Preparation and Characterization of Polymer/Dendrimer Blends

Final Report, March 2000

Eric J. Amis, Barry J. Bauer, Andreas Topp, Franziska Gröhn, Ty J.

Prosa, Brent D. Viers, Dawei Liu, Kathleen A. Barnes, Catheryn L.

Jackson, Giovanni Nisato, Ginam Kim, and Alamgir Karim

Polymers Division

National Institute of Standards and Technology

Gaithersburg, MD 20899

NISTIR 6506
2

Introduction to the Report

This report is a summary of the results of measurement and characterization of

dendritically branched polymers that was done for the Army Research Office under

contract 35109-CH. Three previous NISTIR’s1-3 reported investigations covering

consecutive 12 month periods. This report gathers information from previous reports and

new information gathered within the last year.

The report describes three areas of research on dendrimers. In section 1 we report

on our study of individual dendrimer properties in solution. In section 2, we describe

materials made from a combination of dendrimers and conventional polymers, and in

section 3 materials made from a combination of dendrimers and metals.

The dendrimer solution properties are divided into six categories, size

measurement, internal segment density distribution, comparison of different types of

dendritic polymers, location of dendrimer terminal units, interactions of dendrimers at

high concentrations, and effect of solvent on dendrimer size. This research area was the

first to be explored, and detailed information has been given in several published papers

that can be used to obtain detailed information. In this report, summaries are given of

these results in a concise review.

The research areas of dendrimer/polymer combinations are blends,

interpenetrating polymer networks, and dendrimers tethered to linear chains. The blend

work is divided into four subcategories, hydrogen bonding blends of dendrimers, fatty

acid modified dendrimer/polyolefin blends, ternary blends, and dendrigraft blends. The

ability to disperse a dendrimer in a polymeric matrix is examined by different synthetic

approaches. Methods of structure characterization are developed and thermodynamic

explanations of the results are offered.

The dendrimer/metal combinations have three subcategories, metal containing

polyamidoamine dendrimers in aqueous solution, metal containing hydrophobically

modified polypropyleneimine dendrimers in hydrophobic solvents, and metal containing

dendrimer interpenetrating polymer networks. Measurement methods and techniques of

data interpretation are developed that can be used to identify structural features. These

methods are then used to identify thermodynamic principles that govern the structure

formation process. These principles can then be used on generic materials

Most of the work that is described in this report gives completed areas of research

on generic dendritic materials the results of which may be applied to individual materials

of interest.
3

General Information And Acknowledgments

Throughout this report certain conventions will be used when describing

uncertainties in measurements. Plots of small angle scattering data have been calculated

from circular averaging of two-dimensional files. The uncertainties are calculated as the

estimated standard deviation of the mean and the total combined expanded uncertainty is

not given as comparisons are made with data obtained under the same conditions. In

cases where the limits are smaller then the plotted symbols, the limits are left out for

clarity. In data plots with uncertainties larger than the symbols, representative 95%

confidence intervals are plotted at appropriate places. Fits of the scattering data are made

by a least squares fit of the data giving an average and a standard deviation to the fit.

This would be correct for fit values such as radius of gyration and exponents.

Temperatures are given as expected ranges of values based on previous work.

All concentrations are calculated from weighed samples and are reported as mass

fractions and are nominal values for naming purposes. The ranges of the concentrations

calculated from mass are within one percent of the reported values. The conventional

notation “molecular weight” has been replaced by “relative molecular mass” according to

ISO 31-8 in most cases. occasionally, the conventional notation is used to conform to

previous publications.

Certain commercial materials and equipment are identified in this paper in order

to specify adequately the experimental procedure. In no case does such identification

imply recommendation by the National Institute of Standards and Technology nor does it

imply that the material or equipment identified is necessarily the best available for this

purpose.

This work has been preceded by three progress reports that list in detail the

participants in individual projects from outside of NIST.1-3 We gratefully thank them for

the samples provided and their characterization results. This work is supported in part by

the U.S. Army Research Office under contract number 35109-CH.
4

1 Characterization of Dendritically Branched Polymers by SANS, SAXS, and TEM....14

1.1 Synopsis............................................................................................................ 12

1.2 Introduction....................................................................................................... 12

1.2.1 Unique Structures ...................................................................................... 12

1.2.2 History of Dendrimer Characterization....................................................... 13

1.2.3 Important Technological Questions............................................................ 14

1.2.4 Measurement Methods Used...................................................................... 15

1.3 Dendrimer Size vs. Generation. ......................................................................... 16

1.4 Dendrimer Internal Segment Density Distribution.............................................. 17

1.5 Comparison of Dendrimers, Hyperbranched, and Dendrigraft............................ 18

1.6 Location of the Terminal Groups....................................................................... 20

1.7 Dendrimer-Dendrimer Interactions .................................................................... 22

1.8 Dendrimer Size Change in Different Solvents.................................................... 24

1.9 Summary ........................................................................................................... 25

2 Dendrimer/Polymer Blends ................................................................................... 27

2.1 Blends of Dendrimers and Hydrogen-Bonding Polymers................................... 27

2.1.1 Synopsis .................................................................................................... 27

2.1.2 Introduction ............................................................................................... 27

2.1.3 Experimental.............................................................................................. 27

2.1.4 Results and Discussion............................................................................... 28

2.1.5 Summary ................................................................................................... 29

2.2 Blends of Fatty Acid Modified Dendrimers with Polyolefins............................. 29

2.2.1 Synopsis .................................................................................................... 29

2.2.2 Introduction ............................................................................................... 30

2.2.3 Experimental.............................................................................................. 30

2.2.4 Results and Discussion............................................................................... 31

2.2.5 Summary ................................................................................................... 32

2.3 Ternary Dendrimer Blends................................................................................. 32

2.3.1 Synopsis .................................................................................................... 32

2.3.2 Introduction ............................................................................................... 32

2.3.3 Experimental.............................................................................................. 33

2.3.4 Results and Discussion............................................................................... 33

2.3.5 Summary ................................................................................................... 35

2.4 Blends of Dendrigraft Polymers with Linear Polymers ...................................... 35

2.4.1 Synopsis .................................................................................................... 35

2.4.2 Introduction ............................................................................................... 35

2.4.3 Experimental.............................................................................................. 37

2.4.4 Results and Discussion............................................................................... 38

2.4.5 Conclusions ............................................................................................... 42

2.5 Dispersing Dendrimers in a Solid Polymer Matrix ............................................ 42

2.5.1 Synopsis .................................................................................................... 42

2.5.2 Introduction ............................................................................................... 43

2.5.3 Experimental.............................................................................................. 44

2.5.4 Results and Discussion............................................................................... 45

2.5.5 Conclusions: .............................................................................................. 48

2.6 End Linked Dendrimer Networks ...................................................................... 48
5

2.6.1 Synopsis .................................................................................................... 48

2.6.2 Introduction ............................................................................................... 48

2.6.3 Experimental.............................................................................................. 49

2.6.4 Results and Discussion............................................................................... 50

2.6.5 Summary ................................................................................................... 55

3 Metal Containing Dendrimers................................................................................ 56

3.1 Dendrimers as Templates for the Formation of Inorganic Nanoclusters.............. 56

3.1.1 Synopsis .................................................................................................... 56

3.1.2 Introduction ............................................................................................... 56

3.1.3 Experimental.............................................................................................. 57

3.1.4 Results and Discussion............................................................................... 58

3.1.5 Conclusions ............................................................................................... 64

3.2 Hydrophobically Modified Dendrimers.............................................................. 65

3.2.1 Synopsis .................................................................................................... 65

3.2.2 Experimental.............................................................................................. 66

3.2.3 Results and Discussion............................................................................... 67

3.2.4 Conclusion................................................................................................. 70

References: ................................................................................................................. 151
6

Table 1 Major technological issues. Key to symbols, ++, best technique for measurement;

+, acceptable technique for measurement; -, unsuitable for measurement............... 71

Table 2 Comparison of different dendritically branched polymer types, see Figure 7..... 72

Table 4 Characteristics of Arborescent Polymers with 5000 g/mol Branches................. 73

Table 5. Characteristics of deuterated polystyrene and deuterated poly(vinyl methyl

ether)..................................................................................................................... 74

Table 6. Diameter of G6 – G11 PAMAM dendrimers in methanol solution and in IPN’s

as measured by SAXS and TEM at mass fraction 1 % and 10 %............................ 75
7

Figure 1 Classical Dendrimer Cartoon showing core, branch points and terminal groups.

.............................................................................................................................. 76

Figure 2 SAXS Rg of PPI and PAMAM dendrimers. Straight line is the limit of

PAMAM dendrimers collapsed to bulk density. The 1/3 power law suggests

uniform spherical shape......................................................................................... 77

Figure 3 TEM of G5, G6, G8, and G10 PAMAM dendrimers. Individual molecules are

seen....................................................................................................................... 78

Figure 4 PAMAM dendrimer diameter from SAXS and TEM. ...................................... 79

Figure 5 SAXS curves for PAMAM mass fraction 1% dendrimer/methanol solutions of

generation G3 (top) through G10 (bottom). Power law behavior continuously varies

from –5/3 to –4...................................................................................................... 80

Figure 6 Fits of the G10 PAMAM dendrimer data to a distribution of spheres and a single

ellipsoid of revolution............................................................................................ 81

Figure 7 Cartoons representing dendritically branched polymers listed in Table 2 ......... 82

Figure 8 Zimm and Guinier plots of G4 PAMAM dendrimer and G5 hyperbranched

polyol. The dendrimer fits Guinier (Spherical) and the hyperbranched fits Zimm

(Gaussian). ............................................................................................................ 83

Figure 9 Kratky plots of G1 PS dendrigraft, G3 PS dendrigraft, G4 PAMAM dendrimer,

and G10 PAMAM dendrimer. . Flat high q shows star-like structure, higher order

features shows sphere-like structure....................................................................... 84

Figure 10 Volume fraction interior polymer segments in dendrimer solution. PPI

dendrimer in methanol, PAMAM dendrimer in methanol, hyperbranched polyol in

methanol, and PS dendrigraft in cyclohexane......................................................... 85

Figure 11 Cartoon of possible end group locations. A) whole dendrimer end groups

outside, b) whole dendrimer end groups backfolded, a) matched dendrimer end

groups backfolded, a) matched dendrimer end groups backfolded. Outside end

groups have a larger Rg.......................................................................................... 86

Figure 12 SANS of G7(H) in CD3OH, G7(D) in contrast match methanol, and G7(H) in

contrast match solvent. Labeled dendrimer in core match solvent shows scattering

from labeled terminal generation. .......................................................................... 87

Figure 13 Cartoon showing dendrimers at different concentrations................................ 88

Figure 14 SANS of G5 PPI dendrimer at various mass fractions. Peaks move to higher q

(smaller separation distance) with increased concentration. ................................... 89

Figure 15 Kratky plot of SAXS of G5 PPI dendrimer at various mass fractions. Higher

order feature moves to higher q suggesting shrinkage with increased concentration.

.............................................................................................................................. 90

Figure 16 TEM of aqueous PAMAM G10. Note dendrimers are touching but not

interpenetrating...................................................................................................... 91

Figure 17 Rg of G8 PAMAM dendrimer in alcohol of various types from SANS. Rg of G8

PAMAM dendrimer calculated from HRS results in reference.52 .......................... 92

Figure 18 SANS from G8 PAMAM dendrimer with and without acid and salt additions.

Note constant position of higher order features showing constant size. .................. 93

Figure 19 SANS from blends of G4 PAMAM and PMMA-r-PMAA............................. 94

Figure 20 SANS from Blends of G4.5 PPI and PMMA-r-PMAA. Parameter of the plot is

the temperature as indicated in the figure............................................................... 95
8

Figure 21 SANS from blends of mass fraction 2% dendrimer-h in 98% mass fraction

HDPE-d4. ), G1; ', G3; (, G5. ............................................................................. 96

Figure 22 Guinier plot of the scattering from blends of 2% mass fraction dendrimer-h in

HDPE-d4. Symbols are the same as in.................................................................... 97

Figure 23 Mass fraction 2% G5 Dendrimer-d in PP,); LPDE, '; and E-co-B, (............ 98

Figure 24 SANS from a 1:9 PSD/PVME blend that contains a mass fraction of 1% PPIC8 dendrimer for temperatures in the range 90 °C ≤ T ≤ 140 °C............................. 99

Figure 25 SANS from 3:7 PSD/PVME blends that contain a mass fraction 0% and 1%

PPI-C8 dendrimer. ............................................................................................... 100

Figure 26 . Effect of the dendrimer PPI-C8 on the spinodal temperature of PSD/PVME

blends.................................................................................................................. 101

Figure 27 SANS of PSD/PVME = 1/9 with and without mass fraction 1 % dendrimer at

140 °C and 150 °C............................................................................................... 102

Figure 28 SANS of PSD/PVME = (1/9 and 3/7) with and without mass fraction 1 %

dendrimer at 70 °C. ............................................................................................. 103

Figure 29 TEM of PSD/PVME blend ED-1. The scale bar is one mircon.................... 104

Figure 30 Schematic representation of the growth of arborescent polymers by successive

grafting reactions................................................................................................. 105

Figure 31 SANS curves for all arborescent polymer generations in d-polystyrene at

120 °C................................................................................................................. 106

Figure 32 Rg of arborescent polymers in solutions and in blends as a function of

generation number............................................................................................... 107

Figure 33 Temperature dependence of Rg for arborescent polymers in d-PVME.......... 108

Figure 34 (a) Rg versus molecular mass for arborescent polymers in d-PVME. (b) Rg

versus molecular mass for arborescent polymers in d-polystyrene........................ 109

Figure 35 (a) Scattering functions for power law model compared with G3 polymer in dPVME. (b) Scattering functions for power law model compared with G3 polymer in

d-polystyrene....................................................................................................... 110

Figure 36 Density profiles for G3 arborescent polymer in solutions and blends. .......... 111

Figure 37 I(q) versus q for G3 polymer in d-PVME from 80 °C to the phase separation

temperature. ........................................................................................................ 112

Figure 38 Temperature dependence of Rg for G3 polymer in d-PVME. ....................... 113

Figure 39 Rg of G3 arborescent polymer as a function of molecular mass of the matrix dpolystyrene.......................................................................................................... 114

Figure 40 SAXS for G10 dendrimer solution and IPN’s. High concentration low q peaks

are indicative of dendrimer ordering. The first minimum in the scattering indicates

dendrimer size. The shift to higher q of the minimum for the mass fraction

10% dendrimer in the IPN shows shrinking. ........................................................ 115

Figure 41 SAXS and TEM-FFT dendrimer Rg in solution and IPN’s. The size in mass

fraction10 % dendrimer in the IPN is considerable smaller than in dilute solution or

IPN...................................................................................................................... 116

Figure 42 TEM of mass fraction 10 % G11 dendrimer in the IPN with oso4 staining.

Picture contains images of dendrimers at different levels. .................................... 117

 Figure 43 TEM of mass fraction 1 % G10 dendrimer in PHEMA with

Phosphotungnistinic acid staining........................................................................ 118
9

Figure 44 SAXS of mass fraction 2 % G8 PAMAM dendrimer and mass fraction 2 % G8-

MAA dendrimer stained with phosphotungnstinic acid. Leveling off at low q is an

incipient peak showing uniform spacing. Peak at higher q shows spherical nature

and first minimum gives information on size. ...................................................... 119

Figure 45 TEM of mass fraction 2 % G8 dendrimer in PHEMA with

Phosphotungnistinic acid staining........................................................................ 120

Figure 46 TEM of mass fraction 2 % G8 PAMAM dendrimer in PHEMA-co-PMAA with

Phosphotungnistinic acid staining........................................................................ 121

Figure 47 Fast Fourier transform of TEM micrographs. Features at high q are

representative of spherical shape, the first minimum indicates an average R. Peak in

mass fraction 2 % G8 PAMAM dendrimer samples at low q represents incipient

ordering and is not seen for the mass fraction 1 % G9 or G10.............................. 122

Figure 48 Kratky plots of 32 arm stars with DSM G5 cores. The choice of endlinking

chemistry will affect the ultimate number of arms added. .................................... 123

Figure 49 GPC on the 32 arm stars (Figure 48) demonstrating the differences in reactive

endlinking chemistries......................................................................................... 124

Figure 50. Kinetically Resolved GPC on DSM G4 stars of expected functionality 32. The

star (at low elution volumes) is clearly delineated from the free, reacting arms. A

ratio of the two peaks provides a measure of the conversion. ............................... 125

Figure 51 Kinetic Analysis of Figure 50. The dotted line demonstrates the fit expected

from Equation (2.12). A better fit is obtained when the reaction order is allowed to

float (Equation (2.13)). This demonstrates that arms add very rapidly in early stages,

but further addition is very sterically hindered at late stages. ............................... 126

Figure 52. DSM G5 networks with differing PEG/DSM stoichiometry. The most lightly

crosslinked gels swell most, and there is little variance in swelling for high crosslink

functionality in accord with Equation (2.14) and (2.15) ...................................... 127

Figure 53. PAMAM G4 networks with differing PEG/PAMAM stoichimetries (see.

Figure 52)............................................................................................................ 128

Figure 54. PAMAM networks swollen in solutions of decrasing ph. Gels with the lowest

functionality swell the most, and all gels demonstrate a maximum in swelling due to

repulsion of the (acid charged) dendrimers. The swelling decreases at lower ph

(higher HCl:NR3) due to screening of the repulsive interactions. ......................... 129

Figure 55. Dendrimer nanotemplating in aqueous solution. In a first step, the dendrimer is

loaded with a precursor salt (H+

AuCl4

-

) resulting in a charged dendrimer with the

precursor as counterions. In a second step, the chemical reduction is performed

which yields a colloid inside the dendrimer. ........................................................ 130

Figure 56 UV-VIS spectra for gold-dendrimer hybrid colloids in aqueous solution. The

spectra correspond to G9-PAMAM dendrimer samples loaded with different

amounts of gold (the molar ratio of gold ions to dendrimer end groups is indicated in

the figure.)........................................................................................................... 131

Figure 57. TEM of gold containing G9 PAMAM-dendrimer obtained for 1:1 loading. The

dendrimer has been stained with phosphotungstic acid, it appears gray, the gold

appears black. A: fast reduction (NaBH4 in 0.1 mol/L NaOH) b: slow reduction

(NaBH4 in 0.3 mol/L NaOH)............................................................................... 132

Figure 58 a: Small angle x-ray scattering curve I(q) for the plain G9 PAMAM-dendrimer

along with fit to the data. Error bars are the measured standard deviation in I(q). 134
10

Figure 59 a) Small angle x-ray scattering curve I(q) for the gold containing G9 PAMAM

dendrimer of figure 3 along with fit to the data. B) Pair distribution function P(r)

obtained by indirect Fourier transformation of the scattering data I(q) (program ITP).

A layered-sphere structure with a total diameter of 13 nm becomes evident.135

Figure 60 a) Theoretical pair distribution function P(r) calculated for layered spheres with

different relative contrast of the inner sphere (solvent contrast = 0, outer sphere

contrast =1, inner sphere contrast as given in the figure). The basic shape of the

experimental function in Figure 4b cannot be modeled. ....................................... 136

Figure 61 a) Small angle x-ray scattering curves I(q) for gold containing G9 PAMAMdendrimers obtained for different loading ratios 1:1, 1:2 and 1:4. Pair distribution

functions P(r) obtained by indirect Fourier transformation of the scattering data I(q)

in b) The decreasing gold diameter but constant dendrimer diameter upon decreasing

loading is visible.................................................................................................. 137

Figure 62 a) TEM of gold containing G8 PAMAM dendrimer obtained for 1:1 loading

and slow reduction. (The dendrimer has been stained with phosphotungstic acid.)138

Figure 63 a)Small angle x-ray scattering curves I(q) for gold-dendrimers hybrid

structures obtained with PAMAM dendrimers of generation 7 to 10.................... 139

Figure 64 Small angle neutron scattering curve for the initial G5 poly(propyleneimine)

dendrimer in toluene at 55oC and small angle neutron scattering curve and smallangle x-ray scattering curve after solubilization of gold salt................................. 140

Figure 65 Small angle neutron scattering curve I(q) for the gold-salt loaded G5

poly(propyleneimine) dendrimer along with fit to the data.................................. 141

Figure 66 Pair distance distribution function P(r) obtained by indirect Fourier

transformation of the scattering data I(q) (program ITP). A cylindrical structure with

a diameter of 6 nm and a length of 21 nm becomes evident. ................................ 142

Figure 67 Cross-sectional pair distance distribution function Pc(r) obtained by indirect

Fourier transformation of the scattering data I(q) under assumption of a cylindrical

particle geometry................................................................................................. 143

Figure 68. Radial scattering length density profile ρ(r) obtained by square-root

deconvolution of the cross lectional pair distance distribution function PC(r) in figure

68. The dotted line represents the result from the first multi-step approximation.

The solid line represents the final solution, i.e. the easiest profile corresponding to

the best fit of the data: A two step cross-sectional profile becomes evident.......... 144

Figure 69 Small angle x-ray scattering curve I(q) for the gold-salt loaded G5

poly(propyleneimine) dendrimer along with fit to the data.................................. 145

Figure 70 Pair distance distribution function P(r) obtained by indirect Fourier

transformation of the scattering data I(q) (program ITP). A cylindrical structure with

a diameter of 4 nm becomes evident.................................................................... 146

Figure 71 Cross-sectional pair distance distribution function Pc(r) obtained by indirect

Fourier transformation of the SAXS data I(q) under assumption of a cylindrical

particle geometry (program ITP). ........................................................................ 147

Figure 72 Schematic of the multi-dendrimer cylindrical structure as deduced from the

SAXS and SANS results...................................................................................... 148

Figure 73 Small angle neutron scattering curve I(q) for gold-dendrimer hybrid structures.

............................................................................................................................ 149
11

Figure 74 TEM of gold colloids obtained from hydrophobically modified G5

poly(propyleneimine) dendrimers loaded with gold-salt after reduction with sodium

borohydrate. ........................................................................................................ 150
12

1. Characterization of Dendritically Branched Polymers by SANS,

SAXS, and TEM

1.1 Synopsis

Small angle neutron scattering (SANS), small angle x-ray scattering (SAXS), and

transmission electron microscopy (TEM) have been used to characterize the size, shape

and interactions of dendrimers, hyperbranched, and dendrigraft polymers. Size in terms

of radius of gyration (Rg) from scattering and diameter from microscopy can be routinely

measured. Five technologically important factors of dendritically branched polymers

have been identified and measured. Dendrimers have a uniform spherical structure

without a greatly depressed segment density distribution (SDD) at the center or a broad

outer interfacial transition. Dendrimers are spheres with a uniform SDD and an abrupt

outer transition, hyperbranched polymers are polydisperse in size and have Gaussian

SDD, dendrigrafts have a uniform interior with a star-like outer transition. The terminal

units of dendrimers are predominately on the exterior of the molecule. Dendrimers at

high concentrations tend to align and will shrink rather than interpenetrate at high

concentration. There is negligible size change of dendrimers in solvents of different

quality or when charged.

1.2 Introduction

1.2.1 Unique Structures

Ever since the introduction of the synthetic techniques that produce dendrimers, it

has been quite obvious that they produce structures unlike all previous synthetic

polymers.4,5 The stepwise layering of generations with uniform branching present in

every step produces molecules of elegant symmetry that have become immediately

recognizable. Figure 1 is a classical dendrimer cartoon that is instructive on the synthetic

steps necessary to form the dendrimer, and of the topology of the resultant structure.

At the center of the dendrimer is the core that represents the first synthetic step in

divergent synthesis, or the last step in convergent synthesis. Each concentric circle of

branched units is a generation X, designated GX, of identical repeat units. Hundreds of

chemical repeat units have been reported,6,7 but our characterization has primarily been

for polyamidoamine (PAMAM), -(CH2CH2CONHCH2CH2N)<,4 or polypropyleneimine

(PPI), -(CH2CH2CH2N)<8,9 dendrimers. The discontinuous lines at the perimeter of the

circle in Figure 1 are the terminal units of the dendrimer which are –NH2 for the full

generations of both PAMAM and PPI dendrimers. We are interested in the structure of a

generic dendrimer, however, whose properties result from the connections within a

dendrimer and not primarily from the chemistry involved in the synthesis.

Although the synthetic techniques of dendrimer production have been extensively

studied,6,7 characterization of the size, shape, and interactions of dendrimers have lagged

behind. While the cartoon of Figure 1 is very instructive for learning about the
13

connections resulting from the synthesis, it can be very misleading if it is used to describe

how a dendrimer actually distributes itself in space. If dendrimers were shaped as

depicted by Figure 1 they would be round (circular in 2 dimensions, spherical in 3

dimensions), have a lower segment density on the inside than at the outside, and have all

of the terminal units at the outside. Since these factors have very important technological

implications, it is imperative that measurements be made to characterize the reality of

dendrimers.

The doubling that is inherent in dendrimer chemistry is the dominant process that

controls the dendrimer shape 4. With each generation, the number of terminal units

usually doubles. Since the mass of each generation doubles, the total molecular mass

also approximately doubles with each generation, as does the number of branch points.

While the dendrimer mass doubles with generation, the space to fit the units increases at a

much slower rate. The contour length of any chain from the core to the terminal units is

proportional to the number of chemical bonds and hence the number of generations.

Equations (1.1) to (1.3) show the relationship between the molecular mass, M, and the

molecular volume, V, for a dendrimer of generation G. The ratio of M to V gives a

relative local density ρ and the inverse of this quantity gives an intrinsic viscosity [η].

2G M ∝ (1.1)

3 V G ∝ (1.2)

1 3 [] / 2 / G ρ η MV G − ∝ ∝ ∝ →∞ (1.3)

The increase of the molecular mass proceeds much more rapidly than the space

available and means that after a few generations, there will not be enough room to fit in

all of the required units of the next generation. The result is that the chemistry at a

certain generation cannot be complete and a fraction less than 100 % chemical

conversion will result. It is of interest to study dendrimers up to this limit to find the

effect of such extreme crowding.

