Alliaa 1=lb713 PUBLICATIONS

NBSIR 79-1598

Models for the Migration of

Paraffinic Additives in

Polyethylene

L E. Smith, I. C. Sanchez, S. S. Chang,

and F. L McCrackin

Polymer Science and Standards Division

Center for Materials Science

National Bureau of Standards

Washington, D.C. 20234

Annual Report for the Period

October 1, 1977 - September 30, 1978

issued January 1979

Prepared for Bureau of Foods

Food and Drug AdminisTration

-

9C" Washington, D.C. 20201

: 100

^ . U56

79-1508

C.2

Oalionfil Btnai

MAY 22 1979

fV?' ^

NBSIR 79-1598

MODELS FOR THE MIGRATION OF

PARAFFINIC ADDITIVES IN

POLYETHYLENE

L. E- Smith, I. C. Sanchez, S. S. Chang,

and F L. McCrackin

Polymer Science and Standards Division

Center for Materials Science

National Bureau of Standards

Washington, D.C. 20234

Annual Report for the Period

October 1, 1977 - September 30, 1978

Issued January 1979

Prepared for Bureau of Foods

Food and Drug Administration

Washington, D.C. 20201

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

ABSTRACT

General physical mcxiels of the migration of low molecular weight species

in polymer matrices are needed to provide a basis for the efficient

reg’dlation of plastics used in food contact applications. This report

presents the first year's progress on a project containing both theoretical

and experimental elements aimed at producing such models. Using a modified

equation of state approach, models have been developed for estimating the

equilibrium partitioning of a diffusant in a polymer at a tem.peratijre above

its glass transition in contact with a finite volume of solvent. Some

possible new approaches to a diffusion theory based on volume fluctuations were

outlined. Model calculations using diffusion equations have been made for

the extraction of additives from polymers with concomitant solvent absorption

and for finding a constant extraction temperat'ure equivalent to migration

'under varying temperature conditions. 'The migration of an oligomer, ^'Relabeled ocradecane, from high density linear polyethylene lato various solvents

at different temperatures was measured in order to elucidate the effects

of thickness, temperature, concentration and solvent. Deviations from ideal

Fickean -kinetics la the experimental results may be attributed to the strong

influence of s’welling of the polymer on the migration rates and to the possible

incorporation of a small portion of the oligomer in the crystalline phase of

the polymer.

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TABLE OF CONTENTS

Page

I. INTRODUCTION 1

II. THEORETICAL MODELS OF ADDITIVE MIGRATION ......... 3

Equilibrium Partitioning ...... 4

Partitioning with negligible solvent

absorption 4

Partitioning with solvent absorption 5

Interaction parameters 7

Sample calculations 8

Diffusion Theory 12

Sel f-di ffusion 12

Diffusion of a small molecule in a polymer .... 15

Extraction of Additives with Solvent Absorption .... 16

Graphical results ...... 16

Summary 19

Equivalent Extraction Temperatures for Simulation of Additive Migration in Polymers

Subject to Varying Temperatures 24

III. EXPERIMENTAL MEASUREMENTS OF ADDITIVE MIGRATION 28

Materials 29

Polymers 29

Additives 29

Sample Preparation 31

Method 31

Uniformity estimates .... 33

i i
Page

Luminescence Spectroscopy Measurements 36

Solution concentration measurements ....... 36

Concentration profiles in solids 37

Radioactivity Counting 41

Liquid scintillation counting 41

Calibration of liquid scintillation counter ... 42

Extraction 47

Methods of extraction 47

Results of extraction 49

Discussion 55

IV. REFERENCES 87

Appendix A Determination of Interaction Parameters . . 88

Appendix B Determination of Liquid Densities 89

Appendix C Mathematical Analysis of Additive

Extraction with Solvent Absorption 91

Appendix D Derivation of an Equivalent Extraction

Temperature 94

i i i
I. INTRODUCTION

This report covers progress during the first year of an FDA-sponsored project

on additive migration in plastics. The objectives of this project is the

elucidation of the physical principles underlying the transport of small molecules

in polymers and the development of general material-related models for the

prediction of additive migration in food contact applications. Our semi-annual

report issued in July, 1978, gave a preliminary evaluation of existing physical models

and tabulated available migration data directly applicable to this problem.

The current program consists of two separate, but interacting, parts reflected

in the major division of this report into theoretical and experimental sections.

The theoretical work is aimed at developing and applying current models and

concepts to the prediction of the equilibrium and transport properties of polymermigrant systems. The emphasis has been placed on the most general descriptions

of the broadest possible classes of systems in order to elucidate the fundamental

physical principles underlying these properties. These theoretical models use

basic physical property measurements of the constituent polymers and additives

to predict the partitioning and diffusion observed in direct experiments. Other

theoretical work applies phenomenological models to the analysis of data from

particular experimencal configurations, e.g., solution of diffusion equations using

boundary conditions applicable to a given geometry.

The second major part of this project uses a series of carefully designed and

executed experiments to guide theoretical developments by providing reliable

data on well controlled systems. In addition, the experimental program attempts to

explore significant deviations from idealized behavior and explore the

physical basis for these exceptions. In spite of the recognized importance of

migration phenomena, the number of well-studied systems with significant amounts

of available data is surprisingly small. This was not only our conclusion

following the evaluation of the literature presented in our semi-annual report,

but it was also expressly stated in a recent review on migration phenomena in

food packaging done for the European Economic Community.*

1
In order to have the widest possible application, our work has initially

focused on polyethylene, the food packaging material used in largest volume.

Migration of small molecules through this semi-crystalline polymer occurs

almost exclusively through the amorphous regions which are well above their

glass transition at any realistic use temperature. We have therefore not

dealt as yet with diffusion in the glassy state and its attendant difficulties.

Also, food contact is almost always simplified to mean contact with * so-called

food simulating solvents. We have followed in this assumption. The validity

of this simplification, i.e. the correlation of migration into food stuffs with

migration into solvents, is the subject of a Food and Drug Administration

contract with the Arthur D. Little Corporation and so will not be considered here.

* G. Haesen and A. Schwarze, "Migration Phenomena in Food Packaging", Commission

of the European Communities, Comm-unity Reference Bureau, Brussels-Luxembourg , 1978.

2
II. THEORETICAL MODELS OF ADDITIVE MIGRATION

Migration of minor constituents from a polymeric film to a food or food

simulating solvent is controlled by both transport and thermodynamic factors.

A valid physical model of migration requires a knowledge of migrant's transport and thermodynamic properties in both polymer and solvent phases. These

requisite properties are often very difficult to measure (e.g., diffusion

constants). A useful model of migration theoretically predicts these requisite

physical parameters from known or easily measurable properties of the polymer/

migrant /solvent system.

The general approach that we have adopted in our modeling studies is to

first consider migration in "simple systems". In a simple system migration

satisfies Fick's two laws of diffusion. Based on the accumulated experience

of many others, this type of simple migration occurs in lightly crosslinked

amorphous polymers and in semi-crystalline polymers at temperatures above their

respective glass transition temperatures, T^,. Simple systems have two distinct

advantages: First, since the diffusion is Fickian, one needs only to specify

the boundary conditions to solve the diffusion problem. Second, the amorphous

polymer or the amorphous component of a semi-crystalline polymer can be treated

as an equilibrium liquid. The latter is an important prerequisite for the calculation of the chemical potential of the migrant in the polymer.

The more tractable aspect of the migration problem is the thermodynamic

or equilibrium one. As a result most of our effort has been concentrated in

this area during the past year. In the first of three theoretical sections,

the equilibrium properties of the polymer/migrant/solvent system are addressed.

The main objective is to theoretically calculate the equilibrium partitioning

of a migrant between polymer and solvent phases. In the second section a new molecular theory of diffusion is outlined. The validity of this theory remains

as yet untested. In the third and last section some phenomological aspects of

migration in simple systems is considered.

3
EQUILIBRIUM PARTITIONING

Consider a polymer that initially contains Mq grams of a diffusant in contact

with a solvent of finite volume Vg. At long diffusion times, M grams of diffusant

are transferred to the solvent. Using mass balance yields

( 1 )

a = (V /V ) K (2)

K = cycp (3)

where and CP are the equlibrium concentrations (mass/unit volume) of the

diffusant in solvent and polymer phases, respectively, K is the equilibrium

partition coefficient, Vp is the volume of the amorphous material (it is assumed

that the diffusant is excluded from crystalline domains) and CP refers to the

diffusant concentration within the amorphous regions. (Superscripts s and p are used to designate solvent and polymer phases and subscripts are used, only

when necessary, to designate species.

At equilibrium, the thermodynamic activity of the diffusant in the polymer

aP will equal the activity a® of the diffusant in the solvent:

(4)

^P0P = 7^0=

_ (5)

where x® and ^P are the respective volume fraction activity coefficients. The

partition coefficient is defined as

K = =

7P/75 (6)

Usually the diffusant will be present in low concentrations. In dilute solutions all concentration units (mole fractions, volume fraction, molarity, etc.) are proportional to one another, therefore

K = (pV 0

‘' = CyC^ = ( 7 ) y(“) 1 im Y

Partitioning with Negligible Solvent Absorption .

According to the well-known Flory-Huggins theory of solutions* the activity and volume fraction activity coefficient of component 1 in a binary mixture

of 1 and 2 are given by

In a, = in 0^ + (1 - r^/t2

) 02 +

In 7 i = (1 - ^i/r2) 02 + X^2<?2 ( 10 )

•4
where ?i=l-$2 is the site or volume fraction ot component 1, r^ and r^ are the

respective number of lattice sites occupied by the components, and X is a dimensionless, and symmetrical (Xi 2 "X 2 i^ parameter that characteriras the interaction

between the t~wo components. Usually, r^ /t 2 is equated to the ratio of molar

volumes and the product r;[X ]^2 (designated as in reference 1) is treated as an empirical parameter.

For dilute solutions

In 7^(00) - 1 + r^Xp (qq)

InyMoo) = 1 - r^/r3 + r^X3“ (qq)

where the^^subscr^ts p, s, and d refer to polymer, solvent, and diffusant, respectively; Xp and Xs^re the infinite dilution values of polymer-dif f usant and solventdiffusant interaction parameters. The term r^/rp is absent in Eq. (11) because r a parmeter proportional to the molecular weight of the polymer, approaches infnni

for a crosslinked polymer.

Com.bining Eqs. (7), (11), and (12) yields

In K0 (13)

A zero subscript has been attached to K to remind us that Eq . (13) is only valid

when solvent is not absorbed by the polymer.

Partitioning with Solvent Absorption

liThen solvent is absorbed by the polymer, the polymer phase becomes a ternary

solution; the activity of the diffusant in the polymer phase can be written as

InaP = In0^ + (1- r^/rj 0^ + 0^ + + 0^ X^ - (14)

where, of course.

(b

' + (p + 0 =1 d p (15

and Xsp solvent-polymer interaction parameter for a solvent concentration

of 0s** will assume that the concentrations 0s and 0p are much larger than the

diffusant concentration 0^ so that Xs Xp can be replaced by x“ ^^id xp* l'^ this

limit

107^(00) = (1 - r^/r^)03 + 0p + r^ ^ ~ (16)

P.

4-.J
Combining Eqs . (7, (12), and (16) yields

In K = (1 - cpj [In K^- ( 17 )

Absorption of solvent causes the polymer to swell. Within a swollen polymer,

the pressure acting on the solvent is greater than the atmospheric pressure, Pq.

The excess pressure tt caused by the elastic forces of a crosslinked polymer (crystalline domains act as effective crosslinks) raises the chemical potential of the

solvent Pg within the polymer phase. The condition of equilibrium is

O

(18)

where is the chemical potential of pure solvent at and is the partial

molar volume of the solvent. Since, by definition

h»]/RT (19)

we have by Eq . (9)

tn0s + 0p + = -ttV^RT (20)

As can be seen from the derivation of Eq . (20), the swelling pressure tt is

equivalent to the osmotic pressure developed by a non-crosslinked polymer solution of the same concentration. In the absence of significant swelling, this pressure will be relatively small and to a good approximation the right hand side of

Eq. (20) can be set equal to zero. Thus, a measurement of the equilibrium absorption

of solvent ((j)s) yields an approximate experimental value of Xsp-

'’s^sp ~ ~

/<Pp (21)

If the swelling is appreciable, as it might be for a very good solvent, corrections

can be made to Eq . (21) for both crosslinked amorphous polymers^ and semi-crystalline

-I 4 5 polymers ’ . Substitution of Eq . (21) into (17) yields

In K In K - (b O ' s [l In (1/dj/(1 -

( 22 )

D
where it is understood that is the equilibirum amount of absorbed solvent.

