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31293 01712 0043

This is to certify that the

thesis entitled

THE PERMEABILITY OF BINARY ORGANIC VAPOR MIXTURES
THROUGH POLYMER MEMBRANES BY A DYNAMIC PURGE AND
TRAP/THERMAL DESORPTION PROCEDURE: THEORETICAL AND
PRACTICAL CONSIDERATIONS

presented by

TEERAPONG LAOHARAVEE

has been accepted towards fulﬁllment
of the requirements for

MASTEB— degree in PACKAGINL

Major professor

)Va/t l4. ,ﬁau.

Date FEBRUARY 19, 1998

07639 MS U is an Afﬁrmative Action/Equal Opportunity Institution

 

 

 

LIBRARY

Michigan State
Unlverslty

 

 

 

PLACE IN RETURN BOX
to remove this checkout from your record.
TO AVOID FINES return on or before date due.

 

 

 

 

DATE DUE I DATE DUE DATE DUE
'. Jeugcizojo
(1.30;; “I it? u b
FEB 0 4 2007

 

 

 

 

 

 

 

 

 

 

 

 

 

1/96 WM“

 

 

 

 

THE PERMEABILITY OF BINARY ORGANIC VAPOR MIXTURES
THROUGH POLYMER MEMBRANES BY A DYNAMIC PURGE AND
TRAP/THERMAL DESORPTION PROCEDURE: THEORETICAL AND
PRACTICAL CONSIDERATIONS

By

Teerapong Laoharavee

A THESIS

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
For the degree of

MASTER OF SCIENCE

School of Packaging

1998

ABSTRACT
THE PERMEABILITY OF BINARY ORGANIC VAPOR MIXTURES THROUGH
POLYMER MEMBRANES BY A DYNAMIC PURGE AND TRAP/THERMAL
DESORPTION PROCEDURE: THEORETICAL AND PRACTICAL
CONSIDERATIONS
By

Teerapong Laoharavee

This study was designed to determine the effect of varying concentrations of
organic vapors alone, and in binary mixtures on the barier properties of an oriented
polypropylene ﬁlm and a high barrier PVdC coated oriented polypropylene ﬁhn. The
permeability tests were carried out at 50°C for OPP and 60°C for PVdC coated OPP ﬁlm.
The results obtained indicated that the permeants; ethyl butyrate, ethyl acetate and d-
limonene showed minimal concentration dependency for the mass transfer parameters
within the vapor activity ranges studied for the two test membranes. The effect of a co-
permeant on the permeability of binary mixtures through OPP ﬁlm and the PVdC coated
OPP ﬁlm was studied by determining the permeation rate of the constituents of a series of
binary mixtures of varying compositions using the dynamic purge and trap/thermal
desorption procedure. When combined in a series of binary mixtures, the constituents of
the mixtures showed little propensity of altering the transport properties of the co-

permeant.

Delicated to My Parents

iii

ACKNOWLEDGMENTS

I would like to express my appreciation, ﬁrst of all, to Dr. Jack Giacin for his
persistant support, guidance, and serving as my thesis advisor. Special thanks also goes
to Dr. Susan Selke and Dr. Krishnamurthy J ayaraman for their valuable critical review of
this thesis. Acknowledgement is given to CFPPR for ﬁnancial support, Mobil Chemical
Co., Film Division for supplying materials, and MAS Technology Co. for proper advise
on the instrument.

In addition, a special thanks to my parents for providing ﬁnancial support

throughout the entire study at Michigan State University.

iv

TABLE OF CONTENTS

LIST OF TABLES ................................................................................. viii
LIST OF FIGURES .................................................................................. x
INTRODUCTION ................................................................................... 1
LITERATURE REVIEW ........................................................................... 7
Mathematical Model Describing the Transport Process ............................... 7

Steady State Permeation in a Plane Sheet ................................................ 9
Sorption Mechanism through Polymer Membrane .................................... ll
Diffusion Mechanism through Polymer Membrane .................................. 15
Factors Affecting the Permeation Process ............................................. 17
Temperature ....................................................................... 17

Concentration ..................................................................... 20

Nature of Penetrant ............................................................... 22

Nature of Polymer ................................................................ 24

Permeation of Binary Mixtures .......................................................... 26
Permeation Measurement Procedure and Technique ................................. 30
Dynamic Purge and Trap/Thermal Desorption Technique ........................... 33
MATERIALS AND METHODS ................................................................. 35
Materials and Equipment ................................................................. 36

Methods ..................................................................................... 38

Calibration Curves of d-Limonene, Ethyl Butyrate, and Ethyl Acetate by

Gas Chromatography Analysis: Preparation and Testing ................... 38
Calibration Curves for Dynamic Purge and Trap/Thermal Desorption
Procedure .......................................................................... 41
Permeability Test System ....................................................... 43
Permeability Measurements ..................................................... 45
Dynamic Purge and Trap/Thermal Desorption Procedure .................. 48
Analysis of Test Permeant by Thermal Desorption/Gas Chromatography
Procedure .......................................................................... 49
RESULTS AND DISCUSSION .................................................................. 51

Comparison between MAS2000TM Isostatic Test Procedure and Dynamic Purge
and Trap/Thermal Desorption Procedure ............................................... 51

Estimation of the Detection Sensitivity Limit Between the Two
Procedures ......................................................................... 5 1

Comparison of Permeability Values Between the MAS 2000TM Isostatic
Test Procedure and the Dynamic Purge and Trap/Thermal Desorption

Procedure .......................................................................... 52

Effect of Vapor Activity on the Organic Vapor Diffusion and Permeability
Analyzed by Isostatic Permeability Test Procedure ................................... 57
The Effect of Binary Mixtures Composition on Co-permeant Permeability ...... 69
Statistical Analysis of Binary Mixture Permeability Studies ........................ 83
SUMMARY AND CONCLUSIONS ............................................................ 85
FUTURE STUDY .................................................................................. 87
APPENDICES ....................................................................................... 89
Gas Chromatograph Calibration Procedure ............................................ 89
Dynamic Purge and Trap/Thermal Desorption Calibration Procedure ............. 93

vi

Calibration Curve of Carrier Gas Flow Rate Versus Permeant Vapor Activity ...95

Method of Calculating 12/4Dt for each Value of (AM/At),/( [SM/At)... from
Equation 32 ................................................................................. 97

Statistical Analysis of P, D, and S as a Function of Permeant Vapor Activity ...98

Statistical Analysis of Binary Mixture Permeability Studies ...................... 102

BIBLIOGRAPHY ................................................................................. 106

vii

LIST OF TABLES

Table 1 - Estimated lowest measurable transmission rate between the two
procedures ............................................................................... 52

Table 2 - Permeability coefﬁcient, kg m/m2 s Pa x10'15 , of limonene through OPP ﬁlm

(50°C) determined by the two procedures .......................................... 53
Table 3 - Permeability coefﬁcient, kg m/m2 5 Pa x10'15 , of ethyl butyrate through OPP
ﬁlm (50°C) determined by the two procedures .................................... 53
Table 4 - Permeability coefﬁcient, kg m/m2 s Pa x10'16, of ethyl acetate through OPP
ﬁlm (50°C) determined by the two procedures .................................... 53
Table 5 - Permeance, kg /m2 3 Pa x10'13, of limonene through PVdC coated OPP ﬁlm
(60°C) determined by the two procedures .......................................... 56
Table 6 - Permeance, kg /m2 8 Pa x10'13, of ethyl butyrate through PVdC coated OPP
ﬁlm (60°C) determined by the two procedures .................................... 56
Table 7 - Permeability and diffusion coeﬂicients for limonene through the two
test ﬁlms ................................................................................. 59
Table 8 - Solubility coefﬁcient values for limonene and the estimated % sorbed (v/v) in
the two test ﬁlms ........................................................................ 59
Table 9 - Permeability and diffusion coefﬁcients for ethyl butyrate through the two test
ﬁlms ...................................................................................... 59
Table 10 - Solubility coefﬁcient values for ethyl butyrate and the estimated °/o sorbed
(v/v) through the two test ﬁlms ...................................................... 60
Table 11 - Permeability, diffusion and solubility coefﬁcient values and the estimated %
permeant sorbed for ethyl acetate through OPP ﬁlm at 50°C ................... 60
Table 12 - The Hildebrand solubility parameters (5) values ................................. 68

Table 13 - The permeability coefﬁcient, kg m/s m2 Pa x10'15 , of limonene through OPP
ﬁlm (5 0°C) as a single permeant and in binary mixtures with ethyl butyrate

viii

and ethyl acetate ....................................................................... 70

Table 14 - The permeability coefﬁcient, kg m/s m2 Pa x10'15 , of ethyl butyrate through
OPP ﬁlm (50°C) as a single permeant and in binary mixture with
limonene ................................................................................ 70

Table 15 - The permeance, kg/s m2 Pa x10'13, of limonene through PVdC coated OPP
ﬁlm (60°C) as a single permeant and in binary mixtures with
ethyl butyrate .......................................................................... 71

Table 16 - The permeance, kg/s 1112 Pa x1042, of ethyl butyrate through PVdC coated
OPP ﬁlm (60°C) as a single permeant and in binary mixtures with
d-limonene ............................................................................. 71

Table 17 - Permeation ratios in OPP ﬁlm (50°C) for individual components of the binary
mixtures ................................................................................. 79

Table 18 - Permeation ratios in PVdC coated OPP ﬁlm (60°C) for individual components
of the binary mixtures ................................................................ 80

Table 19 - The permeability coefﬁcient, kg m/s m2 Pa x1046, of ethyl acetate through
OPP ﬁlm (50°C) in single permeant and in binary mixture with limonene ...81

Table 20 — The solution of ethyl butyrate and d-limonene in CCl4 ........................... 89
Table 21 - Calibration data of ethyl butyrate and d-limonene

by gas chromatograph ................................................................ 89
Table 22 - Calibration data of ethyl acetate by gas chromatograph ..................... ....90

Table 23 - Calibration data of ethyl butyrate and d-limonene for dynamic purge and
trap/thermal desorption procedure .................................................. 92

Table 24 - Calibration data of ethyl acetate for dynamic purge and trap/thermal
desorption procedure .................................................................. 92

ix

LIST OF FIGURES

Figure 1 - Control Volume Element (taken from Crank, 1975) ............................... 8
Figure 2 - Permeation through a ﬁlm at steady state .......................................... 10
Figure 3 - Characteristic isotherms plots described by Langmuir, Flory Huggins, and BET

equations. (taken from Roger, 1985) ................................................ 13
Figure 4 - Schematic diagram of permeation test and trap apparatus ........................ 46

Figure 5 - Comparison of permeability of organic vapors through OPP ﬁlm by
MASZOOOTM and DPT/TD procedures (50°C) ...................................... 54

Figure 6 - Comparison between MASZOOOTM and DPT/TD procedures:
organic vapor permeation through PVdC coated OPP ﬁlm (60°C) ......... ....55

Figure 7 - Diffusion of organic vapors through OPP ﬁlm as a function of vapor activity
(50°C) .................................................................................... 61

Figure 8 - Apparent diffusion coefﬁcient of organic vapors through PVdC coated OPP as
a function of vapor activity ........................................................... 62

Figure 9 - Solubility coemcient of organic vapors in OPP ﬁlm as a ﬁmction of
vapor concentration (50°C) ........................................................... 63

Figure 10 - Solubility coefﬁcient of organic vapors in PVdC coated OPP ﬁlm as a
function of vapor concentration .................................................... 64

Figure 11 - Diffusivities of organic vapors through OPP at 50°C as a function of
penetrant molar volume ............................................................ 67

Figure 12 - Effect of ethyl butyrate on permeability of d-limonene through OPP as a
ﬁmction of binary mixture composition (50°C) ................................. 72

Figure 13 - Effect of ethyl butyrate on permeation rate of d-lirnonene through PVdC/OPP
ﬁlm as a function of binary mixture composition (60°C) ...................... 73

Figure 14 - Effect of d-limonene on the permeation rate of ethyl butyrate through OPP as

X

a function of binary mixture composition (50°C) ............................... 74

Figure 15 - Effect of d-limonene on the permeation rate of ethyl butyrate through
PVdC/OPP ﬁlm as a function of binary mixture composition (60°C) ........75

Figure 16 - Transmission proﬁles of binary mixture composition of d-limonene, a=0.05/
ethyl butyrate a=0.04 and its respective individual permeants through OPP
ﬁlm (50°C) ............................................................................ 77

Figure 17 - Transmission proﬁles of binary mixture composition of d-limonene, a=0.2
and ethyl butyrate a=0.2 and its respective individual permeants through

PVdC coated OPP ﬁlm (60°C) ..................................................... 78
Figure 18 - Calibration curve of ethyl butyrate for setting vapor activity .................. 90
Figure 19 - Calibration curve of d-limonene for setting vapor activity ..................... 91
Figure 20 - Calibration curve of ethyl acetate for setting vapor activity .................... 91

Figure 21 - Calibration curve of ethyl butyrate for dynamic purge and trap/thermal
desorption procedure ................................................................ 93

Figure 22 - Calibration curve of d-limonene for dynamic purge and trap/thermal
desorption procedure ................................................................. 93

Figure 23 - Calibration curve of ethyl acetate for dynamic purge and trap/thermal
desorption procedure ................................................................ 94

Figure 24 - Calibration curve of carrier gas ﬂow rate versus limonene vapor activity ...95

Figure 25 - Calibration curve of carrier gas ﬂow rate versus ethyl butyrate and ethyl
acetate vapor activity ................................................................ 96

xi

INTRODUCTION

The use of polymeric materials in food packaging has been increasing in the past
few decades and is expected to continue to increase into the next century. Unlike paper,
glass, or metal, polymeric materials are capable of tailor-made properties to provide light
weight, coupled with strength, lower costs, and ﬂexible shaped packages. Optimal
packaging design requires not only protection ﬁ'om the surrounding environment but also
compatibility with speciﬁc foods to prolong changes in product color, texture, surface
structure, aroma, smell and taste, until the time of consumption (Koszinowski, 1987).

Because of their molecular nature, polymeric materials can allow relatively high
rates of diffusion of gases and vapors through the package, resulting in degradation of the
contained food product. The shelf life of certain food products, based solely on the
prevention of individual permanent gases, such as oxygen and carbon dioxide permeating
both into and out .of packages, can be successfully described and predicted by a simple
shelf life model (Salame, 1996). This is due to the well deﬁned transport behavior of a
permanent gas, a gas that is not easily condensable and small, as compared to the
monomer unit of a polymer. The non-interactive nature of permanent gases with a
polymer results in their diffusion and solubility coefficients being independent of
concentration. These two parameters are related to the permeability coefﬁcient, by the
relationship P = DxS, where D and S are the diffusion and solubility coefﬁcients,

respectively. The permeability coefﬁcient, P, is deﬁned as the amount of substance

2
passing through a polymer ﬁlm of unit thickness, per unit time, per unit area, and at a unit
pressure difference across the ﬁlm. The diffusion coefﬁcient is a kinetic term that
describes how fast a permeant molecule moves through a unit area of a polymer ﬁlm or
slab. The solubility coefﬁcient is a thermodynamic term that describes the amount of a
substance that will be sorbed by a polymer. Both experimental data and techniques for
estimating these parameters for permanent gases and small organic molecules in various
polymers have been reported in the literature (Van Krevelen, 1976; Brandrup, 1975;
Salame, 1986).

Today, the packaging of a food product to prevent deterioration of its original
ﬂavor and aroma presents a challenging problem to packaging engineers. Flavors are
either composed of the same organic compounds with different proportions, or are
speciﬁc and dependent on distinctive chemical entities and structures for their
characteristic proﬁle (Rohan, 1970). These molecules are usually present in extremely
low quantities; often less than one part per million, but are responsible for the unique
ﬂavor of a particular food (Strandburg et. al., 1991). The interaction of these organic
molecules with a polymeric packaging structure, through permeation and/or sorption, can
cause an imbalance in concentration of certain organic compounds, leading to an off-
ﬂavor taste and resulting in a shorter shelf life for the product. The prediction of shelf
life, based on the ﬂavor and aroma retention in food packaging, is complicated due to the
strong interaction between these organic compounds and a polymeric packaging

structure. Thus, making it difﬁcult to monitor a ﬂavor proﬁle in plastic packages.

3

Permeation of gases and organic vapors though polymer membranes includes
diffusion and sorption mechanisms, which are dependent upon a number of parameters.
According to Fujita (1968), the diffusion of permanent gases (i.e. 02, H2, etc.) is
independent of sorbed permeant concentration, because the small molecular size and
chemical inertness of these compounds allow them to move freely within the polymer
matrix, without requiring segmental mobility of the polymer chain. The diﬁ‘usion
mechanism for molecules that have a size comparable to the monomer unit of a polymer,
on the other hand, requires a co-operative movement by the micro-Brownian motion of
several monomer units to take place. As a result, their diffusion coefﬁcients are primarily
controlled by the mobility of the polymer segmental unit. Factors that enhance polymer
segmental mobility, increase the average interchain distance, and weaken the molecular
interaction between neighboring polymer molecules, lead to an increase in permeant
diffusion. Therefore, the diffusion coefﬁcient of organic vapors in polymer membranes
generally increases with increasing sorbed permeant concentration and temperature.