1.2.2 History of Dendrimer Characterization

The earliest work on dendrimer characterization was concerned with aspects of

the organic chemistry – did the proposed chemical reaction take place without side

reactions and what was the conversion? Since near 100 % conversion and near perfect

removal of excess reactants is required for making pure dendrimer, common methods of

spectroscopy and chromatography can be used to verify the structure. In a wide variety

of dendrimer chemistries, nearly perfect structures have been produced, at least for earlier

generations where the techniques are more quantitative.

The development of mass spectroscopic techniques such as MALDI and

electrospray mass spectrometry has allowed the absolute determination of dendrimer

perfection.10,11 For divergent dendrimers such as PAMAM and PPI, single flaws in the

chemical structure can be measured such as an unreacted site of the previous generation,

or a side reaction producing a loop. Mass spectrometric results on dendrimers certainly
14

demonstrate the extreme sensitivity of the technique, but they also demonstrate the

uniformity of the molecular mass. The polydispersity index of Mw/Mn for a G6 PAMAM

dendrimer can be < 1.0006 which is narrower than that of “living” polymers of the same

molecular mass.10

Hydrodynamic sizes from intrinsic viscosity (IV), gel permeation chromatography

(GPC), and holographic relaxation spectroscopy (HRS) map the changes in size with

generation. For example, IV of PAMAM 12 and PPI 9 dendrimers goes through a

maximum with generation suggesting that the dendrimers become more densely packed.

While these techniques give valuable information, they are most sensitive to the external

size of the dendrimers rather than to their internal structure.

Scattering techniques measure the radius of gyration (Rg) of dendrimers which is

an average of the spatial distribution of all of the units. Aharoni and Murthy13 have used

scattering to measure the Rg of dendrimers with alanine repeat units and conclude that

they are spherical. These molecules differ from conventional dendrimers, however, in

that the branch unit is asymmetric and therefore the internal segment distributions are

modified. Other laboratories have begun to publish results of small angle neutron

scattering (SANS)14 and small angle x-ray scattering (SAXS)15,16 of dendrimers, but

only a few studies have had sufficient resolution to resolve the higher order features

characteristic of uniform dendrimers.17-20

Transmission electron microscopy (TEM) 4,21-23 has been used to image

individual dendritic molecules, usually the larger generations. Recently atomic force

microscopy (AFM)24 has also been used to image dendritic molecules.

1.2.3 Important Technological Questions

The unique shape and organization of dendrimers suggests that some important

applications may be possible. We have identified five important factors that pose

questions concerning technological applications. Table 1 lists these factors along with

the applicability of SANS, SAXS, and TEM to address the questions.

The first question concerns the segment density distribution (SDD) of the atoms

in the interior of a dendrimer. Predictions vary from the extremes of a very hollow

structure with a densely packed exterior 25 to a high central segment density with a

gradually tapering concentration of units 26 and a variety of intermediate structures.27-31

If dendrimers have a micelle-like structure, they may be able to solubilize molecules in

the interior for applications such as drug delivery,32 phase transfer,33 etc. If dendrimers

have tapered distributions, they may not be significantly different from linear or slightly

branched polymers for these applications.

Another important factor is the difference between different branched types such

as hyperbranched34 and dendrimers. The different synthetic requirements between the
15

two types make dendrimers orders of magnitude more expensive than hyperbranched.

Are the structures as significantly different as the prices are?

The terminal groups of a dendrimer are large in number and can have

functionalities capable of chemical reactions. If the reactive terminal groups were near

the periphery, they would be readily accessible for attachment to surfaces or to reagents.

Block copolymers or networks with dendrimers as crosslink points would benefit from

having them on the outside.

When dendrimers come in contact by increasing their concentration in solution, or

by placing them on a surface, do they freely pass through one another or do they avoid

interpenetration and align themselves? Dendrimers have sizes in the range (1 to 20) nm

and would be excellent candidates for nanoscopic structures if ordering does occur.

Finally, do dendrimers change greatly in size when placed in different solvents?

For applications as size standards or molecular probes dendrimers having a relatively

fixed size would be preferable. For applications using the release of stored molecules,

however, it would be preferable to “open” and “close” dendrimers by adding appropriate

solvents.

1.2.4 Measurement Methods Used

Dendritically branched polymers have been characterized at NIST primarily by

SANS, SAXS, and TEM. All three techniques are capable of measuring the size of

dendritic materials. SAXS and SANS probe a size scale that reveals information about

the average size of the molecules, the radius of gyration (Rg).17,18,20,35,36 But more

complex fits of the scattering give information on the internal structure of the whole

dendrimer or individual parts of dendrimers.20,35,37 Scattering can also give

information on the spacing between dendrimers.35,38,39 TEM can be used to image

individual polymer molecules, giving direct information on size, shape, polydispersity,

and alignment23.

Both SANS and SAXS probe the same size scale characterized by the scattering

vector q (with q = (4π/λ) sin(θ/2), θ being the scattering angle and λ being the

wavelength of the probing radiation). The intensity of the scattering as a function of

angle (q) gives information on the arrangement and spacing of the polymer segments.

The scattering from a collection of particles can be broken into contributions from a

single particle, P(q), and between particles, S(q).

 () ()() Iq PqSq ∝ (1.4)

The form factor term,P(q), contains information on the distribution of segments within a

single dendrimer. Models can be used to fit the scattering from various types of particles,

common ones being a Zimm function which describes scattering from a collection of

units with a Gaussian distribution (equation (1.5)), a Guinier function which describes the
16

scattering from sphere-like objects (equation (1.6)), and the Sphere function which gives

the exact scattering from a perfect sphere where R = (5/3) 1⁄2Rg (equation (1.7).

2 1 2 ( ) (1 / 3) Pq qRg

− = + (1.5)

2 2 ( ) exp( / 3) Pq qR = − g (1.6)

2 6 P q qR qR qR qR ( ) 9(sin( ) cos( )) /( ) = − (1.7)

Therefore, a fit of the scattering data not only gives information on an average size, Rg,

but also information on the segment density distribution within the dendrimers.

Table 1 compares the usefulness of the three techniques in addressing the

questions posed. SANS has the ability to label parts of the molecule by replacing

hydrogen with deuterium. This allows for the location of parts of the molecules, such as

the end groups, to be measured. SAXS has the advantage of very low background

radiation, which gives the best resolution of the higher q features which are weak in

intensity. TEM is the only way of seeing individual molecules and offers direct

visualization.

Descriptions of the experimental scattering and microscopy conditions have been

published elsewhere and are referenced in each section. Throughout this report certain

conventions will be used when describing uncertainties in measurements. Plots of small

angle scattering data have been calculated from circular averaging of two-dimensional

files. The uncertainties in the text, tables, and figures are calculated as the estimated

standard deviation of the mean and the total combined uncertainty is not given as

comparisons are made with data obtained under the same conditions. In cases where the

limits are smaller than the plotted symbols, the limits are left out for clarity. In data plots

with uncertainties larger than the symbols, representative confidence limits are plotted at

appropriate places. Fits of the scattering data are made by a least squares fit of the data

giving an average and a standard deviation to the fit, this is the case for fit values such as

radius of gyration and exponents.

1.3 Dendrimer Size vs. Generation.

SANS and SAXS have been used to measure the average Rg of dendrimers in

dilute solution.17,18,20,36 Figure 2 is a plot of Rg vs. Theoretical Mw for both PPI and

PAMAM dendrimers. A line giving the theoretical Rg of spheres with a density of

1.23 g/cc, the value reported for PAMAM dendrimers, is also plotted. Therefore, the line

would be the limit of PAMAM dendrimers that have excluded all solvent and shrunken to

single dendrimers of bulk density. The distance of the PAMAM points to the line gives

the relative segment density within the dendrimers. The data points roughly parallel the

line, with the points getting slightly closer to the line for the largest generations.

A slope of 1/3 would suggest that the dendrimers are spherical with similar

internal density profiles. There seems to be a slight increase in internal segment density

as the dendrimers get larger. For the highest PAMAM generations, it is known that the
17

theoretical molecular mass is not reached due to crowding.4 This would shift the high

generation data points to the right and may indicate that the internal densities are uniform

after a certain generation.

TEM has been used to measure the average diameter of PAMAM dendrimers

from G5 to G10.23 Figure 3 shows micrographs of G5, G6, G8, and G10. The G5

micrograph also has a small amount of G10 dendrimers added to help focus the

microscope and to identify the relative sizes. Single dendrimers can easily be

distinguished over the whole size range shown. Individual polymer molecules can easily

be seen, while conventional linear polymers in this molecular mass range are difficult to

image. This attests to the fact that the dendrimers are much more spherical in shape and

have a very high internal segment density compared to conventional polymers.

Size ranges are tabulated from the TEM images and are reported elsewhere.23

Each generation has a well defined average with a relatively narrow range of sizes.

Figure 4 is a plot of the average diameter from TEM23 and from SAXS20 assuming that

the dendrimers are spheres and that therefore the diameter D = (20/3)1⁄2 Rg. There is good

agreement between the two types of measurement.

1.4 Dendrimer Internal Segment Density Distribution

While microscopy can give important information on the average size of

dendrimers, scattering gives much more detailed information on their internal structure.

As has been previously mentioned, there are a variety of predictions on the type of

segment density distributions on the inside of a dendrimer, from a hollow structure with a

dense shell25 to a dense center with a gradually tapering outward distribution.26

The angular dependence of the scattered intensity contains information on the

SDD. In principle, if the SDD is known exactly, then the scattering can be calculated

exactly and vice versa. The uncertainties in the scattering become translated into

uncertainties in the SDD, however, and direct transformation is not practical for samples

that do not scatter strongly. There are some characteristics of the scattering at

intermediate or high q that can provide insight into relative structures, easily

distinguishing the structural class.

Figure 5 is a plot of the SAXS from G3 through G10 PAMAM dendrimers over a

very wide q range37. The scattering at low q is a measure of dendrimer Rg, and a

gradual transition is easily seen from G3 to G10 indicating increasing Rg with generation

number. The high q scattering also has a gradual transition in the limiting power law

slope that is sensitive to the transition of segment densities at the outside of the

dendrimer. The G3 dendrimer has a high q power law of –5/3 which is characteristic of a

polymer in a good solvent such as linear polymers or star polymers.35 This indicates a

relatively diffuse outer boundary. The G10 dendrimer, however, has a power law slope

of –4 which is characteristic of an object with a very sharp outer boundary.35 There is a
18

gradual transition from G3 to G10 showing that dendrimers transform from star-like to

sphere-like.

Another important factor is the appearance of inflections in the high q data that

become multiple peaks as the generation number increases. Equation (1.7), which

describes scattering from a monodisperse, uniform sphere has multiple peaks at high q.

These features also appear in the SAXS data, indicating that the large generation

PAMAM dendrimers are becoming quite sphere-like. Even the relatively small G5

dendrimer is beginning to show this feature and the G10 dendrimer shows at least five

additional peaks in the data.

The strong scattering from the G10 dendrimers and the multitude of subtle

features make it the best candidate for thorough fitting of the structure. Figure 6 is a plot

of the G10 SAXS data in a Porod plot, Iq4

 vs. Q. A Porod plot is a convenient way of

looking at the scattering from objects with sharp outer boundaries since scattering with a

–4 power law will be horizontal line in this type of plot. The data points oscillate around

a horizontal line showing a sphere-like structure with a sharp outer boundary. The

diminished size of the oscillations with increased q is due to the polydispersity of the

sizes of the objects.

The polydispersity can be fit by two limiting cases, as a population of perfect

spheres with a range of diameters, or as a single randomly oriented ellipsoid. The solid

line in Figure 6 is the theoretical scattering from a population of spheres with a Gaussian

distribution of radii with a mean of 69.9 Å and a distribution half width of 4.9 Å. The

dashed line is for a randomly oriented ellipsoid with a major axis of 74.1 Å and a minor

axis of 59.8 Å. It is not possible to distinguish between these two types of

polydispersities, but it is likely that both types are present, resulting from a population of

slightly elliptical molecules with a small size variation.

Therefore, the shapes of dendrimers span the range from stars to spheres. Small

G3 dendrimers have a diffuse, open structure while large G10 dendrimers are spheres

with a uniform interior, sharp outside transition, and low polydispersity.

1.5 Comparison of Dendrimers, Hyperbranched, and Dendrigraft

Dendrimer synthesis involves a repetitive building of generations through

alternating steps which double the size with every generation as has been discussed

earlier4,21. Hyperbranched synthesis involves self-condensation of multifunctional

monomers, usually in a single step34. Hyperbranched polymers and dendrimers of

comparable molecular mass have the same number of branch points and terminal units,

and any application requiring only these two characteristics could be satisfied by either

one. Since dendrimer synthesis requires many synthetic steps and purification processes

while hyperbranched synthesis can have only one synthetic step with no purification step,

the dendrimers will necessarily be a much more expensive material to produce.
19

A third type of branched molecule has been described recently, known

alternatively as dendrigraft40 or arborescent41 molecules. They are made in a stepwise

synthesis as are dendrimers, but the steps involve conventional grafting reactions of end

functionalized linear polymers onto a polymer substrate. Ungrafted linear polymer is

removed by fractionation and the grafting reaction is repeated, forming the next

generation of dendrigrafts. Since many grafts can be added to the previous generation

each time, the molecular mass increases by much more than the doubling that is usual for

dendrimers, with increases of 10 to 100 per generation being typical. Figure 7 is a cartoon

showing the three different types of dendritically branched molecules. The dendrimer

has a uniform doubling of the structure with generation producing a monodisperse

structure. The hyperbranched molecule has polydispersity in both molecular mass

between different molecules, but also internally with the path between the core and

different terminal units varying greatly. A dendrigraft is made by repeated grafting of

“living” linear polymers, each having a very narrow molecular mass distribution, making

the overall distribution narrow.

Table 2 lists some of the typical characteristics of the three types. All have some

characteristics in common, such as a high amount of branching as is defined by having a

low number (typically < 10) of covalent bonds between branch points and a large number

of terminal groups. The most important differences are in the polydispersity, the size of

the end groups, and the number of synthetic and purification steps. The last factor is

mirrored in the resultant cost that can be different by orders of magnitude. It is important

to measure the differences between these three types and linear polymers to see if the

differences are sufficient to justify their enormously different costs.

SANS42-44 and SAXS20,37 have been used to measure the form factors of

various types of dendritic molecules at NIST. As was described earlier, different

structures have different form factors and if the scattering fits a given model over a wide

q range, then the molecular structure is well described by the model distribution. Figure 8

is a plot of the SANS from a G4 PAMAM dendrimer and a G5 hyperbranched polyol

both of which have the same nominal Mw, 14,000 g/mol. Both SANS curves are plotted

as a Zimm plot (I-1) and a Guinier plot (ln(I)). It is quite clear that the dendrimer is linear

in the Guinier plot and curved in the Zimm plot, with the opposite being true for the

hyperbranched. A Zimm plot describes the scattering from particles such as a linear

chain having a Gaussian distribution of segments, while a Guinier plot in this q range fits

the scattering from a uniform spherical object. Therefore, to a first approximation, the

segment density distribution of a dendrimer is relatively uniform while that of a

hyperbranched is quite tapered, with a high density in the center and a gradual decrease in

segment density as one moves outward.

The low q range shown in Figure 8 gives important information, but the most

sensitive q range is at somewhat higher values of q. Figure 9 is a Kratky plot, of

scattering from low generation (G4) and high generation (G10) PAMAM dendrimers20

along with low generation (G1) and high generation (G3) polystyrene dendrigrafts.45 A

Kratky plot, Iq2

 vs. Q, emphasizes the differences in scattering at higher q values. The

uppermost curve is the theoretical scattering from a linear polymer. All of the others
20

show a peak in the scattering which is characteristic of dense internal structure. The G1

dendrigraft has the shape characteristic of a star polymer with a broad peak and leveling

off at higher q. The G4 dendrimer also has this shape, but the peak is much narrower.

This suggests a star-like structure on the outside, but more of a tendency for uniform a

spherical interior than the G1 dendrigraft. As has been seen previously, the G10

dendrimer has several higher order peaks typical of a very sphere-like distribution. The

G3 dendrigraft has a weak higher order peak, but the uniformity is less pronounced than

the G10 dendrimer.

Figure 10 is a plot of the average local segment density (volume fraction polymer)

for typical dendrimers, dendrigrafts, and hyperbranched. The average size is calculated

from the Rg as measured from SAXS or SANS, assuming a spherical shape. The size of a

collapsed molecule calculated from Mw and bulk density, ρ, is then used to calculate the

average internal volume fraction of polymer segments, φp, as is shown in equation (1.8).

3

4 5 2

3 3

/

g

P

w Av

R

M N

π

φ

ρ

      = (1.8)

Where Nav is Avagadro’s number. The hyperbranched molecules have the most open

structure, with values of φp, in the range of (2 to 3) %. PPI and PAMAM dendrimers

form a composite curve with φp, ranging from (20 to 75) % from the smallest to the

largest dendrimers. The dendrigrafts φp, ranges from (10 to 50) % from G0 to G3.

The results are summarized in Table 2. A low generation dendrimer has the shape

of a dense star with an interior having a more uniform density than a low generation

dendrigraft. As the generation number increases, the shape becomes more sphere-like. At

the limit of a G10 PAMAM dendrimer, the molecules have a uniform interior with an

abrupt transition in segment density at the outside, and low polydispersity. A G0

dendrigraft is like a conventional multi-arm star, but a G3 dendrigraft has a uniform

interior with a narrow, star-like zone of transition at the outside. Hyperbranched

molecules have polydispersity both in molecular mass and in the internal structure of

each molecule. They have a much more open structure with a broad, tapered segment

density distribution than do dendrimers of similar size.

1.6 Location of the Terminal Groups

The cartoon representation of a dendrimer is shown in Figure 11 in two forms,

Figure 11a being the classical picture with all of the terminal groups (shown as circles

connected with a single bond) at the outside of the dendrimer. Figure 11b shows how the

terminal groups could enter the interior of the dendrimer by backfolding. SANS of

unlabelled dendrimers can give detailed information on the SDD as was demonstrated in

the SAXS studies20. However, the calculated density distribution cannot distinguish

between the terminal units and all of the other units. Therefore, the types of distributions

described in Figure 11a and Figure 11b would give identical scattering.
21

To distinguish the terminal groups from the groups of the earlier generations,

deuterium labeling is used. PAMAM dendrimers having a tetrafunctional core of

ethylene diamine (EDA) were synthesized according to reported methods46. Fully

hydrogenated G7 PAMAM dendrimers and partially deuterated versions were prepared.

The partially deuterated dendrimer was prepared by reacting the fully hydrogeneous G6

dendrimer with partially deuterated methyl acrylate, CD2=CDCO2CH3 to form G6.5

dendrimer with a hydrogenated interior and deuterated terminal units. The G6.5 was

converted to the partially deuterated G7(D) dendrimer by reaction with hydrogenated

EDA.

Solutions for SANS experiments were prepared with methyl alcohol, CH3OH, and

its partially deuterated counterpart, CD3OH. For the determination of the contrast match

point of the unlabeled parts of the dendrimer, two stock solutions of equal G9 dendrimer

concentrations were made in CH3OH and CD3OH. Various amounts of the two stock

solutions were mixed to make a series of solution with different isotopic contents. The

CH3OH / CD3OH match point was determined as the point at which the coherent SANS

scattering goes to zero. The procedure is described elsewhere.46

After the match point was determined, solutions were made of labeled G7(D) and

unlabeled G7(H) dendrimer in the match solvent along with the unlabeled G7(H) in

CD3OH. Figure 12 shows the SANS of the three samples. The unlabeled in match

solvent is completely flat, showing only incoherent scattering. This proves that the match

solvent completely masks the hydrogenous parts of the dendrimer. The unlabeled G7(H)

in CD3OH shows strong scattering characteristic of dendrimer scattering. The labeled

dendrimer in the match solvent still shows some coherent scattering. This scattering is

from the deuterated half of the last generation.

To ensure that instrumental artifacts do not perturb the results, we collected two

independent data sets for G7(D) in the matching solvent by measuring the solutions on

both 30 m SANS instruments at NIST.47,48 The absolute values of the coherent

scattering intensity of the G7(D) labeled segments were reproduced to high accuracy,

independent of the SANS instrument and its configuration. The values of the Rg are

determined by weighted linear least squares fits to equation 1.6 and give an Rg of nonlabeled dendrimer of (34.4 ± 0.2) Å. For the deuterated segments of the partially

deuterated dendrimer, the results are Rg(G7(D)) = (38.8 ± 1.2) Å and

Rg(G7(D)) = (39.8 ± 1.2) Å for the data taken on NG3 and NG7, respectively

(uncertainties are based on the standard deviation of the fits). We can take the average

value of Rg(G7(D)) as (39.3 ± 1.0) Å for the deuterated segments of G6.5 in a G7

dendrimer. If a uniform distribution of end groups were present throughout the

dendrimer, we would see the same Rg for both the labeled and the whole dendrimer. This

is demonstrated by the cartoon in Figure 11 where the end groups have different

locations. Instead, we see a clear difference between the Rg values for the labeled units

and the unlabeled dendrimers. The distribution of dendrimer terminal groups is not

uniform throughout the interior of the dendrimer but rather the terminal groups are

localized near the periphery of the dendrimer.
22

There have been solid state NMR studies49 on the distribution of end groups by

site-specific stable-isotope-labeling, rotational-echo double-resonance (REDOR) NMR.

REDOR experiments which measure dipolar couplings between C-13 atoms located near

the chain ends and an F-19 label placed at the core of benzyl ether dendrimers

(generations 1-5). They find that average distances are quite small, suggesting that

terminal units do approach the core unit. The important difference between the NMR and

the SANS studies is the moment of the average distribution. The weighting of the Rg

from SANS goes as the square of the distance, R2, so that segments with large distances

from the center of mass are weighted heavily and ones near the core have little weighting.

The NMR technique, however, weighs the cube of the inverse distance, R-3 so that small

distances are weighted heavily and large distances are not seen. Therefore SANS and

NMR are complimentary measurements with the SANS showing that most, but not all of

the terminal units are predominately on the outside of the dendrimer, but some can

approach the core through backfolding.

Most, but not all of the terminal units are near the outside of the dendrimer at any

given time. The SAXS studies20 of the segment density distribution have shown that

there is an abrupt transition region at the outside of large PAMAM dendrimers. The

combination of these two factors suggests that the terminal functionalities of dendrimers

are accessible from the outside and available for chemical reactions such as attachment to

surfaces, mounting of a catalyst, or for use as a crosslink junction.

1.7 Dendrimer-Dendrimer Interactions

As was demonstrated earlier, the internal SDD of dendrimers is quite high

compared to conventional polymers and there is a narrow zone of transition at the

outside. When linear polymers are forced together by increasing their concentration in a

solvent, they freely interpenetrate each other due to their open structure. Dendrimers

may represent a different case, however, due to their compact size. At low

concentrations, dendrimers may avoid interpenetrating each other by occupying space

available away form other dendrimers. As the dendrimer concentration is increased, the

solvent swollen dendrimers will encroach upon each other, first touching, and then

interacting more strongly. Two results could occur, first, the dendrimers could retain the

dilute solution size and start to interpenetrate, mixing the outer segments. The other

extreme result would be for the dendrimers to collapse upon themselves, avoiding

interpenetration. Figure 13 is a cartoon of the three possible states with Figure 13a

showing a dilute solution, Figure 13b showing the overlap concentration at which point

the dendrimers contact one another, Figure 13c showing dendrimer collapse and noninterpenetration, and Figure 13d showing a concentration above the overlap concentration

where the dendrimers retain their size and interpenetrate.

SANS was used to measure the scattering of G4 and G5 PPI dendrimers at

concentrations up to a mass fraction of 80 %.50 The partially deuterated solvent CD3OH

was used throughout the study. It is used instead of CD3OD to prevent exchange of

deuterium with the hydrogen of the terminal primary amines. The scattering experiments
23

were performed at the 30 m SANS facility at NIST.47,48 The spectrometer was operated

at a configuration giving a wide range of the scattering vector, q, 0.05 Å-1 ≤ q ≤ 0.55 Å-1.

The maximum q was required to resolve the scattering at high concentrations. Figure 14

is a plot of the coherent scattering from a G5 PPI dendrimer as a function of

concentration. At concentrations below a mass fraction of 5 % the scattering

monotonically decreases with q. This is typical of dilute solution scattering with no

interactions. A peak in the SANS appears at a mass fraction of 10 % indicating that long

range fluctuations have been suppressed because the dendrimers avoid each other. The

overlap concentration can be calculated from the Rg assuming a spherical shape and is

equal to a mass fraction of about 25 %. At the overlap concentration and higher, the peak

is strong and moves to higher q as the dendrimers are forced together.

A previous SANS study of concentrated PPI dendrimers also noted that the peak

appears and moves in a way consistent with increased concentration51. This peak

suggests ordering, but cannot easily distinguish between dendrimers shrinking or

interpenetrating. It is interesting to note, however, that in Figure 14 at q values higher

than the peak position, there is an excess scattering over the incoherent background. As

was shown earlier, higher order features in scattering from spheres can be used to fit the

size of the sphere. As the sphere size decreases, this feature moves to higher q. If this

feature could be resolved, the size of a dendrimer could be measured at high

concentrations.

