Aggregation processes are studied within a number of different fields--c- loid chemistry, atmospheric physics, astrophysics, polymer science, and biology, to name only a few. Aggregation pro ces ses involve monomer units (e. g. , biological cells, liquid or colloidal droplets, latex beads, molecules, or even stars) that join together to form polymers or aggregates. A quantitative theory of aggre- tion was first formulated in 1916 by Smoluchowski who proposed that the time e- lution of the aggregate size distribution is governed by the infinite system of differential equations: (1) K . . c. c. - c k = 1, 2, . . . k 1. J 1. J L ~ i+j=k j=l where c is the concentration of k-mers, and aggregates are assumed to form by ir k reversible condensation reactions [i-mer + j-mer -+ (i+j)-mer]. When the kernel K . . can be represented by A + B(i+j) + Cij, with A, B, and C constant, and the in- 1. J itial condition is chosen to correspond to a monodisperse solution (i. e. , c (0) = 1 0, k > 1), then the Smoluchowski equation can be co' a constant, and ck(O) solved exactly (Trubnikov, 1971, Drake, 1972, Ernst, Hendriks, and Ziff, 1982, Dongen and Ernst, 1983, Spouge, 1983, Ziff, 1984). For arbitrary K , the solution ij is not known and in some ca ses may not even exist.
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ISBN | 9783540156567 |
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Sprache | eng |
Cover | Kartonierter Einband (Kt) |
Verlag | Springer Berlin Heidelberg |
Jahr | 19850701 |
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