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This is to certify that the

dissertation entitled
Modeling the sorption of water, and the effect of sorbed
water on the solubility and diffusivity of oxygen in an
amorphous polyamide.

presented by

Ruben J. Hernandez-Macias

has been accepted towards fulfillment
of the requirements for

Ph. D. Chemical Engineering

degree in

 

 

 

Major professor

 

Date February 23, 1989

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MODELING THE SORPTION OF WATER, AND THE EFFECT OF SORBED
WATER ON THE SOLUBILITY AND DIFFUSIVITY OF OXYGEN IN AN
AMORPHOUS POLYAMIDE.

by

Ruben J. Hernandez

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemical Engineering

1989

5457fi2I

ABSTRACT

MODELING THE SORPTION OF WATER, AND THE EFFECT OF SORBED
WATER ON THE SOLUBILITY AND DIFFUSIVITY OF OXYGEN IN AN
AMORPHOUS POLYAMIDE.

by

Ruben J. Hernandez

Glassy amorphous polyamides are part of a new kind of
polymeric material that have excellent physical and
mechanical properties. These materials are non-crystalline
and show interesting mass transfer behavior with vapors and
gases. In the case of Nylon 61/6T, a totally amorphous
polyamide recently developed, its interaction with water
vapor affected the transport of oxygen.

Sorption, permeation, FTIR spectroscopy, density and thermal
relaxation studies have been applied to describe the
behavior of the system amorphous polyamide/water and
amorphous polyamide/water/oxygen.

The dual-mode sorption model presented in this study was
found to describe accurately the sorption of water by the
amorphous polyamide, over a broad range of water activity
and predicted clustering of the sorbant. The Langmuir

equation was used to describe the chemisorbed solute and the

Flory-Huggins equation was used to describe the volume
fraction of water that is not chemisorbed.

The sorbed molecules of water in the glassy amorphous
polyamide, showed a depression in the oxygen permeability
values as a function of polymer moisture content. The oxygen
permeability behavior was analysed in terms of the
multiplicative effect of a mobility and solubility term. The
analysis of the oxygen solubility values within the
polymer/water system, provided a complementary framework for

the dual-mode sorption model.

Copyrigth by
Ruben J. Hernandez Macias

1989

To
Natalia and

Daniel Federico.

Let us hold the torch of Science even if it is only for a

'second.

ACKNOWLEDGMENTS

I wish to thank the Department of Chemical Engineering, the
Division of Engineering Research and the School of Packaging
for offering me the support and facilities to carry out
these studies.

I also want to acknowledge the grant received from E. I.
DuPont de Nemours and Company Inc.

I want to thank Drs.E. A. Grulke and J. R. Giacin for
continuous advise and support.

I am grateful to my Guidance Committee members Drs. K.
Jayaraman, L. T. Drzal, from the Department of Chemical
Engineering, and Dr. C. Talkowski from E. I. DuPont Co.

I also want to thank V. Kalankyar, Dr. P. Blatz from E. I.
DuPont Co. and Dr. J. DeLong, from The Division of
Engineering Research for helping to run some tests.

At last, but not least, my deepest appreciation to my
parents Vicente Hernandez and Dolores Macias, and to my wife

Alicia Gardiol. I could not have done it without them.

LIST OF CONTENTS

PAGE
LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . ix
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . xi
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . 1
References. . . . . . . . . . . . . . . . .. . . . 7
CHAPTER I. THE EVALUATION OF THE AROMA BARRIER PROPER-
TIES OF POLYMER FILMS. . . . . . . . . . . . . . . 11
INTRODUCTION. . . . . . . . . . . . . . . . . . . . 11
Modeling Considerations. . . . . . . . . . . . . . .17
Permeability Measurements. . . . . . . . . . . . . .20
Isostatic Method. . . . . . . . . . . . . . . .20
Quasi-isostatic Method. . . . . . . . . . . . .25
Sorption Measurements. . . . . . . .. . . . . . L . 27
Polymer Films. . . . . . . . . . . . . . . . . 27
Polymer Spheres. . . . . . . . . . . . . . . . 28
Desorption Measurements. . . . . . . . . . . . . . 3O
Solubility Coefficient. . . . . . . . . . . . . . . 32
Diffusion Coefficient. . . .'. . . . . . . . . . . .32
METHODS. . . . . . . . . . . . . . . . . . . . . . .34
Determination of Permeation Methods. . . . . . . . .34
Isostatic procedure. . . . . . . . . . . . . . 34
Quasi-isostatic Procedure. . . . . . . . . . . 37
Sorption Measurements. . . . . . . . . . . . . . . .39
APPLICATIONS. . . . . . . . . . . . . . . . . . . . 42
Quasi-isostatic Procedure. . . . . . . . . . . 42
Isostatic Procedure. . . . . . . . . . . . . . 46

vi

Sorption Procedure.
SUMMARY.
REFERENCES.
CHAPTER II. THE SORPTION OF WATER VAPOR BY AN AMORPHOUS
POLYAMIDE.
ABSTRACT.
INTRODUCTION.
DUAL MODE SORPTION MODELS.
Model for Gas Sorption in Glassy Polymers.
Models for Polar Systems at High Solute
Activities.
CLUSTERING OF SOLUTE MOLECULES.
Modified Dual Mode Sorption Model.
EXPERIMENTAL METHODS.
Polymer Films.
Equilibrium Sorption Data.
Density Experiments.
Fourier Transform Infrared Spectroscopy.
DSC and Dielectric Experiments.
RESULTS AND DISCUSSION
Equilibrium Sorption Isotherm.
Parameter Estimation for Equation 8.
Sensitivity Coefficients.
Clustering Analysis.
Physical Evidence for Solute Binding.
Relaxation Temperatures.

Density Data.

vii

.47
.49

50

56
56
57

.58

58

.59

62

.64

65
65
66
66
66
67

.67

67
7O

.74

77

.78

83

.84

Proposed Mechanism for Effects of Water

Sorption on Physical Properties of Amorphous

Polyamide. . . . . . . . . . . . . . . . . . . 87
LITERATURE CITED. . . . . . . . . . . . . . . . . . 88
CHAPTER III. EFFECT OF WATER CONTENT ON THE SOLUBI-

LITY, DIFFUSION AND PERMEABILITY IN NYLON

6I/6T. . . . . . . . . . . . . . . . . . . . . 93
INTRODUCTION. . . . . . . . . . . . . . . . . . . . 93

Oxygen Permeability as Function of Polymer

Water Activity. . . . . . . . . . . . . . . . .95
Oxygen Solubility and Diffusion coefficient. . 96
EXPERIMENTAL METHODS. . . . . . . . . . . . . . . . 99
Polymer Films. . . . . . . . . . . . . . . . . 99
Equilibrium Sorption Data. . . . . . . . . . . 99
Oxygen Permeability Studies. . . . . . . . . .100
RESULTS AND DISCUSSION. . . . . . . . . . . . . . .102
Equilibrium Sorption isotherms. . . . . . . . 102
Calculation of Oxygen Solubility. . . . . . . 108
Conditions for Applying Eqn. 10 . . . . . . . 110
Permeability Data . . . . . . . . . . . . . . 113
Oxygen Solubility. . . . . . . . . . . . . . .123
Oxygen Diffusion Coefficient. . . . . . . . . 132
CONCLUSIONS . . . . . . . . . . . . . . . . . . . 135
SUMMARY. . . . . . . . . . . . . . . . . . . . . . 136
REFERENCES. . . . . . . . . . . . . . . . . . . . .138
APPENDIX A. . . . . . . . . . . . . . . . . . . . .140
APPENDIX B. . . . . . . . . . . . . . . . ... . . .149

viii

CHAPTER TABLE

1

1

10

LIST OF TABLES

Permeability constants and lag time
diffusion coefficients for toluene in
selected polypropylene based structures.
Values for eqn.(23) obtained for the
system Oxygen/Nylon 6I/6T, at 22.00C and
water activity = 0.441.

Models for polar system at high solute
activities.

Experimental data at 23 OC.

Langmuir and Flory-Huggins volume frac-
tion contributions.

Amide I, Amide II and CH absorption
frequencies.

Intensity ratios of Amide I and Amide II
with respect to CH bands.

Water polymer isotherm at 5 0C
Water polymer isotherm at 23 oC
Water polymer isotherm at 42 OC

Values of X_, K and B as a function of
temperature.

Water activity values at the onset of
cluster formation.

Solubility of oxygen in Nylon 6I/6T as
a function of pressure at 24 oC.

Diffusion, solubility and permeability
values of oxygen at 11.9 0C.

Diffusion, solubility andopermeability
values of oxygen at 22.0 C.

Diffusion, solubility andopermeability
values of oxygen at 40.3 C.

Values of the constants for eqn. 6

ix

PAGE

43

48

60
68

73

80

80
103
104
105

109

109

111

114

115

116

123

11

12

13

APPENDIX B

Experimental
of oxygen at

Experimental
of oxygen at

Experimental
of oxygen at

and calculated solubility
11.9 C.

and calculated solubility
22.0 00.

and cglculated solubility
40.3 C.

Activation energy as a function of Aw_

126

127

128

173

CHAPTER FIGURE

1

1

LIST OF FIGURES

Transmission rate profile curve for
toluene vapor Bhrough oriented PET at
90 ppm and 23 C.

Generalized transmission rate profile
curve by quasi-isostatic method test.

A plot of M /M¢,vs. t 1/2 for d-limone-
ne by high density polyethylens/sealant
structure at 1.5 ppm and 20.5 C.

Schematic diagram of the isostatic test
apparatus.

Schematic diagram of the quasi-isostatic
tets apparatus.

Schematic diagram of the electrobalance
test apparatus.

Effect of penetrant concentration onothe
transmission of toluene vapor at 23 C
through coextruded OPP.

Effect of penetrant concentration 8n the
transmission of the toluene at 23 C
through biaxially oriented polypropylene.

Experimental sorption values and Flory-
Huggins fitting.

Experimental sorption values and Flory-
Huggins fitting at low activity values.

Best fit for the Langmuir-Flory-Higgins
model.

Sensitivity coefficients as a function
of activity.

Clustering function as a function of
water act1v1ty.

Typical FTIR spectrum of the amorphous
polyamide recorded at room temperature.

Spectrum region of Amide II as a function
of activity.

xi

PAGE

21

26

29

35

38

41

44

45

69

71

72

75

76

79

81

APPENDIX B

10

11

12

l3

14

Glass transition temperatures as a func-
t1on of act1v1ty.

Density as a function of activity.
Oxygen permeability apparatus.

Water sorption isotherms at 5 C, 23 OC
and 42 C.

Values of K and B of the Langmuir
equation.

Solubility of oxygen as a function of
partial pressure at 240C.

Oxygen permeabiligy values at 11.9 0C,
22. 0 OC and 40. 3 C.

Diffusion coefficient values at 11.9 0C,
22.0 C and 40.3 C.

Oxygeg solubilityO values at 11.9 0C,
22. 0 C and 40. 3 OC.

Solubility and diffusion coefficient of
oxygen at 11. 9 OC.

Solubility and diffusion coefficient of
oxygen at 22.0 C.

Solubility and diffusion coefficient of
oxygen at 40.3 C.

Oxygen solubility at 11.9 0C as function
of a
w

Oxygen solubility at 22.0 0C as function
of a
w

Oxygen solubility at 40.3 0C as function
of aw.

Activation energy as a function of water
activ1ty.

Activation energy versus pre-exponential

term for the diffusion of oxygen in the
amorphous nylon,

xii

85
86
101

106

107

112

117

118

119

120

121

122

129

130

131

134

174

INTRODUCTION

The presence of sorbed or diffusing low molecular weight
penetrants in polymer solids often has a marked effect on
material properties. The way in which the penetrant is
sorbed and distributed within the polymeric matrix can be
expected to affect the penetrant mobility, the local polymer
chain segmental mobility, and related parameters such as
free volume distribution and eventually, efficiency of free
volume utilization [1]. Two major classes of polymer
properties that are controlled by the segmental mobility of
the polymer chain are the transport and mechanical
properties. The mobility of polymer chains is determined by
the polymer structure and its morphology, and is affected by
sorbed molecules and the mode of sorption. For a given
polymer structure, the transport and mechanical properties
will therefore depend on the precise interaction and the

sorbed penetrant.

Penetrant molecules are sorbed within the polymer in
different modes [2]. The nature of interactions between
penetrant and polymer is an important factor in the manner
in which the molecules of penetrant are distributed within
the polymeric matrix. Particular sorption modes of interest
are the localization of penetrant molecules at specific

polymer sites that may be more or less active, randomly

1

dispersed (free) penetrant molecules and sorbed-sorbed
molecules resulting in clustering formation. The total
penetrant sorption process will probably be the result of
the combination of these three different mechanisms or

sorption modes.

The specific sorption process may be described as a function
of penetrant concentration or activity, temperature, and
time to reach equilibrium, as well as the composition of the
penetrant-polymer system. Therefore, polymer structure,
availability of specific active sites of interaction in the
polymer, chain stiffness or segmental mobility, plus the
physico-chemical characteristics of the penetrant (gas,
water or organic compounds) determine the mode and
mechanisms of sorption and transport of the penetrant within

the polymer.

A very common model that describes sorption of penetrants in
glassy polymers was introduced by Matthes in 1944, using

the concept of the dual-mode sorption mechanism [3]. He
combined a Langmuir and a Henry's law type expression to
describe the sorption of water by a cellulosic material. A
large number of other investigators have extended the use of
this model to describe the sorption of fixed gases (most of
them above the critical temperature) such as C02, CH4, C2H6’

etc., by different polymers, [4]-[12]. This model has also

been used to correlate the sorption of mixed gases in glassy
polymers [13].

Although this model based, on Langmuir and Henry equations,
may well describe the sorption of gases by polymers, it
actually overpredicts the sorption of vapors by polymers,
and is not able to predict the cluster formation of the
absorbed molecules.

Another important characteristic of this model is that
Henry's law of dissolution does not distinguish solutions
containing only molecules of ordinary size from those
solutions of very large molecules. Flory [14-15] and Huggins
[l6],derived an equation for the activity coefficient of a
solute in a polymer, as a function of volume fraction of the
solute. At low activity values, this equation underpredicts
the sorption of vapor by polymers and predicts clustering of
the solute within the polymer in the whole range of solute
activity.

The formation of clusters can be predicted by applying the
clustering function to a specific model describing the
sorption behavior of a penetrant-polymer system. The
clustering function ([17], [18]) is a monotone, increasing
function of the probability of finding molecules of the same
kind close to one another. Orofino et al., [19], applied the
clustering function to several polymer-water systems obeying
Flory-Huggins thermodynamics. However, when the clustering
function is applied to the Flory-Huggins model, clustering

is predicted in the whole range of vapor activity.

Polyamides, as most polymeric materials, sorb both water and
organic vapors. In the past years polyamide-water systems
have been the subject of a number of studies, [19]-[23]. The
amide function of the polymer participates in hydrogen
bonding, where the hydrogen on a nitrogen atom associates
with the carbonyl oxygen atom of an adjacent molecule. Such
non-covalent bonds are relatively strong (8 kcal/mol), and
serve to provide a cross-link network between polymer
molecules. They exist in the amorphous as well as in the
crystalline regions of polyamides [20]. Disruption of
hydrogen bonding in the noncrystalline region is necessary
for a solvent to attack polyamides and is a major factor in
the mechanism of absorption of molecules that surround the

polymer [24].

Puffr and Sabenda [23] suggested a mechanism of water
sorption into Nylon 6 at room temperature, which involved
two neighboring amide groups in water-accessible regions
forming a sorption center. This sorption center could
accommodate up to 3 water molecules, involving hydrogen
bonding between adjacent amide groups. Additional sorbed
water molecules may be accommodated via a clustering
mechanism. Papir et al. [25], working also on the nature of
the absorption of water in Nylon 6 confirmed the hypothesis

of Puffr and Sabenda, in that two "types" of water, tightly

bound and loosely bound, can exist within the polymer

matrix.

Fourier transform infrared (FTIR) spectrosc0py is considered
a powerful tool for polymer characterization, [27]-[28]. In
the present study FTIR spectroscopy has been employed to
glean information related to the nature, strength, and
number of intermolecular forces occurring between sorbed
water and an amorphous polyamide. The FTIR spectroscopy
studies focused specifically on the detection of possible
changes in hydrogen bonding between N-H and carbonyl groups.
This was done by observing the vibrational modes of the
amide group, consisting of the Amide I and Amide II bands,

as a function of polymer water content.

In recent years, a totally amorphous polyamide has been
developed, the 6I/6T (70/30) amorphous nylon [29].
Preliminary studies on the effect of water sorption on the
barrier properties of this polymer showed atypical behavior,
as compared to semicrystalline nylons under the same
conditions. For example, oxygen permeability in Nylon 66
increases as a function of moisture content of the polymer,
while it showed a decrease in the amorphous nylon 6I/6T.
Further, the tensile modulus for Nylon 66 decreases as a
function of moisture content, while the tensile modulus for
the amorphous nylon increases with increase in moisture

content. The intriguing behavior of the water-nylon systems

has made evident the need of a model that would provide a
more quantitative description of the mechanism of the
sorption process of water by polar polymers. The thrust is
also to look for a model that may be used to explain the
sorption and diffusion behavior of organic vapor penetrants
in polar polymer. This is important not only for theoretical
but also for practical reasons. Most polymer materials are
normally exposed to vapors (water or organic) and the
interaction that takes place affects the performance of such
polymer as is the case for example, in polymer composites or

product-package interactions.

The present research work has addressed, therefore, two

major objectives:

I. To complete an experimental description of the
equilibrium sorption process of the binary system water-
amorphous polyamide, and to describe the experimental
behavior of the diffusion and solubility of oxygen within

the system water-amorphous polyamide.

II. To develop a theoretical framework for interpreting the
mechanism of sorption equilibrium of the binary system
water-polymer, and of the three components system oxygen-
water-polymer. It is expected that the conclusions of this
work will be valid to describe the equilibrium soption of

organic compounds-polymer systems.

REFERENCES

Sfirakis, A. and C. E. Rogers, Effects of Sorption Modes

on the Transport and Physical Properties of Nylon 6,

Polym. Eng. Sc., 20, 4, 294-299 (1980).

Rogers, C. E., Physics and Chemistry of the Organic
Solid State, Vol II, Chapter 6, Interscience, N. Y.

(1965).

 

Matthes, A., Zur Theorie des Quellungsvorganges an

Gelen, Kolloid-Z. Z., 108, 79-94 (1944).

Michaels, A. S., W. R. Veith and J. A. Barrie, Diffusion
of Cases in Polyethylene Terephthalate, J. Appl. Phys.,
35, (1), 13-65 (1963).

Veith, W. R. and J. A. Eilenberg, Gas Transport in
Glassy Polymers, J. Appl. Polym. Sc., 16, 945-954
(1972).

Veith, W. R., J. M. Howell and J. H. Hsieh, Dual
Sorption Theory, J. Membr. Sc., 1 (1976) 177-220.

Koros, W. J., and D. R. Paul, Transient and Steady State
Permeation in Polyethylene Terephthalate, J. Polym. Sc.

Phys. Ed., 21, 441-465 (1983).

10.

11.

12.

13.

Kulkarni, S. S. and S. A. Stern, The Diffusion of C02,
CH4, C2H4 and C3H8 in Polyethylene at Elevated

Pressures, J. Polym. Sc. Phys. Ed., 21, 441-465 (1983).

Barrie, J. A. and P.S. Sagoo, The Sorption and Diffusion
of Water in Epoxi Resins, J. Membr. Sc., 18 (1984) 197-
210.

Barrer, R. M., Diffusivities in Glassy Polymers for the
Dual Mode Sorption Model, J. Membr. Sc., 18 (1984) 25-
35.

Koros, W. J., R. T. Chern, V. Stannett and H. B.
Hopfenberg, A Model for Permeation of Mixed Cases and
Vapors in Glassy Polymers, J. Polym. Sc. Phys. Ed., 19,
1513-1530 (1981).

Uragami, T., H. B. Hopfenberg, W. J. Koros, D. K. Yang,
V. Stannett and R. T. Chern, Dual-Mode Analysis of
Subatmospheric-Pressure CO2 Sorption and Tramsport in
Kapton H Polyimide Film, J. Polym. Sc. Phys. Ed., 24,
779-792 (1986).

Koros, W. J., Model for Sorption of Mixed Cases in

Polymers, J. Polym. Sc. Phys. Ed., 18, 981-992 (1980).

14.

15.

16.

17.

18.

19.

20.

21.

Flory, P. J., Thermodynamics of High Polymers Solutions,

J. Chem. Phys., 10, 51 (1942).

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

 

University Press, Ithaca, NY, (1953).

Huggins, M. L., Thermodynamic Properties of Solutions of

Long-Chain Compounds, Ann. NY Acad. Sci., 42, 1 (1942).

Zimm, B. H. and J. L. Lundberg, Sorption of Vapors by
High Polymers, J. Phys. Chem., 60, 425-428 (1956).

Lundberg, J. L., Clustering Theory and Vapor Sorption by
High Polymers, J. Macrom. Sci. Phys., B3 (4), 693-711
(1969).

Orofino, T. A., H. B. Hopfenberg and V. Stannett,
Characterization of Penetrant Clustering in Polymers, J.

Macrom. Sci. Phys., B3 (4), 777-788 (1969).

Cannon, C. G., Spectrochim. Acta, 16, 302 (1960).

Starkweather, H. W., The Effect of Water on Some

Properties of Oriented Nylon, J. Macrom. Sci. Phys.,

B3 (4), 727-736 (1969).

22.

23.

24.

25.

26.

27.

28.