Sorption of permeant molecules in a polymer may be described by one or more
different types of sorption modes occurring concurrently, such as those that can be
described by Henry’s law, the Langmuir equation, the Flory-Huggins equation and the
Brunauer, Emmett, Teller (BET) equation. Henry’s law is the common sorption mode for
permanent gases and small organic vapor molecules at a partial pressure up to l
atmospheric (Stannett, 1968). It is the simplest case, where the solubility coefﬁcient is
independent of sorbed penetrant concentration and does not violate the P=DxS

relationship. In general, temperature, sorbed permeant concentration, polymer

4

morphology and the functionality of the polymer, as well as the size and functional
groups of the permeant molecule, affect the sorption and diffusion processes.

A study by Hensley et al.(1991) involving the permeation of ethyl
acetate/limonene binary mixtures through an oriented polypropylene ﬁlm showed that the
permeation rate for the mixture was signiﬁcantly higher than the sum of the transmission
rates for the individual pure components. At the lower activity levels, the increased
permeation rate was attributed to the transmission rate of ethyl acetate, which increased
signiﬁcantly in the presence of limonene. The transmission rate of limonene only
showed a signiﬁcant increase, as compared to the permeability of pure limonene at a
similar activity level, when the vapor activity level of ethyl acetate, as a co-permeant,
was at a high vapor activity level (a=0.48).

In a recent study on the sorption of ethyl acetate/limonene binary mixtures by
oriented polypropylene, Nielson and Giacin (1994) reported that for ethyl
acetate/limonene binary mixtures, limonene as a co-penetrant appears to have little or no
effect on the solubility of ethyl acetate in oriented polypropylene ﬁlm, while signiﬁcantly
changing the inherent mobility of ethyl acetate within the polymer bulk phase. This
accounts for the observed increase in the transmission rates for ethyl acetate through the
OPP ﬁlm in the presence of limonene, as reported by Hensley et al. (1991).

While not fully understood, Nielson and Giacin proposed that there may be co-
penetrant induced relaxation effects occurring during the diffusion of ethyl
acetate/limonene binary mixtures in the oriented polypropylene ﬁlm investigated. Such
relaxation processes, which occur over a longer time-scale than diffusion, may be related

to a structural reordering of the free volume elements in the polymer. Such processes are

5

believed to provide additional sites of appropriate size and frequency of formation, which
promote diffusion and account for the observed increase in the permeation rate of ethyl
acetate in the presence of limonene as a co-permeant.

A review of the literature shows a paucity of data on the permeation of multi-
component mixtures of organic liquids and vapors through barrier membranes (Li et al.,
1965; Huang and Lin, 1968; Weinberg, 1976; Michelson et al., 1985; Hensley et al.,
1991). This lack of data can be attributed to the complexities involved with organic
vapor mixtures exposed to plastics, as well as to the lack of commercial instrumentation
that allows the separation and detection of individual components of multi-component
penetrant mixtures. DeLassus et al. (1988) alluded brieﬂy to the transport of apple aroma
in polymer ﬁlms, where the permeation of binary organic vapor mixtures in low density
polyethylene was studied. Such studies would be more representative of an actual
product/package system, where the product aroma proﬁle contains numerous volatile
components.

In addition to the lack of data on the permeability of organic vapor mixtures
through barrier ﬁhns, only Hensley et al. (1991) have reported on the concentration
dependency of the permeability of organic vapor mixtures, and the effect of the relative
concentration of individual components of the vapor mixture on the transport of each
particular penetrant comprising the mixture.

The present study therefore focuses speciﬁcally on developing a methodology for
determining the permeability of binary organic vapor mixtures of varying composition
through a polymeric barrier ﬁlm, and considers the non-ideality of the mass transfer

process, as indicated by the permeation ratio.

1)

2)

3)

4)

6

The speciﬁc objectives of the study include:

Evaluate and compare the permeability data from a dynamic purge and
trap/thermal desorption procedure to the data obtained from the MAS 2000TM
organic permeability tester.

Evaluate the concentration dependence of the transport process of the individual
permeants selected for study.

Evaluate the effect of co-permeants on the diffusivity of the respective individual
penetrants through the test barrier polymer structures.

Utilize data obtained from the permeability studies to develop a better
understanding of the mechanism and the variables, which affect the diffusivity of
organic penetrants in barrier polymer ﬁlms. In particular, the effect of penetration
(i.e. sorption) of the barrier polymers by a constituent of the binary organic vapor
mixture, on the transport properties of the polymer will be addressed, as indicated
by the permeation ratio.

The signiﬁcance of this study is that it is applicable to permeation of ﬂavor and

aroma components in food, since they are present at very low vapor pressures. The data

from this study can be used to make a relative comparison of barrier properties of

polymeric packaging materials to organic permeants of varying molecular structure and

polarity. In the future, therefore, a means of designing an appropriate barrier structure for

a speciﬁc end use application would be available to researchers. In terms of theoretical

importance, the data from this study may assist in better understanding and developing a

model to accurately predict the permeation proﬁle of different ﬂavor compounds of food

in plastic packages.

LITERATURE REVIEW

Mathematical Model Describing the Transport Process

The transport of molecules through a polymer membrane is based on random
molecular motions as described by Fick’s laws of diffusion (F ick, 1855). Fick’s ﬁrst
law states that the rate of transfer of a diffusing substance through an isotropic membrane

is proportional to the concentration gradient normal to the section.

__ 5’3.
F.— 0(a) (1)

F, ﬂux, is the amount of a substance diffusing across a unit area in unit time, C is the
concentration of diffusing substance, x is the space coordinate measured normal to the
section, and D is the diffusion coefﬁcient. The ﬁrst law only applies to steady state
diffusion, where concentration is not varying with time.

Fick’s second law describes the non-steady state diffusion where the concentration
of the diffusing substance is changing with time. The mathematical treatment of F ick’s

second law, taken from Crank (1975), is brieﬂy summarized as follows.

Assuming a unit square box

 

 

 

 

 

 

 

 

 

 

 

a d
2V
4dydz(F, — 6F, dx) A 4a52dz(F, + 6F, dx)
(3x__> b D ___> 6x
2dz °
15% > C
2dx

Figure 1. Control Volume Element (taken from Crank, 1975)
as a control element with a size of 2 on each length, width, and height, the rate of
diffusing substance entering the plane AabB is 4 dydz (Fx-(de/dx» and that of leaving
the plane Cch is 4 dydz(Fx+(dedx)) (see Figure 1). Thus, the rate of a diffusing

substance accumulating in the volume element in the x direction, Rx, is

6F.
a, (2)

 

R, = —8 dxdydz(

A similar approach is used to derive the rate of accumulation in the y and 2 directions.

 

5F
R =—8 dx dz—" (3)
y 60’ (Q)

077,

Thus, the rate of concentration increase in the volume element is given by

R, +Ry +Rz
8 dxdydz

(5)

 

£5.
a

By substituting equations 2,3 and 4 into 5

=_0"__x_0‘>_y 2
ac a. a.- (6)

e F Fe:
0'?

Differentiating the ﬂux gradient of equation 1 and substituting into equation 6, the change

in concentration can be rewritten as

 

dcz+e2+az2) (7)

When the diffusion is restricted only in the x direction, as in the sheet ﬁlm, equation 7

simpliﬁes to
— = D— (8)

Equation 8 is referred to as F ick’s second law of diffusion, where the
concentration of the diffusing substance is at nonsteady state. The diffusion coefﬁcient in
F ick’s ﬁrst and second laws, written in the form of equations 1 and 8, is assumed to be a
constant and independent of direction, time, and concentration. In cases where D
depends on these three variables, the mathematical treatment can be found elsewhere

(Crank, 1975).
Steady State Permeation in a Plane Sheet.

For steady state in one dimensional diffusion through a plane sheet with thickness,

10

l, the concentration at surfaces x = 0 and x = l are maintained at constant concentration C1

and C2 respectively, as shown in Figure 2 (Crank, 1975).

P1 P2

 

 

V
V

C2

 

 

Figure 2. Permeation through a Film at Steady State

Here, the permeant concentration at all points in the sheet remains constant and equation
8 becomes dzC/dx2 = 0. Further integration with respect to x and restricted boundary

conditions ofC = C1 at x = O and C = C2 at x =1 gives:

 

(9)

This shows that the concentration changes linearly from C1 to C2 through the sheet. The

rate of transfer of the diffusing substance can be written as

_Dd_C=_1%_C_11;22

F: (10)

In permeability experiments, the surface concentrations C. and C2 are unknown and so

equation 10 is replaced by

11

F:P(PII_P2) (11)

where P is the amount of diffusing substance permeated through the ﬁlm of thickness, 1,
per exposed ﬁlm area, time, and partial pressure difference across the ﬁlm. It is referred
to as the permeability constant with SI unit of kg m/m2 3 Pa. When the partial pressure of
the permeant varies linearly with its equilibrium concentration on the surface of the ﬁlm,

Henry’s law states that

Q
ll

Sp (12)

where S is the solubility coefficient of the permeant with the ﬁlm. Substituting equation

12 into equation 11, one can derive the relationship:

P=DxS (13)

This equation states that permeation is dependent on both solubility and diffusion
parameters. According to Stannett (1968), the permeation process through a
homogeneous membrane was described as the condensation and solution of a gas or
vapor at one surface followed by diffusion through the barrier membrane, in the form of a
liquid, and evaporation of the penetrant to the gaseous state at the other surface. Thus,

the permeation process can be discussed in terms of a diffusion and sorption mechanism.

Sorption Mechanism through Polymer Membrane

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12

Whenever a gas is in contact with a solid, there will be an equilibrium established
between the molecules in the gas phase and those which are bound to the surface of the
solid. The amount of gas molecules sorbed onto the surface will depend on the pressure
of the gas above the surface and the temperature of the system. Higher temperatures tend
to increase the internal energy of the sorbate molecules, thus decreasing their sorption by
the polymer membrane. Increasing gas pressure increases collision rates of the sorbate
molecules into the polymer membrane and increases the amount sorbed. Henry’s law,
Langmuir, Flory-Huggin, and Brunauer, Emmett and Teller (BET) equations are some of
the common equations used to describe the behavior of gas sorption into a polymer
membrane, as a function of its pressure at ﬁxed temperature. Characteristic isotherms
described by each respective equation are shown in Figure 3. The derivations,
assumptions, as well as treatments for each equation can be found in Physical Chemistry
of Surfaces (1997).

The Langmuir equation, developed in 1916, was found to ﬁt the experimental data
for a variety of sorbate and substrate systems. As Show in Figure 3, the polymer provides
some kind of speciﬁc sites to sorb the penetrant in the initial stage, such that the sorbed
concentration is linearly proportion to the pressure. When the sites on the surface layer
are nearly all occupied, a small amount of penetrant dissolves in a more or less random
distribution until a single monolayer saturated uptake is reached. In the initial sorption
state, where the pressure is less than 1 or 2 atmospheres, the solubility coeﬁicient is
constant (Stannett, 1968). At high pressure the solubility decreases. In glassy polymers,
where polymer chains have long relaxation times, a two-mode sorption process can occur,

due to a combination of Langmiur and Henry’s law sorption modes. This so-called dual-

l3

mode sorption model has been successfully used to describe the sorption behavior of

carbon dioxide in PET (Stern et al., 1990).

When the sorbate interacts strongly with a solid, such as organic vapors in

polymers, the sorbed vapors have a tendency to plasticize and loosen the polymer

structure, causing subsequent sorbate molecules to cluster within the polymer matrix .

Thus, the observed solubility coefﬁcient is initially constant but signiﬁcantly increases as

pressure increases, causing multiple uptake into the bulk polymer. This type of sorption

is described by the Flory— Huggins equation and is observed in some organic

vapor/polymer systems, as well as for water vapor sorption by hydrophobic polymers.

(Stern, et al., 1973)

Sorbed
concentration

 

   

 

a I
Langrnurr /
equation ’1’

I

I
I

Ix” Flory-Huggins
’ equation

 

 

Pressure

Figure 3. Characteristic isotherms plots described by Langmuir, Flory Huggins,
and BET equations (taken from Roger, 1985)

The BET equation can be thought of as a combination of monolayer sorption, as

in Langmuir, and a multilayer sorption, as in Flory-Huggins sorption. Depending on the

l4

interaction between the sorbate and the polymer, pressure of the sorbate, and temperature
of the system, the sorbate may experience more than one concurrent or sequential modes
of sorption in the polymer materials, according to Henry’s law, Langmuir, and Flory-
Huggins equations.

The degree of interaction between the sorbate and the polymeric material can be
characterized by the solubility parameter, 8, of the sorbate and polymeric material, which
is deﬁned as the square root of the cohesive energy density. Solubility can be expected if
5 values for the sorbate and that of the polymer are less than about 2 (cal/cm3 )“2 ,
provided that there are no strong polar or hydrogen-bonding interactions in either the
polymer or solvent (Rudin, 1982). In general, the closer the values of the solubility
parameters, the more soluble the sorbate will be in the polymer. Experimental values and
estimation techniques of common solvents and polymers can be found in the literature.
(Rudin, 1982, Van Krevelen, 1976).

The barrier properties of a polymer may be seriously impaired by the presence of
organic vapors, which penetrate and plasticize the polymer. Henry’s law is usually
observed for sorption of permanent gases and some low molecular weight organic vapors
by polymer membranes, where the pressure is less than about 1 atmosphere (Rogers,
1985). When the sorption behavior does not follow Henry’s law, the substitution of C =
Sp into equation 11 is in doubt, and the relationship described by equation 13, P = D x S,
is violated. Studying the sorption behavior would allow one to predict the effect of

penetrant plasticization on the transport behavior of the penetrant.

15

Diffusion Mechanism through Polymer Membrane

The hole theory of diffusion states that the rate of diffusion will depend on (a) the
number and size of distribution of pre-existing holes, and (b) the ease of hole formation
(F ujita, 1968). The diffusion process can be thought of as the permeant molecule, in a
series of random “hops” or “jump”, moving through the polymer membrane from an
environment where the concentration of permeant molecules is high, to an environment
where the concentration is low. The unit diffusion involves rearrangement of the
permeant molecule and its surrounding polymer chain segments. For the movement of
permeant to occur, a certain number of van der Walls type or other interactions between
the component molecules and chain segments must be broken to allow a rearrangement of
the local structure. The amount of energy required for this rearrangement or ‘hole
formation’ will increase as the size and shape of the permeant molecule increases (F ujita,
1968)

The diffusion mechanism for permanent gases (i.e. hydrogen, argon, nitrogen and
carbon dioxide), that have a molecular size much smaller than the monomer unit of a
given polymer, is such that a limited rotational oscillation of only one or two monomer
units would be sufﬁcient to give a cross-section area for the diffusant molecule to jump
thermally from one position to a neighboring one, due to a weak thermodynamic
interaction between the penetrants and the polymers. This mechanism follows both
Fick’s linear diffusion law and Henry’s law, and the diﬂ‘usion coeﬂicient is independent
of concentration.

The diffusion mechanism for molecules with a size larger than the monomer unit

16

of a polymer, on the otherhand, requires a cooperative movement by the micro-Brownian
motion of several monomer units to take place. Such a complicated mechanism is
observed for permeants such as water or organic vapors, which interact strongly with the
polymer. As a result, their diffusion coefﬁcient is primarily controlled by the mobility of
the polymer segmental unit. Factors that enhance polymer segment mobility and thus
increase average interchain distance and weaken the molecular interaction between
neighboring polymer molecules leads to an increase in diﬂiision. Therefore, diffusion
coefﬁcients of vapors in polymer generally increase with increasing penetrant
concentration and temperature (Fujita, 1968).

Crank and Park (1951) postulated that polymer molecules rearrange their
conformation toward a new equilibrium conformation with the sorbed state, when they
absorb a vapor. The change toward this new conformation also changes the free volume
within the polymer matrix. Therefore, the level at concentration of sorbed vapor needed
to cause changes in polymer conformation, as well as the time for the polymer chain to
rearrange toward a new conformation, affects the diffusion rate. Furthermore, internal
stresses built up by swelling of the polymer structure during the sorption process cause a
change in polymer conformation to relieve those stresses. For these reasons, diffusion is
believed to be time-dependent (Crank and Park, 1951). At temperatures above Tg, the
change toward a new equilibrium conformation occurs instantaneously with the sorbed
state, when vapor diﬂhses into the polymer, and the internal stresses are relieved by rapid
chain relaxation. Therefore, above Tg, D is independent of time, but depends only on
sorbed penetrant concentration (Crank and Park, 1951). For glassy polymers, where the

Tg is higher than room temperature, the rate of conformational change does not occur

l7

instaneously with sorbed penetrants. Thus, diffusion is expected to be a time-dependent
phenomena, where the mass transfer process cannot be described by Fick’s law. This
anomalous or non-Fickian phenomena can be detected in sorption experiments, where the
shape of the sorption curve does not conform to the characteristic features of a Fickian
sorption proﬁle. The so-called non-Fickian sorption has been reported in describing the
sorption of water by cellulose (Newns, 1956), as well as sorption of organic vapors by
cellulose nitrate (Drechsel et al., 1952), cellulose acetate (Mandelkem and Long, 1951)
and polystyrenes (Odani, 1961).

