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USE OF QCM TECHNOLOGY FOR MEASURING BARRIER
PROPERTIES OF BIODEGRADABLE PACKAGING
MATERIAL

 

presented by

NITIN GULATI

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USE OF QCM TECHNOLOGY FOR MEASURING BARRIER PROPERTIES OF
BIODEGRADABLE PACKAGING MATERIAL

BY
NITIN GULATI

A THESIS

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

MASTER OF SCIENCE

School of Packaging

2008

ABSTRACT
USE OF QCM TECHNOLOGY FOR MEASURING BARRIER PROPERTIES OF
BIODEGRADABLE PACKAGING MATERIAL
By

NITIN GULATI

For measuring the sorption of water vapor on PLA for three different
temperatures with relative humidity ranging from 20 % to 80 %, a new system based on
quartz crystal microbalance (QCM) was built. For this purpose 1 % wt/v PLA was
dissolved in THF at 35°C, and the polymer film was produced on the surface of the
crystal using spin coating. After spin coating the polymer on the crystal, coated crystals
were kept in a vacuum oven for 5 hours at 60 °C. Polymer films having a thickness Of
1.25i0.29 um were Obtained with a crystallinity Of 21.3 i 2.3 %, glass transition
temperature of 62.3 i 1.4°C and melting point temperature of 151.5 :t 1.0° C. Then,
coated crystals were kept in flow cells housed in a peltier chamber and water vapors
generated by a computer control humidity generator were allowed to enter into the flow
cells. Water vapor diffusion coefficients (D) in the range Of 2.6 to 5.67 x 10-15 m2 / sec ,
solubility coefficient (S) in the range Of 0.33 tO 11.0 x 10'2 Kg/m3-Pa and permeability
coefficient (P) in the range of 0.07 to 3.17 x 10"6 (Kg-m/mz-sec-Pa) were obtained at
temperatures of 10, 23 & 40 °C for relative humidity ranging from 20 tO 80 %.

Equilibration time required for determining barrier properties of polymer was
reduced significantly with this technique as compared to traditional methods. QCM

technology was successful to measure water sorption in PLA.

To my parents and friends

iii

Acknowledgements

I would like to sincerely thank Dr Rafael Auras, my major advisor for his
unlimited support and guidance through out my Master’s degree. His valuable continuous
guidance, comments and suggestions for improving presentation and writing skills are
highly appreciated. Also I would like to thank him for providing me with financial
support during my research project which certainly eased off the financial hardships that I
faced during school. Thanks to my committee members Dr Rubino and Dr. Baker for
their comments and suggestions on my research.

Special thanks to all my friends at School and outside School Of Packaging for
motivating me for the graduate studies and their help at times.

Also I would like to thank my parents for giving me an Opportunity to study

outside India and believing in me

Thanks to all

Nitin Gulati

iv

Table of contents

INTRODUCTION 1
LITERATURE REVIEW 6

2.1 INTRODUCTION ........................................................................................................ 6
2.2 OVERVIEW OF PERMEATION PROCESS ...................................................................... 6
2.3 QUARTZ CRYSTAL MICROBALANCE ...................................................................... 10
2.4 POLYLACTIDE (PLA) ............................................................................................. 21
3 MATERIALS AND METHODS 24
3.] MATERIALS ............................................................................................................ 24
3.2 EXPERIMENTAL SET UP .......................................................................................... 24
3.2.1 Water vapor activity generation system ........................................................ 25
3.2.2 Flow cells ...................................................................................................... 26
3.2.3 Temperature control chamber ...................................................................... 27
3.2.4 QCM system .................................................................................................. 27
3.2.5 Data acquisition system ................................................................................ 27
3.2.6 Equipment Run .............................................................................................. 28
3.3 EXPERIMENTAL SET UP .......................................................................................... 28
3.3.1 System calibration ......................................................................................... 28
3.3.1.1 Qcm ......................................................................................................... 28
3.3.1.2 Flow pressure .......................................................................................... 30

3.4 TEMPERATURE CONTROL CHAMBER ....................................................................... 31
3.5 SPIN COATING ........................................................................................................ 31
3.6 THERMAL CHARACTERISTICS ................................................................................ 33
RESULTS AND DISCUSSION 34

4.] PHYSICAL AND THERMAL PROPERTIES .................................................................. 34
4.2 MOISTURE UPTAKE ................................................................................................ 35
4.3 EXPERIMENTAL AND PREDICTED FRACTIONAL MASS UPTAKE ................................ 41
4.4 DETERMINATION OF D, S & P .............................................................................. 46
4.4.1 Difiusion coefiicient ...................................................................................... 46
4.4.2 Solubility coefi‘icient ...................................................................................... 48
4.4.3 Permeability coefficient ................................................................................ 49
4.4.4 Eflect of temperature on Permeability parameters ....................................... 5 I
4.4.4.1 Activation energy Of diffusion (Ed) ......................................................... 51
4.4.4.2 Heat Of sorption (A H,). ........................................................................... 52
4.4.4.3 Activation energy (Ep) ............................................................................. 54
CONCLUSION 57

5. l FUTURE WORK RECOMMENDATIONS ...................................................................... 58
APPENDICES 59

6.] APPENDIX A — EQUATION FOR THE FRACTIONAL MASS UPTAKE FOR ONE SIDED D1 59

7

6.2 APPENDIX B-CODE FOR THE QBASIC PROGRAM .................................................... 60

6.3 APPENDIX C — COMPLETE CALCULATION OF DETERMINING MASS UPTAKE ........... 62
6.4 APPENDIX D - GRAPHICAL PLOTS FOR THE WATER VAPOR MASS UPTAKE ON FILMS
AT 10, 23 & 40°C AT THE RH RANGING FROM 20 % TO 80 % ....................................... 65
6.4.1 10°C-20%RH .......................................................................................... 65
6.4.2 10 ° C — 40 % RH .......................................................................................... 67
6.4.3 10°C - 60 % RH ............................................................................................ 69
6.4.4 10°C- 80 % RH ............................................................................................. 71
6.4.5 23 ° C -20 % RH ........................................................................................... 73
6.4.6 23 ° C -40 % RH ........................................................................................... 77
6.4.7 23° C — 60 % RH ........................................................................................... 79
6.4.8 23 °C - 80 % RH ........................................................................................... 82
6.4.9 40 °C - 20 % RH ........................................................................................... 85
6.4.10 40°C — 40 % RH ........................................................................................... 88
6.4.11 40°C — 60 % RH ........................................................................................... 91
6.4.12 40°C — 80 % RH ........................................................................................... 94
REFERENCES 96

Vi

List of Tables
Table 4-1 Physical and thermal properties of the PLA resin and films ........................... 34

Table 4-2 Summary Of P, D, S values ............................................................................... 56

vii

List of Figures
Figure 2-1 Sorption, desorption and diffusion process across a plastic sheet .................... 7
Figure 3-1 Experimental set up for measuring vapor sorption using QCM ..................... 25

Figure 3-2 Quartz crystal installation in the flow cells. Figure adapted from RQCM
Manual [32] ....................................................................................................................... 26

Figure 3-3 Delta frequencies of crystals when dipped in different weight by percentage
glycerol solution for three different runs and the predicted values from eq 3-1 ............... 30

Figure 3-4 Variation in delta frequency at different relative humidity conditions at gas
flow of 20 sccm ................................................................................................................. 31

Figure 4-1 Drop in resonant frequency as for a film 1.06 x10'4 cm at 23 ° C and 20 % RH
as a function of time according to the Sauerbrey equation ............................................... 36

Figure 4-2 Water vapor mass uptake for a film 1.06 x10“4 cm at 23 ° C and 20 % RH as a
function Of time as a function Of time ............................................................................... 37

Figure 4-3 Water vapor mass uptake for a film 1.06 x 10'7cm at 23°C and 20 % RH as a
function of time calculated from Z-match Equation ......................................................... 40

Figure 4-4 Water vapor mass uptake for a film of 1.06 X 10'7 cm calculated from Z-
match and Sauerbrey equations ........................................................................................ 41

Figure 4-5 Experimental and predicted fractional Mass uptake at 10°C at 20 % RH ...... 43
Figure 4—6 Experimental and predicted fractional mass uptake at 23° C at 20 % RH ...... 44
Figure 47 Experimental and predicted fractional mass uptake at 40° C at 20 % RH ...... 45
Figure 4-8 Diffusion coefficient as a function Of relative humidity ................................. 47
Figure 4-9 Solubility coefficient as a function Of relative humidity ................................. 48

Figure 4-10 Water vapor permeability coefficient as a function Of relative humidity ..... 49

Figure 4-1 1 Confidence interval for activation energy Of diffusion at different RH ....... 52
Figure 4-12 Enthalpy Of sorption (AHS) as a function of relative humidity S ................... 53
Figure 4-13 Confidence interval on EI) and its dependence on relative humidity ............ 54

viii

1 INTRODUCTION

As a product is packaged, it starts undergoing a series of dynamic changes,
such as exchange of small molecule compounds from the external environment into the
package and from the package to external environment. These molecular exchanges
between the product and the package are termed as mass transfer interactions and they
extend through out the Shelf life Of the package. These interactions play a crucial role in
preserving the quality Of the products stored inside the package. Since plastic based
packaging materials are permeable to smaller molecules such as water vapor, organic
vapors and liquids, the extent of mass transfer interactions can have a significant effect
on the barrier performance of plastic based packaging materials. Therefore, it becomes
necessary to understand the mass transfer process or the interactions to predict the barrier

2 performance Of the packaging materials. and for Optimizing the product shelf life.

Mass transfer interactions in polymers are categorized as diffusion Of
compounds through the polymer membrane, sorption of compounds by the polymer and
migration from the polymer into the product. Diffusion can be defined as the movement of
molecules from the area Of high chemical potential or concentration to lOW chemical
potential or concentration. AS the permeant molecules diffuse through the polymer
structure, they move Within the free volume available in the amorphous regions of the
polymer. Diffusion is a concentration—gradient controlled process and may avail reactants
for chemical reactions between the product and the permeant, which can deteriorate the
quality Of the product.

Sorption is the uptake Of moisture, flavor compounds or organic vapors by the

packaging material. The extent Of the sorption process mainly depends on the affinity

between the sorbate molecule and the polymeric material. In rubbery polymers, for low
concentration of permeants, sorption can be explained by the Henry’s law of solubility,
which is expressed as

C = S*p (l-l)
where C is the concentration Of the permeant, p is the partial vapor pressure and S is the
solubility coefficient.

Permeation is defined as the movement Of organic vapors, gases across
homogenous polymeric packaging materials excluding the movement through the
pinholes, cracks or perforations present in the packaging material. Permeation involves
the dissolution of the permeant molecule followed by the transfer through the polymeric
membrane. Permeation process mainly depends on the mobility factor (diffusion Of the .
permeant in the polymer structure) and the solubility, which is the ratio Of equilibrium
permeant concentration inside the polymer and the penetrant partial pressure. Diffusion
coefficient (D) and solubility coefficient (S) are used to calculate permeability coefficient
(P) when the Henry’s law is obeyed

P = D*S (1-2)
Permeability coefficient (P) is a measure Of the ability of the polymer to
allow transport Of permeants through it; low barrier polymers are highly permeable where
as high barrier polymers are less permeable. Even though some polymeric packaging
materials act as a better barrier to specific compounds and they might be poor barrier to
other compounds. Barrier performance Of polymer is significantly affected by the product
— package compatibility and the external environmental conditions. Mass transfer

interactions between the packaging material and product on a very small level can

accelerate further changes such as flavor loss, oxidation of the product, morphological
changes in polymer and its degradation. As fOOd items and drugs are items of direct
consumption, any deterioration in their quality due tO mass transfer interactions may be
highly dangerous and have serious consequences. SO, it becomes very important to
properly understand mass transfer process and the impact Of external environmental
conditions on the barrier performance of the polymer.

Several conventional methods such as isostatic, quasi-isostatic, gravimetric
technique, isopiestic technique, thermal stripping and desorption have been developed to
determine barrier characteristics of polymers [1-4]. Studies measuring the sorption
phenomenon Of various compounds in glassy polymers, using these conventional
methods have produced reliable and accurate results. The challenge involved with using
these techniques is their tendency to become inaccurate at low vapor pressures or at low
‘ concentration Of permeants and long equilibration times required tO reach the steady state
[4-7].

Quartz crystal microbalance (QCM), which works on the principle Of
piezoelectricity, Offers excellent sensitivity, accuracy and Simplicity to measure changes
taking place on the surface Of a crystal. QCM is an excellent mass sensor because of its
capability to measure sub-nanogram changes at the solid-air and solid-liquid interfaces. It
has already been used as an in situ mass detector to study a Wide variety Of materials and
for sorption measurements [8-10].

