Pair distribution function and pair potential of lattice model chains under theta conditions, 2. Theoretical approach

Abstract

AbstractA general expression for the pair potential U and the pair distribution function G for an isolated pair of coiled unbranched macromolecules is derived with special reference to the Θ‐state, using a sort of “square well” potential for the description of segment‐segment interaction. Contrary to former treatments allowance has been made for the fact that at least those segment‐segment interactions which are not of hard sphere character occur at a finite contact distance δ. The “contact sites”, i.e. the locations which–in order to produce this type of interaction–have to be occupied by segments of the second chain of the pair, are shown to obey a broader distribution around the center of gravity of the first chain than its segments themselves. As a consequence the hard sphere (repulsive) and the non‐hard sphere (for the Θ‐state necessarily attractive) interactions between the two chains show a different dependence on the distance R between the centers of mass of the two chains, leading to expressions for U and G—well consistent with numerical Monte Carlo estimates‐which have the general form and respectively, with a always exceeding a′ and for the Θ‐state A>A′. All these parameters are well defined in terms of the model used.