Design of an Apparatus to Measure Gas Solubilities in Polymers

185 Pages·2002·7.84 MB·English

Design of an Apparatus to Measure Gas
Solubilities in Polymers
Esther V. Richards
A thesis submitted in conformity with the requlrements
for the Degree of Master of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
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Design of An Apparatus To Measure Gas Solubilities In Polymers
Esther V. Richaràs
Degree of Master of Applieà Science, 2001
Department of Mechanical and Industrial Engineering
University of Toronto
The design for an apparatus to measure the solubility of gases in polymers is
presented. The apparatus is based on a pressure decay method. and utilizes a threethamber
configuation for achieving multiple experimental pressures with the same sample. The
design was tested using polystyrene (PS) and (CO2) at temperatures of 100 and 160 OC and
pressures up to 12 MPa. The pressure-specific volume-temperature (PVT) data of the PS-
CO2 combination were used to correct the solubility data for the swelling effect of the
polymer. The results indicated that the solubility increased with increasing pressure and
decreased with increasing temperature. However. the data did not compare favorably with
the literature, since the typical Henry's law behavior was not observed. The main source of
error was believed to be due to the pressure transducer setup in which the transducer, because
of its limited tempenture range, was placed extemai to the main experimental setup.
To
my beloved parents:
Thank You,
for your wisdom and guidance
over the years.
Thank You,
for your support.
Thank You,
for your unconditional love.
Thank you,
for king my parents.
Thank you.
iii
ACKNOWLEDGEMENTS
First and foremost, 1 would like to express my thanks to God. Who provided me
with the opportunity to obtain my Master's Degree. 1 thank You for Your continued
blessings and for Your promise, that You'll never put more on me than I cmb ear. To my
family at home, 1 would like to say "thank you" for your continuous love and advice.
May God bless you dl.
This thesis has afforded me a unique leaming opportunity, for which 1 am grateful
to my supervisor. Thank you Prof. Park for your vision, guidance and never-ending
patience. I would also like to express my sincere thanks to Prof. Sinclair for his
continuous support.
Throughout my stay ai the University of Toronto, 1 have also had the honor of
working with the best machinists. Thank you Mark, Patrick, Dave, Mike, and Jeff. 1
could not accomplish half of what 1 did, if it were not for your brilliance.
To Mary-Rose, Teresa, and Sheila in the Receiving Department, thank you for your
patience. Your always-kind reception made my studies a much more pleasant
experience.
Finally to my colleagues at the Microcellular Plastics Manufacturing Lab., it was a
distinct pleasure working with you al]. 1 am especially indebted to Hani, Linda, Patrick,
and Ghaus for your friendship, advice and silent support over the two yeûrs. To
Qingping, thank you for your assistance in the final days-1 could not have finished
without your help.
TABLE OF CONTENTS
..
.............................................................................................................................
ABSTRACT II
...
Dedication ................................................................................................................................III
..................................................................................................................
Acknowledgments iv
......................................................................................................................
Table of Contents v
...
..........................................................................................................................
List of Tables VIII
..........................................................................................................................
List of Figures ix
..
..........................................................................................................................
Nomenclature
XII
Chapter 1: INTRODUCTION
............................................................................................................
1.1 Preamble 1
.................................................................................................
1.2 Foam Processing 3
.......................................................................
1.2.1 Microcellular Processing 3
.................................................................
1.2.2 Physical Blowing Agents 5
............................................................
1.3 Thesis Objectives and Scope of Research 6
...............................................................................................
1.4 Thesis Structure 8
Chapter 2: LITERATURE SURVEY AND THEORETICAL BACKGROUND
............................................................................................................
2.1 Solubility II
.....................................................................
2.1.1 Ideal Sorption Isotherms 11
.............................................................
2.1.2 Non-ldeal Sorption Isotherrns 12
......................................................................
2.2 Solubility Measurement Meihods 14
.........................................................
2.2.1 Gravimetric Sorption Technique 15
...................................................
2.2.2 Pressure Decay Sorption Technique 16
....................................................
2.2.3 Volume Decay Sorption Technique 20
...........................................................
2.2.4 Piezoelectric Quartz Sorption 2 1
..............................................
