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In most of the theoretical work on statistical properties of polymer chains one includes (for mathematical simplicity) configurations which correspond to several monomers located at the same point. Here a mathematical method based on the theory of Markoff chains is used to eliminate short-range excluded volume effects in polymer chains formed on space lattices. Those aspects of the theory of Markoff chains which are important in this problem are briefly reviewed. If as(s=j—k) is the correlation coefficient between the x component of the position of the jth monomer and that of the kth, then the root-mean-square distance between ends of a chain of degree of polymerization N is proportional to N½ (as N→∞) provided that as→0 more rapidly than A/s1+ε (as s→∞). Here A is a constant and ε is an arbitrarily small positive constant. This condition is satisfied in a chain in which any group of n0 successive monomers do not overlap each other or any monomers in neighboring groups of n0 provided n0≪N. A detailed analysis of a polymer chain on a square lattice is given.
Elliott W. Montroll (Mon,) studied this question.