With the increasing focus on using biodegradable polymeric materials in
commercial packaging applications, pOIylactide (PLA), a biodegradable polymer made

from corn starch has emerged as an alternate to the petroleum-based polymers. Growing

demand for PLA in the marketplace as a packaging material in short lived and
commercial food packaging applications, which were initially served by the petroleum-
based polymers such as polyethylene terepthalate (PET), required characterization of
barrier properties Of PLA. Water vapor permeability coefficient (P) for PLA was found
lower than polystyrene (PS) but higher than those Of polyethylene terepthalate (PET)
[11]. Sorption isotherms for PLA films Stored at temperatures Of 5, 23 and 40 °C and
water activity (aw) ranging from 0.11 tO 0.94 were studied, but no values were generated
as the water absorption in those films was lower than the equipment sensitivity [12].
Another emerging issue with the advancement in processing technologies for
producing high barrier polymers is that, it has become more difficult to assess their
barrier characteristics using conventional methods. Therefore, it becomes necessary to
utilize a technique or methodology which has a measurement range of mass uptake lower
than above mentioned methods and Shorten the equilibration times in permeation

measurements while maintaining excellent sensitivity and accuracy [13, 14] .

As water vapor sorption on PLA has been reported tO be lower than 100 ppm,
which is lower than the sensitivity range Of most Of the instruments available. QCM
provides a new alternative for measuring the low levels Of water vapor sorption in PLA.
QCM Offers the advantage Of reducing the equilibration times for reaching the steady
state; it can collectively be used as a tool to derive diffusion coefficient (D), solubility
coefficient (S) and permeability coefficient (P) from the data generated from the

measurements.

The Objective Of this thesis was to determine the water vapor barrier properties

Of PLA at 10, 23 and 40 °C at relative humidity ranging from 20 to 80 % using QCM.

2 LITERATURE REVIEW

2.1 Introduction

The first part Of this chapter presents an overview Of the process, to determine
diffusion (D), solubility (S) and permeability (P) coefficients using the lag-time method.
The second part of this chapter focuses on Quartz Crystal Microbalance (QCM) as a
technique for mass sorption sensing, research done by using QCM, and problems faced
and solutions to those problems. The last part Of this chapter focuses on poly(lactide) as a
commercial packaging polymer, its barrier properties and the problems associated in

measuring its barrier properties.

2.2 Overview of permeation process

Packaging interactions in packaging systems start from the moment the packaging
material and the product come in contact with each other and the external environment
during its production, processing, packaging and storage. These interactions extend
through out the life of the package. For a permeation process to take place through the
polymeric packaging material, the permeant molecule should be first absorbed at the
interacting phase between the polymer and the surrounding environment and then diffuse
through the polymer structure. The main driving force for a permeation process to occur
is the tendency of the permeant molecule to equilibrate its chemical activity. This results
in the transfer Of the permeant molecule from a region Of high chemical activity or high

concentration tO low chemical activity or lOW concentration. Therefore, any molecular

Species which are not in thermodynamic equilibrium will tend to equilibrate their

chemical potential.

 

 

 

 

Phase 1 Phase 2 ' Phase 3
Net Flux

P2 ‘1

Sorption / Desorption
‘
T p1
5‘
V
N

X=0 Package Wall X=I

Figure 2-1 Sorption, desorption and diffusion process across a plastic sheet

Permeation process can be described as a three step procedure which are sorption,
diffusion and desorption as Shown in figure 2-1, which involves the adsorption of
permeant molecule at high concentration Side (p2). The concentration Of the permeant at
this interface may be determined by the Henry’s Law Of solubility which is

C = S.p (2'1)
where S is the solubility coefficient and p is the partial pressure. Solubility coefficient is

a function of partial pressure Of the vapor or the gas in the contacting phase. Henry’s law
of solubility holds well for real solutions as long as they are dilute and there is no
interaction between the polymer and the penetrant molecule [15]. For strong interaction
between the penetrant and the polymer, different models explaining the solubility can be
found elsewhere [15].

After the permeant is adsorbed on the polymer interface, it starts to diffuse

through the polymer film until the concentration Of the penetrant becomes equal at both

sides. The ability Of the permeant molecule to diffuse through the polymer film is greatly
influenced by the physical and chemical structure of the polymer. After diffusing through
the polymer film, the permeant molecule reaches the low concentration Side (p1) and is
desorbed from the polymer interface into the contacting media.

The rate of transfer Of permeant and the amount of permeant transferred through
the polymer film can be derived from Fick’s first law of diffusion, which is based on the
hypothesis that the rate Of transfer of diffusing substance through unit area of a section is
proportional to the concentration gradient measured normal to the section [5]. Fick’s first

law of diffusion can be expressed as

dc
F = -D—— (22)
3x
where F is the rate Of transfer per unit area, C is the concentration Of the diffusing
substance, x is the distance in direction Of diffusion and D is the diffusion coefficient. As
the Fick’s first law describes the rate of transfer Of the permeant diffusing through a
polymeric material of certain thickness during steady state, the diffusion coefficient can
be assumed to be independent Of penetrant concentration and polymer relaxations. For
unsteady or transient state, the rate of flow of permeant can be described by Fick’s
second law which can be written as
2
ER: tile
___.:: l)-——7;
lit it:

where t is the time. Mass sorbed on the polymer film as a function Of time provides the

(2-3)

necessary information to calculate the diffusion coefficient of the permeant in the

polymer and the mass uptake at the equilibrium state provides the solubility Of the

penetrant in the polymer [l6]. Commonly, the diffusion coefficient is calculated from the
half time method, in which sorption reaches 50 % of its extent and can be calculated as
[2
D=0.049—

2-4
’1/2 ( )

But the main disadvantage associated with determining D with this method is that,
if there is any deviations from the ideal conditions, significant errors can be introduced
which can not be corrected by using this method. Duda et a1 [17] calculated the diffusion
coefficient by integrating Fick’s second law under the assumption Of constant diffusivity

and derived the following expression for determining the diffusion coefficient (D)

sz 8(Mt/Moo) 2
_ 4 3,1/2 (2'5)

 

 

D

where M, represents the mass Of the penetrant at time t, M...o is the mass uptake at steady
state, I is the thickness of the polymer film. Since the fractional mass uptake MJM,O
almost follows a linear trend for region less than 0.4, mass sorbed on the polymer as a
function of sqrt(time)/thickness of film can be used to determine the diffusion coefficient
Of permeant in the polymer film. This method for determining the diffusion coefficient is

valid only for diffusion from two sides of the polymer film.

The solubility coefficient can be calculated by dividing the mass uptake at the
steady state (t :00 ) by the volume Of the polymer sample and the vapor pressure at

respective partial pressure

 

S: °°

v. p (2‘6)

where M... is the total amount (mass) Of vapor absorbed by the polymer at equilibrium for
a given temperature, v is the volume Of the polymer sample, and p is the penetrant driving
force in units Of concentration or pressure. The units Of S used are kg/m3.Pa. After that, a
procedure based on the sum of squares technique described by Barr[18] can be utilized to
determine the best estimated diffusion coefficient value. Using the value of permeant
flow at steady state Foo, the permeability coefficient P (in kg.m/m2.s.Pa), can be
determined by the expression
P=D*S (2-7)

Hence , diffusion (D) and solubility (S) coefficients for different temperature and
relative humidity conditions can be Obtained , which can be further used to calculate the
permeability coefficients using P=D'S at respective temperature and relative humidity

conditions

2.3 Quartz Crystal Microbalance

Quartz crystal microbalance (QCM) technology is becoming a promising
technology these days because of its excellent sensitivity to detect small changes on the
surface of a quartz crystal and is already being used for probing adhesion of Visco-elastic
polymer films, in situ Studies Of proteins and for electrolytic solutions. The excellent
sensitivity and accuracy of the quartz crystal can also be used for studying the sorption of

permeants on polymers at a nanO—gram level. A QCM consists of a thin quartz crystal

10

with gold electrodes plated on its both sides. Figure 2-2 represents the front and the back

electrodes of a quartz crystal used in QCM.

 

 

AREA

Figure 2-2 Back and front electrodes on the opposite Sides of the crystal. Figure adapted
from Lu and Lewis (1972) [19]

When an alternating electric field is applied across the opposite sides of a quartz
crystal, by the Virtue of piezoelectricity an internal mechanical stress is produced which
results in a shear acoustic wave propagating normally to surface of the quartz crystal. If a
quartz crystal is coupled with non- rigid materials such as polymer films, the amplitude
and the phase of the acoustic wave can be influenced by mechanical properties of
material As the resonant frequency of quartz crystal is affected both by mass and liquid
loadings, measurement of the resonant frequency alone can not distinguish changes in
surface mass from changes in solution properties .On the other Side, electrical
characteristics can be measured over a range of frequencies; it becomes very convenient
to use a circuit model to describe the electrical behavior of quartz crystal, which can
relate the circuit elements to physical properties of QCM as well as the surface mass

layer and contacting liquid.

11

Butterworth-Van Dyke (BVD) equivalent circuit model can be used to describe
an unloaded (without any mass or liquid loading) and loaded quartz crystal as a network
of electrical parameters such as resistance (R), inductance (L) and capacitance (C) [20,
21]. The BVD circuit for a loaded crystal as Shown in figure 2—3 has two arms—static arm
with static capacitance (Co), the capacitance that arises between the electrodes on the
Opposite sides of the crystal representing the Shunt capacitance of the crystal electrodes
and a motional arm in parallel with the Static arm, which arises due to the
electromechanical and piezoelectric coupling of the quartz crystal. Inductor (L) in the
motional arm, represents the inertial component of the oscillation (related to the
displacement of mass during the Vibration of the crystal), capacitance (Cm) is related to
the energy stored during the oscillation due to the elasticity of crystal and the surrounding
medium and resistor (R) which corresponds to energy dissipated due to oscillation and

from external mounting and the medium in contact.

R L

__ .__/l‘ ‘/‘\\/K\ f—_ __l/N “(I ‘ \(f\\‘L
1

~fo>——— __.___.__. - - ———~———{’f}—
AC . | AC

 

 

Figure 2-3. Electrical equivalent circuit of a quartz crystal
The motional arm in the BVD circuit comes into play when there is a mass
loading on the surface of the quartz crystal. AS an electric field is applied across the Sides
of the crystal, fully charged capacitor (Cm) in the motional arm begins to discharge,

resulting in a flow of current through the inductor (L). By the virtue of self—induction, the

12

inductor (L) resists the current flowing through it , until all Of the current flowing through
the inductor (L) is used to charge up the capacitor (Cm) again in the opposite polarity
[22]. Once the current becomes zero, the capacitor (Cm) begins to discharge again using
the energy gained by charging in the opposite polarity. If the resistance to the flow of
current through the resistor (R) is zero, this process of charging and discharging Of
capacitor (Cm) continues resulting in oscillation of the crystal indefinitely. If R > 0,
resistance to the flow of current will result in damping of amplitude of the oscillation and
with the time, the crystal will stop oscillating. The static capacitance dominates the
admittance away from the resonance, while the motional admittance dominates near the
resonance which implies that the motional arm in the BVD equivalent circuit model
comes into effect when an additional layer is deposited on the surface of the quartz
crystal. When the static arm dominates, the crystal continues to oscillate Without any
dampening of the amplitude of oscillation. Details regarding calculating the physical
properties of the surface layer and the contacting liquid from the electrical measurements
of the quartz crystal can be found elsewhere [19, 23, 24].

As deposition of an additional mass on the surface of the quartz crystal leads to a
decrease in its resonant frequency of oscillation, this frequency Shift is proportional to the
additional mass deposited on its surface. In 1957 Sauerbrey [25] postulated that for small
mass change (up to 20 ug/cmz), addition of foreign mass can be treated as a mass change

on the surface Of quartz crystal, so the resonant frequency shift obeys the relation :

fl = J12 (2-8)

dm in equation 2-8 is the amount of additional mass deposited over the crystal surface, mq

is the mass of the quartz crystal, fq is the resonant frequency of the unloaded crystal and

I3

(ifq is the shift in the resonant frequency Of the crystal as a result of mass loading.

Equation 2-8 can also be written as:

mf =mq(fc —fq)/f (2-9)
where mf is the mass of the film, fC is resonant frequency of the quartz crystal with
deposited film and mf is the mass of polymer film deposited on surface of quartz crystal.

If the density of film deposited on the quartz crystal is known, the film thickness can be
determined by using equation 2-10.

pfrf =<p,r., Imtf. -f.,) (240)
where pq is the density of the quartz crystal, pf is the density of polymer film, tq is the
thickness of quartz crystal, tf is the thickness of the polymer film coated on the surface of
quartz crystal.

