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SORPTION AND DIFFUSION OF ETHYL ACETATE

VAPOR IN POLYIMIDE-CLAY NANOCOMPOSITE FILMS

By

Wenzhen Cheng

A THESIS

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

MASTER OF SCIENCE

School of Packaging

1 999

ABSTRACT

SORPTION AND DIFFUSION OF ETHYL ACETATE VAPOR IN

POLYIMIDE-CLAY NANOCOMPOSITE FILMS
By

Wenzhen Cheng

Sorption and diffusion of an organic vapor are key processes to gain an
understanding of the mass transfer properties of polyimide-clay nanocomposite ﬁlms. The
sorption characteristics of ethyl acetate vapor in polyimide-clay ﬁlms were determined by
micro-gravimetry and the diffusion characteristics were calculated from the sorption
kinetics at different vapor activities, by curve ﬁtting. The vapor activity dependence of the
solubility and diffusion coefﬁcients, S and D, respectively, is represented by a modiﬁed
dual-mode sorption model and a tortuosity model. The montmorillonite clay mineral,
which is hybridized with a polyimide, consists of stacked silicate sheets about 10 A in
thickness, and 800 ~ 2000 A in length. In this nanocomposite ﬁlm, montmorillonite is
dispersed homogeneously into the polyimide matrix and oriented parallel to the ﬁlm
surface. Due to this structure, the nanocomposite showed excellent organic vapor barrier
properties. Only a small volume fraction of clay (i.e. 2.5v/v%) resulted in a signiﬁcant
decrease in the diffusion coefﬁcient. Furthermore, solubility and solubility coefﬁcient
values for the polyimide-clay composites were similar to those obtained for the non-clay
loading polyimide ﬁlms, over the range of ethyl acetate vapor activity levels studied. The
permeant studies indicated that the organic vapor diffusion coefﬁcients increased
exponentially with an increase in local penetrant concentration within the polymer
membrane. The studied also showed that the diffusion coefﬁcients decreased dramatically

with an increase in clay loading level of the polymer membranes.

To

My beautiful wife, Xiaole

Lovely baby boy, Christopher

iii

Acknowledgements

Thank god for giving me a precious opportunity to study and to

have a good time in School of Packaging of Michigan State University.

I would like to thank Dr. Jack Giacin from my heart. During the
years of study, Dr. Giacin has given me a generous ﬁnancial support and
valuable academic advice. Without this, I can't complete my study and
this project. Also, I would like to thank my co-advisor Dr. Ruben
Hernandez and Dr. Thomas Pinnavaia, for their sourceful guidance
through the entire project. I appreciate Christopher Barr, former
graduated student, for helping me get started with this research project.
In addition, I am very grateful to the Center for Fundamental Materials
Research whose funding made this project possible.

Finally, my wife and my son deserve my deepest love for their love,
support and good will during the years studying in this far—away-from-

home country.

iv

Table of Contents

List of Tables .............................................................................. vi
List of Figures ............................................................................. ix
List of Symbols and Abbreviations .................................................... xii
Introduction ............................................................................... 1
Literature Review ....................................................................... 4
Polymer-clay nanocomposites .......................................................... 4
1. General concepts of nanocomposite .......................................... 4
2. Recent study and advance in polymer-clay nanocomposites .............. 6
3. The barrier improvement of polyimide-clay nanocomposites ............. 15
Ideal diffusion and sorption of organic vapor in glassy polymers ................. 19
Non-ideal sorption and diffusion of organic vapor in the glassy polymers ....... 21

Model for the path of a diffusing gas through the polyimide-clay nanocomposite 25

Materials, Instrument and Methods ............................................... 27
A. Materials for synthesis of clay/polyimide nanocomposites ............... 27
B. Materials for sorption tests .................................................... 28
C. Synthesis of clay/polyimide nanocomposite ﬁlms ......................... 29
D. Cahn 2000 Electrobalance ..................................................... 31
E. Gravimetric sorption method .................................................. 33
F. Gas Chromatographic Analysis ............................................... 37
G. Calculation of diffusion coefﬁcient .......................................... 44

1) "Half sorption time" method ......................................... 46

2) Gauss-Newton curve ﬁtting method ................................. 47

3) Least square method ................................................... 49

4) "Consistency for continuous ﬂow" method ........................ 50
H. Calculation of solubility coefficient .......................................... 52
1. Calculation of parameters of dual-mode sorption method ................. 54

Results and Discussion .................................................................. 56

Sorption properties ......................................................................... 56
1. Equilibrium Solubility for Ethyl Acetate Organic Vapor ................... 56
2. Solubility coefﬁcient .............................................................. 62
3. Dual mode sorption parameters .................................................. 65
Diffusion properties ........................................................................ 69
1. Effect of Ethyl Acetate Vapor Activity .......................................... 71

2. Effect of Clay-Loading on Polyimide-clay Nanocomposites ................. 77
3. Aspect Ratio and Tortuosity ....................................................... 80
Error Analysis .............................................................................. 83
1. Uniform of the nanocomposite ﬁlms ........................................... 83
II. Thickness variance of the ﬁlms ................................................. 84
III. Concentration variance of the permeant ..................................... 85
VI. Temperature variance of testing system ...................................... 87
V. Non-Fickian sorption behavior ................................................. 88
Summary and Conclusion .............................................................. 89
Recommendation and Future Research .............................................. 92
Appendices .................................................................................. 94
Bibliography ................................................................................ 99

vi

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

Table 10

Table 1 1

List of Tables

Gas chromatograph condition used for ethyl acetate quantiﬁcation 39
Comparison of the ethyl acetate vapor activity in the hangdown tube
obtained by the experimental and literature ............................... 43
Vapor activity dependence of solubility values in polyimide-clay
nanocomposites ........................................................ 58
Variation in normalized sorption time (tss) to equilibrium in polyimide-
clay nanocomposites (1mil ﬁlm thickness) ............................... 59
Equilibrium solubility values of clay powder and original unﬁlled
polyimide ﬁlm ........................................................... 59
Comparison of experimental and calculated absorption properties of a
polyimide clay hybrid as a function of ethyl acetate vapor activity 60
The calculated solubility coefﬁcients (cc [STP]/cc . pa") for the non-clay
and 1.25 % v/v polyimide clay nanocomposites ............................ 62
Dual-Mode Sorption Parameters for Polyimide ﬁlm ..................... 66
Diffusion coefﬁcients (mz/s) for non-clay polyimide ﬁlms, determined by
the different methods as a function of vapor activity. ................... 69
Diffusion coefﬁcients (mz/s) of clay-loading polyimide ﬁlms, determined
as a function of clay loading and vapor activity. ......................... 70
Vapor activity dependence of diffusion coefﬁcient values in polyimide-

clay nanocomposites. ........................................................ 73

vii

Table 12

Table 13

Table 14

Table 15

Table 16

Effect of ethyl acetate vapor pressure on the permeability of
Clay/polyimide Composite ﬁlms at 23 °C in the Literature (Gu, 1997)
...................................................................................... '76
Comparison of the diffusion coefﬁcient values of non-clay polyimide
composite ﬁlms/ethyl acetate at 23 °C between the Literature (Gu, 1997)
and this study ................................................................... 76
Comparison of the estimated aspect ratio with the literature data .. 82
Thickness distribution of the test ﬁlm ..................................... 84
Residual errors by the Gauss-Newton method as a function ethyl acetate

vapor activity ................................................................... 88

viii

Figure 1

Figure 2

Figure 3
Figure 4
Figure 5
Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

List of Figures

Structure differences in intercalated and exfoliated polymer-clay
nanocomposites .......................................................... 4

A model for the path of a diffusing gas through the polyimide clay

nanocomposite ﬁlms ......................................................... 25
Synthesis of polyimide clay hybrid ....................................... 3O
Schematic of gravimetric sorption experimental .......................... 36
Ethyl acetate calibration curve ........................................ 40
Half sorption time determined by the sorption proﬁle ............... 46

[[(Mcm - Mcxp) 2 /(Mca.c_) 2/n] as a function of the best estimated diffusion
coefficient value for the polyimide ﬁlm ................................. 48
Z[(Mcalc_ - Mexp.) 2] as a function of the best estimated diffusion coefficient
value for the polyimide ﬁlm ................................................. 49
The " l/X versus time" plot of a polyimide ﬁlm ......................... 5]
Determining the Henry's law constant by dual-mode sorption mod :1 .. 55
Determining parameters by Langmuir Plot ............................... 55
A representation plot of Mt/ M55 as a function of time, for the sorption of

ethyl acetate by the non-clay polyimide ﬁlm ........................... 57
A representation plot of Mt/ Ms, as a function of time, for the sorption of

ethyl acetate by the clay-loading polyimide ﬁlm ........................ 57

ix

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Solubility values comparison for the 1.25 v/v% clay loading composite,

between the experimental and calculated values. ........................ 61
Solubility coefﬁcients of non-clay polyimide ﬁlms ..................... 64
Solubility coefﬁcients of 1.25 v/v% clay/polyimide ﬁlms ............. 64

Typical sorption isotherm of ethyl acetate in non-clay polyimide ﬁlms at

Concentration (CD = KD . p) by Henry's Law is a function of the vapor
pressure
Langmuir solubility (CH = C - CD) is not a function of the vapor pressure
at a relatively high vapor partial pressure
Diffusion coefﬁcients of non—clay polyimide ﬁlm versus organic vapor
activity
Diffusion coefﬁcients of 1.25 v% polyimide-clay nanocomposite ﬁlms
versus organic vapor activity ................................................. ‘72
Variation in normalized sorption of ethyl acetate in non-clay polyimide
ﬁlm with time after introduction of vapor at 23 °C ....................... 73
Clay-loading dependence of diffusion coefﬁcients in Polyimide-clay
Nanocomposites
Variation in clay—loading dependency of normalized sorption of ethyl
acetate (av = 0.68) in polyimide/clay ﬁlms with time after introduction of

vapor at 23 °C

Figure 26

Figure 27

Figure 28

Relative diffusion coefﬁcient value of polyimide-clay nanocomposite at
ethyl acetate vapor activity av = 0.68 @23 °C 0%RI-l .................. 81
Equilibrium vapor pressure in the lower portion of the electrobalance
hangdown tube as a function of time. .................................... 86
Polyimide-clay composite sorption proﬁle under alternating system

temperature. ................................................................... 87

xi

av

Cexp

C68!

List of Symbols and Abbreviations

penetrant activity

Fihn thickness, m

represents Ft/Foo

hole afﬁnity constant, pa'l

experimental solubility values, g/g sorbant

calculated solubility values, g/g sorbant

solubility values of polyirrride matrix, g/g sorbant
solubility values of clay powder, g/ g sorbant
concentration of the standard solution for gas chromatography analysis, cc/cc
vapor concentration of point A, cc gas(STP)/cc polymer
vapor concentration of point B, cc gas(STP)/cc polymer
hole saturation constant, cc[STP]/cc polymer
concentration independence diffusion coefﬁcient, mz/sec
limiting diffusion coefﬁcient, mz/sec

thickness of a ﬁlm, m

total path of a diffusing gas, m

diffusion coefﬁcient of nanocomposite, m2 / sec
diffusion coefﬁcient of polymer matrix, m2 / sec
permeation rate of permeation ﬂux aﬁer inﬁnite time
gas ﬂow rate at point A, cc/sec

gas ﬂow rate at point B, cc/sec

xii

Ft

k0

M00 (or M5,)
Mcalc.

Mcxp.

permeation rate of permeation ﬂux at time t

rate of diffusion

Henry's law constant, cc[STP]/cc ' pa'l

length of the clay platelet, m

total amount of the sorbate uptake in the polymer aﬁer inﬁnite time, g
theoretical amount of the sorbate uptake in the polymer at time t, g
experimental data of the sorbate uptake in the polymer at time t, g
total amount of the sorbate uptake in the polymer at time t, g

steady state permeability coefﬁcient, cc[STP] - m/m2 - pa - sec
vapor partial pressure, pa

vapor partial pressure at point A, pa

vapor partial pressure at point B, pa

permeability coefﬁcient of nanocomposite, cc[STP] - m/m2 ~ pa - sec
test vapor partial pressure of ethyl acetate, pa

tortuosity factor

a coefﬁcient of Equation 43

permeability coefﬁcient of polymer matrix, cc[STP] - m/m2 - pa - sec
saturation vapor pressure of ethyl acetate, pa

quantity injected for gas chromatography analysis, g

solubility coefﬁcient, cc[STP]/cc - pa'l

solubility coefﬁcient of nanocomposite, m2 / sec

solubility coefficient of polymer matrix, m2 / see

time of sorption experimental, sec

xiii

DOV AV a“). {‘3

é

Temperature of point A, 0C
Temperature of point B, °C
volume of the system at point A, cc
volume of the system at point B, cc
volume fraction of a clay

width of the clay platelet, m

represents 02/4D t

xiv

Introduction

The sorption and diffusion of low molecular weight compounds, such as water
vapor and organic vapors, are of major concern in the use and application of polymeric
packaging materials, since such product/package systems are typically stored in an
environment which may contain organic and/or water vapors. New packaging materials
with high strength, light weight, high barrier, more ﬁmctionality and low cost are

expected to be developed for future industry use.

For the purpose of these applications, polyimides have been evaluated as a
promising class of material, with potential applications in packaging. Polyimides are
widely used for microelectronics because they exhibit high heat resistance, chemical
stability and superior electric properties (Ghosh, 1996). In recent years, composite ﬁlms
made of polyimide have been used as membranes for the industrial dehydration of
organic vapor by the per-vaporization membrane process (Okamoto et al., 1992).
Polyimide membranes may also have packaging applications, such as in electronic
packaging, where the barrier property of the package system is one of the major concerns.
It would be desirable to reduce the cost and amount of vapor absorption by polyimides, as
well as to enhance their barrier properties, since those properties of polyimides are not

sufficient for advanced electronics use.

Polymer-clay nanocomposites are a new class of material designed to meet these
demands. In this case, the nano-size clay layers (10 A - thick) are homogeneously
dispersed in the polymer matrix. Due to their speciﬁc molecular composition,
nanocomposites usually exhibit signiﬁcant enhancement in mechanical, optical,
conductive, nonlinear optical and barrier properties, as compared to the single

components and conventional composites (Lan, 1994).

As montmorillonite is composed of stacked silicate sheets, it has a low thermal
expansion coefficient and high gas barrier properties (Yano et al., 1993). Polymer-clay
nanocomposites are usually stable after the hybrid complexes are formed, and do not
undergo phase separation. The synthesis and properties of a polyimide-clay
nanocomposite had been reported in the early 90's by Yano (1991). It was found that
when a speciﬁc ammonium ion is chosen as the intercalating reagent, montmorillonite
disperses homogeneously in dimethyl-acetamide, which is a solvent for the preparation of
polyimides. The montmorillonite dispersion can be mixed with the precursor solution of
the polyimide, and after removing the solvent, the polyimide-clay nanocomposite
membranes were obtained. The resultant polyimide-clay nanocomposite showed
excellent gas barrier properties to C02, 02 and water vapor. Organic vapor permeability
of the nanocomposite membranes has also been reported for 2.5 % (v/v) polyimide-clay
nanocomposite ﬁlm and showed an 85% reduction in organic vapor transmission rate,

when compared to the polyimide ﬁlm without clay inclusion (Gu, 1997).

