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This is to certify that the

thesis entitled

MEASURING THE SORPTION AND DIFFUSION OF WATER IN
A MOISTURE SENSITIVE PRODUCT FOR USE IN SHELF
LIFE SIMULATION

presented by

Patricia J. Allen

has been accepted towards fulfillment
of the requirements for

Master Packaging

degree in

 

 

 

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[fine November 4, 1994

 

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1’0 AVOID FINES mum on or baton duo duo.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU loAnAI'fldevkoonIEmd Oppomnly lmtltwon
W1

 

MEASURING THE SORPTION AND DIFFUSION
OF WATER IN A MOISTURE SENSITIVE
PRODUCT FOR USE IN
SHELF LIFE SIMULATION

BY

Patricia J. Allen

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

MASTER OF SCIENCE

School of Packaging

1994

ABSTRACT

MEASURING TEE SORPTION AND DIFFUSION OF WATER IN A MOISTURE
SENSITIVE PRODUCT FOR USE IN SHELF LIFE SIMULATION

BY

Patricia J. Allen

A validation of a finite difference method computer
program for estimating the shelf life of a packaged moisture
sensitive pharmaceutical tablet is described. The parameters
required to execute this computer model include the diffusion
coefficient of the pharmaceutical product and the diffusion
coefficient of the blister packaging material with respect to
water vapor, as well as the solubility of water vapor in the
packaging material. All of these parameters were determined
experimentally using a Cahn electrobalance at various relative
humidity values at 25.0 degrees Celsius.

In addition, the entire blister package / tablet system
was monitored at two upper humidity levels for moisture gain
as a function of time.

The GAB (Guggenheim-Anderson-de Boer) equation was used
to fit the experimental moisture sorption isotherm, data
generated for the tablet.

A finite difference method computer program was found to
be very helpful for predicting the shelf life of a moisture
sensitive product, if all of the key physical characteristics

of the product and packaging material are known.

Copyright by
PATRICIA JEAN ALLEN

1994

Dedicated to my grandmother, Marguerite Allen, who gave

me the inspiration to achieve my goals.

iv

ACKNOWLEDGMENTS

I would like to extend my deepest appreciation for the
assistance on this project from.my major professor, Dr. Ruben
Hernandez. His support, commitment and insight were
invaluable for the completion of this work.

In addition, I want to recognize and thank all of the
members of my Graduate Committee, which included Dr. Jack
Giacin, Dr. Gary Burgess, and Dr. James Steffe. Each
individual provided expertise and valuable input regarding the
research required for this area of study.

It was a privilege to work with the Center for Food and
Pharmaceutical Packaging Research at Michigan State
University. I am grateful for the financial support and
continued interest in this project. I deeply appreciated all
of the materials and information supplied by UpJohn Company,
as well, for use in this research area.

I also want to thank Dr. Rafael Gavara for his time,
knowledge and help in preparing the electrobalance to conduct
the research. In addition, I need to thank Jai Kim for his
assistance in running the computer program.

Finally, I would like to express my gratitude to my
grandfather, Professor Stuart Allen, and my parents, Charles

and Janet Allen, for their patience, love and confidence.

V

TABLE OF CONTENTS

Page
LIST OF TABLES ... ....... .......... ......... ........ viii
LISTor’IGms .0.........OOOOOOOOO.......OOOOOOOOO Xiv
LIBTOF swans ooooooooooooo00000000000000.0000...o Xiii
INTRODUCTION 0.0.0....000............OOOOOOOOOOOOOOO 1
LITERATURE REVIEW ........ .................... ...... 3
Shelf Life of Moisture Sensitive Products ..... 3
Moisture Sorption Isotherm .................... 5
Unit Dose Blister Packaging ................... 7
Diffusion and Permeability .................... 10
Fitting Models for Sorption Isotherms ......... 13
Computer Simulation Programs .................. 16
MATERIALS AND METHODS .............................. 22
Materials ..................................... 22
MOISTURE SORPTION ISOTHERM OF TABLET .......... 24
sample Preparation ......OOOOIOOOOOOO0.0....... 24
Drying the Tablet ............................. 26
Sorption Isotherm of Blister .................. 27
I. R. Identification O00............OOOOOOOOOOO 29
Water Vapor Transmission Rate of Packaging
material ......OOOOOOOOOOOOOOOOOO......OOOOOOOO 30
Moisture Gain of the Tablet and Blister Package 30
RESULTS AND DISCUSSION ........... ............. ..... 32
Tablet Sorption .... ................. . ...... ... 32
Material Sorption ............................. 33
sorption Isotherm ......OOOOOOOOOOOO0.0.0.0.... 36
Solubility of Packaging Material .............. 43
Water Vapor Transmission Rate of Materials .... 43
Diffusion Coefficient ......................... 49
Sorption Isotherm Model for the Tablet ........ 57
Calculations of Package / Product Dimensions .. 61
Other Parameters for Computer Program ......... 62
Moisture Uptake of Blister Package with Product 63

vi

ERROR ANALYSIS .....................................

CONCLUBIONB 00.0.0.........OOOOOOOOOOOOOCOOO00......

Comparison Between Calculated Data and
Validation Experiment .........................

RECOMMENDATIONS FOR FUTURE WORK ....................

APPENDICES
APPENDIX A.
APPENDIX B.
APPENDIX C.

APPENDIX D.
APPENDIX E.

Program Stability Given Q Value,

Input/Output Data Sheets .........
Sorption Experiment of Deltasone

Tablet ...........................
Sorption Experiment of PVC Film ..
Sorption Experiment of Aclar Film
Water Vapor Transmission Rate and
Permeability of Materials ........

BIBLIOGRAPHY 0......0.0.0..........OOOOOOOOOOOOOOOOO

vii

74

76

76

79

80
110
134
141
148

149

Table
1. Tablet dimensions .... ...........................
2. Dimensions of blister package .............. .....
3. Moisture sorption isotherm data for Deltasone
tablet at 25.0 ° C (Experimental and Calculated)
4. Moisture sorption isotherm data for PVC film at
ZSOOOC00......OO00.0.0.0.........OOCOOOOOOOOOO
5. Moisture sorption isotherm data for Aclar film at
ZSOOOC......OOOOOOOOOOOOOOOOOO......OOOOOOOOOO
6. Diffusion coefficient of tablet at R.H.
conditions ..........OOOOOOOOOOOOOOOO000.........
7. Diffusion coefficient of packaging materials at
ROH. conditions ......OOOOOOOOOOOOOOOO00.0.0.0...
8. Values for use in simulation model ..............
9. Moisture gain of complete blister package with
tablets at 80% R.H. and 22.2 deg. C .............
10. Moisture gain of complete blister package with
tablets at 90% R.H. and 22.2 deg. C .............
11. Summary of sorption experiments of 20 mg Deltasone
tablet at ZSOOOC00.0.0.0.........OCOOOOOOOIOOO
12. Moisture sorption isotherm data for Deltasone
tablet at ZSOOOC......OOOOOOOOOOOOOOO00.0.0...
13. Comparison of experimental and calculated Mvflg
for tablet at 0 - 11.50% R.H. and 25.0 ° c with
determination of diffusion coefficient ..........
14. Comparison of experimental and calculated MVQL

for tablet at
determination

LIST OF TABLES

36 - 40% R.H. and 25.0 ° c with
of diffusion coefficient ..........

viii

Page
22

23

38

4O

4O

53

57

64

66

68

110

111

112

118

Comparison of experimental and calculated Ms/M.
for tablet at 40.75 - 48.80% R.H. and 25.0 (I
with determination of diffusion coefficient ..... 120

Comparison of experimental and calculated Mt/M.
for tablet at 60.70 - 66% R.H. and 25.0 ° c with
determination of diffusion coefficient .......... 123

Comparison of experimental and calculated Mvflg
for tablet at 66 - 73.40% R.H. and 25.0 ° C with
determination of diffusion coefficient .......... 125

Comparison of experimental and calculated Mvflg
for tablet at 72.25 - 77.75% R.H. and 25.0 c:
with determination of diffusion coefficient ..... 127

Comparison of experimental and calculated Mgflg
for tablet at 77.90 - 82.45% R.H. and 25.0 (2
with determination of diffusion coefficient ..... 129

Comparison of experimental and calculated Ms/MI,
for tablet at 82.05 - 87.30% R.H. and 25.0 C:
with determination of diffusion coefficient ..... 131

Summary of sorption experiments of PVC film at
ZSOOOC OOOOOOOOOOOOO O ..... ......OOOIOOOOOOOOOOO 134

Moisture sorption isotherm data for PVC film at
25.0 ° c .............................. . ......... 134

Comparison of experimental and calculated Mgflg
for PVC film at 0 - 26.90% R.H. and 25.0 ° c with
determination of diffusion coefficient .......... 135

Comparison of experimental and calculated Mt/M.
for PVC film at 58.20 - 77% R.H. and 25.0 ° c with
determination of diffusion coefficient .......... 139

Summary of sorption experiments of Aclar film at
ZSOOOC00.0.0.0.........OOOOOOOOOOO0.00.0000... 141

Moisture sorption isotherm data for Aclar film at
ZSOOOCOOOOOOOO ........ .... ..... ......OOOOOOOOO 141

Comparison of experimental and calculated M /M.
for Aclar film at 27.35 - 43.50% R.H. and 25.0 ° c
with determination of diffusion coefficient ..... 143

Comparison of experimental and calculated Mt/M,

for Aclar film at 43.50 - 58% R.H. and 25.0 ° C
with determination of diffusion coefficient ..... 145

ix

29. WVTR and Permeability of blister materials at
37.78 ° c and 85% R.H. (Dish Method) .........

LIBT OF FIGURES
Figure

1. Schematic of a blister cavity with thickness
measurements .....0....0.......0......00000......

2. Cahn Electrobalance and hangdown tube for sample
3. Deltasone tablet sample with foil on edge .......
4. Schematic of electrobalance and actual system ...

5. Experimental sorption of tablet at 82.05-87.30%
R.H.’ 25.00C.......................0....0....0

6. Experimental sorption of PVC film at 0 - 26.90%
ROH0' 25.00C0.......0..00................0....

7. Experimental sorption of Aclar film at 43.50-58%
R.H.’ 25.00C..... .......... 0........ ..... ....0

8. Moisture sorption isotherm of 20 mg Deltasone
tablet at 25.0 ° C showing Equilibrium Moisture
Content (EMC) vs. relative humidity .............

9. Moisture sorption isotherm of PVC film at 25.0 ° C

showing Equilibrium Moisture Content (EMC) vs.
relative humidity ...............................

10. Moisture sorption isotherm of Aclar film at

Page

23
25
26

28

34

35

36

39

41

25.0 ° C showing Equilibrium Moisture Content (EMC)

vs. relative humidity ................... ........
11. WVTR of PVC film at 37.78 ° c and 85% R.H. ......
12. WVTR of Aclar film at 37.78 ° c and 85% R.H. ....

l3. WVTR of PVC/Aclar film at 37.78 ° c and 85% R.H.

42
45
46

47

14. Comparison of experimental and calculated Mt/M, for

20 mg Deltasone tablet at 72.25 - 77.75% R.H. and

25.00C....... ..... ......0 ........... ......0...

15. Diffusion coefficient of Deltasone tablet over
ROH. ranges at 25.00C.........................

xi

51

54

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

Comparison of experimental and calculated Mvflg
for PVC film at 58.20 - 77% 12.11. and 25.0 ° c 55

Comparison of experimental and calculated Mvflg
for Aclar film at 43.50 - 58% R.H. and 25.0 °(: . 56

Plot of experimental moisture sorption isotherm
and calculated GAB isotherm of 20 mg Deltasone
tablet at 25.0°c. ........ . ..... 60

Moisture content of tablets in blisters at 22.2 ° C
and 80% R.H. ............ . ...... . ...... . ..... .... 67

Moisture content of tablets in blisters at 22.2 ° C
and 90% R.H. .................................... 69

Moisture content of tablets in blisters at 22.2 ° C
and 80% R.H. for experimental and computer program

data .00....00..........0.......00............00. 7o

Moisture content of tablets in blisters at 22.2 ° C
and 90% R.H. for experimental and computer program
data 000 00000000000000000 000 000000 00 000000 0000000 71

Moisture content of tablets in blisters at 22.2 ° C
and 80% R.H. for experimental and computer program
data (4.5 mils thickness) ............. .......... 72

Moisture content of tablets in blisters at 22.2 ° C
and 90% R.H. for experimental and computer program
data (4.5 mils thickness) ....................... 73

Comparison of experimental and calculated Mvflg for
tablet at 0 - 11.50% 12.11. and 25.0 ° c (SORP Bl) 113

Experimental sorption of tablet at 11.50 - 15.25%
R.H.’ 25.00C (SORP BZ) ......0.....0..0....... 114

Experimental sorption of tablet at 15.75 - 23.20%
R.H.' 25.00C (SORP Cl) .......0...0........... 115

Experimental tablet weight gain at 23.20 - 27%
12.11., 25.0°c (SORP 02) 116

Experimental sorption of tablet at 27.50 - 34.50%
12.11., 25.0°c (SORP C3a) 117

Comparison of experimental and calculated Mvflg for
tablet at 36 - 40% R.H. and 25.0 ° C (SORP C3b) 119

Comparison of experimental and calculated Mt/M. for
tablet at 40.75-48.80% R.H. and 25.0 ° C (SORP C5) 121

xii

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

Experimental sorption of tablet at 48.85 - 60.35%
R.H.' 25.00C (SORP 6C) ......0.00.0.0...0.....

Comparison of experimental and calculated Mt/M_ for
tablet at 60.70 - 66% R.H. and 25.0 ° c (SORP 7Ca)

Comparison of experimental and calculated Mt/M. for
tablet at 66 - 73.40% R.H. and 25.0 ° c (SORP 7Cb)

Experimental sorption of tablet at 72.25 - 77.75%
R.H.' 25.00C (SORP C8) .............0..0.0...0

Comparison of experimental and calculated Mt/M, for
tablet at 77.90-82.45% R.H. and 25.0 ° c (SORP C9)

Comparison of experimental and calculated Mt/M. for
tablet at 82.05-87.30% R.H. and 25.0 ° c (SORP 10)

Experimental sorption of tablet at 86.70 - 91.70%
R.“.’ 25.00C (SORP 13) ......0........0.0..0.0

Comparison of experimental and calculated Mt/M. for
PVC film at 0 - 26.90% R.H. and 25.0 ° c (SORP P1)

Experimental sorption of PVC film at 26.65-43.50%
R.H0’ 25.00C (SORP P2) ......0...0.0.0.0.00000

Experimental sorption of PVC film at 43.50-58.20%
R.H.' 25.00C (SORP P3) .......0.0..0.0...00.0.

Experimental sorption of PVC film at 58.20-77%
R.H., 25.0 °c: (SORP P4) .......................

Experimental sorption of Aclar film at 0 - 27.35%
ROH0' 25.00C (SORP L2) .....0000000.000.000000

Comparison of experimental and calculated Mt/M. for

122

124

126

128

130

132

133

136

137

138

140

142

Aclar film at 27.35-43.50% R.H., 25.0 ° c (SORP L4) 144

Experimental sorption of Aclar film at 43.50 - 58%
R.H., 25.0 °c: (SORP L6) .......................

Experimental sorption of Aclar film at 58 - 74.45%
R.H., 25.0 °c: (SORP L7) .......................

xiii

146

147

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LIST OF SYMBOLS

Surface area

Water activity

Absolute humidity

Weight of filled blister package at time (t)
Statistical parameter for isotherm description
Statistical parameter for isotherm description
Weight of empty blister package at time (t)
Guggenheim constant

Critical Moisture Content

Water concentration in air at saturation
Diffusion coefficient

Package diffusion coefficient

Tablet diffusion coefficient

Weight of water transferred across film
Change in time

Equilibrium Moisture Content

Experimental

Guggenheim-Anderson-de Boer

Henry's Law Constant

Total heat of sorption of first layer on primary
sites

Total heat of sorption of multilayers

Heat of condensation of pure water vapor
Initial Moisture Content

Factor or slope

Average plastic film or product thickness
Tablet weight gain at time (t)

Final tablet weight gain

Moisture content

Number of experimental data points in isotherm
Permeability

Water vapor pressure outside film

Water vapor pressure inside film

Polyvinyl chloride

Water vapor pressure of product

Laminate permeability

Blister radius

Tablet radius

Relative humidity

radius

Root mean square

Solubility coefficient

Temperature

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Time

Half time to reach steady state
Number of shells for tablet
Blister volume

Tablet volume

Water content on dry basis
Final equilibrium tablet weight
Initial tablet weight
Calculated water content

Water content corresponding to saturation of
adsorption sites

Tablet weight at time (t)

Water Vapor Transmission Rate
Weight change

Summation of experimental AH
Monolayer moisture content
Summation of experimental AJEMC
Time lag

GAB constant

GAB constant

GAB constant

INTRODUCTION

In the pharmaceutical industry, a major concern lies in
the determination of the necessary packaging materials to
prevent moisture and other environmental factors from
adversely affecting a product throughout its shelf life. The
Food and Drug Administration requires extensive data
supporting the choice of packaging a pharmaceutical product in
a given packaging component. It would be very beneficial to
have this information as early as possible, so that package
design could be implemented based on actual realistic data as
opposed to assumptions. In response to this need, several
types of computer programs have been written to act as a
simulation of the shelf life under certain conditions.

Many' of ‘these shelf life :models consider' different
aspects of the product and package. One program in particular
uses a finite difference method to compute the shelf life of
a moisture sensitive product. This mathematical model
requires knowledge of the diffusion properties of both the
product and the packaging film. In addition, it takes into
account the solubility of water vapor in the package system.
This project involves experimental validation of a finite
difference method. The objectives of this study are

identified below:

2
To observe the sorption characteristics of a moisture
sensitive pharmaceutical tablet and blister packaging

material experimentally.

To calculate the diffusion coefficient of water vapor

for both the product and package material.

To determine the moisture gain of the complete package/
product system at specific relative humidity levels and

validate the calculated shelf life of the package.

To apply all of the acquired data to a finite difference
computer model in order to generate the shelf life of

the tablet.

To compare the experimental and simulated moisture gain
profile to validate the simulation model based on a

finite difference method.

LITERATURE REVIEW

Shelf Life of Moisture Sensitive Products

A very critical parameter in the selection of packaging
for the food and pharmaceutical industries is the ability to
obtain the proper shelf life needed for a product. Shelf life
may be defined as the amount of time that a package or the
product in the container ‘will remain in a saleable or
acceptable condition under specific storage conditions (Harte
and Gray, 1987). Product shelf life can be altered by
modifying its composition and form, the environment to which
it is exposed, or the packaging system. 'The shelf life can be
affected by environmental conditions, such as temperature and
relative humidity. Therefore, it becomes necessary to have
methods for' predicting the shelf life based on, product
characteristics, external environment, and type of barrier
packaging material utilized. In the case of moisture
sensitive products, predictions for the end of shelf life, due
to»a gain of a critical amount of moisture, can be made if the
temperature and relative humidity conditions are known as a
function of time, and the package permeability to moisture is
also known (Labuza, 1982).

It can be concluded that one of the primary environmental

4
factors that result in increased loss of quality'and.nutrition
for' most products is exposure to increased temperature
(Labuza, 1982). In addition, gain of moisture by dry or semi-
dry substances can lead to several modes of deterioration,
such as microbial growth, softness, hardening, and caking.

The current FDA guidelines for documentation of
acceptable packaging for human drugs and biologics require 3
years of shelf life data based on 2 kinetic concepts, one of
which is reaction and the other is migration (Kim and Gilbert,
1989).

Where solid dosage forms are concerned, moisture plays a
very significant role in preformulation testing.
.Preformulation testing can be defined as an investigation of
the physical and chemical properties of a drug substance -
alone and in combination with excipients. The ultimate
objective of preformulation testing is to gather information
useful to the formulator in the development of stable and
bioavailable dosage forms which can be mass-produced (Schepky
and Thomae, 1989). These sorption studies are designed to
show quantitative relationships between the product samples
and moisture. It is often possible to ensure that a final
formulation exhibits the desired sorption properties by
careful selection of the excipients.

If a container is empty, water vapor will pass through
the container wall until the relative humidity inside the
container is equal to the ambient atmosphere. In a

drug-filled container, the difference in internal and external

5
relative humidity impels moisture to become introduced to the
inside of the package and some amount of it will be absorbed
by the product. The drug absorbs water in a predictable
fashion, following its water absorption properties (Bonis,
1989) . The package contents act as a moisture sink and
retards equilibrium. When the product moisture content has
reached an equilibrium with the ambient relative humidity, the
humidities inside and outside the container are equal,

therefore reducing the driving force to zero.

Moisture sorption Isotherm

In order to analyze a moisture sensitive pharmaceutical
product, it is necessary to produce a moisture sorption
isotherm. The water sorption isotherms of foods and
pharmaceuticals show the equilibrium relationship between the
moisture content and the water activity (Au) at constant
temperatures and pressures. These isotherms are generally
described as a plot of the amount of water sorbed as a
function of Au (Iglesias and Chirife, 1982). Packaging
dehydrated foods is one of the most important applications of
moisture sorption isotherms, since the prediction of storage
life of these items packaged in flexible film materials is of
considerable value in the food preservation area (Iglesias and
Chirife, 1982). The rate of transport of water vapor through

a film sample is shown by Eq. (1)

dw/d6=PA/l (pi-p0) (l)

where w is the weight of water transferred across the film, 9
indicates the time, P is the film's permeability, l is the
thickness of the film, A is film area, pi is the vapor
pressure of water outside the film, and po is the vapor
pressure of water on the other side of the film. ‘This assumes
that moisture entering the package equilibrates with the
product almost immediately.

An interesting finding showed that the particle size
distribution. of a jproduct often does not influence the
sorption isotherm (Iglesias and Chirife, 1982). Isotherm
equations are needed for evaluating the thermodynamic
functions of the water sorbed. The need for mathematical
models in order to use the isotherm with computer techniques
was discovered.

The moisture isotherm serves as the translation between
moisture influx into a hermetically sealed package and the
effects of this water vapor on the product (Marsh, Ambrosio,
and Guazzo, 1991). Computer modeling can be used to predict
the time necessary for the moisture level inside the package
to rise from a production moisture level to a critical level
under specific environmental conditions. Marsh et a1.
developed a model for use in shelf life determination. The
product examined was a Fibre Trim effervescent tablet, which
became the first effervescent tablet to be introduced in a

nonfoil package worldwide. This shelf life model calculates

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the time for the moisture content within the product to rise
from the initial moisture content to the critical content as
influenced by the packaging system andenvironment. Packaging
system refers to the package area, package volume, blister
permeability and product net weight. Marsh's program
considers the change in the driving force of moisture across
the package as moisture traverses the film. Shelf life
differences reflect the varying environmental conditions of 3
climactic regions at differing times in the product life

cycle.

Unit Dose Blister Packaging

Barrier plastics, which may be used for blister
packaging, fill the gap between the infinite barriers to
moisture mass transfer of metals and glass, and the finite
barriers of coated cellulosic products and high permeability
plastics. Often times, combinations of materials - laminates,
coextrusions, or coated substrates - are necessary to provide
for the unique requirements of foods and pharmaceuticals while
supplying needed mechanical, thermal, optical and aesthetic
properties (Brown, 1987).

Blister packages for pharmaceutical products have several
advantages over bottles. Blisters allow for preparation of
unit doses without having to physically handle the drug,
leading to increased hygiene and better conservation of the

drug (Dubouchet and Paisley, 1984). A blister provides good

8

mechanical protection of each individual tablet or capsule,
has tamper evident features, and, being transparent, gives
easy content identification. Also, blister packages aid in
greater flexibility with regard to adapting the package size
to the prescription size, reducing inventory requirements.

Over the last several years, there has been an entirely
new use for coextruded film and sheet in packaging
pharmaceuticals and medical devices in the 0.8. (Bonis, 1989) .
The greatest threats to the physical condition, stability, and
potency of drug products are heat, moisture, light and.oxygen.
Many drug products are completely inactivated by moisture
exposure. Penicillin, for example, becomes totally inert
unless packaged in containers with low water vapor
transmission rates. Moreover, biological products such as
vitamins, hormones, *vaccines, antitoxins and. certain
antibiotics can degrade and be inactivated by excessive heat.
Light‘ and oxygen together may reduce or nullify the
effectiveness of other substances, such as antibiotics,
hormones, alkaloids, glucosides, vitamins, steroids
(cortisone, prednisone) and vaccines.

Polymonochlorotrifluoroethylene (Aclar) is nearly
impermeable to moisture, but it is an expensive material
(Bonis, 1989). Aclar is suitable for packaging of
pharmaceuticals because of its very low WVTR, fairly low gas
transmission rate, inertness to most chemicals, resistance to
ozone, clarity, good tear strength and excellent dimensional

stability (Brennan, 1992). Due to its dramatically different

9

softening point from other thermoforming materials, Aclar
laminates can complicate the thermoforming process. PVC
(unplasticized) is one of the most commonly used materials
because of low cost and ease of thermoforming. Unfortunately,
it generally does not provide decent barrier protection to
moisture. However, its barrier characteristics can be
improved by lamination with different resins, especially
Aclar.

Guise (1984) discussed some of the advantages of blister
packaging. Blister packages offer protection against cross
contamination, elimination of tablet abrasion caused by
vibrations during distribution, decreased chance of overdose
by over-the-counter (OTC) users, and storage space savings for
reels of base and lidding materials over empty bottles.

Pires et al. (1988) conducted a study which evaluated
Ibuprofen product stability in two multiple unit containers
(30 and 50 count) and three blister package types. This
project ultimately compared the effects of opening and closing
the multiple unit containers with the different blister packs
(PVC, Aclar/PVC and Saran coated PVC). Moisture sorption
isotherms and WVTR data were generated. At the abusive
storage conditions (78"F‘and 85% R.H.), the moisture content
of the tablets increased.over time, with the greatest increase
being in the PVC blister package and followed by the multiple
unit 30 and 50 count containers subjected to repeated opening
and closing. The Aclar blisters showed the best performance

against moisture. Ambient conditions resulted in no

10
significant differences for the five package types. There are
advantages to blister packaging in terms of barrier options

and the one-time use feature.

Diffusion and Permeability

Hernandez et al. (1986) applied the equilibrium vapor
pressure and microbalance gravimetric method (i.e., sorption
technique) to study the sorption and diffusion of toluene
vapor in.OPP'and Saran film samples as a function of penetrant
concentration. As part of this approach, the polymer sample
was hung directly from one of the arms of the electrobalance
while a constant concentration of penetrant vapor was flowed
continually through the sample hang-down tube, such that the
sample was completely surrounded by vapor (Hernandez et al.,
1986).

Understanding the diffusion, solubility and.permeability
of penetrants through plastic film structures is of both
theoretical and practical importance. Theoretically, this
knowledge can increase the understanding of diffusion
mechanisms of penetrants through polymer membranes.
Solubility and diffusion of organic penetrants will be
critical for instances when product quality is related to the
transfer of organic vapors from one element of the package to
another element. Diffusion and solubility coefficients are
usually determined by weight change observations of a polymer

sample during a sorption process (Hernandez et al., 1986).

11

Diffusion and permeability values can be found from
permeability studies where permeant transport through a film
sample is monitored (isostatic procedure) or by quantifying
the amount of permeant which has passed through the polymer
and accumulated over time (quasi-isostatic procedure). The
Cahn electrobalance is a very efficient tool for generating
data of a vapor being sorbed by a film sample or any other
product over a given time period.

At low concentrations, where plasticization is negligible
and sorption kinetics are Fickian, the diffusivities of gases
and vapors in glassy polymers are extremely strong functions
of the size and shape of the penetrant molecules (Berens,
1989).

The rate of permeability is affected by the temperature,
humidity, and package surface area: polymer'properties such as
density, molecular orientation, plasticizer content and chain
stiffness. In laddition, the hydrophobic or' hydrophilic
character of the film will affect permeability (Brennan,
1992). Permeation through a plastic film occurs in three
stages:

1. Absorption and solution of the penetrant on one polymer
surface

2. Diffusion of the penetrant through the polymer

3. Desorption and evaporation of the penetrant from the
other polymer surface.

There are several ways in which a gas can permeate a

membrane. This will depend on the membrane structure. A

12

material with a capillary porous structure will produce gas

transport by the phenomena which takes place in the pores,

while a non-porous material will give rise to migration by

molecular diffusion (Rudobashta et al., 1978).

