Osmotic pressure of ring-polymer solutions

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Abstract
For a pair of ring polymers in a solution, the number of mutual entanglements is invariant and, hence, a frozen variable. Such restriction on thermally accessible configurations causes a new type of intermolecular interaction. This paper theoretically studies the nature of molecular interaction caused by topological constraints. Observed depression of the theta temperature by 6 °C in the solution of ring polystyrene compared with that of linear polymer is explained by the existence of repulsive force, which acts between disjoint rings and originates in topological constraints. By the use of Gauss’ linking number for the topological invariant, the second and third virial coefficients are calculated as a function of molecular weight and compared with the experimental observation on ring polystyrene in cyclohexane.