The solubility and diffusivity of a penetrant in a polymer membrane depends on
the temperature and the vapor activity in contact with the polymer. Knowledge of the
correlation between the solubility and diffusion coefﬁcients of the penetrant in the
polymer membrane and penetrant vapor activity in the atmosphere surrounding the
membrane, would make possible the calculation of either the variation of penetrant
sorption extent with time on the speciﬁc conditions, or its permeability rate through the
membrane. Yano (1993) reported that the diﬁusion coefﬁcient of Oz and water vapor in
polyimide/clay hybrid could be well explained by the tortuosity model. In the present
study, the sorption and diffusion characteristics of ethyl acetate vapor in polyimide were

described by microgravimetry and the tortuosity model.

The objective of the study is to gain an understanding of the mass transfer
properties of nanocomposites derived from organic polymers and plate-like inorganic
inclusions (i.e. clays) and organic penetrants, and the principles governing the barrier
properties of nanocomposites derived from organic polymers and plate-like inorganic

inclusions.

The present study therefore includes measurements of the sorption and dirfusion
of ethyl acetate into polyimide membranes with and without clay inclusion, over a range
of sorbate activities. Isotherms were determined gravimetrically at 23 i 1 °C, 0% RH at
O, 1.25, 2.5 and 5 % (v/v) clay loading. To provide insight into the activity dependence
of the mass transfer process, seven vapor activity levels were evaluated: 0.15, 0.21 , 0.27,

0.34, 0.44, 0.55 and 0.68, respectively.

Literature Review

Polymer-Clay Nanocomposite

1. General Concepts of Nanocomposites

 

lnlcrcalation Exfoliarion

Figure 1. Structure differences between intercalated and exfoliated polymer-clay
nanocomposites.

In general, there are two categories of polymer-clay nanocomposites, as presented
above in Figure 1. As shown, the intercalated and exfoliated nanocomposites exhibit
structural differences. Compared to the nanocomposite, the clay tactoids in conventional
composites exist in their original aggregated state with no intercalation of the polymer
matrix into the clay gallery regions. The intercalated polymer-clay nanocomposites are of
interest because organic polymer layers and inorganic silicate layers are alternatively
interstratiﬁed at the molecular level --- at least one dimension in the size range of a

nanometer (l x 10'9 meter, or 1/25 x 106 inch) (N anocor, Inc. web page, 1997).

Polymer/clay nanocomposites are differentiated from conventional composites by
the fact that the size of the ﬁllers is so small that the nanocomposite is macroscopically
homogenous. Exfoliated polymer—clay nanocomposites possess unique structural and
mechanical properties. For example, the exfoliated clay layers (10 A - thick), which are
dispersed into the polymer matrix, simulate the ﬁbers in ﬁber-reinforced-plastics (Lan,

1994)

The physical and mechanical properties of a nanocomposite are determined not
only by the bulk properties of each component, but also by complex interactions between
the building blocks and their interface. Nanocomposites usually exhibit a signiﬁcant
enhancement in mechanical, optical, conductive, nonlinear optical and barrier properties,
over the individual components and conventional composites containing simple ﬁllers

(Pinnavaia, 1997).

2. Recent Studies and Advances in Polymer-clay Nanocomposites

Polymer-clay composites have been studied since 1965 (Blumstein, 1965) (Lagaly
and Beneke, 1975). It was not until Toyota researchers developed several nanoscale
polymer-clay hybrid composites, however, that polymer-clay nanocomposites have
become the subject of signiﬁcant research efforts (Fukushima and Inagaki, 1987). These
studies were based on the dispersion of an (yo-amino acid and alkylammonium exchanged
forms of montomorilonite clay into:

i) semicrystalline nylon-6 (Fukushima and Inagaki, 1987), (Usuki et al., 1995)

ii) amorphous epoxy (Usuki et al., 1989),

iii) acrylic resin (U suki et al., 1995(a)),

iv) polyimide (Yano et al., 1993), (Lan and Pinnavaia, 1994(a)).

At present, there are three major research groups working on polymer-clay
nanocomposites. These include Giannelis's group at Cornell University, the Toyota
group at Toyota Centgal R&Dl;b_, Inc. Japan, and Pinnavaia's group at Michigan State

University.

Two different synthetic methods are commonly used to prepare intercalated clay
polymer nanocomposites. One procedure involves preformed-polymer-intercalation,
where the preformed polymer and clays, respectively, are dissolved and dispersed in a

compatible solvent, and then mixed. Water-soluble polymers can be intercalated into

clay galleries by this method. Such systems include (i) polyethylene oxide (Ruiz-Hitzky,
1993); (ii) ethylene-vinyl alcohol copolymer (Tohoh, 1992); and (iii) polyvinyl alcohol
(Greenland, 1963). Molten polymers can also be intercalated in this way. For example,
polystyrene was intercalated into organo-montrnorillonite clays (V aia et al., 1993). The
second method is the “in situ” intercalative polymerization procedure. In this procedure,
the desired monomers are adsorbed or intercalated into the clay galleries. The
intercalated monomers are then polymerized within the clay galleries to form the
polymer-clay nanocomposite. This method has been used extensively to modify a
number of engineering polymers to include: polyamide (Kato et al., 1979), polymethyl
metharcylate (Blumstein, 1965), polyimide (Yano et al., 1993), polyaniline (Mehrotra
and Giannelis, 1990), poly(e-caprolactone) (Messersmith and Giannelis, 1993),

polyacrylonitrile (Blumstein, 1974), and polyfurfuryl alcohol (Bandosz, 1992).

Lan and Pinnavaia (1994) studied the intercalation of a polyarnic acid into the
galleries of a series of montrnorillonites and the subsequent conversion of the polyamic
acid to polyimide. The results indicated that the polyimide intercalates in large part as a
monolayer and the composite exhibits enhanced barrier ﬁhn properties, as judged from
C02 permeation measurements. Although face-face clay layer aggregation is extensive,
the clay-polyimide hybrid composite ﬁlms exhibited greatly improved C02 barrier
properties at low clay content. Less than 8.0 volume % clay results in nearly a ten-fold
decrease in permeability rate. A self-similar or fractal dispersion of the clay platelets in

the polyimide matrix may explain the barrier property enhancement.

In addition, the incorporation of low loading levels of clay into the polyimide
hybrid results in a signiﬁcant reduction in the permeability of water vapor, oxygen, and
ethyl acetate vapor, as compared to the pure polyimide ﬁlm. The results demonstrated a
non-linear dependence of permeability on clay loading. The temperature dependency of
the transport process, over the temperature ranges studies, followed well the Arrhenius
relationship. Under humidiﬁed conditions, the polyimide ﬁlm showed a loss in barrier
property, while the polyimide-clay ﬁlm showed an enhancement in the barrier properties

to ethyl acetate vapor. (Gu, 1997)

The morphology or crystallization behavior of nylon 6/montmorillonite
nanocomposites has been studied by means of wide-angle x-ray diffractive (WAXD),
small-angle laser scattering (SALS), and differential scanning calorimeter (DSC). The
nanoplastics of montmorillonite dispersed in the nylon-6 matrix were found to act as a
nucleating agent. Surface modiﬁcation of montmorillonite particles was found to
increase adhesion between nylon-6 and montmorillonite, which prohibits the
crystallization of nylon, thus leading to an increase in crystallization activation energy.

(Li et al., 1997).

In order to improve the thermal stability and mechanical properties of polyimides,
a series of polyimide/silica composite ﬁlms, which ranged in silica content up to 45 wt%,
were successfully prepared by sol-gel reaction of tetraethoxysilane in the presence of
polyarnic acid, a precursor of polyimide. The density, decomposition temperature and

modulus increased with increasing silica content. In addition, the linear thermal

expansion coefﬁcient of the silica in the composite ﬁlms decreased, whereas tensile
strength and elongation at break displayed a maximum with the change of silicate

content. (Chen, et al., 1997).

Based on the results of these studies, polymer-clay nanocomposites processing
has been developed for the plastics industry. Nanocor Inc., a branch of AMCOL
International Corporation, has claimed that their unique, chemically modiﬁed clays, when
added to polymers, form nanocomposites. Compared to the base polymer, the
nanocomposites demonstrate improved heat resistance, as well as enhanced structural and
barrier properties. Nanocor has partnered with plastic resin producers and users to
develop the special technologies and products suitable for several different polymer
types. Targeted applications being considered range from ﬂexible and rigid barrier
packaging to structural components for trucks and automobiles. Pilot plant facilities have
been established to advance process operations and produce trial quantities of
NAN OMER® ’ nano-sized platelets. The initial commercial production of some products
was launched in the second half of 1997. Nanocor received its ﬁrst patent pertaining to
the preparation of chemically modiﬁed clays and nanocomposites in September 1996.

(N anocor web page, 1997)

 

' NANOMER® is the trademark of Nanocor Inc.

Because of their unique properties, polymer-clay hybrids have been considered
for a number of applications in both manufacturing and research areas, as reviewed

below:

0 Food Packaging

In 1997, Triton Systems (Triton Systems, Inc., 1997) proposed an irmovative
nanotechnology that would develop an inexpensive, recyclable, and mechanically durable
material for a food tray with sufﬁcient barrier properties to provide food with a three-year
shelf life. A new generation of polymeric sheet stock material with a high barrier
embedded glass structure, capable of being thermoforrned into a retortable food-
container, was to be produced. This unique and innovative technology involves
embedding a highly elastic barrier glass structure within a polymer sheet stock during
extrusion. This single-layered, recyclable food tray can replace the current non-recyclable
co-extruded 3-layered tray. A reduction in energy and die costs may also be realized
because of the use of a single extruder for processing of the single-layered tray. This
technology has tremendous potential as a high gas and moisture barrier material in food
packaging applications in the form of rigid and semi-rigid food containers, as well as
ﬂexible pouches. Other applications include airplane interiors, brakes, tires, fuel yanks,
components in electrical and electronic parts, and under-the-hood structural components.
Replacement of current ﬁlled-polymer systems in automobiles, and airplanes offers

tremendous potential.

10

o Multi-chip Packaging Material

Polyimides are widely used for microelectronics because of their heat resistance,
chemical stability, and superior electric properties. However, it would be desirable to
reduce the cost and dielectric constant of the polyimide employed. Kim (1997) reported
that a silica-polyimide hybrid could improve the electric properties and reduce the cost of
the pure polyimide ﬁhn. The structure of silica-polyimide composites, prepared as thin
ﬁlms, was studied by small-angle x-ray scattering and microscopy. Nanometer—scale
composites were successfully obtained from S 30% tetraethoxysilane-loaded mixtures
with poly (amic diethyl ester) and poly (amic acid). The microstructure of the composite
ﬁlms, based on poly (amic diethyl ester) was not signiﬁcantly affected by the inorganic
particles, i.e., the structure of the homo-polyimide was maintained, while those based on
poly (amic acid) showed changes in structure due to the growth of nanoparticles in situ

during the sol-gel process.

11

0 Electronic Industries

M (1997) reported that nanocomposites of vanadium pentoxide (V205)
aerogel and conducting polymers have applications in the preparation of high
performance intercalation materials for rechargeable lithium batteries. Vanadium
pentoxide (V 205) has been proposed as a cathode material in electric energy storage
batteries, due to its high electrode potential and capacity. Aerogels of V205 (ARG) are
materials characterized by high porosity with a solid phase thickness in the nanometer
scale (10 ~ 50 nm). They were shown to be almost free of lithium diffusion limitation
during the electrochemical insertion and release processes, because of the very short
diffusion length of the intercalate cation in the V205 solid phase. Using a conducting
polymer with a nanometer size structure was found to help enhance the electronic
conductivity of the ARG. The addition of a nanometer thick conducting polymer layer
covering to the vanadium penetrates covered structure, provides electronic conductivity
throughout the ARG particle without loosing the merits of ARG. In this case, the
polypyrrole coating exhibits electronic conductivity with ionic transparency. The
resultant ARG-Polypyrrole nanocomposite material showed improved electrochemical

performances compared to the bare ARG.

12

0 Automobile industries

The Toyota researchers reported that the nylon-6-clay nanocomposites exhibited
mechanical and thermal properties which were remarkably superior to those of the
individual components. At a loading of 5.0wt% exfoliated clay, the tensile strength of the
composite increased by 50% and the heat distortion temperature increased from 65 °C to
152 °C (Fukushima and Inagaki, 1987). Transmission Election Microscopy studies revealed
that the improved performance observed was due to the formation of a nanoscopic
composite. The nanocomposite immediately found application in the automobile industry,
as the structural material of bumpers (Okada et al., 1990). According to a recent report
(U suki et al., 1995), it was found that a nylon 6-clay hybrid using montmorillonite was
superior to the other types of clay minerals in mechanical properties. This was attributed to

the montmorillonite interacting strongly with nylon 6 by ionic interaction.

13

0 Material Industries

To evaluate the feasibility of controlling polymer ﬂammability via a nanocomposite
approach, Gilman et. al. (1997) have examined the ﬂammability properties of nylon-6
clay-nanocomposites. The ﬁre retardant (FR) properties of this new class of materials,
organic-inorganic nanocomposites, were reported by the authors. The cone calorimeter
data showed that the peak heatrelease rate (HRR), the most important parameter for
predicting ﬁre hazard, is reduced by 63 percent in a nylon-6 clay-nanocomposite
containing a clay mass fraction of only ﬁve percent, as compared to the simple
polyanride. Not only is this a very efﬁcient FR system, but, it does not have the usual
drawbacks associated with other FR additives. That is, the physical properties are not
degraded by the additive (clay), instead they are greatly improved. Furthermore, this
system does not increase the carbon monoxide or soot produced during the combustion,
as many commercial ﬁre retardants do. The nanocomposite structure appears to enhance
the performance of the char through reinforcement of the char layer. Indeed, transmission.
electron microscopy (TEM) of a section of the combustion char from the nylon-6 clay-
nanocomposite (ﬁve percent) shows a multilayered silicate structure. This layer may act
as an insulator and a mass transport barrier slowing the escape of the volatile products

generated as the nylon-6 decomposes.