Steffe and Singh (1980) conducted a study to determine
the liquid.diffusivity of the starchy endosperm" bran.and hull
of rough rice. Mathematical equations based on Fick's Law of
Diffusion were used to model the thin-layer drying of brown,
white and rough rice. Diffusion coefficients were found by
minimizing the sum of squared deviations between the
theoretically predicted and observed drying curves. The
distinct feature of this research is that this rough rice
product is viewed as a composite body with different diffusion
properties for each component.

Several assumptions were made in order to develop the
drying models used. Specifically:

1. Liquid diffusion is the mechanism of moisture movement.

2. Diffusion coefficients are not a function of moisture
concentration.

3. Rice was considered to be isothermal during the drying
process.

4. The rough rice kernel was considered as a sphere
(starchy endosperm) surrounded by two concentric shells
(bran and hull) for geometric purposes.

5. Rough rice components are homogeneous, isotropic
materials.

6. Rice kernel shrinkage is negligible during drying.

13

Fitting Models for Sorption Isotherms

Several mathematical models exist to fit the experimental
sorption isotherm data for a given pharmaceutical tablet or
food substance. One example is the BET (Brunauer-Emmett-

Teller) equation (Iglesias and Chirife, 1982) found below

aH/(l-aH)X=1/X,.C + a,<c-1)/x,,c (2)

which calculates x" (the monolayer moisture content). This
parameter (x_) has significance in the physicochemical
stability of foods.

Another such example is the Henderson equation (Iglesias

and Chirife, 1982)

1 - a, = exp 1 - [b2 00", 1 1 (3)
where X is the moisture content expressed on a percent dry
basis, and b1 and b2 are statistical parameters to be used for
the isotherm description. To represent sorption data for
interpolations or inclusion into computer models of drying
processes, closed functions are used: the Guggenheim-Anderson-
De Boer (GAB) equation is one of the relations most often
applied (Spiess and Wolf, 1986).

Until recently, most of the mathematical models for
prediction of the shelf life were simple in nature. Some of

these models were developed by Labuza, Karel and coworkers and

l4

focused on water vapor and oxygen deterioration. Peppas and
Khanna have analyzed a mathematical theory of gaseous
transport through polymer films, which in connection with a
variety of food sorption models, can lead to concise
prediction of shelf life of foods in storage environments
(Peppas and Sekhon, 1980). With this approach, it is possible
to predict shelf life of food products for moisture transport
through plastic films, with minimal or no swelling due to
sorption, and for sorption on food described by linear,
Langmuir, BET, Halsey, Oswin, Freundlich and other isotherms.
Generalized graphs were produced which exhibit the dependence
of internal water activity on storage time for packaging
systems characterized by a permeability-sorption constant.
This constant is a packaging system quality and can be found
from food sorption and polymer diffusion characteristics, as
well as from specific geometric properties of the food
package. Additionally, this theory was extended to include
such parameters as oxygen diffusion, sorption and reaction on
the food product.

The previous mathematical analysis combined diffusive and
sorptive concepts in a simple, but accurate fashion.
Assumptions inherent in this development include
thermodynamically ideal systems, no swelling of the polymer
film due to water vapor diffusion (i.e., thermodynamic
incompatibility between moisture and polymer), isothermal
conditions, single polymer packaging, no pressure difference

during packaging, and constant temperature and relative

15
humidity (R.H.) storage conditions (Peppas and Sekhon, 1980).
The model also assumes that there is no degradation or
physical change of the polymer from time-temperature history,
that sorption on the food is the rate limiting step once the
vapors have diffused through the film, and that water
diffusion through the food is not significant.

The specific amount of water associated with a solid at
a particular relative humidity and temperature depends on its
chemical affinity for the solid and the number of available
sites of interaction. Zografi et al. (1988) studied the
situation where various solids of differing moisture contents
are mixed together into a solid dosage form and stored in a
sealed container at a known temperature and headspace volume.
Assumptions include a completely closed system and transfer of
moisture occurs via the vapor phase.

A mathematical method to predict the amount of moisture
associated with each ingredient in a mixture was presented.
This model requires the initial moisture contents of the
individual components, their dry weights, headspace volumes,
temperature and.an.equationuwhich can describe the sorption or
desorption isotherms for the solid. This approach is
significant for desiccant prediction and quantity necessary to
maintain a relative humidity in a package. In addition, the
headspace volume to be used to reduce moisture sorbed to an

active ingredient may be estimated.

16

Computer simulation Programs

Various computer simulation programs have been developed
at the School of Packaging (Michigan State University, East
Lansing, MI) to predict shelf life of moisture sensitive
products for a range of temperature and relative humidity
values. Kirloskar (1991) interpolated data of the isotherm
from data at three temperatures. Two different pharmaceutical
products generated the experimental results which were being
sought for this program. An orange flavored multivitamin
tablet and an Ibuprofen tablet were evaluated. This
development provides the effect of temperature on the
coefficients of the equation selected to describe the
equilibrium sorption isotherm of the tablet. The program
combines the expression for the isotherm as a function of
temperature and the expression for the water vapor
permeability of the package with the equation for predicting
the moisture gain of the tablet as a function of storage
condition and time, within the three sorption isotherm
temperatures.

Kirloskar evaluated three moisture sorption fitting
equations as part of the shelf life program. The equations
used were the Chen equation, the Henderson equation and the
BET equation. The BET and Henderson equations were presented
in Eq. (2) and Eq. (3), respectively. Chen's equation is

shown in Eq. (4).

17

M = (k - ln(-ln Au)) / a (4)

These equations were used to fit the experimental sorption
isotherm data. The following criteria were used to select the
best fitting equation out of the three possible: 1.) the best
linear regression coefficient and, 2.) the minimum sum of the
squared difference between the equation and experimental
values. Kirloskar's shelf life predictive modeling assumed a
steady state mass transfer of moisture through a package
expressed as a permeability.

A different approach of a shelf life computer program was
presented by Kim (1992). This program estimates the shelf
life of a packaged moisture sensitive pharmaceutical product
based on the solutions of a set of partial differential
equations that correlate the amount of sorbed water by the
product and the diffusion coefficient of water of the
packaging material and the tablet. The set of differential
equations is solved using the finite difference method. Some
of the key parameters which are taken into consideration
include the diffusion coefficient of water in the
pharmaceutical product and the packaging material, as well as
the solubility of the material to water.

One conclusion found as part of Kim's work was that the
shelf life tends toldecrease and reach an equilibrium state as
the diffusion coefficient of the tablet and material
increases. In addition, Kim observed that when the diffusion

coefficient of water in the product is significantly higher

18
than the diffusion coefficient of the packaging material, the
shelf life value for a circular plate shaped product was in
agreement with an analytical solution. This model should
prove to be extremely useful and accurate for package and
material selection for a moisture sensitive product.

The shelf life of the pharmaceutical product is
associated with the total moisture content in the tablet.
Product performance depends on other characteristics besides
moisture. The shelf life modeling does not provide
information about these issues, such as any degradation from
oxygen, light sensitivity, dissolution rate or change in
potency of active ingredients. Perhaps at the present time,
there is no predictive mathematical model which addresses all
product areas. Moisture is the key parameter considered as
part of this finite difference model to predict the shelf life
by calculating moisture content at different levels (shells)
of the tablet and determining the amount of water in the
package headspace. All other changes in the quality of the
product that affect the product's shelf life has to be
correlated with the moisture content.

Contrary' to the :model that ‘uses permeability, this
program, based on a finite difference method, considers the
unsteady steady state transfer of moisture through a packaging
material, into the headspace of the package and into the food
or pharmaceutical product. Due to the development of many
polymers with strong resistance to water vapor, this study of

mass transfer'is useful. Several assumptions are made as part

19

of this simulation program and are found in the following

list.

10.

11.

Water is transferred through the packaging film and
pharmaceutical product by molecular diffusion.
Moisture sorption isotherms of packaging material and
product are known.

The shelf life of the product depends on physical and/or
chemical qualities which are only related to the
moisture content of the product.

The temperature and relative humidity outside the
package are constant.

Sorption/desorption hysterysis in the product is
negligible.

The water vapor concentration in the headspace
surrounding the product is homogeneous.

Initial concentrations of moisture in the product,
headspace, and packaging material are all in
thermodynamic equilibrium.

The diffusion coefficient of the polymer and product
depend solely on temperature.

Product has simple geometry, such as a sphere or
circular plate.

If the shape is that of a circular plate, moisture
transfer occurs through the circular faces only and not
through the edge of the tablet.

Diffusion of water vapor into the product is one

20
dimensional.
12. Product responds to changes in relative humidity
instantly by absorbing moisture immediately.
13. Computer model considers only single layer packaging

film materials.

The necessary parameters needed to execute this shelf
life simulation model include all external conditions and
specific characteristics of the packaging material and
pharmaceutical product. External conditions were those such
as relative humidity, absolute humidity and temperature.
Package properties required were blister volume, blister
surface area, package thickness, package diffusion
coefficient, number of package layers and Henry's Law constant
found from the solubility data. For the pharmaceutical
tablet, characteristics investigated for this program included
the tablet diffusion coefficient, both the initial and
critical moisture contents, the dry tablet weight, the tablet
radius and thickness, the number of shells used and the three
GAB (Guggenheim-Anderson-de Boer) constants. All of these
parameters comprised the input data for the mathematical model
using the finite difference technique for unsteady state
moisture uptake of a packaged product.

The diffusion coefficient of the tablet and the polymer
film to water, as well as the solubility of the film to water,
are the most critical parameters of this program. These

characteristics1have the greatest impact on the outcome of the

21

shelf life and exhibit adsorption and diffusion behavior of
the water molecules. Polymer structure and percent
crystallinity, along with product composition, affect the
diffusion. It is important to know the constant temperature
and relative humidity conditions outside of the package for
the model. Diffusion coefficients of the tablet and material
are dependent on the temperature.

Moisture content is the only indicator of moisture the
product held before exposure to the external conditions. When
the critical moisture content is reached, the shelf life is
determined based on the period of time needed to obtain this
value. Therefore, the CMC is a required variable of the
program.

The GAB equation describes the moisture sorption isotherm
of thejproducta From this equation of sorption character, the
GAB coefficients are derived and are needed for the model to
function. The GAB equation is ideal for analysis of food and
pharmaceutical isotherms.

Blister volume determines package headspace available for

the product with specific dimensions.

MATERIALS AND METHODS

Materials

As part of this experimental project, UpJohn Company
(Kalamazoo, MI) supplied pharmaceutical tablets and blister
packaging materials. The pharmaceutical product was a 20 mg
Deltasone tablet (Lot No. 286 HW), which is a brand of
Prednisone. This drug is often used as an anti—inflammatory
agent for the treatment of arthritis. Deltasone (20 mg) is
the active ingredient in these tablets. calcium stearate,
corn starch, FD & C Yellow No. 6, lactose, sorbic acid and
sucrose are listed.as the inactive ingredients. 'The following
dimensions and characteristics were determined and are listed

in Table 1.

Table 1. Tablet dimensions

 

 

 

 

 

 

 

 

0.392 cm i 0.001 cm
Tablet Radius 0.50 cm i 0.005 cm
Tablet Mass 0.4077 g 1 0.0016 g
Surface Area of Tablet 1.57 cm2 i 0.005 cm2
Volume of Tablet 0.308 cm' i 0.005 cm3
L__¥Shape of Tablet Flat cylinder plate

 

The blister packaging film sheet construction consisted

22

23
of 7.5 mil Polyvinyl Chloride / Adhesive layer / 1.6 mil Aclar
from inside to outside. The following dimensions and
characteristics were determined in Table 2. Figure 1 shows a
schematic of a single blister cavity with thickness variations

of the formed blister.

Table 2. Dimensions of blister package

   

 

 

 

 

 

 

 

Height of Blister 0.65 cm i 0.005 cm

Radius of Blister 0.625 cm i 0.005 cm I

Surface Area of Blister 3.78 cm2 i 0.005 cm2

Package

Inner Volume of Blister OLgIg-cm3 i 0.005 cm’
0.0114 cm

1
Fr 1p“

 

 

 

 

 

 

 

 

 

0.0127 cm
0.0127 cm
085cm
1 *>0195cm1<h I 1
1 Aluminum Foil/Paper f
0.023 cm 0.023 cm

Figure 1. Schematic of a blister cavity with thickness
measurements

24

MOISTURE SORPTION ISOTHERM OF TABLET

Sample Preparation

For the determination of moisture gain over a specific
period of time, the Cahn D-200 Model Electrobalance was used.
This is a very sensitive mass measurement instrument. The
electrobalance is able to detect mass changes as small as 0.1
microgram and is computer operated. The data which was
generated by the electrobalance was stored in and retrieved
from the hard disk in the computer, and plotted on a plotter
using the Cahn software package. A detailed drawing of the
electrobalance and.the hangdown tube where the sample was held
is shown in Figure 2.

The sample tablet used to generate data for the moisture
sorption isotherm was prepared in the following manner. A
thin strip of aluminum foil was cut to the same dimension as
the tablet thickness and attached with adhesive around the
entire edge of the tablet. Epoxy resin/hardener (Elmers) was
used as the adhesive. The two end tabs of the foil were
adhered to one another to form a "tab" and the tablet/foil
arrangement was allowed to set for at least two hours. This
aluminum strip surrounding the tablet was done in order to
fully seal off the edge of the product so that moisture
exposure could occur only at the two tablet faces. It was
desirable to have water vapor enter only the tablet faces and

not the edge, due to the single dimension diffusion character

DOME
\

 

 

 

255

HOVOR

 

 

00H! CLAHP

 

 

 

 

 

unncoowu
ASSInULv
ans: .
PLAIE 1
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Figure 2.

 

 

 

 

 

 

 

I _
' T
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CABLE
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Cahn Electrobalance and hangdown tube for sample

26
of the shelf life predictive model. A sketch of the
tablet/foil sample is in Figure 3. A tiny pinhole was formed
in the foil "tab" producing an area for a hanger-shaped wire

to be placed.

 

 

 

 

Figure 3. Deltasone tablet sample with foil on edge

Drying the Tablet

The tablet was dried to nearly 0% moisture content in a
vacuum oven for '4 - 6 hours at room temperature. A metal
stand was put into a large glass beaker in order to support
the tablet and wire while drying. During this time, the

electrobalance went through a calibration process. After

27

drying the sample, it was quickly moved to the electrobalance
tube inside of the environmental chamber and hung from the
electrobalance hangdown wire. Additional drying took place

through nitrogen flushing until the sample displayed a steady
state conditions The sample tablet. was contacted, with
several relative humidity values ranging from 11.50 to 91.70%
R.H. at 25.0 ° Celsius. It was possible to measure the
relative humidity condition with the use of hygrosensors
attached to a hygrometer (Newport Scientific HYGRODYNAMICS,
Newport Scientific, Inc., 8246 E. Sandy Court, Jessup, MD
20794-0189). The relative humidities considered were 11.50%,
15.25%, 23.20%, 27%, 34.50%, 40%, 48.80%, 60.35%, 66%, 73.40%,
77.75%, 82.45%, 87.30% and 91.70%. These values were used to
construct the moisture sorption isotherm for the product. A
schematic of the electrobalance and system can be fbund in

Figure 4.

Sorption Isotherm of Blister

The blister film material, a laminate of PVC film and
Aclar, was delaminated in order to analyze the components of
the structure on an individual basis for moisture sorption
character. This was necessary to determine the diffusion
coefficient of water through both polymers. Also, this
delamination can ultimately show that separation of these
materials doesn't affect their overall properties, such as

water vapor transmission and permeability. Each material

EC

 

 

 

 

 

 

 

 

 

 

 

7 V
NZ {— HE
R
2 A.
z /
: B
I
T - Nitrogen tank S - Humidity sensor
Te - Tee connection N - Needle valve
EC - Environmental Chamber R - Rotameter
EB - Cahn electrical balance B - Gas washing bottle
Vv - Venting valve

Figure 4. Schematic of electrobalance and actual system

29
sample was 6.45 cm2 and was cleaned with Hexane to remove any
remaining adhesive. Each sample was given a pinhole in order
to hang from a small wire. A similar procedure employed to
dry the pharmaceutical tablet was utilized for drying these
film samples. Relative humidities studied were approximately

26.90%, 43.50%, 58.20%, and 77%.

I. R. Identification

The two blister packaging film samples, PVC and Aclar,
were analyzed using a Perkin Elmer Infrared Spectrophotometer.
The PVC sample required the Attenuated Total Reflectance unit
(ATR) due to its thickness being in excess of a few mils.
This unit, with the aid of specific angled mirrors and a
crystal attachment, allows a clear scan to be obtained on
thicker plastic films. Standard IR transmission techniques
were used to generate a scan of the Aclar material. Before
running the samples on the IR Spectrophotometer, they were
cleaned with Hexane in order to remove any adhesive that could
have been remaining after delamination of the material. IR
scans provide the distinct identification that is
characteristic of various materials. IR transmissions were
conducted to verify that the PVC and the Aclar had no
additional adhesive left.after'delamination.and for individual

film identification purposes.

30

Water Vapor Transmission Rate of Packaging Material

Water Vapor Transmission Rates (WVTR) were determined for
the blister materials using a dish method (ASTM E96). Three
different samples were prepared in triplicate. There was a
PVC sample, an Aclar sample, and a sample of the PVC/Aclar
lamination which were tested. Each dish was cleaned
thoroughly and enough fresh desiccant was added to cover the
bottom of the dish. Circular samples of each material were
cut out and sealed to a dish with a hot paraffin wax mixture.
The dishes were weighed on a Mettler Analytical Balance and
placed into an environmental chamber at 37.78 ° C and 85% R.H.
These dishes were weighed 4 separate times over a 1.25 month
time period. The WVTR of these materials was calculated

based on the weight gain of the dish samples.

Moisture Gain of the Tablet and Blister Package

As an experimental way to validate the calculation of
shelf life, Deltasone tablets packaged in blisters were also
studied for moisture uptake over time. Two separate relative
humidity environments with controlled conditions were created
using salt solutions in tightly closed 5 gallon plastic (high
density polyethylene) buckets. Salt solutions were prepared
by adding the specific salt to a crystallization dish
containing warm distilled water until saturation was clearly

visible. One humidity condition was 78.5 - 80% R.H. and was

31
prepared with Ammonium Sulfate (NH‘)ZSO,. The other
environmental container used Potassium Nitrate (KN03) to
provide a humidity condition of 88.5 - 90% R.H. The relative
humidity levels were measured with a digital hygrometer
periodically.

Five full blister cards were placed inside of each
bucket, along with one empty blister card to be used as a
control. Each blister card contained 10 blisters and held a
total of 10 tablets. ‘The packages were weighed over a several
month period in order to monitor weight gain with a Mettler
Analytical Balance. Forceps were used to handle the blisters
at all times. Before placing in to the controlled humidity
buckets, all of the blister packages were dried in a
convection oven at 40.0 ° C, until a steady state weight

occurred.

RESULTS AND DISCUSSION

Tablet Sorption

Sorption equilibrium experiments were conducted using the
Cahn electrobalance at 25.0 °CL Equilibrium.moisture values
of the tablet were obtained at selected conditions of
humidity, such as 0, 11.50, 15.25, 23.20, 27, 34.50, 40,
48.80, 60.35, 66, 73.40, 77.75, 82.45, 87.30 and 91.70% R.H..
Since the electrobalance operates by a stepwise change of the
humidity value surrounding the tablet, several sorption
experiments were necessary to carry out the whole isotherm.
Besides obtaining the moisture equilibrium value, this mode of
operation allowed the determination of the diffusion
coefficient of water at various values of relative humidity.

The electrobalance, in combination with the computer and
software, allowed for storage of the tablet weight at a
specific time point. The amount of time between each tablet
weighing was selected prior to the experimental test at a
given relative humidity; For each.humidity test, the time was
expressed in hours, and the weight gain of the tablet (Mt) was
calculated" IFor«each.experiment, there was an initial weight,
In, and an equilibrium weight. The equilibrium weight of one

experiment became the initial weight for the next interval of

32

33
humidity. Moisture weight gain, Mt, of the tablet is

calculated as

M ==FV - W. (5)

where Wt is the tablet weight at time (t) and Wi is the initial
tablet weight. The final tablet weight gain (M;) is

calculated as

Mo=wf'wi (5)

where Wf indicates the equilibrium weight of the tablet at the
end of an experimental humidity value. From these values,
Mt/M, was determined by dividing each consecutive weight gain,
Mt, by the final weight gain, Mu. Values of M/M. were plotted
against time (t), as well as Mt vs. time (t). An example of
this is represented in Figure 5. INearly all of the graphs for
the tablet displayed a rapid weight gain of water vapor and

then leveled off at steady state.

Material Sorption

The individual PVC and Aclar film samples were also used
to calculate the moisture sorption for the packaging material.
Similar graphs were produced to illustrate the moisture gain
of PVC and Aclar at selected relative humidities. A typical

graph of the moisture uptake by PVC film is presented in

34
Figure 6, and Aclar film shows a similar type plot which is
presented in Figure 7. This allows a graphical analysis to be
generated of the films' sorption character over a given

humidity range. It was found that

 

L2

Nfi/hfinfi

 

 

 

 

0 1 1 1 1 1 1
0 5 10 15 20 25 30 35
TIME (hours)

Figure 5. Experimental sorption of tablet at 82.05-87.30%
12.11., 25.0 ° c

35
both films absorbed moisture rapidly and.attained.steady state
within 5.0 hours for relative humidity levels ranging from 0
to 26.90% R.H. for PVC film and within 2.0 hours for relative

humidity levels ranging from 43.50 to 58% R.H. for Aclar film.

 

L2

Nh/hfinfl

 

 

 

0 1 1 1

 

0 S 10 15 20
TIME (hours)

Figure 6. Experimental sorption of PVC film at 0 - 26.90%
12.11., 25.0 ° c

36

 

L4

L2 —

Nh/hfinfl

 

 

0 - 1 1 1 1 1 1
0 2 4 6 8 10 12 14

TIME (hours)

 

Figure 7. Experimental sorption of Aclar film at 43.50-58%
R.H., 25.0 ° c

Sorption Isotherm

For each value of relative humidity, the equilibrium
moisture content (EMC) of the product is defined as the gain
of moisture per 100 grams dry weight of product or packaging

material and is calculated in the following equation.

37

EMC = [(wf - w,) / (W,)] x 100 (7)

A moisture sorption isotherm can be generated by plotting EMC
against relative humidity. The isotherm gives the amount of
water per unit of dry weight of the substance at a particular
humidity value at a given temperature. A sorption isotherm
describes the manner in which the moisture content will change
due to relative humidity fluctuations. Isotherms can also be

plotted using EMC vs. A. (water activity) per Eq. (8). For

the Deltasone tablet, the greatest increase in the moisture
content occurred between 87.30 and 91.70% R.H. (last point on
isotherm). The actual isotherm data is given in Table 3.

This isotherm is presented in Figure 8. Equation 8 is

described below.

AH = p/po = Relative Humidity/100 (8)
In this equation, p is the water vapor pressure of the product
and p5 is the saturation vapor pressure of pure water at the
temperature of test (Iglesias and Chirife, 1982). Isotherms
are typically similar for most pharmaceutical products.

The sorption isotherms for the.Aclar and PVC film samples
were generated using the same techniques described for the
Deltasone tablet above in Eq. (7). The moisture sorption
isotherms for the packaging materials showed fairly linear
curves. Increases in moisture content were quite consistent

at the various levels of relative humidity. Tables 4 and 5

38

Table 3. Moisture sorption isotherm data for Deltasone
tablet at 25.0 ° C (Experimental and Calculated)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Exp. Equilibrium Calc. Equilibrium
Moisture Content Moisture Content
(9 PIG/100 9 dry) (9 H0/___g dry

11.5 0.375 0.441

15.25 0.394 0.485

23.2 0.524 0.562

27.0 0.642 0.598

34.5 0.699 0.673

40.0 0.743 0.734

48.8 0.932 0.851

60.35 1.05 1.062

66.0 1.221 1.202

73.4 1.365 1.451

77.75 1.606 1.653

82.45 1.904 1.938

87.3 1.976 2.351

91.7 3.514 2.917

 

 

 

 

39

 

W
I

EMC (g water! 100 g dry product)
1—s N
I F

 

 

 

 

0 l l I I l 1 J l l
0 10 20 30 40 50 60 70 80 90 100
Relative Humidity (%)

Figure 8. Moisture sorption isotherm of 20 mg Deltasone
tablet at 25.0 ° C showing Equilibrium Moisture
Content (EMC) vs. relative humidity

provide the sorption data for' the PVC and .Aclar film.

Moisture sorption isotherms for the PVC and Aclar material

samples are presented in Figures 9 and 10, respectively.

Table 4. Moisture sorption isotherm data for PVC film at

25.0 ° c

Relative Humidity (%)

Equilibrium Moisture
Content (g H 0/100 g dry) 1

 

 

 

 

 

 

0 0
26.9 0.036
43.5 0.076
58.2 0.10
77.0 0.133
- a 1-—-=—=--

 

 

Table 5. Moisture sorption isotherm data for Aclar film at

25.0 ° c

    

   

 

    

 

 

r—_—"-““m***‘*“——“—*_—‘_”“*‘———‘ "* “7
1 Relative Humidity (%) Equilibrium Moisture 1
Content (g H 0/100 9 dry) !
__.___.____—___________—__~_______________4

 

 

 

 

 

 

0 0
27.35 0.055
43.5 0.084
58.0 0.121
74.45 0.131

 

 

 

41

 

0.15

EMC (g water/100 3 PVC)

 

 

 

 

0 1 1 1 1
0 20 40 60 80 100
Relative Humidity (%)
I, Experimental _ Calculated

Figure 9. Moisture sorption isotherm of PVC film at 25.0 °<2
showing Equilibrium Moisture Content (EMC) vs.
relative humidity

42

 

EMC (g water/ 100 g Aclar)

 

 

 

 

0.15
0.1
0.05
0 . 1 1 1 1
0 20 40 60 80 100
Relative Humidity (%)

e Experimental _Calculated

Figure 10. Moisture sorption isotherm of Aclar film at
25.0 ° C showing Equilibrium Moisture Content
(EMC) vs. relative humidity

43

Solubility of Packaging Material

The linear change in moisture content by the PVC and
Aclar'materials can be described by Eq. (9). The slope of Eq.

(9) gives the solubility coefficient of'both the PVC and Aclar

materials.

EMC = k Relative Humidity (9)

For this equation, k is the slope of the sorption isotherm.
For PVC, the solubility coefficient was found to be 0.001704
g “20/100 9 PVC % R.H. (see Appendix C). A solubility
coefficient of 0.001838 9 H20/100 g Aclar % R.H. was

calculated for Aclar film (see Appendix D).

later Vapor Transmission Rate of Materials

The ASTM dish method (ASTM E96) was applied to determine
the Water Vapor Transmission Rate (WVTR) of the various
blister packaging materials. Continuous weight gain of the
desiccant filled metal dishes was monitored over a specific
period of time. This illustrated the passage of water through
the material over time, which resulted in moisture gain of the

desiccant.

WVTR-=AW/A*T (10)

44
AW is the weight change over time (g), A is the surface area
of the exposed material (m2), and T is the time period of the
test (day). The WVTR test was conducted at 37.781° C and 85%

R.H. over a 35 day interval. Surface area is calculated using

A = n r2 (11)

where r is the radius of the circular film section within the
dish. Graphs of dish weight gain over time for each material
display water vapor transmission properties. Results are
presented graphically in Figure 11 (PVC), Figure 12 (Aclar),
and Figure 13 (PVC/Aclar). Film samples of PVC, Aclar, and
PVC/Aclar were analyzed in triplicate for this experiment (see
Appendix E).

In order to evaluate the packaging materials, it was
necessary to determine the permeability and the diffusion
coefficients for the PVC and the Aclar samples. The WVTR and
P were measured experimentally for each individual material
and for the laminate structure in order to compare the
results. With the following equation, the calculated
composite WVTR (WVTRT) may be analyzed against the actual data
generated.

l/WV'I'RT = 1/wv'rRWC + 1/WVTRA (12)

clar

It was found that the calculated WVTR was very close to the
WVTR obtained in the laboratory with 0.169 g/m’ day

45

 

0.2

0.15

Weight Gain (grams)
9
1.1

0.05

 

Figure 11.

