N8S

Publl - cations

>iBSIR 81-2264

A1110S 6671

Models for the Migration of Low

Molecular Weight Additives in

Polyolefins

L. E. Smith, S. S. Chang, F. L. McCrackin

G. A. Senich and F. W. Wang

Polymer Science and Standards Division

Center for Materials Science

U S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

Annual Report for the Period

October 1 , 1 979 - September 30, 1 980

Issued April 1981

Prepared for Bureau of Foods

QC Food and Drug Administration

100 Washington, DC 20201

,U56

81-2264

1981
V
NBSIR 81-2264

MODELS FOR THE MIGRATION OF LOW

MOLECULAR WEIGHT ADDITIVES IN

POLYOLEFINS

0AT1OVAL lUfttA

U

09 MTAUDAUm

bUBUT

JUN . 0 1381

nof (lccaaoo

<?l '9&(s

m\

L. E. Smith, S. S. Chang, F. L. McCrackin

G. A. Senich and F. W. Wang

Polymer Science and Standards Division

Center for Materials Science

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

Annual Report for the Period

October 1, 1979 - September 30, 1980

Issued April 1981

Prepared for Bureau of Foods

Food and Drug Administration

Washington, DC 20201

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
^ f • v ^ * t*'

: ». . 'ft 1

If J

f 0 3 tfUl
Abstract

Food Packaging is an important encounter in the daily life. The

low molecular weight components in the packaging materials may migrate

into the foods. This program, sponsored by the Bureau of Foods of the

Food and Drug Administration, is to provide theoretical models, reliable

data base, and methodology to study the migration phenomena and to

provide reasonable worst-case estimates for the concentrations of the

indirect additives in food. In this annual report we present a relationship

of diffusion coefficients of gaseous diffusants in polyolefins based on

free volume theory, procedures and results of inverse gas chromatography

for migrant-polymer interaction parameters and diffusivities of oligomers

in polyethylene, methods and preliminary results of spectrofluorimetry

on the migration of antioxidants in polyethylene, results and correlations

of extraction experiments with radioactive labeled migrants. It was

found that anhydrous ethanol and lower members of pure triglycerides can

successfully simulate the extractive behavior of food oils. The accelerating

action of n-heptane over that of the food oil is quantified.

Key Words: Antioxidants, Diffusion, Food Packaging, Spectrofluorimetry,

Inverse Gas Chromatography, Migration, Oil Simulants, Oligomers, Radioactive

Tracer, Polyolefins

Table of Contents

Page

INTRODUCTION ii

I. An Empirical Relationship Between the Diffusion Coefficient

in Hydrocarbon Polymers and Its Interpretation by

Fractional Free Volume 1-1

II. Activation Energies for Diffusion in Polyolefins I I -1

III. IGC Measurement of the Polymer-Migrant Interaction Parameter . . . III-l

IV. IGC Measurement of Polymer-Migrant Diffusion Coefficients .... IV-1

Theory IV-1

Experiment and Calculations IV-7

Gas Phase Contributions IV-8

Polymer Phase Contributions IV-11

Concentration Effects IV-1

7

Capillary Columns IV-1

8

Adsorption Effects IV-1

Other IGC Studies of Diffusion in Polymers IV-1

9

Conclusions and Future Work IV-21

V. Fluorescence Measurements of Antioxidant Migration from

Plastics V-l

Introduction V-l

Experimental V-l

Results and Discussion V-6

VI. Experimental Measurement of Migration by Extraction VI-1

Introduction VI-1

Experimental Run Designation VI-5

Estimation of Diffusion Coefficients VI-6

Results of Extraction Experiments VI-10

Typical Examples of Extraction Experiments VI-11

Correlation of Diffusion Coefficients VI-12

Effect of Temperature VI-13

Effect of Solvent VI-14

Effect of Different Polyolefins VI-16

Effect of Migrants VI-19

Effect of Migrant Concentrations VI-20

Summary of Conclusions VI-21

i

Introduction

The daily encounters of food packaging materials become an important

aspect of life as more foods are sold in packaged form for the purpose of

preservation and ease of distribution. The Bureau of Foods of the Food and

Drug Administration has regulatory responsibility of the use of packaging

materials in contact with food. Any substances that migrate from the food

packaging materials into foods are considered to be indirect food additives.

The regulatory decisions on the types of packaging materials to be used on

various types of foods are based on the indirect food additives that can be

expected to migrate from the package into the food, its toxicological knowledge

and expected amount of migration during storage and usage. Since it is impossible

to test every conceivable case of combinations of polymer-migrant-food, the

program at the National Bureau of Standards, sponsored by the Food and Drug

Administration, is aimed to provide sound technical assistance and reliable

data to the Food and Drug Administration and to recommend theoretical or

empirical estimation and extrapolation methods to yield at least a reasonable

worst-case estimates for regulatory purposes. However, this report represents

only the technical opinions of the authors as representatives of the National

Bureau of Standards and should not be taken in any way as regulatory decisions

or recommendations of the Bureau of Foods.

In this report we present an empirical relationship of diffusion coefficients of gaseous diffusants and polymers based on free volume theory,

procedures and results of inverse gas chromatography and spectrofluorimetry,

results and correlations of extraction experiments with radioactive labeled

migrants.

An empirical relationship between the zero concentration diffusion

coefficient of gases in polyolefins, similar to the one presented in a previous

report, has been interpreted by means of free volume theory.
Inverse gas chromatography has been used to generate the specific retention

volume V

° and then to estimate the polymer-migrant interaction parameter

y

x°° needed to calculate the partition coefficients from solution theory. Relative

ranking of diffusivities of probe molecules in the polymer phase above the

polymer glass transition temperature or in the liquid phase can also be estimated

from inverse gas chromatographic method.

A procedure for using spectro-fl uorimeter as a selective and sensitive

method detection of migrants, especially antioxidants, have been developed and

presented in this report together with preliminary results on the migration of

N,N' -di phenyl -p-phenylenediamene from low density polyethylene into n-heptane.

In the past year we have substantially completed a large number of tests

14 involving the migration of radioactive C-labeled straight chain paraffinic

oligomers (n-octadecane and n-dotriacontane) and an antioxidant (butylatedhydroxytoluene) from two different polyethylenes (high density or linear polyethylene and low density or branched polyethylene) and isotactic polypropylene

into various solvents including a variety of triglycerides, alcohols, hydrocarbons and water at temperatures from room temperature to 60°C. Among the

correlations for various parameters, it was found that either the pure triglycerides, such as tributyrin and trioctanoin, or anhydrous ethanol may successfully be employed as an oil simulant in all cases studied. The accelerating action of n-heptane over that of the food oil is quantified.

Future works in the additive migration program would be mainly in the

area of migration from glassy polymers, where the diffusion coefficients are

many orders of magnitude slower than that in the amorphous or semi -crystal! ine

polymers above their glass transition temperatures.
SECTION I

An Empirical Relation for Diffusion of Gases in Hydrocarbon Polymers

and in Interpretation in Terms of Fractional Free Volume
v ?
The zero concentration diffusion coefficient, D, of gases in polyolefins

1 ,

( polyethyl enes of different crystallinity and natural rubber) shows a remarkable

regularity. Not only is the order of the gases according to D the same for all

polyolefins, but the diffusion coefficient of a gas in a polymer is given in

terms of its diffusion coefficient, Dr

, in natural rubber by

D * KDTM (1)

where the values of K and m depend only on the polyolefin and not on the gas.

For natural rubber, K and m must equal 1. Experimental diffusion coefficients

at 25°C of eleven vapors in three polyethylene films and in natural rubber are

given in table 1 and plotted on log-log scales in figure 1. The points lie on

straight lines, justifying equation (1). The relative standard deviation of the

fit of the diffusion coefficients to equation (1) is 9.5 percent. This compares favorably with the wide variation of D which varies by a factor of 1000.

The empirical rule formulated in equation (1) can be derived on the basis

of the fractional free volume concept of the transport properties of polymers.

In a rough approximation, the zero concentration diffusion coefficient of a gas

in a polymer depends, according to Fujita , on the fractional free volume f of

the polymer by

D = Ae" B/f

(2)

i 1-1
ft 7

Table 1. Diffusion Coefficients D x 10 cm /s, at 25 °C in

Natural Rubber (a

y = 0) and Three Polyethyl enes and

The Corrected Value D in Natural Rubber.

ra

a v Volume Crystallinity

Gas 0 0.29 0.43 0.77 Dra

2

173 120 46 17 169

A 136 96 36 11.6 136

co

2

125^ 91 37.2 • 12.4 134

CO 135 82 33.2 9.6 126

n

2

117 74 32 9.3 117

ch

4

89 54 19.3 5.7 86.1

CH

3

- CH

3

40 24 6.8 1.46 . 39.5

CH

2

:C:CH

2

50 31 10.5 2.5 52

CH

3

^CH:CH

2

31 20 5.8 1.1 33.1

ch

3

-ch

2

-ch

3

21 12 3.22 0.49 21.2

sf

6

11.5 5.6 1.35 0.16 11.1

I
CD CD CD CD

Q

three

polyethylenes

at

25

°C

versus

the

diffusion

coeffi-
as long as the whole interaction of the gas and polymer can be taken into

account by f which is a characteristic property of the polymer at the temperature of the experiment. B depends on the size and shape of the diffusing

molecule but is independent of the polymer. The factor A is certainly dependent

on the polymer. According to Fujita, A also depends on the size and shape of

the diffusing molecule, but is independent of the temperature of the diffusing

molecule.

The four polymers in this study are very similar chemically and differ

mainly in their volume crystallinity, shown in table 2 which varies from 0 to

0.77. The crystallinity affects the diffusion coefficients mainly by the detour

3 4

and blocking factors 8. The detour factor decreases the diffusivity because

the crystal lamellae are impermeable to the diffusing molecule so that it must

travel a longer path through the amorphous component than would be the case for

a purely amorphous material. Because the detour factor depends only on the

supercrystalline morphology of the sample, it does not depend on the diffusing

molecule or the fraction free volume of the amorphous component of the polymer.

Thus, the detour factor only affects the factor A in equation (2).

The blocking factor reduces the diffusivity because some of the more narrow

passages in the amorphous layers between the parallel lamellae become impassable

to larger molecules. Thus the blocking factor is dependent on both the polymer

through its morphology and on the diffusing molecule through its size. The

blocking factor affects both A and f in equation (2). Because the size of the

diffusing molecules used in this study, from 0

2

to SF^, covers a limited range,

the effect of the blocking factor on the diffusion coefficients is assumed to

1-2
Table 2. K, m and Volume Crystallinity, for Three Polyethylenes

and Natural Rubber (a„ = 0) at 25 °C

a . K m

V _

0 . 1 1

0.29

k

2.791 1.105

0.43 18.72 1.314

0.77 1326. 1.712
be small; A is therefore assumed to depend only on the polymer. This automatically excludes very small ( » He) and very large penetrant molecules.

With these assumptions, equation (1) is derived from equation (2). Let A

r and f be the values of A and f for natural rubber. Then by equation (2),

D

r

- A

re'

8/f

r (3)

Eliminating B from equations (2) and (3) gives

D - (A/A

r

f

r/f

)D

rVf

(4)

Equation (4) is identical to equation (1) if one defines

m = f

r/f (5)

K = A/A" (6)

with both m and K dependent on the polymer but independent of the diffusing

molecule.

The fractional free volume of the amorphous phase of a polymer is given by

f. Therefore, if the amorphous material in the semi -crystal line polymers were

unaltered by the crystals, its fraction free volume f would be equal to that of

natural rubber, f and the value of m would be one by equation (5). In fact, the

fractional free volume of the amorphous phase is seen to be reduced by the

crystals; for the polyethylene as a volume crystallinity of 0.77, one obtains

f = 0.584 f

r

1-3
i.e., a little more than half the fractional free volume in the fully arcorphu*-

natural rubber. Figure 2 shows the values of f/f for the polymers investigated.

The polymer molecules in the amorphous phase of a semi -crystalline polymer

are more constrained than those of a completely amorphous polymer, so that the

fractional free volume is expected to be less. However, its reduction by almost

a factor of two is surprising.

Equation (1) was found to fail for diffusion coefficients of hydrogen and

helium. This may be understood from the derivation of equation (1). The blocking

factor was assumed to be independent of the diffusing molecule. This assumption

is not valid for hydrogen or helium which are very small and can diffuse in many

channels in the polymer that block larger molecules.

A similar consideration can be applied to the B/f term in equation (2). If

the interactions between the diffusing molecules and the polymer vary with the

diffusing molecules, the fractional free volume of the polymer does not adequately describe this interaction. Then the value of B depends on this interaction so that it also depends on the polymer instead of depending only on the

diffusing molecule. Because all of the polymers investigated were chemically

similar, the interaction of a particular molecule is nearly the same in all of

the polymers.

One of the sources of the derivation between the experimental values of D

and the values computed by equation (1) is experimental errors of D

r

, the

diffusion coefficients of the gases in natural rubber. Therefore, the values of

D

r were adjusted to improve the fit. The adjusted values, equation (1) fit the

diffusion coefficients with a relative standard error of 4.7 percent. The

values of K and m are shown in table 2.

1-4
o >

<3

LD3OOE

03

<U JC

+Jo

Q)E3

r—o>

<u

<u

sf0co

'r—

4-> u

03

5-

O) jC

-*-> V-oo

•r—

+-> fD

S-

<u JCI—

CsJ

a;

i-3

O) o

a>E3O>

<u

<u

s_

03co

-pu

03

s_

<u jc

-Po

•p

s-

<1) E

>>

r

o

CL

a> JC

-P

0Jto

<TJ x:

CL o0 CD 00 CD• LD°

T-.

O CD o o O

tu/1 = JJ/J

rubber

versus

crystallinity.
References

1. A. S. Michaels and H. J. Bixler, J. Polym. Sci., 50, 413 (1961).

2. H. Fujita, Adv. Polymer Sci., 3, 1 (1961).

3. C. H. Klute, J. Appl. Polym. Sci., 1^, 340 (1959).

4. A. S. Michaels and R. B. Parker, Jr., J. Polym. Sci., 41^, 53 (1959).

5. A. Peterlin and F. L. McCrackin, J. P. Sym. Sci., Physics, in press.

SECTION II

Activation Energies for Diffusion in Polyolefins

Diffusion coefficients and activation energies for diffusion of man”

migrants in polyolefins have been collected by Flynn. The activation energies

for high and low density polyethylene given by Flynn as well as those given in

the Polymer Handbook are shown in Figure 1 versus the molecular weight of the

migrant. Despite the large scatter, the activation energies in high and low

density polyethylene are seen to be the same, and to increase with increasing

molecular weight of the migrant.

Figure 2 shows the activation energies of five other polyolefins. The

line is the same line as in Figure 1 and gives the average value for polyethylene.

The increase in the activation energies with the molecular weight of the migrant

is again observed. The activation energies of migration in isotactic polypropylene and polyisbutylene are seen to be larger than in polyethylene, while

the activation energies in stereoblock polypropylene and hydrogenated polybutadiene are seen to be larger than in polyethylene. The data for poly (4-

methylpentene-4) are not sufficient to draw any conclusions.