As predicted in equation 2-10, the shift in the resonant frequency of the quartz
crystal is linearly proportional to the mass deposited and is not affected by the
mechanical properties of the film. Stockbridge [26] applied Rayleigh perturbation
analysis to justify this fact and obtained the same frequency- mass relationship as in
equation 2-10. The basic assumption in this equation was that there is no potential energy
stored in the mass added on the surface of the crystal. during its oscillation, which further
implied that the mechanical energy of the crystal did not have any impact on the crystal
oscillation. This approach for determining the mass frequency relationship was termed as
“frequency measurement technique” [25].The maximum frequency Shift allowed by the
“frequency measurement technique” was only about 2 % of the original frequency for
measuring the thickness of the layer deposited with reasonable accuracy. Lu et al reported

that accuracy in mass determinations can be minimized to an error of less than 2 % if the

14

mass loading of the crystal is kept less than 2 pig/cm2 [9, 27]. However, when the mass of
the deposited material becomes appreciable and forms a uniform layer of finite thickness,
the basic assumption that acoustic waves do not propagate in the film becomes less
acceptable and errors in mass determination become less tolerable.

With improved crystal design and attempts to improve the mass loading capability
of quartz crystal, a new theory termed as “period oscillation technique” was introduced in
1971 by Behmdt [28, 29] which correlates the change in period of oscillation and the

deposited mass as

—————-———=———-— (2-11)

If and tq in equation 2-11 are the oscillation periods for QCM before and after
mass loading respectively. Equation 2—11 when compared with equation 2-10 is
remarkably accurate and makes more sense mathematically as the deposited mass is now
linearly proportional to the change in period of oscillations where as Sauerbrey’s

equation is based on an inverse proportionality .

AM AZ :Arq= qu

M l r fq

q q q

 

 

 

(2—12)

By using “period oscillation technique” for measuring the frequency Shift, more
than 10 % of the resonant frequency could be measured. However, the elastic properties
of the deposited material were not considered into this mass frequency relationship. Lu et
al suggested a different approach for improving the accuracy of QCM, and stated that the

resonant frequency of a composite system Of quartz crystal and film can also be

15

determined by considering the acoustic properties of the film and derived the following

equation:

tan(7I-f. / fq) =-(1/ Z) tanQr-fc / f f) (2-13)

Z
where Z = —Z—q- : pqvq /,0fl)f (2'14)
f

2,, is the acoustic impedance Of quartz crystal, Z] is the acoustic impedance of polymer
film, Uf and uq are the shear wave velocity in coated film and in the crystal. By solving

equation (2—13) algebraically, it can be reduced to

SE = _i.fiarctan(z.tan 57:) (2-15)
M z 79‘

q
where AM is the mass change, Z is the shear mode acoUstic impedance ratio between the
quartz crystal and film deposited on the quartz’s surface. Equation 2—15 was termed as Z-
match equation [22, 30-32], and it considers the acoustic impedance of the deposited film
and quartz crystal for determining the mass uptake on the polymer film deposited on the
quartz crystal. The only drawback Of using this technique is the fact that information
regarding the shear modulus of different polymer films is not always readily available.
These polymer films coated on crystal surface may result in deviations in the frequency
shift predicted from the Sauerbrey equation and introduce non-gravimetric behavior in
the measurements. Carsten et a1 [33] demonstrated a method for quickly determining the

shear modulus of the polymer films coated on a crystal surface.

16

Gas sorption in glassy polymers is traditionally studied by using conventional
methods like gravimetric techniques, pressure decay method and inverse gas
chromatography [10]. The results Obtained from traditional measuring methods regarding
the solubility of sorbents in glassy polymers have been found accurate and can be further
utilized for investigating pure gas diffusion measurements [4-6]. The main disadvantage
associated with using these techniques is that they become inaccurate at low vapor
pressures which tend to increase the equilibration times required to reach the steady state,
which can be extended up to weeks or more . QCM technique has been reported as a
very accurate, rapid and reliable technique for measuring the gas sorption phenomenon in
polymers as it significantly reduces the equilibration times required to reach the steady
state [10, 34-37].

Various studies have been done for studying the sorption of gases and organic
vapors in glassy polymers using QCM technique, and this technique has been established
as a valuable tool for assessment of solubility and diffusion parameters in rubbery
polymer systems [16]. Zhang et a1 [3 8] explored the fundamental phenomenon associated
with the sorption of carbon dioxide in thin glassy polymers films such as poly(ethylene
terephthalate) (PET), poly(methyl methacrylate) (PMMA), and polysulfone using a
QCM. Polymer films in thickness range of 350 - 550 nm were coated on the crystal
surface using spin coating method, and the sorption levels Of carbon dioxide and other
organic vapors associated with these polymer systems compared favorably well with the
previous reported values on thick films obtained from conventional methods. Wong et a1.
[10] developed an isopiestic apparatus using a QCM to measure the solubilities of

benzene, toluene and chloroform in poly(styrene) in a concentrated polymer regime.

l7

Significant adsorption especially for the polar solvents on the metal electrodes was
expected at higher solvent pressures so both faces of the crystal were coated completely
using spray coating process. Adhesion of the polymer film to quartz crystal electrode is
very crucial factor in sorption studies using QCM, as the changes in inertial coupling of
film coated on the quartz crystal leads to hysteresis and might introduce error in the
frequency measurements. Equilibration times were reported to be achieved much faster in
thin films in these experiments as compared with other techniques. Spin coating has been
recommended as the preferred method for coating the polymer film on the surface of the
crystal, as it also helps in producing thin and uniform films on the crystal surface[10].
Thermally treating the coated polymer films at 5°C above their glass transition
temperature also helps in producing more uniform films, without any cracks and surface
irregularities [39].

Rigorous control over the flowing regime of the carrier gas for studying transient
and steady State in sorption measurement is described as very crucial as deviations in the
flow of the carrier gas can have an effect on the frequency shift resolution of the crystal
[40]. Any instability in the flow of the carrier gas will induce fluctuations Of the vibrating
frequency due to local density fluctuation in boundary layer of the carrier gas adherent to
the vibrating surface The carrier gas to be used for carrying the vapors into the flow cell
for the sorption experiments should be chemically inert against the electrodes of the
quartz crystal and must not react with the deposited layer, as it will block the sites of
adsorption for vapors at the layer on the surface of the crystal and will interfere with

sorption Of vapors of interest.

18

Another important parameter that affects the stability of the resonant frequency
of quartz crystal is the hydrodynamic regime of the carrier gas which sweeps through the
cell. Oliveira et al. [11] considered the frequency change due to the injection of gas or
solvent into the flow cell housing the coated and the uncoated crystal as a sum of four
independent terms, a) AFp — the frequency change to due to hydrostatic pressure b) AFv -
change in frequency as a function of properties of gas and crystal, c) AFS frequency
change associated with the sorption of vapor on the polymer/crystal interface and d) the
frequency change associated with the hydrostatic pressure of the carrier gas. These
parameters Should be measured using uncoated crystal for each temperature and pressure
condition and should be established as a baseline and subtracted from the actual
frequency shifts during experimental runs, so as to accurately calculate the frequency
Shifts associated with mass uptake of vapors on the crystal.

Vogt et a1. [41] investigated the frequency and the dissipation factor Of quartz
resonators coated with poly(4-amOnium stryenesulfonic acid) films of thickness ranging
from 3 to 205 nm during exposure to saturated water vapors. At some applied layer
thickness, viscoelastic nature of the layer becomes a significant part of the response Of
the quartz crystal, and as the films absorbed more water, they become less rigid allowing
for deviations from the Sauerbrey equation. These deviations in Sauerbrey equation were
Observed for films thicker than 90 nm and were mainly governed by three parameters:
film Viscosity, thickness and the resonator frequency.

Anomalous shifts in the measured frequency were reported by Banda et a1. [42]
for quartz crystals coated with glassy polymers, due to non gravimetric effects.

Significant errors in mass uptake measurements may arise, if the precautions related with

19

the film thickness and viscoelastic compliance are ignored. As described above,
deviations from Sauerbrey equation were observed for films thicker then 90 nm , Similar
deviations were observed for film thicker then 100 nm [42].

Vapor phase doping of poly(p-phenylene vinylene) with fuming sulfuric acid was
studied by Shah et al. [8] by using a QCM. Mass uptake information derived from Fick’s
second law was applied to the QCM data to determine the diffusion coefficient, which
was found comparable to other studies. However, an unusual frequency response after an
initial drop was observed which can be attributed to out of phase resonance behavior of
film due to large mass uptake of water on its surface which accounted for the viscoelastic
behavior and a deviation from the Sauerbrey equation.

Polymer film coated on the surface of quartz crystal, if thicker than 100 nm
should be considered as a viscoelastic media since both its elastic and viscous character
contribute to the mechanical compliance [43]. Morray et al. [21] proposed the use of
thickness Shear mode quartz resonator for determining the polymer mechanical
properties, primarily the complex shear modulus. They used the BVD equivalent circuit
model of surface loaded quartz resonator to characterize the impedance/ admittance
characteristics to extract the film mechanical properties.

For using QCM, as a mass sensing device with polymer films thicker than 100
nm, frequency response Should be corrected for viscoelastic effects as the mass uptake
then holds its linearity with the change in the frequency as per the Sauerbrey equation.
This corrections can be done using the Z—match equation (equation 2-15), which requires
the characterization of film’s mechanical properties such as shear modulus, which can be

determined by using the methodology as explained by Carsten et al. [33].

20

2.4 Polylactide (PLA)

A major proportion of packaging materials used in commercial packaging
applications comprises of synthetic polymers which are derived from non renewable
sources, and their consumption rate has been growing steadily. As plastics have low
weight to volume ratio, they occupy more space relative to the other materials in landfills.
Due to the moisture free anaerobic environment in the landfills, degradation process for
the plastic materials is extremely Slow. As a result of very Slow degradation or no
degradation at all in some plastic materials, concerns have been growing regarding the
degradability of plastic polymers and the increase of municipal solid waste. Increasing
environmental concerns with the depletion of non-renewable sources, degradability of
plastic materials, demand for developing polymers which are truly biodegradable has

been increasing.

Polylactide, a biodegradable polymer, derived from lactic acid is obtained from
renewable sources and presents numerous advantages over conventional petroleum based
polymers such as Significant energy savings, recyclability and 'compostability. Extensive
research studies have been able to demonstrate polylactide as an economically feasible

packaging polymer (43-45).

Widespread availability of PLA in marketplace has helped to develop commercial
applications in the packaging industry, initially assigned for petroleum based polymers.
Auras et al. [44] reported that PLA showed comparable barrier properties such as C02,
Oz permeability coefficients to those of PET and lower than PS. PLA is a very good

barrier to d-limonene, ethyl acetate, and its barrier to these compounds can be compared

21

to PET and Nylon-6. The amount of lactic acid which migrates from PLA to solutions iS
even lower than current dietary intake of lactic acid values as reported by Food Drug
Administration, US Department of Agriculture. These properties of PLA make it a
popular choice for replacing traditional polymers in commercial food packaging
applications. Now a days, PLA is being used as a primary packaging material in short life
food packaging applications for fresh fruits and vegetables such as thermoformed
containers, salad trays, and dairy packaging. In addition to that, PLA is also being used in
consumer goods and display packaging, threaded containers, bottles and jars. In these
short lived food packaging applications for fresh fruits and vegetables, primary containers
are exposed to varying relative humidity conditions which might trigger the mass transfer
interactions between the primary package and the surrounding environment resulting in
deterioration of the product contained inside. To be successfully accepted for these
commercial short lived food packaging applications, understanding of water vapor barrier
properties of the polymer remains a very crucial factor.

Auras et al. [44] reported that the PLA films stored for more than one week at 5 ,
23 and 40 ° C and in water activity (aw) ranging from 0.11 to 0.94 did not absorb
measurable amounts of water. These low moisture sorption values in PLA can be
described by the difference between the solubility parameter of water and PLA.

Shogren et al.[45] reported the water vapor transmission rate (WVTR) of an as-
cast PLLA specimen much higher than that of crystallized PLLA specimen. Tsuji et a1.
[46] investigated the effects of molecular weight, D- lactide unit content and crystallinity

of poly(lactide) on water vapor permeation of PLA and reported that WVTR of films

22

decreased with increasing crystallinity (1,.) from 0 to 20 %, where as WVTR values

leveled off with further increase in crystallinity.

Water vapor permeability coefficient (W VPC) values reported by Auras et al. [12]
for PLA films with different lactic acid content were found to be practically constant
over the range studied. It was Observed that for those films, permeability values were
found to increase with decrease in the temperature. Also no significant change in the
permeability coefficient values was observed as a function of relative humidity.

Solubility and diffusivity parameters of different gases in PLA were determined
using a QCM by Oliveira et al. [11] and a variation in these values is reported when
compared with the values determined by time lag method. For measuring these values
very thin films of 2.6 pm were used, and it is very likely that deviation from Sauerbrey
equation due to the viscoelastic and non-gravimetric effects during frequency
measurements might have resulted in the discrepancies in the reported values, so to better
understand the water vapor sorption model in PLA using a QCM these non-gravimetric

effects should be considered.

