Uncovering the Impact of Surface-Grafted Chains on the Experimental Glass Transition of Polymer Matrices and an Evaluation of Bayesian Inference to Robustly Fit Noisy Data Open Access

Abstract

In this dissertation, I investigate how polystyrene (PS) chains end-grafted to a silica substrate impact the local glass transition temperature Tg(z) of an adjacent PS matrix for a variety of grafted chain lengths, grafting densities, and grafting chemistries. We find that while the Tg value measured directly next to the grafted interface is the same across different molecular weights of grafted chains, the lengthscale of the perturbation to local Tg(z) varies significantly, in a manner similar to the molecular weight dependence of Tg for bulk polymers. These results show that chain connectivity and its impact on Tg are not adequately described by existing theories of polymer glassy dynamics.

We also introduce a Bayesian inference method of fitting Tg from ellipsometric temperature-dependent film thickness data that demonstrates marked improvements over the existing techniques typically used by the field. The method is benchmarked off of existing data collected by our lab for supported PS films for a wide variety of film thicknesses. The fitting approach is unbiased, robust, and flexible, enabling new conclusions to be drawn from existing data for PS and poly(2-vinyl pyridine) (P2VP) all with less human intervention required than existing fitting techniques. Application of this technique could contribute toward robust unsupervised labeling of training data for artificial intelligence systems for polymer discovery.

We also describe complementary fluorescence measurements for an extensive set of physical aging rate measurements for rubbery-glassy polymer bilayers of poly(n-butyl methacrylate) (PnBMA). These measurements together improved our understanding of how physical aging rate and Tg are related in the presence of a polymer-polymer interface. The result also suggested that the effect of finite domain size on local Tg gradients is an issue worth exploring in future work. Control measurements that provided the baseline for comparison for local Tg(z=0) measurements next to adsorbed layers formed in different ways will also be discussed. These measurements helped to disentangle how adsorbed chains with different structures do (or do not) impact the local glass transition Tg(z=0) in an overlying matrix. Taken together, my work moved forward our understanding of interfacial changes in Tg near interfaces where chain connectivity is relevant, while improving the quality of analysis for data obtained from measurements of these systems.

Table of Contents

Contents

1 Introduction 1

1.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Introduction to Polymeric Glass-formers . . . . . . . . . . . . . . . . 2

1.2.1 Basics of Polymers . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.2 The Glass Transition . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.3 Molecular weight dependence of Tg in bulk polymers . . . . . 10

1.3 Interfacial changes to the glass transition in polymer glasses . . . . . 12

1.3.1 Nanoconfinement effect and the free surface . . . . . . . . . . 12

1.3.2 Grafted chains at interfaces . . . . . . . . . . . . . . . . . . . 13

1.3.3 Summary of the literature on the glass transition with grafted-

surface interfaces in films and composites . . . . . . . . . . . . 16

1.4 Outline of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 Experimental Methods 34

2.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.2 Fluorescence background . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3 Fluorescence instrumentation . . . . . . . . . . . . . . . . . . . . . . 36

2.4 Measuring the Glass Transition by Pyrene Fluorescence . . . . . . . . 38

2.5 Ellipsometry principles and instrumentation . . . . . . . . . . . . . . 40

2.5.1 Light reflection with a single air-dielectric interface . . . . . . 41

2.5.2 Light interaction with a film of finite thickness between two

semi-infinite domains . . . . . . . . . . . . . . . . . . . . . . . 43

2.5.3 Optical layer modeling for ellipsometry . . . . . . . . . . . . . 45

2.6 Comparison of Physical Aging and Glass Transition in Glassy-Rubbery

Polymer Bilayer Films . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.6.2 Aging of PS films capped with PnBMA . . . . . . . . . . . . . 51

2.6.3 Layer-average Glass Transition Temperature of PS layers

capped with PnBMA . . . . . . . . . . . . . . . . . . . . . . . 56

2.7 Comparing the impact of different adsorbed layers on the local glass

transition of polymer matrices . . . . . . . . . . . . . . . . . . . . . . 64

2.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.7.2 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . 66

2.7.3 Comparing Solvent Grown Adsorbed Layers and Solvent

Washed Melt Annealed Films . . . . . . . . . . . . . . . . . . 69

2.7.4 Inferring the Structure of Adsorbed Chains and Understanding

Their Impact on Local Tg . . . . . . . . . . . . . . . . . . . . 76

3 End-Tethered Chains Increase the Local Glass Transition Tempera-

ture of Matrix Chains by 45 K Next to Solid Substrates Independent

of Chain Length 95

3.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4 Gradient length-scale of local polystyrene matrix Tg next to end-

grafted silica substrate exhibits striking dependence on the length

of the grafted chains 127

4.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

4.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 131

4.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.4.1 Local glass transition temperature as a function of distance

from a grafted interface . . . . . . . . . . . . . . . . . . . . . . 134

4.4.2 Breadth of local glass transition temperatures near the grafted

interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

5 A Bayesian Inference Approach to Accurately Fitting the Glass

Transition Temperature in Thin Polymer Films 163

5.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

5.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 170

5.4.1 Common method of identifying Tg via intersection of two linear

fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

5.4.2 Nonlinear fitting to Equation 5.1 . . . . . . . . . . . . . . . . 176

5.4.3 Functional form of temperature-dependent thermal expansion

coefficient α(T ) . . . . . . . . . . . . . . . . . . . . . . . . . . 178

5.4.4 Bayesian Inference by Hamiltonian Monte Carlo . . . . . . . . 182

5.4.5 Brute-force exhaustive search of linear-fitting ranges . . . . . . 194

5.4.6 Comparing Tg(h) for PS Films Obtained from the Different Fit-

ting Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

5.4.7 Bayesian Inference Fitting Applied to P2VP Thin Films . . . 205

5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

6 Summary and Conclusions 230

About this Dissertation

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School	Laney Graduate School
Department	Physics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Physics, General Physics, Condensed Matter
Keyword	Glass Transition Polymers
Committee Chair / Thesis Advisor	Connie Roth, Emory University
Committee Members	Justin Burton, Emory University Stefan Boettcher, Emory University Marcus Cicerone, Georgia Institute of Technology Daniel Sussman, Emory University

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