Date of Award


Degree Type


Degree Name

Doctor of Philosophy in Chemical Engineering


Chemical Engineering

First Advisor

Michael L. Greenfield


The goal of this research is to quantify and analyze elastomer chain conformations and their role in affecting rubber tire viscoelastic properties through the development of novel numerical methods. The hypothesis is that changes in the statistical mechanics of chain conformations at the microscopic scale provide a direct molecular link towards quantifying macroscopic properties of elastomers. The molecular level investigation began with simulating chains in the unperturbed state to study the impact of chain size and temperature on overall chain size statistics. To understand changes in the chain conformations under stress, a numerical model was developed that encompasses effects from multiple forms of deformation. The probabilistic approach implemented in this work allowed for molecular level understanding of chain behavior.

Flory's Rotational Isomeric State (RIS) approach was used to generate numerous uncorrelated, isolated, random conformations of amorphous cis- and trans-1,4- polybutadiene single chains under unperturbed conditions of different molecular weights and over a range of temperatures. Probability density distributions of squared end-to-end distances of these chains were quantified to study size properties. Characteristic ratios were in good agreement with prior experimental and theoretical findings, and increased with increasing molecular weight of cis and trans chains, with this effect being more pronounced for trans than for cis chains. Chain swelling was observed on heating indicated by an increasing characteristic ratio with temperature and positive temperature coefficients for both cis and trans chains. Chain size and shape properties were mutually dependent, with most changes in shape occurring due to changes along the principal direction. A larger relative increase in probability density distribution of unlikely larger chains and a smaller relative decrease in probability density distribution of more likely smaller chains resulted in increased average chain size and characteristic ratios with increasing temperature. This has been termed the “taut conformation effect" and had a significant impact on chain swelling with heating. This effect motivated further work into investigating its presence in other polymers such as polypropylene and polystyrene which is discussed in chapter 4.

After the unperturbed state of chain ensembles were analyzed through size and shape studies, the perturbed or deformed state of the ensembles were explored through molecular modeling techniques to exert and quantify external stresses. Uniaxial, equibiaxial deformation and shear were applied to unperturbed chain ensembles which resulted in changes in their probability density distributions and elastic free energy. The approach for computing changes in elastic free energy involved developing a probability-based numerical method that can be applied across multiple forms of deformation. In order to determine the accuracy of the numerical method, it was initially applied to generated Gaussian chains and compared against known analytical equations. The numerical results and known analytical solutions of Gaussian chains were in excellent agreement and hence the numerical model was extended to computing elastic free energy change, force, and stress on RIS cis- and trans-1,4-polybutadiene chains. Compression forces were much greater than tension forces. Equibiaxial and uniaxial stresses were equivalent in a single extension direction, and greater than shear. Forces and stresses increased with deformation and showed dependence on chain volume and temperature. Significant variation was observed in moduli with chain repeat unit size while only minor variations were observed with temperature. Fewer repeat unit size chains correspond to lower molecular weight between cross-links causing a more tightly cross-linked chain network. This resulted in greater moduli as compared to chains of more repeat units. A slight linear increase in moduli with temperature of chains of the same repeat unit size was observed. Young's and shear moduli computed from the numerical model were in good agreement with experimental results. The novelty in this approach is the ability to incorporate polymer-polymer and polymer-filler interactions.

The “taut conformation effect" was identified as a significant contributor to chain size behavior for polybutadiene, and its presence in vinyl polymers, such as polypropylene and polystyrene, were investigated. Random conformations of numerous single chains of amorphous, isotactic polypropylene and polystyrene were generated using Flory's RIS approach. Characteristic ratios were in decent agreement with prior experimental and theoretical results. These ratios increased with molecular weight and were higher for polystyrene than polypropylene. Chain heating resulted in shrinkage for both polypropylene and polystyrene, indicated by decreasing characteristic ratios and negative temperature coefficients, which were in decent agreement with experimental results. Probability density distribution and chain size subset analysis indicated that only the least probable long size chains or taut conformations showed a decrease in probability density distribution and characteristic ratio with temperature. The most probable medium size chains hardly showed any change in their probability density distributions and characteristic ratios with temperature, while short size chains showed marginal increase. Hence, much like polybutadiene chains, less probable taut chain conformations had a significant impact on the average chain size indicating “taut conformation effect.

The primary focus of this dissertation was analyzing chain conformation statistics. In addition to that work, rheology experiments were performed on asphalt systems, and models were developed in order to predict the experimental results. Rheological studies were done to analyze viscoelastic properties of asphalt binders from different sources and under various aging conditions. Time-temperature superposition (TTS) was applied to frequency sweep data to produce master curves, and discrete and continuous Maxwell models were applied to predict stress relaxation modulus, relaxation and retardation time distributions, and creep compliance. Moduli increased upon aging indicating increased binder stiffness. Zero-shear viscosities decreased with increasing temperature for all binders due to increasing molecular motion and flexibility. At shorter times, stress relaxation moduli and creep compliance were similar for all binders, but with increasing time, unaged binders relaxed more rapidly than aged binders. Low creep compliance at shorter times corresponded to the absence of any configurational re-arrangements of asphalt binders. TTS allowed for computation of creep compliance at very low temperatures (-18° C) to predict Pressure Aging Vessel (PAV) aged binder stiffness and resistance to thermal cracking at such low temperatures. Two binder samples were analyzed and showed similar low temperature flexibilities. The low temperature stiffness results predicted by our rheological model were in good agreement with bending beam rheometer experimental results, hence corroborating the efficiency of our model.

This work encompasses three significant contributions to the scientific community. For polybutadiene, polypropylene and polystyrene, the impact of less likely, taut conformations on the overall chain size was identified and termed the “taut conformation effect". A probability based, reliable numerical tool was developed to predict mechanical properties of elastomers subjected to multiaxial deformations. Finally, an example of applying rheology models to experimental data was shown by accurately predicting asphalt binder stiffness and resistance to low temperature thermal cracking.

Available for download on Saturday, April 20, 2019