Reference

AlllOl

NATL INST. OF STAND & TECH RI.C.

AlllDS D3t.771

NBSIR 80-1999

Models for the Migration of

Additives in Polyolefins

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

I. C. Sanchez and G. A. Senich

Polymer Science and Standards Division

Center for Materials Science

National Bureau of Standards

U.S. Department of Commerce

Washington, D.C. 20234

Annual Report for the Period

October 1 , 1 978 - September 30, 1 979

Issued February 1 980

Prepared for -QC of Foods

100 Administration

gton, D.C. 20201

80-1999

i980

NBSIR 80-1999 • « * MODELS FOR THE MIGRATION OF

ADDITIVES IN POLYOLEFINS

HATlOnAL BmUCAO

or BtAMDABDS

UBBABT

SFP 1 9 1980

7\ U ; > '

2o-/qQi

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

I. C. Sanchez and G. A. Senich

Polymer Science and Standards Division

Center for Materials Science

National Bureau of Standards

U.S. Department of Commerce

Washington, D.C. 20234

Annual Report for the Period

October 1 , 1 978 - September 30, 1 979

Issued February 1 980

Prepared for Bureau of Foods

Food and Drug Administration

Washington, D.C. 20201

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick. Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
iniAilHlkTS «0

T*s>j»"aj

C8€! ^ I

=!<> i^orfAiwmwrsiCT BJBca

8MWajOYJ'3’5 H! gSVSTiC

-A ^ is(ite^«8,^P it’

noiWi^Md rb'UixiflilS brt9 iwrkj|^|iO*i

wit

3di’'

-» ftfrtitjO; Itf vii^yi6^«42( ti' , j-tI

rYSMfcffi’SaM.'' 'i *. .

' .Wl

A' ..; V’l

IS'' '''**^;' .-<tW|L

0'^e'r\o^:

'„ ''?flaB!L " iST '^!; . .It' 08Cr

', M/'fi

^

.'Ij. ’

', ; '4

II

. •#%y '. « V

3... Pi Vv.^^^Pjl

4kK»4^ 'tp.

roS0!: .

I ^ ’^f ;v,

.l!»

t**

. >! ^'

"i’

—M« m^pi .i '''- *th

V ’ Av

vvi-ik»«V4 ”Q-'

'.•'.'IF,

» '

•rifl
TABLE OF CONTENTS

Introduction .

I. Migration Models

Boundary Layer Limited Migration

Quiescent Migration

A General Migration Model

(a) Exact Analysis .

.’ . .

(b) Approximate Analysis . . .

(c) Migration Bounds

II. Effect of Sample Thickness on the Migration

III. Errors in Temperature Extrapolations

IV. An Empirical Formula for Migration in Polyolefins

Physical Interpretation of the Empirical Formula

V. Inverse Phase Gas Chromatography of Polymers

A Description of the Experiment

Generalized Semicrystalline Polymer Behavior

Experimental Considerations

Thermodynamic Studies

Kinetic Studies

Gas Chromatography Determinations of the Purity of the Radio

labeled Alkanes

VI. Experimental Measurements of Migration by Extraction . . .

Materials

Sample Coding Scheme and Sample Plaque Designations . . . .

Experimental Methods .

Presentation of Results

Migration of n-Octadecane into n-Heptane . . .

Migration of Labeled Octadecane into Unlabeled Octadecane .

i,

1

2

3

7

10

10

14

18

20

23

25

27

38

38

40

43

45

48

51

65

66

68

70

73

78

79
Migration of Octadecane into Corn Oil, Ethanol and Trioctanoin . . 80

Migration of Octadecane into Ethanol 83

Migration of Octadecane into Ethanol/Water Mixtures 83

(a) Solubility and the Mixed Solvent System 83

(b) Extraction Results 84

(c) Partition Coefficients 87

Migration of n-Octadecane into/from Polyethylene and 50/50

Ethanol/Water Mixture 88

Appendix A 109

Appendix B 126

ii
Given

a

packaging

plastic

of

mass

Mp

containing

Mg

grams

of

additive,

compare

the

migration

of

additive

into

a

food

simulating

solvent

of

mass

Mg

to

the

max*

imum

permissible

dose

or

concentration

sV

os

o

u

V

(/)

iii

Introduct ion

The Bureau of Foods of The Food and Drug Administration has regulatory

responsibility for the use of packaging materials in contact with food. Their

regulatory decisions demand an estimate of the amount of material that can

reasonably be expected to migrate from the package into the food. Worst-case

estimates are generally needed and may be obtained from analysis of packaged food,

laboratory migration data, extrapolation from closely related data, or by calculation using some theoretical framework. Clearly, direct analysis or laboratory

migration measurements are less efficient and therefore less desirable than

extrapolation or estimation methods. This program at the National Bureau of

Standards aims to provide technical suggestions and data to the Food and Drug

Administration that can be useful in increasing the applicability of more efficient

estimation and extrapolation methods to this challenging regulatory problem. This

report, however, represents only technical opinions of the authors as representatives

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

decisions or recommendations of the Bureau of Foods, the principal sponsor of this

work.

In order to organize the specific technical questions involved in regulating

packaging materials, it is useful to consider a formal decision tree. A general,

but incomplete example of such a decision tree is shown on the facing page.

In this chart and in all acompanying discussion several facts are presumed

as given, either because they can reasonably be assumed to be generally available

or because their determination is beyond the scope of our considerations. Specifically, the basic geometry and size of package is assumed to be known as well as

the range of food stuffs to be contained. Further, an appropriate simulating

solvent or solvents are to have been chosen. The comparison of simulating solvent

extraction with that found in actual food is the subject of current work by the
2

Arthur D, Little Corp., under contract to the Bureau of Foods. Worst-case limits

of shelf life and use temperatures for the package are also needed in some cases.

Finally, to simplify the discussion we assume that a critical amount or concentration of additive exists. This critical value must be based on toxicological considerations and might represent points between different tiers of required testing

or an action level that determines an allowed or a disallowed application.

There are four general phenomena that can limit the amount of an additive

that will migrate into a food, or a food simulating solvent. First, migration is

obviously limited to the total amount of additive present in the packaging material.

This is called load limited migration. Secondly, migration may be limited by insufficient solubility of the additive in the simulating solvent. Third, the additive partitions between the polymer and solvent f)hases. Finally, the total additive

migration may be limited by the diffusion of the additive during the estimated

shelf life. The limiting transport rate may occur in diffusion through the polymer or, in some cases, in diffusion through the solvent phase. A more detailed

description of these possible diffusion processes is given in the following section.

Other sections of this annual report present some estimation methods as well as

experimental results on laboratory measurements of migration in polyethylene.

I. Migration Models

A large number of mathematical models of diffusion have been derived to

cover conditions having various boundary conditions or simplifying relationships

among some of the pertinent variables. Although many of these equations are available in the literature, it is valuable to derive a relatively complete set here

using consistent arguments and notation. The following sections organize and

collect such equations and derive some new experessions for a few special cases.
3

Boundary Layer Limited Migration

In migration experiments with solvent agitation, diffusion of the additive

in the polymer is usually rate determining. This is not the only possibility.

For example, if the solubility of the additive in the food simulating solvent is

limited, diffusion through a relatively stagnant boundary layer of solvent may

become rate determining. The concentration profile for strong boundary layer

limited diffusion is schematically shown below:

CQ-«,

I is the thickness of the stagnant solvent layer (I is determined by the degree

s s of solvent agitation), is the additive concentration in the solvent phase and

C is the additive concentration in the polymer sheet.

At the boundary between polymer and solvent, we assume equilibrium; i.e..

Cg(0,t) = KC(0,t) (D*

where K is the partition coefficient.

A necessary but not sufficient condition for the above concentration profile

to prevail is for the difference in additive concentration between polymer and

solvent, C - C^(°°,t), to be very large compared to the concentration difference

across the boundary layer KC - C^(°°,t). Thus, this condition prevails when K<<!

and we can approximate the concentration gradient across the boundary as a linear

gradient (a quasi-stationary approximation):

*A11 numbers for equations, figures, references and tables are local reference

numbers for each section of the report.
3c

r

"1 [kcu) - c^Kt)J

(

2 )

By Fick's first law (flux is proportional to the concentration gradient),

the rate at which additive migrates to the solvent is given by

dM 2AD

p 1

s

*-

where is the diffusion coefficient of the additive in the solvent boundary

layer and A is the cross-sectional area of the polymer sheet. The factor of

2 appears because diffusion occurs from both sides of the polymer sheet of thickness 5.. We now make use of the following relations:

C = (M^-M^)/Vp

Cs(“»t) = M^/V^

s p

M /M 00 O

g

1+g

where and are the volumes of solvent and polymer, respectively, is the

amount of additive in the polymer at t=0 and is the equilibrium amount of additive extracted as t-x». Now Eq. (3) can be rewritten as

d(M^/M ) 2D K

t °° _ s dt Sil s

(4)

which has the solution

(5)

( 6 )

At short times where st<<l, we have to a good approximation
5

or A

"

M /M ='st

t °°

-j , J2vr\

':%

'if

(7)

That is, is "initialiy linear in time.

A good procedure for determining s in Eq. (5) is to plot In (1-M /M )"

against t. The slope of this plot is equal to -s. In*-''Fig. 1, migration data of

n-C^gH^g from linear polyethylene (LPE) into a 50/5D ethanol/water mixture at 60°C

(E50B60L) are plotted in this manner. Data for M^7m^ values greater than 0.9 were

omitted from the plot because small errors in M^/M^ in this range yield large

errors in calculated s values. From the slope, we obtain

o

1 -1

s = 2 X 10 sec

For this system we know that

K = 10

-3

= 0.07 cm

M /M = 0.18 oo o

—6 2 D = 9 X 10 cm /sec

s

and thus we find from Eq. (6) that

f'

a = .007 cm or 70 microns

s

The diffusion coefficient D of n-octadecane in the 50/50 ethanol/water mixture

® > s

• * 1 was estimaced from the Wilke-Chang correlation .

The idea of diffusion through a relatively stagnant boundary layer is not

novel. For example, similar ideas have been invoked in theories of dissolution

rates of crystals^^ and electrode overvoltage^^. Estimates of the thickness of
6

I-l
7

the boundary layer for turbulent flow typically are in the 10 micron range

To illustrate that Eq. (5) cannot describe migration when diffusion in the

polymer is rate determining, a plot of ln(l-M^/M^) against t for the migration

of radiolabeled C^gH^g from LPE into non-labeled C^gH^g used as a solvent (0E30)

is shown in Fig. 2. Notice the strong deviation from linearity for these data.

Quiescent Migration

We now address the situation where diffusion through the solvent phase is

rate determining. This type of migration will be important in an unstirred solvent or when the food stuff is a solid or viscous liquid.

Consider an ideal system of an infinitely thick polymer in contact with an

infinite solvent reservoir. There is only one polymer- solvent interface located

at x=0. The following conditions hold:

3c a^c

x<0 (8)

3C 3^C

® = D

®

= 3x2

x>0 (9)

C=C x<0 and C =0

o s x>0 at t=0 (10)

C^(0,t)/C(0,t) = K (11)

'3C \

^ / x=0

(12)

Equation (11) indicates that we have assumed that equilibrium holds at the interface (x=0) . Equation (12) indicates that the flux, J, on either side of the

plane at x=0 is the same (an equation of continuity)

.

A general solution of this problem is

( 13 )
-

M4/M

8

Fig. 1-2
9

(14)

y E K(D /D)^/2

s (15)

and where erf(z) is the error function. From Eqs. (12) and (13) it is easy to

show that the flux across the plane at x=0 is

J(0,t)

C

y o (16)

At time t the amount of additive, that will have crossed the plane at x=0 and

of cross-sectional area A is

J(0,t')dt'

4AC y o rrn (17)

Now

C = M /Ail o o (18)

where I is the polymer sheet thickness. An additional factor of 2 appears because we assume that both sides of the polymer sheet are in contact with the solvent. Although we assumed that the polymer is infinitely thick, all that is

really required is for I » /Dt^ . Therefore, for sufficiently thick polymer

sheets Eq. (17) is valid and with the help of Eq. (18) it can be rewritten as

M^/M

o 4y

y + 1

(19)

For finite sheets for which £ < v^dF and/or finite solvent amounts, Eq. (19) will

slightly overestimate the amount of migration; thus, Eq. (19) is always a conservative measure of quiescent migration.

Notice that
10

(Dt/TTi,^) if y>>l

4

1/2

( 20)

K(D t/TTil^) s if y<<l

The result for y>>! is the familiar one for polymer limited migration with strong

solvent agitation.

The above analysis of quiescent migration as well as boundary layer limited

migration clearly shows that partition coefficients can have ^ strong influence

on migration rates .

A General Migration Model

(a) Exact Analysis

Polymer limited migration as well as the boundary layer and quiescent migration models represent particular extremes of migration behavior. What is needed

is a more general model which can span the total range of migration behavior.

The most general model that we might consider is diffusion from a polymer sheet

of thickness £ through a stagnant solvent layer of thickness to a solvent reservoir of volume V . We can simplify the analysis considerably by allowing £ to

s be very large. Our results for an infinitely thick polymer will always accurately

represent migration from a finite polymer sheet for times less than about 0.1 t^:

The characteristic time t^ is approximately equal to the time required for

a molecule to diffuse a distance £ in the polymer sheet. Therefore, for t<t^

only molecules within a distance £ of the polymer surface will significantly contribute to migration. A more careful analysis of this "thick polymer approximation" will be given later in Section II.

Locating the polymer-solvent interface at x=0, we wish to solve the folE £^/D ( 21 )

lowing two diffusion equations;
u

3C

s at

x<0

x>0

subject to the following initial conditions:

C(x,0) = C and C (x,0) = 0

o s

and boundary conditions:

C^(0,t) = K C(0,t)

D

s J(0,t)

9x

x->-<» 0

( 22 )

(23)

(24)

<25)

(26)

(27)

9C

s 9t

x>Jl — s

=

- ^ J(0,t)

s

(28)

Boundary condition (27) is the thick polymer approximation. Boundary condition

(28) reflects the condition that the solvent reservoir is finite and is being

agitated. It also implicitly assumes that the volume of the boundary layer, 2A£^,

is very much smaller than the total solvent volume V . s The above diffusion problem can be solved by the Laplace transform method.

The solution is outlined in Appendix B. The Laplace transform of the flux J(0,t)

is given by

_ oM cosh(t p)^^2

-A J(O.p) °

2 + a(t 1/2 Ur

p) [cosh(t p) + y sinh(t p) ]

X/ s s

where
a = KV /V 5 KV /Ail (30)

s p s

2 2 U E K D /D

s (31)

t E il^/D

s s s (32)

and p is the transform variable. The Laplace transform of a variable, such as J,

is denoted as J. The characteristic time t^ is approximately the average time

required for a molecule to diffuse a distance in the solvent phase. Under

normal conditions of solvent agitation t^>>t^ since and D<<D^.

The amount of additive that migrates to the solvent is given by (two sided

migration) :

M. J(0,t’)dt' (33)

and its Laplace transform is

Mp = -2A J(0,p)/p (34)

Thus, to obtain M^, we must invert J/p. To date we have been unable to carry out

this inversion except for some special cases which we now consider.

Case I Zero Boundary Layer and Finite Solvent Reservoir

aM

lim -A J(0,p) =

s

5. -K) 2 + a(tgp) 1/2

(35)

The inverse of J/p is tabulated and the result is

M /M = a 1 -

t o L

'] (36)

V where t is a dimensionless time variable defined by

- / t = t/t, (37)

This is the same thick polymer approximation given by Crank for a plane sheet .
13

Case II Zero Boundary Layer and Infinite Solvent Reservoir

For an infinite solvent reservoir, we obtain from Eq. 36

r 4 lim M /M = lim a I 1 - (1 •- . . . to I /-a ct-x» I

1/2

M /M = — = A

which is the familiar result for polymer limited migration .

Case III Infinite Boundary Layer

M

lim -AJ(0,p) =

1 / 2 ,, . - 1 > I (t p) (1+y )

The inverse of J/p is tabulated and the result is

which is the result previously obtained, Eq. (19), for quiescent

Case IV y<<l ( Boundary Layer Limited Migration)

When y<<l we can approximate J by (expand cosh x and sinh 3

aM

-AJ(0,p) -

2 + ay“^(t^t^)^^^p

In making this approximation we assumed that

(t^p)^/^«l

and

y ^(tgp)^/^»l

(38)

(39)

(AO)

migration .

(Al)

(A2)

These conditions on the reciprocal time variable p are equivalent to restricting
14

the validity of this approximation to the following time interval:

t <<t<<y”^t

s s

Again the inverse of J/p is tabulated and the result is

(43)

(44a)

(44b)

Equation 44b is identical to Eq. (7), the short time linear ”t law" for boundary

layer limited migration . Notice that the leading term in Eq. (44b) is the only

non-zero one in the infinite solvent reservoir limit (a-x») . What the above result tells us is that t law type migration can only be expected in the time interval defined by relationship (43).

(b) Approximate Analysis

Because we have in general been unable to invert J/p with J defined by Eq.

(29), we present here an approximate analytical solution to this problem. At

time t the concentration profile will look similar to the one shown below.

O X
We approximate the concentration gradients at the polymer- solvent interface by

C -C(0,t)

o

IX

(45)

KC(0,t)-C^(<»,t)

I

S' (46)

where I is given by

Z = /irDt (47) X

Equation (45) would be exact if 2.^ where known exactly as a function of

time. Our choice of Eq. (47) for 2,^ is the exact value for polymer limited migration and quiescent migration. For example, from Eq. (13) we have

and

C(0,t) (48)

(49)

Combining Eqs. (45), (48) and (49) we obtain Eq. (47). Thus, we know Eq. (47)

is exact in certain extremes and should be a good approximation for intermediate

cases.

