  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.