14

3. The Banier Improvement of Polyimide-clay Nanocomposites

Polyimides which exhibit excellent thermal, chemical and mechanical durability
have attracted much attention for their potential use in gas separation processes. When
montmorillonite was intercalated with the ammonium salt of 12-aminododecanoic acid, it
dispersed at the molecular level into the polyimide matrix. Due to this unique structure,
this polyimide hybrid exhibited high strength, high modulus, low thermal expansion
coefﬁcient and a low permeability coefﬁcient. Only 2 wt % addition of montmorillonite
reduced gas (water, 02) permeability values to less than half of that of the non-clay

loaded polyimide. (Okamoto et al. 1992)

Polyimides also have electronic, composite and adhesive applications. In these
applications, it would be desirable to increase their moisture and organic vapor barrier
properties and dielectric constant, since these properties of polyimides are not sufﬁcient
for advanced electronics use. As montmorillonite is composed of stacked silicate sheets,
it has high gas barrier properties. Therefore, this polyimide-clay nanocomposite would

be expected to exhibit enhanced barrier properties.

Montrnorillonite is one of the clay minerals whose size is about 2000 A in length
and 10 A in thickness. Recent studies evaluated the effect of the size of clay minerals on
the barrier properties of the resultant polyimide-clay nanocomposites (Yano, 1997). Four
different sizes of clay minerals were synthesized and compared. These clays consisted

of stacked silicate sheets of about 460 A (hectrite), 1650 A (saponite), 2180 A

15

(montmorillonite), and 12300 A (synthetic mica), respectively in length and 10 A in
thickness. Yano (1997) found that the longer the length of the clay platelet, the more
effectively the barrier properties of the polyimide were improved. In the case of the
polyimide-mica hybrid, only 2 wt % addition of synthetic mica reduced the permeability
coefﬁcient of water vapor to a value less than one-tenth of that of ordinary unﬁlled

polyimide.

The earliest studies on the barrier properties of polyimide-clay nanocomposites
were carried out by the Toyota group (F ukushimaand and Inaganki, 1987, 1988). They
found that the addition of only 2 wt% montmorillonite, reduced the permeability
coefﬁcients of various gases to values less than half of those of the ordinary unﬁlled
polyimide (Yano, 1993). Furthermore, it has been suggested that nearly complete
dispersion of the IO-A-thick clay layer is needed to optimize the aspect ratio of the ﬁller
(the aspect ratio is deﬁned as the ratio of the length of a face of a ﬁller plate to the
thickness of the ﬁller plate), which in the case of montmorillonite can reach a value of
200 (Yano, 1993). Lan and Pinnavaia (1994) showed that similar composites, with an
aspect ratio of 192, had enhanced C02 barrier properties. To describe the mechanism of
the barrier property enhancement of polyimide-clay nanocomposites, Lan and Pinnavaia
(1994) compared the structural difference between exfoliated and intercalated polyimide-
clay hybrids. In the exfoliated structure, the single clay layers act as ﬁller elements. The
aspect ratio of the individual clay plates and the ﬁller loading were found to determine
the barrier property improvement. And for the intercalated structure, the clay fractal

aggregates, and not single layers, function as ﬁller elements. The formation of the fractal

I6

clay structure for natural clay minerals is due to a water swelling effect. When water
molecules have been pre-intercalated into the clay galleries and then evaporated from the
system, they tend to form a water domain region. This causes the clay layers to slip and
change their stacking pattern from turbostratic to a staircase fashion. During the
synthesis of the polyimide-clay nanocomposites, a rearrangement of the clay stacking
occurs to form the fractal structure of the clay within the polyamic acid matrix during the
pre-intercalation process. After ﬁrrther heating, the clay fractal structure will simply

remain because of the low mobility of the preformed polymer chains.

While various researchers have proposed different mechanisms to account for the
barrier property enhancement of polyimide-clay nanocomposites, the observed non-linear
dependence of the diffusion coefﬁcients as a function of clay loading and the very low
content of the inorganic phase, is crucial in developing light-weight composites of

enhanced barrier properties.

In an earlier study, Gu (1997) determined the permeability of water vapor,
oxygen, carbon dioxide, and ethyl acetate vapor through the same polyimide-clay
nanocomposite ﬁlms. These permeability values were determined with the MOCON
Permatran-W, 0x-Tran 200, Permatran C-IV, and the Aromatran 1A permeability test
systems, respectively. Gu (1997) found that the mass transfer process for the respective
penetrants, i.e. water, C02 and 02, is highly dependent on the clay loading level and
exhibited a non-linear dependency with the respect to the decrease in permeability. With

a clay loading level of 2.5 % (v/v), the permeability coefﬁcients to H20, 02 and C02

17

were reduced to 39 %, 47 % and 54 % of the permeability value of the pure polyimide
ﬁlm, while the permeability coefficients of the 5% (v/v) clay loading ﬁlm were deceased
by nearly 70 %, when compared to the single polyimide. Gu (1997) also found that the
temperature dependency of the oxygen transport process followed well the Arrhenius
relationship, over the testing range evaluated (0 °C - 30 °C). The obtained activation
energies for the pure polyimide and the 2.5 % v/v polyimide-clay ﬁlm were 16.9
KJol/mol and 19.6 KJol/mol, respectively. Furthermore, when ethyl acetate vapor was
evaluated as a penetrant, the following results were obtained. a) The 2.5 % v/v
polyimide-clay nanocomposite ﬁlm under dry conditions showed an 85 % reduction in
the permeability coefficient, as compared to the polyimide ﬁhn without clay loading.

b) Within the test temperature range from 15 °C to 30 °C, the effect of temperature on the
permeability coefﬁcient is minimal. Less than 3200 Pa ethyl acetate vapor pressure, the
activation energies for the pure polyimide and the 2.5 % v/vpolyimide-clay ﬁlm are 7.1
KJol/mol and 4.1 KJol/mol, respectively. c) Over an ethyl acetate vapor pressure
range from 1700 Pa to 3200 Pa, the permeability coefficient appeared to be independent
of vapor concentration. There was no indicated effect of penetrant vapor pressure on the
activation energies for the polyimide-clay composite ﬁlm, while the activation energy of
the pure polyimide showed a minimal dependency on penetrant concentration. d) When
water vapor (50% RH) was introduced to the test system, the permeability coefﬁcient
value of the pure polyimide ﬁlm doubled as compared to that obtained under dry
conditions. However, the permeability coefﬁcient for the polyimide clay nanocomposite
(2.5 % v/v) ﬁlm under humidiﬁed conditions showed a decrease of approximately 50 %

when compared to permeability coefﬁcient obtained under dry conditions.

18

Ideal Diffusion and Sorption of Organic Vapor in Glassy Polymers

Diffusion is the net transport of matter in a system, by means of random
molecular motion. This results in the removal of chemical potential differences in a
system and eventually produces a uniform state of equilibrium, if the boundary
conditions are not held constant for a permeation experiment. (Hopfenberg and Stannett,

1973)

Frequently the rate of diffusion (J) is proportional to the concentration gradient,
although the proportionality constant, known as the diffusion coefﬁcient, may be a

function of the diffusant concentration in the polymer:

J = 43¢);— (1)

This is Fick’s ﬁrst law of diffusion and it has been found experimentally to represent
diffusion in many systems. Based on Fick's ﬁrst law, for vapors above their critical
temperature, the diffusion coefﬁcient is independent of penetrant concentration. Fick’s

second law may be derived from Fick’s ﬁrst law:

dc 6 6c
97-3;[D(C)5;) (2)

When the boundary conditions are ﬁxed, such that a steady-state diffusion ﬂux is
maintained, equation (1) can be used to calculate the steady state permeability, deﬁned as
the ﬂux per unit pressure gradient across a polymer membrane of unit thickness;
assuming Henry's law to describe the gas-membrane equilibrium. Henry's law simply
states that the concentration of penetrant in the polymer, C, is directly proportional to the

gas partial pressure, p, to which the polymer is exposed:

C=Sp (3)

The relationship between the permeability, diffusion, and solubility coefﬁcients can be

described by:

P D S ( 4 )
where P is the steady state permeability coefﬁcient, cc[STP] - m/m2 . pa 2 sec
D is the concentration independence diffusion coefﬁcient, mz/sec
C is the solubility of vapor absorbed in the polymer

or concentration of vapor in the polymer, cc[STP]/cc polymer
S is the solubility coefﬁcient, cc[STP]/cc - pa'l

p is the vapor partial pressure, pa

Strictly idealized behavior results not only from Fickian diffusion but also additionally

from a Henry's law description of solution.

20

Non-ideal Sorption and Diffusion of Organic Vapor in the Glassy Polymers

The magnitude of the negative enthalpies of sorption of organic vapors by polymers
reported by Barrer (1957) were inconsistent with the sorption theories of Henry's law and
led Barrer to suggest a dual-mode, concurrent sorption mechanism for glassy polymers,

namely ordinary dissolution and 'hole' ﬁlling.

Michaels et a1. (1963) also reported and proposed that a two-mode sorption model of
ordinary dissolution and adsorption in microvoids ("holes") for gas sorption in glassy
amorphous polymers. The authors (Michaels et al., 1963) assumed that the total
concentration of the sorbate in the polymer, C, consisted of two thermodynamically
distinct molecular populations; molecules 'adsorbed' in the 'holes' or microvoids, CH, and

molecules dissolved in the amorphous polymer matrix, CD, as shown in equation (5):
C = CH + CD (5 )
The concentration Cy was described by a Langmuir isotherm:
C H bp

C =——— 6
H 1+bp ()

and the concentration C D by Henry's law:

21

where C 'H = hole saturation constant cc[STP]/cc polymer
b = hole afﬁnity constant (pa '1)
p = vapor partial pressure (pa)
k0 = Henry's law constant for dissolution in the amorphous matrix,

cc[STP]/cc - pa"

The equilibrium concentration for the "dual mode sorption model" can be described by:

C=C..+C..=C”"p +k..p (8)
1+bp

 

This model was applied by Okamoto et al.(l992) to the sorption isotherm of water vapor
by a polyimide ﬁlm and gave an excellent ﬁt of water vapor sorption by the glassy,
amorphous polymer. The isotherm for this sorbate/polymer sorption was described by

the following expression:

__ 0.01356 p
1+2.26 x10‘3p

 

+6.32 x10-3p (9)

It is instructive to show the two limiting cases from the dual mode sorption model.

At low partial pressure (b p<<l ), equation (8) reduces to :

C =C'H bl? + [top (10)

22

For many glassy polymer systems, C'H b is signiﬁcantly larger than k0 Therefore

reducing the equation (10) to:
C = C 'H b p (11)
At high partial pressure, b p >>1 which reduces the equation (8) to:

C=Cp+gp am

At sufﬁciently high pressure the term C 'H/ p becomes negligible as compared to kD,
therefore indicting that the available 'holes' have become saturated and that ordinary
dissolution dominates. Later investigations by Vieth et a1. (1966) on glassy polymers

indicted that the gas molecules are sorbed in the "hole" site, only as monolayers.

The dual-mode sorption model therefore predicts that an isothermal plot of C versus p
will consist of a low-pressure linear region and a high-pressure linear region connected
by a nonlinear region. So, kD can be obtained from the slope of the sorption isotherm at
high pressures. By subtracting the solubility of the normally dissolved gas, CD, from the
total solubility C, the solubility of the sorbate in the microvoids, Cy, can be calculated at
each partial pressure:

CH=C-CD=C—kpp (13)

23

Once CH as a ﬁmction of p has been detemrined, it can be tested in terms of the assumed

Langmuir model:
CH=C,pr/(I+bp) (14)

Equation (14) can be rearranged to:

p 1 p. (15)

 

 

 

Therefore, to test whether a single Langmuir expression ﬁts the data for the hole-ﬁtting
process a least-mean-squares plot of p/CH versus p is made and is checked for linearity.
The constants C ’H , and b can be determined from the slope and y-intercept of such a

Langmuir plot.

24

Model for the path of a diffusing gas through the polyimide/clay nanocomposite

The signiﬁcant reduction of the permeability coefﬁcients of the polyimide-clay
nanocomposite ﬁlms, as compared to the non-clay loading control, was explained by the
increase of the total path of the diffusing gas through the structure. As clay is composed
of stacked silicate sheets, it exhibits high gas barrier properties. The diffusing gas has to
go along the length of the clay instead of the width, which is a hundred time less than
lengthwise. Therefore, the total path of the diffusing gas will increase. If a plate of
length L and thickness W is dispersed parallel in a polymer matrix, the tortuosity model
for the path of a diffusing gas through the polyimide clay nanocomposite is shown by

Figure 2 (Nielsen, 1967):

For montmorillonite, length of a clay L = ~ 2000 A, width of a clay W = 10 A.

The value of L was determined from transmission electron micrograph (TEM) (Yano et

 

 

 

 

 

 

 

a1,1993)
‘ i. .................
1:3;
dd’ 'w
HL>I
E:::I

 

 

 

Figure 2 A model for the path of a diffusing gas through the polyimide clay
nanocomposite.

25

Total path of a diffusing gas
d'=d+dLVf/2W (16)

where d is the thickness of a test ﬁlm and VfiS the volume fraction of a clay.

Tortuositv factor

t=d'/d =1 +(L/2W) vf (17)
where Vf represents a volume fraction of a clay plate. The permeability coefﬁcient ratio
is given by:

P, 1_ 1
P r 1+(L/2W)vj

P

 

 

(18)

where PC and Pp are a permeability coefﬁcient of composite and polymer matrix,

respectively.

According to the equation above, the permeability coefﬁcient ratio should be smaller as

aspect ratio (ratio of length versus width) of plate becomes bigger.

26

Materials and Methods

Materials for synthesis of clay/polyimide Nanocomposite

Natural montmorillonite

Source clay mineral Depository
University of Missouri, Columbia, Missouri
Unit 06112 Naose [Mg086 A1514 (Si 8.00) 020 (OH)4]

4, 4' - diaminodiphenylether (4, 4' - ODA)
Aldrich Chemical Co. (Milwaukee, WI)
Molecular Weight: 200.24

Melting point: 190-192 °C

Purity: 99%

Pyromellitic Dianhydride (PMDA)

Chriskev Company, Inc. (Leawood, KS)
Molecular Weight: 218.12

Melting Point: 286.7 °C
Purity: 99 %
Dimethylacetarnide (DMAC)

Aldrich Chemical Co. (Milwaukee, WI)
Molecular Weight: 87.12

Melting Point: - 20 °C
Boiling Point: 164 ~ 166 OC
Purity: 95 %
Octadecylarnine (18 A)

Aldrich Chemical Co. (Milwaukee, WI)
Molecular Weight: 269.52

Melting Point: 55 ~ 57 °C
Purity: 99 %

27

Materials for Sorption tests

Ethyl acetate (CH3-C00-C2H5)

J. T. Baker Chemical Co. (Phillipsburg, NJ)

Analytical Reagent grade
Molecular Weight: 88.11
Boiling Point: 77.2 i 0.5 °C
Purity: 99.9 %

Ethylene Glycol (H0-CH2-CH2-0H)

J. T. Baker Chemical Co. (Phillipsburg, NJ)

Laboratory grade

Molecular Weight: 67.07
Boiling Point: 197 i 0.5 °C
Purity: 100 %

Acetonitrile (used as a solvent when preparing standard solutions for construction
of an ethyl acetate calibration curve)

EM Science, Gibbstown, NJ

Laboratory grade

Molecular weight: 41.05
Boiling point: 81.2 i 0.5 °C
Purity: 99.8 %

Nitrogen gas (carrier gas of the sorbate vapor)

AGA Gas, Inc., Cleveland OH
Dry grade nitrogen: 99.98%

28

C. Synthesis of Clay-Polyimide Nanocomposite Film

In the present study, montmorillonite/polyimide nanocomposites were prepared in
a two step process involving condensation polymerization, followed by a

cyclodehydration reaction, as described by Lan (1994).

