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thesis entitled

SORPTION OF ORGANIC PENETRANTS BY AMORPHOUS POLYAMIDE

presented by

MYUNGHOON LEE

has been accepted towards fulfillment
of the requirements for

MASTER degree inPACKAGING

 

Major professor

DateélliIL 1. 1994

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SORPTION OF ORGANIC PENETRANTS BY AMORPHOUS
POLYAMIDE

By

Myunghoon Lee

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

School of Packaging

1994

ABSTRACT

SORPTION OF ORGANIC PENETRANTS BY AMORPHOUS
POLYAMIDE

By

Myunghoon Lee

Sorption studies involving the sorption of n-propanol by an amorphous
nylon ( Nylon 61 /6T ) were carried out as a function of sorbate vapor
activity at 23 0 C.

Vapor activity levels from 0.035 to 0.91 were investigated to evaluate
the concentration dependency of sorption mechanism.

Sorption behavior of propanol by Nylon 6I/6T showed distinctive two
mode sorption phenomena as a function of vapor activity . At vapor
activity levels below a=0.11, equilibrium sorption was achievediwithin a
short period of time ( less than 20 hours ) , which can be interpreted as
fellowing a Fickian diffusion model. i

A Langmuir- Flory-Huggins dual mode sorption model can also be
applied at these concentration levels. However , for vapor activities above
a=0.11, the sorption process appeared to be non-Fickian and resulted in a

lack of equilibrium being attained.

ACKNOWLEDGEMENTS

I'd like to express my heartfelt thanks to my major advisor Dr. Jack . R .
Giacin. His devoted and endless supports enabled me to complete this
research. I would also like to thank Dr. Ruben Hernandez and Dr. Eric. A.
Grulke for their precious advice and discussion throughout the course of
research. I also thank to Dr. Heidi and Mr. Bob Hurwitz for helping me to
design and assemble the test system and to provide comfortable
circumstance during the research.

I am deeply indebted to the Korea Institute of Industrial Design and
Packaging , which sent me to study in the School of Packaging. Finally ,
my lovely wife and two daughters deserve to have my deep thanks and love

for their devoted supports during the research.

ii

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

INTRODUCTION

LITERATURE REVIEW
Characteristics of Amorphous Polymers
Properties of Amorphous Polyamide
Properties of Penetrant
Sorption Mechanisms
Ideal sorption and diffusion
Non ideal sorption
Modified dual mode sorption
Factors affecting the sorption process
Temperature
Crystallinity
Orientation
Sorption measurement

iii

Page

vi

13
14
14
16
20
22
22
25
27

30

Diffusion and relaxation in glassy polymers

Correlation of sorption with penetrant size

MATERIALS AND METHODS
Polymer film
n-Propanol
Sorption measurement

Density experiment

RESULTS AND DISCUSSION
Data preparation and prelimenary test
Equilibrium sorption
Analysis of sorption at vapor activity a < 0.11

Analysis of sorption at vapor activity a > 0.11

CONCLUSION

APPENDIX

Appendix A Procedure for standard calibration
curve constraction

Appendix B Electrobalance calibration procedure

Appendix C Vapor activity fluctuation

BIBLIOGRAPHY

iv

31

33

35
35
35
36
39

47
49

53

67

68

70
71

76

LIST OF TABLES

Table Title Page

1. Comparison of the properties between Amorphous 12
Nylons and Nylon 66

2. Relationship between rotameter readings and 45

vapor activities

3. Volume fraction vs. vapor activity from Flory- 51
Huggins equation

4. Average vapor activity and standard deviation 52
in each step of vapor activity

Figure
l.

2.

10.
ll.
12.
13.
14.
15.
16.

17.

LIST OF FIGURES

Title
Structure of Nylon 61 / 6T
Structural formulas of various alcohols
Schematic diagram of electrobalance test apparatus

Saturated vapor pressure of n-propanol
Standard calibration graph of n-propanol at 23 0 C

Illustration of sample flushing by nitrogen at 23 0 C

Evaluation of the reproducability of the sorption system
at a = 0.06

Interval sorption of n-propanol at a = O - 0.035

Interval sorption of n-propanol at a = 0 .035- 0.050
Interval sorption of n-propanol at a = 0.050 - 0. 80
Interval sorption of n-propanol at a = 0.080 - 0.110
Interval sorption of n—propanol at a = 0.110 - 0.295
Interval sorption of n-propanol at a = 0.295 - 0.390
Interval sorption of n-propanol at a = 0.390 - 0.490
Interval sorption of n-propanol at a = 0.490 - 0.840
Interval sorption of n-propanol at a = 0.840 - 0.910

Successive interval sorption of n-propanol into Nylon 61/6T
at 23 OC(a=0-0.9l)

vi

Page
10
13
41

42

43

56

56
57
57
58
58
59
59
60
6O
61

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

Successive interval sorption of n- propanol into Nylon 61/6T
at 23 OC(a=0-0.110)

Experimental sorption isotherm for n-propanol in Nylon
6I/6T at the low vapor activities ( a< 0.11 )

Flory - Huggins plot when x = 1.6 from the equation
Ina1=1nV1+ v2 + xv22,v,=1- V3

Plot of Mt/Moo vs. t 1/2 for n-propanol sorption by
Nylon 6I/6T, at 23 0C ( a = 0 - 0.035)

Plot of Mt/Moo vs. t 1/2 for n-propanol sorption by
Nylon 6l/6T, at 23 0C ( a = 0.035 - 0.050)

Plot of Mt/Moo vs. t 1/2 for n-propanol sorption by
Nylon 61/6T, at 23 OC ( a = 0.050 - 0.080)

Plot of Mt/Moo vs. t 1/2 for n-propanol sorption by
Nylon 6I/6T, at 23 0C ( a = 0.080 - 0.110)

Comparison between experimental and calculated
data at vapor activity a =0.035

Deviation from Equation(21) due to non - Fickian
sorption for sorption of n-propanol by Nylon 6I/6T

at 23 0C( a = 0.11 - 0.295): Graphic estimation of
Fickian Moo value

Plot of Mt/Mco vs. t 1/2 for n-propanol sorption by

Nylon 6I/6T, at 23 0C; a = 0.11 - 0.295, Equation
(21) for Moo = 0.275 and t 1/2 = 84 sec.

Plot of Mt/Moo vs. t 1/2 for n-propanol sorption by

Nylon 6I/6T, at 23 0C; a = 0.11 - 0.295 ; points
observed curve,Equation(21) for Moo = 0.275

and t 1/2 = 84 sec.

vii

61

62

62

63

63

65

65

66

66

29.

30.

32.

33.

35.
36.

37.

Distribution of vapor activity at
Distribution of vapor activity at
Distribution of vapor activity at
Distribution of vapor activity at
Distribution of vapor activity at
Distribution of vapor activity at
Distribution of vapor activity at
Distribution of vapor activity at

Distribution of vapor activity at

a = 0.035
a = 0.050
a = 0.080
a = 0.1 10
a = 0.295
a = 0.390
a = 0.490
a = 0.840
a = 0.910

viii

71
71
72
72

73

74
74

75

INTRODUCTION

Over the past decade , the development and use of high barrier
plastic materials has increasingly replaced traditional glass and metal
containers for food and beverage packaging.

The advantages of plastic packaging are numerous and include :
low cost . light weight , a wide range of mechanical properties ,transparency.
flexibility , direct food contact , and general consumeripreference
because of convenience and microwaveability ( Salame , 1986).

However , with the use of plastic packaging there are concomitant
concerns related to product / package interactions. This is a broad based
topic that includes transport of gases and organic vapor of low molecular
weight : (i) from the product through the package , as well as (ii) from
the environment through the package to the product.

The specific mass transport ( permeability ) process may be described as
a function of penetrant concentration , temperature , and time to equilibrium,
as well as the composition of the penetrant / polymer system.

Therefore , polymer structure , free volume , chain stiffness or
segmental mobility , and the availability of specific sites of interaction in the

polymer,plus the physicochemical characteristics of the penetrant (gas, water

vapor , or organic vapor) determine the mode and mechanism of sorption

1

2

and thus . the resultant transport and mechanical properties of the polymer
( Blatz , 1989 ).

The dual mode sorption model has been widely used to describe the
solubility of gases in glassy polymers . and in glassy , polar polymers
as well. This model assumes that the solute molecules in the glassy
polymer consist of non-specifically absorbed and specifically adsorbed

species , which are in dynamic equilibrium in the medium ( Michaels et al.,
1963 )

The solubility of the absorbed species is represented by Henry's law ,
and the solubility of the adsorbed species is described by a Langmuir type
adsorption isotherm. The Langmuir sorption is believed to occur at
specific sites , usually considered to be units of stable free volume present in
the amorphous polymer structure.

Local equilibrium between the absorbed and adsorbed populations is
maintained throughout the polymer matrix. The total amount of solute

sorbed by both mechanisms is :

CH' b
C=CD+CH=KDP+——— (1)
l + bp

where C is the total concentration of sorbed solute in the polymer ,

CD and CH are the solubilities due to absorption ( Henry's Law ) and

Langmuir type adsorption respectively , K1) is the Henry's law

3

constant . b is the hole affinity constant . CH' is the hole saturation
constant and p is the pressure.

Recently , Hernandez et a1. ( 1991 ) have studied the sorption
of water vapor into an amorphous polyamide ( Nylon 61 / 6T ).
The authors have applied a dual mode sorption model , based on
Langmuir and Flory - Huggins equations , to describe the sorption
process. The total amount of water sorbed by the polymer was described
by the summation of a Langmuir type association , and by a solution
component mode given by the Flory-Huggins model , which is given by:

V1 = V1L + V1FH (2)

Where V1 is the total volume fraction of water within the polymer , and the
superscript L and FH refer to Langmuir and Flory - Huggins water sorption

contributions , respectively. These contributions are expressed as :

 

K a
V1L= (3)
1 + Ba
and
a=exp[1nV1FH+(l~V1FH)+x(1-V1FH)2] (4)

Where a is water activity , x is the Flory - Huggins interaction parameter ,
and K and B are parameters of the Langmuir equation ( Hernandez et a1.,
1991).