The scatter in these curves are not unexpected. Many experimental measurements of the activation energies are based on few measurements of the diffusion

coefficients so they are inaccurate. Also, the activation energy in a given

polymer depends on the chemical structure and shape of a migrant in addition to

the molecular weight of the migrant. However, these figures can still provide

the best estimate of the activation energy for diffusion of a migrant in a

polyolefin when no other information is available.

II-I
<DC

<1> >X-4-1 0>0

CL>wC Li. I <D CL kJ a cl > 2 -*-> > 0 -4- J _J w - C \fl ~u 0 c; c a © o a x X 0) -1 o-o - r _j r + a cc0w( »- k-aL0

k-LU

COr i °W/ ! no

r

Figure
Activation

Energy

for

Diffusion

of•

PoIyi

sobut yi

ene

-r

Isotsact ic

PoI

ypropy 1

ene O

Stereb I

ock

PoI

y^y I

ene

21

Hydrogenated

Poi

ybu t

adi

ene ^

PoIy

C4-he

thy I

pentene-4)

<> I OU'/O I no' r ^ (A

hoi

ecu I

ar

Weight

cf

Migrant

SECTION III

IGC Measurement of the Polymer-Migrant Interaction Parameter

The polymer-migrant interaction parameter, x» can be determined experimentally

from the results of osmotic pressure, swelling, sorption, vapor pressure, and heat

of mixing studies. Such studies are often conducted at relatively high migrant

\ concentrations. This necessitates extrapolation to zero migrant concentration in

order to estimate the interaction parameter x°° needed to calculate the partition

coefficient describing the distribution of a migrant between the solvent and polymer

phases. Inverse gas chromatography ( I GC ) provides a method for the determination of X°°

at migrant or probe levels so low that extrapolation to zero concentration may not

be required. The specific retention volume, V^, is the IGC result from which

9

is calculated as previously outlined in NBSIR 80-1999. In order to investigate the

capabilities and limitations of this method, we have determined both V° and x°° y for several migrants in the linear polyethylene SRM 1475 at temperatures above and

below the polymer melting point. The results for decane-SRM 1475 and an analysis

of the source of errors encountered in this typical determination are given in

the previously cited NBS report. Determination of the total mass of polymer in

the column makes a significant contribution to the overall uncertainty in V°. We

have found that this quantit^ can be obtained more reliably from gravimetric determinations on a calcined diatomite or glass bead support than by solvent refluxing treatments. When these methods are applied our results for decane-SRM 1475

are identical, within the limits of uncertainty, to literature data available for

similar systems.

The X°° parameter can be calculated from an IGC determined V° with the aid of

a theory which describes the behavior of polymer solutions. These theories provide

O oo a link between V and X by relating X to the weight fraction activity coefficient

y

of the probe. The latter quantity is readily calculated from the experimentally

determined V?.

III-l
Several theoretical treatments are possible but all lead to a similar relati on

between x°° and V°. The accuracy of x°° depends on the uncertainties in V° and

y 9

input parameters needed for the solutions theories. The latter are difficult

to ascertain, however, and errors in x°° have not been estimated in our work.

The agreement between values calculated from the Flory equation-of-state theory

and the Sanchez and Lacombe lattice fluid based treatment of polymer solutions

is generally good.

A large body of IGC-determined polymer-solvent interaction parameters is

available. Table I is a compendium of references to x values derived from major

IGC studies on a variety of polymer-sol vent systems. It should be noted that all

the studies cited have been conducted at temperatures above the polymer glass

transition. Values of x°° derived from IGC experiments are in good agreement with

those obtained from other methods of measurement, as discussed in two interlaboratory comparisons (1,2).

Specific retention volumes and interaction parameters determined below the

melting point of a semi crystal 1 ine polymer have a greater degree of uncertainty

than the corresponding results obtained from the molten polymer. The crystalline

material present below Tm

does not contribute to bulk sorption; therefore, the

effective mass of polymer in the column is that of the amorphous fraction. As

the crystalline content of a semi crystal 1 ine polymer is a nominal value that can

be determined to an accuracy of about 5% at best, this additional uncertainty

will contribute to the error in the effective mass of polymer in the column and

be reflected in the experimental and the x value derived therefrom.

References

1. W. E. Hammers and C. L. DeLigny, J. Polym. Sci., Phys., ]_2, 2065 (1974).

2. Y.-K. Leung and B. E. Eichinger, J. Phys. Chem. , 78, 60 (1974).

1 1 1-2
TABLE 1

Literature Sources of IGC X Values

Polymera Probe T.ype

b

Reference

Linear polyethylene A,B,D,E 1 Branched polyethylene A,B,C,D,E,F 1,2,14

Polyethylene copolymers a,c,d,e,f 2,3,14

Polypropylene A,C,D,E,F 3,14

Poly(vinyl acetate) A,C,D,E 4

Poly(vinyl methyl ether) A,C,D,F 5

Poly(vinyl chloride) A,F 6

Poly(e-caprolactone) A,F 6

Polystyrene A,B,C,D,E,F 5, 7, 8,

9

Poly(methyl methacrylate) A,B,D,E 9

Polyisoprene A,B,D,E 3,10

Polyisobutylene A 11 Polysiloxanes A,B,D,E 12,13

d

all measurements reported are above the polymer

b

A = normal alkane B = branched alkane C = chlorinated alkane

D = aromatic E = branched aromatic F = compounds containing

heter atoms

H. P. Schreiber, Y. B. Tewari, and D. Patterson, J. Polym. Sci . Phvs , 11, 15 ( 1973 ). R. D. Newman and J. M. Prausnitz, AIChE J., 1_9, 704 (1973).

K. Ito and J. E. Guillet, Macromol., 12, 1163 (1979).

D. D. Deshpande and 0. S. Tyagi, Macromol., 1J_, 746 (1978).

C. S. Su and D. Patterson, Macromol., ljO, 708 (1977).

0. Olabisi, Macromol., 8, 316 (1975).

M. Gal in and M. C. Rupprecht, Polymer, 19 , 506 (1978).

F. H. Covitz and J. VJ. King, J. Polym. Sci. A-l , K), 689 (1972).

G. Di Paol a-Baranyi and •!. E. Guillet, Macromol . , 11, 228 (1978)

Y. B. Tewari and H. P. Schreiber, Macromol., !5, 329 (1972).

Y.-K. Leung and B. E. Eichinger, J. Phys. Chem., 78, 60 (1974).

W. R. Summers, Y. B. Tewari, and H. P. Schreiber, Macromol., 5, 12 (1972)

M. Gal in, Macromol., 1J), 1239 (1977).

G. DiPaola-Baranyi , J. E. Guillet, H.-E. Jeberien, and J. Klein, Macromol

Chem. , 181 , 215 (1980).
.
SECTION IV

IGC Measurements of Polymer-Migrant Diffusion Coefficients

THEORY

The probe or migrant injected onto a chromatographic column resides partly

in the carrier gas and partially in the stationary phase during transit through

the column. Diffusion of the probe vapor in the gas phase can occur parallel to

the background flow of carrier gas sweeping the vapor through the column both with

and opposed to the carrier flow direction. This longitudinal gaseous diffusion

process, that is, diffusion in the gas phase along the carrier flow direction

through the column, causes an increase in width of the eluted peak over its

initial injection distribution. An additional gas phase peak spreading mechanism

originates in the multiplicity of path lengths possible around the packed support

particles and leads to an associated broadened distribution of elution times.

Peak spreading can also be attributed to diffusive processes in the stationary

phase. If the carrier gas flow rate is very rapid, equilibrium partitioning of

the vapor between the gas and stationary phases cannot be established. The

residence time in the stationary liquid phase is influenced by both the diffusivity and the distance in the stationary phase over which diffusion must occur,

among other factors. Longitudinal diffusion in the liquid phase, however, has

been found to be insignificant compared to peak spreading arising from the corresponding gas phase process and can be ignored in all cases. Peak broadening is

commonly quantified by the construct of the height equivalent to a theoretical

plate H, related to the width at half-height w-j^ for an eluted gaussian-shaped

peak as follows:

where L is the column length, a the standard deviation, and t

R the retention

time of the peak at the maximum.

An equation attributed to van Deemter et al . (3) is often used to relate

H to the carrier gas flow velocity u and is of the form:

(

1 )

IV-1
H = A + B/u + Cu (2)

where the A term arises from the number of possible gas paths through the column,

B from longitudinal diffusion of the probe in the carrier gas, and C from the

resistance to mass transfer in the liquid or stationary phase. The coefficients

in equation 2 are defined as follows:

A = 2Ad

P (3)

B = 2YD

g

(4)

8 £ k r =

T (5)

u 0 ? " d

£

(i + kr

where A is a measure of support packing irregularities, d the average support

r particle diameter, y a correction for the tortuosity of the gas flow in the

column, D the probe diffusivity in the gas phase, d

f the effective thickness

of the liquid phase film, the diffusivity of the probe in the liquid phase,

and k the column capacity factor commonly given as:

( 6 )

t

M being the time taken to elute an unsorbed material, such as methane or air,

from the column. Equation 2 indicates that at high flow rates H will be proportional

to u as illustrated in Figure 1. The probe-liquid diffusion coefficient can

then be determined from the constant of proportionality C by Equation 5 if the

film thickness is known. Equation 5 is applicable for diffusion into a spherical particle. A more commonly encountered situation is diffusion into a

uniform stationary phase film on a planar solid surface which leads to a similar relation for C:

2 d? k

C

= 7 (7)

3 (1 + kr

While equation 2 gives a suitable explanation of peak spreading in some

cases, other results have raised questions about its utility. Bohemen and

IV-2
Figure

1.

van

Deemter

plot

of

HETP

vs.

carrier

gas

flow

velocity

d!3H

Eddy

Diffusion
Purnell (4) determined the coefficients in equation 2 for several systems and

II found A values which were unexpectedly independent of the particle size and

sometimes negative, a result not predictable by the van Deemter treatment.

Giddings (5) has developed a theory which postulated that the A term is

velocity dependent, having a zero value at low flow rate and reaching the limiting value of equation 3 at high velocity. A serious question to this prediction

was raised by experiments with air samples where there is no sorption by the

stationary phase (k=0). The expected asymptotic approach to a limiting value of

A at high flow rates was not realized; rather, a minimum in the H vs. u plot

was observed in all cases as typified by the work of Kieselbach (6). These discrepancies indicate that the simplifications made by van Deemter in neglecting other

mechanisms of diffusion are not valid for all systems. Giddings and coworkers (7)

examined several modified forms of the van Deemter equation and found that none

could account for the experimental results obtained on columns of varying length and

outlet pressure.

An equation proposed by Jones (8) takes several additional sources of peak

spreading into consideration: resistance to mass transfer in the gas phase

normal to the carrier gas flow direction (D), velocity distribution effects (E),

and a correlation between these two processes (F). This equation is given as:

H = A + B/u + (C + D + E + F)u (8)

where C is as in equation 7 and

D

=

2 2 C

D

k

g Dg(l + k)

2

E =

C

E d

”~D g

2P

F

= 20 (C

D

C

E

) 1/2

k d

p

d

q

D

g O + k)

(9)

( 10 )

( 11 )
d being the diffusion path length in the gas, 0 the correlation coefficient

between the D and E terms, and Cp and geometric constants. The D term was

discounted by van Deemter in the derivation of equation 2 because of the much

greater magnitude of D

g compared to D^. This simplification is valid for

the thick liquid films used in their work, studies of columns with roughly 0.3

mass fraction stationary phase loading. If low column loadings which reduce d

f

to about 0 . 01 d

Q are used, then the expected difference in diffusivit.y between

liquid and gas phases is overcome and the D term cannot be ignored. In addition,

if the support surface is not completely covered then Cp must increase by a factor

of the average number of times for diffusion to the wall before contact with the

liquid phase is made. The functional form of the D term given in equation 9 is

not correct since its plate height contribution is predicted to approach zero as

the vapor becomes increasingly insoluble in the liquid phase. This difficulty has

been examined by Purnell (9) who concludes that the discrepancy is a consequence

of neglecting the nonuniform velocity profile. For an infinite value of k, equation

9 is expected to give a result about an order of magnitude less than the theoretical

limiting Cp value of 0.115 derived for an ideal distillation process.

The E contribution to spreading arises from diffusion caused by differences

in the velocity of the carrier gas in various parts of the column. When the

support is porous the carrier gas in the interior of the particles is relatively

stagnant. The time taken by the probe vapor to diffuse from the particle interior

to the flowing carrier stream contributes to the peak broadening process. The

diffusion distance from the particle interior to the fast flowing carrier stream

is on the order of the particle radius. Other velocity differences can arise from

short and long range channels formed by support packing irregularities and transcolumn effects caused by the influence of the tube walls and coiling of the column.

These effects are summarized by Giddings (10) who estimates approximate magnitudes

for contributions of the many possible velocity gradients combined in the E term

of equation 8.

I V4
While the first three terms in equation 8 are independent of one another, the

D and E terms are not since molecules which have a lower average velocity will

spend a smaller fraction of time in the gas phase and therefore not experience

as much gaseous diffusion as molecules with higher than average velocity. The

total variance of two dependent contributors to the variance is given as:

a

2

ij °i +

°j + 26

ij oi°j ( 12 )

The F term of equation 11 originates from the final term in the above equation

and corresponds to the interaction between the D and E terms.

Giddings (11) has given an expression similar to equation 8 which accounts

for all known plate height terms contributing at least 1% of the total plate

height for packed GC columns in the absence of interfacial adsorption as:

H -E 1/A. + vqu i C^u + Du + H tc ( 13 )

The term represents the contribution of column-wide velocity inequality

effects, such as that arising from column coiling, and could alternatively

be included in E. If the A term is small, a situation often encountered at

normal operating velocities, it can be neglected and the gaseous diffusion

D and E terms combined. A compilation of the C, D, and E coefficients expected to apply in various situations and a means of calculating their magnitude

from measurable column parameters is given in reference 10.

The plate height equations discussed to this point apply only to the peak

spreading in a localized area of the chromatographic column. A final modification

should be made to equations 8 and 13 to account for the variation in local carrier

velocity along the column caused by the drop in pressure from column inlet to

outlet. The effect of this correction is primarily on the liquid mass transfer

term, as discussed by Dal Nogare and Juvet (12). The final expression for the

I V5
experimentally accessible column average plate height H dependence on the carrier

gas outlet velocity uQ

is similar to equation 8 and is given as

H = A + ir

0

2p

o

c + D + E + F (14)

Pi + P0

where p^ and pQ are the column inlet and outlet pressure. The gas phase diffusivity found in equations 4, 9, 10, and 11 must be stated at the outlet

pressure of the column. The form of this modification is based on the relationship between the local column velocity and the average carrier gas velocity.

The preceeding treatment assumes a distance average of this velocity. Other

methods (7) involve the use of a pressure average velocity and yield a slightly

different equation for H but agree reasonably well with equation 14 even at

large values of the inlet pressure.