 

l l 1

10 20 30
TIME (days)

... Sample 1 _._ Sample 2

WVTR of PVC film at 37.78 ° c and 85% 11.11.

 

46

 

0.05

.o .c
8 3

Weight Gain (grams)
9
8

0.01

 

 

0 1 1 1

 

 

0 10 20 30 40

TIME (days)

_._ Sample 1 ... Sample 2

Figure 12. WVTR of Aclar film at 37.78 ° C and 85% R.H.

 

Atacafiexv rem-.... v .—~l...v>)

Fh

47

 

0.04

0.03 1-

Weight Gain (grams)
9
8

0.01 —

 

 

 

0 4 l l l
0 10 20 30 40
TIME (days)

+ Sample 1 ... Sample 2

Figure 13. WVTR of PVC/Aclar film at 37.78 ° C and 85% 12.11.

(calc

(expe

resu'

P. i
tote

PVC

aqre

8&2;

exte

48
(calculated) and 0.1616 g/m2 day (average experimental).
In addition, a comparison of the permeability
(experimental) for the laminate blister material and the
calculated permeability was determined. Eq. (13) provided the

results of the permeability for the total laminate.

P1 = LT / ((LPVC / PPVC) + (LAclsr / PAclsr)) (13)

P1 is the permeability for the total film structure, 1..Y is the
total thickness of the laminate, an is the thickness of the

PVC sample, L is the thickness of the Aclar, and th and

Acler

P are the permeability values for the PVC and the Aclar,

Aclar

respectively. Permeability is calculated from the following
equation. Experimental permeability (average) was found to be
0.0348 g mil/m2 day mmHg and the comparative calculated
permeability was 0.0364 g mil/m2 day mmHg showing outstanding

agreement of the laminate structure.
P=WVTR*L/Ap (14)

P is the permeability, L is the thickness of the material
sample and ap is the change in pressure of the internal and
external environment of the film.

Permeability may also be expressed using other variables

as noted below.

p=o*s (15)

49

D is the diffusion coefficient and S is the solubility

coefficient.

It was critical to show the correlation between the
calculated WVTR and permeability of the laminate and the
experimental WVTR and permeability values for the laminate.
This helped to verify that separation of the composite film
into PVC and Aclar layers can yield expected and accurate

results for most film characteristics.

Diffusion Coefficient

The diffusion coefficients for water vapor through both
the Deltasone pharmaceutical tablet and the packaging films
need to be determined as a parameter in the finite difference
method computer program (Kim, 1992). For the circular plate
shaped pharmaceutical product, the diffusion coefficient is

described by the following expression

D = 0.049 L2 / 1:1,2 (16)

where L is the average thickness of the tablet (cm) and tvz
(seconds) is half the time required for Mt/M. to reach the
equilibrium steady state condition at any given relative
humidity value.

It is important to discuss the procedure used to
calculate the diffusion coefficient for the tablet, as well as

the packaging materials. The diffusion coefficient takes into

50

account the t1/2 value as seen from Eq. (16) . T1/2' the time
required to reach one half of the steady state, was difficult
to identify exactly. Therefore, several t1,2 values were
analyzed to produce several D values. Based on Eq. (17),
various curves of M/M. were generated using the different
tablet diffusion coefficients. At any given relative humidity
range, the experimental Mt/M_ vs. time was compared to the
calculated Mt/M_ vs. time using a least squares method. This
method involved taking the sum of the differences squared for
the Mt/M. values (calculated and experimental). The diffusion
coefficient which provided for the least sum was used as the
result for a particular humidity level (see Appendix B).
Product diffusion is a required component of the shelf life
model. This process should improve the accuracy for the
determination of the diffusion coefficient.

The mass uptake of a flat specimen surrounded by a
sorbate at constant concentration is given by the following

equation (Crank, 1975).

Mt/M. = 1--8/1r2 [exp (-D 1r2 t/L’) + 1/9 exp (-9 D 11’ t/L’)] (17)

This equation allows a comparison between the calculated Mt/M.
values and the experimental Mt/M. values. Figure 14 presents
a comparison of the calculated and experimental moisture
uptake curves for the Deltasone tablet. It is evident from
the two curves that the agreement is excellent for the

experimental and calculated data.

51

 

1.2

Mt / Minf.

 

 

 

 

0 1 1 1
0 5 10 15 20
TIME (hours)
. Experimental __Calculated

Figure 14. Comparison of experimental and calculated Mt/M. for
20 mg Deltasone tablet at 72.25 - 77.75% R.H. and

25.0 ° c
The values for the diffusion coefficient which were
calculated for the Deltasone tablet had some degree of
variability across the different humidity levels. This

variability may have been caused by the change in

environmental conditions (relative humidity). Based on the

52

calculation for the diffusion coefficient, the t“? value is
the only variable which can fluctuate with the humidity as the
average thickness of the tablet remains constant. Therefore,
the time required to obtain half of the steady state condition
varied with the R.H. in this instance. Diffusion coefficient
results extended through the range of 0.603 E -06 cmz/sec. at
40.75 - 48.80% R.H. to 1.62 E ~06.Cm’/seC. at 66 - 73.40% R.H.
The standard deviation was found to be 3.30 E -07 cmz/sec.
Table 6 summarizes the values for the diffusion coefficient of
water at various relative humidity levels. Figure 15 shows
the graphical presentation of the tablet diffusion coefficient
and the relative humidity. It is evident that there is no
trend in the data.

For the tablet, the average diffusion coefficient value
was used in the shelf life computer program.

Equation (16) was used to compute D for the film samples
and the tablet. Figure 16 and Figure 17 demonstrate the same
concept for the packaging materials as Figure 14 showed for
the tablet comparison (see Appendices C and D). Again, the
experimental and calculated moisture uptake profiles are very
similar. Many of the points coincide graphically. These
figures are shown below; Table 7 lists the diffusion
coefficients of water for the PVC film sample and the Aclar
film sample at two relative humidity ranges.

When.a laminate is composed of two layers of thickness in
series, L1 and L2, and two diffusion coefficients, D1 and D2,

the effective diffusion coefficient, D, is given by the

53

following equation (Crank, 1975).

(111/01) + (Lg/Dz) = (L1+L2) /0 (18)

This equation can also be written as shown in Eq. (19).

D = (L1 4' 17) / ((L1/’I%) + (Lg/’15)) (3»

The effective diffusion coefficient was used in the shelf life

computer program and was calculated to be 2.0 E —09 cmz/sec.

Table 6. Diffusion coefficient of tablet at R.H.

 

 

 

 

  
  
  
  
   
  

 

 

 

 

   
 

 

 
 

 

   
 

 
 

conditions.
Relative Humidity (%) Diffusion Coefficient l
(cm3/sec.)
0 - 11.50 1.22 E -06
36 - 40 0.85 E -06 I
40.75 - 48.80 0.603 E -06 l
60.70 - 66 1.26 E -06 I
66 - 73.40 1.62 E -06
72.25 - 77.75 1.27 E -06 I
77.90 - 82.45 1.60 E ~06
‘fl82.05 - 87.30 (0.996 E
s, - “9% __ __ _1°__9____
Standard Deviation 3.30 E -07

 

 

54

 

 

 

1.5 L

 

 

 

Millionths
(.3
I

 

 

Diffusion Coefficient (sq. cm/sec.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.75 38 44.78 63.35 69.7 75 80.18 84.68
Relative Humidity (%)

Figure 15. Diffusion coefficient of Deltasone tablet over
R.H. ranges at 25.0 ° C

55

 

1.2

 

Mt/ Minf.

 

 

 

oi . . 1 .

0 5 10 15 20 25
TIME (hours)

I Experimental _Calculated

 

Figure 16. Comparison of experimental and calculated Mt/M. for
we film at 58.20 - 77% R.H. and 25.0 ° c

56

 

1.2

Mt/ Minf.

 

 

 

 

o 1 1 1 1
0 1 2 3 4 5
TIME (hours)
. Experimental _Calculated

Figure 17. Comparison of experimental and calculated Mt/M. for
Aclar film at 43.50 - 58% R.H. and 25.0 ° C

57

Table 7. Diffusion coefficient of packaging materials at
R.H. conditions

PVC Film - 7.5 mils ;
Relative humidity (%) Diffusion Coefficient I

0 - 26.90

 

 

 

Average 7 5.04 E -09

 

 

   
    

 

 

  

 

Aclar Film - 1.6 mils I
27.35 - 43.50 3.36 E -10 I
_-

Borption Isotherm Model for the Tablet

The GAB (Guggenheim-Anderson-de Boer) sorption isotherm
model was used to fit the experimental isotherm data of the
tablet obtained in the present study. The equation is given

in Eq. (20) (Bizot, 1991).
W/Wm=CkAu/ (l-kA') (1-kAH-l-CkAH) (20)

A“ is water activity, W is water content on a dry basis” “5 is
water content corresponding to saturation of all primary
adsorption sites by one water molecule (previously called the

monolayer in BET theory), C is the Guggenheim constant.= c'exp

58

(H1 - H.)/R T, Hq is total heat of sorption of the multilayers
(which is different from the heat of condensation of pure
water), H. is total heat of sorption of the first layer on
primary sites, k is a factor correcting properties of the
multilayer molecules with respect to the bulk liquid [k =
k'exp (I111 - Hq)/R T], and H1 is the heat of condensation of
pure water vapor.

This GAB model has been reported as a very good model for
fitting sorption isotherms over a range of water activities.
It also provides a means to evaluate the amount of water
tightly bound by the primary adsorption sites (fig).

Equation (20) can also be written in the following manner

A/W = 01A“2 + 3A,, + y (21)
where

a = k / Wm [l/C - 1] (22)

fi=1/W,.[1-2/C] (m)

y = 1 / Wu C k (24)

and a regression (quadratic) can be conducted on

experimental numbers. From Eq. (23)

wm=1/8[1-2/c1 (25)

and combining Eq. (22) and Eq. (23) gives the following

equation.

59

a = k B / [1 7 2/C] [1/c ' 1] (26)
Eq. (24) and Eq. (25) provided

7 = 3 / [1 - 2/C] c k (27)
which simplified to Eq. (28).

k = 8 / y [c - 2] (28)
From Eq. (26) and Eq. (28), Eq. (29) is defined.

a = 3’ (1 ' C) / Y (C ’ 2) (C ’ 2) (29)

The constants (GAB) were calculated to be

a = -1.79
8 = 1.922
y = 0.064

and can be used in the above computations. The constants (a,
B, and 7) were figured using matrices which consisted of
combinations of X, X1, X3, X5,‘Y, XY, X’Y, and N. X was the
summation of experimental A", ‘Y was the summation of
experimental A/EMC, and N was the number of experimental
points. A plot of the experimental moisture sorption isotherm
against the GAB model produced a very good fit of the two
curves. This plot is found in Figure 18.

The quality of the fit can.be analyzed from the result of

60

 

w
I

EMC (3 water/ 100 g dry product)
1—1 N

 

 

 

 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Aw

. Experimental _ Calculated (GAB)

Figure 18. Plot of experimental moisture sorption isotherm
and calculated GAB isotherm of 20 mg Deltasone
tablet at 25.0 ° c

the relative percent root mean square (% RMS)

% RMS = I [2 (WII - wi*/wi)2 / N] x 100 (30)

where N is the number of experimental points, W1 is the

experimental water content, and w; is the calculated water

61
content (Bizot, 1991). The RMS was calculated to be 11.11%,
which verifies the strength of the fit for the experimental

and calculated data.

Calculations of Package / Product Dimensions

There are four additional parameters of the packaging
material and the pharmaceutical product which must be
determined. They include the surface area of the tablet, the
volume of the tablet, the surface area of the blister package,
and the inner volume of the blister package. The surface area

of the Deltasone tablet (A1) is found by

.A ==2 x R; (30
where R' is the radius of the tablet. Likewise, the volume of
the pharmaceutical tablet (V}) is deduced from the following
equation.

V, = (1r 12,2) (1",) (:2)

I} is the tablet thickness. The surface area of the blister

package (A?) is as follows

15 ==n'rgz + 2 1'19 TP (1»

where R, is the radius of the blister, and TP is the height of

62
the blister package. Lastly, the inner volume of the blister

package (v;) has the following calculation.
VP==”I%2 T9 0“)

For this project, the permeable blister package area did not
include the aluminum foil backing, as it would be impermeable

to moisture.
Other Parameters for Computer Program

The absolute humidity (A.H.) is a necessary component for
the finite difference computer model since the driving of
water is based on the absolute concentration of water through
the system. The absolute humidity can be located from a
psychrometric chart at saturation temperature.

c = 11.11. / 1.5829 '1' (35)

Slt

C is the concentration of water in the air at saturation

sat
(gram / ml) and T is in ° R.

Henry's Law Constant needed to be determined as well
using different units as those described by Eq. (9) with the

following equation.

CE (39

63
ML is Henry's constant (9 HZO/cm’ polymer) / (g HZO/cm’ air)
and is dependent on packaging material and temperature. CLE
is the concentration of absorbed water vapor on the outer
surface of the package (constant). (M is the concentration of
water vapor outside the package (constant).
Table 8 lists all of the experimental values which were

used in this finite difference simulation computer model.
Moisture Uptake of Blister Package with Product

Over a several week period, the water uptake of the total
10 cavity blister package with tablets was monitored. Five
samples were contained in an 80% R.H. condition, and five were
also stored in a 90% R.H. condition at 22.2 ° C. Each
container also held one empty 10 cavity blister package in
order to factor in the moisture sorption of the packaging
material alone. The percent moisture content of an individual

tablet was calculated with the following equation
M.C. = [((a-b) /10) / (W)] * 100 (37)

where W is the dry weight of the tablet, "a" is the weight of
the filled blister package at any timepoint, and "b" is the
weight of the empty blister package at the same timepoint.
The results of this portion of the study are presented in
Table 9 (80% R.H. level) and Table 10 (90% R.H. level),

respectively. Graphical presentations are shown in Figures

64

 

 

 

Table 8. Values for use in simulation model
I Variable Value Reference l
E l
Temperature (T) 25.0 ° Celsius' Given
Storage Relative 80%, 90% Given

Humidity (R.H.)

 

Absolute Humidity 0.0163, 0.0183 Equation (35)
(A.H.) g HEO/g Air 1

 

 

 

 

 

Package Diffusion 0.02 E -07 Equation (19)
Coefficient (DL) cmz/sec.
Henry's Law 125.12 Equation (36)
Constant (H1)
Package Thickness 0.023, 0.0114 cm Measured
(L)
Blister Surface 3.78 Cm2 Equation (33)
Area (A,)
Blister Volume 0.80 cm’ Equation (34)
(V5)
Number of Package 5 Selected
Layers (L)

I
Tablet Diffusion 0.1179 E -05 Equation (16)

 

 

 

 

 

 

 

 

 

 

Coefficient (DR) cmz /sec.
Initial Moisture 0.0001 0 H4) Estimated
Content (INC) 100 g dry product
Critical Moisture ____2‘Q_g_figl____ Selected
Content (CMC) 100 g dry product
Dry Tablet Weight 0.4077 9 Measured
(W)
Tablet Radius (Ra 0.50 cm Measured
Tablet Thickness 0.392 cm Measured
( T1)
G.A.B. Constant a -1.79 Equation (22)
G.A.B. Constant 8 1.922 Equation (23)
G.A.B. Constant 7 0.064 Equation (24)
Number of Shells 5 Selected

 

 

(U)

 

 

 

* HL has units of (g H20/cm’ PKG) / (g HZO/cm’ Air)

65
19 and 20.

Tables 9 and 10 give the moisture gain for each of the
five sample blister packages and.the empty control sample over
time for each environmental condition. The average moisture
gain and standard deviation of these packages are also
provided. The average moisture content per tablet calculated
using Eq. (37) is tabulated and plotted. It is apparent from
the standard deviation that there is variability among the
samples for moisture uptake. All blister packs did show a
steady increase in mass over the duration.

Figure 21 and Figure 22 compare the experimental packaged
tablet moisture content curves with the curves generated by
the shelf life simulation model using a finite difference
method at 80 and 90% R.H., respectively. For these figures,
the blister laminate thickness used in the computer program
was 9.1 mils, which was the thickness of the flat sheet
material. In addition, the program was tested with a package
thickness of 4.5 mils, which was the measured value for the
formed blister. The comparative results are available in
Figures 23 and.24. With the decrease in thickness, there were
significant variations between the experimental and calculated

data.

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50

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69

 

L5

..a

Moisture Content (%)
;>
M

 

Figure 20.

 

l l l I

10 20 30 40
IHNHEOMMTS)

Moisture content of tablets in blisters at
22.2 ° c and 90% 12.11.

 

50

70

 

I“
tn
l

Moisture Content (%)

 

 

 

 

05
0 1 1 1 J
0 10 20 30 40 50
Tflhflifiwwhfl
s Experimental _ Computer Program

Figure 21. Moisture content of tablets in blisters at
22.2 ° C and 80% R.H. for experimental and
computer program data

71

 

I"
M

Moisture Content (%)
...L

9’
UI

 

 

 

0 1 1 1 1
0 10 20 30 40 50
quHEOMflfls)

I Experimental __ Computer Program

 

Figure 22. Moisture content of tablets in blisters at
22.2 ° C and 90% R.H. for experimental and
computer program data

72

 

I"
tn

Moisture Content (%)

.°
VI

 

 

 

 

0 1 1 L 1
0 10 20 30 40 50
TIME (weeks)
I Experimental _ Computer Program

Figure 23. Moisture content of tablets in blisters at
22.2 ° C and 80% R.H. for experimental and
computer program data (4.5 mils thickness)

73

 

p
v:

N

Moisture Content (%)
...:
'JI

 

 

 

 

1
05
0 1 1 1 1
0 10 20 30 40 50
Tlhfl30mufls)
I Experimental _ Computer Program

Figure 24. Moisture content of tablets in blisters at
22.2 ° C and 90% R.H. for experimental and
computer program data (4.5 mils thickness)

ERROR ANALYSIS

Throughout the process of performing this research-based
project, there were many opportunities to introduce both
operator and machine error. Errors are possible even in the
most controlled situations. For example, the relative
humidity produced within the hangdown tube of the
electrobalance, where the sample was located, was dependent on
both the humidity sensors (hygrosensors) and the hygrometer
unit used. The hygrometer and hygrosensors had been
calibrated, but there may have been some error of
approximately +/- 1%.

Secondly, there were a few instances when the light in
the chamber where the hangdown tube was located was left on
causing a potential temperature fluctuation of +/- 1-2 ° C.
This increased.heat.in the chamber could.have resulted in some
changes in the tablet weight gain during the creation of the
sorption isotherm. The extra heat in the chamber decreased
the relative humidity for a short period of time.

Another error in relative humidity could have occurred
inside of the five gallon buckets containing the salt
solutions. Therefore, there could be a greater or lesser
weight gain over time due to this inaccuracy of about 4-5%.

Also, temperature variations could have existed in the storage

74

75
location of +/- 2-3 ° C.

It is uncertain whether or not the Deltasone
pharmaceutical tablet was thoroughly dried to 0% moisture
content at the onset of this experiment. However, initial
desorption studies showed that the product had reached
equilibrium during the nitrogen flush.

Lastly, calibration of the electrobalance could have been
inaccurately performed with the calibration weights. This
calibration occurs before the sample product is put into the
hangdown tube. Calibration weights are placed in the sample

dish for a specified period of time for the process to take

place.

CONCLUSIONS

Comparison Between Calculated Data and Validation Experiment

A finite difference computer program for shelf life
simulation calculated the shelf life of the 20 mg Deltasone
tablet packaged in such a way as described in this research
project, using the values in Table 8. This simulation program
estimated the shelf life to be 10,010 hours (417 days) under
the conditions of 25.0 ° C and 90% R.H. for a package
thickness of 9.1 mils. This translates into a shelf life
value of nearly 60 weeks. The finite difference program
showed that at 25.0 ° C and 80% R.H., the product would not
reach the critical moisture content of 2.0 g H20/100 g dry
product from an initial moisture content of 0.0001 g H20/100
g dry product. This occurs since the equilibrium moisture
content at 80% R.H. is less than 2.0 g H20/100 g dry product
from the sorption isotherm in Figure 18. For this case, the
maximum value for the moisture content came out to be 1.5477
g H20/100 g dry product at 9,200 hours (383 days). Through
several trials using the model, it was evident that the value
-of the dimensionless constants, Q and G, played a key role in
the stability of the computational process (see Appendix A).

When compared to the experimental blister packages which

76

77
were stored at 80% R.H., the program agreed quite well with
the data, when the packaging film thickness used was 9.1 mils.
For example, when the EMC reached 0.6412 g H20/100 g dry
product, the shelf life was calculated to be 6.6 weeks from
the finite difference program. The experimental data of the
packaged product found the shelf life to be 6.6 weeks at a
moisture content of 0.64 g H20/100 g dry product. This can be
seen in Figure 21. In addition, the 90% R.H. condition had
satisfactory agreement with the shelf life simulation model,
when using a value for the package thickness of 9.1 mils.
This program computed a shelf life of 13.9 weeks at an EMC of
1.1321 g H20/100 g dry product. Experimental data at 90% R.H.
revealed a shelf life of 13.9 weeks at 1.1023 g 1120/100 g dry
product- Also, this is expressed in Figure 22. The
input/output results of the computer program with all of the
data can be found in Appendix A.

It was found.that the formed.blister structure of PVC and
Aclar had a package thickness close to 4.5 mils, as seen in
Figure 1. An assumption was made that the two laminated
materials are proportionally formed during the blister
manufacturing process in relation to the original unformed
film sheet (9.1 mils). At this value of 4.5 mils, the finite
difference program computed changes in moisture content over
time which far exceeded the experimental data. This deviation
became more pronounced with an increase in time. There could
be several reasons for these results. The relative humidity

in the buckets could have been decreasing over time causing

78
less moisture to be gained in later weeks. 0n the other hand,
this computer program for the prediction of shelf life may be
overestimating the moisture content _. of this product. In

addition, this program was designed for single layer packaging

materials.

RECOMMENDATIONS FOR FUTURE WORK

A recommendation for future work in this area of
mathematical modeling and shelf life prediction for packaged
food and pharmaceutical products would include some research
into a program which could evaluate multi-layer packaging
films. In addition, another interesting project for further
development would be an expansion of the shelf life program
using the finite difference method to analyze other packaging
containers. Currently, the focus of this model is blister
packaging, but could possibly also involve bottles with
closures and bulk materials, such as boxes or lined fiber
drums. This type of predictive model could have value for the
pharmaceutical industry as various package configurations need
to be considered. Ideally, a program with the capabilities to
advise on product quantity per container based on product
size, available headspace and product characteristics would be
a useful tool.

Another addition to a shelf life model might be the
incorporation of oxygen transmission rates through a package
component, which can also cause product degradation. A
program which integrates all environmental conditions

surrounding a product/package system would have great benefit.

79

APPENDICES

APPENDIX A

APPENDIX A

Program Stability Given Q Value, Input/Output Data Sheets

This finite difference computer program uses a number of
dimensionless constants as part of the computation of the
shelf life. The dimensionless constant, Q, was of particular
interest while running various trials with this model.
According to Kim (1992), Q is used to solve the diffusion
equation of the packaging material to moisture. In any
application of this program, Q must be less than 0.5 in order
to avoid a negative concentration value using (1-2Q). Q is
also dependent on the geometry of the product under
investigation.

With the data generated for this project, Q needed to be
determined by trial and error as to the optimum value for
use. It was found that an appropriate Q constant for the data
was between 0.001 and 0.00142. It was apparent that as the
critical moisture content increased, Q needed toidecrease. In
addition, Q affects G, another dimensionless constant, which
must be less than 0.3 for purposes of numerical stability
(Kim, 1992).

All input and output data used from the computer program

are found in the following section.

80

81.

computer Program Input/Output Data

All data are checked successfully !!!
Re-check all data entered
Temperature of storage environment incelsius -25.00
Relative humidity of storage environment in % -80.00
Absolute humidity of storage environment ingfl20/gAir -.0163
Diffusion coefficient of packaging materialin 10“-7 cm‘2/sec -0.020
Henry constant of packaging material in(gH20/cm“3 PKG)/(9H20/cm‘3 Air) - 125.12
000
Thickness of packaging material in cm - 0.01140
Surface area of packaging material in cm‘2 - 3.78000
Volume of packaging material in cm‘3 - 0.80000
Diffusion coefficient of product in lO‘-5cm‘2/sec - 0.11790
Initial moisture content in gHZO/lOOg dryproduct -0.00
Critical moisture content in gMZO/IOOg dryproduct -2.00
Dry weight of product in g - 0.40770
Chemical reaction rate - 0.0
Chemical reaction order - 0.0
Aw/M--.l79OE+Ol Au‘z + 0.19222+01 Aw+ 0.64OOE-Ol
Radius of product in cm - 0.50000
Thickness of product (Only Plate shape) incm - 0.39200

Hit any key to continue .....

 

Concentration of outside environment (CE) - 0.01534 g/L
Concentration of outside surface of PKGtCLE) - 1.91945 g/L
Concentration of inside surface of PKGtCLH) - 0.00002 g/L
Concentration of headspace (CH) - 0.00000 g/L

Concentration of outside surface of product(CRM) - 0.00132 g/L

Q-0.l4ZOE-02

s-o.1szos-oz

A1-0.18228-04

Bl-O.l9OZE-03

S-0.l9BlE+Ol

x-o.9ooor+03
- 7

 

Enter the number of time to caleulateconcentrations at once.

