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

Abstract

We present an off-lattice statistical model of a single polymer chain in mixed solvent media. Taking into account a polymer conformational entropy, renormalization of solvent composition near the polymer backbone, the universal intermolecular excluded volume and Van-der-Waals interactions within the self-consistent field theory the reentrant coil-to-globule-to-coil transition (co-nonsolvency) has been described in this paper. For convenience we split the system volume in two parts: the volume occupied by the polymer chain and the volume of bulk solution. Considering the equilibrium between two sub-volumes, the polymer solvation free energy as a function of radius of gyration and co-solvent mole fraction within internal polymer volume has been obtained. Minimizing the free energy of solvation with respect to its arguments, we show two qulitatively different regimes of co-nonsolvency. Namely, at sufficiently high temperature a reentrant coil-to-globule-to-coil transition proceeds smoothly. On the contrary, when the temperature drops below a certain threshold value a coil-globule transition occurs in the regime of first-order phase transition, i.e., discontinuous changes of the radius of gyration and the local co-solvent mole fraction near the polymer backbone. We show that, when the collapse of polymer chain takes place, the entropy and enthalpy contributions to the solvation free energy of globule strongly grow. From the first principles of statistical thermodynamics we confirm earlier speculations based on the MD simulations results that the co-nonsolvency is the essentially enthalpic-entropic effect and caused by enthalpy-entropy compensation.We show that the temperature dependences of solution heat capacity change due to the solvation of polymer chain are in qualitative agreement with the Differential scanning calorimetry data for PNIPAM in aqueous methanol. a) urabudkov@rambler.ru 2

Statistical description of co-nonsolvency suppression at high pressures

“…Fig. 4 shows that at rather low pressure the chain collapse is accompanied by the increase in the co-solvent mole fraction x 1 in the internal polymer volume (see also 26 ). However, the rather high pressure imposed suppresses the co-solvent concentration enhancement in the internal polymer volume and, simultaneously, the polymer chain collapse.…”

“…The contour length of the polymer chain is N b (N is the polymerization degree and b is the bond length). As in our previous works 26,[34][35][36] and in works 42,43 , for convenience the whole solution volume is divided into two sub-volumes -the first is the volume occupied by the polymer chain (gyration volume) and the rest is the volume of the solution (bulk). The gyration volume is chosen to be spherical V g = 4πR 3 g /3, where R g is the gyration radius.…”

“…Recently, the authors of this communication have formulated the Flory-type self-consistent field theory based on the modern liquid-state theory of the flexible polymer chain in the mixed solvent and applied it to the co-nonsolvency description 26 . It was confirmed that co-nonsolvency could be obtained within the theory taking into account only the universal Van der Waals and excluded volume interactions.…”

On a new application of the path integrals in polymer statistical physics

“…It should be noted that the limiting laws (64) for d = 3 are widely used in the different applications of polymer physics [11][12][13][14][15][16][17].…”

Polarizable polymer chain under external electric field: Effects of many-body electrostatic dipole correlations

“…where F conf (R g ) is the free energy of the ideal polymer chain which can be calculated by the following interpolation formula [8][9][10][11][12][13][14]…”