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In accurate coagulation measurements, the observed coagulation rate should be extrapolated to time zero to find the rate of formation of doublets from singlet particles. In the theoretical calculation of coagulation rates, generally a steady state is assumed. At the onset of coagulation, however, a transient state is present. The results are given of numerical computations of the transient-state coagulation rate for the cases of Van der Waals attraction only and of Van der Waals attraction combined with double layer repulsion. The duration of the non-steady state is about tile same as the one calculated by Von Smoluchowski for the case of no long-range interaction. It is expected that no transient effects will be found in classical coagulation experiments, but they may interfere with rapid (stopped-flow) measurements of the rate of rapid coagulation.

The Flory–Huggins formulation of the combinatorial entropy, supplemented with residual free energy, is applied locally to obtain the interfacial free energy and the concentration profile of polymer in the interface between two demixed polymer solution phases. Two choices were investigated for the residual free energy: a “regular solution” formulation and an empirical formulation of Koningsveld for polystyrene in cyclohexane. Asymptotic, analytical solutions of the equations near the critical solution point and solutions obtained by numerical calculations are given as a function of temperature for several molecular weights. At temperatures farther below the critical temperature the equations have no solutions. The reason for this is not entirely clear. The local formulation of the free energy used here is an improved version of a previous one, which gave wrong results for asymmetric systems (polymer in a low molecular weight solvent). This newer version is consistent with our theory of critical opalescence and gives a relation between the interface “thickness” and the correlation range of the concentration fluctuations. The calculated correlation ranges were in good accord with those found experimentally by Debye, Chu, and Woerman. That the newer version of our equations for an interface gives no acceptable solutions at lower temperatures could be caused by a “collapse” of a diffuse to a sharp interface as suggested by Nose.

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