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  Home > JCE Print > Journal of Chemical Education > Issues > 2007  > February  >
Research: Science and Education
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
Cover
February 2007
Vol. 84 No. 2
p. 361
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.
Supplement
The versatility of the random-climb model is illustrated further by three additional problems that are presented in this issue of JCE Online. The first problem examines molecules that have a nonlocal intrachain attraction and calculates their average sizes as functions of the interaction strength. The second problem adapts the random-climb model to a network of polymer chains and predicts a force-elongation relationship for rubbery materials that is surprisingly realistic. Finally, equilibrium constants for the partitioning of polymeric solutes between bulk solution and nonadsorbing, porous solids are calculated as well as the average chain sizes in the unobstructed directions.
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Contents
  JCE2007p0361W.pdf
 
JCE2007p0361W.zip
Sup_2005-0531.doc (Microsoft Word)
More Information
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Citation
Hladky, Paul W. J. Chem. Educ. 2007, 84, 361.
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Keywords
Mathematics / Symbolic Mathematics; Molecular Properties / Structure; Physical Properties; Polymer Chemistry; Statistical Mechanics; Theoretical Chemistry; Upper-Division Undergraduate
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History
Created:
Last Updated:
1/9/2007
2/23/2007
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