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A Statistical Theory of cosolvent-induced coil-globule transitions in dilute polymer solution

We present a statistical model of a dilute polymer solution in good solvent in the presence of low-molecular weight cosolvent. We investigate the conformational changes of the polymer induced by a change of the cosolvent concentration and the type of interaction between the cosolvent and the polymer. We describe the polymer in solution by the Edwards model, where the partition function of the polymer chain with a fixed radius of gyration is described in the framework of the mean-field approximation. The contributions of polymer-cosolvent and the cosolvent-cosolvent interactions in the total Helmholtz free energy are treated also within the mean-field approximation. For convenience we separate the system volume on two parts: the volume occupied by the polymer chain expressed through its gyration volume and the bulk solution. Considering the equilibrium between the two subvolumes we obtain the total Helmholtz free energy of the solution as a function of radius of gyration and the cosolvent concentration within gyration volume. After minimization of the total Helmholtz free energy with respect to its arguments we obtain a system of coupled equations with respect to the radius of gyration of the polymer chain and the cosolvent concentration within the gyration volume. Varying the interaction strength between polymer and cosolvent we show that the polymer collapse occurs in two cases - either when the interaction between polymer and cosolvent is repulsive or when the interaction is attractive. The reported effects could be relevant for different disciplines where conformational transitions of macromolecules in the presence of a cosolvent are of interest, in particular in biology, chemistry and material science.