A ﬂow chart of the synthesis of the polyimide-clay nanocomposites is depicted in
Figure 3. Polyamic acid was synthesized by the condensation reaction between 4,4'-
diaminodiphenylether and pyromellitic dianhydride in dimethyl acetamide (DMAC). An
amount of pyromellitic dianhydride was slowly added to the 4,4'-diarninodiphenylether/
DMAC solution with vigorous stirring at 15 - 20 °C and kept stirring for 1 hr at room

temperature. The ﬁnal polyamic acid solution has a concentration of 7 wt%.

Polyamic acid-clay intercalates were prepared by reaction of the desired
organoclay (2 -10 wt%) with the polyamic acid solution at 25°C. The clay suspension, in
polyamic acid/ DMAC solution, was then vigorous stirred for 24 hrs, followed by a 2hr
settle down period. Allowing the polyamic-organoclay suspensions to dry on a clean
glass plate yielded self-supporting ﬁlms. The air-dried polyamic acid-clay ﬁlms were
heated at 1°C/min to 300 °C and kept at 300 °C for 3 hrs to form the cured polyimide-clay

hybrid composites.

29

 

4,4'-Diaminodiphenylether
DMAC

 

 

 

 

 

 

< Pyromellitic dianhydride

 

 

 

 

L Polymerization I

l

Poly (amic acid) solution

1

Mixing

 

 

 

 

 

 

Organoclay (2 ~ 10 wt %)

 

 

 

 

 

 

 

 

 

 

Poly(amic, acid) ﬁlm

1

Heating 300 °c 3hr |

l

Polyimide clay nanocomposite/Hm I

 

 

 

 

 

Figure 3 Synthesis of polyimide clay hybrid.

30

D. Cahn 2000 Electrobalance

Sorption experiments conducted using the gravimetric technique are usually
carried out at equilibrium vapor pressure and employ an apparatus that continuously
records the weight gain or loss of a polymer sample as a function time. A recording

electrobalance, such as the Cahn 2000, is commonly used for such studies.

The Cahn 2000 is a very sensitive weighting instrument and is designed to
measure weights up to 3.5g. It has a 0.01mg resolution and a 0.02mg precision, for a
measuring scale of 100.00mg. The electrobalance can be described as a torque-to-current
converter. The apparatus consists of a balance beam mounted to, supported by and
pivoting about the center of a taut ribbon; a torque motor coil, located in a permanent
magnetic ﬁeld and also mounted to the taut ribbon; sample suspension ﬁxtures; a beam

position sensor system; and controls, circuitry and indicators.

When conducting a sorption measurement by the continuous ﬂow method, the
polymer sample is suspended from the arm of the electrobalance, and a sorbate of
constant concentration is continuously ﬂowed through the sample hangdown tube. The
sorbate vapor is produced by bubbling pure nitrogen gas through the liquid sorbate. This
can be achieved by constructing a vapor generator system, consisting of an Impinger
Bubbler, containing the organic liquid. As the weight of the polymer test sample
changes, a torque is produced about the axis of rotation. The electrobalance effectively

measures the amount of electric current needed by the torque converter to maintain the

31

balance beam in a level position. By calibrating the electrobalance using calibration
weights, the change in electric current can be related to weight change of the polymer
sample. By interfacing the electrobalance control unit to a computer, the polymer

sample's change in weight can be continuously recorded, as a function of time.

32

E. Gravimetric Sorption Method

Sorption studies were conducted on a Cahn 2000 electrobalance (Cahn
Instruments, Inc., Cerritos, CA) by the continuous ﬂow method. A schematic of the test
system is shown in Figure 4. A polymer sample weighing approximately 25 ~ 60 mg
was suspended from the arm of the electrobalance. A sorbate vapor stream of constant
concentration was produced by bubbling pure nitrogen gas through the liquid sorbate.
This was achieved by constructing a vapor generator system, consisting of an Impringer
Bubbler, 824/40, 25ml (Ace Glass Inc. 1430 N West BLVD, Vineland, NJ 08360), which
contained the organic liquid. The Impringer Bubbler, or sparger unit, was maintained in
a constant temperature control bath (N ESLAB, Endocal RTE-100, Refrigerated
Bath/Circulator, Neslab Instruments, Inc. Nevvington, NH) as a means of controlling the

vapor pressure of sorbate delivered to the hangdown tube of the electrobalance unit.

To provide insight into the concentration dependency of the mass transfer process,

seven vapor activity levels were evaluated: 0.15, 0.21, 0.27, 0.34, 0.44, 0.55,0.68.

Flow meters (Cole Parmer, Chicago, IL) and needle valves (Nupro 'M' series,
Nupro Co., Willoughby, OH) were used to regulate the gas ﬂow and indicated a constant
ﬂow rate. The sorbate uptake was continuously recorded with a computer, until steady

state was reached.

33

The test gas delivered can be a certiﬁed gas or sparging gas. In this study, a
sparging gas was used. The organic liquid is added to the sparger, and a carrier gas is
passed through the liquid in such a manner so as to obtain a known and stable
concentration of the permeant in the test gas stream. The test gas stream is connected
directly to the test gas inlet of the hangdown tube. Test gas ﬂows were normally set at 15

cc/min.

When the temperature controller bath is set at a speciﬁed temperature, the organic
liquid inside the sparger generates a ﬁxed and constant saturation vapor pressure at that
speciﬁc temperature. It is suggested that the sparging system should be maintained at a
temperature below ambient so as to insure that there is no condensation in the delivery
lines. In this study, the bath was set at temperatures ranging between -10 °C to 16 °C,
depending upon the desired vapor activity. The resultant organic vapor partial pressure
in the hangdown tube is equal to the saturation vapor pressure generated in the sparger.

The conclusion is based on the following reasoning (Hernandez, 1994):

The vapor pressure is generated at TA (point A), while the ﬁhn is evaluated within
the test system maintained at a higher temperature TB (point B). The parameters of
partial pressure, concentration and volume for the organic vapor generator and test

conditions are denoted as pA , pB , C A , CB , V A and VB , respectrvely.

Assumption:

i) At point A and B, the mass ﬂows are equal.

34

Therefore, MA = MB = M, where M is the mass ﬂow (mass/time).

ii) The organic vapor pressure is usually low, therefore the mass ﬂow consists
primary of nitrogen (N2). For this case, it can therefore be assumed that the
organic vapor behaviors as an ideal gas. In follows then, that FB = FA * TB/ TA,
and by deﬁnition:

C = M /F, where F is the gas ﬂow rate (volume / time).

So, the concentration ratio is CB /CA = TA / TB
When expressing C or p by the ideal gas law, at point A:
p=nRT/v=R/MW*m/v*T=R/MW*C*T
pB/pA = CB TB/CA TA
1’13 =pA * I/CA TA * CA TA/TB * TB :pA
So, at point A and B:
o Temperatures are different
0 Mass ﬂows are equal
0 Flow rates are different

0 Partial pressures are equal

The composition of the vapor stream was determined by using a high
performance, gas tight syringe (Hamilton 1750, Supelco Inc., Bellefonte, PA) to take
samples from the sampling port located on the hangdown tube and performing gas
chromatography (GC) analysis. All of the gravimetric sorption studies were conducted

at a temperature of 23 i 1 °C.

35

 

SP: Sampling port SP 1

(To GC)

Figure 4

 

 

oooooooooooooooooooooooo
-----------------------
-----------------------

 

 

 

 

 

 

 

 

IExhaust

 

 

 

 

meter

 

 

 

 

 

 

 

 

 

 

 

Schematic of Gravimetric Sorption Experimental

36

F. Gas Chromatographic Analysis

Gas chromatographic analyses were performed using a Hewlett-Packard 5890A
gas chromatograph, equipped with a dual ﬂame ionization detector and interfaced with a
Hewlett-Packard 3395 integrator for quantiﬁcation (Avondale, PA). The column used in
this study was a Supelcowax 10 fused silica capillary column (60m, 0.25mm ID, 0.25 pm
ﬁhn thickness) (Supelco Inc., Bellefonte, PA). A detailed summary of the procedure for

calibration curve construction is presented below:

Materials:
0 25mL and IOOmL volumetric ﬂasks with stoppers
- 500uL high performance gas tight syringe
o 1 and SmL sterile pipettes with automatic pipette ﬁxtures
0 Lab grade ethyl acetate and acetonitrile
Procedure:

To determine the relationship between area response and the ethyl acetate

quantity injected, a calibration curve was constructed using the following procedure:

37

1.

Prepare a 1000ppm (v/v) standard stock solution

3.

Using a high performance gas tight syringe, add 0.1mL of ethyl acetate to a 100ml
volumetric ﬂask. Fill to 100mL with acetonitrile. Stopper the ﬂask and swirl to

ensure proper mixing.

From the 1000ppm stock solution, prepare 25mL standard solutions of the

following concentrations: 10, 20, 40, and 80ppm (v/v).

To the four 25mL volumetric ﬂasks, add 0.25, 0.5, 1.0 and 2.0mL of the 1000ppm
stock solution, respectively. Fill to 25mL with acetonitrile. Stopper the ﬂasks

and swirl to ensure proper mixing.

Using the GC settings presented in Table I, analyze each standard solution by
injecting a luL aliquot directly into the gas chromatograph for quantiﬁcation.

Repeat until a consistent response value is obtained for each concentration.

38

Table 1. Gas chromatography conditions used for ethyl acetate quantiﬁcation

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Column Supelcowax 10
Injection temperature 220 °C
Detector temperature 250 °C
Initial temperature 100 00
Initial time 9 min
Rate 7.5 °C/min
Final temperature 220 °C
Final time 15 min
He (carrier gas) 7.0 mL/min
H2 40 mL/min
Air 400 mL/min
Nitrogen (make-up gas) 30 mL/min l

 

4. Plot the average area response value obtained for each concentration as a function
of the ethyl acetate quantity injected. The injected quantity of ethyl acetate can be

calculated from the following expression:

‘1: = v,xcx0.902 %L (19)

Where qi represents the quantity injected, v,- is the injection volume, c is the
concentration of the standard solution (v/v), and 0.902 g/mL is the density of

ethyl acetate. The ethyl acetate calibration curve is presented in Figure 5:

39

4. OOE +05

 

   
 
 

 

 

 

3 3.00505 .
S
8‘ 2.00505 .
2
G
2 1.00505 . y= 5E+10x
< R2 = 0.9951

0.00500 , . 5
0.00500 2.00506 4. 00506 6.00506 8.00506
Quantity Injection (9)
Figure 5. Ethyl acetate calibration curve
5. Using linear regression, determine the slope of the standard curve. Take the

inverse of this value to obtain the ethyl acetate calibration factor.

A calibration curve was constructed to determine the relationship between area
response and ethyl acetate quantity injected. Retention times for ethyl acetate and
acetonitrile were found to be 7.2 and 8.4 minutes, respectively. In addition, the
saturation vapor pressure of ethyl acetate at 23 °C was experimentally determined using
gas chromatographic analysis. The following is the method used to calculate the ethyl

acetate vapor activity levels employed in this study.

40

Materials

- SOOuL gas tight syringe

o 50mL crimp seal vials

0 Aluminum crimp cap

0 Teﬂon coated septa seals

0 5mL sterile pipettes with automatic pipette ﬁxtures

0 Lab grade ethyl acetate

Procedure

The saturation vapor pressure and the vapor activity of ethyl acetate were

experimentally determined using the following procedure:

1. Add IOmL of ethyl acetate to each vial and seal using a Teﬂon coated septa seal

and an aluminum crimp cap.

2. Store the sample at 23 °C for one week, to allow the vial headspace to equilibrate,

3. Using the same GC conditions as the calibration curve in Table 1, determine the
ethyl acetate saturation vapor pressure within the headspace by withdrawing a
SOuL aliquot and injecting the sample directly into the gas chromatograph for

quantiﬁcation.

41

Determine the ethyl acetate saturation vapor pressure from the ideal gas law:

pV=nRT (20)

Determine the vapor activity of the ethyl acetate test vapor.

Using GC conditions identical to those described above, determine the vapor
pressure of the test ethyl acetate vapor by withdrawing a SOuL aliquot from the
vapor stream sampling port and injecting the sample directly into the gas
chromatograph for quantiﬁcation. Vapor activity is determined from the

following expression:

a. = pi/ps (21)

where a, represents the vapor activity, p,- is the test vapor partial pressure of ethyl

acetate, and p, is the saturation vapor pressure of ethyl acetate.

42

The saturation vapor pressure value obtained from the literature (see appendix A)
was 85.7 mmHg at 23 °C. The ethyl acetate vapor activity for the ethyl acetate permeant
determined experimentally was compared with the values obtained from the literature
(Appendix A) and are summarized in Table 2. The average percent deviation from the
experimental was 3.3 % below the values obtained from the literature. The variation
between the two procedures can be attributed to a number of factors, such as deviation of
the permeant from the ideal gas law at or near the saturation point of the vapor, as well as
errors introduced by the gas chromatography procedure and errors involved in the

possible condensation in the test system.

Table 2. Comparison of the ethyl acetate vapor activity in the hangdown tube

obtained by the experimental and literature.

 

 

 

 

 

 

 

 

Bath System vapor activity System vapor activity Deviation
Temperature obtained from literature determined from experimental based on the
( °C) literature data
-10 0. 150 ~ 0. l 5 0 %

-4 0.21 8 0.21 3.7 %

0 0.284 0.27 4.9 %

4 0.361 0.34 5.8 %

8 0.453 0.44 3.0 %

12 0.566 0.55 2.8 %

16 0.700 0.68 2.9 %

 

 

 

 

 

 

43

G. Calculation of diffusion coefficient

When a polymer sample of known shape and size, which is at an initially
equilibrium state (uniform penetrant concentration), is suddenly exposed to an
atmosphere of constant penetrant vapor pressure, the sample weight changes with time
towards the sorption equilibrium value, according to kinetics governed by the penetrants
diffusion coefﬁcient. For dense polymeric materials such as polyamides, polyimides and
polyethylene terephthalate, surface sorption is generally considered to be negligible,
when compared with the sorption levels in the bulk polymer. As polyimide ﬁlms are
quite dense and uniform, a vapor absorption in the bulk materials is assumed. (Perrin et

al., 1996)

If M, denotes the total amount of the diffusing substance which has entered a ﬂat
sheet at time t, and M.o (or M5,), the corresponding quantity after inﬁnite time, the change

in the mass of the sample, as a function of time, is given by: (Crank 1975)

 

M — ,,, (2n+1)27r2

w

 

 

(22)

M, °° 8 [-Dn2(2n+1)2t]
— 6X 12

where D is the diffusion coefﬁcient (mz/s), 0 the ﬁlm thickness (m) and t is time (s).
This equation is valid when the vapor penetrates bi-directionally in the material with a
constant diffusion coefﬁcient from both planer surfaces. If the ﬁhn was bonded to an
impermeable substrate (aluminum sheet) or vapor penetrates unidirectionally in the ﬁlm

from one surface, the thickness value in equation (22) is double that of the true sample.