The previous description of the theory of peak broadening in packed gas

chromatographic columns is complicated by the ill-defined nature of packing

regularity, stationary phase geometry, and gas flow paths in the column. Such

variables necessitate the introduction of empirical geometry or flow coefficients

into the equations describing peak spreading. This limitation is overcome when

the geometrically simple open tubular column is employed. Golay (13) has obtained

an exact solution for the case of peak broadening arising from a capillary

column with a uniform liquid phase coating on the inner wall of the tube and

a parabolic carrier gas flow velocity distribution. In this instance H is given

by the equation:

H

=

2 D

g 1 + 6k + Ilk

2 r uo u7“

+ —77 7772“ + 75“

2k d

2

u J D,

(15)

o 24 (1 + k) 3(1 + k)

U

Z

where r is the inner radius of the capillary tube and d the liquid phase thickness. Although the apparent simplicity of this equation when compared to equation

13 would indicate that capillary columns are the medium of choice for the chromatographic study of diffusion phenomena, these systems suffer from the same diffiI V6
culty encountered for packed columns, the poor definition of the stationary phase

film thickness, which will be discussed in the following section.

EXPERIMENTS AND CALCULATIONS

IGC determinations of diffusivity in the polymer phase are made from a

study of probe peak broadening at varying carrier gas velocities; a schematic

illustration of typical results is shown in Figure 1. The slope at high flow

rates is often identified with the quantity C in the van Deemter equation

(equation 2) and the diffusion coefficient can be calculated from C according

to equation 7. Such a calculation assumes that liquid phase mass transfer is

the primary mechanism of peak spreading in this region of high carrier gas flow

velocity. If the other kinetic processes discussed in the previous section are

operative then the limiting slope at high flow rate of Figure 1 should also reflect these contributions as indicated by equations 8 and 14. The contribution

of each of these terms is calculated for the system octadecane-1 inear polyethylene

(SRM 1475) studied in this laboratory as described below. The polymer was coated

onto 180-150 qm diameter (80-100 mesh) glass beads from a hot xylene solution by

slowly evaporating the solvent. The coated beads were then packed into 6.35 mm

j| outer diameter stainless steel mass fraction of polymer were employed. These are

designated as column A and B respectively in the remainder of the report. About

0.1 y a of liquid, either neat octadecane (C-jg) or a 0.5% by mass heptane solution

of C-|g, was injected and the output of a flame ionization detector recorded on a

strip chart recorder operating with a high chart speed. At least three symmetrical

peak were collected for a determination of the mean width at half maximum at each

carrier gas flow rate. A symmetrical peak is defined as that having a front to

rear tangent slope ratio of 1 + 0.2. The helium carrier gas flow rate was measured

with a soap film flow meter. Inlet pressure was monitored with a calibrated pressure

gauge of appropriate range while the outlet pressure was atmospheric in all cases.

Concurrent injections of methane gas, assumed to have k = 0, were employed to

IV-7
determine of equation 6. An electronic integrator was used to time the

peak maxima to within 0.01 min. All experiments were conducted at a column

temperature of 150 + 0.3°C. The column capacity factor is 17.84 for A and

118.8 for B under these conditions. A plot of H vs u was constructed for eight

flow velocities in the high flow rate region and linear least squares fit yielded

_3

a slope for column A of 7.05 x 10 s with calculated standard deviation of 8.8%

_2

and 1.89 x 10 s with calculated standard deviation of 7.4% for B.

Gas Phase Contributions

Before the gas phase contributions to the experimentally determined slopes

can be estimated, a value for the diffusivity of C-jg in helium at 150°C is required. Two methods were used to estimate this diffusion coefficient, one attributed to Arnold (14) and a treatment of Fuller, Schettler, and Giddings (15).

The following parameters were used in the calculation according to Arnold:

= 7.21 cm^/mol , Vg = 407 cm^/mol , = 78, Cg = 866. The FSG treatment

employed v^ = 2.88 and Vg = 372.2. At 150°C and a column outlet pressure of 1

2

atm the two treatments give values of 0.317 and 0.268 cm /s respectively for

2

the diffusion coefficient. An intermediate value of 0.292 cm /s is used in all

subsequent calculations.

Mass transfer in the gas phase can be estimated from equation 9 if values

of Cg and d^ are available. The distance over which lateral gaseous diffusion

must take place depends both on the average separation between two liquid phase

areas and the degree of coverage of the support surface. A probe vapor molecule

diffusing to a support surface not covered by the polymer phase will continue

to diffuse in the gas phase until the polymer is encountered, thus lengthening

the diffusion path. The distance d

g is assumed to be on the order of the average

particle diameter. A value of 0.115 is assumed for the constant Cg based on the

theoretical limiting result discussed earlier. For average size particle of lfi.S^m,

D for column A is calculated as follows:

IV- 8
D = 0.115 (17.84)' (1.65 x 10~ 2 cm)

2

(0.292cm

2

/s) (1 + 17. 84)

2

= 9.61 x 1 0~ 5

s -4

A value of 1.05 x 10 s is obtained for column B. The choice of the average

particle diameter for the distance d

o was checked by calculating D for the systems

studied by Kieselbach (6) and comparing the calculated values to his experimental

results. The agreement to within a factor of 2 in the five cases studied lends

support to the choice of d

g for the mean path length.

The E term employed to account for interaction of different flow chanels of

unequal velocity has been studied by Giddings (16). When parameters typical of

a packed nonporous support are assumed the following approximate equation is

obtained for C^:

r 0.63 k + 0.43 (16) U

E k + 1

Substituting this equation and data for column A into equation 10 allows the E

term to be calculated as shown:

E = (0.63(17.84) + 0. 43) (1 . 65 x 10~ 2 cm)

2

(17.84 + 1) (0.292 cm

2 /s)

= 5.77 x 10'4

s -4

The corresponding value for column B is 5.86 x 10 s.

The correlation between the D and E terms can be estimated from equation 11

if the correlation coefficient 0 is known. Independent variables have a 0 of

zero while strict correspondence between two variables gives a value of unity.

The value of this coefficient is not certain but estimates for capillary columns

(8) suggest that 0.8 is a reasonable choice. Substituting into the equation for

column A gives:

2(0.8) ^0 .115 x 0.619j

1/2 (17.84) (1.65 x 10" 2 cm)'

p = —- in ' (0.292 citt/s) (1 +17.84)

= 3.77 x 10' 4

s

I V9
-4

The corresponding result for column B is 3.98 x 10 s.

The last gas phase contribution to peak spreading that will be considered

arises from column coiling, a component of the term of equation 13. The

contribution of this term can be estimated from an equation given for columns of

circular tube cross section (10) as:

H

tc

7 4 x2 7r

o 12R

o D

g

(17)

where r

Q

is the tube radius, R

Q

the coil radius, and t the tortuosity, which should

have a value of 0.63 for packed, impenetrable spheres (17). The columns employed in

this study have an inner radius of 0.229 cm and a coil radius of 5.72 cm leading

to an H. term of 6.62 x 10

tc

-5

s.

The gas phase contributions to peak spreading are summarized in the following

table and compared to the limiting slope C calculated from the van Deemter equation

least squares fit.

Table 2 Gas Phase Contributions to Peak Spreading

Col umn

A

B

D(ms)

0.096

0.105

H tc

0.577

0.586

0.377

0.398

0.066

0.066

Z gas phase

1.12

1.16

7.05

18.9

2 gas phase

C

0.16

0.06

It is evident that the peak spreading attributed to gas phase diffusion can make

a significant contribution to the overall kinetic broadening and plate height.

Equations that neglect these contributions should be applied only when they are

assuredly negligible. Gas phase diffusion contributions can be minimized by employing low molecular weight carrier gases at high temperatures to increase the

diffusivity D .

The capacity factor also contributes to the magnitude of the C, D, and F

terms. As the magnitude of k increases, the k /(I + k) term of D (equation 9)

o approaches unity while the k/(l + k) term of C approaches zero as illustrated in

Table 3.

IV-10
Table 3 Magnitude of Various k-dependent Terms

k k

2

k 1 + 6k + Ilk

2

k (1 + k)

2

(1 + k)

2 1 + k 24(1 + k)

2

1 .25 .25 .5 .118

10 .083 .83 .909 .399

100 .0098 .98 .990 .452

1000 .0010 .998 .999 .458

A large capacity factor may cause the gas phase mass transfer terms to greatly

exceed the stationary phase term; an example is provided in a study by Kieselbach

(6). His findings indicate that the C term is dominant for early sample peaks

(K2) but becomes insignificant for late peaks (K30) primarily due to the influence of the k/ ( 1 + k) factor as indicated in Table 3. The gas diffusion terms

are thought to be large when k is not near unity and the stationary phase loadings

are less than a mass fraction of 0.1. A determination of the probe-stationary phase

diffusion coefficient is favored when the probe has a k value near unity since

the C term should be prominent. Increasing the stationary phase loading in order to

maximize the C term by thickening the coating can be partially offset by the expected increase in retention time and corresponding decrease in k/(l + k) .

Polymer Phase Contribution

The stationary phase contribution to peak broadening is customarily related

by the van Deemter C term, found from a plot of H vs. u at large u, to the diffusivity

as indicated in equation 7. Such a procedure can only succeed if the other contributions to peak spreading discussed previously are small when compared to that

arising from liquid or stationary phase mass transfer. This has been assumed to

be the case in many previous studies of probe-polymer diffusion. A further consideration is the nature of the carrier velocity on which the plate height depends. Equation 14 indicates that while the plate height contribution of the

B, D, E, and F terms are directly or inversely proportional to the carrier

IV-11
outlet velocity uQ

, the C term contribution to H depends on the average velocity,

in this case a distance average. Consequently, the often-employed plot of H vs.

carrier velocity suggested by equation 2 will not be linear at high flow velocity

for any variant of velocity if both liquid and gas phase mass transfer effects are

nonnegl igble. Purnell (9) has suggested a method for resolving the liquid and

gas phase mass transfer contributions which involves first determining A and B

of equation 14 and employing these values to reduce the experimental IT to the peak

spreading arising only from mass transfer effects, In terms of an equation:

Wuo -I H - A -

2 Pp

P . + P C + D + E + F (18)

When the left-hand side of this equation is plotted against the pressure correction

( 2p

Q /(Pi + pQ

) a straight line with slope C and intercept (D + E + F) should be

obtained. Evaluation of the constants A and B requires that experiments be conducted over a wide range of carrier gas flow velocities. Limited low velocity data

precludes experimental determination of these constants in many cases; however,

they can be estimated from theoretical considerations. The multipath A term defined

in equation 3 has been found to have a A value between one half and unity in many

studies (18) and a value of 0.5 is assumed for these calculations. The longitudinal

diffusion B term most often has a y value near one (18) and unity is assumed here.

These values were used to calculate the A and B terms of equation 18 and a fit of

HMj/u

q

against the pressure correction term gives a linear least squares line with

_2

a slope of 1.64 x 10 s and calculated standard deviation of 5.5% for column A

_2

and 2.19 x 10 s with calculated standard deviation of 6.6% for B. The smaller

standard deviations of these slopes compared to the corresponding values for the

van Deemter fit discussed earlier indicate the better applicability of the Purnell

method. The C value obtained by this method for Column A is more than twice that

obtained from the simple van Deemter analysis. This is attributed to the latter's

combination of the effects of polymer and gas phase mass transfer in a nonlinear manner

I V- 1

2
which can be noted by comparing the C term obtained from equation 2 to its complement

in equation 14, the expression in parenthesis. For the case of column A where the

gas phase terms contribute significantly to the peak broadening, the van Deemter

equation based analysis underestimates the magnitude of C. Gas phase mass transfer effects for column B contribute only 6% to the total broadening, as indicated

in Table 2, and this is reflected in the similar results of the two methods for determining C which differ by only 15%.

While the method of determining the polymer phase mass transfer contribution

can be important under certain column conditions, the most significant parameter

affecting a diffusivity determination is the distance over which diffusion occurs.

This distance is identified with the effective film thickness d^ of equation 7.

It is often assumed that the stationary phase is distributed as a uniform thin

film over the surface of the spherical glass bead column packing. The effective

film thickness for this geometry can be calculated from the expression:

M

d

f

= (19)

where is the mass of polymer phase in the column, r the average support particle

radius, N the number of support particles in the column, and p the polymer density.

-6 -5

The results are 3.46 x 10 cm for A and 3.24 x 10 cm for column B. Such a

configuration requires a high amount of stationary phase surface area, however, and

a geometry in which the liquid phase is confined by capillary forces into annular

regions around the contact points between support particle spheres has been advocated

as a means of minimizing the exposed stationary phase area. This geometry has

been observed for both low molecular weight (11) and polymeric (19) stationary

phases coated onto glass bead supports. A factor of three decrease in the surface

to volume ratio of polystyrene coatings in IGC columns on prolonged treatment at

180°C led Klein and Waltnitzki (20) to suggest that surface tension can be effective

in minimizing the surface area of the supported polymer at elevated temperatures.

IV -13
Giddings (21) has compared the contribution to peak spreading expected from a

hypothetical support coated with two regions, a thin film of uniformly adsorbed

stationary phase and a second region where the liquid phase collects at the support

contact points, and concludes that for glass bead supports at mass fraction loadings

up to about 0.015 the bulk of the liquid phase is present at the bead contact points

and controls the plate height performance by virtue of its greater thickness. An

equation has been proposed (22) to relate C to measurable column parameters for this

geometry and is as follows:

C

= 12 (1 + k)

/ m

2 ps 2 l 18.7 5p

1/2

( 20 )

where p

s is the density of the support particles and m

2

the mass fraction of polymer

phase in the column. This treatment assumes that the spherical support particles

pack randomly and are surrounded by 6.25 nearest neighbors. The relation for C is

similar to equation 7 differing only by the explicit expression for d^, given in

terms of the particle diameter as:

/ m

2p

s \ 1/4

°f ' \18.75p ) 4/T

( 21 )

The average film thickness calculated for a polymer stationary phase collected at

-4 -4

bead contact points is 5.28 x 10 cm for column A and 9.24 x 10 cm for column B.

Both equations 7 and 20 have been used to calculate the diffusion coefficient

of octadecane in HDPE. For column A assuming a thin uniform film, can be calculated by substituting equation 19 into equation 7:

2 17.84 / 6.10 x 10~ 4

g

3

(1 + 1 7 . 84

)

2 (1.64 x 10' 2

s) \

4tt( 8. 25 x 10~ 3

cm)

2 x 2.11 x 105 x 0.978 g/cm

3

= 2.4 x 10" 11 cm

2

/s

Assuming a geometry where the polymer collects at the bead contact points for column

A, is calculated according to equation 20 as follows:

I V- 1

4
D = (1.65 x 10~ 2 cm)

2 (17.84) / 6.10 x 10~ 4

g x 2.019 q/cm3 \

1/2

£

12 (1.64 x 1 0~ 2 s) (1 + 17.84)^ l 18.75 x 0.978 g/cm

3

)

= 5.7 x 10”^cm2

/s

The corresponding values for column B are 2.6 x 1Q~ 10

and 2.1 x 10~ 7 cm

2 /s respectively. It is evident that the uniform thin film geometry assumption leads

to unreasonably low values of the diffusion coefficient. In addition, an order

of magnitude discrepancy exists between results for the two columns. The

assumption of a collection of polymer stationary phase at bead contact points

yields diffusion coefficients of reasonable magnitude and column-to-column agreement

within a factor of three. Limited data are available in the literature on diffusion

of the higher alkanes in HOPE; however, studies of similar diffusants, linear

aliphatic esters with 25 to 45 backbone units, have been conducted by Klein

and Briscoe (23). Extrapolating their experimental results to an 18 unit chain

- 6 2 leads to an expected diffusion coefficient of 5 x 10 cm /s in linear polyethylene at 152°C. While the two results cannot be compared directly due

to the different chemical nature of the diffusion species and the chain length

extrapolation required, their agreement within an order of magnitude is encouraging.