23

3 MATERIALS AND METHODS

3.1 Materials

Polylactide (PLA) resins made with 94 % L-Lactide provided by Nature Works ®
LLC (Blair, NE) were used for measuring the sorption of water vapor on these films.
Quartz crystals of 5 MHz base frequency, crystal holders, and flow cells were obtained
from Maxtek Inc. (Santa Fe, CA). A humidity generator RH-200 used to generate the
required relative humidity for the experimental work previously calibrated was obtained
from VTI Corp (Hialeah, FL). A peltier chamber for controlling the temperature between
5 and 60°C with a precision of 0.1°C and for housing the flow cells with the coated and
uncoated crystal was obtained from Sable Systems International Inc. (Las Vegas, NV).
Tetrahydrofuran (THF) which was used for making the polymer solutiOn was obtained
from Sigma—Aldrich (St. Louis, MO). A spin coating machine for coating the polymer
films on the quartz crystal was obtained from Laurell Technologies Corporation (North

Wales, PA).

3.2 Experimental set up

The system built for measuring the sorption of permeant on the polymer film
using a QCM consists of five parts: a) water vapor activity generation system, b) flow cells,
c) temperature control chamber, (1) QCM, and e) data acquisition system. A complete

schematic of the apparatus is Shown in Figure 1.

24

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cbll 1. derrer-Oystd (Mauve) I

.Mtual Cell WOWS‘CIOGTC

 

 

 

75% III “as R
WmValw Ewan rm 1.. WWW

 

 

 

 

Figure 3-1. Experimental set up for measuring vapor sorption using QCM

3.2.1 Water vapor activity generation system

AS the dry nitrogen splits in two parts (see figure 3-1), one entering the mass flow
controllers and the other entering the flow cells through the four way valve, the RH
generator reduces its pressure to less than 15 psi and is split into branches passing
through the wet mass flow controller (MFCl) and the dry mass flow controller (MFC2).
Through the wet mass flow controller the gas enters into an evaporator where it becomes
saturated with the water vapor. The gas flowing through the dry mass flow controller
mixes up the dry gas at the output of the evaporator. The final mixed stream enters into

the Dew Point Analyzer (DPA) and flows out to the four way valve from which it is

25

carried into the flow cells containing the coated and the uncoated crystals. Based on the
target relative humidity the software controls the flow of the gas in the wet and dry mass
flow controllers. This system can also be used to generate organic vapor at different

vapor activities.

3.2.2 Flow cells

The flow cells containing the crystals were made up of Kynar® and two stainless
steel inlet and outlet tubes with a .047” ID. x .062” 0D. A Viton® o-ring provides
sealing between the flow cell and the face of the sensor crystal which creates a flow
chamber of approximately 0.1 cm3. The flow cells were connected to the QCM to
monitor the change of frequency. Figure 3-2 represents the flow cells used for the study

and how the quartz crystals are installed into the flow cells.

RetainerCover

Crystal Retainer

,.
Crystal e
Female BNC -

—-—>
Or SMBJack
‘ Pogo
I - I Pins
7
Holder
Housing

Figure 3-2 Quartz crystal installation in the flow cells. Figure adapted from RQCM
Manual [32]

26

3.2.3 Temperature control chamber

The peltier temperature-controllable chambers have a volume of approximately 8
liters. These cabinets can achieve a temperature control over a range of approximately 5 -
60°C with a precision of 0. l0 C and was obtained pre-calibrated from factory (factory

information).

3.2.4 QCM system

The QCM system used in this study was equipped with a built in Phase Lock
Oscillator (PLO) to support its use in measurement with lossy films and in liquid
applications. PLO utilizes an internal Voltage Controlled Oscillator (VCO) to monitor the
current flowing through the crystal. At the cancellation of the crystal’s electrode
capacitance, there is zero phase difference between the current and the voltage which is
the exact resonant frequency of the crystal. If the crystal’s resonant frequency moves up .
or down due to the phase differences between the current and the voltage, VCO keeps the
frequency of the crystal locked to the crystal resonant frequency through a phase detector.
After the frequency is locked to series resonant frequency, the crystal current is
demodulated to DC voltage, there by amplifying the voltage, which is further converted

into resistance value which QCM outputs to the computer.

3.2.5 Data acquisition system

To support data logging of parameters such as delta frequency, resistance, mass
uptake, the QCM was connected to a data acquisition system which transfers the data to a
computer. The water vapor activity generation system was also connected to a data

acquisition system which controls the flow of wet and dry stream in the mass flow

27

controllers to generate the desired relative humidity level and storing the data in the

computer.

3.2.6 Equipment Run

AS the dry nitrogen gas flows into the system it splits in two branches, one flowing
into the RH-generator and the other one flowing into the flow cells. As soon as the
polymer coated crystals are placed in the flow cells after being thermally treated, the flow
cells are purged with dry nitrogen gas for a period of at least 60 minutes for drying the
surface of the polymer film coated on the crystal. AS the target humidity level in the RH
generator is reached the flow of dry nitrogen gas is stopped by closing the four way valve
which opens the flow of wet stream of nitrogen gas into the flow cells. Before the wet
stream of nitrogen is allowed to enter in the flow cells, it is split into three branches,
entering the flow cell at a constant flow of 20 sccm (standard cubic centimeter per
minute). With the wet stream entering into the flow cells it results in a frequency change
and mass is absorbed on the polymer film. The water vapor sorption on the polymer film
is allowed to run until no change in frequency is recorded. The frequency shift and the
change in mass associated with the crystals during the experimental run is logged into the

QCM and recorded in a computer.

3.3 Experimental set up

3.3.1 System calibration

3.3.1.1 QCM

With the technological developments done on QCM technology, measurements

can be done in liquids and viscoelastic deposits. 1n liquids, the viscoelastic material in

28

contact with the crystal play an important role in characterizing the resonant frequency
and the series resonant frequency of the crystal. Like the decrease in the resonant
frequency of the crystal when an additional mass is deposited on its surface, there is also
a decrease in the resonant frequency of the crystal when it comes in contact with a liquid.
This decrease in the frequency of the crystal in a liquid medium can be calculated from

the Kanazawa’s equation

Af :_f3/2 (3_])

 

where f is the resonant frequency of the crystal, or is the density of liquid in contact with
the crystal, 1’11 is the Viscosity of the liquid in contact with the crystal, rig is the Shear
modulus of the crystal, pq is the density of the quartz crystal. Before proceeding for any
experimental runs the crystals were calibrated to match the accuracy of the crystals with
the specified manufacturer limits. Figure 3-2 represents the changes in resonant
frequencies measured, when the crystals were dipped in different weight percentage
solutions of glycerol in water at 20 °C. The recorded values of the delta frequencies in
different weight percentage solutions of glycerol were fitted to a straight line up to 45 wt
% Of glycerol and were found to agree well with the calculated values. At higher weight
percentage values of glycerol, the delta frequency Showed higher deviation. Drop in the
resonant frequency up to 1500 Hz for crystals when dipped in different weight percentage
of glycerol solution was established as acceptable in the calculations as they agreed well

with manufacturers Specified limits.

29

-400

 

 

 

 

0 Run 1
0 Run 2
'500 v Run 3
A Predicted Value
N
I, -800 P 3
>1
8
a ' 2
g -1000 -
‘1: o
C
._ o
o. 9 o
e -1200 P
Q o
-1400 ~ A
-1600 . - L 4
0 10 20 30 40 50

Glycerol, wt %

Figure 3-3 Delta frequencies of crystals when dipped in different weight by percentage
glycerol solution for three different runs and the predicted values from eq 3-1

3.3.1.2 Flow pressure

For keeping accuracy in measurements in gaseous environment, it was required to
maintain a constant gas flow during the experimental runs. To remove the discrepancies
associated with the flow pressure of the carrier gas, drop in resonant frequencies of the
crystals at different flow pressures of 10, 20, 30 seem at relative humidity levels of 20%,
40 %, 60 % & 80% to be used in experimental runs was measured. Based on the
consistency of the results obtained from three different runs, flow pressure of 20 sccm
was selected as the flow pressure for all experimental runs. Figure 3-4 shows the drop in
the resonant frequency of the uncoated crystals at a gas flow of 20 sccm. The drop in the
resonant frequency for all crystals at this flow pressure was no more than 2 Hz, SO this
flow pressure of the carrier gas was used to establish a baseline for further experimental

work. This baseline Shift was subtracted from the drop in the resonant frequencies of the

30

coated crystals during the experimental runs to correct for the actual mass
adsorbed/absorbed on the surface of the crystals.

0.2

0 4
~02
-0.4
~06 I ‘
0.8

Time. in mins

 

    
 
 

, Reference

E
:ii
p

.E 1 “““‘o
e H
E 1.2 . “‘o
m 0"s‘0
>‘ 1 4 \."."‘
g ‘O'I'ys'osohn
g ‘ ' -"u I
U- 16 |‘ ""'.o‘-.OI-"D..a,.4'
2
LL. 1.8

-2

Figure 3-4 Variation in delta frequency at different relative humidity conditions at gas
flow of 20 sccrn

3.4 Temperature control chamber

The temperature control chamber used for maintaining the temperature was
calibrated before performing the experimental runs. Temperature readings were taken
after every hour for a period of 8 hours from a thermometer (factory calibrated) dipped in
a flask containing HPLC grade water kept inside the chamber at the respective

temperatures. A temperature variation of less than 0.50 C was observed during this time.

3.5 Spin coating

A uniform and homogenous polymer film on the surface Of the quartz crystal was
produced by Spin coating. For this purpose polymer resins were dissolved in tetra hydro

furan at 35 0C and a solution 1 ‘70 wt/v was made. Before coating the crystals, they were

thoroughly cleaned with acetone to remove any particles on their surface which can have
an affect on the resonant frequency of the crystals. Subsequently their resonant
frequencies were measured. After washing Off the crystals, they were spin coated with the
1% wt/v polymer solution to produce a uniform polymer coating. The Spin coating was
done in three consecutive steps; a) after properly mounting the crystal on the chuck, they
were rotated for 5 seconds at a 100 rpm, and Simultaneously starting off the dispensing of
the polymer solution on the crystal; b) dispensing of polymer solution was completed
within the first 5 seconds. After that, the crystal was allowed to spin over the next 5
seconds at a Speed of 200 rpm giving sufficient time and Speed for the polymer solution
to Spread uniformly on the crystal surface; c) In the last drying step, the crystal was
rotated for 5 seconds at 50 rpm allowing the solution to evaporate Off from the surface of
the crystal. After this step, the coated crystals were kept on the stationary chuck for
around 10 minutes providing enough time for the solution to evaporate. After this the
coated crystals were moved to a vacuum chamber for a period of 5 hours at a temperature
of 60° C. This temperature treatment was done for allowing the polymer chains to relax,
remove any impurities present on the surface and further drying it producing a uniform
polymer film on the crystal. After vacuum drying, the coated crystals were taken out in a
desiccator for measuring the thickness of the polymer film. The thickness of the polymer
film coated on the crystal was evaluated by measuring the frequency shift associated with

the coating of the film on the crystal surface in absent of flow.

AI -Af.

— (3-2)

1 f.

 

32

where l is the thickness of the quartz crystal, Af is the frequency shift associated with the
coating of the polymer film on the crystal, and f0 is the resonant frequency of the crystal

before coating.

3.6 Thermal Characteristics

A differential scanning calorimeter (DSC) from TA Instruments (New Castle,
Delaware) was used to determine the glass transition (T3) and melting temperatures (Tm)
of the polymer films as per ASTM D 3418-97. Crystallinity of the polymer films were
determined by determining the enthalpies of fusion (AHf) according to ASTM D 3417-

97.

33

4 RESULTS AND DISCUSSION

4.1 Physical and Thermal Properties

Before producing the polymer films from the actual PLA resin, its physical and
thermal properties such as glass transition and melting temperatures and percentage
crystallinity were determined by DSC. The physical properties of the polymer films
produced by spin coating were also determined during each experimental run. Table 4-1

shows the values of these physical properties of the resin and polymer films.

Table 4-1 Physical and thermal properties of the PLA resin and films

 

Property Resin Film
Film thickness, pm NA 1.2i0.2
Glass Transition Temperature , °C 66.03.20 62.0:20
Melting Temperature, °C 1480:] .0 151.1120
Crystallinity, % 16.0120 21.0i2.0

 

As diffusion of permeant on a polymer film depends on thickness of the sample,
extreme care was taken to produce polymer films of uniform thickness for this study. The
thickness of the polymer films were determined by dividing the mass deposited on the
crystal before the beginning of the sorption by the density and surface area of the
polymer sample. Polymer films produced by Spin coating method were found to have a
thickness of 1.25 :L- 0.29 pm. In addition as the crystallinity of the polymer film greatly

affects permeation process, to keep consistency in our experiments, proper attention was

34

given to produce polymer films of approximately same crystallinity. To do so, polymer
solution was allowed to Spread uniformly over the crystal surface during the Spin coating
process and after Spin coating, coated crystals were thermally treated. This thermal
treatment of polymer films at a temperature 5 °C above their glass transition temperature
for 5 hours allowed the polymer chains to relax, thereby Obtaining the films of
approximately same crystallinity. All the films used in the study had an overall

percentage crystallinity of 21$ 2 %, as Shown in table 4- l.