Different modes of vapor sorption in polymers usually occur and the diffusion
constants are often highly dependent on the concentration of penetrant in the polymer
(Rogers, 1985). In general, the permeability rate for vapors is a function of many
parameters, including temperature, concentration, the nature of the penetrant and the

nature of the polymer.

Factors Affecting the Permeation Process

Temperature

Temperature dependency of the diffusion, solubility, and permeability
coefﬁcients, expressed by the Arrhenius equation, are found to ﬁt the experimental data
for a variety of permeant/polymer systems, within a limited temperature range. The
Arrhenius equations describing the temperature dependency of the respective mass

transfer parameters are as follows.

 

 

—ED
D — Doexp( RT ) (14)
S — Saexp(_AHS) (15)

(16)

where Do, and So are pre-exponential terms. ED and AHs are diffusion activation energy,
and heat of solution, respectively. E1) is the apparent activation energy of permeation and
is equal to ED+ AHs, when Henry’s law is obeyed and the P=DxS relationship holds. R
is the gas constant and T is the absolute temperature. Do includes both the entropy of
activation and the jump length, and would also be expected to increase with the size of
the diffusing molecule. The diffusion coefﬁcient increases with increasing temperature,
as an increase in temperature provides the energy for a general increase in segmental
motion and hole formation, which increases the free volume within the bulk polymer.
The solubility coefﬁcient decreases or increases with increasing temperature, depending
on the physical state of the penetrants. Values of D, ED, and Do for gases in various
polymers have been gathered and reported by Crank and Park (Crank and Park, 1968).

The heat of solution may be expressed as the sum of the molar heat of

condensation, Aﬁcond , and the partial molar heat of mixing, A17: .

AHS = Aﬁcond + AH] (17)

The value of AH: can be related to the Hildebrand solubility of the permeant and the

19

polymer.

AHI mi, =99. —6.)’¢§ (18)

The solubility parameters 61 and 82 are the square roots of the cohesive energy densities

of the penetrant and polymer. 6, is the partial molar volume of the penetrant and (I), is

the volume fraction of the polymer in the mixture. For permanent gases, such as H2, He,

02, and N2, where their critical point is much lower than room temperature, the value of

AIL—1m, would be very small, and Ms is governed by AH] , which is a small positive

value. Thus, the solubility coefficient usually shows a slight increase with increasing

temperature. For condensable organic permeants, the value of AHs depends mostly on

the value of [SH—cm, , which is generally negative. Thus, for organic vapors, solubility

coefficients generally decrease, as the temperature increases (Rogers, 1985; Delaussus,
1985)

The Arrhenius relationship of diffusion and solubility coefficients versus
temperature is not observed at the glass transition temperature, because the rate of change
of free volume changes at the glass temperature (Mears, 1954). The glass transition
temperature, Tg, is deﬁned as the temperature that marks the freezing of micro-brownian
motion of chain segments of 20 to 50 carbon atoms in length. According to Frisch (1965)
diffusion occurs by localized activated jumps from one pre-exiting cavity to another.
When the size of the penetrants is much less than the average hole size in the polymer,
the glass temperature has no effect on the diffusion process. However, as the size of the

penetrant increases, or the hole size decreases, a change in the slope of the Arrhenius plot

20

at the glass transition temperature occurs, with a lower energy of activation for a polymer
in the glassy state. The restraints of segmental mobility of the polymer makes the
diffusion process more dependent, not only on the size and shape of the penetrant
molecule, but also more dependent on concentration (Rogers, 1985). At temperatures
well above Tg, log D increases linearly with diffusant concentration, the slope being
smaller as the temperature is raised. As the temperature is lowered toward the Tg, the
Arrhenius plot becomes curved downward at low concentrations and a linear relationship
is not observed (Mears, 1958a; Kishimoto and Matsumoto, 1959). Below the Tg of a
polymer, not enough energy is provided to produce the micro-Brownian motion and the
chains are ﬁxed in a speciﬁc conformation, related to processing conditions. The kinetics
of sorption of organic vapors by polymers is almost invariably complicated by various
non-Fickian anomalies that occur at temperatures below Tg and up to at least 10-15°C

above Tg (Fujita, 1968).

Concentration

For the permeation of gases and small organic vapors, where solubility in the
polymer is very limited, the diffusion and solubility coefﬁcients can be thought of as
being constant. For organic vapors, where the size is larger, the permeant is more soluble
in polymers. These highly soluble permeants are capable of swelling and plasticizing the
polymeric structure, leading to an increased mobility of both polymer chain segments and
penetrant molecules. Thus, an increase in solubility, with increasing penetrant size,

usually results in an increase in the concentration dependence of S, D, and therefore P

21
(Roger, 1985).
In systems where the concentration of sorbed vapor is small, or the temperature
sufﬁciently high such that sorption follows Henry’s law, the dependence of the diffusion
coefﬁcient on sorbed penetrant concentration or vapor activity has usually been

empirically represented by the following equations.

D = D(0)exp(}c) (19)

D = D(O)exp(aa) (20)

where c is sorbed concentration and a is the vapor activity, p/ps. D(0) is D at zero
penetrant concentration. 7 and or are the characteristic parameters of the system at the
given temperature (Roger, 1985).

At high vapor activity, where the sorption process does not conform to Henry’s
law, a number of penetrant/polymer combinations involving the sorption of organic

vapors follow the Flory-Huggins equation, in the simple form (Suwandi and Stern, 1973).

S = 5(0) exp(0'c) (21)

where S(0) is S at zero penetrant concentration and o is the characteristic parameter of
the system at the given temperature.
D can be written as a function of sorbed concentration that obeys the Flory

Huggins equation.

22

 

D = 13(0) epr ex 9:00] (22)

At low concentration, when Henry’s law is obeyed, o = 0 and equation 22 is reduced to
equation 19. When the system follows Flory-Huggin sorption, o—) 1 and by expanding
the exponential term in ac and neglecting higher order terms equation 22 can be written

as

 

D = D(O) epr (23)

ac
(l + 09)
Taken as o=1, D can be expressed in terms of penetrant volume fraction, 11)], as shown in
equation 24

D = D(O)eXP(a'¢I) (24)

CI

(1+cl)

 

where 411 is equal to . y, a, and a' measure the effectiveness with which equal

amounts of various penetrants plasticise a polymer to facilitate segmental mobility and,
hence, to increase the rate of diffusion of the penetrant. The values are expected to be
higher for any systems that cause a decrease in polymer segmental mobility, for instance,
a decrease in temperature, an increase in solvating power of the penetrant, an increase in

polymer-polymer interaction, etc. (Rogers, 1985).

Nature of Penetrant

23

At a given temperature the more easily condensable vapors are more soluble in a
given polymer. Larger size penetrants condense easier and are more soluble in a polymer
matrix. Thus, the linear relationship between the solubility coefﬁcient and either the
boiling point temperature, critical temperature or other parameters that measure the ease
of condensibility of penetrants have been observed by many investigators (Van
Amerongen, 1950, 1964; Barrer and Skirrow,l948; Strandburg et al., 1991). The
increase in the size of a penetrant in a series of chemically similar structures, generally
increases solubility and decreases the diffusion coefficients. Shirnoda e1 at. reported that
the permeability, diffusion, and solubility coefﬁcients in PE relate linearly with increasing
carbon atoms for n-alkanes, aliphatic ethyl esters, n-aldehydes, and n-alcohols up to 10
carbon atoms (Shimoda et.al., 1987). The dependence of the solubility coefﬁcient, on
increasing the number of carbon atoms, is higher than that of the diffusion coefﬁcient.
Thus, the permeability coefﬁcient increases with an increase in the carbon number. A
study by Berens and Hopfenberg (1982) showed that diffusion coefﬁcients of simple
gases and organic vapors, up to C6, in a series of glassy polymers, PVC, PS, and PMMA,
decreases exponentially and the diffusion activation energy (ED) increases linearly, with
increasing average diameter of “spherical” penetrant molecules. The diffusivity of
elongated or ﬂattened molecules is higher by a factor of up to 103, relative to spherical
compounds with similar molecular weight, suggesting that elongated molecules tend to
align and transport along their long dimension through a polymer membrane. For
rubbery polymers, however, several investigators have observed that the diffusion of a
series of organic vapors in natural rubbers is much higher and much less dependent upon

molecular size than in glassy polymers (Fujita, 1968). The results of sorption studies of

24

gases and vapors by PVC, as reported by Beren (1990) show that the difference in
diffusivity between the glassy and rubbery state of PVC can vary by as much as 1 order of

magnitude for small gas molecules and as much as 12 times for plasticizers of size 8 to

10 A . Also, the same studies suggest that the activation energy is constant and

independent of penetrant size but varies with different kinds of rubbery polymers.

Nature of Polymer

The barrier properties of polymeric materials are determined by the chemical
structure of the chain and the systems morphology. A symmetrical, regular structure,
with strong cohesive energy between the polymer chains, allows efficient chain packing,
which minimizes the free volume within the polymer matrix and thus reduces sorption
and diffusion processes. The two properties can be manipulated through the parameters
derived ﬁom the chemical structure, such as degree of polarity, inter-chain forces, and
chain stiffness.

The crystalline region obtained with regular molecular structures increases
packing efﬁciency of the polymer chains, so that the crystalline regions can be regarded
as impermeable, relative to the amorphous region (Shimoda et al., 1987). Several
investigators have shown that sorption and diffusion processes vary with amorphous

phase content in semi-crystalline polymers by the following equations (Michaels, 1961).

s = S.¢. (25)

25

D = D I»: (26)

a

where Sa is the solubility coefﬁcient and D, is the diffusion coefﬁcient for a completely
amorphous polymer. (1) is the amorphous volume fraction in a polymer. The parameter m
is constant and varies among different polymers. It has been reported as varying from
about 0.3 for polyethylene to about unity for PET (Michaels et al., 1959 and 1963).

The effect of the crystalline region on the diffusion process is related to polymer
morphology, mainly the tortuosity and immobilization effects. Since the penetrant
diffuses around the amorphous region, its average path length is higher than the nominal
dimensions of the polymer membrane and this extra path length is referred to as the
tortuosity effect. Also, the tie molecules between crystallites and other chains anchored
to the crystal would reduce the mobility of the amorphous phase. Reducing polymer
chain mobility, reduces hole formation and thus the diffusion rate. The tortuosity and

immobilization effect on diffusion in a semicrystalline polymer can be expressed as

 

w (27)

where T and B are tortuosity and immobilization factors, respectively. These two effects
are experimentally found to decrease the diffusion rate but not the sorption in the
amorphous region of a senricrystalline polymer (Weinkauf et al., 1990).

Polymer morphology can be improved to a higher molecular order by orientation
of polymer ﬁlms, resulting in improved barrier properties. Orientation is a process of

stretching the polymer ﬁlm above the glass transition temperature, in order to rearrange

26

and align the polymer chains in the direction in which it is stretched. The more ordered
morphology obtained usually resulted in a decrease in free volume and sorption sites,
which resulted in a substantial decrease in the diffusion coefﬁcient and a smaller decrease
in the solubilty coefﬁcient. For instance, an eighty percent decrease in the diﬁusion
coefﬁcient and less than a forty percent decrease in the solubility coefﬁcient has been
observed for carbon dioxide permeation in oriented polystyrene (Weinkauf et al., 1990).
The eﬂ'ect of orientation on diffusion is greater in crystallizable polymers than those
observed in noncrystallizable polymers, because the deformation in crystallizable
polymers causes additional stress-induced crystallization and orientation of the remaining
amorphous phase, which tend to increase the tortuosity. In general, the degree of
orientation achieved and its effects on barrier properties of polymers depends on the draw

ratio and mode of deformation mechanism (Choy et al., 1984)

Permeation of Binary Mixtures

A number of permeability studies have been reported for single component
organic vapor/polymer systems (Rogers et al., 1960; Gilbert et al., 1983; Neibergall et al.,
1978; Zobel, 1982; Baner et al., 1986; and Hernandez et al., 1986). However, only a
limited number of studies have been reported on the permeation of multi-componenet
mixtures of organic liquids and vapors through barrier membranes (DeLassus et al., 1988;
Huang et al., 1968; Mickelson et al., 1985; and Hensley et al., 1991). The importance of
multi-component mixture permeation is such that it would be more representative of an

actual product/package system, where the product aroma proﬁle contains numerous

27

volatile components at relatively low concentrations.

Studies on the permeability of permanent gas mixtures through various rubbery
ﬁlms by Pye et al.(1976), Stannett et al.(1957) and Meyer et al.(1957), indicated that there
was no effect of one penetrant gas on the permeation of another in the mixture. The rate
of the permeation of a gas mixture was equal to the sum of the rates of its constituents.

Studies reported dealing with the permeation and diffusion of organic liquid
mixtures through barrier polymer ﬁlms showed that varying degrees of interaction can
occur between the components of the mixture and the polymer. For example, the
permeation studies of binary organic liquid mixtures of varying composition by
Michelson et a1. (1985) led the authors to generalize three possible modes of interaction
occurring with organic mixtures. First, the mixture may decrease the lag time or
breakthrough time of the components. Second, a component that does not permeate as a
pure liquid may be transported through the membrane by another component, when
present in the mixture. Third, the collective permeation rate for the mixture may be
higher than the transmission rate of either pure component of the mixture. Huang et al.
(1986) conducted extensive studies on the permeation of various binary organic liquid
mixtures through polyethylene (PE) and made three observations regarding the effect of
molecular size, shape, and chemical nature of the permeants to the permeation of binary
organic mixtures. First, for a given binary mixture containing two members of a
homologous series, the lower molecular weight member permeates preferentially.
Second, with similar molecular weight and chemical nature in the mixture, molecules
with smaller cross sections will permeate at a faster rate than the other. Third, when the

mixture contains molecules with a large difference in chemical nature, permeation is not

28

as affected by their size and shape, but depends more on the chemical nature of the
molecule, as can be measured by the solubility parameter. Molecules with a solubility
parameter closer to that of the polymer tend to permeate at a higher rate than the other
molecules in the mixture. Furthermore, the effect of temperature on the permeation rate
of the binary mixture is such that the selectivity of the membrane to the constituents of
the mixture is decreased as the temperature is increased. When the temperature rises,
increasing the free volume within the polymer matrix, more of the less diffusive
molecules can therefore diffuse through the membrane (Huang etal., 1968).

The higher permeation rate of the mixture relative to the sum of permeation rates
of the pure components, is attributed to the combined internal plasticizing and solubility
effects. The results of permeation and sorption experiments involving d-limonene and
ethyl acetate binary mixtures through OPP ﬁlm, by Hensley et al.(1991) and Nielson and
Giacin (1994), led the authors to propose that d-limonene, a more soluble compound in
the ﬁlm, plasticizes the ﬁlm, which increases the free volume and therefore increases
diffusion of its co-permeant, ethyl acetate. While the solubility coefﬁcient of the two
compounds in the mixture was not affected by the presence of the co-permeant, the
observed increase in total permeation of the mixture was proposed to be the result of
increased internal mobility of ethyl acetate caused by plasticization of the OPP ﬁlm by d-
limonene. Similarly, carbon dioxide under high pressure is found to plasticize certain
glassy polymers and inﬂuence the transport of low molecular weight penetrants in glassy
polymers (Berens, 1989). In the polyvinyl chloride (PVC)/CO2/dimethyl phthalate
(DMP) system, liquid carbon dioxide was found to increase the sorption of DMP in PVC

ﬁ'om 1%wt to 40% wt in less than one third the time taken for PVC to absorb 1% DMP in

29

single component sorption. Thus, high-pressure carbon dioxide has practical potential
use in incorporating low molecular weight additives into polymers. In the absence of
plasticization, the sorption and permeability of a gas in a glassy polymer will be
depressed, relative to its pure gas values, by the presence of a second gas (Koros, 1989).
The competitive sorption model explains the behavior by which different gas molecules
in a mixture compete for sorption sites within the polymer matrix, resulting in
suppressing overall permeability.

The effect of mixture composition on the transport process of the individual
components can be expressed by the permeation ratio 0, which is deﬁned as the ratio of
the sum of permeation rates for components A and B in the mixture, Q, to the sum of

permeation rates of pure components A and B, Q°.

 

.. (28)

The permeation ratios for the individual components can be expressed as

_ ‘1_A
a’a cm
93 = ‘1—8 (30)
Q8

where 9A and 03 are the permeation ratios of components A and B, qA and qB are the
permeation rates of components A and B in the binary mixture, and QA and Q3 are the

permeation rates of pure components A and B, respectively.

30

Thus, the permeation ratio should be equal to unity when a binary organic liquid
mixture exhibits ideal permeation behavior. The value of the permeation ratio may be
higher or lower than unity for non-ideal permeation. If the permeation ratio of a system is
higher than unity, the system can be said to exhibit a permeation enhancement effect,

while a value lower than unity indicates a permeation depression effect.