SANS often has a large amount of incoherent scattering that is a flat background

containing no structural information. The higher order peaks are in a q range that has low

coherent scattering so that a large fraction of the scattering is a noisy baseline, and

resolving features becomes difficult. SAXS, however, has only weak background

scattering in this angular region. The experiments were repeated at the Advanced

Polymers PRT beamline (X27C; SUNY Stony Brook/ NIST/GE/Allied Signal/Montell)

at the National Synchrotron Light Source, Brookhaven National Laboratory. Figure 15 is

a Kratky plot of the scattering of a G5 PPI dendrimer at various concentrations. The

mass fraction 1% scattering can be fit with the scattering from a sphere giving R = 18.6 Å

and Rg = 14.4 Å which is consistent with previous results of fitting the low q scattering

alone. It is easy to distinguish the higher order features in these plots. As the

concentration increases, the minimum remains stationary until the overlap concentration

of 25 % is reached. Beyond this point, the minimum moves to higher q showing that the

dendrimers are becoming smaller. At the highest concentration, the resolution is lost, but

at moderate concentrations above the overlap concentration, the dendrimers tend to

shrink in size rather than overlap. Figure 16 is a cryo-TEM image of G10 PAMAM

dendrimers in water. The cryo technique involves flash freezing of the solvent that is in a

thin film on a grid and is described in detail elsewhere.23 Individual dendrimers can be

seen that are lined up in what is probably an array of a single dendrimer thickness. While

there are complicating factors due to the sample preparation, the picture is consistent with

dendrimers touching, but not interpenetrating. AFM studies of G3 dendrigraft

polystyrene can resolve individual molecules in a surface monolayer24. This is

consistent with our PAMAM results and is further evidence of dendrimer noninterpenetration.
24

Dendrimers remain discrete objects in dilute solution, avoiding interpenetration.

As the concentration increases above overlap, the dendrimers preferentially shrink in size

rather than interpenetrating. When dried to a solvent free condition, the dendrimers must

either deform from their spherical shape into polyhedrons, or must interpenetrate. The

solvent free condition would require deuterium labeled dendrimers, and experiments are

underway to probe this last concentration regime.

1.8 Dendrimer Size Change in Different Solvents

The effect of solvent quality on the dimensions of linear chains has been studied

for many years, and chain dimensions can change a large amount, especially at high

molecular mass. There are reports in the literature that the size of dendrimers is largely

influenced by the solvent quality. A molecular dynamics study by Murat and Grest29

resulted in an increasing internal segment density of dendrimers when the dendrimersolvent interactions are less favorable, which leads to a considerable decrease of the

average dimensions of the simulated structures. A holographic, relaxation spectroscopy,

HRS, study by Stechemesser and Eimer52 concluded that the radius of higher generation

PAMAM dendrimers would be extremely sensitive to solvent conditions. The effect of

charging of the dendrimer in aqueous solution was investigated by Welch and

Muthukumar 53 through Monte Carlo simulations. They found that charging a simulated

PPI dendrimer could change its linear dimension by as much as a factor of 1.8.

Small angle scattering is a direct method of determining dendrimer size. SANS

was used to measure dendrimer size by two methods. Dilute solutions of noninteracting

dendrimers can be fit by equation (1.6) to determine Rg as a function of dendrimer

generation, solvent type, and temperature. The effect of charging is more complex

because long range ionic interactions can impose a uniform spacing between dendrimers

that affects the low angle scattering. In this case, higher q scattering can be used to

measure a size if a higher order feature can be resolved as was the case for the high

concentration dendrimer solutions discussed earlier.

The SANS experiments were performed at the NIST 8 m facility. SANS

experiments were performed with solutions of G8 PAMAM dendrimer in D2O, methyld4, ethyl-d6, and n-butyl-d10 alcohol at a temperature of T = 20.0 °C. PAMAM

dendrimers do not dissolve in acetone, but they readily dissolve in methyl

alcohol/acetone mixtures over a wide range of composition. Solvents of different

composition, were prepared and added to a weighed amount of dried G5 or G8

dendrimer. In a separate set of experiments, the NIST NG7 30 m instrument was used to

measure the effects of charging on the dendrimer size. PAMAM G8 dendrimers in D2O

were charged by addition of HCl. Various amounts of NaCl were also added to the

charged dendrimers to screen the electrostatic interactions.

Guinier plots were made of the scattering from G8 PAMAM dendrimers to

measure the Rg in alcohols of different chain length. Figure 17 is a plot of the Rg values

vs. Alcohol chain length. There is a small but consistent drop in Rg as the length of the
25

hydrocarbon chain goes from 0 to 4, with the total relative change being 10 %. The range

of solvents goes from very good (water) to very poor (n-butanol). This is considerably

lower than the range predicted from dynamic calculations. Also plotted in Figure 17 are

results of holographic relaxation spectroscopy from the literature.52 The large changes

in the reported hydrodynamic size are not found in the SANS results.

Similar results were found with mixtures of acetone-d6 and methanol-d4. The Rg

of the dendrimers is not significantly affected by the fraction of acetone in the solvent.

The same result is found over the whole range of temperature studied, i.e. In the range –

10 °C ≤ T ≤ 50 °C. Only the data taken in the solvent of the composition xs = 0.50 show

some consistent decrease of Rg, relative to the other solvent compositions. This may

indicate the onset of a shrinkage of the dendrimers in the vicinity of the solubility gap,

which is around xs ≈ 0.52. However, the difference from the value of Rg for xs = 0.50 is

less than 5 % of the mean value of Rg for the other solvent compositions.

Ionic effects were used in an attempt to modify the size of a G8 PAMAM

dendrimer. Monte Carlo calculations53 have predicted that there should be a strong

effect, with Rg varying by as much as 1.8 by charging with acid and by screening the

charges by addition of salts. Figure 18 shows SANS of the dendrimer under three

conditions54. A dendrimer solution without acid or salt addition has a ph of 10.1 and has

scattering typical of a dilute non-interacting sphere. The Rg of the dendrimer can be

calculated from the position of the higher order feature of the sphere scattering and is

consistent with previous measurements. The dendrimer is then charged by addition of

acid until the ph becomes 4.7. At this point the low q scattering changes dramatically,

developing a peak that is characteristic of ordering of the dendrimers by long range ionic

effects. As with the high concentration dendrimer studies, the minimum in the scattering

can be used to calculate a dendrimer Rg, even when the interactions occur. The Rg has

changed only very slightly, increasing by no more than 5 %. Upon addition of salt to

screen the long range interactions, the peak disappears, indicating that the long range

ordering has been lost. The position of the minimum has not changed, however,

indicating that charging and screening the dendrimers does not significantly modify the

dendrimer size.

Both large (G8) and small (G5) PAMAM dendrimers do not significantly change

size when the solvent environments are changed. When the solvent is made increasingly

hydrophobic by increasing the hydrocarbon chain length, only a 10 % change occurs.

Also the addition of a nonsolvent to a good solvent does not significantly change the

dendrimer size up to the point of phase separation. Charging a dendrimer in aqueous

solution also does not change the size of the dendrimer by more than 5 %.

1.9 Summary

Dendritically branched molecules have shapes and interactions that are radically

different from conventional linear polymers. SANS, SAXS, and TEM have been used to

measure the properties of dendrimers and a generic understanding of their properties has
26

emerged. Five technologically important questions on the nature of dendrimers have

been posed and generalized observations can be made.

Dendrimers are very spherical in shape when compared to conventional linear

polymers.20,37 The lowest generation dendrimers have internal segment density

distributions similar to star molecules, but even the smallest are more compact than stars.

As the generation number increases, the sphere-like characteristics increase and the

largest dendrimers form a population of spheres with uniform internal density (roughly

half dendrimer units - half solvent)50, sharp interfaces on the outside, and a small

polydispersity in shape.

Dendrigraft molecules are star-like in the 0th generation, but have a uniform

interior with an exterior transition zone for G3.20,37 Hyperbranched molecules have

broad distributions in molecular mass and in shape.20 The scattering from

hyperbranched is more similar to that of linear polymers than to spheres, indicating that

there is a gradually tapering distribution on units from the center to the exterior.

The terminal units of a dendrimer are predominately towards the exterior of the

dendrimer.46 While some terminal units may fold inwards, most of the terminal units are

on the outside. Combined with the fact that there is a narrow interface on the outside of

large dendrimers,20 most terminal groups should be accessible for chemical manipulation

such as attachment to surfaces, mounting of catalysts, or attachment of linear chains.

As dendrimers are forced together by increasing the concentration, they avoid

interpenetrating each other and preferably shrink in size rather than overlap.38,50 This

should provide a strong thermodynamic force for ordering dendrimers on surfaces or in

the bulk. Dendrimers seem to be well suited for forming well ordered nanostructures.

The size of dendrimers in dilute solution is relatively constant. Changing the

quality of the solvent or charging the dendrimers results in only a very small change in

dimensions. Therefore, dendrimers seem well suited for applications as standards or as

probes of other materials.
27

2 Dendrimer/Polymer Blends

2.1 Blends of Dendrimers and Hydrogen-Bonding Polymers

2.1.1 Synopsis

Blends of PAMAM and PPI dendrimers were made with linear polymers. SANS

of these blends indicated good mixing between the linear components, but heating the

mixtures to temperatures above 100 °C causes irreversible changes in the scattering. The

samples became insoluble due to crosslinking after the heating cycles of the SANS

experiments. This is due to covalent bonds formed between the components. While

hydrogen-bonding seems capable of making dendrimers miscible with linear polymers,

the side reactions make further processing impossible. This is probably due to the

dendrimer samples available to this study and is not representative of dendrimers in

general.

2.1.2 Introduction

Miscible blends of high molecular weight polymers have been studied for many

years. They are polymer combinations that form thermodynamically favorable

interactions causing the polymers to dissolve in each other giving intimate mixing and

molecular lever dispersions. Combinations of polymers that form miscible blends,

however, are exceedingly rare. Arbitrary combinations of two linear polymers

overwhelmingly form immiscible blends. This is primarily due to unfavorable heats of

mixing that dominate the thermodynamics and result in morphologies with relatively

large domains of individual polymers.

An important way to induce miscibility in polymer blends is to make the heat of

mixing more favorable through the use of hydrogen bonding.55,56 By placing hydrogenbonding groups on one polymer and hydrogen-bond acceptors on the others, the

favorable heat of mixing can be used to induce miscibility. This approach has been

successful with linear polymers and may be an important approach in forming miscible

dendrimer blends.

The most commonly available dendrimers, PAMAM and PPI, both have internal

tertiary amino groups and terminal primary amino groups which are candidates for ionic

or hydrogen-bonding interactions. The PAMAM dendrimers also have carbonyl groups

in amide linkages that may be susceptible to hydrogen-bonding. It was therefore of

interest to use linear polymers with a few hydrogen bonding or ionic groups to determine

if miscibility could be induced.

2.1.3 Experimental

Full generation G4 and G11 PAMAM, and generation G5 PPI, each terminated

with primary amines (-NH2) were used as hydrogen bond donors. Half generation G4.5

PPI dendrimers dendrimers of generation 4 (G4) were purchased from Aldrich Chem.
28

Comp., And G11 PAMAM (StarburstTM) dendrimers were obtained from Dendritech

(Michigan Molecular Institute, Michigan). The PPI (AstramolTM) dendrimers were

provided by DSM (Geleen, The Netherlands). The full generation dendrimers are

terminated by primary amines (-NH2), while half generation PPI dendrimers have cyano

groups (-CN) as terminal units. These dendrimers were used as received. Random

copolymers were synthesized from mixtures of methylmethacrylate-d8 or styrene-d8

(PSD) with methacrylic acid or 1,1,1,3,3,3-hexafluoro-2-hydroxy-isopropyl-α-methyl

styrene (HFIS) with azobisiso-butyronitrile as initiator in bulk at 60 °C for 2 hours. They

were purified by dissolution in THF and precipitation into methanol.

Blends were prepared by dissolving the components in a mixture of methanol and

THF and evaporating the solvents slowly in a fluorinated copolymer dish. They were

then pressed into disks of 0.5 mm thickness for the neutron scattering experiments. The

NIST 8 m instrument was used in the standard manner. A sample to detector distance of

3.6 m was used with a wavelength λ = 6 Å and a wavelength spread of ∆λ/λ = 0.25. 

2.1.4 Results and Discussion

The blends of hydrogen bonding polymers with dendrimers were first screened

for cloudiness by simple visual inspection. Out of all the combinations tried, a large

majority could be identified as phase separated, and were rejected from further study.

Among these are mixtures of PAMAM and full generation PPI dendrimers with

poly(styrene)-d8 that contained a small fraction of comonomers of either methacrylic acid

or FHIS.

Figure 19 shows the scattering from a blend of G4 PAMAM dendrimer with

PMMA-r-PMAA containing mass fraction 2 % PMAA. The scattering is typical of a

single phase mixture. The scattering decreased with increasing the temperature from

140 °C to 180 °C, indicating decreased concentration fluctuations due to enhanced

mixing. DSC results from this combination, with the blend having a Tg intermediate

between the pure materials. At higher temperatures, the blend showed an anomalous

change in the heat flow. This is often found in systems that are undergoing chemical

reactions.

Blends of a copolymer of methyl methacrylate-d8 with mass fraction 1 %

methacrylic acid produced films that were optically transparent when blended with

PAMAM dendrimers or the cyano terminated half generation PPI dendrimers. Both of

these were examined with SANS for miscibility, and the temperature dependence of the

scattering was studied.

Figure 19 shows an example of the SANS results of PAMAM dendrimers in

poly(methacrylate) as described above, heating the sample from 130 °C up to 180 °C and

cooling back to 130 °C. The scattering intensity decreases with increasing temperatures,

suggesting that an upper critical solution temperature might be present. However, when

the sample is cooled back to previous temperatures, the scattering is not reproducible, i.e.

Does not regain the intensity recorded previously at 155 °C or 130 °C. This can be
29

caused by a chemical reaction between the dendrimer and the methacrylate polymer

during the time of study. After the SANS experiments, the samples were no longer

soluble, indicating that crosslinking took place.

Figure 20 shows the SANS results from a blend of mass fraction 5 % G4.5 PPI

dendrimer with a PMMA-d8 copolymer containing mass fraction 2 % PMAA. As the

temperature is increased, the scattering increases as the phase boundary is approached.

For short periods of heating of only a few hours, lowering the temperature reproduces the

previous scattering, but longer times at high temperatures produced samples that did not

reproduce the scattering as in the previous example. After the scattering experiment was

concluded, the samples did not redissolve, indicating crosslinking.

The terminal units of both the PAMAM and the PPI dendrimers are possible sites

for chemical reactions. Although, the SANS experiments show that the dendrimers can

be dispersed in this polymeric matrix, the material does not exhibit the characteristics of a

truly miscible polymer blend, but rather should be considered as a covalent

dendrimer/polymer network after reaction.

2.1.5 Summary

Hydrogen bonding can increase the miscibility of PAMAM and PPI

dendrimer/polymer blends, forming systems where dendrimers are uniformly dispersed in

a polymeric matrix. Elevated temperatures cause chemical reaction to result in a

crosslinked network, however. This limitation is due to the fact that only PAMAM and

PPI dendrimers were available for this study. We can make no conclusions on the

dendrimeric nature of the molecules on the thermodynamic drive for miscibility.

This technique is available for producing molecularly dispersed dendrimers in a

matrix of linear polymers. Other methods such as IPN and end-linked polymers also

form intractable structures, but have several synthetic advantages of structure control

over the ones shown in this section.

2.2 Blends of Fatty Acid Modified Dendrimers with Polyolefins

2.2.1 Synopsis

Blends were made by solution and melt mixing fatty acid modified dendrimers

with various polyolefins. Small angle neutron scattering (SANS) was used to determine

the miscibility of the blends. Poly propylene imine (PPI) dendrimers G1, G3, and G5

(DAB-dendr-(NH2)y) with y = 4, 16, and 64, were reacted with stearic acid or stearic

acid-d35 forming amide bonds. The modified dendrimers were then blended with high

density polyethylene (HDPE), high density polyethylene-d4 (HDPE-d4), low density

polyethylene (LDPE), amorphous polypropylene (PP), or an ethylene-butylene

copolymer (E-co-B). Limiting power law behavior shows that all of the blends are

immiscible. It is likely that the dendrimers form a second phase, being finely dispersed,

but thermodynamically immiscible.
30

2.2.2 Introduction

Recently, dendrimers have been modified by attaching hydrophobic groups to the

terminal units of dendrimers.57,58 This further accentuates the micellar nature of the

dendrimers. Hydrophylic dendrimers such as polyethyleneimine dendrimers

(ASTRAMOLTM)59 can be reacted with stearic acid resulting in amide bonds between

the dendrimer and the hydrophobic stearic acid groups. The solubility characteristics are

changed dramatically, with the dendrimers becoming soluble in hydrocarbon solvents.

From recent work it appears that the combination of fatty acid modified

dendrimers (FAD’s) with polyolefins leads to interesting new applications. It turns out

that FAD’s can stabilize the dispersion of polar dye molecules in apolar polyolefins such

as polyethylene,59 by complexing the dye molecules as guests into the modified

dendrimer, followed by blending the dendrimer-dye complex into the polymer matrix.

Another application, which makes use of FAD’s, is a dendrimer-modified polypropylene

(PP) fiber. This is obtained by blending a small quantity of FAD with PP, followed by

spinning. The resulting dendrimer-containing fibers can be dyed by aqueous solutions or

dispersions of conventional dyes.

The nature of the dispersion of the FAD’s in the polyolefins in these applications

is not known. One possibility is that the dendrimers are molecularly dispersed in the

polymeric matrix. Another possibility is that the dendrimers form a second phase, being

finely dispersed, but thermodynamically immiscible.

2.2.3 Experimental

In order to gather this information from a SANS experiment, it is necessary that

sufficient neutron contrast exists. This is most commonly achieved by deuterium

labeling of one of the components. In this study, three generations G1, G3, and G5 of

poly(propylene imine) dendrimers,8 with y = 4, 16, and 64 primary amine groups (DABdendr-(NH2)y), were modified with fatty acid (octadecanoic, C18). The modification

consisted of the conversion of the primary amine groups into amides.60 In this case,

about 2.5 mmoles of fatty acid, hydrogenous or deuterated, was added to an equivalent

amount of poly(propylene imine) dendrimer and 20 ml of xylene. The mixture was heated

to 160 °C while stirring under a slow stream of nitrogen in a two-necked flask with a gas

inlet and a Dean-Stark trap. After 1 h. Of reaction at 160 °C all xylene was distilled off

carefully, and the product was allowed to cool to room temperature. The dendrimer

modified with octadecanoic acid-d35 is designated dendrimer-d and with octadecanoic

acid-h35 is designated dendrimer-h.

HDPE-d4 was purchased from Cambridge Isotope Laboratories (DLM-220).

HDPE 42,799-3, PP 42,818-3, ,LLDPE 42,809-4, LDPE 42,804-3, and E-co-B 43,473-6

were purchased from Aldrich. All were used as received except for the PP which was
31

extracted with toluene at 60 °C and precipitated into methanol to produce an atactic,

amorphous polymer.

Samples were prepared by two methods, solution mixed and melt mixed. The

solution mixed samples are dissolved in xylene at 140 °C and precipitated into methanol.

They were dried in vacuum and pressed at 150 °C into disks for SANS. The melt mixed

samples were pressed at 150 °C and folded twice and repressed. The folding and

pressing is repeated 10 times.

SANS experiments were carried out on the 8m (NG1) and 30m (NG7)

instruments in the standard manner. The wavelength λ of the incident beam was 6Å.

2.2.4 Results and Discussion

Differential scanning calorimetry was used to determine the melting points of the

crystalline regions of the polyolefins so that blending and SANS could be carried out on

amorphous samples. Miscible blends can be made to phase separate upon crystallization

of one component. The highest melting point was for HDPE-d4 which showed complete

melting by 130 °C. Therefore all of the melt mixing was carried out at 150 °C and the

scattering was done at 140 °C.

The first set of experiments checked for miscibility of HDPE-d4 with dendrimers

of different size. Figure 21is a plot of the SANS from binary blends of mass fraction 2 %

dendrimer-h in HDPE-d4. A log-log plot shows that there is an extensive region with a

slope of q-4.

35 This is characteristic of Porod scattering from a morphology that is

strongly phase separated with negligible mixing within the phases and a negligible

interfacial region between the phases. In this q range, there is no leveling off of the

scattering intensity at low q. This extended range of power-law behavior indicates that

the characteristic size of the two phase morphology is larger than can be measured under

these instrumental conditions.

Figure 22 is a Guinier plot of the scattering from blends of mass fraction, 2 %

dendrimer-h HDPE-d4. The measurement was taken with the 8 m SANS instrument

which had a low q value of 0.008 Å-1. An estimate can be made of the characteristic

phase size if data is available in the range q Rg << 1. As can be seen, there is still

curvature in the lowest accessible q region, so fits in this region only give a lower bound

of the phase size. The fits over a q range of 0.008 < q/Å-1 < 0.012 give Rg = 220 Å,

200 Å, and 190 Å for G1, G3, and G5 respectively. Since qrg > 1 under these conditions,

the measured size is limited by the instrument resolution. These sizes therefore represent

a lower bound of the true phase size.

Other polyolefins were blended with dendrimers to see if miscibility was possible

for other combinations. Figure 23 is a log-log plot of mass fraction 2 % G5 dendrimer-d

in PP, LDPE, and E-co-B. As with the blends of PE described earlier, there is an

extended region with a slope of q-4, indicating strong phase separation. Since there is no

plateau region at low q, as was the case of the other blends, these also have relatively
32

large phase sizes, larger than the resolution of the SANS instrument. Also, the results

shown are for both melt (LDPE, E-co-B) and solution processed (PP) samples with both

giving identical power law scattering. No differences could be seen resulting from

different preparation methods.

2.2.5 Summary

While melt mixed samples of fatty acid modified PPI dendrimers appear

transparent when kept above the melting temperature, SANS shows that they are actually

phase separated on a size scale much greater than the individual dendrimer size. This was

true for all of the fatty acid modified dendrimers studied, G1, G3, and G5, in both

hydrogen and deuterium forms. All polyolefins tested were immiscible with the

dendrimers, HDPE, LDPE, PP, and E-co-B, in both hydrogen and deuterium forms. Melt

mixing by mechanical kneading of virgin material or with samples previously solution

mixed all produced immiscible blends. Premixing in solution also did not change the

miscibility of the binary blends. Extended annealing did not produce any morphological

changes in a size scale accessible to SANS.

The ultimate goal of blending fatty acid modified dendrimers is to promote long

time stability of additives to the polyolefins. Even if the size scale of the dendrimer phase

is relatively large, small molecules such as dyes that are permanently affixed to the

dendrimers may be lodged in the polyolefin matrix. If this is the case, then the use of

fatty acid modified dendrimers to promote long time stability of additives may be

applicable to a wide range of polymers other than polyolefins, independent of specific

miscibility conditions.

2.3 Ternary Dendrimer Blends

2.3.1 Synopsis

Miscible blends were made of polystyrene-d8 (PSD) and poly(vinylmethyl ether)

(PVME) with and without addition of a fatty acid modified PPI dendrimer. SANS shows

that the phase separation of the PSD/PVME blends can be inhibited by several °C with

the addition of a small amount of dendrimer. The scattering from the ternary blends

shows an upturn at lowest q, however, suggesting a large size component in the

morphology. TEM reveals very large aggregations of the dendrimer in a matrix of a

miscible PSD/PVME phase, so that while the dendrimer affects the phase boundary of the

miscible binary blend, it itself is not miscible at a mass fraction 1 % level.

2.3.2 Introduction

Dendrimers may act as modifiers of binary blends if they could change the point

of phase separation. The branched structure of dendrimers may act as an interfacial agent

and modify the thermodynamics or rate of phase separation. Hydrophobically modified

PPI dendrimers are soluble in toluene which is the preferred solvent for casting films of

PSD/PVME. The binary blend of PSD/PVME has been extensively studied by SANS. It
33

has a lower critical solution temperature and phase separates at temperatures around

150 °C. A ternary blend of PSD/PVME/dendrimer is a good candidate for the study of

the effect of dendriticly branched additives on blend miscibility.

2.3.3 Experimental

Hydrophobically modified dendrimers were synthesized from a G5 PPI dendrimer

with -NH2 terminal groups by addition of an excess mass fraction 80 % 1,2-epoxy octane

in vacuum at 140 °C for 8 h. Fatty acid modified G5 PPI was synthesized as described in

the experimental section of the Blends of Fatty Acid Modified Dendrimers with

Polyolefins section.

Blends were made with PSD and PVME by solution in toluene, evaporation of the

solvent, drying in vacuum, and pressing into disks. SANS from blends with and without

added dendrimer demonstrate that the presence of the dendrimer gives the sample

stability, causing it to remain miscible when blends without the dendrimer phase separate.

All SANS experiments were performed in the normal manner. A sample to

detector distance of 3.6 m was used with a wavelength λ = 6 Å and a wavelength spread

of ∆λ/λ = 0.25.

The PSD:PVME (1:9) samples, ED-1 and ED-4 (containing mass fraction (1 to

10) % G5 DSM dendrimer reacted with 1-2 epoxy octane), were ultramicrotomed to a

thickness of (60 to 80) nm at –70 °C and transferred to 200-mesh, carbon coated Cu

grids. The sections were stained with OsO4 vapors by exposing the grids to a aqueous

solution containing 0.04 g OsO4/g H2O at room temperature for 2 h. The blend samples

were imaged by transmission electron microscopy (TEM) at 120 kV in a Philips 400T

using low-dose conditions.

2.3.4 Results and Discussion

A series of SANS experiments was run on the ternary system consisting of the

hydrophobically modified dendrimer PPI-C8 and the polymer blend PSD/PVME.

Samples were prepared with between mass fraction 0 % and mass fraction 10 % of the

dendrimer added to a blend of PSD/PVME having mass ratios of 1:9, 3:7, 5:5, and 7:3.

The samples with 1:9 and 3:7 were optically clear, but were hazy for higher PSD content.