29.

10

Skirrow, G. and Young K. R., Sorption, Diffusion and
Conduction in Polyamide-Penetrant systems: I. Sorption

Phenomena, Polymer, 15, 771-776 (1974).
Puffr, R. and J. Sabenda, On the Structure and
Properties of Polyamides: XXVII. The Sorption of Water

in Polyamides. J. Polym. Sc. Part C, 16, 79-93 (1967).

Kohan, M. I., Nylon Plastics, J. Wiley, N.Y. (1973).

 

Papir, Y. S., Kapur, S., C. E. Rogers and E. Baer,
Effect of Orientation, Anisotropy, and Water Vapor on
the Relaxation Behavior of Nylon 6 From 4.2 to 300 0K,

J. Polym. Sc. A-2, 10, 1305 (1972).

Koening, J. L., Fourier Transform Infrared Spectroscopy

of Polymers, Advances in Polymer Science, 54, 87 (1984).

Painter, P. C., M. M. Coleman and J. L. Koening, Theory
of Vibrational Spectroscopy with Application in

Polymers, J. Wiley, N. Y. (1981).

Siesler, H. W. and K. Holland-Moritz, Infrared and Raman

 

Spectroscopy of Polymers, M. Dekker Inc. N. Y. (1980).

 

Blatz, P. and C. Talkowski, Personal Communication

(1987).

CHAPTER I

THE EVALUATION OF THE AROMA BARRIER PROPERTIES OF POLYMER
FILMS**

Key Words: Aroma barrier, organic penetrants, diffusion,
sorption, permeability, barrier polymer films,

polypropylene, high density polyethylene.

INTRODUCTION

The shift from absolute barrier type packages, such as cans
and bottles, to semi-permeables polymeric packaging systems
has created a need to develop a better understanding of the
transport of gases, vapors, and other low molecular weight
moieties through polymer films. The transport of permeants
such as oxygen, carbon dioxide and water vapor through
polymer structures has been the subject of numerous
investigations, and standard test methods are availables for

determining transmission rates for these permeants (ASTM

E96-66, ASTM D3985-81).

 

** This review paper was published in the Journal of Plastic

Film and Sheeting. Volume 2, 187-211 (1986).

11

12

In contrast, while the transport of organic penetrants
through packaging materials have been the subject of several
recents investigations, there is a paucity of data
available in this area.

This paper will, therefore, focus on the various procedures
developed for quantifying the rate of diffusion of organic
penetrants through barrier membranes and describe in detail
the specific procedure employed in the studies reported.

Pye et al. (1976) described a continuous or isostatic
procedure for measuring the diffusivity properties of
polymer membranes that employed two gas chromatographs
connected to a cell. One chromatograph was equipped with
flame ionization detection and the second was based on a
thermal conductivity cell. This was achieved by
incorporating gas sampling valves in the carrier gas stream.
With multiples detectors, the authors were able to study the
diffusion of gases as well as organic vapors through polymer
films. The system described by Pye et al. also included a
gas and organic vapor mixture generating apparatus.
Niebergall et al. (1978) also described a method for
determining the difusivity values of the various organic
penetrant/barrier film systems based on the isostatic
procedure of test. The apparatus developed by these authors
was designed to allow measurement of transmission rates for

mixtures of organic vapors through barrier structures as

13

function of penetrant concentration, temperature and
relative humidity.

Zobel (1982) has also reported an isostatic method for
measuring the permeability rate of films to organic vapors
at low penetrant concentrations and, in recent articles,
described a modification of the previous procedure which
incorporated an absorption/desorption cycle, Zobel (1984,
1985).

An isostatic procedure was described by DeLassus (1986), who
studied the transport of d-limonene vapor through a series
of polymer films typically used for food packaging. The
author employed techniques on photoionization and
atmospheric pressure ionization, Caldecourt and Tou (1985),
for quantifying the permeation rate of d-limonene through
the respective test films. Hernandez (1984) and Bauer et a1.
(1986) also employed an isostatic procedure for determining
the diffusion coefficient from permeability data of organic
penetrants through polymer membranes. Analysis of permeated
vapor was based on a gas chromatographic technique with
flame ionization detection. Smith and Adams (1981) and
Pasternak (1970) also reported permeability studies using a
continous flow or isostatic method.

Hilton and Nee (1978) developed an accumulation or quasi-
isostatic test method for determining the permeability of
organic vapors through barrier films, where the polymer film
was mounted in a permeability cell above a reservoir of

liquid permeant. The permeant vapor which has diffused

14

through a barrier film accumulates in the low concentration
chamber of the test cell and was quantified by a gas
chromatographic technique. A similar procedure for
determining the permeability of organic vapors through
barrier films was reported by Murray and Dorschner (1983).
In a more recent publication, Murray (1985) expanded on this
procedure and reported a number of examples for which the
test apparatus was employed to determine the relative
permeation rates of organic vapors through barrier
structures. These methods are limited, however, to
determining the transmission rates and permeability constant
values at only one concentration given by the saturation
equilibrium vapor pressure of the liquid penetrant at a
given temperature.

Gilbert et a1. (1983) also evaluated the barrier properties
of polymeric films to various organic penetrants by a quasi-
isostatic test procedure. To provide a constant
concentration or partial presure gradient, wherein the net
movement for the penetrant is from high partial pressure to
low partial pressure, these author continually flowed a
penetrant vapor stream through the high concentration
chamber of the permeability cell. Baner et al.(1984)
described a test apparatus based on the quasi-isostatic
procedure for determining the diffusion of organic penetrant
through polymer films, and also employed the continous flow

of organic vapor through the high concentration cell chamber

15

to assure a constant vapor gradient. A chromatographic
method was developed for the permeation rate measurements.
Peterlin (1975) has studied the concentration dependence of
the diffusion and permeability coefficient in a homogeneous
membrane.

In addition to the permeation methods described above, the
transport of small molecules in polymers can also be
evaluated by absorption-desorption methods. Fujita (1961)
has decribed the general behavior of sorption and
permeability of organic vapors. Bischoff et a1. (1984) have
studied the effect of the polymer molecular orientation on
the sorption of toluene by high density polyethylene (HDPE).
Applying a succesive sorption method, Choy et al. (1984)
studied the sorption and diffusion of toluene vapor in
oriented polypropylene (OPP) film of varying draw ratios. By
this method the authors obtained values of the difussion
coefficient (D), solubility (S) and permeability (P) of the
polymer, as well as information on the structure and
molecular dynamics of OPP as a function of draw ratio.
Berens (1978) described vapor sorption studies on polyvinyl
chloride (PVC) powders as a mean of studying the transport
of low molecular weight organic molecules in glassy
polymers. For a detailed rewiew of the sorption method for
measuring the sorption and diffusion coefficients of small
molecules in polymers, the reader is referred to Berens

(1978) and references cited therein.

16

Bauer (1986) applied the sorption equilibrium method by
using a electrobalance to studiy the sorption and diffusion
of toluene vapor in OPP and Saran (trademark of the Dow
Chemical Company for its polyvinylidene chloride and
copolymers) film samples as a function of penetrant
concentration.

Knowledge of the diffusion, solubility and permeability of
organic penetrants through polymer structures has both
theoretical and practical importance. In terms of
theoretical importance, such studies can aid developing a
better understanding of the mechanism of diffusion of
organic penetrants through polymer membranes and
particularly for the case of permeant molecules that have
strong interaction with the polymer. The diffusion and
solubility of organic penetrants will be of practical
importance for example in the case of packaged goods, when
product quality is related to the transfer of organic vapors
when polymers materials are used. For example, the aroma
barrier properties of a package system are important, since
the retention of product aroma constituents and the
exclusion of sensorially objectionable organic molecules
from the package external environment contribute to the
keeping quality and, thus, the shelf life of the product.
Further, knowledge of the aroma barrier propeties of
polymeric packaging materials can provide a mean of
designing and/or selecting a barrier structure for a

specific end use application.

17

Knowing solubility data for essential flavor ingredients in
certain polymers is of paramount importance in avoiding the
effect of "flavor scalping". For example, d-limonene, a
common flavor component present in foods has a relative high
solubility in HDPE, Mohney et al., (1986). Since the flavor
compounds are normally present in low concentration in the
foodstuffs, there is a potential risk to "lose" aroma
constituent due to absorption by the package polymeric

material.

MODELING CONSIDERATIONS

Diffusion (D) and solubility (S) coefficients are usually
determined by observing the change in weight (increase or
decrease) of a polymer sample during a sorption process.
Such a process can involve the absorption or the desorption
of low molecular weight moieties by the polymer sample.
Diffusion and permeability (P) values can be obtained from
permeability experiments where the transport of a permeant
through a polymer membrane is continually monitored
(isostatic procedure) or by quantifying the amount of the
penetrant that has passed through the film and accumulated
as a function of time (quasi-isostatic procedure).

The basic equations for decribing the diffusion process are

Fick‘s first and second law of diffusion (Crank, 1975).

18

 

dc
F = - D (1)
dx
and
dc d dc
—-=-—-[D—] (2)
dt dx dx

Where F is the flux or the rate of transfer of penetrant per
unit area, expressed as a mass of diffusant per unit area
per time; c is the concentration of the penetrant in the
film, expressed in the same unit of mass of diffusant per
unit of volume or mass of the polymer; D is the mutual
diffusion coefficient, in unit of (length)2/time; t is time
and x is the length in the direction in which the transport
of the penetrant molecules occurs. To obtain the flux F, or
the diffusion coefficient D, equation (1) or (2) must be
solved together with the initial and boundary conditions

associated with the experiment to give the desired values.

Solution to eqn. (2), and respective initial and boundary
conditions, can be performed analytically or numerically to
calculate D. In the first case a power-series of solutions

usually arises when solving for the unsteady state case.

19

In this paper, simplified equations related to the first
approximation of the power-series are presented (Crank,
1975). It should benoted that when the diffusion
coefficient is calculated using these equations, only
approximated values will be obtained. More accurate
estimation of this parameter D, can be carried out by using,
for example, a non linear maximum likelihood sequential
method based on the Gauss linearization method (Beck and

Arnold, 1977).

To relate the concentration of the penetrant in the polymer,
(solubility), to the penetrant concentration in the gas or
vapor phase in equilibrium with the polymer, Henry's law is

assumed

S.p (3)

0
ll

Where p is the partial pressure of the penetrant in the gas
phase and S is the solubility coefficient of the penetrant
into the polymer. The partial pressure of the penetrant is
further related to the penetrant concentration in the gas
phase through, for example, the ideal gas law. Application
of the ideal gas law is justified when the concentration of

the diffusant in the gas phase is lower than one atmosphere.

20

The diffusion coeffient D, can be independent or, a function
of the penetrant concentration c in the polymer. In the
latter case, the diffusion coefficient would not be constant
but would be concentration dependent. In either case, it is
assumed that the diffusion process is fickian. If the
diffusion coefficient is time dependent, the diffusion

process is said to be non-fickian (Meares, 1965).

Permeability Measurements

 

Isostatic Method

A representative transmission rate profile curve for
describing the transport of a permeant through a polymer
membrane by an isostatic method is shown in figure 1. From
such an experiment, diffusion and permeability coefficient
values are obtained, and while the specific experimental
configuration may vary among investigators, the basic
equations describing the permeation phenomenom are similar.
Solution of eqn. (1) depend on the boundary conditions of

the experiment, in this case given by:

(
(

Ahd
At

A1

:31
Aha

).

21

 

L0?

0.8-

0.6»-

0.4

U

0.2!-

 

 

 

130 150 170 190
Time (hours)

G L
90 110

Figure 1. Transmission rate profile curve for toluene vapor
through oriented polyethylene terephthalate (PET) at 90 ppm

and 23 C (thickness of the film was 3.49 x 10"5 m, crystali-
nity 27%).

22

 

c = CO at x = 0 t = 0
c = 0 at x = L t > O
L-x
C=c2 at O<x<1t=°° (4)
l

where L is the thickness of the film, co is the
concentration at x = L.in equilibrium with the permeant
flow. These B.C. represent the change from one steady state,
t = 0 and CI, to the final c2 at t = <9, with the partial
pressure of the permeant on the downstream side of the

membrane always kept at zero since pure gas nitrogen is

continuously flowed.

A solution of eqn. (1) subject to boundary conditions given
by eqn. (4) was presented by Pasternak et al. (1970) and is

given as a first approximation in Equation (5)

 

A11
At: t 4 12 1/2 _L2

=—— —— 5
(AM) [51—][40t] exp[4Dt] ()

 

 

 

23

where (AM/At)t and (AM/At)mare the transmission rate of
the penetrant at time t and at steady state, respectively.
For each value of (AM/At)t/(AM/At)ao a value of 12/4Dt can
be calculated, and by plotting 4Dt/12 as a function of time,
a straight line is obtained. From the slope of this graph, D

is calculated by substitution in eqn. (6).

(slope) x I?

4

 

(6)

Smith and Adams (1981) used this method to study the effect
of the tensile deformation on gas permeability in glassy
polymers. From a different general expression for
(AM/At)t/(AM/At)m , Ziegel et a1. (1969) derived equation

(7), to solve for D:

L2

D = (7)
7.199 tl/2

 

where t1/2 is the time required to reach a rate of
transmission (AM/At)t equal to half the steady state

(A M/At)°o value.

24

DeLassus (1985) applied eqn. (7) to calculate the diffusion
coefficient of limonene vapor for different polymer films

tylically used for food packaging.

The permeability coefficient P, can be calculated from the

isostatic method by substitution in eqn. (8)

a.G.f.L
P = (8)
A.b

 

where

a = calibration factor to convert detector response to
units of mass of permeant/unit of volume [(mass/vol)
/signal units]

G = response units from detector output at steady state
(signal units)

f = flow rate of sweep gas conveying penetrant to detector
(volume/time)

b = driving force given by the concentration or partial

pressure gradient (pressure or concentration units).

25

Quasi-Isostatic Method

In this method, the permeated gas or vapor is accumulated
and monitored as a function of time. A generalized
transmission rate profile curve describing the transport of
permeant through a polymer membrane by the quasi-isostatic
method is shown in Figure 2. As shown, the total quantity of
penetrant to have transmitted through the film is plotted as
a function of time. Barrer (1939) presented a solution of
equation (2) for this specific set of experimental
conditions, which allowed determination of D,

L2

D=—— (9)
69
where e is the intersection of the projection of the steady-
state portion of the transmission curve and is called the
lag time. The steady-state permeability coefficient P can be
determined from the quasi-isostatic method by substitution
into eqn. (10).
y.L.
P = ---- (10)
A.b
where y is the slope of the straight line portion of the
transmission rate curve (mass/time).

By plotting log [tl/2

(AM/Ant] as a function of l/t, it is
possible to obtain information about the concentration

dependency of the diffusion coefficient.

26

     
 

I
l

.5. Q Ouantlt
I

O Mlcrograms Permeated

 

Figure 2. Generalized transmission rate profile curve by quasi-
isostatic method test. '

27

Sorption Measurements

 

Polymer Films

Sorption experiments are usually carried out at equilibrium
vapor pressure, using a gravimetric technique in an
apparatus that records continually the gain or the loss of
weight by a test specimen as a function of time. A recording
electrobalance (Cahn Instrument Co., Cerritos, California)
is commonly used for such studies.

The diffusion equation that describes appropriately the
sorption of penetrant by a polymer sample in film or sheet
form for large time is described by Crank (1975), and taking

the first two terms of the serie solution, eqn. (11) is

obtained,
M 8 -D.t.n2 1 -9D.t.n2
—'L' = 1 '71 eXp(——2—) + - €XP(_—2'—)] (11)
Moo Tl - 1.. 9 1.

where Mt and M¢,are the amount of penetrant sorbed by the
polymer film sample at time t and the equilibrium sorption
uptake after infinite time, respectively; and L.is the
thickness of the sample.

The sorption diffusion coefficient DS can be calculated by a
non-linear regression analysis of the above equation or
approximated by setting Mt/M“° equal to 0.5 an solving for

DS to obtain,

28

0.049-1?
D = (12)

t1/2

 

where t1/2 is the half sorption time or the time required to
attain the value Mt/Mm.

A graphical representation of eqn. (11) and data from an
experimental sorption process are shown in figure 3, where
values of Mt/M¢,are plotted as a function of square root of
time, t1/2.
In the early stage of the diffusion process, the uptake by a

film is described by,

 

M‘ 4 ( Dt )“2 [ 1 2 ' f 1 ] (13)
-- = -- -- + 1er c
M., 1? H172 (2Dt)1/2

Polymer Spheres

The ratio of the amount of vapor absorbed at any time t over
the equilibrium sorption uptake at infinite time Mt/M¢,for
polymer samples of spherical geometry and of diameter d is

given by the expression:

Mt 6 -D.t.n2 1 -16D.t.n2
—— =1-716XP(——7—)+ - eXP( 2 )1 (14)
M“, ‘n d 4 d

 

29

 

 

 

 

0 EXPERIMENTAL DATA
"2 —CALCULATED FROM'
THEORETICAL EQUATION
1.0 -
0.8 -
0.6 -
0.4 -
0.2 -
O l l l n I
0 100 200 ' 300

Time"2 (secondsV')

Figure 3. A plot of M /M vs. t”2 for d-limonene by high

density polyethylene/sealant lamination (thickness, 4.8 x 10'“5
m); vapor concentration 1.5 ppm; temperature 20.5 C.

30

which is the first two terms of the serie solution presented
by Crank (1975). The diffusion coefficient is also readily
obtained from eqn.(14) by setting Mt/Mwequal to 0.5 to give

the expression,

 

(15)
t1/2

Berens (1977, 1978) conducted absorption experiments to

study the characteristics of the transport of vinyl chloride

monomer in polyvinyl chloride (PVC) using powdered polymer

samples. Application of equations (14) and (15) showed that

the PVC powder particles could be treated as spheres.

Desorption Measurements

When desorption experiments are performed and the value of
the mass transfer coefficient of the moiety in the gas phase
is negligible, eqns. (11) and (14) can also be applied to
the desorption process by considering the loss of the
penetrant at any time t and the amount of penetrant loss
after infinite time as Mt and Ma” respectively.

The diffusion coefficient for the desorption process Dd is

given by:

 

(16)

31

for film samples and, for polymer samples of spherical
geometry by:
d2
Dd = 0.00745-—-— (17)
t
1/2
When DS and Dd are different the diffusion coefficient may

be better represented by the average of these two values.

However, when the mass transfer coefficient of the diffusing
molecule in the gas phase cannot be neglected the power-
series of solution must include this parameter, Crank
(1975). The expression that includes only the leading term

of the solution for the above boundaries conditions is

 

given by:
Mt 2L.exp(-B.D.T/12)
—=1" 2 2 2 (18)
M00 B(B+L+L)
where
B.tan(B) = L
and

L=L.k.D

k is the mass transfer coefficient in the gas phase. A
simplified method to solve for both the diffusion and the
mass transfer coefficients has been presented by Han et a1.
(1986), but the numerical solution presented by the authors

is probably incorrect.

32

Solubility Coefficients

The solubility coefficient S is readily calculated from

absorption experiments by substitution into the expression
8 = ---— ' (19)

where S is expressed as mass of vapor sorbed at equilibrium
per mass of polymer per unit of driving force concentration
or penetrant partial pressure. M¢,is in the total amount
(mass) of vapor absorbed by the polymer at equilibrium for a
given temperature, w is the weight of the polymer sample
under test, and b is a value of the penetrant driving force

in units of concentration or pressure.
Diffusion coefficients

Implicit in the expression to calculate D is the assumption
that the diffusion coefficient is independentéflof the
concentration of the penetrant. However, unlike the
transport of less-interactive penetrants (such as oxygen or
nitrogen), the molecular transport of most organic vapors
show non-ideal diffusion and solubility behavior due to
their ability to interact with, and swell the polymeric
matrix. Since those effects is a function of the
concentration of the vapor, both D, S, and also P are

function of the penetrant concentration.

33

Nevertheless, these equations can also be applied when the
polymer sample swells and the thickness changes as the vapor
enters the film. As Crank and Park (1968) showed, D (the
mean diffusion coefficient) can be related to the variable

diffusion coefficient D by the approximation

D = -- D dc (20)

where the range of concentration goes from zero to Co“

A graphical or numerical derivation of DCC versus CO gives a
first approximation of the relationship between D and C. In
many cases, this first approximation may be sufficiently
accurate. However, successively better approximatiion can be
obtained.

When the diffusion process is dependent upon the time
necessary for polymer molecule chain reaccommodation, the
diffusion coeffient is considered non-fickian. Such non-
fickian behavior of the diffusion process is usually
determined by experimentation. For example, the plots for
permeation and sorption data exhibiting non-fickian behavior
are different from those presented in Figures 1-3. There is
not available a general theory for predicting the non-
fickian behavior. Readers interested in this subject are
referred to Fujita (1961), Meares (165) and Crank and Park

(1968) and references found therein.

34

METHODS

Determination of permeation rates

 

Isostatic Procedure

A shematic diagram of the isostatic test apparatus is shown
in Figure 4.

The test system allows for the continuous collection of
permeation data of a molecule (gas or organic vapor),
through a polymer membrane from the initial time zero to
sgady state conditions, as a function of temperature and
permeation concentration. The permeability cells are of our
own design and consist of two stainless steel chambers, with
the upper and lower cell chambers each being equipped with a
gas sampling port and inlet and outlet valves. The film to
be tested is placed between the two stainless steel plates
forming the cell, with the two cell chambers each leaving a
volume of 5 cc. The surface area of the film exposed to the
permeant is 50 cm2. Hermetic isolation of the chambers from
the environment is achieved by the compression of
overlapping Viton "0" rings on the film.