4.2 Moisture uptake

After purging the flow cells containing the coated and uncoated crystals with the
dry nitrogen gas for approximately 60 minutes, N2 with specific relative humidity
between 20 and 80 % was allowed to enter into the flow cells. Due to the sorption of the
water vapor on the surface of the polymer film on the coated crystal and the bare crystal
surface, a drop in the resonant frequency of the crystals occurs. Once the drop in
frequency iS stabilized, the steady state is achieved. The data generated was used to
calculate the mass uptake on the polymer film in accordance to the Sauerbrey equation

which can be expressed as

 

MIT-91:: (fq—f)“p"#" (4-1)

C1 2nf2

where n = number of harmonic at which the crystal is driven
f is the resonant frequency of the uncoated crystal
fq is the frequency of the coated crystal

pq is the density of the quartz crystal

35

1.1,, is the shear modulus of the crystal

Figure 4-1 Shows the drop in the resonant frequency of the coated and uncoated
crystals as a function of time. Drop in the resonant frequency is found to be more
pronounced for coated crystals as compared to the uncoated crystals, which is due to

additional affinity of the film deposited on the crystal towards the moisture.

Trme,m'm

fl—————“

A 10 20 30 40 50 60 70
A
-20 2
A
I i A Coated Crystal
‘45 I A 0 Reference
=75 2
u: .
<1 i
-70 I
-95 .
-120

Figure 4-1 Drop in resonant frequency as for a film 1.06 x104 cm at 23 ° C and 20 % RH
as a function of time according to the Sauerbrey equation

Sorption of water vapor on the surface of the polymer film was calculated as a
function of time, as Shown in figure 4-2. The process of mass uptake on the polymer film
takes place in two Steps; transient state and the steady state. During the transient stage,

mass uptake continues to increase with time until it reaches a steady state termed as

equilibrium or steady state.

36

 

2i)

N
E
i.
(5’ 1.5 -
2
X
E
0)
“g 1.0 P 3
g. 0
3 o
a o
E
,5 o
a. 0.5 - '
c>3 o
:6 0
cc 0
3 o

 

 

I l l l

10 20 30 40 50 60 70

00

°L.

Time,mins

Figure 4-2 Water vapor mass uptake for a film 1.06 x10'4 cm at 23 ° C and 20 % RH as a
function of time

The mass uptake calculated from the Sauerbrey equation (Eq. 4-1) as Shown in
figure 4-2 represents the water vapor mass uptake on the polymer film coated on quartz
crystal.

AS the thickness of the polymer films used in the experimental runs had a
thickness greater than 100 nm, deviations from the Sauerbrey equation due to non-
gravimetn'c effects have been previously observed in films thicker than 100 nm by Banda
et a1 [42]. Deviations from the Sauerbrey equation may account for some errors in mass
uptake measurements. Therefore, in order to check for these errors, mass uptake on the

surface of the crystal was calculated from Z- match equation, which can be expressed as

Am: fi'gq—Jtan‘l Rz.tan 7r.[f°—J:—£J

7r.R f

Z.

Where:

. . . . 2
Am rs change In mass per unrt area expressed In g/cm

Nq is the frequency constant for AT —cut quartz crystal
f is the resonant frequency of the uncoated crystal,

fq is the frequency of the coated crystal,

    

pq'uq . . .
—— = — = acoustic Impedance ratio
pf 'qu Z I
pq is the density of the quartz crystal

pq is the shear modulus of the crystal in g.cm".s2

pf is the density Of the polymer film , g /cm3

W is the Shear modulus of the film in g.cm".s2

(4-2)

(4-3)

To determine the mass uptake on the polymer film from the Z-match equation, the

acoustic impedance ratio is required. Quartz crystal can also be used as a tool to extract

the mechanical properties of the film such as shear modulus from impedance analysis.

For viscoelastic polymer films, generalized impedance Z equals the conventional acoustic

impedance and can be expressed as
Z = ,0.G
where:

p is the density of the polymer

G is the complex Shear modulus of the polymer film.

38

(4-4)

Behling et al [33] characterized polymer properties such as Shear modulus using a
quartz crystal resonator by doing impedance analysis. The acoustic load impedance
generated from the Single film on the crystal surface after taking into account the phase
shift difference between of acoustic wave between the quartz crystal and outer coating

surface can be described as
_ . [p
Z, — 11/p.G tm((t)sh (4—5)

p is the density of the polymer

where

G is the complex shear modulus of the polymer film
h is the thickness of polymer coating on crystal surface
(0 is the series resonant frequency of the crystal
After considering the gravimetric response corresponding to very small acoustic
phase Shifts and the non-gravimetric response corresponding to high acoustic Shifts, the

shear modulus of the polymer film is calculated from the expression
2
G=16.pf.fr.df (4-6)

where
f, is the series resonant frequency of crystal
d-f is the thickness of the polymer film coated on crystal

The shear modulus of the film calculated from equation 4-6 iS used in equation 4-
4 to Obtain the conventional acoustic impedance of the material. Conventional acoustic
impedance for the viscoelastic film and the crystal obtained from equation 4-4 is used in

equation 4-3 to obtain the acoustic impedance ratio, which finally is used in equation 4-2

39

to predict the permeant mass uptake on the polymer film after considering the non-
gravimetric errors induced. Mass of polymer film coated on the quartz crystal is
normalized, to calculate actual water vapor mass uptake on the polymer due to the
sorption of water vapors on it surface. Figure 4-3 Shows the water vapor mass uptake on

the polymer film, calculated from the Z-match equation.

 

20

2

6
5’.

Water vapor mass uptake ( M x 10 ), ugm/cm

F’
c>
on

—L
O
I

.o

U1

I
oooooooooo

 

 

1 l l l

10 20 30 40 50 60 70

Time, mins
Figure 4-3 Water vapor mass uptake for a film 1.06 x 10'7cm at 23°C and 20 % RH as a
function of time calculated from Z—match Equation
The water vapor mass uptake calculated from Z-match equation match the water
vapor mass uptake calculated from Sauerbrey equation. Figure 4-4 represents the
comparison between the water vapor mass uptakes calculated from two different

equations. The root mean square difference between the water vapor mass uptake values

40

on the polymer film predicted from the Z-match and Sauerbrey equation was found to be

less than 3 % , which shows a very good agreement.

 

 

 

 

 

 

 

20
or
E
E.
3
r: 1.5'-
“’2
x
2
15° 1.0 — 8
’5. o
P o
g o
O
0.5 - 0 ,
. O O Sauerbrey Equation
E O O Z—Match equation
a O
3 O
0.00i l l l l l 1

 

10 20 30 4O 50 60 70

C

Time, mins

Figure 4-4 Water vapor mass uptake for a film of 1.06 x 10'7 cm calculated from
Z-match and Sauerbrey equations

As Z-match equation considers the errors induced in the mass uptake
measurements due to the non-gravimetric errors, but no significant difference in the
measured values was observed by using the Sauerbrey and Z-match equation, to generate
more accurate and reliable measurement data, the Z-match equation was used for all

calculation purposes and data analysis in this thesis.

4.3 Experimental and Predicted Fractional Mass Uptake

Six different films of comparable thickness were used to for each relative
humidity condition at a particular temperature condition to study the water vapor sorption

on polylactide films.

41

AS the water vapors were allowed to enter into the flow cells containing the
coated crystals, it usually takes some time for them to get sorbed on the polymer surface.
Therefore, it becomes quite necessary to correct for the time at which the actual mass
uptake of water vapor started on the surface of the polymer film.

During our experimental procedures, only one side of the polymer film was
exposed to the water vapors since the other Side was directly in contact with impervious
crystal surface. In this case, the permeable surface is at concentration C: Co, whereas the
impermeable surface is at concentration C = 0. Under these boundary conditions Fick’s

second law is solved to obtain the following expression. The detail solution of the system

is Shown in Appendix A
M 1 . . .
—'—=1———°7 —————2—exp(—(2n +1)-7z-Dz/41~) (4-6)
Moo 7: (2 +1)

Fractional mass uptake was predicted using the equation (4-6) and then compared
with the experimental mass uptake for each experimental run at different conditions.
Figure 4-5 to 4-6 Shows the plot of experimental and predicted fractional mass uptakes

for 10° C, 23°C, and 40°C at a relative humidity of 20 %.

42

Mt/Moo

 

1.2

 

1.0 r

0.8 -

0.6 —

0.4 -

 

 

0.2 - o Mt/MO0 - Experimental
—- Mt/MOO - Predicted

l L

 

 

 

 

 

O
F

0.04
0 1 2 . 3 4 5 6

7 1/2
Sqrt(t)/lx10.,s /m

Figure 4-5 Experimental and predicted fractional Mass uptake at 10°C at 20 % RH

43

1.2

 

 

1.0” Ar

0.8 ~

Mt/Moo

0.6 P

0.4 - °

 

L . . Mt/Moo - Experimental
0-2 - Mt/Moo - Predicted

 

 

 

 

 

 

 

7 1/2
Sqrt(t)/lx10 ,s /m

Figure 4-6 Experimental and predicted fractional mass uptake at 23° C at 20 % RH

44

1.2

 

 

 

 

 

 

 

 

 

 

1.0 a
0.8 s
o
O
2.. 0.6 -
2
0.4 -
0.2 - 0 Mt/Moo - Experimental
Mt/M00 - Predicted
O
0.0 . I I I I
0 l 2 3 4 5

7 1/2
Sqrt(t)/l x 10 , S /m

Figure 4-7 Experimental and predicted fractional mass uptake at 40° C at 20 % RH

Root mean square (RMS) values of less than 10 % were found between the
experimental and the predicted mass uptake values. Steady state predictions were very
closely match, though minor deviations were observed in transient stage. Deviation
between the predicted and experimental fractional mass uptake values can be explained
with two possibilities. Thickness at different points on the spin coated film can be
variable, causing different local diffusion coefficients. It was not possible to measure the
thickness of the film at different points. Other possibility of the model not fitting the
experimental data in the transient stage may be because of the absence of factor in the

model that would compensate the interaction between the PLA and moisture. Earlier

45

 

studies have shown that PLA is affected by relative humidity. Probably, a better fit can be
obtained if a compensation factor is included in the model equation itself. At steady state,
experimental fractional mass uptake values seemed to agree well with the predicted

values for all the temperature and relative humidity conditions.

4.4 Determination of Diffusion, Solubility & Permeability Coefficient

Diffusion, solubility and permeability coefficients were calculated under different
environmental conditions. Additionally, the effect of different environmental conditions

was predicted and compared with the previously reported values.

4.4.1 Diffusion coefficient

Diffusion coefficient determined from the half time method in the sorption range
Of 35% to 85 % can thus be used to accurately predict the diffusion coefficient of water
vapors in the polymer film.

Sum of squares of residual errors (SSE) was calculated for the optimal solution
using different values obtained for the diffusion coefficient and the diffusion coefficient
corresponding to minimum SSE taken as the best solution. This procedure was followed
for each experimental run. Complete code for the QBasic program used for the
calculation can be found in Appendix B (Burgess, 2007). The values of the diffusion
coefficient (D x 10'5, m2/S) for temperatures 10 °C, 23 °C, 40 °C are summarized in
Table 4-2.

Figure 4-8 represents the values of the diffusion coefficient (mz/Sec) at 23 °C and
40 °C for relative humidity values ranging from 20 % to 80 %. Diffusion coefficient

values obtained using 23 °C and 40 °C conditions shows large variability though they do

46

 

not show statistically significant difference. Determining diffusion coefficient when the
sorption reaches 50 % of its extent can also introduce significant errors, if there is any

deviation from the ideal conditions.

 

 

 

 

 

 

 

 

 

10
. 23°C
3 _ __ 0 40°C
0
8 6 _ T
N\
E.
‘2
E
>< 4 -
Q
2 _
0 l 1 l 1
0 20 40 60 80 100

Relative Humidity, %

Figure 4-8 Diffusion coefficient as a function Of relative humidity

As for deriving the diffusion coefficient, we assume that initially the polymer is in
equilibrium with the cell environment and at t=0, the sorbate concentration has a step
change to Co and is maintained constant during the experiment. In actual experiments,
the concentration surrounding the film specimen changes continuously from the initial to
the final concentration. Assuming the sorbate concentration in the cell is homogeneous,
kinetics of this process might depend on the volume of the cell and the flow rate Of the
stream. This process also leads to the deviation from the ideal behavior and assumptions;

it might have resulted in the high variability in the diffusion coefficient results.

