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We present an off-lattice statistical model of a single polymer chain inmixed solvent media. Taking into account a polymer conformational entropy,renormalization of solvent composition near the polymer backbone, the universalintermolecular excluded volume and Van-der-Waals interactions within theself-consistent field theory the reentrant coil-to-globule-to-coil transition(co-nonsolvency) has been described in this paper. For convenience we split thesystem volume in two parts: the volume occupied by the polymer chain and thevolume of bulk solution. Considering the equilibrium between two sub-volumes,the polymer solvation free energy as a function of radius of gyration andco-solvent mole fraction within internal polymer volume has been obtained.Minimizing the free energy of solvation with respect to its arguments, we showtwo qulitatively different regimes of co-nonsolvency. Namely, at sufficientlyhigh temperature a reentrant coil-to-globule-to-coil transition proceedssmoothly. On the contrary, when the temperature drops below a certain thresholdvalue a coil-globule transition occurs in the regime of first-order phasetransition, i.e., discontinuous changes of the radius of gyration and the localco-solvent mole fraction near the polymer backbone. We show that, when thecollapse of polymer chain takes place, the entropy and enthalpy contributionsto the solvation free energy of globule strongly grow. From the firstprinciples of statistical thermodynamics we confirm earlier speculations basedon the MD simulations results that the co-nonsolvency is the essentiallyenthalpic-entropic effect and caused by enthalpy-entropy compensation. We showthat the temperature dependences of solution heat capacity change due to thesolvation of polymer chain are in qualitative agreement with the Differentialscanning calorimetry data for PNIPAM in aqueous methanol.

A statistical theory of coil-to-globule-to-coil transition of a polymer chain in the mixture of good solvents