An IGC study of diffusion of benzene and carbon tetrachloride in polyethylene containing columns has shown that the diffusion coefficient increases

by a factor of four to nine as the stationary phase film thickness is increased

to four times the original value (24). These authors propose that the short

contact time between probe vapor and polymer results in only a portion of the

film, termed the effective layer, taking part in probe exchange between the polymer

and vapor phase. The thickness of the effective layer is thought to increase

more slowly than the overall increase in film thickness. The existence of

an effective layer could further complicate the film geometry question since

the geometrical ly determined thickness would not correspond to the distance

over which diffusion takes place. The diffusion coefficient determined in

I V- 1

5
this study decreased by a factor of three as the thickness of the film

collected at the support contact points approximately doubled. This trend is

contrary to the benzene and carbon tetrachloride results previously discussed.

The effective layer concept does not apply to these polyethylene-octadecane

studies since the contact time between polymer and probe is sufficiently long

that diffusion of at least two thirds of the probe molecules through the entire

film thickness is possiole for each "theoretical plate" of column length.

The distribution of film thickness also plays an important role in determining the magitude of the diffusivity. The previous calculations assume

that the film thickness is constant. In an actual column, however, the film

thickness would be expected to be distributed about the mean values employed here.

An alternate form of equation 7 can be used to estimate the effects of different

film thicknesses. The equation is:

C

= D, (1 k)

,

2 £ Vid

i

( 22 )

where umn q^ is a configuration factor and x^ the volume fraction per unit col

volume of stationary phase segments with thickness d^ (25). Assuming a uniform

configuation factor and holding x^ constant gives:

C

= kqx

(1 + k)

i£ * £d

i

2

(23)

which reduces to:

C =Zd2

(24)

for a uniform film of thickness d. For a distribution with an equal volume of

film O.ld and lOd in thickness:

c

1 + 25 (

10d

)

2

= 5.05 d

2

This distribution, resulting from the same volume of stationary phase present

in the uniform thickness case, leads to a liquid mass transfer coefficient five

I V- 1

6
times larger and a diffusivity value five times smaller than those corresponding

to a uniformly distributed film. Table 4 summarizes the effects of different

thickness distributions on the diffusion coefficient compared to that expected

from a uniform film of thickness d, D^. All the geometries considered require

the same volume of stationary phase per unit column volume and have an average

thickness of d.

Table 4 Effect of Thickness Distribution on Diffusivity in the Polymer Phase

Thin Section

Depth

Thick Section

Depth C'/C d ;/°

d/2 2d 1.25 0.80

d/4 4d 2.13 0.47

d/10 lOd 5.05 0.20

d/50 50d 25.01 0.04

d/100 lOOd 50.01 0.02

It is evident from these examples that thick sections of the polymer film

can exert a disproportionate influence and lead to a considerable reduction

in the polymer-probe diffusion coefficient when compared to the value calculated for an IGC experiment that assumes an ideal polymer layer with uniform thickness.

Concentration Effects

The diffusivity is often quite sensitive to the concentration of the

diffusing species, depending approximately either linearly or exponentially on

concentration (26). In the IGC determination of the diffusion coefficient discussed previously, the probe concentration in the polymer film varies both along

the column length due to increasing peak broadening with transit time and

with trie depth of penetration into the polymer film expected from Fickean diffusion.

The diffusivity determined is therefore a concentration-averaged value over all

column conditions. The actual concentration of octadecane in the polymer film

I V- 1

7
has been estimated to range from 0.01 to 1.5 weight percent for column A and

from 0.001 to 0.16 for column B. The diffusion coefficients calculated for

column B correspond to concentrations about an order of magnitude lower than for

column A.

Capillary columns

The plate height equation for capillary columns (equation 15) is superior

to that for packed columns by virtue of its analytic expression for the gas phase

mass transfer terms. Experiments with low capacity factor probes favor operation

in a region where liquid mass transfer effects are prominent, as indicated by

Table 3, a situation similar to that for packed columns. Equation 15 was derived for a uniform thin coating of stationary phase on the inner tube wall.

In actual practice the stationary phase coating will never be uniform and the

film geometry is envisioned as similar to the case of a porous diatomite support

where most of the stationary phase is contained in surface pores of varying

dimensions (11). The geometry of the polymer film on the capillary wall is

thought to be even more irregular than that of a film collected at the contact

points of a spherical glass bead support. An ill-defined diffusion distance,

a consequence of the uncertain film geometry, leads to similar difficulties in

calculating the polymer-probe diffusivity from the liquid mass transfer term

as discussed above for packed columns.

Adsorption effects

This discussion has neglected any effect of interfacial adsorption on peak

spreading but such a mechanism may be operable at the polymer-support interface

and even override the liquid phase mass transfer induced broadening in some cases

if the sorption isotherm is nonlinear. Several expressions for adsorption-desorption kinetic contributions are available (11). The nonpolar nature of the

system examined in these studies and the symmetry of the resulting chromatographic

elution peaks suggest that adsorption contributions to peak spreading are minimal.

I V- 1

8
OTHER IGC STUDIES OF DIFFUSION IN POLYMERS

Several attempts have been made to compare experimental C terms to those

calculated from equation 20 for the low molecular weight stationary phase trio-tolyl phosphate on glass bead supports. Such a comparison can serve as an

indication of the maximum possible accuracy to which the stationary phase-probe

diffusion coefficient can be determined. The two quantities agree within about

30% for loadings between 0.1 and 0.25% by mass on 540 and 980 pm diameter beads

with the calculated value becoming too small by a factor of two as the loading

reached 1% by mass (22). A more detailed study (27) revealed that the calculated

and experimental C agreed to about 10% for 230 pm diameter beads whereas for

smaller beads (95 pm diameter) the two terms concur within a factor of 1.5. Column

loadings ranged between 0.09 and 1.05%. Agreement is poor when smaller support

diameters (40 pm) or liquid loadings greater than 1% are examined, the calculated

value being at least a factor of three smaller than the experimental. These

data suggest that a minimum uncertainty in D^ of about 10% is likely even under

the most favorably conditions.

A number of IGC studies have been concerned with diffusion in silicone

elastomers (28-31). Each of these involve determinations with the polydimethyl

siloxane SE-30; however, data on diffusion in the oligomers of this material

(28-31), polysiloxanes with aromatic sidegroups (30), and polyethylene glycol (29)

are also reported. All the SE-30 studies assume that the polymer is held solely

at the supporting bead contact points. Experimental problems with sample injection process and neglect of gas phase mass transfer effects complicate the

interpretation of results presented in the early studies (28-30). These problems

have been overcome in the work of Millen and Hawkes (31) who studied diffusion

of alkanes in SE-30 at temperatures from 50 to 200°C. Diffusion coefficients

in the range of 10 to 10 cm /s are reported for the alkanes undecane to

octadecane and Arrhenius activation energies of 25 to 60 kJ/mol can be calculated

from their data.

I V- 1

9
Diffusion of decane and tetradecane in LDPE has been examined in the 1GL

studies of Gray and Guillet (32). They base their calculations on a uniform

polymer film present on the surface of the glass bead support. They found

diffusivi ties for tetradecane ranging from 1 to 7 x 10” cm /s over the temperature

interval from 125 to 170°C while a decane diffusant gave values of 0.4 to 1.3

x TO"** cm

2

/s from 30 to 80°C. The LDPE- tetradecane results obtained above the

polymer melting point follow an Arrhenius type temperature dependence and an

activation energy of 67 kJ/mol can be calculated from their data. The authors

attribute a changing degree of polymer crystal 1 inity with temperature for the

failure of the LDPE-decane results to reflect an Arrhenius temperature dependence. If the polymer is assumed to reside primarily at the bead contact points

rather than being uniformly distributed on the support surface, equation 20 can

be used to calculate the diffusion coefficient from the tabulated C data of

reference 32. For the mean support particle diameter of 340 pm, the diffusivi ty

“6 2

in LDPE is calculated to be 5.1 to 44 x 10 cm /s for tetradecane and 2.1 to

"6 2

8.1 x 10 cm /s for decane over the same temperature ranges indicated previously.

The desorption and time lag experiments on decane diffusion in LDPE by McCall and

-9 2 Slichter (33) yield a diffusivity of 7.5 x 10 cm /s, in better agreement with

the result of Gray and Guillet based on a uniform film assumption.

Further studies on diffusion in LDPE above the melting point are reported

by Braun, Poos, and Guillet (34). Results are given for dodecane, tetralin, two

-7 2 isomers of decal in, BHA, and BHT and are on the order of 10 cm /s in all cases.

Activation energies are also given and range from 38 to 42 kJ/mol . A uniformly

distributed polymer film was again assumed. These diffusion data were criticized

by Millen and Hawkes (35) who maintained that equation 5 was employed incorrectly

for the calculation. They present revised results obtained by recalculating with

equation 7 and indicate that the initial work's neglect of gas phase mass transfer

effects could introduce an error of about 5% in the recalculated diffusivity values.

IV-20
Diffusion of toluene and decane in polystyrene has been studied by Gal in

and Rupprecht (36) for temperatures of 160 to 180°C. They determined diff-

-7 2 usivities by IGC of about 3x10 cm /s from the van Deemter equation, determining the film thickness from the surface to volume ratio by studying the

surface adsorption of decane below the polymer Tg.

Three amorphous polymers have been examined at temperatures above and below

their glass transition by Tait and Abushihada (37). They studied diffusion of

buytl ether, ethyl benzene, and propyl benzene in PVC, PS, and PMMA at 45 and

110°C. The polymer was assumed to be uniformly distributed on the Chrom-W and

glass bead supports employed. Diffusion coefficients on the order of 1 to

2x10" cm /s were determined in all cases. Very little change in the diffusivity

was noted for a given polymer-solvent pair when the measurement temperature shifted

from below to above the polymer glass transition, a finding contrary to the expected increase in diffusivity by several orders of magnitude when passing from

a glassy, solid polymer below Tg to a viscous liquid with greatly increased free

volume above Tg.

CONCLUSIONS AND FUTURE WORK

The previous discussion has shown that gas phase mass transfer effects can be

estimated and their interference with IGC studies of probe-polymer diffusion

minimized by the choice of appropriate column conditions. A more difficult problem

arises in accurately defining the mean polymer phase thickness and thickness distribution. These parameters have a strong influence on the magnitude of the diffusivity, yet there is considerable uncertainty associated with them as discussed

above. For these reasons the probe-polymer diffusion coefficient probably cannot

be determined any more accurately than within a factor of ten even under the most

favorable conditions.

While accurate absolute diffusivity measurements seem beyond the reach of

the IGC method, the possibility exists for using the technique to rank the relative

IV-21
ease of diffusion of many probes in a given polymer. A calibration of a specific

column can be accomplished by conducting experiments with a probe-polymer combination of known diffusivity to calculate the mean polymer layer thickness from

the measured peak broadening. The same column can then be used under similar

operating conditions to determine other probe diffusivities and a relative ranking

of many probe diffusion coefficients established. Such experiments are now in

progress.

The diffusivity determinations described in this report have been conducted

above the polymer glass transition temperature. Studies below the polymer Tg are

also being attempted. These experiments are complicated by a competition between

surface adsorption and bulk sorption as the primary probe retention mechanism. In

addition, the slow nature of diffusion in glass-like materials may prohibit the

entire polymer layer from taking part in probe sorption and only an "effective

layer" may participate, again complicating the film thickness issue.

IV-22
References

1. W. E. Hammers and C. L. DeLigny, J. Polym. Sci., Phys., 12_, 2065 (1974).

2. Y.-K. Leung and B. E. Eichinger, J. Phys. Chem. , 78, 60 (1974).

3. J. J. van Deemter, F. J. Zuiderweg and A. Klinkenberg, Chem. Eng. Sci.,

5, 271 (1956).

4. J. Bohemen and J. H. Purnell, "International Gas Chromatography Symposium

at Amsterdam, 1958", D. H. Desty, ed., Butterworths , London, 1958, p. 6.

5. J. C. Giddings, Nature, 188 , 847 (1960).

6. R. Kieselbach, Anal. Chem., 33^ 23 (1961).

7. J. C. Giddings, S. L. Seager, L. R. Stucki, and G. H. Stewart, Anal.

Chem., 32, 867 (1960).

8. W. L. Jones, Anal. Chem., 33, 829 (1961).

9. H. Purnell, "Gas Chromatography" , Wiley, New York, 1962, Ch. 8.

10. J. C. Giddings, "Dynamics of Chromatography", Marcel Dekker, New York,

1965, Ch. 2.

11. J. C. Giddings, Anal. Chem., 35, 439 (1963).

12. S. Dal Nogare and R. S. Juvet, "Gas-Liquid Chromatography", Interscience,

New York, 1962, Ch. 5.

13. M. J. E. Golay, "International Gas Chromatography Symposium at Amsterdam,

1958", D. H. Desty, ed., Butterworths, London, 1958, p. 36.

14. J. H. Arnold, Ind. Eng. Chem., 2^2, 1091 (1930).

15. E. N. Fuller and J. C. Giddings, J. of Gas Chromatogr., 3, 222 (1965).

16. J. C. Giddings, Anal. Chem., 34, 1186 (1962).

17. J. C. Giddings, "Dynamics of Chromatography", Marcel Dekker, New York,

1965, p. 246.

18. H. Purnell, "Gas Chromatography", Wiley, New York, 1962, Ch. 9.

19. G. J. Courval and D. G. Gray, Can. J. Chem., 54, 3496 (1976).

20 . J. Klein and G. Waltnitzki, Polym. Bull. Berlin, 1_ 9 451 (1979).
21. J. C. Giddings, Anal. Chem., 34, 458 (1962).

22. J. C. Giddings, K. L. Mallik and M. Eikelberger, Anal. Chem., 34, 1026

(1962).

23. J. Klein and B. J. Briscoe, Proc. R, Soc. Lond. A., 365 , 53 (1979).

24. Ye. N. Rosolovsaya and Ya. Sal'vinski, Polym. Sci. USSR, 1J3, 1638 (1976).

25. J. C. Giddings, "Dynamics of Chromatography", Marcel Dekker, New York,

1965, p. 141.

26. J. Crank and G. S. Park, "Diffusion in Polymers", Academic Press, London,

1968, p. 17.

27. S. J. Hawkes, C. P. Russell, and J. C. Giddings, Anal. Chem., 37^, 1523

(1965).

28. S. J. Hawkes, and D. J. Carpenter, Anal. Chem., 3£, 393 (1967).

29. L. Butler and S. Hawkes, J. Chromatogr. Sci., TJO , 518 (1972).

30. J. M. Kong and S. J. Hawkes, J. Chromatogr. Sci., ~\A_, 279 (1976).

31. W. Mi lien and S. Hawkes, J. Chromatogr. Sci., 1_5, 148 (1977).

32. D. G. Gray and J. E. Guillet, Macromolecules, 6, 223 (1973).

33. D. W. McCall and W. P. Slichter, J. Amer. Chem. Soc., 80, 1861 (1958).

34. J.-M. Braun, S. Poos, and J. E. Guillet, J. Polym. Sci., Letters,

14, 257 (1976).