Permeation Measurement Procedure and Technique

The experimental methods for measurement of S, D and P can be divided into
permeation and sorption experiment categories, which have been described by a number
of investigators (Stannett et al., 1972, Zobel, 1982, Baner et al., 1986, Hernandez et al.,
1986). The permeation test methods are based on static state (quasi-isostatic) and
dynamic permeation (isostatic) procedures, both of which use different mathematical
treatments to ﬁnd P and D. When the solubility coefﬁcient follows Henry’s law, S can
be determined from the relationship S=P/D. The agreement between the solubility
coefﬁcient of gases and vapors in polymers measured by equilibrium sorption and
permeation experiments is good at test temperatures above the polymer glass transit? on
temperature (Meares, 1958; Barr, 1996). Barr (1996) reported that the solubility
coeﬁicients for ethyl acetate in low density polyethylene, linear low density polyethylene,
and ionomer, determined by a gravimetric procedure, was approximately 25 to 30% lower
than the values obtained from isostatic permeability techniques. Because the methods of
calculating the solubility coefﬁcient values by the two procedures are inherently different

this agreement is considered to be within acceptable limits. Since the isostatic

31

permeation test method will be employed in the present study, the system and the
mathematical treatment will be brieﬂy described here, while other methods can be found
elsewhere (Hernandez et al., 1986).

The design of the isostatic test system is that permeation data for an organic vapor
or gas through a polymer membrane is continuously collected from the initial time zero to
steady state conditions, as a function of temperature and penetrant concentration. A
constant, desired concentration of penetrant is maintained in the high concentration cell
chamber, while a constant ﬂow of carrier gas in the lower cell chamber removes any
permeated penetrant and conveys it through to the detector. The detector utilized must be
able to give a good response to the kind of permeant tested. Since a ﬂame ionization
detector gives a good signal to noise ratio for most organic vapors, it is commonly used in
the commercial isostatic test apparatus. The lower concentration cell chamber is
maintained at zero penetrant concentration and thus a constant penetrant concentration
gradient is achieved during the entire test run. At pre-selected time intervals the
concentration of penetrant from the lower cell chamber is determined, and the
transmission rate is monitored continuously until steady state is attained. The

permeability coefficient at steady state is then calculated as

_ 4Q!
_ AtAp (31)

where AQ / At is the transmission rate at steady state, 1 is the thickness of the ﬁhn, A is
the exposed area of the ﬁlm, and p is the penetration concentration gradient.

The diffusion coefﬁcient is determined using the solution of Fick’s ﬁrst law of

32

diffusion given by Pasternak, et al. (1970).

If.)

_ _‘L 1.24/2 _
(AM) —(J7?)(4Dt) exP(4Dt) (32)

 

737

where (AM/ A t) and (AM/ At)... are the transmission rate of the penetrant at time t and at
steady state, respectively, t is the time and l is the thickness of the ﬁlm. For each value
of (AM/ A t), /(AM/ At)”, a value of 12/4Dt can be calculated by using a Newton-Raphson
method (Chapra and Canale, 1985). The method is brieﬂy described in appendix D. By
plotting the reciprocal of these calculated values, 4Dt/12, against time, a straight line is

obtained and the diffusion coefficient, D, is calculated by

:(slope) x l2 (33)

4

D

 

Another approach to determine a ﬁrst approximation of D is given by the

expression derived by Ziegel, et. al.(Ziegel et. al., 1969).

12
D :
7.1994,,

 

(34)

where to_5 is the time to reach a rate of transmission ( M/ t). equal to half the steady state
(M/ t)... value.

The most common error involving permeation experiments is usually caused by
the failure to obtain the true steady state transmission rate, and inaccuracy of thickness

determination. According to equations 33 and 34, these two factors thus constitute a

33

variation in the estimation of D.

Dynamic Purge and Trap/Thermal Desorption Technique

The dynamic purge and trap/thermal desorption technique is another approach to
determine the permeation rate. The technique involves the use of adsorbents to trap and
concentrate the permeated penetrant at steady state. The vapors concentrated in the
adsorbent trap are subsequently recovered by the desorption system and transferred to a
gas chromatograph for analysis. The amount recovered per trapping time is treated as the
permeation rate. Since quantiﬁcation of the amount of vapor permeated is achieved by
gas chromatography, the permeation rate of constituents in a gas mixture can be
quantiﬁed, if the corresponding peaks of the constituents can be separated by a gas
chromatography colunm.

The application of a dynamic purge and trap/thermal desorption procedure
coupled with the MAS 2000TM Permeation Test System was developed and performed by
Chang (1996). Validation of the method was obtained by comparing the permeance
values for OI-pinene through a PVdC coated OPP ﬁlm, determined by the dynamic purge
and trap/thermal desorption technique, with the values obtained from the MAS 2000TM
Permeation Test System operated in the continuous ﬂow isostatic method. The
permeability values obtained by the two procedures were found to be in good agreement.
The permeance of OI-pinene vapor through a series of high barrier composite membranes,
which could not be tested by the normal isostatic procedure, was determined by the

dynamic purge and trap/thermal desorption procedure (Chang, 1996). The lowest

34

detection sensitivity of the dynamic purge and trap/thennal desorption procedure was
found to be 0.2 rig/hr which is three to four orders of magnitude less than the continuous
ﬂow isostatic procedure. The increased detection sensitivity of the method provides the
ability to determine the permeation rate of aroma/ﬂavor permeation rates through high

barrier ﬁlms, where the conventional techniques fail.

MATERIALS AND METHODS

Materials and Equipment
Films:

PVdC-coated OPP ﬁlm, BICOR 70 HES-2, one—side sealable, one-side high barrier
PVdC-coated OPP ﬁhn (Mobil Chemcal Co.)

Total Thickness: 0.7 mil

Biaxially oriented polypropylene ﬁlm (Mobil Chemical Co.)

Thickness 2 mil
Density : 890 kg/m3
Percent Crystallinity: 45.7% determined by differential scanning calorimetry
analysis
Level of Elongation: 420% machine direction
800% cross machine direction
Hildebrand Solubility Parameter: 8.3 (cal/cc)”2 poor H-bonding
(taken from Van Krevelen, 1976)

Permeants:

d-limonene (Aldrich Chemical Co., Milwaukee, WI)

Molecular Structure (CIOHI6)
Density at 25 °C 0.840 g/cc
Molecular Weight 136.24
Boiling Range 175.5-176 °C

Hildebrand Solubility Parameter 8.21 (cal/cc)“2 poor H-bonding
(taken from Halek and Luttmann, 1991)

Molar Volume 162 cc/mol
Refractive Index 1.4730
%Purity 97%

Ethyl Butyrate (Aldrich Chemical Co., Milwaukee, WI)

Molecular Structure (CH3CH2CH2C02C2H5)

l

35

36

Density at 25 °C 0.878 g/cc
Molecular Weight 116.16
Boiling Range 120 °C

Hildebrand Solubility Parameter 3.5 (cal/cc)1/2 moderate H-bonding
(taken from Nielsen et al., 1992)

Molar Volume 132.3 cc/mol
Refractive Index 1.3920
%Purity 99%

Ethyl Acetate (Aldrich Chemical Co., Milwaukee, WI)

Molecular Structure (CH3CO2C2H5)
Density at 25 °C 0.894 g/cc
Molecular Weight 88.11

Boiling Range 77.1 °C

Hildebrand Solubility Parameter 9.11 (cal/cc)”2 moderate H-bonding
(taken from Van Krevelen, 1976)

Molar Volume 98.56 cc/mol

Refractive Index 1.37

%Purity 99.9 %
Solvent:

Carbon Tetrachloride (Mallinckrodt, Inc., Paris, Kentucky)

Molecular Structure (CC14)

Density at 25 °C 1.585 g/cc

Molecular Weight 153.84

Boiling Range 76.3-76.8 °C
Thermal Desorption Apparatus:

Dynatherrn 890/891 thermal desorption unit (Supelco Inc.,
Bellefonte, PA)

Carbotrapm300 multi-bed thermal desorption tubes, 6 mm OD. x 4 mm ID. x
11.5 cm length (Supelco Inc., Bellefonte, PA)

Gas Chromatograph:

37

Hewlett Packard model 5890A interfaced with HP 3395 integrator
(Avondale, PA),

Gas Chromatography Column:
Fused Silica Capillary Column
SPBTM-s, 30 meters long, 0.32 mm ID, 1.0 nm ﬁlm thickness
(Supelco Inc., Bellefonte, PA)
Permeation Test Apparatus:
MASZOOOTM Organic Permeation Detection System
(Testing Machines Inc., Amityville, N.Y.)
Water Bath
Blue M Magni Whirl (Blue M, A Unit of General Signal, Blue Island, IL)
250 ml Gas Washing Bottle
(Fisher Scientiﬁc, Pittsburgh, PA)
Needle Valves
Nupro ‘M’ series (Nupro Co., Willoughby, OH)
Swagelok Fitting
(Supelco Inc., Bellefonte, PA)
Electronic Mass Flow Meter
Model Top-Trak 821 (Sierra Instruments, Carmel Valley, CA)
Syringe

500 m1 gas-tight syringe (Hamilton Co, Reno, Nevada)
5 ul syringe (Hamilton Co, Reno, Nevada)

38
Methods

Calibration Curves of d-Limonene, Ethyl Butyrate, and Ethyl Acetate by Gas
Chromatography Analysis: Preparation and Testing
The vapor activities of the respective permeant vapors evaluated with the
MAS2000TM Organic Permeation Detection system were determined by gas
chromatography analysis. Standard solutions of the respective test compounds in carbon
tetrachloride were prepared by a serial dilution procedure and calibration curves for the

respective permeants were constructed according to the following analytical conditions.

Gas Chromatography Condition:

Injection temperature 220°C

Detector temperature 250°C

Head pressure 10 psi

Total ﬂow port (split vent) 27.8 ml/min
Septum purge (purge vent) 2.76 ml/min
Helium ﬂow rate 1 ml/min

Temperature Programming

Two sets of temperature programming conditions were employed, one for d-
limonene and ethyl butyrate analysis and the other was for analysis of ethyl acetate. Both

programming runs utilized two temperature cycles in order to reduce the total run time.

For d-limonene and ethyl butyrate

Initial oven temperature 50°C
Initial time 2 min

Rate 7°C/min

Final temp 110°C

39

Final time 0 min

Rate A") 30°C/min

Final temp A“) 200°C
Final time A“) 3 min
Total rim time 16.58 min.

(“L the second temperature programming cycle
For ethyl acetate

Initial temperature 40°C
Initial time 5 min

Rate 7°C/min

Final temp 110°C

Final time 0 min

Rate A") 30°C

Final temp A") 200°C
Final time A") 3 min
Total run time 21 min

(a) the second temperature programming cycle

The above conditions gave retention times for ethyl acetate, ethyl butyrate, and d-

lirnonene of 2.25, 3.95, and 8.94 min, respectively. The quantity of permeant detected

was determined by multiplying the standard concentration (v/v) times the volume

injected (1 ul), which is then multiplied by the density of the permeant, to give quantity

injected. The quantity injected plotted versus the corresponding area response gave the

calibration curves which established the linearity and sensitivity of the assay procedure

for the respective permeants. The reciprocal of the slope is taken as the calibration factor

in grams per area unit. These calibration factors were used to set the vapor activities for

the MASZOOOTM Organic Detection System. The calibration curves for the test

compounds are found in Appendix A.

40

In order to check the accuracy of the calibration curves determined for the test
compounds, their actual saturated vapor pressures were experimentally determined and
compared to the literature values. Approximately three ml of each test compound were
separately stored in 5 ml septa seal glass vials at 23°C and allowed to equilibrate for at
least 48 hours. The vials were sealed with Teﬂon-faced silicone septum and aluminum
crimp cap. A 500 Ill gastight syringe was used to withdraw a 50 ul gas sample from the
headspace of the septa seal vial and injected directly into the gas chromatograph. The
area response was then converted to grams of permeant injected through its calibration
factor. The vapor in the vial was assumed to have reached equilibrium and behave as an
ideal gas. Therefore, the ideal gas law was used to determine the saturation vapor

pressure of each compound at 23°C, by substitution into equation 35.

MWxV

 

where P = partial pressure [mmHg]
CF = calibration factor [g/AU]
AU = Area Response from GC [AU]
R = gas constant, 6.236x107 [mmHg 111 /mol K]
MW = molecular weight of compounds [g/mol]
V = gas sample volume [111]

The experimentally determined saturated vapor pressures were then compared
with the interpolated values obtained from Perry’s Chemical Handbook (1984). The
accuracy of the calibration factors for d-lirnonene, ethyl butyrate, and ethyl acetate was

within 10% between experiment and literature saturation vapor pressure values.

Saturated Vapor Pressure in mmHg at 23° C

 

 

 

 

 

 

Experiment“) Perry’s Chemical % difference
Handbook“)
d-limonene 2.34 2.32 0.73%
Ethyl butyrate 14.23 15.34 7.23%
Ethyl acetate 79.82 82 2.65%

 

 

 

(a)

(b) average of 10 samples.

values were interpolated by polynomial function to the fifth power.

Because of the wide variation in the saturation vapor pressure of the various penetrants,
at the respective temperatures of test, the partial pressure gradient for the permeability
experiments was expressed as vapor activity. This allowed for barrier performance to be
compared at a standard driving force for the permeants evaluated. Vapor activity values

were calculated by:

a = _P_ (36)

where p = partial vapor pressure
p, = saturated vapor pressure

Calibration Curves for Dynamic Purge and Trap/Thermal Desorption Procedure

The choice of adsorbents to efficiently trap the components in the mixture and the
desorption conditions to ensure a complete recovery of penetrants is important. The
Carbotrap 300TM adsorbent tube ﬁom Supelco was selected for the present study because
its multi-bed adsorbent design allows trapping of various organic compounds with

different size and different functional groups. Also, its sampling capacity within

 

42
trapping time in the present study is sufﬁcient and the recovery of trapped penetrants is

near quantitative. Problems may arise when preparing a standard calibration curve by
this procedure, as some solvents do not desorb instantaneously during the thermal
desorption process. This leads to a broad solvent peak with a tailing baseline. Only the
desorption of carbon tetrachloride solvent from Carbotrap 300TM was found to give a
satisfactory ﬂat baseline, with accurate and precision peak areas for the trapped
penetrants, following their desorption.

To establish the linearity and sensitivity of the thermal desorption procedure,
standard calibration curves for the respective test compounds were prepared. A 1 pl
sample of standard solutions of limonene, ethyl buryrate, and ethyl acetate of known
concentration in carbon tetrachloride, was directly injected onto the sorption tube. The
sorption tube was then inserted into a heating chamber of the thermal desorption unit,
which is interfaced directly to the column of the gas chromatograph for quantiﬁcation.
The gas chromatography column is the same as that described previously for vapor
activity determination. The test compounds, which are sorbed onto the trap, are desorbed
by heating and then separated into the individual components, according to the following

analytical conditions.

Thermal desorption unit condition

Tube desorption chamber temperature 370°C

Valve compartment temperature 250°C

Transfer line temperature 250°C

Tube preparation chamber temperature 350°C

Desorption time 8 min

Preparation time 30 min.

Desorption carrier gas ﬂow rate at ﬂow check port 9 ml/min
Preparation carrier gas ﬂow rate at side port 15 ml/min

43

Gas chromatography condition:
For d-Iimonene and ethyl butyrate
Initial temperature 50°C
Initial time 5 min
Rate 10°C/min
Final temperature 200°C
Final time 3 min
Total run time 23 min.
For d-limonene and ethyl acetate
Initial temperature 35°C
Initial time 5 min
Rate 10°C/min
Final temperature 200°C
Final time 3 min
Total run time 24.50 min
The gas chromatographic conditions gave retention times for ethyl butyrate and d-
limonene of 6.8 and 11.4 min, respectively. The second set of conditions gave retention
times for ethyl acetate and d-limonene of 3.41 and 12 min, respectively. Again, plotting
grams of permeant introduced onto the sorption trap against its corresponding area
response provided a series of calibration curves. The reciprocal of the slope was taken as
the calibration factor for quantiﬁcation. The calibration proﬁles for each test compound

are shown in appendix B. After 8 min. of desorption time, the tube is cleaned to remove

any residual compounds by heating at 350°C for 30 min.

Permeability Test System

Permeability studies were carried out with a MAS 2000TM Organic Permeation

44

Detection System, which was modiﬁed with a device for trapping permeated organic
vapors employing a dynamic purge and trap technique. The MAS2000TM Organic
Permeation Detection System is based on an isostatic permeation test procedure. This
system allows for the continuous collection and measurement of the permeation rate of
the organic vapor through a polymer membrane, from the initial time zero to steady state
conditions. The MAS 2000TM system incorporates a ﬂame ionization detector (FID),
and precisely controls the cell temperature (range from ambient to 100°C) and all gas
ﬂow rates (nitrogen as carrier, air, and hydrogen as fuel). An IBM 486SX computer
system with a very user friendly software package was interfaced to the system to control
many of the test parameters. The computer can also activate and deactivate the gas ﬂow
direction, cell opening/closing, as well as display data, while recording all pertinent
instrument parameters. All permeation data can be stored in the computer hard drive, and
LOTUS 1-2-3 is used to recall the permeation data to calculate the respective mass
transfer parameters and give the transmission rate proﬁle curve.