The assembled cell and film is placed horinzontally in a
constant temperature bath. A constant concentration of
permeant vapor is continually flowed through the upper (high
concentration) cell chamber. Concurrentely a constant flow
of inert gas (nitrogen) is passed through the lower cell
chamber removing permeant vapor at a constant rate and

conveying it to the detector apparatus.

35

 

fir.
In
8
A m ' a 'l
| .. ' I-
a I |
I J 5 I
N l____._...|
flak ' a

1

 

 

  

I
1
I
I

 

 

 

. ‘1 "2
Automatic
Simon VIM to N,
Gas Tank
cutout-town»!
VI
3

B1 - Water bath, generation 0! pennant vapor

photo dllutod In NWO
B2 - Wat-r bath ($0.1'C)
C - Coll
F - an flow bubble m

R. - Roguhtor

8 - 80mph port

T - Thu. way valve
w - Wot-r mom

Figure 4. Schematic diagram of the isostatic test apparatus

36

This detection system consist of a gas chromatograph,
equipped with a flame ionization detector, interfaced to the
permeability cell via a computer controlled gas sampling
valve. At preselected time intervals the concentration of
penetrant in the carrier stream flowing through the low
concentration chamber is determined and the the flow is
monitored continually until steady state conditions are
attained. Values of ZAMLAt can be then calculated for each
time. The diffusion and permeability coefficient values are
then computed by substitution into eqns. (6) and (8).

A constant concentration of permeant vapor is produced by
bubling nitrogen gas through liquid permeant. This is
carried out by assembling a vapor generator consisting of a
glass gas washing botlle containing the organic liquid, and
a fritted dispensor tube. The concentration obtained in this
way can be adjusted to a required value by mixing it with a
pure gas carrier steam. Before being directed to the
permeation cell the vapor stream is passed through a glass
reservoir to damp perturbations in the concentration. The
vapor generator system is mounted in a constant temperature
bath. As shown, flow meters were used to provide a continous
indication that a constant rate of flow is mantained. Gas
flow are regulated using needle valves. Prior to initiate a
run, care is taken to purge the lower cell chamber, the
capillary tubing and the sampling valve of residual permeant

vapor.

37

Quasi-Isostatic Procedure

Figure 5 represents a schematic diagram of the quasi-
isostatic permeation test apparatus. The permeability cell,
constructed of stainless steel (or aluminium), is comprised
of two cell chambers and a hollow center ring. Each cell
chamber have a volume of 50 cc; the volume of the center
cavity is aproximately 50 cc. The area of the film exposed
to the permeant is 50 cm2. In operation, two test films are
placed between the center ring and each of the cell
chambers. Isolation of the interior of the chamber from the
environment is achieved by using a Viton "O" ring on each of
the side of the center ring providing a Viton/film/metal
contacting surfaces seal. Each cell chamber and the center
ring are equipped with an inlet and oulet valve and a
sampling port. The films to be tested are mounted in the
permeability cell and the cell is assembled. The constant
concentration flow of permeant is flowed through the center
ring. As showed in Figure 5, to perform simultaneously
multiple runs, several cells can be attached to a dispensing
manifold. Each permeant stream running into each cell may
have a different concentration value.

During the diffusion process, the change in penetrant
concentration in the accumulation cell chamber is determined
by gas chromatography. At predetermined time intervals an

aliquot (.5 ml) of head space is removed from the cell

38

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Farmeation Cells PM“: 4:02:35
I I
Ho Ho
31 - Organic vapor huhhlar II - Iaalla valve
32 - Organic/water vapor huhhlar ll - notanatar
83 - Watar huhhlar ll. - llaoaIator
9: - Four way valva T - Nitrogen tank
II - Ilvgromatar TV - Thraa way valva
ll - Band III - Water Ilatll

Figure 5. Schematic diagram of the quasi-isostatic test apparatus

39

chamber with a gas tight syringe and injected into the gas
chromatograph. To keep the pressure constant inside the
cell, 0.5 ml of pure nitrogen is re-injected into the cell.
Further, to ensure a quasi-constant driving force of the
permeant through the film during each run,the permeant
concentration in the low concentration cell is not allowed
to exceed l-2% of the permeant concentration at the center
ring.
To determine the diffusivity and the permeability values,
the increase in penetrant quantity in the accummulation
chamber is plotted as a function of time and the resultant
transmission rate profile is related to the permeability of
the film sample. The time lag is obtained as the intercept
on the time axis of the steady rise portion of the
penetrant-time plot. By using eqn. (9) the diffusion
coefficient can be determined from the lag time values.
The lag time diffusion coefficient for laminted structures
is considered to be an effective diffusion coefficient
value, being the result of the combination of different

diffusion coefficients of the respective individual layers.

Sorption Measurements

Sorption measurements can be carried out on a Cahn
electrobalance (Cahn Instruments Inc. Cerritos, California).
The electrobalance is maintained in a constant temperature

environment.

40

A sample film between 25 and 100 mg is normally used for
sorption experiments, and the sensibility of the apparatus
is around 1 microgram. A schematic diagram of the test
system is shown in Figure 6. The test system allows for the
continuous collection of sorption data of an organic or
water vapor by a polymer film from the initial time zero,
when the film is first exposed to the vapor, to the steady
state condition, when the equilibrium is reached.

As shown, the polymer film sample to be tested is suspended
directly from one of arm of the electrobalance and a
constant concentration of penetrant vapor is continually
flowed through the sample tube (hang-down tube), such that

the polymer sample is totally surrounded by the vapor. A
constant concentration of penetrant vapor is produced by the
same procedure as explained before. The gain in weight of
the sample due to penetrant sorption is monitored
continually until the gain is zero at equilibrium. To
determine D and S, the ratio of the amount of penetrant
vapor absorbed at any time and the equilibrium sorption
uptake at infinite time, Mt/M“” is plotted as a function of
time. For film samples, the diffusion coefficient DS is
determined by proper substitution into eqn. (12), and the

solubility coefficient into eqn. (19).

 

 

 

 

 

41

B - Water bath, generation of permeant
Vapor phase diluted in Nitrogen

Ct - Computer terminal

Cu - Control unit

F - Gas flow bubble meter
Ho - Hood

N - Needle valve

P - Printer

r
T - Nitrogen tank

 

 

 

 

 

Sc

. c
i S. ‘ ICI
5' __le'
F.__.

 

 

R - Rotameter

R. - Regulator

S - Sample port

Sf - Sampling iilm

Sc - Strip chart

Si - Electrical Input/output signal
Tv - Three way valve

wm- Cahan electrical balance

Figure 6. Schematic diagram of the microbalance test apparatus.

42
APPLICATIONS
Quasi-Isostatic Procedure

A limited number of penetrant/polymer film combinations have
been studied using the quasi-isostatic procedure and test
apparatus described above. Interested readers are referred
to Baner et al. (1986) and Baner (1986) for detailed summary
of these findings. In this review two examples are presented
on the diffusion of toluene vapor through polypropylene
based structures:

1) Two ply coextruded Oriented Polypropylene, 2.3x10-5 m
(0.9 mil) thick; and

2) Two side acrylic heat seal coated, biaxially oriented

polypropylene, 2.4x10-5 m (.93 mil) thick.

Those fims were supplied by Mobile Cemical Corporation and
were identified as Bicor 90 and Bicor 310 respectively. The
results are presented in Table 1 and Figures 7 and 8.

As shown, the permeation behavior of the films had an
initial non-steady state period followed by steady state
constant flow portion. The shape of the curve indicated that
the diffusion process was fickian even at the higher
concentration values.

The results of these studies clearly showed the flux or
permeability rate to be affected drastically by the level of

vapor concentration.

43

TABLE 1. Permeability and lag time diffusion coefficients

for toluene vapor in selected polypropylene based

 

 

structures.
Film Toluene Temp. Flux Lag
Structure Concent. Time
(ppm) (00) (mg/hr.m2) (min)
Bicor 90 28 22 6.0 54
33 22 17.0 96
74 22 900 24
84 22 900 24
Bicor 310 39 22 .02 --
73 22 23 1920
88 22 400 108

120 22 2200 36

 

44

 

 

 

 

500 P
84 ppm
72°F
13 4£X3_.
0
“
m
o
E
B
n. 300 -
E
3 28 ppm
3 20° ' 72°F
.‘2’
2
O
100 -
l L I
2 4 6 8 10

time, hours

Figure 7. Effect of penetrant concentration on the trasmission
of toluene vapor at 23.0 C through coextruded OPP.

1400

1200

1000 '

 

I
1600 I 3399'"
I
I
I
I

O Micrograms Permeated

§ §fi§ §

 

45

 

73 ppm
time, hours

39 ppm

 

i .

100

Figure 8. Effect of penetrant concentration on the trasmission
of toluene at 23.0°C through biaxially oriented polypropylene

acrylic coated.

46

Since the change of the lag time values are not equally
affected, it may be suggested that sorption behavior of the
toluene into the polypropylene structure, as a function of
concentration, is a dominant phenomenon. This behavior is
normally related to configurational changes and alteration

of the polymer chain conformational mobility.
Isostatic Procedure

Equation (5) can be written as:

A = XII2 exp (-X) (21)

where

A = -——

(22)

:3
A

D DID'
rt 3
\J
n

and

4Dt

To solve the non-linear equation (22), the Newton Raphson

method can be used, Chapra and Canale (1985). In this case,
eqn. (22) is written as,

1/2

c = x exp (-X) - A = 0 (23)

A iteration calculation method for eqn. (23) can be
implemented to solve for X, Hernandez (1984).
This procedure can be applied to both organic vapors and

gases.

47

In Table 2 data are shown for the permeation of oxygen
through an amorphous polyamide.

The diffusion coefficient is calculated from the slope of a
linear regression analysis of l/X versus time. For the

10

values shown in Table 2, D was 6.73x10— cmz/sec, and the

correlation coefficient was .998.

Sorption procedure

1/2 for d-limonene

Shown in Figure 3 is a plot of Mt/Ma,vs. t
sorption by a laminate structure made of High Density
Polyethylene (HDPE) and a sealant (blend of ethylene vinyl
acetate/surlyn ionomer/polubutylene). The sorption
experiment was carried out at vapor concentratiion of 1.5
ppm (mg/1). Also shown in Figure 3 is the sorption profile
obtained by subatitution into eqn. (11), the diffusion
coefficient was calculated by eqn. (12). As seen, good
agreement was obtained between the experimental and
calculated sorption curve, supporting the theory that at low
penetrant concentration the diffusion process is fickian.
Mohney et a1. (1986) have shown, however, that for HDPE at
d-limonene concentration higher than 5 ppm there is an onset
of non-fickian relaxation controlled sorption, which results
in an uptake larger than the expected. Similar sorption

behaviors has been described by Berens (1977), Bagley and
Long (1958) and Fujita (1961).

48

TABLE 2. Values for eqn. (23) obtained for the system

Oxygen/Nylon 6I/6T, at 22.00C and water activity = 0.441.

 

 

Time (min) Flow Percent 1/X
30 .56 .611
33 .63 .676
36 .67 .727
39 .72 .794
42 .76 .852
45 .79 .912
48 .81 .960
51 .83 1.006
54 .86 1.078
57 .87 _ 1.108
60 .89 1.165
63 .90 1.218

66 .91 1.247

 

49

For the sorption process of HDPE/sealant laminate film
sample and d-limonene vapor concentration of 1.5 ppm,

10

calculations gave a D = 4.3x10- cmZ/sec and a solubility

3

coefficient, 8 = 7.6x10- g of limonene per gram of polymer

structure.
SUMMARY

For penetrant such as organic vapors which can exhibit
physicochemical interactions with a polymer matrix, the
diffusion coefficient D, solubility S, and permeability P
should be determined experimentally in order to describe
accutarely the mass transfer behavior of penetrant /barrier
system. Concentration and time dependent processes should be
also considered when dealing with organic penetrants.

In terms of practical applications, the loss of volatile
aroma compounds from a polymeric package system can be the
result of both sorption and permeation process and both
mechanism must be considered for the prediction of changes

in the quality of a packaged product.

1.

4.

50

REFERENCES

ASTM Designation E96-66, Standard Method of Test for Water

Vapor Transmission of Materials in Sheet Form.

ASTM Designation D3985-81, Standard Method of Test for Oxygen
Gas Transmission Rate Through Plastic Film and Sheeting Using

A Coulometric Sensor.

. Bagley, E. and Long, F.A. , “Two-Stage Sorption and Desportion

of Organic Vapor in Cellulose Acetate," J. Am. Chem. Soc.,

77:2172(l958) .

Baner, A.L., Hernandez, R.J., Jayaraman, J., and Giacin, J.R.,
"Isostatic and Quasi-Isostatic Methods for Determining the
Permeability of Organic Vapors Through Barrier Membranes," in
Current Technologies in Flexible Packaging. ASTM STP
912(1986) .

Baner, A.L. , "Diffusion and Solubility of Toluene in Polymeric
Films," Presented at the 13th Annual IAPRI Symposium, Oslo,

Norway (May, 1986).

Beck, J .V. and Arnold, R.J., Parameter Estimation in
Engineering and Science, John Wiley and Son, New York, NY

(1977).

10.

11.

12.

13.

51

Barrer, R.M. , “Permeation, Diffusion and Solution of Gases in

Organic Polymers,“ Trans. Faraday Soc., 35:628 (1939).

Berens, A.R., “Diffusion and Relaxation in Glassy Polymer
Powders: 1. Fickian Diffusion of Vinyl Chloride in Poly (Vinyl
Chloride), Polymer, 18:697 (1977).

Berens, A.R., "Analysis of Transport Behavior in Polymer

Powders," J. Membrane Science, 3:247 (1978).

Bischoff, M. and Everer, P., "Effect of Orientation on the
Sorption of Toluene by High Density Polyethylene,“ J. of
Membrane Sci. 23:333 (1984).

Caldecourt, V. and Tou, J., "Atmospheric Pressure Ionization
Mass Spectrophotometric and Photoionization Techniques for
Evaluation of Barrier Film Permeation Properties," TAPPI
Proceedings, Polymers, Laminations and Casting Conference, 441

(1985).

Chapra, S.C. and Canale, R.P., Numerical Methods for

Engineers, McGraw-Hill Book Company (1985).

Choy, C.L., Leung, W.P., and Ma, T.L., “Sorption and Diffusion
of Toluene in Highly Oriented Polypropylene," J. Polymer
Science: Polymer Physics Edition, 22:707 (1984).

14.

15.

l6.

17.

18.

19.

20.

52

Crank, J. and Park, G.S., Diffusion in Polymers, Academic

Press, New York, NY (1968).

Crank, J., The Mathematics of Diffusion, 2nd Edition,

Clarendon Press, Oxford, England (1975).

DeLassus, P., "Transport of Unusual Molecules in Polymers
Films," TAPPI Proceedings, Polymers, Laminations and Coating

Conference, 445 (1985).

Fujita, J., "Diffusion in Polymer-Diluent Systems," Fortsch-

Hochpolym-Forsch, 3:1 (1961).

Gilbert, S.C., Hatzidimitriu, E., Lai, C., and Passy, N.,
"Studies on Barrier Properties of Polymeric Films to Various

Organic Aromatic Vapors," Instrumental Analysis of Food, 1:405

(1983).

Han, J.K., Miltz, J., Harte, B.R., Giacin, J.R. and Gray,
J.I., "Loss of 2-tertiary-butyl-4-methoxy phenol (BHA) from
High Density Polyethylene Film," Polymer Engineering and

Science (1986) .

Hernandez, R.J., "Permeation of Toluene Vapor Through Glassy
Poly(ethylene) Terephthalate Films," M.S. Thesis, Michigan

State University, East Lansing, MI 48824-1223 (1984).

21.

22.

23.

24.

25.

26.

53

Hilton, B.w. and Nee, S.Y., "Permeability of Organic Vapors
Through Packaging Films," Ind Eng. Chem. Prod. Res. Dev.,
17(1):80 (1978).

Meares, P., "Transient Permeation of Organic Vapors Through

Polymer Membranes," J. Appl. Polymer Sci., 9:917 (1965).

Mohney, S., Hernandez, R.J., Giacin, J.R., and Harte, B.R.,
"The Aroma Permeability of Packaging Films and Its
RelationShip to Product Quality," Presented at 13th Annual

IAPRI Symposium, Oslo, Norway (May, 1986).

Murray, L.J. and Dorschner, R.W., "Permeation Speeds Tests,
Aids Choice of Exact Material," Package Engineering,‘March:76
(1983).

Murray, L.J., "An Organic Vapor Permeation Rate Determination
for Flexible Packaging Materials," J. Plastic Film and
Sheeting, 1:104 (1985).

Niebergall, W., Humeid, A., and. Blochl, W., "The Aroma
Permeability of Packaging Films and Its Determination by Means
of a Newly Developed Measuring Apparatus," Lebensm. Wiss U.

Technol., 11(1):1 (1978).

27.

28.

29.

30.

31.

32.

54

Pasternak, R.A., Schmimscheimer, J.F., and Heller, J., "A
Dynamic Approach to Diffusion and Permeation Measurements,"

J. Polymer Sci. Part A-2, 8:467 (1970).

Peterlin, A. , "Dependence of Diffusive Transport on Morphology
of Crystalline Polymers," J. Macromol. Sci. Phys., Bll(1):57
(1975).

Pye, D.G., Moehr, M.M., and Panar, M., "Measurement of Gas
Permeability of Polymers, II. Apparatus for Determination of
the Permeability of Mixed Gases and Vapors," J. Applied
Polymer Sci., 20:1921 (1976).

Smith, T.L. and Adam, R.E. , "Effect of the Tensile Deformation
on Gas Transport in Glassy Polymer Films," Polymer, 22(3):299
(1981).

Ziegel, K.D., Frensdorff, B.R., and Blair, D.E., "Measurement
of Hydrogen Isotope Transport in Poly(Vinyl Fluoride) Films
by Permeation Rate Method," J. Polymer Sci., Part A-2, 7:809
(1969).

Zobel, M.G.R. , "Measurement of Odour Permeability of
Polypropylene Packaging Films at Low Odourant Levels," Polymer
Testing, 3:133 (1982).

33.

34.

55

Zobel, M.G.R. , "Aroma Barrier Properties of Coextruded Films,"
Presented at COEX‘84 in Proceedings of the 4th Annual
International Conference and Exhibition on Coextrusion Markets

and Technology, September 19-21, Princeton, NJ (1984).

Zobel, M.G.R., "The Odour Permeability' of Polypropylene

Packaging Film," Polymer Testing, Vol. 5, No. 2:153 (1985).

CHAPTER II

The Sorption of Water Vapor by an Amorphous Polyamide **

am

The dual-mode sorption model presented here was found to describe

accurately the sorption of water vapor by an amorphous polyamide at 230 C
over a broad range of water activity. The Langmuir equation is used to
calculate the volume fraction of chemisorbed solute and the Flory-Huggins
equation is used instead of Henry's Law to calculate the volume fraction of
water which is not chemisorbed. This model describes the data over the
range of water activities from zero to one and predicts clustering of the
sorbant. Fourier Transform Infrared (FTIR) spectroscopy data and dielectric
measurements of the gamma relaxation temperature suggest that the water
binds to amide groups at low water activities. This physical evidence of
binding corresponds well with the predictions of the Langmuir factor of the

sorption model.

 

** Paper submitted to the Journal of Membrane Science.

56

57

W

An amorphous polyamide recently has been synthesized and characterized
[1]. This polymer is made from hexamethylenediamine and a mixture of
isophthalic and terephthalic acid. The random placement of these isomers in
the polymer chain prevents crystallization of the material. Preliminary
studies on the effect of water sorption on the barrier properties of this
amorphous polymer show atypical behavior, compared to semicrystalline
polyamides. For example, oxygen permeability increases as a function of
moisture content in Nylon 66 (a semicrystalline polyamide) but decreases as
a function of moisture content in amorphous material. The tensile modulus
decreases with moisture content in Nylon 66 but increases with moisture
content in the amorphous material [1].

The intriguing behavior of the amorphous polyamide system in the
presence of water demonstrates the need for equilibrium models which
describe sorption phenomena well over a wide solute activity range.

Improved models are needed for binary systems and hopefully can be extended
to describe ternary systems (non-condensible gas - water - polymer) in order
to interpret and control barrier properties. This study models the sorption
phenomena of water vapor into amorphous polyamide as the first step in
describing the effects of water on the barrier and mechanical properties of

this polymer.

58

W

Model for Gas Sorption in Glassy Polymers

Sorption of gases, such as helium, nitrogen, oxygen, carbon dioxide,
and methane above their critical temperature, into glassy polymers has been
studied by many researchers. The dual mode sorption model proposed by
Michaels et a1 [2] is the most widely used model for analyzing these data.
This model assumes that the solute molecules in the glassy polymer consist
of freely diffusing and bound species which are in dynamic equilibrium with
the medium. The solubility of the freely diffusing species is represented
by Henry's Law and the solubility of the bound species is described by a
Langmuir type adsorption isotherm. Local equilibrium between the freely
diffusing and the bound species is maintained throughout the polymer matrix

[3]. The model is:

C ' b
C - CD + CH - kD p + B (1)
1 + b p

where C is the total solubility of sorbant in the polymer, CD and CH are the
solubilities due to Henry's law and Langmuir sorption, kD is the Henry's law

constant, b is the hole affinity constant, CH. is the hole saturation

constant and p is the pressure. The plot of the penetrant solubility, C, as
a function of pressure for eqn 1 is always monotonically convex to the
pressure axis.