2.2.5 In-Line Measurement of Gas Solubility 23
...................................................................................
2.3 Physicd Blowing Agents 27
.......................................................................................
2.4 Theoretical Treatments 29
Chapter 3: PROBLEM STATEMENT AND PROPOSED DESIGN
............................................................................................................
Overview 35
........................
Principle of Solubility Measurement (Pressure Decay Method) 35
...........................................................
Problem Statement and Overall Strategy 39
.................................................................
3.3.1 Effect of Poly mer Dilation 3 9
..................................................
Background on Axiomatic Design Approach 4 4
.........................................................
Axiomatic Design of the Overall Process 4 6
...............................................................................................
3.5.1 Design 1 46
3.5.2 Design II ..............................................................................................4 7
............................................................................................................
Summary 53
Chapter 4: DETAILED DESIGN
.......................................................................................................
4.1 Overview 5 6
................................................................................
4.2 Pre-solu bility Calculations 5 6
......................................................................
4.2.1 Theoretical Sample Size 56
........................................................................
4.2.2 Sorption Cell Size 6 0
I .......................................................................
4.2.3 Thennostatted Oil Bath 64
...................................................................................
4.2.4 Vacuum System 66
.....................................................................................
4.3 Solubility Calculations 67
............................................................................................................
4.4 Summary 69
Chapter 5: EXPERIMENTAL
........................................................................................................
Overview 8 3
..............................................................................
Experimental Apparatus 8 3
......................................................................................
Experimental Materials 87
.....................................................................................
Experimental Procedure 8?
.......................................................................
5.4.1 Volume Measurements 8 7
..........................................................................
5.4.2 Sorption Experiments 88
......................................................................................
Results and Discussion 9 1
....................................................................................................
Error Analysis 93
...................................................
5.6.1 Erron in Temperature Measurement 93
....................................................
5.6.2 Emrs in Pressure Measurement 9 4
vi
..............................................
5.6.3 Errors due to Transducer Configuration 94
Chapter 6: SUMMARY. CONCLUSIONS AND FUTURE WORK
..........................................................................................................
6.1 Summary 107
......................................................................................................
6.2 Conclusions 108
.....................................................................................................
6.3 Future Work 109
....................................................................................................................
REFERENCES 111
vii
Table 3.1 Parameters for calculating PiA and PIB.. ....................................................5 4
Table 4.1 Parameters for calculating the pressure drop due to
...............................................................................
diffennt sample sizes 7 1
..............................................
Table 4.2 Parameters for calculating chamber thickness 7 2
................................... . ...........
Table 4.3 Properties of air and Heat Transfer Fhid 7 3
............................................
Table 4.4 Parameters for determining the heating capacity 74
..................................................................
Table 5.1 High-pressure chamber volumes 9 7
.....................................................................
Table 5.2 Experimental Solubility Data 9 8
...........................................................
Table 5.3 Error contribution of externd volume 9 9
viii
LIST OF FIGURES
.....................................................................
Figure 1.1 Microcellular foam production 10
............
Figure 2.1 Schematic representation of sorption isotherms in rubbery pol ymers 32
...............
Figure 2.2 Schematic representation of sorption isotherms in glassy polymers 32
............................................................................
Figure 2.3 Schematic of electrobalance 33
.................
Figure 2.4 Schematic diagram of the piezoelectric-quartz sorption apparatus 33
...........................................................
Figure 2.5 Basic Principle of ultrasonic technique 34
......................
Figure 3.1 Schematic of pressure decay method based on three Chambers 55
Figure 4.1 Schematic for determining the pressure drop due to solubility
...........................................................................
for different VpNc ratios 7 5
. .....
Figure 4.2 Relative sample size vs pressure drop due to 0.94% solubility at 140 75
O C
...................................................
Figure 4.3 Determination of relative sorption cell sizes 76
. . .................
Figure 4.4 Stepwise Pressure Increase vs Iteration No for 4 chamber ratios 76
Figure 4.5 Stepwise Pressure Increase vs . Iteration No . for 7 chmber ratios ................. 77
...........................................
Figure 4.6 Detailed schematic of high-pressure chamber #I 78
Figure 4.7 Detailed schematic of high-pressure chamber #2 and
..............................................................................
high-pressure chamber lids 79