Thermodynamics of Dilute Solutions of High Polymers

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Abstract
Whereas extensive efforts have been directed recently toward improving the mathematical exactness of the statistical mechanical theory of polymer solutions, fundamental limitations set by the nature of the physical approximations have not received adequate attention. A careful comparison between theory and experiment in dilute solutions reveals a large discrepancy between the calculated and the observed departures from the ideal entropy of dilution. The assumption of random occupancy of lattice sites by polymer segments, which is employed in previous treatments, is at fault. In very dilute solutions of high polymers the solution is microscopically discontinuous. Two regions of the volume can be distinguished: one is totally unoccupied by segments of polymer molecules; the other consists of regions encompassed by the irregularly coiled polymer molecules. In the latter the concentration of lattice cells occupied by polymer segments is determined by the configuration of the polymer molecule, being independent of the over‐all average concentration. The above concepts have been employed in the formulation of a new statistical mechanical theory of the thermodynamic properties of very dilute high polymer solutions. The deviation from ideality, e.g., the slope of the osmotic pressure: concentration ratio plotted against concentration, is related to the ``effective volume ratio'' of the irregularly coiled solute molecule. This ratio, or ``swelling factor,'' can be estimated from the intrinsic viscosity of the polymer. Satisfactory agreement between theory and experiment is obtained in this way. The comparatively small deviations from ideality which are observed for protein molecules, not extremely dissymmetric in shape, receive semi‐quantitative interpretation under the present theory. The failure, of the van Laar expression to account for heats of mixing in polymer solutions at all concentrations is a necessary consequence of the discontinuities in the dilute region.

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