Figure 24 shows the scattering for a 1:9 blend containing mass fraction 1 % PPI-C8. The

scattering is plotted in the Ornstein-Zernike (OZ) method, i.e. As I(q)-1 versus q2

. The

scattering fits the OZ relation well, suggesting a miscible blend. The scattering was

shown to be reproducible in temperature cycles, and the samples could be redissolved

after the SANS experiments. Size exclusion chromatography before and after the SANS

experiments showed that the PSD and PVME had not degraded or crosslinked during the

experiment.

Figure 25 shows the SANS of a 3:7 blend containing mass fraction 0 % or mass

fraction 1 % dendrimer. Both samples show OZ type of scattering at 120 °C, indicating
34

miscibility, but the mass fraction 1 % sample shows a much higher scattering intensity

suggesting that it is closer to phase separation. The 130 °C results confirm this

observation. The intensity of the 1 % sample has shifted slightly, being closer to the

phase separation temperature, but remaining a single phase. The mass fraction 0 %

sample had phase separated at this temperature, however, as is indicated by the negative

intercept of the OZ plot, and was confirmed by its optical cloudiness.

The results shown in Figure 25 suggest that the ternary blends have an increased

range of miscibility over blends that do not contain the dendrimer. Fits were made to an

OZ form as

2 2 Sq Sq q ( ) ( 0) /(1 ) == +ξ (2.1)

Where S(q) is the scattered intensity and ξ is the correlation length. In a mean field

polymer system, S(q = 0) and ξ vary with temperature as:

Sq T kT s ( ) = =+ − − − 0 1

1

1 1 (2.2)

ξ − − − = + 1 2 1

2

/ 1 T kT s (2.3)

Plots of S(q = 0) -1 versus T -1 or ξ -1/2 versus T -1 give the value Ts

-1 as an intercept, Ts

being the spinodal temperature (e.g. Critical onset of phase separation).

Figure 26 is a plot of the relative shift in Ts as a function of dendrimer content for

1:9 and 3:7 blends. There is a dramatic increase in the spinodal temperature when

dendrimer is added, with as large as a 30 °C shift for the 1:9 blend. These results suggest

that for PSD/PVME blends with high PVME content, the addition of dendrimer improves

the miscibility significantly.

Experiments were continued with G5 PPI dendrimers that were modified by

reaction with stearic acid forming amide bonds on all 64 terminal amino groups. Figure

27 shows the SANS from PSD/PVME = 1/9 blends with and without mass fraction 1 %

of the dendrimer added. Two types of dendrimer were used, one that had stearic acid -d35

and one that was -h36. At 140 °C, all three samples has scattering typical of a miscible

blend. At 150 °C, however, the blend without dendrimer showed increased scattering at

low q indicating phase separation is taking place. The blends with the dendrimer still

showed scattering typical of micibility at 150 °C. These results are qualitatively similar

to previous results of blends with the 1,2-epoxy octane modified dendrimers.

Experiments were repeated under experimental conditions that gave results

extending to lower values of q. Figure 28 shows SANS of blends of PSD/PVME = 1/9

and PSD/PVME = 3/7 containing mass fraction 1 % dendrimer. The data were taken at

70 °C which is well within the range of miscbility for the blend without dendrimer. At

lower q there is an upturn in the scattering which is typical of a large dispersed phase.

The q range shown in Figure 28 gives a linear relationship, but when lower q is probed,

the 2 phase structure is evident.
35

Figure 29 is the TEM result of ED-1. It shows dark domains of sizes <100 nm,

presumed to be aggregates of the dendrimers in the single phase, PS/PVME blend. A

PS/PVME (1:9) blend without dendrimer was examined as a control and did not contain

any similar domains; this control sample showed a single phase morphology. ED-4

(mass fraction 10 % dendrimer) contained dark domains of larger and more varied sizes,

from 100 nm-1.0 μm, also presumed to be the dendrimer aggregates.

2.3.5 Summary

The addition of dendrimer promotes miscibility of binary PSD/PVME, blends as

is demonstrated by SANS, causing the phase separation temperature of the PSD and

PVME componentsto increase by several °C. However, the dendrimer itself is not itself

miscible with the PSD/PVME binary blend. This is apparent from the upturn in the very

low q of the scattering curves and by TEM. The cause of the effect is not known. It may

be that a small amount of dendrimer does enter the PSD/PVME phase.

2.4 Blends of Dendrigraft Polymers with Linear Polymers

2.4.1 Synopsis

 Small angle neutron scattering (SANS) was used to measure the size and shape of

styrene-based arborescent polymers blended with linear deuterated polystyrene (d-PS)

and linear deuterated poly(vinyl methyl ether) (d-PVME). For generation 0, 1, and 2

arborescent polymers, the Rg values were the same in going from d-PVME to d-PS as the

matrix material while for generation 3 (G3) the Rg in d-PS was found to be smaller than

in d-PVME. For comparison, the Rg of a sphere was calculated assuming the size of the

sphere was equivalent to a G3 molecule collapsed to bulk density. The Rg obtained was

162 Å, which is quite close to the Rg of the G3 polymer in d-PS (Rg = 164 Å). This

indicates that the G3 molecules should behave as essentially non-interpenetrating spheres

with the linear d-PS matrix chains being largely excluded from the interior of the

arborescent molecules. In the single phase region of the phase diagram it was difficult to

establish a clear temperature dependence of the Rg for the generation 0, 1 and 2

molecules in d-PVME. For the G3 molecules in d-PVME a small decrease in Rg with

increasing temperature was observed in the single phase region with an abrupt decrease

in Rg of 21 % on phase separation between 110 °C and 115 °C. The single particle form

factor of arborescent polymers in blends was studied using a power law model for the

density profile. In comparison with a hard sphere or a shell model, the scattering

function calculated from the power law function for the density profile provided the best

fit to the experimental scattering data.

2.4.2 Introduction

Various types of dendritic polymers with a controlled architecture such as

dendrimers, hyperbranched polymers, and arborescent polymers have been developed

recently.4,24,34,41,61-66 This special class of branched polymers has gained increasing
36

interest from both theoretical and practical points of view. For example, they can be used

as crosslinking agents, sensors, catalysts, size standards, and drug release systems. 4,30

For many applications it is necessary to have detailed information on the intramolecular

density profile, molecular size and shape in solution and in mixtures with other polymers.

Arborescent polymers are branched macromolecules synthesized by successive

cycles of functionalization and grafting reactions.4,24,30,41,62-66 The structure of

arborescent polymers is represented schematically in Figure 30. The structure of

arborescent polymers has features distinct from the classical dendrimer molecules. The

building blocks used in the synthesis of arborescent polymers are polymer chains rather

than small molecules. The grafting sites in arborescent polymer molecules are randomly

distributed, rather than strictly controlled like in dendrimer molecules. In our previous

paper the size of arborescent polystyrenes in solution was measured as a function of

temperature and molecular mass using small angle neutron scattering (SANS).45 In this

paper small angle neutron scattering is used to study arborescent polystyrenes in blends

with linear polymers for comparison to the results obtained in solutions. Deuterated

polystyrene (d-PS) and deuterated PVME (d-PVME) are used as matrix polymers to

study arborescent polymer blends as a function of molecular mass and temperature.

According to classical Flory theory for a linear polymer chain in a good and a

theta solvent, the scaling exponent for Rg ~ Mν is 0.6 and 0.5, respectively, where Rg is

the radius of gyration and M is the molecular mass (or chain length). Linear polymer

chains are fractal objects which means that as the molecular mass of a linear polymer

chain increases, the average density of the linear chain decreases. The density is taken as

an average coil density estimated as ρ ~ M/ Rg

3

.67 In the work by Zimm and Stockmayer

who studied this scaling relation for branched polymers, the scaling exponent was found

to be 0.25 for a Cayley tree in the limit of large molecular mass.68 This value of the

scaling exponent is smaller than the value of 1/3 for a constant density object, which

means that as the size of a (highly) branched polymer increases the (average coil) density

of branched polymer increases.68 de Gennes and Hervet studied the scaling relation for

dendrimers using an analytical calculation and the scaling exponent was found to be

0.2.25 According to numerous computer simulations and limited experimental work on

dendrimers, the values of this scaling exponent have been reported in the range of 0.2-

0.4.26-29,52 In our previous work on arborescent polymers in solution, the scaling

exponent was found to be ν = 0.25 ± 0.01 in deuterated cyclohexane and ν = 0.32 ± 0.01

in deuterated toluene.45 These values of ν are less than 1/3, indicating again that the

average segment density in the polymer coil is increasing. This creates a self-limiting

condition where the coil density approaches bulk density, and arborescent polymers of

higher generations can no longer be synthesized with a constant branching density.

The intramolecular radial density profile of dendrimer molecules proposed by de

Gennes and Hervet has a minimum density at the center of the molecule.25 However, a

number of computer simulations 25,27-29,52 and theoretical work by Boris and

Rubinstein30 predict a maximum in the radial density profile at the center of the
37

molecule, and a decreasing density gradient to the outer edge of the molecule. According

to recent small angle x-ray scattering (SAXS) work, generation 10 polyamidoamine

(PAMAM) dendrimers in solution do not exhibit any sizable minimum in density near the

core.20 More recent results by Prosa et al. Show that the dendrimers exhibit sphere-like

characteristics.37 In our previous work on arborescent polymer in solution, a power law

model for the radial density profile which has a maximum density at the center of

molecule was used to successfully model the single particle form factor.45 This function

has a relatively constant interior density and an outer zone of transition that is dependent

on the solvent used.

2.4.3 Experimental

The arborescent polymers used in this study were synthesized by successive

grafting reactions of polystyryl anions onto a linear polystyrene substrate.65 The

molecular mass of the branches used for grafting for each generation was determined by

gel permeation chromatography (GPC). The molecular mass of the arborescent polymers

was not determined by GPC, but was measured in this work as part of the SANS analysis.

The characteristics of the arborescent polymers used in the study and the branches are

given in Table 3. The relative precision in molecular mass from GPC is ± 10 % as is

typical of this technique. The core and the side chains used in the synthesis of each

generation had a molecular mass of around 5000 g/mol. The total number of branches in

a given generation G polymer was calculated using eq (2.4);

( )- ( -1) ( ) ( -1) ( )

w w

w w

w

M GM G f tot f G M branch

= + (2.4)

Where Mw(G), Mw(G-1) and Mw(branch) are the molecular masses of a generation G

polymer, of the previous generation and of the grafted side chains, respectively. If the

molecular mass of the branches for all generations is the same, eq (2.4) can be reduced to

simpler form:

( )- ( ) ( ) ( )

w w

w

w

M G M linear core f tot M branch = (2.5)

The branching density of the core portion of a generation G polymer is given by eq (2.6):

number of branches added per molecule in a grafting reaction Branching Density total number of repeat units of previous generation = (2.6)

Blends of the arborescent and linear polymers were prepared using deuterated

linear polystyrene or deuterated linear poly(vinyl methyl ether). The deuterated linear

polystyrene samples were either purchased or synthesized, depending on the molecular

mass. Deuterated styrene purchased from Cambridge Isotope Laboratories, Inc and a

tetramethylpiperidinyloxy (TEMPO) based unimolecular initiator obtained from Dr. C.
38

Hawker of IBM Almaden Research Center were used to synthesize deuterated linear

polystyrene by living free radical polymerization.69 Deuterated linear PVME was

synthesized by cationic polymerization of d3-vinyl methyl ether, CH2=CHOCD3, in

toluene using boron trifluoride-ethyl ether complex as the initiator.43 The molecular

mass of deuterated polystyrene and deuterated PVME were determined using GPC and

the mass average molecular massess were found to be 102,900 g/mol and 8,280 g/mol,

respectively. Universal calibration was used with the Mark-Houwink-Sakurada

parameters a = 0.739 and k = 1.35×10-4 for d-PVME in tetrahydrofuran (THF) at 30

°C.43 In addition to the deuterated polystyrene synthesized by living free radical

polymerization, several anionically polymerized deuterated polystyrenes of different

molecular masses were purchased from Polymer Laboratories, Ltd. The characteristics of

the linear polymers are summarized in Table 4. Samples for neutron scattering were

prepared by dissolving the appropriate deuterated linear polymer and the arborescent

polymer in toluene and then allowing the solution to evaporate in a Teflon petri dish to

form a thin film. The film was then dried in vacuum to remove any remaining toluene.

The film was pressed into disk of 1.4 cm diameter and 0.05 cm thickness for the SANS

experiments using a hot press at approximately 150 °C. The concentration range of the

blends studied was mass fraction (0.5 to 2) % arborescent polymer.

Small angle neutron scattering experiments were carried out at the Center for

Neutron Research of the National Institute of Standards and Technology on the 30 m

NIST-NG3 instrument in the normal manner.47 The q range was from 0.0046 Å-1 to

0.0520 Å-1 with a neutron wavelength, λ = 6 Å and a wavelength spread, ∆λ/λ = 0.15.

All temperatures reported are within ± 1 °C as determined by previous experience.

2.4.4 Results and Discussion

A typical set of SANS data for all generations (T = 120 °C, mass fraction 1 % in

deuterated polystyrene) is shown in Figure 31. The radii of gyration were measured

using Guinier plots at small q as given by eq (2.7):

2 2

( ) (0) exp 3

R qg Iq I   = − 

 

(2.7)

Where Rg is radius of gyration of the object.70,71 A typical Guinier plot of ln I(q) versus

q2 for a generation 3 (G3) polymer is displayed as an inset in Figure 31. The Rg of the

arborescent polymer molecules in blends was plotted as a function of generation number

(molecular mass) and compared with data from solutions measured previously in Figure

32.45 The error bars in Figure 32 represent one standard deviation calculated from the

linear least-squares fit of the Guinier plot data. The Rg decreases in going from solutions

to blends, and the observed Rg is smaller in linear deuterated polystyrene than in

deuterated PVME (Note that the molecular masses of the two polymers are quite different

at 103 k and 8.2 k, respectively). As will be discussed in detail later in the paper, the Rg

of the G3 polymer was studied as a function of the molecular mass of the d-PS matrix
39

polymer. The Rg of the G3 polymer in d-PS with N = 38 (Mw = 4.3 k) and N = 238 (Mw =

27 k) was found to be 206 Å and 182 Å, respectively, while Rg in d-PVME with N = 131

(Mw = 8.2k) was 205 Å (N is the average number of monomer units in the chains).

Although the d-PVME chain length falls between the two d-PS molecular massess

studied, it appears that for equivalent chain lengths the Rg would be smaller with d-PS as

the matrix.

The radii of gyration for the arborescent polymers in deuterated PVME are plotted

as a function of temperature in Figure 33. Polystyrene/poly(vinylmethylether) blends are

well known to exhibit a low critical solution temperature (LCST) type phase diagram

with a critical point between 110 °C and 160 °C depending on molecular mass and

deuteration effects.35 The polystyrene/poly(vinylmethyl ether) blends studied in this

work contain deuterated PVME. All previous neutron scattering work on PS/PVME

blends used polystyrene as the deuterated component. All the data in Figure 33 are from

blends in the single phase region of the phase diagram. It is difficult to interpret the data

in Figure 33 in terms of any systematic temperature dependence of Rg in the single phase

region of the phase diagram. The temperature dependence of Rg for arborescent

polymers in deuterated polystyrene was not studied.

A scaling relation given by Rg = kMw

ν

 exists between the Rg and the molecular

mass, Mw, where ν is the scaling factor and k is a constant. A log-log plots of Rg versus

M for the arborescent polymers in deuterated PVME and deuterated polystyrene are

shown in Figure 34(a,b). Two dashed lines are shown in Figure 34(a,b), one calculated

for a Gaussian linear polystyrene chain and one for a sphere with the bulk density of

polystyrene, assuming the chain is completely collapsed. As observed in previous work

on arborescent polymers in solution, the arborescent polymers exhibit a crossover

between a Gaussian linear chain (ν=1/2) and an object with constant density (ν = 1/3).45

The exponent of ν for the arborescent polymers in deuterated PVME and deuterated

polystyrene was found to be ν = 0.28 ± 0.02 and ν = 0.26 ± 0.06, respectively, which

indicates that the average polymer segment density inside the sphere defined by the Rg

increases with increasing generation.

A power law function for the radial density was used to calculate the expected

scattering and fit to the SANS data for the G3 polymer. The fitting procedures and

uncertainties are reported elsewhere. The fit was optimized by varying the value of α.

The power law function is given by

max

() 1 rr

R

α

ρ   = −   (2.8)

Where Rmax corresponds to the hydrodynamic radius. The scattering was calculated using

eq (2.9).35
40

2

2 sin( ) () () qr I q dr r r

qr ρ  

   

∝ ∫ (2.9)

The best fit to the SANS data for the G3 molecule was found when α = 12 and

α = 18 for deuterated PVME and deuterated polystyrene, respectively, and the fits to the

scattering data are shown in Figure 35(a,b). The fits to the data in Figure 35(a,b) include

a 9 % polydispersity of the polymer and the effect of instrumental smearing with I(0),

Rmax and a base line as floating parameters. 72,73The values of Rmax=(260 ± 4) Å and

Rmax=(221 ± 4) Å were obtained from the fit of the scattering data in Figure 35(a,b) for

the G3 polymer in deuterated PVME and deuterated polystyrene, respectively. The error

bars for the values of Rmax were calculated from the errors in q based on the SANS

instrument configuration. A comparison of the radial density profiles in blends with

those previously obtained for solutions is shown in Figure 36.45 The density profile for

arborescent polymers in blends with linear chains decreases more rapidly at the outside

edge of molecules in comparison with that in solutions (α = 4). The density profile for

arborescent polymers in deuterated polystyrene is close to that of a hard sphere. Using

the power law density function given by Equation (2.8), the radius of gyration can be

calculated from Equation (2.10).

4

2

2

 (r) r

 (r) r g

dr

R

dr

ρ

ρ = ∫

∫ (2.10)

The relation between Rg and Rmax for arborescent polymer in deuterated

polystyrene was found to be Rg = (63/115)1/2 Rmax (for α = 18) and the calculated Rg was

164 Å. For comparison the Rg of a sphere was calculated assuming that the G3

molecules were collapsed to bulk density. The Rg obtained was approximately 162 Å,

which is close to the Rg of the G3 polymer in deuterated polystyrene. This indicates that

the G3 molecules in deuterated polystyrene should be non-interpenetrating and the

deuterated linear polystyrene is largely excluded from the interior of the arborescent

molecules.

The measured scattering for the G3 in deuterated poly(vinylmethyl ether)

(PVME) was essentially constant as the temperature was changed from 80 °C to 105 °C.

No increase in the concentration fluctuation scattering was observed as the phase

separation was approached, as is typically observed for polymer blends.74,75 Phase

separation occurs above 105 °C and two peaks develop as shown in Figure 37. Upon

phase separation, the single particle form factor peak (the second peak located at q =

0.023 Å-1) shifts to higher q, indicating that the size of the molecules decreased. The size

of the molecules after phase separation was estimated from the position of the second

form factor peak using the power law model and plotted as a function of temperature in

Figure 38. As noted previously, there is no appreciable temperature dependence of Rg in

the single phase region, but a collapse of the G3 molecules by about 21 % is observed

with phase separation. The collapse transition has long been of interest and has generated
41

much theoretical and experimental work, because of its relevance to local polymer

structure, fractionation, and biological applications such as protein folding.76,77 To the

authors’ best knowledge this is the first direct observation of a collapse transition

observed in polymer blends, although it has been predicted in simulations78 and

theoretically.79 It should also be noted that the deuterated PVME is of quite low

molecular mass. The variation in the size of a linear polystyrene chain in cyclohexane as

a function of temperature near the theta temperature has been studied by many authors

and the collapse transition for a linear chain in deuterated cyclohexane has been observed

below the theta temperature.76,77,80-84 In our previous experiments on arborescent

polymers in deuterated cyclohexane there was a 15% decrease in Rg when phase

separation occurred.45 At 115 °C two peaks are found in the I(q) versus q data for the

G3 in deuterated poly(vinyl methyl ether). The first peak is due to the interference

between molecules, while the second peak arises from the single particle form factor.

The scattering intensity for a particulate system can be expressed as20

( ) ( ) S(q) n Iq k NPq = (2.11)

Where kn is the contrast factor for neutrons, N is the concentration of the

scatterers (arborescent polymer molecules), P(q) is the single particle form factor

(intraparticle interference), and S(q) is the structure factor (interparticle interference). In

the single phase blends, the molecules are in the dilute concentration range and noninteracting, and only P(q) is observed. For the phase separated G3 arborescent polymers

in d-PVME at high temperature, it is expected that S(q) should play a role. The first peak

observed in the scattering curve from the phase separated solution is due to the first

neighbor interference (i.e. S(q)), as observed in many systems such as latex spheres and

spherical block copolymers.85-89 The second peak in the scattering curve has the same

general shape and is in the same general q range as the peak observed in P(q) for the nonphase separated samples. The interpretation of this peak as being associated with P(q) is

also consistent with previous work on latex spheres and block copolymer

systems.85,90,91 From the position of the first peak the center to center distance between

nearest neighbor molecules was estimated using the relation, d = (1.23×2π)/q, which is

valid for a structure controlled by two body (noncrystalline) correlations.70,71 This

distance was found to be (505 ± 14) Å. From the position of the second peak, the

diameter of a single molecule was estimated using the single particle scattering function

derived from the power law function density profile (Equation (2.8)). The data in the

range q = (0.018 to 0.05) Å-1 was fitted to the scattering function calculated using the

power law model with α=12. Rmax was found to be (232 ± 4) Å and the calculated

density profile for phase-separated G3 polymer in deuterated PVME is shown in Figure

7. The error on the value of Rmax was calculated from the errors in q based on the SANS

instrument configuration. The diameter of a single dendrimer molecule is dmax = 2Rmax =

 (464 ± 8)Å, which is smaller than the distance between nearest neighbors, indicating

that the molecules are not quite in contact with each other. Using the power law density

function given by Equation (2.8) the radius of gyration was calculated from eq 7 and

found to be Rg = (9/17)1/2 Rmax (for α = 12). The Rg for a G3 arborescent polymer in
42

deuterated PVME at 115 °C (which is slightly inside the two-phase region of the phase

diagram) calculated using this relation is (169 ± 3) Å. This is close to the Rg calculated

for a sphere assuming the G3 molecule is collapsed to bulk density. This indicates that

deuterated PVME is largely excluded from the interior of the arborescent molecules after

phase separation occurs.

The Rg of G3 arborescent polymer molecules was studied as a function of the

molecular mass of the linear d-polystyrene matrix. The matrix molecular mass was

varied from 4,300 g/mol to 430,000 g/mol. The Rg obtained using Guinier analysis, is

plotted as a function of the molecular mass of the matrix polymer in Figure 39 shows that

as the molecular mass of the matrix polymer increases, the Rg of the G3 polymer

decreases. The largest decrease in Rg is observed when the matrix molecular mass

increases from 4300 g/mol to 26600 g/mol. There appears to be additional small

decreases in Rg with further increases with molecular mass of the matrix polymer, but

their magnitude is close to the errors on the measurements. The larger Rg observed for

the lowest molecular mass matrix polymer indicates that the regions within the volume of

the G3 arborescent polymer are limited in size and shape and only accessible to the

shortest chains. The configurational entropy penalty for higher molecular mass polymers

to penetrate the coil of the arborescent polymer is too great compared to the (relatively

small) gain in mixing energy.

2.4.5 Conclusions

The radius of gyration of arborescent polymers decreases in going from solutions to

polymer blends. The size of arborescent polymers in deuterated polystyrene is smaller

than in deuterated poly(vinyl methyl ether). The scaling exponent for Rg ~ Mν

 is found to

be ν = 0.28 ± 0.02 in d-PVME and ν =0.26 ± 0.06 in d-PS, which indicates that

arborescent segment density is increasing as a function of generation. The scattering

curve calculated using a power law model is in reasonable agreement with the measured

scattering. The value of α in the power law model is largest for arborescent polymers in

deuterated polystyrene, and the sequential density calculated from the molecular mass

divided by the volume of coil of the arborescent polymer in deuterated polystyrene is

found to be close to bulk density. This indicates that the molecules are essentially noninterpenetrating and exclude the linear matrix chains. For G3 polymer in deuterated

poly(vinylmethyl ether), two peaks in the I(q) versus SANS data are observed above the

phase separation temperature (105 °C) and the Rg of the phase separated sample

decreases by about 21 % upon phase separation. In the two phase blends, G3 polymer

molecules are found to be not in contact with each other.

2.5 Dispersing Dendrimers in a Solid Polymer Matrix

2.5.1 Synopsis

Dendrimers can be uniformly dispersed in a solid, polymeric matrix by the use of

interpenetrating polymer network (IPN) synthetic methods. Small angle x-ray scattering

(SAXS) and transmission electron microscopy (TEM) demonstrate that polyamidoamine
43

(PAMAM) dendrimers are well dispersed in a poly(2-hydroxyethyl methacrylate)

PHEMA matrix that has been crosslinked with mass fraction 0.5 % ethylene glycol

dimethacrylate. The dendrimer size can be measured by SAXS through fitting of the

minimum before the first higher order feature of the sphere-like scattering. The size can

also be measured by TEM through either measurement of individual dendrimers in the

micrograph, or by taking a fast Fourier transform (FFT) of the micrograph and comparing

the features of the transform to those of circles. All three methods give equal sizes within

the error estimates. When the concentration of dendrimers in the IPN reaches mass

fraction 10 %, a shrinkage of the dendrimers occurs with the dendrimers shrinking to near

bulk density. This concentration is lower than the concentration at which the dendrimers

shrink when in solution. The G8 dendrimers at mass fraction 2 % have a weak peak in

the FFT indicating that a correlation in the spacing is beginning, but the addition of acid

to the IPN polymerization does not increase order.