In order to determine the permeability of binary organic vapor mixtures, the test
unit employed in the present study incorporated a dynamic purge and trap system to
allow accumulation of the permeated vapor. In the original MASZOOOTM system, the
permeated vapor is directly conveyed to a ﬂame ionization detector (FID) for
quantiﬁcation. However, in the modiﬁed system, a bypass line was inserted to convey
the permeated vapor to a sorption trap. The trapping system was designed to ensure that
the low concentration cell chamber is continuously ﬂushed with the carrier gas and the
permeated vapor is conveyed to the trapping tube attached. The sorption trap was

connected to the exit port of the bypass line, which is incorporated on the instrument

45

chassis, via a Mt” thumb wheel swagelok ﬁtting for easy removal. Figure 4 shows a
schematic of the permeation test and trap system. The glass thermal desorption tubes,
CarbotrapTM 300, were employed as adsorption traps, which were prepacked by Supelco
Inc. The trapping tubes contain 300 mg of Carbotrap C adsorbent, 200 mg of Carbotrap

B adsorbent, and 125 mg of Carbosieve S-III adsorbent.

Permeability Measurements

The permeability studies were carried out at 50°C for OPP and 60°C for PVdC-
coated OPP. A minimum of three different concentrations were run for each test
compound as a pure vapor and a minimum of six different binary mixture combinations
of varying composition were run, except for ethyl acetate. For ethyl acetate, three binary
mixture combinations with limonene through OPP were studied. Tests for each vapor
activity evaluated were carried out in duplicate.

Prior to initiating a test run, the test ﬁlm was conditioned at 60°C +/- 1°C for 6
hours, to desorb any residual monomer, or other low molecular weight volatiles from the
ﬁlm, which could interfere with detection of permeated vapor. For each test run, a
sample ﬁlm approximately 6” x 6 V2” was cut, mounted on a paperboard ﬁlm holder with
tape, and then placed in the permeability cell. The area of the test ﬁlm was 0.0081 m2
(12.6 inz).

A constant concentration of permeant vapor for the high concentration cell
chamber was produced by bubbling nitrogen through the liquid permeant, with the flow

rate equal to 30 ml/min. The liquid permeant is contained in a vapor generator consisting

 

 

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47
of a 250 ml gas washing bottle. The gas washing bottles were placed in a constant

temperature water bath and the temperature maintained at 23+/-1°C, throughout.

In order to obtain a wide range of vapor concentration levels, the permeant vapor
stream was mixed with another stream of pure carrier gas (nitrogen). Flow meters and
needle valves were used to adjust the ﬂows and to indicate constant ﬂow rates.

For studies involving the permeation of binary mixtures, separate vapor streams
were generated and mixed to provide a series of binary vapor mixtures of varying vapor
activity values.

The vapor activity was correlated linearly with the ﬂow of carrier gas through the
bubbler as shown in appendix C. The digital mass ﬂow meters were used to select vapor
activity levels required and to monitor a constant ﬂow throughout the test run.

In order to provide an accurate measurement of the permeant vapor concentration
or activity, a gas sampling port was installed between the dispensing manifold and the
test cell. To determine the speciﬁc vapor concentration, a 50 I11 sample was withdrawn
ﬁ'om the sampling port with a 500 I11 gas-tight syringe, and injected directly into the gas
chromatograph for quantiﬁcation. The GC analysis conditions were the same as that for
determining the saturated vapor pressure.

The computer software monitors the transmission rate by recording and plotting
the signal output in picoamps against time, until it reaches a steady state. The picoamp
signal is converted to transmission rate by calibrating a known amount of vapor against
the integration value in picoamp per second from the area of picoamp versus time plot.
The calibration procedure is done by manually introducing a known amount of vapor

through the injection port of the MASZOOOTM. The average calibration factor determined

48

hour different vapor activity levels was then used to quantify the transmission rate of the
respective permeants through the ﬁhn. The permeability constant and diffusion

coefﬁcient are determined manually from raw data of the MASZOOOTM.

 

 

 

 

Organic Vapors Average calibration factor“
picogram/pamp x sec
Ethyl acetate 33 l . 14
Ethyl butyrate 278.571
d-limonene 1 52.42

 

 

 

 

* Average value determined ﬁom three vapor activity levels.

Dynamic Purge and Trap/Thermal Desorption Procedure

Once the operational parameters of gas ﬂow rates, temperature, vapor pressure,
and signal base line became stable, the permeation tests were started. In conducting a
permeability run, the test ﬁlm is initially exposed under isostatic conditions at the
required test temperature and permeant concentration and the permeation process
conﬁnle monitored until a steady state transmission rate is attained. After attaining a
steady state rate of transmission, the switching valve was activated and the system was
operated in the accumulation or dynamic purge and trap mode for a predetermined time
interval. The trapping time for the low barrier OPP ﬁlm was 30 seconds, while the
trapping time for the high barrier PVdC coated OPP ﬁlm was 3 nrinutes. The sorbant
tube was then removed and immediately replaced by a new trapping tube and the
permeated vapor again accumulated for quantiﬁcation. This sample collection procedure

was repeated in triplicate. The sorbant tube removed from the permeability test system

49

was then transferred to a thermal desorption unit, which thermally desorbs any organic
volatiles from the sorbant tube and transfers them to the gas chromatograph for
quantiﬁcation. The sorbed volatiles were desorbed by heating for 8 minutes at 370°C
with the valve and transfer line held at 250°C to maintain the desorbed compounds in the
vapor phase, while being transferred to the gas chromatograph. Helium was used as a
carrier gas through the thermal desorption unit at a ﬂow rate of 9 ml/minute at 40 psi.
After sample desorption, the sorbant tubes were conditioned at 350°C for 30 minutes
prior to re-use. The trapping and subsequent thermal desorption of volatiles allows their
effective release, undiluted, and allows monitoring of otherwise undetectable levels of
penetrant concentration.

After each test run, the switching valve in the MASZOOOTM was checked for any
possible residual volatiles that might have been retained from the previous run. There
was no indication of residual volatiles retained by the switching valve on testing, thus,

cleaning of the switching valve was not carried out in the present experiment.

Analysis of Test Permeant by Thermal Desorption/Gas Chromatography Procedure

Gas chromatographic (GC) analysis was carried out with a Hewlett-Packard
Model 5890 gas chromatograph, equipped with a ﬂame ionization detector and interfaced
to a Hewlett-Packard Model 3395 integrator (Avondale, PA), for quantiﬁcation of
permeated vapor. The GC conditions were the same as that for determining the
respective calibration curves. The permeance or permeability constant was determined

by substitution into

50

P = CFxA U (37)
txAxAp

 

where P*= permance [kg / sec m2 Pa]
AU = area unit response from integrator [AU]
A = exposed area of the ﬁlm
CF = dynamic purge and trap/thermal desorption calibration factor
t = trapping time [sec]
Ap = vapor pressure gradient [Pa]

*permeability coefficient is calculated by multiplying permeance by the ﬁlm thickness

RESULTS AND DISCUSSION

Comparison between MA82000TM Isostatic Test Procedure and Dynamic Purge and
Trap/Thermal Desorption Procedure

Estimation of the Detection Sensitivity Limit Between the Two Procedures

The lowest detection limit for the dynamic purge and trap/thermal desorption
procedure depends upon the trapping time and the gas chromatographic output signal for
each particular permeant. Applying the dynamic purge and trap/thermal desorption
procedure, Chang (1996) reported that the lowest signal output from the gas
chromatograph, with good precision and accuracy, was assumed to be around 5,000 area
response units. The longest trapping time in the present study is 3 min. Thus, the

minimum measurable transmission rate of limonene is calculated as follows.

5000AU x 5.26x10‘l4 g x 3600 see x 1000mg
180 sec AU 1hr lg

 

= 5.26x10‘° E (38)
hr

The 5.26x10’M g/AU is the calibration factor of limonene determined by the thermal
desorption procedure (Appendix B).

Operating the MASZOOOTM Organic Permeation Detection System by the isostatic
procedure, the calibration factor in pg/pamp see was the average value determined at the

respective vapor activity levels for each permeant. Assuming that 0.5 pamp is the lowest

51

52
detection signal, since it was the lowest signal output obtained for limonene permeability

through PVdC coated OPP that was accurate and repeatable, the minimum measurable

transmission rate of limonene is calculated as follows.

 

 

 

 

 

 

.4
152.42 pg x0. Spampx 1mg x 3600 see = 2.74x10 mg (39)
pamp sec 10 pg 1hr hr
Table 1. Estimated lowest measurable transmission rate between the two
procedures
. MAszoooTM Dynamic Purge and.
Organrc Vapors Isostatic Mode Trap/Thermal Desprptron
Procedure
limonene 2.74 x104 mg/hr 5.26x10'° mghr
Ethyl butyrate 1.00x10'3 mg/hr 1.14x10‘5 mg/hr

 

 

 

(a) Values are based on a 3 minutes trapping time

Based on this analysis, the sensitivity of the transmission rate measured by the
dynamic purge and trap/thermal desorption procedure is two orders of magnitude greater
than the MASZOOOTM isostatic procedure for both limonene and ethyl butyrate (see Table
1). Chang (1996) also reported similar ﬁnding for permeability studies involving the

permeability of Ot-pinene through high barrier polymer membranes.

Comparison of Permeability Values Between the MAS 2000TM Isostatic Test
Procedure and the Dynamic Purge and Trap/Thermal Desorption Procedure
A comparison of the permeability coefﬁcient values obtained for d-limonene,
ethyl butyrate, and ethyl acetate by the isostatic and dynamic purge and trap/thermal
desorption procedures for OPP ﬁhn is shown in Tables 2, 3, and 4, respectively. Tables 5

and 6 summarize the permeance values for d-limonene and ethyl butyrate through PVdC

 

53

coated OPP ﬁlm. For better illustration the data is presented graphically in Figures 5 and

6, where the permeability parameter (i.e. permeability coefﬁcient or permeance) values,

obtained by the respective procedures, are plotted as a function of vapor activity.

Table 2. Permeability coefﬁcient, kg m/m2 s Pa 1110'”, of limonene through OPP

ﬁlm (50°C) determined by the two procedures“)

 

 

 

 

 

 

 

 

 

 

Vapor . . .
Vapor TM Dynamic Purge and % devratron from
activity a” “3:3“ MASZOOO Trap/TD Procedure MAszoooTM
0.3 93 4.15+/- .37 3.67+/-.15 11.57%
0.2 62 4.54+/—.15 3.34+/-.017 26.43%
0.13 41 3.65+/-.07l 3.24+/-.031 1 1.23%
0.05 16 3.30+/—.42 2.68+/-.40 18.79%

 

(a) All values are the average of duplicate runs.
”’4 Vapor activity values were determined at room temperature (24°C).

Table 3. Permeability coefﬁcient, kg m/m2 3 Pa x10”, of ethyl butyrate through

OPP ﬁlm (50°C) determined by the two procedures (a)

 

 

 

 

 

Vapor . . .
Vapor TM Dynarnlc Purge and % devratron from
activity (9 ”:32?” MASZOOO Trap/TD Procedure MAS2000TM
0.2 404 1.83+/-.19 2.07+/-.30 13.11%
0.12 241 l.47+/-.039 l.56+/-.012 6.12%
0.04 73 1.53+/—.13 1.41+/-.25 7.84%

 

 

 

 

 

(‘0 All values are the average of duplicate runs.
(1’) Vapor activity values were determined at room temperature (24°C).

Table 4. Permeability coefﬁcient, kg m/rn2 3 Pa x10“, of ethyl acetate through OPP

ﬁlm (50°C) determined by the two procedures (a)

 

 

 

 

 

Vapor Vapor Dynamic Purge and % deviation from
activity a” Pressure MA32000TM Trap/TD Procedure MAszoooTM
(P3)
0.2 3287.5 6.34+/-.14 6.40+/-.28 0.95%
0.12 1093 4.91+/-.O79 5.29+/-.33 7.74%
0.04 404 4.21+/-.46 4.68+/-.26 1 1.16%

 

 

 

 

 

(a) All values are the average of duplicate runs.
(b) Vapor activity values were determined at room temperature (24°C).

 

 

 

54

 

 

 

 

 

 

 

6I I III V I T "WWI
I I
I I
5 I . I
m I d-lrmonene I
7.2 I I
x I I
N ’ I
a. I _ ~
g . -- ~
E i
on { I
2‘: I i ethyl butyrate I
. Jar-’M’r/LA , ‘ ' V ‘L I
2 I g A. ﬁ' I
I ethyl acetate
_ ___~ A I
I l:##:9~_————— I
I
0 I.-- . . ___2 . , ‘- _ __._ I _-.-
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
vapor activity
+ MAS2000 I DTP/TP Procedure

Figure 5. Comparison of permeability of organic vapors
through OPP ﬁlm by MA52000TM and DPT/TD
procedures (50°C)

55

12 I ethyl butyrate

10“

    

d-limonene

Permance, kg/m2 8 Pa x 10'‘3

O 4,--- ~-,__ __vrie_vr . .___.#A; _. . _.-.r_ _i___ﬁ_-._

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

 

vapor activity
—O-— MASZOOO —I— DPT/TD Procedure

Figure 6. Comparison between MA82000TM and DPT/TD
procedures: organic vapor permeation through PVdC

coated OPP ﬁlm (60°C)

M—‘ﬁ

 

 

0.4

56

Table 5. Permeance, kg /m2 s Pa 1:10“, of limonene through PVdC coated OPP ﬁlm
(60°C) determined by the two procedures“)

 

 

 

 

 

Vapor Vapor . . .
. . (1,) TM Dynamlc Purge and % devratron from
act1v1ty 1371::ng MASZOOO Trap/TD Procedure MAS2000TM
0.35 108 8.06+/-.62 7.04+/-.41 12.66%
0.2 68 6.49+/-1.0 6. l 6+/-.53 5.08%
0.09 28 4.15+/-.O71 4.78+/-.31 15.14%

 

 

 

 

 

(“7 All values are the average of duplicate runs.
a” Vapor activity values were determined at room temperature (24°C).

Table 6. Permeance, kg /m2 s Pa 1:10“, of ethyl butyrate through PVdC coated OPP
ﬁlm (60°C) determined by the two procedures“)

 

 

 

 

 

 

 

 

 

Vapor Vapor . . .
. . (1,) TM Dynam1c Purge and % devratron from
actrvrty P713231” MAS2000 Trap/TD Procedure MA82000TM
0.21 436 9.85+/-.21 11.6+/-.14 17.77%
0.12 251 8.90+/-.28 10.2+/-.028 14.61%
0.04 73 7.73+/-.53 8.90+/-.86 15.14%

 

(a) All values are the average of duplicate runs.
(1’) Vapor activity values were determined at room temperature (24°C).

As shown by the results presented in Tables 2 through 6 and from Figures 5 and

6, there was good agreement between the permeability values obtained by the two test

methods for the respective permeant/barrier ﬁlms systems studied, which considered

permeants of various chemical structure, as well as low and high barrier ﬁlms. The %

deviation between the permeability values obtained from the dynamic purge and

trap/thermal desorption procedure, as compared with the MAS2000TM isostatic

procedure, was less than 20%, except for the permeability of limonene through OPP at a

= 0.2, which gave a 26% deviation between the respective permeability coefﬁcient

values. The average % deviation between the permeability values obtained by the two

procedures for limonene, ethyl butyrate, and ethyl acetate was 14%, 12%, and 7%,

respectively. Because of the procedure differences between the isostatic and dynamic

 

 

57
purge and trap/thermal desorption techniques, this agreement is considered to be within

acceptable limits.

The average % deviation between the permeability values obtained by the two test
procedures was 12%. Thus, establishing the suitability of the proposed dynamic purge
and trap/thermal desorption method for measuring permeation rates of binary organic
vapor mixtures through barrier ﬁlms.

The variation between the permeability values obtained by the two procedures can
be attributed to a number of factors, such as errrors introduced by the gas
chromatography procedures and to calibrating both the MAS 2000TM system and the
thermal desorption unit. Fluctuation in temperatures and ﬁlm thickness can also
contribute to the observed variation. With respect to the dynamic purge and trap/thermal
desorption procedure, variation in trapping time, incomplete trapping during sample
collection and incomplete desorption of the trapped volatiles during the desorption

process can also introduce sources of error.

Effect of Vapor Activity on the Organic Vapor Diffusion and Permeability Analyzed
by Isostatic Permeability Test Procedure
Isostatic permeability studies were carried out to determine the effect of vapor
activity on permeability, diffusion, and solubility coefﬁcient values for d-limonene, ethyl
acetate, and ethyl butyrate through OPP and PVdC OPP ﬁlms. The permeability tests
were conducted at 50°C for the OPP ﬁlm and at 60°C for the PVdC coated OPP ﬁlm at
three different vapor activity levels for each respective penetrant, except for the

limonene/OPP system, where four vapor activity levels were evaluated. Under these

58
experimental conditions, the time required for the permeants to reach steady state through

the OPP ﬁlm ranged from 6 hours for ethyl acetate and ethyl butyrate to 8 hours for d-
limonene. A steady state rate of permeation through PVdC coated OPP ﬁlm was
achieved within 12 hours for ethyl butyrate and 20 hours for d-limonene, under the
experimental conditions.