Notice that K-^Kq as cp^O and K^l as as it should.

A further check of the self-consistency of Eq. (22) is obtained by considering

the partitioning of a diffusant in which the diffusant is radiolabeled (RL) solvent.

In this case Xg = 0 , and r^=rs . Substituting these results into Eq . (22) or (17)

yields

In K = - In (/) (23) ' S

The RL solvent should partition exactly as the non-RL solvent. The partition

coefficient for the non-RL solvent. Kg, is equal to the volume fraction of the bulk

solvent in the solvent phase (unit^/) divided by the volume fraction of the solvent

in the polymer phase (Is) or K = 1 /0 (24)

s

which agrees with the result obtained from Eq . (22) for the RL solvent.

Interaction Parameters

In the original formulation of the Flory-Huggins theory^Xij was strictly

an energetic parameter that was proportional to the energy required to form

an i-j bond from a i-i and j - j bond. It also had a simple 1/T temperature dependence and was independent of solution composition. Experimentally, y,-.: often has

a large positive entropic component which arises, according to the Flory and

lattice fluid (LF)^*^”"^ theories, from differences in the equation of state properties

of the pure components.

Both the Flory and LF theories require three equation of state parameters for

each pure component which are determined from PVT data. Each component satisfies

a theoretical equation of state; the LF equation of state is

p^ + P + T[ln(1-p) + (1- ^ /r) p] = 0 (25)

where T, P and p are the reduced temperature, pressure, and density. Three equation

of state parameters, T*, P* , and p*, are used to reduce the experimental temperature,

pressure, and mass density of the fluid; r is the number of lattice sites occupied

by a molecule and is proportional to its molecular weight, M:

r = (P*/RT*p*) M (26)

For the LF, equation of state parameters have been tabulated for about 60 low

molecular weight fluids^'^and the ten different polymers^^. Methods for determining

these parameters are discussed in the Appendix A.

From the LF theorv, the interaction parameters ^.nd required in Eqs. (13)

and (22) are given by ‘

= p.^p; P*T +

d d Pj/% ^ ln(p^/p,)/i ( 27 )

+ (1 - p^) In (1 - p^)/p^ - (1 - p^) In (1 - pj/p^

/
and a similar expression holds for '^p (replaces s by p) . The parameter which

has units of pressure is the only unknown parameter in Eq . (27). All other quantities are calculable from the equation of state properties of the pure components.

The physical meaning of APg is that it is a measure of the net change in the

energetics that occurs upon mixing solvent and diffusant at the absolute zero of

temperature. At absolute zero, the sign of AP* determines the sign of the heat of

mixing

.

In both the Flory and LF theories, the cohesive energy density of a fluid

at absolute zero equals its characteristic pressure, P*. It is, therefore, convenient to define a dimensionless parameter Ag in terms of the characteristic pressures

of the pure components:

AS AP' (28)

Combining Eqs. (13, (27) and (28) yields

A<PAPd* + 'll -At'- AIPp‘/Pd* + ')l]h' (29)

+ (1 - In (1 - - II - pj ln(l - + r~' In ip^/pj +

where r^ and r^ are defined by Eq. (26) and Pg and Pp are calculated from the

equation of state (25)

.

Sample Calculations

In principle the dif f usant-solvent or the dif f usant-polymer interaction

parameter can be empirically determined from a single solution datum such as a heat of mixing, a critical temperature, a solution density, etc. However,

in some systems intelligent choices of Ag and Ap can be made from limited data.

An example of this kind is the partitioning of the n-alkanes between linear

polyethylene (PE) and n-heptane. In Table I, the partition coefficients Kq and

K are calculated from Eqs. (29) and (22) for selected n-alkanes at 25°C. Equation of state parameters required in the calculations were obtained from references 8 and 9. For PE, the equilibrium amount of n-heptane absorbed is d)g=0.26

Entries enclosed within parentheses are K values and those without are Kq values.

Entries that are crossed out with solid lines are considered unlikely values

of the partition coefficient; those with broken lines are considered more probable

than those crossed out with solid lines, but less probable than the clear entries.

The rationale for selecting Ap in the range between 0.01 and 0.03 is based on

tne calculation of Ap for polyisobutyiene (PIB) solutions of the n-alkanes from

heats of mixing and the experimental result that K=Kg = 1/0.26 =3.8 for n-heptane.

For PIB, Ap=0.016 for n-pentane and decreased monotonically with chain length

to Ap=0.002 for n-decane^^. Since PIB and PE are chemically very similar, it is

not unreasonable to expect that Ap values in the PE/n-alkanes are similar to those

in PIB/n-alkanes . Selection of Ag=0 is certainly correct for n-heptane (assumed

to be radiolabeled n-heptane) and is probably an excellent approximation for the

n-alkanes between pentane and decane. Of course, as the chain length of the n- alkane increases, As^Ap and Ap^O, which explains the choice of Ag and Ap values for

the partitioning of PE of molecular weight 10^*. Because the partition coefficient

is proportional to the chain length of the diffusant [see Eqs. (13) and (22)], the

calculated values of the partition coefficient become more uncertain as chain length

increases

.

In Table II calculated values of are shown for the partitioning of some n-alkanes between linear PE and ethanol. Here the estimates of Ag , and conse- quently Kq, are much more uncertain. However, we have some crude guidelines to

go by. We know that the n-alkanes exhibit limited miscibility in ethanol which

is qualitatively indicative of a large, positive A^, value. Also, because ethanol

is polar and PE and the diffusants are non-polar , we :an reasonably expect that

O
dif

fusant

0.04

0.03

ro' Q-

<2 <1

O

a

o

CMo

o

o

o

O r— O '=3’ CM

CMO

O

CO CTi LD CM

O LD

I— CO

CT> -y

O)c

1T3

4—

CO o

CM

CD

"St CM

CO CO

CD ro

CD ro

CO CM

{ <t

ro 'CM Cm

r o c

CO ro

CTi

c

<DCl

CTi 53-

CD CO ro LO

cuC

raQ.

QJ

CM 00

03 ro

N, _/l

CM >0

03 'to'

O' LD

03 00CO

C<J

cuc

fC3 u

<11 TO

I c

m

o

cu 30

<T3

CM LD / C3J cm/

I ' I, X \X

<33

CO CD o o

X X

r"' 1

CO CO

ro I o o

X X

ro LD

tor— CM/ O <p

X.' X

LO' ro

,CM <03

O'

LlJ O

a. <—

S- II <T3 cu 2: c

t/1

<1) o

<T3 -X

03

I c

-a

<uu

OJ

O) . U3 <0

i- o

o LD

<4- CM

iX ro 30 OJ

ro 33 +J

CCC. x; <u

'•

I uo C

+->C 30

<u c

•I— ro U

•r- QJ M- O

M- QJ

CU r— O

<J ^4-> c a; o >,

4-) o

I- Cl

5_ i_ ro ro C. <11 C

30 •—

QJ r—

ra SO r— O) O O)2

I— +-> ro CJ CJ JD

LO

ro

9
diffusant

0,025

0.025

0.025

“O H3

QJ

-l-J f— U o

QJ t—

<T3 QJ

(/) QJ

S-O -a

H- c

03 0<D

OJ r—

ut

4-J C 4-J QJ QJ

•r-u r—

•r— o

M- CL

Mo; S- o 03 u QJC c •r-* o r—

•r4-> •1— QJ

4-> QJ

i. 3

ra -M C- QJ -c

QJ (y^ -M QJ

113

C

r— 03 Z3U r—

f— <13< ra 1 C

fT3 I—

10
Inspection of Eq . (22) reveals that if Kq> 1; i.e., if partitioning favors the

solvent phase, absorption of solvent lowers the partition coefficient (K<Kq) as is

illustrated for the partitioning of the n-alkanes between PE and n-heptane in Table I. This effect on partitioning is best understood by imagining the partitioning to occur in two steps. In the first step the diffusant partitions in the absence of

solvent absorption preferentially toward the solvent phase. In the second step,

solvent containing some of the diffusant is absorbed by the polymer. Thus, the

diffusant is reabsorbed literally on the "coattails” of the solvent.

When Kq< 1, Eq. (22) suggests that it is possible for solvent absorption to

increase the partition coefficient (K>Kq)

The exact conditions for this to occur

are

X“s > 1/r

s +X”p + 0 X

P sp = X* + In (1/0^)/ r^(1 (30)

Under these conditions we have a reverse coattail effect. It can be understood

as follows: A small implies a poor solvent-dif fusant interaction (.large positive x*s) diffusant prefers to remain in the polymer phase in the absence

of solvent absorption. When solvent is absorbed, the diffusant now "sees" a thermodynamic environment in the polymer phase that is similar to the one in the

solvent phase, neither of which it likes. Since the disparity in thermodynamic

environments is reduced by solvent absorption, the diffusant tends to redistribute

itself more evenly between the two phases.

11
DIFFUSION THEORY

Self-Ditf usion

Consider a system of N molecules in a system of macroscopic volume V. The

average volume per molecule I7=V/N; the average distance between molecular centers

is V

/

^ . In the liquid state we can imagine that each molecule in the system is

confined to a 'cage" formed by neighboring molecules. This cage has an average

size of ^ average volume v. The cage fluctuates in size with time as is

schematically illustrated below:

OO o

O *0

COq

o

o o

The hypothesis is invoked that a molecule is confined to its cage until the

cage volume exceeds a certain critical value v*. If the cage is larger than v*

the molecule "escapes". Escape followed by capture (collision) constitutes a successful diffusive displacement. This physical picture of diffusion is one in

which a molecule spends an average residence time Tin its cage before it escapes

and travels a mean distance H before it is captured. The time required for the

molecule to travel a distance £ is assumed to be much smaller than 1. While confined

to its cage, a molecule suffers many molecular collisions and is constantly being

displaced, but its average location remains the same in the time interval!. Below

we schematically trace the diffusing path of a molecule. Each straight line seghave used a very similar physical description in their theory of diffusion.

Let P(v)dv equal the probability that a molecule has a cage volume between

V and V + dv; P(v) possesses the following properties:

X”p(v)dv = 1 (31)

_y^”vP(v)dv = V (32)

12
( 33 )

The probability that the cage volume exceeds v* is

P(v>v‘) = X”P(v)dvNow radiolabel a very small number of the molecules in the system,

these N* and their density p''=N*/V. Suppose that their distribution is

in the x-direction as illustrated below:

Call

non-uniform

All labeled molecules within a distance £ of the plane at x are capable of

crossing that plane when they undergo a diffusive displacement. The average

velocity u of a molecule of mass m at a temperature T is

ii = (kT/m)'''"

by virtue of the equipartition theorem. Roughly 1/3 of the molecules will be

moving in the x-direction; 1/6 will be moving in the positive direction, and

1/6 will be moving in the negative direction, but only P(v>v*) of these molecules

will be executing diffusive displacements of average length £. The mean number

of labeled molecules which in unit time cross a unit area of the plane from the

left is

Jx = ii P(v>v’) 1 1 1 ><; -1 (35) L J

but

p'(x- 1 ) .-p(x)- j’p

(36)

and therefore

Jx = -Ddp'/dx

D = u ZP(v>^’•)/3

13
That is, the net flux of labeled molecules passing through the plane at x is

proportional to the concentration gradient at that point (Pick's first law of

diffusion). The proportionality constant D is the diffusion coefficient.

The numerical coefficient of 1/3 in Eq. (38) should not be taken too seriously

since our estimate of the number of molecules with velocity components in the

x-direction is very crude.