This model has been used to describe the solubility of gases in glassy

polymers, and in glassy, polar polymers as well. Uragami et al [4] studied

59

the sorption and equilibrium for CO2 in a polyimide film for pressures up to

0.78 atmospheres. Chern et al [5] applied eqn 1 to the permeability of CO2

through Kapton polyimide for pressures up to 16.3 atmospheres. Koros and
Sanders [6] described a bicomponent sorption process by the dual mode

sorption model (COZ/C2H4 and COZ/NZO in poly(methyl methacrylate)). Henry’s

law is an adequate description of the solubility for many gases, although it

may fail at high solute activities.

Models for Polar Systems at High Solute Activities

Solutes below their boiling point (such as organic solvents and water
at room temperature) often exhibit an inflection point in the solubility
versus pressure curve. For these cases, eqn. 1 does not describe the data

well over the activity range, 0 < a1 < 1, and usually underpredicts the

actual solubility values at high activities. This lack of agreement has
been explained as a "positive deviation" of the Henry's law caused by the
swelling of the polymer network as the penetrant is sorbed. It is
postulated that the network swelling exposes more binding sites and
increases the sorption level of the penetrant synergistically [3].

Table 1 lists some recent data sets for polar systems at high solute

activities and models used to describe the solute solution factor (CD of

eqn. 1) for these data. The Henry's Law description of solute solution has
been modified to include a concentration effect [8], [10]. In the case of
vinyl chloride/poly(vinyl chloride), the new term has been related to the

Flory-Huggins equation. Berens [9] reported that this equation adequately

60

Table 1. Models for Polar Systems at High Solute Activities

 

 

System Solution Factor Comment Ref.
HZO/Polyacrylonitrile kd exp(oc) p data of [7] [8]
Vinyl Chloride/Poly- Flory-Huggins1 fits for O<a1<l [9]

(vinyl Chloride)
kd exp(oc) p data of [9] [10]
a - 2(1+x)A
HZO/Kapton2 kd p [11]
3 1,4
HZO/Nylon 6 Flory-Huggins fit by authors [12]
HZO/Epoxy5 kd p hysteresis [13]
HZO/Epoxy6 kd - exp(l+x) two Langmuir factors [14]

 

l - Flory-Huggins model only, no Langmuir term

2 - Registered trademark, 3.1. du Pont de Nemours and Company, for a

aromatic polyether diimide.

3 - trademark of E.I. duPont de Nemours, Inc.

4 - best fit model as determined by authors of this work.

5 - TGDDM/DDS epoxy resins (MY720, Ciba-Geigy, Ltd.)

6 - DBEBA/TETA (Epikote 828, Shell. Italy) and TBDDM/DDS (Araldite MY720

Ciba-Geigy, Ltd.)

61

described his data. For high molecular weight polymers, the Flory-Huggins

expression [15-17] is:

2
ln a1 - 1n V1 + V2 + x V2 (2)

where x is the interaction parameter. Although eqn. 2 does not provide the
most accurate description of the thermodynamic performance of polymer
solutions, it does contain most of the essential features which distinguish
such solutions [18]. Eqn. 2 usually fits equilibria data over a wider range
than Henry's law. For example, sorption data of toluene in poly(vinyl

chloride) is well fit by the Flory-Huggins equation especially for 0.5 < a1

< 1.0 [19].

Sfirakis and Rogers [12] studied the sorption of vapors by Nylon 6
but did not present a mathematical model to describe the sorption process.
However, this data set can be fit to eqn. 2 with a x value of 1.88. The
Henry's Law term seems adequate for fitting the water/Kapton data. Either
hole filling or chemisorption might be occurring in the polyimide for the
Langmuir contribution, as Kapton is known to hydrogen bond with water.
Water is known to hydrogen bond with a variety of epoxies and the dual mode
sorption model describes some data well [13]. Apicella et a1 [14] tested
the hole-filling hypothesis with an epoxy system by sorbing water between 0
and 60 atm. Two Langmuir factors were needed to model these data: one for
chemisorption (probably to hydroxyl or secondary amine groups) and one for
sorption into holes. The use of eqn. 2 to describe solvent solution seems
an obvious extension of the work summarized in Table l. The constant I

describing solute solution is usually determined at high solute

62

pressures. It would be desirable to develop criteria for determining how to

choose the constants.

W

Self-association of the solute to form clusters has been used to
explain a number of transport phenomena occurring in polar systems. For
example, the clustering of water molecules in polyacrylonitrile coincides
with a maximum in the diffusion coefficient [20]. Clustering could reduce
the effective mobility of water since the size of the diffusing group
increases. A similar effect has been reported for Kapton by Yang et a1
[11]. The authors calculated the clustering of water by differentiation of
a fourth order polynomial fit. Puffr and Sabenda [21] reported the
clustering of water in several polyamides. Skirrow and Young [22] described

the clustering of water, methanol and propanol in Nylon 6 by plotting al/V1

versus al. In Nylon 6, clustering has been associated with a change in the

diffusion coefficient [12]. Aronhime et a1 [23] reported clustering of
water in epoxy resins. It would be useful to predict the onset of
clustering by direct analysis of the model used to describe the solute
sorption.

The clustering function developed by Zimm and Lundberg [24-25] has been
used with binary systems in equilibrium to give a measure of the tendency of

like molecules to cluster. Their clustering function, Gll/Vl’ is:

11 - - v 5 (a1/V1) - 1 (3)

63

where V1 is the volume fraction of the solute, V2 is the volume fraction of
the polymer, and a1 is the solute activity. When Gn/V1 is greater than -1,

the solute is expected to cluster.

Equation 1 is not written in a convenient form for the analytical
determination of the derivative in eqn 3. Popular methods for evaluating
the clustering function are either fitting activity versus volume fraction
data with polynomials and taking their derivatives or doing a numerical
differentiation of the data. Equation 1 can be rearranged to express the
concentration, C, as volume fraction and to express the Henry's law and

Langmuir contributions in terms of activity:

V1 - V1 + V1 - KD a1 + 1 (4)

l + B a1

.where V H and V

1 1L are the Henry's law and Langmuir volume fraction

contributions, KD - kD ps, K - C ' f b p8, B - b p8, ps is the saturation

H
vapor pressure of the solute and f is a conversion factor. Applying eqn 3

to eqn 4 gives:

2
11 _ _ V2 V1 - [KD a1 + K al/(l + B a1) ] (5)

 

2

V V1

Since the term in brackets is always less than V1, Gll/V1 is always less
than -1 for the range, 0 < a1< 1. Therefore, a system which follows Henry's

law solubility and Langmuir binding should not have clustering.

64

The clustering function for the Flory-Huggins equation has been derived

previously [26] and is:

> -1 (6)

 

V1 1 - 2 x V

l
for a constant value of x. eqn 6 always predicts clustering in the range, 0

< V1 < l/2x. The equation is not defined at the upper limit of the range
(Vl - l/2x), which is the spinodal point indicating phase separation.

Neither the conventional dual mode sorption model or the Flory-Huggins model
with a constant value for x correctly describe the apparent clustering in
the systems mentioned above (Table 1).
M d d u

In this study, eqn 1 has been modified by using the Flory-Huggins
equation to describe non-specific solution rather than Henry's law. This

modification should allow the model to fit over the activity range, 0 < a1 <

1. Other choices for the solution model are possible, but the Flory-Huggins
equation is relatively simple to apply. Because the non-specific sorption
term is nonlinear, the complete model can have an inflection point and
should predict clustering somewhere over the range of activity values. For
convenience, the modified dual mode sorption model is expressed in terms of

volume fractions and solute activity:

1 + V1 (7)

65

where V1FH refers to the Flory-Huggins contribution to the solute volume
fraction. Since eqn 2 is nonlinear, it is convenient to determine the value
for V1FH by numerical methods, such as the Newton-Raphson technique and eqn

7 becomes:

K a

 

V1 - FH (a1, X) +- ______1__ (8)
l + B a1
The clustering function based on eqn. 8 is:
G V K a V PH 1
_11 - _.Z __l._ + 1 - __ (9)
2 2 FR FH
V1 V1 (1+3 a1) l-V1 (1+2sz ) V1

Equation 9 predicts clustering for some values of the constants but is
undefined when:
1-v1m(1+2xv2m)-0 (10)

This occurs when V1 is 1.0 (pure solvent) or l/2x (phase separation).

W

Pol er ms

The amorphous polyamide used in this study was provided by E. I. du
Pont De Nemours and Company. The polymer was synthesized from hexamethylene
diamine and a mixture of 70/30 isophthalic and terephthalic acids. The

random placement of the acid isomers in the polymer chain prevents

66

crystallization. No evidence of a crystalline melting point was found for

this polymer.

Equilibrium Sorptign Data

Equilibrium sorption data was taken on polymer films using a Cahn
Electrobalance Model RG. A stream of nitrogen adjusted to specific values
of water activity provided the source of water vapor in equilibrium with the
polymer films. The apparatus and operation are described elsewhere [27].
Closed containers with salt solution to provide selected values of water
activity were also used. The experiments were conducted at room

5

termperature. The film samples, of 2.93 x 10- m thickness (1 mil), were

dried under vacuum at 1000 C before each run.

De it
Film densities were determined in a density gradient column with the

gradient made of toluene and carbon tetrachloride.

Fourier T s o d

The sample for infrared analysis was prepared by casting a thin film
onto a zinc sulfide (ZnS) crystal from a 2% solution with l,l,l,3,3,3-
hexafluoro-Z-propanol (Kerr Company, Novi, Michigan). After evaporation of
the solvent at room temperature, the sample was dried in a vacuum oven at
1000 C to remove residual solvent and water. The sample was then

equilibrated with water vapor at selected water activity values. After

67

attaining equilibrium, the sample was immediately covered with another

crystal of ZnS and transferred to the instrument.

Diffe ential ca n a e e 5
Film samples were prepared for these analyses by vacuum drying at 1000
C and equilibrating with the vapor over salt solutions to give selected

water activities.

W191!

Equilibrium Sogptiog Isgthgzm

Sorption equilibrium values of water weight fraction and volume
fraction in the amorphous polyamide at 230 C are presented in Table 2.
Experimentally determined and calculated densities for the water-polymer
solution also are presented. Isotherm data was obtained over a wide
activity range (0.046 < a1 < 0.96) in order to provide a good test of the
modified dual mode sorption model. Figure 1 shows the sorption isotherm for
water in the amorphous polyamide. - ~ The solid curve
through the data is the Flory-Huggins equation (eqn 2) with a x value of
1.632. The value of the interaction parameter was calculated by using a
Box-Kanamazu modification of the Gauss method of minimization of sum of
squares for nonlinear models [28]. This model represents the data at high

activities very well.

68

 

Table 2. Experimental Data
Temperature: 23C

Water Uptake Uptake Experim. Calcul. weight Volume

Activity Weight Percent Density Density Fraction Fraction
0.0000 0.00000 0.0000 1.1938 1.1938 0.00000 0.00000
0.0460 0.00470 0.4700 --- 1.1939 0.00468 0.00560
0.0560 0.00657 0.6572 --- 1.1940 0.00653 0.00781
0.0720 0.00752 0.7520 --- 1.1941 0.00746 0.00893
0.0800 0.00787 0.7870 1.1938 1.1942 0.00781 0.00935
0.0900 0.00836 0.8360 --- 1.1943 0.00829 0.00992
0.1100 0.00938 0.9380 --- 1.1944 0.00929 0.01113
0.1550 0.01211 1.2110 --- 1.1950 0.01197 0.01433
0.1890 0.01290 1.2900 --- 1.1955 0.01274 0.01526
0.2520 0.01670 1.6700 --- 1.1964 0.01643 0.01970
0.2690 0.01596 1.5960 --- 1.1967 0.01571 0.01884
0.3080 0.02200 2.2000 1.1975 1.1973 0.02153 0.02583
0.4100 0.03040 3.0400 1.1986 1.1989 0.02950 0.03545
0.4400 0.03568 3.5680 --- 1.1993 0.03445 0.04142
0.5650 0.04180 4.1800 --- 1.2008 0.04012 0.04829
0.5800 0.04580 4.5800 --- 1.2009 0.04379 0.05272
0.5850 0.04340 4.3400 --- 1.2010 0.04159 0.05007
0.6350 0.05050 5.0500 1.2012 1.2014 0.04807 0.05789
0.7350 0.06190 6.1900 1.2017 1.2019 0.05829 0.07022
0.7900 0.07110 7.1100 --- 1.2020 0.06638 0.07998
0.8600 0.07870 7.8700 --- 1.2021 0.07296 0.08791
0.8800 0.08200 _ 8.2000 1.2022 1.2022 0.07579 0.09132
0.9630 0.09000 9.0000 1.2022 1.2024 0.08257 0.09951

Volume Fraction x (E + 03]

B}
CD

69

 

100 -
—Florv-lluuins
a Experimental .
80 -
60 -
40 r-

 

: l 1 L I 1
0 .2 .4 .5 .8

Water Act!

Figure 1. Experimental sorption values and Flory-Huggins
fitting.

    
 
  
 
 
 
 
 

 

1.0

70

Parameter stimatio o E us 7

Parameter values estimated for eqn 7 were sensitive to the method used
to determine them. A nonlinear regression method was used to determine the
values of the three parameters simultaneously. This resulted in Langmuir
coefficients with a high amount of error and a fit using eqn 7 which was no
better than the fit using eqn 2. The least squares technique was not
sensitive to deviations between the data and the model at low activities.
However, the deviation of eqn 2 from the data is systematic. Figure 2 shows
an expanded view of the low water activity data and the underprediction of
eqn 2.

An alternative parameter estimation method gave coefficients with lower
error. The data for a1 > 0.4 were used to determine a range of x values
which could represent this portion of the curve. x should be between 1.6
and 1.85 to minimize the least square error for this data set. The data for
a1 < 0.4 were used to determine the Langmuir coefficients. The nonlinear
regression method gave the coefficients and the R2 parameter for a set of X
values in this range. The R2 value was plotted as a function of x to find
the best estimates of the parameters. Figure 3 shows eqn 8 as the solid
curve (x - 1.7, K - 0.395 and B - 95.2) and the complete data set. Table 3
shows the contribution of the Langmuir and Flory-Huggins factors to the
solute volume fractions over the activity range. At low activities, the
Langmuir contribution is high compared to the Flory-Huggins contribution and
at a1 - 0.4, it is just over 10% of the total volume fraction of solute.

The Langmuir contribution is nearly constant (> 90% of its maximum value) at
activities greater than 0.11 and the curve at high water activities should
be insensitive to the values of the Langmuir coefficients. Therefore, the

estimation method is consistent with the parameter values.

Volume Freotlon x (E + 03)

71

 

—FIorv-Ilogoins a
a Experimental

hi
:3

d
C:

 

 

 

0J— ' I I

0 .l .2 .3 .4
Water Activity

Figure 2. Experimental sorption values and Flory-Huggins fitting
at low activity values.

72

 

100

    
   
  

— tang. + Fii
a Experimental

CD CD
CD :3
I I

Volume Fraction x (E + 03)
a
l

 

l l l l J I

.4 .o .8 1.0
Water Activity

 

   

 

Figure 3. Best fit for the Langmuir-Flory-Huggins model.
Values of the parameters are7-= 1.70, K = .385 and B -= 95.15.

73

 

Table 3. Langmuir and Flory-Huggins volume fraction contributions.

x - 1.7

k - .384707

B - 95.14954
Activity Lang. F-H Total
0 0 0 0
.01 1.9713458-03 6.7405093-04 2.6453968-03
.02 2.6504188-03 1.3521268-03 4.0025458-03
.03 2.9942288-03 2.0342783-03 5.0285078-03
.04 3.2019022-03 2.720568-03 5.9224628-03
.046 3.2912265-03 3.1343323-03 6.4255588-03
.056 3.4042853-03 3.827329E-03 7.2316153-03
.072 3.5281782-03 4.9450292-03 8.4732085-03
.08 3.5736998-03 5.5080513-03 9.0817498-03
9.000001E-02 3.620418-03 6.215795E-03 9.8362048-03
.11 3.6905748-03 7.6447413-03 1.1335312-02
.155 3.7864432-03 1.09277eE-02 1.471418E-02
.189 3.8301963-03 1.347346E-02 1.7303662-02
.252 3.8813112-03 1.8349342-02 2.2230658-02
.269 3.8911573-03 1.9702435-02 2.3593598-02
.308 3.9097718-03 2.2870325-02 2.6780093-02
.41 3.9421328-03 3.1612522-02 3.5554655-02
.44 3.94886E-03 .0343221 3.8270963-02
.565 3.9693493-03 4.6401532-02 5.0370882-02
.58 3.9712233-03 4.7946433-02 5.1917665-02
.585 3.9718263-03 4.8466413-02 5.243823E-02
.635 3.9773555-03 5.381052E-02 5.778788E-02
.735 3.9861875-03 6.538535E-02 6.9371543-02
.79 3.9900998-03 7.2345758-02 7.633585E-02
.86 3.9943688-03 8.194831E-02 8.5942688-02
.88 3.9954632-03 8.4867963-02 8.8863423-02
.963 3.9995312-03 9.7993338-02 .1019929

74

Sensitivit Coef ent

Sensitivity coefficients indicate the magnitude of the change of a
function due to perturbation in the values of its parameters [28].
Sensitivity coefficients for eqn 8 are given by the first derivative of the

volume fraction with respect to x, B and K.

XK_5V1-_31 (11)
6 K 1 + B al
6 V -K a 2
XB-__1-_1_ <12)
6 B (l + B a1)2
m m
xx-L‘ii-‘h—YL (13)
5x 2v1FH-1

Where XK’ XB’ and XX are the sensitivity coefficients of K, B and x. These
coefficients were evaluated as a function of activity, al. at the optimum
values of K, B, and x and the results are plotted in Figure 4.

For a1 > 0.1, XX changes with activity while XR and XB are essentially
constant. For high activity values, it will be difficult to distinguish
between K and B parameters. At low activity values, they are non-linear
dependent and better estimates for them can be obtained. The results shown
in Figure 4 suggest that a simultaneous search for the three parameters will
be difficult over the entire activity range, that high activity data will be
insensitive to K and B, and that the best estimates for K and B will be
obtained at low activity values. Eqs. 11-13 give a protocol for evaluating

the method of determining the constants and are an improvement over the

75

 

 

 

 

 

 

 

-1 5 1 1 1 1 1 1 1 1 1
0 .2 .4 .6 .8 I . 0
WI!" Activity

Figure 4. Sensitivity coefficients as a function of activiy.

76

 

 
 
  

 

 

 

 

1.0
Langmuir-FIory-liuppins (eqn. 01— 4
3th. Order Polynomial ---
4th. 0rder Polynomial ---°
0.8 -
3' 0.0 h
E
‘5
a:
0.4 -
0.2 -
0.0 ' 1 1 1 1 1 1
-3l -21 -II -I 4

Cluster Function

Figure 5. Clustering function as a function ofactivity.

77

suggestion that the constant(s) for the solution phenomenon should be
determined when the solute partial pressure is much larger than the Langmuir

affinity constant, b [10].

Clustering Analysis

Equation 9 and polynomial expressions were used to compute the
clustering function for the water sorption data. The polynomial expressions
fit the data with similar least square errors. Both expressions approached
but did not pass throught the zero activity-zero volume fraction point, and
neither expression replicated the S-shaped curve of the data. Figure 5
shows the clustering function estimated from two polynomial fits (third and
fourth order) and the modified dual mode sorption model. All three
equations predict clustering (Gll/V1 > -1) but differ in the solute activity
at which this should occur. The fourth order polynomial predicts clustering

in the activity range, 0.34 < a < 0.96. The third order polynomial

1
predicts clustering for a1 > 0.27 but the clustering function does go
through a maximum at a1 - 0.60. There is no obvious physical explanation

for why clustering should decrease, or disappear, at high water activities.

78

Equation 9 predicts clustering at a1 - 0.38 and the function is increasing

monotonically over the whole activity range.

Ph sica vi e e fo 0 u e

The Langmuir isotherm was derived based on chemisorption of a chemical
species to a specific binding site characterized by a single activation
energy. Solute sorption described by this isotherm for the water-polyamide
solution might result in observable changes in physical properties of the
polymer, particularly if the water is associated with a specific group on
the polymer backbone. One obvious possibility is water interaction with the
amide group. FTIR spectroscopy studies were done to detect possible changes
in hydrogen bonding between N-H and carbonyl groups by observing the
vibrational modes of the amide group (Amide I and Amide 11 bands).

The Amide I mode includes contributions from C-O stretching, C-N
stretching and C-C-N deformation vibrations. The Amide II band includes N-H
plane bending, C-N stretching and C-C stretching vibrations. Figure 6 shows
a typical FTIR spectrum taken at room temperature over the range, 800-4000
cm'1 for a cast polyamide sample. The Amide I and Amide II modes occur at
1640 and 1541 cm'l, respectively, for the dry sample and are the most
intense bands. The frequency scale and the relative intensity of the Amide
I and Amide II modes were internally calibrated with reference to the CH2
stretching band at 2858 cm-1. Table 4 lists the absorption frequencies, and
Table 5 lists the intensity ratios for the Amide I and Amide II bands of the
sample recorded as a function of water volume fraction and activity. The
frequency of the CH2 stretching band, which served as the interal

calibration band, is presented for reference. Figure 7 shows the absorption

79

 

 

 

 

 

 

 

 

too
80 '-
5
la; all"-
.2
g 1
a .—
,: 40 i? :5 U u
_ Z 9
20 - :3
ES
- SE
‘3
‘I l l . l l,
4000 3000 2000 1000 1200
cm"1

Figure 6. Typical FTIR spectrum of the amorphous polyamide
recorded at room temperature.

80

Table 4. Amide I, Amide II and CH absorption frequencies.

