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XIII.—The Graph-like State of Matter. I. Statistical effects of correlations due to substitution effects, including steric hindrance, on polymer distributions.

Published online by Cambridge University Press:  14 February 2012

M. Gordon  and
T. G. Parker
M. Gordon
Affiliation:
Department of Chemistry, University of Essex
T. G. Parker
Affiliation:
Department of Chemistry, University of Essex
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Synopsis

Models which treat molecules as graphs provide the first approximation to practically all chemical and physical theories of polymers. This paper, worded so as to aim at intelligibility by both chemists and mathematicians, deals with statistical effects of correlations on distributions of molecules in their graph-like states. The correlations are formally equivalent to fertility correlations in family trees, and the theory covers the range of correlation to the point where a man's fertility expectations depend on how many brothers he has. Chemically, this describes the ‘second shell substitution effect’ which includes certain steric hindrance situations; mathematically, the problem is solved by restoring the Markovian nature of a conventional Galton-Watson process. Long-range correlations are an inevitable and troublesome aspect of the structure of gels and this work represents a step towards improving models for real gels.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 69 , Issue 3 , 1971 , pp. 181 - 198
Copyright
Copyright © Royal Society of Edinburgh 1971

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References

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