W. Millen and S. J. Hawkes, J. Polym. Sci., Letters, ]_5, 463 (1977).

36. M. Gal in and M. C. Rupprecht, Polymer, 19^, 506 (1978).

P. J. T. Tait and A. M. Abushihada, J. Chromatogr. Sci., 17, 219 (1979).

SECTION V

Fluorescence Measurements of Antioxidant Migration from Plastics

I. Introduction

Since the fluorescence technique is selective and sensitive and does

not require inordinately expensive equipments, it is suitable for the study

of the migration from plastics of antioxidants that are often strongly

fluorescent. We have developed a procedure to measure by fluorescence

technique such migration and have applied the procedure to determine the

migration of N,N'-diphenyl-p-phenylenediamine from low-density polyethylene

films immersed in n-heptane. We describe here the procedure we have developed

and the preliminary results of its application.

II. Experimental

Antioxidant - N,N' -diphenyl-p-phenylenediamine, hereafter referred to as

DPPD, was purified by recrystallization from toluene according to the following

procedures. A mixture consisting of 20.0 grams of DPPD and 950 cc of toluene

was slowly heated with stirring in a nitrogen-filled glove-bag until the

temperature of the mixture reached 43°C, whereupon DPPD solids seemed completely dissolved. The solution thus obtained was filtered by gravity with

a Whatman number-42 filter paper in the glove-bag. After 5 hours during

which the filtrate thus obtained cooled down slowly to 22°C, some DPPD

crystals formed. The filtrate with the crystals was placed overnight in a

refrigerator at 0.5°C. The crystals were collected on a Buchner funnel,

washed with tolune chilled to 0.5°C, and dried in a dessicator at 22°C and

_? ca 10 mm Hg.

V-l
Polyethylene - National Bureau of Standards Standard Reference Material (NBSSRM) 1476, a branched polyethylene whole polymer containing 50 ppm of the

antioxidant Santonox (Monsanto) which is 4,4' -thio-bis-(6-t-Butyl-3-cresol

)

and soluble in toluene, was purified as follows. To a 2-liter, one-neck,

round-bottom flask equipped with a magnetic stirrer were added 100 grams of

NBS-SRM 1476 and 2 liters of toluene. A slow stream of purified nitrogen was

bubbled in the mixture for about 30 minutes and then was admitted to the flask

through a ground joint loosely stoppering the flask. The contents of the

flask were stirred and slowly heated with an oil bath until the bath temperature

reached 110°C, whereupon NBS-SRM 1476 seemed completely dissolved. At this

point, the heating was stopped and the solution was allowed to cool down with

stirring. When the bath temperature was 66°C, the solution turned turbid.

After the slurry thus obtained cooled down to 22°C, polyethylene solids were

collected on a Buchner funnel, washed with 2 liters of toluene, and dried in a _2 dessicator at 22°C and ca 10 mm Hg.

Solvent - Commercial "Distilled in Glass" n-Heptane was used for fluorescence

measurements and for extraction without further purification.

Blending of DPPD and Polyethylene - To a 500-ml , one-neck, round-bottom flask

equipped with a magnetic stirrer were added 300 ml of Toluene "Distilled in

Glass", and 30.0 grams of polyethylene. The flask was loosely capped with a

ground joint through which a slow stream of purified nitrogen flowed. Then,

the contents of the flask were stirred and slowly heated with an oil bath

until the bath temperature reached 105°C, whereupon polyethylene completely

dissolved and the heating was stopped, while the stirring was maintained.

When the bath temperature was 100°C, 0.030 gram of DPPD in 10 ml of toluene

was added to the polyethylene solution. The solution which turned turbid at

66°C was allowed to cool down to 51 °C, whereupon the flask was stoppered with

a teflon-lined stopper and stored overnight in a refrigerator at 0.5°C. The

V-2
slurry thus obtained was stripped of solvent at reduced pressure with the use

of a rotary evaporator, the heating being provided by a water bath at 20°C.

The DPPD-polyethylene powder thus obtained was then dried in a dessicator at

22°C and ca 10~^mm Hg.

Fusion of DPPD-Polyethylene Powder - DPPD-polyethylene powder was fused to

form a void-free mass with the use of a two-part tubular device shown in

Figure 1. The lower end of the tube was lined with a portion cut from a 22mm x

80mm soxhlet extraction thimble made from TFE (Teflon/Halon) . A quantity of

DPPD-polyethylene powder was pulverized in a glass mortar and 13.1 grams of it

was placed in the TFE-lined portion of the tube with the use of a long-stem

powder funnel, care being taken not to let the powder touch other part of the

tube. The powder was then pressed into a compact mass with the use of a flatended glass rod. The two parts of the device were then joined by sealing and

then the device was connected to a vacuum line equipped with a diffusion pump.

The device was kept at 22°C and ca 10 ^ mm Hg for about 16 hours and then

immersed in an oil bath at 95°C. The temperature of the oil bath was raised

to 178°C in two hours, whereupon the valve between the device and the vacuum

line was closed. Two days later, the temperature of the oil bath was reduced

from 178°C to 95°C in 90 minutes, whereupon the melt in the device became

frozen and the heating of the oil bath was terminated. When the temperature

of the oil bath dropped to 22°C, the aforementioned valve was opened to the

vacuum line and then the device was sealed at the constriction.

V3
20.5 cm

Figure 1

.
DPPD- Polyethylene Films - The void-free DPPD-polyethylene mass was shaped into a

cylinder with the use of a lathe. Immediately before an extraction experiment,

films were sectioned from the DPPD-polyethylene cylinder with the use of a

microtome whose knife, as well as the DPPD-polyethylene cylinder, was chilled to

1°C just before sectioning. The average thickness, diameter, and density of the

-2 3 seven films thus obtained were 2.67 x 10 cm, 1.60cm, and 0.91g/cm , respectively.

Thermal Analysis - The thermal property of DPPD was determined with the use of a £

differential scanning calorimeter (Perkin-Elmer, DSC-2).

Fluorimetry - With the exception of the spectra shown in Figure 3 which were

obtained with a Fluorolog Spectrofluorimeter (SPEX Industries, Inc.), all *

fluorescence measurements were obtained with an Amino-Bowman Spectrofluorimeter.

An Analytical working curve relating DPPD concentration to fluorescence intensity

was obtained with the use of a device which consisted of a fluorescence cell,

a bulb where the DPPD solution was kept during the degassing operations, and

a valve for connection to the vacuum line. All solutions were degassed by

three freeze-pump-thaw cycles. The excitation wavelength was 300 nm and the

fluorescence intensities at 380 nm for n-heptane solutions of DPPD were measured

to establish the analytical working curve.

The extraction of DPPD from polyethylene films was carried out with the

use of an extraction cell shown in Figure 2. It consisted of a fluorescence

cell, a solvent chamber, an extraction chamber, and a valve for connection to

a vacuum line.

At the beginning of an extraction experiment, a quantity of n-heptane arid

DPPD-polyethylene films were placed in a thoroughly cleaned extraction cell

according to the following procedure. A teflon-coated stirring magnet and

*Certain commerical materials and equipment are identified in this paper to

adequately specify the experimental procedure. This identification does not

imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best

available for the purpose.

V-4
TO

VALVE

Figure
seven DPPD-polyethylene films weighing 0.343 gram were placed in the extraction

chamber. After the extraction cell was evacuated with a vacuum line equipped

with a diffusion pump, 7.2 grams of n-heptane (previously degassed at other

part of the vacuum line) was distilled into the solvent chamber. Then the

valve was closed and the extraction cell was taken to a 22.0°C water bath

where its lower part including the two chambers and the fluorescence cell was

immersed in the bath water and allowed to equilibrate at 22.0°C. At the beginning of the extraction experiment, all the n-heptane was poured into the

extraction chamber, the lower part of the extraction cell was reimmersed in

the 22.0°C water bath, and the magnetic stirrer was turned on. At various

elapsed times, some n-heptane solution was poured into the fluorescence cell

and its fluorescence intensity at 380 nm was measured with an Aminco-Bowman

spectrofluorimeter whose cell holder was kept at 22.0°C. The solution was

then poured back to the extraction chamber for additional extraction.

V-5
III. Results and Discussion

N, N'-diphenyl-p-phenylenediamine ( DPPD )

(a) Thermal Property - From measurements with a differential scanning

calorimeter on DPPD samples in nitrogen atmosphere, we concluded

that DPPD may crystallize in two forms, one with the melting point

at 146.4 °C and the other with the melting point at 151.6 °C. The

DPPD we purified was mostly in the lower-melting form. However,

the relative amounts of the two forms may be altered by thermal

treatment. Povet'eva and coworkers 1 reported a melting point of

147 °C for a DPPD sample recrystallized from n-heptane while

Nespurek and Tlustakova 2 reported a melting point of 152 °C for a

DPPD sample recrystal 1 ized from ethanol.

(b) Fluorescence Property - Figure 3 shows the fluorescence spectra of

a DPPD solution in n-heptane, the solid curve and the dashed curve

being for the solution after and before degassing, respectively.

The concentration of DPPD was 14.3 ppm. Degassing not only increased

the overall fluorescence intensity but also made detectable fluorescence below 340 nm which was completely quenched by oxygen. We

do not know yet whether the latter fluorescence is an inherent

characteristic of the DPPD-n-heptane system or it is due to some

impurities

.

Analytical Working Curve - Figure 4 shows the relative fluorescence

intensity F of DPPD-n-heptane solution as a function of DPPD concentration C in ppm. These data for fourteen solutions have been

fitted to the equation

F = 131 C - 1.6 C

2

.

The standard deviations for the first and the second coefficients

are 3.7 and 0.4, respectively.

V-6
Figure 3.
1200

1000

eoo

600

400

200

0

2 4 6 8

DPPD CONCENTRATION, ppm

•5

t.

Figure 4.
Migration of DPPD From Polyethylene Films

A preliminary result of the extraction of DPPD-polyethylene films

with well-stirred n-heptane at 22.0 °C is shown in Figure 5. There, the

DPPD concentration of the solution in the extraction chamber is plotted

1 /

2

as a function of t , where t is the elapsed time in minutes. From the

initial slope of the plot, we have obtained D = 2.8 x 10" 9 cm

2 /sec as an

estimate of the diffusion coefficient of DPPD in these polyethylene films

at experimental conditions.

Concluding Remarks

The degradation of antioxidants during film-forming processes and

extraction experiments has been an obstacle to the measurements of antioxidant migration by the fluorescence technique. We have developed a

procedure that overcomes this obstacle and have applied it to measure

the migration of N, N'-di phenyl -p-phenylenedi amine from low-density

polyethylene films. Additional experiments are being pursued to confirm

the preliminary result described here, and to measure the migration of

other antioxidants from polyethylene films.

References

1. Z. P. Povet'eva, L. A. Chetkina, and V. V. Kopylov, Sov. Phys.

Crystal logr. , 21_, 168 (1976).

2. S. Nespurek and M. Tlustakova, Czech. J. Phys., B21 , 1225 (1971 ).

V7
Figure 5
SECTION VI

Experimental Measurement of Migration by Extraction

INTRODUCTION

Diffusion coefficients of low molecular weight migrants moving from

polymeric materials into surrounding liquid media under well stirred conditions

are measured in this laboratory for the following combinations of base polymer,

migrant, migrant concentration, solvent and temperature:

Polymer Linear Polyethylene (LPE), SRM 1475

Branched Polyethylene (BPE), SRM 1476

Polypropylene (PP)

Migrants n-Octadecane, n- C-j q

H 38

n-Dotriacontane, n-C

32

H 66

BHT or 3,5-di-t-butyl-4-hydroxytoluene

Migrant ConcentrationFrom less than 100 ppm to greater than 10%

Solvents Accelerating solvents: n-heptane, n-octadecane,

Fat and Oil Simulating Solvents: Corn Oil, Ethanol,

n-Octanol Tributyrin, Trioctanoin, HB307

Aqueous Solvents: Water, Ethanol -Water Mixtures

Temperatures 24, 30, 60°C

Except experimental works on polypropylene and extractions involving noctanol and HB307 as solvents, most experiments are now completed. Therefore,

in this report we present mostly empirical correlations from the large sets of

data being collected in the past two years.

EXPERIMENTAL

Materials

The characteristics of the base polymers and of the base radioactive

labeled migrants are listed in Table 1A and IB respectively.

IV-1
TABLE 1A

Characteristics of Polyolefin Samples

Linear Branched Isotactic

Polyethylene Polyethylene Polypropylene

NBS-SRM 1475 NBS-SRM 1476 Pro-fax 6301 *

M

n 18.310 (GPC)

Mw 53,070 (GPC) 290,000

Mw 52,000 (LS)

VMn

11

Cn] CN 0.890 0.8132

TCB - 1.010 0.9024

dl/g DHN 1.180 1.042 2.1

Melt Flow

Rate, g/10 min.

2.07 1.19

Isotacticity, % 95-96

GPC -- Gel Permeation Chromatography

LS -- Light Scattering

CN -- 1 -chloronaphthal ene

TCB -- 1 ,2,4- trichlorobenzene

DHN -- decahydronaphthalene. Decal in

t = 130°C for polyethyl enes

t = 135°C for polypropylene

Melt Index by Procedure A, ASTM Method D 1238-65T, Test Condition D, 190°C,

load 325 g for SRM 1475 and 2160 g for SRM 1476.

Density by ASTM Method D 1505-67; sample prepared by Procedure A, ASTM

Method D 1928-68.

Isotacticity is determined as fractional insoluble in Decal in at room temperature

after entire sample has been dissolved at 160°C and allowed to cool.

*Certain commercial materials and equipment are identified in this paper to

adequately specify the experimetnal procedure. This identification does not

imply recommendation or endorsement by the National Bureau of Standards, not

does it imply that the material or equipment identified is necessarily the best

available for the purpose.
TABLE IB

Characteristics of Radioactive Tracers

yC^/mg ng/25 dpm

H l

^ 18

m381 L 86.0

13.3

0.13

0.83

32

H 66" 16,17 " 14c 45.5 0.25

S^-di-tert-butyl-A--,*

hydroxytoluene- 7- x

(BHT)

57.9 0.19
Sample Plaque Preparation

The following procedure for the mixing of additives to the polymer stock

and the molding of the sample plaques was chosen. A large quantity of polyethylene powder stock was prepared from either NBS-SRM 1475 or 1476 pellets

first by dissolution in hot toluene or xylene. Most of the polyethylene

precitates out upon cooling. The precipitate, together with the residue

obtained by evaporationg the solvent, was dried in a vacuum oven to remove the

last trace of solvent.

To a quantity of the polyethylene powder stock, a specific amount of

labeled additive dissolved in a highly volatile solvent is mixed. The mixture

is then evaporated to dryness in a rotary evaporator, together with a number

of glass beads to act as a ball mill, under reduced pressures at relatively

low temperatures and further dried in a vacuum oven.

The mixture is then compression molded in a hydraulic press operated at

about 180°C for oligomers and 165°C for BHT. Plaques of 125 mm x 125 mm or

less are molded with brass or stainless steel shim stocks of appropriate

thickness sandwiched between two sheets of teflon or teflon coated plates.