 

Activity CH Peak Amide I Amide II
0 2858 1640 1541
0.08 2858 1640 1545
0.308 2858 1641 1545
0.56 2858 1641 1545
0.88 2858 1641 1546

Unite: cm

 

Table 5. Intensity ratios of Amide I and Amide II with respect to CH bands.

 

ACTIVITY AHIDE I / C-H AHIDE II / C-H
0 1.77 5.47
0.08 1.78 5.44
0.308 1.87 5.11
0.56 1.80 5.43

0.88 1.84 5.14

81

 

 

 

 

 

 

1.8
8.8 ' n
8.8 -
= 1
g ,
3 ' / ‘
88
a
C
8.4 F “W
8.2 - -
o.o' - . . .
1888 1588 1528
cm"1

Figure 7. Spectrum region of Amide II as a function
of activity.

82

region from 1500 to 1600 cm.1 (Amide II mode) as a function of al. The
spectrum are displayed on an absolute absorbance scale.

The Amide I band remained essentially constant at 1640 cm.1 as did its
intensity. The peak maxima of the Amide II band shifted to higher
frequency, 1541 to 1546 cm'l, over the range, 0% to 9.1%, water volume
fraction. The intensity ratio of the Amide II band remained essentially
constant. The shift of the Amide II band to higher frequency with
increasing water content is consistent with an increase in the average
hydrogen bond strength [29]. These data suggest that the water does not
change the hydrogen-bonding strength of the carbonyl group but does change
the hydrogen bonding strength of the N-H group. The shift in the Amide II
band is completed at the water activity at which 90% of the Langmuir sites
would be filled (Table 3).

In linear, aliphatic homopolyamides there is essentially 100% hydrogen
bonding, as evidenced by the absence of bands in the infrared spectra above
3300 cm"1 [30]. In structurally irregular copolymers, such as amorphous
polyamide, both the N-H stretching region and the Amide11.region can be
resolved into "free” and hydrogen bonded stretching modes. Skranovek et a1
[29] resolved the N-H stretching region into three components: a "free" N-H
mode, a hydrogen-bonded N-H stretching mode and an Amide II mode. The Amide
I band was resolved into a ”free" and hydrogen-bonded carbonyl mode.

Most of the first water molecules sorbed form hydrogen bonds with the
"free" N-H groups of the amorphous polyamide. This would be an exothermic
process and should have a single activation energy associated with it. The
formation of these new hydrogen bonds should have a negligible enthalpic
effect [21],[31]. The extent of disruption of the self-association of

polyamide neighboring groups by water molecules is not known. Both the

83

model and the FTIR data suggests that chemisorption has been completed at
activities well below those at which clustering occur.

At a water activity of 0.08 (where the Langmuir sites are 89%
saturated), the total amount of chemisorbed water is only 4% of the total
water volume fraction. This amount corresponds to 3.34 x 10"3 g of water
per gram of polymer, or one molecule of water per 22 repeating units of the

polymer. Each repeat unit contains 2 amide groups so only 2.3% of the amide

groups available form hydrogen bonds with water.

Relaxation Temperatures

Several relaxation temperatures have been described for semicrystalline
polyamides. Papir et a1 [31] related the gamma relaxation peak (1400K) of
Nylon 6 to the movement of methylene and polar groups. Sfirkis and Rogers
[12] reported that the gamma peak for the Nylon 6-water system was affected
by water concentration. The change in intensity of the gamma peak with
changing water concentration leveled off at a concentration corresponding to
the apparent onset of water clustering. The gamma relaxation temperature
was measured via the dielectric constant at 1 kH. The gamma peak of the
amorphous polyamide was 1730 K in the dry state. The peak was not observed
for samples equilibrated at a1 > 0.08. The difference could be due to the
interaction of water with the amide group decreasing the units available to

participate in the relaxation process.

84

Data for the alpha relaxation temperature (glass transition
temperature) were obtained by DSC measurements. The effect of sorbed water
on T8 is shown in Figure 8, where Tg values are plotted with water volume
fraction. There is an apparent change in slope of T8 with activity near a1
- 0.40. A similar trend was observed on T8 versus water volume fraction
obtained from the dielectric experiments. The slope change occurs near the
activity at which clustering is predicted. A similar trend was observed by

Sfirakis and Roger [12] for the change in the 1 peak intensity for the

system water-nylon 6.

Density Data

Figure 9 shows the change in total density with water activity. The
amorphous nylon solution becomes more dense as water is added. This is the
opposite effect expected from a mixing rule depending on additive molar
volume fractions. A similar result has been reported for an epoxy system
[32]. Notice that there is little change in density below water activities
of 0.1, where the Langmuir coefficients suggest that chemisorption (or "hole
filling") is essentially completed. It is interesting to point out that the
permeability of this amorphous nylon to oxygen decreases by a factor of 2
for films at water activities greater than 0.10 compared to a sample from
which water has been removed. An inflection point occurs in the density
curve near the water activity range (0.30 - a1 at the maximum of d0/da1 for
these data) over which clustering is predicted to begin. The water activity
at this inflection point is similar to that near the apparent change in Tg

vs a1 curve (Fig. 8).

19,0

85

 

 

 

 

To Versus Volume traction
130 f
” a
l 10 -
A
90 -
£3
70 -
(3
so . °
; 1 1 1 l 1 11. 1 1 1
3"0 . .3 .5 .7 .9 t .01
Volume traction [x 10]

Figure 8. Glass

transition temperature as a function of activity.

1.2

Density p/cc

86

 

 

 

 

 

t
A 1.9..
1.2 -
l
1.19 1 1 1 1 1 1 1 1
0 .l .3 .5 .7 .9
Water Activity

Figure 9. Density as a function of activity.

87

Pro osed Mech i £0 E ec s W e o s Pro erties of
Amor hous 0 am de

At water activities less than 0.10, water preferentially chemisorbs to
amide bonds, although a low mole fraction of the total hydrogen bonding
sites on the polymer are occupied. The chemisorption process can be
detected by observing the wave shift in the amide group absorbance. The
filling of these "open" positions reduces the permeability of the polymer
system to other, nonchemisorbing, species, such as oxygen. Chemisorption is
essentially completed at a1 - 0.1 (about 1 vol % water). There is no
measurable change in system density at this water activity. As with other
dual mode sorption systems, polymer history and relaxations probably affect
the Langmuir sorption capacity, C'H, although such data have not been taken
in this study.

At higher water activities, the permeability of oxgyen and water change
little, even though water clustering is predicted. System density increases
nonlinearly as water activity increases. A change in the T3 of the system
with respect to water activity coincides with the clustering predictions as
does the inflection point in the density-activity curve. Clustering may be
associated with the increase in density (and decrease in system volume).

The effects of water sorption on transport properties will be treated in
another paper. The dual mode sorption model with a Flory-Huggins term to
represent non-specific sorption predicts clustering at activities similar to

those determined by numerical analysis of the data.

88

LTTERNTURE CITED

1)P. Blatz and C. Talkowsky, Personnel Commicuation, (1987).

2)A.S. Michaels, w.R. Vieth and J.A. Barrier, J. Appl. Phys.,
Solution of Gases in Poly (Ethylene Terephthalate), 34(1),
(1963), 13-

3)w.R. Vieth, J.M. Howell and J.H. Hsieh, Dual Sorption Theory,
J. Membrane Sci., 1, (1976), 177.

4)T. Uragami, H.B. Hopfenberg, W.J. Koros, D.K. Yang, V.T.
Stannett and R.T. Chern, Dual-Mode Analysis of Subatmospheric

-Pressure C0. Sorption and Transport in Kapton H Polyamide

Films, J. Appl. Polym. Sci., 24, (1986), 779.

syR.T. Chern, w.J. Koros, E.S. Sanders and R. Yui, J. Membrane
Sci., Second Component "Effect in Sorption and Permeation of

Gases in Glassy Polymers," 15, (1983), 157.

(”w.J. Koros and 2.5. Sanders, J. Polym. Sci., Multicomponent
Gas Sorption in Glassy Polymers, 72, (1985), 141.

7yv. Stannett, M, Haider, v.3. Koros and 3.8. Hopfenberg, Poly.
Eng. Sci., Sorption and.Transport of Water Vapor in Glassy
Poly (Acrylonitrile), 20, (1980), 300.

89

8)G.R. Mauze and S.A. Stern, J. Membrane Sci., The Solution and
Transport of Water Vapor in Poly (Acrylonitrile): A

Reexamination, 12, (1982), 51.

9)A.R. Berens, Angew. Makromol. Chem., The Solubility of Vinyl
Chloride in Poly (Vinyl Chloride), 47, (1985), 97.

1o)G.R. Mauze and S.A. Stern, J. Membrane Sci., The Dual-Mode
Solution of Vinyl Chloride Monomer in Poly (Vinyl Chloride),
18, (1984), 99.

11)D.K. Yang, w.J. Koros, 1,-1.3. Hopfenberg and V.T. Stannett, _J_._
Appl. Polm. Sci. , Sorption and Transport Studies of Water in
Kapton Polyamide I, 30, (1985), 1035.

12)A. Sfirakis and C.E. Rogers, Poly1_o. Eng. Sci., Effects’of
Sorption Modes on Transport and Physical Properties of Nylon

6, 20, (1980), 294.

13)J.A. Barrie, P.S. Sagoo and P. Johncock, J. Membrane Sci., The
Sorption and Diffusion of Water in Epoxy Resins, 18, (1984) .
197.

14)A. Apicella. R. Tessieri and C. DeCataldis, J. Membrane Sci. ,
Sorption Modes of Water in Glassy Epoxies, 18, (1984), 211.

9O

15)P.J. Flory, J. Chem. Phys., Thermodynamics of High Polymer
Solutions, 10, (1942), 51.

.16)P.J. Flory, Principles of Polymer Chemistry, Cornell
University Press, Ithaca, NY, (1953).

171111.11. Huggins,, Ann. NY Acad. Sci., Thermodynamic Properties

of Solution of Long-Chain Compounds, 42, (1942), 1.

18)J.M. Prausnitz, R.N. Lichtenthale, and E. Gomez deAzevedo,

Molecular Thermodyaamics of Fluid-Phase Egailibria, 2nd Ed.,
Prentice-Hall, Inc., NJ, (1986).

19)A.R. Berens, J. American Water Works Assoc., Prediction of
Organic Chemical Permeation through PVC Pipe, Nov., (1985),
S7.

20)V.T. Stannett, G.R. Ranade and w.J. Koros, J. Membrane Sega,
Characterization of Water Vapor Transport in Glassy
PolyaCrylonitrile by Combined Permeation and Sorption
Techniques, 10, (1982), 219.

21)R. Puffr and J. Sabenda, J. Polm. Sci., 0n the Structure and
Properties of Polyamides XXVII, The Mechanism of Water
Sorption in Polyamides, Part C, 16, (1967), 79.

91

22)G. Skirrow and 14.12. Young, Polmer, Sorption Diffusion and
Conduction in Polyamide-Penetrant Systems: I Sorption

Phenomena, 15, (1974), 771.

23M.T. Aronhime, X. Peng and J.K. Gillhan, J. Appl. Polym. Scig,
Effect of Time-Temperature Path'of Cure on the Water

Absorption of High T. Epoxy Resins, 32, (1986), 3589.

203.11. Zimm and J.L. Lundberg, J. Phys. Chem., Sorption of
Vapors by High Polymers, 60, (1956), 425.

25)J.L. Lundberg, J. Macromol. Sci. Phsy., Clustering Theory and
Vapor Sorption by High Polymers, 4, (1969), 693.

267r.A. Orofino, H.B. Hopfenberg and V.T. Stannett, J. Macromol.
Sci. Phys. Ed. , Characterization of Penetrant Clustering in

Polymers, 4, (1969), 777.

27)R.J. Hernandez, I..A. Baner and J.R. Giacin, J. Plast. Films
8. Sheeting, The Evaluation of the Aroma Barrier Properties of
Polymer Films, 2, (1986), 187.

28)J.V. Beck and K.J. Arnold, Parameter Estimation in Engineering
and Science, J. Wiley and Sons, NY, (1977).

92

29)D.J. Skronovek, S.E. Howe, P.C. Painter and M.M. Coleman,
Macromolecules, Hydrogen Bonding in Polymers: Infrared
Temperature Studies of an Amorphous Polyamide, 18, (1985),
2218.

30)D.S. Trifan and J.R. Terenzi, J. Polm. Sci., Extends of
Hydrogen Bonding in Polyamides and Polyurethanes, 28, (1958) ,
443.

31)Y.S. Papir, S. Kapur and C.E. Rogers, J. Polym Sci., Effect
of Orientation, Anisotropy, and Water on the Relaxation

Behavior of Nylon 6, from 4.2 to 300°K, A-2, 10, (1972), 1305.

32)E.L. McKague, J.D. Reynolds and J.E. Halkias, J. Appl. Polym.
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Material in Humid Environments, 22,(1978\, 1643.

CHAPTER III

EFFECT OF WATER CONTENT ON THE PERMEABILITY, SOLUBILITY, AND
DIFFUSION OF OXYGEN IN NYLON 6I/6T.

INTRODUCTION

In general, physical properties of hydrophylic polymers such
as polyamides are affected by the presence of water within
the polymer matrix. Nylon 6I/6T, a totally amorphous
polyamide which was recently developed, is synthesized from
hexamethylenediamide and a 70/30 (weight percent) mixture of
isophthalic and terephthalic acids. Preliminary studies on
the effect of water sorption on the barrier properties of
this polymer showed atypical behavior, as compared to
semicrystalline Nylons under the same conditions. For
example, oxygen permeability in Nylon 66 increases as a
function of moisture content of the polymer, while the
permeability of oxygen in Nylon 6I/6T shows a decrease in
value, with increasing water content of the polymer.
Further, the tensile modulus for Nylon 66 decreases as a
function of moisture content, while the tensile modulus for

Nylon 6I/6T increases with increasing moisture content.

9'!

94

The behavior of this amorphous polyamide has lead Hernandez
et al. [1] to study the mechanism of water sorption into
this polymer.

The authors proposed a dual-mode sorption model, based on a
Langmuir and Flory-Huggins mechanism. At water activities
below 0.1, water preferentially chemiabsorbs to amide bonds,
although, only a low mole fraction of the total hydrogen
bonding sites on the polymer are occupied (2.3%). Chemisorp-
tion is essentially completed at water activity a1 =0.1, and
represented about 4% of the total water absorbed. At the
same time, randomly non-chemisorbed water molecules dissolve
within the polymer matrix are described by Flory-Huggins
equation. At higher water activities, a1< 0.3-0.4 the model
predicts that water molecules start clustering among
themselves. This mechanism results in an increased capacity
of the polymer to accommodate water molecules. The model is
given by:

+ V PH (1)

where V1 is the total volume fraction of water within the
polymer, and the superscripts L and FH refer to Langmuir and
Flory-Huggins water sorption contributions, respectively.

These contributions are expressed as:

 

vL= (2)

95

and

FH FR 2]

a1 = exp [1n vl + (1-v1FH) +1: (1-v1 ) (3)
where 31 is water activity,)(is the Flory-Huggins
interaction parameter, and K and B are parameters of the
Langmuir equation.

Equation (3) can be written in implicit form as:

V1FH = FH(al,X) (4)

Applying cluster function to equation (1), the following

expression is obtained [1]:

 

 

 

 

(1+3 a1) 1—v1FH(1+2 xv1 ) v1

Where Gll/Vl is the cluster function.

Oxygengpermeability as a function of polymer water activity
When oxygen permeability experiments were carried out on

films of Nylon 6I/6T as a function of water content, it was

found that permeability values decreased with an increase in

96

water content, with the largest relative percent decrease
being observed at low water activity values, al<0.2.

Similar results were reported by Chern et al., [2], for CO2
permeability through Kapton Polyimide at 60°C, for upstream
pressure levels up to 240 psia (16.33 atm), with and without
water vapor in the feed stream. The authors found that CO2
permeability was depressed by the presence of water
molecules (experiments were carried out at 0, 5.5 and 9.3%
relative humidity). These results suggested that competition
between the two species for Langmuir sorption sites takes
place [2].

The effect of a low partial pressure of water and pentane on
the permeability of H2 and CH4 through several polyimide
films has been measured by Pye et al., [3]. These
investigators reported a decrease in the flux or permea-
bility for H2 and CH4, when the experiments were performed

at values of 50% of water vapor.
Oxygen solubility and diffusion coefficient

In the present study, a series of experiments was carried
out to characterize the effect of water content of Nylon
6I/6T on the permeability of oxygen, as well as on the
solubility and diffusion coefficient of oxygen. The
experimental conditions covered water activity values from 0
to 1 and temperatures of 11.9, 22.0 and 40.30C. Upstream

oxygen pressure was maintained at 1 atm, while the

97

downstream oxygen partial pressure value was approximately
zero, as a nitrogen carrier gas was flowed continually
through the downstream cell chamber. From permeability
experiments, values of the solubility and diffusion
coefficient of oxygen were calculated [4]. Solubility data
showed that oxygen competes with water molecules for
Langmuir active sites.

A semiempirical model is presented, based on the depression
of oxygen solubility, and is described in terms of the

Langmuir component of eqn. (1):

 

V = V - F (6)

Where V is the solubility of oxygen in the polymer,
expressed as cc 02 (of critical volume)/ cc polymer-water
system, V* is the solubility of oxygen in the polymer at dry
conditions and F is a empirical constant that relates
sorption values of oxygen and water associated with Langmuir

sorption mode, and is defined by:

 

F = (7)

98

J—

Where V“ is the solubility of oxygen, expressed as volume
fraction of liquid oxygen (at critical conditions) in the
dry polymer, Veq is the solubility of oxygen, expressed as
volume fraction of oxygen liquid (at critical conditions) at
water activity 31 = 1, and VlLeq is the volume fraction of
liquid water given by the Langmuir mode at a1=l, according
to eqn. 2.

Values of the diffusion coefficient of oxygen increased
initially and then showed a plateau as a function of water
activity, suggesting that its numerical values depend both

on the effect of plasticization of the polyamide by the

water molecules and by the clusters of water.

99

EXPERIMENTAL METHODS

Polymer films

 

An amorphous polyamide, known as Nylon 6I/6T, was provided
by the E.I. Du Pont De Nemours and Co. The polymer was
synthesized from hexamethylenediamine and a mixture of
isophthalic (70%) and terephthalic (30%) acids. Since the
acid isomers were randomly placed into the polymer backbone,
resulting in structural irregularity, no crystallization of
the polymer matrix was observed. No evidence of crystalline
melting point was found, by performing differential scanning

calorimeter (DSC) analysis.

Equilibrium Sorption Data

 

Equilibrium sorption data was taken on polymer films using a
Cahn Electrobalance Model RG, (Cahn Instuments Inc.,
Cerrito, California). A stream of nitrogen gas adjusted to
specific values of water activities provided the source of
water vapor in equilibrium with the polymer films. The
apparatus and its operation were described in Chapter I.
Closed containers with salt solutions were also used to

obtain equilibrium sorption values.

100

5 m thickness (2 mils) dried under

Film samples of 5.1 x 10-
vacuum at 100 0C for two hours before each run, were used in

each experiment.
Oxygen Permeability Studies

Oxygen permeability studies were performed using a
continuous gas flow system similar to the one described in
Chapter I. These studies were carried out on an Ox-Tran 100
Permeability Tester (Modern Controls, Inc., Elk River,
Minnesota). This apparatus was modified to allow the two
streams, oxygen and carrier gas, to be adjusted to specific
water vapor activities. An schematic of the modified
apparatus is shown in Figure (1). As shown, each stream is
formed by mixing a wet and a dry gas component to obtain the
required activity value. Water activities were measured
using hygrometer sensors (Hygrodynamic Co., Silver, Spring,
Maryland). Samples of 2.93 x 10.5 m thickness (1.15 mils),
were dried under vacuum at 100 0C before each run. The
equilibration process between the polymer film and the gas
phase, at the selected values of water activities, was done
with the sample film mounted into the permeation cell. The
required time to reach equilibrium was previously determined
by gravimetric method, using the Cahn electrobalance.
Although time consuming, this procedure avoided sample

handling and assured correct conditions of tests.

101

 

PACKAGE LOOP

        
    
 
     

  
  
   
 

 
   
 

\/ ._

DIFFUSION
CELL

31311
CATALYST 3?:

SPECIMEN T

 

 

 

 

   

 

 

 

 

 

 

OXYGEN CARRIER
PURSE q PURSE
INSERT -“~
SENSOR BYPASS v
., SENSOR 2
v1 ‘ A
ll
SENSOR ::
I i
i
l i
LOAO RESISTOR

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1. Oxygen permeability apparatus.

102

RESULTS AND DISCUSSION_

Equilibrium Sorption lsotherms

 

Values of the equilibrium sorption of water in Nylon 6I/6T
at 5, 23 and 420C, expressed as fraction volume, are
presented as a function of water activity in Tables 1, 2 and
3, respectively. Density data were only available at 230C

and these were used to calculate the volume fraction values.

Figure 2 presents a plot of the three isotherms and, as
Shown, the solubility of water in the polymer decreases when
temperature increases. The apparent Shape of the three
isotherms indicates that they follow the Lamgmuir-Flory-

Huggins model, given by eqn. (1).

As outlined in Chapter II, equilibrium sorption data was
treated to obtain the parameters of the model. Table 4
shows the values forJK , K and B at 5, 23 and 42°C.

An Arrhenius plot of K and B is presented in Figure 3, and
the following expressions correlate the constants B and K

with the temperature:

U5
II

15.7 x exp(-0.232/T) (8)

751
ll

2.05E-03 x exp(0.9135/T) (9)

103

TABLE 1. Water/polymer isotherm at 5°C.