Equation (46) is an excellent approximation for small 2^, but a poor one

if 2 is large. Thus, our approximate calculation is limited to small 2 . s s Notice in Eqs. (45) and (46) that C(0,t) is unknown. However, from the continuity condition Eq. (26), we can solve for C(0,t):

C(0,t)

1 + (KD /DHd /I ) S X s (50)

where
16

C (o°,t) = M^/V

s t s

( 51 )

The flux across the polymer-solvent interface is given by Eq. (26). For two-sided

migration, we multiply this result by two and then integrate to obtain

iln

We now look at the special cases as before:

l+y(irt/tg) 1/2

]/

y(iTt/t^)^^^-l (52)

Case I Zero Boundary Layer and Finite Solvent Reservoir

As or equivalently as t^-^0, Eq. (52) becomes

(53)

This approximate solution (two-sided migration) is compared with the exact solution Eq. (36) in the Table below:

M /aM

t o ^1/2 , t /a Eq. (36) Eq. (53)

0.00 0.00 0.00

0.05 0.104 0.107

0.10 0.191 0.202

0.20 0.329 0.363

0.30 0.432 0.492

0.40 0.511 0.594

0.50 0.572 0.676

1.0 0.745 0.895

CO 1.00 1.00

As (see below) or as t->0 the two solutions become identical. The small t

limit for both equations is

M^/M00 (54)
17

Since Eq. (36) or (53) is only applicable for values _<(l+a)

Case II Zero Boundary Layer and Infinite Solvent Reservoir

As a.-^ Eq. (53) reduces to Eq. (38), the correct result for polymer limited

migration .

Case III Infinite Boundary Layer

Our approximate solution is invalid in this limit because of our assumption

of a linear concentration gradient, Eq. (46), becomes invalid.

Case IV y<<l (Boundary Layer Limited Migration)

If y is very small and we restrict ourselves to times such that

we can expand Eq. (53) to recover Eqs. (7) and (44b). Notice that the time restrictions (43) and (55) are for practical purposes identical.

Case V Finite Boundary Layer and Infinite Solvent Reservoir

This is an especially useful result that is obtained from Eq. (52) by lett ing a-^oo

:

y(TTt/t )^^^<<1

s s (55)

M /M = 4(t/7T)^'^^ 1

t o (56a)

which can also be written as

(56b)

where

(57)

When 3t is small, Eq. (56) reduces to Eqs. (7) or (44b) and when 3t

‘yl/2 »1, it
18

reduces to Eq. (38); i.e., initially obeys a t law (pure boundary layer limited

1/2 migration), but at longer times it follows a t law (polymer limited migra1/2 tion) . Evidence of the transition from t to t behavior has been observed for

the migration of n-octadecane from high density PE to ethanol, corn oil and

trioctanoin as shown in Fig. E-3 in the experimental section VI.

Figure 3 illustrates the general effects of boundary layer limited migration

according to Eq. (56).

(c) Migration Bounds

Assuming that the additive is uniformly distributed throughout the polymer

and is not supersaturated, we can place meaningful upper and lower bounds on migration. The upper bound is Case II or polymer limited migration and the lower

bound is Case III or quiescent migration. These bounds, of course, are not the

best ones, but in both cases we err on the safe or conservative side. Thus

^

(t/7T)^/^ < M /M < 4(t/7T)^/^ (58) 1+y — t o —

For one-sided migration the above factors of 4 become factors of 2.

Boundary layer limited migration. Case V, as calculated from Eq. (56) will

always be less than or equal to Case II and greater than Case III for t>4t^.
18 a

®IAI/*IAI

Fig. 1-3

19

References

1. C. R. Wilke and P. Chang, AIChE J., 1, 264 (1955).

2. K. J. Vetter, "Electrochemical Kinetics", Academic Press, New York, 1967.

(a) p. 160 and references therein. (b) pp. 188-193.

'^3. H. Bateman, "Tables of Integral Transforms", Vol. I, McGraw-Hill, New York,

» 1954, Ch. V.

4. J. Crank, "The Mathematics of Diffusion", Clarendon Press, Oxford, England,

2nd Ed., 1975. Ch. 4. In Crank's treatment, I is the half-thickness of

the plane sheet.
20

II. Effect of Sample Thickness on Migration

'\j We have asserted, without proof, that for times less than 0.1 t^ (or t<0.1)

we can accurately treat migration from a polymer sheet of thickness as if it

were infinitely thick. We have called this procedure the "thick polymer approximation". The utility of this approximation is especially transparent for Case II

or polymer limited migration. The exact solution of this problem is

00 M^/M^ =1-53 ~ exp[-(2n+l)^ir^t] (1)

t j< it/16

( 2 )

t > tt/16

The series in Eq. (1) converges very slowly for small values of t and is awkward

to use.

Equations (1), dashed line, (2), solid line, are compared in Figure 1. As

can be seen, for values less than or equal to 0.6, the thick polymer approximation is very accurate. This corresponds to times

t f 0.07 (3)

f\j The maximum error occurs at t = tt/16 0.2 and even here it is acceptable (1.0

versus 0.87). Besides it convenience, use of the thick polymer approximation

always yields a conservative estimate (i.e., an overestimate) of migration.

A corollary of the above result is that for times t^0.07, the migration per

unit area will be Independent of polymer thickness. By using Eq. (1.18), ^ can

be eliminated from Eq. (2) and we obtain

n=0 (2n+l) IT

whereas the thick polymer approximation is

4(t/iT)^'*^^

M^/M =

t o

( 4 )
MJM

20a

Fig. 1-4
'aT'.

(?

i*'. ,

V \

• It

'Vr.

y;.. ‘i " ~yif '
21

Thus, if inequality (3) is satisfied, migration measured at one sheet thickness

can be safely used for thicker samples.

On the other hand, migration per unit area at sufficiently long times becomes independent of time and proportional to thickness:

Mto/A M /A = £C (5) o

Equation (5) will apply within an accuracy of 1% for times

t > 0.44 (6)

Figure 2 illustrates migration per unit area plotted versus the square root of

time for three thicknesses. The initial concentrations in all three samples were

identical.
Ml/A

1 .0

0 .8

0 .6

0 . 4

0.2

0 .0

0.0 0.4 0-8 1.2 1.6

I L

Fig. II-2, Migration curves of films of three thicknesses.

i\
23

III. Errors in Temperature Extrapolations

Let the diffusion coefficient of a migrant in a polymer be at a temperature with an activation energy E. Then the diffusion coefficient at a temperature T

2 may be extrapolated to be;

exp[E/R(l/Tj^ - l/T^) ] (1)

Let an estimated activation energy E + AE in error by AE be used instead of the

true activation energy E. Then the error in the predicted diffusion coefficient

at temperature T

2

, expressed in percent, is:

where R is the gas constant and the temperature T^^ and T

2 are in degrees Kelvin.

Notice that the extrapolation error, when expressed in percent, depends only on

the error in the activation energy and on the temperatures; the percent error

does not depend on the activation energy or the diffusion coefficient. Table 1

gives percent errors of the extrapolated diffusion coefficient for extrapolations

from 80“C to 60, 40 and 20®C for errors AE in the estimated activation energy of

2, 5, 10 and 15 kcal/mole.

Table 1 shows that accurate values of the activation energy are required for

temperature extrapolation. Thus, if the activation energy is estimated to within

2 kcal/mole, the diffusion coefficient may be extrapolated for 80 to 20°C with

less than 50% error. However, if the activation energy is only known to within

10 kcal/mole, the diffusion coefficient may not be extrapolated from 80°C to even

60“C with less than 50% error.
24

Table 1

Percent Error in Diffusion Coefficients Extrapolated

From 00 o

0 O ft O Given Temperature

Error in activation 20“C 40°C 60°C

energy, kcal/mole

2 44 31 16

5 77 60 35

10 95 84 58

15 98 93 72
IV. An Empirical Formula for Migration in Polyolefins

A selected compilation of literature values of diffusion coefficients for

migrants in polyolefins reported^ in a preceding progress report was extended.

Values for which the same migrant was tested in several polyolefins at 25 °C or

80°C were selected from this compilation. For comparison purposes, values of the

diffusion coefficients of gases in polyolefins at 25“C were selected from other

2

sources . These diffusion coefficients were fit to the empirical equation

D = PM^ (1)

where the value of M depends only on the migrant and temperature while the values

of P and F depend only on the polyolefin. This approach is similar to the simple

3 4 functional relationships developed by Stannett and Szwarc , Rogers et al , and

Frisch^ to correlate permeabilities and diffusion coefficients of gases through

polymer films. Values of M are given in Table 1 and the values of P and F

are given in Table 2. In the correlation discussed here, M is the diffusion

2 constant of the migrant in low density polyethylene. The units of D is cm /sec.

Eq. 1 may be written

In D = In P + F In M (2)

so that a log-log plot of D for a polyolefin versus the M values of migrants is a straight line. Eq. 2 is plotted in Figures 1 to 6 for the nine polyolefins and

compared with the experimental values of D. The experimental values of the

diffusion coefficients are seen to agree with the line predicted by Eq. 2 to

within a factor of 2 in almost all cases. These figures also illustrate the

paucity of data available for fitting some of the polymers. Values of P and F

for these polymers should be considered very tentative.

The diffusion coefficients of hydrogen, helium and benzene did not fit Eq. 1

jti so were eliminated from the fitting. Hydrogen and helium are very small mole-
26

cules, so that their rate of diffusion is probably overly sensitive to features

of the structure of the polyolefins that do not affect the diffusion of larger

molecules. Benzene is strongly absorbed by polyolefins and the diffusion coefficients measured for benzene are probably not representative of the pure polyolefin but of the polymer swollen with benzene.

The application of Eq. 1 can best be illustrated by the following examples:

Example 1. Estimate the diffusion coefficient of Didodecyl,3,3-thio Dipropinate in Isotactic Polypropylene at 80®C.

From Table 1, M = 4.18 x 10

^

From Table 2, P = 500 and F = 1.523

By Eq. 1, D = 500 x (4.18 x lO"®)^’^^^

-9 2 = 2.9 X 10 cm /sec.

Example 2. The diffusion coefficient of Thiodiphenylamine in isotactic poly-

-9 2 propylene at 80®C is 2.1 x 10 cm /s. Estimate is diffusion coefficient at 80°C

in low and high density polyethylene.

From Table 2, for isotactic polypropylene, P = 500 and F = 1.523. Substituting

in Eq. 1,

-Q 1 2.1 X 10 = 500 M

Solving, the M value for Thiodiphenylamine

M = (2.1 X 10"^/500)^^^*^^^

= 3.4 X 10"®

For low density polyethylene, P = F = 1 so the diffusion coefficient is

D=M=3.4xl0^ cm^/s

The diffusion coefficient in high density polyethylene is by Eq. 1,

D “ 915 (3.4 X 10 = 5 X 10 ^ cm^/s.
27

This empirical formula, Eq. 1, is not expected to predict highly accurate

values of diffusion coefficients. Some of the limitations in its derivation are:

1. The form of Eq. 1 is purely correlative and has no intrinsic

physical basis.

2. The polyolefins have been grouped into general classes. For

example, different samples of low density polyethylene differ

in crystallinity, morphology, etc. so will have different diffusion coefficients. Ideally, the variation of diffusion coefficients with at least the crystallinity of the polyolefins

should be taken into account.

3. The data of Table 1 is incomplete. Only a few migrants other

than gases are included. Also, only a few diffusion coefficients

are available for some of the polyolefins.

4. The experimental accuracy of some of the diffusion coefficients

^ ^

* j. is low, especially some of the measurements by radioactive analysis.

5. Small errors were introduced by temperature extrapolation of some

^ t of the diffusion coefficients.

6. This formula does not apply to solvent extraction of the migrant.

For example, if a polyolefin is immersed in pentane, the effective diffusion coefficient may be an order of magnitude greater

than that given by the formula.

In spite of these limitations, it is hoped that the empirical formula will

be of value in estimating diffusion coefficients in polyolefins when no other

method is available.

Physical Interpretation of the Empirical Formula

For diffusion of a migrant in low density polyethylene (LDPE) , P=F=1, so D=M
28

by Eq. 1. That is, the value of M for a migrant is simply its diffusion coefficient in low density polyethylene.

If F=1 for a polyolefin, Eq, 1 becomes

D = PM (3)

so that the diffusion coefficient in the polyolefin is P times its diffusion

coefficient in LDPE by Table 5, P=4 and F=1 for ET-C-PR. Therefore, the diffusion coefficient of a migrant in Hydrogenated Butadiene is 3.25 times its

diffusion coefficient in LDPE. If F is not 1 for a Polyolefin, a constant ratio

between the diffusion coefficient of a migrant in the Polyolefin and in LDPE does

not exist.

The compilation of diffusion coefficients in Polyolefins is being extended

and an empirical fit of the diffusion coefficients based on more data will be

given in a later report. Also, an empirical fit of the activation energies will

be attempted. The correlation of the M values with the molecular weight, size or

other properties of the migrants will be investigated. This will allow the

estimation of the diffusion coefficient of a migrant prior to any measurements

using the migrant.
29

Ref erences1. NBSIR 79-1779, Progress report for period Jan. 1 to Mar. 31, 1979.

2. Polymer Handbook, edited by J. Brandrup and E, H. Immergut, John Wiley & Sons, Inc. (1975)

.

3. V. Stannett and M. Szwarc, J. Polym. Sci. , 1^, 89 (1955).

4. C. Rogers, J. A. Meyer, V. Stannett and M. Szwarc, Tappi, 741 (1956).

5. H. L. Frisch, Polymer Letters, j^, 581 (1963).
Table 1

Values of M

Migrant

Oxyg en Carbon Dioxide

Carbon Monoxide

Nitrogen

Argon

Sulfur Tetraf luoride

Methane

Ethane

Allene

Propene

Propane

n-Pentane

n-Octane

n-Decane

2 -A Dihydroxy Benzophenone

2-5-Di-Tert-Butyl-A-Hydroxy Toluene

2-Hydroxy-A-Methoxy Benzophenone

2-Hydroxy~A-Butoxy Benzophenone

2-Hydroxy-4-Octoxy Benzophenone

N-Octadecyl-Diethanol Amine

2-Hydroxy-4-Dodecoxy Benzophenone

Di(2-Ethyl-l-Hexyl)Pthalate

2-Hydroxy-4-Octadecoxy Benzophenone

Didodecyl,3,3-thio Dipropionate

n-Butane

Cyclohexane

Methylene Chloride

n-Hexane

g Temperature, **C M x 10

25 40.2

25 33.4

25 25.7

25 30.1

25 29.3

25 18.8

25 1.73

25 17.2

25 7.15

25 9.96

25 6.00

25 3.64

25 1.69

25 .895

25 .346

80 5.19

80 9.21

80 4.50

80 2.71

80 3.29

80 12.0

80 2.61

80 .392

80 1.34

80 4.18

25 2.22

25 .677

25 7.23

25 1.51
Table 2

Values of P and F

Polyolefin

Low density polyethylene

High density polyethylene

Isotactic Polypropylene

60-64% Crystallization

Stereblock Polypropylene

24% Crystallization

Poly ( isobutene-co- isoprene)

98/2 (Butyl Rubber)

Poly (4-methylpentent-l)

Poly (ethylene-co-propylene)

49/51

Hydrogenated Butadiene

p F

1 1

915 1.509

500 1.523

5.45 X

10“^ 0.694

7,1 X lO”'^ 0.623

2.13 1

8.0 1.053

3.25 1

Polyisobutylene .093 1
Figure

IV-1.

Low

density

polyethylene

34

oes /uio 'q

H

i

i
oes/, uip <(]

Figure

IV-4

.

+

Poly

(ethylene-co-propylene)

49/51
36

/

{jJO '(3

Figure

IV-5

.

+

Stereblock

Polypropylene
M

D0S/ mo' Q

Figure

IV-6.

Hydrogenated

Butadiene
38

V. Inverse Phase Gas Chromatography of Polymers

Inverse phase gas chromatography (IGC) was first reported by Guillet^^^ less

than ten years ago. The experiment differs from conventional gas chromatography

(GC) in that the material of interest, a polymer with negligible vapor pressure,

is employed as a stationary phase which sorbs various volatile organic species,

often referred to as probes. Processes of solution, adsorption and diffusion can

be studied in addition to morphological characteristics of polymers, such as the

glass and melting temperature and degree of crystallinity. Studies of this nature

(2-4) have been reviewed by several authors

A Description of the Experiment

The experiment involves injecting a pulse of the volatile probe and a noninteracting marker, usually methane or air, into a stream of flowing carrier gas

which sweeps the injected substances through a column containing the polymer of

interest. 'The polymer can be coated as a thin film onto the tube wall or on an

inert support packed within the tube. The carrier gas is usually helium or

nitrogen supplied at an accurately measured pressure and flow rate. An appropriate detector senses the elution of the marker and solvent vapor from the

polymer-containing column. The time from injection to elution of the marker (t^^)

and vapor (t ) and the width at half height of the resulting chromatographic peaks

are noted from the chart recorder output. Figure 1 gives a schematic representation of the chromatographic system and Figure 2 a typical chromatogram of the

inert marker peak and the probe peak with the various quantities of experimental

interest indicated.

At low rates of carrier gas flow, the vapor or probe reaches a steady-state

distribution between the vapor and polymer phase and the thermodynamics of

polymer-solvent or polymer-migrant Interaction can be studied. Since the

probe concentration is very low, a condition of infinite dilution is approxi-
39

mated and the interaction parameter x can be obtained. At high carrier gas flow

rates, the equilibrium state is not approached and the kinetics of polymer-solvent

interactions can be studied. The diffusion constant of the probe in the polymer

can be determined at low probe concentrations.

The parameter directly measured in IGC experiments is the retention volume or

the volume of carrier gas required to elute the injected probe. The adjusted

retention volume, V', corrects for dead volume in the system and is given by

the equation;

’'r * - V''

where V is the volumetric flow rate. A correction for nonuniform flow velocity

along the column length is required in order for the final specific retention

volume (V ) equation to be obtained:

V =

g

273.2 j

( 2 )

where j is the velocity correction;

j = (Pl/p„)^ - 1

(3)

p^ and p^ the column inlet and outlet pressure respectively, T^ the column temperature and W

2

the weight of polymer phase in the column. V should also be

g

corrected for carrier gas nonideality and vapor-carrier gas interactions when

very accurate results are required^^\ The symbol is denoted as V° when this is

done.

