Kinetics Of Homogeneous Nucleation Research Articles

Studies on the freezing of pure liquids - II. The kinetics of homogeneous nucleation in supercooled liquids

A modified form of Turnbull & Fisher’s equation for the rate of nueleation in pure liquids is derived from the more general solution of Frenkel to the non-equilibrium steady -state kinetic problem . Recent developments in relaxation theory, based on the Zeldovich— Frenkel formulation of the time-dependent flow of embryos over the size variable g , show that under certain conditions the nucleation time lag may be exceedingly sensitive to the initial state of the condensing system. Frisch’s integral for the nucleation time lag is evaluated for two initial distributions of embryo size. The results, which are of general form, are used to derive expressions for the time lag in supercooled liquids. Methods are given for estimating certain parameters required in the computation of time lags in supercooled liquids.

Theory of Formation of Polymer Crystals with Folded Chains in Dilute Solution.

A detailed interpretation of the kinetics of homogeneous nucleation and growth of crystals of a linear homopolymer from dilute solution is given. The probability of forming both nuclei with folded chains, and conventional bundlelike nuclei, from dilute solution is analyzed. It is predicted that at sufficiently high dilution, critical nuclei of length will be formed from single polymer molecules by sharp folding of the chain backbone. The step height of the nucleus is given approximately by . Here σe is the free energy required to form a unit area of the loop-containing end surfaces, and Δf is the free energy difference per unit volume of crystal between the crystalline and solution states. The quantity Δf is approximately proportional to the degree of supercooling ΔT. The growth of these nuclei is then analyzed. After growth, the resulting crystal is flat and platelike, the loops formed by the chain folds being on the upper and lower surfaces. Kinetic factors determine that the distance between the flat surfaces in the grown crystal will vary over only a narrow range about a value that is in the vicinity of 1*=4σe/Δf. (Neglecting effects due to edge free energies, the theoretical upper and lower limits are 1*=4σe/Δf and 1*=2σe/Δf, respectively.) In some cases the predicted temperature dependence of the step height of the grown crystal, 1* = const./ΔT, may be modified by the existence of a constant term resulting from the presence of an edge free energy ϵp. A grown loop-type crystal is predicted to be stable in comparison with a bundlelike crystal of the same shape and volume in a sufficiently dilute solution. The logarithm of the nucleation rate is approximately proportional to 1/(ΔT)2 near the melting point. The exponent n in the free growth rate law is predicted under various assumptions. To the extent that comparison is possible, the predictions given agree with the experimental results obtained by Keller and O’Connor and others on single crystals of unbranched polyethylene grown from dilute solution.A survey is given of homogeneous nucleation in bulk polymers, where the conventional bundlelike nucleus containing segments from many different molecules is valid, and the essential results compared with those calculated for the dilute solution case.The theory given for loop nuclei is both general and precise enough at the critical points to suggest that, on crystallization from sufficiently dilute solution, crystals of a definite step height are commonly to be expected for other crystallizable linear polymers than polyethylene, provided loop formation is sterically possible.