 

 

Experimental Calculated Calculated
Water Volume Flory-Huggins Langmuir
Activity Fraction Component Component
Aw leloo VlFHx100 Vle100
0 0 0 0
0.096 1.21 0.692 0.51
0.185 1.90 1.38 0.52
0.36 3.37 2.84 0.53
0.402 3.76 2.84 0.53
0.60 5.78 5.24 0.53
0.685 6.80 6.23 0.57
0.83 8.72 8.17 0.55
0.91 9.98 9.42 0.56
0.975 11.15 10.57 0.58

 

104
TABLE 2. Water/polymer isotherm at 23°C

 

 

Experimental Calculated Calculated
Water Volume Flory-Huggins Langmuir
Activity Fraction Component Component

Aw lelOO VlFHxIOO vle100

0.046 0.56 0.313 0.329
0.560 0.781 0.383 0.340
0.072 0.893 0.494 0.353
0.080 0.935 0.551 0.357
0.090 0.992 0.622 0.362
0.110 1.113 0.764 0.369
0.155 1.433 1.093 0.378
0.189 1.526 1.347 0.383
0.252 1.970 1.835 0.388
0.269 1.884 1.970 0.389
0.308 2.583 2.287 0.391
0.041 3.545 3.161 0.394
0.440 4.142 3.430 0.395
0.565 4.839 4.640 0.396
0.580 5.272 4.795 0.397
0.585 5.007 4.847 0.397
0.635 5.789 5.381 0.398
0.735 7.022 6.538 0.399
0.790 7.998 7.235 0.399
0.860 8.791 8.195 0.399
0.880 9.132 8.487 0.400
0.963 9.995 9.800 0.400

105

TABLE 3. Water/polymer isotherm at 42°C.

 

 

Experimental Calculated Calculated

Water Volume Flory-Huggins Langmuir
Activity Fraction Component Component

Aw V1x100 VlFHx100 VleIOO

0 0 0

.078 0.67 0.505 0.165
.265 2.00 1.820 0.18
.395 3.01 2.838 0.172
.48 3.74 3.561 0.179
.57 4.56 4.383 0.177
.777 6.75 6.567 0.183
.82 7.27 7.086 0.189
.91 8.46 8.27 0.19

000000000

 

Volume Fraction

.09

.08

.07

.06

.05

.03

.02

.01

106

 

U

I

 

23°C

5°C

42°C

p

J l J

.2 .3 .4 .5 .8 .7 .8 .9

aw(Water Activity)

Figure 2. Water sorption isotherms at 5 °C, 23 °C and l+2"C.

 

107

2x52

 

1x52 . *k a

 

1x E1 1 fl,

 

 

 

3.15 3.3 3.45

1ITXE03

Figure 3. Values of K and B of the langnuir equation.

3.6

108

The clustering function values were calculated from the
equilibrium sorption values. The onset of the cluster
formation was taken to be when the value of Gll/Vl = -l,
[5]. Table 5 shows the corresponding values of water
activity for the onset of clustering at 5, 23 and 420C. The
computer program used to calculate the cluster function
values, as well as the output are included in Appendix A.

Calculation of Oxygen Solubility

 

Oxygen permeability experiments were conducted at 11.9, 22
and 40.3OC. Diffusion coefficient and solubility values were
obtained from these experiments according to the procedure
outlined in Chapter I. Permeability experimental data
obtained for this study are tabulated in Appendix B. The
diffusion coefficient was calculated from a least-squares
linear analysis of values from the unsteady state region for
each permeability run. Values of 4Dt/L2 were used as the
dependent variable versus time. The corresponding values of
the correlation coefficient were also calculated, to I
indicate the goodness of fit. Solubility values were
calculatated from the expression,

S = P/D (10)
Where P, S and D stand for permeability, solubility and
diffusion coefficient, respectively. The solubility of
oxygen is expressed as S in cc 02 (STP)/cc polymer-water
system or V in cc (liquid 02 at its critical Specific

volume)/cc polymer-water system.

109

TABLE 4. Value of X., K and B as a function of temperature.

 

 

Parameter SOC 220C 420C
X. 1.66 1.70 1.76
K 0.46 0.385 0.19
B 81.36 95.15 102.0

 

TABLE 5. Water activity values at the onset of cluster

 

 

formation.
Temperature Water Activity
00
5 0.42
22 0.37

42 0.28

 

110

Conditions for ApplyinggEqn. 10

AS previously discussed in Chapter I, when eqn. 10 is
applied to calculate solubility values from permeability and
diffusion coefficients, it is assumed that the
permeant/polymer system follows the Henry's law of
solubility, [6]. For this work, which was intended to Study
the effect of water activity on the diffusion of oxygen, it
is necessary to show that the oxygen diffusion coefficient
is independent of the oxygen pressure in the range up to 1
atmosphere.

To show that the solubility of oxygen in Nylon 6I/6T follows
a Henry's law behavior and that the oxygen diffusion
coefficient was independent of the pressure (in the range of
the experimental conditions of this work), permeability
experiments were conducted in the range of 0 to 1 atmosphere
oxygen. Summarized in Table 6 are the values of the oxygen
solubility and diffusion coefficient in Nylon 6I/6T at 0.2,
0.366, 0.50, 0.745 and 1.0 atm of pressure and a temperature
of 24°C. AS shown, D remains constant through the
experimental range of pressure.

For better illustration, Figure 4 presents a plot of the
oxygen solubility values. The solubility of oxygen in Nylon

61/6T as a function of oxygen partial pressure is given by:

s = 0.144 x p (11)

1.11

TABLE 6. Solubility of Oxygen in Nylon 6I/6T as a function

of pressure at 240C.

 

 

Pressure D x E9 S x 10 V x E4
atm (a) (b) (C)
0.2 1.08 0.277 0.91
0.366 1.11 0.530 1.73
0.50 1.04 0.750 2.53
0.745 1.18 1.073 3.52
1.0 1.13 1.44 4.71

 

(a)- in (cm2/sec)
(b)- in (cc 02/cc polymer)
(c)- in (cc O2 liq./cc polymer)

D = 1.11 x 10E09

Standard error = 5%

 

s, ccoz (STPilcc polymer

112

 

8.2

0.15 - /

 

 

 

O
0.1 -
0.05 >
0 a 1 .1 1
0 e4 .8 1.2

Pressure, atm

Figure 4 . Solubility of oxygen as a function of partial pressm'e
at 24 ’C.

113

where S is the solubility in cc 02 (STP)/cc polymer and p is

the pressure in atm.

Permeability Data

 

Tables 7, 8 and 9 present the values of permeability,
diffusion coefficient and solubility of oxygen in Nylon
61/6T at 11.9, 22 and 40.3OC, respectively. Figures 5, 6
and 7 illustrate the effect of temperature on the
permeability coefficient, the diffusion coefficient and the
solubility of oxygen in Nylon 6I/6T, as a function of water
activity. Figures 8, 9 and 10 Show the Simultaneous change
of the diffusion coefficient and the solubility of oxygen aS
a function of water activity at 11.9, 22 and 40.30C.

AS shown in these figures, oxygen permeability values
decreased as a function of water activity. The values of
oxygen permeability were factored into a solubility and a
mobility term according to eqn. 11. The solubility term
decreased 5 times and the D values increased by 2 as a fun-
ction of water activity (average values for all temperatu-
res). From these findings it became apparent that the in-
crease in the diffusion coefficient was not enough to com-
pensate for the depression of the oxygen solubility values,
and the result was a depression in the permeability values.
An attempt is made here to interpret these results in the
framework of the dual-mode sorption model presented in

Chapter II.

114

TABLE 7. Diffusion, solubility and permeability values of

oxygen at 11.9OC.

 

 

Water D x E10 S x 10 P V x E4
Activity (a) (b) (c) (d)
0 3.06 3.46 31.3 11.33
0.06 3.65 1.67 18.1 5.47
0.175 3.65 1.34 ' 14.3 4.39
0.32 3.70 1.13 12.4 3.70
0.452 4.03 0.85 11.4 2.78
0.594 4.84 0.72 10.4 2.36
0.74 4.9 0.73 10.6 2.39
0.753 4.91 0.71 10.3 2.32
0.881 4.90 0.69 10.0 2.26

 

(3)“ in (cmzlsec)
(b)- in (cc O2/cc polymer)
(c)- in (cc 02/m2.day)

(d)- in (cc 02 1iq./cc polymer)

 

115

TABLE 8. Diffusion, solubility and permeability values of

oxygen at 22.00C.

 

 

Water D x E10 3 x 10 P V x E4
Activity (a) (b) (c) (d)
0 5.54 2.97 48.8 9.71
0.048 7.19 1.58 33.7 5.13
0.153 7.36 1.21 26.3 3.96
0.275 7.90 1.04 24.4 3.40
0.445 9.34 0.774 21.4 2.53
0.545 9.54 0.71 20.2 2.32
0.75 9.89 0.67 19.52 2.19

 

(a)- in (cmz/sec)
(b)- in (cc 02/cc polymer)
(c)- in (cc 02/m2.day)

(d)- in (cc O2 1iq./cc polymer)

 

116

TABLE 9. Diffusion, solubility and permeability values of

oxygen at 40.300.

 

 

Water D x E10 8 x 10 P V x E4
Activity (a) (b) (c) (d)
0 11.5 2.56 87.6 8.37
0.040 13.6 1.50 60.7 4.91
0.096 12.5 1.3 50 4.25
0.15 14.38 1.10 48.5 3.6
0.253 17.54 0.87 45.1 2.84
0.392 22.25 0.65 42.6 2.13
0.535 24.41 0.52 37.3 1 7
0.67 27.42 0.46 37.6 1.5
0.81 27.67 0.45 36.5 0.1.47

 

(a)- in (cm2/sec)
(b)- in (cc 02/cc polymer)
(c)- in (cc 02/m2.day)

(d)- in (cc 02 liq./cc polymer)

 

117

 

 

 

 

 

 

 

 

 

N
E. 5 A
> 0.
fi \
~ A
9- \
1- A
9 \A
o A A
9 A
n.’ \A o
\A 22 C
\A
N A 119°C A
o 4 - 1 .
0 .1 .2 .3 .4 .5 .6 .7 .8 .9
aw( Water Activity)

Figure 5. Oxygen permeability values at ll.9°C, 22.0°C and
40.31:.

Dx Eta, cmzleec

118

 

 

 

 

 

 

30
A—————A
403°C /
/A
A
20
/A
A’ A’A
f 22°C
10 ' A—— A—— A
A/
A-—— 4/
119°C A
A AA
0 1. . 1 1

 

0 .1 .2 .3 .4 .5 .8 .7 .8 .9

“(Water Activity)

Figure .6. Diffusion coefficient values at ll.9°C, 22.0'C and

L10.3”C.

 

Sxto, cc02 (STPllcc polymer

4.0

119

 

E"
0

1°
0

 

 

 

 

 

 

10 K °\\e°
' . \OSOi'Q‘?
0
°\' "22°c°
°-o o-40.3°C

0 4 4 1 1
o 1 .2 .3 .4 .5 .e .7 .s .9 1

”Water Activity)

Figure 7.

Oxygen solubility values at ll.9°C, 22.0'C and l+0.3"C.

011 E10, cmzlsec

120

 

 

 

 

 

5.0 4.0
O/& o
A Solubility
o Diffusion Coefficient
4,5 1- 1 3.0
4.0- ° «2-0
A
\ <0
o—m
3.5 - \ 1 o
‘ ‘~—Ae-——A
3L0 - .1 1 o

 

0.1 .2 .3 .4 .5 .o .7 .a .9 1

“(Water Activity)

Figure 8. Solubility and diffusion coefficient of oxygen
at ll.9°C.

8x10, cc02 (STPilcc polymer

Dx E10, cm2/eec

121

3.0

 

 

 

1"
o

'3
3x10, cc02 (S‘i’Pllcc polymer

 

 

10
0......
ASoiublllty
O/
olefuslon Coefficient o /
9.
1
8 _ o
A /
o
7b A
\‘ q
\‘
6 \7 “
5_ 1, . . ,
O .1 .2 .3 .4 .5 .8 .7 .8 .9 1
”Water Activity)

Figure 9. Solubility and diffusion coefficient of oxygen
at 22:0 C.

011 E10, cmzlsec

122

 

30-
:: Solubility
A Diffusion Coefficient o —————°-—
25
o
/ t 2.0
o
20 - A\
A
\‘ O
15 .
’o’o \A\
o

 

3.0

. 1.0

 

10 - _. - 1 o
1

O .1 .2 .3 .4 .5 .6 .7 .8 .9
”Water Activity)

Figure 10. Solubility and diffusion coefficient of oxygen
at 40.3 C.

51110, cc02 (STPilcc polymer

123

Oxygen solubility

 

Equation (6) was applied to model the solubility of oxygen
in Nylon 6I/6T, as a function of water activity at 11.9,
22.0 and 40.300.

The values of the constants necessary for eqn. (6) are

presented in Table 10.

 

TABLE 10. Values of the constants for Eqn 6.

 

 

 

Temperature F K B
cc 02(Liq) cc water
0 -1
C a1
cc water cc polymer
11.9 .187 .42 86.7
22.0 .188 .385 95.15
40.3 .373 .19 102

 

Numerical values of F indicate that at the same temperature
the volume fraction of liquid oxygen associated with active
Sites within the polymer is only 0.19-0.37 of the volume
fraction of the chemiabsorbed water. The value of the

constant F at 40.30C appears to be somewhat higher than the

124

other two values. This lack of trend may be due to the
numerical error associated with the values of the constants
of the Langmuir equation that describe the chemisorbed
molecules of water into the polymer. As Shown in Chapter II,
the sensibility coefficients of the parameters K and B
indicated the importance of the values at low water activity
when calculating these constants. In order to get better
values for the constants, K and B, more data at low water
activity values may be required. '
Tables 11-13 present experimental and calculated (using eqn.
6) values of oxygen solubility at 11.9, 22.0 and 40.30C
respectively. For better illustration, the tabulated data is
presented graphicaly in Figures 11-13 where oxygen
solubility is plotted as a function of water activity of the
polyamide. The experimentally determined solubility values
are also included to Show the validity of the model.
AS Shown, good agreement between calculated and experimental
data is observed, except in the range of 0.1 to 0.3 of water
activity, where the model predicted a lower solubility than
that found experimentally.
These findings indicate that the solubility of oxygen in
Nylon 6I/6T is comprised of two components: one, simple
dissolution of O2 molecules within the polymer matrix and
not affected by the presence of water molecules, and

second, 02 molecules related to active Sites of the polymer
and able to be easily displaced by water molecules. The

simple dissolved molecules contribution is about 20% of the

125

total oxygen solubility (20% at 11.900, 21% at 22.000 and
18% at 40.300). The fact that 80% of the total dissolved
oxygen was displaced by molecules of water associated with
active sites of the polymer matrix, indicates the
importance of these active Sites in the mechanism of the
solubility of oxygen within the Nylon 6I/6T. Polarity and
molecular size may be important factors in determining the
final equilibrium sorption values of water and oxygen

molecules within the polymer matrix.

126

TABLE 11. Experimental and calculated solubility of oxygen

 

 

 

 

 

at 11.9OC.
Aw Experimental Calculated
(cc 02(Liq) per cc of polymer-water) x E4
0 11.32 11.32
0.06 5.41 3.73
0.175 4.39 2.81
0.32 3.70 2.59
0.452 2.59 2.49
0.594 2.42 2.42
0.74 2.39 2.39
0.753 2.26 2.31
0.881 2.26 2.31
v* - v (11.36-3.26)XE-4
eq.
F = = = 0.187
v L 0.00484

 

127

TABLE 12. Experimental and calculated solubility of oxygen

 

 

 

 

 

at 22.000.
Aw Experimental Calculated
(cc 02(Liq) per cc of polymer) X E4
0 9.72 9.72
0.048 5.15 3.43
0.153 3.96 2.53
0.275 3.41 2.31
0.445 2.53 2.21
0.545 2.32 2.18
0.75 2.19 2.15
V - Veq. (9.72-2.19)xE-4
F = = = 0.188
L
V1 eq. 0.004

 

128

TABLE 13. Experimental and calculated solubility of oxygen

 

 

 

 

 

at 40.3OC.
Aw Experimental Calculated
(cc 02(Liq) per cc of polymer) x E4
0 8.34 8.34
0.04 4.91 2.78
0.096 3.92 2.06
0.15 3.60 1.86
0.253 2.80 1.70
0,392 2.12 1.60
0.535 1.70 1.57
0.67 1.50 1.54
0.81 1.47 1.50
v* — veq_ (8.34-l.47)xE-4
F = = = 0.373
v L 0.00185

 

S, cc02 (STPi/cc polymer

oe‘ ‘

P
or

9
no

0.1

 

129

A Experimental
— Calculated

 

A AA

 

 

A

‘ J

 

.3 .4 .5 .6 .7 .8 .9
aw(WSter Activity)

Figure 11. Oxygen solubility at ll.9'C as function of aw.

 

S, cc02 (STPllcc polymer

130

 

 

 

 

 

0.4
A Experimental
- Calculated
0.3
0.2
A
0.1 ’ \A
A A A
0 1 - 1

 

 

o .1 .2 .3 .4 .5 .9 .7 .a .9
a“,( Water Activity)

Figure 12. Oxygen solubility at 22.0°C as function of aw.

s, cc02 lSTPl/cc polymer

131

0.3

 

A Experimental

 

 

 

 

- Calculated
002‘ h
A
A
0.1 i
A
A
A A A
0 c A 4 A

 

 

 

—‘V

O .1 .2 .3 .4 .5 .6 .7 .8 .9
aw(Water Activity)

Figure 13. Oxygen solubility at HO.3°C as function of aw.

132

Oxygen diffusion coefficient

Values of the oxygen diffusion coefficient D in the
amorphous polyamide/water system were presented in Figures
8-10 as a function of water activity al, for three
temperatures. As shown, the general trend in the change of D
values as function of a1 was similar in the three cases. In
general, the diffusion coefficient increased with increasing
water activity up to a value of 0.5-0.6 activity, after
that, D values showed a plateau. The value of water activity
at which the diffusion coefficient approached a constant
value (0.5-0.6), was immediatelly above the value of a1 at
which the clustering of water within the polyamide was
predicted (0.3-0.4). This behavior was observed for all
temperatures except at 11.9 0C where D showed constant
values for O.05<a1<0.20.

The observed increase in D the region of low water activity
(a1<0.5), may be attributed to a plasticization of the
polyamide chain backbone by sorbed water. This
plasticization effect would tend to increase the mobility of
oxygen molecules within the polymer bulk phase. This 18
consistent with the behavior of the glass transition
temperature of the system polymer/water. As shown in Figure
8 Chapter II, the glass transition temperature of Nylon
6I/6T had a sharp decrease in its value for O<a1<0.5. For

values of water activity larger than 0.5 the slope of Tg

versus a1 changed at a lower value.

133

The plateau shown by the oxygen diffusion coefficient for
values of 31 above 0.4-0.5 suggests that clusters of
molecules of water formed within the polymer, may have a

retardant effect on the mobility of oxygen molecules.

A better appreciation of the effect of the distribution of
water molecules within the polymeric matrix on the mobility
of oxygen molecules can be obtained by analyzing the
activation energy of the oxygen diffusion process as a
function of water activitity. The activation energy is
related to the diffusion coefficient by the following

equation:

 

(12)

Where ED is the activation energy, D0 is a pre-exponential
term, R is the gas constant and T is the absolute
temperature. Figure 14 presents a plot of the activation
energy of the diffusion process of oxygen as a function of
water activity in equilibrium with Nylon 6I/6T. Values of
the activation energy at selected values of a1 and a plot of
ED vs. DC (to show consistency of the data)are presented in
Appendix B.

As shown in Figure 14, values of the activation energy

shifted from the region of low water activity values,

134

 

ED KcallMol

 

L A l

0.13.3.4 .5 .o .7 .a .9 1
aw(Water Activity)

 

 

 

Figure 11+. Activation energy as a function of water activity.

135

O<al<0.15, (about 8.2 Kcal/mole) to a higher value (about
10.7 Kcal/mole) for a1 >O.4. The change of ED values took
place for the range O.15<a1<0.4.

An increase in the activation energy is interpreted as an
increase in the energy required by the oxygen molecules to
overcame the intermolecular forces within the polymer, to
move from one position to another [7-9]. The fact that
oxygen molecules require more energy to diffuse through the
polymer water-system for a1>0.4 may be a indication that
clusters of water molecules opposes the passage of oxygen
molecules, creating a more tortuose path to the diffusing
molecule [8]. If this is true, the oxygen diffusion
coefficient studies as a function of water activity may be
considered as a experimental proof of the clustering of

water molecules within the polymer.
CONCLUSIONS

Results from the study of oxygen solubility and diffusivity
complemented the Fourier Transform Infrared spectroscopy,
temperature relaxation and density studies that were
performed on the polyamide water system. Further, these
results provided additional supportive evidence for the
dual-mode sorption model proposed in Chapter II. Water is
rapidly chemisorbed to dry Nylon 6I/6T, bounded to amide
groups through hydrogen bonds. Saturation of the amide

actives sites is completed before water activity reaches a

136

value of 0.1. There is also a simultaneous process of
dissolution of water non-chemisorbed and randomly
distributed within the polymer. This water is easily removed
from the polymer and does not present hystersis during the
desorption process. When water activity reaches a value
between 0.3 and 0.4 molecules of water tend to self
associate forming clusters of molecules. The degree to which
molecules of water preferentially self associate rather than
exist as loosely dissolved within the polymer is not known.
However, it appears to be large enough to result in a
increase in the activation energy for the diffusion process
of oxygen molecules. Techniques such Nuclear Magnetic
Resonance spectroscopy and isotopes tracers studies may

help to elucidate this important question.