44

As the sample ﬁlms were thin sheets (thickness less than a hundredth of the width or
length), penetrant sorption by the edges was assumed to be negligible, when compared

with that by the plane surfaces.

In the case of sorption of vapors or condensable gases, the difﬁrsion may progress
locally at different rates due to the dependence of the difﬁrsion coefﬁcient on the local
concentration. The dependence, known as the 'plasticization' effect on the polymer by the
penetrant, is caused by an increase in the mobility of polymer segments with the local

penetrant concentration. (Perrin et al., 1996)

To solve numerically Fick's second law equation, a trial-and-error method is
typically employed to ﬁt the experimental kinetics by varying the values of the
parameters of the concentration dependence law. The simplest law, the one in which
diffusion is Fickian with a constant value for the diffusion coefﬁcient, is tested ﬁrst.
This is based on the assumption that the value of the diffusion coefﬁcient can be
calculated by different approximation methods, such as the method of half-sorption time
t1/2, or by a method using a transform of equation (22), with only the ﬁrst term of the
series. Nevertheless, with such methods, it is not possible to check the validity of the
assumption of a constant diﬁusion coefficient. In this study, equation (22) was used for
the ﬁtting of the entire curve by the "Least square curve ﬁtting method". A statistical
treatment of the data [[(Mcalc, - Mcxp. )2] showed that the total departure of the calculated
from the experimental values should be minimized in order to obtain a good ﬁt of the

experimental data.

45

1)

luv/A'mmmu)0"99¢nﬂﬂ

"half sorption time" method

Diffusion coefﬁcient values, D, can be estimated using the following expression

derived by Ziegel (1969):

D = 0.049 — (23)

tl/Z

0n the assumption that the diffusion process followed Fickian sorption behavior,
this equation can only be used when there is a good agreement between the
experimental and theoretical sorption proﬁles. Estimation of t1/2 is illustrated in
Figure 6 for the penetrant/polymer system of ethyl acetate (3 = 0.68) and the non-

clay loading polyimide ﬁlm.

 

 

 

 

 

 

1.25
4
120 150 180
Time (houn
Figure 6 Half sorption time determined by sorption proﬁle of 0.675mil non-

clay polyimide ﬁlm at ethyl acetate vapor activity a = 0.68 and T = 23 °C. (t1/2 =

15.3 hours, D = 2.58 x 10 '16 mz/sec)

46

2)

Gauss-Newton curve ﬁtting method

Equation (22) can be used for ﬁtting the entire sorption curve, based on the
"Gauss-Newton curve ﬁtting" method. In this procedure, diffusion coefﬁcient
values are selected and for each selected D value, a value of M, is calculated from
Equation (22) for each data point (11) on the sorption curve. Statistical treatment
of the data [[(Mcmc. - Mcxp, )2 /((Mc,,.c,)2 . n)] showed the average relative departure
of the calculated values from the experimental values. The best estimated D
values can be determined by the least sum of the {[(Mcm, - Map, )2 /((M,,,,k,_)2 . n)].
A value less than 1% is considered to be a likely good ﬁt of the data to the
theoretical equation (Penin, 1996). A typical plot of the statistical treatment of
the data ZKMcarc. - Mexp, )2 /((Mc,uc)2 . n)] is presented in Figure 7, where the sum
of X[(Mca.c, - Mexp, )2 /((Mc,.c,)2 . n)] is plotted as a function of selected diffusion
coefﬁcient values. Here the diffusion coefﬁcient giving the lowest value of
[[(Mcarc. - Mexp, )2 /((Mc,,.c.)2 . n)] is assumed to give the best ﬁt of the

experimental data to Equation (22).

47

0.12

 

0.11 .L
0.1 ..
0.09 .. V
0.08 -.
0.07 a

0.06 1.

sum 0f (M exp ' "only, (Meal2 ' n)

 

 

0.05 , , , ,
0.00500 1.00516 2.00E—16 3.00516 4.00516 5.00516

Diffusion Coefﬁcient (m’Isec)

 

Figure 7. £[(Mcalc. — Mex, )2 /((Mc,,)c_)2 . n)] as a function of the best estimated
diffusion coefﬁcient value for the system of 0.675mi1 non-clay polyimide ﬁlm at

ethyl acetate vapor activity a = 0.68 and T = 23 °C. (D best = 2.8 x 10 '16 m2/sec)

48

3)

Least square method

Equation (22) can also be used for ﬁtting the entire sorption curve, based on the
least square method. For the least square curve ﬁtting method, diffusion
coefficient values are selected and for each diffusion coefficient value selected,
values of M, are calculated by solution of Equation (22). Statistical treatment of
the data [[(Mcalc, - Map, )2] shows the total departure of the calculated values
from the experimental values. The best estimated D value is determined from the
minimum sum of the squares value, which is considered to be the likely best ﬁt.

A typical graphical treatment is presented in Figure 8, where the sum of squares is

plotted as a function of the selected diffusion coefﬁcient values.

 

1.8
E 1.6
a
3
"6
:5, 1.2
(D
1 .
0.8

 

 

 

0.00E+00 1.00516 2.00516 3.00516 4.00516 5.00516 6.00516

Diffusion coefﬁcient (mzlsec)

Figure 8. [[(ch, - Map) 2] as a function of the best estimated diffusion
coefﬁcient value for the system of 0.67 5mil non-clay polyimide ﬁlm at ethyl

acetate vapor activity a = 0.68 and T = 23 °C. (D best = 3.2 x 10 '16 mz/sec)

49

4) "Consistency for continuous ﬂow" method

The consistency test for continuous ﬂow permeability experimental data has been
described in detail by Gavara and Hernandez (1993) and is summarized brieﬂy

below.
The permeation rate or permeant ﬂux at any time F. during the transient state

portion of the permeability experiment, varies from zero at time zero, up to the

value F.o reached at steady state. This is described by the following expression

2 w _ 22
5’_= 4 J 1 exp n 1 (24)
Fan J7? 4D! n=1.3.5... 4D! ,

where F(/F.o is the permeant ﬂux ratio. F t is the permeant ﬂux at time t, and F... is

(24):

 

 

the permeant ﬂux at steady state. In this equation, D is assumed to be time and

concentration independent. For short times, the ﬁrst term of the convergent series
in Equation (24) gives a good description of the permeation process from t = 0 up
to the time when 95% of the steady-state ﬂow has been reached. Equation (24) is

then simpliﬁed to read:

(J?) 6... (25)

50

1

where (0 represents Ft/Fm in Equation (25) and X = 122/4Dt . By using a Newton-
Raphson method, the value of X can be calculated for each value of t and the
diffusion coefﬁcient D can be obtained from the slope of 1/X versus t. The plot
of I/X versus time is expected to be a straight line and to intercept the ordinate
axis at zero. This is illustrated in Figure 9 for the ethyl acetate (a = 0.68) / non-

clay loading polyimide ﬁlm system.

1.600

 

1.400 ..
1.200 _
1.000 .

0.600 .
0.400 _
0.200 -
0.000 , , . . -

 

 

 

0 5 10 15 20 25 30 35 40 45
Time (hour)

Figure 9 The " I/X versus time" plot of 0.675mil non-clay polyimide ﬁlm at
ethyl acetate vapor activity a = 0.68 and T = 23 0C. (Slope = 0.0329, R2 = 0.965,

D = 6.6 x 10 "6 mZ/sec)

51

H. Calculation of solubility coefﬁcient

The solubility coefﬁcient (S) is usually determined by observing the change in
weight of a polymer sample during a sorption process. Such a process can involve the

absorption or desorption of low molecular weight moieties by the polymer sample.

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

assumed:
C = S p (3)

where p is the partial pressure of the penetrant in the gas phase. The partial pressure of
the penetrant is further related to the penetrant concentration in the gas phase through the

ideal gas law.

As discussed in the Results and Discussion section (see page 65), the ethyl acetate
sorption isotherm, assumes a dual-mode sorption model of ordinary dissolution and
adsorption into the microvoids ("hole") for vapor sorption in the glassy amorphous
polyimides. The sorption isotherm for this polymer was accurately described by the

dual-mode sorption model (Equation 8).

C'b
C=CH+CD=i—+%+kbp (8)

52

 

ll

 

 

From the isotherm, the changes in the vapor partial pressure are not consistent
with the changes in the solubility values. If the Henry's law component contributes only
a portion of the ethyl acetate uptake described by the sorption model, the solubility
coefﬁcient (S) will be given by:

EC = CHb 2 +ko
6p (1+bp)

 

S = (26)

Solving Equation (26) thus gives the tangent value of the sorption isotherm at each vapor
partial pressure. The S values determined by this procedure, show how the vapor partial

pressure affects the solubility values.

53

I. Calculation of parameters of dual-mode sorption methods

Calculation of the sorption parameters C 'H, [(0, b from the sorption isotherm data was

carried out as following:

C=CH+kDp (27)

This form of equation (27) indicates that a quantitative separation of the sorption
contributions is possible at high partial pressures, assuming the dual mode sorption model
adequately describes the data. Since the expression is in a linear form, a plot of C as a
function of p give a slope equal to kg and the y-intercept equal to C 'H . After kn has been
determined from the slope of the best straight lines through the high partial pressure data,
the 'hole' contribution, C”, for each vapor pressure can be determined by subtracting kD p

fromC.

CH=C—kDp (28)

Also the expression for C” can be rearranged to the form;

 

 

 

1’: 1+le (29)

54

Then the Langmuir plot, p/CH versus p, should yield a straight line of slope 1/C'H

and intercept at (p = 0) of l/C'Hb. This procedure, as in most procedures involving curve

ﬁtting of the data, is of a trial and error nature and it is continued until the best (least

mean-squares) ﬁt of the data on the Langmuir plot is achieved. This procedure is

illustrated in Figure 10 & 11.

Sorption lsotherm

 

SIOPC=KD

 

C (cc[STP]/cc polymer)
0 a 8 8 8 8 8

 

—I

0 2000 4000 6000

 

I

8000 10000

Vapor partial pressure, p (pa) ,

Figure 10. Determining the Henry's law constant by dual-mode sorption model

Langmuir Plot
0.35

 

0.3 .
0.25 _
0.2 _
0.15 -
0.1 -
0.05 _

P/CH

 

slope = l/C 'H
y-intercept = l/b C'”

 

 

0 2000 4000 6000

8000 10000

Vapor partial pressure, p (pa)

Figure 11. Determining parameters by Langmuir Plot

55

Results and Discussion

Sorption Properties

1. Equilibrium Solubility for Ethyl Acetate Organic Vapor

The solubility at equilibrium of ethyl acetate in a polyimide ﬁlm was obtained
from the weight gain of the sample at long sorption times, where weight gain is
determined at steady state. A representative plot of Mt/ M55, as a function of time, for
the sorption of ethyl acetate by the non-clay polyimide ﬁlm, is presented in Figure 12.
The theoretical sorption curve obtained by solution of Equation 22 is superimposed for

comparison.

 

 

 

-D7r2(2n+1)2t] (22)

M °° 8
' =1- ex
M, giannfnz p[ 12

The sorption behavior of clay-loading polyimide ﬁlm (2.5 v/v%) is illustrated in
Figure 13 and is representative of the sorption proﬁle curves obtained for the respective
clay/polyimide composites studied. The theoretical sorption curve for the clay/polyimide

ﬁlm is also presented in Figure 13 for comparison.

56

1.2

 

0.8 -
0.6 .

0.4 .

M 1’" cs (mm/(m9)

 

Figure 12

 

 

. Experimental (mg/mg)
— Theoretical (mg/mg)

 

 

 

 

 

50 100 150 200 250
Time (hour)

A representation plot of M,/ M55 as a function of time, for the sorption of

ethyl acetate by the non-clay polyimide ﬁlm. (av = 0.68)

1.2

 

1.0 -

0.8 4

0.6 .

0.4 .

M , m“ (mg/mg)

 

0.2 .

0.0

Figure 13

 

 

 

 

 

 

 

O. 0 Experimental (mg/mg)
—— Theoretical (mg/mg)
50 100 150 200 250 300 350 400
Tlme (hour)

A representation plot of Mt/ Ms, as a function of time, for the sorption of

ethyl acetate by the 2.5 v% polyimide-clay ﬁlm. (av = 0.68)

57

It can be seen that the theoretical curve lacks a good ﬁt to the experimental data,
and as shown, the initial portion of the experimental data is approximated by a straight
line. The lack of good agreement between the experimental and calculated sorption data
can be explained by the fact that a calculated D value can not accurately account for the
whole sorption kinetics in the limited range of diffusion coefﬁcient variations. The
equilibrium solubility values (C) and the time values to equilibrium (tss) determined for
ethyl acetate in non-clay and clay loaded polyimide composites ranging from 1.25 % to
5% (v/v) are summarized in Table 3 and Table 4, respectively. As shown, while the
sorption time to equilibrium varied dramatically as a function of clay loading, the
equilibrium solubility of ethyl acetate in the unﬁlled polyimide and clay/polyimide
composite membranes was relatively constant at the respective vapor activity levels
studied. It can be concluded that the polymer matrix and clay ﬁller have similar organic
vapor absorption properties, and the clay has neither a synergetic or antagonistic effect on

the solubility of organic vapor in the polyimide matrix.

Table 3 Vapor activity dependence of solubility values in polyimide-clay
nanocomposites (23 i 1 0C)

 

 

 

 

 

 

 

 

 

Ethyl acetate 0 v% clay a 1.25 v% clay 2.50 v% clay 5.0 v% clay
vapor activity Polyimide ﬁlm Polyimide ﬁlm Polyimide ﬁlm Polyimide ﬁlm
(mg/mg polymer) (mg/mg polymer) (mg/mg polymer) (mg/mg polymer)
0.68 0.141 21:0.002 0.130 0.124 0.116
0.55 0.126 :t0.004 0.120 0.1 15
0.44 0. 112 i0.002 0.108 0. 104
0.34 0.101 $0.001 0.096
0.27 0.091 :t0.002 0.082
0.21 0.082 2120.002
0.15 0.067 i0.002

 

 

 

 

 

 

‘1 Solubility values are the average of at least two sorption tests.