The teflon surfaces are used for the easy removal of the sample plaques without

the aid or contamination of mold release agents.

The isotactic polypropylene was received in a granular form from the

supplier without any additives. Therefore, it was used directly to form a

slurry with the migrant in solution as mentioned above.

Experimental Methods

Two extraction methods were used, i.e., (1) continuous extraction into

limited solvent volume and (2) discrete extraction into simulated infinite

solvent volume.

VI-2
In method (1) an extraction vial of 25 ml in volume with a teflon valved

cap is used. The solvent in the vial will only meet glass walls and the teflon

surfaces during normal experimental processes. A silicon plug is situated above

the valve. A small area of the silicon rubber, less than 1 mm in diameter and

used as a septum for the hypodermic needle, may be exposed to the solvent vapor.

The polymer sample may sometimes be surrounded by a ni chrome or stainless steel

screen to prevent it from sticking to the walls or another sample has lower

density than the solvent.

The total amount extracted, M^, at time t is

t-1

H

t

C

st

W

st + si=l

c .w . si ai

where C , W and W a represent the concentration of the migrant, total weight of

o 5 a the solution (including that of the aliquot) and the weight of the aliquot,

respectively. At equilibrium the partition coefficient is estimated as

C

Cco C W

s°° s°° p Mn-M

= Mn-M

U 00 U 00

where Mq is the amount of migrant originally present in the polymer of weight

Wp, and is the total amount extracted at long times calculated from the

concentration, aliquot weights and solution weights as mentioned above. The

amount of migrant present in the aliquot is obtained via radioactivity indicated

by liquid scintillation technique.

In method (2), the polymer sample is immersed in about 10 ml of extracting

solvent in a typical 20 ml liquid scintillation counting vial. At specific

times the sample is removed from the solvent, rinsed and placed in another vial

with fresh solvent to repeat the extraction process. The total amount extracted

at time t is simply the sum of all extracts:

t

M. = E M.

z i=i1

VI-3
Method (1) is able to yield information about the equilibrium partition

coefficient at infinite extraction time. However, it suffers from rigid requirements of knowing accurately the ratio of aliquot versus total solution

and of keeping track of materials lost during the sampling process for material

balance purposes. As extraction time increases, there is only very small

change in the concentration of extracted material in the solution, whereas the

weighing or ratio error may persist. Therefore, the results at long time or

high degree of extraction will show considerable degree of scatter.

Method (2) is much simpler in operation, but simulates a condition of migration into infinite media, and is relatively free from aforementioned experimental

difficulties. However, it cannot be used to generate partitioning information

nor migration kinetics for migrant that is sparingly soluble in the solvent.

It should only be used for convenience when the migrant is highly soluble or

miscible with the solvent.

For all the methods mentioned the extraction vials are shaken inside a

temperature controlled aluminum block on a shaking table at a rate of about

200 reciprocations per minute.

When the extraction process is ended, radioactivity of the residual low

molecular weight species remaining in the polyethylene sample is monitored by

dissolving the sample in toluene at high temperatures. We found that the

single crystals or precipitates of polyethylene in the counting vial does not

interfere with the counting efficiency beyond the normal scattering of the

counting results.

VI -4
Experimental Run Designation

In order to utilize the rather limited graphical BASIC language resident in

the graphics terminal, we have changed designations for each of the experiments

into an all numerical representation as follows:

1) Least significant digit method of observation and

repetition number.

2) Tens and Hundreds digits temperature in °C.

3) Thousands and Ten Thousands digits solvent code.

4) Hundred Thousands and Millions digits sample code

'N

TT

SS

PP

Method or Repetition

Temperature in °C

Solvent Code

Polymer Code

This coding scheme is described in more detail in Table 1C and ID.

VI5
Polymer

Migrant

Migrant

Cone.,

%

Sp.

Act.

Thickness CM CT» o o of VO OO 00 cn o LO LO

VO , 00 LO

p— IT**. CVJ 00 CM iO VO UO VO VO VO to CM LO VO CM CNJI VO CM CM CM CM CM CM o o o o o o o o o CM o o o o o o o O o o O o O o o

o o o o o o o o o o o o o o o d d o o o o d o o o

s-a>

r— CM

vo to cn CO CMO

COCM CM VO o CM o 00 co LO CO cn CO CM CM 1— o o o o o d r- CO CO LO CO <3

* CO r— CM LO r~ M- LO

o

m

x x

«— X X

X XX X

X X XXXXXX XX

00 XXXXXX X X

CM

coo

X X X X X

f-XXXXXXXXXXXXXX 00o

Q.

Q.

Q.

00 X X X X XXX XXX

O. X X X X X X X X X X X X X

Co

tn +J 3 rO o c

•f- cn >

os _o </i s_ <o a> a. _j q

< co c_> o lu u. o i—« 'O X zo o_ cr a; co i

<=c

Ls_ U. CM CM =3 Z3CO

n. oOu

ino •— CM CO M- Lf> CO co <y» o r— cm co to co r-- oo o> oCM

CM

CM CM

LT) CMCO

CM

00

CM

cnCM

LPD
Table ID

XI

0

3 Solvent

10, Corn Oil

20, Ethanol

XI 0^ Temp.

24, 24°C

30, 30°C

60, 60°C

21, 10% Ethanol

23, 30% Ethanol

25, 50% Ethanol

27 70% Ethanol

29 90% Ethanol

30 n-Heptane

40 n-Octadecane

50 n-Octanol

60 Tributyrin

70 Trioctanoin

80 Water

XI 0° Method

0, Limited Solvent Volume

1, Unlimited Solvent Volume

N, Number of Repetitions
Estimation of Diffusion Coefficient

One of the widely used solutions for the diffusion equation 3C/3t=D

2 2

3 C/3x , solving for the case of diffusion between a plane sheet p of

thickness 2fi, and a stirred liquid s of finite volume V

g

, is presented by

J. Crank^

= 1 z n=l

2a ( 1 +a

)

. , 2 n 2

I +a+a q

n e-%2r

( 1 )

where a = /M„

s°° p° = V / KV . K = C /C and T = Dt/JT.S P

poo s°° The solution for the non-zero positive roots, q , of

lies between ott when a=0 and ( n-1 /2 )tt when a=°°. At a<<l

,

q

n ^ n/(l+a)

.

For other values of a,

q

n ^ [n - a/2 ( 1 +a ) ]tt

may be used as the starting value in a reiterative numerical computation.

Equation (1) converges rather slowly, thus enough terms must be used

to avoid premature termination of the computation. At small values of

T(<<1), approximately 3”^ og

]0

T terms are required to reach a reasonable

precision. Either of the two approaches described as follows may be used

to simplify the computational effort.

1) Crank, J., "The Mathematics of Diffusion", Oxford University, Press, 1975.

VI-6
Simplified Computation

At small values of a(«l), a master curve of M

it /(l+a)Moo

, which is equal to

? M . M/ for absorption or M ./aM for extraction, as a function of T/a may be

pt so st po

constructed from equation (1) as listed in Table 2Ae However, by limiting the

computations to 0. 1>T>0.Q01 , the number of terms required will be limited to

about 5 at T^O.l and about 45 at T^O.OOl. The values of M

t

/(l+a)Mco at smaller

2

a, but at corresponding T/a , are set to equal to the values calculated for

larger a. The results of this selective computation deviates about 0.001%

at T^O.l from the more rigorous and tedious computations, and much less than

0.001% at lower T.

Table 2A may be divided into three regions.

Region I, T<0.1. The system is far from equilibrium, M^/O+ajM^ is a

2 function of T/a only.

Region II, 5>T>0. 1 . The system is approaching equilibrium, detailed computation must be carried out for different a values (only 2 to 6 terms are required for equation (1) in this region). The results of the computation for

the regions approaching equilibrium are listed in Table 2B. For a<<l and

2 3 T/a >10 , M

t

/(l+a)Moo = 1 - a/vVT before reaching equilibrium.

Region III, T>5. For all practical purposes, equilibrium has been reached

with the deviation 6=1- M./M < 10" T

, where M = M /(1+a) in the case of

t oo — oo so absorption and M = M a/(l+a) in the case of extraction. For a<l, equilibrium

oo po

' ' may be reached much earlier (Table 2B).

Alternate Approximation

An alternative form of the solution^

2 M

t

/Moo = (1+a) {1 - e T/a erfc(T1/2 /a)> (2)

VI-7
Table

2A

4J

CO o u

•M | O

ns0 I

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pH rH

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ON 00 I 8

I*'. \o in list© cm 1 t

Region

1.

T<0.1

Master

Curve

Region

2.

5>T>0.1

Approaching

Equilibrium

[bracketed

area]

Region

3.

T>5

Equilibrium
Table

26

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1

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• 00 oo 00 00 CO O' O' O' O' O' O' O' O' O' o O' O' O' O' O' O' O' O' O' O' O' O' O' O'

CM CM o vO O' o o o o o o o o o

iH CM O' O' O' o o o o o o o o o

o OO 00 00 00 oo O' O' O' O' O' O' O' O' O' o O' O' O' O' O' O' O' O' O' O' CTi O' O' Cn

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i—#••••••••••••• ievjcn'^u“'\0r^aoo'00000 ooooooooOiHcsim^m
may be used in some cases and is relatively simple in computation.

rational approximations^ for the error function yields the followi

5

M,/(l+a)M =1- E ax^+e

t 00 n

One of the

ng

(3)

where t=1/(1+0. 327591 1 T 1/2 /a), a

] =0. 254829592, a2 =-0. 28449636, a

3

=l .42141 3741

,

a 4=-l .453152027, a

g

=l .061405429, and |e|<1.5 x 10" 7.

At a«l, results computed from equation (2) or (3) deviates less than

0.00001 from that of equation (1) at T/a

2 <5 or at M^/ ( 1 +a ) M00< 0.75. Maximum

deviation of 0.0035 occurs at T/a 2fv5QQ or at M^/O+a ^1^0.97. Therefore,

equation (2) or (3) may be used to generate the master curve for equation (1)

at T<0. 1 (Region I). However equation (2) or (3) does not yield any information

about the region approaching equilibrium at larger values of a, and hence

should be used with discretion.

Computation for Infinite Bath

When a-*», MjVM^ approaches a limit, and equation (1) can be reduced to a function of T only,

where q

n

=

in Table 2.

( n - 1 / 2 )

tt .

For T<0.1

M./M, = 1-2 z L e" q

n T

n=l orM

n

Values of M^/M^ in the range 5>T>0 .

1

1 /2

, M./M is a linear function of T

* t “

H

t

/Mm= 2 (T/ti) 1/2 = 1.128379

are also listed

t

1/2

( 4 )

(5)

Deviations of equation (5) from equation (4) is less than 10

^

at T<0.05,

about 10~ 6at T = 0.1, about 5 x IQ"

4

at T = 0.2 and becomes much greater than

0.0 at T = 0.3 or higher.

VI-8
By combining the use of Equation (2) or (3) at T<0.1 (Region I) and the

use of Equation (1) at T>0.1 (Region II and III), computational requirements

for the solutions of the diffusion equation between a plane sheet and a well

stirred liquid may be reduced to a minimum.

The results of computations are shown graphically in Figure 1A, where

2 T/a is used as the abscissa and in Figure IB, where the more familiar reduced

2

time T = Dt/& is used as the abscissa, for various values of a as noted along

the curves.

By regressive means, diffusion coefficient at any point may be estimated

from the above computation method.
Pig.

1A I
Fig.

IB

W °+l w

Od

Ts

W

W

X)
Results of Extraction Experiments

The results of extraction experiments are summarized in Table 3A through 31

for the extraction of n-octadecane by triglycerides, by ethanol, by ethanol /water

mixtures, by n-heptane and by n-octadecane, of n-dotriacotane and of BHT by

triglycerides, by ethanol, ocatanol and water and by n-heptane, respecti vely.

The tables provide information on the test pieces on to their weight, thickness

L, exposed area A, specific activity in yCi/g of polymer, amount extracted at the

end of experiment M^/M

o

, the amount of solvent absorption and the maximum of

diffusion coefficient observed.

Special problems are encountered in the preparation of sample plagues with

BHT as additive. A much longer time is required to mix BHT with polymeric powder

in a rotating flask with glass beads acting as a ball mill. Apparently, BHT is

relatively insoluble in the polymer even in the molten state therefore, sample

plagues made from insufficiently mixed batch of powder mixtures yield autoradiographs

of distinctive sharp regions of streaks and patches. Each molding at 185°C seems

to "fix" some 15-20% of BHT, i.e. only 80% of the BHT may be extracted exhaustively

even by n-heptane. When plagues being remolded at 185°C for 5 times, only 20% of

original amount of BHT would be extractable. The remainders of the BHT are combined with the polymer. The residual radioactivities remain with the powderous

precipitate, even after the plagues were dissolved in toluene at high temperatures.

However, molding at 165°C of well mixed batches of BHT and polymeric powder seem to

offer rather uniformly distributed sample plagues with less than 5% of BHT being

combined with the polymer. The M^/M of n-heptane extractions of BHT samples, as

listed in Table 3G through 31, qive indication of the extractable fraction of BHT

in those samples.

In order to provide quick cross references the diffusion coefficients from

Table 3 are arranged according to migrant, then polymers, temperature and solvents

in Table 4 A to 4D.

VI-10
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3G

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of

BHT

by

Triglycerides

*

x v. c*cm £ £

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a-a.OLa_a-a_a.a_ o —I —J —1 —I 1 ifl ai rn m
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of

BHT

by

Ethanol,

Octanol

and

Water

fo AJ

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of

BHT

by

Heptane

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c*CM

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Table

4A

Diffusion

Coefficients

of

nC

-j

8

H

38

in

Linear

Polyethylene

(D/ym

CXI CO

CO 0 1

00 0 C\J 0 O O LO 0 r—

r-^ l— • • • • 0 O 0 0

0 0 CO CO

rsi LO LO CO 0 0 • • • • • • • 0 CXJ 0 CO 0 CO

i CO

(XI

• • co cr> LO

a_ r— CO t— 0 CO CXJ CO LO 8 00

rn 0 • r— * • • • ® • • CO r~ e» CXJ CXJ 0 0 00 0 0 00

CXI

CO UJ

CXI CO

r^.

ioI

X

co

oo

i o

X

I"- co

LO LxJ CXI ._n oVOo

o’

LOo

o’ oo

COo

o*

r-.