2.5.2 Introduction

Various applications of dendrimers take advantage of the spherical shape, such as

the use as covalently bonded micelles or as an agent for encapsulation (“dendritic

box”).92 The design of materials with specialized optical properties, or for use as highcapacity magnetic storage devices is currently being discussed.93,94 These applications

require the isolation of entrapped functionalities from their counterparts in neighboring

dendrimers. Recently, PAMAM dendrimers have been used as templates to produce

metallic nanoclusters that are incorporated into the dendrimer structure.95

To fabricate a useful device based on these ideas, incorporation of the dendrimers

into solid polymeric matrices is desirable. It would be very advantageous to be able to

“freeze” the dispersion of dendrimers in solution by replacing the solvent with polymer.

This could possibly be accomplished by the use of interpenetrating polymer network

(IPN) techniques.

IPN technology has been studied for many years96. It involves forming an

intimate mixture of two polymer types, with at least one of the polymers being

polymerized in the presence of the other. The word “interpeneterting” described the

attempts to make two polymers form continuous, independent structures, either as

intertwined networks in a single phase, or more commonly, as a two phase morphology

with co-continuous phases. While the word “interpenetrating’ implies a certain

morphology, the designation, IPN, has taken on a broader meaning than the morphology

alone. In this paper “IPN” will be used to describe the method of polymerization as is

commonly used, and does not imply that the dendrimer phase is continuous.

A Semi-II IPN is formed when a linear polymer is dissolved in a monomer of

another type which acts as a solvent. The monomer is then polymerized, most often with

a certain amount of multifunctional comonomer present to form a crosslinked network.

In most cases, the dissolved polymer phase separates during the polymerization of the

second polymer, forming a multi-phase morphology. The presence of the crosslinked

second phase, however, can induce a very fine size scale on the phase separation.
44

Previous work on semi-II IPN’s of linear polymers has shown that there is a

strong thermodynamic push to phase separation.42,97,98 Only when the first polymer is

of low molecular mass, generally having a lower molecular weight than the molecular

mass between crosslinks, does the linear chain stay molecularly dispersed. If this is also

the case with dendrimers, large dendrimers, which can be greater then 1,000,000 g/mole,

may be difficult to disperse in an IPN matrix at a molecular level.

2.5.3 Experimental

2.5.3.1 Synthesis

PAMAM dendrimers diluted with methanol to produce the desired concentration.

The ipns were prepared by dissolving the dendrimers in 2-hydroxyethylmethacrylate

(HEMA) containing either mass fraction (1⁄2 or 1) % ethylene glycol dimethacrylate with

AIBN as an initiator99,100. They were polymerized at 35 °C for 72 h and at 70 °C for an

additional hour.

2.5.3.2 SAXS

SAXS experiments were measured in the standard manner. The IPN samples were

soaked in aqueous HBr to increase the x-ray contrast. They were then dried in vacuum

for the SAXS experiments. A second set of samples were soaked in the same

Phosphotungstinic acid solution as was used in the TEM experiments.101 The stained

samples were mounted in a solution cell.

2.5.3.3 TEM

Samples of thickness approximately (60-80) nm were ultramicrotomed at -80 °C,

transferred to carbon-coated Cu grids of 200 mesh, and stained with OsO4 vapors by

exposing the grid to a solution of 0.04 g OsO4/g H2O at room temperature for 1 h. The

images were obtained at magnification of 17,000X or less on a Philips 400T model TEM

operated at 120 kV using low-dose conditions99,100.

Dendrimer blends were stained with a mass fraction 2% aqueous phosphotungstic

acid (PTA) solution that has been neutralized with sodium hydroxide (ph = 7), for 1 d

and dried for 3 d in air. The blends looked optically transparent, even after Na-PTA

staining. Electron transparent films of (60 to 80) nm thickness were cryo-microtomed at

–30 °C, transferred to carbon coated Cu TEM grids, and the morphology of these

materials was studied using TEM (Philips EM 400T) operated at 120 kV under low-dose

conditions101.

2.5.3.4 Data Analysis
45

The Rg values of solutions were from Guinier fits of the scattering data.35 The

values for the IPNs were calculated from the positions of the higher order features38,50

and are reported as a relative range of ± 10 % that is typical of such measurements.

Micrographs were scanned at (40 to 120) pixels/cm. Sections 512 by 512 pixels

were cut and fast Fourier transforms were taken with Scion Image102 to produce 2-

dimensional images that were anisotropic in all cases. The 2-dimensional images were

averaged to produce I(q) files and calibrated by taking transforms of model objects.

2.5.4 Results and Discussion

Figure 40 shows the SAXS from a G10 dendrimer at high and low concentration,

in methanol solution and in a PHEMA matrix. The IPN contrast was enhanced by

treatment with hbr as described in the experimental section. The maxima at q > 0.05 Å-1

in Figure 40 result from P(q) with the higher order scattering features from spherical

particles (Equation (1.7)35). This function has minima at qr = 4.49, 7.73, 10.90 ... which

can be used to estimate the R and Rg of a sphere. This is useful at high concentrations

where S(q) interferes with the size measurements at low q. Such a procedure has been

used to measure dendrimer size at high concentrations38,50. It is easy to see in Figure 40

that the first minimum of P(q) is quite similar for the G10 dendrimer at mass fraction 1 %

in both solution and IPN. At mass fraction 26 % solution concentration, the minimum is

the same as the low concentrations, indicating that the dendrimer is unchanged in size.

At mass fraction 10 % dendrimer in the IPN, however, the minimum is shifted to higher

q, showing that the dendrimer has shrunken in size. This is similar to the findings that

dendrimers shrink in size at concentrations higher than overlap concentration, even

though the mass fraction 10 % dendrimer in IPN is presumably below the overlap

concentration.

Figure 41 is a plot of dendrimer size in dilute solution and in ipns at mass fraction

(1 and 10) % versus generation. There is a consistent trend in the range G6 through G11

where the dilute solution sizes are similar in both methanol solution and in HEMA IPN.

At mass fraction 10 % concentration, however, the size has shrunken by about 20 %.

Such sizes are close to dendrimers that have excluded all of the linear PHEMA chains.

The peaks at low q of the mass fraction 10 % dendrimer in the IPN and the mass

fraction 26 % dendrimer in solution are from the S(q) contributions and can be used to

calculate the characteristic spacing between dendrimers, D, from the peak position, qmax

by D = 1.23 × 2π / qmax.35 The spacing of the mass fraction 26 % dendrimers in

solution is (187 ± 19) Å and of the mass fraction 10 % dendrimer in the IPN is

(224 ± 22) Å. Also, there is no sign of an upturn at the lowest resolvable q that would be

an indication of dendrimer aggregation. Therefore, SAXS shows that dendrimers from

G6 through G11 can be uniformly distributed in IPNs.

Figure 42 is a TEM of a G11 PAMAM dendrimer at mass fraction 10 %

concentration. Individual dendrimers can be seen, but due to the thickness of the sample,
46

dendrimers at different levels can be seen, making them appear to overlap. The

dendrimers appear round, with uniform sizes and distributions. Lower magnification

images of this sample showed that the dendrimer concentration was uniform without any

sign of clustering. These results are consistent with the SAXS results.

 Figure 43 is a TEM of an IPN with mass fraction 1 % PAMAM G10. The

staining in this sample was with a mass fraction 2 % aqueous PTA as was described in

the experimental section. Individual dendrimers can be seen. A comparison to results

using oso4 stain for the mass fraction 10 % G11 dendrimer in the IPN shown in Figure

42. The dendrimers are visible in this image, but the differentiation between dendrimer

and matrix is much less apparent than seen in Figure 40 for the same sample stained with

NaPTA.

Previous work54,103 has shown that the addition of acid to an aqueous dendrimer

solution causes ordering of the dendrimers. If such ordering can be induced in the solid

IPN, it may produce morphologies with potential applications as electrical, optical, or

information storage devices93,94. SAXS was performed on samples that were stained

with phosphotungstinic acid. The samples were made with mass fraction 2 % G8

dendrimer (G8) and with added methacrylic acid comonomer (G8-MAA) as was

described in the experimental section. Figure 44 shows the scattering from the two

samples. The two curves are nearly identical, suggesting that the morphology is

unchanged with and without the acid addition. In previous solution studies54,103 a

strong peak appears when the acid is added. This peak if from the S(q) function which

can be used to calculate a characteristic spacing. While no peak is apparent, there is a

leveling of the intensity at low q, which may be a shoulder or an incipient peak. The

absence of a strong peak shows that no pronounced ordering exists in these samples. The

electrostatic forces that cause the ordering in dilute aqueous solution are not sufficient to

increase the ordering under the IPN conditions since the scattering from.

Figure 45 is a TEM of sample G8. Individual dendrimers can be seen, and they

appear to be well dispersed in the matrix. Micrographs of all of the different areas

examined in this sample were indistinguishable from this one, suggesting that the

dispersion is macroscopically uniform. Figure 46 is of a sample similar to the one in

Figure 45, except that the matrix is made from PHEMA containing a small amount of

methacrylic acid sample G8-MAA, an amount calculated to be the molar equivalent to

the PAMAM dendrimer terminal amine groups. These are the same samples that were

used in the SAXS experiments shown in Figure 44.

Figure 45, however, is indistinguishable from Figure 44 showing that there is no

detectable change in the morphology. This is in agreement with the SAXS results. To

better estimate the size and dispersion of the dendrimers, a 2-dimensional Fourier

transform was performed on the micrographs and the resulting anisotropic pattern was

circularly averaged to produce the curves shown in Figure 47. The SAXS and TEM-FFT

curves differ in that the SAXS scattering is from a 3-dimensional array, while the TEMFFT is from a 2-dimensional projection. Both, however, have similar features. First, the

curves of the two samples are identical in both samples in each figure, indicating that the
47

morphology is not significantly affected by the addition of the MAA to the IPN. Second,

the incipient peak at low q in the SAXS has become a weak peak in the TEM-FFT

indicating that there is a weak correlation between the dendrimer spacing. A TEM-FFT

of the mass fraction 1 % G9 and G10 dendrimers in IPN’s is included in Figure 47 to

show the complete absence of a peak in the transform. Third, both figures show higher

order features in the scattering which can be used to measure the R and Rg of the

dendrimers. The sizes from SAXS are Rg = (37.4 ± 3.7 and 36.2 ± 3.6) Å for the G8 and

G8-MAA sample respectively. The TEM-FFT size is Rg = 36.8 ± 3.7 Å for both samples.

Table 5 is a compilation of the sizes of the dendrimers in IPNs and in solution of

samples of various generations. Also listed in Table 5 are the sizes from TEM calculated

by measuring the sizes of a population of dendrimers from each micrograph23,101. As

can be seen in Table 5 and in Figure 41, all of the dendrimer sizes form a composite line

except for the mass fraction 10 % dendrimer in IPN samples which are approximately

20 % smaller. Therefore there appears to be a shrinkage in size with increased

concentration as was seen in previous solution studies,38,50 however, the shrinkage

comes at a somewhat lower concentration for the solid ipns.

All of the SAXS and TEM results suggest that the dendrimers are well dispersed

in the matrix with no dendrimer aggregation evident. This is contrary to previous results

on ipns made from linear polymers. Bauer and Briber42 have found that ipns made with

poly(vinylmethyl ether) in a crosslinked polystyrene (PS) matrix will phase separate

when the crosslink density is large enough. In this study, the Flory-Huggins interaction

parameter was negative, which is a strong driving force for miscibility. Even under these

favorable conditions, phase separation was induced by the crosslinking. Similarly, linear

PS phase separated from a deuterated PS network during the IPN polymerization.97

Another study98,104 with dilute linear PS in a deuterated PS network found that the

linear chains collapsed as the network density was increased and phase separated, even at

low concentrations, when the molecular mass between crosslinks was equal to the

molecular mass of the linear chains.

For the dendrimer ipns, however, phase separation did not occur, even though the

dendrimer molecular weight of the largest dendrimers was around 1,000,000 g/mol. The

dendrimer/PHEMA interaction parameter is unfavorable as is evident since a solution

cast film of PAMAM G8 and linear PHEMA phase separations upon solvent evaporation.

The fact that the dendrimer ipns do not phase separate upon polymerization may be due

to their compact size. In linear ipns, phase separation occurs when the size of linear

chain is approximately that of the size of the linear chain between crosslink points. For a

mass fraction 0.5 % ethylene glycol dimethacrylate, the molecular mass between

crosslink points is approximately 80,000 g/mol. For a mer step length of 7 Å, this makes

the average spacing between crosslink points of 170 Å which is smaller than the

dendrimer diameters. The compact size of the dendrimers may contribute to the stability

of the ipns.
48

2.5.5 Conclusions

Dendrimers can be uniformly dispersed in a solid, polymeric matrix by the use of

IPN synthetic methods. PAMAM dendrimers from G6 – G11 were placed in IPN’s of

PHEMA crosslinked with mass fraction 0.5 % ethylene glycol dimethacrylate. SAXS and

TEM show that there is a uniform dispersion of dendrimers at mass fraction 1 %

dendrimer. SAXS of mass fraction 10 % dendrimer IPN’s also shows good dispersion,

with a peak forming that indicated ordering. G8 dendrimers at mass fraction 2 %

dendrimer show an incipient peak in SAXS and a weak peak in TEM-FFT. This may be

the concentration at wich ordering first appears. The addition of MAA to the IPN does

not measurably change the ordering of the dendrimers.

The dendrimer size can be measured by SAXS through fitting of the minimum

before the first higher order feature of the sphere-like scattering. The size can also be

measured by TEM through either measurement of individual dendrimers in the

micrograph, or by taking a Fourier transform of the micrograph and comparing the

features of the transform to those of circles. All three methods give equal sizes within the

error estimates.

When the concentration of dendrimers in the IPN reaches mass fraction 10 %, a

shrinkage of the dendrimers occurs with the dendrimers shrinking to near bulk density.

This concentration is lower than the concentration at which the dendrimers shrink when

in solution.

2.6 End Linked Dendrimer Networks

2.6.1 Synopsis

Networks and star polymers are former by reacting end functionalized

polyethylene glycol (PEG) with PAMAM or PPI dendrimers. Four end functionalities,

Vinyl Sulfone (VS), Isocyante (IS), Acrylate (AC), and Epoxide (EP) are used and SANS

and GPC are used to measure the extent of reaction. The EP is unreactive under the

conditions used, AC reacted efficiently but quickly hydrolyzed in aqueous conditions,

and IS reacted well, but formed large size byproducts in aqueous conditions. The VS

proved best, giving high conversion and hydrolytically stable linkages. Swelling

experiments show similar swelling for samples with high crosslink functionality, but the

amount of swelling is methanol < water < acid. Aqueous solutions swell with acid

addition, reaching a maximum, and then deswelling with more acid addition.

2.6.2 Introduction

A variety of model networks made from end functionalized low polydispersity

linear polymers have been studied. The functionality of the crosslinks is either small

molecules with 3 or 4 functionallity or a polydisperse, multifunctional gel such as

divinyl benzene. The use of dendrimers as a multifunctional branch point should give
49

high functionality since dendrimers have up to several thousand attachment sites and low

polydispersity.

Dendrimers are polymeric molecules that are made in a stepwise synthesis that

doubles the terminal functionality with each set of two synthetic steps, or generation.4,21

Dendrimers have been found to be spherical with a narrow interfacial transition on the

outside.20 The terminal units are predominately on the outside.46 These factors make

dendrimers ideal multifucntional crosslinking agents, with many functional units easily

accessible at the periphery of the dendrimer. Dendrimers also have a very narrow

polydispersity with between 4 and 4096 theoretical crosslink sites.4,21

The efficiency of the reaction is difficult to measure in networks, analytical

methods that measure end group conversion are difficult and subject to uncertainties at

high conversions. Extraction experiments are also inexact at high conversions. Studies

of the reactions of polymers with a single end functionality are simpler since they form

stars rather than networks which are soluble and can be more easily characterized.

Reactions of end functionalized PEG with dendrimers have been reported for

amino terminated dendrimers and NHS terminated PEG.105 High conversions have been

reported forming stars with large numbers of arms. Only the high conversion results

were studied, however. No measures of the kinetics were made. This work reports the

use of chromatography to follow the conversion of arms to stars.

By changing the generation of the dendrimer, the crosslink functionality can be

continuously changed. Similarly, by changing the ratio of linear chains to dendrimer

terminal units, the crosslink functionality can be changed. Thus, samples can be made

with a constant degree of polymerization, N, between crosslinks, but with a wide range of

functionalities. Swelling of the networks with solvents of varying power, i.e. Varied

Flory-Huggins interaction parameter, χ, can be used to measure the effect of crosslink

functionality.

2.6.3 Experimental

All endfunctionalized poly(ethylene glycol) was used as received from

Shearwater Polymers. Monofunctional Vinyl Sulfone (VS), Isocyante (IS), Acrylate

(AC), and Epoxide (EP) terminated PEG had nominal Mn = 5,000 g mol-1 and

Mw/Mn < 1.1. Difunctional Vinyl Sulfone (VS) terminated PEG had nominal

Mn = 20,000 g mol-1 and Mw/Mn < 1.1. Polyamidoamine (PAMAM) dendrimers G5

through G10 were obtained from Dendritech and generations G2 through G4 were

purchased from Aldrich Chemical Company. Polypropyleneimine (PPI) G5 dendrimer

was purchased from Aldrich Chemical Company.

Stars were formed by reacting the monofunctional PEGs with PPI or PAMAM

dendrimers in methanol, water, or DMSO solution. Networks were made in a similar

way and fluorinated polymeric containers were used for easy removal of the gels for

swelling measurements. Swelling measurements were made by immersing the gels in a
50

large excess of the new solvent. Swelling ratios were measured by weight and soluble

fractions were measured by evaporation of the extracting solvent. Ipns were synthesized

by swelling the gels with methyl methacrylate containing mass fraction 0.5 %

axobisisobutyronitrile as a free radical initiator and polymerizing at 35 °C for 72 hours

and an additional hour at 70 °C.

Gel permeation chromatography (GPC) was done with volume fraction 0.1 %

triethylamine in H2O as a mobile phase with a Phenomenex Polysep-GFC P column.

Kinetic GPC runs were done by adding appropriate amounts of VS-PEG and dendrimer

at total mass fraction 10 % in the mobile phase solvent were mixed and 10 μl quantities

were repeatedly injected. Detection was by an evaporative light scattering detector

(Varex, model Mark iia).

The SANS experiments were performed at the 8 m facility at the National

Institute of Standards and Technology Center for Cold Neutron Research (Gaithersburg,

Maryland) in the normal manner. Scatterring was done at ambient temperatures which

were nominally (20 ± 2) °C. A sample to detector distance of 360 cm was maintained

throughout the study, operating at a wavelength λ = 6 Å, with a wavelength spread of

∆λ/ = 0.25. Based on the hydrogen content of the materials, an estimate for the

incoherent scattering was subtracted from the values of the absolute solution scattering

intensity, to give the final form of the experimental data, which is the absolute intensity

of the coherent scattering, I, as a function of q.

SAXS data were collected at the Advanced Polymer Beamline at Brookhaven

National Laboratory, X27C. X-ray contrast was enhanced by soaking the samples in

dilute sodium phosphotungstinate solution as is described in the experimental section of

the dendrimer IPN section. The usable span of scattering vector ,q , was in the range

0.07 Å-1 < q < 0.3 Å-1.

2.6.4 Results and Discussion

PEG has many advantages over other end functionalized polymers. It has

solubility characteristics similar to that of PAMAM and PPI dendrimers, being soluble in

water, alcohols, and DMSO. Solubility in common solvents is a requirement for the

chemical reaction to form a large, uniform sample. PEG is also soluble in non-solvents

for dendrimers such as benzene. Also PEG forms miscible blends with polymers such as

poly(methyl methacrylate) (PMMA) and poly(methyl acrylate) (PMA) which can be

exploited in forming solvent-free samples.

PEG is available with a variety of end functionalizations that are capable of

forming covalent bonds with the terminal primary amines of PAMAM or PPI dendrimers.

It is important that the reaction tales place at a rate fast enough for high conversions to

be reached in a reasonable time, but slow enough so that mixing and film casting can take

place before gelation takes place. Side reactions that would cause unwanted bonding or

polymerizations or cleave the functionalities from the chain have to be avoided.
51

 Four functionalities were chosen for screening, acrylate, epoxy, isocyanate, and

vinyl sulfone. An acrylate reacts with a primary amine through a Michael addition. This

is the same reaction that is used to form half generations in both PAMAM and PPI

dendrimers. The vinyl sulfone also reacts through a Michael addition. The isocyanate

forms a urethane linkage and is perhaps the most common reaction used in linking

polymers. The epoxy forms an amine linkage and generated a hydroxy group. The

epoxy-amine reaction is commonly used in forming networks, but usually requires high

temperatures.

PEGs of Mw = 5000 g/mol with these four functional groups on one end were

reacted with PPI G5 dendrimer. The ratio of PEG end groups to PPI end groups

examined was 1:2, which would produce 32 arm stars at 100 % conversion. Mixtures

were made in DMSO-d6 at a total mass fraction of 10 % and allowed to react for one

week. The mixtures were placed in 1 mm thick quartz cells for SANS experiments.

Figure 48 shows Kratky plots of the results of mass fraction 0.5 % dilutions of the four

samples. The plot is Iq5/3 vs q which gives a plateau region at high q for flexible chains

in a good solvent. The plots are normalized so that the curves go to 1 at this point. The

IS, VS and AC samples all have a strong peak in the Kratky plots which is characteristic

of many arm stars.35 The ratio of the peak to the plateau is function of the average

number of arms. Assuming that the scattering is from a mixture of stars and unreacted

arms with an arm conversion, p, the scattering can be calculated for stars with Gaussian

arms, and an estimate of conversion and arms per star can be made.

The conversion of the IS, VS, and AC, is 0.76, 0.73, and 0.66, respectively. The

average arms per star are 24.4, 23.3, and 21.6. It is clear that the reaction is efficient and

produces large star molecules. The EP sample, however does not produce a peak in the

Kratky plot. A peak appears in the Kratky plot at a conversion of 0.21 under these

conditions, so it is obvious that the reaction is quite incomplete. Also plotted is the

SANS of a mass fraction 5 % PEG arm for comparison. It appears that the epoxy does

not react significantly under these conditions.

The SANS samples were examined with GPC to separate the stars from the

unreacted arms. Figure 49 shows chromatograms of the four groups and an unreacted VS

terminated PEG. The chromatographic conditions used gives good separation of the two

peaks. The VS star shows good conversion into a narrow star peak, with only a small

peak from the unreacted PEG, giving a conversion of 0.82. The IS chromatogram shows

good conversion of the arms, but an additional peak appears at even lower elution

volume, indicating a larger hydrodynamic volume. This peak is at the exclusion limit of

the column and indicated that very large structures exist. This additional peak is

probably due to a side product from the isocyanate reaction producing larger molecules.

It seems likely that the reactions happened when the sample was placed in the aqueous

solution since the SANS results do not show such large structures. The EP sample shows

little conversion, consistent with the SANS results. The AC sample also shows no star

molecules present, in contrary to the SANS results which indicated high conversion. The

EP terminated PEG was the only sample that has an ester linkage. It probably has

hydrolyzed under the aqueous GPC conditions.
52

Out of the four reactions, the EP is not useful due to the low conversion under the

reaction conditions. The IS reacts well, forming stars, but side reactions make the

product heterogeneous. The AC reaction is quite efficient and the bond formed stable in

aprotic solvents such as DMSO, but is sensitive to impurities such as water. The VS is

by far the most useful of the four reactions. It gives good yield in a reasonable time and

is not subject to side reactions. The bond formed is hydrolytically stable, and good

conversions can be obtained even with water or methanol as a reaction solvent.

The VS reaction allows for detailed study of the kinetics of the linking due to its

reaction in aqueous media. GPC was done on a reaction mixture in which the dendrimer

and PEG-VS was mixed in water with volume fraction 0.1 % triethylamine which was

the GPC mobile phase. Roughly equimolar amounts of a G4 PPI dendrimer (32 terminal

–NH2 groups) and PEG-VS at a total mass fraction of 10 %. A slight excess of G4 PPI

dendrimer would give 30 arms at complete conversion. Injections were repeatedly made

from this reaction mixture over the period of one day. Figure 50 shows the GPC of six

injections over this time period. The PEG-VS peak drops continuously during this time

span and the star peak increases in size. The position of the star peak also shifts to lower

elution volume and becomes narrower with conversion. This suggests that the stars are

becoming larger and more uniform. Figure 51 shows the conversion of arms with time

with GPC data were taken between (4 and 1383) min. The kinetics of the reaction can be

modeled by kinetics that are first order in VS-PEG and first order in dendrimer end

groups as in equation (2.12).

2 ∂ ∂ =− − [ ]/ [ ][ ] PEG t k PEG NH (2.12)

 The solid line in Figure 51is a fit of equation (2.12) to the first order kinetics. The fit

is quite poor, underestimating the rates at low conversion and overestimating the rates at

high conversion. The reaction seems to be slowing down considerably with conversion

due to the crowding that occurs when a large number of arms are placed on the star.

If the crowding that occurs when a large number of arms are on the dendrimer, the

reaction may not obey first order kinetics in the concentration of available dendrimer

terminal groups. The kinetics was refit to equation (2.13), which allows the order of the

reaction with respect to dendrimer end groups to float.

2 [ ]/ [ ][ ] PEG t k PEG NH α ∂ ∂ =− − (2.13)

It is quite possible that the reaction in also not first order in PEG-VS

concentration, but the reaction orders will be too closely correlated to separate them from

a single kinetic run. The dashed line is a fit of Equation (2.13) and it is quite good,

giving an exponent a = 3.6 with a standard deviation of ± 0.2. The kinetic experiment

has been repeated with different concentrations, stoichiometries, and dendrimer type and

the slowing down of the conversion is typical of this reaction, but high conversions can

still be reached. In Figure 51 a conversion of 80 % is reached within a day. A more

detailed investigation of the kinetics will be published separately.
53

A network with degree of polymerization, NC, when swollen with a solvent with a

solvent having a Flory-Huggins interaction parameter, χ, will swell from the volume

fraction polymer during synthesis, ν2c, to a swollen volume fraction, ν2 , according to

equation (2.14).