The diffusion coefﬁcient values reported were the best estimated diffusion
coefﬁcient values (D351) based upon the sum of squares technique. The sum of squares
method selects the diffusion coefﬁcient which gives the least differences between the
experimental transmission rate curve and the theoretical transmission rate curve, obtained
by the relation of Fick’s ﬁrst law, as given by Pasternak et al. (1970) (see equation 32).
Mathematically the method sums the squares of the differences between experimental
and calculated transmission rate values at each point of the transmission rate proﬁle
curve. A plot of the corresponding sum of squares values versus diffusion coefﬁcient is
then used to determine the least sum of squares diffusion coefficient value. Since the
PVdC coated OPP ﬁlm investigated in the present study is a coated structure, permeance
values were calculated to describe the barrier properties of the total structure and the
diffusion coefficient values reported were apparent diffusion coefﬁcients, representative
of the speciﬁc structure. Assmning that the relationship P = D x S is valid, the solubility
coefficients can also be determined. Permeability, diffusion, and solubility coeﬂicient
values determined for limonene, ethyl butyrate, and ethyl acetate through the respective

polymer membranes, as a function of vapor activity, are summarized in Tables 7-11.

 

59

Table 7. Permeability and diffusion coefﬁcients for limonene through the two test

 

 

 

 

 

ﬁlms (a)
OPP ﬁlm (50°C) PVdC OPP ﬁlmg60°C)
Vapor Vapor Vapor Vapor
activity Pressure P,Pkg Ill/“i: S D’ “if/483 activity Pressure P’ kg/ “3:35 Pa D’ mzlgec
(b, @a) a x 10 x10 (1,) (Pa) x10 x10
0.3 93 4.15+/-.37 5.88+/-.18 0.35 108 8.06+/-.62 2.73+/-.035
0.2 62 4.54+/-. 15 5.3 8+/-. 1 8 0.2 68 6.49+/- l .0 2.33+/-.46
0.13 41 3.65+/—.07 1 5.05+/-.O71 0.09 28 4.15+/-.071 2.25+/-.35
0.05 16 3.30+/-.42 5.13+/-.18

 

 

 

 

 

 

 

 

 

 

(a) All values are average of duplicate runs.

(b) Vapor activity values were determined at room temperature (24°C).
(0) D determined by the sum of squares method

Table 8. Solubility coefﬁcient values for limonene and the estimated % sorbed (v/v)

 

 

 

 

 

 

in the two test ﬁlms
OPP ﬁlm (50°C) PVdC OPP ﬁlm(60°C
Vapor Vapor S, kg/m3 % sorbed Vapor Vapor S, kg/m3 % sorbed
activity (a) Pressure Pa 0” (v/v) activity (a) Pressure Pa 0’) (v/v)
(Pa) (Pa)
0.3 93 .071 0.79% 0.35 108 .0052 0.07%
0.2 62 .084 0.62% 0.2 68 .0050 0.04%
0.13 41 .072 0.35% 0.09 28 .0033 0.01%
0.05 16 .064 0.12%

 

 

 

 

 

 

 

 

 

(a) Vapor activity values were determined at room temperature (24°C).
(b) S determined by P =DxS relationship.

Table 9. Permeability and diffusion coefﬁcients for ethyl butyrate through the two

test ﬁlms 0')

 

 

 

 

 

 

 

OPP ﬁlm (50°C) PVdC OPP ﬁlm(60°C)
Vapor Vapor 2 2 2 2
. . P,k m/rn sPa D,m/sec P,k sm Pa D,m/sec
“(ﬁlmy P3336 gx 10'15 x10"3(°) fie” x10“5‘°>
0.2 436 1.83+/—.19 2.08+/-.035 9.85+/-.21 11.5+/-1.4
0.12 251 1.47+/-.039 2.20+/-0.00 8.90+/-.28 9.78+/-.035
0.04 73 1.53+/-.13 1.95+/-0.00 7.73+/-.53 9.88+/-.88

 

 

 

 

 

 

7"} All values are average of duplicate runs.

a” Vapor activity values were determined at room temperature (24°C).

’0 D determined by the sum of squares method.

 

60

Table 10. Solubility coefﬁcient values for ethyl butyrate and the estimated %
sorbed (v/v) through the two test ﬁlms (a)

 

 

 

 

 

 

OPP ﬁlm (50°C) PVdC OPP ﬁlm(60°C)
Vapor o o
Vapor Pressure S, k g/m3 Pa /0 sorbed S, kg/m3 Pa /0 sorbed
actrvrty (Pa) (v/v) (v/v)
0.2 436 0.0088 0.40% 0.0015 0.07%
0.12 251 0.0067 0.18% 0.0016 0.05%
0.04 73 0.0078 0.06% 0.0014 0.01%

 

 

 

 

 

 

(“1 S determined by P =DxS relationship

Table 11. Permeability, diffusion and solubility coefﬁcient values and the estimated
% permeant sorbed for ethyl acetate through OPP ﬁlm at 50°C (‘0

 

 

 

 

 

Vapor Vapor P, kg m/rn2 8 Pa D, mz/sec S, kg/m3 Pa (d) % sorbed
activity 9) Pressure x 10''6 x 10'l3 ‘0 (v/v)
(P3)
0.3 3287.5 6.34+/-0.14 5.58+/-0.1 1 0.0011 0.40%
0.14 1093 4.9l+/-0.079 5.25+/-.035 0.00094 0.11%
0.04 404 4.21+/-0.46 4.3 8+/-0. 1 8 0.00096 0.04%

 

 

 

 

 

 

 

(“I All permeability and diﬁusion values are average of duplicate runs.
(1’) Vapor activity values were determined at room temperature (24°C).
(0) D determined by sum of squares method.
(J) S determined by P=DxS relationship

To better illustrate the effect of vapor activity on the permeability of the test
ﬁlms, the results are presented graphically in Figures 5 and 6, where the permeability
parameters (permeability coefﬁcient or permeance) are plotted as a function of vapor
activity. Figures 7 and 8 plot the diffusion coefficient values of each permeant through
OPP and PVdC coated OPP ﬁlms as a function of permeant vapor activity. The
relationship between the solubility coefﬁcient values for the respective permeant/barrier
membrane systems, as a function of vapor activity, is presented graphically in Figures 9
and 10, respectively.

A single factor statistical analysis, using Minitab software, was performed to

determine whether the experimentally obtained permeability, diffusion and solubility

 

D, mz/sec x10'‘3

61

 
   
 

 

 

 

5'00 I y = 4378608805):
4.00 ll I
I
I
. I
3.00 I i
I ethyl butyrate y = 1.9781 e0.3883x ;
I I
2.00 I r ' I
I I
A I
1-00 I d-limonene y = 048418-585" l
- A 4,. I
I ' ' ' I
I I
0.00 ~ I — I
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
vapor activity

Figure 7. Diffusion coefﬁcient of organic vapors through OPP ﬁlm as
a function of vapor activity (50°C)

62

12 a
I ethyl butyrate L

 

10 1

D, mz/sec x10'IS

d-limonene y = 2.0630207621x

 

I.
i

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

vapor activity

Figure 8. Apparent diffusion coefﬁcient of organic vapors
through PVdC coated OPP as a function of vapor activity

s, kg/m3 Pa

0.10 — ~ ~— — ~ 7*7 * ﬁ “ s,#,n______gv_w
0.09
0.08 I d-limonene
0 y = 0.0673e0'4462"

0.06 3

I .I
0.05 I

I
0.04 ’

I
0.03
0'02 I y=0.0071e0'7445x
0.01 ' ethyl butyrate

I T A

I ethyl acetate

0.00 I — —a!4———e~—r-e»:1:_ﬂ- .4» ”ﬁn“; __ __

0

63

 

 

 

0.05 0.1 0.15 0.2 0.25
Vapor activity

 

y = 000093-7007" I

Figure 9. Solubility coefﬁcient of organic vapors in OPP ﬁlm as

a function of vapor concentration (50°C)

S, kg/m3 Pa

64

 

      

 

7.008-03 I —v 7, ,M 7 7 5,, .7 - - I
I I
6.00E-03 I I
I d-limonene I
5 DOE-O3 a: y = 0.003161693x i I
I I I
4.00E-03 I I
I I
3005-03 I I
I I
2.00E-03 i ethyl butyrate I
1.00E-03 J y = 0.0015305044)‘ I
0.00E+00 . . ﬁe”? . _ I __

 

 

 

 

 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Vapor activity

Figure 10. Solubility coefﬁcient of organic vapors in PVdC coated OPP
ﬁlm as a function of vapor concentration

65

coefﬁcient values differed signiﬁcantly over the vapor activity ranges evaluated. The
signiﬁcant level of test is at alpha 0.05. A detailed description of the statistical analysis
performed is presented in appendix E. The analysis indicated a statistically signiﬁcant
effect of vapor concentration on the diffusion coefﬁcients obtained for OPP ﬁlm and the
respective permeants. However, there was no statistically signiﬁcant effect of vapor
concentration on the diffusion coefﬁcient values determined for the PVdC coated OPP
ﬁlm. The effect of vapor concentration on the solubility coefficient for the respective
permeants and the test ﬁhns evaluated was not statistically signiﬁcant, except for the
limonene/PVdC coated OPP ﬁlm permeant/polymer system. The permeants showed a
statistically signiﬁcant effect of vapor concentration on the permeability values obtained
for both OPP and PVdC coated OPP (permeability coefﬁcient or permeance), except for
the ethyl butyrate/ OPP system.

Even though there was a statistically signiﬁcant effect of vapor concentration on
the diffusion coefﬁcient for selected permenant/ ﬁlm systems, the effect is small.
According to equation 20 in the literature review, the slope of the plot of the diffusion
coefﬁcient vs vapor activity, which is deﬁned as on, measures the plasticizing effect that

each sorbed penetrant has on the polymer chains.

D = 0(0) exp(aa) (20)

The maximum value of 0: found in the present study is less than 1. The small value of 0L
suggests that there was no plasticization of polymer chains by the permeants at the test

conditions.

66

The respective solubility coefﬁcient values and the estimated % permeant sorbed
(v/v) for each permeant in OPP and PVdC coated OPP ﬁlms are summarized in Tables 8,
10, and 11. Figures 9 and 10 show a plot of the solubility coefﬁcients for each permeant
in the OPP and PVdC ﬁlms, as a function of vapor activity. The overall % permeant
sorbed by either ﬁlm is less than 1%, on a volume/volume basis. The observed transport
behavior suggests that the sorption of the permeants at the test temperatures and the
concentration range evaluated does not result in strong penetrant/polymer interaction and
thus swelling of the polymer matrix. The transport process therefore appears to behave
like that of a permanent gas, where the permeant driving force concentration has little or
no effect on the permeability values.

In the present study, the effect of permeant size and its chemical nature on the
diffusion and sorption processes follows that predicted by mass transfer theory. In OPP
ﬁlm the diffusion coefﬁcient is highest for the lowest molecular weight permeant, ethyl
acetate and lowest for the highest molecular weight permeant, limonene. This is
illustrated graphically in Figure 11, where log Do, the diffusion coefficient at zero
penetrant concentration through OPP ﬁhn at 50°C, is plotted against the penetrant molar
volume. The diffusion coefﬁcient decreases by nearly one order of magnitude as the
penetrant molar volume increases by approximately 150%. Diffusion of the permeants
through PVdC coated OPP also behave in a similar way.

The Hildebrand solubility parameters (8) values for the permeants and OPP,
calculated by the component group contributions method of Hoﬁ'yzer and Van Krevelen
(1976), are presented in Table 12. The solubility parameters of d-lirnonene and

polypropylene are equivalent, while the difference for ethyl butyrate and OPP is 0.2, and

67

Ethyl acetate

    

F’
A
1

Ethyl butyrate

O

longo x 10’”. m2/s
53
N

 

SF 100 120

d-Limonene
o

 

 

 

414%-..- V ._-____.

penetrant molar volume, cc/mol

Figure 11. Diffusivities of organic vapors through OPP at 50°C as
a function of penetrant molar volume

68
the difference between the solubility parameter values of ethyl acetate and polypropylene

is 0.6. Both ethyl acetate and ethyl butyrate have moderate polar bonding force
contribution, while polypropylene and d-limonene have no polar bonding force
contribution. This would predict limonene to have the highest solubility coeffcient in
OPP and PVdC coated OPP ﬁlm, where the bulk of the ﬁlm is OPP, followed by ethyl
butyrate and ethyl acetate, respectively. Experimental solubility data for OPP and PVdC
coated OPP ﬁlms agreed well with the trend of the estimated values of the solubility
parameters. The solubility coefﬁcient of limonene is the highest in both ﬁlms because of
the similar nonpolar structures of limonene and polypropylene, which tend to maximize
solubility, as compared to the relatively polar ethyl acetate and ethyl butyrate structures.
Moreover, when comparing ethyl acetate and ethyl butyrate, two permeants of similar
chemical structure, the solubility coefﬁcient in OPP ﬁlm for the higher molecular weight
permeant, ethyl butyrate, is greater than that of ethyl acetate, the lower molecular weight
permeant. As the size of the permeant molecule increases, the diffusion coefﬁcient
decreases and the solubility coefﬁcient increases. Many investigators have observed a

similar trend (Zobel, 1982; Hotchkiss et al., 1988).

Table 12. The Hildebrand solubility parameters (5) values

 

 

 

 

 

 

Permeant/Polymer Hildebrand Solubili Polar-bonding
Parameters, (cal/cc)l character
PP 8.3“) Poor
d-Limonene 8.21“” Poor
Ethjl acetate 9.1 1““) Moderate
Ethyl butyrate 8.5“) Moderate

 

 

 

“) Values taken from Van Krevelen, 1976
(b) Value taken from Halek and Luttmann, 1991
(c) Value taken from Nielsen et al., 1992

 

69
The Effect of Binary Mixtures Composition on Co-permeant Permeability

The effect of a co-permeant on the permeability of binary mixtures through the
OPP ﬁlm and the PVdC coated OPP ﬁlm was studied by determining the permeation rate
of the constituents of the binary mixture for a series of binary mixtures of varying
composition using a dynamic purge and trap/thermal desorption procedure. The results
are summarized in Tables 13, 14, 15, and 16. Tables 13 and 14 summarize the
permeability coefficient values for d-limonene and ethyl butyrate as both single
permeants and in binary mixtures through OPP ﬁlm at 50°C. Table 13 also summarizes
permeability coefficient values for limonene/ethyl acetate binary mixtures. Tables 15 and
16 summarize permeance values for d-limonene and ethyl buryrate, as both single
permeants and in binary mixtures, through PVdC coated OPP at 60°C. As shown in
Tables 13 and 15, the permeability runs were carried out at limonene vapor activity levels
of a=0.3, 0.2, 0.13, and 0.05 for the OPP ﬁlm and at vapor activity levels of a=0.2 and
0.13 for the PVdC coated OPP ﬁlm. For the respective limonene vapor activity levels,
three different ethyl butyrate vapor activity levels were studied, except for the limonene
vapor activity of a = 0.3 in OPP ﬁlm, where only two ethyl butyrate vapor activity levels
were evaluated. For better illustration, the results from Tables 13 and 15 are presented
graphically in Figures 12 and 13, where d-limonene permeability rates are plotted as a
function of ethyl butyrate vapor activity. It follows from Tables 13 and 15 and ﬁom the
graphical presentation (Figures 12 and 13) that at the concentration levels evaluated,

ethyl butyrate did not appear to affect the transport charateristics of limonene vapor

70

Table 13. The permeability coefficient, kg m/s m2 Pa :10“, of limonene through

OPP ﬁlm (50°C) as a single

butyrate and ethyl acetate (' (b) I“)

meant and in binary mixtures with ethyl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Limonene co-perrneant with ethyl butyrate vapor activity of
Vapor Vapor 81%; a = 0.2 a = 0.12 a = 0.04
activity Pmssme PC (404 Pa) (241 Pa) (73 Pa)
(Pal
0.3 93 3.67+/-.15 3.95+/-.1 1 3.59+/-.21
0.2 62 3.34+/-.017 4.32+/-0.67 3.93+/-0.35 3.56+/-0.13
0.13 41 3.24+/—.031 3.66+/-0.15 3.65+/-0.09 3.47+/-0.29
0.05 16 2.68+/-.40 3.30+/-0.28 3.12+/—0.01 3.30+/-0.06
Lirnonene co-perrneant with ethyl acetate va r activity of
Single a = 0.3 a = 0.14 a = 0.04
Vapor
535:; Page? permeant 3287.5 Pa 1093 Pa 404 Pa
a
0.2 62 3.34+/-0.017 4.2+/-0.0064 3.65+/—0.0042 3.52+/-0.00

 

 

 

 

 

 

“9 All values are average of duplicate runs.

(5) All values were determined by dynamic purge and trap/thermal desorption procedure.
(c) All vapor activity levels are determined at room temperature.

Table 14. The permeability coefficient, kg m/s m2 Pa x1045, of ethyl butyrate
through OPP ﬁlm (50°C) as a single permeant and in binary mixture with

 

 

 

 

 

 

 

limonene ('0 0’) (‘9
Ethyl butyrate co-permeant with limonene vapor activity of
vapor Vapor Suﬁgefm a = 0.3 a = 0.2 a = 0.13 a = 0.05
activity Pressm 1’" (93 Pa) (62 Pa) (41 Pa) (16 Pa)
(Pa)

0.2 404 2.07+/-.30 2.24+/-.46 l.80+/-.099 1.92+/-.127
0.12 241 1.56+/-.012 l .95+/-.15 1.70+/-.15 1.55+/-.035 1.62+/-.078
0.04 73 1.41+/-.25 2.10+/-.24 1.68+/-.071 1.65+/-.29 1.75+/-.071

 

 

 

 

 

 

 

R" All values are average of duplicate runs.