47

4.4.2 Solubility coefficient

Water vapor mass uptake at equilibrium (M...) was used to determine the solubility
coefficient. Dividing the mass uptake at equilibrium (M...) by the density of the polymer
sample and partial vapor pressure, gave the solubility coefficient which can be expressed
as

S = M°° (4-8)

v.p

 

Values of solubility coefficient (S x102, kg/m3-pa) for temperatures 10° C , 23°
C, and 40° C are summarized in Table 4-2 at the end of the chapter. Figure 4-9 represents

the solubility coefficient as a function of relative humidity.

 

 

 

 

 

 

 

 

12- E O 10°C
0 23°C
v 40°C
10-
EU
‘3': 8-
("’1
-§
00
>4 5_
N
9..
>< 4-
”’ i
2.—
1
0- T T
0 20 40 60 80

Relative Humidity , %
Figure 4-9 Solubility coefficient as a function of relative humidity

48

Solubility coefficients at 23 °C & 40 °C were found to be independent of the
permeant concentration. However, solubility coefficient at 10 °C showed a reduction in
the solubility values at higher partial pressures. Solubility coefficient (S) measured at
temperature 10 °C, 23 °C & 40 °C for relative humidity ranging from 20 % to 80 % was
found to be in the range of 0.72 x 10'2 to 11 x 10'2 kg/m3—Pa. Large discrepancies exist

between the solubility values determined by QCM and the time lag methods.

4.4.3 Permeability coefficient

 

 

 

 

 

 

 

 

 

2.5
O 23°C
2.0 — O 40 C
c:
‘3.-
§ 1.5 - 0
("II
E
E
60 1.0 —
x ..
2 ’ i
E 0.5 ~
K
°‘ 1
D
00 i
-05 I r I 1_ J r 1
10 20 30 40 50 60 70 80 90

Relative Humidity,%
Figure 4-10 Water vapor permeability coefficient as a function of relative
humidity
Water vapor permeability coefficient of PLA films at 23° C, 40°C for
relative humidity ranging from 20 % to 80 % are shown in figure 4-10. Values of
permeability coefficients for different temperature and relative humidity conditions are

summarized in table 4-2.

49

No statistical Significant change in the water vapor permeability coefficient values
was observed with the increasing permeant concentration. So the water vapor
permeability was observed to be independent of the relative humidity. Auras et al. [47]
also reported the water vapor permeability coefficient values for PLA to remain constant
with the changes in relative humidity, despite PLA being a polar polymer.

Analysis of the water vapor permeability coefficient values for polylactide films
showed large variability as shown in table 4-2. The values determined using this
technique was found to be two orders of magnitude lower than previously reported
values. Bao et al. [48] determined permeation properties of poly(lactic acid) which were
about one order of magnitude lower then previously reported results and showed
considerable disagreement with previously reported values. They indicated non—
unifonnity of the film thickness as a major source Of uncertainty in their results.

AS during our experimental runs, we used extremely thin films, which are very
hard to handle. There is a possibility of presence of structural defects such as pin holes,
cracks in such thin films, which might have contributed to the large variability in
permeability values.

Condensation of the water vapors in the flow cells or on the surface of the film at
low temperatures such as 10 °C might have also contributed to the high variability in the
permeability values at 10 °C . As we know that little amount of permeant such as water is
enough to bring in some morphological changes in polymer architecture and lower its
glass transition temperature which directly would have affected its permeability

coefficient values.

50

Larger deviations in the water vapor permeability coefficient values during this
research can be due to the extremely thin films used in this measurement. With extremely
thin films, the possibility of structural defects such as pinholes, cracks in films is

increased, which can result in unpredicted behavior during the sorption of permeants.

4.4.4 Effect of Temperature on Permeability Parameters

Temperature dependence of transport parameters is usually described by Arrhenius
relationship, and can be expressed as

—E)/RT

D 2 Doe ‘ (4-9)
s = 50.3“”5 ”’T (410)
P=Pe‘EP/RT (4-11)

I where
Ed is the activation energy of diffusion
AH, is the enthalpy of sorption
Ep is the activation energy of permeation.
Activation energy of permeation can also be expressed as a sum of enthalpy of
sorption and activation energy of diffusion

E, z E, . AH, (442)

3.3.1.1 Activation energy of diffusion (Ed)

Activation energy of diffusion (Ed) was determined for the experiment
runs at 100 C, 23° C, 40°C for the relative humidity ranging from 20 % to 80 %. Figure

4—11 represents the plot of confidence interval of activation energy of diffusion. Due to

51

the higher variability of diffusion coefficient at 10 °C, only the values of diffusion

coefficient at 23 °C & 40 °C were used to estimate the energy of diffusion (Ed).

 

 

 

 

 

 

 

30
V 0 Lower 95 %
25 - 0 Average
v Upper 95 %
20 -
_ O
9
i 15 I v
'6 o v
1.1.1 o O
10 -
o o
5 l' V .
o
O 1 l l 1
0 20 40 60 80 100

Relative Humidity , %

Figure 4-1 1 Plot of Confidence interval for activation energy of diffusion at different RH

The average values of energy of diffusion (Ed) showed no statistically significant

difference as relative humidity increases, however some unpredictable values of energy

of diffusion were observed at 60 % RH. Energy of diffusion was found to be in the range

of 2.81 kJ/mol to 27.75 kJ/mol in relative humidity range of 20 % to 80 %.

3.3.1.2 Heat of sorption (AHS)

Enthalpy of sorption (A H,) can also be considered as sum of two terms

AHS =AHC +AHm

(4-13)

where AHC is the enthalpy of condensation of pure gaseous penetrant to the liquid phase

and AH", is the partial molar enthalpy of mixing the condensed penetrant with polymer

52

segments. AS the solubility depends on the heat of sorption and unlike activation energy
of diffusion, it can take positive or negative values. Figure 4-7 represents the enthalpies

of sorption (AH,) and its dependence on relative humidity.

 

 

 

 

 

 

 

 

-30
o
-40 -
-50 ..
O
_ o
o
E50 ” v
2 0 v
(I)
<70 - O
-30 - a 0 Lower 95 %
o 0 Average
v Upper 95 %
_90 r 1 r 1
20 40 60 80

Relative Humidity,%

Figure 4-12 Enthalpy of sorption (AHS) as a function of relative humidity s

Heat of sorption (AHS) was found to be in the range of -68 kJ/mol to -54 kJ/mol
for relative humidity ranging from 20 %to 80 %. For negative heat of sorption, solubility

coefficient decreases with increasing temperature.

53

3.3.1.2 Activation energy (E)

Activation energy of permeation depends on relative magnitudes of the activation
energy of diffusion and heat of sorption. For E, > AH,, resulting values of Ep will be
positive, which means that permeability coefficient values will increase with the increase
in the temperature. Where as for E; < AHS, resulting values of Ep will be negative,
resulting in decrease in the permeability values with the increase in temperature. Figure
4-13 represents the confidence interval on the activation energy of permeation measured
at different relative humidity. Activation energy of permeation (Ep) was calculated to be
in the range (— 55) kJ/mol to (~85) kJ/mol for relative humidity ranging from 20 % to 40

%.

 

 

 

 

 

 

 

 

0
0 Lower 95 %
’20 ” 0 Average
7 Upper 95 %
-40 _
-50 _ 8
o o
of“ v o 5
-80 ~ 0
0 V o
-100 r
-120 b
-140 ~
0 2O 40 6O 80

Relative Humidity, %

Figure 4-13 Confidence interval on Ep and its dependence on relative humidity

54

As the energy of diffusivity (Ed) is always positive, negative activation energy
(Ep) indicates that heat of sorption (AHS) plays a dominant role in water vapor
permeation through PLA. So, water vapor permeation process in Polylactide can be best
described by sorption —diffusion model. With the negative values of the energy of

activation, permeability coefficient decreased with increasing temperature.

55

 

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56

5 CONCLUSION

In this research study, water vapor barrier properties of polylactide (PLA) at 10 °C ,

23°C & 40 °C for relative humidity ranging from 20 % to 80 % were determined using

quartz crystal microbalance (QCM) technology. This study demonstrates how QCM can

be used for determining the barrier properties of polymeric packaging materials. The

main findings or the conclusions of this study can be outlined as

l.

A complete system using QCM was built, calibrated and used to measure the
water vapor sorption of PLA at different temperature and relative humidity
conditions.

Carrier gas (N2) flow of 20 sccm was established as the optimal flow rate for the
different relative humidity conditions and was used as a baseline in the
experimental work.

Spin coating conditions for producing extremely thin films were optimized and
with those conditions, polymer films with a thickness 1.25: 0.29 pm having a
crystallinity of 21 i 2 % were able to be produced.

QCM has been found as an effective tool for reducing the equilibration times
significantly as compared to other conventional techniques currently in use.

This study demonstrated the ability of QCM to measure and obtain diffusivity,
solubility and permeability data. Diffusion coefficient (D) in the range of 2.6 to
5.67 x 10'” m2 / sec , solubility coefficient (S) in the range of 0.33 to 11.0 x 10'2
Kg/m3-Pa and permeability coefficient (P) in the range of 0.07 to 3.17 x 10"6
(Kg-m/mz—sec-Pa) were obtained for temperature at 10 °C , 23 °C & 40 °C and

relative humidity ranging from 20 % to 80 %.

57

6. Even though QCM was able to be used to measure the diffusivity, solubility and
permeability data, a large variability was found in the final results , which needs

to be looked into in future studies.

5.1 Future work recommendations

0 As the variability in thickness of the films used can be a major source of
variability in the final results, a more detailed study on the spin coating
conditions should be done to determine the best conditions which produce
films with lower variability.

0 In addition to the variability in thickness of films, there is a need to find
out the presence of pin holes, cracks or any other surface irregularities in
the surface of films and analyzing them with techniques such as atomic
force microscopy.

0 Factors such as flow cell volume in the deriving the model with proper

boundary conditions should be included for deriving the best suited model.

58

6 APPENDICES

6.1 Appendix A - Equation for the fractional mass uptake for one sided diffusion

A is the area of the film

L is thickness of polymer film

Using boundary conditions as x = 0 to x =1

C (x,t) is the concentration is point x in the film at time t
C0 is concentration at impermeable surface (C0 = 0)

Mt is the mass uptake at time t

M00 is mass uptake at steady state

By using Fick’s second law

M, = (i)[c(x, t) —c0]Adx

MT=Ai[(c,—c0)—fl(£'—_—CQZ }x=A(cl—co)i[l—£Z }7x
0 7r 0 7t

 

 

 

 

 

 

 

 

 

 

(-1)"' 8—1
=Ac— -—c l———Z Ic —— dx
( °)[4 71' 2m+loc(2 ml)
4 (_1)m TE (_1)me _( 7 I (_l)m
=Ac—c l-—Z e 2’ =Ac— —c l——2—— (“(("M’r
(' 0) 7r 2m+1 (' 0) 2m+l
81 e—
=Ac-c)l-—Z
(‘ °[ 7&2 (2m+1)]
8 (m l/2)27r?'D.T/12 7
MT 3 (C|_C0)(Al) 1—-fl_'2 "E08 (2m+l)“
Ast—>oo,M, —)c><>=(cl —c0)A.l
M 8 0° e—(2m+1)27rth/412
’=1— — Z 2
MW JIZHI (2m+1)

59

6.2 Appendix B-Code for the QBasic Program, developed by Dr G.Burgess

10 Dim T(100), R(lOO) ‘T=TIME,R=MASS RATIO

20 N = 20: For I = 1 To N: READ T(I), R(I): Next I 'EXPERIMENTAL DATA
30 DATA

40 L = thickness of film

50 D1=Dl: D2=D2 'search range

70 For D = D1 To D2 Step (D2 - D1)/ 10

80 SSE = 0

90 For I = 1 to N

100 Sum = O

110ForM =OTo 100:2 = (2 * M +1)A 2 'USE 100 TERMS IN SERIES
1208um=Sum+Exp(-Z* 3.14"2*D*T(I)/4/L"2)/Z

130 Next M

14OSSE=SSE+(R(I)- l +(8/3.l4"2)*Sum)"2

150 Next I

160 Print "D="; D;” SSE="; SSE

170 Next D

Symbols

D — Diffusion coefficient

L — Thickness of the polymer film

T (I) — Time

R (I) — Mt/Moo

6O

SSE — Sum of squares

Procedure for running the program

1.

2.

3.

4.

Input T(I) and R ( 1) values from the experimental data collected

Divide range N based on the data points selected from the experimental data
Pick range of diffusion coefficients D1 & D2

Input the thickness of the polymer film

Save the program for each time new data values are entered

After saving the program, run the program by pressing function key F2.