1/3

2 2

2

22 2

(1 2 / )( / ) (1 ( ))

ln(1 )

c

C

f K N νν λ

ν ν χν

− + = − ++

(2.14)

Where f is the functionality of the crosslinks and K(λ) is an elastic contribution

that is a function of chain extension ratio, λ, which depends on the elasticity theory used.

Therefore the swelling ratio of a network is a constant for any given value of NC / (1 -

 2/f). Therefore changing the crosslink functionality has the effect of changing the

molecular mass between crosslinks. The change in going from f = 4 to f → ∞ involves

an effective change of NC by a factor of 2.

Equation (2.14) has different forms depending of the theory of elasticity used.

For the Phantom Network assumption, where the chains do not experience the effects of

neighboring chains, the term K(λ) = 0 so equation (2.14) described the swelling without

the final term. For an Affine Network assumption, where the microscopic crosslink sites

move proportionate to macroscopic deformation, the term K(λ) = 1 – λ-2. The functional

form for the swelling is given in equation (2.15), and is known as the Flory-Rehner

equation.

1/3 2/3

22 2 2

2

22 2

( / ) (1 2 / ( / ))

ln(1 )

c c

C

f N νν ν ν

ν ν χν

+ = − ++

(2.15)

Two series of networks were synthesized with PEG-VS2 chains attached to PPI or

PAMAM dendrimers. In the PPI series, G5 dendrimers were used in all samples, but the

stoichiometry was changed giving between 4 and 64 theoretical crosslink functionality

for 100 % conversions. Therefore, the mass fraction dendrimer and the fraction of

reacted terminal groups changed in the samples of the series, but the dendrimers were all

the same size. In the PAMAM series, the dendrimer generation changed from G2 to G7,

but the ratio of VS groups to dendrimer terminal groups was kept at 1:2 in all cases

giving between 16 and 256 theoretical crosslink functionality. Therefore, the mass

fraction dendrimer and the fraction of reacted terminal groups were constant in the

samples of the series, but the dendrimers changed in size.

Both series had a mass fraction of 10 % solids in methanol during the synthesis

and the reaction was allowed to proceed for seven days. In the PPI series, three

additional samples were made but were reacted for only one day. Figure 52 is a plot of

the mass swelling ratio of the PPI series samples. The samples were first placed in

excess methanol and allowed to swell to equilibrium. The samples were then placed in

excess water and the water was exchanged twice. HCl was then added in a stoichiometric

amount to that of the dendrimer terminal groups. The increased mass in methanol was

quite small with the exception of the lowest crosslink functionality. In water, the
54

swelling ratio increases for all samples and was relatively constant with the exception of

the lowest functionality again. This is qualitatively in agreement with equations 3 and 4

which predict only a weak effect of the crosslink functionality on the swelling for large f

and an increase of swelling as f gets close to the critical value of 2.

The data points for the one day reaction time all lie above the seven day points.

This is due to the lower extent of reaction. The theoretical value of f is not achieved and

the curves would be shifted to the left if the actual values of f were printed. In fact, the

study of the reaction rated of the stars shows that the reaction is not complete and this is

undoubtedly true for the networks also. In an effort to judge the effectiveness of

equations (2.14) and (2.15), fits can be made to the swelling data. There are considerable

uncertainties in the variables needed for the fits, particularly the crosslink functionality,

but the fits can give qualitative trends that can provide some insight in the swelling.

Equations (2.14) and (2.15) were fitted to the swelling data, using χ as the fitting

parameter. When 100 % conversion is assumed and the theoretical f is used, the fits are

poor, with the low f swelling values underestimated and the high f values overestimated.

The fits were repeated but the average conversion was also fitted. An assumption that the

probability of a chain attaching, p, is the same for all samples. While there is

undoubtedly different conversions for the samples, the results should qualitatively be the

same.

The fits of the PPI series are shown in Figure 52 for both the Phantom and Affine

networks. Fits of both theories have common features, a relative level swelling at high f

with an upturn at low f. The fit parameters merely show that the value of c is small and

the conversion is around one half. Extraction studied of these samples gives an average

extractable fraction of (2.9 ± 2.7) % which represents a value of p = (83 ± 16) %. The

fits of equations (2.14) and (2.15) are therefore qualitatively consistent with other

measurements.

The addition of acid causes the samples to swell considerably more than with

neutral water. Figure 53 shows the swelling that results when HCl is added to the

aqueous solution in a stoichiometric amount to the terminal amines. The amount of

swelling is also no longer flat for the larger crosslink functionality, but varies

continuously. For these samples, the mole fraction dendrimer increases proportionately

to the crosslink functionality so that the acid amount increases also.

Another set of samples was made with PAMAM dendrimers of generations 2

through 7. The molar ratio was kept at one PEG end group to two PAMAM terminal

units. These samples therefore have a constant mass fraction dendrimer in each case, but

the crosslink functionality changed continuously with the generation number. The

swelling curves shown in Figure 54 look qualitatively like those of PPI dendrimers in

Figure 53. The fits also give values similar to those in Figure 53, but as before, the can

be considered qualitative only. As with the PPI networks, the swelling ratios increase as

methanol > water > acid.
55

The PAMAM samples were titrated with HCl and swelling measurements were

taken from well below to well above the stoichiometric amounts. The swelling results

are shown in Figure 54and clearly show a maximum swelling ratio at intermediate acid

additions. There is a large initial increase with the first relatively small acid addition with

a maximum at approximately the stoichiometric amount to the total amine concentration,

both the internal tertiary amines, and the terminal amines, both unreacted and attached to

the PEG vinyl sulfone. Additional acid additions causes a decrease in swelling ratio, but

no abrupt volume decrease is seen.

2.6.5 Summary

Networks can be synthesized by reacting α−ω end functionalized PEG with the

terminal amines of PAMAM or PPI dendrimers. The relative reactivity and susceptibility

to side reactions of four functional groups, EP, AC, IS, and VS were examined by SANS

and GPC. The EP group did not react at ambient temperatures. The AC reacted

efficiently, but upon solution in basic water, the bonds broke to the dendrimer, probably

due to hydrolysis of the ester linkage from the PEG to the dendrimer. The IS reacted

efficiently, but upon solution in basic water, very large structures formed, possibly due to

additional side reactions. The VS proved to be best with 80 % conversion possible and

was hydrolytically stable.

The reaction kinetics of the VS-dendrimer reaction can be conveniently followed

by repeatedly injecting a reaction mixture into a GPC column. The reaction was found to

slow down considerably with conversion, probably due to the crowding that results when

a large fraction of the dendrimer terminal units have reacted with a PEG chain. Even

with the crowding, a conversion of more than half of the terminal amines was possible.

Swelling of dendrimer networks shows that these is a strong effect of going from

relatively poor (methanol) to relatively good (water) solvents. The swelling of the

networks in only weakly affected by the crosslink functionality, however. Addition of

aqueous acid to the dendrimer increases the swelling a large amount, with a maximum in

swelling being seen when there is a stoichiometric amount of acid to amine added.
56

3 Metal Containing Dendrimers

3.1 Dendrimers as Templates for the Formation of Inorganic Nanoclusters

3.1.1 Synopsis

Charged poly(amidoamine) (PAMAM) dendrimers are used to create organicinorganic hybrid colloids in aqueous solution. The formation of gold colloids upon

reduction of a gold salt precursor serves as a model reaction to study the influence of

reaction conditions and dendrimer generation on the resulting nanostructures.

Characterization by transmission electron microscopy (TEM), small angle neutron

scattering (SANS), and small angle x-ray scattering (SAXS) show that the gold particles

are formed inside the dendrimer and located offset from the center. Although lower

generation dendrimers aggregate when stabilizing the metal particles formed, dendrimers

of generation 6 to 9 can template one gold colloid per dendrimer molecule, the size of

which is well-controlled by the number of gold atoms added per dendrimer. For

generation 10, multiple smaller gold particles per dendrimer are observed. The

effectiveness of PAMAM dendrimers as templates in the host-guest nanoscale synthesis

is confirmed for different chemical reactions.

3.1.2 Introduction

Organic-inorganic hybrid nanostructures have generated great interest due to a

variety of potential applications as electrical, optical, medical and information storage

materials. In order to design hybrid structures of organic and inorganic material,

templating a growing inorganic crystal within a polymeric matrix, a method that was

initially inspired by nature, has been evaluated as an effective synthetic route for a variety

of polymer-inorganic systems.106

Since dendrimers are well defined organic molecules in the size range of (1 to 15)

nm and are known to act as hosts for guest molecules,107,108 they are promising

candidates as templates for the formation of inorganic nanoclusters. Organic-inorganic

hybrid materials based on dendrimers have been recently reported by several authors.109-

114 The results from these studies show that dendrimers are able to stabilize metal

clusters in solution. Furthermore, the nanoclusters have been demonstrated to be effective

high surface area catalysts in solution that allow substrates to penetrate the dendrimer

interior and access the cluster surface.112 Predictions have been made about the

selectivity of such catalysts.115 Although several studies propose that dendrimers can act

as “nanotemplates”,109-114 none of those studies show whether the colloid is formed

inside the dendrimer nor investigate how the colloids formed can be influenced by

varying the so-called “template”.

Our motivation for using dendrimers comes from a desire to understand the

mechanisms of polymer nanotemplating with a model system. Dendrimers are

monodisperse and well characterized molecules.20 The size of different generation
57

dendrimers spans the characteristic sizes of low molecular mass molecules, polymers and

colloids, thereby offering a unique mesoscopic system.

In this study, we use charged poly(amidoamine) (PAMAM) dendrimers in

aqueous solution as potential nanotemplates. We investigate dendrimers of generation 2

to 10 (G2 to G10) for the formation of inorganic-organic hybrid colloids, whereas

previous reports employed only low generation dendrimers (G6 and below). Our

approach relies on the attraction between charged dendrimers and oppositely charged

metal ions. Performing chemical reactions on the inorganic precursor that is physically

attached to the dendrimer should produce colloid structures that are controlled by the

dendrimer. The concept of using charged, solvent-penetrable nano-polymer-particles as

templates in aqueous solution was first applied to polyelectrolyte microgels.106 This is in

contrast to the specific coordination chemistry, i.e. Complexation of metal ions by amine

groups, used by other authors and is presumed to be more general. In this study, we use

the reduction of gold as a classical model reaction. Transmission electron microscopy

(TEM), small angle neutron scattering (SANS) and small angle x-ray scattering (SAXS)

are employed to characterize the resulting organic-inorganic nanocomposites. We also

investigate how the reaction rate and other parameters influence the colloid formation.

3.1.3 Experimental

3.1.3.1 Synthesis

Poly(amidoamine) (PAMAM) dendrimers of generations 2 to 4 were purchased

from Aldrich Chemical Company and generation 5 to 10 were supplied by Dendritech

(Michigan Molecular Institute). Aqueous solutions with a dendrimer mass fraction of

0.1 % to 1 % were prepared by diluting concentrated dendrimer/methanol solutions

(dendrimer mass fraction of 20 % to 25 %) with deionized water. Dilute aqueous

solutions of PAMAM dendrimers were mixed with aqueous solutions of HAuCl4 at

controlled stoichiometries. After stirring these solutions for 1 h, sodium borohydride in

basic aqueous solution (0.025 mol/L to 0.5 mol/L sodium hydroxide) was added. The

light yellow dendrimer/ HAuCl4 solutions immediately turned brown or red, indicating

the formation of colloidal gold.

UV-VIS spectra of the dendrimer-gold colloid solutions were obtained on a

Perkin-Elmer Lambda 9-spectrometer in the wavelength range of 400 nm to 800 nm.

TEM was also performed on these solutions as well as on dialyzed samples. The resulting

TEM images for both cases are the same. For the SANS experiments, samples were

either dialyzed against deuterium oxide or directly synthesized in deuterium oxide.

3.1.3.2 Transmission Electron Microscopy (TEM)

Carbon coated copper grids, 300-mesh, were washed in chloroform reflux in order

to remove formvar. Grids were then treated for (2 to 5) s in a glow-discharge tube in

partial vacuum to impart hydrophilic character to the carbon substrate. Stained specimens

were prepared by depositing the sample solutions on the grid and inverting the grid on a
58

drop of aqueous phosphotungstic acid solution that had been neutralized with NaOH

(mass fraction of phosphotungstic acid = 2 %). The grid was then blotted on filter paper

and air-dried. TEM images were obtained at 120 kV with a Phillips 400T at a

magnification of 46000 X and 100000 X. The relative error is within 10 % of the

magnification.

3.1.3.3 Small Angle Neutron Scattering (SANS)

Samples for SANS measurements were transferred into optical quality quartz

banjo cells with 2 mm path length. SANS studies were performed at the Center for

Neutron Research at the National Institute of Standards and Technology in the normal

manner. Measurements were made using the 30 m SANS instrument with a neutron

wavelength λ = 0.6 nm and wavelength spread of ∆λ/λ = 0.15

3.1.3.4 Small Angle X-ray Scattering (SAXS)

SAXS data were collected at the Advanced Polymer Beamline at Brookhaven

National Laboratory, X27C in the normal manner. The radiation spectrum from the

source was monochromated using a double multilayer monochromator and collimated

with three 2° tapered tantalum pinholes to give an intense X-ray beam at λ = 1.307 Å.

Two configurations were used with a linear position sensitive detector (European

Molecular Biology Laboratory, EMBL) or a 2D image plate detector (BAS2000, Fuji).

The sample to detector distance was varied between (1 to 1.5) m. The span of scattering

vector magnitudes q was in the range 0.15 nm-1< q < 3.2 nm-1 and 0.2 nm-1< q < 4.4 nm-1

for the two configurations used.

The scattering curve I(q) was Fourier transformed into the pair distance

distribution function P(r) using the program ITP (Indirect Transformation for the

Calculation of P(r)) by O. Glatter.116-118 This includes smoothing of the primary data

by a weighted least square procedure (estimation of the optimum stabilization parameter

based on a stability plot) and transformation into real space by the indirect transformation

method with minimized termination effects.

3.1.4 Results and Discussion

3.1.4.1 Nanocomposite Synthesis

The nanotemplating by dendrimers in aqueous solution is depicted schematically

in Figure 55. The addition of HAuCl4 to a neutral dendrimer with primary and tertiary

amine groups results in a protonated dendrimer with AuCl4

-

 counterions. The gold ions

are then reduced to metallic gold without the formation of a macroscopic metal

precipitate. The stable brown to red solutions of colloidal gold formed indicate that the

metal colloids were stabilized by the dendrimer. The brown or red color of the solutions

and UV-visible spectra (Figure 56) are typical of gold colloids in the size range of (1 to

5) nm. In the following discussion, we will show that the location of the gold colloid
59

inside the dendrimer as sketched in Figure 55 is an accurate representation of the

dendrimer-colloid structure.

3.1.4.2 Optimization of the Reaction Conditions

The stabilization of gold colloids in aqueous solution by the PAMAM dendrimers

is possible over a wide range of reaction conditions. In order to control the size of the

particles, one needs to optimize the ratio of the added gold ions to dendrimer, the

dendrimer concentration in solution, as well as the reduction rate. In the first step, the

gold/dendrimer ratio has to be adjusted so that no precipitation occurs. We found that

gold could be added to the solution without precipitation of the dendrimer up to the

amount corresponding to a gold salt to dendrimer end-group ratio of 1:1. We refer to the

number of end groups as a reference value and do not imply any specific binding to the

end groups. Furthermore, the dendrimer contains an equivalent number of inner, tertiary

amine groups, which can also be protonated.

At higher concentration (dendrimer mass fraction ≥ 2 %), precipitation occurs

upon reduction of the gold salt. When the concentration of the dendrimer is sufficiently

low (for example a dendrimer mass fraction of 1 %) a stable colloidal solution is formed,

but the resulting gold colloids are relatively polydisperse. It is only when the dendrimer

mass fraction is 0.12 % or lower that the reduction can result in uniform gold colloids,

and the dendrimer acts as a true template. Therefore, we employ a dendrimer mass

fraction of 0.12 % for all subsequent experiments.The third parameter to be optimized is

the reaction rate, i.e. Mass transfer and growth in comparison to nucleation. We

performed the reduction with sodium borohydride in order to control the reduction rate

by the pH of the solution.119 If the reduction is fast (NaBH4 in (0.025 to 0.1) mol/L

NaOH), again polydisperse colloids are observed (Figure 57). For slower reduction rates

(NaBH4 in 0.3 mol/L NaOH), uniform encapsulated particles can be formed (Figure 57).

Under much slower reduction conditions (NaBH4 in 0.4 mol/L NaOH), a red-violet

precipitate is observed. Thus the dendrimer is an effective template only when

sufficiently slow reduction rates are used. This trend corresponds to results for other

systems, but the specific optimal conditions are different. We have chosen the slowest

reduction that results in stable colloidal solutions (NaBH4 in 0.3 mol/L NaOH) for further

investigations, hereafter referred to as “slow reduction”. Furthermore, the precipitate

obtained at even slower reduction is also a dendrimer-metal composite material since the

color indicates nanometer dimensions of the metal. This complex material is an

interesting hybrid system, but is not the focus of this study.

3.1.4.3 Characterization of the Hybrid Particles

The particles synthesized are investigated by TEM, SANS and SAXS. The

characterization procedure is demonstrated for a representative G9-gold sample (loading

ratio 1:1, slow reduction) in this section. TEM on the dendrimer-gold-particles was

performed after staining the dendrimer; thus both components are evident in Figure 57b.

The image indicates that the colloid particles are formed inside the dendrimer. Under

these slow reaction conditions, one gold particle per dendrimer is predominantly formed.
60

The gold colloids observed are relatively monodisperse. The sizes estimated for the

dendrimer and gold are 13 nm and 4 nm, respectively. The measured dendrimer size

corresponds to previous reports of the size of the unmodified PAMAM dendrimers.20

The TEM image in Figure 57b suggests that some of the dendrimers aggregate. From the

TEM experiments one cannot determine whether the aggregates are present in the parent

solution or formed while casting on the grid. Solution characterization methods must be

applied to resolve this issue.

SANS measurements were performed on solutions of the dendrimer-gold hybridparticles in deuterium oxide. Scattering curves for the unmodified dendrimer and the gold

containing dendrimers are shown. For the dendrimer-gold hybrid particles, the radius of

gyration obtained from Guinier extrapolation is (5.1 ± 0.1) nm. This is within the

experimental error the same as for the unmodified dendrimer. The result indicates that the

hybrid particles also do not form larger aggregates in solution. Furthermore, the higher

order sphere form factor features, which are pronounced in case of the unmodified

dendrimer, nearly completely disappear for the hybrid samples. This will be understood

in the context of the SAXS results.

SAXS provides more detailed information about the colloid structures. In Figure

59, data for an unmodified G9 dendrimer are shown. Figure 60 shows data for dendrimergold hybrid-particles, which correspond to the TEM sample in Figure 57b. The scattering

curves I(q) (Figure 59a and Figure 60a) can be Fourier transformed yielding the pair

distance distribution functions P(r) (Figure 59b and Figure 60b).

Transformation into real space, which does not include geometric assumptions

about the particle, demonstrates the different particle features more obviously than the

inverse space scattering curves, in this case. The shape of the P(r) for the unmodified

dendrimer in Figure 59b corresponds to a homogenous sphere of 13 nm diameter, which

is in agreement with earlier modeling results.20 In contrast, the shape of the P(r) for the

hybrid particle in Figure 60b is typical of a layered sphere. An estimate of the dimensions

of the inner sphere and outer sphere diameter confirms the diameters of the gold (4 nm)

and the dendrimer (13 nm) estimated from TEM. More importantly, this result proves

that the gold is formed inside the dendrimer.

A further deconvolution of the pair distance distribution function P(r) under the

assumption of a specific geometry (which has been deduced from the P(r) function itself)

generally leads to the particle electron-density-profile, ρ(r). In case of the hybrid particles

(Figure 60), by assuming spherical symmetry, a satisfactory description of the P(r)

function, specifically the relative peak heights, is not possible. Deviation from strict

spherical particle symmetry is one possible reason for such a discrepancy.

Additional modeling has been performed in order to understand this issue: We

calculated the scattering curves and the pair distance distribution functions for several

model layered particles. At this point, one can compare the scattering curves or the realspace pair distance distribution functions in order to understand the basic trends. We will

refer to the pair distance distribution functions here, since the effects are more obvious.
61

Figure 61a displays the calculated pair distance distribution functions for layered spheres

with different relative contrast of the inner sphere. The variation does not allow the

modeling of the basic shape of the experimental pair distance distribution function

(Figure 60b). This points to deviations from a perfect spherical symmetry, as was already

indicated by the problem with the deconvolution of the P(r). When considering potential

structures with non-spherical symmetry, one has to remember that the maximal diameter

of the unmodified dendrimer and the gold containing dendrimer is the same (Figure 59b

and Figure 60b). Thus, the best hypothesis for non-spherical symmetry in our system is a

non-centered placement of the gold particle within the dendrimer. In Figure 61b we

calculated pair distance distribution functions for layered particles with constant relative

contrast, but an increasing offset of the inner sphere from the center of the outer sphere.

The experimental pair distance distribution function (Figure 60b) is best represented for

an offset of 4.7 nm (Figure 61b, bold line). Thereby it is clearly indicated that the gold

particle is offset from the center of the dendrimer. We do not perform a quantitative curve

fitting within this model, since no new information is expected. The displacement of the

gold from the dendrimer-center is also visible in some of the particles in the TEM in

Figure 57b. (Because the TEM is a two-dimensional projection, only a fraction of the

gold colloids appears off-centered.) In addition, this off-center placement of the gold in

relation to the dendrimer can also explain the loss of sharp features in the SANS

scattering curve shown above.

Thus we have shown that the gold colloid is inside the dendrimer and it is located

with an offset from the center as was depicted schematically in Figure 55. The good

agreement between the gold colloid diameter determined from TEM and SAXS allows a

quantitative comparison with the model sketched: The G9 dendrimer was loaded with

gold salt corresponding to a gold-ion to end-group ratio of 1:1, i.e. 2048 gold ions per

dendrimer molecule. Assuming the formation of one gold colloid from the loading of one

dendrimer molecule upon reduction, one would expect a gold particle consisting of 2048

gold atoms. This means an expected particle size of 4 nm when assuming bulk density for

the gold. This calculated value is in good agreement with the experimental results. Thus,

the postulate that the gold ions from the load of one dendrimer form one particle has been

demonstrated to be true. The gold-colloid formation is indeed templated by the

dendrimer. We will hereafter refer to this template mechanism as “fixed loading law”.

3.1.4.4 Influence of the Gold to Dendrimer Loading Ratio

As stated above, the maximal loading of the dendrimer with gold (1:1 molar ratio

of gold ions to dendrimer end groups) is determined by the solubility of the gold salt

loaded dendrimer. Although we have extensively studied the structure of the hybrid

formed under these maximal loading conditions, we have also investigated the variation

of the structures formed with loading ratios below the maximum value. We have studied

systems with gold-ion to dendrimer end-group ratios of 1:1, 1:2 and 1:4. UV-VIS spectra

for samples formed upon reduction were shown in Figure 56, SAXS results for the G9

sample are given in Figure 62. It can be seen from the SAXS data as well as from TEM

(not shown) that a lower loading yields smaller particles. Gold diameters of 4 nm, 3.3 nm
62

and 2.5 nm (within ranges of ± 0.2 nm) for 1:1, 1:2 and 1:4 loading are observed. Again,

this corresponds well with the expected values for 2048, 1024 and 512 atoms.

In other polymer template systems, it has been observed that one part of the

polymer particles ends up “fully” filled with gold while another part is completely empty,

indicating a more complicated growth mechanism.106 In contrast, with the dendrimers

investigated here, the size of the metal colloids formed is precisely determined by the

number of gold atoms that were added per dendrimer, introduced before as the “fixed

loading law”.

Although one might be interested in putting as much gold as possible into a single

dendrimer, the samples resulting from a lower loading also represent well-defined

composite particles which may be of importance for certain applications. For example,

dendrimer-stabilized metal colloids represent an interesting system for heterogeneous

catalysis in aqueous solution. The hybrid particles containing smaller metal colloids may

be more effective because of the larger surface area provided per mass, or changed

selectivity due to their different morphology.120,121

3.1.4.5 Effect of Dendrimer Generation on Colloid Size

Table 1 summarizes some TEM and SAXS results for hybrid structures obtained

for different generation dendrimers under the same reduction conditions (1:1 loading,

slow reduction). The effect of the dendrimer generation on the colloid size is not simple,

i.e. For G2, the colloids formed are larger than those obtained with G4. For G6 to G9 the

gold diameter increases with increasing generation number. For G10, multiple smaller

gold particles per dendrimer are formed. In the following paragraphs we describe the

results of the particle characterization and discuss the different structures. In this context,

one has to consider how the dendrimer structure itself changes with generation: G2 is a

star-like molecule with 16 end groups, G3 to G5 have star-like as well as sphere-like

features, and higher generation dendrimers show a spherical structure.37

For G2 and G4 dendrimers, gold colloids of 4 nm and 2 nm diameter,

respectively, are detected by TEM as well as by SAXS. In addition, we observe the

existence of larger dendrimer aggregates. For the G4 sample these have a well-defined

dimension of 7 nm as evident from the pair distance distribution function as well as from

our TEM staining experiments. Larger particles obtained with G2 rather than G4

dendrimer are in agreement with recent results from other authors who are studying these

lower generation dendrimers as colloid stabilizers.122 A schematic of multiple

dendrimers attached to one gold colloid was inferred in that work, but not verified

experimentally. Small angle scattering and Guinier analysis revealed aggregated

structures formed upon colloid preparation using a G4 dendrimer by Beck Tan et al.123

Thus, our results for low generation dendrimers are in agreement with the results of other

authors.
63

The formation of multiple dendrimer aggregates may be understood because for

these “small” molecules a single dendrimer cannot provide enough material to stabilize

the surface of one gold colloid. In addition, very small metal clusters are less stable, so

that colloids from the gold loading of more than one dendrimer are formed. This results

in a hybrid structure of a metal colloid surrounded by several dendrimers. The colloidformation mechanism for these low generation dendrimers is different than for high

generation dendrimers. The gold colloids are not formed inside a “pre-existing

container”, but the nanostructure organizes only when the colloid is produced chemically.

