The Pair Distribution Function of Athermal Model Chains

Abstract

Abstract Using a Metropolis‐Monte Carlo‐process equilibrated self‐avoiding unbranched model chains consisting of 50–400 segments have been generated on a 5 way cubic lattice, no attractive potential being operative between the segments (“athermal” chains). By checking all possible pairs of chains for absence of overlaps (double occupancies of lattice points) for several intermolecular separations R within an ensemble of such chains consisting of 100–200 individuals the pair distribution function G ( R ) has been evaluated as the fraction of pairs which are free of intermolecular overlaps. G ( R ) qualitatively has the form which is predicted by the Flory‐Krigbaum‐theory (FK‐theory), a quantitative inspection, however, shows that it is substantially higher than it should be according to the FK‐theory, which is also reflected in much lower excluded volumes compared to the FK‐prediction. ‐ This disagreement can be explained by inspection of the frequency distribution of the overlaps in the chain pairs: While it is implicit in the FK‐treatment that the overlaps form independently of each other and, as a consequence, their distribution should obey a Poisson‐statistics, the actual distributions show that the existence of one (or more) overlaps favors the formation of further ones. As on the other hand the average number of overlaps within a pair, Z. which has been evaluated numerically, is well consistent with the FK‐theory this leads to an increase of the fraction of pairs which are free of overlaps, i.e. G ( R ). relativ to a Poisson‐distribution. ‐ It is proposed, therefore, to subdivide the chains not ‐ as in the FK‐treatment ‐ into n segments of volume V , but into n ' clusters of segments of volume V ′( nV = n′V′ ) where n ' should be chosen in a way that the resulting clusters can be considered to behave actually independently in the overlap formation process. On this basis a substantial improvement of the theory of G ( R ) for linear chains will be possible.