(NOTICE 3!! It must be over 200 and be times of 200)

 

82

(Plate Shape)
Each step is

152000. steps (83.6379hrs)

 

 

<0 of the divided shell of product is 5
01.8 01.1 01.2 01.3 01.4 01.11 011 Meg
CRH CR1 CR2 CR3 CR4 CRC GAIN '1‘ IKE (h :3)

1.9194 1.6483 1.3771 1.1060 0.8349 0.5639 0.2930 0.0222
0.0002 0.1134

1.5014 1.4755 1.4560 1.4430 1.4366 1.4366 0.1100 83.6379
1.9194 1.6535 1.3877 1.1219 0.8562 0.5906 0.3252 0.0600
0.0005 0.2253

2.9841 2.9587 2.9397 2.9270 2.9206 2.9206 0.2220 167.2758
1.9194 1.6635 1.4076 1.1518 0.8962 0.6409 0.3858 0.1312
0.0010 0.3340

4.4225 4.3981 4.3799 4.3677 4.3616 4.3616 0.3307 250.9138
1.9194 1.6827 1.4460 1.2096 0.9736 0.7380 0.5030 0.2686
0.0021 0.4361

5.7747 5.7523 5.7355 5.7243 5.7186 5.7186 0.4331 334.5517
1.9194 1.7114 1.5036 1.2960 1.0888 0.8822 0.6763 0.4713
0.0038 0.5274

6.9836 6.9640 6.9493 6.9395 6.9346 6.9346 0.5248 418.1896
1.9194 1.7402 1.5612 1.3823 1.2039 1.0259 0.8485 0.6719
0.0054 0.6063

8.0291 8.0122 7.9996 7.9911 7.9869 7.9869 0.6041 501.8275
1.9194 1.7638 1.6083 1.4530 1.2980 1.1434 0.9892 0.8356
0.0067 0.6746

8.9334 8.9187 8.9077 8.9004 8.8967 8.8967 0.6727 585.4654
1.9194 1.7824 1.6455 1.5087 1.3721 1.2359 1.1000 0.9646
0.0077 0.7344

9.7256 9.7127 9.7030 9.6965 9.6933 9.6933 0.7327 669.1033
1.9194 1.7972 1.6750 1.5530 1.4311 1.3095 1.1881 1.0672
0.0085 0.7876
10.4292 10.4177 10.4090 10.4032 10.4003 10.4003 0.7860 752.7413
1.9194 1.8092 1.6990 1.5889 1.4789 1.3692 1.2597 1.1505
0.0092 0.8353
11.0615 11.0510 11.0432 11.0380 11.0354 11.0354 0.8339 836.3792
1.9194 1.8191 1.7188 1.6186 1.5185 1.4186 1.3189 1.2195
0.0097 0.8786
11.6351 11.6256 11.6184 11.6137 11.6113 11.6113 0.8774 920.0171
1.9194 1.8275 1.7355 1.6437 1.5519 1.4603 1.3688 1.2776
0.0102 0.9182
12.1596 12.1509 12.1443 12.1399 12.1378 12.1378 0.9171 1003.6550
1.9194 1.8346 1.7498 1.6651 1.5804 1.4959 1.4115 1.3273
0.0106 0.9547
12.6424 12.6343 12.6283 12.6242 12.6222 12.6222 0.9536 1087.2930
1.9194 1.8408 1.7622 1.6836 1.6051 1.5267 1.4485 1.3704
0.0110 0.9884
13.0892 13.0817 13.0761 13.0724 13.0705 13.0705 0.9874 1170.9308
1.9194 1.8462 l.7730 1.6998 1.6267 1.5537 1.4808 1.4081
0.0113 1.0198
13.5046 13.4976 13.4924 13.4889 13.4872 13.4872 1.0189 1254.5687
1.9194 1.8510 1.7825 1.7141 1.6458 1.5775 1.5094 1.4414
0.0115 1.0491
13.8924 13.8859 13.8810 13.8778 13.8762 13.8762 1.0482 1338.206?
1.9l94 1.8552 1.7911 1.7269 1.6628 1.5988 1.5349 1.4710
0.0ll8 1.0765

14.2557 14.2496 14.2450 14.2420 14.2405 14.2405 1.0757 1421.8446
1.9194 1.8591 1.7987 1.7384 1.6781 1.6178 1.5577 1.4977
0.0120 1.1023

14.5971
1.9194
0.0122

14.9187
1.9194
0.0123

15.2223
1.9194
0.0125

15.5097
1.9194
0.0126

15.7822
1.9194
0.0128

16.0409
1.9194
0.0129

16.2870
1.9194
0.0130

16.5215
1.9194
0.0131

16.7451
1.9194
0.0132

16.9587
1.9194
0.0133

17.1628
1.9194
0.0134

17.3582
1.9194
0.0135

17.5453
1.9194
0.0136

17.7246
1.9194
0.0136

17.8967
1.9194
0.0137

18.0620
1.9194
0.0138

18.2208
1.9194
0.0138

18.3734
1.9194
0.0139

18.5203
1.9194
0.0139

18.6617
1.9194
0.0140

.5913
.8625
.1266
.9132
.8656
.1495
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.8685
.1712
.5048
.8711
.1918
.7775
.8735
.2113
.0365
.8757
.2299
.2829
.8778
.2476
.5175
.8797
.2645
.7413
.8815
.2806
.9550
.8831
.2961
.1593
.8847
.3108
.3548
.8861
.3249
.5421
.8875
.3385
.7216
.8888
.3515
.8938
.8900
.3640
.0592
.8911
.3759
.2181
.8922
.3875
.3708
.8933
.3986
.5178
.8942
.4092
.6593
.8952
.4195

.5870
.8056

.9092
.8118

.2134
.8175

.5012
.8228

.7741
.8276

.0333
.8320

.2798
.8361

.5146
.8399

.7385
.8435

.9523
.8468

.1567
.8499

.3524
.8528

.5397
.8556

.7193
.8581

.8916
.8606

.0571
.8629

.2161
.8650

.3689

.5159
.8690

.6575
.8709

14.5841
1.7487

14.9065
1.7581

15.2108
1.7666

15.4988
1.7745

15.7718
1.7817

16.0311
1.7883

16.2777
1.7945

16.5126
1.8002

16.7366
1.8055

16.9505
1.8105

17.1550
1.8152

17.3507
1.8195

17.5381
1.8236

17.7178
1.8275

17.8902
1.8311

18.0557
1.8346

18.2147
1.8378

18.3676
1.8409

18.5147
1.8438

18.6563
1.8466

£33

14.5827
1.6918

14.9051
1.7043

15.2095
1.7157

15.4976
1.7262

15.7706
1.7358

16.0300
1.7447

16.2766
1.7529

16.5116
1.7605

16.7357
1.7676

16.9496
1.7742

17.1542
1.7804

17.3499
1.7863

17.5373
1.7917

17.7170
1.7969

17.8894
1.8017

18.0550
1.8063

18.2140
1.8106

18.3669
1.8147

18.5141
1.8186

18.6557
1.8223

14.5827
1.6351

14.9051
1.6507

15.2095
1.6649

15.4976
1.6780

15.7706
1.6900

16.0300
1.7010

16.2766
1.7113

16.5116
1.7208

16.7357
1.7297

16.9496
1.7380

17.1542
1.7457

17.3499
1.7530

17.5373
1.7598

17.7170
1.7663

17.8894
1.7723

18.0550
1.7780

18.2140
1.7835

18.3669
1.7886

18.5141
1.7934

18.6557
1.7981

1.1015
1.5783

1.1259
1.5971

1.1488
1.6141

1.1706
1.6298

1.1912
1.6442

1.2108
1.6575

1.2294
1.6698

1.2471
1.6812

1.2640
1.6918

1.2802
1.7018

1.2956
1.7111

1.3104
1.7198

1.3245
1.7280

1.3381
1.7357

1.3511
1.7430

1.3636
1.7498

1.3756
1.7563

1.3871
1.7625

1.3982
1.7683

1.4089
1.7738

1505.4825
1.5217

1589.1204
1.5435

1672.7583
1.5634

1756.3962
1.5817

1840.0342
1.5985

1923.6721
1.6139

2007.3101
1.6283

2090.9480
1.6416

2174.5859
1.6540

2258.2236
1.6656

2341.8616
1.6764

2425.4995
1.6866

2509.1375
1.6962

2592.7754
1.7052

2676.4133
1.7136

2760.0510
1.7216

2843.6892
1.7292

2927.3269
1.7364

3010.9651
1.7432

3094.6028
1.7496

18.7979
1.9194
0.0140

18.9291
1.9194
0.0141

19.0557
1.9194
0.0141

19.1777
1.9194
0.0142

19.2955
1.9194
0.0142

19.4092
1.9194
0.0142

19.5190
1.9194
0.0143

19.6252
1.9194
0.0143

19.7277
1.9194
0.0144

19.8269
1.9194
0.0144

19.9228
1.9194
0.0144

20.0156
1.9194
0.0144

20.1054
1.9194
0.0145

20.1923
1.9194
0.0145

20.2764
1.9194
0.0145

20.3579
1.9194
0.0146

20.4369
1.9194
0.0146

20.5134
1.9194
0.0146

20.5876
1.9194
0.0146

20.6595
1.9194
0.0146

18.7956
1.8960
1.4294

18.9269
1.8969
1.4390

19.0535
1.8977
1.4482

19.1756
1.8984
1.4571

19.2935
1.8991
1.4657

19.4073
1.8998
1.4740

19.5172
1.9005
1.4820

19.6233
1.9011
1.4897

19.7260
1.9017
1.4972

19.8252
1.9023
1.5045

19.9211
1.9029
1.5115

20.0140
1.9034
1.5183

20.1038
1.9039
1.5248

20.1908
1.9044
1.5312

20.2750
1.9049
1.5373

20.3566
1.9053
1.5433

20.4356
1.9058
1.5491

20.5121
1.9062
1.5547

20.5863
1.9066
1.5601

20.6583
1.9070
1.5654

18.7938
1.8726

18.9252
1.8743

19.0519
1.8759

19.1741
1.8774

19.2920
1.8788

19.4058
1.8802

19.5158
1.8816

19.6220
1.8828

19.7247
1.8840

19.8239
1.8852

19.9199
1.8863

20.0128
1.8874

20.1027
1.8884

20.1897
1.8894

20.2739
1.8903

.3555
1.8912

.4346
1.8921

20.5112
1.8929

20.5854
1.8937

20.6574
1.8945

84

18.7927
1.8492

18.9241
1.8517

19.0508
1.8541

19.1730
1.8564

19.2910
1.8586

19.4049
1.8606

19.5148
1.8626

19.6211
1.8645

19.7238
1.8663

19.8231
1.8681

19.9191
1.8697

20.0120
1.8713

20.1019
1.8729

20.1889
1.8743

20.2732
1.8758

20.3548
1.8771

20.4339
1.8784

20.5105
1.8797

20.5848
1.8809

20.6567
1.8821

18.7921
1.8258

18.9235
1.8292

19.0503
1.8323

19.1725
1.8354

19.2905
1.8383

19.4044
1.8410

19.5144
1.8437

19.6206
1.8462

19.7233
1.8486

19.8227
1.8509

19.9187
1.8532

20.0116
1.8553

20.1015
1.8573

20.1886
1.8593

20.2728
1.8612

20.3545
1.8630

20.4335
1.8648

20.5102
1.8664

20.5844
1.8681

20.6564
1.8696

.7921
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.8066

.0503
.8106

.1725
.8144

.2905
.8180

.4044
.8215

.5144
.8248

.6206
.8279

.7233
.8309

.8227
.8338

.9187
.8366

.0116
.8393

.1015
.8418

.1886
.8443

.2728
.8466

.3545
.8489

.4335
.8511

.5102
.8532

.5844
.8552

.6564
.8572

1.4192
1.7791

1.4291
1.7841

1.4387
1.7889

1.4479
1.7934

1.4568
1.7978

1.4654
1.8019

1.4737
1.8059

1.4818
1.8096

1.4895
1.8133

1.4970
1.8167

1.5043
1.8201

1.5113
1.8233

1.5181
1.8263

1.5246
1.8293

1.5310
1.8321

1.5372
1.8348

1.5431
1.8374

1.5489
1.8400

1.5545
1.8424

1.5599
1.8447

3178.

3261.

3345.

3429.

3512.

3596.

3680.

3763.

3847.

3930.

‘01‘ O

4098.

4181.

4265.

4349.

4432.

4516.

4600.

4683.

4767.

2407

.7558

8787

.7616

5166

.7672

1545

.7725

7925

.7775

4302

.7824

0684

.7870

7061

.7914

3442

.7956

9819

.7997

6201

.8036

2578

.8073

8960

.8109

5337

.8143

1719

.8176

8096

.8208

4473

.8238

0854

.8267

7231

.8296

3613

.8323

20.7292
1.9194
0.0147

20.7968
1.9194
0.0147

20.8624
1.9194
0.0147

20.9260
1.9194
0.0147

20.9878
1.9194
0.0147

21.0477
1.9194
0.0148

21.1059
1.9194
0.0148

21.1623
1.9194
0.0148

21.2172
1.9194
0.0148

21.2704
1.9194
0.0148

21.3221
1.9194
0.0148

21.3724
1.9194
0.0149

21.4212
1.9194
0.0149

21.4686
1.9194
0.0149

21.5147
1.9194
0.0149

21.5595
1.9194
0.0149

21.6031
1.9194
0.0149

21.6454
1.9194
0.0149

21.6865
1.9194
0.0149

21.7266
1.9194
0.0150

20.7280
1.9074
1.5705

20.7957
1.9077
1.5754

20.8613
1.9081
1.5802

20.9249
1.9084
1.5849

20.9867
1.9087
1.5894

21.0467
1.9090
1.5938

21.1049
1.9093
1.5981

21.1614
1.9096
1.6022

21.2162
1.9099
1.6062

21.2695
1.9102
1.6101

21.3213
1.9105
1.6139

21.3715
1.9107
1.6176

21.4204
1.9110
1.6212

21.4678
1.9112
1.6247

21.5139
1.9114
1.6281

21.5588
1.9117
1.6314

21.6023
1.9119
1.6346

21.6447
1.9121
1.6377

21.6858
1.9123
1.6407

21.7259
1.9125
1.6436

20.7271
1.8953

20.7948
1.8960

20.8604
1.8967

20.9241
1.8974

20.9859
1.8980

21.0459
1.8986

21.1041
1.8992

21.1607
1.8998

21.2155
1.9004

21.2688
1.9009

21.3206
1.9015

21.3709
1.9020

21.4197
1.9025

21.4672
1.9030

21.5133
1.9034

21.5582
1.9039

21.6018
1.9043

21.6441
1.9047

21.6853
1.9051

21.7254
1.9055

20.7265
1.8832

20.7942
1.8843

20.8599
1.8853

20.9236
1.8863

20.9854
1.8873

21.0454
1.8882

21.1036
1.8892

21.1602
1.8900

21.2151
1.8909

21.2684
1.8917

21.3202
1.8925

21.3705
1.8933

21.4193
1.8940

21.4668
1.8947

21.5130
1.8954

21.5578
1.8961

21.6014
1.8967

21.6438
1.8974

21.6850
1.8980

21.7250
1.8986

.7262
.8711

.7939
.8726

.8596
.8739

.9233
.8753

.9851
.8766

.0451
.8778

.1034
.8791

.1599
.8802

.2148
.8814

.2682
.8824

.3199
.8835

.3702
.8845

.4191
.8855

.4666
.8865

.5128
.8874

.5576
.8883

.6012
.8892

.6436
.8900

.6848
.8908

.7248
.8916

20.7262
1.8590

20.7939
1.8608

20.8596
1.8626

20.9233
1.8643

20.9851
1.8659

21.0451
1.8675

21.1034
1.8690

21.1599
1.8704

21.2148
1.8718

21.2682
1.8732

21.3199
1.8745

21.3702
1.8758

21.4191
1.8770

21.4666
1.8782

21.5128
1.8794

21.5576
1.8805

21.6012
1.8816

21.6436
1.8826

21.6848
1.8837

21.7248
1.8846

1.5652
1.8470

1.5703
1.8491

1.5753
1.8512

1.5801
1.8532

1.5848
1.8552

1.5893
1.8571

1.5937
1.8589

1.5980
1.8606

1.6021
1.8623

1.6061
1.8640

1.6100
1.8656

1.6138
1.8671

1.6175
1.8686

1.6211
1.8700

1.6246
1.8714

1.6280
1.8727

1.6313
1.8740

1.6345
1.8753

1.6376
1.8765

1.6406
1.8777

4850.9990
1.8349

4934.6372
1.8374

5018.2749
1.8399

5101.9126
1.8422

5185.5508
1.8445

5269.1890
1.8467

5352.8267
1.8488

5436.4644
1.8509

5520.1021
1.8528

5603.7407
1.8547

5687.3784
1.8566

5771.0161
1.8584

5854.6538
1.8601

5938.2920
1.8618

6021.9302
1.8634

6105.5679
1.8650

6189.2056
1.8665

6272.8438
1.8680

6356.4814
1.8694

6440.1196
1.8708

21.7655
1.9194
0.0150

21.8033
1.9194
0.0150

21.8401
1.9194
0.0150

21.8759
1.9194
0.0150

21.9107
1.9194
0.0150

21.9446
1.9194
0.0150

21.9776
1.9194
0.0150

22.0096
1.9194
0.0150

22.0408
1.9194
0.0150

22.0712
1.9194
0.0150

22.1008
1.9194
0.0151

22.1295
1.9194
0.0151

22.1575
1.9194
0.0151

22.1848
1.9194
0.0151

22.2113
1.9194
0.0151

22.2372
1.9194
0.0151

22.2623
1.9194
0.0151

22.2868
1.9194
0.0151

22.3107
1.9194
0.0151

22.3339
1.9194
0.0151

21.7648
1.9127
1.6465

21.8027
1.9129
1.6493

21.8395
1.9130
1.6520

21.8753
1.9132
1.6546

21.9101
1.9134
1.6572

21.9440
1.9135
1.6596

21.9770
1.9137
1.6621

22.0091
1.9139
1.6644

22.0403
1.9140
1.6667

22.0707
1.9142
1.6689

22.1003
1.9143
1.6711

22.1291
1.9144
1.6732

22.1571
1.9146
1.6753

22.1843
1.9147
1.6773

22.2109
1.9148
1.6792

22.2367
1.9149
1.6811

22.2619
1.9151
1.6830

22.2864
1.9152
1.6848

22.3103
1.9153
1.6866

22.3335
1.9154
1.6883

21.7643
1.9059

21.8022
1.9063

21.8390
1.9066

21.8748
1.9070

21.9097
1.9073

21.9436
1.9076

21.9766
1.9080

22.0087
1.9083

22.0399
1.9086

22.0703
1.9089

22.0999
1.9091

22.1287
1.9094

22.1567
1.9097

22.1840
1.9099

22.2106
1.9102

22.2364
1.9104

22.2616
1.9107

22.2861
1.9109

22.3100
1.9111

22.3332
1.9114

21.7640
1.8991

21.8018
1.8997

21.8387
1.9002

21.8745
1.9008

21.9094
1.9013

21.9433
1.9018

21.9763
1.9022

22.0084
1.9027

22.0396
1.9031

22.0700
1.9036

22.0996
1.9040

22.1284
1.9044

22.1565
1.9048

22.1838
1.9052

22.2103
1.9056

22.2362
1.9059

22.2614
1.9063

22.2859
1.9066

22.3098
1.9070

22.3330
1.9073

86

.7638
.8924

.8017
.8931

.8385
.8938

.8744
.8945

.9092
.8952

.9432
.8959

.9762
.8965

.0083
.8971

.0395
.8977

.0699
.8983

.0995
.8989

.1283
.8994

.1564
.8999

.1836
.9004

.2102
.9010

.2361
.9014

.2613
.9019

.2858
.9024

.3097
.9028

.3329
.9033

21.7638
1.8856

21.8017
1.8865

21.8385
1.8874

21.8744
1.8883

21.9092
1.8891

21.9432
1.8900

21.9762
1.8908

22.0083
1.8915

22.0395
1.8923

22.0699
1.8930

22.0995
1.8937

22.1283
1.8944

22.1564
1.8951

22.1836
1.8957

22.2102
1.8963

22.2361
1.8969

22.2613
1.8975

22.2858
1.8981

22.3097
1.8987

22.3329
1.8992

1.6435
1.8788

1.6464
1.8800

1.6492
1.8810

1.6519
1.8821

1.6545
1.8831

1.6571
1.8841

1.6596
1.8850

1.6620
1.8860

1.6644
1.8869

1.6666
1.8877

1.6689
1.8886

1.6711
1.8894

1.6732
1.8902

1.6752
1.8910

1.6772
1.8917

1.6792
1.8924

1.6811
1.8932

1.6829
1.8938

1.6847
1.8945

1.6865
1.8952

6523.7573
1.8721

6607.3955
1.8734

6691.0332
1.8746

6774.6709
1.8759

6858.3091
1.8770

6941.9473
1.8782

7025.5850
1.8793

7109.2227
1.8804

7192.8604
1.8814

7276.4990
1.8824

7360.1367
1.8834

7443.7744
1.8844

7527.4121
1.8853

7611.0508
1.8862

7694.6885
1.8871

7778.3262
1.8880

7861.9639
1.8888

7945.6021
1.8896

8029.2402
1.8904

8112.8779
1.8911

22.3565
1.9194
0.0151

22.3785
1.9194
0.0151

22.4000
1.9194
0.0151

22.4209
1.9194
0.0151

22.4412
1.9194
0.0151

22.4611
1.9194
0.0151

22.4804
1.9194
0.0152

22.4992
1.9194
0.0152

22.5175
1.9194
0.0152

22.5354
1.9194
0.0152

22.5528
1.9194
0.0152

22.5697
1.9194
0.0152

22.5862

22.3561
1.9155
1.6899

22.3782
1.9156
1.6915

22.3996
1.9157
1.6931

22.4205
1.9158
1.6947

22.4409
1.9159
1.6962

22.4607
1.9160
1.6976

22.4800
1.9161
1.6990

22.4989
1.9162
1.7004

22.5172
1.9163
1.7018

22.5351
1.9163
1.7031

22.5525
1.9164
1.7044

22.5694
1.9165
1.7056

22.5859

22.3558
1.9116

22.3779
1.9118

22.3994
1.9120

22.4203
1.9122

22.4406
1.9123

22.4605
1.9125

22.4798
1.9127

22.4986
1.9129

22.5170
1.9131

22.5348
1.9132

22.5522
1.9134

22.5692
1.9135

22.5857

22.3556
1.9076

22.3777
1.9079

22.3992
1.9082

22.4201
1.9085

22.4405
1.9088

22.4603
1.9091

22.4796
1.9093

22.4985
1.9096

22.5168
1.9099

22.5347
1.9101

22.5521
1.9103

22.5691
1.9106

22.5856

87

22.3555
1.9037

22.3776
1.9041

22.3991
1.9045

22.4200
1.9049

22.4404
1.9053

22.4602
1.9056

22.4795
1.9060

22.4984
1.9063

22.5167
1.9067

22.5346
1.9070

22.5520
1.9073

22.5690
1.9076

22.5855

22.3555
1.8997

22.3776
1.9003

22.3991
1.9008

22.4200
1.9012

22.4404
1.9017

22.4602
1.9022

22.4795
1.9026

22.4984
1.9030

22.5167
1.9035

22.5346
1.9039

22.5520
1.9043

22.5690
1.9047

22.5855

1.6882
1.8958

1.6899
1.8964

1.6915
1.8970

1.6931
1.8976

1.6946
1.8982

1.6961
1.8987

1.6976
1.8993

1.6990
1.8998

1.7004
1.9003

1.7017
1.9008

1.7030
1.9012

1.7043
1.9017

1.7056

8196.5156
1.8919

8280.1543
1.8926

8363.7920
1.8933

8447.4297
1.8940

8531.0674
1.8946

8614.7051
1.8953

8698.3438
1.8959

8781.9814
1.8965

8865.6191
1.8971

8949.2568
1.8977

9032.8945
1.8982

9116.5332
1.8988

9200.1709

8E3

All data are checked successfully 2!!
Re-check all data entered
Temperature of storage environment incelsius -25.00
Relative humidity of storage environment in 4 -90.00
Absolute humidity of storage environment ingflZO/ghir -.0183
Diffusion coefficient of packaging materialin 10“-7 cm‘2/sec -0.020
Henry constant of packaging material in(gHZO/cm‘3 PKG)/(gflZO/cm‘3 Air) - 125.12
000
Thickness of packaging material in cm - 0.01140
Surface area of packaging material in cm‘2 - 3.78000
Volume of packaging material in cm‘3 - 0.80000
Diffusion coefficient of product in 10‘-50m‘2/sec - 0.11790
Initial moisture content in gHZO/lOOg dryproduct -0.00
Critical moisture content in gH2o/100g dryproduct -2.00
Dry weight of product in g - 0.40770
Chemical reaction rate - 0.0
Chemical reaction order - 0.0
Aw/H--.17908+01 Au‘2 + 0.19228+01 Aw+ 0.64008-01
Radius of product in cm - 0.50000
Thickness of product (Only Plate shape) incm - 0.39200

 

Hit any key to continue .....

 

INITIAL CONCENTRATION
Concentration of outside environment (CB) - 0.01938 g/L
Concentration of outside surface of PKG(CLE) - 2.42433 g/L
Concentration of inside surface of PKG(CLB) - 0.00002 g/L
Concentration of headspace (CH) - 0.00000 g/L
Concentration of outside surface of product(CRfl) - 0.00132 g/L

 

oxuznsszoutsss consranw
Q-0.12608-02

e-o.1vooa-02

A1-0.18158-04

31-o.21270-03

s-o.221se+01

x-o.9ooos+03

 

 

 

nit any key to continue ......

 

Enter the number of time to calculateconcentrations at once.

(NOTICE !!! It must be over 200 and be times of 200>

 

85)

(Plate Shape)
Each step is

137000. steps (84.3120hrs)

CONCENTRATON PROFILE IN PRODUCT

 

 

<4 of the divided shell of product is S
01.1: 01.1 01.2 01.3 01.4 01.11 011 Meg
CRH CR1 CR2 CR3 CR4 CRC GAIN TIME(hrs)

2.4243 2.0819 1.7395 1.3971 1.0549 0.7127 0.3707 0.0290
0.0002 0.1273

1.6856 1.6564 1.6346 1.6200 1.6127 1.6127 0.1234 84.3120
2.4243 2.0894 1.7545 1.4198 1.0852 0.7509 0.4169 0.0833
0.0007 0.2540

3.3635 3.3351 3.3137 3.2995 3.2924 3.2924 0.2502 168.6240
2.4243 2.1053 1.7863 1.4676 1-1493 0.8316 0.5145 0.1983
0.0016 0.3760

4.9788 4.9518 4.9316 4.9181 4.9114 4.9114 0.3724 252.9361
2.4243 2.1366 1.8492 1.5622 1.2758 0.9904 0.7060 0.4230
0.0034 0.4882

6.4646 6.4405 6.4224 6.4104 6.4044 6.4044 0.4850 337.2481
2.4243 2.1758 1.9276 1.6797 1.4326 1.1862 0.9410 0.6970
0.0056 0.5861

7.7616 7.7408 7.7252 7.7149 7.7097 7.7097 0.5834 421.5601
2.4243 2.2092 1.9943 1.7797 1.5656 1.3521 1.1396 0.9280
0.0074 0.6706

8.8809 8.8629 8.8493 8.8403 8.8358 8.8358 0.6683 505.8722
2.4243 2.2350 2.0457 1.8567 1.6681 1.4800 1.2926 1.1060
0.0088 0.7446

9.8605 9.8446 9.8327 9.8248 9.8208 9.8208 0.7425 590.1841
2.4243 2.2549 2.0856 1.9165 1.7477 1.5793 1.4114 1.2441
0.0099 0.8105

10.7325 10.7183 10.7076 10.7005 10.6969 10.6969 0.8086 674.4962
2.4243 2.2708 2.1173 1.9640 1.8109 1.6582 1.5059 1.3540
0.0108 0.8699

11.5196 11.5067 11.4970 11.4905 11.4873 11.4873 0.8682 758.8082
2.4243 2.2837 2.1431 2.0027 1.8625 1.7225 1.5829 1.4437
0.0115 0.9242
12.2381 12.2263 12.2174 12.2114 12.2085 12.2085 0.9226 843.1202
2.4243 2.2945 2.1646 2.0349 1.9054 1.7761 1.6471 1.5184
0.0121 0.9741
12.8999 12.8890 12.8808 12.8753 12.8725 12.8725 0.9727 927.4323
2.4243 2.3036 2.1829 2.0623 1.9418 1.8215 1.7015 1.5818
0.0126 1.0205

13.5140 13.5038 13.4961 13.4910 13.4885 13.4885 1.0192 1011.7443
2.4243 2.3114 2.1985 2.0858 1.9731 1.8606 1.7483 1.6363
0.0131 1.0638

14.0871 14.0776 14.0704 14.0657 14.0633 14.0633 1.0625 1096.0563
2.4243 2.3182 2.2122 2.1062 2.0004 1.8947 1.7891 1.6838
0.0135 1.1044

14.6248 14.6159 14.6091 14.6046 14.6024 14.6024 1.1032 1180.3683
2.4243 2.3243 2.2242 2.1243 2.0244 1.9246 1.8251 1.7257
0.0138 1.1427

15.1314 15.1229 15.1165 15.1123 15.1102 15.1102 1.1415 1264.6804
2.4243 2.3296 2.2349 2.1403 2.0457 1.9513 1.8570 1.7629
0.0141 1.1788

15.6103 15.6023 15.5963 15.5923 15.5903 15.5903 1.1778 1348.9923
2.4243 2.3344 2.2445 2.1546 2.0649 1.9752 1.8857 1.7963
0.0144 1.2131

16.0646 16.0570 16.0513 16.0475 16.0456 16.0456 1.2121 1433.3044
2.4243 2.3387 2.2531 2.1676 2.0821 1.9968 1.9115 1.8264

0.0146
16.4967
2.4243
0.0148
16.9087
2.4243
0.0150
17.3024
2.4243
0.0152
17.6793
2.4243
0.0154
18.0407
2.4243
0.0155
18.3880
2.4243
0.0157
18.7220
2.4243
0.0158
19.0437
2.4243
0.0159
19.3540
2.4243
0.0160
19.6536
2.4243
0.0162
19.9431
2.4243
0.0163
20.2232
2.4243
0.0164
20.4943
2.4243
0.0165
20.7571
2.4243
0.0165
21.0119
2.4243
0.0166
21.2592
2.4243
0.0167
21.4993
2.4243
0.0168
21.7327
2.4243
0.0168
21.9596
2.4243
0.0169
22.1803
2.4243

