Random Walks on a Simple Cubic Lattice, the Multinomial Theorem, and Configurational Properties of Polymers

Paul W. Hladky
Department of Chemistry, University of Wisconsin–Stevens Point, Stevens Point, WI 54481-3897
J. Chem. Educ., 2007, 84 (2), p 361
DOI: 10.1021/ed084p361
Publication Date (Web): February 1, 2007
History, Education, and Documentation

Abstract

A random walk or, more correctly, a random climb on a simple cubic lattice is a very simple model of a polymer molecule that is easily visualized and, as we show, can be utilized to describe a variety of physical properties. The model is used to calculate average sizes of homopolymers and copolymers in solution when the segments either have or do not have orientational biases. We also employ it to treat molecules that have many local intrachain attractions and calculate their average sizes as functions of the interaction strength. In spite of these capabilities, the random-climb model is rarely, if ever, presented in the polymer educational literature. This article attempts to remedy that situation by drawing attention to the model's inherent advantages and serving as an introduction to polymer physical properties for students studying chemistry, chemical engineering, material science and related fields.

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Polymer Chemistry

Keywords (Subject):

Mathematics / Symbolic Mathematics
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  • Received: August 03, 2009

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