The primary problem is to calculate P(v) and P(v>v*). Cohen and Turnbull^^

assumed that a multinomial distribution of volumes exist in a liquid and proceeded

to calculate P(v) from this hypothesis. The disadvantage of this approach is that

the calcualted P(v) is not easily related to the physical properties of the liquid.

The approach that we adopt is to use classical fluctuation theory to calculate

P(v). Bueche^"^ has used a similar approach to describe self-dif f us ion in polymeric

liquids. According to fluctuation theory, the distribution of volumes is a Gaussiam

function given by

P(v) = ( 27TCT“)2\-!/3’exp

iv-vy- 1

J

(39)

a' = kTv /?/N (40)

where 3 is the isothermal compressibility of the medium. The mean square volume

fluctuation equals . Notice the varies inversely with the number of molecules N in the system. We are interested in volume fluctuations on the microscopic scale; i.e., fluctuations associated with a single molecule (N=l) . The

derivation of Eq . (39) becomes highly approximate for N=l. Nevertheless, we shall employ Eqs. (39) and (40) for P (v) fully aware of its shortcomings.

For N=l, the volume fluctuations predicted by Eq . (40) are still relatively

small. For example, for the typical liquid values of T=300K,B=10“‘^ bar~^ and

v=100 cm^/mole, a/v equals about 0.15 or the volume fluctuations are about 15%

of the average molecular volume. Because the distribution is relatively narrow, we can safely extend the limits of integration (for the purposes of normalisation)

from 0 to CO to -co to without introducting appreciable error. We now have by Eq . (33)

P(v>v') = k 1 -erf

V —V

V2a S

/2

P(v>v*) = erfc ry^l

[_ V2cr J

/2 (41)

where erf x and erfc x are the error and complementary error functions, respectively.

Notice that for

( 42 )
To complete the calculation of the self-dif fus ion coefficient we must specify

the mean distance £ that a molecule travels during a diffusive displacement. One

approximation is to assume that £=(v*)^/^ , but other approximations are possible.

One can argue that £ should be a unique function of v and the molecular collision

cross-section a . Dimensional analysis then suggests that £-v/a. This is the

functional form for the mean free path of a gas molecule that is calculated from

the classical kinetic theory of gases. Using the kinetic theory result (£-v/ i ^o)

has the virtue of yielding the correct diffusion coefficient for a gas in the limit

v>>v* (D=u£ / 3) .

Diffusion of a Small Molecule in a Polymer

Now consider a system comprised of a polymeric liquid and a trace amount of

a small molecule diffusant. The effective volume of the diffusant molecule in the

polymer is the diffusant 's partial molar volume at infinite dilution v? If N(j is

the number of diffusant molecules then

^is given by

V

(43)

where V is the volume of polymer + diffusant.-

The volume fluctuations that are occurring in this system are characteristic

of those occurring in the pure polymer. If we focus attention on a small volume

within the polymer of size v“, the volume fluctuations about this volume would be

approximately given by = kT(3v° (44)

where S , of course, is the isothermal compressibility of the polymer liquid. The

distribution of volumes about v°o would be approximately Gaussian with a variance

given by Eq . (44). Thus, we can assume that the volume fluctuations that a diffusant molecules "sees" in diffusing through the polymer are those given by Eq . (44)

and its diffusion coefficient is

D = u(v’)‘'^^erfc r

V -V

(2k T/?v-)

t/3 1 ./6

J

( 45 )

where £ has been taken to be equal to (v*)^^^

Equation (45) embodies all of the physical factors judged important for

diffusion in polym.ers through v*,v°°, and 3 ; v* is a unique property of the shape

and size of the diffusant; v°° is the property which depends sensitively on the

po lymer-dif f usant intermolecular interaction; and 3 is a characteristic property

of the polymer.

15
EXTRACTION OF ADDITIVES WITH SOLVENT ABSORPTION

The race of migration of an additive from a plastic in contact with a liquid is often increased by simultaneous migration of the liquid in the plastic, that is, by extraction by the liquid. The migration curves for extraction

cannot be found by analytical formulas. Therefore, the diffusion equation for

extraction has been solved by a finite difference method. The calculated migration curves will first be qualitatively compared with the experimental extraction

curve. Later, they will be fit to experimental extraction curves and applied

to studies of extraction from plastic containers in use.

Graphical Results

First, the symbols that are used will be defined. Let the diffusion

coefficient of the liquid in the plastic be D^^ and the diffusion coefficient

of the additive be given by

D = Dg + k c (46)

where Dq is the initial diffusion coefficient, k is a constant and c is the

concentration of the liquid in the plastic. Because c depends on the position in the plastic and time, D also depends on position and time.

Let c be the concentrat ion of the liquid in the plastic at infinite time, on the equilibrium concentration, and let D^ be the corresponding diffusion coefficient of the additive. Then

D* CO Do + k c

CO (47)

The diffusion coefficient of the additive varies from D^ to D^ during its migration.

The migration curves for Dj^/Dq = 2, that is, the liquid diffuses twice as fast as the initial rate for the additive are shown in Fig. 1. The amount of

additive, that has migrated from the plastic to the liquid at time t over

the initial amount, M , of additive in the plastic is plotted versus the sauare

OO root of the reduced time. Z is one-half the thickness of the plastic sheet.

Curves are given for 4 values of D /D^. The solid curve for D /D_ = 1 corresponds

to zero increase of diffusion of the additive due to liquid absorption. The

amount of additive migrated out of the plastic is seen to increase linearly with

the square root of time for the first 60% of the migration of the additive. For

increasing values of D /D , corresponding to increasing diffusion of the additive

due to liquid absorption, the migration of the additive increases, as expected.

However, the shape of the migration curve does not markedly change; the migration

still increases linearly for the first 60% of the migration of the additive.

Fig. 2 shows the migration curves when the liquid diffuses at 10 times the

rate of the initial rate of the additive. The migration is somewhat larger for

this case, but the migration curves are similar to those of Fig. 1. The preceeding analysis considered the migration of the liquid in the plastic to be ideal with a constant diffusion coefficient D^ . However, for some

systems D^ is expected to increase with increasing concentrations, , of the

liquid in the plastic. When D,^ is very dependent on concentration, the diffusion

of the liquid at a position in the plastic will be very small until the plastic

has been "opened up" by the first penetrating liquid. Therefore, the plastic

will contain an essentially unswollen region and a highly swollen region, separated

by a well defined front. The penetration depth of this front will be proportional

16
oo

Fig. 1, ^ou.t Of f.o. a plastic sheet when the surtoun.in, ii^af

migrates in the sheet at twice the rate of the additite. The curves,

reading fron. the lower to the upper curves, are for D /D of 1 is

2 and 5.
oo

Fia, 2, Amount of migration from a plastio sheet when the surrounding liquid

migrates in the sheet at ran times the rate of the additive. The

cur^/es, reading from the lower to the upper curves, are for D /D of oo Q

1 , 1.5, 2 and 5

.

I*»

I

I

I

P

I

2
to the square root of time. Fig. 3 shows schematically the concentration distribution of the liquid for three equally spaced times.

The penetration depth of the front is taken to be wv t . Fig. 4 shows the

migration curves for the additive for this concentration-dependent diffusion

of the liquid. The lower solid curve corresponds to zero increase of the additive due to absorption of liquid by the plastic, and is included for comparison

with the other curves. The other curves are for D /D„ = 5 and for values of the

r— 20 U reduced parameter - of 0.05, 0.1, 0.2 and 0.5, the upper curves correspond

to larger values o' w/vD^.

The migration at a given time is seen to increase for increasing velocities

of the front of the liquid diffusion, corresponding to larger values of w. However, the shape of the migration curve does not change m.arkedly; the curves remain

linear for small times.

The effect of non-uniform initial distribution of the additive in the plastic

sheet was also calculated. The increase of migration of the additive due to

absorption of the surrounding liquid was not included in these calculations.

The three initial distributions of the additive shoxvn in Fig. 5 were considered.

The solid line represents a uniform distribution; the dashed line represents a con- centration of the additive near the sides of the sheet that is one-half the concen- tration in the center of the sheet; and the dotted line represents a concentration

that increases linearly from zero at the sides of the sheet to a maximum value at the

center of the sheet. These distributions were chosen so that they all have the same average concentration.

The migration curves calculated for these distributions are sho^vm in Fig. 6.

The amount of migration is proportional to v t for the uniform distribution, as has been previously observed. However, the migration for low concentration of

additive at the sides, shown by the dashed curve, is smaller and shows an inflection point for small times. This is similar to some of the experimentally observed

migration curves. The migration curve for the dotted triangular distribution shows

a pronounced decrease at small times.

Summarv

The migration curves of an additive from a plastic have been computed for

the case there the rate of migration is increased by the surrounding liquid migrating into the plastic. The migration curves have been computed both for a constant

liquid diffusion coefficient and for a liquid diffusion coefficient strongly dependent

on the concentration of the liquid in the plastic. Although the rate of migration

of the additive was increased by migration of the extracting liquid, the shapes of

the migration curves were not markedly different from the case where the migration

of the additive in the plastic is not affected by migration of the surrounding

liquid into the plastic.

The migration curves have also been calculated for a non-uniform initial

concentration distribution of additive in the plastic. The shapes of the migration

curves were found to depend on the additive distribution, showing inflection points

similar to those observed in some of the experimental migration curves.

19
Fig. 3 The concentration distribution for three equally spaced times of the

liquid in the plastic for the case that the diffusion of the liquid

is very concentration dependent. The front of penetration of licuid

in the plastic mcves a distance w /F' in time t.

8

o

o

1 .0

0 .8

0 .6

0 . 4

0 .2

0 .0

0-0 0*2 0-4 0-6 0»8 1

- Plastic

20
oo

Fig . 4 The nig-ation curves for the additive when the concentration distribution

of the liquid in the plastic is that shown in fig. 3. The curves, readin;

^ron the lower to upper curve, are for values of w/ of 0, 0.05, 0.1,

0.2, and 0.5.

1 .

0 .

0 .

0 .

0 .

0 .

21
a

V

Three assu„ied initial distributions of the

additive in the plastio sheet.

concentration, c , of the

o

o

o

o

0=0 0=2 0=4 0=6 0=8 1 = Plastic
oo

Fig. 6. The migration curves for the distributions shown in fig. 5.

1 .

0 .

0 .

^-5

0 .

0 .

0.0 0.2 0-4

„

0

6

_ 0-8

Dt/1^

1-0 1-2
EQUIVALENT EXTRACTION TEMPERATURES

FOR SIMULATION OF ADDITIVE MIGRATION

IN POLYMERS SUBJECT TO VARYING TEMPERATURES

A polymer in use is exposed to a range of temperatures. Migration of an additive in the polymer will vary with the temperature, being greatest at the

highest temperature. On the other hand, tests of the migration of additives

are generally performed at a constant temperature. In this section, an equivalent test temperature, Te, is derived such that the migration of an additive

in a test of temperature Te is the same as the migration of the additive at the

range of temperatures of the polymer in use. The diffusion constant, D, of the additive in the polymer will vary with

temperature, T, according to the relationship

D = Dq exp(-E/RT) (48)

where E is the activation energy of diffusion and R is the gas constant.

Consider first the simple case that the polymer in use is exposed to a temperature T^ a fraction f of the time, and is exposed to a temperature T

2 the remaining fraction (1-f) of the time. Then the equivalent test temperature is sho^m in Appendix D to be given by

^ ^ -E/R

e Logg[f exp(-E/RT^) + ( 1- f ) exp (-E/RT^ ) ] (49)

For the general case in which the polymer is exposed to any variation of temper

ature T with time, t, the equivalent test temperature is shown in Appendix D to

be given by

- ^ ^ lE/R

Logg [ (1/t) ^ exp (-E/RT) dt ] (50)

If the activation energy E is known for a polymer-additive system, the

equivalent test temperature, Tg, corresponding to any variation of temperature

may be computed by Eq. 49 or 50.