1.2458
16.4894
2.3426
1.2769
16.9018
2.3462
1.3066
17.2957
2.3495
1.3351
17.6729
2.3525
1.3624
18.0346
2.3553
1.3886
18.3821
2.3579
1.4138
18.7164
2.3603
1.4381
19.0383
2.3626
1.4615
19.3488
2.3647
1.4841
19.6485
2.3667
1.5060
19.9382
2.3686
1.5272
20.2184
2.3703
1.5476
20.4897
2.3720
1.5675
20.7527
2.3735
1.5867
21.0076
2.3750
1.6054
21.2550
2.3765
1.6235
21.4953
2.3778
1.6412
21.7287
2.3791
1.6583
21.9557
2.3803
1.6750
22.1765
2.3815

16.4840
2.2610

16.8966
2.2681

17.2908
2.2747

17.6682
2.2808

18.0301
2.2863

18.3777
2.2915

18.7121
2.2964

19.0342
2.3009

19.3448
2.3051

19.6447
2.3091

19.9345
2.3128

20.2149
2.3163

20.4863
2.3196

20.7493
2.3228

21.0044
2.3257

21.2519
2.3286

21.4922
2.3313

21.7258
2.3338

21.9528
2.3363

22.1737
2.3386

16.4804
2.1794

16.8931
2.1901

17.2875
2.1999

17.6650
2.2090

18.0270
2.2174

18.3748
2.2252

18.7093
2.2324

19.0315
2.2392

19.3422
2.2455

19.6422
2.2514

19.9321
2.2570

20.2125
2.2623

20.4840
2.2673

20.7471
2.2720

21.0022
2.2765

21.2498
2.2807

21.4902
2.2847

21.7238
2.2886

21.9509
2.2923

22.1718
2.2958

90

16.4786
2.0978

16.8914
2.1121

17.2858
2.1252

17.6634
2.1373

18.0255
2.1485

18.3733
2.1588

18.7079
2.1685

19.0302
2.1775

19.3409
2.1859

19.6409
2.1939

19.9309
2.2013

20.2113
2.2083

20.4829
2.2150

20.7460
2.2213

21.0011
2.2272

21.2487
2.2329

21.4892
2.2383

21.7228
2.2434

21.9499
2.2483

22.1709
2.2529

16.4786
2.0163

16.8914
2.0342

17.2858
2.0506

17.6634
2.0657

18.0255
2.0796

18.3733
2.0926

18.7079
2.1046

19.0302
2.1159

19.3409
2.1264

19.6409
2.1363

19.9309
2.1456

20.2113
2.1544

20.4829
2.1627

20.7460
2.1706

21.0011
2.1780

21.2487
2.1851

21.4892
2.1918

21.7228
2.1982

21.9499
2.2043

22.1709
2.2101

1.2448
1.9350

1.2759
1.9564

1.3057
1.9760

1.3342
1.9941

1.3615
2.0109

1.3878
2.0264

1.4131
2.0408

1.4374
2.0543

1.4608
2.0670

1.4835
2.0789

1.5054
2.0900

1.5265
2.1006

1.5470

2.1105 ,

1.5669
2.1199

1.5862
2.1288

1.6048
2.1373

1.6230
2.1454

1.6406
2.1530

1.6578
2.1604

1.6745
2.1674

1517.6163
1.8537

1601.9285
1.8787

1686.2404
1.9016

1770.5525
1.9227

1854.8646
1.9422

1939.1765
1.9603

2023.4886
1.9771

2107.8005
1.9929

2192.1125
2.0076

2276.4248
2.0214

2360.7366
2.0345

2445.0486
2.0467

2529.3608
2.0583

2613.6729
2.0693

2697.9846
2.0797

2782.2966
2.0896

2866.6089
2.0990

2950.9209
2.1079

3035.2327
2.1165

3119.5449
2.1246

0.0170
22.3951
2.4243
0.0170
22.6043
2.4243
0.0171
22.8081
2.4243
0.0172
23.0068
2.4243
0.0172
23.2006
2.4243
0.0173
23.3896
2.4243
0.0173
23.5740
2.4243
0.0174
23.7541
2.4243
0.0174
23.9300
2.4243
0.0175
24.1018
2.4243
0.0175
24.2697
2.4243
0.0175
24.4339
2.4243
0.0176
24.5944
2.4243
0.0176
24.7514
2.4243
0.0177
24.9051
2.4243
0.0177
25.0554
2.4243
0.0177
25.2026
2.4243
0.0178
25.3467
2.4243
0.0178
25.4878
2.4243
0.0178
25.6261
2.4243

1.6912
22.3914
2.3826
1.7070
22.6008
2.3836
1.7224
22.8047
2.3847
1.7374
23.0034
2.3857
1.7520
23.1973
2.3866
1.7663
23.3864
2.3875
1.7802
23.5709
2.3884
1.7938
23.7510
2.3892
1.8071
23.9270
2.3900
1.8201
24.0989
2.3908
1.8327
24.2669
2.3915
1.8451
24.4311
2.3923
1.8573
24.5917
2.3930
1.8691
24.7488
2.3936
1.8807
24.9024
2.3943
1.8921
25.0528
2.3949
1.9032
25.2001
2.3955
1.9141
25.3442
2.3961
1.9247
25.4854
2.3967
1.9352
25.6237
2.3972

22.3887
2.3408

22.5981
2.3430

22.8021
2.3450

23.0009
2.3470

23.1948
2.3489

23.3839
2.3507

23.5685
2.3524

23.7488
2.3541

23.9248
2.3557

24.0967
2.3572

24.2647
2.3587

24.4290
2.3602

24.5896
2.3616

24.7468
2.3629

24.9005
2.3642

25.0509
2.3655

25.1982
2.3667

25.3424
2.3679

25.4836
2.3690

25.6220
2.3702

.3869
2.2991

.5963
2.3023

.8003
2.3054

.9992
2.3083

.1932
2.3111

.3823
2.3138

.5670
2.3164

.7472
2.3190

.9233
2.3214

.0952
2.3237

.2633
2.3259

.4276
2.3281

.5883
2.3302

.7454
2.3322

.8992
2.3342

.0496
2.3361

.1969
2.3379

.3412
2.3397

25.4824
2.3414

25.6208
2.3431

91

.3860
.2574

.5954
.2616

.7995
.2657

.9984
.2697

.1923
.2734

.3815
.2770

.5662
.2805

.7465
.2838

.9225
.2871

.0945
.2902

.2626
.2932

.4269
.2961

.5876
.2988

.7447
.3015

.8985
.3042

.0490
.3067

.1963
.3091

.3406
.3115

.4818
.3138

.6202
.3160

22.3860
2.2157

22.5954
2.2210

22.7995
2.2261

22.9984
2.2310

23.1923
2.2357

23.3815
2.2402

23.5662
2.2446

23.7465
2.2488

23.9225
2.2528

24.0945
2.2567

24.2626
2.2604

24.4269
2.2640

24.5876
2.2675

24.7447
2.2709

24.8985
2.2741

25.0490
2.2773

25.1963
2.2803

25.3406
2.2833

25.4818
2.2862

25.6202
2.2889

1.6907
2.1740

1.7065
2.1804

1.7219
2.1866

1.7369
2.1924

1.7516
2.1981

1.7658
2.2035

1.7798
2.2087

1.7934
2.2137

1.8067
2.2185

1.8197
2.2232

1.8324
2.2277

1.8448
2.2320

1.8569
2.2362

1.8688
2.2402

1.8804
2.2441

1.8917
2.2479

1.9029
2.2516

1.9137
2.2551

1.9244
2.2586

1.9349
2.2619

3203.

3288.

3372.

3456.

3541.

3625.

3709.

3794.

3878.

3962.

4046.

4131.

4215.

4299.

4384.

4468.

4552.

4637.

4721.

4805.

8569

.1324

1689

.1399

4807

.1470

7930

.1539

1050

.1604

4170

.1667

7292

.1728

0410

3530

.1843

6653

.1897

9773

.1950

2891

.2000

6011

.2049

9136

.2096

2251

.2142

5371

.2186

8496

.2228

1616

.2270

4731

.2310

7856

.2349

0.0179
25.7616
2.4243
0.0179
25.8943
2.4243
0.0179
26.0245
2.4243
0.0179
26.1521
2.4243
0.0180
26.2772
2.4243
0.0180
26.3999

1.9454
25.7593
2.3978
1.9554
25.8921
2.3983
1.9652
26.0223
2.3988
1.9749
26.1499
2.3993
1.9843
26.2751
2.3998
1.9936
26.3978

25.7575
2.3712

25.8904
2.3723

26.0206
2.3733

26.1483
2.3743

26.2735
2.3752

26.3962

26

.7564
.3447

.8893

.3463

.0195

.3478

.1472
.3493

.2724
.3507

.3952

92

25.7558
2.3182

25.8887
2.3203

26.0189
2.3223

26.1466
2.3243

26.2719
2.3262

26.3947

25.7558
2.2916

25.8887
2.2943

26.0189
2.2968

26.1466
2.2993

26.2719
2.3017

26.3947

1.9451
2.2651

1.9551
2.2683

1.9650
2.2713

1.9746
2.2743

1.9840
2.2772

 

SHELF-LIFE OF THIS PRODUCT IS

FORTRAN STOP

5

£93

All data are checked successfully !!!
Re-check all data entered

Temperature of storage environment incelsius -25.00

Relative humidity of storage environment in 4 -80.00

Absolute humidity of storage environment ingHZO/gAir -.0163
Diffusion coefficient of packaging materialin 10‘-7 cm*2/sec -0.020
Henry constant of packaging material in(gHZO/cm“3 PKG)/(gHZO/cm‘3 Air) -
000

Thickness of packaging material in cm - 0.02300

Surface area of packaging material in cm‘2 - 3.78000

Volume of packaging material in cm“3 - 0.80000

Diffusion coefficient of product in 10‘-5am‘2/sec - 0.11790
Initia1 moisture content in gHZO/lOOg dryproduct -0.00

Critical moisture content in gHZO/lOOg dryproduct -2.00

ary weight of product in g - 0.40770

Chemical reaction rate - 0.0

chemdcal reaction order - 0.0

Ay/M--.179OE+01 1992 + 0.19228+01 Aw+ 0.64008-01

Radius of product in cm - 0.50000

Thickness of product (Only Plate shape) incm - 0.39200

 

Hit any key to continue.....

 

INITIAL CONCENTRATION

 

concentration of outside environment (CE) - 0.01534 g/L
Concentration of outside surface of PKG(CLE) - 1.91945 g/L
Concentration of inside surface of PKG(CLH) - 0.00002 g/L
Concentration of headspace (CR) - 0.00000 g/L

Concentration of outside surface of product(CRH) - 0.00132 g/L

DIMENSSIONLESS CONSTANT

 

Q-0.1420£‘.-02
e-o.15200-02
A1-o.19220-04
BJ-o.19ozr-03
S~0.19a1z+01
x-o.9oooa+03
- 14

Hit any key to continue ......

 

 

Enter the number of time to calculateconcentrations at once.

<NOTICE !!! It must be over 200 and be times of 200)

 

125.12

(Plate Shape)
152000. steps (83.6379hrs)

Each step is

94:

 

 

<4 of the divided shell of product is 5
CLE CL1 C12 CL3 CL4 CLH CH Meg
CR3 CR1 CR2 CR3 CR4” CRC GAIN TIME(hrs)

1.9194 1.7828 1.6462 1.5096 1.3730 1.2365 1.0999 0.9634
0.8269 0.6904 0.5540 0.4175 0.2812 0.1449 0.0086 0.0001
0.0504

0.6676 0.6545 0.6448 0.6382 0.6350 0.6350 0.0487 83.6379
1.9194 1.7837 1.6479 1.5122 1.3764 1.2407 1.1050 0.9693
0.8337 0.6980 0.5625 0.4269 0.2915 0.1560 0.0207 0.0002
0.1071

1.4189 1.4059 1.3962 1.3897 1.3865 1.3865 0.1054 167.2758
1.9194 1.7848 1.6501 1.5154 1.3807 1.2461 1.1115 0.9769
0.8424 0.7079 0.5735 0.4391 0.3048 0.1705 0.0364 0.0003
0.1634

2.1642 2.1514 2.1417 2.1353 2.1321 2.1321 0.1617 250.9138
1.9194 1.7862 1.6529 1.5197 1.3864 1.2533 1.1201 0.9870
0.8539 0.7209 0.5880 0.4552 0.3224 0.1898 0.0572 0.0005
0.2191

2.9017 2.8890 2.8795 2.8731 2.8700 2.8700 0.2174 334.5517
1.9194 1.7881 1.6568 1.5255 1.3942 1.2630 1.1318 1.0007
0.8697 0.7388 0.6079 0.4772 0.3466 0.2161 0.0857 0.0007
0.2740

3.6285 3.6160 3.6067 3.6004 3.5973 3.5973 0.2724 418.1896
1.9194 1.7908 1.6622 1.5336 1.4051 1.2766 1.1482 1.0199
0.8917 0.7636 0.6357 0.5079 0.3803 0.2528 0.1256 0.0010
0.3278

4.3404 4.3282 4.3191 4.3130 4.3100 4.3100 0.3262 501.8275
1.9194 1.7946 1.6698 1.5451 1.4204 1.2958 1.1713 1.0469
0.9227 0.7986 0.6748 0.5511 0.4277 0.3045 0.1816 0.0015
0.3799

5.0314 5.0196 5.0108 5.0049 5.0020 5.0020 0.3784 585.4654
1.9194 1.7998 1.6803 1.5607 1.4413 1.3220 1.2028 1.0838
0.9649 0.8463 0.7280 0.6099 0.4921 0.3747 0.2576 0.0021
0.4300

5.6936 5.6824 5.6740 5.6684 5.6656 5.6656 0.4285 669.1033
1.9194 1.8064 1.6934 1.5805 1.4677 1.3549 1.2424 1.1301
1.0180 0.9061 0.7946 0.6834 0.5725 0.4621 0.3521 0.0028
0.4772

6.3194 6.3089 6.3010 6.2957 6.2931 6.2931 0.4758 752.7413
1.9194 1.8138 1.7082 1.6027 1.4972 1.3919 1.2868 1.1819
1.0773 0.9729 0.8688 0.7651 0.6617 0.5588 0.4564 0.0036
0.5214

6.9042 6.8944 6.8871 6.8822 6.8798 6.8798 0.5201 836.3792
1.9194 1.8213 1.7231 1.6250 1.5271 1.4292 1.3316 1.2341
1.1369 1.0399 0.9432 0.8469 0.7510 0.6554 0.5603 0.0045
0.5624

7.4476 7.4386 7.4317 7.4272 7.4249 7.4249 0.5612 920.0171
1.9194 1.8283 1.7372 1.6461 1.5551 1.4643 1.3736 1.2831
1.1928 1.1027 1.0130 0.9235 0.8344 0.7456 0.6573 0.0053
0.6005

7.9521 7.9437 7.9374 7.9331 7.9310 7.9310 0.5994 1003.6550
1.9194 1.8346 1.7499 1.6652 1.5805 1.4960 1.4116 1.3274
1.2434 1.1596 1.0760 0.9928 0.9098 0.8271 0.7448 0.0060
0.6359

8.4214 8.4135 8.4076 8.4037 8.4017 8.4017 0.6349 1087.2930
1.9194 1.8403 1.7612 1.6822 1.6032 1.5243 1.4455 1.3669

1.2885
0.6690
8.8593
1.9194
1.3285
0.7000
9.2693
1.9194
1.3641
0.7291
9.6545
1.9194
1.3958
0.7565
10.0177
1.9194
1.4243
0.7824
10.3612
1.9194
1.4499
0.8070
10.6868
1.9194
1.4731
0.8304
10.9963
1.9194
1.4942
0.8527
11.2911
1.9194
1.5134
0.8739
11.5726
1.9194
1.5311
0.8942
11.8417
1.9194
1.5474
0.9137
12.0996
1.9194
1.5625
0.9324
12.3470
1.9194
1.5764
0.9503
12.5848
1.9194
1.5894
0.9676
12.8135
1.9194
1.6015
0.9842
13.0338
1.9194

1.2102

8.8519
1.8454
1.2552

9.2624
1.8498
1.2952

9.6481
1.8538
1.3308

10.0116
1.8574
1.3628

10.3554
1.8606
1.3916

10.6813
1.8635
1.4176

10.9910
1.8662
1.4413

11.2861
1.8686
1.4630

11.5678
1.8708
1.4828

11.8372
1.8728
1.5011

12.0952
1.8747
1.5181

12.3428
1.8765
1.5337

12.5807
1.8781
1.5483

12.8096
1.8796
1.5620

13.0300
1.8811

1.1322

8.8464
1.7713
1.1821

9.2572
1.7802
1.2264

9.6432
1.7882
1.2660

10.0070
1.7953
1.3014

10.3510
1.8018
1.3334

10.6771
1.8076
1.3623

10.9871
1.8129
1.3886

11.2824
1.8177
1.4126

11.5642
1.8222
1.4346

11.8337
1.8263
1.4549

12.0919
1.8300
1.4737

12.3397
1.8335
1.4911

12.5777
1.8368
1.5073

12.8067
1.8398
1.5224

13.0272
1.8427

1.0545

8.8427
1.6972
1.1092

9.2538
1.7107
1.1579

9.6399
1.7226
1.2013

10.0040
1.7333
1.2402

10.3481
1.7430
1.2753

10.6744
1.7517
1.3070

10.9845
1.7597
1.3359

11.2799
1.7669
1.3623

11.5618
1.7736
1.3865

11.8315
1.7797
1.4088

12.0898
1.7853
1.4295

12.3376
1.7906
1.4486

12.5757
1.7955
1.4664

12.8047
1.8000
1.4830

13.0253
1.8043

95

0.9769

8.8409
1.6233
1.0366

9.2521
1.6412
1.0895

9.6383
1.6571
1.1368

10.0024
1.6714
1.1792

10.3467
1.6842
1.2174

10.6730
1.6959
1.2520

10.9832
1.7064
1.2834

11.2786
1.7161
1.3122

11.5606
1.7250
1.3385

11.8303
1.7331
1.3628

12.0887
1.7407
1.3853

12.3365
1.7477
1.4062

12.5747
1.7542
1.4256

12.8037
1.7603
1.4436

13.0244
1.7659

0.8997

8.8409
1.5494
0.9642

9.2521
1.5717
1.0214

9.6383
1.5916
1.0725

10.0024
1.6095
1.1184

10.3467
1.6255
1.1596

10.6730
1.6401
1.1970

10.9832
1.6533
1.2310

11.2786
1.6654
1.2621

11.5606
1.6764
1.2907

11.8303
1.6866
1.3169

12.0887
1.6961
1.3413

12.3365
1.7048
1.3638

12.5747
1.7129
1.3848

12.8037
1.7205
1.4044

13.0244
1.7276

0.8228

0.6680
1.4756
0.8920

0.6991
1.5024
0.9536

0.7282
1.5263
1.0085

0.7557
1.5476
1.0577

0.7817
1.5669
1.1021

0.8063
1.5843
1.1423

0.8297
1.6002
1.1788

0.8520
1.6146
1.2122

0.8733
1.6279
1.2429

0.8936
1.6402
1.2712

0.9131
1.6515
1.2973

0.9318
1.6620
1.3216

0.9498
1.6717
1.3441

0.9671
1.6808
1.3652

0.9838
1.6893

0.0066

1170.9308
1.4020
0.0071

1254.5687
1.4332
0.0076

1338.2067
1.4610
0.0081

1421.8446
1.4859
0.0085

1505.4825
1.5083
0.0088

1589.1204
1.5287
0.0091

1672.7583
1.5471
0.0094

1756.3962
1.5640
0.0097

1840.0342
1.5795
0.0099

1923.6721
1.5938
0.0102

2007.3101
1.6069
0.0104

2090.9480
1.6192
0.0106

2174.5859
1.6305
0.0107

2258.2236
1.6411
0.0109

2341.8616
1.6511

1.6129
1.0003
13.2462
1.9194
1.6235
1.0158
13.4513
1.9194
1.6335
1.0307
13.6494
1.9194
1.6429
1.0452
13.8411
1.9194
1.6517
1.0592
14.0265
1.9194
1.6601
1.0728
14.2062
1.9194
1.6681
1.0859
14.3803
1.9194
1.6756
1.0987
14.5492
1.9194
1.6828
1.1111
14.7132
1.9194
1.6896
1.1231
14.8724
1.9194
1.6960
1.1348
15.0272
1.9194
1.7022
1.1461
15.1777
1.9194
1.7081
1.1572
15.3240
1.9194
1.7138
1.1680
15.4665
1.9194
1.7192
1.1784
15.6052
1.9194

1.5747

13.2426
1.8824
1.5866

13.4478
1.8836
1.5979

13.6461
1.8848
1.6084

13.8378
1.8859
1.6184

14.0234
1.8870
1.6278

14.2031
1.8880
1.6368

14.3774
1.8889
1.6452

14.5464
1.8898
1.6533

14.7104
1.8907
1.6609

14.8697
1.8915
1.6682

15.0245
1.8923
1.6752

15.1751
1.8930
1.6818

15.3215
1.8937
1.6881

15.4640
1.8944
1.6942

15.6028
1.8950

1.5366

13.2399
1.8453
1.5498

13.4452
1.8478
1.5623

13.6435
1.8502
1.5740

13.8353
1.8524
1.5851

14.0210
1.8545
1.5956

14.2008
1.8565
1.6055

14.3751
1.8584
1.6149

14.5442
1.8602
1.6238

14.7083
1.8619
1.6323

14.8677
1.8635
1.6404

15.0226
1.8651
1.6481

15.1732
1.8666
1.6555

15.3196
1.8680
1.6625

15.4622
1.8693
1.6693

15.6010
1.8706

96

1.4985

13.2381
1.8083
1.5131

13.4434
1.8120
1.5268

13.6418
1.8156
1.5397

13.8337
1.8189
1.5519

14.0194
1.8221
1.5634

14.1993
1.8251
1.5743

14.3736
1.8279
1.5846

14.5428
1.8306
1.5944

14.7069
1.8331
1.6038

14.8663
1.8356
1.6126

15.0212
1.8379
1.6211

15.1719
1.8401
1.6292

15.3184
1.8422
1.6370

15.4610
1.8443
1.6444

15.5998
1.8462

1.4606

13.2372
1.7713
1.4764

13.4426
1.7763
1.4914

13.6410
1.7810
1.5054

13.8329
1.7854
1.5187

14.0186
1.7896
1.5312

14.1985
1.7936
1.5431

14.3729
1.7974
1.5544

14.5420
1.8010
1.5650

14.7062
1.8044
1.5752

14.8656
1.8076
1.5849

15.0206
1.8107
1.5942

15.1712
1.8137
1.6030

15.3178
1.8165
1.6114

15.4604
1.8192
1.6195

15.5992
1.8218

1.4227

13.2372
1.7343
1.4399

13.4426
1.7405
1.4560

13.6410
1.7464
1.4712

13.8329
1.7520
1.4856

14.0186
1.7572
1.4991

14.1985
1.7622
1.5120

14.3729
1.7669
1.5242

14.5420
1.7714
1.5357

14.7062
1.7756
1.5467

14.8656
1.7797
1.5572

15.0206
1.7836
1.5673

15.1712
1.7873
1.5768

15.3178
1.7908
1.5859

15.4604
1.7942
1.5947

15.5992
1.7974

1.3849

0.9998
1.6973
1.4033

1.0153
1.7048
1.4207

1.0303
1.7119
1.4371

1.0448
1.7185
1.4525

1.0588
1.7248
1.4671

1.0724
1.7308
1.4809

1.0855
1.7364
1.4940

1.0983
1.7418
1.5065

1.1107
1.7469
1.5183

1.1227
1.7518
1.5296

1.1344
1.7564
1.5404

1.1458
1.7609
1.5507

1.1569
1.7651
1.5605

1.1676
1.7692
1.5699

1.1781
1.7730

0.0111

2425.4995
1.6604
0.0112

2509.1375
1.6691
0.0114

2592.7754
1.6773
0.0115

2676.4133
1.6851
0.0116

2760.0510
1.6925
0.0117

2843.6892
1.6994
0.0118

2927.3269
1.7060
0.0119

3010.9651
1.7123
0.0120

3094.6028
1.7182
0.0121

3178.2407
1.7239
0.0122

3261.8787
1.7293
0.0123

3345.5166
1.7345
0.0124

3429.1545
1.7394
0.0125

3512.7925
1.7442
0.0125

3596.4302
1.7487

1.7243
1.1886
15.7403
1.9194
1.7293
1.1986
15.8720
1.9194
1.7341
1.2083
16.0004
1.9194
1.7386
1.2177
16.1256
1.9194
1.7430
1.2270
16.2477
1.9194
1.7473
1.2360
16.3670
1.9194
1.7513
1.2447
16.4834
1.9194
1.7553
1.2533
16.5971
1.9194
1.7591
1.2617
16.7081
1.9194
1.7627
1.2699
16.8167
1.9194
1.7662
1.2779
16.9228
1.9194
1.7697
1.2858
17.0265
1.9194
1.7729
1.2934
17.1279
1.9194
1.7761
1.3009
17.2272
1.9194
1.7792
1.3082
17.3243
1.9194

1.7000

15.7380
1.8957
1.7056

15.8697
1.8962
1.7110

15.9982
1.8968
1.7161

16.1234
1.8974
1.7211

16.2457
1.8979
1.7258

16.3649
1.8984
1.7304

16.4814
1.8989
1.7348

16.5951
1.8994
1.7391

16.7062
1.8998
1.7432

16.8148
1.9003
1.7471

16.9209
1.9007
1.7510

17.0247
1.9011
1.7547

17.1262
1.9015
1.7583

17.2255
1.9019
1.7617

17.3226
1.9023

1.6757

15.7363
1.8719
1.6819

15.8680
1.8731
1.6879

15.9965
1.8742
1.6936

16.1218
1.8753
1.6991

16.2441
1.8764
1.7044

16.3634
1.8774
1.7095

16.4799
1.8784
1.7144

16.5937
1.8793
1.7191

16.7048
1.8802
1.7237

16.8134
1.8811
1.7281

16.9196
1.8820
1.7323

17.0234
1.8828
1.7364

17.1249
1.8836
1.7404

17.2242
1.8844
1.7443

17.3214
1.8851

1.6515

15.7351
1.8481
1.6583

15.8669
1.8499
1.6648

15.9954
1.8516
1.6711

16.1208
1.8532
1.6772

16.2430
1.8548
1.6830

16.3624
1.8563
1.6886

16.4789
1.8578
1.6939

16.5927
1.8592
1.6991

16.7039
1.8606
1.7042

16.8125
1.8619
1.7090

16.9187
1.8632
1.7137

17.0225
1.8645
1.7182

17.1240
1.8657
1.7226

17.2233
1.8668
1.7268

17.3205
1.8679

97

1.6273

15.7345
1.8243
1.6347

15.8664
1.8267
1.6418

15.9949
1.8290
1.6487

16.1202
1.8312
1.6552

16.2425
1.8333
1.6616

16.3619
1.8353
1.6677

16.4784
1.8373
1.6735

16.5922
1.8392
1.6792

16.7034
1.8410
1.6847

16.8120
1.8428
1.6900

16.9182
1.8445
1.6951

17.0220
1.8461
1.7000

17.1236
1.8477
1.7048

17.2229
1.8493
1.7094

17.3201
1.8508

1.6031

15.7345
1.8005
1.6111

15.8664

1.8035
1.6188

15.9949
1.8064
1.6262

16.1202
1.8091
1.6334

16.2425
1.8118
1.6402

16.3619
1.8143
1.6468

16.4784
1.8168
1.6532

16.5922
1.8191
1.6593

16.7034
1.8214
1.6652

16.8120
1.8236
1.6709

16.9182
1.8258
1.6765

17.0220
1.8278
1.6818

17.1236
1.8298
1.6870

17.2229
1.8317
1.6920

17.3201
1.8336

1.5789

1.1883
1.7768
1.5876

1.1983
1.7803
1.5959

1.2080
1.7838
1.6038

1.2174
1.7871
1.6115

1.2267
1.7903
1.6189

1.2357
1.7933
1.6260

1.2445
1.7963
1.6328

1.2531
1.7991
1.6394

1.2615
1.8018
1.6458

1.2697
1.8045
1.6520

1.2777
1.8070
1.6579

1.2855
1.8095
1.6636

1.2932
1.8119
1.6692

1.3007
1.8142
1.6746

1.3080
1.8165

0.0126

3680.0684
1.7530
0.0127

3763.7061
1.7572
0.0128

3847.3442
1.7612
0.0128

3930.9819
1.7650
0.0129

4014.6201
1.7688
0.0129

4098.2578
1.7723
0.0130

4181.8960
1.7758
0.0131

4265.5337
1.7791
0.0131

4349.1719
1.7823
0.0132

4432.8096
1.7854
0.0132

4516.4473
1.7883
0.0133

4600.0854
1.7912
0.0133

4683.7231
1.7940
0.0133

4767.3613
1.7967
0.0134

4850.9990
1.7993

1.7822
1.3154
17.4193
1.9194
1.7851
1.3224
17.5123
1.9194
1.7879
1.3293
17.6034
1.9194
1.7906
1.3361
17.6926
1.9194
1.7933
1.3427
17.7800
1.9194
1.7958
1.3491
17.8656
1.9194
1.7983
1.3555
17.9495
1.9194
1.8007
1.3617
18.0317
1.9194
1.8031
1.3678
18.1123
1.9194
1.8053
1.3737
18.1913
1.9194
1.8076
1.3796
18.2687
1.9194
1.8097
1.3853
18.3447
1.9194
1.8118
1.3909
18.4192
1.9194
1.8139
1.3965
18.4923
1.9194
1.8158
1.4019
18.5641
1.9194