The behavior of oxygen solubility within the polymer / water system

4

was related to V114 , according to the following expression.
V0:2 = V* - FV]L (5)
where V02 is the solubility of oxygen in the polymer as a function of a ,

V* is the solubility of oxygen in the dry polymer , and F is a factor that
relates sorption values of oxygen at dry conditions and the fraction volume
of water described by the Langmuir sorption mode , when water activity
equals one. The fact that 80 % of the total oxygen dissolved by the
polymer at dry conditions was displaced by molecules of water associated
with active sites of the polymer matrix , indicated the importance of these
active sites in the mechanism of the solubility of oxygen within the
Nylon 61 / 6T bulk phase. These results also suggested that molecular size
may be an important factor in determining the final equilibrium sorption
values in the three component system of polymer , water and oxygen
( Hernandez et al. , 1991 ).

Based on the results described above , it can be proposed that a similar
model can be applied to the binary system of polymer and organic penetrants
,which has not yet been reported.

A quantitative relationship between molecular weight of sorbates and
active sites concentration in polyethylene was reported by Gedraitite et a1.

( 1989) , who studied the sorption by polyethylene , of selected low

molecular weight compounds dissolved in n - hexane , and in isopropanol.

D

In addition to the limited amount of data describing the effect of
moisture content on the mass transport and solubility of oxygen in
hydrophilic polymers , no references have been found in the literature
which considered the importance of size distribution of sorption sites in
determining the final equilibrium sorption values for the sorption of organic
penetrants by hydrophilic polymers , such as the amorphous polyamide.

There is also a paucity of data describing the effect of organic vapor
concentration on the solubility and diffusion of organic penetrants in
hydrophilic polymers , and the importance of active binding sites associated
with the polymer matrix in determining the final equilibrium sorption value
for the binary system of polymer / organic vapor.

The proposed studies will provide for a better understanding of the
parameters contributing to the diffusion and sorption of organic penetrants
in hydrophilic polymer membranes .

In terms of practical application , the data obtained describing the
relationship between sorption parameters and the molecular weight of
the sorbate molecule may allow calculation of the solubility of a
penetrant in the polymer matrix from knowledge of the penetrants solubility
in a contact phase , and its molecular weight. This could further provide a
means of designing a barrier structure for a specific end use application.

For example , in the packaging of a juice product , when there is

concern for flavor loss due to sorption _. or sorption of ingredients from a

 

6

pharmaceutical preparation . which could result in loss of product efficacy.

Objectives

1. Determine the equilibrium sorption isotherm for n-propanol in an

amorphous polyamide ( Nylon 61 / 6T ) at water activity 2 0.

2. Provide an empirical framework to study the sorption of organic vapor by
a glassy polymer , and the relationship of Langmuir type association
( active site binding) , to the solubility of organic penetrants in

hydrophilic polymers.

3. Evaluate the appropriateness of the Langmuir-Flory-Huggins dual mode
sorption model to describe the sorption isotherm of n-propanol in the

amorphous polyamide( Nylon 61 / 6T ).

LITERATURE REVIEW

Characteristics of Amorphous Polymers

A vast majority of well-known polymers are characterized by their
structural differences. The conformation of flexible chain molecules in the
melt or glassy state is determined both by the local position and
orientational distribution of chain segments belonging to the same chain
( intramolecular correlations ) or belonging to different chains
(intermolecular correlations ) (Wendorff , 1987 ).

Polymers differ from other low molecular weight organic or inorganic
materials , in that they are composed of long chain molecules , usually
containing a huge number of atoms. This gives rise to a very large number
of internal degrees of freedom for flexible chain molecules ( Blumstein ,
1978 ). The chain is represented by a line in space , the curvature of
which depends upon the persistence length A1. The parameter(Ai) is thus a
measure of the chain stiffness. It corresponds to the distance along the
chain over which correlations in the orientation of successive chain units
extend. The mean square end-to-end distance < h2 > is given by

<h2>/2AiL=[1-(l/x)][1-exp(-x)] (6)
where L is the contour length of the chain and x = L /Ai. A worm- like

chain becomes a flexible Gaussian chain for x —> 00 , and a rigid rod- like

7

8
chain for x —> 0 ( Wendorff . I987 )-

Flexible chain molecules have a persistence length of the order of 1 or
2 nm. A flexible chain in a random configuration occupies only a small
portion of the space it pervades. The density of an isolated chain molecule
is typically of the order of l % of that of the condensed state , and it
decreases with increasing chain length ( Wendorff , 1987 ).

Intermolecular forces require , however , that the empty space be filled in
the condensed , amorphous state. This may be achieved in various ways as
described below. i
(l) The chains may collapse , a process which is known to occur in solutions
with poor solvents ( Williams et al. , 1981) ; (2) The chains may aggregate
in bundles in which neighboring chains or chain segments are parallel to
each other as in a nematic liquid crystalline phase ( Pechhold et al. , 1979 ) ;
(3) The chains may remain in their random configuration and many different
chains are able to pervade the space taken up by the reference chain.

This leads to a highly entangled system ( Gennes , 1979 ).

The distribution of the centers of the chains as well as their orientation is
as close to random , as in a real gas. Macroscopic properties of amorphous
polymers are known to depend heavily on the local spatial and orientational

distribution of chain segments , belonging to the same or to a different

chain (Wendorff, 1987).

 

9

Properties of Amorphous Polyamide

Polyamides containing aromatic residues are normally very high melting,
highly insoluble semi-crystalline materials , which are difficult to process.

In recent years , a number of more easily processed amorphous
polyamides , based on iso— and terephthalic acids have been claimed in the
patent literature. In general , amorphous polyamides can possess a wide
range of good mechanical properties , including tensile and impact
strength , and a high specific modulus , which are desirable for engineering
applications ( Dolden , 1976 ).

The amorphous polyamide ( Nylon 61 / 6T ) which was developed by
the E.I.Du pont De Nemours & Co., Ltd., has a random structure based on
hexamethylenediamine and a 70/ 30 mixture of isophthalic and
terephthalic acids ( Fig. l ), and when dry has a glass transition temperature
(Tg ) of 125 0 C ( Blatz ,1989).

It has good processability by primary extrusion and molding
operations , as well as secondary processing such as thermoforrning.

Film has been produced by both the blown film and flat cast processes.
Coextruded film and sheet can be produced using three to five layers , at

thicknesses from 2 mils to 60 mils.

IO

NHz CH2 - (CH2)4 - CH2 NHz -> Hexamethylene diamine

+

COzH C02”

| + |

\
COzH

|

COzH
lsophthalic acid Terephthalic acid

(70 % ) ( 30 % )

Figure 1. Structure of the Nylon 61 / 6T

Nylon 61 / 6T also has good tensile strength , elongation and tensile
modulus. These properties are similar to those for the other resins used
for quality packaging applications. The tensile strength of amorphous
polyamide is higher than nylon 66 dry , but decreases in a manner
similar to nylon 66 at 50 % RH. The tensile modulus , a measure of
stiffness , shows an atypical trend with increasing humidity. As
expected , the modulus of nylon 66 decreases substantially as the

humidity increases , however the modulus of amorphous polyamide

11

increases slightly. Thus . it maintains its stiffness at high
humidities ( Blatz , 1989 ).

The barrier properties of amorphous polyamide approaches the
levels of polyvinylidene chloride , ethylene vinyl alcohol copolymer
and the extrudable acrylonitrile copolymers. As was previously indicated,
water vapor has an unexpected effect on the permeability of
amorphous polyamide. Whereas the oxygen permeability of nylon 66
film increases on exposure to water vapor , that for the amorphous
polyamide film decreases. Thus , a film of amorphous polyamide has
a significantly better barrier as the humidity increases ( Blatz , 1989 ).

The chemical resistance is usually not as good as the semi-crystalline
resins , such as PET or 6 and 66 Nylon. The resin is unaffected by
dilute acids and bases , but is attacked by acetic acid ( Blatz, 1989 ).

It is also attacked by the common low molecular weight alcohols such as
ethyl alcohol and solutions containing more than 10 % ethyl alcohol.

The amorphous nylon is resistant to both aliphatic and aromatic
hydrocarbons , to chlorinated solvents , ketones , and esters. However ,
methylene chloride will cause swelling ( Blatz, 1989 ).

As with all glassy polymers , as the melt is cooled down and
reaches the glass transition temperature ( Tg ) , the molecular motions

are frozen at that temperature , which results in a void content that is higher

12

than that in a polymer with low Tg . For an amorphous glassy polymer .
the larger the difference in temperature between the Tg and the test
temperature the greater the amount of unrelaxed volume ( sometimes called
the free volume ). Table 1 summarizes selected mechanical and barrier

properties of amorphous nylon ( Nylon 61 / 6T ) and nylon 66.

 

 

Items Unit Amorphous Nylon* Nylon 66
Tensile strength K Psi 10.0 8.0
Elongation % 50.0 70.0
Tensile modulus K Psi 330 340

Heat deflection T. @ 66 psi 26] 0 F (128 0 C) 365 0 F (185 0 C)
of packaging resin @ 264 psi 248 0 F (120 0 C) 151 0 F (66 0 C)

Oxygen Dry 3.3 2.5
Permeability (1) 50 % RH 1.4 5.0

CO2 8.0 10.0( 50 % RH)
Permeability (2)

Water vapor 5.0 5.7
Permeability (3)

 

* SELAR® PA of Du Pont Co.,

(1) CC-mil / 100 SQ. IN. / 24 Hours-Atm. at 30 0 C
(2) CC-mil / 100 SQ. IN. / 24 Hours- Atm. at 80 % RH, 30 0 C
(3) g-mil / 100 SQ. IN. / 24 Hours- Atm. at 90 % RH, 23 0 C

Table 1. Comparison of mechanical and barrier properties of amorphous
nylon* and nylon 66

 

13

Properties of penetrant : l - Propanol

Alcohols may be viewed as alkyl derivatives of water and are indicated
by the formula R - OH. They are structurally similar to water , but have
one of the hydrogens replaced by an alkyl group.