CXI UJ «=t- o’

2: CXI CTl LlI CO

CXJ 00 o

r-» o 2: in

CXJ QJ O

co O O r— 00

I— <_> O <sj- o o

>st o o CXJ CO CO

a>CL

03 OO

8

”

O* O*

<sjcxi

sj- O

*st Oo

o

*=1-00

CXI CO CO

«st

(XI oCO oCO oCO 00

coco

CXJ CO •Sfo o CO CO

LO

o O CO CO

CO
Table

4B

Diffusion

Coefficients

of

nC-jgH^g

in

Branched

Polyethylene

(D/ym

cn O O r— O I— • O -=3-

O CQ O CM

VO h- • O CM

O O •3- o

co

IT) CT»

• o oo

•> CM CO CM CM

CTt O Q. • • ro I M- O oo

LO

z: CO

LO LlJ o 00 CO

CM LO r—

. o o • • • o o o

VO O ^ 00 o o CM LlJ • • co ro

*3- o o

rs

c!> CM r- (_> • • • • o CO O CM

4-> C

a>>

o

oo

oo

-t-> o o CO VO o o o o o CO VO CO VO VO

a>CLE

ro oo

CT* 00 CO
Table

4C

2

Diffusion

Coefficients

of

from

Polyolefins

(D/um S

O <D 00 4-> rO

a O»—X

f^.

o

c VO

03 i CVJ JC o r—

4-> r— o LO UJ X

CM o • • Oin

CO o

cor;(Q

LO

CVJ oCOo CO O 4-> o <3- o CVI O • • • • •r— o o o o iI

c

•r* i- O 4-> VO =3 -Q

CVJ O

COO

o CO c CO o *3 • LO 4~> o

oo

r— in CO o r—

>

CVJ c o o CO O 03 o in cr» crt CO

CVJ sz o o o CVJ CVJ CVI

+-> • • • • • • UJ o o o o o o

r— CVJ

• r— r— CO o o o o CO o CO o LO

«— c o o o cvj o t- • • • • • o o o o o o c_>

CDc

03

4-> O COat

LOo

COo CO <D • • • • • • • I

c

1 c o o ' CVI lO

r—

<D r—

Q.E a> LO Ot CT* LO VO at

03 r— iCVI r— r— r— CVI UO

S-o> UJ UJ Q- UJ UJ UJ QQ_ Q- Q- Q_ Q_ a. Q- o —

1

CO CQ CQ

a.

<D

s-3

4-> r0

S~CDCLs

CD I—

OCO oLO
Table

4D

2

Diffusion

Coefficients

of

BHT

From

Polyolefins

(D/um S

0)c

a3

4-> C£X CO CM o CM r— CM o CL • co a> r— CM CM CM Kt in vo co — CM r- VO in VO

r— r— r— CO co CM CM CM co

ic

00

t- o 00 vo VO o a) o vo in CO

oo +-> o o o o o 03 o o o o o 3: . . . • • o o o o o

o

c

03 O u

o

cf" O

O

O LO

CM VO O O

O C>

cod

i s->> O -M CO =3 JD

<D>O

CO o

c O 03 in 4-> oo

COo

d

<x> o

d

cod

to

00d

r—o

c O 03

co1^o

o\

o

VOCM

00n

voCM VO

VO 00VO VO in

CM -C o o o o O o o CO 1— o>

+-> LU o o o o O o o o o r— O

•r* CM <r~ o r— r— CXI o o o r— CM

r— c o o o O l- • • • o o o o d o

s

d

o> in

in o o in o o o

co

00

0>o. o cvj cocotor^o «— cvj co co to E CM CM CVJ Cvj CVJ CVJ CM CVJ CVJ CVJ CM CM CM CM

03 oo

s.0) J,o

Q.

LU

CL LU CL LUCL Q. CL CO —I

LU

CL

OO

CL

CL

Oo

<yu

u

L>

03

J-a>CLE

CD

oco oCO

0.032

0.096

0.070
Typical Examples of Extraction Experiments

Typical extraction results may be separated into three categories,

namely, ideal Fickian behavior, effect, of highly swelling solvents and

intermediate cases.

In order to demonstrate the ideal Fickian behavior, in special cases,

we may employ the same chemical species as the solvent as well as the

migrant, except that the migrant is radioactively labeled, n-octadecane

was chosen for these experiments. The polymer was saturated with the

migrant/solvent before the extraction experiment. Therefore, change of

diffusion coefficient due to swelling or absorption of solvent will not

be observed. Under these conditions, the extraction experiments follow

an ideal Fickian behavior as shown in Figure 2A, B and C for branched

polyethylene saturated with radioactively labeled n-octadecane being

extracted by n-octadecane at 30°C (840302). The curves are calculated

1/2 as afore mentioned. Both the linear time (Figure 2A) and linear t

'

(Figure 2B) representations are commonly used in the literature. The

1 /2 linear t

' representation will show a linear region below 0.6 fractional

extraction for partition coefficients favoring the solvent. The log-log

1 /2 representation can also show this linear t region as a straight line

of slope 0.5 as well as behavior at regions below 0.1 fractional migration.

In a highly swelling solvent, the diffusion coefficient of the

migrant will increase drastically as the polymer matrix expands. A

typical example is shown as Figure 3A and B for the extraction of ndotriacotane from polypropyl ene by n-heptane at 60°C (2930601). The

diffusion coefficient changes at minimum by a factor of more than 10.

The maximum diffusion coefficient observed in this case at high degree

of extraction is only the lower bound of the diffusion

VI-11
Figure

2A.

Diffusion

of

n-Octadecane

in

BPE

at

30°C

Time /

Hour
Figure

2B.

Diffusion

of

n-Octadecane

in

BPE

at

30°C

00

CD

CM

O

CM

°ifii /

lm

(Time

/

Hours)
Figure

2C.

Diffusion

of

n-Octadecane

in

BPE

at

30°C

OO©

Time /

Hour
Figure

3A.

Migration

of

nDotriacotane

from

PP

into

n-Heptane

at

60°C

O . °m i l m

OOa OOoe

Time /

Hour
Figure

3B.

Migration

of

n-Dotriacontane

from

PP

into

n-Heotane

at

60°C

°1AI /

l

IAI

(Time

/

Hour)
coefficient under equilibrium swelling, as most of the migrant have already been

extracted by the time the sample reaches equilibrium swelling.

For most cases of extraction experiments the results would fall in between of

these two examples shown above. A moderate swelling or absorption of solvent may

occur before the majority of migrant being leached out. Therefore the typical

behavior will show up as a shift between two diffusion coefficients, one for the

“dry" polymer and the other for the "equilibrium swollen" polymer. A typical

example is shown in Figure 4A and B for the extraction of n-octadecane from polypropylene by ethanol at 30°C (2820300). In general either the lower or the higher

diffusion coefficient regions are expanded or reduced depending on the rate of

solvent equilibration. One should also note that if the migration curve is shown in

1 /2 Figure 4B, commonly as linear Mt/Mo versus linear t , one may draw the conclusion

that the behavior is rather ideally Fickian. However, the log-log plot in Figure

3A indicates detail behavior below 10% of extraction. The log-log plot does suffer

from resolution at high degree of extraction, i.e. above 70% of extraction. However,

for regulatory purposes, the detailed behavior in this region is less important.

As with such high degree of extraction, one may simply use M as the extractables

without producing serious errors.

Correlation of Diffusion Coefficients

In the following we present empirical correlations of diffusion coefficients

as a function of temperature, solvent, migrant, migrant concentration, or polymer,

while keeping all other parameters constant.

o Due to the wide span of the diffusion coefficients (10 ), log-log plots are

used. The solid diagonal line in the correlation plot denotes a 1:1 correspondence

between the subject diffusion coefficient and the reference diffusion coefficient.

VI-H2
Figure

4A.

Migration

of

n-Octadecane

from

PP

into

Ethanol

at

30°C

Time /

Hour
Figure

4B.

Migration

of

n-Octadecane

from

PP

into

Ethanol

at

30°C

O

if)

COo

CO

CMo

CM

LO

in

CM

00a O 0 a OCMd

(InoH /

Quin)
Effect of Temperature

Temperature will have pronounced effect on solvent extractibil ities not

only through the changes in solubilities, partition coefficients, swelling

powers but also through the possible change of states of the polymer, migrant

as well as the solvents. However in the limited temperature ranges that is

of interest to food packaging, for instances from -10 to 100°C, the change in

the diffusion coefficient is generally less than a factor of 1000.

For the limited temperature range baring any change of states, the

effect of temperature may be best described by the activation energy defined

by E in the following expression:

D

2

/D

1 = exp R

k J

2

where and D-j are the diffusion coefficients at temperatures and T-j (in

K), respectively.

Estimation of activation energies are tabulated in Table 5A through F

and presented graphically in Figure 5A through F for n-octadecane in triglycerides,

in ethanol and ethanol/water mixtures, in n-heptane, in n-octadecane, for ndotriocotane and BHT in various solvents, respectively. A straight-line is

used to link the two data points at 30 and 60°C. A majority of the results

listed in Table 3 and 4 are presented in these tables and figures.

The groupings of the diffusion coefficient in each of the figures are

due to polymers or solvents. In general, the behavior of PP is rather similar

to that of BPE, although the magnitudes of the diffusion coefficients in PP

are closer to that in LPE. The behaviors in ethanol, pure triglycerides and

corn oil are very similar to each other in magnitudes of activation energies

as well as diffusion coefficients. In Figure 5G, diffusion coefficients of

BHT in both corn oil and water as measured by NBS for Authur D. Little (ADL)

samples as well as data from ADL are plotted together. The agreements in

corn oil are excellent. The measurements in water are probably within a factor of 3 from mean values.

VI-13
Table

5A.

Diffusion

Coefficient

and

Activation

Energy

of

n-Octadecane

in

Triglycerides

o

K

s. UJ —

JC

MW ei cm CM CM CM

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ui z tn*r moat®

v <0=3$

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«aaf «e=^9 to fO •M-CVS

CM CM ®© CftCTi©

<8^ cd3> QaS) '^=3 w C5>© © © CD ®<®> ® N. I S § s S § 3 rocy us Ui US UJ USUIUJ

Ci e ^CM

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•s — > t£9 £®> CD® CD ®©

a— —»|X, ^ »=< L®

c ©

© CO

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r-op*> SVpwjy,

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.

LULU Ldl Lai LlS lii LsJ O D-O. G= £L- 0.£JuO_

o_ _i_J _J_J 00 OO 0Q
Figure

5A.

Diffusion

coefficients

of

n-Octadecane

in

Triglycerides

s/^uio

1

/J,

t/K
Table

5B.

Diffusion

Coefficient

and

Activation

Energy

of

n-Octadecane

in

Ethanol

and

50%

Ethanol

o

£

CM SO <0& «.£> fw

C'J CM CM CM CMS n

u

o -« C<0 c* cy. yj £ 0^8 «-* CP

v *“« <55*^1 n»

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®

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u • • © • ©

(DOG® «»S <3J»S CM

w ®> ®®® <D ® X Sill 8 yjLyyj&y &y

Cl £

u • •no «s fO

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CM CM CM CM CM

£ 0

e?i»

<vj cm r«- cr« m

>

z. o yjyjyjyj yj m HI

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c QDC&OO 00 m

CS <®=® <a?=-a **§»*4 JL oo oo o

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a

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©“€ 'Hot6 '*'—9 •«—

«

»— yjLULiJtji LU

o Q-Ha.£L a.

CL. 00
Figure

5B.

Diffusion

coefficients

of

n-Octadecane

in

Ethanol

and

50%

Ethanol 1

/T,

1/K
roro

O£ c• r

«E?

Cij c

tj> 2£

<0u j Oi "O

O

(O tjJ £ +-> u0 “i 1 c

4—0

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cd ^r«jow

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05 fw*. fw © ®® © ® ffi © i 1 S 8 LU LULU LU

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fw cr, « ® m © ro© ©© ®

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Bf-S -B-# -©—a

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_j _J_J OQ
Figure

5C.

Diffusion

coefficients

of

n-Octadecane

in

n-Heptane
Table

5D.

Diffusion

Coefficient

and

Activation

Ener

<uc

fOo

a> ofS

+-> 0o1 co

>5

cr,

<uc

»o0

<u •o

(O +Juo1 c o£% fO so©

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LU •—

tj

2L

cj r«i OJ

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Ci £ §oto ro tOfv OJ <M U

s*>ro OJ gp* *-« <ga^ ourvi 0SCT8 m 00 ® <r« ©00 ©Q © ®®

w ©®

© ®®

©

©

©

© \ S i i § 9 i i f rocu LULU LU LULU 4U LULU

c. c r*-is- r=fl »o<js fO OS® u • ® ro ^r4 SO rooi - > ©Q © ©© © ©©

!!»” -"S* ft ft ft ^r ft ft £ O & tjy m

foro mm a\ mm > oo o o oo o

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d -*-* <o-a vH *r~« yf

i_ OO o OO o oo .v- .V .V •V .V «v « v ,\‘

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w ©©'V"< » *

08

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u_ _j _J_J

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Figure

5D.

Diffusion

coefficients

of

n-Octadecane

in

n-Octadecane

T

9/£\tlO '<3
Table

5E.

Diffusion

Coefficient

and

Activation

Energy

of

n-Dotriacontane

o

z

lf> m p-©^ us — CM ro u

o ro VC 05® MJ

US E © iocx>-*r NOda

v *»« =3^=0 ^*=0 -SP®*® CM «•>< -X

<55 r*. ffl <?» © © w<w=# •***=« ©©©

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u « 9 © 0

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© © WOiW CM CM CM

<^*a© «a=3 <^=0 v*$ S=s w © © ®cs>® <S®6> © N. 1 t 8 1 1 i 8 8 TO CM Ui LU UJUilxi UKuui

Ck & or. fw cMintn *rro —

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run «w=»^ V* <e»e <**€ <««fi CO

>

a. a. 0X0 0X0

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p

c CM CVS CVS CVI CVS CM CMOS

ro ro rororo rororo

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51 • 'T .V -vr .sr -v -v .\r

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LlJ Ll! LULU LlJ iii »ii »ii o A £>,_ Q.£L£L a. a_ a_

CL -J 0Q idoilq
Figure

5E.

Diffusion

coeficients

of

nDotriscontsne 1

/T,

1/K
Table

5F.

Diffusion

Coefficient

and

Activation

Energy

of

BHT

o

z

UJ

&

VJ x

CM 0-1 CM Aj All CM CM Al

lu e ‘•^'sr'^r'^-'sraoioar/^j <y« <r« cm po

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iL ©mmmca CO moa oa 03 m mmmmmm mmm mOQ mm

fR .NT .Nr .NT B\“ .V -V .Nf .Nf .Nf »N? «>r .N? X- „N- .v .Nr .Nr .NT .NT .Nr -Nr .V JO Jv*

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o a. a. o_ o_ Q_ a. a. a, cl. a_ a_ a. «x a. o_ a_ o_ a_ cu a. cl. a. ma.

a_ j_j_i jjffiosmm _u.x._j.u^mmmmmmmm _j oq
Migration

of*

BHT

s/^uio 'q

1

/T,

t/K
I UJ

CD

in

O)

sZ3o>

© © Q © © © ©

S/^WO 'Q

t/T
The diffusion coefficients at 30°C are less than that of at 60°C as

expected as shown in Figure 6. There is a general trend that the effect of

change of temperature is greater at lower diffusion coefficient. By grouping

into migrants, empirical correlation may yield a scatter of less than a

factor of 5. n-Octadecane and BHT may be grouped together without effecting

the correlation significantly. Better correlation for n-dotriacontane may be

obtained by separating into LPE and BPE.

The average activation energies for various combinations of polymer,

migrant and solvent are listed in Table 6A, B and C. No estimated range is

given for activation energies obtained from a single pair of estimation. The

activation energies or ratios of ( D60^ D 30 ^ ^or n_dotri acontane and ^HT are

plotted in Figure 7. The activation energies for n-octadecane show similar

trend but with a higher scatter of the data points. It is somewhat surprised

to find the four combinations having linear correlations of identical slope.