58

Table 4

clay nanocomposites (23 i 1 °C, 1mil ﬁlm thickness)

Variation in normalized sorption time (t,,) to equilibrium in polyimide-

 

 

 

 

 

 

 

 

 

Ethyl acetate 0 v% clay 1.25 v% clay 2.50 v% clay 5.0 v% clay
vapor activity Polyimide ﬁlm Polyimide ﬁlm Polyimide ﬁlm Polyimide ﬁlm
(hours) (hours) (hours) (hours)

0.68 188 255 313 509

0.55 369 457 788

0.44 569 787 1089

0.34 700 1667

0.27 957 2034

0.21 1 108

0.15 1358

 

 

 

 

 

* The time value to equilibrium (t,,) is calculated by the time value which is equal to 6
times of t1/2 (half-sorption time value).

The sorption capacity of the organo-clay inclusion was also determined and

compared to the solubility of ethyl acetate in the non-clay loading polyirrride membrane.

The results are summarized in Table 5. As shown, the clay ﬁller and the polymer matrix

exhibit comparable sorption properties for ethyl acetate vapor.

 

 

 

Table 5 Equilibrium solubility values (mg/mg sorbant) of clay powder and unﬁlled
polyimide ﬁlm.
Ethyl acetate vapor activity 0.68 0.44 0.27
Clay powder 0.131 0.082 0.055
Original polyimide 0. 141 0. 1 12 0.09 1

 

 

 

 

 

With regard to the equilibrium solubility determined for the respective

clay/polyimide hybrid membrane, it can be assumed that the solubility value is the sum of

the polymer equilibrium solubility value and the clay inclusion solubility value.

59

 

 

Equation 30 can therefore be used to estimate the solubility values of the clay loading

polyimide nanocomposites.

6,... =(1-Mf)Cp+Mch (30)

where M; is the weight fraction of the clay inclusion in the composite. In this case, the
weight fraction of the clay is equal to two times the volume fraction of the clay (Vf). Cp
and Cc are the solubility values of the non-clay polymer and the clay powder itself,
respectively. Estimated values for the equilibrium solubility of ethyl acetate in the
1.25% (v/v) clay/polyimide hybrid are summarized in Table 6. The determined
solubility values are also listed for comparison. As shown, good agreement was
obtained between the experimental and calculated solubility values. This is also shown
graphically in Figure 14, when calculated and experimental solubility values are

compared for the 1.25 v/v% clay/polyimide composite at selected ethyl acetate activity

 

 

 

 

 

levels.
Table 6 Comparison of experimental and calculated absorption properties of a
polyimide clay hybrid as a function of ethyl acetate vapor activity
w a = 0.68 a = 0.44 a = 0.27

Solubility (wt/wt sorbant)
Cp Polyimide 0.141 0.1 12 0.091
Cc Clay powder 0.131 0.082 0.055
chp 1.25 v% polyimide-clay hybrid 0.130 0.108 0.082
Cest 1.25 v% clay + 98.75 v% polyimide 0.141 0.110 0.090

 

 

 

 

 

60

 

 

 

 

3

E 1

§ I

B

.5.

o“

2

'1'

z. I Experimental 1
g DEstimated .
2

o

m

 

 

 

 

 

 

 

 

 

 

a = 0.44 a = 0.27
Vapor activity , pip,

 

Figure 14 Solubility values comparison for the 1.25 v/v% clay-loading polyimide
composite, between the experimental and calculated values.

61

 

2. Solubility coefﬁcient

The equilibrium solubility coefﬁcient values (S) determined for the respective
polyimide-clay nanocomposites membranes are summarized in Table 7. The S values
reported were determined by the tangent methods, as discussed in the Materials and
Methods section. Typical plots of the calculated solubility coefﬁcient (S) as a function of
ethyl acetate vapor pressure for the non-clay loading and clay-loading (1.25 % v/v)
polyimide membrane are presented in Figures 15 and 16, respectively. As shown, with
increasing vapor activity, the solubility coefficient (S) decreases and approaches a
constant at high activity levels (i.e. av > 0.5). The Henry's law constant, k0, would be the

lower limit of the solubility coefficient.

 

 

 

 

 

 

 

Table 7 The calculated solubility coefficients S (cc [STP]/cc . pa") for the non-
clay and 1.25 % v/v polyimide clay nanocompOsites.
Vapor Vapor partial Solubility coefﬁcient Solubility coefﬁcient
activity pressure (pa) (0% v/v polyimide ﬁlms) (1.25 % v/v polyimide ﬁlms)
0.15 1694 0.00456 0.00438
0.21 2458 0.00440 0.00424
0.27 3205 0.00434 0.00419
0.34 4065 0.00431 0.00417
0.44 511 1 0.00429 0.00415
0.55 6326 0.00427 0.00414
0.68 7894 0.00426 0.00413

 

 

 

 

 

 

 

As shown, with increasing vapor activity, changes in the solubility coefficient
between the hybrid and polyimide matrix are almost imperceptible, over the whole range
of vapor activities studied. Clay did not appear to inﬂuence the sorption of ethyl acetate
vapor by the polyimide ﬁlm, at the concentrations evaluated. For the respective

nanocomposite ﬁlms, the solubility coefficients were similar to the solubility coefﬁcient

62

values obtained for the non-clay polyimide ﬁlms, at comparable vapor activity levels.

As shown in Table 7, and from Figures 15 and 16, it was found that the solubility
coefﬁcient values were independent of vapor activity, at vapor activity values great than
0.5. For the polyimide-clay nanocomposite, the clay appears to have little effect on the
solubility of ethyl acetate in the polyimide ﬁhn, while signiﬁcantly changing the inherent
mobility of ethyl acetate vapor within the polymer bulk phase. Okamoto et a1. (1992)
observed similar behavior for water sorption by the same type of polyimide ﬁhn, where
the solubility coefﬁcient increased at low water vapor activities and leveled off at

medium and high water activities.

63

0. 0050

 

0.0045 .

0. 0040

0. 0035

Solubility coefficient
(cc [STP] cc ' pa ')

 

 

0.0030 . . . . . . .
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0. 700 0.800

Vapor Activlty, p/p ,

 

Figure 15 Solubility coefﬁcients of non-clay polyimide ﬁlms

0.0050

0.0045 3' v
r 4

0.0040 .

 

 

0.0035 .

Solubility coefﬁcient
(cc [STP] cc pa ')

 

 

0.0030

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800
Vapor Activity, p/p ,

 

Figure 16 Solubility coefﬁcients of 1.25 v/v % clay/polyimide ﬁlms.

64

3. Dual mode sorption parameters

The sorption isotherms obtained for the non-clay polyimide and 1.25 v/v %
clay/polyimide nanocomposite are presented in Figures 17 and 18, respectively, with the
calculated sorption isotherm curve obtained from Equation 8 superimposed for
comparison. As shown, the sorption isotherm obtained for this polymer is concave to the
activity axis at low activity and linear at higher activity levels and was accurately
described by Equation 8, the dual-mode sorption model. Okamoto et a1. (1992) found
that for water sorption by the same type of polyimide ﬁlm, the sorption isotherms of
water vapor in polyimide ﬁlms were in good agreement with the dual-mode sorption
model. Okamoto et a1. (1992) proposed that the large values of both kg and b and the
small values of C 'H are characteristic of water vapor sorption in the polyimide ﬁlms, as
compared with the respective constants describing C02 sorption. The large values of
both kg and b are suggestive of interaction between imide groups and water molecules.
Large values of both kg and b and a small value of C '2; cause appreciable deviation from

the Henry's law isotherm, in the low vapor activity region.

Cszp+m (8)

The dual mode sorption parameters for the ethyl acetate vapor/polyimide ﬁlm
system are summarized in Table 8. The constants for water vapor sorption by the same
type of polyimide ﬁlm, as reported by Okamoto et a1. (1992), are also given for

comparison. According to the dual mode sorption model, the total quantity of penetrant

65

sorbed (C) is comprised of the Henry’s law component (CD) and the “hole” ﬁlling
components (CH). The Henry’s law solubility (CD) and the Langmiur solubility (CH)
values are plotted as a frmction of vapor pressure for the ethyl acetate/polyimide system
in Figures 19 and 20, respectively. As shown in Figure 20, the "hole" ﬁlling component
of the polymer matrix is saturated by organic vapor, when the vapor pressure exceeded
1600 pa. The small values of k0 (Henry's law solubility constant) and the large values of
C 'H (Langmuir capacity constant) are characteristic of organic vapor sorption in the

polyimide ﬁlms, as compared to water vapor sorption.

 

 

 

 

Table 8 Dual-Mode Sorption Parameters for Polyimide ﬁlm
[(1) b C 'H
CC(STP)/Cco pa pa’l [cc(STP)/cc]
Ethyl acetate vapor 0.00425 0.0218 20.5
23 °C (Non-clay)
Ethyl acetate vapor 0.00412 0.0252 19.6
23 °C (1.25 v% clay)
Water vapor 0.00630 0.0022 6.0
50 °C “ (Non-clay)

 

 

 

 

 

 

3'" Okamoto K., 1992. " Sorption and Diffusion of Water Vapor in Polyimide Films ".
Journal of Polymer Science: Polymer Physics Edition 30: 1223.

66

60.0

 

50.0 .
40.0 .
30.0 .
20.0 - z’

/ |.- ._

 

C [cc(STP)/cc]

Q Experimental
_ Theoretical

10.0 J

 

 

 

 

0.0 .5.. , ,5,
0100020003000400050006000700080009000

Vapor Partial Pressure, pa

Figure 17. Typical sorption isotherm of ethyl acetate in non-clay polyimide ﬁlms at
23°C

 

 

 

C [cc(STP)/cc]
S
O

l— . Experimental
— Theoretical

 

 

 

 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Vapor partial pressure, pa

Figure 18. Typical sorption isotherm of ethyl acetate in 1.25 v/v % clay/polyimide
ﬁhns at 23°C

67

40.0

 

35.0 -
‘g 30.0 .
E 25.0 .
m 20.0 .
‘0
o 15.0 9
9- 100
a . .
o 5.0 .

0.0

 

 

 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Vapor Partial Pressure, pa

Figure 19. Concentration (CD = KD . p) by Henry's Law is a function of the vapor
pressure.

30. O

 

25.0 -
20.0 . ‘__-_.n_.l__.——r——o
15.0 .
10.0 .

5.0 .

CH, (cc[STP]Icc)

 

 

0.0

 

O 1000 2000 3000 4000 5000 6000 7000 8000 9000
Vapor Partial Pressure , pa

Figure 20. Langmuir solubility (CH = C - CD) is not a function of the vapor pressure at a

relatively high vapor partial pressure.

68

Diffusion Properties

For the sorption of the ethyl acetate by the non-clay polyimide ﬁlms and clay-
loading ﬁlms, the experimental sorption curve was found to deviate from the theoretical
data. These ﬁndings would indicate that the sorption process might follow non-Fickian
behavior. Thus, the difﬁrsion coefﬁcient values were determined by the application of
the curve ﬁtting methods described in the Materials and Methods section (see Page 44 -
51). Tables 9 & 10 summarize the diffusion coefficient values determined by the
respective curve ﬁtting methods, over a range of vapor activity levels. As shown, in
Tables 9 and 10, the calculated diffusion coefﬁcients appear to be similar, for the
respective methods. In the present study, the Least Squares Method was used to
calculate the diffusion coefficients. For validating the diffusion coefﬁcient variance, the
Least Squares Method provides an integration procedure which includes the entire
sorption data. Also, the diffusion coefficients would be consistent with the data obtained

from earlier studies, which used the same least square method (Barr, 1997).

Table 9 Diffusion coefﬁcient values (mz/s) for non-clay polyimide ﬁlms,
determined as a function of vapor activity.

 

 

 

 

 

 

 

 

Vapor Diffusion Coefﬁcients Diffusion Coefﬁcients Diffusion Coefﬁcients
Activity By By By

(a,) Gauss-Newton method Half sorption time method Least Squares method
0.15 0.347 x 10 '“f 0.388 x 101° 0.401 x 10 'j‘j
0.21 0.460 x 10 i": 0.476 x 10 "I 0.537 x 10::I
0.27 0.479 x 10 'I° 0.551 x 10 I° 0.608 x 10 III
0.34 0.700 x 10 ‘16 0.754 x 10 1‘: 0.875 x 10 ‘j‘j
0.44 0.884 x 10 4“ 1.036 x 10 'jj 1.290 x 10 'j‘j
0.55 1.380 x10 'I° 1.429 x10 "III 1.725 x10 "I
0.68 2.780 x 10 'I° 2.808 x 10 'I° 3.290 x 10 'I°

 

 

 

 

 

 

69

Table 10

Diffusion coefficient values (mI/s) for clay-loading polyimide ﬁlms,
determined as a function of clay loading and vapor activity.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Clay Vapor Diﬁ‘usion coefﬁcients Diffusion coefﬁcients Diffusion coefﬁcients
Loading activity By Gauss-Newton By Half sorption time By Least Squares
(3,) method method method
1.25v% 0.27 0.215 x 10 "6 0.259 x 10 "6 0.292 x 10 "6
0.34 0.255 x 10 "5 0.305 x 10 "5 0.351 x 10 "6
0.44 0.515x10’I° O.669x10°I° 0.715x101°
0.55 1.025x10'I° 1.153x10'I° 1.280x10’I°
0.68 1.995 x 10 "6 2.066 x 10 “6 2.290 x 10 "5
2.5 v% 0.44 0.451 x 10 "6 0.484 x 10 '1‘ 0.555 x 10 "6
0.55 0.611 x 10 "6 0.669 x 10 "6 0.745 x 10 "6
0.68 1.555 x 10 "6 1.684 x 10 "6 1.903 x 10 "6
5.0 v% 0.68 0.885 x 10 “6 1.035 x 10 "5 1.160 x 10 "6

 

70

 

1. Effect of Ethyl Acetate Vapor Activity

Diffusion coefﬁcient values obtained from the gravimetric experiments are
presented in Table 11. For better illustration, the results obtained for the non-clay
loading polyimides and the 1.25 v/v % polyimide/clay nanocomposites ﬁlms are
presented graphically in Figures 21 and 22, respectively. As shown, in Table 11 and
Figures 21 & 22, for the non-clay loading polyimide and the 1.25 v/v % clay composites,
diffusion coefﬁcient values increased with an increase in vapor activity of ethyl acetate,
indicating a concentration dependency of the diffusion coefficient. Okamoto et a1.
(1992) found that for water sorption by a similar polyimide ﬁlm, the diffusion coefﬁcient
increases at low water vapor activities and leveled off at medium and high water

activities.

Integral sorption from zero pressure was investigated. Figure 23 shows typical
normalized sorption curves of non-clay polyimide nanocomposites. M, and Mss refer to
the mass sorbed at time t and the mass sorbed at steady state, respectively. Plots of M. ./
Mss versus time initially were linear. As shown, equilibrium sorption was achieved
within 100 hours at av = 0.68 and 500 hours at av = 0.27, judging from the diffusion
coefﬁcient. At low vapor activity, the approach to equilibrium is extremely protracted,
indicating the presence of a slow, minor component of sorption in addition to the normal,

major mode of sorbate uptake.