The reactions of alcohols are those of the -OH functional group , known
as the hydroxyl group .

Figure 2 lists both the IUPAC and common names for a variety of

simple alcohols , which include the 1 - propanol used in this study.

 

CH3OH CH3CH20H CH3CH2CH20H
methanol ethanol l-propanol
methyl alcohol ethyl alcohol n-propyl alcohol
CH3CHCH3 CH3CHCH20H CH3
| |
OH CH3 CH3COH
l
CH3
2-propanol 2-methyl-l-propanol 2-methyl-2-propanol
isopropyl alcohol isobutyl alcohol tert-butyl alcohol

 

Figure 2. Structural formulas of alcohols.

14

Sorption Mechanisms

Organic vapors can exhibit concentration dependent mass transport
and sorption processes. The permeant vapor pressure and the type of
vapors that come in contact with the package will also determine the
magnitude of sorption and permeation into and out of polymeric packaging
systems.

The study of the solubility of gases in polymers has a twofold
objective : (1) it permits the establishment of correlations of gas
solubilities , with readily available gas molecular parameters ; and (2) it also

supplies information on the morphology of polymers ( Vieth ,1966 ).

Ideal sorption and diffusion

In ideal gas - polymer systems , both the solubility and diffusion
coefficients are constant at any given temperature , and so the permeability
is also a constant.

Permeation or transport through a polymer film can be described in
terms of its component parts by Equation (7):

P = D S (7)
where S is the solubility coefficient , and D is the diffusion coefficient.

S characterizes the amount of permeant that can be dissolved into the

15

polymer under the given vapor pressure . and D describes the rate at
which the permeant molecules are advancing through the barrier film.

For a simple permeation process , the sorption and desorption steps are
described by the assumption of Henry's law , which relates the
concentration of the penetrant in the polymer , to the vapor pressure in
equilibrium with the polymer. The partial pressure of the penetrant is
further related to the penetrant concentration in the gas phase through the
ideal gas law.

Generally , the application of the ideal gas law is justified since the
concentration of the diffusant in the gas phase is very low. The
diffusion step is described by Fick's first (8) and second laws (9) of
diffusion ( Hopfenberg , 1973 ).

dc
F = - D(c)

 

(8)
6x

dc 6] 6c\

= —| D(C)- | (9)
dt 6x \ 6x)

 

where F is the flux or the rate of transfer of penetrant per unit area ,
expressed as mass of diffusant per unit area per time ;c is the
concentration of the penetrant in the film , expressed in the same unit of
mass of diffusant per unit of volume or mass of the polymer.

D is the mutual diffusion coefficient , in ( length )3/ time ; t is time ;

and x is the length in the direction in which transport of the penetrant

16

molecules occurs.

To obtain the flux (F) or the diffusion coefficient (D) from
Equations (8) or (9) , initial and boundary conditions associated with the
experimental method are needed , and the expressions solved to give the
desired values.

It should be recognized that when the diffusion coefficient is calculated
using Equations (8) and (9) , only approximate values will be obtained.

More accurate estimations of this parameter can be carried out by using ,
for example , a nonlinear maximum likelihood sequential method , based
on the Gauss linearization method ( Beck and Arnold, 1977).

The partial pressure of the penetrant is further related to the penetrant
concentration in the gas phase through the ideal gas law. Application of
the ideal gas law is justified since the concentration of the diffusant in the

gas phase is , in general , very low ( Hernandez et al. , 1986 ).

Non-ideal sorption

The sorption of a low molecular weight compound proceeds by two steps.
Firstly the sorbate penetrates into the relatively ordered polymeric
substance , forming a true solution. The concentration of the
homogeneously dissolved compound is related to the concentrations outside

the polymer by Henry's Law. Secondly the dissolved compound is

1 7

reversibly sorbed by certain centers . which are the zones of destruction of
the short range order. The total sorbate concentration in the polymer will
be the sum of the concentrations of the homogeneously dissolved compound.
and of that sorbed by the sorption centers ( Shlyapnikov and Mar'in , 1987 ).

For systems in which the solubility doesn't conform to Henrys law , both
the diffusion and the solubility parameters are concentration dependent.
The solubility coefficient often is essentially constant at low vapor activities
for the more volatile vapors, and only the diffusion coefficient exhibits
significant concentration dependence ( Rogers et a1. , 1960 ). This
concentration dependence can be understood in the context of the free
volume theory ( Cohen and Tumbull , 1959 ; Fujita , 1961; Kwei and Wang,
1972 ; Peterlin , 1975 ) , which gives a relationship between the diffusion
coefficient D and the fractional free volume f :

D=Aexp(-B/f) (10)
where A is a frequency factor and B is a measure of the minimum hole size
for the jump process ( Choy et al. , 1984 ). Fujita ( 1961 ) further assumed
that

f = fo + B Cs (11)
where Cs is the mass fraction of the penetrant and 8 denotes the
effectiveness of the penetrant molecule for increasing the free volume of the
polymer. Substituting Equation ( l 1) into Equation (10) and assuming

BCs << fo , Equation (10) becomes

 

18

D=Doexp(st) (12)
where

y = 86/ to2 (13)
Peterlin ( 1975 ) has obtained an alternative expression for y in terms of the
fractional free volume of the penetrant , but the physical meaning is
essentially the same.

Equation (13) shows that the concentration coefficient 7 depends on fo
and f3 ; i.e.,y is a function not only of the fractional free volume but also of
the interaction between the penetrant and the polymer. For the two
penetrant-polymer systems , methylene chloride-HDPE and methylene

chloride-LDPE , B does not seem to vary significantly with drawing , so the

change in y is determined largely by the I / fo2 factor , which gives rise to a
substantial increase in y with increasing draw ratio ( Choy et al. , 1984 ).
The idea that the molecules of the penetrant present in a polymer are
of two different types (those mobile , homogeneously dissolved , and those
immobile , sorbed in certain centers ) , was called the dual mode sorption
model. This model has been widely applied to describe nonideal sorption ,
which can explain the irregularities of diffusion and sorption of low
molecular weight compounds ( i.e. , additives ) in glassy polymers ( Paul
and Koros , 1976 ).

The magnitude of the negative enthalpies of sorption reported by

19

Meats ( 1954 ) for neon . nitrogen . oxygen and argon in glassy polyvinyl
acetate and by Barrer et al. ( 1957 ) for organic vapors in ethyl cellulose
were inconsistent with the sorption theories of rubbery systems . and led
Barter et al. to suggest a two-mode , concurrent sorption mechanism for
glassy polymers , namely ordinary dissolution and 'hole' filling. In glassy
polymers , substantial deviations from linearity are often observed in
sorption isotherms at penetrant pressures above 1 atm.

Barrer et al. ( 1957 ) first suggested that two distinct mechanisms may
be operating in the sorption of low molecular mass species by glassy
polymers. They observed isotherms for the sorption of C4 and C5
isomers in glassy ethyl cellulose that curved towards the pressure axis , and
appeared to become asymptotically linear at high penetrant pressures.

These results were interpreted in terms of a "dual mode" sorption model ,
which assumes a combination of Langmuir - type trapping within preexisting

vacancies , plus "true" Henry's law solution. Quantitatively , this may be
written :
C'H P
C = 1(1) p + -——— (14)
l + b p
where C is the total sorbate concentration , K1) is the effective Henry's

law solubility constant , Cu is the Langmuir "capacity factor", b is the

Langmuir site affinity parameter , and p is the gas pressure.

20

Michaels et al. ( 1963 ) also reported the sorption of helium . nitrogen .
oxygen , argon and methane in glassy amorphous , and glassy
semi-crystalline polyethylene terephthalate. For penetrant partial pressures
up to 1.0 Henry's law was followed. However , carbon dioxide at 25 0 C
and 40 0 C , and ethane at 25 0 C, in the same pressure range , deviated from
Henry's law.

The carbon dioxide isotherms prompted Michaels et al. ( 1963 ) to
propose a two - mode sorption model of ordinary dissolution and adsorption
in microvoids ( 'holes' ) , for gas sorption in glassy amorphous polymers.

Michaels and Bixler( I961 ) attempted to adapt the Flory — Huggins
theory of polymer solution to the sorption of simple gases, picturing the
process as first condensation of the gas , followed by mixing of the polymer

and liquid penetrant.

Modified dual mode sorption model

Recently , Hernandez et al. ( 1991 ) also proposed a modified dual
mode sorption model , which described the sorption of water vapor by an
amorphous polyamide at 23 0 C. They modified Eqn. (14) by using the
Flory-Huggins equation to describe non-specific solution , rather than

Henry's Law. This modification allowed the model to fit over the

21

activity range . 0 < a < l . Although other choices for the solution
model are possible , they applied the Flory - Huggins Equation (15)
because of its simplicity.

Ina =an1+ V2 + )(V22 (15)
where x is the interaction parameter. The non-specific sorption term
is nonlinear , the complete model can have an inflection point and should
predict clustering somewhere over the range of activity values
( Hernandez et al., 1990 ). The modified dual mode sorption model is
expressed in terms of volume fractions and solute activity:

V1 = VlFH + V1L (2)
where V 1FH refers to the Flory - Huggins contribution to the solute
volume fraction , and V1L is Langmuir volume fraction contribution.
Since Equation (2) is nonlinear , it is convenient to determine the value
for V 1FH by numerical methods , such as Newton - Raphson technique
and Equation (2) becomes:
K a

V1: FH(a,x)+ (16)
1+ Ba

 

Factors affecting sorption behavior

Temperature

The temperature dependence of the sorption parameters have been
studied for a number of penetrant / polymer systems. The K1) and b
terms are generally decreasing as a function of T , and appear to be well
correlated at a given temperature with the penetrant Lennard - Jones
energy parameter E/K values ( Pace and Datyner , 1980). The data for
C‘ H are more ambiguous.