SUMMARY

The sorption of water molecules by a glassy amorphous
polyamide, Nylon 6I/6T, showed a depression in the oxygen
permeability values as a function of polymer moisture
content. The oxygen permeability behavior was analysed in
terms of the multiplicative effect of a mobility and a
solubility term. The analysis of the solubility values of
the oxygen within the polymer-water system, provided a
complementary framework for the dual sorption model

presented in Chapter II. The model provided a theoretical

137

basis for interpreting transport behavior in polymer-vapor-
gas systems. This may prove important in relation with the
new generation of materials that are characterized by high
glass transition temperature, molecular backbone rigidity

and eventually made of polar groups such as Nylon 6I/6T.

138

REFERENCES

. Hernandez, R. J., J. R. Giacin and E. A. Grulke, The

sorption of Water by an Amorphous Polyamide, submmitted

to the Journal Membrane Science.

Chern, R. T., w. J. Koros, E. S. Sanders and R. Yui,
”Second Component" Effect in Sorption and Permeation in

Glassy Polymers, J. Membrane Sc., 15 (1983) 157-169.

Pye, D. G., M. M. Moehr and M. Panar, Measurement of gas
Permeability of Polymer, II. Apparatus for Determination
of the Permeability of Mixed gases, J. Applied Sc., 20
(1976) 287-301.

. Hernandez, R. J., J. R. Giacin and A. L. Baner, The
Evaluation of the Aroma Barrier Properties of Polymer

Films, J. Plastic Film Sheeting, 2 (1986) 187-211.

Lundberg, J. L.,Clustering Theory and Vapor Sorption by
High Polymers, 4 B3 (1969) 263-711.

Crank, J. and G. S. Park, Diffusion in Polymers,

Academic Press, London, (1968).

139

DiBenedetto, A. T. and D. R. Paul, An Interpretation of
Gaseous Diffusion Through Polymers Using Fluctuation

Theory, J. Polym. Sc.: Part A, 2 (1964) 1001-1015.

Paul D. R. and A. T. DiBenedetto, Diffusion in Amorphous

Polymers, J. Polym. Sc.: Part C, 10 (1965) 17-44.

Kumins, C. A.,Transport Through Polymer Films,

J. Polym. Sc.: Part C, 10 (1965) 1-9.

APPENDIX A

100
110
120
130
140
150
160
165
170
175
180
190
191
195
200
205
210

140

REM BOX KANAMAZU METHOD FOR FLORY HUGGINS MODEL

CLS: DIM A1(20),v1(20),ETA(20),X(20)

INPUT "HOW MANY POINTS?", N

INPUT "HOW MANY ITERATIONS?", ITE

INPUT "ENTER THE FIRST ESTIMATE OF CHI", B

PRINT "ENTER FIRST Al'S AND THEN Vl'S"
A1(1)=.056:A1(2)=.08:A1(3)=.11 : A1(4)=.189 :A1(5)=.252
A1(6)=.308

A1(7)=.41 : A1(8)=.44 :A1(9)=.565 : Al(10)=.585

A1(11)=.63S : A1(12)=.735

Al(l3)=.79 :A1(l4)=.86 :Al(15)=.88 : Al(16)=.963 : A1(l7)=.58
V1(l)=.0076 : Vl(2)=8.000001E-03 : V1(3)=.0109 :Vl(4)=.0139
Vl(5)=.0912

REM

V1(6)=.02515 : V1(7)=.03442 : V1(8)=.04016 :Vl(9)=.05097
V1(10)=.04843

Vl(11)=.05591 : Vl(12)=.06768 :Vl(l3)=.07696:Vl(14)=.0845:

V1(15)=.0877 :Vl(16)=.0955:V1(17)=.0109

215
220
225
230
240
250
255
260
270
280
290
295

300‘

310
315
320
330

PRINT " H", " Sl", " CHI"
RL =0!

RL=RL+1

XTX=O£ : XTY=0£ :SO=0! :Sl=0!

REM EQUATION FOR THE MODEL

FOR K=l TO N

V2=1 -V1(K)
ETA(K)=V1(K)*EXP(V2+B*V2*V2)

NEXT K

REM EQUATION FOR THE SENSITIVITY COEFF
FOR K=l TO N

V2=1!-V1(K)
X(K)=Vl(K)*V2*V2*EXP(V2+B*V2*V2)
NEXT K

REM CALCULATE SO, XTX, XTY

FOR K=l TO N

SO=SO+ (Al (K) -ETA (K) ) * (Al (K) -E TA (K) )

340
350
360
370

380
390

400
410
420
430
440
445
450
460
560
570
580
590
600
610
615
620
630
640
650
660
670
680

141

XTX=XTX+X(K)*X(K)
XTY=XTY+X(K)*(A1(K)-ETA(K))
NEXT K

DELTAB=XTY/XTX

REM CALCULATE G
G=DELTAB*DELTAB*XTX

IF (G<0!) OR (G=0!) GOTO 670
H=11

B=B+DELTAB*H

REM CALCULATE ETA'S WITH B'S
FOR K=l TO N

V2=ll-V1(K)
ETA(K)=Vl(K)*EXP(V2+B*V2*V2)
NEXT K

REM CALCULATE $1

FOR K=l TO N

51 =Sl+ (A1 (K) -E TA (K) ) * (Al (K) 'E TA (K) )
NEXT K

JJ=SO-(2-(1/l.l))*G

IF (Sl<JJ) OR (Sl=JJ) GOTO 640
B=B-DELTAB*H
H=G/(Sl-SO+2!*G)
B=B+H*DELTAB

PRINT H,Sl,B

IF (RL<ITE+1) GOTO 225

IF (RL=ITE) GOTO 680

PRINT "G=",G

END

90

100
110
112
115
118
121
122
125
130
132
133
135
136
137
140
150
155
160
170
180
190
200
210
215
220
225
230
235
240
245
250
255
260
265
270

142

REM CALCULATES VALUES OF THE CLUSTER FUNCTION

REM CALCULATES VOLUME FRACTION FOR FLORY-HUGGINS MODEL
REM (USING NEWTON -RAWSON METHOD) AND THE LANGMUIR
REM CONTRIBUTION

REM GIVEN BY PARAM(l)*ACTIVITY/1+PARAM(2)*ACTIV.

DIM A(100),W(100),V(100)

FOR I=l TO 100

A(I)=.01*I

NEXT I

INPUT "ENTER VALUE OF CHI ",CHI
INPUT "ENTER VALUE OF PARAM(1)' ",K
INPUT "ENTER VALUE OF PARAM(2) ",B
LPRINT "CHI VALUE USED=";CHI

LPRINT "PARAM (l),K = ":K

LPRINT "PARAM (2),B = ":B

LPRINT "ACTIVITY "; v1 ";" CLUSTER FUNCTION"
FOR I=1 TO 100
REM FIRST GUESS FOR VOLUME FRACTION : X=A(I)/10
FOR II =1 TO 4

z=1-x

Y=Z+CHI*Z*Z

F=X*EXP(Y)-A(I)
FP=EXP(Y)*(l-X*(2*CHI*Z+1))

X=X-F/FP

W(I)=X

NEXT II

v(I)=W(I)+K*A(I)/(1+E*A(I))

NEXT I

FOR I=2 TO 99 STEP 2
x1=(A(I+1)/V(I+1))-(A(I-1)/V(I-1))
X2=A(I+1)-A(I-1)

DER=x1/x2

CLUST=-(1-V(I))*DER-1

LPRINT A(I),V(I),CLUST

NEXT I

END

10
30
31
32
33
35
36
37
38
39
40
50
60
70
80
90
100
110
120
160
170
180
190
195
200
205
210
220
230
240
250
260
270
280
290
300
310
320
330

143

REM THIS PROGRAM CALCULATES THE DIFFUSION COEFFICIENT FROM
REM PERMEABILITY CONTINUOUS FLOW EXPERIMENTS.

REM PROGRAM WRITTEN BY RUBEN J. HERNANDEZ. JAN/1988

DIM F(50),T(50),X(50),DF(50)

REM TIME SHOULD BE IN MINUTES TO GIVE THE UNITS

REM OF THE DIFFUSION COEFFICIENT IN cmZ/sec

PRINT
INPUT
PRINT
REM

INPUT
PRINT

"ENTER
HUM
"ENTER

SUN
"ENTER

INPUT W

PRINT
INPUT
PRINT
FOR I=
PRINT
INPUT
PRINT
INPUT
NEXT I
PRINT

"ENTER
D
"ENTER
1 TO D
"ENTER
T(I)
"ENTER
F(I)

"ENTER

INPUT GUESS

PRINT
INPUT

"ENTER
FI

RELATIVE HUMIDITY IN PERCENT"

THE RUN IDENTIFICATION NUMBER"

THE TEMPERATURE AT STEADY STATE "
THE NUMBER OF DATA POINTS"

THE FLOW F(in mV) AND TIME T(min) STARTING FROM ZERO'
TIME"

FLOW"

YOUR GUESS FOR X"

STEADY STATE VALUE OF FLOW"

REM NEWTON-RAWSON METHOD

FOR I=

DF(I)=F(I)/FI

1 TO D

A=.44313*F(I)/FI

X=GUES
FOR J=
B=SQR(
C=EXP(
L=l/B

H=(.5*
E=(B*C
X=X-(E
NEXT J
X(I)=X
GUESS=
NEXT I

S

1 TO 7
X)

-X)

L-B)*C

)-A
/H)

X

380
390
400
410
420
430
440
445
450
460
470
480
490
500
510
520
530
540
550
560
562
563
564
570
600
610
620
630
635
636
637
638
639
640
642
645
646
647
648
649
650
655
659

144

REM LINEAR REGRESSION
ST=0

SX=0

SXT=0

STSQ=0

SXSQ=0

FOR I=l TO D

X(I)=l!/X(I)

ST=ST+T(I)

SX=SX+X(I)

SXT=SXT +(X(I)*T(I))
SXSQ=SXSQ+(X(I)*X(I))
STSQ=STSQ+(T(I)*T(I))

NEXT I
SLOPE=(ST*SX-D*SXT)/(ST*ST-D*STSQ)
DUM1=(D*SXT)-(SX*ST)
DUM2=(D*STSQ)-(ST*ST)
DUM3=(D*SXSQ)-(SX*SX)
DUM4=SQR(DUM2*DUM3)

R=DUM1/DUM4

LPRINT "RUN NUMBER: " SUN

LPRINT

LPRINT "TIME (MIN) ","FLOW (mV)", " l/X", "FLOW PERCENT"
FOR I=l TO D

LPRINT T(I),F(I),X(I),DF(I)

NEXT I

LPRINT

LPRINT

DIFF= (3.555E—08)*SLOFE

LPRINT "DIFFUSION COEFFICIENT (cm2/sec.) =" DIFF
LPRINT

LPRINT "PERMEABILITY COEFFICIENT (cm3/m2.day) =" FI*12.5156
LPRINT

LPRINT "SOLUBILITY (cc OZ/cc polymer) =" (4.22994E-ll)*FI/DIFF
LPRINT

LPRINT "CORRELATION COEFFICIENT =" R

LPRINT

LPRINT "TEMPERATURE (C) =" w : LPRINT

LPRINT "WATER ACTIVITY, aw =" HUM/100 : LPRINT

LPRINT "STEADY STATE FLOW, mV =" FI

REM THE VALUE OF THE DIFF. COEFF. IS FOR TIME IN MINUTES
REM THE THICKNESS IS L=2.93E-03 cm.
END

110
115
118
121

145

100 REM CALCULATES VOLUME FRACTION FOR FLORY-HUGGINS MODEL
REM (USING NEWTON -RAPHSON METHOD) AND THE LANGMUIR CONTRIBUTION

REM G
DIM A(
A(1)=O

IVEN BY PARAMII]*ACTIVITY/1+PARAM[2]*ACTIV.
30),W(30)
1 : A(6)=.046:A(7)=.056:A(8)=.072:A(9)=.08:A(10)=.0901

ll)=.ll:A(12)=.155:A(13)=.189:A(14)=.252:A(15)=.269:A(16)=.308:
7)=.41:A(18)=.44:A(19)=.565:A(20)=.58:A(21)=.585:A(22)=.635:A(23)
35:A(24)=.79

122
130
132
133
135
136
137
140
150
155
160
170
180
190
200.
210
215
220
225
230
235
240
260

A(2)=.01 : A(3)=.02 : A(4)=.03 : A(5)=.04

INPUT "ENTER VALUE OF CHI ",CHI

INPUT "ENTER VALUE OF PARAM(l) ",K

INPUT "ENTER VALUE OF PARAM(2) ",B

LPRINT "CHI VALUE USED=";CHI

LPRINT "PARAM l= ":K

LPRINT "PARAM 2 = " :B

LPRINT "ACTIVITY "3 " LANG.";" F-H ";" TOTAL "
FOR I=l TO 27

REM FIRST GUESS FOR VOLUME FRACTION : X=A(I)/10
FOR II =1 TO 4

Z=l-X

Y=Z+CHI*Z*Z

F=X*EXP(Y)fiA(I)

FP=EXP

(Y)*(1-X*(2*CHI*Z+1))

X=X-F/FP

W(I)=X
NEXT I

I

V=W(I)+K*A(I)/(1+B*A(I))

LPRINT
NEXT I
END
END

A(I),V-W(I),W(I),V

146

CHI VALUE USED= 1.66

PARAM (l),K = .46

PARAM (2),B = 81.36

ACTIVITY V1 CLUSTER FUNCTION Eff
.02 4.909319E-03 -90.90162
.04 7.15727E-03 -64.81381
.06 8.9675923-03 -48.22278
.08 1.063685E-02 -37.01073
9.999999E-02 .0122507 -29.07661
.12 1.384331E-02 -23.25473
.14 1.543119E-02 -18.85523
.16 1.702347E-02 -15.44847
.18 1.862575E-02 -12.75571
.2 2.024176E-02 -10.5894
.22 2.187418E-02 -8.81987
.24 2.352508E-02 -7.354772
.26 2.519619E-02 -6.127185
.28 2.688893E-02 -5.087882
.3 2.860463E-02 -4.199164
.32 3.034454E-02 -3.432935
.34 .0321098 -2.766167
.36 3.390159E-02 -2.182774
.38 3.572106E-02 -l.667958
.4 3.756939E-02 -1.210921
.42 3.944775E-02 -.8029108
.44 .0413574 -.436193
.46 4.329963E-02 -.1050007
.48 4.527576E-02 .1956189
.5 4.728722E-02 .4702143
.52 4.933547E-02 .7221345
.54 5.142208E-02 .9541478
.56 5.354873E-02 1.169004
.58 5.571716E-02 1.369228
.6 5.792922E-02 1.556429
.62 6.018697E-02 1.732119
.64 6.249248E-02 1.89784
.66 6.484811E-02 2.055503
.68 6.725629E-02 2.204984
.7 6.971966E-02 2.348459
.72 7.224111E-02 2.486567
.74 7.482374E-02 2.619742
.76 .0774709 2.749503
.78 8.018624E-02 2.875573
.8 8.297378E-02 2.99972
.82 8.583789E-02 3.12211
.84 8.878334E-02 3.243133
.8599999 9.181541E-02 3.364202
.88 9.493999E-02 3.485315
.9 9.816351E-02 3.607294
.9199999 .1014932 3.730898
.94 .1049372 3.856965
.96 .1085045 3.986406
.9799999 .1122056 4.12035

147
CHI VALUE USED= 1.7

PARAM (1),K = .385

PARAM (2),B = 95.15

ACTIVITY V1 CLUSTER FUNCTION 23%)
.02 4.004555E-03 -109.8264
.04 5.924888E-03 -72.53325
.06 7.548856E-03 -51.0288
.08 9.084456E-03 -37.49783
9.999999E-02 1.058944E-02 -28.43002
.12 1.208647E-02 -22.05536
.14 1.358643E-02 -17.40221
.16 1.509535E-02 -13.90056
.18 1.661697E-02 -11.19784
.2 1.815385E-02 -9.067458
.22 1.970787E-02 -7.356995
.24 2.128052E-02 -5.962404
.26 2.287309E-02 -4.808938
.28 2.448669E-02 -3.843528
.3 2.612237E-02 -3.026233
.32 2.778114E-02 -2.32777
.34 2.946397E-02 -1.725049
.36 3.117185E-02 -1.201051
.38 3.290575E-02 -.7411583
.4 . 346667 -.3353634
.42 3.645574E-02 2.531791E-02
.44 3.827395E-02 .3484278
.46 4.012246E-02 .6389959
.48 4.200245E-02 .9025192
.5 4.391517E-02 1.142076
.52 4.586192E-02 1.362017
.54 .0478441 1.563781
.56 4.986316E-02 1.751476
.58 5.192066E-02 1.925771
.6 5.401825E-02 2.088488
.62 5.615769E-02 2.241869
.64 5.834089E-02 2.386677
.66 .0605698 2.523843
.68 6.284664E-02 2.655386
.7 6.517371E-02 2.781028
.72 6.755351E-02 2.902389
.74 .0699887 3.020126
.76 7.248222E-02 3.134567
.78 7.503723E-02 3.246629
.8 7.765715E-02 3.356855
.82 8.034578E-02 3.466034
.84 8.310711E-02 3.574474
.8599999 8.594568E-02 3.68273
.88 8.886645E-02 3.79195
.9 .0918748 3.901837
.9199999 9.497685E-02 4.013824
.94 9.817922E-02 4.127654
.96 .1014896 4.245092
.9799999 .1049162 4.366406

148

CHI VALUE USED= 1.76
PARAM (1),K = .19
PARAM (2),B = 102

ACTIVITY V1 CLUSTER FUNCTION “2°C

.02 2.523137E-03 -135.1841
.04 4.057181E-03 -73.0991
.06 5.465441E-03 -45.03116
.08 6.842509E-03 -29.96472
9.999999E-02 8.214356E-03 -20.94153
.12 9.591216E-03 -15.1085
.14 1.097809E-02 -1l.11884
.16 1.237786E-02 -8.267276
.18 1.379239E-02 -6.157206
.2 1.522304E-02 -4.550576
.22 1.667089E-02 -3.297645
.24 1.813686E-02 -2.300347
.26 1.962179E-02 -1.492445
.28 2.112646E-02 -.8276245
.3 2.265163E-02 -.2731706
.32 2.419806E-02 .1951207
.34 2.576649E-02 .5948483
.36 2.735772E-02 .9403656
.38 2.897253E-02 1.240473
.4 3.061176E-02 1.505156
.42 3.227627E-02 1.739242
.44 3.396694E-02 1.948834
.46 3.568473E-02 2.136946
.48 .0374306 2.307936
.5 3.920563E-02 2.464288
.52 4.101084E-02 2.607499
.54 4.284744E-02 2.740478
.56 4.471666E-02 2.864259
.58 4.661973E-02 2.980225
.6 4.855809E-02 3.089716
.62 5.053315E-02 3.193428
.64 5.254651E-02 3.292421
.66 5.459977E-02 3.387795
.68 5.669473E-02 3.479759
.7 .0588333 3.568708
.72 .0610175 3.655758
.74 6.324952E-02 3.741069
.76 6.553169E-02 3.825558
.78 6.786656E-02 3.908974
.8 7.025688E-02 3.992309
.82 7.270565E-02 4.0757
.84 7.521605E-02 4.15959
.8599999 7.779161E-02 4.244279
.88 8.043621E-02 4.330721
.9 8.315405E-02 4.418622
.9199999 8.594977E-02 4.508579
.94 8.882847E-02 4.601832
.96 9.179582E-02 4.697719
.9799999 9.485813E-02 4.797932

APPENDIX B

149

RUN NUMBER: 1 A

TIME (MIN) FLOW (mV) 1/X
30 .62 .3695568
36 .86 .4353971
42 1.09 .5031636
46 1.21 .5416824
50 1.33 .5832294
54 1.43 .6207683
58 1.5 .6531465
62 1.6 .6926031
66 1.67 .7259575
70 1.74 .7621256
75 1.8 .7957972
80 1.86 .8324215
85 1.91 .8656294
90 1.95 .8942747
100 2.06 .9853724

DIFFUSION COEFFICIENT (cmZ/sec.)
FERMEABILITY COEFFICIENT (cm3/m2.day)
SOLUBILITY (CC OZ/cc polymer)
CORRELATION COEFFICIENT

TEMPERATURE (C)

..a
\0

II
N O l-'

WATER ACTIVITY, aw

STEADY STATE FLOW, mV

FLOW PERCENT

.248
.344
.436

.4840001

.532
.572
.604
.64

.668
.696
.72

.744
.764
.78

.824

3.056011E-10
31.289
.3460344

.9960481

150

RUN NUMBER: 1D

TIME (MIN) FLOW (mV) 1/X
20 .08 .2242855
25 .175 .2805958
30 .29 .3370263
35 .41 .3930966
40 .53 .4506895
45 .63 .5019877
50 .725 .5551573
55 .805 .6046123
60 .88 .6561946
55 .95 .710357
70 1 .753656
75 1.05 .801886
85 1.14 .9059511
94 1.2 .99379

DIFFUSION COEFFICIENT (cmZ/sec.)
PERMEABILITY COEFFICIENT (cm3/m2.day)
SOLUBILITY (CC OZ/cc polymer)

CORRELATION COEFFICIENT

TEMPERATURE (C) = 11.9
WATER ACTIVITY, aw = .06
STEADY STATE FLOW, mV = 1.45

FLOW PERCENT
5.517241E-02
.1206897
.2
.2827586
.3655172
.4344828
.5
.5551724
.6068965
.6551725
.6896551
.7241379
.7862068
.8275863

3.684086E-10
18.14762

.166484
.9995706

RUN NUMBER:

TIME (MIN)
25
30
35
40
45
50
55
60
65
/0
75
80
85
90
100

DIFFUSION COEFFICIENT

1E

151

FLOW (mV)

.12
.21
.3

.39
.48
.55
.62
.68
.73
.77

.815

.85
.88
.91

.965

PERMEABILITY COEFFICIENT

SOLUBILITY

l/X
.2686466
.326189
.3798029
.4340633
.4916768
.5404004
.594054
.6453394
.6930058
.7352706
.78843
.8350044
.879576
.9296001
1.041357

(cmZ/sec.)