Several considerations must be taken into account in the experimental determination of V^. A sufficiently low concentration of the probe must be introduced

to avoid operating in the nonlinear sorption isotherm range which can contribute to

skewing of elution peaks and corresponding anomalous values of the net retention

time as illustrated schematically in Figure 3. If the surface to volume ratio of
the supported polymer film is high, surface adsorption can make a significant

contribution to the retention time. When both bulk and surface sorption mechanisms occur the measured net retention volume is given by the expression;

40

Vr = + K A

a 2 (A)

where and are the bulk and surface partition coefficients and the total

polymer surface area. The contribution of these concurrent retention mechanisms

can be resolved by conducting experiments with several polymer films of differing

surface to volume ratio. Carrier gas flow rate can also have an effect on V .

If the flow rate is too rapid then partitioning of the probe molecules between

the polymer and the vapor will be incomplete. A linear extrapolation of determinations at several flow rates to zero flow rate is often necessary to eliminate

this influence. The capillary column studies of Lichtenthaler et al^^^ suggest a

relationship of the form;

V = a-exp(-bV ) g(5)

a and b being temperature dependent constants characteristic of each polymersolvent pair. Such a relationship was found to give a good fit to their data at

low flow rates, however, its derivation has limited physical justification.

Generalized Semicrystalline Polymer Behavior

A retention diagram, a plot of log V vs. inverse temperature as shown in Figg ure 4, is constructed by determining V at a series of temperatures for a particular

g

polymer-probe system. Several types of information about the polymer-probe system

can be deduced from the retention diagram, as discussed in references 1-3, provided

that the vapor pressure of the probe is accurately known as a function of temperature.

The retention diagram is usually linear below the glass transition temperature,

as in region AB. This region generally corresponds to condensation and adsorption

of the probe onto the polymer surface. The slope of the curve can be used to
41

give AH , the heat of adsorption, when the heat of vaporization of the probe

and the surface area of the film are known, provided that a judicious choice

of the probe molecule precludes penetration of the probe into the bulk polymer.

Adsorption isotherms can be determined from analysis of the shape of the eluted

probe pulse. A more conmon occurence is for both surface and bulk sorption to

be operative in this region particularly for nonpolar systems. The contribution

/• of each mechanism may be resolved by varying the polymer surface to volume ratio

as described previously.

At point B on the diagram the polymer glass transition temperature is

reached. The retention mechanism begins to shift from a predominantly surface

mode at B to a largely bulk mode at C. Over this region the diffusion coefficient of the probe in the polymer increases by several orders of magnitude.

IGC can be used to determine the glass transition temperature of a polymer by

noting the first departure of a strongly adsorbed probe from the linear behavior

exhibited below the glass transition.

As the temperature is increased, equilibrium absorption of the probe molecules

in the amorphous phase will occur in region CD. Retention in this region is

primarily attributed to solution in the bulk polymer but may also be caused by

adsorption at the polymer-support, polymer-vapor or amorphous-crystalline interfaces and condensation on the polymer-vapor surface. If the portion of retention

due to various modes of adsorption is evaluated experimentally, the enthalpy of

mixing may be found from the slope of the retention diagram. Activity coefficients

may also be calculated when the vapor pressure of the probe is known. From the

activity coefficients and their temperature coefficients, the partial molal excess free energy, enthalpy and entropy of mixing and the polymer-solvent interaction parameter x ^^in be evaluated. The particular solution theory employed

will determine the exact formulations of equations used to obtain these

quantities. Operation at low flow rates and probe concentrations is preferable

and the surface to volume ratio of the polymer film should be low. The utility
of GC in obtaining activity coefficients in low molecular weight systems has been

demonstrated by the work of Tewari, Martire and Sheridan^^^ who report results

thought to be accurate to within 1% at four temperatures for sixty nine binary

systems; eleven probes with n-tetracosane, n-triacontane and n-hexatriacontane as

the sorbing phases.

Diffusion coefficients can also be determined above the glass transition

temperature. Several conditions must be met in order to employ the van Deemter

equation that allows calculation of the diffusion coefficient in the stationary

phase. Polymer film thickness must be uniform, equilibration in the vapor phase

must be instantaneous, and trans-column diffusion must be much faster than diffusion in the stationary phase. The experiments must be conducted at extremely

low probe concentration, or extrapolated to infinite dilution, and peak broadening from other sources must be minimized. Under these conditions the flow rate

dependence of the plate height yields the diffusion coefficient at the temperature of measurement.

Polymer melting begins at point D on the retention diagram. A perfectly

ordered crystalline polymer would show a sharp increase in retention volume at

the melting temperature but because of the distribution of crystal size and

perfection normally present, melting occurs gradually as the temperature is increased to the final melting point. An increase in the amorphous content at the

expense of crystalline regions impervious to penetration occurs as the melting

region is traversed, giving rise to the gradual increase in V over region DF.

S

/O') Such information has been employed by Gray and Guillet^ to obtain the degree of

crystallinity at various temperatures in a study of LDPE and HDPE using a decane

probe. In addition to melting and recrystallization as a function of temperature, isothermal crystallization of both materials was carried out. Crystallization half-times for LDPE agreed with previously reported studies conducted by

dillatometric methods. The sharp discontinuity in slope at point F has been

found to correspond to the complete disappearance of crystallinity and compares
43

favorably with the peak position of the melting endotherm determined by differential scanning calorimetry experiments.

The thermodynamic and kinetic parameters studied in region CD can also be

determined for the poljmier melt in region FG. The presence of polymer crystals

in region CD reduces the retention volume by a constant amount over that predicted by extrapolation of line FG since the crystals present below T^ cannot

be penetrated by the probe molecules.

Experimental Considerations

The use of IGC for the acquisition of physicochemical data requires a knowledge of some parameters that are unimportant in analytical GC, for example, the

weight of polymer phase and the column outlet pressure. The many variables of

the experiment must be controlled to ensure that the final V value calculated is

(9) sufficiently accurate. The studies of Wicarova and coworkers on elution of

hexane from a squalane column have shown that each experimental error can be

considered to be random and independent of other error sources. They have treated

the variance of V as a propagation of errors for the generalized function Q:

Q

= a“b^ (6)

with the standard deviation of Q given by:

This relation can be applied to equation 2 and used to estimate the standard

deviation of V as measured by the present IGC apparatus. Typical values of the

measured variables, their estimated or calculated standard deviation and their

contribution to the total variance of are shown in Table 1 for a study of

decane-SRM 1475 at 150°C carried out in our laboratory. The flow meter temperature, and the vapor pressure of water at this temperature, p^, are required
to correct the flow rate measured with a soap film flow meter downstream of the

detector to the column temperature and outlet pressure. For an ideal gas the

correction is of the form;

( 8 )

where is the experimentally measured volumetric flow rate and p the atmospheric pressure. The standard deviation of j is obtained by treating j , a

function of the column inlet and outlet pressures as given by equation 3, in the

same manner as the generalized function Q. Fluctuations in the column temperature have the greatest effect on the probe partition coefficient which in turn

influences the retention time by the relation:

t R

(1 + k') , 2

(P^-P

(9)

where 1 is the column length, K the packing permeability coefficient, n the

carrier gas viscosity and k' the capacity factor, defined as:

V, k’ = M

''A

( 10)

where is the partition coefficient and and the mobil and stationary

phase volumes, repsectively . Equation 9 was developed by Guiochon^^*^^ and has

been employed by Goedert and Guiochon^^^ in studies of the influence of

pressure and temperature variations on the precision of measured retention times.

Their findings show that the change in carrier gas viscosity with temperature is

negligible compared with the variation of k' . The uncertainty of T^ is accounted

for in the experimentally determined a and is therefore not included as a

separate source of variance in Table 1.

The overall standard deviation in expected from contributions of random

errors is found to be about 5%. The primary contributions to are the high

S
uncertatinty in determining the retention times and the column loading. As the

concentration of polymer coated onto the glass beads is small, typically 0.5% by

weight, precise determination of the polymer loading is critical for obtaining a

reliable value of W

2

. The most common methods reported in the literature are

gravimetric in nature. Calcination or solvent refluxing are employed to remove

the film from the beads and the weight of polymer deposited is obtained by difference. The accuracy of these methods has been evaluated for a SRM 1475 coated

glass bead packing. Calcination in a 380 °C oven gave a polymer weight fraction

_3 loading of 6.20 x 10 with standard deviation of ±3.5%. The weight change of a

blank was less than 2% of the weight lost from destruction of the polymer. A

-3

loading of 6.97 x 10 with standard deviation of ±21% was found by solvent ret fluxing experiments. The weight change of the blank was sizeable in this instance, comparable to the weight lost from dissolution of the polymer. The calcination method gave more consistent results at these low loadings and was used

for other determinations. A standard deviation as low as 0.5% has been achieved

in one case. Retention times can be measured at higher precision by the use of a

data handling system with a more rapid sampling rate or by employing a high chart

speed recorder. A reduction in 0 and a to 0.2 s and o /w„ to 1% would allow

^ ^ (14) the standard deviation of V to be reduced to 2%. Laub and Pecsok suggest

g

that the inherent precision in is limited to about 0.5% by the determination

of W^.

Thermodynamic Studies

The specific retention volume is related to the polymer-probe interaction

parameter, x» through the activity coefficient of the probe molecule, a concept

originally developed for GC by Porter, Deal and Stross^^^\' Patterson and coworkers have obtained an expression which relates the polymer-probe inter00 action parameter, x » derived from the Flory-Huggins lattice theory in the limit

of vanishing probe concentration to V“
4 6

= In

273.2 R V, - 1 - (Kll-V,)p°

RT ( 11 )

where is the molecular weight, the pure liquid vapor pressure, the molar

volume and the gas phase second virial coefficient of the probe, v^ the specific volume of the polymer and R the gas constant. These workers have derived a

similar relation for the Flory equation of state theory which is given as:

X

= In

273.2 R V,

V°V.p“

R

1*^1

- 1 - RT ( 12 )

where the superscripted volumes correspond to the close-packed specific volumes of

the hypothetical liquids at An equation of state treatment of polymer

solutions based on the lattice fluid theory has been described by Sanchez and

(X7“20) 00 Lacombe . The relation between x and V° is:

8

00 X = In

273.2 R p. ^?lP^2

- 1 - (Bii-Vi)pi

RT

(13)

where and p^ are the close-packed densities of probe and polymer. The the00 oretical relation for x Is given by equation 73 of reference 20. The three

00 theories yield an identical dependence of x on V°.

8

The interaction between a decane probe and NBS SRM 1475, a high density polyethylene, has been studied by IGC at this laboratory. The net retention time between a

methane marker and the decane probe was determined from the flame ionization detector

output as a function of decane concentration and carrier gas flow rate at 70 and

150°C. The net retention time was found to remain constant at 70°C for decane

concentrations below about 2 ppm. Concentrations below this amount were employed

in all subsequent measurements. A linear relationship between and V and one of

the form of equation 5 were used to extrapolate to zero flow rate and gave retention volumes identical within 3%. The range of flow rates examined is in-
47

sufficient to distinguish the preferable relation.

Two determinations of V were made at 70°C, one before and one after heating

g

to 150°C. These are shown as 1 and 2 respectively in Figure 5. Different V

g

3 values were obtained in each case, 234 and 258 cm /g respectively. Part of this

10% discrepancy could be due to a different percent crystallinity for each determination. Below the melting temperature, only the amorphous fraction contributes

to bulk sorption and any change in the amount of amorphous material present will

affect W_, and in turn V , as can be seen from equation 2. The accuracy of the

g

percent crystallinity determination probably limits the maximum reliability to

which V may be determined below the polymer melting temperature. An IGC study

g

of crystallization in Tenite 3310 high density polyethylene by Gray and Guillet ( 8 )

gives a V of 260 ml/g for decane at 70®C, in reasonable accord with the SRM 1475

g

results.

3 The limiting V at 150 °C was found to be 70.2 cm /g. Previous studies by

( 21) Braun et al employed two linear polyethylenes, Marlex 50 and Marlex 6050, and

( 22 ) decane at temperatures from 145 to 153 °C. Schreiber and coworkers have also

studied Marlex 50 and decane over the same temperature region. These results are

interpolated to 150°C and compared to SRM 1475-decane results in Table 2. The

' 3 three sets of results for V differ from the average value of 72.5 cm /g by about

g

oo 3.5%. The X calculated from the Flory equation of state based theory of polymer

solutions and the lattice fluid theory agree quite well, while the Flory-Huggins

result is found to be somewhat lower. The agreement among the x values calculated from various sources is about that expected based on other interlaboratory comparisons available in the literature^^^* These two studies also

favorably compare IGC derived interaction parameters to those obtained by the

classical method of vapor sorption for different rubbers above T^ with a variety

of hydrocarbon probes.

Interaction parameters from IGC experiments on many polyethylene-probe com-

( 22 ) binations are given in the extensive study of Schreiber and coworkers . For
48

these nonpolar systems, x values range between 0.2 and 0.4. When one component

OO is polar the value of x is expected to be much larger in magnitude, for example,

00 X values for PVC and ethanol, acetonitrile and hexane of 2.35, 1.85 and 1.76,

(25) °° respectively have been determined in IGC studies . Large values of Xp can make

a significant contribution to the partition coefficient calculated from the equation:

OO lnK=lnS + x+ l (1^)

o ^p

derived in progress report NBSIR 79-1779.

Kinetic Studies

Diffusion coefficients can be determined from IGC experiments at high carrier

gas flow rates where slow diffusion of the probe in the polymer phase can be

studied. The affect of this diffusion process is to broaden the emerging chromatographic peaks. Other factors such as vapor transverse and longitudinal diffusion in the gas phase, non- instantaneous equilibration of the vapor with the

stationary phase, chemical reaction at the interface and non-linearity of sorption

isotherms can also cause peak broadening and must be minimized in a determination

of the probe-polymer diffusion coefficient. These and other causes of broadening

of elution peaks are reviewed by Littlewood^ \ When the primary mechanism is

that of slow diffusion in the stationary phase, the diffusion coefficient is

related to the height equivalent of the theoretical plate H by the van Deemter

equation:

H = A + B/u + Cu (15)

where u is the linear flow velocity and A, B and C are constants having the

following values:

A = 2Xd

P (16)
A9

B = 2yD

gas

L. k*

2 —^2

(17)

(18)

where X is a measure of packing irregularities, is the average solid support

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

column, the probe diffuslvity in the gas phase, d^ the effective thickness of

the polymer film, the diffusion coefficient of the probe in the polymer and

k' the capacity factor. At high flow rates, a plot of H vs. u is linear and l*2.iq can be determined from the slope. Such a plot is illustrated schematically in

Figure 6. Equation 18 is only applicable for a uniform carrier gas velocity

profile. Several groups have derived a relation similar to equation 18 for the

case of a parabolic velocity profile and a uniformly distributed film on a solid

surface.

c=l k' ^ ®liq d+k')^

(19)

(27) Purnell gives an expression for the case of a thin continuous film on spherical particles obtained by approximating the packed column as a series of parallel

capillaries:

(k»)^

d+k')^

( 20 )

This treatment eliminates the effective film thickness term. A non-equilibrium

(28) treatment of Glddlngs' , taking into account peak dispersion from many sources,

reduces to equation 19 for uniform film thickness but allows a distribution of

(29) film thickenss to be considered. Jones has developed an extended van Deemter

equation to take into account resistance to mass transfer in the gas phase, a

distribution of carrier velocities, and a correlation between the two. These and

other rate theories of chromatography have been discussed in several texts ^ ’ ’
50

Several methods are available for determining the height equivalent to a

theoretical plate. For a gaussian peak, any of the following expressions can be

used

where Z is the column length, A the peak area and w the width at the inflection

point, half height, and baseline as indicated in Figure 2.

We have made a preliminary determination of the diffusion coefficient of

decane in SRM 1475 at 70°C by assuming a uniform pol3oner film thickness and api —8 2 plying equation 19. A diffusion coefficient of 2.2 x 10 cm /s is calculated.

(31) No other HDPE-decane IGC data are available, however Gray and Guillet have

studied LDPE-decane diffusion from 30 to 80°C. Interpolation of their results to

—8 2 70°C gives a diffusion coefficient of 1.5 x 10 cm /s. Weight-loss gravimetric

(32) measurements on LDPE-decane from 30 to 50°C are available and an extrapolation

-7 2

to 70°C gives D = 1.6 x 10 cm /s. The latter diffusion coefficient value is

obtained at a much higher diffusant concentration than those present in the IGC

determinations and as such is not strictly comparable to the IGC results. The

result from the SRM 1475-decane determination are of an acceptable order of

magnitude but further consideration is necessary to fully evaluate the technique.

(33) Rosolovskaya and Sal'vlnski have indicated that this method cannot be used for

accurate measurements due to the difficulty in determining the effective thickness

of the film. Scanning electron microscopy studies of solution coated polystyrene

films used in IGC experiments have shown that the film thickness can be highly

(34) non-uniform at both low and high loadings . These issues will be addressed in

future IGC diffusion studies.

Few IGC studies of diffusion in polymers have been reported in the litera-

(31) ture. Gray and Guillet have studied decane and benzene diffusion in LDPE

below the polymer melting point and LDPE-tetradecane in the melt. Braun and

(35) coworkers studied diffusion of BHA, BHT, dodecane and three naphthalene
51

/ O g\

derivatives in molten LDPE. Millen and Hawkes' maintain that the results of

the latter study should be calculated from equation 19 rather than equation 18

and present a table of corrected diffusion coefficients.

Gas Chromatography Determinations of the Purity of the Radiolabeled Alkanes

Radiolabeled alkanes employed in migration studies have been examined by GC

using both a flame ionization detector for its extreme sensitivity and a thermal

conductivity detector to allow for collection of the effluent peaks and subsequent determination of their radioactivity by liquid scintillation counting.

This was accomplished by passing the TCD effluent through a heated transfer line

to dry ice chilled counting vials containing heptane.