The diffusion of the ultraviolet stabilizer 2 , 4-d.ihydroxybenzophenone in

polyolefins has been measured by Westlake and Johnson. The measured values ot

the activation energies, E^ , of diffusion are 18, 23 and 34 kcal/mole for lowdensity polyethylene, high-density polyethylene and polypropylene, respectively

As these values are probably typical for activation energies, calculations of

equivalent test temperatures were performed for activation energies of 15 and

30 kcal/mole. The calculations were performed for temperatures varying from

20 to 75°C for variations of the temnerature with time shown in Figs. 7, 8,

and 9. For Fig. 7, the test temperature is 20°C for half the time and 75°C for

the other half of the time. For Figs. 8 and 9, the temperature varies between

20 and 75°C in a manner that is more realistic. The equivalent test temperatures calculated by Eqs. 49 and 50 are shown in Table 3. Fig. 10 shows the equivalent test temperatures for the time variation

shoxTO in Fig. 7 except that varying amounts of time are spent at the high temper

ature of 75°C. The solid line is for an activation energy E of 15 kcal/mole

and the dashed line is for E of 30 kcal/mole.

24
* Figure 7 Ass’dmed time variation of temperature of plastic.

Figure 3 Assumed time variation of temperature of elastic.

Figure 9

Assumed time variation of temperature of plastic.

25
TABLE 3

Equivalent Test Temperatures in °C for Temperatures

Varying Between 20 to 75°C

Variation of Temperature Activation Energy of Diffusion, E,

given bv k.cal/mole

15 30

69.5

60.0

59.3

Fig.

Fig

.

Fig. 3

64 .

5

54.9

54.8

26
LquivaleiiL

L-esl

tempera

tun '

lor.

versus

the

pei'ceiitage

of

the

time

O

00

00Q

(DO

OJ o

LO0

U)0s0

(Pa

0/0s0XV 4-

in o Q

(O LO

Q <s

CO

Q

CM 1
III. EXPERIMENTAL MEASUREMENTS OF ADDITIVE MIGRATION

Polyethylene

There are a number of reasons for the choice of polyethylene as the

polymer substrate for migration studies. As the largest vol'ume packaging material,

there are a wide variety of commercial resins and formulations available so

general physical models would have broad application and case by case testing

would be tedious. The commercial importance of polyethylene and the simplicity

of its chemical structure have prompted enough scientific investigation

that a great deal is already known about the detailed structure and morphology of

the solid state. There is a wide range of crystallinities available with

different resins and the crystallinity in a given resin is controllable within

limits by well known thermal treatments. This presents a challenge to any

theoretical model and another variable to control and alter in experiments. Finally,

polyethylene is relatively stable chemically. It does not degrade thermally under

usual processing conditions and can be adequately protected from oxidation.

The firsu migrating species to be considered are the polyethylene oligomers.

Some octadecane migration results are presented in this report. Further data

including other oligomers will be presented in the next report as well as

initial experiments with polar additives.

28
MATERL^S

PolyiTiers

The basic polymer used for the extraction experiment is the National

Bureau of Standards Standard Reference Material (NBS-SRT4) 1475, Linear Polyethylene Nhiole Polymer. This SRM is well characterized and certified^® for

its molecular weights , molecular weight distribution , density , melt-flow rate

,

viscosity and heat capacity. The weight averaged molecular weight of SRM 1475

is 52,000.

When the FDA extraction procedure (Code of Federal Regulations, Title 21,

Chapter I, Part 177.1520) was applied to the SRM 1475 sarnrle in pellet form,

tne hexane extractives at 50'^C are in the order of 0.05 to 0.1%, either by

weighing the residue from hexane extract or by the weight loss of the sample

pellets. Additional experiments with heptane at 50°C on a 0.2 mm fiLm ma.de

from SRM 1475 yielded a weight loss figure about 0.2%.

Future polymeric materials will include ^^BS-SP^M 1476, Branched Polyethylene

('/hole Polymar, and other polyethylenes of commercial grade especially those used

for bottling purposes.

Additives

The low molecular weight paraffinic hydrocarbons are oligomers of linear

polyethylene. We have now on hand ’^^C-labeled decane, octadecane and lotriacontane with total activities of about 5 mCi (millic’uries ) each. Labeled hexadecane

is also readily available in small quantities as NBS-SRM 4222.

We have chosen octadecane as the first hydrocaroon for the migration study

because of its relatively low volatility (b.p. 316°C). The molecules of octadecane are still small enough to have relatively large diffusion coefficient, so

that the experimLents may be completed in reasonable ti.me scale.

_ lu , . ^ n-Oc Ladecane-i- C was obtaaned from comumercial sc'urce as hexane solution

sealed in glass ampules. The specific activity in one of the ampule was stated

as 13.3 mCi/g, but was foiand to be 12.2 mCi/g. The total activity is

29
1.65 mCi in 135 mg of dissolved in hexane. The entire content of the

arrpule was diluted into 50 ml (33 yCi/ml). One ml of this solution is further

diluted into 50 ml (0.66 uCi/mJ.). These dilutions provide much easier handling

of the labeled compound. Further isotopic dilution by unlabeled octadecane

may be desirable in some cases to reduce unneccessary waste of radioactive

materials. The amount of dilution depends upon the minimum detection level

desired and the concentration of the additives in the polymer.

The FDA’ s extraction procedures for the determination of total non-volatile

extractives (Code of Federal Regulations, Title 21, Chapter I, Part 177.1010)

uses a ratio of 10 ml of solvent per square inch of plastic surface for a sample

of 5 in.2 of surface area. The extractives in parts per million are then

obtained as 100 times the weight of extractives in milligrams per square inch

of plastic S’urface. Strickly spe.aking this expression for extractives is

expressed in terms of mlcrogramiS per milliliter of solvent or per 0 . 1 in^

of the plastic surface.

If we desire a detection limit of 10 ppb (10 ng/ml) for rhe extractives

in food simulating solvents, we are required to detect tlie presence of 100 ng

of the extractives in 10 ml of solvent or from each square inch of the plastic

S’urface. 3y ass^uming a minimumi counting rate at twice the background rate

as the instrumental detection limit, then this requirement amounts to a minimum

activity in the order of 25 pCi. Therefore the minimum specific activity of

the extractives should be about 0.25 mCi/g. However if we desire to have a 1%

precision of the data at the 10 ppb level , then a minimum activity of 2 . 5 nCi

or about 5000 dpm in the 10 ml solvent would be more desirable.

30
SAMPLE PREPARATION

Method

After several attempts we have chosen the following procedure for the

mixing of additives to the polymer stock and the molding of the sample plaques

.

A large quantity of polyethylene powder stock was prepared from NBS-SRM 1475,

Linear Polyethylene Whole Polymer, pellets by first dissolving in hot toluene,

and then followed by cooling. Most of the polyethylene precipitates out. Tne

precipitate was filtered and dried in a vacuum oven to remove the solvent.

To a quantiry of the polyethylene powder stock, a specific amount of labeled

additive dissolved in a highly volatile solvent is mixed. The mixtiure is then

evaporated to dryness in a rotary evaporator under reduced pressures at relatively

low temperatures , and further dried in a vacuum oven . The mixtijre is then compression molded in a hydraulic press operated at about 180°C.

Four sample plaques were prepared by the aforementioned techniq^ues, i.e. ,

by wetting the SRM 1475 polyethylene precipitate with hexane solution of ^'Relabeled C-]qH 33 , followed by evaporation and compression molding. The four sample

plaques, designated as A, B, C and D respectively, are molded into two different

thicknesses from two powder mixes of different Cq 3H38 additive levels as shown

in Table 4

.

The plaques (50 X 125 mm) were molded with brass shim stocks of 0.76 (30 mil)

and 0.25 mm (10 mil) thickness sandwiched between two sheets of teflon, Ihe

teflon sheets are used for the easy removal of the samples from the mold. 'The

finished plaques have nominal thicknesses of slightly less than 0.7 and 0.2 mm

respectively. The thickness at the edge is generally Thicker than that in the

center. Part of the shrinkage is due to the large coefficient of expansion of

polyethylene. The depression of the teflon sheets may also contribute to the

apparent total shrinkage. The variaiion in the thickness can often reach ± 0.05 mmi

(± 2 mil)

.

31
Table 4

Description of Polyethylene Samples

Sample

Tliickness

inm

Concentration

of added Specific .Activity

.Mdpm/

g

A 0.7 1 5

B 0.2 1 5

C 0.7 0.01 3 .

5

D 0.2 0.01 9

32
We have now obtained teflon coated top and bottom plates to replace the

teflon sheets in order to eliminate some of the sources of shrinJ<age and thickness non-uniformity. Stainless steel shims will be used instead of the brass

ones to eliminate possible contamination and reaction during the molding process

.

Uniformity

Besides the non-ijniformity in the thickness the samples are not too miform

in the additive distribution. The sample plaques were checked for the uniformity

of the distribution of the added radioactive C]_3 H

23 by autoradiography. NoScreen X-ray film type NS-oT was used because of its speed. Exposure time in

the order of 16 hours is sufficient to register the activities of these plaques

.

The distribution in the 0.7 mm plaques seems to be more uniform than that in the

0.2 mm. plaques, the distribution is especially poor for the 0.01% C-| gH 33 sample (D)

.

Therefore .sample (D) was cut up and compression molded again. The distribution,

although still not uniform, was improved greatly as shown in Fi,gure 11 . Typical

microdensitometer scans across the width on these sample plaq_ues are shown in

Figure 12 , along with the scar.s of background of the film adjacent to the images

of the plaques . The variation in the optical density levels are quite obvious

,

and can often reach 20% or higher.

33
34
i 1glare 12. .^ci'cxierisi'tcme’cer scare of the AutoradiograDhs of Sa,ncle olao’je D.

Top Cup'/es: first molcirg. Bottom CLirves: second .molding. Steps:

Calibration strip.

35
LL'MII'JESCENCE SPECTROSCOPY MEASURH1ENTS

The migration of antioxidant from polymers will be studied by two types

of experLments: extraction experiments and concentration profile experiments.

In an extraction experiment, a plane sheet of polymer with uniform concentration of an antioxidant is immersed in a limited amount of well stirred solvent.

The migration of an antioxidant is then deduced from, the change in antioxidant

concentration in the solution surrounding the plane sheet. The antioxidant

concentration can be determined either by fluorimetry at room temperat’ure or

phosphoricetry at a lower temperature. If the diffusion coefficient for the

antioxidant is constant, it can be deduced from an extraction experiment. In

a concentrarion profile experiment, a plane sheet of polymer with uniform concentration of an antioxidant is immersed in a large volume of well stirred solvent.

The concentration profiles along the direction normal to the larger surfaces of the

sheet can be determined at various times by mdcrofluorimetry after sectioning

the sheet. The diffusion coefficient of an antioxidant can then be deduced from

the concentration-distance curve.

Solution Concentration Meas'urements

In late FY 78, we made room-temperature fluorescence measurements on Irganox

1076 (n-0ctadecyl-3-( 3, 5-di-t-butyl-4-hydrox}/phenyl) -propionate) in hexane, Agerite

Wh.ite (N, N'-di-3-naphthyl-p-phenylenediamine) in ethanol, BHA ( S-t-Butyl-P-hydroxyanisole) in ethanol, and BHA in heptane. We found that, of these three antiooxidants, only Agerite White and BHA show room temperature fluorescence sufficiently

intense to be useful for trace analysis. In FY 79, we will develop a procedure to

follow the extraction of Agerite Wnite or BHA from low density polyethylene. This

development entails principally the preparation of polyethylene films of about

0.025 cm containing an antioxidant, uniformly distributed and 'undegraded by the

preparation, the construction of an extraction device equipped with a cell for

36
making fluorescence measurements without exposing antioxidant to oxygen, and

the establishment of an analytical working curve relating antioxidant concentration to fluorescence intensity.

Since , for most antioxidants , the phosphorescence is known to be more

intense than room-temperature fluorescence, we plan in late FY 79 to begin

the development of a procedure to follow the extraction of an antioxidant

such as Santonox R ( Bis (2-methy1-4-hydroxy- 5-t-butyIphenyl ) sulfide ) , by phosphorescence measurements

.