This resembles the concept of double-hydrophilic block copolymers in

mineralization.124,125 In contrast, the dendrimers are chemically uniform and no

complex architectures result. From this point of view, the colloid stabilization can be

considered as an analogue to the classical stabilization mechanism with low molar mass

molecules like citric acid. The molecules can become attached to the colloid surface and

act as stabilizers, but they do not template the colloid.

While the analysis of the G5 hybrid structure proved to be more difficult, for the

G6 sample, a gold colloid of about 2 nm diameter is observed, thus the size corresponds

to 1:1 loading. However, the dendrimers at least partially aggregate in solution in this

case. For G7 to G9, individual dendrimer molecules containing single gold colloid

particles are found. The TEM for the G8 sample is shown in Figure 63a. The structure of

the hybrid particles corresponds to the G9 sample discussed before. Pair distance

distribution functions obtained from SAXS data for G7, G8 and G9 (Fig.10b, solid lines)

show the increasing gold colloid size with increasing dendrimer size. The colloid

diameters of 2.5 nm, 3.2 nm and 4 nm (within ranges of ± 0.2 nm) agree well with the

expected sizes.

The mid-generation dendrimers (G6 to G9) obviously offer the best conditions in

terms of a “host-guest nanoscale” synthesis. This may be explained by the fact that their

structure provides sufficient polymer to stabilize the surface of the forming colloidal

particle, along with enough flexibility for the growth of only one particle from all of the

gold ions loaded in the dendrimer. Thereby, the number of gold atoms that build one

colloid can be precisely controlled with these dendrimers (“fixed loading law”).

For G10, multiple smaller gold particles inside one dendrimer are observed in the

TEM (Figure 63b). In addition, the decreased gold diameter in comparison to the G9

sample is evident in the P(r) function (Figure 64b, dotted line). In general, the growth of a

colloid is determined by the free energy of the crystal formation and surface tension.

However, when the colloid grows inside a polymeric matrix the elastic forces of the

surrounding polymer become important. The growth of a nucleated colloid is limited by

the finite extension of neighbouring polymer chains. In this context, one must note that

with each generation number G the mass of the dendrimer is roughly doubled, while the

size increases only linearly (mass: Mw~2G, radius: R~G, volume: V~G3

, compare Table

1). This means, as the generation number increases, the internal dendrimer segment

density increases slightly37 and the flexibility of the dendrimer chains decreases. The

volume of a single gold nanocluster would double with each generation, yet the space

available for its formation would decrease. For the G10 dendrimer, it may be that the
64

chain flexibility is not sufficiently high to allow for the growth of one colloidal particle.

On the other hand, the increased surface to be stabilized for multiple smaller particles is

likely to be provided by the G10 dendrimer. From this point of view, the G10 dendrimer

still realizes a host-guest nanotemplating, and the different dendrimer structure results in

a different colloid morphology. Similarly, in microgels of high cross-linking density only

multiple small colloid particles can be formed, while the larger flexibility of lower crosslinking density microgels allows for the formation of continuous structures through the

microgel.106 But for the case of dendrimer nanotemplates, the “fixed-loading law”

remains valid. About four 3 nm-gold colloids inside one G10 dendrimer are formed,

which is in good agreement with the expected amount of 4096 atoms.

3.1.5 Conclusions

PAMAM dendrimers are shown to be effective as nanotemplates in the formation

of inorganic colloids. They not only stabilize the colloidal metal in aqueous solution, but

also determine the architecture of the forming nanostructures. G2 to G4 dendrimers

behave more like low molecular mass colloid stabilizers, i. E. Several dendrimers become

attached to the surface of the metal particle formed. G6 to G10 dendrimers act as

effective “polymeric” templates. One colloid particle is completely formed inside one

dendrimer, a template mechanism known as “host-guest nanoscale synthesis” or

“exotemplating”.106 For G6 to G9, the size of the inorganic colloid can be precisely

controlled by the dendrimer generation without changing the morphology of the hybrid

structure. Also, hybrid particles with different morphology can be synthesized in a welldefined manner (G10). To our knowledge, this is the first time such a transition has been

shown from colloid “stabilization” by low molecular mass molecules to “polymer

nanotemplating” with increase of molecular mass but unchanged chemistry of the

stabilizing species.

A detailed study has been presented on the parameters that influence the colloid

formation for the reduction of gold salt. With respect to future applications, it is certainly

interesting to extend this concept to other chemical reactions leading to different

inorganic colloids. For this purpose, we have also synthesized other metal colloids like

copper, silver and platinum inside the dendrimers as well as cadmium sulfide

nanoclusters, which will be subject of future reports. These examples demonstrate that

the dendrimer nanotemplating is not restricted to a specific chemistry, but it represents a

fundamental mechanism, which may be widely applied. The inorganic “filled”

dendrimers in solution are promising candidates for multiple applications due to the

colloidal size of the inorganic crystal, e.g. Specific optical and electrical behaviour

caused by quantum size effects, or catalytic activity enhanced by the large surface area.

Since the hybrid particles also represent well-defined inorganic colloids in a polymeric

matrix, they pave the way to new materials, which combine the mechanical properties of

polymers with special colloidal effects. Furthermore, incorporating the gold-dendrimer

hybrids further within a polymeric matrix could lead to promising solid composite

materials.
65

3.2 Hydrophobically Modified Dendrimers

3.2.1 Synopsis

Poly(propyleneimine) dendrimers with stearyl end groups are investigated as

inverse micelles in toluene. While these dendrimers exhibits a spherical structure with a

collapsed core, solubilization of metal salt hydrate leads to the formation of cylindrical

multi-dendrimer structures with swollen, metal-salt filled dendrimer cores. The

cylindrical structure can be deduced from both small angle neutron (SANS) and x-ray

scattering (SAXS) pair distance distribution function. While the neutron scattering leads

to a two-step cross section density profile, the x-ray scattering visualizes only the inner,

metal-salt-stained part. Chemical reduction was performed on the salt-filled inverse

micelles to form colloidal particles. Upon reduction, the cylindrical structure breaks up

and spherical colloids are formed. This indicates that the inorganic matter from several

dendrimers is combined.

3.2.1.1 Introduction

Higher generation dendrimers appear as homogeneous spheres in solution.20

There is sufficient space available inside the dendrimer molecule that allows them to act

as a “host” for smaller guest molecules. Meijer first showed encapsulation of Bengal rose

as a guest into the “dendritic box” of poly(propyleneimine) dendrimers modified with

amino acids.107 This observation has motivated a number of further studies and initiated

the consideration of a variety of potential applications in areas such as drug delivery,

catalysis or gas detection.

The “molecular encapsulation” has been applied to different kinds of dendrimers

and modified dendrimers in different solvents: Hydrophobically modified PAMAM

dendrimers have been shown to transport copper(II)sulfate from an aqueous solution into

an organic phase.126 Dendrimers with a fluorinated shell are soluble in supercritical

carbon dioxide and can extract an ionic dye from water into supercritical carbon

dioxide.33 Sulfonate-terminated amphiphilic dendrimers with hydrophobic carbosilane

cores were demonstrated to enhance the solubility of lipophilic molecules in water.127 In

all of these experiments, the amphiphilic dendrimer is basically acting as a micelle, or

inverse micelle, solubilizing the guest in a solvent of different polarity. Thus a dendrimer

may be considered an “unimolecular micelle”.

Several studies on the binding of the guest to the dendrimer-host have been

performed by photometric measurements and different kinds of spectroscopy. In this

study, we are interested in characterizing the nanoscale structure of dendrimers acting as

inverse micelles. We use dendrimers with a hydrophilic poly(propyleneimine) cores

which have been modified with hydrophobic chains attached to the dendrimer terminal

groups.
66

We investigate how the structure changes when filling a hydrophobically

modified dendrimer with a gold salt hydrate HAuCl4·3H2O in toluene solution. The use

of the gold salt hydrate not only allows for the addition of a very well defined number of

water molecules, but also allows study of the structure formed by scattering techniques.

The water provides contrast for a small angle neutron scattering (SANS) experiment

when using deuterated toluene as solvent, and the gold can provide contrast for a small

angle x-ray scattering (SAXS) experiment. Furthermore, the gold salt hydrate can serve

as a precursor to investigate if dendrimeric micelles can be used as confined reaction

space for the formation of noble metal colloids.

3.2.2 Experimental

Fifth generation (G5) poly(propyleneimine) dendrimers (PPI)8 with 64 primary

amine groups (DAB-dendr-(NH2)64) that were modified with octadecanoic acid were

provided by DSM.58,128 Mass Fraction 1% solutions of G5 fatty acid modified

dendrimer were prepared at 55 oC in toluene. The desired amount of HAuCl4·3H2O is

added as a solid salt and the solution is gently stirred at 55 oC resulting in a clear yellow

solution. For SANS experiments, deuterated toluene is used as solvent. Reduction of the

gold is performed by addition of a solution of sodium borohydrate in diglyme.

Samples for SANS measurements were transferred into optical quality quartz

banjo cells with 1 mm path length. SANS studies were performed at the National Center

for Neutron Research at the National Institute of Standards and Technology.

Measurements were made using the 30 m SANS instrument with a neutron wavelength

λ = 0.6 nm and wavelength spread of ∆λ/λ = 0.15. All measurements were performed at

55 oC.

SAXS data were collected at the Advanced Polymer Beamline at Brookhaven

National Laboratory, X27C in the normal manner. The span of scattering vector

magnitudes was in the range 0.15 nm-1 < q < 3.2 nm-1. All measurements were performed

at 55 oC.

The scattering curve I(q) is Fourier transformed into the pair distance distribution

function P(r) using the program ITP (Indirect transformation for the calculation of P(r))

by O. Glatter,116-118 which includes smoothing of the primary data by a weighted least

square procedure (estimation of the optimum stabilization parameter based on a stability

plot), desmearing and transformation into real space by the indirect transformation

method with minimized termination effects. For the SANS measurements, we include

desmearing by the wavelength distribution of the incident beam as well as the measured

beam profile. For the SAXS measurements, the wavelength distribution ∆λ/λ is smaller

than 1 % and the beam is focused via a pinhole collimation system to (100 to 200) μm

diameter. Therefore smearing effects are not accounted for in case of the SAXS data

analysis.

Scattering-length-density and electron-density profiles are calculated from the

pair distance distribution function P(r) by calculation of the convolution square root
67

(“deconvolution”) using the program DECON by O. Glatter.129-131

Carbon coated copper grids, 300-mesh, were extensively washed in chloroform

reflux in order to remove formvar. Specimens were prepared by depositing the sample

solutions on the grid and drying in air at 55 oC. TEM images were obtained at 120 kV

with a Phillips 400T at a magnification of 46000 X.

3.2.3 Results and Discussion

3.2.3.1 Structure of Inverse Micelles

When stirring solutions of hydrophobically modified poly(propyleneimine)

dendrimer over solid HAuCl4·3H2O, the color of the solution turns yellow, indicating the

solubilization of the gold salt in the dendrimers. We have prepared samples with an

excess of gold salt as well as samples with controlled stoichiometries of gold salt. The

maximum amount that is completely dissolved in the toluene solution corresponds to a

stoichiometric ratio of gold salt to dendrimer terminal amine groups (64 per dendrimermolecule) of 1:1. In addition, the UV absorption of the gold salt in different solutions

agrees with the saturated and the 1:1 loaded solution. Solutions with loading ratios 1:2,

1:4 and 1:8 show a smaller absorption.

The scattering results from a sample with a maximum load of gold salt, i.e. A

molar ratio of 1:1 to dendrimer end groups are shown in Figure 65. It shows the SANS

scattering curve for the initial plain dendrimer and the SANS and SAXS scattering curves

after solubilization of gold salt. Diagrams are also given which show the areas of high

contrast in the dendrimers for the different scattering experiments.

The initial dendrimer exhibits a spherical structure. The radius of gyration for the

scattering curve shown is 2.2 nm. This is in agreement with previous reports on the

single-chain form factors of the fatty acid and the dendrimer components of these

hydrophobically modified dendrimers58 and their size in different solvents at different

temperatures.3 The size of the dendrimer measured under these conditions is for a

collapsed dendrimer core plus a fatty acid shell.

The neutron scattering curve for the sample after addition of gold salt hydrate

shows a shift of the first minimum to lower scattering vector, q, i.e. The size of the

structure increases, Figure 66. This is due to the swelling of the dendrimer upon

solubilization of the gold salt hydrate. In addition, the shape of the scattering curve also

changes. In order to analyze the structure of the gold-filled dendrimers in more detail, we

Fourier transform the scattering curve I(q) into the pair distance distribution function

P(r), which is shown in Figure 67. The P(r) shows a shape typical of a cylindrical

structure. The diameter of the cylinder is about 6 nm (inflection point after the

maximum), while the length of the cylinder, i.e. The largest correlation found, is about 21

nm. The 21 nm dimension corresponds to the smallest q measured and could possibly

represent an experimental limit. However, the fit of the data is stable and the error bars of

the calculated P(r) do not dramatically increase for higher r-values, so that we consider
68

21 nm a good estimate for the length of the cylinder. While the cylinders might in fact be

longer, the scattering results clearly show that they are not shorter than 21 nm. In

addition, some polydispersity in average length cannot be excluded. Most importantly,

the scattering result shows the existence of a cylindrical structure in solution, which has

to result from an aggregation of multiple dendrimers, since the length is clearly larger

than the diameter of one dendrimer.

Since the data gives conclusive evidence of the cylindrical structure from the P(r),

we can now assume cylindrical geometry as input for further calculations. We repeat the

Fourier transform of the scattering curve from Figure 67, this time using the zero-order

Bessel function J0(qr)-transformation instead of the sin(qr)/(qr)-transformation used

before, and thereby calculate the cross-section pair distance distribution function Pc(r) of

the cylinder. The result is shown in Figure 68. From this, a better estimate of the diameter

can be made, giving 6.4 nm. In addition, the shape of this cross-section P(r) roughly

indicates a circular cross section. Furthermore, we deconvolute this cross-section pair

distance distribution function into a radial scattering length density profile of the

cylinder. First, we allow a multiple step density profile. The resulting radial profile is

shown in Figure 68 as the dotted line. Secondly, we estimate from this multiple step

profile how many actual steps are present in the density profile and the range in which

they are located. We then calculate the radial density profile again, under the assumption

of a one-step, a two-step and a three-step profile, respectively, looking for the simplest

solution that gives the best fit to the cross-sectional P(r). The result is shown in Figure 69

as solid line. We find two pronounced steps in the radial density profile: an inner part

with a radius of 1.9 nm, plus an outer shell of 1.3 nm thickness. The total diameter is 6.4

nm. The resolution of the fit values due to the limited q range measured is expected to be

within the range of ±1 nm .

The measured two-step density profile of the cylinder cross-section can be

interpreted as a swollen dendrimer core plus a fatty acid shell. The diameter of the

“swollen dendrimer” of 3.8 nm is in agreement with previous measurements on G5

polypropyleneimine dendrimer (without fatty acid chains attached) in aqueous

solution.20 The thickness of the fatty acid shell is also in agreement with the length of

C18-alkyl chains. Since the hydrogen-containing dendrimer is filled with aqueous salthydrate, the contrast of the inner core is higher than the contrast of the outer shell.

In order to further confirm the cylindrical structure, we have performed SAXS on

the same sample. In the x-ray experiment, only the inner gold-containing core gives

contrast, since the electron density difference between the fatty acid chains and the

toluene is relatively small. The scattering curve and resulting pair distance distribution

function are shown in Figure 70 and Figure 71, respectively. Again, the P(r) reveals a

cylindrical structure. The diameter estimated is 4 nm, while the length is 20 nm. The

cross-section pair distance distribution function is given in Figure 71and the cross-section

density profile in Figure 72. One obtains a one step-profile, the diameter of the cylinder

being confirmed as 4 nm. This corresponds well to the gold-salt filled inner part of the

cylindrical structure, i.e. The first step of the neutron density profile from Figure 67.
69

Figure 73 displays a schematic of the multi-dendrimer cylindrical structure that has been

deduced from the SANS and SAXS.

It is interesting to consider the approximate relative volumes in the dendrimernanostructures. A G5 poly(propyleneimine) dendrimer, having a molecular mass of

7166 g/mol, having a density of 1.01 g/mL, has a volume of 11.8 nm3, i.e. In a collapsed

spherical state a radius of 1.4 nm in agreement with the experimental results. As

mentioned before, an amount of gold salt to dendrimer end groups of 1:1 was added, i.e.

64 molecules of HAuCl4·3H2O, which means 192 water molecules, were solubilized per

dendrimer molecule. These 192 water molecules have an additional volume of 5.74 nm3.

If the analogy of the hydrophobically modified dendrimers to surfactant micelles

is valid, then the same factors may determine the phase behaviour. The relative volume of

the inner hydrophilic part and the outer hydrophobic part, or more accurately the ratio of

the surface area of the dendrimer end group to the volume of the inner part, may

determine whether spherical or cylindrical structures are formed. Upon solubilization, the

volume of the hydrophilic part increases, i.e the ratio of surface area to volume decreases

and cylindrical structures are favored. To confirm of this postulate, however, different

samples with a variation of these parameters would be needed.

As mentioned before, we have also prepared samples with different loading ratios.

The SANS curves from the saturated and the 1:1 filled sample are the same as would be

expected from the UV-vis results which give similar spectra. However, it was not

possible to perform the SANS measurements on the samples that had less than

stoichiometrically loading, since the ions became reduced when exposed to the neutron

beam for a time period needed to perform the scattering measurement. It is known that

gold salts can be easily reduced when exposed to x-ray or neutron beams. Why the

samples with less gold salt are less stable than the 1:1 loaded, is not apparent. An

investigation of the influence of the loading ratio on the structure formed should be

possible if metal salts of less noble metals are used, which is an issue that will be

addressed in future studies.

3.2.3.2 Use of Dendrimeric Micelles as Confined Reaction Space

Although the poly(propyleneimine) dendrimers are not unimolecular micelles

when filled, but rather consist of multiple dendrimers, the expression emphasizes the

difference from classical surfactant micelles. Due to the highly branched structure of the

inner core, the dynamics are different from those of conventional micelles. Blockcopolymer micelles have been claimed to have advantages over low-molecular mass

surfactant based micelles for use as a confined nano-scale reaction space, not only

because of the larger size range covered, but also due to the different dynamics of the

system. Due to the slower exchange of surfactant molecules, the stability of the

nanoreactor is enhanced. This feature is obviously further improved in a “unimolecular”

or “few-molecular” dendrimeric micelle, which should therefore be an interesting new

system for use as a potential nanoreactor. This approach has been recently used with
70

inner-crosslinking of block-copolymer micelles, after the micelles have formed, but prior

to their use as a nanoreactor.

We have therefore tested the use of dendrimeric “few-molecular” micelles as a

confined reaction space for the reduction of gold salt. Upon addition of reducing agent,

the solution turns purple, indicating the formation of colloidal gold. No macroscopic

precipitate is observed. The SANS curve of the reduced sample is shown in Figure 74 and

a TEM of the gold colloids is shown in Figure 75. As is evident from the shape of the

scattering curve and the TEM, reduction of the gold salt yields spherical dendrimer

structures and spherical gold particles. This can be due to the density difference of the

reduced gold compared to the gold-salt hydrate. For all of the reducing methods tested,

the gold colloids are bigger than expected when formed within one dendrimer. This may

be explained by the intermediate connection of dendrimers in the gold salt-filled

structure. Thereby, the amount of gold salt from multiple dendrimers is combined,

forming one colloidal particle.

All experiments described previously have been performed at 55 °C, since the

fatty acid modified dendrimer is not soluble in toluene at lower temperatures. When

cooling the gold-colloid containing solution to room temperature, the gold precipitates

with the dendrimer, as can be seen from the purple color of the precipitate, while a clear

toluene solution remains. This observation proves that the gold colloids are indeed

connected to the dendrimers. It also allows for an easy separation of the hybrid material

from the solvent. The precipitate can be easily redissolved in toluene when re-heated to

55 °C.

Although the hydrophobically modified dendrimers form cylindrical structures

when filled with gold salt, these cylinders cannot be used as template for the formation of

cylindrical metal particles. This is in agreement with experiments on the use of

cylindrical micelles or hexagonal morphologies as confined reaction spaces However, we

consider the large gold particles produced by the reduction as a further evidence of the

intermediate cylindrical connection of multiple dendrimers.

3.2.4 Conclusion

The structure of poly(propyleneimine) dendrimers modified with stearyl end

groups in toluene changes from mono-molecular spherical dendrimers to cylindrical

multi-dendrimer structures when filled with gold-salt hydrate. Upon reduction of the gold

salt to metallic gold, spherical gold colloids are formed and the cylindrical structure splits

up. Small angle neutron scattering and small angle x-ray scattering have been used as a

powerful tool for the characterization of the solution-structures.

The dendrimer-gold hybrid particles may have certain properties that could allow

for them to be incorporated into other polymer systems, or their use as selective catalysts.

Although the volume change upon reduction of gold is large, other reactions leading to

inorganic materials of lower density could eventually be performed without destruction

of the multi-dendrimer cylinders. This issue will be investigated in future studies.
71

Factor Question Application SANS SAXS TEM

Segment

Distribution

Uniform or

Diffuse?

Solubilization + ++ +

Type of

Branching

Important

Differences?

Major Cost

Differences

+++

Terminal Group

Location

Surface or

Interior?

Attachment

Networks

++ + -

DendrimerDendrimer

Interactions

Interpenetration

or Collapse?

Ordering

Nanostructures

+ ++ +

Size Variation

with Solvent

Large Changes

of Stable Size?

Standards

Release

++-

Table 1 Major technological issues. Key to symbols, ++, best technique for measurement;

+, acceptable technique for measurement; -, unsuitable for measurement.
72

Dendrimer Dendrigraft Hyperbranched

Interior Branching High High High

Terminal units Small Linear Chains Small

Molecular Mass

Distribution

Narrow Narrow Broad

Shape – Low

Generation

Dense Star Star-like Polydisperse,

Diffuse

Shape – High

Generation

Dense Sphere Uniform Center

Star-like Exterior

Polydisperse,

Diffuse

Synthetic Steps 4-20 2-5 1

Purification Steps 4-20 2-5 0

Cost Very High Moderate Low

Table 2 Comparison of different dendritically branched polymer types, see Figure 7.
73

Generation

 Branches Graft Polymer

Mn (g/mol) Mw/Mn Mw (g/mol) fw(tot) Branching

 Density

0

1

2

3

4,300 1.03 5.7×104

 12 0.25

4,600 1.03 5.7×105

 120 0.20

4,200 1.04 3.2×106

 720 0.11

4,400 1.05 2.4×107

 5200 0.15

Table 3 Characteristics of Arborescent Polymers with 5000 g/mol Branches
74

Mw /Mn Mw Mn

D-PS 1.03 4300 4170

1.03 26600 25800

1.51 102900 68100

1.04 244000 235000

1.05 424900 404700

D-PVME 2.05 8280 4040

Table 4. Characteristics of deuterated polystyrene and deuterated poly(vinyl methyl

ether).
75

Measurement

Method

 G6 G7 G8 G9 G10 G11

The average size

in IPN from TEM

(Average in

Image)

9.6 ± 0.4 11.7 ± 0.8 14.7 ± 1.6

The average size

in IPN from TEM

(FFT of Image) 9.5 ± 1.0

12.2 ± 1.2

14.3 ± 1.4

The average size

in IPN from

SAXS (low

concentration)

8.0 ± 0.8 9.6 ± 1.0 13.7 ± 1.4

The average size

in IPN from

SAXS (mass

fraction 10 %)

5.9 ± 0.6 11.4 ± 1.1 13.4 ± 1.3

The average size

on a surface from

TEM 6.9 ± 0.5 8.0 ± 0.7 10.2 ± 0.8 12.4 ± 0.5 14.7 ± 1.1

The average size

in methanol from

SAXS 7.3 ± 0.7 8.4 ± 0.8 10.0 ± 1.0 11.8 ± 1.2 14.0 ± 1.4 15.5 ± 1.6

Table 5. Diameter of G6 – G11 PAMAM dendrimers in methanol solution and in IPN’s

as measured by SAXS and TEM at mass fraction 1 % and 10 %.
76

Figure 1 Classical dendrimer cartoon showing core, branch points and terminal

groups.
77

Figure 2 SAXS Rg of PPI and PAMAM dendrimers. Straight line is the limit of

PAMAM dendrimers collapsed to bulk density. The 1/3 power law suggests uniform

spherical shape.

10

20

30

40

50

60

1000 104 105 106

PPI

PAMAM

R

g / Å

Molecular Mass / g mol-1

slope = 1/3

ρ = 1.23/cc
78

Figure 3 TEM of G5, G6, G8, and G10 PAMAM dendrimers. Individual molecules are

seen.
79

Figure 4 PAMAM dendrimer diameter from SAXS and TEM.

2

4

6

8

10

12

14

16

18

5 6 7 8 9 10

SAXS TEM

Diameter / nm

Generation
80

Figure 5 SAXS curves for PAMAM mass fraction 1% dendrimer/methanol solutions of

generation G3 (top) through G10 (bottom). Power law behavior continuously varies from

–5/3 to –4.