(b) All values were determined by dynamic purge and trap/thermal desorption procedure.
(c) All vapor activity levels are determined at room temperature.

through either OPP or PVdC coated OPP ﬁlms. For the respective ethyl

butyrate/limonene vapor activity combinations evaluated, the permeability coefficient for

 

 

71

Table 15. The permeance, kg/s m2 Pa x1043, of limonene through PVdC coated
OPP ﬁlm 60°C) as a single permeant and in binary mixtures with ethyl
butyrate (b (c) (d)

 

 

 

 

 

 

Limonene Co-perrneant with ethyl butyrate vamr activity of
Vapor Vapor Suﬁ; a = 0.2 a = 0.12 a = 0.04
activity Presme 9" (436 Pa) (251 Pa) (73 Pa)
Pa
0.2 62 6.16+/-.53 6.50+/-.3l8 5.24+/-.332 4.64+/-.9
0.13 41 4.78+/-.31(") 4.73+/-.643 5.02+/-.594 5.59+/-.11

 

 

 

 

 

 

I“) Value based upon limonene vapor activity of a = 0.09

(b) All values are average of duplicate runs
(‘7 All values were determined by dynamic purge and trap/thermal desorption procedure.
@ All vapor activity levels are determined at room temperature

Table 16. The permeance, kg/s m2 Pa xlO‘”, of ethyl butyrate through PVdC
coated OPP ﬁlm 60°C) as a single permeant and in binary mixtures with

 

 

 

 

 

 

 

d-limonene (a) (b) (‘
Ethyl bu tyra te S. l Co-permeant wrth limonene vapor actrvrty of
mg e _ _
Vapor Vapor rmeant a -' 0.2 a — 0.13
activity Pressure PC (62Pa) (41 Pa)
a
0.2 436 1.16+/-.014 1.40+/-.0071 1.36+/-.028
0.12 251 l.02+/-.0028 1.13+/—.064 l .04+/-.18
0.04 73 0.89+/-.086 1.04+/-.0021 l.16+/-. l4

 

 

 

 

 

 

 

1") All values are average of duplicate runs.
(1’) All values were determined by dynamic purge and trap/thermal desorption procedure.
“7 All vapor activity levels are determined at room temperature.
limonene remained constant and was statistically equivalent to the permeability
coefﬁcient value obtained for pure limonene vapor, at similar activity levels.

Tables 14 and 16 summarize the results of permeability studies carried out to
evaluate the effect of d-limonene on the permeability of ethyl butyrate. Permeability
studies were carried out at ethyl butyrate vapor activity levels of a=0.2, a=0.14 and 0.04

for both OPP and PVdC coated OPP ﬁlms. Three to four different limonene vapor

activity levels for the OPP ﬁlm and two different limonene vapor activity levels for the

d-limonene permeation rate, kg/m2 5 x10'9

72

 

8 ., — 7 i 7 23 z 2 ~,ﬁ_,
I i
I l I
6 I ‘
h
4 I '
I I A 4
I A
O limonene a=0.3
2 I I limonene a=0.2
A limonene a=0.13
I X limonene a=0.05
i x X 3
0I h I- _ c4_ .I_A- 2 .....
-0.05 0 0.05 0.1 0.15 0.2

ethyl butyrate vapor activity

Figure 12. Effect of ethyl butyrate on the permeation rate of d-

limonene through OPP as a function of binary
mixture composition (50°C)

d-limonene permeation rate, kg/m2 sx 1 0'”

73

6.00 .A-ﬁwm— ~— 4 4 ,- -_ . -.ﬁ--,____________ ._- «DI

A

LII

0
1—0—1

 

 

I O d-limonene a=0.2 I

0.00 I ~k~ — — ‘ _*---h__ _-._. ___ ..___#I
-0.05 0 0.05 0.1 0.15 0.2 0.25

I I d-limonene a=0.13

ethyl butyrate vapor activity

Figure 13. Effect of ethyl butyrate on permeation rate of d-limonene
through PVdC/OPP ﬁlm as a function of binary mixture

composition (60°C)

Ethyl butyrate permeation rate, kg/m2 sec x10'8

74

 

 

2.40 +—— 44—4 t - - ——-_ u a-
2.00

' 0
1.60 - I I

I ._ l
1.20 {
0.80 - . i i i

{ I'
0.40 I

A i 4‘ E

0.00 I

 

 

e ethyl butyrate a=0.2

I ethyl butyrate a=0.12

I A ethyl butyrate a=0.04
-0.40 ~ ———— —-———~ I I NI» +——-

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

d-limonene vapor activity

 

Figure 14. Effect of d-limonene on the permeation rate of ethyl
butyrate through OPP as a function of binary

mixture composition (50°C)

ethyl butyrate permeation rate,
kg/m2 5 x10 ‘0

75

 

I
400;
o ethyl butyrate a=0.2
I ethyl butyrate a=0. 12
A ethyl butyrate a=0.04
*r i
‘ - l
i

 

000-9—--—.—. ~—- 1-_ ..- ..-H---_c_wnmy_n .

-0.05 0 0.05 0.1 0.15 0.2

d-limonene vapor activity

Figure 15. Effect of d-limonene on the permeation rate of ethyl
butyrate through PVdC/OPP film as a function of

binary mixture composition (60°C)

76
PVdC coated OPP ﬁlm were evaluated for the respective ethyl butyrate vapor activity

levels. Limonene did not appear to inﬂuence the permeability of ethyl butyrate vapor
through either OPP or PVdC coated OPP ﬁlms, at the concentrations evaluated.
Statistical analysis indicated that the permeability of one binary mixture composition
through OPP ﬁlm and two mixture compositions through PVdC coated OPP ﬁlms
showed a statistically signiﬁcant increase in ethyl butyrate permeability in the presence of
limonene. In general, for the respective binary vapor mixtures studied, d-limonene does
not appear to affect the transport characteristics of ethyl butyrate vapor, as compared to
the permeability values obtained for ethyl butyrate as a single permeant, run at
comparable vapor activity levels. The results summarized in Tables 14 and 16 are
presented graphically in Figures 14 and 15, where ethyl butyrate permeability rates are
plotted as a function of d-limonene vapor activity.
By direct measurement of the permeation rates (Tables 13 to 16) it was found that

the permeability values for d-limonene and ethyl butyrate were not affected by the
1 presence of a co-permeant, over the range of vapor activity levels studied. This is
illustrated graphically in Figure 16, where the transmission rate proﬁle curves for ethyl
butyrate (a= 0.04) and d-limonene (a = 0.05), determined as pure single component
vapors and as a binary mixture (ethyl butyrate a = 0.04/d-limonene a = 0.05) through
OPP, are superimposed. As shown, the total permeation rate of the binary mixture is
equal to the sum of the permeation rates of the individual permeants.

Similar results were obtained for the permeability of ethyl butyrate/ limonene

binary mixtures through PVdC coated OPP ﬁlm, as illustrated in Figure 17, where the

transmission rate proﬁle curves for the pure permeants (ethyl butyrate a = 0.21 and d-

81

Table 19. The permeability coefﬁcient, kg m/s m2 Pa x1046, of ethyl acetate through
OPP film (50° in single permeant and in binary mixture with

 

 

 

 

 

 

limonene (a) (b) (c
Ethyl acetate Co-permeant with limonene
Vapor Pressure Single permeant vapor activity of a=0.2
activity Pa (62 Pa)
0.3 3287.5 6.40+/-0.28 8.99+/-0.31
0.14 1093 5.29+/-0.33 6.71+/-0.042
0.04 404 4.68+/-0.26 4.82+l-0.28

 

 

 

 

(a) All values are average of duplicate runs.
(1’) All values were determined by dynamic purge and trap/thermal desorption procedure.
(c) All vapor activity levels are determined at room temperature.

While statistical analysis showed a signiﬁcant difference, at a conﬁdence level of
95%, between the permeability of pure ethyl acetate and for ethyl acetate in the binary
mixtures described above, the effect of the co-permeant (i.e. limonene) was minimal
when compared to the synergistic effect of d-limonene on the permeability of ethyl
acetate vapor reported by Hensley et al. (1991), who found that limonene as a co-
permeant increased the permeability of ethyl acetate through OPP ﬁlm by as much as 40
times.

To account for the observed dramatic increase in the permeability coefﬁcient for
ethyl acetate in the presence of limonene as a co-permeant, Nielson and Giacin (1994)
proposed a co-penetrant dependency of the diffusion coefﬁcient, due in part to co-
penetrant induced relaxation effects occurring within the polymer matrix. The absorption
of organic vapors can result in polymer swelling and thus change the conformation of the
polymer chains. These conformation changes are not instantaneous, but are controlled by
the retardation times of polymer chains. If these times are long, stresses may be set up
which relax slowly. Thus, the absorption and diffusion of organic vapors can be

accompanied by concentration as well as time-dependent processes within the polymer

 

82

bulk phase, which are slower than the micro-Brownian motion of polymer chain
segments which promote diffusion (Mears, 1965).

Thus, the previously reported dramatic increase in the permeability of ethyl
acetate through OPP in the presence of limonene may be attributed to co-penetrant
induced relaxation effects occurring during the diffusion of ethyl acetate/limonene binary
mixtures through the oriented polypropylene ﬁlm investigated. Such relaxation
processes, which occur over a longer time-scale than diffusion, may be related to a
structural reordering of the free volume elements in the polymer. Thus, providing
additional sites of appropriate size and frequency of formation, which promote diffusion
and account for the observed increase in the permeation rate of ethyl acetate in the
presence of limonene as a co-permeant.

In comparing the results of the permeability studies of ethyl acetate/limonene
binary mixtures through OPP ﬁlm reported by Hensley et al. (1991) with the results of
the present study, it should be noted that Hensley et al. carried out the permeability
studies at ambient temperature (i.e. 23+/-1°C), while the present studies was carried out at
50°C. The results of their two studies suggest that the effect of limonene on the
permeability of a co-permeant in binary mixtures at high temperature is minimized. At
high temperature, the sorption of limonene might not be at a level required to cause
changes in polymer chain conformation. The estimated solubility values of d-limonene
by OPP ﬁlm in the present study ranges from 0.064 to 0.084 kg/m3 Pa. The values are
four times less than the value of 0.33 kg/m3 Pa reported by Nielson and Giacin (1994).
Therefore, such co-permeant induced relaxation mechanism as proposed by Nielson and

Giacin (1994) might not have occurred in oriented polypropylene at the present test

83

temperature of 50°C. Thus, a substantial increase in the permeation rates of the co-
permeants, ethyl acetate and ethyl butyrate, in the presence of limonene were not

observed in the present study.

Statistical Analysis of Binary Mixture Permeability Studies

For each concentration level of limonene and ethyl butyrate, statistical analysis,
using single factor AN OVA, was performed on MINITAB to determine whether there
was a difference between the permeation rate of the pure permeant and the permeant in a
binary mixture. If such a difference was detected at 95% conﬁdence interval, a Dunnett
pairwise comparison test was further performed to determine which pairwise comparison
between the permeability of a permeant in a binary mixture and the permeability of the
pure permeant, at similar concentration level, is signiﬁcant at the 95% conﬁdence level.
For all limonene vapor activity levels evaluated in both OPP and PVdC coated OPP
ﬁlms, the addition of ethyl butyrate did not result in a statistically signiﬁcant increase or
decrease in permeability values of d-limonene, with a conﬁdence level of 95%. Further,
the addition of ethyl acetate to limonene vapor at an activity level of a=0.20 did not
signiﬁcantly change the permeability of limonene through OPP ﬁlm, at a conﬁdence
level of 95%. The addition of limonene to ethyl butyrate vapor resulted in a signiﬁcant
increase in the permeability of ethyl butyrate with a 95% conﬁdence level, only at one
mixture composition for OPP ﬁlm and two binary mixture compositions for PVdC coated
OPP ﬁlm. The binary mixture compositions are limonene a=0.3/ethyl butyrate a=0. 12 for

OPP; limonene a=0.2/ethyl butyrate a=0.2] and limonene a=0.13/ethyl butyrate a=0.2]

84
for PVdC coated OPP ﬁlm.

For comparing ethyl acetate permeability coefficients through OPP ﬁlm as a
single vapor vs. the permeability of ethyl acetate in binary mixtures with limonene vapor
activity of a=0.2, a two sample t-test was performed to determine whether the
permeability values at each respective vapor activity level are signiﬁcantly different at a
95% conﬁdence level. Of the three ethyl acetate/ limonene mixture compositions, two
mixture compositions showed that the ethyl acetate permeability coefﬁcients are
signiﬁcantly different at 95% conﬁdence level. They are limonene a=0.2/ethyl acetate
a=0.30 and limonene a=0.2/ethyl acetate a=0.14. Appendix F summarizes details of

statistical analysis utilized in the present study.

SUMNIARY AND CONCLUSIONS

The dynamic purge and trap/thermal desorption procedure developed was found
to increase the sensitivity of the permeability values by as much as two orders of
magnitude, as compared to the isostatic permeation test procedure employed by the
MASZOOOTM Permeation Test System. Both procedures showed good agreement
between the permeability values obtained, with the % deviation between the permeability
values obtained being less than 20%. The average % deviation between the permeability
values obtained by the two procedures for limonene, ethyl butyrate, and ethyl acetate was
14%, 12%, and 7%, respectively. While the MASZOOOTM Permeation Test System lacks
the ability to detect the constituents of a binary mixtures, the dynamic purge and
trap/thermal desorption procedure developed, proved to be an effective analytical
procedure to study the permeability of multi-component organic vapor mixtures through
polymer membranes.

This study was designed to determine the effect of varying concentrations of
organic vapors alone, and in binary mixtures on the barrier properties of an oriented
polypropylene ﬁlm and a high barrier PVdC coated oriented polypropylene ﬁlm. The
permeability tests were carried out at 50°C for OPP and 60°C for PVdC coated OPP ﬁlm.
The results obtained indicated that the permeants; ethyl butyrate, ethyl acetate and d-
limonene showed minimal concentration dependency for the mass transfer parameters,

permeability coefﬁcient and permeance constant, and D, within the vapor activity ranges

85

86

studied, for the two test membranes. The effect of a co-permeant on the permeability of
binary mixtures through OPP ﬁlm and the PVdC coated OPP ﬁlm was studied by
determining the permeation rate of the constituents of the binary mixture for a series of
binary mixtures of varying composition using the dynamic purge and trap/thermal
desorption procedure. When combined in a series of binary mixtures, the constituents of
the mixtures showed little propensity of altering the transport properties of the co-
permeant. For the respective ethyl butyrate/limonene vapor activity combinations
evaluated, the permeability values for limonene remained constant and were statistically
equivalent to the permeability values obtained for pure limonene vapor at similar activity
levels.

The results of permeability studies carried out to evaluate the effect of d-limonene
on the permeability of ethyl butyrate showed that limonene did not inﬂuence the
permeability of ethyl butyrate vapor through either OPP or PVdC coated OPP ﬁlms at the
vapor concentrations evaluated, as compared to the permeability values for the ethyl
butyrate as a single permeant, run at comparable vapor activity levels.

Similar results were obtained for the permeability of d-limonene/ethyl acetate
binary mixtures through OPP ﬁlm and while statistical analysis showed a signiﬁcant
difference, at a conﬁdence level of 0.05%, between the permeability coefﬁcient of ethyl
acetate and for ethyl acetate in selected binary mixtures evaluated (see Apendix F ), the

effect of the co-permeant (i.e. limonene) was minimal.

FUTURE STUDY

A number of additional studies can be proposed to develop a better understanding
of the factors inﬂuencing the permeability of multi-component vapor mixtures. With
limonene, which is known to plasticize polymers having a similar chemical structure such
as OPP, it is interesting to determine how molecular size, geometry, or the chemical
nature of the co-permeant contributes to the effect of d-limonene on the permeability of
the co-permeant. Other permeants, such as oxygen and carbon dioxide, which have a
smaller molecular size than organic compounds, should also be affected by limonene in
the mixture as well. While the results from this study suggest that there was a minimal
effect of co-permeant on the permeability of the respective constituents of limonene/ethyl
acetate binary mixtures at an elevated temperature, it is not fully understand what the
relationship is between temperature and the effect of limonene as a co-permeant on the
permeability of binary vapor mixtures. It is therefore proposed that a study be carried
out to evaluate the effect of temperature on the permeability of binary vapor mixtures,
such as d-limonene/ethyl acetate. The proposed studies would be carried out at constant
vapor pressures, with the temperature of test ranging from ambient (i.e. 23°C) to 50°C. It
has been proposed, based on the studies of Hensley et al. (1991) and Nielson and Giacin
(1994), that the plasticization of OPP by d-limonene leads to an increase in free volume

within the polymer bulk phase and thus an increase in the rate of diffusion of a co-

permeant. It is not clear whether such plasticization would occur in the crystalline or

87

88
amorphous regions of the polymer matrix. By varying the % crystallinity of the test ﬁlm

and conducting permeability studies with binary vapor mixtures, a better understanding
of how % crystallinity inﬂuences the co-permeant effect of limonene may be gleaned.
The proposed studies can all be carried out using the dynamic purge and trap/thermal
desorption procedure coupled with the MASZOOOTM Permeability Test System, as
described in the present study. The data from these studies might help develop or test a
mathematical model to accurately predict the permeation characteristics of multi-
component organic vapor mixtures through polymer based packages. Such a model, or
actual experimental data, would help in the design of an aroma barrier package system
for packaging a product whose quality is based solely upon maintaining its original

aroma proﬁle.

