Role of Free Volume Change on Polymer Solutions; Osmotic Pressure of Moderately Concentrated Polyisobutene–Normal Alkane Systems

Abstract

ABSTRACT:An attempt was made to verify the effect of free volume dissimilarity, which is predicted by the cell (or free volume) theory, upon the x parameter. Osmotic pressures of moderately concentrated polyisobutene solutions in n-pentane, n-hexane, and n-heptane were measured at various temperatures, and values of the x1 parameter were obtained. It was found that x1 increases with increasing temperature in each system, and decreases with the increasing chain length of n-alkanes used as solvents at fixed temperature. This effect is in agreement with the cell theory. It has been considered that the statisticalmechanical approximation for the thermodynamical nature of polymer solutions achieved an essentially satisfactory form through the FloryHuggins theory 1 which is based on a strictly regular solution theory for the mixtures of spherical molecules of equal size. It appears, however, that the qualitative physical picture of solutions has to be changed in view of many experimental results for the thermodynamical nature of polymer solutions, e.g., the behaviour of polymer-solvent interactions and the x parameter, the temperature dependence of polymer solubility, and the phase separation which takes place in all polymer solutions at an elevated temperature (called the lower critical solution temperature). Although the traditional ideas, such as the Flory-Huggins theory, have been refined, they can not explain these results even qualitatively. Apparently a new factor is needed.In the traditional treatment, the factor which lowers the mutual solubility of solute and solvent concentrates on the dissimilarity of contact energies or cohesive energies between segments of polymer and solvent molecules of different chemical nature. In the early 1950's Prigogine, et al., 2 -4 introduced into solution theory a new factor which was due to the dissimilarity between the free volumes of the polymer and solvent molecules. This free volume dissimilarity exists, even between a polymer and a chemically identical homologous solvent of low molecular weight, due to the inescapable difference of size or chain length. The free volume theory gives a picture much different from the Flory-Huggins theory for the solution properties. Nevertheless many recent investigations by Patterson, et a/.,[5][6][7][8][9][10][11][12][13][14][15] et al.,[16][17][18][19][20][21][22][23][24][25][26][27][28] are based on the free volume theory.The residual chemical potential parameter x presented by Flory 18 for a polymer solution depends on the dissimilarity of either the cohesive energies or the free volumes between segments of polymer and solvent molecules. Hence it is expected that measurement of x for various polymer-solvent systems gives significant information for understanding the solution thermodynamics.In this work, measurements of osmotic pressures were made, in order to obtain the x value directly at various temperatures in a concentration range of more than 10% where the segments of the polymer chain are supposed 747

Statistical Thermodynamics of Polymer Solutions Based on Free Volume Theory

“…For a binary mixture, assuming a random mixing, the energy E0 can be given by ~Ei$/fN = (cqSiSiTJn 4" c202s2t)22 4" 2ff102Si»?i2)/2L> (12) where ; is the segment fraction of component i {i = 1,2) defined by ,• = / + r2N2) = r¡Ni/rN (13) and 0¿ is the site fraction of component i defined by 0; = s^iNi/is^Nx + s2r2N2) (14) Flory7 assumed that segments of both molecules in the mixture were arbitrarily chosen to be of equal core volume. (This assumption leads to linearity of the molecular core volume in the mole fraction.)…”