A mixture of labeled and unlabeled dodriacontane used in the preparation of

samples for migration studies contains several impurities as can be seen from the

chromatogram in Figure 7. The identity of these impurities can be determined

from a plot of retention volume vs. carbon number as discussed in references 27

and 30. Several alkanes of known chain length were used to construct such a

plot, as shown in Figure 8. This plot allows the identity of the impurity peaks

to be estimated from their retention time. Such a procedure is best carried out

with at least two stationary phases to insure unequivocal assignments, however,

this was not done since the few stationary phases suitable for high temperature

(>280“C) analysis of these nonvolatile materials are of similar selectivity.

Assuming that the detector response to the impurities is the same as toward

^32^66* approximate concentration of the impurities are as follows: 0.2%

SA4» ^28^58’ So^62 SAo’ ^6^54 ^3^68*

^29^60' impurities are also present in unlabeled dotriacontane obtained

from two sources. Scintillation counting studies of fractions collected under

the same chromatographic conditions but substituting a TCD for the FID indicates

that about 2% of the total radioactivity arises from the more volatile alkanes

which elute before while another 2% is from the higher chain length impurities.
52

A similar analysis has shown that undiluted radiolabeled octadecane contains

about 0.25% of as the primary impurity with small amounts of less volatile

impurities, about 0.01% 0*0^^ of an unidentified material. Only about

0.02% of the total radioactivity originates from the heptadecane.

The presence of radiolabeled alkane impurities may have to be taken into

account in interpreting results from future migration experiments.
53

References

1. J. E. Guillet, Macromolecules, 1669 (1970).

2. J. E. Guillet In Adv. in Analyt. Chem. and Inst. , Vol. 11, H. Purnell, ed.,

John Wiley, New York (1973) p. 187.

3. J.-M. Braun and J. E. Guillet in Adv. in Polym. Sci. , Vol. 21, SpringerVerlag, Berlin (1976) p. 107.

4. D. G. Gray in Prog. Polym. Sci. , Vol. 5, Pergamon Press, London (1977)

p. 1

.

5. C. L, Young, Chromatogr. Revs., 3^, 129 (1968).

6. R. N. Lichtenthaler, D. D. Liu and J. M. Prausnitz, Macromolecules, 1_, 563

(1974).

7. Y. B. Tewari, D. E. Martire and J. P. Sheridan, J. Phys. Chem., 2345

(1970).

8. D. G. Gray and J. E. Guillet, Macromolecules, 129 (1971).

9. 0. Wicarova, J. Novak and J. Janak, J. Chromatogr., 3 (1970).

10.

G. Guiochon, Chromatogr. Rev., 1 (1967).

11. M. Goedert and G. Guiochon, Analyt

.

Chem.

,

962 (1970).

12. M. Goedert and G. Guiochon, Analyt

.

Chem.

,

1180 (1973)

.

13. M. Goedert and G. Guiochon, Analyt

.

Chem.

,

1188 (1973).

14. R. J. Laub and R. L. Pecsok, Physicochemical Applications of Gas

Chromatography , John Wiley, New York (1978) p. 55.

15. P. E. Porter, C. H. Deal and F. H. Stress, J. Amer. Chem. Soc., 7^, 2999

(1956).

16. D. Patterson, Y. B. Tewari, H. P. Schreiber and J. E. Guillet, Macromolecules, 356 (1971).

17. I. C. Sanchez and R. H. Lacombe, J. Phys. Chem.

,

2352 (1976)

.

18. I. C. Sanchez and R. H. Lacombe, J. Polym. Sci. , Letters, 1^, 71 (1977)

19. R. H. Lacombe and I. C. Sanchez, J. Phys. Chem . , 2568 (1976)

.

20. I. C. Sanchez and R. H. Lacombe, Macromolecules

,

11. 1145 (1978)

.

21. J.-M. Braun, M. Cutajar, J. E. Guillet, H. P. Schreiber, and D. Patterson,

Macromolecules, 1^, 864 (1977).

22. H. P. Schreiber, Y. B. Tewari and D. Patterson, J. Polym. Sci., Phys.,

11,

15 (1973).
54

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

24. Y.-K. Leung and B. E. Eichinger, J. Phys. Chem. , 7^, 60 (1974).

25. 0. Olabisi, Macromolecules, 316 (1975).

26. A. B. Littlewood, Gas Chromatography , 2nd ed.. Academic Press, New York,

1970, ch. 6.

27. H. Purnell, Gas Chromatography , John Wiley, New York, 1962, ch. 8.

28. J. C. Giddings, Dynamics of Chromatography , Part 1, Marcel Dekker, New

York, 1965.

29. W. L. Jones, Analyt. Chem., 33 , 829 (1961).

30. S. DalNogare and R. S. Juvet, Gas-Liquid Chromatography , John Wiley, New

York, 1962, ch. 5.

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

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

33. Y. N. Rosolovskaya and Y. Sal'vinski, Polym. Sci. USSR, 1638 (1976).

34. G. J. Courval and D. G. Gray, Can. J. Chem., _W, 3496 (1976).

35. J. M. Braun, S. Poos and J. E. Guillet, J. Polym. Sci., Letters, 1^, 257

(1976).

36. W. Millen and S. J. Hawkes, J. Polym. Sci., Letters, 1^, 463 (1977).
Table 1

Standard deviation of variables for the elution of decane from a

HDPE column at 150 °C

Variable

Nominal

Value, X

lOOo^

X

T

c 150°C ±0.3 0.1 a

”2 100 mg ±2.0 2.0 2.00

•^R 40 s ±0.6 1.5 4.89

21 s ±0.6 2.9 4.89

•V

m

0.5 ml/s ±2.5 X

10”^ 0.5 0.13

25“C ±0.2 0.1

-4

3 X 10

P 101 kPa ±0.7 0.7

-4

3 X 10

Pw 3.3 kPa ±0.03 0.8

-4

4 X 10

Pi 148 kPa ±0.3 0.2 b

Po 107 kPa ±0.3 0.3 b

j 0.831 ±0.009 1.0 0.55

V

g

70.8 ml/g ±3.5 5.0 E = 12.4

a) contributes to o

b) used to calculate a,

J
Table 2

Polymer

SRM 1475

Marlex 50

Marlex 50

Marlex 6050

a)

b)

HDPE-decane Results at 150 °C

V

g

9 3 cm //g

K FH FES LF

70.2

69.9

74.6

75.1

a

b

b

0.24 0.38 0.37

0.18 0.32 0.30

interpolated from data of reference 22.

interpolated from data of reference 21.
Schematic

Drawing

ofa

Gas

Chromatoraphic

System

57 E
Elution

chromatogram

showing

a

marker

peak

at

tj^

and

a

probe

peak

at

tp

58

CM

C

CM

b b

> b CM CM

r" CM

II

II b 0)

II

11 £

<

b

IIJD

§

^ £0|

1

< U-!

I

I

I

I

I

I

esuodsey jope^ea
Shape

of

isotherms

and

resulting

peaks

59

10 IBuBjs

Time
Generalized

retention

diagram

for

semicrystalline

polymer

60
Figure

V-5

61

VOLUMETRIC

FLOW

RATE

(jV.

cm^/min)
HETP

Against

Gas

Velocity

dl3H

C

Resistance

to

Mass

Transfer
Detector

Response

63
6A

O

lO

CO

o

CO

ir> CM

o

CM

in

(S ‘‘''*1-^1)

Carbon

Number
65

VI. Experimental Measurements of Migration by Extraction

Of the four important branching points in the Decision Making Tree (DMT) —

Mq, C^, K and D — we are attempting to study at least the latter two parameters,

partition coefficient K and diffusion coefficient D. The third parameter, solubility C^, may also be studied, as it is closely related to K. The original

amount of migrant present in the polymer is considered known.

We have studied the migration of oligomers and antioxidants from two base

polymers — branched (low density) or linear (high density) polyethylene. Three

migrants are under study — two oligomers: n-octadecane and n-dotriacotane, and

an antioxidant; BHT (3 , 5-di-tert-butyl-4-hydroxytoluene) . Five pure solvents are

used — two non-polar solvents: n-heptane and n-octadecane, and three polar

solvents: corn oil, ethanol and trioctanoin. One mixed solvent system, ethanolwater, is also used. The migration studies are carried out at two temperatures,

60 and 30°C, to show temperature effect. Sample plaques of different thicknesses

are also studied to show the correlation of thickness.

Only a few of the n-C

22

H^^ and BHT observations are completed at this time,

therefore, the details of these observations are not given here in this report.

The following highlights are related to n-C-oH„o migration from polyethylene

lo Jo

only.

1/2 Fickian behavior, i.e., the amount migrated is proportional to t for up to

M /M =0.6, is only observed in the following cases: (a) from polyethylene samples

saturated with into or C^gH^g, (b) from branched polyethylene into

ethanol.

Near Fickian behavior is observed for ethanol, oil and trioctanoin extractions at high temperatures or for absorption experiments.

In poor solvents, near linear t behavior is observed.

Solvent absorption or swelling tends to increase the migration.
66

Migration kinetics in corn oil, ethanol and trioctanoin are practically

identical.

Solubility of ethanol-water varies over a range covering six

orders of magnitude.

Partitioning of migrant in polymer and the surrounding solvent has been observed .

Partition coefficients may also be estimated from solubilities.

At low partition coefficients, absorption of migrant into polymer from the

surrounding media is possible.

Besides the effect of migrant, polymer and solvent, rate of migration depends

on the level or concentration of the initial migrant in polymer, temperature as

well as crystallinity.

Effect of crystallinity is minimized either in the case of saturated migrant

or in the case of poor solvent.

Materials

(a) Polymeric Materials

The base polymers used in this report are the two National Bureau of Standards Standard Reference Materials (NBS-SRM) 1475 and 1476 for linear and branched

polyethylene (whole polymers), respectively. These two SRMs have been well characterized*. The essential characteristics of these two materials are listed in

Table E-1.

(b) Radioactive Tracers

Two n-paraffins, octadecane and dotriacontane, are used to spike the oligomer

level of the polyethylene samples for oligomer migration studies. A commonly used

antioxidant, BHT or 3 , 5-di-tert-butyl-4-hydroxy toluene, are used for the study of

*cf. NBS Special Publication 260-42, September 1972, and Certificates for National

Bureau of Standards Standard Reference Material 1475 and 1476, November, 1969.
TABLE E-1

Characteristics of Polyethylene

Linear Branched

SRM 1475 SRM 1476

Gel Permeation M

n 18,310

Chromatography M

w

53,070

Light Scattering M

w

52,000

[n] CN 0.890 0.8132

130°C TCB 1.010 0.9024

dl/g DHN 1.180 1.042

Melt Flow

Rate, g/10 min.

2.07 1.19

o P g/cm 0.97844 0.9312

CN — 1-chloronaphthalene

TCB — 1,2,4-trichlorobenzene

DHN — decahydronaphthalene

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

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

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

190°C

ASTM Method D 1928-68.
68

additive migration. The characteristics of these tracers are shown in Table E-2

for their specific activities and the minimum detection levels.

(c) Sample Plaque Preparation

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

the molding of the sample plaques was chosen. A large quantity of polyethylene

powder stock was prepared from either NBS-SRM 1475 or 1476 pellets first by dissolution in hot toluene or xylene. Most of the polyethylene precipitates out upon

cooling. The precipitate, together with the residue obtained by evaporating the

solvent, was dried in a vacuum oven to remove the last trace of solvent.

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

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

evaporated to dryness in a rotary evaporator, together with a number of glass

beads to act as a ball mill, under reduced pressures at relatively low temperatures and further dried in a vacuum oven.

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

180“C. Plaques of 125 mm x 125 mm or less are molded with brass or stainless

steel shim stocks of appropriate thickness sandwiched between two sheets of

teflon or teflon coated plates. The teflon surfaces are used for the easy removal

of the sample plaques without the aid or contamination of mold release agents.

Sample Coding Scheme and Sample Plaque Designations

Only a small modification of the coding scheme detailed in the Semi-Annual

Report for the period (October 1, 1978 - March 31, 1979) was required, such that

the fractional notation for the composition of solvent mixture was replaced by the

percentage notation. This change was necessary in order that the coding scheme is

compatible with the code for file and element names that are acceptable by our

central computing system.

The code sequence is
69

TABLE E-2

Characteristics of Radioactive Tracers

^ . ; yC^/mg ng/25 dpm

86.0 0.13

13.3 0.83

45.5 0.25

3 , 5-di“tert-butyl-4-^^ 57.9 0.19

< ; hydroxytoluene-7- C

(BHT)

i
70

(1) First Character — Solvent Type

C : Corn Oil

E: Ethanol (the numeral following the letter E denotes the percentage ethanol content of the composition of aqueous

ethanol mixtures)

H: n-Heptane

0: n-Octadecane

T; Trioctanoin

(2) Second Character — Sample Plaque Designation

Refer to Table E-3

(3) Extraction temperature in ®C follows the second character

(4) Third Character — Condition of Extraction

No third character: simulated infinite bath or unlimited volume extraction

L: Limited volume extraction

R: Reverse of extraction — absorption

(5) Additional experiments with identical experimental conditions are

distinguished by a dashed line followed by a number.

For example, E50M60R indicates an absorption experiment on a branched polyethylene sample M, which contains no labeled octadecane additive, carried out in

50% aqueous ethanol at 60®C.

Experimental Methods

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

limited solvent volume and (2) discrete extraction into simulated infinite solvent volume.

In method (1) an extraction vial of 25 ml in volume with a teflon valved

cap is used. The solvent in the vial will only meet glass walls and the teflon

surfaces during normal experimental processes. A silicone plug is situated

above the valve. A small area of the silicon rubber, less than 1 mm in diameter
7

Linear Polyethylene

(SRM 1475)

Branched Polyethylene

(SRM 1476)

TABLE E-3

Sample Plaque Designations

^ ^18^38 ^ ^32^66

0 0.01 1 5 10 0 1

ii,cm

0.02

0.07

0.26

N

D

C

K

B

A,L

0.02

0.07 M G,I,J H

Q

R P

% BHT

0.01

U
72

and used as a septum for the hypodermic needle, may be exposed to the solvent

vapor. The polymer sample may sometimes be surrounded by a nichrome or stainless

steel screen to prevent 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 than the solvent.

The total amount extracted, M^, at time t is

M

t

t-1

C W + E St St . , 1=1

C .W . SI ai

where C , W and W represent the concentration of the migrant, total weight of

S S ci the solution (including that of the aliquot) and the weight of the aliquot, respectively. At equilibrium the partition coefficient is estimated as

k =

Soo M--M

0 °

c w

s°° p

M--M

0 “

where Mq is the amount of migrant originally present in the polymer of weight W^,

and M is the total amount extracted at long times calculated from the concentre- |

i tion, aliquot weights and solution weights as mentioned above.

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

i solvent in a typical 20 ml liquid scintillation counting vial. At specific times j

the sample is removed from the solvent, rinsed and palced in another vial with

fresh solvent to repeat the extraction process. The total amount extracted at j

time t is simply the sum of all extracts:

|

^ I = E M. i t . 1 1 i" 1=1 i,|

f! Method (1) is able to yield information about the equilibrium partition

coefficient at infinite extraction time. However, it suffers from rigid require- |

I ments of knowing accurately the ratio of aliquot versus total solution and of i

keeping track of materials lost during the sampling process for material balance

I

I

. !i
73

purposes. As extraction time Increases, there is only very small change in the

concentration of extracted material in the solution, whereas the weighing or ratio

error may persist. Therefore, the results at long time or high degree of extraction will show considerable degree of scatter. 7

Method (2) is much simpler in operation, but simulates a condition of migration into infinite media, and is relatively free from aforementioned experimental

difficulties. However, it cannot be used to generate partitioning information nor

migration kinetics for migrant that is sparingly soluble- in the solvent. It

should only be used for convenience when the migrant is highly soluble or miscible

with the solvent.

An absorption experiment, the reversal of extraction, can be performed

similar to that of the limited volume extraction by starting with unlabeled polymer and labeled migrant in solution.

For all the methods mentioned the extraction vials are shaken inside a temperature controlled aluminum block on a shaking table at a rate of about 200

reciprocations per minute. ' :

' '

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

the polyethylene sample is extracted by dissolving the sample in toluene at high

temperatures. We found that the single crystals or precipitates of polyethylene

in the counting vial does not interfere with the counting efficiency beyond the

normal scattering of the counting results.