Some results suggest that OH is independent , or varies only weakly
with temperature , and others suggest that OH is a strongly decreasing
function of T(Pace, 1980). However, it is reasonable to assume that the
immobile species is contained in microvoids formed by local segmental
motions in the rubbery state which have become ”frozen" in the glass.

This frozen void fraction must be , to a first approximation , at least
independent of T to explain the low thermal expansivity of the glass ,
which is comparable to that of the crystalline state. Hence C'H should
also be essentially independent of T ( Pace and Datyner , 1980 ).

The glass transition temperature ( T8) of any amorphous substance ,
whether polymeric or not , is defined as the point where the thermal

expansion coefficient undergoes a discontinuity. In polymers , there

22

23

expansion coefficient undergoes a discontinuity. In polymers . there
may be more than one discontinuity associated with the thermal expansion
coefficient term.

The largest discontinuity is usually associated with the loss of the
molecular mobility . which permits configurational rearrangements of the
chain backbones ( Ferry , 1970 ).

Below the Tg of a polymer , not enough energy is provided to produce
the Micro-Brownian motion of chain segments 20-50 carbon atoms in
length , and the chains are locked into the position created from the
processing history. Sorption and diffusion in polymers at temperatures
below the polymer's Tg consist of more complex behaviors , and are not
well understood at this time ( Hernandez , 1984).

Above the Tg of a polymer , it seems likely that hole filling is an
important sorption mechanism , which is supported by the fact that the
low-pressure ( Henry's law ) solubility for simple gases varies smoothly
on going through Tg , although the apparent heats of solution are different
and constant in the glassy and rubbery regions.

Meares ( 1957 ) proposed the following idealised concept of the gaseous
sorption and diffusion process in polymers at temperatures above and below
Tg , based on the relative activation energies for diffusion and heats of

solution for polyvinyl acetate in the two temperature regimes , and the zone

24

of activation theory.

Above Tg , gas molecules which dissolve in the polymer must create
their own "holes" by separating the interchain polymer contacts.

The penetrant then diffuses through the polymer matrix along cylindrical
voids created by the synchronized rotation of polymer segments about the
C - C bonds ( Meares , 1957). Below Tg , the polymer consists of regions
of densely packed and arranged chains which have limited freedom for
rotation , separated by less dense regions of disordered chains that form the
'holes' into which the gas sorbs. The gas molecules diffuse between these
'holes' by the slight compressing of localized chains in the dense regions
enabling the gas molecules to pass through. This compression in the glassy
state does not create the long cavities common to the rubbery state,
indicating that the zone of chain activation is much larger in the rubbery
state. This zone of activation was found to be essentially independent of
the size of the penetrating molecule ( Meares , 1954 ).

Above the Tg the polymer is assumed to be in thermodynamic
equilibrium , while below Tg the hole concentration is that which was
frozen in at Tg , provided the glass is formed by slow cooling from the
rubbery region. One therefore expects

C'H=Coexp(—Hh/RT), T>Tg (17a)

C'H:Coexp(’Hh/RTg), T<Tg (17b)

25

where Hh is the enthalpy of hole formation . C0 is a pre~exponential term .
and R is the gas constant ; b is also expected . over moderate temperature
ranges , to have a van't Hoff form

b=boexp(- Ead/RT) (18)
where Bad is the energy change of hole filling. Either above or below Tg ,
gas sorption may be thought to take place either :( 1) within an existing hole ,
or (2) at a "site" on the polymer lattice , after creating a hole at that point

( Pace and Datyner . 1980 ).

Crystallinity

It is assumed that even the smallest gas molecule cannot penetrate or
diffuse through a polymer crystallite. Therefore , the higher the degree of
crystallinity in a polymer . the lower the permeability.

Michaels et al.( 1961 ) have found that the solubility constants for
a particular gas were proportional to the amorphous volume fraction , a ,
that is :

K = a K* (19)
where K* is the solubility constant of a hypothetical completely amorphous
polyethylene , and K is the solubility constant of partially crystalline

polyethylene. This relationship suggests that the gases are sorbed entirely

26

in the amorphous phase of rubbery crystalline polymers . and that the
quantity sorbed is directly proportional to a( Hopfenberg and Stannet .
1973).

The relationship discussed in Equation (19) was used by Michaels et al.
( 1963 ) in studying the effect of crystallinity on the sorption of several
gases in glassy semi-crystalline polyethylene terephthalate.

Unlike the rubbery semi-crystalline polyethylene , it was found that
gas solubility , with the exception of helium , is not directly proportional to
the amorphous volume fraction. The decrease in solubility accompanying
crystallization , (C* - C) / C* ( C* is the amorphous polymer solubility and
C is the crystalline polymer solubility ), was smaller than the corresponding
reduction in amorphous volume fraction , l - or. ; and this solubility
decrease on crystallization tended to become less with increasing Lennard -
Jones force constants , e / K of the sorbed gas.

This result can be satisfactorily accounted for in terms of the 'hole'
model of the glassy amorphous phase. Upon annealing the polymer ,it is
more probable that the denser regions crystallize first , tending to remove
more of the amorphous phase used for gas dissolution , therefore leaving
the residual amorphous phase with a higher concentration of 'holes' than in
the previously amorphous polymer. This means that crystallization in
glassy polymers tends to increase the relative contribution of 'hole' filling as

indicated by the CH / a values ; by definition the 'hole' saturation — limit per

 

27

unit volume amorphous phase. Also such an increase in concentration of
'holes' with increasing crystallization accounts for the decreased reductions
in solubility with increasing a / K of the gas , a measure of the tendency of
the gas to condense ( Michaels et al., 1963 ).

Michaels et al.( 1963 ) generalized their original dual sorption model to
include the effects of crystallinity on the solubility of the dissolved species
as shown in Equation ( 20 ).

CH 9 P

C : + (1K*D p (20)
I+bp

 

The usual methods for assessment of degree of crystallinity in nylons
are by measurement of density , differential scanning calorimetry ( DSC )
or by infrared techniques. Density measurement is perhaps most
satisfactory because it is rapid , precise , and unaffected by sample

calibration - the assumption of amorphous and crystalline densities.

Orientation

Polymer chain orientation will "line - up" the crystallites , and cause the
permeating molecule to take a more tortuous path.
Vieth et al. ( 1961 ) have investigated the effects of chain orientation.

The sorption mechanism was found to be similar in oriented and unoriented

 

. 28
polyethylene terephthalate . but the solubility of gas is higher in the oriented

film. An analysis of the sorption data gives higher Henry's law solubility
constants , higher hole-filling constants , and higher hole affinity constants in
the oriented polyethylene terephthalate film. The diffusion of vapors into a
two dimensionally restricted piece of polymer will result in the polymer
molecules being oriented and extended in the direction of diffusion
( Hartley, 1946 ). A number of ingenious optical experiments were
devised to illustrate these effects. Hartley ( 1946 ) also studied directly
the effect of orientation on the rate of penetration of solvents by stretching
cellulose acetate films and following the sorption optically.

The oriented samples were penetrated up to 24 times faster than the
unoriented films. Hartley suggested that the higher sorption rate was due
at least partly to the greater transverse oscillation of the polymer chains
contributing to the sorption process. The magnitude of the penetrant
activity not only affects the rate of sorption but the relative contributions
of Fickian diffusion and relaxation controlled transport.

The penetrant activity , therefore, biases the effect of orientation on
these processes. At low activities Fickian diffusion predominates , and the
effect of orientation on the Fickian diffusion rate is small.

Conversely , at high activities where the transport is controlled by
polymeric relaxations , the relaxation rate is a strong function of orientation ,

which in turn strongly affects the rate of sorption.

 

29
Choy et al. ( 1984 ) studied the sorption and diffusion of toluene vapor at

30 0 C in polypropylene with draw ( orientation ) ratio from 1 to 18.
Drawing leads to the transformation of the initially spherulitic material into
the fibrous structure , with many taut tie molecules lying mainly on the outer
boundary of the microfibrils. The free volume and hence the sorption sites
are thereby reduced , and the microfibrils become less and less permeable as
the draw ratio increases. As a result , the equilibrium concentration and the
zero concentration diffusion coefficient drop by factors of 4 and 30 ,
respectively. The diffusion coefficient increases exponentially with toluene
concentration but the concentration dependence becomes weaker with
increasing draw ratio , indicating that the severely constrained chain
segments in the drawn samples have much less freedom to mix with

penetrant molecules ( Choy et al. , I984 ).

 

3O

Sorption measurement

Sorption experiments are usually carried out at equilibrium vapor
pressure , using a gravimetric technique in an apparatus that records
continually the gain or loss of weight by a test specimen as a function of
time ( Hernandez et al. , 1986 ).

