The 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.