Presentation of Results

The results of completed experiments on the extraction, as well as absorption, of octadecane into and front polyethylene are presented in the Appendix and

summarized in Table E-4. Several slow experiments involving the extraction of

octadecane are still in process, it may take another 3-6 months before leveling

off occurs. ,

Only a few of the experiments on the extraction of and BHT are com-
74

c

o U -H -I C 4-> (Q 0) 0.»« U > U

O iH O HO®Ui ^

<l

fHintn<.^cMiO(nvoO(na\^i-i'^o

m'4'sr'<rmmmfn'ij-<Tr-tmr^vrQ0

•tfO-*Jr-IOO'd'CMmOOrO

LOinmin%i'^Lnoot^r^

oo

3

CO

rjc

®

®

CJ

0)o

®

M

®

J3O

c 1 ® /-s « o ^ iH m m o m 00 o CM en o CM o cn o o CM O CM 00 m vO o C3N o '3' sr ® Hc>J ® a a rH t—

<

fH ON ON fH CM o o O 00 o vO vO o CO o CM <r CJN CO CM O 00

o. a X o pH Mf fH pH CM <

®

C

o

•H •o

4JO ® 00 o 00 00 <n CM O CM ON 00 in vO CM CO CO o pH vO pH m “cr ® o ® a • • • • • • • • • • • • • • • • • • • • • • • M q. H o in sf *!f m in «o in sr sr 00 00 •o 'O' vO m 00 CJN pH CO CO v£> vO U r-4‘ pH X Cd

Cda® ® 4J

CJ iH JS m o> 00 o cn «o o o •o m CO pH o 00 m CM pH. o m vO 00 C3N vO CM a 60 00 vA -O’ •4* ro m CO vO •o sr m o pH 'O- CM CO CO 00 m pH CM -O' ON ON m m

•o a H fH iH fH o o fH fH o cn CM CM pH pH o pH pH CO CO pH o O pH iH ® <3 ® • 4J CO ^ o o O o o o o o o o o o O o o o o o o o o o o o o o

o

T3C o >» 00 ON ® •H 4J 00 -o pH pH CO CM pH CO CO pH. PH.

dl »W -H "*, tH ^ *H fO m fH PO <n CM fH vO r* VO o fH o o CM pH CO r* CO pH fH pH CM CM pH iH

•>T G ci d CN CN fM «N| CM CM CM rH pH iH o o o O CM CM pH pH o o o o o o O

J ® ® u

Cd u O. CJ 3. o. CO -<

Cd <u

I-] s

M-l H o ®

®

o 00 »H r«* ON ON ON o ON ON cn CM vO vO CM 00 ON ON ON m p" m in vO M3 u fi a \0 vO vO fH vO VO CM 00 vO vO vO pH iH vO VO 00 00 CM vO vO m m

JiH

4J *J c a

® (U u iJ ^e

00 a H O S CJ

ooooooooooooooo

cocoddddddddddddd

ooooooooooo ddddddddddo

iHHOOOO«n«-ti-IO • • • • iH o o o o

r-IOOtniTtmOOrHiH

• • iH iH O O

a 00 00 CO OO OO ON ON m in in ON vO 00 00 00 ON in m vO VO vO O o

o vO vO VO vO vO VO vO vO vO vO vO M3 CM CM M3 VO vO VO vO M3 vO cn cn ON ON ON ON CJN ON ON ON ON ON ON CJN ON ON ON ON ON ON ON ON ON C3N ON

00 • •

U

I,o

H4tJ)i-)iJ)hJi-Ji-4paPQnPQ

u H ®

a a

0 00 ® tH

CO ®

fH CS

tJ I I •fl' sr o o o *4 o O '3- O o o o o o o o o o O o o o

CM m vO CM cn cn vO vO cn vO cn M3 vO cn vO cn O CJ CJ O Cd CJ o prt X CJ o X X X X X M

sa S3 33 33 X X X S o o o o O O o o o o
75 IIIIIIiiin ao U •H rH a 4J CM cn m d <Ti o\- o^ y£> m ^43 cr> CM

n) 0) 0. 5^

4-1 > U cn CM iH iH

O

d

d tH

O o o CM CM CM

O iHO

H o CO cn -O 4»4 < - u CO CM vO in a 1 CO CO 00 cn 1-H cn rH pH in CM

(U

X

O '«*. sf 0 in <r 0 0 0 00 sr tH 0 00 vO pH 0

CO

M (0 iH CM c (0 3 8 0 0 cn 0 0 0 0 0 0 0 0 cn 0 0 o a a X cj •H 04 U C O

cO . ‘ .V Uu

r

X •a

ca (U

CO CCJCM o\ r~- sf 0 ONm rH pH ON cn cn CM 0 in

a

O (U s

•r4 O4

V4 CJ cn

m r>»m 'S’ 00 sr vO vO

mmm cn o X < a ta

(0 Uo ; - o

•H (U 4J M r-l X o> CM CJN CM iH

m vO iH ON 0 0 m 0 fH

H 0< 00 00 p*. 0 in !>. cn vn in

m ON ON CM NO

a *H fH iH CM fH 0 0 0 0 0 iH pH fH iH iH pH

T3 CD (U a CO s 0 0 0 0 0 p 0 0 0 0 0 0 . 0 0 0 a 0 >N pH ON CM

cd •H 4J 00 CM pH pH CM Ji CM •H 0 'S' 0 ON cn cn rH 00 iH 'S 0 0 pH NO 0 u •H > •H

CO

U 0 •H CJ CM iH 0 iH CM CM CM iH CM pH 0 0 •CM P^ 0

(U 4J 1 04 CJ 3.. bl CO <

•H

U 0

‘3

C < M CO H 0 CO CJ <i>

a

in CM r>. cn 00 ON cn cn cn ON CM nS

m rH •S'

G n- f" NO pH rH rH rH fH NO NO NO p" r" NO

14-1 Si CJ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

•H

d 0 0 0 0 0 0 d

d 0 0 0 0 0 0 >Nu H 3

CO 4Ju

G 0 , •3 Cd 3 pH pH pH G >-t 4J fH 0 pH pH rH fH fH rH iH 0 pH pH pH 0 pH

cd 00 3 • • • •H 0 0 0 0 CO 0

CJ •H

4J

CO •H >N

Vm ijcn

(U •H

a 00

m 00 00 ON ON cn cn ON

m 00 00 00

m 00

4J CO

u NO NO CM NO NO NO NO nO no NO CM CM NO NO CM 0 0 '

. ON cn cn cn cn ON ON ON ON cn cn cn cn ON cn

Cd (U 00 M

rt

a

j2

CJ Io

04

hJ I-) 0Q »-3 h-] PQ

cu 4J hO. >-3 ^3

h4 ' h4 - hJ iJ rd rH Cd 0 0 0 ‘ O' 'S' >s 0 0, 0 0 0 0 0 0 0 O4 G. NO NO NO NO CM CM cn NO NO NO cn NO NO NO NO a 00 0 CJ < P9 CO CO. CO CJ CJ CJ c 0 CJ

cd •H 0 CJ CJ U' w- » CO te] CO CO Cd

HHH

cn CO

(U a
Characteristics

and

Summary

of

Ethanol/Water

Mixture

Extractions

76

u

'^(0 u

<n NO o o

O O iH o o o

o o o • • • o o o

in CM ON QO 00

iH O O O O O

o o o o o o

o o o o o o • ••••• o o o o o o

ONO n* O «N O O CO

• • • o o o

ao

-H ^ fi iJ

(0 0) 4J > h

O fH O H O CO CO ^

OrHiHOcnCN|iHr-ICV»Ot-»OCONOON dddi-Iododooodooo

4J 00 a 1 09

4) X O ^ M A rH<N

(0 a a a Q X O

OsrOfHr>>oaoomoor^ONOON

CSOCNlOOcSOrO'^'S’vOcnrHOO

(fl dCM o s a

a. H u r'r^mcOi-t(-iinmminoo<r<TON

NOvomr«NO^vONOr^r^aooor«r*oNO

4) u

O. M 00 i 0) cn 3

oomvomfsinmooooncnin CSCNIiHOOr^HiHCSCNlCNICSlNCNJO

ddddddddddddddd

o >* •HUM •W *H

•H >

O -H O

4) U

a u 3. to -<

r^iHOoof^r^iHtHOr-OsroNi-iON

OiHCNi-liHfHOOOCSOCNr-tCstr-t

09

(0

4) 5

o

FHrHiHONOiHl^NO">d’'^'^'>d’'TNOON

i^r^t>.i-iCNjn«.m»nNONONONOr>»r»H ooooooooooooooo ddddddddddddddd

4J u

a a

CO 0) U U K 00 a

o X o

IrHOiHiHOinOmiHrHi—

I

• • • o o o

4J<n

•H a m 00 ON ON in o o ON ON m m m m ON

09 o NO NO NO NO NO CO CO CM CM NO NO NO NO NO d ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON

4) 00

O

04

hJ i-l i-q hJ hJ PO iJ bl hJ h1

4) 4J O o o O o o o o o o o o o O o

NO NO NO NO NO CO NO NO NO NO NO NO NO NO

04 a o o CQ pq o M M X 5g 2 z <3 <4 pq a 00 o o o o O o O o o o o o o o o

3 •H CO m m m m m m in m in m ON ON

C/9 09 bl bl b) M b) bl M bl Cd bl bl bl bl bl

4) Q
IIIIIIIIIIIIIii 3

U3•Oa

(Q

COO

•H

4J

CO •H

<0 uo

COu

CJ

75 co U *H iH C W

CO <u a&'S

4-t > O r-(

O

H

O CO cn ^

<!

CMm »n • • • cn CM r-lO ov ov o>

iH

O

O

O iH

vO 40 vO o d d

C3N CM

CM CM CM

4J 00 CM \om

d 1 CO 00 00 cn rW CO iH tH

m CM

d

X

O '»s. '0* o in «o- o o o 00 ST f-4 o 00 vO rH o

CO }4 (0 <-ICM d CO S S o o cn o o o o o o o o CO

d o 'T o O.Q X O

•H o< < * O ‘ .V. CO , * V MuX •d u (UCO C0<N CT» o ON in fH fH ON CO CO CM o sf

m

d

O

d s

•H a.

H

u CO

m f>.

m sr 00 sr vO NOm 1^mm CO

O

X < d

cO u

(J0

•H

d 4J

M rM JS ON CM o> CM fHm vO iH C3N p«. o o in o H Oi 00 00 r- o m <r n* CO m in m ON ON CM NO a -H iH rH CM fH o O o o o tH rH iH iH rH iH

•d CO

d c

CTt cn 5 o o o o o p o o o o o O . o o p d O >N iH ps ON CM

CO •H

H 00 CM fH

H CM

.d IH •H

OO ON CO CO rH 00 fH <r o o fH NO o H •H > -H

03 bl

O •HO CM iH o rH CM CM CM tH CM iH o o -CM o 'T d 4J I o. CJ 3.^ M rH CO < •H

td o

hJ

•5

d < CO H O CO U d in CM n. CO 00 ON ON

C3N ONC3N CM ST

m iH ST

da px. n. vO rH iH fH fH

H vO vO NO px. NO

iw is CJ

OO o o o o o o o o o o o o O 0 u d d o o o o o o o o o o o o o

4J

aa

<0 (U

S-l 4J 00 do s u

O iH oiH rM <H iH iHO rH rH o

'H

OO

a 00 in 00 00 ON C3N ON OV ON in 00 00 oo

m OO o vO NO CM NO NO NO NO NO NO NO CM CM NO NO CM ON C3N ON ON ON ON ON ON CTN ON CJN ON ON ON ON M

0)IiHO

PUd

0)u

iH CO o. d. e 00

cO "H M CO

(U Q

h3 hJ PQ )-3h3i-3hJi-Ji-Ji-3pQpQ •-4 hJ PQ

h3a 1-3 P h4 - p- h3

a hd

O o o O' O 0.0 o O

O o o o NO NO NO NO CM CM cn NO NO NO cn.NO NO NO NO o o < M 03 PQ. 03 03 O o CJ < CJ CJ

CJ CJ CJ Cd td Ed' Ed- Ed Ed' Ed Ed Ed

H

HH
Characteristics

and

Summary

of

Ethanol/Water

Mixture

Extractions

76

(0 u

ro vO o o O O fHO

O O

m CM cT» 00 00

iH O O O O O

o o o o o o

o o o o o o

ooo oooooo

a>O

CNO CO

• • • ooo

C3o a u o fH ^ o cn cs fH pH cs o pH o cn so os

<0 4) 4J > M ooo pH o o o o o o o o o o o

o O H O 09 cn <

CO a 1 09

4) X o O sf o iH o oo o cn o O C" o so OS M (13 rH <N • • • • • • • • • • • • • • • CO ti ^ a cs O cs o o cs o cn ST sr so cn pH o o

O. a X U

o. <

•S

(0 (0C4 ^ cn cn fH pH m cn cn cn O O '0- '4’ OS o S a

Q. d so cn so '«• so so n* QO CO t'' so

4) fH «C3 O f-t i*H '0' cs 'O’ <t 'O’ 'O’ so sr sf

Ot O o m VO m cs m cn O o o o cn cn cn a CS cs iH O O pH pH pH cs cs cs cs CS cs o

3 4) CO :s O d d o o o o o o o o o o o o

O >\

•H U 00

M-t "rl •>**. <rt > 1-i O -H o

(U u

a u =L

r^p^Ooor*«r^THr-loi^O*TO't-io\

OHCSr-liHrHOOOCSOCSiHCNr-J

OSC9

0) 5

o a r^r^r»i-(csr»io»nvovOsovor^p«.H

o ooooooooooooooo

dooooodooocsoodd

U

e a

(0 (U M iJ M

00 c

o S o

f-liHiHrHr-IOrHr-IOinOiniHiHr-l

• • • o o o

>» 4J<n

•H a cn cn s

OS OS cn o o os OS in cn m in os

09 u so so so so so cn cn cs cs so so so so so a os os OS OS OS OS OS os os OS os os os os C3S 4) 00

0

01

•H •J hJ h3 •d •d •d 04 •d 04 hJ d id

4) U o O O O o o O o o o o o o O O

so so so so so so cn so so so so >o so so so

CC. d o O <5 ca tP O M M s X z z c Ed a 00 o O O o o o O O o o o o O <5 o

3 •H rH cn cn cn m cn m cn m in cn in C'. os OS

cn CO M C4 Ed Ed Cd Ed Ed Ed Cd Ed Ed Ed Ed Ed Ed

(U Q
pleted, therefore it would be more desirable to discuss them when more information is available. Some preliminary information indicates that the migration of

into corn oil is about 20 times as slow in comparison with the migration

of C-oH»o at 60°C, and having a much greater temperature coefficient. The rate

Lo Jo

of migration of BHT into corn oil is at similar magnitudes as that of the ^32^

55

*

In the tables of experimental results given in the Appendix, the fractional

migrant migrated, M^/Mq, was listed as a function of time. Other units of concern, for example, M^/A may be calculated as (M^/Mq) (C^W^/A) from the various

parameters listed in Table E-3.

. r2-' The results are generally shown as graphs of versus t/L to allow

easier identification of other parameters. In cases is used in

place of M /M for simplicity. Thickness scaling is generally observed except

t ^

for a couple of isolated cases. The long dash lines or the dotted lines in the

1/2 graphs denote the linear t or t behavior, or a slope of 0.5 or 1 in the log

2 M /M vs. log (t/L ) plots, respectively.

U In many cases, especially when a large amount of solvent swelling occurs, a 1/2 pronounced enhancement from the normal linear t behavior is seen. For semiquantitative or trend analysis purposes, a may be estimated from the maximum

1/2 slope of a tangential line that passes through the origin in a M^/M^ versus t

plot, or from the highest tangential line having a slope of 0.5 in a log (M /M )

2

versus log t/L plot. Often in the extraction of octadecane by heptane, is

1/2 reached around M^/M^ 0.8. This is a much higher fraction than the linear t

region of a Fickian type diffusion behavior. Since most of the original migrant

has now been removed from the polymer, the so estimated represents the

minimum of the diffusion coefficient under the equilibrium swollen condition. On

1/2 the other hand, when a long initial linear t behavior is observed, the so

estimated may represent the maximum diffusion coefficient for the original unswollen polymer. Since D and t are inversely proportional, the interpretation in
78

the following section may use either the change in D or t, the fastness or slowness, in describing the experiments.

The interpretation of the extraction results from Sample C and D requires

special caution. The added amount of 0.01% labeled octadecane is probably not

very far from the concentration of the original oligomer fraction of octadecane in

polyethylene. The original oligomer fractions near the molecular weight of octadecane may also contribute to the total migration and having effects on the solubility.

The samples loaded with 1% of octadecane seem to lose some 10-20% of their

activities in 6 mo. - 1 year period to the surroundings. No significant change in

the efficiency of the liquid scintillation counter was detected over the same

period.

The amount of solvent intake listed in Table E-4 is generally obtained from

gravimetric method, and includes the amount of solvent absorbed to compensate for

the loss of migrant. In the case of extraction or exchange of pre-saturated

samples by unlabeled octadecane, the amount absorbed by the polymer may be checked

both by the radioactivity as well as by gravimetric weightings.

Migration of n-Octadecane into n-Heptane

Heptane has long been used as a fat-simulating solvent in a large number of

studies for migration of indirect food additives. The study reported here focuses

on the migratory behavior of an oligomer, n-octadecane, of polyethylene into nheptane. The results are summarized in Table E-4A, listed in the Appendix and are

shown in Figures E-lA, B and C for 24 “C, 30“C and 60"C extractions, respectively.

The following conclusions may be deduced from the results.

In general, thickness may be scaled as “ l/®<, as seen by comparing

(HA24, HA24L, HB24), (HC24, HD24) and (HA30, HB30) . For high solubility or

complete miscibility of the migrant in the solvent, there is no difference in the
79

results of the two methods of extraction, namely finite bath vs. infinite bath

(HA24L, HA24) .

.

' -

"

The only experiment in this series that caii be subjected to simple theoretical treatment is HE30, where the linear polyethylene ’sample has been saturated

with the oligomer octadecane to about 5% weight content prior to the extraction

experiment. The extraction or exchange of octadecane by heptane in this case

behaves as a normal Fickian diffusion. The final content of heptane in the

sample is also about 5%. . ; -

The migratory behavior is strongly dependent upon the initial oligomer content (HE30, HB30, HA30) since the oligomer may behave as a plasticizer or a

swelling agent to the polymer. At lower oligomer content and lower temperatures,

1/2 the initial extraction behavior seems to be linear with t . However, soon the

migration rate increases due to the absorption of the solvent. Maximum extraction rate is reached when the solvent intake has reached its maximum. However as

most of the migrant in the polymer has now been removed by the solvent, the

apparent maximum rate is far below that of a pre-swollen sample. Therefore the

apparent maximum diffusion coefficient is not a true characteristic of the migratory behavior but is an indication of the minimum diffusion coefficient under

the combined swollen condition caused by the migrant and the solvent.

The influence of temperature and crystallinity of the polymer may also include the effects due to the more rapid absorption of solvent at higher temperature or at higher amorphous content if the polymer has not been fully saturated

with low molecular weight hydrocarbons.

Migration of Labeled Octadecane into Unlabeled Octadecane

In order to gain more insight of the migratory behavior of oligomers of

polyethylene into light hydrocarbons, the migration of octadecane in the polymer

into octadecane as solvent was studied (Figures E-2A and B)

.

Similar conclusions may be drawn as that discussed in the section concerning
80

heptane as the solvent. When the polymer samples have been pre-saturated with 5%

octadecane for linear polyethylene (0E30, 0E60, 0F60) and 10% for branched

polyethylene (OH30, 0H60), the subsequent extraction or exchange of octadecane

follows a Fickian behavior. Deviations from a Fickian behavior become more

pronounced at lower temperatures and at lower initial octadecane content. Judging

from the results of the experiment OE60, it might have been performed on a sample

not yet fully saturated with octadecane. The amount of labeled octadecane intake

is estimated from the activities, which compares favorably with the gravimetrically

determined amount of unlabeled species moved in later on.