The diffusion equation appropriate for the sorption of penetrant by a
polymer sample in sheet or film form was described by Crank ( 1975 ) as :

Mt 8 -D.Jt2.t l -9D.Jt2.t

=1-—[exr)( )+—exp( )‘l (21)
M... n2 L2 9 L2

 

 

 

where Mt and Mac are the amount of penetrant sorbed by the polymer film
sample at time (t) and the equilibrium sorption level after infinite time ,
respectively ; t is the time to attain Mt , and L is the thickness of the film
sample.
The sorption diffusion coefficient ( D3) can be calculated from Equation
( 21 ) by setting Mt/ Mo: equal to 0.5 and solving to give D5.
0.049 L2
D5 = —— (22)
1;0.5

where to_5 is the "half-sorption time" or the time required to attain the value ,

MIL/Mo: = 0.5

 

31

Diffusion and relaxation in glassy polymer

It is now widely agreed that transport involves both a diffusion process ,
controlled by a concentration gradient , and a relaxation process , controlled
by a time dependent response of the polymer to a swelling stress. The
observed effects may vary not only with the particular polymer / penetrant
system considered , but also with the range of vapor activities or'
concentrations covered in specific experiments ( Berens , I977 ). Logers
(1965) has pointed out that sorption vs. time curves may be pseudo-Fickian ,
sigmoid , or two stage as the penetrant concentration is increased.
Hopfenberg (1970) has also pointed out , however , that at the low
temperatures and activities ,where simple Fickian behavior in the glassy state
might be expected , experimental times become prohibitively long with
conventional polymer film samples. Berens and Hopfenberg( 1977 )
reported that sorption by initially penetrant free polymer samples is
dominated by a rapid Fickian diffusion process , while incremental sorptions
show larger relative contributions from slow relaxation processes. The
relaxation processes appear to be related to slow redistribution of available
free volume through relatively large scale segmental motions in the relaxing
polymer. The diffusion - relaxation model seems to provide a meaningful

analysis of several non - Fickian "anomalies" . including a very slow

 

32
approach to apparent equilibrium . two stage and sigmoidal sorption curves .
and sorption curves involving an initial maximum followed by temporary
desorption and subsequent resorption ( Berens and Hopfenberg . I977 ).

In sorption experiments at very low activities , simple Fickian kinetics
were obeyed and equilibrium was achieved within a short time. In sorption
experiments covering a larger concentration interval , the initial rapid
sorption was followed by a slower further uptake of penetrant which was
qualitatively attributed to a relaxation - controlled swelling process ( Berens
and Hopfenberg , 1977 ).

Berens ( 1977 ) suggested the sorption model for the vinyl chloride
monomer by polyvinyl chloride powder sample , which can be useful for
calculation of numerical values of equilibrium and kinetic parameters ; the

equation is

6 oo 1 1
Mt: Mqu I1 —— Z — exp(-n2kpt | + ZMooj l1 - exp(-kit)'| (23)
l 32 n=1 n2 J i

where M”: is the contributions of the Fickian process at time t , ki is the
respective relaxation rate constant and each MooJ represents the equilibrium
sorption of the i th relaxation process. k}: represents as 43r2D / d2~ where
D is the diffusion coefficient and d is the particle diameter. This model
provides a means for calculating a meaningful and useful diffusion

coefficient from complex sorption data involving long term relaxations

 

33

which may overshadow the rapidly achieved Fickian diffusion. The model
is also used to analyse the unexpected differences in sorption kinetics
between experiments starting with penetrant-free samples ( integral sorption)
and those involving a finite initial penetrant concentration ( incremental

sorption ).

Correlation of sorption with penetrant size

The density of the polymeric substance in the sorption centers is lower
than that for the surrounding polymer , so that the centers may be considered
as units of stable free volume present in the polymer (Gedraitite , 1988 ).

Thus , the free volume associated with the sorption centers corresponds
to the maximum volume of a molecule which can be sorbed by this center.

Most of the usual organic compounds possess approximately the same
density. Thus for each elementary unit of the free volume , there exist a
certain maximum molecular weight of the compound sorbed by the center
( Gedraitite et al. , 1989 ).

In each polymer , there must be a certain size distribution of the
sorption centers , according to which the Langmuir sorption capacity of the
polymer must decrease with increasing molecular mass of the penetrant

under study. On the other hand , the energy of interaction of the

 

34

penetrant molecule with the polymer depends not only on the area of its

contact with the polymer , which may be a function of the molecular

mass of the penetrant , but also on a number of other factors , including

the chemical nature of the penetrant and polymer , so that one cannot expect

an unambiguous dependence of the sorption constants such as capacity

factor and site affinity parameter on the molecular weight of the penetrant

( Gedraitite , 1989 ). As previously described , one measure of molecular

size is the constant b of the Van der Waals equation of state (Berens , 1975 ).
n2 a

(P+ ——-)(V-nb)=nRT (24)

V2

where b is the effective volume of the molecules in one mol of gas , in

liter / mol.

 

MATERIALS AND METHODS

MATERIALS

Polymer Films

An amorphous polyamide , known as Nylon 61 / 6T , provided by the
El. Dupont De Nemours and Co. was used for all studies. The polymer
was synthesized from hexamethylenediamine and a mixture of isophthalic
( 70% ) and terephthalic ( 30% ) acids. Since the acid isomers were
randomly placed into the polymer backbone , resulting in structural
irregularity , no crystallization of the polymer matrix was observed.

No evidence of crystalline melting point was found. A 1 mil thickness
film was used for all studies. The volume fraction of n-propanol within the

polymer as a function of vapor activity was measured by the density gradient

technique ( ASTM D 1505-68 , 1979 ).
n - Propanol
Used as a penetrant.

Supplied from Fisher Scientific Co., Pittsburgh , PA
Specific Gravity ( at 25 0 C ) 0.801

Molecular Weight 60.09 g / mol

Solubility soluble in water and ether
Boiling Range 96.7 - 97.1 0 C

Purity 99.998 %

35

 

3 6
Dichlorobenzene

Used as a solvent for constructing a n-Propanol calibration curve.

Nitrogen

Used as a carrier gas. High purity dry nitrogen 99.98 % by the Union -:~

Carbide Corporation , Linde Division , Danbury , CI‘.

 

EXPERIMENTAL METHODS

Sorption measurements

Equilibrium sorption studies were carried out using a Cahn
Electrobalance , Model D 200 ( Cahn Instruments Inc., Cerrito , California),
which has a sensitivity of 10 '7 g. A schematic diagram of the sorption
apparatus is shown in Figure 3.

A constant concentration of n-propanol vapor was produced by bubbling
nitrogen through the liquid n-propanol. The liquid n-propanol is contained
in a vapor generator consisting of a Pyrex glass gas washing bottle , 250 mm
long and 50 mm diameter, with a frittered dispersion tube. The organic
vapor stream can then be mixed with another source of pure nitrogen , if

further dilution is needed.

37

Before actual testing was conducted. rotameter setting were determined
to provide a range of vapor activities. Vapor activity was calculated by
dividing the experimentally determined vapor pressure by the saturated
vapor pressure ( Perry Handbook.) Figure 4 is the saturated vapor pressure
curve of n-propanol plotted as a function of temperature.

Rotameters were used to provide an indication of the settings required
for the desired vapor activities. The gas flows to the rotameters were
regulated by N upro "M"series needle valves. The relationship between the
rotameter settings and vapor activities is described in Table 2. Each value
of the rotameter column in Table 2 indicates the rotameter reading , when
the middle zone of a spherical bead inside the rotameter is aligned with the
rotameter calibration line. Digital mass flowmeters were also incorporated
between the dispensing manifold and the test cell (inside sampling port ) , to
provide a continuous indication that a constant rate of flow was maintained.

As shown in Figure 3, two sampling ports were installed, both inside and
outside the chamber , to determine accurately the vapor activity within the
hangdown tube , which contained the film sample. Table 2 also shows the
difference in vapor concentration between the two sampling port locations.

For the calculation of vapor activity, a standard calibration curve for
n-propanol was prepared. A detailed procedure and data are presented in
Appendix A and Figure 5 , respectively. A Hewlett Packard 5890A gas

chromatograph equipped with dual flame ionization detection , interfaced to

 

38

3 3390A GC Hewlett Packard terminal was used for propanol detection.
The 5890A GC is a keyboard controlled instrument with a multifunctional
digital processor. From the digital processor . the area under the peak and
retention time was obtained.

Before starting a run , a film sample ,1 1/4"W x 3 1/2"L , and

 

approximately 100 mg weight was cut from the sample roll and dried in the F
vacuum oven ( 24 hours , 70 0 C , 30 psi ). The dried film sample was
transferred quickly into the hangdown tube of the electrobalance which is ._

installed inside a constant temperature chamber ( Thermotron Model SM-
32S-SH , Therrnotron Industries , Holland , Michigan). The film sample
was suspended directly from the arm of the electrobalance , and the system
purged with nitrogen until a constant weight was attained. This process
was monitored by computer screen display. Figure 6 is a graphical display
of a typical sample weight profile prior to initiating the sorption run.

Care must be taken to calibrate the electrobalance prior to performing
sorption experiments. Appendix B provides a brief description of the
procedure for electrobalance calibration.

When the sample weight change during the purging process reached a
constant value the sorption experiment test was initiated , starting with the
lowest vapor activity. This was accomplished by careful control of the
rotameter settings ( Vapor and Nitrogen ) , whose values were predetermined

( Table 2 ). Sorption data was compiled on a computer disc at one hour

39

intervals. Simultaneously the sorption procedure was followed on the
monitor screen through a linear graph , which enables continuous monitoring
of the sorption process.

The sorption of n-propanol was measured at 23 0 C by the successive
sorption or interval sorption method ( Bagley and Long , 1955 ).
For interval sorption studies , the film sample was permitted to equilibrate
with the propanol vapor of fixed vapor activity.

When the sorption reached the equilibrium state , the vapor activity was
quickly changed to the next level ( a ), and the same procedure repeated until
sorption data values for the highest vapor activity were obtained. During
each sorption experiment , the vapor activity was checked twice daily to
insure a constant sorbate concentration throughout the course of the
experiment. Appendix C shows the fluctuation of vapor activity in each

stage.

Density experiments

The test procedure followed was in accordance with the ASTM D
1505 ( Standard test method for Density of Plastics by the Density Gradient
Technique ).

Film densities were determined in a density gradient column with the

 

4o

gradient made of toluene and carbon tetrachloride , which have densities of
0.87 and 1.59 respectively.

