Abstract
A general linear response theory is presented to calculate the zero-wavevector and zero-frequency reaction rate coefficient for particles diffusing into absorbing spheres. Allowance is made for possible incomplete particle absorption. A Faxén-like theorem for chemical reactions is derived. The problem is solved completely for a simple regular array of sinks. Exact analytic expressions for the rate coefficient as a function of sink volume fraction are obtained for the sc and fcc lattices. The case of a disordered array of sinks is also considered and the leading order nonanalytic density dependence of the rate coefficient is calculated. In both cases an increase in the rate coefficient with sink density in a local region of the system is found. The general formalism is extended to examine the modification to the particle diffusion coefficient due to the presence of the spheres. For regular arrays of spheres, the mean field result is reproduced.
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References
M. v. Smoluchowski,Phys. Z. 17:557 (1916).
R. M. Noyes,Prog. Reac. Kin. 1:128 (1961) and references therein.
B. U. Felderhof and J. M. Deutch,J. Chem. Phys. 64:4551 (1976).
P. Mazur and D. Bedeaux,Physica 76:235 (1974).
L. M. Hafkensheid and J. Vlieger,Physica 75:57 (1974);79A:517 (1975).
R. Kapral and D. Bedeaux,Physica 91A:590 (1978).
D. Bedeaux, R. Kapral, and P. Mazur,Physica 88A:88 (1977).
F. C. Collins and G. E. Kimball,J. Colloid Sci. 4:425 (1949).
A. Albano, D. Bedeaux, and P. Mazur,Physica 80A:89 (1975).
B. R. A. Nijboer and F. W. de Wette,Physica 23:309 (1957).
H. L. Friedman,Ionic Solution Theory (Interscience, New York, 1962).
K. F. Freed and M. Muthukumar,J. Chem. Phys. 69:2657 (1978); and C. Y. Mou and S. A. Adelman,J. Chem. Phys. 69:3135 (1978).
P. A. Hiltner, Y. S. Papir, and I. M. Krieger,J. Phys. Chem. 75:1881 (1971).
B. U. Felderhof,J. Chem. Phys. 66:4385 (1977), esp. Section VII.
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Research supported in part by a grant from the National Research Council of Canada.
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Lebenhaft, J.R., Kapral, R. Diffusion-controlled processes among partially absorbing stationary sinks. J Stat Phys 20, 25–56 (1979). https://doi.org/10.1007/BF01013745
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DOI: https://doi.org/10.1007/BF01013745