1.7651

17.4177
1.9026
1.7683

17.5107
1.9030
1.7715

17.6019
1.9033
1.7746

17.6911
1.9037
1.7775

17.7785
1.9040
1.7804

17.8641
1.9043
1.7832

17.9480
1.9046
1.7859

18.0303
1.9049
1.7885

18.1109
1.9052
1.7911

18.1899
1.9054
1.7936

18.2674
1.9057
1.7960

18.3434
1.9060
1.7984

18.4180
1.9062
1.8007

18.4911
1.9065
1.8029

18.5628

1.9067‘

1.7480

17.4165
1.8858
1.7516

17.5095
1.8865
1.7551

17.6007
1.8872
1.7585

17.6899
1.8879
1.7618

17.7774
1.8885
1.7650

17.8630
1.8891
1.7681

17.9470
1.8897
1.7711

18.0292
1.8903
1.7740

18.1099
1.8909
1.7769

18.1889
1.8915
1.7797

18.2664
1.8920
1.7824

18.3424
1.8925
1.7850

18.4170
1.8930
1.7875

18.4902
1.8935
1.7900

18.5619
1.8940

98

1.7309

17.4156
1.8690
1.7349

17.5087
1.8701
1.7387

17.5999
1.8711
1.7425

17.6892
1.8721
1.7461

17.7766
1.8730
1.7496

17.8623
1.8740
1.7530

17.9462
1.8749
1.7563

18.0285
1.8758
1.7596

18.1092
1.8766
1.7627

18.1882
1.8775
1.7657

18.2658
1.8783
1.7687

18.3418
1.8791
1.7716

18.4164
1.8798
1.7744

18.4895
1.8806
1.7771

18.5613
1.8813

1.7138

17.4152
1.8522
1.7182

17.5083
1.8536
1.7224

17.5995
1.8550
1.7264

17.6888
1.8563
1.7304

17.7762
1.8576
1.7342

17.8619
1.8588
1.7380

17.9459
1.8600
1.7416

18.0282
1.8612
1.7451

18.1088
1.8624
1.7485

18.1879
1.8635
1.7518

18.2654
1.8645
1.7550

18.3415
1.8656
1.7582

18.4160
1.8666
1.7612

18.4892
1.8676
1.7642

18.5610
1.8686

1.6968

17.4152
1.8354
1.7015

17.5083
1.8372
1.7060

17.5995
1.8389
1.7104

17.6888
1.8405
1.7147

17.7762
1.8421
1.7189

17.8619
1.8437
1.7229

17.9459
1.8452
1.7268

18.0282
1.8467
1.7306

18.1088
1.8481
1.7343

18.1879
1.8495
1.7379

18.2654
1.8508
1.7414

18.3415
1.8521
1.7448

18.4160
1.8534
1.7481

18.4892
1.8547
1.7513

18.5610
1.8559

1.6798

1.3152
1.8186
1.6848

1.3222
1.8207
1.6897

1.3291
1.8228
1.6945

1.3359
1.8248
1.6991

1.3425
1.8267
1.7035

1.3489
1.8285
1.7079

1.3553
1.8304
1.7121

1.3615
1.8321
1.7162

1.3676
1.8338
1.7202

1.3735
1.8355
1.7240

1.3794
1.8371
1.7278

1.3851
1.8387
1.7315

1.3908
1.8402
1.7350

1.3963
1.8417
1.7385

1.4017
1.8432

0.0134

4934.6372
1.8019
0.0135

5018.2749
1.8043
0.0135

5101.9126
1.8067
0.0135

5185.5508
1.8090
0.0136

5269.1890
1.8112
0.0136

5352.8267
1.8134
0.0136

5436.4644
1.8155
0.0137

5520.1021
1.8176
0.0137

5603.7407
1.8196
0.0137

5687.3784
1.8215
0.0138

5771.0161
1.8234
0.0138

5854.6538
1.8252
0.0138

5938.2920
1.8270
0.0139

6021.9302
1.8288
0.0139

6105.5679
1.8305

1.8178
1.4072
18.6345
1.9194
1.8197
1.4124
18.7035
1.9194
1.8215
1.4175
18.7713
1.9194
1.8233
1.4226
18.8379
1.9194
1.8251
1.4275
18.9033
1.9194
1.8268
1.4323
18.9674
1.9194
1.8284
1.4371
19.0304
1.9194
1.8300
1.4418
19.0923
1.9194
1.8316
1.4464
19.1531
1.9194
1.8332
1.4509
19.2129
1.9194
1.8347
1.4553
19.2715
1.9194
1.8362
1.4596
19.3292
1.9194
1.8376
1.4639
19.3858
1.9194
1.8390
1.4681
19.4415
1.9194
1.8404
1.4723
19.4962
1.9194

1.8051

18.6333
1.9070
1.8072

18.7024
1.9072
1.8093

18.7702
1.9074
1.8113

18.8368
1.9076
1.8133

18.9021
1.9079
1.8152

18.9663
1.9081
1.8171

19.0294
1.9083
1.8189

19.0913
1.9085
1.8207

19.1521
1.9087
1.8224

19.2118
1.9088
1.8241

19.2705
1.9090
1.8258

19.3282
1.9092
1.8274

19.3849
1.9094
1.8290

19.4406
1.9096
1.8305

19.4953
1.9097

1.7924

18.6323
1.8945
1.7948

18.7015
1.8949
1.7971

18.7693
1.8954
1.7993

18.8359
1.8958
1.8015

18.9013
1.8963
1.8036

18.9655
1.8967
1.8057

19.0286
1.8971
1.8078

19.0905
1.8975
1.8097

19.1513
1.8979
1.8117

19.2111
1.8982
1.8136

19.2698
1.8986
1.8154

19.3275
1.8990
1.8172

19.3841
1.8993
1.8190

19.4398
1.8997
1.8207

19.4946
1.9000

1.7798

18.6317
1.8820
1.7824

18.7009
1.8827
1.7849

18.7687
1.8834
1.7874

18.8353
1.8840
1.7898

18.9007
1.8847
1.7921

18.9650
1.8853
1.7944

19.0280
1.8859
1.7966

19.0899
1.8865
1.7988

19.1508
1.8871
1.8009

19.2105
1.8876
1.8030

19.2693
1.8882
1.8050

19.3270
1.8887
1.8070

19.3836
1.8893
1.8089

19.4394
1.8898
1.8108

19.4941
1.8903

99

1.7671

18.6314
1.8695
1.7700

18.7006
1.8704
1.7727

18.7684
1.8713
1.7754

18.8351
1.8722
1.7780

18.9005
1.8731
1.7806

18.9647
1.8739
1.7831

19.0277
1.8747
1.7855

19.0897
1.8755
1.7879

19.1505
1.8763
1.7902

19.2103
1.8770
1.7925

19.2690
1.8778
1.7947

19.3267
1.8785
1.7968

19.3834
1.8792
1.7989

19.4391
1.8799
1.8010

19.4939
1.8806

1.7545

1.8571
1.7576

18.7006
1.8582
1.7605

18.7684
1.8593
1.7634

18.8351
1.8604
1.7663

18.9005
1.8615
1.7690

18.9647
1.8625
1.7717

19.0277
1.8635
1.7744

19.0897
1.8645
1.7770

19.1505
1.8655
1.7795

19.2103
1.8664
1.7819

19.2690
1.8674
1.7843

19.3267
1.8683
1.7867

19.3834
1.8692
1.7889

19.4391
1.8700
1.7912

19.4939
1.8709

1.7419

1.4070
1.8446
1.7452

1.4122
1.8460
1.7484

1.4174
1.8473
1.7515

1.4224
1.8486
1.7546

1.4273
1.8499
1.7575

1.4322
1.8512
1.7604

1.4369
1.8524
1.7633

1.4416
1.8536
1.7660

1.4462
1.8547
1.7688

1.4507
1.8559
1.7714

1.4552
1.8570
1.7740

1.4595
1.8580
1.7765

1.4638
1.8591
1.7789

1.4680
1.8601
1.7814

1.4721
1.8612

0.0139

6189.2056
1.8321
0.0139

6272.8438
1.8337
0.0140

6356.4814
1.8353
0.0140

6440.1196
1.8368
0.0140

6523.7573
1.8383
0.0140

6607.3955
1.8398
0.0141

6691.0332
1.8412
0.0141

6774.6709
1.8426
0.0141

6858.3091
1.8439
0.0141

6941.9473
1.8453
0.0142

7025.5850
1.8466
0.0142

7109.2227
1.8478
0.0142

7192.8604
1.8491
0.0142

7276.4990
1.8503
0.0142

7360.1367
1.8514

1.8417
1.4763
19.5500
1.9194
1.8431
1.4803
19.6029
1.9194
1.8444
1.4842
19.6549
1.9194
1.8456
1.4881
19.7060
1.9194
1.8468
1.4919
19.7563
1.9194
1.8481
1.4956
19.8057
1.9194
1.8492
1.4993
19.8543
1.9194
1.8504
1.5029
19.9021
1.9194
1.8515
1.5065
19.9491
1.9194
1.8526
1.5100
19.9954
1.9194
1.8537
1.5134
20.0409
1.9194
1.8548
1.5168
20.0856
1.9194
1.8558
1.5201
20.1297
1.9194
1.8568
1.5234
20.1730
1.9194
1.8578
1.5266
20.2157
1.9194

1.8321

19.5491
1.9099
1.8335

19.6020
1.9101
1.8350

19.6540
1.9102
1.8364

19.7051
1.9104
1.8378

19.7554
1.9105
1.8391

19.8048
1.9107
1.8405

19.8535
1.9108
1.8418

19.9013
1.9110
1.8430

19.9483
1.9111
1.8443

19.9946
1.9112
1.8455

20.0401
1.9114
1.8467

20.0849
1.9115
1.8479

20.1289
1.9116
1.8490

20.1723
1.9117
1.8502

20.2149
1.9119

1.8224

19.5484
1.9003
1.8240

19.6013
1.9007
1.8256

19.6533
1.9010
1.8272

19.7045
1.9013
1.8287

19.7548
1.9016
1.8302

19.8042
1.9019
1.8317

19.8528
1.9022
1.8332

19.9007
1.9025
1.8346

19.9477
1.9027
1.8360

19.9940
1.9030
1.8373

20.0395
1.9033
1.8386

20.0843
1.9035
1.8400

20.1284
1.9038
1.8412

20.1717
1.9040
1.8425

20.2144
1.9043

100

1.8127

19.5479
1.8908
1.8145

19.6009
1.8913
1.8163

19.6529
1.8917
1.8180

19.7040
1.8922
1.8197

19.7543
1.8927
1.8214

19.8038
1.8931
1.8230

19.8524
1.8935
1.8246

19.9002
1.8940
1.8261

19.9473
1.8944
1.8276

19.9936
1.8948
1.8291

20.0391
1.8952
1.8306

20.0839
1.8956
1.8320

20.1280
1.8960
1.8334

20.1713
1.8963
1.8348

20.2140
1.8967

1.8030

19.5477
1.8812
1.8050

19.6006
1.8819
1.8069

19.6527
1.8825
1.8088

19.7038
1.8831
1.8107

19.7541
1.8837
1.8125

19.8036
1.8843
1.8142

19.8522
1.8849
1.8160

19.9000
1.8855
1.8177

19.9471
1.8860
1.8193

19.9934
1.8866
1.8210

20.0389
1.8871
1.8225

20.0837
1.8876
1.8241

20.1278
1.8881
1.8256

20.1712
1.8886
1.8271

20.2138
1.8891

1.7934

19.5477
1.8717
1.7955

19.6006
1.8725
1.7976

19.6527
1.8733
1.7996

19.7038
1.8740
1.8016

19.7541
1.8748
1.8036

19.8036
1.8755
1.8055

19.8522
1.8763
1.8074

19.9000
1.8770
1.8092

19.9471
1.8777
1.8110

19.9934
1.8783
1.8128

20.0389
1.8790
1.8145

20.0837
1.8797
1.8162

20.1278
1.8803
1.8178

20.1712
1.8809
1.8195

20.2138
1.8815

1.7837

1.4762
1.8621
1.7860

1.4802
1.8631
1.7883

1.4841
1.8641
1.7905

1.4880
1.8650
1.7926

1.4918
1.8659
1.7947

1.4955
1.8668
1.7968

1.4992
1.8676
1.7988

1.5028
1.8685
1.8008

1.5064
1.8693
1.8027

1.5099
1.8701
1.8046

1.5133
1.8709
1.8065

1.5167
1.8717
1.8083

1.5200
1.8725
1.8101

1.5233
1.8732
1.8118

1.5265
1.8740

0.0143

7443.7744
1.8526
0.0143

7527.4121
1.8537
0.0143

7611.0508
1.8548
0.0143

7694.6885
1.8559
0.0143

7778.3262
1.8570
0.0143

7861.9639
1.8580
0.0144

7945.6021
1.8590
0.0144

8029.2402
1.8600
0.0144

8112.8779
1.8610
0.0144

8196.5156
1.8619
0.0144

8280.1543
1.8629
0.0144

8363.7920
1.8638
0.0145

8447.4297
1.8647
0.0145

8531.0674
1.8655
0.0145

8614.7051
1.8664

1.8588
1.5298
20.2576
1.9194
1.8598
1.5329
20.2989
1.9194
1.8607
1.5360
20.3396
1.9194
1.8616
1.5390
20.3796
1.9194
1.8626
1.5419
20.4190
1.9194
1.8634
1.5449
20.4577
1.9194
1.8643
1.5478
20.4959

1.8513

20.2569
1.9120
1.8523

20.2982
1.9121
1.8534

20.3389
1.9122
1.8544

20.3789
1.9123
1.8555

20.4183
1.9124
1.8565

20.4571
1.9126
1.8574

20.4953

1.8437

20.2564
1.9045
1.8449

20.2977
1.9048
1.8461

20.3384
1.9050
1.8472

20.3784
1.9052
1.8484

20.4178
1.9054
1.8495

20.4566
1.9057
1.8506

20.4948

101

1.8361

20.2560
1.8971
1.8375

20.2973
1.8974
1.8388

20.3380
1.8978
1.8400

20.3780
1.8981
1.8413

20.4175
1.8984
1.8425

20.4562
1.8988
1.8437

20.4944

1.8286

20.2558
1.8896
1.8300

20.2972
1.8901
1.8314

20.3378
1.8905
1.8328

20.3779
1.8910
1.8342

20.4173
1.8914
1.8355

20.4561
1.8919
1.8368

20.4943

1.8211

20.2558
1.8821
1.8226

20.2972
1.8827
1.8241

20.3378
1.8833
1.8256

20.3779
1.8839
1.8271

20.4173
1.8844
1.8286

20.4561
1.8850
1.8300

20.4943

1.8135

1.5297
1.8747
1.8152

1.5328
1.8754
1.8168

1.5359
1.8761
1.8185

1.5389
1.8768
1.8200

1.5419
1.8774
1.8216

1.5448
1.8781
1.8231

1.5477

0.0145

8698.3438
1.8672
0.0145

8781.9814
1.8681
0.0145

8865.6191
1.8689
0.0145

8949.2568
1.8697
0.0145

9032.8945
1.8704
0.0146

9116.5332
1.8712
0.0146

9200.1709

1132

All data are checked successfully !!!
Re-check all data entered

Temperature of storage environment incelsius -25.00

Relative humidity of storage environment in 4 -90.00

Absolute humidity of storage environment ingflZO/gAir -.0183
Diffusion coefficient of packaging materialin 10“-7 cm‘2/sec -0.020
Henry constant of packaging material in(qHZO/cm‘3 PKG)/(9820/cm‘3 Air) - 125.12
000

Thickness of packaging material in cm - 0.02300

Surface area of packaging material in cm‘2 - 3.78000

Volume of packaging material in cm‘3 - 0.80000

Diffusion coefficient of product in 10‘-50m‘2/se0 - 0.11790
Initial moisture content in 9820/1009 dryproduct -0.00

Critical moisture content in thO/lOOg dryproduct -2.00

Dry weight of product in g - 0.40770

Chemica1 reaction rate - 0.0

Chemical reaction order - 0.0

Aw/M--.179OB+01 Aw‘2 + o.1922:+o1 Aw+ 0.64008-01

Radius of product in cm - 0.50000

Thickness of product (Only Plate shape) incm - 0.39200

Hit any key to continue .....

 

INITIAL CONCENTRATION

Concentration of outside environment (C8) - 0.01938 g/L
Concentration of outside surface of PKG(CLB) - 2.42433 g/L
Concentration of inside surface of PKG(CLH) - 0.00002 g/L
Concentration of headspace (CH) - 0.00000 g/L

Concentration of outside surface of product(CRH) - 0.00132 g/L

DIMENSSIONLESS CONSTANT
Q-0.1260£-02
c-o.1vooa-02
A1-0.1815£-04
B1-o.21270-o3
s-o.221ss+o1
x-o.9ooos+o3

- 13

Hit any key to continue ......

 

 

Enter the number of time to calculateconcentrations at once.

(NOTICE !!! It must be over 200 and be times of 200>

Each step is

(Plate Shape)
137000. steps (84.3120hrs)

103

 

 

<4 of the divided shell of product is 5
CLE CL1 CLZ CL3 CL4 CLH CH Meg
CRH CR1 CR2 CR3 CR4 CRC GAIN TIME (hrs)
2.4243 2.2386 2.0528 1.8670 1.6813 1.4956 1.3099 1.1243
0.9387 0.7532 0.5678 0.3824 0.1971 0.0118 0.0001 0.0607
0.8037 0.7879 0.7761 0.7682 0.7642 0.7642 0.0586 84.3120
2.4243 2.2399 2.0554 1.8710 1.6866 1.5023 1.3179 1.1337
0.9495 0.7653 0.5813 0.3973 0.2135 0.0297 0.0002 0.1299
1.7200 1.7043 1.6925 1.6847 1.6808 1.6808 0.1278 168.6240
2.4243 2.2417 2.0591 1.8765 1.6939 1.5114 1.3289 1.1466
0.9643 0.7821 0.6000 0.4181 0.2363 0.0546 0.0004 0.1984
2.6272 2.6117 2.6001 2.5923 2.5884 2.5884 0.1963 252.9361
2.4243 2.2443 2.0643 1.8843 1.7044 1.5246 1.3448 1.1652
0.9857 0.8063 0.6271 0.4481 0.2693 0.0908 0.0007 0.2659
3.5213 3.5061 3.4947 3.4871 3.4833 3.4833 0.2639 337.2481
2.4243 2.2482 2.0721 1.8961 1.7202 1.5443 1.3687 1.1931
1.0178 0.8427 0.6679 0.4933 0.3191 0.1452 0.0012 0.3320
4.3960 4.3811 4.3700 4.3626 4.3589 4.3589 0.3300 421.5601
2.4243 2.2542 2.0841 1.9141 1.7442 1.5744 1.4049 1.2357
1.0667 0.8981 0.7299 0.5621 0.3947 0.2280 0.0018 0.3958
5.2408 5.2266 5.2160 5.2088 5.2053 5.2053 0.3939 505.8722
2.4243 2.2628 2.1013 1.9399 1.7788 1.6178 1.4571 1.2968
1.1369 0.9774 0.8185 0.6601 0.5024 0.3455 0.0028 0.4563
6.0426 6.0292 6.0192 6.0125 6.0092 6.0092 0.4545 590.1841
2.4243 2.2736 2.1229 1.9723 1.8220 1.6719 1.5221 1.3728
1.2239 1.0755 0.9277 0.7806 0.6342 0.4886 0.0039 0.5128
6.7904 6.7780 6.7687 6.7625 6.7594 6.7594 0.5111 674.4962
2.4243 2.2850 2.1457 2.0065 1.8676 1.7289 1.5905 1.4525
1.3150 1.1780 1.0415 0.9057 0.7706 0.6363 0.0051 0.5649
7.4812 7.4698 7.4612 7.4555 7.4526 7.4526 0.5634 758.8082
2.4243 2.2957 2.1671 2.0387 1.9104 1.7823 1.6546 1.5271
1.4001 1.2736 1.1476 1.0222 0.8974 0.7733 0.0062 0.6131
8.1188 8.1082 8.1003 8.0950 8.0924 8.0924 0.6117 843.1202
2.4243 2.3052 2.1861 2.0672 1.9483 1.8297 1.7114 1.5933
1.4756 1.3584 1.2415 1.1252 1.0095 0.8943 0.0071 0.6577
8.7092 8.6994 8.6920 8.6871 8.6847 8.6847 0.6564 927.4323
2.4243 2.3135 2.2027 2.0920 1.9814 1.8710 1.7608 1.6509
1.5413 1.4321 1.3233 1.2149 1.1069 0.9995 0.0080 0.6992
9.2586 9.2495 9.2426 9.2381 9.2358 9.2358 0.6980 1011.7443
2.4243 2.3207 2.2171 2.1135 2.0101 1.9069 1.8038 1.7010
1.5984 1.4962 1.3942 1.2927 1.1916 1.0910 0.0087 0.7380
9.7725 9.7639 9.7575 9.7532 9.7511 9.7511 0.7368 1096.0563
2.4243 2.3270 2.2296 2.1323 2.0352 1.9381 1.8413 1.7446
1.6482 1.5520 1.4562 1.3607 1.2655 1.1708 0.0094 0.7744
10.2553 10.2473 10.2412 10.2372 10.2352 10.2352 0.7734 1180.3683
2.4243 2.3325 2.2406 2.1489 2.0572 1.9656 1.8742 1.7829
1.6919 1.6011 1.5106 1.4204 1.3304 1.2409 0.0099 0.8088
10.7109 10.7033 10.6976 10.6938 10.6919 10.6919 0.8078 1264.6804
2.4243 2.3373 2.2504 2.1634 2.0766 1.9899 1.9033 1.8168
1.7306 1.6445 1.5587 1.4732 1.3879 1.3030 0.0104 0.8414
11.1424 11.1352 11.1298 11.1261 11.1243 11.1243 0.8405 1348.9923
2.4243 2.3417 2.2590 2.1764 2.0939 2.0115 1.9292 1.8470
1.7650 1.6832 1.6016 1.5203 1.4392 1.3583 0.0109 0.8724
11.5525 11.5456 11.5404 11.5370 11.5353 11.5353 0.8715 1433.3044
2.4243 2.3456 2.2668 2.1881 2.1095 2.0309 1.9525 1.8741
1.7960 1.7179 1.6401 1.5625 1.4852 1.4080 0.0113 0.9019

11.9432
2.4243
1.8239

12.3166
2.4243
1.8492

12.6743
2.4243
1.8723

13.0175
2.4243
1.8935

13.3475
2.4243
1.9130

13.6654
2.4243
1.9311

13.9721
2.4243
1.9478

14.2683
2.4243
1.9634

14.5548
2.4243
1.9780

14.8323
2.4243
1.9916

15.1013
2.4243
2.0044

15.3624
2.4243
2.0164

15.6159
2.4243
2.0277

15.8625
2.4243
2.0384

16.1023
2.4243
2.0486

16.3359
2.4243
2.0582

16.5634
2.4243
2.0673

16.7853
2.4243
2.0760

17.0018
2.4243
2.0843

17.2131
2.4243
2.0922

11.9367
2.3491
1.7493

12.3104
2.3523
1.7778

12.6682
2.3552
1.8037

13.0117
2.3578
1.8275

13.3420
2.3603
1.8495

13.6601
2.3625
1.8698

13.9669
2.3646
1.8886

14.2633
2.3666
1.9061

14.5500
2.3684
1.9224

14.8276
2.3701
1.9377

15.0968
2.3717
1.9521

15.3580
2.3733
1.9656

15.6117
2.3747
1.9784

15.8583
2.3760
1.9904

16.0982
2.3773
2.0018

16.3319
2.3785
2.0126

16.5596
2.3796
2.0229

16.7815
2.3807
2.0327

16.9981
2.3818
2.0420

17.2095
2.3828
2.0508

11.9317
2.2738
1.6749

12.3057
2.2802
1.7065

12.6637
2.2860
1.7353

13.0074
2.2913
1.7617

13.3378
2.2962
1.7860

13.6560
2.3008
1.8085

13.9630
2.3050
1.8294

14.2595
2.3089
1.8488

14.5464
2.3125
1.8670

14.8241
2.3160
1.8840

15.0934
2.3192
1.8999

15.3546
2.3222
1.9149

15.6084
2.3250
1.9291

15.8552
2.3277
1.9424

16.0952
2.3303
1.9551

16.3289
2.3327
1.9671

16.5567
2.3350
1.9785

16.7787
2.3371
1.9893

16.9953
2.3392
1.9997

17.2068
2.3412
2.0095

11.9285
2.1986
1.6007

12.3025
2.2082
1.6354

12.6607
2.2169
1.6670

13.0045
2.2249
1.6960

13.3350
2.2322
1.7227

13.6533
2.2390
1.7474

13.9604
2.2453
1.7704

14.2570
2.2512
1.7917

14.5439
2.2567
1.8116

14.8218
2.2618
1.8303

15.0911
2.2666
1.8478

15.3524
2.2711
1.8643

15.6063
2.2754
1.8798

15.8531
2.2794
1.8945

16.0932
2.2832
1.9084

16.3269
2.2868
1.9216

16.5547
2.2903
1.9341

16.7768
2.2936
1.9461

16.9935
2.2967
1.9574

17.2050
2.2996
1.9683

104

11.9268
2.1235
1.5267

12.3009
2.1362
1.5644

12.6592
2.1478
1.5989

13.0030
2.1585
1.6305

13.3336
2.1683
1.6596

13.6520
2.1773
1.6865

13.9591
2.1857
1.7114

14.2558
2.1935
1.7347

14.5427
2.2008
1.7564

14.8206
2.2077
1.7767

15.0899
2.2141
1.7958

15.3513
2.2201
1.8138

15.6052
2.2258
1.8307

15.8520
2.2311
1.8467

16.0921
2.2362
1.8619

16.3260
2.2411
1.8762

16.5538
2.2456
1.8899

16.7759
2.2500
1.9029

16.9926
2.2541
1.9152

17.2041
2.2581
1.9270

11.9268
2.0484
1.4529

12.3009
2.0643
1.4937

12.6592
2.0788
1.5310

13.0030
2.0921
1.5651

13.3336
2.1043
1.5966

13.6520
2.1156
1.6257

13.9591
2.1261
1.6527

14.2558
2.1359
1.6778

14.5427
2.1450
1.7013

14.8206
2.1536
1.7233

15.0899
2.1616
1.7439

15.3513
2.1691
1.7633

15.6052
2.1762
1.7817

15.8520
2.1829
1.7990

16.0921
2.1893
1.8154

16.3260
2.1953
1.8309

16.5538
2.2010
1.8457

16.7759
2.2064
1.8597

16.9926
2.2116
1.8731

17.2041
2.2166
1.8859

0.9010
1.9734
0.0116
0.9293
1.9925
0.0119
0.9563
2.0099
0.0122
0.9823
2.0258
0.0125
1.0072
2.0405
0.0128
1.0312
2.0540
0.0130
1.0544
2.0666
0.0132
1.0768
2.0783
0.0134
1.0985
2.0893
0.0136
1.1194
2.0995
0.0138
1.1398
2.1091
0.0139
1.1595
2.1181
0.0141
1.1787
2.1267
0.0142
1.1973
2.1347
0.0144
1.2154
2.1423
0.0145
1.2331
2.1495
0.0146
1.2503
2.1564
0.0148
1.2670
2.1629
0.0149
1.2834
2.1692
0.0150
1.2994
2.1751
0.0151