71

4.00
3.50 .
3.00 .
2.50 .
2.00 .
1.50 .
1.00 .
0.50 .

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Ethyl Acetate Vapor Activity, P/Ps

 

(m’lsec) x 10 "‘

Diffusion Coefﬁcient

 

 

 

Figure 21 Diffusion Coefﬁcients of non-clay polyimide ﬁlm versus organic vapor
activity.

2.50

 

2.00

1.50 .

1.00 .

(m’lsec) x 10 '“

Diffusion Coetl'lclent

0.50 .

 

 

0.00 0. 10 0. 20 0.30 0.40 0.50 0.60 0.70 0.80 0. 90 1.00

Ethyl Acetate Vapor Activity, P/Ps

 

Figure 22 Diffusion Coefficients of 1.25 v% polyimide-clay nanocomposite ﬁlms
versus organic vapor activity

72

1.2

 

 

 

 

 

 

 

 

 

 

3
E
B
.5.
3
2
gr —e—a=0.68
+a=0.44
+a=0.27
0 100 200 300 400 500
Time(hou r)

 

 

 

 

 

 

 

 

Figure 23 Variation in normalized sorption of ethyl acetate in non-clay polyimide
ﬁlm with time after introduction of vapor at 23 °C. Diffusion coefficients
are 3.2, 1.2, and 0.6 (x 10'I°m2/s), respectively.

Table 11 Vapor activity dependence of diffusion coefﬁcient values (x 10’[6 1n2/s) in
polyimide-clay nanocomposites.

Vapor Clay loading Clay loading Clay loading Clay loading
aCﬁVit)’ 0 v/v% II 1.25 v/v% 2.50 v/v% 5.00 v/v%
0.68 3.25 i 0.04 2.29 1.90 1.16
0.55 1.69 i 0.04 1.28 0.75
0.44 1.13 i 0.14 0.72 0.56
0.34 0.89 i 0.05 0.35
0.27 0.65 :i: 0.06 0.29
0.21 0.48 i 0.06
0.15 0.36 :t 0.06

 

 

 

 

 

 

a. Diffusion coefﬁcient values are the average of at least two sorption tests.

73

 

The data obtained showed a signiﬁcant increase in the diffusion coefﬁcient with
an increase in vapor activity for the non-clay loading polyimide and the 1.25 v/v %
clay/polyimide nanocomposite. Such dependence is well known for a number of
polymer-permeant systems, for which an exponential relationship was proposed (Crank,
1951). The permeation data through a ﬁlm can be accounted for by a diffusion
coefficient, which increases exponentially with an increase in the local solute content in

the polymer ﬁlm, as described by Equation (31):

D = D* exp(y C) (31)

Where D* is the limiting diffusion coefﬁcient and y is a coefﬁcient that can be
interpreted as characterizing the ability of a penetrant to 'plasticize' a polymer, i.e. to

increase the polymer segmental chain mobility.

Schematically, the polymer structure is loosened as penetrant molecules are
inserted between polymer segments, and more free volume is available for penetrant
diffusion. The molecular origin of the exponential dependence of the diffusivity on both
penetrant concentration and polymer free volume can be found in the free-volume theory
(Neogi, 1996) (Meares, 1993). Figures 21 and 22 indicate that the diffusion coefﬁcient
for ethyl acetate increases exponentially with its local concentration in the polymer

membranes.

74

0n the other hand, it should be noted that the observed increase in the diffusion
coefficient, with increased solute content in the polymer, must not lead to a value larger
than that of the solute self-diffusion coefﬁcient. In fact, being limited by the extent of
penetrant sorption, the diffusion coefﬁcients increase less than tenfold, over a vapor
activity range from the vacutun state to saturated state. In the case of the polyimide-clay
nanocomposite of 1.25 v% clay loading, the diffusion coefficients increase about six-fold,

when vapor activity increased from 0.3 to 0.7.

The exponential relationship found between the diffusion coefﬁcient and vapor
activity for the polymer ﬁlm is consistent with the results obtained by Perrin (1996) on
the water/polyvinyl alcohol (PVA) system, but shows a lack of agreement with the results
reported by Okamoto et a1. (1992) on the water/Polyimide system and Gu (1997) on the
ethyl acetate/Polyimide system. Gu (1997) reported that ethyl acetate vapor
concentration did not signiﬁcantly affect the permeability coefficient values for the same
polyimide ﬁlms, over a vapor pressure range between 1700 to 3200 Pa. The results of the
permeability studies reported by Gu are summarized in Table 12. The diffusion
coefficient values determined by Gu (1997) and the values obtained in the present study
are summarized in Table 13. The lack of agreement between the diffusion coefﬁcient
values reported by Gu and those obtained in the present sorption studies is not fully
understood and a clear explanation for the discrepancy between these two cases can not

be provided. The present studies suggest that the behavior of the diffusion coefficients is

75

the result of the effect of local chain organization, clay dispersion, polymer matrix

morphology and the distribution of clay domains.

Table 12.

composite ﬁlms at 23 °C in the Literature (Gu, 1997).

Effect of ethyl acetate vapor pressure on the permeability of Clay/polyimide

 

 

 

 

 

 

 

 

 

Vapor activity Ethyl acetate partial Permeability Coefﬁcient ( Kg nV(m?sec pa) )
(a,) pressure (Pa) 0 v/v % Clay 2.5 v/v% Clay
0.27 3200 1.24 x 10 '"I 0.188 x I?“
(24.36 mmHg) -- --
0.15 1700 1.14x10'I° 0.127x10'I°
(12.87 mmHg)
Table 13. Comparison of the diffusion coefﬁcient values of Non-clay polyimide

composite ﬁlms/Ethyl acetate at 23 °C between the Literature (Gu, 1997) and this study.

 

 

 

 

 

 

 

 

Vapor activity Ethyl acetate partial Diffusion Coefﬁcient ( m‘ /sec )
(av) pressure (Pa) Literature This Study
0.27 3200 (3.1 i 0.2) x 10 "4 (6.5 i 0.6) x 10 "7
(24.36 mmHg)
0.15 1700 (5.7:1.3)x10'” (3.6i0.6)x10'I7
(12.87 mmHg)

 

76

 

 

2. Effect of Clay-Loading on Polyimide-clay Nanocomposites

 

 

.a=0.68
Aa=0.55
*— .a = 0.44

Diffusion Coefficient
(x 10’" m‘lsec)

 

 

 

 

 

 

 

 

O. 00 , . . 2 . . . . a . - .
0 0.01 0.02 0.03 0.04 0.05 0. 06

Clay loading (vlv)

 

Figure 24 Clay-loading Dependence of diffusion coefficients in Polyimide-clay
Nanocomposites

 

 

 

 

 

 

 

 

 

a

E

3

E

:3 -—o—0 V/V%

E- _._1.25 vlv %
+2.5 vlv 96
+5.0 WV 96

0 .. . f . . . . f
0 100 200 300 400 500 600 700 800

Time(hour)

Figure 25 Variation in clay-loading dependency of normalized sorption of ethyl

acetate (a = 0.68) in polyimide/clay ﬁlms with time after introduction of vapor at 23 °C.

Diffusion coefﬁcients are 3.3, 2.2, 1.9, and 1.1 (x 10'1° mz/s), respectively.

77

Figure 24 shows the variation of the diffusion coefﬁcient as a ﬁmction of the clay loading
level. Also, Figure 25 presents typical normalized sorption curves, as a function of clay
loading. As shown in Figure 25, at high clay loading, the approach to equilibrium
sorption levels is extremely protracted, indicating the presence of a longer diffusion path
through the ﬁlm. This is illustrated in Figure 24, which shows that, with an increase in clay
loading, the diffusion coefﬁcient decreased dramatically. The function of the clay can be
interpreted as characterizing the ability to 'modify' the polymer, i.e. to increase the
diffusion path of a diffusing gas through the polymer matrix. For a gas-impermeable clay,
the diffusion coefﬁcient values may only be determined by the aspect ratio (L/W) of the

clay inclusion and the clay loading v).

These results also show that the effect of clay loading and organic vapor activity are
independent. As a result, the degree of improvement of the barrier properties of
polyimide/clay nanocomposites depends on the clay inclusion. It appears that the clay
restricts the permeant mobility by decreasing the diffusion coefﬁcient. The decrease in
the diffusion coefﬁcient can be explained by an increase in the tortuosity of the diffusion
path and also by a restriction of the mobility of the polymer segments blocked in the
impermeable clays. The greater the level of clay loading, the lower the effectiveness of
penetrant diffusivity, at the same penetrant concentration. However, no model is

available to account for the above effects.

78

Such dependence found between the diffusion coefﬁcient and the volume fraction of
clay inclusion in the polymer ﬁlm is consistent with the results obtained by Gu (1997) (See
Table 12), who reported that the clay-loading level dramatically affected the permeability
coefﬁcient values for the same polyinride ﬁlms. The results of the sorption and permeability
studies show that the mineral clay inclusion dramatically improved the barrier properties of

intercalated and exfoliated polyimide-day nanocomposite ﬁlms.

79

3. Aspect Ratio and Tortuosity

As shown by transmission electron microscopy (TEM), for the clay/polyimide
composites, montmorillonite is disposed parallel to the ﬁhn surface. (Lan, 1994) In this
case, the total path of diffusing gases is increased. If montmorillonite plates of length L
and width W, are dispersed parallel within the polymer matrix, the tortuosity factor I,
which can be directly calculated by the aspect ratio (L/W), is the main factor in

controlling the diffusivity of the vapor through the polymer matrix (Nielsen, 1967).

As previously discussed, (see page 56 - 58), the clay loading level doesn't appear
to effect the solubility values and the respective solubility coefﬁcients, where S, and Sp
(Sc and Sp are the solubility coefﬁcient values for the composite and polymer matrix,
respectively) are equivalent. In Equation (18), the relative permeability data can
therefore be replaced by the relative diffusion coefﬁcient data. Therefore, the relative
diffusion coefﬁcient ratio (Dc / DP), where Dc and DI, are the diffusion coefﬁcients for the

composite and polymer matrix, respectively, is given by Equation (32):

 

 

D P DS 1 .
__c-§_c.___ c c = (32)
DP Pp DpSp 1+ (L/2W)v,

where V; represents the volume fraction of clay, and the aspect ratio (L/W) can be

estimated ﬁ'om the experimental diffusion coefﬁcient data.

80

 

 

 

 

0.8 -

a 0.6 -
Q

a” 0.4 -

0.2 _

0 . . a . . . .
0 0. 025 0. 05 0. 075 0. 1
Volume Fraction
Figure 26 Relative diffusion coefﬁcient value of polyimide-clay nanocomposite at

ethyl acetate vapor activity = 0.68 @23 °C 0%RH.

Based on this expression, an effective aspect ratio was estimated from the diffusion
coefficient data (DC/DP). Figure 26 illustrates the results obtained by application of
Equation 44 to the experimental data. The solid curve represents the best ﬁt of the
calculated values from Equation 45 to the experimental data. The best-ﬁt curve yields an
effective clay aspect ratio of approximately 100 from the ethyl acetate sorption studies.
Table 14 summarizes the estimated aspect ratio values obtained from the permeability
data reported in the literature for similar clay/polyimide composites. The aspect ratio
determined in the present study fell within the range reported in the literature. It should
be noted that the ﬁlms used in this study were the same ﬁlms employed by Gu (1997).
Also, it is further assumed that the clay texture in the nanocomposite ﬁlms evaluated in

the present study is similar to that obtained by Lan (1994) and Yano (1993), since the

81

methodologies employed in the respective studies in preparing the nanocomposite ﬁlms

were similar.

 

 

 

 

 

 

 

Table 14 Comparison of the estimated aspect ratio with the literature data.
Penetrant (23 °C) Source Estimated Aspect Ratio
Ethyl Acetate This study 100
Water Gu, 1997 132
C02 Gu, 1997 83-
02 Gu, 1997 87
C02 Lan, 1994 192
Water Yano, 1993 200

 

 

 

 

 

It should be pointed out that the diffusion path model described is based on the
assumption that the impermeable clay layers are perfectly oriented and evenly spaced
within the matrix of the polymer. However, this situation is not likely to be realized in

actual composite structures (Messersmith 1995).

As described above, a low loading level (i.e. 5% wat) of clay improves the
barrier properties of polyimide nanocomposite drastically. In general, for polymer ﬁlms
containing conventional clay type ﬁllers, clay loading levels of up to 40%(wt/wt) are
required to reduce the permeability of the clay ﬁlled structure. The observed increase in
the barrier performance of the nanocomposite is attributed to the molecular level
dispersion and speciﬁc geometry (thin plate) of the clay layers in the polymer entity.
Those facts result in a large interfacial area between the clay and the polymer matrix and

lead to excellent barrier properties.

82

Error Analysis

I. Uniformity of the nanocomposite ﬁlms

The uniformity of the test ﬁlms introduced the most variation in this study. Each
sample of ﬁlm was prepared by an individual batch procedure. Even for the pure
polyimide ﬁhns, variations may occur when using polymer solutions from a different
condensation polymerization series. In addition, when preparing polyimide-clay
composites, variation in stirring efﬁciencies in the reaction vials may result in different
aspect ratios (L / W) for the clay particles. Finally, each ﬁlm was cast on individual glass
plates. Differences in surface properties of the respective glass plates may result in
variation of ﬁlm structure which may effect the orientation of the ﬁlms and tortuosity of

the permeant diffusing through.

It is assumed that the diffusion coefﬁcient would be most impacted by a lack of

uniformity of the polyimide ﬁlms.

83

II.

Thickness variance of the ﬁlms

All of the variables described above can contribute to differences in the individual
ﬁlm samples in terms of the ﬁlm thickness. The following is an example of
thickness variation for a 2.5 v/v% Polyimide-clay ﬁlm, at an ethyl acetate vapor

activity of av = 0.68. (Table 15)

Table 15. Thickness distribution of the test ﬁlm (2.5v% polyimide-clay) for
the sorption of ethyl acetate at av = 0.68 and T = 23°C.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 2 3 4 5 6 u 0'
Thickness 0.75 0.80 0.85 1.05 0.90 0.85
(mil)

7 8 9 10 ll 12 0.908 0.090
Thickness 1.00 0.90 1.00 1.00 0.90 0.90
(mil)

 

The variation of the thickness can account for the variation observed for the

diffusion coefﬁcient values.

84

III.

Concentration variance of the permeant

The concentration of the ethyl acetate vapor in the hangdown tube can
effect the partial pressure of the sorbate, which can directly impact the sorption
value used in calculating the diffusion coefﬁcient, especially in the very
beginning of the experiment. The volume of the hangdown tube (i.e. 500cc) is
signiﬁcant. At the start of the sorption experiment, the volume is void of
permeant vapor. While in an ideal test simulation, the volume in the
electrobalance hangdown tube should instantaneously be ﬁlled with the desired
vapor concentration at the time of experiment initiation, the physical design of the

apparatus do not make this possible.