Let the program print SSE vs. D for each point

61

6.3 Appendix C - Complete calculation of determining mass uptake on one film

Table 6-1 Physical dimensions and mechanical properties of film and quartz crystal

 

 

 

 

 

 

 

 

 

 

 

Thickness (cm) 0.000105
Thickness (m) 1.05E-06
Nq 166800
Film Density (gm/cc) 1.24
Quartz Density (gm/cc) 2.648
Shear Modulus of film 5357281
Accosutic Impedance of Quartz 883383
Accoustic Impedance of Film 3236619
Impedance Ratio 0.272934
Area 5.064506

 

 

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6.4 Appendix D - Graphical plots for the water vapor mass uptake on films at 10,
23 & 40°C at relative humidity ranging from 20 % to 80 %

6.4.1 10 ° C -20 % RH

 

 

 

 

 

 

 

 

 

1.0 r
0.8 -
o 0.6 ~
0
E
E
0.4 *-
0.2 - _._ Mt/Moo - Experimental
.0... Mt/MOO-Predicted
0.0V 1 I L l l
0 1 2 3 4 5 6

7 l/2

Sqrt(t)/lx10 ’s /m

Figure 7-1 Experimental & predicted mass uptake for 1.05 x 10'6 m at 10°C & 20 % RH

 

 

 

 

 

 

 

 

 

1.0 -
0.8 ~
0 0.6 ~
EC)
2
0.4 -
02 _ Mt/M00 - Experimental
Mt/Moo—Predicted
0.0V I l l l L
O 1 2 3 4 6

Sqrt(t)/l x 107’ 31/2 /m

Figure 7-2 Experimental & predicted mass uptake for 6.84 x 10'7 m at 10°C & 20 % RH

 

MI/M 00

    

 

Mt/M00 - Experimental
Mt/Moo-Predicted

 

 

 

 

 

h
h—

3

Sqrt(t)/l x 107’51/2/m

Figure 7-3 Experimental & predicted mass uptake for 1.06 x 10'6 m at 10°C & 20 % RH

66

 

 

 

Mt/Moo - Experimental
Mt/MOO-Predicted

   

 

 

 

 

 

_
p

l l l

1 2 3 4 5 6

Sqrt(t)/l x 107’51/2/m
Figure 7-4 Experimental & predicted mass uptake for 1.06 x 10'6 m at 10°C & 20 % RH

6.4.2 10 ° C—40 % RH

 

 

 

 

 

 

 

 

 

1.0 -
0.8 ~
0 0.6 ~
2c:
2
0.4 -
0.2 - Ml/M00 - Experimental
M‘IMOO-Predicted
0.0f ‘ 1 l l
0 1 2 3 4 5

.,
Sqrt(t)/l x 107‘ 5”" /m

Figure 7-5 Experimental & predicted mass uptake for 1.45 x 10‘6 m at 10°C & 40 % RH

67

 

 

 

 

 

 

 

 

 

1.0 _
0.8 -

8 0.6 —

2H
0.4 -
, Mt/Moo - Experimental
0-2 L ,- Mt/Moo-Predicted
00: 1 1 l
0 1 2 3 4
Sqrt(t)/l x 107’ 51/2 /m

Figure 7-6 Experimental & predicted mass uptake for 1.57 x 10‘6 m at 10°C & 4O % RH

 

 

 

 

 

 

 

 

 

1.0 F
0.8 -
o 0.6 L
20
2
0.4 -
Mt/M00 - Experimental
0'2 M‘lMoo—Predicted
00-1 1 l 1 1
O 1 2 3 4 5 6

7
Sqrt(t)/] x 107’ 5”“ /m

Figure 7-7 Experimental & predicted mass uptake for 1.06 x 10'6 m at 10°C & 40 % RH

68

6.4.3 10°C - 60 % RH

 

 

 

 

 

 

 

 

 

1.0
0.8 L
o 0.6 -
o
E
\a
2
0.4 ~
Mt/M00 -Experimental
Mt/Moo-Predicted
0.2
00' l l L 1
0 1 2 3 4 5 6
Sqrt(t)/l x 107’51/2/m

Figure 7-8 Experimental & predicted mass uptake for 1.46 x 10'6 m at 10°C & 6O % RH

 

 

 

 

 

 

 

 

 

1.0 -
0.8 —
o 0.6 *-
E?
E
0.4 ~
Mt/M00 -Experimental
0-2 Mt/Moo-Predicted
0.0 1 l l l l
o 1 2 3 4 5 6
Sqrt(t)/1 x 107’51/2/m

Figure 7-9 Experimental & predicted mass uptake for 1.06 x 10’6 m at 10°C & 6O % RH

69

 

OO

 

 

Ml/M00 - Experimental
MMMOO-Predicted

   

 

 

 

 

 

l l

1 2 3 4

y—

Sqrt(t)/l x 107' 51/2 lm

Figure 7-10 Experimental & predicted mass uptake for 1.62 x 10'6 m at 10°C & 6O % RH

 

 

 

 

 

 

 

 

 

1.0 e
0.8 ~
0 0.6 -
o
2
\t-l
E
0.4 -
Mt/Moo - Experimental
02‘ Mt/MOO-Predicted
0.0- J 1 l l
0 1 2 3 4 5

71/

Sqrt(t)/l x 10 ‘s 2/m

Figure 7-11 Experimental & predicted mass uptake for 1.34 x 10'6 m at 10°C & 6O % RH

70

6.4.4 10°C- 80 % RH

 

 

    

 

 

 

 

 

 

 

1.0
0.8 -
8 0.6 -
0.4 ~
Mt/M00 -Experimental
0.0' l l l 1
0 1 2 3 4
Sqrt(t)/l x 107’ s1’2/m

Figure 7-12 Experimental & predicted mass uptake for 1.45 x 10'6m at 10°C & 8O % RH

 

 

 

 

 

 

 

1.0 -
0.8 P
o 0.6 e
z:
E
0.4 -
Mt/Moo -Experimental
0.2 Mt/Moo-Predicted

 

Sqrt(t)/l x 107' 51/2 /m
Figure 7-13 Experimental & predicted mass uptake for 1.47 x 10'6 m at 10°C & 80 % RH

71

 

0.8 '-

 

 

 

 

 

 

 

 

o 0.6 ~
0
2
\O-l
2
0.4 ~
0 2 M‘IM00 - Experimental
' M‘lMoo-Predicted
0.07 1 l l l l
0 1 2 3 4 5 6

Sqrt(t)/l x 107‘ 51/2 /m

Figure 7-14 Experimental & predicted mass uptake for 1.06 x 10'6 m at 10°C & 80 % RH

 

 

 

Mt/M00 - Experimental

 

 

0.2 Mt/Moo-Predicted

 

 

 

 

Sqrt(t)/l x 107’ 51/2 /m

Figure 7-15 Experimental & predicted mass uptake for 1.34x 10'6 m at 10°C & 80 % RH

72

 

 

 

 

 

 

 

 

 

1.0 ~
0.8 ~
0 0.6 -
:3

0.4 -
Mt/M00 - Experimental
M/M -Predicted

0.2 ‘ °°

0.0V 1 1 1 1

0 1 2 3 4 5

Sqrt(t)/l x 107’ 51/2 /m

Figure 7-16 Experimental & predicted mass uptake for 1.51x 10'6 m at 10°C & 80 % RH

6.4.5 23 ° C ~20 % RH

 

1.2

Mt/Moo

   

 

 

 

 

 

.—

 

; 3 A 5 e
sqrt(t)/l x10 7 , 81/2/m
Figure 7-17 Experimental & predicted mass uptake for 1.06 x 10'6 m at 23°C & 20 % RH

73

 

 

   
 
   

-.— Mt/M00 - Experimental
—0— MIIMO0 - Predicted

 

 

 

 

l 1 l l

2 3 4 5 6
7’ 51/2

 

sqrt (t)/l x 10 /m

Figure 7-18 Experimental & predicted mass uptake for 1.46 x 10'6 m at 23°C & 20 % RH

 

 

—O— MIIM00 - Experimental
—0— MI/M00 -Predicted

   

 

 

 

 

 

 

1 I I

0 1 2 3 4

sqrt(t)/1 x107, sl/zlm
Figure 7-19 Experimental & predicted mass uptake for 1.62 x 10'6 m at 23°C & 20 % RH

74

 

1.2

   
    

 

—o— Mt/M00 - Experimental
—0— Mt/Moo - Predicted

 

 

 

 

 

l

2 3 4

p-

sqrt (t)/ l x 107, sllzlm
Figure 7-20 Experimental & predicted mass uptake for 1.44 x 10’6 m at 23°C & 20 % RH

1.2

 

MIIMOO

 

—O— M/Mon - Experimental
—0— M/Mon - Calculated

 

 

 

 

 

l L l

1 2 3 4 5 6

sqrt(t)/|x 107. 51/2

Figure 7-21 Experimental & predicted mass uptake for 1.04 x 10'6 m at 23°C & 20 % RH

_

Im

75

 

1.2

1.0 r

0.8 ~

0.6 r

 

   

Mt/Moo

-O— M/M00 - Experimental
—0— Ml/Mno - Predicted

   

0.4 r

 

 

 

 

 

L l l l

2 3 4 5 6

sqrt(t)/lx107 , sllzlm
Figure 7-22 Experimental & predicted mass uptake for 6.81 x 10'7 m at 23°C & 2O % RH

76

6.4.6 23 ° C -40 % RH

 

1.2

Mt/MOO

   

 

—O— Mt/M00 - Experimental

   

 

 

 

 

 

l 1 l

2 3 4 5

sqrt (t)/ l x 107 /2/m

Figure 7-23 Experimental & predicted mass uptake for 1.06 x 10'6 m at 23°C & 4O % RH

’51

1.2

 

 

—0— Mt/M00 - Experimental
-0— Mt/M00 - Predicted

   

 

 

 

 

 

l 1

2 3 4 5
7, 81/2

1.

sqrt (t)/1 x 10 /m

Figure 7-24 Experimental & predicted mass uptake for 1.46 x 10'6 m at 23°C & 4O % RH

77

 

1.2

Mt/M00

 

   

_._ M!/M00 - Experimental
_0_ Mt/M00 - Predicted

   

 

 

 

 

 

l l l

1 2 3 4

7 1/2

sqrt (t)/1 x10 , s /m

Figure 7-25 Experimental & predicted mass uptake for 1.57 x 10‘6 m at 23°C & 40 % RH

 

 

   

 

 

 

 

 

1.2
1.0 ~
0.8 ~
E 0.6 ~
2
0.4 r-
..._ Mt/Moo - Experimental
..0.. Ml/M00 - Predicted
1 l l

 

1 2 3 4

7l/

’7
sqrt(t)/lx10 ,s "/m

Figure 7-26 Experimental & predicted mass uptake for 1.22 x 10'6 m at 23°C & 40 % RH

78

6.4.7 23° C — 60 % RH

 

1.2

1.0 r

0.4 '-

  

 

 

—O— Mt/Moo - Experimental
0.2 —0— Mt/Moo - Predicted

 

 

 

 

 

.-

l l l

0.0 1
0 1 2 3 4 5 6

7 1/2

sqrt(t)/l x 10 , s /m

Figure 7-27 Experimental & predicted mass uptake for 1.06 x 10’6 m at 23°C & 6O % RH

 

0.8 ~

0.4 -

 

—.-— Mt/M00 - Experimental

 

0 2 —O— M‘IM00 - Predicted

 

 

 

 

 

y-

00' l l l l
O 1 2 3 4 5 6

71/

sqrt (t)/l x 10 .s 2/m

Figure 7-28 Experimental & predicted mass uptake for 1.46 x 10'6 m at 23°C & 6O % RH

79

 

1.2

1.0’

0.8 ~

0.6 ~

0.4 -

  

 

 

—.— MllM00 - Experimental

0'2 b —O— Mt/Moo - Predicted

 

 

 

 

 

.-

0,0- l l
0 1 2 3 4

7 1/2

sqrt(t)/1 x 10 , s /m

Figure 7-29 Experimental & predicted mass uptake for 1.62 x 10'6 m at 23°C & 6O % RH

 

  

 

 

 

 

 

 

 

1.2
1.0 r
0.8 i
o
o
E 0.6 —
E
0.4 -
_._ Mt/Moo‘ Experimental
0.2 _o_ Mt/Moo' Predicted
0.0v l l 1
0 1 2 3 4

7
sqrt(t)/1 x107 ,sl/‘Vm

Figure 7-30 Experimental & predicted mass uptake for 1.45 x 10'6 m at 23°C & 6O % RH

80

 

  

 

 

 

 

 

 

 

 

1.0 *-
0.8 -
O
0
g o 5 —
2
0.4 e
—O— M‘IM00 - Experimental
02 —0— Mth00 - Predicted
0.0 l l l l l
0 1 2 3 4 5 6

sqrt (t)/1 x 107,51/2/m

Figure 7-31 Experimental & predicted mass uptake for 1.06 x 10'6 m at 23°C & 60 % RH

 

 

 

 

 

 

 

 

 

1.2
1.0 ~
0.8 1-
o
o
E 0.6 —
2
0.4 ~
+ Mt/M00 - Experimental
02 .0— Mt/MOO- Predicted
0‘0 1 l l 1 J_
0 1 2 3 4 5 6
a
sqrt (t)/l x 107,51/‘lm

Figure 7-32 Experimental & predicted mass uptake for 1.06 x 10'6 m at 23°C & 6O % RH

81

6.4.8 23 °C — 80 % RH

1.2

 

1.0 r

0.8 *-

0.6 r

MI/MOO

   

 

_._ M‘lMo0 - Experimental
._0_ Mt/M00 - Predicted

   

 

 

 

0.2

 

 

sqrt (t)/1 x 107,5”2/ m

Figure 7-33 Experimental & predicted mass uptake for 1.06 x 10'6 m at 23°C & 8O % RH

 

 

—O— MI/M00 - Experimental

   

-O— Mt/M00 - Predicted

 

 

0.2

 

 

 

l L l l

0 1 2 3 4 5 6

,,
sqrt (t)/l x 107 . sl/“lm

0.0

Figure 7-34 Experimental & predicted mass uptake for 1.46 x 10'6 m at 23°C & 80 % RH

82

 

0.8 .

