# A rotational isomeric state approach towards understanding elastomer chain conformations in tires

#### Abstract

Experiments have found that strengthening interactions between rubber and reinforcement fillers can be used to maintain a balance between reducing tire rolling resistance without compromising on wear resistance and traction, but why this works is not known. Understanding the statistical mechanics of elastomer chain conformations provide us a vital molecular link towards quantifying rolling resistance. This thesis provides a first step towards this link. ^ Molecular modeling is used to study the size and shape distribution, and characteristics of cis- and trans-1,4-polybutadiene chains. Computations are conducted using Flory's Rotational Isomeric State approach (RIS), in which energy distribution is considered over discrete rotational isomeric states. The Rotational Isomeric State approach is chosen because it allows generating a large number of polybutadiene chains in a computationally cheap manner using less resources and computation time , and also because the RIS approach allows each chain realization to be treated as an independent sample. ^ Numerous (100,000) isolated single cis- and trans-1,4-polybutadiene chains of uncorrelated random conformations are considered under unperturbed conditions (balanced attractive and repulsive polymer-solvent interactions, i.e. theta-conditions). Using a single chain in each computation is justified because a flexible polymer surrounded by the same polymer takes on the same average shape as a single random polymer chain in a theta solvent. Chain size and shape properties are computed at different chain lengths and over a range of temperatures. ^ Characteristic ratios are in good agreement with experimental and prior computed values (cis-1,4-polybutadiene), and slightly higher than prior computed values (trans-1,4-polybutadiene). Characteristic ratios increased with increasing chain length for both cis and trans chains with this effect being more prominent for trans than for cis chains. Small absolute changes in chain size probability densities with temperature are observed. Larger relative increase in probability density of larger chains and smaller relative decrease in probability density of smaller chains result in increased average chain size with increasing temperature. This effect increases characteristic ratios with increasing temperature. The larger chains show a much higher increase in characteristic ratios with temperature than smaller chains, and this effect is stronger for trans than for cis chains. ^ Eigenvalues of the radius of gyration matrix quantify chain shapes by providing eigenvalues along the three principal directions (eigenvectors). Average shape measures differ between cis and trans chains. With increasing chain length, trans chains are slightly compressed along the principal direction while cis chains are slightly stretched. Resultantly, trans chains are slightly more spherical with increasing chain length while cis chains are slightly less spherical. At the same chain length, trans chains are slightly less spherical than cis chains. At long chain lengths, trans and cis chains have similar spherical shapes. With increasing temperature, little or no variation in shape is computed for cis chains, whereas trans chains are slightly stretched along the principal direction, and thus are slightly less spherical. Most changes in shapes arise from changes along the longest principal direction. ^ Cis and trans chains show similar asphericity at longer chain lengths. Little or no change in acylindricity is computed for either cis or trans polybutadiene chains. Relative shape anisotropy follows the same trends like asphericity as functions of both chain length and temperature for cis and trans polybutadiene chains. ^ Joint correlation studies reveal that size and shape parameters are mutually dependent properties of chains. For asphericity, rod-like small size and spherical medium size cis chains show anti-correlation between chain size and shape. Spherical small size, near rod-like medium and large size chains show correlation between chain size and shape. ^ For acylindricity, medium size chains of flattened cross section, and small and large size chains of round cross section showed correlation between chain size and shape. Round cross section medium size chains show anti-correlation between chain size and shape. Trans chains show similar behavior as cis chains with correlation and anti-correlation between chain size and shape occuring to a greater extent. ^ The next use for the detailed conformation results in this work is to relate probability densities to the work done to alter chain size and shape. Cis and trans chains show different probability density distributions implying different amounts of deformation work to alter chain size and shape. When a tire revolves and deflects while in motion, affine deformation of the elastomer-filler system takes place. The deformation leads to changes in elastomer chain conformations, which results in entropy losses of the elastomer-filler system (since entropy is related logarithmically to chain conformations). These entropy losses lead to computing irreversible work, viscoelastic losses and rolling resistance. The effects of fillers on these conformation distributions thus will quantify interaction effects on loss modulus and rolling resistance. (Abstract shortened by UMI.)^

#### Subject Area

Engineering, Chemical

#### Recommended Citation

Suvrajyoti Kar,
"A rotational isomeric state approach towards understanding elastomer chain conformations in tires"
(2014).
*Dissertations and Master's Theses (Campus Access).*
Paper AAI1555658.

http://digitalcommons.uri.edu/dissertations/AAI1555658