A decrease in the diffusion coefficient by a factor of 2 to 4 from that of

octadecane into heptane is observed. However, the crystallinity of the poljmier

seems to have no effect on the migration of octadecane into octadecane.

By increasing the temperature from 30 to 60®C, an increase of diffusion

coefficient by a factor of about 5 is observed. Thus the effects from changing

of good solvent and from changing of temperature could be viewed as having a common cause, changing in the viscosity of the solvent. Such a view may be tested

by measuring the viscosity concerned, in the future.

The literature values* for the diffusion coefficient of octadecane in low

—8 —8 2 density polyethylene are 4 x 10 and 16 x 10 cm /s at 40 and 60°C, respec-

—8

tively. These values are in good agreement with our findings of 4 x 10 and

—8

22 x 10 at 30 and 60“C, respectively.

Migration of Octadecane into Corn Oil, Ethanol and Trioctanoin

By comparing the results of corn oil extractions (CA60L, CC60L, CG60) with

that of heptane extractions (HA60, HC60, HG60) , it appears that at an initial

loading of 1% octadecane the diffusion constant changes by a factor of about 15.

Much greater differences are seen at lower initial loading. It seems that even

*1. Auerbach, W. R. Miller, W. C. Kuryla and S. D. Gehman, J. Polym. Sci., 28 , 129 (1958).
81

though both solvents may extract almost all of the migrant added to the polymer,

the kinetic behavior is vastly different. Hence heptane should not be considered

as a fat simulating solvent if migration kinetics may be involved. The estimated

diffusion coefficients along with that for heptane extractions are listed in

Table E-5.

In working with corn oil extractions, caution must be exercised to minimize

or compensate for the effect of chemiluminescence during the liquid scintillation

counting process. This is achieved by keeping the extract sample vial in the refrigerated counter overnite before counting data are accepted, and also by using

the random coincidence monitor feature to detect and correct for the remaining

single photon events.

Trioctanoin, a pure triglyceride, was selected as a fat-simulant, while it

was rather readily available. Along with the results of corn oil and trioctanoin

extractions, corresponding results of ethanol extractions on two linear and one

branched polyethylene samples are compared together in Figure E-3 . It is obvious

that all three corresponding sets of extractions behave practically identical to

each other, even the small irregularity at short times and low extraction level

for Sample A and C shows up in each of the extractions. At 60°C, all the results

at above 0.02 behave rather Fickian-like, especially for the cases of

branched polyethylene samples.

Unlike the results of migration of octadecane into octadecane, there is an

eight-fold increase in diffusion coefficient from linear to branched polyethylene. There appears also an five-fold increase in D when the initial octadecane

loading changes from 0.01 to 1%.

It seems that, at least for the case of octadecane, anhydrous ethanol could

act as a fat-simulant in a much more rational way than the use of heptane. One

shall reserve the comments about general suitability until the results on

and BHT migrations, as well as results from 30®C extraction, are completed.
TABLE E-5

Diffusion Coefficients

D X 10 ^ cm^/s

max

Sample Corn Oil Ethanol Trioctanoin Heptane*

A, LPE 1% 0.48 0.43 0.6 9

C, LPE 0.01% 0.08 0.11 0.12 7

G, BPE 1% 3.5 3.8 4.0 46
83

Octadecane is miscible with corn oil and trioctanoin at temperatures above

the melting point of n-C^gH^g. The solubilities rise sharply in a narrow temperature range just below the melting point of n-C^gH^g.

Migration of Octadecane into Ethanol

Results of extraction of octadecane by the more readily available anhydrous

ethanol are represented in Fig. E-4A for 24 and 30®C and Fig. E-4B for 60°C. The

results of extraction by 90% aqueous ethanol is also shown in Fig. E-4. Kinetically, the difference between the finite bath and infinite bath extractions,

e.g., (EB24, EB24L) and (EB60, EB60L) , are rather small. This is, however, a

borderline case where the convenience of a infinite bath experiment should be

abandoned in favor of a definitive finite bath experiment for kinetic as well as

equilibrium studies. The solubilities of octadecane in the solvent now is

finite. At 60®C the solubility of octadecane in anhydrous ethanol remained high

at 23%. However, the solubilities in 90% ethanol at 60®C and in anhydrous

ethanol at 30®C have dropped to about 3% and 11% respectively.

Therefore, at long times, indications of reaching an equilibrium partitioning of octadecane in the solvent and in the polymer may be seen from these

two latter cases and from the lower temperature and aqueous ethanol experiments.

There is definitely an influence of the original migrant level (EA60L, EC60L) and

influence of the crystallinity of the base polymer (EA60L, EB60) to the diffusion

coefficient. The magnitude of solvent intake and the subsequent enhancement of

the migration rate are far less pronounced in ethanol than that in heptane.

Fickian behavior is observed for the extraction of octadecane from branched polyethylene. Near Fickian behavior may be seen in other ethanol extractions. A

greater temperature dependency is seen for ethanol than for heptane.

Migration of Octadecane into Ethanol/Water Mixtures

(a) Solubility and the Mixed Solvent System

One of the most important factors to consider, in order to determine the
84

amount of migration, is the solubility of the migrant in the solvent. The solubility of n-octadecane in ethanol-water system spans over a range of more than

six orders of magnitude (Table E-6, Figure E-5) . These results were first obtained by gravimetric observations and were later more precisely determined by

14

means of C-labeled octadecane. The reproducibilities of the data at low ethanol

content are rather poor, partly due to evaporation of the solvent mixture and

partly due to contamination problems. Any contamination during the sampling

process by minute amount of undissolved suspension may cause an error in the

orders of magnitude above that of the solution itself.

It was thought that the wide-range of solubilities of the ethanol-water

system may be used to simulate a wide variety of solvents of interest. However,

as we may conclude from the following that, unless meticulous care is taken, the

extraction results may be somewhat difficult to Interpret using ethanol-water

mixtures as solvents. For extraction experiments lasting a long time, it is

1 difficult to keep the evaporation through the sample cbntalner seals to a very

low figure or to prevent the removal of some of the vapor phase during sampling

process. Since the vapor phase is ethanol-rich, the remaining liquid composition

drifts toward lower ethanol composition than the original composition. This

results to a drastic change in the solubility as well as the partition coefficient. A better mixed solvent system should be rather non-volatile. Perhaps

the system ethylene glycol-water would perform much better in this respect. In

any event, the absorption of the more compatible component of the solvent system

by the polymer may also change the composition of mixed solvent.

(b) Extraction Results

The results of migration of octadecane into a number of the ethanol-water

mixtures are shown in Figure E-6A, where the amount migrated is normalized by the

original amount of migrant in the polymer, Mq, and in Figure E-6B, where the

amount migrated is normalized by the final amount migrated, M^. In certain
85

TABLE E-6

Solubility of in Ethanol/Water System

Weight Fraction of C-gH.g

C2H^0H 11°C 30“C 60°C

0 1.2 X 10"^ 1.5 X

10"^ 1.7 X 10'^

5 5 X

10"^ 6 X 10"^

10 1.5 X 10"^ 1 X 10"^ 8 X 10"^

30 1.9 X

10"^ 2.5 X lO"^

50 1.9 X lO”^ 1.1 X

10"^ 1.3 X lO"'^

75 3.7 X 10"^ 0.0018 0.004

90 0.00183 0.0156 0.0316

95 0.0036 0.0387 0,0736

100 0.0089 0.113 0.226
-o

cases, where the loss of solvent is serious, the migrated amount or the solution

activity starts to drop drastically after a maximum value was reached, due to the

change in solubility and partition coefficient. This maximum amount of extraction

is the lower bound corresponding to the equilibrium concentration value as dictated by the partition coefficient.

The migration behavior is Fickian-like at high ethanol content but changes

toward a linear time dependency at lower ethanol content. When the polymer is

only loaded with 0.01% of octadecane, the estimated partition coefficient may be

lower than the actual value, since there is an undetermined amount of octadecane

present in the original polymer at comparable levels. At such a low additive

level, even the dissolution or extraction of species other than octadecane from

the original polymer may also effect the observation of the partition coefficient

for octadecane alone.

Some of the 50% aqueous ethanol extractions were subject to renewed extractions after each apparent equilibrium condition has been reached. Aside from the

experimental result from E50B60L, all the results on 50% aqueous ethanol extractions at 60°C (Figure E-7A and B) seem to behave in similar fashion and magnitude,

regardless of the crystallinity of the original polymer.

Figure E-8A and B show the results of 50% aqueous ethanol extraction on

branched polyethylene samples at two different temperatures. The 30°C extraction

seems to be about 4 times slower.

At low ethanol content, the solubility is low, therefore, a local partition

equilibrium may easily be established by only a very small amount of migrant. The

extraction of the migrant may depend more on the surface characteristics, mass

transport kinetics similar to that of dissolution, as well as agitation. Although

the eventual partition of the migrant is still determined by the partition coeff icient

.
87

(c) Partition Coefficient

Figure E-5 shows the observed partition coefficient from the experiments

shown in E-6A and B. The partition coefficient, K, is defined, at equilibrium,

as

M

s W + M

s s

W + M M W

_2 2. ^ _s • _E.

M . W M

P s P

where C and M represent the concentration and the weight of the migrant in either

the solvent, s, or the polymer, p. W and W represent the weights of polymer or

P ® solvent, respectively.

As a first approximation, one may estimate a reasonable partition coefficient from the more readily available or more easily obtainable solubility

data, such that

C

K V

C

p, sat

where C ^ and C ^ represent the independent saturation solubilities of the

s,sat p,sat

migrant concerned in the solvent and the polymer, respectively. The maximum

level of swelling of the migrant in the polymer is taken as the saturation solubility of the migrant in the polymer. For octadecane in linear and branched

polyethylene C is about 0.05 and 0.1, respectively. If the solubility is

further normalized to the amorphous content of the polymer, then C =0.25, or

P3> y K =4C , where the subscript denotes the amorphous region of the polymer.

^ S y s&c

The lattice theories yield a relationship

lnK=lnC + x "hi

s

GO Since the parameter x » which characterizes the thermodynamic interaction at infinite dilution of the migrant with the polymer, usually falls in the range

0 < x” < 2
It follows

2.7 C < K < 20 C

s s

The observed partition coefficients are listed in Table E-7 . These values

compare favorably with the assumption of K C /C and are also within

the range as predicted by lattice theories.

Migration of n-Octadecane into /from Polyethylene and 50/50 Ethanol/Water Mixture

When the distribution or partition coefficient is strongly in favor of the

polymer, the absorption of a migrant from the solution into the polymer will

cause a substantial change in the solution activity. Thus it is possible to

study the migration phenomenon via absorption into the polymer, in addition to

the commonly employed technique of extraction of the migrant out of the polymer.

Let the parameter a be defined as

W

P

Therefore,

M

s _ g

Mq “ 1+g ’

where the total amount of migrant M^ is defined as

M_ = M + M

0 s p

For extraction and absorption experiments, it is common to have

W

77^ 100 or a 100 k . W

P

Under this condition, and neglecting the amount of aliquot removed for analysis

(the weight of solvent and the total amount of migrant available for redistribution will change slightly from the original amount) , the following values
TABLE E-7

Partition Coefficients

of n-Octadecane in Aqueous Ethanol/Polyethylene

Solubility,

Weight Fraction

Sample % Ethanol K = C /C

s p

^18^38

30*C >

I, BPE 50

-4

2 X 10 1 X

10"^

60**C

C, LPE 10 3 X

10"^ 8 X

10"^

C, LPE 30 6 X

10”^ 2.5 X

10”^

C, LPE 50

-4

5 X 10

-4

1.3 X 10

A, LPE 50 0.001 1.3 X

10"^

B, LPE 50 0.001 1.3 X

10"^

I, BPE 50 ' 0.0009 1.3 X 10"^

M, BPE 50 0.0008 1.3 X

10“^

N, LPE 50 0.009 1.3 X 10"^

A, LPE 70 0.027 0.002

A, LPE 90 (0.3) 0.032
90

may be estimated for equilibrium conditions:

K

1 0.99

0.1 0.90

0.01 0.50

0.001 0.091

0.0001 0.0099

0.00001 , 0.0010

Therefore, in an experiment where the solvent weight is 100 times that of the

polymer weight, more than 90% of the migrant will be extracted if K is greater

than 0.1. Alternatively, more than 90% of a migrant in the solution will be absorbed by the polymer if K is less than 0.001. If the migration kinetics are to

be followed experimentally, it is quite possible to produce reliable data from

extraction aliquots even at relatively low solution concentrations or small

values of K, limited mainly by the background and the instrumental sensitivity.

In absorption experiments, however, the important parameter is the change in the

solution concentration from a relatively large value. When the total change

in is small, the data will be imprecise. Therefore, the value of a should be

less than 1 or K less than 0.01 at W /W 100 for a substantial solution cons p

centration change to occur during an absorption experiment.

I

Results from experiments involving absorption (immigration) of the migrant

octadecane into branched and linear polyethylene samples (E50M60R, E50N60R) from

a 2.5 ppm octadecane solution in 50% aqueous ethanol, and the subsequent extraction (emigration) experiments (E50M60L, E50N60L) are shown in Figure E-9A, where

the solution activity is normalized by the total activity of the system, M^, and

in Figure E-9B, where the absorbed or extracted activity is normalized by the

equilibrium amount migrated, M^, across the polymer /solvent interface. The partition coefficients for all four experiments reach a value about 0.001. The

_o

estimated maximum diffusion coefficients based on M{-/Moo are all about 4 x 10

—2 cm /s. Both of these figures compare favorably with the results of separate

[
extraction experiments (E50I60L, E30A60L, E50B60L) . The two absorption and

extraction experiments behave almost identical to each other, in spite of the

differences in the crystallinity of the base polymer. Similar observations were

91

noted as that for other experiments using 50% aqueous ethanol as solvent

same comments will apply here. However, the absorption experiments show

Fickian-like behavior rather than the behavior of close to a linear time

pendence as noted in the extraction experiments.

therefore

a quite

de-
92

(D

O (S>

(\J <E

U

\

L. X

Cvl <-J

OW /
93

PQ

I—

I

I U

0) 3

bO

•H

<M

<

<9

C»

O

(M —

I(9

OW / 1W

/

L^2

.

hr

/

cm
94

1...

N

CO 1 ®

•i

CM 4 O

C^J <£

U

\

i. X

CM

CN

-4

CD

CD

CD CM -

ICD

OW / IW
MI

grai !

on

of

n— C1

8H38

from

PoI

yothy I

ono

Inio

C18H38

95 IIIJI OW /

ti /

L'^2,

hr/

cm
Ml

oral I

on

of

n—

C18H38

from

Polyoihylono

Inio

C18H38 III

CM<

CM<N

ow /

cm
IIIIiiii

97

cnI M

(U

l-i 3

bO

•H

e»

Q G)

®W /

cm
98

C

><rI

(UU3

bO

•H

(O

U)

O CM<\ ^ X

G9^ % (M<N

(0

CM

G»

a

®W /

cm
fi

IIIiII1IIIIII

99

U) /

L^2,

hr/

cm
Solubility

and

Partition

Coeff*

I

c

I

ents

C

1

8H38

I

n

Aqu«ous

Ethano

I

and

Po

1

y«thy I

ene

100

Ic

0

00

(O

Q

(NJ

I CJI(9

CO

I I u>

1 (O

I

>1 JO *0

I

j

I

^

Ethanol
III

101 IIIII*I /

L*^2,

hr/

cm
MiQrallon

o*f

n—

C18H38

•From

Poly«ihyl*n«

into

Eihanol

/

Uoi«r

Mixiures

ai

60

C

102

OW /

/

L*^2

j

hr

/

cm
Migration

of

n-C18H38

from

Polyolhylono

into

50/50

Ethono

I

/Uator

Mixture

103
104

to

1 w

(Uu

d

60

- ®

0 ;

C'Jac

a.

M I ^ N

“ ®

<]•

i I i i 1 I ( a

(S

I i t i 1 i

©

J

CJ

i©

i ©

oOi^ / iw
105

II

li

II

T

I

me

.