(cm3/m2.day)

(CC OZ/cc polymer)

CORRELATION COEFFICIENT

TEMPERATURE (C)

WATER ACTIVITY, aw

STEADY STATE FLOW, mV

FLOW PERCENT
.1052632
.1842105
.2631579
.3421053
.4210527
.4824562
.5438597
.5964912
.6403509
.6754386
.7149123
.7456141
.7719298
.7982457
.8464912

3.595235E-10

14.26778

.1341256
.9995285

152

RUN NUMBER: 5

TIME (MIN) FLOW (mV) 1/X
25 9.529999E-02 .2681289
30 .1737 .330636
35 .2542 .3905649
40 .339 .4554396
45 .4068 .5114006
50 .4662 .5652788
55 .519 .6185303
60 .572 .6789239
65 .6145 .7341264
75 .678 .8327998

DIFFUSION COEFFICIENT (cmZ/Sec.)
PERMEABILITY COEFFICIENT (cm3/m2.day)
SOLUBILITY (CC OZ/Cc polymer)
CORRELATION COEFFICIENT

TEMPERATURE (C) = 11.9

WATER ACTIVITY, aw = .452

STEADY STATE FLOW, mV .911

FLOW PERCENT
.1046103
.1906696
.2790341
.3721185
.4465423
.5117454
.5697036
.6278815
.6745335
.7442371

4.032022E-10

11.40171

.0955718
.9993317

153

RUN NUMBER: 6

TIME (MIN) FLOW (mV) 1/X
30 .213 .3753858
35 .298 .4460538
40 .373 .5136517
45 .447 .5891816
50 .5 .6514816
55 .554 .7253016
60 .596 .7929905
65 .628 .8530728
70 .66 .9234472

DIFFUSION COEFFICIENT (cmZ/sec.)
PERMEABILITY COEFFICIENT (cm3/m2.day)
SOLUBILITY (CC OZ/CC polymer)
CORRELATION COEFFICIENT

TEMPERATURE (C) = 11.9

WATER ACTIVITY, aw = .5940001

STEADY STATE FLOW, mV = .83

FLOW PERCENT
.2566265
.3590362
.4493976
.5385543
.6024097
.66747
.7180723
.7566266
.7951808

4.868098E-10

10.38795

7.211955E-02
.9998113

154

RUN NUMBER: 1F

TIME (MIN) FLOW (mV) l/X FLOW PERCENT
25 .115 ~.2914978 .1352941
30 .195 .3569971 .2294118
35 .28 .4251765 .3294118
40 .36 .4935652 .4235294
45 .435 .5652957 .5117647
50 .495 .6309945 .582353
55 .55 .7007728 .6470589
60 .595 .7675537 .7
65 .615 .8009851 .7235294
70 .67 .9098404 .7882353
75 .7 .9842807 .8235294
80 .72 1.042877 .8470588
90 .76 1.195295 .8941176

4.900779E-10

DIFFUSION COEFFICIENT (cmZ/sec.)

10.63826

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY (CC 02/Cc polymer) = 7.336486E-02
CORRELATION COEFFICIENT = .9991102
TEMPERATURE (C) = 11.9

WATER ACTIVITY, aw = .74

STEADY STATE FLOW, mV = .85

155

RUN NUMBER: 7

TIME (MIN) FLOW (mV) 1/X FLOW PERCENT
30 .2136 .3775252 .2597908
35 .316 .4643096 .3843348
40 .3844 .5281584 .4675262
45 .4485 .5955592 .5454877
50 .5125 .6738917 .6233277
55 .555 .7347388 .6750183
60 .598 .8066253 .727317
65 .632 .8737842 .7686695
70 .662 .9438266 .8051569
75 .683 1.00124 .8306981

DIFFUSION COEFFICIENT (cmZ/sec.) = 4.909014E-10

PERMEABILITY COEFFICIENT (cm3/m2.day) 10.29033

SOLUBILITY (cc OZ/CC polymer) = 7.084635E-02
CORRELATION COEFFICIENT = .9995529
TEMPERATURE (C) = 11.9

WATER ACTIVITY, aw = .753

STEADY STATE FLOW, mV = .8222

RUN NUMBER: 8

TIME (MIN) FLOW (mV)
25 .13845
30 .22365
35 .30885
40 .3834
43 .426
45 .4558
48 .49
50 .5112
53 .54315
55 .5538
60 .5964
70 .6284

DIFFUSION COEFFICIENT

156

1/X
.3184585
.3909239
.4655729
.5377478
.5836809
.6185755
.6621512
.6914581
.7397224
.7570992
.8348215
.9046042

(cmZ/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY

CORRELATION COEFFICIENT

TEMPERATURE (C)
WATER ACTIVITY, aw

STEADY STATE FLOW,

(CC 02/CC polymer)

mV

11.9

.881

.8

FLOW PERCENT
.1730625
.2795625
.3860625
.47925
.5325
.56975
.6125
.639
.6789375
.69225
.7455
.7855001

4.891418E-10

10.01248

6.918142E-02
.9940052

RUN

TIME
15
18
20
23
25
28
30
35
40
45
50
55

NUMBER:

(MIN)

13

F

L W

.69

1.18
1.34
1.64
1.82
2.11
2.26
2.55
2.76
2.93
3.05
3.15

(mV)

DIFFUSION COEFFICIENT

157

l/X
.3211444
.4066213
.4351081
.4912659
.5274619
.5914451
.628141
.7087757
.7781929
.8442052
.8980966
.9491737

(cm2/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY

CORRELATION COEFFICIENT

TEMPERATURE (C)

(cc OZ/cc polymer)

WATER ACTIVITY, aw

STEADY STATE FLOW, mV

FLOW PERCENT

.1769231
.3025641
.3435898
.4205128
.4666667
.5410256
.5794871
.6538461
.7076923
.7512821
.7820513
.8076923

5.541952E-10

48.81084

.2976707
.9925459

RUN NUMBER:

TIME (MIN)
14
18
22
26
30
34
38
42
46
50
60
70

2A

FLOW (mV)

.43

a)
N

thJNBOkHHF‘HPJP”

O O O O O O O O O

Ulbtuk‘OHO~JOhbt‘
Lnuunnau

U

158

l/X
.3091848
.4030821
.4881121
.5729102

4.6435948

.7137386
.7867717
.8623256
.9316498
1.015341
1.187729
1.519134

FLOW PERCENT

.1598513
.2973978
.4163569
.5204461
.5947955
.6579926
.7137546
.7620818
.7992565
.8364312
.8921933
.9479554

DIFFUSION COEFFICIENT (cmZ/sec.) 7.185359E-10

PERMEABILITY COEFFICIENT (cm3/m2.day) = 33.66697
SOLUBILITY (CC OZ/Cc polymer) = .1583573
CORRELATION COEFFICIENT = .9958065
TEMPERATURE (C) = 22

WATER ACTIVITY, aw = .048

STEADY STATE FLOW, mV = 2.69

159

RUN NUMBER: 2B

TIME (MIN) FLOW (mV) 1/X FLOW PERCENT
12 .2 .2605724 9.523811E-02
14 .33 .3072656 .1571429
16 .47 .3532068 .2238096
18 .61 .3983534 .2904762
20 .75 .4447045 .3571429
23 .92 .5047915 .4380953
26 1.19 .6155871 .5666668
29 1.22 .6295978 .5809524
32 1.34 .6904246 .6380953
35 1.45 .7547426 .6904763
38 1.53 .8085104 .7285715
41 1.6 .8620221 .7619048
45 1.7 .9530811 .8095239

DIFFUSION COEFFICIENT (cmZ/sec.) 7.364255E-10

PERMEABILITY COEFFICIENT (cm3/m2.day) = 26.28276
SOLUBILITY (CC OZ/cc polymer) = .1206215
CORRELATION COEFFICIENT = .9973829
TEMPERATURE (C) = 22

WATER ACTIVITY, aw = .153

STEADY STATE FLOW, mV = 2.1

RUN NUMBER: 2C

FLOW (mV)

TIME (MIN)

12 .17
14 .3
15.5 .4
17 .5
19 .63
21 .76
23 .86
25 .96
27 1.07
29 1.17
31 1.24
36 1.4
41 1.55
46 1.62

DIFFUSION COEFFICIENT

160

1/X
.2538611
.3049202
.3405245
.3752396
.4207709
.4682719
.5070758
.5486355
.5985596
.6489706
.6879242
.7928111
.9228322
1.001412

(cmZ/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY

CORRELATION COEFFICIENT

TEMPERATURE (C)

WATER ACTIVITY,

STEADY STATE FLOW, mV

(CC 02/cc polymer)

aw

22
.275
1.95

FLOW PERCENT
8.717949E-02
.1538462
.2051282
.2564103
.3230769
.3897436
.4410257
.4923077
.548718
.6
.6358974
.7179487
.7948718
.8307693

7.901757E-10

24.40542

.1043867
.9994421

RUN NUMBER: 2D

FLOW (mV)

TIME (MIN)

10 .075
12 .17
14 .295
16 .43
18 .555
20 .685
22 .8
24 .905
26 1

28 1.08
30 1.16
35 1.31
40 1.42

DIFFUSION COEFFICIENT

161

l/X
.2120374
.2639706
.3180766
.3718956
.4218016
.4762826
.5284098
.5807443
.6334406
.6830525
.7389876
.8692451
1.000543

(cmZ/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY

CORRELATION COEFFICIENT

TEMPERATURE (C)

WATER ACTIVITY,

STEADY STATE FLOW, mV

(CC OZ/CC polymer)

aw

22
.445

1.71

FLOW PERCENT
4.385965E-02
9.941521E-02
.1725146
.251462
.3245614
.4005848
.4678363
.5292397
.5847953
.631579
.6783626
.7660818.
.8304093

9.338639E-10
21.40168
7.745451E-02

.9999887

162

RUN NUMBER: 2E

TIME (MIN) FLOW (mV) l/X FLOW PERCENT
12 .155 .2614194 9.627329E-02
14 .27 .314712 .1677019
16 .395 .3677611 .2453416
18 .525 .422862 .326087
20 .65 .478622 .4037267
22 .76 .5318381 .4720497
24 .86 .5851842 .5341615
26 .95 .6387602 .5900621
28 1.03 .6923183 .6397516

-30 1.1 .745248 .6832298
34 1.22 .8549849 .757764
38 1.31 .9620561 .8136646
42 1.38 1.070902 .8571429
47 1.44 1.196458 .8944099

9.546139E-10

DIFFUSION COEFFICIENT (cm2/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day) 20.15012

SOLUBILITY (cc OZ/CC polymer) = 7.133988E-02
CORRELATION COEFFICIENT = .9999728
TEMPERATURE (C) = 22

WATER ACTIVITY, aw = .545

STEADY STATE FLOW, mV = 1.61

RUN NUMBER:

TIME
10
12
14
16
18
20
22
24
26
28
31
34

(MIN)

2

FLOW (mV)
.07
.16
.28
.405
.53
.65
.765
.86
.95
1.03
1.125
1.2

DIFFUSION COEFFICIENT

163

l/X
.2131914
.2664996
.3229229
.3774066
.4324036
.4883466
.5470177
.6009548
.6583942
.7164725
.7974862
.8747756

(cmZ/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY

CORRELATION COEFFICIENT

(cc OZ/cc polymer)

TEMPERATURE (C)

WATER ACTIVITY,

aw

STEADY STATE FLOW, mV

22
.75

FLOW PERCENT

.0448718
.1025641
.1794872
.2596154
.3397436
.4166667
.4903847
.5512821
.6089744
.6602565
.7211539
.7692308

9.888553E-10

19.52434

6.673075E-02
.9999458

164

RUN NUMBER: 1C

TIME (MIN) FLOW (mV) 1/X FLOW PERCENT
6 .55 .2464279 7.857143E-02
7 .95 .2918066 .1357143
8 1.4 .3370263 .2
9 1.9 .385404 .2714286
1 2.35 .4295787 .3357143
11 2.8 .4758481 .4
12 3.15 .5141279 .45
14 3.84 .5984231 .5485715
16 4.34 .6702503 .62
18 4.75 .7392545 .6785714
20 5.05 .7978894 .7214286
25 5.5 .9050119 .7857143
30 5.8 .9961334 .8285715

1.15189lE-09

DIFFUSION COEFFICIENT (cmZ/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day) = 87.6092
SOLUBILITY (cc OZ/Cc polymer) = .257052
CORRELATION COEFFICIENT = .9846563
TEMPERATURE (C) = 40.2

WATER ACTIVITY, aw = 0

STEADY STATE FLOW, mV = 7

RUN NUMBER: 2G

TIME (MIN) FLOW (mV)
6 .36
7 .65
9 1.35
11 2
13 2.53
15 2.95
17 3.25
19 3.55
21 3.72
23 3.85
25 3.98
27 4.13

DIFFUSION COEFFICIENT

165

1/X
.2425544
.2905604
.3901006
.4851021
.573975
.6576235
.7285702
.8136434
.8708681
.9207344
.9775943
1.055105

(cmZ/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY

CORRELATION COEFFICIENT

TEMPERATURE (C)

WATER ACTIVITY,

STEADY STATE FLOW, mV

(cc OZ/CC polymer)

aw

40.3

4.85

FLOW PERCENT
7.422681E-02
.1340206
.2783505
.4123711
.5216495
.6082475
.6701031
.7319588
.7670103
.7938145
.8206186
.8515464

1.363489E-09'
60.70066

.1504611
.9949336

166

RUN NUMBER: 3

TIME (MIN) FLOW (mV) l/X FLOW PERCENT
12 .25 .2323619 6.329114E-02
15 .68 .3178236 .1721519
18 1.175 .4031303 .2974683
21 1.68 .4949314 .4253164
24 2.17 .5991648 .5493671
27 2.55 .6990365 .6455696
3 2.885 .8112427 .7303798
33 3.135 .9204504 .7936709
36 3.325 1.028941 .8417721
39 3.49 1.155459 .8835442

DIFFUSION COEFFICIENT (cm2/sec.) 1.215242E-09

PERMEABILITY COEFFICIENT (cm3/m2.day) = 49.43663
SOLUBILITY (cc 02/Cc polymer) = .1374892
CORRELATION COEFFICIENT = .998459
TEMPERATURE (C) = 40

WATER ACTIVITY, aw = .096

STEADY STATE FLOW, mV = 3.95

167

RUN NUMBER: 4

TIME (MIN) FLOW 1/X
10 .42 .2232762
13 1.3 .3147401
16 2.49 .4195317
19 3.62 .5278103
22 4.67 .6516603
25 5.5 .7809827
28 6.1 .9076528
31 6.6 1.055288
34 6 9 1.180514

DIFFUSION COEFFICIENT (cm2/sec.)
PERMEABILITY COEFFICIENT (cm3/m2.day)
SOLUBILITY (CC 02/Cc polymer)
CORRELATION COEFFICIENT

TEMPERATURE (C) = 40

.15

WATER ACTIVITY, aw

STEADY STATE FLOW 7.75

FLOW PERCENT
5.419355E-02
.1677419
.3212903
.4670968
.6025807
.7096774
.7870968
.8516129
.8903226

1.437803E-09

48.4995

.1140004
.9980205

R
UN NUMBER: 5

TIME (MIN) FLOW
10 .75
12 1.51
14 2.44
16 3.35
18 4.15
20 4.8
22 5.35
24 5.8
26 6.1
28 6.32

DIFFUSION COEFFICIENT

168

l/X
.2677766
.3436512
.4318037
.5263384
.6250758
.7243094
.8309175
.9446628
1.043316
1.135357

(cm2/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY

(CC 02/CC polymer)

CORRELATION COEFFICIENT

TEMPERATURE (C)

WATER ACTIVITY,

aw

STEADY STATE FLOW

40
.253
7.2

FLOW PERCENT
.1041667
.2097222
.3388889
.4652778
.5763889
.6666667
.7430556
.8055556
.8472222
.8777778

1.754137E-09

45.0576

8.681068E-02
.9991106

RUN NUMBER: 6

TIME (MIN) FLOW
9 .93
10 1.45
11 1.95
12 2.51
13 3.01
14 3.55
15 4
16 4.42
17 4.76
19 5.35
21 5.75

DIFFUSION COEFFICIENT

169

1/X
.2925775
.3460382
.3958234
.4532766
.5083436
.5743376
.6369081
.7042227
.7675534
.9070168
1.038951

(cm2/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY

(cc OZ/cc polymer)

CORRELATION COEFFICIENT

TEMPERATURE (C)

WATER ACTIVITY,

aw

STEADY STATE FLOW

40

.392

FLOW PERCENT
.1367647
.2132353
.2867647
.3691177
.4426471
.5220588
.5882353
.65
.7
.7867647
.8455882

2.225163E-09

42.5544

6.463255E-02

.9987307

RUN NUMBER: 7

170

TIME (MIN) FLOW l/X FLOW PERCENT
7 .4 .2360046 .0671141
8 .85 .2968458 .1426175
9 1.33 .3527632 .2231544
10 1.88 .4154808 .3154363
11 2.44 .4828646 .409396
12 2.96 .5523021 .4966443
13 3.43 .6242035 .5755034
14 3.84 .6975561 .6442953
15 4.19 .7716989 .7030201
16 4.47 .8421059 .75
17 4.7 .9105256 .7885906
18 4.9 .981093 .8221477

DIFFUSION COEFFICIENT (Cm2/sec.) = 2.44146E-09

PERMEABILITY COEFFICIENT (cm3/m2.day) = 37.29768

SOLUBILITY (cc OZ/cc polymer) = 5.162986E-02
CORRELATION COEFFICIENT = .9993703
TEMPERATURE (C) = 40
WATER ACTIVITY, aw = .535

= 5.96

STEADY STATE FLOW

171

RUN NUMBER: 8

TIME (MIN) FLOW 1/X
7 .63 .268438
8 1.13 .3290299
9 1.73 .3968923
10 2.36 .4709141
11 2.97 .5509088
12 3.49 .6303095
13 2.92 .5439042
14 4.29 .788556
15 4.61 .8731919
16 . 4.87 .9577005
17 5.1 1.050848

DIFFUSION COEFFICIENT (cm2/sec.)
PERMEABILITY COEFFICIENT (cm3/m2.day)
SOLUBILITY (CC OZ/CC polymer)
CORRELATION COEFFICIENT

TEMPERATURE (C) = 40

WATER ACTIVITY, aw .67

STEADY STATE FLOW 6

FLOW PERCENT
.105
.1883333
.2883333
.3933333
.495
.5816666
.4866667
.715
.7683334
.8116667
.8499999

2.741845E-09

37.548

4.628205E-02
.9788098

RUN NUMBER: 9

TIME (MIN) FLOW
7 .72
8 1.26
9 1.88
10 2.46
11 3
12 3.49
13 3.9
14 4.26
15 4.55
16 4.7
17 5

DIFFUSION COEFFICIENT

172

l/X
.2827206
.3479984
.4203497
.4923645
.5677521
.6475471
.7271404
.8117335
.8951025
.9459649
1.072316

(cmZ/sec.)

PERMEABILITY COEFFICIENT (cm3/m2.day)

SOLUBILITY

(CC 02/CC polymer)

CORRELATION COEFFICIENT

TEE 1P ERATURE (C)

W TER ACTIVITY,

aw

STEADY STATE FLOW

40
.81
5.83

FLOW PERCENT
.1234992
.2161235
.32247
.4219554
.5145798
.5986278
.6689537
.7307033
.780446
.806175
.8576329

2.767158E-09
36.48414

4.455934E-02

.9986682

173

Table Of activation energy as a function Of water activity.

 

 

 

Aw Diffusion Coefficient xElO E O

cm2/Sec.

Kcal/mol

11.900 22.000 40 3°C
0 3.06 5.54 11.50 8.18 6.00E-4
0.05 3.55 7.19 13.65 8.22 7.70E-4
0.10 3.65 7.27 13.90 8.18 7.33E-4
0.15 3.65 7.36 14.38 8.39 1.07E-3
0.20 3.67 7.36 15.91 9.00 3.15E-3
0.30 3.70 8.00 19.12 10.10 2.23E-2
0.40 3.90 8.95 22.30 10.73 7.07E-2
0.50 4.30 9.45 24.08 10.64 6.50E-2
0.60 4.84 9.63 25.86 10.43 4.90E-2
0.75 4.91 9.89 27.56 10.74 8.58E-2
0.8 4.91 9.89 27.67 10.76 8.87E-2

 

Do 1: 504 cmzlsoc

174

 

 

 

 

553

153 . A/

IV:
A/
A{//
152(-
/A
151 . A)
150 . L . .
7 8 9 1o 11 12

ED KcallMol

Plot of the activation enrgy versUs pre-exponential term

for the diffusion process of oxygen in water/Nylon 6I/6To

l .. .‘ll'i’ul

I" .ill 5" l ‘\

"Illlllll'lllllllf