Lattice theory of polymer solutions

The chemical potential of the solute particles in a solution can be written as 

When there is no interaction, the activity is given by y = 1 and f = so that the diffusion coefficient reduces to the marker diffusion coefficient 

The factor in the parenthesis of (2.76) appears due to the molecular interaction, and is called the thermodynamic factor of the diffusion coefficient. The diffusion coefficient can be expanded in powers of the concentration in the dilute region as 

We modify the conventional regular solution model [5] of low-molecular weight molecules to apply it to solutions of long chain molecules in which the molecular weight of the solute molecules is much larger than that of the solvent molecules. The entropy of mixing decreases with the molecular weight of polymers due to the reduction of the freedom in the translational motion of the molecules. 

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Fig. 17 B/E-p dependence of the critical temperatures of liquid-liquid demixing (dashed line) and the equilibrium melting temperatures of polymer crystals (solid line) for 512-mers at the critical concentrations, predicted by the mean-field lattice theory of polymer solutions. The triangles denote Tcol and the circles denote T cry both are obtained from the onset of phase transitions in the simulations of the dynamic cooling processes of a single 512-mer. The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...

It has been remarked in the preceding sections that the equilibrium concentration of monomer in solution of its living polymer is affected by the nature of the solvent and by the polymer concentration, because these factors influence the activities of the components. A quantitative treatment of these effects, based on Scott s modification of the standard lattice theory of polymer solutions (33), has been outlined recently by Bywater (34). 

Hory-Huggins Lattice Theory of Polymer Solutions... 

The linear relationship between the melting points and values in (4.14) is further confirmed by Monte Carlo simulations of polymers, and the results are shown in Fig. 4.8. The high consistency in the results between the lattice theory and Monte Carlo simulations validates the mean-field treatment in the lattice theory of polymer solutions. 

It has been widely confirmed with numerous experiments that polymer solutions reveal remarkable deviation from the behaviour expected for an ideal solution [5]. According to the Flory-Huggins lattice theory of polymer solutions [6,7], Apo is given by ... 

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