Kinetics of Solid State Reactions With Fractal Reagent

Journal of Materials Synthesis and Processing - Tập 6 - Trang 305-309 - 1998
S. V. Kalinin1, A. A. Vertegel1, N. N. Oleynikov1, Yu. D. Tretyakov1
1Inorganic Chemistry Division, Department of Chemistry, Moscow State University, Moscow, Russia

Tóm tắt

In the present research we theoretically studied the kinetics of nucleation-limited solid state reactions as influenced by the fractal properties of solid reagent. We consider the model of equal-sized primary particles assembled in fractal cluster. The geometry of such an object is assumed to be described solely by its fractal dimension D and by upper (R max) and lower (R min) cutoffs of fractality further identified with the overall size of the object and the size of the primary particle correspondingly. Depending on the ratio between R max, R min and the radius of the critical nucleus R nucl the following cases are considered: (1) R max ∼ R nucl. In this case the reaction kinetics is described by the equation: α = 1 − B{ln(k′ τ + 1)}D/(D−3), where B, k′ are constants. Numerical solution of this equation gives rise to n-order reaction kinetics with n & 1. (2) R min ≪ R nucl ≪ R max. In this case under certain conditions there can exist non-trivial critical density ρcrit ≠ 0, 1 that favors the formation of the critical nuclei of the new phase. The asymptotic kinetic equation for large times corresponds to n-order reaction with n = (D + 3)/(D + 1). (3) R min ≪ R nucl ∼ R max′. In this case the reaction follows the first-order kinetics with D-dependent rate constant.

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Tài liệu tham khảo

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Thông tin xuất bản

Journal of Materials Synthesis and Processing

Tập 6

305-309

Thông tin tác giả