Hours
Migration

of

n-C18H38

•Trom

Polyothylone

Into

50/50

Ethano I

/Wotor

Mixturo

1,06

cm
<JONI Cdu3

00 ft

I/) CO

<s

CO

I/)

CVJ

(9

(\J

inQ

LO

(9

<9 <90 (O 'T CM

<9U.30X9£

I- I liJ
108

C\J

03o\

I

U

3

CO

•H

o

Q

0

CSi

1 0

0

0 0 0

®w / qw

T

I

me^

Hour*
APPENDIX A

List of Experimental Data

CA60L, CC60L, CG60

EB24, EB24L, EB30L, EG30

EA60L, EB60, EB60L, EC60L, EG60

E50A60L, E70A60L, E90A60L

E50B60L, E50B60, E90B60

E10C60L, E30C60L, E50C60L

E50I30L, E50I60L

E50M60R, E50M60L, E50N60R, E50N60L

HA24L, HA24, HB24, HC24, HD24

HA30, HB30, HC30

HE30, HG30, HH30

HA60-1, HA60-2, HC60, HG60

OA30, OC30

OE30, OH30, 0130

OB60, 0C60

OE60, OF60, OH60, 0160

TA60L, TC60L, TG60
CA60L

CC60L

no

I

, CO CO CO c» 00 CT» Lo 00 o o CTv o>

*->1 o covoa^coooiOvo«^cT^coi— «!j-Lnr'^oooocT> 2: IS ooor-r— cMco^mr^oocno^cPicncrvcn

00 00000000000 000*0

oo

o

M

t/) i- CO CO

I— COOCOLO UO LDLO OOOi— CSJinOUOOCMOOOOOJCVJO

OOOOOOr— I— COLOr^»;i-CVJLr)«sJ-^t^

CVJ CO IT) CM O LT>

I— CO r—

+J O

Lf) f—

CM«^r^cor— oO'd-sj-r««.coir>cT>OLnocM OOOi— CMCOUDC^CTii— COCDLnCncOCDCri OOOOOOOOOi— I— I— CMCMCO^un

OLncoLnvocr>r— ococM

cOf— oocoo'^i-r^coco'^

r^oooocr>(T>cr>criCJ^cr»o

p

to

i-3

O

CO CO r— CO CD CO in oooi— CMLOOuoLOOLnLnooooooootocrimr^ooto^

r— I— CM's^-LOCO'^CMLOi— oor>.ooococricocytcoo

CMcoir)oOLr)<;t-cooocMLncnoOr- oco

I— CMC0 «?j-r^i— coLnc7^•^o

(— r— I— I— CM CO

•P o

OCT>^OOtOLOlf>OLOr^OO^O«:l-r-i— «;t- 0 <;d-<TiLf)tDr- r— r-CMCOmOOCMLOOOCMtOOr^CMCOmCOlDr— LOOOCTiOO oooooof— I— r— cMCMCo«sfLf>totDoooocn<T>cncno^

ooooooooooooooooooooooo

J

i' V

I

CO CO r— CO to CO in ooOi— cMiooLnmoooinomocMLnotooocMO

ooooooi— f— CM^tooocor— oo^or^oocototnin CMCO^tnCMCMCTiOOinCMtO

I— I— r— CM ^ cn
I

I

i

i

i

I

I

I

II

I

II

I

I(

II

I

I

I

ij 1

oCO

C3

UJ

oor— Lno<T>c\jCMcr>ooocvj^voiocriCT<cOr— «;j-cyicsjc3^Lno Oioooooooooi — r— cs!c>j<;fLf)tocrvoco«4-Lr>uncx3 ooc^coo«— nro«d-Ln — r— CMromior^oocoo'CT'cncyicrio OOOOOOOOOOOOOOOOCDOOOOOOcdi

CO CO

CO uD CO Ln tf> ooi— cviLnointnoLOOr— cvjoor—

U

3 LOOOOOOO oooooi— 1— <Nj*d-Lncx5 ';j-cooix5 LO>^Lnr— r^cMi— t— <n CMr+CMi— COlOUDOOCOCVJOOOCO

r— OJCOLDOOr— UOO'^OOCO

I— I— C\J CM CVJ CO

OCO

CO

UJ

+J o

«a- CO CM

CM Lft c» 00 CT» O I— r— CM CO LO 00 o o o o o o o

ir> CO r~. >— o r—

1— 'a' CO

r- r— 1— CM CM CO ^

or^co«o«a-or^co

cM^cx3O^«d'C0crico

uoLOvovor^r^r^oo ^ 00 CO O CM CM

lO C'. O'! O cr> Oreo 00 00 cr> 00 Cjc CTC

(O Cv CO

<— CO CO CO lO CO ooOl— cMcnounLnocooooooooooooooooooo • ••••••••••*« • OOOOOOt— r— CM<d-lOr^COi— COlOOOOOOCO«d-«;i-LOOOOCOrOCM

CMCO'3’CnCMCMCOCMCr»COCOCM<T»CDCOOI^

I— I— ,— cMCMcounr-~cMcocri^Lr)

r- I— I— CM CM

M- ior^cyiir>ooc3NiocMt>»iocoo

+j o I— cDcooofocoi^cTir— commooo S Iz: r— f— co«;#-coi^r^r^oooooooooocyv

oooooooooooooo

4J O

Is

CO CO ir» CM cr>

I— CM CO LT> CO o o o o o

o o o o o

cci CD cn O CD CO CO oo

I— F— CM CO *M" o o o o o

00 O <T> CO CM

CM o CO o

CD 00 00 cn o o o o o

CM

03

(/) t-3O

J= oominoooooooooo

r- CO Cn I— CO CfJ CO

I— ir> t— CT> 00 I— I— CM

LO 00

CO 00 o CO CM IT) CO O O COCM CM LO

00 CM LO

«#

CM

CO

c/1 ico r>~ 00 LO CO Oi— fOLDOOOOOOOOOOO

OOOOi— CM«3-00>:J-C0C0cDO1LOrCM ^ I— O •d' CO CM «d- o
EA60L

EB60

EC60L

112

CO CO VO UO Lf) csjrj-r*^Lr)r^«d-oc\j<T\counvoa^r^Or— csjcOi— c\j m cr» c\j vo r— (t» oooi— oo«^ooocNj^r^coc\jrocoovDcr^fOLnr>«..r*^r^co<T*o ooooooo*— r- r-r— csjfo^ir>r^r>.r^oocococooooooooo

rocj*'d“vocovo<— csjcr»r^r^ococn<T> u^r^o^crtcx)'— oor^r^r— CTiC7^(^o> oor— »— r-CM^unr^coa^a^o^o^ch

oVO

CD

I"II

p>. m CO ^ ro vo ro vn OOOf— CSJ lOLOLOOlOOOOOOOOOOCOOOOOOO

o o o o o o

.

•cvj^ioco^csjvDioOr— ^LDOvocorotooro

CNj CO If) o ^ ^ o csj 00 00 O 00

»— r— csjromrN.oc\jioo^^oO

r— r- r- r- CNJ CM

I"

II

r*^ CO h«* CO

r— CO VO CO tf> If) ooo»— CMLOOOOOLOOCSJOOO

O O O O O O I cM«^ior^^cocoi^

csj CD oLO CM

r— vncvjr— COtOOOOO«^»— Of— fOVOvOt^OO hN.COCOCOCM^C0^CDC\jr^C0C0C00000C000 O^CVJC0^Lf)V0C0000)O0)OO)0)CD0)O OOOOOOOOOOQOOOOOOO £ l£ o<x> CO

Or— CMI^O>OnrOOOOO^r— COVOOOlOO>i— 00 Lnr-oif)rounoot^crvOir)i— vovooiocMt^vo OOr— r-CMrO«^ir)lOOOCOO'CT'CT>OCT><7lO'CTk

CMF- m CO m LO _ OOl— COlOOOOlOLOOlOOuOLOVOOO

OOOOOf— CVJ<3-LOr^^Lf)CM^VOC0^*^

CMlf)r^<3*«4“r-r-rO

r— CM CO If)

CO CO

I— CO VO CO If) CM CM O CM _ ooor— cMLOOLf)vftOtno)voocoa>r-r«*iro

OOOOOOr— r— CM’Sd’LOr^COi— Lf)i— ocovo

CM CO If) CM CM 00 CM i— CM CO VO

^f>O^O^VOO^OLOO^^>«O^Lf)CO^^lf)OO^^r— CM^VOOCOinOCOr^CMCM^CMCOOVO OOOOOt— I— r— f— CMCMC0Lf)r^ChO)a)O)

It

II

CO CO *— CO VO CO If) CO OOOf— CMLf)OLOLf)OLnOOCOC)CO^O oooooof— r— cM'^vnco^LOOvo^oo

CM LO r— r- 00 LO f— CM ^ LO

r

t

I

I

I

I

721.1

.970
I

i

I

I

\

I

I

I

oVOcocr> LU

o CO o VO 00 CM r— O VO VO in VO 00 00 cn o m VO CO o tn CM CO V£> cr» CM 00 CM vr> 00 LT> f“ vn r-» CM 00 00 CTi CTi o

o O o o o O *— »— CM CM CM IT) VO VO 00 00 OD 00 00 00 00 cr» o O o o o O o o o O O O O o o o o o o o o o o o

VO ro VO CO r— CO VO CO to O ooof— cvjLOOLomoLOLOioiotoOioiocsiuomr^a^o

o o o o o o f— csj^Lor^coi— 00^000 CsJ CO lO CM CM »— I— CM

00 lO

00 00 CM

CM CO lO

CM

CT» O 00 CM

I

I

I

I

. c^«^Ln«;rI— t>>ococouDOCMCocnLno^ooo>r^

-t-> I o O'— CNjcounr^i— rovo<T>cvitnoocvjioior^vor^

s: Is oooooof—r— r— ^cvie\jco«:tLntOLf>i/>Ln

ooooooooooooooooooo —IoVOcoI

UJ

CM n cn ^ cn VO

I— r- CM CO

ui CO CO

S- r— CO VO CO UO 3 ooo.— cMvnoLOvnovnuo vno vn vn cm ^ o

XZ OOOOOOr— >— CM*^vnr^^OVOVOVO«TCO

I

I

I

II

i I

t

2: Is

CTi 00 00 O r— CM ooo ooo

ovcMc^cocoi— CMLor^^

>^oo<d-vO'a-r^r^cor^co OOi— CMCO"^UOVOVOVO OOOOOOOOOO

p^cM«d-cocor^<»vor^vo O'— CM«^f'«*a-vocMcr>^ oooooi— CM«;i-Lr)cri OOOOOOOOOO

cjvvor— vovnvoooo CMLnoi^covor>.cM ooi— I— cMcOLor^ oooooooo

O 00 O O00 OOOOOOOOOOOOO OOOOOOOOOO OOOOOOOOOOO

OVOcovr> LU

C'. CO CO

I— CO VO CO Lf> LO o o o I— cMLOovovnoLDOr-.

oooooOlI— CM"^vor^ro

CM

CO CO

I— CO VO CO m OOOr— CMIOOOIOLO

CO r~. CO oovocovootn LOLf) Or— COvDOr^OOCMf'.C'.

OOOOOOi— CMCOO

CM O o o o •vf 00 CO

CM

II

fi

II

It

I
E10C60L

E50C60L

114

'd" r-~ CM CM 00 CD cn 1— CO CO CO CO CD CM o CM 'd- r— cn CD CO 00 CO CM 'd" 00 CO LD CD o o O o r— 1— CM CO ID o o o 1— 1— CM CM CM o o O o o o O O O o O o o o o o O O O

coooooooooo oooooooo

(/) CO

1— CD CD CO CD 1^ LD CD

CO 1^ CO CD ID LD

S- oOl— cooooocDOr^ r— CO CD O O o C'.. o OOOOi— CM'd-r'^COOLD o O O 1— CM <=a- CD CO

CM CO CTi CM

fd

(X) cvj <T> 00 O CM OJ CM OJ CM o o o o o o

o o o o o o

o o o o o o

0*00000

od"oo

o

<x>

C_) oCO

to o o o o o

s_D CD CM 00 CM o CM C3^ CM CD

1 LD

CO o

s- • D

O CVJ

oCO

CQoLD

I— o 1—

, COLOCTlI^COOr— r^OCM«d-OOCMCM'd-<OCO

+-> o ooOl— cocDoocTii— Locor^r^r^r^r^r^

e: Is; OOOOOOOOr— i— r— — i— i— r— — r— ooooooooooooooooo

O OO lO

CD ro CD CO

CO CO CO CO

I— cococoLoocn ooOl

cMLor^OLOLOLnuncoLOLoOLn

o o o o o o o CM'd-C'-cot— 'd-coco

CM CO LO CD «d- t— CO

I

96.0

0.00070

192.0

0.00068

528.0

0.00064

792.0

0.00061

1464.0

0.00066
115

I

I

I

I

I

I

I

I

I

I

I

-p o

r>. I— CO r— CM r^ o o o o o o o

I— ro CT> I— ^ CO Lf) o I— CM CO Lf> o o o o

CM CO I—

00 CM n 00

Lf) CO CO CO o o o o

CD CT> ro

LO CM CO

CO CO CO CO o o o o

o

o

oCO

t—

t

oIT) UJ

1/1 S-3

o

CO CO CO CO CO Lo CM o oOr— cMLf)OLnunouooc^»oocoo^c^lco

OOOOOr-r— CM^LOOOCOi— r^oicnoo

CM CO <T> CO LO O r— CO LO

oCOoLO

LiJ

I CMco'ij-r^ooLocococooor^r^r^ -•-» Ip OOOOl— r— I— I— I— r-r-r— I—

s: is: oooooooooooooo ***•••••••••••

CO

00 CO OOCMCMlOr^LO ololooc^ocolooc^locmocm

I— I— CM«^fLn00COr— OOUOi— CO«:t CO CMCO«^COCMi— 00 00 I— CM CO
E50M60R

E50N60R

116

«;^•CSJ^^CO^Uf>^^^0<^J^^^OCS4COCOO^O^VOO> o »^vor— cr>cocNjcr»cr»coo«^«^r— ooo^oooo^*^ S Is a^CnO^OO^^r^LO^^O^OC^JC^JC^JC^JCSJr-r-^-r— ooooooooooooooooooo

CNJCSiiOOinr^^OCM«^ 0>CM^CM^Of^C^

^^^(sjfOr^rof0 ^ro<sir^OvDfOCNJtn<^jfi

o OOOOOOOOOOOOOOOOOO OOOOO^CSJCO^LOl^^^^^^gJg

oooooooooooooooooo

oVDoir>

I"11

CO fO

I— COt^rOlT) CVILOLO ooor- csjLnouoir)Oir>o^cvjcouf>o^r^

O O O O O O r~ 1 CM^lDOOvO^mCSJOOrCNj fo uo o o wo m r- CO CO ir>

rs. ro fo

r- fo lO CO LO CO CO ooor— cvjLnOLnunoir>a»woa\p^coa^o OOOOOOi— r— CSJ«5j*lf>r^COr— o^wocooo

CO CO r- I— CO m r- CU CO Sjcowoo^cocowocsicocoocoootor^ mr-.-roLOr^or^^^i'^corocoro

OOr^VO^CNJCJr-f— ^r— f— r— ^r—

oooooooooooooo

r— o>\o^rowocooo^^co<oroinroroir)ir>^

r— rowocvjr-rN.voLr>r-ro^wor^<T>c\jotr>r^ OOOOOr-cvjcvjro^mLf>if)t/)u>^tr)u>iom oooooooooooooooooooo

oooooooooooooooooooo

\t

u

mevjLnoooowcMLOevj

CT> CM CNJ CO O

OOl— cvj^vot'.'i' • • ••••

CM I— in VD O O ro in I— i— VD CM CM CO CO

\t

Li

CO CO ^ ^ _ r— ro wo CO LO LD CO CO ooor— csjLOOir>LOOLOO>p^Q>or^r^r^CNJtn

ooooooi— r— cj«3-Lor^«^*— loom^co^

OJCOLOr— f— COtOCSJ

r- csj CO m
117

^ cn o CO ro ^ VO ^ o to 00 csj ^ ir>

' O cocsjoooounooovoOr-LnLnvor^h^r^

Is Op-f— <^J^vooocoo^o^o^o^a^ovo^a»

oooooooooooooooo

CO <n

r- CO VO CO IT) ooor- csjioooooooooom

OOOOOOr^CNJ«^VOC\JO^OOVOVO

CSJ CO 0> <• r— 00 ^ e^j csj

I

I

III

II

I

eTIsP

•I

(Oa^roroinrocNJOocstcvir^cvioooo^^m CMromeO'— (O>^r^voo^vovor^r^r^r^^ ooooi— r-csiroioat9>o>aio>9iotato»

oooooooooooooooooo

lA

esi lA o lo OOi— CMlAOOOOOOOlAtOLOOLOir)

ooooo>— csj^cooocNj>— ^ror^csip-oo

r— CSJ csj ^ in lA

lOkOi— CMin^wcuin*^' ^roo^r^miDiDr«.r^t^ O 00 00 o> Ot Ot oooooooooo

_l 1 M 1 ? CSJ 1 $ o

1 X

r— oooooommtA

ovo •nooioioooinin >— c\j«a-r~ni— or~-io

»— esj po ro VO

I

I

I

I

iOvo^cococMCMr^fOcsjr^coOr— CO r— c\j^vooo«^r^o^coi— coir>vor>^ OOOOi— CSJCO«d'<X>f> 00 C000 C000

ooooooooooooooo

Lf) 00

00o

^1csj| qI

CO CO CO VO CO m ooi— CNjvnooooooooooio OOOOO*— CM^OOOCSJVO^Oa^OCSJ

CMCSJ<y»^Cr» 00 vOC7\ f— CVJ ^ VO

. oovf)Oa>a^vovooovof>^oor^^GOcoa^cocor^^

t O Of— c\)CMoouococsjo>vovDcoco«^io‘or^r^ooa^ S IS O O O O O O O f— I— VO r-* 00 00 CO 00 00 00 CO 00 oooococ>oooociooc:>o’cic>c)oo

CO Cn. CO

CO VO CO vn LOLnOLOLOLOLOLDm OOf— OJ iooooOfvJCsjLnr^r^r^r^r^r^OO OOOOOf—

C

vJc^COr^r— OrOCSJVDOOCOlOOD CNjr^LO^Or-VOr— or^o F— cvjcgco^mvoc^o
118

ro

, r^or^iDooovor^coi— oc\Jr^i— «;a- 0 '^i-cT>oorovDOJC\JCOro

+-> o Or— I— cMcoLnr^OLoOi— '^or^cnooor— coLr>(X)r^cX)coo^

2: Is: OOOOOOOi— I— (NJOLnVOOOr^OOOOOOOOCOOOOOOOOO 0000000000000000000000000

oCOo

CO CO LO tocoocoun un t^oo s- ooi— CMLnOLnLnoLDOOOOooocor^LnOLT) • • • +J 3 COVOCTi O OOOOOi— I

CM'd-LDCJ^'^fCOOOOOLn^OOOOOOCOO -c c\jco«^Lr>c\jr^CMcooocMr^c\jLncTi

I— I— cMco^r^cOi— r— I—

«;j- o o

O I— I— 0 CM Lf) CM IT) CO CT» CTi CTi CM CO 00 cr> 0 P— (Ti 0 CO LT> LO CO CO CO CO

CO •5^- r>^ 00 00 00 00 CT« cn CTi <T> CTt CTt cn CTi CT> oCO

CQ

+->

(/I s-3

o

1^ CO CO r— COOCOUO COOJOCO OOOl— CMliOOmmOLOi— CXDCX3COO «c»- CM LO CM ooooool— I— CM^LOoococ>.cr>^r^'?t-r^Ln

