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Toward a Universal Behavior of Linear Athermal Model Chains in the Limit of Infinite Chain‐length
Author(s) -
Olaj Oskar Friedrich,
Zifferer Gerhard
Publication year - 2012
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.201200040
Subject(s) - extrapolation , limit (mathematics) , chain (unit) , intramolecular force , gaussian , function (biology) , distribution function , distribution (mathematics) , statistical physics , physics , mathematics , chemistry , thermodynamics , mathematical analysis , computational chemistry , quantum mechanics , evolutionary biology , biology
Athermal chains of various stiffness embedded in several types of lattices were analyzed with respect to their pair distribution function G ( R ). Extrapolation to infinite chain‐length on a reduced distance scale made all the G ( R ) data coincide within extremely narrow limits, thus suggesting the existence of a universal pair distribution function for polymers in good solvents in the long‐chain limit. The ratio –ln( G ( R ))/ Z ( R ) with Z ( R ) being the reduced distribution of overlaps is also universal in type and varies only little with distance R . Further, a likewise universal function could be established that allows the construction of Z ( R ) from the Flory–Krigbaum expression taking into account not only the deviations from Gaussian behavior but also the effect of intramolecular repulsion present in athermal chains.