Concentration Profile Experiments

Figure 13 gives the block diagram of the microfluorometer used for our

concentration profile experiments. The most noteworthy feature of the microfluorometer is a vertical illuminator equipped with a dichroic mirror with

high reflectance for the exci^"ing wave length and high transmission for other

wavelengths (see Figure 14). The dichroic mirror thus reflects an intense exciting

light into the objective u"d allows an intense fluorescent light to reach she

eyepiece. In addition, a relatively dark background can be obtained since the

dichroic mirror also deflects the exciting light that is reflected by the glass

surfaces of the objective and by the cover glass or the sample. A barrier filter

is used to eliminate the weak exciting light that passes the dichroic mirror.

Measurements have been made with our microfluoromieter on solids of Agerite

hhire, solids of Nonox WSP (Bis (I-hydroxy-S-a-m.ethyl-cyclohexyi-S-methylphenyDmethane), a high density polyethylene film containing 3100 ppm. Irganox 1076,

and a low density polyethylene fiLm containing 1000 ppm. Agerite White. We foiund that, o

these three antioxidants, only Agerite White shows rcom-remperat'jre fluorescence

sufficiently intense to be useful for measuremients with our microfluorometer.

In FY 79, we shall develop a procedure for concenTrration profile meas’urements

on lov7 density polyethylene films containing Agerite White. This developm.ent

37
1 % i»". '-j

I

j

’> ^ i

:0

;

-T)

I \

Figiure 13. Block diagram of microfluorometer . XE S - xenon source; LA S

-

laser source ; R PM^P - reference photomultip lier Aube ; SAL! - sample

DM-FC - dichroic mirror - bar-rier filter combination; MO - monocular;

MT - meas'uring telescope; '/A - m.easuring aperture; X-Y FO-x-y

focusing optics; MONO - monochromator; FMT - photomultiplier; R -

ratio amplifier; X-Y RFC - x - y recorder; V TO F - voltage to

frequency converrer; PS- p’ulse shaper; MCA - m;ultichannel analyzer;

TT - teletype; and CL - crystal clock.

38
(orange)

fluorescence

39
will involve, in addition to the film preparation mentioned earlier, the sectioning of a film, the construction of a holder for the sectioned film, and

the measurement of concentration profile maintained unperturbed by antioxidant

degradation

.

Because of the limitation of the available dichroic mirrors , our microfluorom.eter is not suitable for measurements on films containing BKA or Agerite

superlite (mixture of polybutunrated bisphenol A) which is excited by light of

shorter wavelengths than Agerite l^/hite. In late FY 79, we shall modify our

microfluoromerer to make it useful for measurements on films containing BEA or

Agerite superlite.

40
xRADIOACTIVITY COUMTING

Liquid Scintillation Counting

We have chosen the liquid scintillation technique to monitor the level of

radioactivity. This method is capable of detecting relatively low levels of

radioactivity with the background counts being in the order of 20-30 counts

per minute (cpm). It is also free from, affects of sample geometry. However,

the radioactive material should be soluble in the counting cocktails or in solvents Gomnatible with the counting cocktails. This method is a desrructive

testing, therefore the test meterial is not easily recoverable from the counting

solution

.

Tne general methodology is described in several books .

° A commercial liquid

scintillation counter with microprocessor control is used in this work.

In the determination of radioactivity in numbers of disintegration per ma_nute

(dpm) from, the observed counts per m±nute, we have adopted the method of locating

the upper edge of the pulse height distribution for the Com.pton electrons , generated

in the counting solution by an external radioactive -^-^'Cs source, as the measure

of the degree of quenching. This method provides a leather universal calibration

cuime of counting efficiency versus degree of quench over a verp^ wide range of

quenching conditions . With extensive testings , we have found that the ultimate

precision in dpm for the counter operated in the above mentioned mode is of che order

of 0.2%, even when the total counts are much greater than 10®. In general, a precision of 0.5% can generally be realized. Thus at low counts the precision is

llmired by the counting statistics (although the actually observed precision is

often about twice that indicated by Poisson staristics ) , however at high counts

the precision is limited by tne stability/ of the instrument and the reproducibility in the determin.ation of the Compton edge or of the shift of the Compton edge

41
from an unquenched counting solution. Therefore we have generally used a limit

of 2 a = 0 . 2 % ( 10 ^ counts) and/or 10 minures of counting time to terminate the

counting process for routine work. A collection of repeated counts' to increase

the reliability of the results is usually recorded on a tape and then processed

by the NBS central computing facilities.

Calibration of Liquid Scintillation Counter

The calibration results are listed in Table 5 and shown graphically in Figure

15 . The results were obtained on a commercial unquenched standard , a commercial sraridarc quenched set and on a variety of quenched solutions made fromi a

Mational 3'ureau of Standards Standard Reference Material (MBS-SRM) 4222 and

various commercial counting cocktails . The commercial unquenched and quenched

set are sealed in glass vials and use CCI 4 as the quenching agent. All these

standards are Traceable to iBS-SRH NaoCO^ and are cuoted with an mcer^aintv of 3%.

In calibrating the liquid scintillation counter by NBS-SRiM 4222 , Carbcn-14

standard ( Hexadecane ) , 14 samples were weighed out. The samples weighed from

0.02 to 0.1 g. 'The certified specific activity is 3.832 X 10*^ disintegration

per second per gram (dps/g). To each of the samples, a certain amount of counqing

cocktail was added and then counted . To these , ethanol and counting cocktails

in q'arious ratio were added to vary the quenching levels and then counted. The

liquid level in the counting vials varied from 0.5 ml to 20 ml. From previous

experiments we have established that the liquid level in the counting vial , varying

from 1 to 20 ml, does not effect the counting efficiency beyond the precision of

the counting process.

The degree of quenching is represented by the so-called H^, which indicates

a shift in the position of the Compton edge from that of an unquenched solution.

Tne Hf is a logarithmic representation of the energy snectrijm where

Lnteger numbers from 0 to 10.00 are used to indicate the energy level up to 2 MeV.

42
Table 5

Calibration of Liquid Scintillation Counter

1.

Efficiency

Cornmercial Unquenched Standard

Efficiency

(31500 dpm.)

Hr? Efficiency

0 0.963 0 0.956

9 Cornmercial Quenched Set (190300 dpm)

19 0.957 19 0.958 20 0.959

~'3 0.933 80 0.929 80 0.929

14:’ 0.8"! 1 5o 0.864 152 0.867

200 0.~90 210 0.""4 206 0.785

21" 0.^56 228 0. '58 224 0 . "48

248 0.676 263 0.646 255 0 . 666

5

.

XBS-SRM 4222 (Carbon-14, hexadecane, 5.93-. x

10'^ dps/g )

EP GP HP

I. 86300 dpm I

.

67240 dpm I . 257200 dpm

48 0.934 •69 0.927 65 0.925

55 0.931 55 0.933 54 0.956

89 0.915 91 0.915 85 0.920

116 0.889 113 0.89" 109 0.901

141 0.867 136 0.880 130 0.884

168 0.838 162 0.852 157 0.858

191 0.799 182 0.820 180 0.824

TI. 112900 dpm 11. 134500 dpm II. 112200 dpm

514 0.48" 283 0 . 566 510 0.501

203 0. ""9 192 0.804 19" 0. '99

217 0. "42 225 0. "58 204 0."6^

43
Table 5 (continued)

H// Efficiency H// Efficiency

NA OCS

I. 120200 dpm I. 51120 dpm

323 .442 27 .934

192 .805 21 .936

205 . 784 63 .924

217 .747 76 .916

112 .889

142 .865

159 .843

II. 148100 dpm II. 134100 dpm

44 .942 309 .495

25 .948 182 .822

89 .919 192 .807

119 . 897 208 . 772

182 .824

III. 105000 dpm III. 162400 dpm

278 .573 36 .937

303 .514 208 . 770

146 .866 108 .897

171 .836

212 .762

259 .634

IV. 187900 dpm IV. 194600 dpm

56 .933 48 .933

288 .574 285 .561

387 .241 418 . 116

427 .111 457 .033

459 .031 349 . 362

351 . 349 282 .613

245 .679 269 .'612 238 .701

44
K 'A0N3I0IJJ3

45

i.oiency

ver’su;j

Quench

L,oveJ

.
is obvious from the composite graph, Figure 15, that regardless of the

tyzes of counting cocktails , -^C sources , liquid levels in the counting vial

qjuenching agents used, the calibration curve for non-aqueous sample is quite

universal in nature with a scatter of about 1% in counting efficiency which

is well within the accuracy quoted or certified by the various standards.

and

46
EXTRACTION

Methods of Extraction

Two extraction methods were used, i.e. , (1) continuous extraction into limited

solvent volume and (2) discrete extraction simulating infinite solvent voiume.

In method (1) an extraction vial of 40 ml in volume with a teflon valved

cap is used, Figure 16 . The solvent in the vial will only meet glass walls and

teflon surfaces. A silicone rubber plug is situated above the valve and may be

exposed to the solvent vapor only while an aliquot of 1 ml is taken through syringes

from time to time. The plastic sample may sometimes be surrounded by a nictrome or

stainless steel screen to orevent it from sticking to the walls or another sample if

more than one piece is being extracted in the same vial or if the sample has lower

density then the solvent.

In method (2), the plastic sample is immersed in about 10 ml of extracting

solvent in a 20 ml counting vial. At specific times the sample is removed from

the solvent, rinsed and placed in a vial with fresh solvent to repeat the extraction process.

Method (1) should be 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 tima increases , there is only very small change in the concentration

of extracted material in the solution, whereas the weighing or ratio error nay 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 experinental

difficulties

.

We may employ a third method: many plastic samples are placed in individual

vials with solvents at similar surface to volume ratio. Each vial is then counted

at different times (both the solution and the plastic sample for ins residue activity).

47
Figure

16.

-'ly^yica]

Extraction

Vial.
This method may be operationally simpler than that of Method (1). It yields similar

results and has similar shortcomings to those of Method (1). Furthermore,

additional scattering of the results may arise from the non-uniformity of the

sample

.

For all the methods menrioned the extraction vials may be shaken by a wristaction shaker in a temperature environment chamber, or placed in a temperamure

controlled aiuminum block on a shaking table as shown in Figure 17 . When the

extraction process is ended, the residual radioactivity remaining in the polyethylene

sample is extracted by dissolving the samiple in toluene at nigh temperarures . We

found that the single crystals or precipitates of polyethylene in the counting

vial does not effect the counting efficiency beyond the normal scattering of the

counting results

.

Resulrs of Extraction

The experimental results on the extraction of labeled C-, polyethylene

are listed in Table 5 and S'ummarized in Table 7

.

The experiments are coded by two letters followed by a number to facilitate

easy identification. ‘The first letter denotes the sample plaque designation as that

in Table . The second letter denotes rhe extracting solvent , e . g . , F for

ethanol, H for heptane, 0 for octadecane and W for water. 'The number denotes the

test number of the sample-solvent combination.

The results are expressed in terms of M-|-/Mq, where M^ is the original am.ount

of labeled Cj_ 0 H

2 q in the polyethylene, and M^ is the cumulative amount of labeled

C-igH^g extracted at time t.

In Method (1) the amount extracted between time t-1 and t is obtained by

A* = {[(Nt/Et)/Wa,tl - (5D

where A is the activity increment , N the count rate , E the efficiency of counting

,

W^ the weight of aliquot and Wg the weight of total solution . In Method ( 2 ) the

49
50

Figure

17.