At an operating ﬂow rate of 15 cm3/min, the time required for the vapor
concentration in the hangdown tube to approach 95% of the desired level would
be approximately 2 hours. Figure 27 shows the plot of the ethyl acetate vapor
concentration as a function of time. Compared to the time values to equilibrium
(Table 4, Page 59), the time to reach the desired vapor concentration level would
likely be minimal. Thus, the time required for displacement of the electrobalance
hangdown tube volume by the penetrant vapor stream has introduced a small

fraction of error into the diffusion coefficient values.

85

1.20

 

1.00 _

 

0
0

0.80 _

0.60 _

Pressure (96)

0.40 -

0.20 -

 

Partial Pressure/Equilibrium vapor

0.00 . , ,

 

 

.4

0 1 2 3 4 5
Time (hour)

Figure 27 Equilibrium vapor pressure in the lower portion of the

electrobalance hangdown tube as a function of time.

86

IV.

Temperature variance of testing system

Temperature changes would effect the speed of the molecular movement and
would effect the equilibrium solubility, as well as result in a change in the ratio of
diffusivity. This is therefore an important variable in determining the diffusion
coefﬁcient. In the present study, the temperature of the test system was at
ambient temperature (23 i 1 °C) and would ﬂuctuate with building temperature
ﬂuctuation. A typical plot of temperature versus time is presented in Figure 28.

The solid line in Figure 28 is the vapor uptake proﬁles.

30.0
29.0
- 28.0
_ 27.0
. 26.0
. 25.0
24.0
23.0
22.0
21.0
, , 1 , 20.0
0 50 100 150 200 250 300
Time (hour)

 

   

 

Vapor uptake (mg)

 
 

‘ 7‘ ’.e :5 ,
'wht: ‘4 4"“ “'1:

+1.25 v% clay Poiyimide@ a=.55
_ _ .- - Roorn'i'emperature

 

Room tempearture (° C)

 

 

 

 

QANQAOIQV

Figure 28 1.25v% Polyimide-clay composite sorption proﬁle under
alternating system temperature.

As shown, the highest temperature was 27.2 °C, the lowest temperature was

221°C, with a mean temperature at 23.23 i 1.04 °C.

87

V. Non-Fickian sorption behavior

During the sorption of ethyl acetate by the non-clay polyimide ﬁlms and clay-

loading ﬁlms, the experimental curve was found to deviate ﬁ'om the theoretical data.

The higher the vapor activity, the greater the departure from the theoretical data and the

higher the residual error. These ﬁndings can be explained by sorption induced swelling

of the polymer matrix, resulting in the sorbate/polymer system exhibiting non-Fickian

behavior. Table 16 summarizes the residual error, over the whole vapor activity range.

The dramatic changes observed at the vapor activity values greater than 0.3 are evident.

 

 

 

 

 

 

 

Table 16 Residual errors by the Gauss-Newton curve ﬁtting method as a ﬁrnction
ethyl acetate vapor activity.
Vapor Residual Error Diffusion Coefﬁcient Difﬁrsion Coefﬁcient II
Activity By By By
Gauss-Newton method Gauss-Newton method Least Squares method

0.15 0.044 0.347 x 10 III 0.401 x 10 III
0.21 0.045 0.460 x 10 I° 0.537 x 10 I°
0.27 0.045 0.479 x 10 III 0.608 x 10 II
0.44 0.084 0.884 x 10 I° 1.290 x 10 'I°
0.55 0.085 1.380 x 10 I° 1.725 x 10 'II
0.68 0.090 2.780 x 10 'I° 3.290 x 10 'I°

 

 

 

 

 

 

88

Summary and Conclusion

The sorption of ethyl acetate vapor by polyimide-clay nanocomposite ﬁlms was
determined with the Cahn 2000 electrobalance, using a gravimetric technique and
recording the weight gain by the polymer sample as a function time and vapor activity.
The clay loading content and the organic vapor activity are the two major factors
affecting the sorption and diffusion properties of polyimide-clay nanocomposites. For
this nanocomposite ﬁlm, montmorillonite is dispersed homogeneously within the

polyimide matrix and oriented parallel to the ﬁlm surface.

No signiﬁcant change was found in the solubility values at equilibrium between
the non-clay ﬁhns and clay loading ﬁlms, over the range of testing vapor activity levels
studied. The equilibrium solubility values of polyimide-clay nanocomposite ﬁlms could
be accurately estimated by the total value of the independent unﬁlled polymer and the
clay powder itself. The results of sorption studies showed that the polymer matrix and
clay ﬁller have similar organic vapor absorption properties, and the clay has neither a
synergetic or antagonistic effect on the solubility of organic vapor in the polyimide

matrix.

Comparison of the solubility coefﬁcient values obtained for the non-clay ﬁlms
and clay loading ﬁlms showed the values to be reasonably consistent, over the range of
vapor activity levels studies. Because of the imperceptible changes in equilibrium

solubility between the polyimide-clay hybrid and the simple polyimide matrix, over the

89

entire range of activity levels studied, the organic vapor solubility coefﬁcient values were
not effected by the presence of the clay inclusion. According to the dual mode sorption
model, the solubility coefﬁcient value would appear to be a constant value, represented
by Henry's law constant, kg, at medium and high vapor activity. Compared with the
water sorption data, the small values of kg and the large values of CH (Langmuir capacity

constant) are characteristic of ethyl acetate vapor sorption in the polyimide ﬁlms.

The exponential relationship found between the average diffusion coefﬁcient and
the vapor activity for the test systems evaluated can be explained by 'plasticizing' of the
polymer matrix by the organic vapor, thus enhancing polymer chain segmental mobility
as penetrant molecules are inserted between polymer segments, and resulting in an
increasing in more free volume available for penetrant diffusion. The free-volume
theory well described the molecular origin of the exponential dependence of the
diffusivity on penetrant concentration and polymer free volume. The observed increase
in the diffusion coefﬁcient, with increased solute content in the polymer, should not lead
to a value larger than that of the solute self-diffusion coefﬁcient. In this study, the
difﬁrsion coefﬁcient increase around tenfold, over a vapor activity range from the
vacuum state to saturated state. In the case of the polyimide-clay nanocomposite of 1.25
v/v% clay loading, the diffusion coefficients increase about six-fold, when vapor activity

increased from 0.3 to 0.7 .

Such dependence found between the diffusion coefﬁcient and the clay loading

content of the nanocomposites can be the result of the effect of the aspect ratio and

90

tortuosity. Due to the speciﬁc structure, it is assumed that montmorillonite was
dispersed homogeneously and disposed parallel to the ﬁlm structure. As a result, the
polyimide-clay nanocomposite had excellent vapor barrier properties. Only a small
volume ﬁ'action of clay will result in a signiﬁcant decrease in the diffusion coefﬁcient.
The diffusion coefﬁcient of a 5.0 v/v% clay/polyimide ﬁlm at vapor activity a, =I0.68 is
only one third of the diffusion coefficient value of the comparable non-clay polyimide
ﬁlm. The greater the level of clay loading, the lower the effectiveness of penetrant
diffusivity, at the same penetrant concentration. This result is well explained by an
increase in the tortuosity factor. The effective clay aspect ratio of approximately 100
from the ethyl acetate sorption in the present studies fell within the range reported in the
literature. The observed increase in the barrier performance of the nanocomposite is
attributed to the molecular level dispersion and speciﬁc geometry (thin plate) of the clay
layers in the polymer entity. Those facts result in a large interfacial area between the clay

and the polymer matrix and lead to excellent barrier properties.
Thus, the clay loading content, sorbate concentration and speciﬁc geometry of the

clay layers in the polymer matrix would provide the polyimide-clay nanocomposites with

unique properties for application in the packaging area.

91

Recommendation and Proposed Future Studies

Base on the results of this study, a number of recommendations for future
research can be suggested. The following proposed studies might lead to a better
understanding of the mass transfer of low molecular weight penetrants through the

polyimide nanocomposites.

1. Due to the time constriction, this study only conducted one run for the sorption
experiments involving the polyimide-clay nanocomposite ﬁlms. It is proposed to
duplicate the sorption experiments for the clay-loading polyimide ﬁlms (1.25

v/v% ~ 5.0 v/v%) at vapor activity av = 0.21, 0.27, 0.34, 0.44, 0.55, 0.68.

2. Ethyl acetate was picked as the sorbate in this study because of its presence in
many food ﬂavor proﬁles. A similar study comparing the solubility and diffusion
coefficient values should be made using a series of sorbates of varying molecular

mass.

3. The current studies was conducted at RH = 0. It can be proposed that a similar
investigation be conducted as a function of relative humidity (i.e. 50%, 95%) to
investigate how the moisture affects the sorption mechanism for organic

penetrants. .

92

"..‘..4. IF: “I” i
. r

 

 

 

In this study, all sorption measurements were conducted at ambient temperature.

It is proposed that additional experiments be conducted over a range of

temperatures, to investigate:

i) whether the temperature dependence of the solubility, and diffusion
coefﬁcient values can be described by the Arrhenius equation,

ii) whether the solubility, and diffusion values agree as a function of

temperature.

Sorption by non-clay and clay loading-polyimide ﬁhns should be determined at

lower ethyl acetate activity levels (i.e. a, = 0.01, 0.02, 0.05, 0.1) where feasible,

to understand how well the experiment data ﬁts the dual-mode sorption model.

93

APPENDICES

94

Appendix A

Vapor-Liquid Equilibria for pure substances (V LPT)‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ethyl acetate (Ethanoic acid ethyl ester, Ethyl ethanoate): C4 H3 02
141-78-6 M = 88.1063
Coefﬁcients: a] = 21.1891 a2 = 2838.03 a3 = -56.5630
T (°C) P (mmHg)
—20 6.390
-15 9.149
-10 12.874
-8 14.629
-5 17.262
-4 18.681
0 24.359
2 27.462
4 30.893
6 34.679
8 38.848
10 43.432
12 48.463
14 53.973
16 59.998
18 66.576
20 73.745
21 77.564
22 81.546
23 85.697
24 90.022
25 94.527
30 119.950
40 187.850
60 417.980

 

 

 

 

 

I CRC Handbook of Thermophysical and Thermochemical Data. (David R. Lide & Henry V. Kehiaian)

95

Appendix B

Basica Program for Diffusion Coefﬁcient by "Consistency for Continuos Flow" Method"

10
20
30
40
50
60
70
80
90
100
110
120
130
140

150
160
170
180
190
200
210
215
220
230
235
240
250
260
270
280
290
300

305
310
320
330

REM sorption continuous ﬂow experiment

DIM F980), T(80), x(80), DF(80)

REM time -- minute, D -- m /sec

INPUT "Enter the thickness of the ﬁlm (MIL) -- ", LL
INPUT "Enter the steady state sorption value (mg) -- ", Fl
NUM=0:N1=1:N2=1

DF(NUM+1) = F(NUM+1)/FI

READ T(NUMI), F(NUM+1)

DF(NUM+1) = F(NUM+1)/FI

IF T(NUM+1) = 99.99 THEN 140

PRINT T(NUM+1), F(NUM+1)

NUM = NUM+1

GOTO 80

GUESS = 10 ’SET INITIAL GUESS

REM NEW-RAPHSON METHOD

FOR 1=1 T0 NUM

IF DF(I) < 0.05 AND DF(I+1) >= 0.05 THEN N1=I+1

IF DF(I) < 0.95 AND DF(I+1) >= 0.95 THEN N2=1

NEXT I

FOR I = N1 T0 N2
A = 0.44313 * DF(I) 'SQRT(rr)/4 = 0.44313
x = GUESS

FOR J: 1 To 10

B = SQR(X)

c = EXP(-X)

H=(0.5/B-B)* C

x = x- ((B'l'C - A)/H)

IF x <0 THEN GUESS = SQR(GUESS) : GOT0 215

NEXT J

X(I) = 1/x

GUESS = x

NEXT 1

REM LINEAR REGRESSION
ST = 0

SX = 0 : SXT = 0

STSQ = 0

 

‘ Referenced by Burgess and Hernandez, 1998.

96

340 SXSQ = 0
350 NN =N2 -N1 +1
360 FOR I =N1 T0 N2

370 ST = ST + T(I)

380 sx = sx + X(I)

390 SXT = SXT + X(I) * T(I)
400 SXSQ = SXSQ + X(I) * X0)
410 STSQ = STSQ + T(I) * T(I)
420 NEXT 1

430 SLOPE = (ST * SX - NN * SXT)/(ST * ST - NN * STSQ)

440 DUMI = (NN * SXT) - (SX * ST)

450 DUM2 = (NN * STSQ) - (ST * ST)

460 DUM3 = (NN * SXSQ) - (SX * SX)

470 DUM4 = SQR(DUM2 * DUM3)

480 R= DUMl/DUM4

490 LPRINT LL; "MIL, "; ' 1.25V% Clay/Polyimide Film at Ethyl Acetate Vapor"
500 LPRINT

510 LPRINT "Time (min) ", "Weight gain", " l/X", "Relative Percentage"
520 FOR I =' 1 TO NUM

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

540 NEXT I
550 LPRINT
555 LPRINT "STEADY STATE SOLUBILITY "; FI; "mg"
560 LPRINT

570 DIFF = ((LL * 0.0000254)"2)/4/60 * SLOPE

580 LPRINT "DIFFUSION COEFFICIENT (mZ/sec) ="; DIFF
590 LPRINT

600 LPRINT "CORRELATION COEFFICIENT =", R

610 REM CONSISTENCY

620 F11 = F] / 4

630 I = 1

640 1 =1 + 1

650 IF DF(I) < 0.25 GOTO 640

660 T14 = T(I-1)+(T(l)- T(I-1))/(F(I)- F(I-1))*(F11 - F(I-1))
670 I: I + 1

680 IF DF(I) < 0.5 GOTO 670

690 T12 = T(I-1)+(T(I)- T(I-1))/(F(I)- F(I-1))*(F11* 2 - F(I-1))
700 IF I = NUM THEN 730

710 1 =1 +1

720 IF DF(1) < 0.75 GOTO 700

730 T34 = T(I -1)+(T(I)- T(I-1))/(F(I)- F(I - 1)) * (F11 * 3 - F(I-1))
740 LPRINT

750 LPRINT "T El"; T14, " T U"; T12, " T U"; T34

760 x14 = 1/(SLOPE*T14) : x12 = l/(SLOPE'l‘TlZ) : x34 = 1/(SLOPE*T34)
770 PRINT "x14 "; x14, " x12 "; x12, " x34 "; x34

97

780 LPRINT "K1 "; X34/X14, " K2 "; X12/Xl4
790 LPRINT

800 END
810 DATA
820 DATA

830 DATA 99.99,99.99

98

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