0.6 '-

Mt/M00

0.4 *-

      

 

_._ Mt/Moo - Experimental

0-2 _o_ MIIM00 — Predicted

 

 

 

 

 

 

00 i i l
O 1 2 3 4

sqrt (t)/l x107, sllz/m

Figure 7-35 Experimental & predicted mass uptake for 1.62 x 10'6 m at 23°C & 80 % RH

 

1.2

 

   
 

Mt/M00
O
a)

_._ MIIM00 - Experimental

0.4 _o_. MIIM00 - Predicted

 

 

 

0.2

 

 

l 1

0 1 2 3 4

7
sqn (t)/1 x107, SI/‘lm

0.0

Figure 7-36 Experimental & predicted mass uptake for 1.45 x 10'6 m at 23°C & 80 % RH

83

1.2

 

   
 

 

 

 

 

 

 

 

1.0 r-
0.8 -
O
0
E... 0.6 -
E
0.4 —O— Mt/Moo - Experimental
—0— Mr/M00 - Predicted
0.2
0.0 ‘ L 4
0 1 2 3 4
sqn(t)/1 x 107 , sllzlm

Figure 7-37 Experimental & predicted mass uptake for 1.57 x 10'6 m at 23°C & 80 % RH

1.2

 

Mt/Moo
O
a)

   
 

 

0_4 + Mt/M00 - Experimental

—0— Mth00 - Predicted
0.2

 

 

 

 

 

l l

0 1 2 3 4

7
sqrt(t)/1 x 107 . sl/‘Vm

0.0

Figure 7-38 Experimental & predicted mass uptake for 1.92 x 10'6 m at 23°C & 8O % RH

84

6.4.9 40 °C - 20 % RH

 

  

 

 

 

 

 

 

 

 

1.2
1.0 -
0.8 -
o
0
E 0.6 ~
2
0.4 —
_._ Mt/Moo - Experimental
_0_ Mt/M00 - Predicted
0.2
0.0 1 ‘ L
0 1 2 3 4

sqrt (t)/l x107,s“2/m

Figure 7-39 Experimental & predicted mass uptake for 1.62 x 10'6 m at 40°C & 2O % RH

 

1.2

0.8 -

0.6 -

Nil/M00

 

   

_._ Mt/M00 ~ Experimental
—0— M‘IM00 - Predicted

   

 

 

0.2

 

 

 

tn-

0.0r ‘ ‘
0 1 2 3 4

sqrt (t)/l x 107,51/2/m

Figure 7-40 Experimental & predicted mass uptake for 1.44 x 10'6 m at 40°C & 20 % RH

85

1.2

 

Mt/Moo

 

  
 
    

.4.- M‘IM00 - Experimental
-0-— MIIM00 - Predicted

 

 

 

 

 

1 l l

2 3 4 5 6
7

)—

1/2
sqrt(t)/1x10 ,s /m

Figure 7-41 Experimental & predicted mass uptake for 1.1 1 x 10'6 m at 40°C & 20 % RH

 

Mt/M00

 

_._ Mt/M00 - Experimental
_0- Mt/M00 - Predicted

 

 

 

 

l l L

1 2 3 4 5 6

7
sqrt (t)/1 x107,sl/'/m

p—
i—

 

Figure 7-41 Experimental & predicted mass uptake for 1.34 x 10'6 m at 40°C & 20 % RH

86

1.2

 

Mt/Moo

   
   

 

._._ Mt/M00 - Experimental
-O- MllMOO - PI’CdlCICd

 

 

 

 

 

_
-

3 4 5 6

71/2

sqrt(t)/1x10 ,s /m

Figure 7-42 Experimental & predicted mass uptake for 1.51 x 10'6 m at 40°C & 20 % RH

1.2

 

MllM00

 

_._ Mt/Moo - Experimental
-0—- MIIMOO -Predicted

 

 

 

 

 

l l l l

1 2 3 4 5

7 1/2

sqrt(t)/l x10 ,3 /m

Figure 7-43 Experimental & predicted mass uptake for 1.22 x 10’6 m at 40°C & 20 % RH

87

6.4.10 40°C - 40 % RH

 

  
 

 

 

 

 

 

 

1.2
1.0 ~
0.8 ~
0
o
2.. 0.6 ~
2
0.4 —
_._ Mt/M00 - Experimental
..0_ Mt/M00 - Predicted

 

1 2 3 4 5 6

sqrt (t)/l x 107, sin/m

Figure 7-44 Experimental & predicted mass uptake for 1.23 x 10'6 m at 40°C & 40 % RH

 

1.2

1.0 r

0.8 e

0.6 *-

Mt/M00

 

 

0.4 - —.— Mt/Moo - Experimental
—0— Mt/Moo - Predicted

 

 

 

0.2

 

 

)-
l-

1

0 1 2 3 4 5 6

sqrt(t)/l x107,s“2/m

.0

o

1
1.

Figure 7-45 Experimental & predicted mass uptake for 1.23 x 10'6 m at 40°C & 40 % RH

88

 

Mt/MOO
o
m

 

 

_._ Mt/Moo - Experimental
0.2 _0.- Mth00 - Predicted

 

 

 

 

 

 

0.0 1 l 1 1
0 1 2 3 4 5

7 1/2

sqrt(t)/1x 10 , s /'m

Figure 7-46 Experimental & predicted mass uptake for 1.34 x 10'6 m at 40°C & 4O % RH

 

0.8 ~

0.6 -

Mi/Moo

0.4 -

    

 

_._ Mt/M00 - Experimental
0.2 _o_ MllM00 - Predicted

 

 

 

 

 

 

0.0V 1 1 1 1
O 1 2 3 4 5

sqrt (t)/1 x 107, 51/2

Figure 7-47 Experimental & predicted mass uptake for 1.1 1 x 10‘6 m at 40°C & 40 % RH

89

 

1.2

1.0 r

0.8 -

0.6 ~

Mt/Moo

0.4 e

 

 

_.— Mt/M00 - Experimental
0.2 _0— MW“) - Predicted

 

 

 

 

 

’-
b-

o.o 1 1 1
o 1 2 3 4 5 6

sqrt (t)/l x 107, slnlm

Figure 7-48 Experimental & predicted mass uptake for 1.12 x 10'6 m at 40°C & 4O % RH

 

 

 

 

 

 

 

 

 

1.2
1.0 -
0.8 -
o
o
E. 0.6 r
2
0.4 ~
+ Mth00 - Experimental
0.2 _o— Mt/Moo - Predicted
00 J l l 1 l
0 2 3 4 5 6

sqrt (t)/l x 107, SIB/m

Figure 7-49 Experimental & predicted mass uptake for 1.21 x 10‘6 m at 40°C & 4O % RH

90

6.4.1140°C - 60 % RH

 

ituttltltiitumtttttttu.

   

0.6 -

Mt/Moo

0.4 -

 

_._ Mt/Moo - Experimental

0.2 _o_ Mt/M00 - Predicted

 

 

 

 

 

l l l l l

0 1 2 3 4 5 6 7

sqrt (t)/l x 107, slnlm

Figure 7-50 Experimental & predicted mass uptake for 1.20 x 10'6 m at 40°C & 60 % RH

1.2

 

((1((ttittmumtttmm.

1.0“

0.8 >-

0.6 -

Mt/M00

0.4 -

 

 

.9— Mth00 - Experimental
0.2 _o_ Mt/Moo - Predicted

 

 

 

 

 

 

sqrt (t)/1 x 107, sla/m

Figure 7-51 Experimental & predicted mass uptake for 1.12 x 10'6 m at 40°C & 6O % RH

91

 

1.2

1((11“(HUHHHUHUUC

1.0 r

0.8 ~

0.6 ~

MI/M00

0.4 -

 

 

_._ Mt/M00 - Experimental
0.2 ._o_ Mt/M00 - Predicted

 

 

 

 

 

0,0- 1 i 1 1 1 1
0 1 2 3 4 5 6 7

sqrt (t)/l x 107, sl/z/m
Figure 7—52 Experimental & predicted mass uptake for 1.11 x 10‘6 m at 40°C & 6O % RH

 

 

((((((((((((((((((((ttllfl.

0.8 -

0.6 -

Mt/Moo

0.4 P

  

 

_._ Mt/M00 - Experimental
0.2 _o_ Mr/M00 - Predicted

 

 

 

 

 

 

.0

O

1
i—
p—
1..

0 1 2 3 4 5 6 7

sqrt (t)/l x 107, sin/m

Figure 7-53 Experimental & predicted mass uptake for 1.34 x 10'6 m at 40°C & 60 % RH

92

 

 

  
   
 

 

 

 

 

 

 

1.0 r
0.8 r
O
O
E 0 6 r-
2
0.4 -
_._ Ml/M00 - Experimental
0.2 _o_ Mt/M00 - Predicted
00v 1 1 1 1
0 1 2 3 4 5
sqrt (t)/l x 107, sl/Zlm

Figure 7-54 Experimental & predicted mass uptake for 1.51 x 10’6 m at 40°C & 60 % RH

 

1.2

10*-

0.8 -

0.6 -

Mt/Moo

0.4 -

 

_._ M‘IM00 - Experimental

0.2 _o_ Mt/M00 - Predicted

 

 

 

 

 

l l J

0 1 2 3 4 5

sqrt (t)/1 x 107, sl/zlm

.—

0.0

Figure 7-55 Experimental & predicted mass uptake for 1.23 x 10’6 m at 40°C & 60 % RH

93

6.4.12 40°C - 80 % RH

1.2

 

1.0 ~

0.6 -

MIIMO0

0.4 -

 

 

+ Mt/M00 - Experimental
0.2 _o_ M‘IMO0 - Predicted

 

 

 

 

 

.—
1-

0 1 2 3 4 5 6

sqrt (t)/1 x 107, SIR/m
Figure 7-56 Experimental & predicted mass uptake for 1.11 x 10‘6 m at 40°C & 80 % RH

1.2

 

0.8 ~

0.6 r

MllM00

 

_._ Mt/M00 - Experimental
0.2 _o— Mt/Moo - Predicted

 

 

 

 

 

 

 

sqrt (t)/1 x 107, s llzlm

Figure 7-57 Experimental & predicted mass uptake for 1.34 x 10'6 m at 40°C & 80 % RH

94

 

  
   
 

 

 

 

 

 

 

 

1.0 ~
0.8 e
o
o
E 0.6 -
2
0.4 -
_._ Ml/M00 - Experimental
0.2 _o_ Mt/Moo - Predicted
0.0. L l 1 l
O 1 2 3 4 5

7 1/2

sqrt (t)/1 x 10 , s /m

Figure 7-58 Experimental & predicted mass uptake for 1.51 x 10’6 m at 40°C & 80 % RH

 

 

 

 

 

 

 

 

1.2
1.0 -
0.8 r
o
o
E 0.6 -
E
0.4 _
_._ MIIM00 - Experimental
0.2 _o_ Mt’Moo - Predicted
00 1 1 1 1
0 1 2 3 4 5
sqrt (t)/l x 107, sla/m

Figure 7-59 Experimental & predicted mass uptake for 1.23 x 10'6 m at 40°C & 80 % RH

95

10.

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Wong.C. H. , Bhethanabotla.V. R. , and CS. W., Sorption of benzene, toluene and
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Barr . C . D A Comparison of Solubility Coefficient Values Determined by
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Lu, Chih-Shun , and L. Owen, Investigation of film-thickness determination by

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