For the gradient tube preparation , method C( ASTM D 1505
Appendixes A 2.3 ) was adopted where the liquid entering the gradient tube
becomes progressively more dense. Care should be taken to fill up the
density gradient tube with toluene and carbon tetrachloride mixtures , since
the calibration floats would not be placed correctly unless the filling
procedure is performed at a slow enough rate ( approximately 30 min / 300
mm length of column ).

Test samples whose change in density on conditioning may be greater
than the accuracy required of the density determination should be
conditioned before testing in accordance with the method listed in the

applicable ASTM material specification.

 

41

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chamber Wm Si
I" ——————— ‘1 J I
I
T
l A 5v? I l CU
Tv N | | —
Re Sf
I B (Sp _ I Com
1. _ _ _ _____ _| l-Io
T N Fl
CP 1
PO
8 : Organic vapor Bubbler Fl : Rotameter
Ch: Temperature constant PO: Plotter

Chamber

CU: Control Unit (By
Computer

C : Cell for sampling (Vapor
activity check)

COM2Computer

Ho :Hood

N : Needle Valve

Re: Regulator

Sf: Sample film

Si: Electric signal

Sp: Sampling pot

T: Nitrogen Tank

Tv: Three way Valve

Wm: Cahn Electrobalance
(0200-02)

Figure 3. Schematic diagram of the electrobalance test apparatus

800

 

I

600

 

400 '-

200 '-

Vapor Pressuretmmttol

 

 

 

 

 

o - a
-20 0 20 40 60 80 too
Temperature(oC)

. y = 3.1970 + 0.27732x + 1.013762%? 4- 1.2757e-4x"3 + 3.075996)!“ 4- 2.593598%“.5 3‘2 = 1.000

Figure 4. Saturated Vapor Pressure of n-Propanol

( using polinomial # 5)

Arcanesponao

43

 

20000

I

10000

 

 

 

 

X Y
12025 5830
20.025 9580
40.050 19200
0 A L ' L I L L 1‘ L
1 0 20 30 40 50

Ouantlty(ng-9)

y = 55.596 + 477.71): 8‘2 = MID

Figure 5. Standard calibration graph of n-propanol at 23 0C

 

44

 

 

 

 

      

 

 

97.1 __.__.
98.8 .J
7?
o
5 ~
13
‘ .4

.4
98.1 _.

./ Start the

~ flushing

.1

.4 ‘/ Slnrl the sorption of propanol
95.6 I ' ‘ y I I I I

0: 002 00 102 00: 00 20: 002 00 30'. 00: 00

TIME (HHS: HIN: SECI

Figure 6. Illustration of sample flushing by nitrogen at 23 0C

44: 00: 0

 

4S

 

No Rotameter

Inside sampling port

Outside sariipiihg port

 

 

 

 

 

 

 

vapor N2 1 AR 3 X '50 AR 3 X SD

1 0.5 55 1.129x56.C2m ~- 1.145xE6 .0207
1.2015 .0217 .021 .0008 1.1459 .0207 .021 .0003

1.1834 .0213 5 1.1293 .0204

1.103 .0199 1.1705 .0211

2 1 50 1.466xE6 .0265 1.253xE6 .0226

1.725 .1311 ' 1.503 .0271
1.681 .0303 .029 .0026 1.453 .0262 .027 .0020

1.373 .0248 . 1.488 .0269

1.718 .0310 1.558 .‘1

1.573 .0284 1.581 .0286

3 1 40 2.442xE6 .0441 2229XE6 .0402
25586 .0462 .046 .0012 2.4556 .0443 .043 .0027

25648 .0463 . 25141 .0454

4 2 50 274XE6 .0495 262x56 .0473
2824 .0510 .051 .001 27274 .0492 .048 .0026

28418 .1513 26359 .0476

5 5 50 4.783(56 .0864 4.84xE6 .0873
4.9522 .0895 .087 .0037 4.8783 .0881 .088 .0008

4.5309 .0818 5.1716 .0934

4.9841 .0899 4.534 .0819

6 7 50 5.65xE6 .1021 5.74xE6 JMS
5.8577 .1058 .102 .0029 5.5998 .1011 .099 .0042

5.5078 .0995 5.4223 .0979

5.5406 .1000 5.2013 .0939

7 15 4O 1.58xE7 .2856 1.59xE7 .2883

1.5723 .2848 1.6972 .3074
1.5198 .2753 .287 .0091 1.5124 .2739 .287 .0184

1.6611 .3008 1.4522 .2630

2 1.5784 .2859 1.6613 3&9

 

Table 2. Relationship between rotameter readings and vapor activities

RESULTS AND DISCUSSION

Data preparation and prelimenary test

All sorption experiments of n-propanol in Nylon 6I/6T were determined
at 23 0 C. Prior to carrying out the sorption studies, several parameters
which were related to the sorption measurements were determined.

These include :

 

(1) Calibration curve for n—propanol vapor to calculate the vapor
concentration levels was prepared ( see Figure 5 ). The detailed
procedure is described in Appendix A.

(2) The relationship between the rotameter settings and vapor activities at
the inside and outside sampling port was determined and presented in
Table 2. This results showed good agreement between the vapor
activity values with an error of 6 %.

(3) Dried film samples, which were quickly transferred from the vacuum
oven to the hangdown tube showed a weight loss during the purge step
which was assumed to be due to rapid moisture uptake during sample
transfer to the sorption system.

It was found that to insure complete drying , it was necessary to wait at
least 5 or 6 hours after the film sample attained a constant weight to
initiate sorption studies. The initial sorption experiment was then
started by adjusting the rotameters ( N2 , vapor) to predetermined
values. Figure 6 illustrates the weight change of the polymer film
sample, following purging the electrobalance hangdown tube with dry

nitrogen gas.

46

47
(4) Saturated vapor pressure of propanol at 23 0 C was calculated as 17.52

mmHg from the equation in Figure 4.

In accordance with the above considerations , preliminary studies were
also carried out using two separate film samples in order to evaluate the
reproduceability of the sorption experiment. Initial sorption studies were
carried out under the condition of vapor activity a=0.06 , and repeated with a
second film sample without changing test conditions. Sorption profile
curves are presented in Figure 7. As shown, good reproduceability was
obtained between the two runs with an error less than 3%, which proves that
the apparatus was reliable.

Over the course of the entire experiment , vapor activities were carefully
monitored , and the results are summarized in Table 4 and presented
graphically in Figures 29 to 37, in Appendix C. Plots show the scatter band
of vapor activities versus time and , each data point represents the average
value of four or five replicate analysis at the corresponding time interval.
Vapor activity fluctuation did not exceed 1 7 % throughout the course of

the studies.

Equilibrium Sorption

The sorption of n-propanol in Nylon 61 / 6T , as a function of vapor
activity was determined at 23 0 C. Figures 8 to 16 present the weight
gained for each successive interval sorption measurement, where the uptake

mass fraction is plotted as a function of time.

 

48

Figure 17 shows the overall sorption profile , that includes the
experiments carried out over the entire vapor activity range (i.e. 0.035-0.91).
This figure indicates that "true" equilibrium was obtained within a period of
time less than 20 hours , for n-propanol vapor activity below 0.11.

As shown in Figures 12 to 16 , above a vapor activity of 0.11 , the
sorption process for the propanol / Nylon 61 / 61‘ system appears to be best
described by the diffusion - relaxation model proposed by Berens and
Hopfenberg( 1977 ) , who interpreted the sorption mechanism of vinyl
chloride monomer by polyvinyl chloride as following a Fickian diffusion
process at the low vapor activity levels , and an anomalous relaxation
process at the high vapor activity levels. .

As shown in Figure 18 , for n-propanol activity levels a < 0.11 , the
sorbate uptake was very rapid and the sorbate / polymer system attained
equilibrium conditions. This process can be described as Fickian , where
the diffusion coefficient is a function of vapor concentration , but is not time

dependent.

49

Analysis of sorption behavior at vapor activity below 0.11

As shown in Figure 18 , when the interval between the initial and final
concentration , Ci and Cf is small . equilibration times of less than 10 - 12
hours were observed for the Fickian diffusion process. Thus , the Fickian
diffusion pathway may be assumed to be essentially completed before
applicable stress - relaxation has occurred. This suggests that the
concentration differential is not a variable that determines whether the
process is Fickian , but rather the level of vapor concentration determines
sorption behavior. Above a = 0.11 the sorption process is not Fickian and
exhibits anomalous behavior, while the sorption process appears to follow
Fickian behavior at vapor activities a < 0.11. The limited amount of
sorption data , excludes any possibility of fitting the data to the Langmuir-
FIory-Huggins model , over the whole range of vapor activity. However ,
the data obtained at a vapor activity below 0.11 can be modelled.

As shown in Figure 19, a plot of the weight fraction as a function of
vapor activity shows a linear relationship. Where the weight fraction (Wf)
is defined as the weight gain over the total sample weight

Ws
Wf = (25)
Ws + Wp

Where W5 is the mass of the sorbate and Wp is the mass of the sample.

 

This can be interpreted in two ways ; (i) a simple Henry's law is.
applicable , which suggests simple dissolution of n-propanol in the polymer
film at the low vapor activity levels ( a < 0.11 ) , or (ii) the Langmuir-Flory-

Huggins model can be applied at low concentration levels since the Flory-

50

Huggins equation is quasi-linear at low vapor activity levels and the
Langmuir equation ( see Equation (1)) can also be simplified by reducing the

denominator l + bp _. where it is assumed that

bp << 1 at low vapor activity levels ( a < 0.1 l ) , and
C = CH P (26)

353111999 Maine 9:12.62 J a theoretical plot can be obtained which illustrates
the linearity of the Langmuir-FIory-Huggins model. The calculated data
and the associated plot are presented in Table 3 and Figure 20 respectively.