APPENDICES

Appendix A

Gas Chromatograph Calibration Procedure

A stock solution of 500 ppm (v/v) is prepared by dissolving 5 ul of d-limonene,

ethyl butyrate, and ethyl acetate into a 10 ml volumetric ﬂask ﬁlled with carbon

tetrachloride to make 10 ml of 500 ppm stock solution. Standard solutions of ethyl

butyrate and d-limonene, with concentrations of 20, 40, 100, and 200 ppm (v/v), were

prepared by diluting from the stock solution according to the following table.

Table 20. The solution of ethyl butyrate and d-limonene in CCl4

 

 

 

 

 

 

 

 

#1111 StOCk #ml stock solution
Conc, ppm (v/v) solution th 1 b #ml CC14 Total volume
d—limonene e y utyrate
20 .4 .4 9.2 10
40 .8 .8 8.4 10
100 2 2 6 10
200 4 4 2 10

 

 

 

 

The ethyl acetate solution was separately prepared by diluting from its stock solution in a

similar fashion.

Table 21. Calibration Data of Ethyl Butyrate and d-limonene by Gas

 

 

 

 

 

chromatograph.
ams of eth 1 area res onse, ams of d- area res nse,
Conc, (WV) Erutyrate, x 10:8 AU, £104 lirfrbnene, x10'8 Au, xplci)s
20 1.8 8.2 1.7 1.4
40 3.5 12.5 3.4 2.5
100 8.8 33.4 8.4 6.4
200 17.6 86.5 16.8 14.8

 

 

 

 

 

 

89

 

90
Table 22. Calibration Data of Ethyl Acetate by Gas Chromatograph.

 

 

 

 

 

 

 

 

 

 

Con, (v/v) grams of ethyl acetate, Area response,
x10'8 AU, x104

20 1.8 9.8

40 3.6 16.7

100 9.0 36.7

200 18.0 82.7
100 7
90 "i

l e

80 -{
7.1
,2 60 i
’1 50 ,
:3 .
< 40 -~

    

y = 4.66E+12x
R2 =0.98l
Cal factor = 2.15E-13g/AU

 

 

0 5 10 15 20
grams of ethyl butyrate, x10‘8

Figure 17. Calibration curve of ethyl butyrate for setting vapor activity.

AU, x 10’

91

  

y = 8.49E+12x

R2 = 0.993
Cal factor = l.18E-l3 g/AU

 

0 5 10 15 20

grams of d-limonene, x 10'8

Figure 18. Calibration curve of d-limonene for setting vapor activity

     
 

50 .
40 y = 4.49E+12x
R2 = 0.994
30 cal factor = 2.23E-l3 g/AU
20

0 5 1O 15 20

grams of ethyl acetate, x10'a

Figure 19. Calibration curve of ethyl acetate for setting vapor activity.

Appendix B

Dynamic Purge and Trap/Thermal Desorption Calibration Procedure

The same solutions prepared for vapor activity setting were used to generate

calibration curves for the desorption thermal/desorption procedure. The following tables

show the calibration proﬁle for each test compound.

Table 23. Calibration data of ethyl butyrate and d-limonene for dynamic purge and

trap/thermal desorption procedure.

 

 

 

 

 

 

 

 

 

 

Conc, (v/v) grams of ethyl area response, grams of d- area response,
butyrate, x 10'8 AU, x105 limonene, x10'8 Au, x105
40 3.5 3.0 3.4 6.0
100 8.8 8.2 8.4 15.1
200 17.6 15.5 16.8 31.8
500 44.0 38.6 42.1 80.2

 

Table 24. Calibration data of ethyl acetate for dynamic purge and trap/thermal

 

 

desorption procedure.

 

 

 

 

 

 

 

 

Con, (v/v) grams of ethyl acetate, Area response,
x 10'8 AU, x105
20 1.8 1.4
40 3.6 2.4
100 9.0 6.2
200 18.0 10.1

 

92

 

93

45 ~,
40 J
35 l
30

25%;

AU.x10’

    
    

y = 8.81E+12x
R2 =0.99
Cal factor = 1.13E-13 g/AU

 

 

0 5 10 15 20 25 30 35 40 45 50
grams of ethyl butyrate, )th'8

Figure 20. Calibration curve of ethyl butyrate for dynamic purge and trap/thermal
desorption procedure.

904
l
804
l
70!
60.

501

Auxio’

404'

y = 1.90E+13x
R2 = 0.99
Cal factor = 5.26E-14 g/AU

 

 

grams of limonene,x10'8

Figure 2]. Calibration curve of d-limonene for dynamic purge and trap/thermal
desorption procedure.

 

94

12-

   
 

"‘2
’i 6
E; ,
1 y=5.90E12x
4 { R‘=0.9818
1 Cal factor 1.69E-13 g/AU
21
o — - -r-———- - A -- ~ ,, t ~- -. .———
0 2 4 6 s 10 12 14 16 1s 20

grams of ethyl acetate, x10‘8

Figure 22. Calibration curve of ethyl acetate for dynamic purge and trap/thermal
desorption procedure.

Appendix C

Calibration Curve of Carrier Gas Flow Rate Versus Permeant Vapor Activity

~ ~
A O\
1 . _ I

y—s
N

  
 

—a
O

y = 63.432x + 0.932
R2 = 0.9984

A O\
. 1 l

nitrogm ﬂow rate through the bubbler, mllmin
N W

 

 

 

1
I
‘

Tk ___ _ _ . __.....

O 0.05 0.1 0.15 0.2 0.25

vapor activity levels

Figure 23. Calibration curve of carrier gas flow rate versus limonene vapor
activities

95

96

0—1
A
.___J

    
 

 

 

 

g 12
g: 1
,9 .
.D
a 8 j
g» g o y=64.375x+0.1417
g 6 R2=0.991
3
a I
E 4
=1
e?» 2;
8 1
'a
0 0.05 0.1 0.15 0.2 0.25

vapor activity levels

Figure 24. Calibration curve of carrier gas ﬂow rate versus ethyl butyrate and ethyl
acetate vapor activities

Appendix D
Method of Calculating l2/4Dt for each Value of (AM/At)./( AM/At)... from Equation 32

Equation 32 can be written as

AzX”2 exp(—X)

 

 

where
(M)
A_\/; At ,
41%)
At .0
And
[2
‘41):

To solve for value of X for each value of (AM/At),/( AM/At)... a Newton-Rawson method

was employed. Equation 32 can be rewritten as
G=X”2 exp(—X)—A

With G being equal to zero, the iteration process is described by

G(k)

X<k+l> ___ X“) _
expt-X‘*’1{%1X‘“1‘V2 —1X"‘>1V2}

 

(k+l) .

where x 1s the k+1 iteration step for x value.

97

Appendix E

Statistical Analysis of P, D, and S as a Function of Permeant Vapor Activity

ANOVA for d-limonene permeability coefficient through OPP (50°C) as a function
of vapor activity.

Source DF SS MS F P
Between 3 1.8 0.6 7.00101 0.04535
Error 4 0.34 0.085

Total 7 2.1

. MS and SS 2210‘”

ANOVA for d-limonene diffusion coefﬁcient through OPP (50°C) as a function of
vaporacﬁvﬁy.

Source DF SS MS F P
Between 3 83.0 28.0 11.2532 0.02028
Error 4 9.9 2.5

Total 7 93.0

MS and ss x104°

AN OVA for d-limonene solubility coefﬁcient through OPP (50°C) as a function of
vaporacﬁvﬁy.

Source DF SS MS F P
Between 3 0.00042 0.00014 3.56415 0.12564
Error 4 0.00016 0.00004

Total 7 0.00058

AN OVA for ethyl butyrate permeability coefﬁcient through OPP (50°C) as a
function of vapor activity.

Source DF SS MS F P
Between 2 0.15167 0.0758 4.22635 0.13407
Error 3 0.053831 0.0179

Total 5 0.2055

MS and ss x104°

98

 

99

ANOVA for ethyl butyrate diffusion coefﬁcient through OPP (50°C) as a function of
vapor activity.

Source DF SS MS F P
Between 2 625 312 75 0.00275
Error 3 12.5 4.17

Total 5 637.5

. MS and 33 x10“30

ANOVA for ethyl butyrate solubility coefﬁcient through OPP (50°C) as a function of
vapor activity.

Source DF SS MS F P
Between 2 4.5946 2.3 6.61576 0.07946
Error 3 1.0417 0.347

Total 5 5.6364

. MS and 88 x10'6

ANOVA for ethyl acetate permeability coefﬁcient through OPP (50°C) as a function
of vapor activity.

Source DF SS MS F P
Between 2 0.0472 0.024 30.6257 0.01026
Error 3 0.00234 0.00078

Total 5 0.0495

MS and SS x10'3O

AN OVA for ethyl acetate diffusion coefﬁcient through OPP (50°C) as a function of
vapor activity.

Source DF SS MS F P
Between 2 1.54 0.77 13.7985 0.0307
Error 3 0.168 0.056

Total 5 1.71

. MS and 33 x10‘26

AN OVA for ethyl acetate solubility coefﬁcient through OPP (50°C) as a function of
vapor activity.

Source DF SS MS F P
Between 2 4.83 2.4 8.27714 0.06009
Error 3 0.876 0.29

100
Total 5 5.71

0 ‘MS and SS x10'8

ANOVA for d-Iimonene permance through PVdC coated OPP (60°C) as a function
of vapor activity.

Source DF SS MS F P
Between 2 15 7.7 15.8519 0.02542
Error 3 1.5 0.49

Total 5 17

MS and 58 x10'26

ANOVA for d-limonene diffusion coefﬁcient through PVdC coated OPP (60°C) as a
function of vapor activity.

Source DF SS MS F P
Between 2 2.6 1.3 1.15926 0.42364
Error 3 3.4 1.1

Total 5 6

MS and 53 x10'31

ANOVA for d-limonene solubility coefﬁcient through PVdC coated OPP (60°C) as a
function of vapor activity.

Source DF SS MS F P
Between 2 4.4 2.2 13.8897 0.03043
Error 3 0.48 0.16

Total 5 4.9

0 MS and SS x10"6

ANOVA for ethyl butyrate permance through PVdC coated OPP (60°C) as a
function of vapor activity.

Source DF SS MS F P
Between 2 4.53 2.27 16.7511 0.02356
Error 3 0.406 0.135

Total 5 4.94

MS and 58 x10'26

AN OVA for ethyl butyrate diffusion coefﬁcient through PVdC coated OPP (60°C)
as a function of vapor activity.

101

Source DF SS MS F P

Between 2 3.75 1.88 2.02201 0.27794
Error 3 2.78 0.928
Total 5 6.53

0 MS and SS x10'30

AN OVA for ethyl butyrate solubility coefﬁcient through PVdC coated OPP (60°C)
as a function of vapor activity.

Source DF SS MS F P
Between 2 1.14 0.572 1.56024 0.34317
Error 3 1.1 0.366

Total 5 2.24

0 MS and 35 x10‘7

 

Appendix F

Statistical Analysis of Binary Mixture Permeability Studies

ANOVA for d-limonene permeability coefﬁcient at a=0.3 vs d-limonene
permeability coefﬁcient in the binary mixture with ethyl butyrate (OPP ﬁlm)

Source DF SS MS F P
Between 2 0.1416 0.0708 2.66 0.216
Error 3 0.0799 0.0266

Total 5 0.2215

. MS and ss x10'3°

AN OVA for d-limonene permeability coefﬁcient at a=0.2 in single vapor vs d-
limonene permeability coefﬁcient in the binary mixture with ethyl butyrate and in
the binary mixture with ethyl acetate (OPP ﬁlm)

Source DF SS MS F P
Between 6 1.6188 0.2698 3.15 0.080
Error 7 0.6003 0.0858

Total 13 2.2191

SS and MS value x10"3o

AN OVA for d-limonene permeability coefﬁcient at a=0.13 vs d-limonene
permeability coefﬁcient in the binary mixture with ethyl butyrate (OPP ﬁlm)

Source DF SS MS F P
Between 3 0.2277 0.0759 2.63 0.186
Error 4 0.1154 0.0288

Total 7 0.3431

SS and MS value x10'3o

ANOVA for d-limonene permeability coefﬁcient at a=0.05 vs d-limonene
permeability coefﬁcient in the binary mixture with ethyl butyrate (OPP ﬁlm)

Source DF SS MS F P
Between 3 0.5180 0.1727 2.93 0.163

102

Error 4 0.2355
Total 7 0.7535

SS and MS value x10”3o

103

0.0589

AN OVA for ethyl butyrate permeability coefﬁcient at a=0.2 vs ethyl butyrate
permeability coefﬁcient in the binary mixture with d-limonene (OPP ﬁlm)

Source DF SS
Between 3 0.2127
Error 4 0.3254
Total 7 0.5382

SS and MS value x10'3o

MS F P
0.0709 0.87 0.526
0.0814

AN OVA for ethyl butyrate permeability coefﬁcient at a=0.12 vs ethyl butyrate
permeability coefﬁcient in the binary mixture with d-limonene (OPP ﬁlm)

Source DF SS MS F P
Between 4 0.2162 0.0541 5.25 0.049
Error 5 0.0514 0.0103
Total 9 0.2677
0 SS and MS value x10'30
Comparison Mean Difference
Critical Values = 0.348 x10'15
Pure ethyl butyrate Ethyl butyrate in Permeability Dunnett’s test
Vapor activity binary mixture with coefﬁcient difference
d-limonene vapor x10'15
activity of

012 03 0-3900 *

0.12 0.2 0 . 14 0 0

0.12 0.13 ‘0-0100

0.12 0.05 0-0500

* Signiﬁcant at 95% CI

ANOVA for ethyl butyrate permeability coefﬁcient at a=0.04 vs ethyl butyrate
permeability coefﬁcient in the binary mixture with d-limonene (OPP ﬁlm)

Source DF SS
Between 4 0.4972
Error 5 0.2097
Total 9 0.7068

SS and MS value x1040

104

MS F
0.1243 2.96
0.0419

ANOVA for d-limonene permeance at a=0.2 vs d-limonene permeance in the binary
mixture with ethyl butyrate (PVdC coated OPP ﬁlm)

Source DF SS
Between 3 4.3398
Error 4 1.2994
Total 7 5.6392

0 SS and MS value x 10'26

MS F
1.4466 4.45
3.2485

0.092

AN OVA for d-limonene permeance at a=0.13 vs d-limonene permeance in the

binary mixture with ethyl butyrate (PVdC coated OPP ﬁlm)

Analysis of Variance for

Source DF SS
Between 3 0.938
Error 4 0.876
Total 7 1.815

SS and MS value x 1046

.13b
MS F
0.313 1.43
0.219

0.359

AN OVA for ethyl butyrate permeance at a=0.2] vs ethyl butyrate permeance in the
binary mixture with d-limonene (PVdC coated OPP ﬁlm)

Source DF SS
Between 2 0.064300
Error 3 0.001050
Total 5 0.065350

SS and MS x10'24

Comparison Mean Difference

Critical Values = 0.387 x10'13

MS F
0.032150 91.86
0.000350

0.002

105
Pure ethyl butyrate Ethyl butyrate in Perrnance difference Dunnett’s test

Vapor activity binary mixture with x10'12
d—limonene vapor
activity of
0.21 0.2 .24
0.2 1 O. 1 3 .34

* Signiﬁcant at 95% CI

AN OVA for ethyl butyrate permeance at a=0.12 vs ethyl butyrate permeance in the
binary mixture with d-limonene (PVdC coated OPP ﬁlm)

Source DF SS MS F P
Between 2 0.0119 0.0060 0.52 0.640
Error 3 0.0344 0.0115

Total 5 0.0463

58 and MS x10‘24

ANOVA for ethyl butyrate permeance at a=0.04 vs ethyl butyrate permeance in the
binary mixture with d-limonene (PVdC coated OPP ﬁlm)

Source DF SS MS F P
Between 2 0.0192 0.0096 0.80 0.528
Error 3 0.0362 0.0121

Total 5 0.0554

58 and MS x1044

Two sample t-test for comparing ethyl acetate permeability coefﬁcient in pure vapor
vs the permeability coefﬁcient in binary mixture with limonene vapor activity level
a=0.2.

Comparing Mean Difference

Ethyl acetate in Signiﬁcant
Pure ethyl acetate binary mixture with I to | p-value at 95%
Vapor activity d-limonene vapor conﬁdence
activity of level
0.30 0.20 8.83 0.013 *
0.14 0.20 6.12 0.026 *

0.04 0.2 0.51 0.66

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