These correlations indicate that although the changes in activation energies

due to changes in the reference diffusion coefficients are the same, the

activation energies are higher in the case of BPE than that of LPE, and

higher in the case of n-dotriacontane than that in n-octadecane. These

correlations are not to be extrapolated toward high diffusion coefficients,

as such extrapolations may soon lead to a situation that

VI-14 \
Figure

6.

Diffusion

Coefficients

asa

Function

of

Temperature
Table 6A

Activation Enerqies of Migration of n-Octadecane at Different Concentrations

(E, kJ mol" 1 )

LPE BPE

0.01% 1% 5% 1% 10%

n-Heptane 88 55 72

n-Octadecane 8 5 56 30+10 8 5 53±5

Ethanol

,

Triglycerides

99+8 114+5

151+4 100+1 93+15

50% Ethanol 111

Table 6B

Activation Energies of Migration of n-Dotriacontane

(E, kJ mol" 1 )

• ."T^^from

i nto

LPE BPE

n-Heptane 103 146

Ethanol, Triglycerides 155+12 188+11

Table 6C

Activation Energies of Migration of BHT

(E, kJ mol" 1 )

. .'''''^Jrom into

LPE BPE

n-Heptane 45+3 56+4

Ethanol, Triglycerides 103+4 94+3

Water 124 39
Figure

7.

Activation

Energies

of

Migration

of

n-Dotriacontane

and

BHT

!

ioui n

(/> CM

E

o

o

CO

o

CM

o o

o

o

OoOSg/OoOSg

0o09
Effect of Solvent

Solvent is the single most important parameter effecting both the amount

extractable and the diffusion coefficient of the migrant through solubilities

and its swelling action upon the polymer.

By comparing diffusion coefficients in other solvents to one of solvent,

e.q. ethanol, while keeping all other parameters constant, it is possible to

O reduce the large range of 10 in the diffusion coefficient for individual

solvent to a factor of 5 or less from the correlation.

For partitioning or lower solubility solvents, the correlations may

depend not only on the solvent but also on the migrant or polymer. However

for solvents having moderate solubilities toward the migrants, the correlation

seems to be independent of migrant, polymer or temperature.

The most significant correlations are that for pure triglycerides and

ethanol as food oil simulants and that for accelerating solvent, n-heptane.

As shown in Figure 8A, the diffusion coefficients of migrants (n-octadecane,

n-dotriacontane or BHT) moving from polyolefins (LPE, BPE or PP) into either

tributyrin or trioctanoin at either 30 or 60°C are almost the same as the

corresponding diffusion coefficient into corn oil. The diffusion coefficients

in the pure triglycerides are slightly higher than that in corn oil with a

ratio of D(pure triglycerides)/D(corn oil) less than 1.5 over most of the

range studied. Ethanol seems to behave almost identically to the lower

members of pure triglyceride in its extractions behavior as shown in Figure

8B. However the correlation for the data of ethanol extractions versus that

of corn oil scatters more than that for triglycerides, at a factor of about 3

or less.

From the above observations, either ethanol or low members of pure

triglycerides may be used successfully as food oil simulants, regardless of

their dissimilarities in solvation power for the migrants, swelling power for

the polymers and viscosities.

VI-15
Figure

8A,

Comparison

of

Diffusion

Coefficients

in

Pure

Triglycerides

and

in

Corn

oil

DCcorn

oi

O,

err>2/«
Figure

8B.

Comparison

of

Diffusion

Coefficients

in

Ethanol

and

in

Corn,

oil

DCcorn

oil

em2/i
The accelerating action of n-heptane over that of food oil was long recognized.

However no quantitative figures have been attached to this accelerating action.

The accelerating power of n-heptane is clearly demonstrated in Figure 9, where

diffusion coefficients in n-heptane and in triglycerides (including corn oil)

are plotted against that of ethanol for identical test samples and conditions.

The accelerating power is greater at low diffusion coefficients than that at

-7 2-1

high diffusion coefficients. While at D(ethanol) around 10 cm s the accelerating power is about 10, the power may be increased to about 1000 at

D(ethanol) around 10”^ or 10~^ 2cm

2

s”^.

The accelerating action of n-heptane versus that of ethanol (and that of

triglycerides), coupled with the differences in solubilities of oligomers of

polyolefins, has dramatic effects on the total extractables of polyolefins. We,

therefore, subjected large quantities (50 g) of the raw polymer stocks of SRM

1475 (LPE) and SRM 1476 (BPE) to be extracted by both 500 ml of ethanol and nheptane at 70°C for 160 days with occasional shaking. By assigning a minimum

-9 2 diffusion coefficient of about 10 cm /sec for n

" C 32

H 66

and a pellet size of

2

0.1 cm radius, the effective time T = Dt/£ = 1.4. Thus according to the generalized solution for the diffusion equation, the extraction should be at least 95%

completed. The results of the 160-day extractions are listed in Table 7. For

each polymer, about 6 to 8 times as much in polymer fraction was extracted by nheptane than that by ethanol.

The extracts were than subjected to gel permeation or size exclusion

chromatographic analysis by Roger C. Snyder of FDA to find out their molecular

weight distributions, as summarized in Table 8 and shown in Figure 10A for

linear polyethylene SRM 1475 extracts and in Figure 10B for branched polyethylene SRM 1476 extracts. The molecular weight scales were calibrated by

means of analyzing five NBS polyethylene standard reference materials, three

VI-16
Figure

9.

Effect

of

Accelerating

Solvent

DCEfcOH:>,

cm2/«
Table 7

Extraction of 50 g of Polyethylene

by 500 ml of solvent at 70®C for 160 days

Fraction Extracted

IPE BPE

Solvent SRf-1 1475 SRM 1476

Ethanol

%

0.0008 0.0023

n-Heptane 0.0047 0.018

/
'

Table 8

Molecular Weight Distributions of Ethanol and

n-Heptane Extractions of Polyethylene

-Vw

Solvent

Ethanol

n-Heptane

M

r IPE

SRM 1475

250 : 310

560 : 1020

M.w

BPE

SRM 1476

310: 410

620 : 3000
n-alkane from Cg to C^. The molecular weight scale for branched polyethylene

is only approximately correct, however it should be sufficient for comparison

purposes.

The extracts from the linear polyethylene show rather normal symmetrical

distributions with peaks of molecular weight centering at about 300 for

ethanol and at about 800 for n-heptane extracts. This type of result is

expected from the practice of molecular weight fractionation by solvents of

different solubility power. At the low molecular side, e.q. n “C]

3

H

3 g> there

is large enough solubility or even total miscibility of the oligomer fraction

in both solvents, such that almost all of the low molecular weight fraction

will be dissolved by the extraction processes, cf. label A in Figure 10A and

10B. As molecular weight gets higher, e.g. the solubility in the

solvent, especially ethanol, decreases which causes a partitioning of the

particular component between the polymer and the extracting solvent to occur,

cf. label B in Figure 10A and 10B. The partitioning of n_C

32

H66^ as ^een

confirmed by extractions with ethanol. The diffusion coefficient for larger

molecules also drop significantly. Thus the combination of the effects of

solubility, partitioning and diffusion created the shape of the molecular

weight distribution curve beyond the peak molecular weight extracted.

A similar compariosn for branched polyethylene is seen in Figure 10B.

The skewed curves are most likely due to the incorrectness of the size versus

molecular weight calibration until one could identify the individual branched

low molecular weight hydrocarbon species. The peak of apparent molecular

weight extracted is about 350 for ethanol and about 3200 for n-heptane extracts.

Therefore, n-heptane can not only accelerate the diffusion process but

also remove high molecular species of oligomers that may be hardly detectable

in ethanol or triglyceride extracts.

VI-17
Figure

10A.

Molecular

Weight

Distributions

of

Ethanol

and

n-Heptane

Extracts

of

LPE

jeuiA|Od 3|0i|/\/v %

*v

Molecular

Weight
n-Heptane

Ethanol

Oo

CM

D *-

* O

o o

O)

'5

<e

jaiuAjOd a|Oi|M %

Fiqure

10B.

Molecular

Weight

Distributions

of

Ethanol

and

n-Heptane

Extracts

of

BPE

n-Hepta.no

extract,

-

-

-

Ethanol

extract
Effect of Different Polyolefins

In all c^ses studied , the maximum reduction L, u.anginy ui uase

polymer from BPE to LPE or PP is by a factor of around 30 as shown in

Figure 11. The mean effect throughout the entire range of diffusion

coefficients from 10~ 14 to 10~ 6 cm

2 s"

1 is a factor of 6 (dashed line),

or D

BPE ^ ® DLPE PP*

observation 1s beyond a factor of 5 from this

mean correlation.

Finer correlations are possible by specifying the temperature and

the migrant involved. However, the change is greater for higher temperatures. For oligomeric migrants, constant factors (DLpE pp/ D

Bpf: =

at 30 °C and 1/6 at 60 °C) may be assigned independent of solvents used.

For the migration of BHT, although the effect is greater at higher

temperatures, no constant factors may be assigned. A general trend of

great effect at lower diffusion coefficients prevails.

Therefore, the influences of different polyolefins on the diffusion

coefficient cannot be directly related to the crystallinities of the

polyolefins alone. The crystallinities of BPE, LPE, and PP are about

55, 75, and 90%, respectively. Since the diffusion coefficient, as a

first approximation, may be proportional to the amorphous content or the

mean free volume of the entire system, the effect of different polyolefins on migration is relatively small. Slight perturbations in the

temperature coefficient or activation energy, as well as in solubilities,

may produce just as large an effect as due to amorphous content alone.

VI-18
Figure

11.

Effect

of

Different

Polyolefins

t.- UIO dd‘3dlQ
Effect of Migrants

As expected, the diffusion coefficient of oligomers of higher

molecular weight species will be less than that of lower molecular

species, as shown in Figure 12, where diffusion coefficients of ndotriacontane is plotted versus tnat Of n-octadecane. There can be a

change in the diffusion coefficients by a factor of 500. Quantitative

assessment of the effect of changing in molecular weight of oligomers is

rather difficult because of other factors and perturbations. Nevertheless, the general trend of having greater effect at lower diffusion

coefficient prevails. The trend of the effect is greater at 30 °C than

at 60 °C. However, the effect is greater in BPE than in LPE and that

the trend of the effect seems greater for n-heptane extractions than

that for ethanol and triglyceride extractions.

As seen in Figure 13, the extraction behavior of BHT and n-octadecane are almost identical when n-heptane is used as the extracting

solvent. However, the diffusion coefficient of BHT is generally about 4

to 10 times lower than that of n-octadecane when ethanol or trigylcerides are used as extracting solvents.

VI-19
Diagonal

Line:

Dq-jq

Dc32 :a

lpe v

BPE

Figure

12.

Effect

of

Molecular

Weight

of

Oligomers
Diagonal

Line:

DQ-jg

I^Sgiuo /

iHaa

Figure

13.

Effect

of

Different

Migrants
Effect of Migrant Concentrations

For relatively insoluble migrants in polyolefin, such as BHT, no

significant difference in diffusion coefficient was observed as a

function of the migrant concentration.

Oligomers may be viewed as either a plasticizer or low molecular

weight swelling solvents for the polymer. Therefore, their contents are

expected to have marked influence on the migration behavior.

Figure 14 shows the influence of added n-C 18 H 38 concentration

toward the diffusion coefficients of n-Ci 8 H 38 from LPE into various

solvents at different temperatures. For changes of concentration

between 0.01% and 1% loading of n-C i8 H 38 , the diffusion coefficients

change by a factor of 1 to about 30. For change of concentration from

1% to 5 or 10% loading (saturated), the diffusion coefficient changes by

a factor of 5 to 20, with hydrocarbon as solvents.

Again, a general trend of greater influence at lower diffusion

coefficient prevails. The effect of oligomer concentration seems to

disappear at diffusion coefficient around 10~ 6 cm

2 s"

1

.

VI-20
Figure

14.

Effect

of

n-Octadecane

Concentration

CO

I</> CM

v .s

z

uio / °Q

I

cm
Summary of Conclusions

® Maximum amount of extractables depends on the original migrant

concentration in the polymer, the solubilities of the migrant

in solvent and in polymer or the partition coefficient.

o Migration behavior is mainly Fickian.

§ Diffusion coefficient may be increased by absorption of the

solvent or swelling of the polymer by the solvent.

• Activation energies for the change of diffusion coefficient as

a function of temperature generally lies between 40 to 200 kJ

mol” 1

. In general, the activation energy is lower at higher

diffusion coefficients.

« Lower members of pure triglycerides may be used to simulate

the extraction behavior of corn oil in oligomers and antioxidants, such as BHT, from polyolefins.

« Anhydrous ethanol may also be considered as food-oil simulant.

• Accelerating action of n-heptane over that of food-oils or oil

simulants is more pronounced at lower diffusion coefficients.

• n-Heptane will remove higher molecular weight fraction of

oligomers which may hardly be detected in food oil or oil

simulants.

« Diffusion coefficient increases with increased oligomer content.

« Increase of amorphous content in polyolefin produces a corresponding change in diffusion coefficient.

• The following is the ranking of importance of the parameters

effecting the diffusion coefficient of a migrant from polymer

matrix into surrounding media.

Solvent > Temperature (limited range) > Swelling

> Migrant Concentration > Amorphous content.

VI-21
NBS-I14A (REV. 2-60) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

' 2. Pcformfng Organ R "

** r> « • • r> . m

4. TITLE AND SUBTITLE

Models for the Migration of Low Molecular Weight Additives in Polyolefins - FDA Annual Report for the Period October 1, 1979 to September 30, 1980

5. AUTHOR(S)

L. E. Smith, S. S. Chang, F. L. McCracken, G. A. Senich, F. W. Wang

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. national bureau of standards FDA 224-77-2443

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

Annual, 10/1/79 - Q/3n/8n

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

Food and Drug Administration

Rockville, MD 20857

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here)

Food Packaging is an important encounter in the daily life. The low molecular

weight components in the packaging materials may migrate into the foods. This program,

sponsored by the Bureau of Foods of the Food and Drug Administration, tends to provide

theoretical models, reliable data base, and methodology to study the migration phenomena

and to provide reasonable worst-case estimates for the concentrations of the indirect

additives in food. In this annual report we present a relationship of diffusion co- efficients of gaseous diffusants in polyolefins based on free volume theory, procedures

and results of inverse gas chromatography for migrant-polymer interaction parameters

and dif fusivities of oligomers in polyethylene, methods and preliminary results

of spectrof luorimetry on the migration of antioxidants in polyethylene, results and

correlations of extraction experiments with radioactive labeled migrants. It was found

that anhydrous ethanol and lower numbers of pure triglycerides can successfully simulate

the extractive behavior of food oils. The accelerating action of n-heptane over that

of the food oil is quantified.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

antioxidants; diffusion', food packaging; spectrof luorimetry; inverse gas chromatography;

migration; oil simulants', oligomers; radioactive tracer', polyolefins

13. AVAILABILITY

[33~Wnl i mi ted

| | For Official Distribution. Do Not Release to NTIS

H Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

Q3) Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

15. Price

USCOMM-DC 6043-P80
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