1517.6163
1.8986
0.9301

1601.9285
1.9208
0.9571

1686.2404
1.9410
0.9830

1770.5525
1.9596
1.0079

1854.8646
1.9767
1.0319

1939.1765
1.9925
1.0551

2023.4886
2.0072
1.0775

2107.8005
2.0208
1.0991

2192.1125
2.0336
1.1201

2276.4248
2.0455
1.1404

2360.7366
2.0567
1.1601

2445.0486
2.0672
1.1792

2529.3608
2.0772
1.1979

42613.6729

2.0865
1.2160
2697.9846
2.0954
1.2336
2782.2966
2.1039
1.2508
2866.6089
2.1119
1.2675
2950.9209
2.1195
1.2839
3035.2327
2.1267
1.2999
3119.5449
2.1336
1.3154

17.4195
2.4243
2.0998

17.6212
2.4243
2.1070

17.8184
2.4243
2.1139

18.0113
2.4243
2.1205

18.2001
2.4243
2.1269

18.3850
2.4243
2.1330

18.5660
2.4243
2.1389

18.7434
2.4243
2.1445

18.9173
2.4243
2.1500

19.0878
2.4243
2.1552

19.2550
2.4243
2.1603

19.4190
2.4243
2.1652

19.5801
2.4243
2.1699

19.7382
2.4243
2.1745

19.8934
2.4243
2.1789

20.0459
2.4243
2.1832

20.1957
2.4243
2.1874

20.3429
2.4243
2.1914

20.4877
2.4243
2.1953

20.6300
2.4243
2.1991

17.4160
2.3837
2.0593

17.6178
2.3846
2.0674

17.8151
2.3855
2.0752

18.0081
2.3863
2.0827

18.1969
2.3871
2.0898

18.3818
2.3879
2.0967

18.5629
2.3886
2.1033

18.7404
2.3893
2.1097

18.9143
2.3900
2.1158

19.0849
2.3907
2.1217

19.2521
2.3913
2.1274

19.4163
2.3919
2.1329

19.5773
2.3925
2.1382

19.7355
2.3931
2.1434

19.8907
2.3936
2.1483

20.0433
2.3942
2.1531

20.1932
2.3947
2.1578

20.3404
2.3952
2.1623

20.4852
2.3957
2.1667

20.6276
2.3961
2.1710

17.4134
2.3431
2.0189

17.6152
2.3449
2.0280

17.8126
2.3466
2.0366

18.0056
2.3483
2.0449

18.1945
2.3499
2.0528

18.3795
2.3514
2.0604

18.5606
2.3529
2.0678

18.7381
2.3543
2.0748

18.9121
2.3557
2.0816

19.0827
2.3570
2.0882

19.2500
2.3583
2.0945

19.4142
2.3595
2.1006

19.5753
2.3607
2.1065

19.7334
2.3618
2.1122

19.8888
2.3629
2.1178

20.0413
2.3640
2.1231

20.1912
2.3650
2.1283

20.3386
2.3660
2.1333

20.4834
2.3670
2.1382

20.6258
2.3680
2.1429

105

17.4116
2.3025
1.9786

17.6135
2.3052
1.9885

17.8109
2.3078
1.9980

18.0040
2.3103
2.0071

18.1929
2.3127
2.0158

18.3779
2.3150
2.0242

18.5591
2.3172
2.0323

18.7366
2.3193
2.0400

18.9106
2.3213
2.0475

19.0812
2.3233
2.0547

19.2486
2.3252
2.0617

19.4128
2.3271
2.0684

19.5739
2.3288
2.0749

19.7321
2.3306
2.0812

19.8874
2.3322
2.0872

20.0400
2.3338
2.0931

20.1900
2.3354
2.0988

20.3373
2.3369
2.1043

20.4821
2.3384
2.1097

20.6246
2.3398
2.1149

17.4107
2.2619
1.9383

17.6126
2.2655
1.9491

17.8100
2.2690
1.9595

18.0031
2.2723
1.9694

18.1921
2.2755
1.9789

18.3771
2.2785
1.9880

18.5583
2.2815
1.9968

18.7359
2.2843
2.0053

18.9099
2.2870
2.0134

19.0805
2.2897
2.0213

19.2479
2.2922
2.0289

19.4121
2.2947
2.0362

19.5732
2.2970
2.0433

19.7314
2.2993
2.0501

19.8868
2.3015
2.0567

20.0394
2.3037
2.0631

20.1893
2.3058
2.0693

20.3367
2.3078
2.0754

20.4815
2.3097
2.0812

20.6240
2.3116
2.0869

17.4107
2.2213
1.8981

17.6126
2.2258
1.9098

17.8100
2.2302
1.9210

18.0031
2.2343
1.9317

18.1921
2.2383
1.9420

18.3771
2.2421
1.9519

18.5583
2.2458
1.9614

18.7359
2.2493
1.9706

18.9099
2.2527
1.9794

19.0805
2.2560
1.9879

19.2479
2.2592
1.9961

19.4121
2.2623
2.0040

19.5732
2.2652
2.0117

19.7314
2.2681
2.0191

19.8868
2.2709
2.0263

20.0394
2.2735
2.0332

20.1893
2.2761
2.0399

20.3367
2.2786
2.0464

20.4815
2.2811
2.0528

20.6240
2.2835
2.0589

1.3150
2.1808
0.0152
1.3302
2.1862
0.0153
1.3451
2.1914
0.0154
1.3597
2.1963
0.0154
1.3740
2.2011
0.0155
1.3879
2.2057
0.0156
1.4016
2.2101
0.0157
1.4150
2.2144
0.0157
1.4282
2.2185
0.0158
1.4410
2.2224
0.0159
1.4537
2.2262
0.0160
1.4661
2.2299
0.0160
1.4782
2.2334
0.0161
1.4902
2.2369
0.0161
1.5019
2.2402
0.0162
1.5134
2.2434
0.0163
1.5247
2.2465
0.0163
1.5359
2.2495
0.0164
1.5468
2.2525
0.0164
1.5576
2.2553
0.0165

3203.8569
2.1402
1.3307

3288.1689
2.1466
1.3456

3372.4807
2.1526
1.3601

3456.7930
2.1584
1.3744

3541.1050
2.1640
1.3883

3625.4170
2.1693
1.4020

3709.7292
2.1745
1.4154

3794.0410
2.1794
1.4285

3878.3530
2.1842
1.4414

3962.6653
2.1888
1.4540

4046.9773
2.1932
1.4664

4131.2891
2.1975
1.4786

4215.6011
2.2017
1.4905

4299.9136
2.2057
1.5023

4384.2251
2.2095
1.5138

4468.5371
2.2133
1.5251

4552.8496
2.2169
1.5362

4637.1616
2.2205
1.5471

4721.4731
2.2239
1.5579

4805.7856
2.2272
1.5685

20.7700
2.4243
2.2027

20.9077
2.4243
2.2063

21.0431
2.4243
2.2098

21.1764
2.4243
2.2132

21.3076
2.4243
2.2164

21.4368
2.4243
2.2196

21.5640
2.4243
2.2227

21.6893
2.4243
2.2258

21.8126
2.4243
2.2287

21.9342
2.4243
2.2316

22.0539
2.4243
2.2344

22.1719
2.4243
2.2371

22.2882
2.4243
2.2398

22.4029
2.4243
2.2424

22.5159
2.4243
2.2450

22.6273
2.4243
2.2474

22.7372
2.4243
2.2499

22.8456
2.4243
2.2522

22.9526
2.4243
2.2546

23.0580
2.4243
2.2568

20.7676
2.3966
2.1751

20.9053
2.3971
2.1791

21.0408
2.3975
2.1830

21.1742
2.3979
2.1868

21.3054
2.3983
2.1905

21.4346
2.3987
2.1941

21.5618
2.3991
2.1976

21.6871
2.3995
2.2010

21.8105
2.3999
2.2043

21.9321
2.4002
2.2076

22.0519
2.4006
2.2107

22.1699
2.4009
2.2138

22.2862
2.4012
2.2168

22.4009
2.4016
2.2197

22.5140
2.4019
2.2226

22.6254
2.4022
2.2254

22.7354
2.4025
2.2281

22.8438
2.4028
2.2308

22.9507
2.4031
2.2334

23.0562
2.4034
2.2359

20.7658
2.3689
2.1475

20.9036
2.3698
2.1520

21.0391
2.3706
2.1563

21.1725
2.3715
2.1605

21.3037
2.3723
2.1646

21.4330
2.3731
2.1686

21.5602
2.3739
2.1725

21.6855
2.3747
2.1763

21.8089
2.3754
2.1799

21.9305
2.3761
2.1835

22.0503
2.3768
2.1870

22.1684
2.3775
2.1905

22.2847
2.3782
2.1938

22.3994
2.3788
2.1970

22.5125
2.3795
2.2002

22.6240
2.3801
2.2033

22.7340
2.3807
2.2064

22.8424
2.3813
2.2093

22.9494
2.3819
2.2122

23.0549
2.3824
2.2150

106

20.7646
2.3412
2.1199

20.9024
2.3425
2.1248

21.0379
2.3438
2.1296

21.1713
2.3451
2.1342

21.3026
2.3463
2.1387

21.4319
2.3475
2.1431

21.5591
2.3487
2.1474

21.6844
2.3498
2.1515

21.8079
2.3509
2.1556

21.9295
2.3520
2.1595

22.0493
2.3531
2.1634

22.1674
2.3541
2.1671

22.2838
2.3551
2.1708

22.3985
2.3561
2.1744

22.5116
2.3570
2.1779

22.6231
2.3580
2.1813

22.7330
2.3589
2.1846

22.8415
2.3598
2.1879

22.9484
2.3606
2.1911

23.0540
2.3615
2.1942

20.7640
2.3135
2.0924

20.9018
2.3152
2.0977

21.0374
2.3170
2.1029

21.1708
2.3187
2.1080

21.3021
2.3203
2.1129

21.4313
2.3219
2.1177

21.5586
2.3235
2.1223

21.6839
2.3250
2.1268

21.8074
2.3265
2.1313

21.9290
2.3279
2.1356

22.0488
2.3293
2.1398

22.1669
2.3307
2.1439

22.2833
2.3320
2.1479

22.3980
2.3333
2.1518

22.5111
2.3346
2.1556

22.6226
2.3358
2.1593

22.7326
2.3370
2.1629

22.8410
2.3382
2.1665

22.9480
2.3394
2.1699

23.0535
2.3405
2.1733

20.7640
2.2858
2.0649

20.9018
2.2880
2.0706

21.0374
2.2902
2.0763

21.1708
2.2923
2.0817

21.3021
2.2943
2.0870

21.4313
2.2963
2.0922

21.5586
2.2983
2.0973

21.6839
2.3002
2.1022

21.8074
2.3020
2.1069

21.9290
2.3038
2.1116

22.0488
2.3056
2.1162

22.1669
2.3073
2.1206

22.2833
2.3089
2.1249

22.3980
2.3106
2.1291

22.5111
2.3122
2.1333

22.6226
2.3137
2.1373

22.7326
2.3152
2.1412

22.8410
2.3167
2.1451

22.9480
2.3182
2.1488

23.0535
2.3196
2.1525

1.5681
2.2581
0.0165
1.5785
2.2607
0.0165
1.5888
2.2634
0.0166
1.5988
2.2659
0.0166
1.6088
2.2683
0.0167
1.6185
2.2707
0.0167
1.6281
2.2731
0.0168
1.6376
2.2754
0.0168
1.6469
2.2776
0.0168
1.6561
2.2797
0.0169
1.6651
2.2818
0.0169
1.6741
2.2839
0.0169
1.6828
2.2859
0.0170
1.6915
2.2878
0.0170
1.7000
2.2898
0.0170
1.7085
2.2916
0.0171
1.7168
2.2934
0.0171
1.7250
2.2952
0.0171
1.7330
2.2970
0.0172
1.7410
2.2987
0.0172

4990.0972
2.2304
1.5799

4974.4097
2.2335
1.5991

5059.7217
2.2366
1.5991

5143.033;
2.2395
1.6091

5227,3457
2.2424
1.6188

5311.6577
2.2452
1.6294

5395.9692
2.2479
1.6379

5490.2917
2.2506
1.6472

5564.5933
2.2531
1.6564

5648.9058
2.2557
1.6654

5733.2179
2.2591
1.6743

5917,5293
2.2605
1.6831

5901.9419
2.2629
1.6919

5986.1538
2.2651
1.7003

6070.4653
2.2673
1.7097

6154.7778
2.2695
1.7170

6239.0898
2.2716
1.7252

6323.4019
2.2737
1.7333

6407.7139
2.2759
1.7412

6492.0259
2.2777
1.7491

23.1621
2.4243
2.2590

23.2648
2.4243
2.2612

23.3661
2.4243
2.2633

23.4662
2.4243
2.2654

23.5649
2.4243
2.2675

23.6624
2.4243
2.2694

23.7586
2.4243
2.2714

23.8536
2.4243
2.2733

23.9474
2.4243
2.2752

24.0401
2.4243
2.2770

24.1316
2.4243
2.2788

24.2220
2.4243
2.2806

24.3113
2.4243
2.2823

24.3995
2.4243
2.2840

24.4867
2.4243
2.2857

24.5728
2.4243
2.2873

24.6579
2.4243
2.2889

24.7420
2.4243
2.2905

24.8251
2.4243
2.2921

24.9073
2.4243
2.2936

23.1603
2.4037
2.2384

23.2630
2.4039
2.2409

23.3644
2.4042
2.2433

23.4644
2.4045
2.2456

23.5632
2.4047
2.2479

23.6607
2.4050
2.2501

23.7569
2.4052
2.2523

23.8520
2.4054
2.2545

23.9458
2.4057
2.2566

24.0385
2.4059
2.2587

24.1300
2.4061
2.2607

24.2204
2.4064
2.2627

24.3098
2.4066
2.2646

24.3980
2.4068
2.2665

24.4852
2.4070
2.2684

24.5713
2.4072
2.2702

24.6564
2.4074
2.2721

24.7406
2.4076
2.2738

24.8237
2.4078
2.2756

24.9059
2.4080
2.2773

23.1590
2.3830
2.2178

23.2617
2.3835
2.2205

23.3631
2.3841
2.2232

23.4632
2.3846
2.2258

23.5619
2.3851
2.2283

23.6594
2.3856
2.2308

23.7557
2.3861
2.2333

23.8508
2.3866
2.2356

23.9446
2.3870
2.2380

24.0373
2.3875
2.2403

24.1288
2.3879
2.2425

24.2193
2.3884
2.2447

24.3086
2.3888
2.2469

24.3969
2.3892
2.2490

24.4841
2.3897
2.2511

24.5702
2.3901
2.2532

24.6553
2.3905
2.2552

24.7395
2.3909
2.2571

24.8226
2.3912
2.2591

24.9048
2.3916
2.2610

107

23.1581
2.3623
2.1972

23.2608
2.3631
2.2002

23.3622
2.3639
2.2031

23.4623
2.3647
2.2060

23.5611
2.3655
2.2088

23.6586
2.3662
2.2115

23.7549
2.3669
2.2142

23.8499
2.3677
2.2168

23.9438
2.3684
2.2194

24.0365
2.3691
2.2219

24.1281
2.3697
2.2244

24.2185
2.3704
2.2268

24.3078
2.3711
2.2292

24.3961
2.3717
2.2316

24.4833
2.3723
2.2338

24.5695
2.3729
2.2361

24.6546
2.3735
2.2383

24.7388
2.3741
2.2405

24.8219
2.3747
2.2426

24.9041
2.3753
2.2447

23.1577
2.3416
2.1767

23.2604
2.3427
2.1799

23.3618
2.3438
2.1831

23.4619
2.3448
2.1862

23.5607
2.3458
2.1892

23.6582
2.3468
2.1922

23.7545
2.3478
2.1952

23.8495
2.3488
2.1980

23.9434
2.3497
2.2008

24.0361
2.3506
2.2036

24.1277
2.3515
2.2063

24.2181
2.3524
2.2089

24.3075
2.3533
2.2115

24.3957
2.3541
2.2141

24.4829
2.3550
2.2166

24.5691
2.3558
2.2190

24.6543
2.3566
2.2214

24.7384
2.3574
2.2238

24.8216
2.3582
2.2261

24.9038
2.3589
2.2284

23.1577
2.3210
2.1561

23.2604
2.3223
2.1596

23.3618
2.3237
2.1631

23.4619
2.3250
2.1664

23.5607
2.3262
2.1697

23.6582
2.3275
2.1730

23.7545
2.3287
2.1761

23.8495
2.3299
2.1792

23.9434
2.3311
2.1823

24.0361
2.3322
2.1853

24.1277
2.3334
2.1882

24.2181
2.3345
2.1911

24.3075
2.3355
2.1939

24.3957
2.3366
2.1966

24.4829
2.3377
2.1993

24.5691
2.3387
2.2020

24.6543
2.3397
2.2046

24.7384
2.3407
2.2072

24.8216
2.3416
2.2097

24.9038
2.3426
2.2121

1.7489
2.3003
0.0172
1.7566
2.3020
0.0173
1.7643
2.3035
0.0173
1.7718
2.3051
0.0173
1.7793
2.3066
0.0173
1.7867
2.3081
0.0174
1.7939
2.3096
0.0174
1.8011
2.3110
0.0174
1.8082
2.3124
0.0174
1.8152
2.3138
0.0175
1.8221
2.3152
0.0175
1.8289
2.3165
0.0175
1.8357
2.3178

0.0175 ‘

1.8423
2.3191
0.0176
1.8489
2.3203
0.0176
1.8554
2.3216
0.0176
1.8619
2.3228
0.0176
1.8682
2.3239
0.0176
1.8745
2.3251
0.0177
1.8807
2.3263
0.0177

6576.3379
2.2797
1.7568

6660.6499
2.2816
1.7645

6744.9614
2.2834
1.7721

6829.2739
2.2853
1.7795

6913.5859
2.2870
1.7869

6997.8979
2.2888
1.7941

7082.2100
2.2905
1.8013

7166.5225
2.2922
1.8084

7250.8340
2.2938
1.8154

7335.1460
2.2954
1.8223

7419.4585
2.2970
1.8291

7503.7700
2.2985
1.8359

7588.0820
2.3001
1.8425

7672.3945
2.3016
1.8491

7756.7061
2.3030
1.8556

7841.0186
2.3044
1.8620

7925.3306
2.3059
1.8684

8009.6421
2.3072
1.8747

8093.9546
2.3086
1.8809

8178.2661
2.3099
1.8870

24.9885
2.4243
2.2951

25.0688
2.4243
2.2966

25.1482
2.4243
2.2980

25.2266
2.4243
2.2994

25.3042
2.4243
2.3008

25.3810
2.4243
2.3022

25.4569
2.4243
2.3035

25.5319
2.4243
2.3049

25.6061
2.4243
2.3062

25.6795
2.4243
2.3075

25.7521
2.4243
2.3087

25.8240
2.4243
2.3100

25.8950
2.4243
2.3112

25.9653
2.4243
2.3124

26.0349
2.4243
2.3136

26.1037
2.4243
2.3147

26.1718
2.4243
2.3159

26.2392
2.4243
2.3170

26.3058
2.4243
2.3181

26.3718
2.4243
2.3192

24.9871
2.4082
2.2790

25.0674
2.4084
2.2806

25.1468
2.4085
2.2822

25.2253
2.4087
2.2838

25.3029
2.4089
2.2854

25.3797
2.4091
2.2870

25.4556
2.4092
2.2885

25.5306
2.4094
2.2900

25.6048
2.4096
2.2914

25.6783
2.4097
2.2929

25.7509
2.4099
2.2943

25.8227
2.4100
2.2957

25.8938
2.4102
2.2971

25.9641
2.4103
2.2984

26.0337
2.4105
2.2997

26.1025
2.4106
2.3010

26.1706
2.4108
2.3023

26.2380
2.4109
2.3036

26.3047
2.4110
2.3049

26.3707
2.4112
2.3061

24.9861
2.3920
2.2629

25.0664
2.3924
2.2647

25.1458
2.3927
2.2665

25.2243
2.3931
2.2683

25.3019
2.3934
2.2700

25.3787
2.3938
2.2717

25.4546
2.3941
2.2734

25.5297
2.3944
2.2751

25.6039
2.3948
2.2767

25.6773
2.3951
2.2783

25.7500
2.3954
2.2799

25.8218
2.3957
2.2814

25.8929
2.3960
2.2829

25.9632
2.3963
2.2844

26.0328
2.3966
2.2859

26.1016
2.3969
2.2874

26.1697
2.3972
2.2888

26.2371
2.3975
2.2902

26.3038
2.3978
2.2916

26.3699
2.3980
2.2930

108

24.9854
2.3758
2.2467

25.0657
2.3764
2.2488

25.1451
2.3769
2.2507

25.2236
2.3775
2.2527

25.3013
2.3780
2.2546

25.3780
2.3785
2.2565

25.4539
2.3790
2.2583

25.5290
2.3795
2.2602

25.6033
2.3800
2.2620

25.6767
2.3805
2.2637

25.7493
2.3810
2.2654

25.8212
2.3814
2.2672

25.8923
2.3819
2.2688

25.9626
2.3823
2.2705

26.0322
2.3828
2.2721

26.1010
2.3832
2.2737

26.1692
2.3836
2.2753

26.2366
2.3841
2.2768

26.3033
2.3845
2.2784

26.3693
2.3849
2.2799

24.9850
2.3597
2.2306

25.0654
2.3604
2.2328

25.1448
2.3611
2.2350

25.2233
2.3618
2.2371

25.3009
2.3625
2.2392

25.3777
2.3632
2.2413

25.4536
2.3639
2.2433

25.5287
2.3646
2.2453

25.6029
2.3652
2.2472

25.6764
2.3659
2.2492

25.7490
2.3665
2.2510

25.8209
2.3671
2.2529

25.8920
2.3677
2.2547

25.9623
2.3683
2.2565

26.0319
2.3689
2.2583

26.1007
2.3695
2.2601

26.1689
2.3701
2.2618

26.2363
2.3706
2.2635

26.3030
2.3712
2.2651

26.3690
2.3717
2.2668

24.9850
2.3435
2.2146

25.0654
2.3444
2.2169

’25.1448

2.3453
2.2193
25.2233
2.3462
2.2216
25.3009
2.3471
2.2239
25.3777
2.3480
2.2261
25.4536
2.3488
2.2283
25.5287
2.3496
2.2304
25.6029
2.3505
2.2325
25.6764
2.3513
2.2346
25.7490
2.3520
2.2367
25.8209
2.3528
2.2387
25.8920
2.3536
2.2407
25.9623
2.3543
2.2426
26.0319
2.3551
2.2445
26.1007
2.3558
2.2464
26.1689
2.3565
2.2483
26.2363
2.3572
2.2501
26.3030
2.3579
2.2519
26.3690
2.3586
2.2537

1.8868
2.3274
0.0177
1.8929
2.3285
0.0177
1.8989
2.3296
0.0177
1.9048
2.3306
0.0178
1.9107
2.3317
0.0178
1.9165
2.3327
0.0178
1.9222
2.3337
0.0178
1.9279
2.3347
0.0178
1.9335
2.3357
0.0178
1.9390
2.3366
0.0179
1.9445
2.3376
0.0179
1.9499
2.3385
0.0179
1.9553
2.3394
0.0179
1.9606
2.3403
0.0179
1.9659
2.3412
0.0179
1.9711
2.3421
0.0180
1.9762
2.3430
0.0180
1.9813
2.3438
0.0180
1.9863
2.3446
0.0180
1.9913
2.3455
0.0180

8262.5781
2.3112
1.8931

8346.8906
2.3125
1.8991

8431.2021
2.3138
1.9050

8515.5146
2.3150
1.9109

8599.8271
2.3162
1.9167

8684.1387
2.3174
1.9224

8768.4502
2.3186
1.9280

8852.7627
2.3198
1.9337

8937.0742
2.3209
1.9392

9021.3867
2.3220
1.9447

9105.6992
2.3232
1.9501

9190.0107
2.3242
1.9555

9274.3232
2.3253
1.9608

9358.6348
2.3264
1.9660

9442.9463
2.3274
1.9712

9527.2588
2.3284
1.9764

9611.5713
2.3294
1.9815

9695.8838
2.3304
1.9865

9780.1943
2.3314
1.9915

9864.5068
2.3323
1.9964

109

26.4371 26.4360 26.4352 26.4346 26.4343 26.4343 1.9963 9948.8193

SHELF-LIFE OF THIS PRODUCT IS 10013.31445hr3

FORTRAN STOP

 

APPENDIX B

APPENDIX B
Sorption Experiment of Deltasone Tablet

Table 11. Summary of sorption experiments of 20 mg Deltasone

tablet at 25.0 ° C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

110

 

Test Number Ewmive Humidity I
Range (%) '
1 SORP 91 0 - 11.50 )
2 SORP 92 11.50 - 15.25 i
3 SORP 01 15.75 - 23.20 T
4 soap 02 23.20 - 27 l
5 SORP C3a 27.50 - 34.50 .
6 SORP C3b 36 - 4o ,
7 SORP 05 40.75 - 49.90 '
9 SORP 60 49.95 - 60.35 2
9 SORP 7Ca 60.70 - 66 g
10 sonp 7Cb 66 - 73.40 i
11 sonp 09 72.25 - 77.75 5
12 sonp 09 77.90 - 92.45 1
13 SORP 10 92.05 - 97.30
14 sonp 13 96.70 - 91.70 H
======L

111

Moisture sorption isotherm data for Deltasone
tablet at 25.0 ° 0

Table 12.

 

 

 

 

 

 

 

   

 

  

 

   

 

   

 

   

 

   

 

   

 

   

 

 

Absolute
Tablet Weight

0 407.7421 0 0 ,
0.115 409.2698 1.5277 0.375 H
0.153 409.35 1.6079 0.394
0.232 409.8798 2.1377 0.524
0.27 410.36 2.6179 0.642
0.345 410.593 2.8509 0.699
0.4 410.7729 3.0308 0.743
0.488 411.5429 3.8008 0.932
0.604 412.0246 4.2825 1.05
0.66 412.7226 4.9805 1.221
0.734 413.3085 5.5664 1.365
0.778 414.2913 6.5492 1.606
0.825 415.5057 7.7636 1.904
0.873 415.7983 8.0562 1.976
0.217 422.0713 14.3292

 

 

An = Water activity
= Equilibrium Moisture Content

EMC

 

 

 

    

Table 13. Comparison of experimental and calculated ngL for

112

tablet at 0 - 11.50% R.H. and 25.0 ° 0 with
determination of diffusion coefficient

Time
[ (hours)

meadows-0010940

 

 

Sum of diff. 1

0.427244
0.63193

0.73483

0.785625
0.819533
0.842836
0.859789
0.873208
0.883943
0.893042
0.900242
0.906592
0.911828
0.91641

0.920665
0.923545
0.924789
0.925313
0.923807
0.931138
0.948616
0.955227
0.960136
0.96354

0.967467
0.973555
0.975453
0.976239
0.979577
0.979053
0.980101
0.981606
0.984094
0.987039
0.990116
0.992996
0.995352
0.997185
0.998756

sum of the difference2 between exp.

 

Calculated
"/__

0
0.397925
0.540453
0.653264
0.739693
0.903099
0.951632
0.999202
0.915759
0.936523
0.952169
0.963959
0.972942
0.979536
0.99459

0.999391
0.991245
0.993403
0.995029
0.996254
0.997179
0.997973
0.999397
0.999792
0.99909

0.999314
0.999493
0.999611
0.999707
0.999779
0.999933
0.999975
0.999905
0.999929
0.999946
0.99996

0.99997

0.999977
0.999993
0.999997
0.99999

0.999992

T12

1.52
1.54
1.58
1.62
1.66
1.70
1.71
1.72
1.73
1.74
1.75
1.76

Diffusion
Coeff. =
0.004404
cmz/hour

 

 

um of ?