However , this approach to modelling the sorption process for the
n-propanol / Nylon 6I/6T system could not be verified due to the lack of data
points and the extrordinary amount of time needed to complete the studies.

Figure 20 represent the relationship between volume fraction and vapor
activity at the low vapor activities ( a < 0.11 ). Similar to Langmuir plots
of P/ CH versus P , the straight line in Figure 20 gives clear evidence of a
Langmuir type sorption model for the sorption of n-propanol by Nylon 6I/6T
,at the low vapor activities. From the sorption studies diffusion coefficients
can be determined, when sorption levels are at the equilibrium state. The

Mt/ Mac vs tl/Z curves for the low vapor activities are presented in Figure 21

to 24. The sorption diffusion coefficient (Ds) was then calculated from
Equation 22 by setting Mt/ Moo equal to 0.5 and solving t give Ds As the
sorption uptake levels were measured by hours, the diffusion coefficient
value might have some inherent errors.

Figure 25 presents a comparison between experimental and calculated
data for an independant integral sorption experiment carried out at a = 0.035.
Good agreement was obtained at the low vapor activities whereas significant

differences between the experimental and calculated curves were obtained at

5 1
the high vapor activities, this can be explained as Fickian diffusion at the
low vapor activities and time dependent diffusion by relaxation - controlled

swelling at the high vapor activities.

 

 

Volume fraction (V1) Vapor activity
0.002 -- — -0.027 ----
0.003 0.040
0.004 0.053
0.005 0.066
0.006 0.079
0.007 0.092
0.008 0.104
0.009 0.117
0.010 0.129

 

Table 3. Volume fraction vs. vapor activity from Flory-Huggins equation
lna1=ln V1+ V2+xV22whenx= 1.6,V1=1- v2

 

 

Step Average vapor activity Standard deviation
1 0.035 i 0.003
2 0.050 i 0.0016
3 0.080 t 0.0042
4 0.110 i 0.003
5 0.295 :t 0.0069
6 0.390 i 0.0084
7 0.490 :t 0.015
8 0.840 i 0.027
9 0.910 i 0.0046

 

Table 4. Average vapor activity and standard deviation for each

successive vapor activity interval

 

53

Analysis of sorption behavior at vapor activities above 0.1 l

A somewhat similar "two stage" sorption process has been observed by
Bagley and Long ( 1958 ) for the sorption of acetone by ethyl cellulose and
by Fujita ( 1961 ) for several other systems. Berens and Hopfenberg
(1977) also observed a two stage sorption process as previously discussed.

The “two stage” sorption process can be discussed as follows:

when a solid polymer is brought into contact with a penetrating vapor ,
the penetrant diffuses into the polymer and the polymer swells. Swelling of
the polymer involves larger scale segmental motion resulting , ultimately , in
an increased distance of separation between polymer molecules and it shows
a long term relaxation. This interpretation also seems to be applicable to
the n-propanol / amorphous polyamide system ; in the early stage of
sorption , the n-propanol concentration gradient provides the major driving
force and the transport process is dominated by the Fickian diffusion
(Flgure8- 11 ).

When the concentration of n-propanol resulting from this process is
sufficient to develop a significant swelling stress , the slow response of the
glassy polymer to this stress produces gradual swelling of the amorphous
polyamide structure and permits additional sorption ( Figure 12 - 16 ).

This swelling-relaxation process may continue even after the Fickian process
has produced a virtually uniform concentration of propanol through the

amorphous polyamide.

54

In this event , the sorbate concentration resulting from Fickian diffusion
becomes negligible , and the later stage of sorption is dominated by the
relaxation - controlled process ( Berens , 1977 ).

As discussed above , a distinct two stage sorption process was

observed at the high vapor activities ( a1 > 0.11 ). The rate of sorption in

the initial stage is principally controlled by the Fickian process and
therefore, may be used to estimate a true diffusion coefficient, even when the

total sorption does not follow the Fickian model ( Berens , 1977) .

Furthermore , since the second sorption stage is almost entirely

relaxation - controlled , the kinetic and equilibrium parameters describing

the slow relaxation process can be obtained from long time sorption data.

To determine if the initial portion of the sorption profile , which
exhibited "two stage" sorption behavior , followed Fickian behavior , and to
estimate the diffusion coefficient the following treatment was applied with
the aid of a computer - assisted fitting routine.

Initially , values of M.» were intuitively selected by inspection of a plot
0f the experimental Mt vs. 1 data. This is illustrated for sorption studies
discribed in Figure 26, as shown, the Mac value for a Fickian diffusion
process is assigned , the t 1/ 2 value can be obtained from a plot of Mt / Moo
versus t“2 ( Figure 27 ) and the diffusion coefficient ( Ds ) calculated by
solution of equation (22).

By substituting the Ds value into Equation (21) , calculated values of Mt
are obtained.

The calculated and experimental values of Mt / Moo versus t“2 are then
plotted and the quality of the fit is evaluated by graphical analysis.

If the experimental and calculated values show poor agreement , this

55

procedure is repeated with a new value of Moo until a satisfactory f it
between the calculated and experimental values is obtained ( Figure 26 ).

As shown in Figure 28, an assigned value of Moo = 0.275 ,
gave good agreement ( Figure 28 ) between the experimental and calculated
data for the sorption profile plot at a = 0.295. The estimated diffusion
coefficient for the initial stage of the sorption profile ( i.e, Fickian ) was

1.264 13—10 cm2/sec.

Wt. Gain [m glm 9]

Weight Gainlm g]

56

 

0.07 _
0.06
0.05

 

002: —-o-- WLGng
“n.6mn1

 

 

 

I k I l l 1 4

. I
00 50 100 150 200 250
Time(hours)

 

Figure 7. Evaluation of the reproducability of the sorption
system at a = O - 0.06 ,

 

001 l

 

 

000

000

000

000

000 ‘ ' ‘ 4‘ ‘ '
0 10 20 30

fimaHm)

Figure 8. Interval sorption of n- propanol at a = O - 0.035

Wt. Gain[m 9]]

 

 

 

 

 

0.03

0.02 ’

0.01 '

0.00 . 1 1 1 1 1 . . 1
:13 35 37 39

Times(Hrs)

Figure 9. Interval sorption of n- propanol at a =0035 - 0.050

Weight Gain [m g]

 

0.10

 

0.05

 

 

 

0.00
0 2 4 6 8 10 12

Times(Hrs)

Figure 10. Interval sorption of n- propanol at a = 0.050- 0.080

Weight Gain [mg]

wt. gainImg]

 

 

 

 

0.0 A L A I 1 L l l

0.0 5.0 10.0 15.0 20.0
Times(Hrs)

Figurei 1. Interval sorption of n- propanol at a=0.080-0.110

 

 

 

 

 

80

Times(Hrs)

Figure12. Interval sorption of n- propanol at a=0.11-0.295

Wt. Gejn[m 9]

WI. Gain[mg]

59

 

 

 

 

 

Times(Hrs)

Figure13. Interval sorption of n- propanol at a=0.295-O.390

 

 

 

 

I l 1 l l L l 4 J

'0 so 100

 

Times(Hrs)

Figure14. Interval sorption of n- propanol at a=0.39-0.490

Wt. GainIm 9]

WI. Gain[m g]

60

 

 

 

 

0.0 1 l . l .
50 100 150

Times(Hrs)

Figure15. Interval sorption of n- propanol at a=0.49-0.840

 

 

 

 

l

0.0 A a 4 1 a a 1 a n A
50 1 00
Times(Hrs)

Figure16. Interval sorption of n- propanol at a=0.84-0.910

 

61

 

oooooooooooooo

 

 

 

1.5 - ,.-- 9
.8 .........
I .........
:I'
’3 1 O _ "7 ........... "
E ' f..-
g 6.
=3 5 1: a = 0.035 6: a = 0.390
E o s _ / """"" 2:a=0.050 7:a=0.490
' 3: a=0.080 8: a=0.840
3‘3"; 4:a=0.110 923:0.910
1 2 .---: 5: a = 0.295
0.0 ("""" 1 I 1 1 I 1 1 I L 1 I 1 1 I 1 1 I L 4
0 100 200 300 400 500 600 700

Time(hrs.)

Figure 17. Successive interval sorption of n- propanol into Nylon 61/6T
at 23 0C (a = 0 - 0.91)

 

     

 

 

 

 

P
0.20 -
g a=0.05 - 0.08
I.
‘E’
'8
Q
g 0.10 _ a=0.035 - 0.05
a = 0 - 0.035
0.00 1 1 I 1 1 I
0 50 100

Time(hrs.)

Figure 18. Successive interval sorption of n- propanol into Nylon 6I/6T
at2300(a=0-0.110)

Volume Fraction

Weight Fraction[glgx100)

0.30

0.25

0.20

0.05

0.00

62

 

 

 

 

 

1 I 1 J I 4 1 I 1 1 l #4 I J 4
0.02 0.04 0.06 0.08 0.10 0.12
Vapor Activity

Figure 19. Experimental sorption isotherm for propanol in

0.011

0.009

0.007

0.005

0.003

0.001

Nylon 61/6T at low vapor activities (a < 0.11)

 

I

I ' Y T T V I

 

4

 

j A L M J l A j l l L

 

I I 1
0.06 0.08 0.10 0.12 0.14

Vapor activity

I
0.04

Figure 20. Flory-Huggins plot when I =1.6,from the equation

Ina=InV1+V2+V2

63

 

 

 

 

 

 

 

 

8
2
‘2"
1 I 1 I 1 l 1 l 1
0 40 80 120 160 200
t1/2,Sec1/2
Figure 21. Plot of Mthoo vs t1/2 for n- propanol sorption
by Nylon 6|I6T, at 23 00 (a: 0.0 - 0.035)
110 _
100 [-
90 fi-
80 :-
70 :-
6 60 E
5 so 3
5 40 Z-
30 Z-
20 E-
10 r
0 g I 1 L 1 l 1
0 4o 80 120 160
11/2,sec1/2

Figure 22. Plot of Mt/Moo vs t1/2 for n- propanol sorption
by Nylon 6|/6T,at 23 00 (a = 0.035 - 0.050)

MIIMoo

Mtllvloo

110
100

64

 

 

 

I L I m I 1 I

 

40 80 120 160 200

t1l2,sec1l2

Figure 23. Plot of Mt/Moo vs t1l2 for n- propanol ’sorption

100'

90
80
70
60
50
40
30
20
10

by Nylon 6l/6T,at 23 0C (a = 0.05 - 0.08)

 

 

 

I 1 J

40 80 120 160 200

t1l2,sec1/2

Figure 24. Plot of Mthoo vs t1l2 for n- propanol sorption

by Nylon 6|/6T,at 23 00 (a = 0.08 - 0.11)

65

 

110

100' ‘1 J
90 ..

