Abstract
According to the Mayer model, the properties of a long-chain polymer molecule are crudely but sufficiently well represented if one supposes that the successive atoms occupy adjacent sites of a regular tetrahedral† lattice. If one treats all such configurations as equally probable, the positions of the atoms in a chain of (n+1) atoms are distributed in exactly the same way, relative to the position of one end, as the sites passed through in n steps of a Pólya walk (random walk) on the same lattice. One may then appeal to the theory of Pólya walks for the various information that one requires; of particular interest is the mean square distance \(\left\langle {r_n^2} \right\rangle\) between the ends of the chain.
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© 1964 J. M. Hammersley and D. C. Handscomb
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Hammersley, J.M., Handscomb, D.C. (1964). Long Polymer Molecules. In: Monte Carlo Methods. Monographs on Applied Probability and Statistics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5819-7_10
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DOI: https://doi.org/10.1007/978-94-009-5819-7_10
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