Typical

Set

up

for

Extraction

Experiment
Table 6

Migration of from Polyethylene

t Mt t Mt t Mt

hours Mo hours Mo hours Mo

I. Into Heptane at 24°C

AHl AH 2 BHl

0.1 0.046 0.025 0.026 0.017 0.086

16 0.836 0.05 0.039 0.033 0.124

23 0.891 0.1 0.053 0.067 0.183

40 0.932 0.25 0.083 0.133 0.28

70 0.955 0.5 0.115 0.25 0.458

136 0.964 1 0.163 0.5 0.683

216 0.969 2 0.242 1 0.804

308.5 0.972 4 0.378 2 0.866

357.5 0.975 8 0.662 4 O.904

665.5 0.974 28 0.902 6 0.919

72 0.947 22 0.950

151 0.962 30 0.955

244.5 0.968 94 0.968

293.5 0.970 148 0.972

437.5 0.97 216 0.974

462 0.974 286.5 0.975

511.5 0.974

578.5 0.975

CHI

0.,033 0.,008

0.,067 0.,015

0.,133 0.,020

0.,25 0.,029

0., 5 0.,039

1 0.,056

2 0.,086

4 0,,128

8 0.,196

27,,25 0.,467

71,,25 0.,663

150,,5 0., 787

243,,75 0,,834

292

,

, 75 0.,848

316., 75 0.,853

460., 75 0.,869

510,, 75 0,,873

603,, 75 0.,878

775 0,,887

1008 0.,894

DHl

0.033 0.015

0.067 0.026

0.133 0.041

0.25 0.063

0.5 0.108

1 0.202

2 0.342

4 0.477

20 0.693

28 0.732

92 0.817

146 0.838

196 0.85

289 0.861

460 0.373

692.5 0.885

51
Table 6 (continued)

t Mt t Mt

hours Mo hours Mo

II. Into Heptane at 60°C

AH 3 AH4

0.25 0.265 0.25 0.26

0.5 0.382 0.5 0.378

1 0.576 1 0.572

2 0.860 2 0.859

4 0.968 4 0.968

8 0.982 8 0.982

24 0.986 24 0.986

48 0.988 48 0.988

120 0.990 120 0.990

168 0.991 168 0.991

III. Into Ethanol at 24°C

BEl BE2

1 0.114 0.083 0.016

3 0.16 0.167 0.023

19.5 0.335 0.33 0.035

51.5 0.^87 0.67 0.052

116 0.639 1 0.069

195 0.735 2 0.109

288 0.778 4 0.166

337 0.799 8 0.237

387 0.816 24 0.367

505 0.832 48 0.485

648 0.857 78 0.578

820 0.855 216 0.720

1220 0.883 409 0.809

1556 0.900 745 0.865

1081 0.902

IV. Intc) Octadecane at 60°C (BOl)

BOl

0.25 0.687

0.5 0.922

1 0.978

2 0.984

4 0.987

8 0.990

24 0.992

48 0.993

127 0.994

168 0.995

52
Table 7

Summary of Extraction of Cj_gH 3 g from Polyethylene

Weight ^0 £ (nom. ) C^(nom.) t °i Solvent

Sample g Mdpm/

g

mm wt% C^gHgg °C Solvent cm.^ / s Absorption

AHl 0.449 5.03 0.7 1 24 H (1X10-^) 4.5

AH2 0.165 5.20 0.7 1 24 H 7X1 0~5 5.1

AH3 0.138 5.10 0.7 1 60 H 7X10~® 4.4

AH4 0.150 5.14 0.7 1 60 H 7X10"^ 5.2

BEl 0.075 5.21 0.2 1 24 E (2X10-’^^ ) 1.0

BE2 0.041 5.18 0.2 1 24 E 8X10"^

1.0

BHl 0.043 4.91 0.2 1 24 H 9X10-^ 3.6

BOl 0.160 5.16 0.2 1 60 0 (3X10-®) 5.1

CHI 0.160 3.51 0.7 0.01 24 H 1X10-® 4.3

DHl 0.054 2.13 0.2 0.01 24 H 2X10“^ ^ 2.0

Solvents = E - Ethanol, H - Heptane

,

0 - Octadecane

Thickness 1 = the variation in the thickness is generally within + 0 .05 mm.

Solvent Absorption = measured right after the sample was removed from the solvent

53
activity extracted between t and t-1 is simply the total activity ini the extracting

solution, i.e., = N-(-/E-|-.

In Method (3) M^/Mq i-S obtainable directly from each vial, thus

where is the activity in the solution and Ap the residue activity in the polymer.

The initial Dp is estimated from the approximate expression of

wh.ere D is the diffusion constant, t the time, I the thickness and M the amount

extracted at infinite time. Substitution of M for M should make less than 10%

0 “ error (cf. section on the discussion of the results).

The amount of solvent absorbed was obtained by blotting the rinsed test

specimen at the last measurement with filter papers and weighing immediately.

Adjustments have also been made to the weight loss due the loss of the migrant.

Data on the extraction of CP 3 H38 from polyethylene, BWl, is not presented

here, because of the inconclusiveness of the result. The radioactivity in the

aqueous extract is very close to that of the background even after 2 -months of

extraction at 2UOC.

As all the results are listed and shown here in terms of IL/M , it is someL o tLmes more convenient to express them^ in terms of the FDA's expression for extractives in terms of ppm (ug of extractives per m.l of solvent or per 0.1 in^ of

polymer surface area) . To do this one may convert the values by a factor

expressing the original concentration of the extractives in 10~^g per square inch

of surface area. By approximating the density of polymer as 1 g/cm^ , the factor

is 0.32 X 10~® CQil , where '^o is the concentration of the additive in weight

fraction and i is thickness in cm.

(52)

CO

54
DISCUSSION

The experimental results are grouped together to show the eofects of thickness, additive concentration in the polymer, temperat’ure and solvent. Tlnree time u -U

scales, i.e., log]_gt, t^, and t -, are used to plot the results with each scale

emphasizing a different time domain. Figijre 18 shows the corresponding scale in

t versus the three scales . For all the subsec:uent graphs , the dashed lines in

graphs A and 3 denote the extension of a linear dependence, whereas the cashed

lines (where n is an integer) denotes the factor for the coordinates as lO”^, whereas

in C denote the extension of a linear t“^ dependence.

Fig'ure IS and 20 show the effect of 0.7 and 0.2 mm nom.inal thicknesses

for AHl, TU2 and 3H1 at 1% C^gK^g concentration, and for CHI and DHl an 0.01%

C. aH-a, resoectively. Over most of the ranges, IL/M^ for 3H1 is about four times

that of AH2 , with a thickness ratio of 3K1 : AH2 = 1 ; 3.5. The initial diffusion

constants , estimated from the initial portions of the extraction experiments

,

for AH2 and 3H1 are in good agreements with the thickness variation as per Eq. (52).

Therefore initially either the rate or the amount of additive migration per '-unit

surface area should be the same regardless of the sample thicknesses . At long

times, when most of the additive has been extracted, the total amount migramed per

surface area will be proportional to the thic^tness. Only qualitative agreements

may be -draim from the results of CHI and DHl.

The effect of concentration varying from 1% to 0.01% of added C. .,H,„ is

la 00

shown in Figure 21 and 22 for AHl, AK2 and CHI at 0.7 mm thic]<ness, and for 5H1

and DHl at 0.2 mm thickness, respectively. Over most of ranges there is only a

change by a factor of 3 in the for a hundred fold change in the added C-, gkgg

for the 0,7 mm samples. Decreasing the concentration by a factor of 100 seams to

decrease D^ by a factor of 10. However there appears a 10 fold change in the

amount migrated at short times between the 0 . 2 mm samples 3H1 and DHl.
Ml

oral

Ion

of

n*~C18H38

from

Polyothyl^no

Into

C7H16

CO

Q

OJ

QQ

Q

QI Q

C\JI Q G)

'J? w0\ a / "tW

58

Figui’e J

'jA.

Migration

of

Cjgll^g

irom

Polyethylene -

1%

C-|^gHgg

Sheets

into
MONTHS

57

.

(HOUR)
It aDDears that the results from the experiment DHl or the sample D is

somewhat peculiar. Unlike AH2 , BHl and CHI, even the initial portion of the DHl

extraction curve does not have a t^ dependency. It also absorbs least amount of

solvents, C.^H^g (Table 7). If one artificially brings the initial DHl curve up

so that it has a t^ dependency and that its initial diffusion constant for DHl

is simular to that of CHI, then the new curve will also indicate a 3-fold change

in ^ 10-fold change in D^.

Tne effect of temperature is shown in Figiure 23. A 36°C temperature increment

from 24 to 6Q0C increases D^_ by a factor of 10 or the amount migrated by a factor

of 3 at short t.

Changing fromi non-polar solvent to polar solvent from to ethanol

decreased the D^ by a factor of 100 or the amount extracted by a factor of 10 at

short times as shown in Figure 24

.

At this time rhe results on BOl, Figure 25, may not be compared directly with

other results collected for the effect of a single variable. However if we assume

the migration of C^gH^g has the same temperature dependency as that of C^gHgg into

C.yH^g then the amount migrated into (^2.8^38 about 2/3 of that migrated into C.^H^g

at the same temeprature under otherwise the same conditions

.

In comparing the two extraction methods , i . e

.

, continuous extraction with

aliquot taken at different times and discrete extraction- with new solvent each

time, the differences are very small even at large t as shown in Figure 19 anti

21 (C) for AHl and AH2 and in Figure 24 (C) for BEl and BE2 . A set of duplicate

measurements, AH3 and AH4, was made at 60°C with virt^ually identical results as

shown in Figure 23.

56
• • •

(VJ N

H59

Figure

19

H.

Mignlion

ul" 1

r'l^ni

Po

[yell

ly

Lei

leL%

i|g

^^33

SheeLs

into

0,^11

e)l

240

('g

(iro.7

nun:

,.AH1,

AT2.

V,=

0.2

niia:[)BHl
MlQpation

of*

n"~Cl0H38

f*rom

PolyotHyl

Into

C7H16

at

24C

<9C

<9 o II ;±J I

<D

Q; S

CO Im

CO r—

'Cn I

0) I IIIi

60
Mi

Grot

ion

of

n—

C18H38

from

Polyethylene

Into

C7H16

cs>

<n3

<s

G3

0^1 GJ

GJ

'Sf / ^ 1^1

61

I'igiire

20

A.

MLgrvition

of

C,'

^loo

fi'oni

F'o I

ye

lliy

Lene0.01% C

Sheets

into
Migration

of

n—C18H38

from

Polyethylene

Into

C7H16

at

24C

in

CO

Q

CO

in

CNJ

;Ms,

GJ X

C\J

in

%

9

<D

in

Q

oo CO 'T OJ cs

/ 1/1

62

I'igure

20

B.

Migration

of

Irom

Polyethylene

-

0.0J%

C^gH^g

Sheets

into
Mitral

Ion

of

n—

C18M38

from

Po1

yolhy i

«ne

Into

C7H16

at

24C

53

rigut'C

'/t.)

Mig'i'alioii

t;l'

liMiii

l-'olya

Lhy

laneO.UL%

‘^'j

inlo
Ml

O'Neil

Ion

of

n—

C18H38

from

Po1

yolhy 1

ono

Into

C7H16

at

24C

T

CO

GJ

CMCDG

<>1

'SU*10\ £

JGG

CJq

Oj M

OJo; cn

<vc0) rH • /—

OJo

a.g

CO

CO

o~' Oco• HM<I—I Z3 MH

o\o OO

II

OO<

o\° i 1

II cado

CN

64
'S) CO I!i Q

CO

'J3

v'J N

r\L

QX

CNJ 'V

vMN

10^ QC O

'XO / ‘W ( 65

I'iyui’C!

:M

1^.

Mi.gr

’citioi’i

of

C,

Jl,,o

U.7

nun

lV).lye U

ly

l.cj

le

Shuels

iiilcr

C.,!!
Mlgrallon

of

n~C18H38

from

Polyelhyleno

66
Migration

of*

n—C18H38

from

Polyethylono

into

C7H16

at

24

C

COQ

cyo

CNi

1 O

CVJ

i

a5

0

<

67

Migr'dlioii

ol"

I'uii

Fo

l.yo

Uiy

lene

Sheets

iiilcj
Migration

of

n—

C18H38

from

Polyothyleno

Into

C7M16

at

24C

OO

<vi X

r\

<0

ur

•N. « T E

hCMO

LOm

rigure

22

B.

