Theory of phase transition kinetics with growth site impingement. I. Homogeneous nucleation

Abstract

The nonlinear integral equations governing phase transition kinetics with homogeneous nucleation and growth site impingement are developed and solved to the first order for the two‐dimensional case. It is shown that the fractional transformed area at time t is given approximately by a(t) = Kt3/(1 + Kt3). The iteration method used to get the solution is applicable to certain other nonlinear differential and integral equations. It is shown that the theory predicts the total number of growth sites formed, and that the nucleation rate and growth constants can be deduced from this and the gross kinetic data. The extension of the method of three‐dimensional growth is indicated.

Kinetics and thermodynamics of adsorption of congo red on cellulose

“…Aiming at improving the Avrami model, Tobin [22][23][24] proposed a different expression. The Tobin equation is generally expressed as (15) The linearized form of this equation is presented as: (16) where k t is the Tobin kinetic constant, and n t is the Tobin exponent.…”

Isothermal crystallization kinetics of poly(ethylene terephthalate) and poly(methyl methacrylate) blends

“…k a and n a are temperature dependent parameters and are specific to a given crystalline morphology and type of nucleation [14]. The Tobin equation [16] is proposed on the basis of kinetic phase transformation and is given as Equation (4): (4) k t and n t are the Tobin rate constant and Tobin exponent respectively. The Tobin exponent, n t , is governed by different types of nucleation and growth mechanisms [16].…”

“…The Tobin equation [16] is proposed on the basis of kinetic phase transformation and is given as Equation (4): (4) k t and n t are the Tobin rate constant and Tobin exponent respectively. The Tobin exponent, n t , is governed by different types of nucleation and growth mechanisms [16]. Urbanovici and Segal [19] developed a new kinetic equation, which is a modification of the Avrami model.…”

“…Although a knowledge of the crystallization kinetics of polymeric materials is important from the aspects of both fundamental and practical applications, only few studies have been carried out on the crystallization behaviour and rheological characterization of PET/PMMA blends. For studying the isothermal crystallinity a number of mathematical models [14][15][16][17][18] have been proposed. Unlike Avrami model, use of the Tobin [18] and model to analyze the isothermal crystallization data of semi-crystallineamorphous polymers is rarely reported in the literature.…”

Theory of phase transition kinetics with growth site impingement. III. Mixed heterogeneous–homogeneous nucleation and nonintegral exponents of the time

“…This is hardly a satisfactory explanation, since such overlap occurs in pure homogeneous nucleation, which leads to integral exponents. 3 Heterogeneous nucleation where the nuclei induce growth sites in a first-order process leads to the fractional exponents 2.85 (two dimensions) and 3.74 (three dimensions),4 but cannot account for other exponents. In heterogeneous nucleation, where all nuclei initiate growth simultaneously, the time exponent is two for two-dimensional growth and three for three-dimensional g r~w t h .~,~ There is no obvious reason why, after such nuclei have started to grow, homogeneous nuclei could not start to form in untransformed material.…”