Concentration Dependence of Polymer Chain Configurations in Solution

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Abstract
On the basis of the theory of fluids and of the fashion prevailing in the statistical thermodynamics of dilute chain polymer solutions, the segment distribution functions are formally derived as a power series in concentration. The mean‐square radius of gyration and end‐to‐end distance at finite concentrations are calculated by using the general equations derived and introducing the modified random flight model. Evaluation is carried out up to the linear term in concentration. The coefficients of the linear terms are obtained as a power series in the excluded volume parameter, and also appropriate closed forms for those are proposed, which might be properly applied to good solvent systems. The results show that the polymer chain dimension decreases with increasing concentration. Then the concentration‐dependent term in the intramolecular intensity function in light scattering is evaluated. It is pointed out that the separation of this term and the intermolecular correlation leads to the possibility of estimation of the polymer chain dimension at finite concentrations by light‐scattering measurements. Finally, the Huggins constant k′ in the viscosity‐concentration relation is phenomenologically calculated. The concentration dependence of polymer chain dimensions proves to explain satisfactorily the effect of solvent power on the k′ constant.