MigraLion

ot

ir^oni

(J.2

iran

Polyethylene

Sheets

into

C^H
Migration

of

n—

C18H38

from

Po1

yolhy

1

one

Into

C7H16

at

24C

69
Migration

of

n—

C18H38

from

Polyelhyleno

Into

C7H 16

at

24

and

60C

COo

<D

(\J1 1G) 1 O

03

4-1 (U03 00

CO

ro

x:00I—i u

o\oI

'03 5

03>, ^ d L ^

cn O3• H4-

j!

b£) <

CO

CNJ9

bO <

CJoa

CO

Cc<

r-J

CJo

cJCO

CJ IIIIIIIIII\JIIIItI

70
Migration

of

n-”C18H38

from

Polyethylene

Into

C7H16

at

24

and

60

C

• • #

CO

CO

I

q)

<

/

1
O) O) O) o

'T

CO

#

OJ

N

T

r\

9

S

on /

72

Fdgur'e

23

C.

Migraton

of

C^gH^g

from

0.2

iran

Polyethyierie

-

1%

C^gHgg

Sheets

into

C

H

.

240C:.A.AH1,

/.xAdl2.

60°C; L

,

AH3

,>

A114

.
Migration

of

n*“Cl8H38

from

Polyethylene

Into

C7H16

and

Ethanol

at

24C

T

-i_) (U

OJ CO

CO

CO

'~coI—!

CJ1—( I

q;3

>>

QJ>1 I—I O

o£} 2

oO / td

73

aI

Into

C.,H. :!

BHl.

Into

Ethajiol:

.'cE5El,'"''Bi:2.
Mitral

Ion

of

n*-Cl

81138

from

Polyolhylen©

Into

C7H16

and

Hilhanol

al

24C 1 / t'd

74 1I

^''ip j

%[- |

At []

oA |fi\

iinii

,;•(] I

ll”

\')

uoi
• •••••

00

iMN

7

• S

V-/

0-i

o

w

4-^ CUo;

(f)00-o

CO a

o\°

>.

30oo O

O

co

n3

Vi30

a

OJc

5o

75

dt.

2UO('_

Into

Bill.

liit:o

litlidnol:

'.BL'l,

'

BL:B.
Migration

of

n“C18H38

from

Polyelhylono

Into

C18H38

1

76

Sheets

into

uniabeled

C,

at

60°C.
Mlarollon

of

n“CI8H38

from

Poiyolhyleno

Into

C18H38

at

60C '1' / / inIo

ui

ilabe

led C.

p^'ioo *

bO°C.
Ml

or

at

Ion

of*

n—

C18H38

from

PoI

yolhy 1

one

Into C1

8M38 / V/^

78

SheoLs

inlo

ui11

abe 1

ec'l
Fig'oi^e 26 A and B show the migration beha'/ior as calculated from a solution

for the diffusion from a plane sheet with the assumption that the diffusion coefficient is concentration independent and that the sheet does not swell

il _ - 3 \ ' 1

M

= - - -2 > _ . [-D(2n+D

n=0 "

At M-/M < 0.5, M^/M is oroDortional to Thus the

may be esrimated by the approximation for short tim.es

,

initial diffusion constanr

Eg. (52). At long times

^ [in(M -M)] (5U)

Tnerefore the plot of InCl-lh/M ) versus t at 1-h/M >0.5 is highly linear, as shown

in Figure 27. Tne behavior at long times, or as approaches 1, as calculated

from the series solution is shown in Figure 26 C and D for (i^/M versus l/t"2 . it

seems that when the time scale is expressed in 1/t^, the approach of to is quite

sudden. The experimental results, Figure 19-25 (C), however seem to indicate

a strong linear 1/t^ dependence at long times, and this linearity may start to

aDoear - in some cases when M^/M is about 0.5. 'Thus the above m.entioned soluricn - u oo

is not sufficient to describe the overall behavior of these experl'ients . 'The difference mav be due to swelling by solvent, concentration dependent diffusion constants and perhaps edge effects

.

Additional general conclusion may be drawn from the limited set of the extraction data

;

(1) No "blooming" of additives was observed in these experiments. This was Indicared in Figures 19-2 o (B) where Liie exiraciion c-urves Con oe ex urc;.i^ola.ted

through the origin at t=0. An intercept at positive values of -T t=0

would indicate the presence of blooming. This observation is expected for

oligom.ers ar moderate concentration, as they should be himhly

79
/ IW

80

Figure

26

A.

Calculated

Diffusion

Cui'ves

versus

log(m)ii^t/)i^

)

.
81

C!a

Iculalc'd

DiJ 1

is1i.

)i1

(djtve;;
® OO CO CJ <s

* * A A

82

Figure

26

C.

Calculated

Diffusion

Curves

M^/M^

versus

1

/

(

4

I>

iT ^t

/£^

)'2
000

’

83

2l)

D.

C>-j

Iculal

t\l

Di.llusic^n

('urves

M(./M

v/e^rsu:;

l/(*i!);r
- 1

84

TIME

Figure

27.

Calculated

Diffusion

Cur’ves

logd-M-^/M

)

versus
compatible in the polymer matrices.

(2) The initial migration kinetics obeyed Fickiari behavior, i.e. , M- cc t^. This

behavior may be seen as a slope of d log(FLj-)/d logt = in Figures 19-25

(A) and a linear portion at small t for ti. vs t^ in Figures 19-25(8). However this behavior only lasted to ^ 0-2, or less for these experiments.

(3) There is an apparent enhancement of the diffusion of the additive molecules

by solvent penetration or swelling of the polymer, as seen in Figure 19-25

(3). The behavior cannot be fully described by Fq. (53) and Figure 26, nor

by some simple model described in section II of this report. In Table 7

we see that the amount of solvent absorbed by the test pieces at long times

are generally in the order of 4-5%, with the exception of DHl, for heptane

or octadecane either at 24 or at 60°C. The amount of ethanol absorbed

seemiS to balance out the weight loss of C

2_ 3 H3 g of 1%.

Separate weight uptake measurements on unlabeled polyethylene plaques also

indicated a leveling off of weight_gain at 4% C^Hi ^ at 24°C after 4 to 48

hours. Approximately 95% of the absorbed C^H-, may be driven off in 24

hours by air* drying or by vacu'um evaporation. 'The remaining 5% of the absorbed

solvent takes much longer time to come out. The weight uptake of octadecane

at 37°C is about 4.5% at 24 hours and about 5% after 500 to 1000 hours.

Tne time when the polymer reaches sat'uration swelling by the solvent seems

to correspond to the time with maximum increase in the extracrion rare.

(4) When t is large, vs. 1/t^ plots generally give a linear appearance

as in Figure 19-25 (C). These plots thus yield a reasonable estimare of

M^. We used Mq, the initial total amount of additive in the polymer, to

normalize the results here instead of the customary M^, the amount desorbed

at infinite time. For die case d lnQi,-M,u)/dt - at large t, it would

take a fitting procedure and some judgment in order to estimate the or

values . is more readily a.vailable in higher precision than the exrra85
polated value of In most experiments, except for AHl and BEl, and

should be identical. However it is obvious from Figure 19-25 ( C)i that

is about 99% of for the 1% C^gH^g samples and about 93-94% of for

the 0.01% C^gHgg samples. One of the likely explanations is that a small

portion of the oligomer additive gets incorporated in the crystalline portion of the polyethylene and thus migrates at much slower rates and behaves

differently from the additive in the amorphous portion of the polyethylene.

Therefore it is rather difficult for the experiments described here to yield

any reasonable estimate of the equilibrium partition coefficients for systems

favoring the solvents

.

(5) The average labeled C-,oH^o content for all samples derived from both sample

lo oo plaques A and B with sample sizes greater than 1.5 cm X 1.5 cm., is within

1% of 5.15 Mdpm/g—with the exceptions that AHl and BHl are about 3-5% off.

Both claques A and B were molded from, the same 1% C^oH^q - colyethylene

powder mix. This indicates a relatively 'oniform sample on -a macroscopic

scale. The labeled C^gHgg concentrations in sample plaques C and D are

very much different, even though both plaques were molded from the same

0.01% C., gl-igg - polyethylene powder mix.

86
IV. REFERENCES

1. Flory, P.J. , "Principles of Polymer Chemistry", Cornell

Univ. Press, Ithaca, N. Y. 1953.

2. Tomoa, H. , "Polymer Solutions", Academic Press, New York

1956.

3. Flory, P.J. and Rehner, J. , J. Chem. Phys., (1943), 11,

521.

4. Rogers, C.E. , Staruiett, V., and Szwarc, M. , J. Phys. Chem.,

(1959), 1406.

5. Kwei, K.P. and Kwei, T.K., J. Phys. Chem., (1962), 66,

2146.

6. Flory, P.J., Orwoll, R.A. , and Vrij , A., J. Amer. Chem.

Soc. , (1964), 86, 3515.

7. Flory, P. J. , J. .4mer. Chem. Soc. , (1965), 1333.

3. Eichinger, B.E. and Flory, P. J. , Trans. Faraday Soc.

(1968) , 2035.

9.

Flory, P.J. , Discuss. Faraday Soc. , (1970), 7.

10. Sanchez, I.C. and Lacomte, R.H. , J. Phys. Cnem. , '(1976),

2352, 2568.

11. Sanchez, I.C., "Polymer Blends", D.H. Paul and S. Newman,

editors. Academic Press, N. Y. , 1978, Ch. 3.

12. Sanchez, I.C. and Lacorabe, R.H. , J. Poly. Sci. , Pol'/mer

Letters Ed. , (1977), 71.

13. Sanchez, I.C. and Lacombe, R.H. , Macromolecules , 11 , 1145 (1978).

14. Bueche, F. , J. Chem. Phys . , 21 , 1850 (1953)

15. Turnhull, F. and Cohen, M.H. , ibid , 31 , 1164 (1959).

16 Westlake, J.F. arid Johnson, M. , J. Appl. Pol. Sci., 19, 319 (1975).

17 Crank, J. , "Mathematics of Diffusion", Oxford University Press, London (1975).

18 Wagner, H.L., md Verdier,_ P.H. , Editors, N3S Snecial Publication 260-42,

"The Characterization of Linear Polyethylene SRF: 1475" (1972)

19 Wang, C.H. , Willis, D.L. and Loveland, W.D., "Radiotracer Methodology in

the Biological, Environmental and Physical Sciences." Prentice Hall,

1975.

20 Meame, K.D. and Homewood, C.A. , "Liquid Scintillation Counting". John

Wiley and Sons , 1974

87
APPENDIX A

Molecular parameters for low molecular weight fluids can be estimated

from a knoiTO heat of vaporization AH^, a vapor pressure P, and a liquid

specific volume V£ all at the same temperature T:

AH^/RT - iln(vg/v£) V ' 6' K' (A.l)

1 + (v-1) £n (1-p)

T* E £*/R = (AEv/R)/rp (A. 2)

P* = 1/PV£ (A. 3)

V* = M/rp* (A. 4)

P* = RT*/v* (A. 5)

The reduced density p required above satisfies the following equation which

must be numerically evaluated:

[2AEv/RT - £n(vg/v£)][p + £n(l-p)] - [AE^/RT - l]p£n(l-p) = 0 (A.&)

xj’nere AE^ is the energy of vaporization and v^ is the specific volume of the gas

phase

.

In deriving the above results we assumed that P was low enough so that the

vapor phase could be treated as an ideal gase and that Vg>>V£. Under these con- ditions the entropy of vaporization AS^ is given by

AS-y/R = AHy/RT = r [ l+(v-l) £n (1-p) ] + £n(vg/v£) (A. 7)

and

AEy = AH^ - RT = rp/T (A. 8)

Using equations (A. 7) and (A.8),^r and T can be eliminated in the equation of

state (12) to obtain (A. 6) with P = 0.

For a binary solution the only unknown parameter is AP* or A (see text)

.

There are variety of experimental methods by which this parameter can be determined. One of the simplest methods is to use solution densities. The equation

of state for the solution is formally identical to that for a pure fluid (see

Eq . 25) except that the reducing parameters, T* , P*, and p* are compostion

dependent (see reference 13). At atmospheric pressure P - 0, and the equation

of state can be solved for T* which is a function of AP*

;

T*(AP*) = - T[£n(l-p) + (l-Vr)p]/p^ (A. 9)

Thus measurements of density will yield values of T* and AP*.

In Appendix 3 a brief description is given on how liquid densities can be

accurately determined on a digital densimeter.

88
Appendix B

Densities of solutions and solvents are being determined by comparison with

standard density fluids in a Mettler/Paar vibrating ceil type densimetry system.