0.01 0.1 1

Intensity (AU)

q / Å-1

q

-5/3

q

-2.4

q

-4

G3

G10
81

Figure 6 Fits of the G10 PAMAM dendrimer data to a distribution of spheres and a single

ellipsoid of revolution

0 0.05 0.1 0.15 0.2 0.25 0.3

G10 Dendrimer

Distribution of Spheres

Single Ellipsoid of Revolution

I(q) q4 (AU)

q / Å-1
82

Figure 7 Cartoons representing dendritically branched polymers listed in Table 2

b) Hyperbranched

c)Dendrigraft

a) Dendrimer
83

Figure 8 Zimm and Guinier plots of G4 PAMAM dendrimer and G5 hyperbranched

polyol. The dendrimer fits Guinier (Spherical) and the hyperbranched fits Zimm

(Gaussian).

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

1 / Intensity, G5 Hyperbranched

ln(Intensity), G5 Hyperbranched

1 / Intensity, G4 Dendrimer

ln(Intensity), G4 Dendrimer

1 / Intensity or ln(I(q)) (AU)

q

2

 / A-2
84

Figure 9 Kratky plots of G1 PS dendrigraft, G3 PS dendrigraft, G4 PAMAM dendrimer,

and G10 PAMAM dendrimer. . Flat high q shows star-like structure, higher order

features shows sphere-like structure.

0.01

0.1

1

0 2 4 6 8 10

Dendrigraft G1

Dendrigraft G3

Dendrimer G4

Dendrimer G10

Linear Chain

P(q) (q Rg

)

2

q Rg
85

Figure 10 Volume fraction interior polymer segments in dendrimer solution. PPI

dendrimer in methanol, PAMAM dendrimer in methanol, hyperbranched polyol in

methanol, and PS dendrigraft in cyclohexane.

0

0.2

0.4

0.6

0.8

1

1000 104 105 106 107 108

Polyol Hyperbranched

PPI Dendrimer

PAMAM Dendimer

PS Dendrigraft

Fraction Dendrimer

Molecular Mass / g mol-1
86

Figure 11 Cartoon of possible end group locations. A) whole dendrimer end groups

outside, b) whole dendrimer end groups backfolded, a) matched dendrimer end groups

backfolded, a) matched dendrimer end groups backfolded. Outside end groups have a

larger Rg.

a) End groups – Outside b) End groups Backfolded

c) Contrast Match – Outside d) Contrast Match - Backfolded
87

Figure 12 SANS of G7(H) in CD3OH, G7(D) in contrast match methanol, and G7(H) in

contrast match solvent. Labeled dendrimer in core match solvent shows scattering from

labeled terminal generation.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

G7[H] in CD3OH

G7[D] in Contrast Match Solvent

G7[H] in Contrast Match Solvent

q / Å-1

I(q) / cm-1
88

Figure 13 Cartoon showing dendrimers at different concentrations.

a) Dilute

b) Contact

c) Collapse

d) Interpenetrate
89

Figure 14 SANS of G5 PPI dendrimer at various mass fractions. Peaks move to higher q

(smaller separation distance) with increased concentration.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.1 0.2 0.3 0.4 0.5 0.6

1%

3 %

5 %

10 %

20 %

30 %

35 %

60 %

80 %

I(q) / cm-1

q / A-1
90

Figure 15 Kratky plot of SAXS of G5 PPI dendrimer at various mass fractions. Higher

order feature moves to higher q suggesting shrinkage with increased concentration.

0

5

10

15

20

25

0 0.125 0.25 0.375 0.5

 1 %

10 %

20 %

25 %

30 %

45 %

55 %

I(q)q2 (AU Shifted)

q /Å-1

R = 18.56 Å

σ = 1.73 Å

Dendrimer mass fraction

Shrinking Particle Size
91

Figure 16 TEM of aqueous PAMAM G10. Note dendrimers are touching but not

interpenetrating.
92

Figure 17 Rg of G8 PAMAM dendrimer in alcohol of various types from SANS. Rg of G8

PAMAM dendrimer calculated from HRS results in reference.52

30

35

40

45

50

55

60

01234

SANS

Stechmesser and Eimer 

R

g

 / Å

m in D(CD2)

m

OD
93

Figure 18 SANS from G8 PAMAM dendrimer with and without acid and salt additions.

Note constant position of higher order features showing constant size.

0.02 0.04 0.06 0.08 0.1

pH = 7.7, CS = 0.5 M, SANS

pH = 7.7, CS = 0.5 M, fit

pH = 10.1, CS = 0, SANS

pH = 10.1, CS = 0, fit

pH = 4.7, CS = 0, SANS

pH = 4.7, CS = 0, fit

I(q) Shifted (AU)

q / Å-1
94

0

1 104

2 104

3 104

4 104

5 104

6 104

7 104

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

130 °C, up

155 °C, up

180 °C

155 °C, down

130 °C, down

q / Å-1

Figure 19 SANS from blends of G4 PAMAM and PMMA-r-PMAA.
95

0

500

1000

1500

2000

2500

0 0.05 0.1 0.15 0.2

100 °C

110 °C

120 °C

130 °C

q / Å

Figure 20 SANS from Blends of G4.5 PPI and PMMA-r-PMAA. Parameter of the plot is

the temperature as indicated in the figure.
96

0.01

0.1

1

10

100

1000

0.01 0.1

G1

G3

G5

Slope = -4

I(q) / cm-1

q / Å-1

Figure 21 SANS from blends of mass fraction 2% dendrimer-h in 98% mass fraction

HDPE-d4. ), G1; ', G3; (, G5.
97

-6

-4

-2

0

2

4

6

0 0.002 0.004 0.006 0.008 0.01

G1, R

g

 = 220 Å

G3, R

g

 = 200 Å

G5, R

g

 = 190 Å

R

g

 = 25 Å

ln( I(q) / cm-1

)

q

2

/ Å-2

Figure 22 Guinier plot of the scattering from blends of 2% mass fraction dendrimer-h in

HDPE-d4. Symbols are the same as in Figure 21.
98

0.01

0.1

1

10

100

0.008 0.01 0.03 0.05 0.07

PP

LDPE

E-co-B

Slope = -4

I(q) / cm-1

q / Å-1

Figure 23 Mass fraction 2% G5 Dendrimer-d in PP,); LPDE, '; and E-co-B, (.
99

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.0005 0.001 0.0015 0.002

90 °C

100 °C

110 °C

120 °C

130 °C

140 °C

q

2

 / Å-2

Figure 24 SANS from a 1:9 PSD/PVME blend that contains a mass fraction of 1% PPIC8 dendrimer for temperatures in the range 90 °C ≤ T ≤ 140 °C.
100

0

0.1

0.2

0.3

0.4

0.5

0 0.0005 0.001 0.0015 0.002

0% Dendrimer, 120 °C

1% Dendrimer, 120 °C

0% Dendrimer, 130 °C

1% Dendrimer, 130 °C

q

2

 / Å-2

Figure 25 SANS from 3:7 PSD/PVME blends that contain a mass fraction 0% and 1%

PPI-C8 dendrimer.
101

Figure 26 . Effect of the dendrimer PPI-C8 on the spinodal temperature of PSD/PVME

blends

0

5

10

15

20

25

30

35

0 0.02 0.04 0.06 0.08 0.1 0.12

W

PS

 = 0.1

W

PS

 = 0.3

T

S

 -T

S0

Mass Fraction Dendrimer
102

Figure 27 SANS of PSD/PVME = 1/9 with and without mass fraction 1 % dendrimer at

140 °C and 150 °C.

10

100

1000

104

0.006 0.008 0.01 0.012 0.014 0.016 0.018

H Dednrimer, 150 °C

D Dednrimer, 150 °C

No Dednrimer, 150 °C

H Dednrimer, 140 °C

D Dednrimer, 140 °C

No Dednrimer, 140 °C

I(q) / cm-1

q / Å-1
103

Figure 28 SANS of PSD/PVME = (1/9 and 3/7) with and without mass fraction 1 %

dendrimer at 70 °C.

0.1

1

10

0 0.0005 0.001 0.0015 0.002 0.0025

PS:PVME:G5 = 30:70:1

Rg = 130 Å

Rg = 30 Å

PS:PVME:G5 = 10:90:1

Rg = 130 Å

Rg = 40 Å

I(q) / Å-2

q

2

 / Å-2
104

Figure 29 TEM of PSD/PVME blend ED-1. The scale bar is one mircon.
105

Figure 30 Schematic representation of the growth of arborescent polymers by successive

grafting reactions.

Arborscent Polymers

Linear Chain Generation 0

Generation 1 Generation 2
106

Figure 31 SANS curves for all arborescent polymer generations in d-polystyrene at

120 °C.

0.001

0.01

0.1

1

10

100

1000

104

105

0 0.01 0.02 0.03 0.04 0.05 0.06

G3

G2

G1

G0

I(q), cm-1

q, Å-1

4.5

5

5.5

6

6.5

5 10-5 0.0001 0.00015 0.0002 0.00025

Guinier Plot

ln I(q)

q

2

, Å-2
107

Figure 32 Rg of arborescent polymers in solutions and in blends as a function of

generation number.

0

50

100

150

200

250

300

01234

d-toluene, 30°C

d-cyclohexane, 30°C

d-PVME, 100°C

d-PS, 120°C

Generation

Rg

Å

φ=1%
108

Figure 33 Temperature dependence of Rg for arborescent polymers in d-PVME

0

50

100

150

200

250

70 80 90 100 110

G3

G2

G1

G0

R

g, Å

T, oC
109

Figure 34 (a) Rg versus molecular mass for arborescent polymers in d-PVME. (b) Rg

versus molecular mass for arborescent polymers in d-polystyrene.

101

102

103

R

g, Å

(a) d-PVME

 T=100 o

C

Hard Sphere

 ν=1/3

Gaussian Chain

 ν=1/2

 ν=0.28 ± 0.02

101

102

103

103 104 105 106 107 108 109 1010

R

g, Å

M

Hard Sphere

 ν=1/3

Gaussian Chain

 ν=1/2

 ν=0.26 ± 0.06

(b) d-PS

 T=120 o

C
110

Figure 35 (a) Scattering functions for power law model compared with G3 polymer in dPVME. (b) Scattering functions for power law model compared with G3 polymer in dpolystyrene.

0.1

1

10

100

1000

104

Experimental data for G3 in d-PVME

Power law model + 9 % polydispersity + instrumental smearing

Scattering function for power law model

I(q), cm-1

(a) d-PVME

0.01

0.1

1

10

100

1000

0 0.01 0.02 0.03 0.04 0.05 0.06

Experimental data for G3 in d-PS

Power law model + 9 % polydispersity + instrumental smearing

Scattering function for power law model

I(q), cm-1

q, Å-1

(b) d-polystyrene
111

Figure 36 Density profiles for G3 arborescent polymer in solutions and blends.

0

0.4

0.8

1.2

1.6

0 50 100 150 200 250 300 350 400

Hard sphere

Power law model (α=18) for G3 in d-PS

Power law model (α=12) for phase separated G3 in d-PVME

Power law model (α=12) for G3 in d-PVME

Power law model (α=4) for G3 in d-cyclohexane

Power law model (α=4) for G3 in d-toluene

ρ(r), g/cm

3

r, Å
112

Figure 37 I(q) versus q for G3 polymer in d-PVME from 80 °C to the phase separation

temperature.

0.001

0.01

0.1

1

10

100

1000

104

0 0.01 0.02 0.03 0.04 0.05 0.06

80 oC

90 oC

100 oC

110 oC

115 oC

120 oC

130 oC

I(q), cm-1

q, Å-1
113

Figure 38 Temperature dependence of Rg for G3 polymer in d-PVME.

100

150

200

250

300

70 80 90 100 110 120 130 140

R

g, Å

T, oC
114

Figure 39 Rg of G3 arborescent polymer as a function of molecular mass of the matrix dpolystyrene.

0

50

100

150

200

250

300

0 1 105 2 105 3 105 4 105 5 105

R

g, Å

M PSD
115

Figure 40 SAXS for G10 dendrimer solution and IPN’s. High concentration low q peaks

are indicative of dendrimer ordering. The first minimum in the scattering indicates

dendrimer size. The shift to higher q of the minimum for the mass fraction

10% dendrimer in the IPN shows shrinking.

0.001

0.01

0.1

1

10

100

1000

104

105

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

26% G10 in Methanol

1% G10 in Methanol

10% G10 IPN

1% G10 IPN

I(q) (Shifted)

q / Å-1
116

Figure 41 SAXS and TEM-FFT dendrimer Rg in solution and IPN’s. The size in mass

fraction10 % dendrimer in the IPN is considerable smaller than in dilute solution or IPN.

20

30

40

50

60

70

5 6 7 8 9 10 11 12

SAXS R

g

 IPN 1 %

SAXS R

g

 IPN 10 %

SAXS R

g

 Solution

TEM R

g

 IPN 1 %

R

g

 / Å

Generation
117

Figure 42 TEM of mass fraction 10 % G11 dendrimer in the IPN with oso4 staining.

Picture contains images of dendrimers at different levels.
118

 Figure 43 TEM of mass fraction 1 % G10 dendrimer in PHEMA with

Phosphotungnistinic acid staining
119

Figure 44 SAXS of mass fraction 2 % G8 PAMAM dendrimer and mass fraction 2 % G8-

MAA dendrimer stained with phosphotungnstinic acid. Leveling off at low q is an

incipient peak showing uniform spacing. Peak at higher q shows spherical nature and

first minimum gives information on size.

0.0001

0.001

0.01

0.1

1

10

0 0.05 0.1 0.15 0.2 0.25

G8-MAA

G8

I(q) (AU)

q / Å-1
120

Figure 45 TEM of mass fraction 2% G8 dendrimer in PHEMA with Phosphotungnistinic

acid staining
121

Figure 46 TEM of mass fraction 2 % G8 PAMAM dendrimer in PHEMA-co-PMAA with

Phosphotungnistinic acid staining
122

Figure 47 Fast Fourier transform of TEM micrographs. Features at high q are

representative of spherical shape, the first minimum indicates an average R. Peak in

mass fraction 2 % G8 PAMAM dendrimer samples at low q represents incipient ordering

and is not seen for the mass fraction 1 % G9 or G10.

104

105

106

107

108

109

1010

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

G8

G8-MMA

G9

G10

I(q) (AU)

q / Å-1
123

Figure 48 Kratky plots of 32 arm stars with DSM G5 cores. The choice of endlinking

chemistry will affect the ultimate number of arms added.

0

1

2

3

4

5

0 0.05 0.1 0.15

Unreacted PEG

Vinyl Sulfone

Isocyanate

Epoxy

Acrylate

Iq5/3 / (Iq5/3

)High q

q / Å-1
124

Figure 49 GPC on the 32 arm stars (Figure 48) demonstrating the differences in reactive

endlinking chemistries.

.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

10 12 14 16 18 20

Vinyl Sulfone

Isocyanate

Epoxy

Acrylate

Detector Response (Normalized)

Elution Volume / mL
125

Figure 50. Kinetically Resolved GPC on DSM G4 stars of expected functionality 32. The

star (at low elution volumes) is clearly delineated from the free, reacting arms. A ratio of

the two peaks provides a measure of the conversion.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

12 14 16 18 20 22

4

26

90

145

329

1383

Detector Response (AU)

Elution Volume / mL

Reaction Time / min
126

Figure 51 Kinetic Analysis of Figure 50. The dotted line demonstrates the fit expected

from Equation (2.12). A better fit is obtained when the reaction order is allowed to float

(Equation (2.13)). This demonstrates that arms add very rapidly in early stages, but

further addition is very sterically hindered at late stages.

.

0

0.2

0.4

0.6

0.8

1

1 10 100 1000

C/C

0

k = constant

k = power law

C/C0

Time / m
127

Figure 52. DSM G5 networks with differing PEG/DSM stoichiometry. The most lightly

crosslinked gels swell most, and there is little variance in swelling for high crosslink

functionality in accord with Equation (2.14) and (2.15)

1

10

10 100

Swelling Ratio Methanol

Swelling Ratio Water

Swelling Ratio Acid

Swelling Ratio Methanol

Swelling Ratio Water

Methanol Phantom

Methanol Affine

Water Phantom

Water Affine

W

T

/W

0

Crosslink Functionality 

PPI Series
128

Figure 53. PAMAM G4 networks with differing PEG/PAMAM stoichimetries (see.

Figure 52)

1

10

10 100

Methanol

Water

1st Acid

Methanol Phantom

Methanol Affine

Water Phantom

Water Affine

W

T

/W

0

Crosslink Functionality

PAMAM Series

G2 G3 G4 G5 G6 G7
129

Figure 54. PAMAM networks swollen in solutions of decrasing ph. Gels with the lowest

functionality swell the most, and all gels demonstrate a maximum in swelling due to

repulsion of the (acid charged) dendrimers. The swelling decreases at lower ph (higher

HCl:NR3) due to screening of the repulsive interactions.

1

10

100

0.1 1 10

G2

G3

G4

G5

G6

G7

W

T

/W

0

HCl : NR

3

 mol / mol

No Acid
130

Figure 55. Dendrimer nanotemplating in aqueous solution. In a first step, the dendrimer is

loaded with a precursor salt (H+

AuCl4

-

) resulting in a charged dendrimer with the

precursor as counterions. In a second step, the chemical reduction is performed which

yields a colloid inside the dendrimer.

PAMAM Charged

dendrimer

Dendrimer

with gold

4

+

++

+

+

+

+

+ +

+

+

+

+

+

+

+ +

+ +

+

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+
131

Figure 56 UV-VIS spectra for gold-dendrimer hybrid colloids in aqueous solution. The

spectra correspond to G9-PAMAM dendrimer samples loaded with different amounts of

gold (the molar ratio of gold ions to dendrimer end groups is indicated in the figure.)

10-1

100

101

102

103

104

0 0.2 0.4 0.6 0.8 1 1.2 1.4

g9nacl

Au31d

Au30d

Au18d I(q)

a.u.

q / nm-1

1:1

1:4

1:2

unmodified
132

Figure 57. TEM of gold containing G9 PAMAM-dendrimer obtained for 1:1 loading. The

dendrimer has been stained with phosphotungstic acid, it appears gray, the gold appears

black. A: fast reduction (NaBH4 in 0.1 mol/L NaOH) b: slow reduction (NaBH4 in 0.3

mol/L NaOH)
133

Figure 58. a) Small angle x-ray scattering curve I(q) for the plain G9 PAMAM-dendrimer

along with fit to the data. Error bars are the measured standard deviation in I(q). b) Pair

distribution function P(r) obtained by indirect Fourier transformation of the scattering

data I(q) (program ITP). A homogenous sphere structure with a diameter of 13 nm

becomes evident

10-1

100

101

102

103

104

0 0.2 0.4 0.6 0.8 1 1.2 1.4

g9nacl

Au31d

Au30d

Au18d I(q)

a.u.

q / nm-1

1:1

1:4

1:2

unmodified
134

Figure 58 a: Small angle x-ray scattering curve I(q) for the plain G9 PAMAM-dendrimer

along with fit to the data. Error bars are the measured standard deviation in I(q).

B: Pair distribution function P(r) obtained by indirect Fourier transformation of the

scattering data I(q) (program ITP). A homogenous sphere structure with a diameter of 13

nm becomes evident.

10-2

10-1

100

101

102

0 0.5 1 1.5 2 2.5

I(q)

cm-1

q / nm-1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10 12 14

P(r)

r / nm
135

Figure 59 a) Small angle x-ray scattering curve I(q) for the gold containing G9 PAMAMdendrimer of figure 3 along with fit to the data. B) Pair distribution function P(r)

obtained by indirect Fourier transformation of the scattering data I(q) (program ITP). A

layered-sphere structure with a total diameter of 13 nm becomes evident.

10-4

10-3

10-2

10-1

100

0 0.5 1 1.5 2 2.5 3 3.5

q / nm-1

I(q)

cm-1

0.0

0.5

1.0

1.5

2.0

2.5

0 2 4 6 8 10 12 14

r / nm

P(r)
136

Figure 60 a) Theoretical pair distribution function P(r) calculated for layered spheres with

different relative contrast of the inner sphere (solvent contrast = 0, outer sphere contrast

=1, inner sphere contrast as given in the figure). The basic shape of the experimental

function in Figure 4b cannot be modeled.

B) Theoretical pair distribution function P(r) calculated for layered spheres with different

offset of the inner sphere inside the outer sphere (outer sphere radius = 6.6 nm, inner

sphere radius = 1.8 nm, offset d between centers given in the figure). The basic shape of

the experimental function is much better represented.

0.0

0.5

1.0

1.5

2.0

2.5

0 5 10 15

100

80

60

40

20

10

r / nm

P(r)

 homogeneous

sphere

 80

 60

 40

 20

100

0.0

0.5

1.0

1.5

0 5 10 15

1

1

1

1

1

1

r / nm

P(r)

d

4.7 nm

4 nm

3 nm

2 nm

1 nm

centered
137

Figure 61 a) Small angle x-ray scattering curves I(q) for gold containing G9 PAMAMdendrimers obtained for different loading ratios 1:1, 1:2 and 1:4. Pair distribution

functions P(r) obtained by indirect Fourier transformation of the scattering data I(q) in b)

The decreasing gold diameter but constant dendrimer diameter upon decreasing loading

is visible.

10-4

10-3

10-2

10-1

100

0 0.5 1 1.5 2 2.5 3 3.5

1

1

1

I(q)

cm-1

q / nm-1

1:2

1:4

1:1

0.0

0.5

1.0

1.5

2.0

2.5

0 2 4 6 8 10 12 14

1

1

1

r / nm

P(r)

1:2

1:4

1:1
138

Figure 62 a) TEM of gold containing G8 PAMAM dendrimer obtained for 1:1 loading

and slow reduction. (The dendrimer has been stained with phosphotungstic acid.) b) TEM

of gold containing G10 PAMAM dendrimer obtained for 1:1 loading and slow reduction.

(The dendrimer has been stained with phosphotungstic acid.)

G 20 G1
139

Figure 63 a) Small angle x-ray scattering curves I(q) for gold-dendrimers hybrid

structures obtained with PAMAM dendrimers of generation 7 to 10. b) Pair distribution

functions P(r) obtained by indirect Fourier transformation of the scattering data I(q) in a).

For G7 to G9 (solid lines) an increasing gold diameter with increasing dendrimer

diameter is seen. Contrary, for G10 (dotted line) the gold diameter is decreased though

the dendrimer diameter is further increased.

10-2

10-1

100

0 0.5 1 1.5 2 2.5 3 3.5

1

1

1

1

q / nm-1

I(q)

cm-1 G10

G8

G9

G7

0.0

1.0

2.0

3.0

0 2 4 6 8 10 12 14

1

1

1

1

r / nm

P(r) G10

G8

G9

G7
140

Figure 64 Small angle neutron scattering curve for the initial G5 poly(propyleneimine)

dendrimer in toluene at 55oC and small angle neutron scattering curve and small-angle xray scattering curve after solubilization of gold salt.

10-4

10-3

10-2

10-1

100

101

0 0.5 1 1.5 2 2.5 3 3.5 4

SANS initial dendrimer

SANS salt loaded

SAXS salt loaded

I(q)

cm-1

q / nm-1
141

Figure 65 Small angle neutron scattering curve I(q) for the gold-salt loaded G5

poly(propyleneimine) dendrimer along with fit to the data.

10-4

10-3

10-2

10-1

100

101

0 0.5 1 1.5 2 2.5 3 3.5

I(q)

cm-1

q / nm
142

Figure 66 Pair distance distribution function P(r) obtained by indirect Fourier

transformation of the scattering data I(q) (program ITP). A cylindrical structure with a

diameter of 6 nm and a length of 21 nm becomes evident.

0

1

2

3

4

5

6

7

0 5 10 15 20 25

r / nm

P(r)
143

Figure 67 Cross-sectional pair distance distribution function Pc(r) obtained by indirect

Fourier transformation of the scattering data I(q) under assumption of a cylindrical

particle geometry

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

01234567

P (r) c

r / nm
144

Figure 68. Radial scattering length density profile ρ(r) obtained by square-root

deconvolution of the cross lectional pair distance distribution function PC(r) in figure 68.

The dotted line represents the result from the first multi-step approximation. The solid

line represents the final solution, i.e. the easiest profile corresponding to the best fit of the

data: A two step cross-sectional profile becomes evident.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.5 1 1.5 2 2.5 3 3.5 4

r / nm

ρ(r)
145

Figure 69 Small angle x-ray scattering curve I(q) for the gold-salt loaded G5

poly(propyleneimine) dendrimer along with fit to the data

10-4

10-3

10-2

10-1

100

101

0 0.5 1 1.5 2 2.5 3 3.5 4

q / nm-1

I(q)

cm-1
146

Figure 70 Pair distance distribution function P(r) obtained by indirect Fourier

transformation of the scattering data I(q) (program ITP). A cylindrical structure with a

diameter of 4 nm becomes evident.

0.0

0.5

1.0

1.5

0 5 10 15 20 25

r / nm

P(r)
147

Figure 71 Cross-sectional pair distance distribution function Pc(r) obtained by indirect

Fourier transformation of the SAXS data I(q) under assumption of a cylindrical particle

geometry (program ITP).

0.0

0.1

0.2

0.3

0.4

0.5

01234567

P (r) c

r / nm
148

Figure 72 Schematic of the multi-dendrimer cylindrical structure as deduced from the

SAXS and SANS results.

1.9

3.2

nm

nm
149

Figure 73 Small angle neutron scattering curve I(q) for gold-dendrimer hybrid structures.

10-4

10-3

10-2

10-1

100

101

0 0.5 1 1.5 2 2.5 3 3.5

q / nm-1

I(q)

cm-1
150

Figure 74 TEM of gold colloids obtained from hydrophobically modified G5

poly(propyleneimine) dendrimers loaded with gold-salt after reduction with sodium

borohydrate.

20 nm
151

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