CM«^fr^>^i— oot^uo

r— CM CO UO CO

, COLOCOLOi— COi— COC^>LOCMOOOCOCOCD'^CTlCM«;^^^CX^OCM«^^«^^

+-> o CMCo«;J-cocT>CMir)r^i— CTioO'^J-coo^LomcDcococor^r^i^r^

s; Is: OOOOOi

I— I— cMCM«=j-LncooocT»CTio%ocncT»cricr>cT><n(ncri 00000000000000000000000000

oCO

CO CO

to f— CO CO CO CO 0 Lf) in

s- 0 0 0 >— CM Lf) r>. 0 in LO 0 LO in 0 in 0 CM in CO in in in 0 0 0 0

0 CD 0 0 0 0 0 0 1— CM in , CO CO O) 00 CO CM CO O) CM CO cn CD CO CO CO CO CO CO

r““ r— CM CO in CO 0 CM

I

I

2407.0

0.898

2905.0

0.902

3409.0

0.905

3894.0

0.908

4517.0

0.910
119

I

I

I'

I

I

I

I

I

I

I

I

I

I

I

I

I

oCO

Lnr^«^<nr^«!d-coc\j^i— Lf)<^cM«^Oi— c>jco';a-

«:d‘if)oocvjcor^oooOi— OLOr^cooocTicno^cTicrt oooi

I— c\jcoLncocTi<TicTia^cria^cTicricncri

ooooooooooooooooooo

LO CO CO

(/) LO 00 CO CO CO

S- O o pi* CO CO CO CD CO CO ID o CM 3 O o o o o

CM CD ,0 ,5 .5 O CO LO 00 CM o C7> ID o

C3 o o o o o O O r— I— CM un CO CO 00 CM

CM CO

, vocr>vor^oo<x>o^oc\jcsjcvj«^r>.ovococT>o

+J O ?fvooir)>!^r^<T>CMvOi— <:d-r>.r^oooocooocT>

s: Is: oor— r— c^^^o^^^coo^a^c^>c^c3^c3^a^o^cTl

oCO

C3

(A

i-3

O

x;

CO CO

CO CO CO ID o o CM LO .0 .5 .5 O LD O o O O CO CM <3 o o O O r— 1— CM LD CO CM 00 (T> LD CO 00

CM CO r— r— 00 CM

r— CM CO CO

oro

LiJ r

+j o

ro CO CT» ir> 00

00 •d- 00 00 LO O I— I— cvj CO ^

C\J C\J CO CSJ r— r>. CO

in CO CO r>. 00

CO p>. o cn I—

CM «;i- CO 00 00

CTt CT> CTi CTi CTi <Ti COCyiOr—i—r—

00 00 CT> cr> on CT>

CTi 0^ CT» C7> CTi

+->

V)

s-3

o

CO CO CO

I— cocococoocooLOLOLOLOiOLOLncnooLncx) OOOi— cocni^ocMi^r^ccir^r^cMr^OLor^co

ooooooOi—i—p—cM^Lnr^<^r—co«d-oO'^

CM CO <0^ "sa" C3^ CD

I— t— CM

438.75 533.75 652.25
120

CT> r— un 00 00 00 ocTi<^'^coc\jioooafscr>cr»cno^

^oc\Jcooocrirocr><T«o^cncT>o^cTt

I— c\jrO'^'X>o^cricTiCTi<TicT>CTicri

ooooooooooooo

o<x>

CJ3

I/) &_3

o

SI

CO ro

I— CO VO CO LT) LO LO ooOl— CMLoOLDLOLninr^cM

ooooooi— I— csj«^roLor^

C\J CTi VO

CVJ

oOr— o»oo<hvovooor^ocvjvoO'^LnooocMLnvor^oooo vr>cTirooovocvjc\aocM>^Lnunvovovovor^r>.r^r^r^r>.oooo ooi— c^Jco«d•voooo^c^»cy(cr) 0^o^cTl 0^cr>cT>CT>cy»a^cT>o^o^o^

oVOo

cn CO

CO VO CO LO

(/) o o CM LO ,0 ,5 ,5 O LO O o O o o O o o VO VO O VO o O o

3 o o o O O r— 1— CM LO cn CO LO LO CM VO o 00 o VO O CM CO LO CT> o CO CO CM r— o CO VO sz r— r— CM CO LO 1^ cr> CM LO LO

I oVO

cc

vncvjvoooocvjvoooor—

vooor^vovooooooocno^

cMcoLnoocT>(ncr»cT>cTio^

oooooooooo

(/) S- lOOsJLOOOOOOOOO

o o CM 00 00 O 00

CM ^ CM VO

CM

I OVO

<c

OOOCMCT>OOCMVOOOOi— voi^r^vnvocooooocncn

CMCOLOCX)(T>CTl(T>CTiCr>CT>

oooooooooo

vncMunoooooooo

o o CM 00 00 O 00

CM «^1- CM VO

I

J

I J

I

)

I
121

I

I

I

I

I

I

I

1

I

I

I

I

I

I

I

II

I

ooooo

00 lO CO o 00 CJ 1— LO <n LO ^ r— CM (T> '=d- o LO o

o o J— CM CO r— cn 00 r— o p— CO 00 00 cn o o 1

o o o o o o o 1— CM CM to r>. r>«. 00 00 00 00 00 00 00 CO cn cn cn oooooooooooooooooooooooo

t/) s-3

o

CO CO

00 VO CO kO Or-rOVOOOOOOOOOOOOOOOOOOOOO

OOOOl— CM^rv.rOi— voro«:i-CT>r^ou3«ocsjrocvJO<or^

cMcoCT»o«st-cr>v^«OLn(T>r^i— <^03000

1— I— r— c\jco-^<oc\JvocT>rooOLr>

I— I— I— cvj c\j ro

M O

CO CO CO r— to to CM cn CO CM to CM o to LO LO r>. to cn LO 00 CM r— o r— CM LO 00 o CM LO 00 CO to 00 oo CO =^‘ LO LO to to to o o o O O o o o 1— r— I— r" CM CO 00 00 00 cn cn cn cn cn cn cn cn cn cn oooooooooooooooooooooooooooo

oro

<co

CO CO

to I— cotocotootn

s- ooOl— c\jLor^omLnOLOLnoir>OLOOLOLOcoLOLnunoooo

o o o o o o o c\j un r—^ ^ i— to CM CO CM CO 00 «:3- CTi oo^intDi—

f— r— I— r— CM CO

CO CO CM CO CM

CO CO CO

tr> to o CO

to

un
0H30

122

ro O (Ti O I— O 00 I— CM C\J «!l- Ln «X) 00 o o o o o o o

ocMO^r'.CTi'^a-cooi— cduocmco

covocTir— r^CMOOco«::f-LOcr5r^r^

I— I— I— CMCMco'^(-t'^oocTicr»cr>(3^cn

oCO

CO CO r>^

1— CO to

=5 o o o

o

00 to to 1^ tn I— CM tn 00 oooooooo CMCM^LOOO'^COOOtDCMOOt—

CM CM to

coocr>«Nfi— r^otDr''OOioo<^ocT>i— o^t^i— co co tn CM«^tnt^cT>r— ^r'.(n«^co«!^oooio^cMCMOoocy>cT>cr>cr>cr> OOOOOi— I— I— r— CMCMCO'^«^hlOCOr^OOCT»CJ^CT>CT>CT«CriCTi

(locDcijocjcdocijooczjcocooooooocooocDoo

CM

CO o i-3

o CD

oOl— CO cor^coco corococococococor'^cocor^r^ OCMOOLOOOi—OOCOLO COOOOOOOCOOOOOOOi— OOCOi—i— to OOOOOr— I— CMrOLOI^Cri«^CriC3^<T>CT>CT>OOCriCM<;l-COO

oooooooooooo CMCOtnOOCOi— OOtOCMOO

CM CO <=i- tn to

z:

oCO

cocTir^,— o o CO cn (— cm cm co cooovocMCMcOi— cooococr(cricr>cr>

r— r— CMCO«d"Ur>r^CT'CTlCTlCTlCn<TlCri

oooooooooooooo

CO

1— COCOOOOOOOtOOOOO

ooor— cM^oo«^oocnc30 r>.t— cT> CM «;i- CO 1— CO

I— CM CM CO
0B60

0C60

123

I— ro«:j-^D«X)mcvjcoLOOo<T>fOcoro>=^-ooO'^r«^ocM«:i-Ln ^vo(T>cocr»oOLnvocy»oooojro<;i-LnLnio'sD^or^r^r^r^ OOOr— r— C\JCO«^Lf)r—^OOCT>CT'<T>(T>CriCr>CT»CT>(T>Cr>CT>Cr>

ooooooooooooooooooooooo

cr>

cr> CT> o o

+J

10

i-3

O

CO r>. ro CO cokocoLO CO I— inLOi— OOr— CMLnOLf>LOOLnOOOOOOOCT»VOCsJCOO<£)OOCO

OOOOOt— I— <M«^Lf)00>!^-CMr^C\JUDLf)COOOOOCsJCT«CT>Lf>

cvjcoLT>cvjr>^c\j«:i-ooc\jcoOLncno

r— I— ojco«:i-r^ocoLnoo^

i^cMoo«^r^oc\jco«d-Lo

00CsJr>.00COCT»CT»cy»CT>CT>

<-ocr>cr>cTicricn<Tio^<T>cT>

oooooooooo

+J

CO

S-3

o

inc^iLnoooooooo

OOi— c«j«;^00^00r^00

<NJ C\J CD
oVO

t—

<

o

CM VO CO to IT) o CM CO o 00 o CO 00 00 00

r* VO CM 00 CO 00 cr» o CM VO CT> CT> CTV CTV CTV CTl

4-> o o CM CM CO tn CO (Ti <T> CT> CT> CTV CTV CTv CT> ov

s; 2: ooooooooooooooooooo

124 I

I

I

]

I

CO

s_3o

ro I— ro

r— covoi— oocn in m oooor^ OOOf— r— Ojinr^oinoinor^ocoor-r^ ooooooooi—r— cMCM^inoococsjoor««.

CM CO «a- o

„ 00 cvj 00 00 O O Ln«d-covocooooomoi— vo«^cvjOoo«Mcr>cur^ooooooooooovov coo^vooii— «^OLno^r«*^inr^>;j-covocT>cr>cr>cr>cTiCT>ov<y*cT» Or— r— I— I— C\ICMrOrOCO^mvDI^COCT>O^CT>Cri<TiCTlCTi<TlCr>avO»

oooooooooooooooooooooooooo

oVO

I"u

LDi— r^mroor^ofor^oro Or-i— csjromvDOcovOLrtfoom ooooooor-p-r- csjroii^r^otnoooooooa^r^io OOOOOOOOOOOOOOr-r— CVJCOtnOO^CMOOincOO^

csj CO ^ ir> ^

o 00

iO LT> VO

f— CM CO ^

CO *51“ CM 00 ^ ^ VO Cn.

vr> VO 00

CO CO ^ ^ ^ cv 0>

o> ^ ^

LO VO VO VO 010 0^0%

CTv CTl

4-> O

CO O f—

cn o CO VO

CO I— o CM CO cr^ CT\CM CO CO

o^ o> o^

o% o> o^ ^ ^ lO

o^ o^ o> o> ^ VO

o> oooooooooooooooo ooooooooooooooo

oVO

Ul oVO o CO

00 CO 1^ or-covoounvoooootooooo

OOOOf— n-CM^VDOOCOr— oo^cocr^

CM CO CM VO CM I—

I— r— CM CO

CO CO

in CO 00 CO

i- o o r* CO ,6 ,0 ,5 o o to o o O to IT) o o o o o O 1— 1— CM CO 00 CM 00

JC CM o CTV
125

I

I

\

»

I

I

I

I

I

o

to

. ir> CO CT» »;1' 00 VO r>. to CM to CO VO ^ to O CVJ

4-> o <;t-r^OLnococT>r^cr>i— crvioco'ri-tDr^coo^ £ Is ooi— r^cvjcvjco«;*-inr^r^oocr»cr»crvo^o^CT>

oooooooooooooooooo

CO CO

I— CO to CO to I— to to OOOr— CVJtOOtOtOOtOtOOlOCVJOC\J<T>

OOOOOOr-f— CSI<d-tOr^«;J’r-i— CT^OOtO

csi CO 1^ to «;! CO I— to

, r— r— to 4->0 ct'toootnr^^ro.cM^f— cor— toCTlcooootooooc^>o^«;^•evJ S Is OOOr— CSJ«^tOCOOCOlOCOO>COtOCVJCOr^r— OOOOOOOOr— r-r-r— CVJC0 tnr^00 00 O%Cr»Cy>CT>CT>O%

otoo

+J

(/) i-3

o

CO CO f— CO to CO to OOOr— CVJtOOtOtOOLOOOOOOOOOtOCTttOCOO

r— I— CM^LOOO^CMr— tOO>OOr^-=i-LOr— LOi— cvjcoor^tocooooOLOcocvj

f— r— CVJCO';l-r^r-COLOO

t— r— r— C\J

«!l-CkJCMtOCOt^i— tOCOOOtOOOOOCOr-.f— ^VOOOOOCO

I— cvjco^tootcotoo'csitoooco^fcvj'sfcsjtor^oor-

+J o oooooor— I— I— cvjcsjcM^uocooocTicnatcricri

E S ooooooooooooooooooooo

oto

<c

to

s-3

o

C> CO CO

I— CO to CO to CO CO OOOr— CSJtOOtOtOOtOOtOOCOtOOtOOCOr^

OOOOOOi— r— C\i«^ tor»«^otOfO«^^roi

evicotnot^tocooto

I— I— cvi ^ CTi

L26

APPENDIX B

Here we briefly outline the Laplace transform solution to the diffusion

problem posed in Section I [Eqs. (22)-(28)].

The Laplace transform of the diffusion Eqs. (22) and (23) [subject to the

initial conditions in Eq. (24)] are

2— ^ - q^C + C /D = 0 (B.l)

and

q^C

s s 0 (B.2)

where

q^ = p/D and q^ = p/D (B.3)

s s

Bars over a variable denote the transform of that variable and p is the transform

variable.

Equations (B.l) and (B.2) are ordinary, second-order differential equations

whose general solutions are well-known:

C = a,e^^ + a.,e + C /p (B.4)

i Z o

_ <1 ^ “‘I X

C = b,e si ® + b.e ® (B.5)

2

where a^, b^, and are constants of integration. These constants are determined from the transformed boundary conditions, Eqs. (25)-(28):

C (0,p) = KC(0,p)

s

J(0,p)

dC

s

s dx

(B.6)

(B.7)
I

Taf

1 r< 1 3

ii:.;, 1 .= ! ' , .. ..:

‘

I , j, (';-,; .V .^’T * n;t^/. .’,

. ..

.

; -v ,, > ^

'

Jj- JtOt

i

fi ?.^'

’'

: . ')

1 !' \ li/ ••>" -

'

a-

( ' . ''i..*

I t

‘

>r(i et I! ht^<^ ‘v£*f:ii.H*iev --.'tOiaiJa-i- a*ir

. P'

, i ,. > : o ^i»xB (£ .S)

. la

) . rf ~

I fil . •

j n •>)•'

X;> - qV^n •=

' ' -'I ' ^

.;• n*

1

’

C'’ ,d)

f / T B €

' »rfr ,Tg:)..Jn:l; Ho J

- • -

' ' '

.,,,, ,

. vii';fc’vcr' f V-

' : c

•ii

f «)

' .

,'. Hi " ' 4

•• ' •

I ’. • * I ^ ff xb

\
127

dC

dx

X->-oo 0

— 2k —

pc^0i^,p) - - ~ J(o,p)

s

Boundary condition (B.8) implies that

= Q

The other 3 boundary conditions yield 3 simultaneous linear equations

unknowns a^, b^, and b

2

* These equations are easily solved by Cramer'

From (B.4), (B.7) and (B.IO), we have

J(0,p) = (Dp)^'^^a

where

-a, = aC cosh(t p) o s*^ 1/2

2(Dp)^^^ + a£p [cosh(t^p)^^^ + y ^ sinh(t^p)

]

Combining (B.ll) and (B.12) and using Eq. (1.18) for C^, we obtain Eq.

(B.8)

(B.9)

(B.IO)

in the 3

s rule.

(B.ll)

(B.12)

(1.29)

.
NBS-114A IREV. 9-76)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 80-1999

3. Accession No.

4. TITLE AND SUBTITLE

Models for the Migration of Additives in Polyolefins

5. Publication Date August 1980

5. PwforirJng Organ! z|itlont^o

7. AUTHOR(S) L. E. Smith, S. S. Chang, F. L. McCrackin,

I. C. Sanchez and G. A. Senich

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS fSfreer. City, St^te, ZIP)

Bureau of Foods

Food and Drug Administration

Washington, D.C. 20201

13. Type of Report & Period Covered

15. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.) In addition to continuing our experimental and theoretical program as previously

described during the past quarter we have considered methods of organization and classification which could facilitate the understanding and use of our program outputs.

We have also considered a number of specific technical questions that have been raised

by FDA staff. Our program has focused initially on the class of polymers best described

as polyolefins. These polymers represent the majority of plastics used in packaging

applications and we feel that models of migration developed for the principal members

of the class will be applicable to most members with only minor modifications. The

technical requirement that the polymers be equilibrium fluids rather than glasses can

be established by a glass transition temperature well below the use temperature or by

evidence of some crystallinity at use temperatures. Using these criteria, a preliminary

classification of polymers based on chemical structure has been developed. We have

found a formal decision tree to be a useful device to focus attention on the specific

technical decisions involved in amking regulatory judgments on indirect additive

questions. A simple example of such a decision tree is given. The general form of

this tree is, of course, independent of the polymer-migrant system involved but the

functional forms used in the calculations of partition coefficients and diffusion con- stants are specific for the class of polymer involved. The determination of the appropriate functions for decisions is a principal objective of our work along with an assessment of the experimental data and methods needed a s inputs.

17. KEY WORDS (aix 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;

regulations.

models;

18. AVAILABILITY [^Unlimited

I I For Official Distribution. Do Not Release to NTIS

(T Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

[X Order From National Technical Information Service (NTIS), Springfield, VA. 22161

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF

PRINTED PAGES

134

22. Price

$10.00

USCOMM-DC
II