The densimetry system consists of two external vibrating cells connected to a dual channel processing unit.

For temperature control, thermostat fluid is pumped from an external con- stant temperature both through the thermal control cylinders of the two cells

connected closely in series. With the present temperature control system, the

temperature of the thermostat fluid can be selected to within O.Ol^G and controlled

with a variation of less than ±0.01°C by a thermistor control sensor and a proportional controller. The effects of small variations in temperature on the density

data were suppressed by operating the densimeter in its optional phase-lockedloop mode, in which the oscillation frequency of the cell containing the solution is continuously compared with the oscillation frequency of a second cell

containing either a standard density liquid or a solvent of the solution system

under investigation. The second cell functions as a time interval standard that

responds sympathetically to the same small variations in the thermal environment.

The density measurements in the present report were conducted at temperatures

indicated by a copper-constantan thermocouple and a potentiometer which demonstrated

a sensitivity of 0.003°C. The calibration of the thermocouple-potentiometer combination is traceable to a Mueller bridge and a platinum resistance thermometer which

in turn had been subjected to a certified calibration in the NBS Thermometry Section.

The hot junction of the thermocouple was stationed in the temperature indication

tube of that densimeter cell containing the fluid of density to be determined. The

uncertainty in indicated temperature was estimated to be ±0.01°C. Plans are under

consideration to improve both control and indication of temperature for future density determinations.

The secondary density standard liquids were standardized by comparison in the

densimeter with two primary density standard fluids, the lighter of which was the

ambient air of the laboratory, and the heavier primary density standard was a sample

of xylene. The density of the air was computed from its temperature in the densimeter cell and the absolute barometric pressure. The density of the primary standard

xylene had been determined by Schoonover [1,2] from its buoyancy on high purity

silicon single crystals at a series of nine temperatures from 10°C to 23^C. On the

basis of

[1] Bowman, H.A. , Schoonover, R.M. , and Carroll, C.L.

"A Density Scale Based on Solid Objects",

J.Res. Nat. Bur. Stand. (U.S.), 78A 13 (1974)

[2] Bowman, H.A. , Schoonover, R.N., and Carroll, C.L.,

"The Utilization of Solid Objects as Reference

Standards in Density Measurements",

Metrologia 117 (1974)

these measurements Whetstone et al (3) have reported an expression for density of the

primary standard xylene versus temperature as

0.884671 - 0.00086147 (T, deg C)

with a standard deviation of 1.2 X 10~® in the fit of density to temperature.

89
Subsequent measurements by Greer [4,5], using the magnetically suspended buoy

method, very closely duplicated the thermal density coefficient and indicated

it to be linear in the temperature interval from 14°C to 47°C. This value for

the thermal density

[3] liThetsone, J.R., Cameron, J.M..

Carroll, C.L., and Gallagher, W.H.

NBS Internal Report 77-1533 (September 1978)

[4] Greer, Sandra C., private communication

[5] Greer, S.C., and Hocken, R.

,

"Thermal Expansion Near a Critical Solution Point",

J.Chem.Phys. 6_3_ 5067 (1975)

coefficient will also be used with the secondary density standard xylene.

The densities of a substantial reserve of two secondary standard liquids,

heptane and xylene, were determined at 35°C in the densimeter calibrated with

air and the sample of primary density standard xylene:

Sec. Den. Std. , gcm~^ 35.00°C dt, gcm~^ deg~^

Heptane 0.672157 -0.000840

Xylene 0.854254 -0.00086147

The thermal density coefficient tabulated above for the secondary density

standard heptane is quoted by Riddick and Bunger [6] to be applicable in the

temperature interval from 0°C to 50°C, and it will be used as a provisional

value until either superseded or substantiated by determinations within the present project.

[6] Riddck, J.A., and Bunger, W.B., page 87 in

"Techniques of Chemistry, Vol. II Organic Solvents - Physical Properties and Methods of Purification" 3rd

(1970) Wiley-Interscience , New York

90
Appendix C

Mathematical Analysis of Additive Extraction with Solvent Absorption

The plastic is in the shape

concentration of the additive of

sheet with the surfaces at x = S, tive is given by the solution of

of a sheet of thickness 2£ containing an initial

Cq

•

Let s be the position coordinate in the

and K = -i . Then the concentration of the addioc 3 3c

IF ' Ix

(C-1)

for the boundary conditions

c = Cq at t = 0 , -£ < X < ^ (C-2)

c = 0 at X = 1 and -I for t > 0 (C-3)

In addition to the additive diffusing out of the sheet, the surrounding

liquid will diffuse into the sheet. At zero time, its concentration will be 0. The liquid concentration at the side of the sheet is C and its diffusion

coefficient is D . Then by Crank

s

^

Cg ' (2n+l)2,-x (2n+l)2,+x

yr- = H = 2-- (-1)'^ [erfc—r-niv— + erfc ——p==

n=0 2iDgt 2,/Dgt

Substituting eqs. 46 and C-4 in eq . C-1 gives

(C-4)

3t ^oSx ^

where K = kC /D„

OO The concentration of the additive is thus given by the solution of eqs.

and C-3.

We transform to the reduced variables

T =

X = x/i

C = c/cq

The eqs. 6 and 7 may be written

(C-5)

(C-6)

C-5, C-2

(C-7)

(C-8)

(C-9)

H £ (-1) P " [erfc P-0.5-X/2

v''TDg/Do

+ erfc p-0.5+X/2^ (C-10)

where p = n + 1

91
(c-11)

3 c _ _j C > oT ~ 3X Jx

where F = 1 + KH (C-12)

The boundary conditions eq. C-2 and C-3 become

C = 1 at T = 0 (C-13)

C = 0 at X = 1 and -1 (C-14)

In order to solve eq . C-11 by finite differences, intervals

used, so that,

AX and AT are

X = (I - 1)AX (C-15)

T = (J - DAT

We choose 2M intervals for X so

(C-16)

AX = 1/M

By symmetry

(C-17)

C(X,T) = C (-X,T)

or

(C-18)

C T o ~ C T

The boundary conditons eqs . C-13 and C-14 are

(C-19)

^1,1 " 1 (C-20)

^M+] T " ^-M+1 " 0

, u , J By eqs. C-10, C-l5 and C-16

(C-21)

^ 'p-0.5 , (I-l)AX

^i,j ^

[J-1)ATD„/D ]'2 2 p=l _ so _ — ^ ^ p-0.5 , (1-1) AX

""

' [(J-DATDg/D^]^^ 2 __

(C-22)

The Crank-Nicolson finite difference approximation to eq. C--11 is

^^1,1+1 - j + Fj^j) - Cj^j(Fi+i^j + 2Fi,j +

^I-1,J^ + ^1,J^^I,J ^ ^I-1,J) + - ^1, J+l(^I-rl,J+l ^

2^1, J+1 ^ ^I-l,J+l) -1, j+l(Fi, j+1 + Fx_p^j+q) ]/[4(AX)^j1 (C-23)

Eq. C-23 is rearranged to give

^I,J^I-1,J+1 + ^I,J^I,J+1 +

^I^I+1,J+1 " ^I,J (C-24)

92
(C-25)

Bl,J = + ^'^l,J+l +^I-1,J+1 + (C-26)

^I,J " ^I+1,J ^ ^I,J+1 (C-27)

^I,J " +

^I-l, j)^I-l,J + (^I+1,J + 2 F^^j + - R)Cr,j

- + ^I,j)Cl+l,J (C-28)

R = 4(AX)VAT (C-29)

For 1=1 and M, eq. C-2: must be modified for the boundary conditions eq . C-19

,

C-23 and C-24 to be

+ E^^j)C2,j+i = G^,j

+ %,jCm,J+1 = %,J

(C-30)

(C-31)

The distributions of the concentration of the additive in the plastic sheet

is computed as follov^7s: For J = 1 (T = o) , = 1 by eq . C-13. Eqs . C-24, C-30

and C-3l give linear simultaneous equations for the concentrations at J + 1 in terms

of concentrations at J. Solving these equations for J = 1, 2, 3 etc. give the con- centration distribution versus J or T.

For the case that the liquid diffuses as a front, shown in Fig. 3, the concentration of the liquid is given by

C

OO H

x-£+w/F~

t

= 0

for x>i -/t

for 0<x<2-w/t"

(C-32)

We define the reduced value

U = w/v^

Then Eq. C-32 is written

for X<l-U/T

= 0 for 0<X<1-U/^ (C-33)

The calculation is then the same as previously with Eq. C-33 replacing Eq.C-10.

^ _ X+U /T -1

Uy—

93
Appendix D

Let diffusion occur in a polymer exposed to a temperature that varies with

time, t. The diffusion constant D(t) will then also vary with time. Diffusion

will be controlled by the equation

3t D(t)|^ (D-1)

where C is the concentration of the additive in the polymer. As shown by Crank,

substituting

' t w = D(t^)dt^ (D-2)

' o

gives

3C ^ 3w (D-3)

Now consider diffusion in the polymer exposed to the constant temperature T^.

The diffusion equation is then

K

3t = D(Te)

3C^

3F (D-4)

By the substitution

V - tD(Tg)

,

(D-5)

the diffusion equation D-4 gives

^

3v 3X“ (D-6;

At the equivalent test temperature, the diffusion given by the solution of Eq. D-6

is required to be the same as if the polymer was exposed to a varying test temperature which is given by the solution of Eq. D-4. Because the equations are of Che same form, their solutions will be equal if

w = V

Substituting Eqs. D-2 and D-5 in Eq. D- / gives the condition

, t D(T^) = - D(t^)dt-

(D-7)

(D-8)

94
The dirfusion constant varies with temperature by the relationship

D = DgexpC-E/RT) (DSubstituting Eq . D-9 in Eq . D-8 gives Eq . 50.

Let the polymer be exposed to a constant temperature T

2_ for a time f t and a constant temperature T 2 for a f'me (l-f)t. Substituting in Eq . 3, the

integral may be evaluated to give Eq. 49.

The equations D-1 and D-4 apply to diffusion in a plane sheet. However,

as mentioned in Reference 17 , the same results may be similarly derived for

diffusion in a plane sheet, cylinder or sphere.

USCOm-NBS-DC
t

: V
N8S-114A (REV. a-78)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. Accessiai No. 3. Reeisfent's Accession No,

4. TITLE AND SUBTITLE

"Models for the Migration of Paraffinic Additives in

Polyethylene"

5. Publication Date

6. PerfonntRg Organization Code

7. AUTHOR(S) L. E. Smith, I. C. Sanchez, S. S. Chang, and F. L. McCrackin8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

18. Proiect/Task/Wor{< Unit No.

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS cSfreffr, City, State, ZIP)

Same as Item 9

13. Type of Report & Period Covered Annual

10/1/77 - 9/30/78

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

I

1 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT rA 200^word or less factual summary of most significant information. If document includes a si gni ficant bibliography or I literature survey, mention it here,) General physical models of the migration o-f low molecular weight species in

polymer matrices are needed to provide a basis for the efficient regulation of

plastics used in food contact applications. This report presents the first year's

progress on a project containing both theoretical and experimental elements aimed

at producing such models. Using a modified equation of state approach, models have

been developed for estimating the equilibrium partitioning of a diffusant in a polymer at a temperature above its glass transition in contact with a finite volume

of solvent. Some possible new approaches to a diffusion theory based on volume

fluctuations were outlined. Model calculations using diffusion equations have been

made for the extraction of additives from polymers with concomitant solvent

absorption and for finding a constant extraction temperature equivalent to migration

under varying temperature conditions. The migration of an oligomer, ^"'C-labeled

octadecane, from high density linear polyethylene into various solvents at different

temperatures was measured in order to elucidate the effects of thickness, temperature, concentration and solvent. Deviations from ideal Fickean kinetics in the

experimental results may be attributed to the strong influence of swelling of the

polymer on the migration rates and to the possible incorporation of a small portion

of the oligomer in the crystalline phase of the polymer.

17. KEY WORDS (six to twelve entries; alphabetical order: capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Additives; diffusion; food additives; indirect additives; migration; models;

regulation.

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