Truly Universal? The Behavior of Linear Athermal Polymer Chains

by | Nov 7, 2012

Researchers find a universal pair distribution function for polymers in the long-chain limit.
A universal pair distribution function for polymers in the long-chain limit

A universal pair distribution function for polymers in the long-chain limitThe properties of chain molecules in infinitely diluted solutions may be calculated by use of single chains. For the limiting case of a highly diluted solution of macromolecules, however, they can be evaluated by studying isolated pairs of molecules.

Their non-ideal behavior may be attributed to interactions between two dissolved molecules which do not interfere with further ones in this regime. The fraction of compatible, i.e., non-intersecting pairs then is given by the pair distribution function G(R) which may be calculated by exact enumeration for lattice based polymer models.

As shown by O. F. Olaj and G. Zifferer at the University of Vienna, for finite chain lengths G(R) is dependent on the lattice type and local stiffness of the chains but extrapolation to infinite chain-length on a reduced distance scale makes all the G(R) data coincide within extremely narrow limits, thus suggesting the existence of a universal pair distribution function for polymers (at least in good solvents) in the long-chain limit. Furthermore, G(R) may be related to the number of overlaps Z(R) between the two chains on the lattice, with Z(R) – the average number of intermolecular overlaps – being accessible on the basis of a theoretically concept dating back to Flory and Krigbaum.

In this simple way an approximate close expression for the pair distribution function of chains in the limit of infinite chain-length may be given although it cannot be decided whether the proposed relation between G(R) and Z(R) has a theoretical background or is purely fortuitous.

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