Segmental orientation and conformational dynamics of polymer chains

Abstract

Various remarkable features of polymers, as compared with metallic and inorganic materials, arise from the fact that macromolecules can take up various conformations. The study of macromolecular conformations and dynamics is undoubtedly important in polymer science and technology from both basic and practical viewpoints. Comprehension of the configurational statistics of chain molecules leads to a rational interpretation and understanding of their physical properties. In previous studies, much effort have been devoted to dilute solutions. Though, recently there is a clear trend towards studying molecular properties in condensed systems, studies in the area of dilute solutions still remain a cornerstone of polymer characterization. Orientational motions of segments in polymer chains depend sensitively on both intra- and intermolecular configurational characteristics of the chains, and thus are of special interest for the understanding of polymer behavior. This thesis is mainly composed of two parts. In the first part, segmental orientation of polymers related to the chemical structure and resulting configurational characteristics of the chains are investigated using polyetylene (PE) and polyoxyethylene (POE) networj<s: In the calculations, the orientation of a reference vector m rigidly embedded in a chain of deformed network is considered. As a first step, the mean-square cosine <cos28>r of the angle that m makes with a laboratory-fixed axis is formulated for a chain with fixed end-to-end vector r. A series expression including terms up to fifth inverse power of n, where n is the number of bonds in the network chain, is obtained for <cos2S>r. Next, the corresponding averages over all chains of a network and the associated orientation function S, which is macroscopically observed are found in terms of (i) unperturbed chain moments readily obtainable by the rotational isomeric state scheme(RIS) (ii) the extension ratio A. for uniaxially deformed networks. Such a rigorous expression for S is particularly useful for relatively short chains and for moderate to large deformations that can not satisfactorily be accounted for by the existing simpler formulations. Thus, we estimate ranges of extension ratios A. to which the conventional first order approximation may be confidently applied. Calculations are performed for PE and POE chains of n = 21, 51 and 101 bonds which are generated by Monte Carlo simulation. The results are compared with those obtained by previous theoretical approaches. These comparisons demonstrate the importance of the adoption of higher order terms in the serial expansion of the orientation function for . In the second part, static and dynamic correlations between bond conformations and reorientations are examined by Brownian dynamics simulations for polymer chains with fixed ends. Polyethylenelike model chains are considered. Rates of rotational isomeric transitions and time evolution of orientational correlations are analyzed for various extensions of the chain. The relatively more extended chain exhibits the higher mobility in the short-time scale but possesses lower effective rate of rotational isomerization. This follows from a hazard analysis covering ranges up to 10 ns. The time decays of bond orientational correlations are reproducible by stretch--exponential functions with exponent almost independent of chain extension. The imposition of deformation by fixing chain ends, affects the orientational mobility of the chain down to the scale of individual bonds which may be observed from the biased evolution of time-dependent distribution functions for bond spatial reorientations. The analysis is also extended to the study of local orientational motions as seen by a laboratory fixed-observer. Time-dependent joint probability distribution functions for orientations of a vector affixed to a polymer chain are expressed in terms of double spherical harmonics. An expansion of the distribution function up to the second order harmonics accurately reproduces the results of Brownian dynamics simulations for a 49 bond polyethylene chain whose end-to-end separation is fixed at different extensions. Various functions related to the anisotropy of segmental dynamics such as the mobility, orientation-mobility correlation, directivity of mobility and the sense of mobility are examined and observed to be strongly dependent on the degree of chain extension.