0.090486
0.089439
0.087708
0.086465
0.085695
0.085376
0.085365
0.085381
0.085422
0.085491
0.085587
0.085711

and calc.

Illillllllll

74
5

1.1

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

Mt/ Minf.

113

 

 

 

Ill-lllliiiil""""

 

0 ' 1 1 1 1

Figure 25 .

 

 

0 10 20 30 40

TIME (hours)
. Experimental _Calculated

tablet at o - 11.50% R.H. and 25.0 °<:

50

Comparison of experimental and calculated Mt/M_ for

(sonp 91)

114

 

1.1

Mt / Minf.

 

 

 

O 1 1 1
0 10 20 30 40
TIME (hours)

 

Figure 26. Experimental sorption of tablet at 11.50 - 15.25%
R.H., 25.0 ° 0 ($099 92)

115

 

Ll

IMt/Nfinfl

 

Figure 27.

 

 

l 1 I

10 20 30 40
TIME (hours)

Experimental sorption of tablet at 15.75 - 23.20%
R.H., 25.0 ° 0 ($014? 01)

116

 

0.6

9 P P
w A Ur

Ml: (Weight Gain, mg)
.°
N

0.1

 

 

 

0 l
0 50 100 150
TIME (hours)

Figure 28. Experimental tablet weight gain at 23.20 - 27%
R.H., 25.0 ° 0 (50129 02)

117

 

Nfl/hfinfi

 

 

 

0 1 1 1 1 1
0 S 10 15 20 25 30
TIME (hours)

 

Figure 29. Experimental sorption of tablet at 27.50 - 34.50%
R.H., 25.0 ° 0 (SORP C3a)

118

Table 14. Comparison of experimental and calculated MVGL for

tablet at 36 - 40% R.H.
determination of diffusion coefficient

and 25.0 ° C with

 

 

Time
(hours)

0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
5.25
5.5
5.75
6
6.25
6.5
6.75
7
7.25
7.5
7.75
8
8.25
8.5
8.75
9
9.25
9.5
9.75
10
10.25
10.5
10.75
11
11.25
11.5

 

Sum Of diff.z

 

Exp.
ll/M;

0
0.00603
0.022111
0.052261
0.088442
0.139698
0.18392
0.237186
0.281407
0.333668
0.38191
0.435176
0.478392
0.514573
0.539698
0.560804
0.584925
0.60804
0.634171
0.660302
0.681407
0.702513
0.731658
0.751759
0.769849
0.78995
0.80804
0.826131
0.842211
0.861307
0.870352
0.881407
0.895477
0.911558
0.923618
0.934673
0.950754
0.956784
0.970854
0.975879
0.972864
0.978894
0.98191
0.988945
1.001005
1.001005
1

 

Calculated
mm.

0
0.299699
0.31119
0.330029
0.353041
0.378209
0.404266
0.430419
0.456183
0.481267
0.505505
0.528809
0.551144
0.572502
0.592896
0.612352
0.630899
0.648573
0.66541
0.681446
0.696717
0.711258
0.725104
0.738286
0.750837
0.762787
0.774164
0.784995
0.795307
0.805124
0.814471
0.823369
0.831841
0.839906
0.847585
0.854895
0.861855
0.86848
0.874788
0.880794
0.886511
0.891954
0.897137
0.90207
0.906767
0.911239
0.915496

 

 

— 1
Tu: Sum of j
(hours) diff.2 i
2.10 0.761769 I
2.20 0.721649 !
2.30 0.695722 }
2.40 0.692954 :
2.45 0.69094 7
2.46 0.690994 i
2.47 0.690961 9
2.49 0.691131 1

i

I

l

i

Diffusion g
Coeff. = I
0.003061 1
cmz/hour :
i

I

j

Ji

i

j

l

I

}

r

l

l

1

E

i

l

i

i

l

!

—-_ i

= sum of the difference’ between exp. and calc.

119

 

 

1.2

Mt / Minf.

 

 

 

 

0 1 J 1 1 l 1
0 2 4 6 8 10 12 14
TIME (hours)
. Experimental _Calculated

Figure 30. Comparison of experimental and calculated lat/M. for
tablet at 36 - 40% R.H. and 25.0 ° 0 (SORP 03b)

Table 15. Comparison of experimental and calculated Mt/M. for

120

tablet at 40.75 - 49.90% R.H. and 25.0 ° 0 with

determination of diffusion coefficient

(hours)

P_.——________

35.5

 

I

 

0.27509
0.481551
0.573439
0.629289
0.668916
0.701795
0.728643
0.753625
0.775879
0.799569
0.819239
0.837904
0.861307
0.86748
0.865757
0.854559
0.856138
0.870065
0.884566
0.896482
0.903087
0.909404
0.916296
0.922757
0.927638
0.933094
0.938406
0.943862
0.950179
0.956927
0.964393
0.971285
0.979469
0.986648
0.996698
1

 

 

 

Sum of diff.2 = sum of the difference2 between exp. and calc.

Calculated

0.326579
0.39566

0.468999
0.536574
0.596435
0.648815
0.694469
0.734208
0.768785
0.798865
0.825032
0.847795
0.867597
0.884822
0.899807
0.912842
0.924181
0.934045
0.942626
0.95009

0.956583
0.962232
0.967145
0.97142

0.975138
0.978372
0.981186
0.983634
0.985763
0.987615
0.989227
0.990628
0.991847
0.992908
0.993831
0.994246

 

Tvz

Diffusion
Coeff. =
0.002170
cmz/hour

 

 

0.081304
0.080946
0.080942
0.080951
0.080981
0.081021

 

 

121

 

1.2

Mt/ Minf.

 

 

 

0 l l L
0 10 20 30 40
TIME (hours)

. Experimental _Calculated

 

Figure 31. Comparison of experimental and calculated Flt/M. for
tablet at 40.75-49.90% R.H. and 25.0 ° 0 (5099 05)

122

 

1.2

Mt/ Minf.

 

 

 

0 1 1 1 1 l 1
0 2 4 6 8 10 12 14
TIME (hours)

 

Figure 32. Experimental sorption of tablet at 48.85 - 60.35%
R.H., 25.0 ° 0 (SORP 6C)

123

Table 16. Comparison of experimental and calculated 131/u, for

 

 

 

tablet at 60.70 - 66% R.H.
determination of diffusion coefficient

'1‘"2 Sum of
"WW , _ __

__—
(hours) M /M. M /M.
0 0 0
0.5 0.00294 0.32929
1 0.191102 0.402445
1.5 0.407291 0.478689
2 0.542728 0.548098
2.5 0.633281 0.609038
3 0.696394 0.661967
3.5 0.742062 0.707786
4 0.776362 0.74741
4.5 0.804194 0.781665
5 0.828499 0.811275
5.5 0.849667 0.83687
6 0.868091 0.858994
6.5 0.884555 0.878117
7 0.899647 0.894647
7.5 0.912191 0.908935
8 0.924735 0.921286
8.5 0.935711 0.931961
9 0.945708 0.941189
9.5 0.957076 0.949165
10 0.966484 0.956059
10.5 0.97452 0.962018
11 0.982556 0.96717
11.5 0.988436 0.971622
12 0.989808 0.975471
12.5 0.988044 0.978797
13 0.988044 0.981673
13.5 0.990004 0.984158
14 0.996472 0.986307
14.5 1 0.988164

 

and 25.0

1.60
1.64
1.65
1.66
1.67
1.68
1.70

Diffusion

Coeff. =
0.004536
cm3/hour

O

 

 

 

Sum of diff.2

sum of the difference2

between exp.

C wi

0.164457
0.16293
0.16278
0.162713
0.162736
0.162847
0.16333

1

1

and calc.

124

 

1.2

Mt / Minf.

 

 

 

0 l 1 1
0 5 10 15 20
TIME (hours)

. Experimental _Calculated

 

Figure 33. Comparison of experimental and calculated Mt/M, for
tablet at 60.70 - 66% R.H. and 25.0 ° c (soap 7Ca)

125

Table 17. Comparison of experimental and calculated M /H_ for
tablet at 66 - 73.40% R.H. and 25.0 ° c with

determination of diffusion coefficient

 

 

Calculated T

12
(hours)

M/H.

 

 

 

Sum of diff.2

0.003256
0.092716
0.224507
0.341902
0.435476
0.511397
0.572408
0.622451
0.665124
0.701971
0.732648

0.75904
0.782519
0.802742

0.81988
0.836675
0.850386
0.864096
0.876435
0.887746
0.898543
0.907798
0.917224
0.924764
0.931962
0.938646
0.944987
0.951157
0.956641
0.962639
0.967952
0.973093
0.978406
0.982862
0.987318
0.991945
0.995716
0.998972
1.001371
1.002742
0.991602
1.002913
1.002057

 

 

 

0
0.309764
0.34859
0.397027
0.446755
0.494451
0.538918
0.579853
0.617315
0.651507
0.682674
0.711067
0.736924
0.76047
0.78191
0.801431
0.819205
0.835388
0.850122
0.863538
0.875753
0.886874
0.897
0.90622
0.914614
0.922257
0.929216
0.935552
0.941321
0.946573
0.951355
0.95571
0.959674
0.963284
0.96657
0.969563
0.972287
0.974768
0.977026
0.979083
0.980955
0.98266
0.984212
0.985625
0.986912

1.27
1.28
1.29
1.30
1.36
1.40

0.2142
0.213818
0.213665
0.213742
0.218822
0.226393

 

 

1.43 0.234163
1.46 0.243604

Diffusion
Coeff. =
0.005837
cmz/hour

 

 

sum of the difference2 between exp. and calc.

126

 

1.2

Mt / Minf.

 

 

 

0 1 1 1 I 1

 

0 2 4 6 8 10 12
TIME (hours)

. Experimental _Calculated

Figure 34. Comparison of experimental and calculated 11./M. for
tablet at 66 - 73.40% R.H. and 25.0 ° c (SORP 7Cb)

Table 18. Comparison of experimental and calculated Mvflg for

127

 

 

 

 

 

 

tablet at 72.25 - 77.75% R.H. and 25.0 ° c with
determination of diffusion coefficient
l Time Exp. Calculated T12 Sum of
(hours) M /M_, M /M, (hours) diff.2
0 0 0 1.60 0.051542
0.5 0.126425 0.329647 1.64 0.050668
1 0.332308 0.403324 1.65 0.050656
1.5 0.47819 0.479935 1.66 0.050726
2 0.569321 0.549571 1.68 0.051105
2.5 0.637466 0.610642 1.70 0.051804
3 0.691493 0.663634 1.72 0.052799
3.5 0.733032 0.709468
4 0.768597 0.749071
4.5 0.800271 0.783279
5 0.823077 0.812825 Diffusion
5.5 0.842896 0.838344 Coeff. =
6 0.85991 0.860383 0.004564
6.5 0.874299 0.879417 cmz/hour
7 0.886787 0.895857
7.5 0.897738 0.910055
8 0.907692 0.922318
8.5 0.920271 0.932908
9 0.93276 0.942055
9.5 0.942443 0.949955
10 0.949955 0.956778
10.5 0.95629 0.962671
11 0.9619 0.96776
11.5 0.967149 0.972155
12 0.971222 0.975952
12.5 0.975837 0.97923
13 0.979457 0.982062
13.5 0.982624 0.984507
14 0.985068 0.98662
14.5 0.987692 0.988444
15 0.990407 0.990019
15.5 0.992489 0.99138
16 0.994842 0.992555
16.5 0.997014 0.99357
17 0.999548 0.994447
17.5 1.001448 0.995204
17.75 1 0.995543

 

Sum of diff.’

= sum of the difference’ between exp. and calc.

 

128

 

1.2

Mt / Minf.

 

 

 

0 1 1 1
0 5 10 15 20
TIME (hours)

 

Figure 35. Experimental sorption of tablet at 72.25 - 77.75%
R.H., 25.0 ° c (soap ca)

129

Table 19. Comparison of experimental and calculated MVQL for
tablet at 77.90 - 82.45% R.H. and 25.0 ° c with
determination of diffusion coefficient

 

 

 

 

 

 

 

 

Calculated
M/M.
0 O 0 1.25 0.074536
0.5 0.191391 0.347156 1.30 0.0726
1 0.337666 0.443662 1.31 0.072598
1.5 0.453808 0.534866 1.32 0.072723
2 0.557202 0.61278 1.35 0.073829
2.5 0.645778 0.677956 1.40 0.078014
3 0.720778 0.732221 1.45 0.084958
3.5 0.782368 0.777354 1.50 0.094519
4 0.831871 0.814882
4.5 0.871109 0.846085
5 0.90505 0.872028
5.5 0.932781 0.893599 Diffusion
6 0.953808 0.911533 Coeff. =
6.5 0.969619 0.926445 0.005748
7 0.981043 0.938843 cm1/hour
7.5 0.991142 0.949152
8 0.999338 0.957723
8.5 1.004636 0.964849
9 1.008692 0.970774
9.5 1.012169 0.9757
10 1.015563 0.979796
10.5 1.019123 0.983201
11 1.021689 0.986033
11.5 1.023179 0.988387
12 1.024338 0.990345
12.5 1.022599 0.991972
13 1.020033 0.993325
13.5 1.017881 0.99445
14 1.015811 0.995386
14.5 1.013162 0.996164
15 1.009272 0.99681
15.5 1.007036 0.997348
16 1.004884 0.997795
16.5 1.00207 0.998167
16.75 1 0.998328

 

Sum of diff.2

sum of the difference”

between exp. and calc.

 

130

 

1.2

11 ...-IIIIIIIIIIII

Mt/ Minf.

 

 

l l

10 15 20
TIME (hours)

. Experimental _Calculated

 

Figure 36. Comparison of experimental and calculated Mt/M. for
tablet at 77.90-82.45% R.H. and 25.0 ° c (SORP C9)

131

Table 20. Comparison of experimental and calculated Mvflg for
tablet at 82.05 - 87.30% R.H. and 25.0 ° c with
determination of diffusion coefficient

 

 

 

Calculated
M/M.
0 0 0 2.08 0.038614
1 0.215121 0.37013 2.09 0.038574
2 0.439014 0.490327 2.10 0.038571
3 0.577833 0.593975 2.11 0.038603
4 0.670774 0.677335 2.15 0.039101
5 0.741994 0.74368 2.20 0.040502
6 0.799151 0.796395 2.25 0.042795
7 0.845725 0.838271 2.30 0.045849
8 0.883111 0.871534
9 0.913464 0.897956
10 0.938179 0.918944
11 0.959343 0.935615 Diffusion
12 0.975494 0.948857 Coeff. =
13 0.989 0.959376 0.003585
14 0.999582 0.967731 cm3/hour
15 1.004107 0.974368
16 1.006892 0.97964
17 1.007449 0.983827
18 1.007519 0.987153
19 1.007937 0.989796
20 1.009816 0.991894
21 1.012531 0.993561
22 1.013854 0.994886
23 1.015664 0.995938
24 1.020955 0.996773
25 1.024854 0.997437
26 1.02374 0.997964
27 1.021791 0.998383
28 1.01817 0.998715
29 1.013436 0.99898
30 1.008911 0.999189
31 1.005569 0.999356
32 1.001184 0.999489
32.25 1 0.999517

 

 

 

 

 

Sum of diff.2

sum of the difference’

between exp. and calc.

 

132

 

1.2

Mt / Minf.

 

 

 

 

0 1 1 1 1 1 1
0 5 10 15 20 25 30 35
TIME (hours)
. Experimental _Calculated

Figure 37. Comparison of experimental and calculated Mt/M. for
tablet at 82.05-87.30% R.H. and 25.0 ° C (SORP 10)

133

 

1.2

Mt / Minf.

 

 

 

0 1 1 1 1 1 1

 

0 5 10 15 20 25 30 35
TIME (hours)

Figure 38. Experimental sorption of tablet at 86.70 - 91.70%
R.H., 25.0 ° c (SORP 13)

APPENDIX C

APPENDIX C

Sorption Experiment of PVC Film

 

 

 

 

Table 21. Summary of sorption experiments of PVC film at
25.0 ° c

Test Number Experimental Test Relative Humidity
Range (%)
1 SORP P1 0 - 26.90

2 SORP P2 26.65 - 43.50

3 SORP P3 43.50 - 58.20
4 SORP P4 58.20 - 77

 

 

 

 

 

 

     

   
 
       

Table 22. Moisture sorption isotherm data for PVC film at
25.0 ° c
AH Absolute EMC Calc. EMC
Film Weight (g 1120/ (g 1120/
Weight Change 100 g dry 100 g dry
product) product)

   
      

0 193.9691

 

 

 

 

 

 

M

 

A = Water activity

EMC = Equilibrium Moisture Content
= Calculated

Calc.

134

 

 

0.269 194.0393 0.0702 0.036 0.046
0.435 194.1173 0.1482 0.076 0.074
0.582 194.1622 0.1931 0.1 0.099
0.77 194.2264 0.2573

 

135

Table 23. Comparison of experimental and calculated M,fig for
PVC film at 0 - 26.90% R.H. and 25.0 ° c wit
determination of diffusion coefficient

h

 

 

 

Exp. Calculated
0 0 0 0.74 0.040469
0.5 0.373219 0.39354 0.80 0.03044
1 0.586895 0.532911 0.82 0.029135
1.5 0.696581 0.644594 0.84 0.027906
2 0.762108 0.729935 0.86 0.027173
2.5 0.806268 0.794814 0.026994
3 0.847578 0.844109 0.026993
3.5 0.873219 0.881561 0.02709
4 0.894587 0.910016 0.02729
4.5 0.908832 0.931635
5 0.911681 0.948059
5.5 0.924501 0.960538
6 0.930199 0.970019 Diffusion
6.5 0.935897 0.977222
7 0.935897 0.982694
7.5 0.950142 0.986852 cmz/hour
8 0.951567 0.990011
8.5 0.954416 0.992411
9 0.958689 0.994234
9.5 0.960114 0.995619
10 0.962963 0.996672
10.5 0.972934 0.997471
11 0.974359 0.998079
11.5 0.977208 0.99854
12 0.981481 0.998891
12.5 0.987179 0.999157
13 0.992877 0.99936
13.5 0.994302 0.999514
14 0.998575 0.999631
14.5 0.994302 0.999719
15 1.002849 0.999787
15.5 1.005698 0.999838
16 1.008547 0.999877
16.5 1.012821 0.999906
17 1.014245 0.999929
17.5 1.01567 0.999946
18 1.004274 0.999959
18.5 1 0.999969 J

 

 

 

 

 

Sum of diff.2

sum of the difference2 between exp. and calc.

 

136

 

1.2

   

 

 

 

 

0.8
:5
E 0.6
E

0.4

0.2

0 1 1 1
0 5 10 15 20
TIME (hours)
. Experimental _Calculated

Figure 39. Comparison of experimental and calculated Mt/M. for
pvc film at 0 - 26.90% R.H. and 25.0 ° c (SORP P1)

137

 

1.2

Mt / Minf.

 

 

 

L l l l l l

10 20 30 40 50 60 70
TIME (hours)

9-

Figure 40. Experimental sorption of PVC film at 26.65-43.50%
R.H., 25.0 ° c (SORP P2)

138

 

1.4

1.2 —

0.8 ~

Mt/ Minf.

0.6 r

0.4

0.2

 

 

 

0 i 1 1 1 1 1
0 10 20 30 40 50 60

TIME (hours)

Figure 41. Experimental sorption of PVC film at 43.50-58.20%
R.H., 25.0 ° c (SORP pa)

139

Table 24. Comparison of experimental and calculated Mvflg for
PVC film at 58.20 - 77% R.H. and 25.0 ° c with

 

l

determination of diffusion coefficient

a) \l O) U! ab U N H
0 0 O O O O O O
UI‘OUIQUIQWGUWUIhMUUINUII-‘kflo

)0
H.
O

..-
O
U!

H
..-

11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
16.5
17
17.5
18
18.5
19
19.5
20
20.5
21
21.5
22
22.5
23
23.5

 

Sum of diff.2

Exp.
M/M.

0
0.203288
0.439462
0.596413
0.699552
0.769806
0.814649
0.849028
0.877429
0.896861
0.910314
0.920777
0.932735

0.93722
0.944694
0.947683
0.949178
0.950673
0.964126
0.971599
0.980568
0.979073
0.980568
0.989537
0.995516

1.00299
1.008969
1.017937
1.025411
1.029895
1.035874
1.037369
1.037369
1.037369
1.037369
1.028401
1.019432
1.010463
1.010463
1.007474

1.00299
1.007474
1.004484
1.001495
1.008969
1.014948
1.010463

1

 

 

Calculated

M/M.

0
0.365588
0.48154
0.583157
0.665774
0.73214
0.785346
0.827985
0.862155

.0.889537

0.91148
0.929064
0.943155
0.954447
0.963496
0.970747
0.976558
0.981215
0.984946
0.987937
0.990333
0.992253
0.993792
0.995025
0.996013
0.996805

0.99744
0.997949
0.998356
0.998683
0.998944
0.999154
0.999322
0.999457
0.999565
0.999651

0.99972
0.999776

0.99982
0.999856
0.999885
0.999908
0.999926
0.999941
0.999952
0.999962
0.999969
0.999976

 

1.14

Diffusion
Coeff. =
1.62 E -05
cm1/hour

 

sum of the difference2 between exp.

Sum of
diff.2

 

0.048983
0.048705
0.048296
0.048169
0.048075
0.048112
0.049606

1

——a

and calc.

140

 

1.2

Mt/ Minf.

 

 

 

0 1 1 1 1
0 5 10 15 20 25

TIME (hours)

 

Figure 42. Experimental sorption of PVC film at 58.20-77%
R.H., 25.0 ° c (SORP p4)

APPENDIX D

APPENDIX D

Sorption Experiment of Acler Film

Table 25.

Summary of sorption experiments of Aclar film at
25.0"c

 

 

Test Number

Experimental Test

Relative Humidity

 

 

 

 

Range (%)
1 SORP L2 0 - 27.35
2 SORP L4 27.35 - 43.50 I
3 SORP L6 43.50 - 58 I
4 SORP L7 58 - 74.45 I

 

 

 

Table 26.

Moisture sorption isotherm data for Aclar film at
25.0 C

fl

 

 

 

 

 

1?=-===-F_l—=====—-_ - » - , , 77% ~ ‘
AH Absolute Film EMC Calc. EMC
Film Weight (g 1120/ (g 1120/
Weight Change 100 g dry 100 g dry ‘
1 (mg) (mg) product) product)_;
0 50.7371 0 0 0.003
0.274 50.7649 0.0278 0.055 0.054
0.435 50.7797 0.0426 0.084 0.083
0.58 50.7983 0.0612 0.121 0.11
0.745 50.8034 __19:0§§§__ ‘ ¥_0.131 0'14- 1
An = Water activity
EMC = Equilibrium Moisture Content
Calc. = Calculated

 

 

 

141

 

 

 

142

 

1.2

Mt / Minf.

 

 

 

 

0 1 1 1 1 1
0 5 10 15 20 25 30
TIME (hours)

Figure 43. Experimental sorption of Aclar film at 0 - 27.35%
R.H., 25.0 ° c (SORP L2)

143

Table 27. Comparison of experimental and calculated Mot/M. for
Aclar film at 27.35 - 43.50% R.H. and 25.0 C with

determination of diffusion coefficient

 

 

 

 

 

 

 

Calculated
M/M.
0 0 0 0.50 0.089474
0.25 0.422857 0.348129 0.52 0.077926
0.5 0.508571 0.445762 0.55 0.064347
0.75 0.594286 0.53762 0.58 0.053588
1 0.657143 0.615863 0.61 0.048002
1.25 0.737143 0.681165 0.64 0.045094
1.5 0.754286 0.735422 0.65 0.044979
1.75 0.777143 0.780456 0.66 0.045197
2 0.811429 0.817827 0.67 0.045868
2.25 0.828571 0.848837
2.5 0.822857 0.874568
2.75 0.84 0.895919
3 0.845714 0.913636 Diffusion
3.25 0.868571 0.928337 Coeff. =
3.5 0.891429 0.940536 1.21 E -06
3.75 0.908571 0.950658 cm3/hour
4 0.931429 0.959057
4.25 0.942857 0.966026
4.5 0.954286 0.971809
4.75 0.965714 0.976608
5 0.988571 0.98059
5.25 1.011429 0.983894
5.5 1.011429 0.986636
5.75 1.022857 0.98891
6 1.028571 0.990798
6.25 1.022857 0.992365
6.5 1.011429 0.993664
6.75 0.994286 0.994743
7 1 0.995638
7.25 1.017143 0.99638
7.5 1.017143 0.996996
7.75 1.017143 0.997508
8 1.011429 0.997932
8.25 1 0.998284

 

Sum of diff.’ =

sum of the difference2 between exp. and calc.

 

 

144

 

1.2

Mtl Minf.

 

 

 

 

0 1 1 1 1 1 1 1 1
0 1 2 3 4 5 6 7 8 9
TIME (hours)
. Experimental _Calculated

Figure 44. Comparison of experimental and calculated Mt/M, for
Aclar film at 27.35-43.50% R.H., 25.0 ° c (SORP L4)

145

Table 28. Comparison of experimental and calculated Mt/M.I for

Aclar film at 43.50 - 58% R.H.
determination of diffusion coefficient

 

Tvz

and 25.0 ° C with

 

 

 

E
Calculated
0 0 0
0.25 0.485577 0.454602
0.5 0.644231 0.628646
0.75 0.735577 0.748548
1 0.826923 0.829778
1.25 0.860577 0.884768
1.5 0.903846 0.921994
1.75 0.932692 0.947194
2 0.971154 0.964253
2.25 0.990385 0.975801
2.5 0.995192 0.983618
2.75 1.004808 0.98891
3 1.009615 0.992493
3.25 1.004808 0.994918
3.5 1.009615 0.99656
3.75 1 0.997671
4 1 0.998423
—

 

 

 

Sum of diff.2

Diffusion
Coeff. =

2.53 E -06

cmz/hour

 

0.02068
0.010792
0.004109
0.00372
0.004I5
0.005298

 

= sum of the difference“ between exp. and calc.

146

1.2

 

Mt/ Minf.

 

 

 

 

0 1 1 J 1
0 1 2 3 4 5
TIME (hours)

Figure 45. Experimental sorption of Aclar film at 43.50 - 58%
R.H., 25.0 ° c (SORP L6)

147

 

1.5

Mt/ Minf.

 

 

 

 

0 L 1 4 1 1
0 0.5 1 1.5 2 2.5 3
TIME (hours)

Figure 46. Experimental sorption of Aclar film at 58 - 74.45%
R.H., 25.0 ° c (SORP L7)

APPENDIX E

APPENDIX E

Water Vapor Transmission Rate and Permeability of Materials

 

 

 

 

 

 

 

 

 

 

 

 

WVTR = Water Vapor Transmission Rate (g / 102 day)

Perm. =

Permeability (g mil / m2

Area of dish = 0.00608 m2

148

 

 

day mmHg)

 

Table 29. WVTR and Permeability of blister materials at
37.78 ° c and 85% R.H. (Dish Method)
Weight
Gain
(grams) ___ __ ‘__ 1.1 _ k __
Pkg. 7 days 21.days 35 days WVTR Perm. f
Mat'l. ____________________l____i____
Aclar 1 0.0426 0.086 0.1099 0.5163 0.0196 ‘
Aclar 2 0.0097 0.0264 0.0471 0.2213 0.00838
Aclar 3 0.0063 0.0271 0.0457 0.2147 0.00813
l
PVC 1 0.0554 0.1144 0.1622 0.762 0.135
PVC 2 0.0496 0.1114 0.165 0.7751 0.138
PVC 3 0.0536 0.1088 0.1562 0.7338 0.13
I
PVC/Aclar1 0.006 0.0196 0.0354 0.1663 0.0358
PVC/AclarZ 0.005 0.0156 0.0334 0.1569 0.0338
PVC/Aclar3 0.0655 0.1275 0.1677 0.7878 0.17

 

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