80':- 9
7O "
60
50
40

30 A (Mt/Moo)experi x100

28 r - (Mt/Moo)ca|cu. x100
1

O . I 1 I 1 I
0 100 200 300

11/25601/2

 

'U'

[MtIMoolxIUU

Y'U

 

 

 

Figure 25. Comparison between experimental and calculated
data at vapor activity a = 0.035

 

 

 

 

 

 

 

 

0.45
1
0.40 -
0.35
.
0.30
0.25
._. 0.20
CD
3; 0.15
-§ '1 :Moo 0.275 mg
0 0'10 2 :Moo 0.284mg
is; 0.05 3 :Moo 0.298 mg
g 0.0011I11111I14L11I1PIL41.J
0 10 20 30 4O 50 60 70 80

t, Hrs

Figure 26. Deviation from Eqn.(21) due to non-Fickian sorption
for sorption of propanol by Nylon 6l/6T at 230C(a=0.11-
0.295):Graphical Estimation of Fickian Moo value

66

 

Ivlt I Moo [gig]

 

 

 

 

OJ
0.0 1 I 1 I 1 I 1 I 1 I 1 I4 [*1 1 I 1
O 20 4O 60 100 120 140 160 180 200
11/2 = 84 sec. t1l2.sec1/2

Figure 27. Plot of Mt/Moo vs. t1l2 for n- propanol sorption by
Nylon 6I/6T ,23 00, a = 0.11 - 0.295,Eqn.(21) for

Moo = 0.275 and 11/2 = 84 sec.

 

MI I Moo [gig]

 

 

 

0.0 1 41 J
100 200

tI/2,sec1l2

Figure 28. Plot of Mt/Moo vs. t 1/2 for n- propanol sorption by Nylon
6II6T, 23 0C (a = 0.11 - 0.295 ): point observed,
curve, Eqn.(21) for Moo = 0.275 and t 1/2 = 84 sec.

Conclusion

The sorption of propanol by amorphous polyamide, evaluated by an
incremental sorption technique, showed that simple Fickian kinetics were
obeyed and equilibrium was achieved within a short time at very low vapor
activities ( a1 < 0.11 ) . However , at high activity levels ( a1 > 0.11 ) , the
initial,rapid sorption was followed by a slower further uptake of
propanol,which was qualitatively attributed to a relaxation-controlled
swelling process. The initial rapid stage of sorption may be related to the
Fickian diffusion of penetrant into pre-existing and available vacancies or
sites in the glassy polymer. The relaxation processes , which occur over a
long time scale may be related to a structural reordering or redistribution of
free volume elements to provide additional sites of suitable size and

accessability to accommodate more penetrant molecules.

67

Appendix A

Procedure of standard calibration curve construction

In all cases , a standard curve of response vs. penetrant concentration
was constructed from standard solutions of known concentration.
Calibration solutions were prepared by dissolution of known quantities of n-
propanol in dichlorobenzene. The detailed procedure follows:

1. Bake out vials and syringes in oven prior to use to remove any residual
solvent or permeant. Cool to room temperature.

2. Using the gas chromatograph , check the retention time of each solvent
by head space technique to ensure there is no interferring peaks at the
propanol retention times.

3. Prepare dilute solutions for the permeant standards by the following
procedure:

- fill up 100 ml volumetric flask with 10 ul of n-propanol and dilute to
make with dichlorobenzene. This becomes 100 ppm standard solution.

- make up similar standard solution with dichlorobenzene , which
becomes a standard solution of 50 ppm concentration.

- Make 2 or 3 more different concentration solutions by using the same
method

4. From the lowest concentration solution , inject 0.5 111 sample solution

directly into the gas chromatograph and the area response recorded.

68

69

Replicate the run and calculate the average

Plot the gas chromatograph area unit response vs. the number of grams
injected per sample. The slope of this curve equals the calibration
factor. Injected quantity can be calculated as follows

W .—: concentration(v/v) x 0.5 111 x 1 ml/ 1000 111 x propanol density(g/ml)

Setting conditions of gas chromatograph are as follows :

o Oven temp. : 50 0 C 0 Initial time : 5 min.

0 Rate : 3 0 / min. 0 Final time : 0 min.

0 Final temp. : 165 0 C o Inject temp.: 200 0 C

o Detect temp.: 250 0 C o Oven max. : 250 0 C

0 He carrier gas : 33 ml/min. 0 Sample injected : 0.5 ul

0 Head space test : 100 1.11 inject

0 Concentration used : 100 , 50 , 25 , 10 , 5 ppm ( 5 kinds )

Appendix B

Electrobalance Calibration Procedure

Cahn D-200 Electrobalance can be calibrated by the following procedure.
. Suspend the sample container on the hangdown wire

. Press the down arrow key three times and the NET WEIGHT box will
display the weight that the balance is actually seeing.

. Enter "Y" into the REZERO box. Next, press the up arrow key once to
go back to the Balance Calibrate menu.

. Enter into Tare Balance box "Y" and the balance will tare.

. Press the down arrow key to input the calibration weight

. Remove the hangdown tube so that the pan is exposed. Then put the
100 mg calibration weight onto the sample weight pan. Replace the
hangdown tube for stable reading.

. Place the cursur into the Calibrate Balance box and enter "Y" and press
ENTER when the pan with the calibration weight is steady.

. Lower the hangdown tube and remove the calibration weight.

. Suspend the sample and set up run conditions.

70

Yap or Activity

trap or Actin’ty

7 1
Appendix C.

Vapor activity fluctuation

 

 

 

 

 

 

0.10
0.08 -
0.06 -
0.04 "' Bun B D—
002 .. Mean: 0.035
Standard deviation: 0.003
000 I 1 I 1 l - 1
0 10 20 30 40
Time(Hrs)

Figure 29. Distribution of vapor activityat a = 0.035

0.10

0.08

0.06

0.04

0.02

0.00

 

 

 

 

 

.
.._B___n—-u—F T
Mean:0.050
" Standard deviation:0.0016
1 l 1 I 1 J 1 I L I 1 I 1
1 2 3 4 5 6 7 8
' Times(Hrs)

Figure 30. Distribution of vapor activity at a = 0.050

i.iap or Activity

trap or Activity

\1
N

 

 

 

 

 

 

 

0.12 _
0.10 :-
E a E,
0.08 _ 43—43— r
0.06 _-
0.04 :-
I Mean: 0.08
0,02 :. Standard devration: 0.0042
0.00 : J— 1 J l L l 1 L 4
6 8 10 12 14
Times(Hrs)

Figure 31. Distribution of vapor activity at a = 0.080

 

 

 

 

 

0.30
0.25 1
0.20 -
0.15 1
0.10 fir—”J; F +
O 05 E Mean: 0.110

' - Standard deviation: 0.003
O’COI- l 1 l 1 l 1 I 1

O 10 15 20 25 3O
Times(Hrs)

Figure 32. Distribution of vapor activity at a = 0.110

 

Yap or Activity

Yap or Activity

 

0.50

0.40 -

0.35

0.45 -

h

 

 

 

 

 

 

 

 

 

 

030E. a 3334 W 5'
Mean: 0.295
0‘25 0 Standard deviation:0.0069
0.2011I11I11I11J11l11I1LI11
0 10 20 30 40 50 60 70 80
Times(Hrs)
Figure 33. Distribution of vapor activity at a = 0.295
0.50
0.45 i-
0.40 - fl 4L
.35
0.35 i' Mean: 0.390
Standard deviation: 0.0084
0.30 LIAAIAIIJIIILIAALAIII;
0 10 20 30 40 so 60 70 80
Times(Hrs)

Figure 34. Distribution of vapor activity at a = 0.390

 

Yap or Activity

Yap or Activity

 

0.60
0.58
0.56
0.54
0.52
0.50 in a
0.48
0.46
0.44
0.42

0'40 4 1 1 1 1 L 1 1 1 1 1 I 1 1 1 1
0 50 100 150

Times(Hrs)

U I I I V

ljl

 

l
E)

' I

mean: 0.490
Standard deviation: 0.015

I

 

V ‘l I

J

 

 

Figure 35. Distribution of vapor activity at a = 0.490

 

 

 

 

 

1.00
0.95 '-
O.90 '- a
L In
0.85 . a a
. a a a
0.80 .
: Mean: 0.84
0-75 _” Standard deviation: 0.027
0.70 h 1 l 1 l 1 1 1 l 1 L 1 I 1 l l_ J 1 l 1
0 20 40 60 80 100 120 140 160 180 200
Times(Hrs)

Figure 36. Distribution of vapor activity at a = 0.840

Yap or Activity

1.00

0.95

0.85

0.80

 

 

0.90

 

Mean: 0.91
Standard deviation: 0.0046

 

l 1 1 l 1 1 l 1 1 l l

 

1 1 I 1 1 1 1
20 40 ' 60 80 100 i 20 140
Times(Hrs)

Figure 37. Distribution of vapor activity at a = 0.910

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