Abstract
A study is made of the coupling between chemical reaction and diffusion in a dense fluid. Our analysis utilizes the projection operator formalism and a generalized Langevin equation that is based on irreversible, phenomenological equations of motion instead of conventional Hamiltonian mechanics. It also is shown that this same “non-Hamiltonian” theory provides a simple way of deriving Kawasaki's mode-mode coupling theory of diffusion.
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N. Xystris and J. S. Dahler,J. Chem. Phys. 68:354, 374, 387 (1978).
S. H. Northrup and J. T. Hynes,J. Chem. Phys. 68:3203 (1978).
R. Kapral,J. Chem. Phys. 68:1903 (1978).
K. Kawasaki,Phys. Rev. 150:291 (1966);Ann. Phys. 61:1 (1970).
P. Fulde, L. Pietronero, W. R. Schneider, and S. Strässler,Phys. Rev. Lett. 35:1776 (1975); W. Dieterich, I. Peschel, and W. R. Schneider,Z. Phys. B 27:177 (1977); W. Dieterich, T. Geisel, and I. Peschel,Z. Phys. B 29:5 (1978).
R. Zwanzig, inLectures in Theoretical Physics, W. E. Britten, B. W. Downs and J. Downs, eds. (Interscience, New York, 1961).
H. Mori,Progr. Theor. Phys. 33:423 (1965).
F. C. Collins and G. Kimball,J. Colloid. Sci. 4:425 (1949); R. M. Noyes,Prog. Reac. Kin. 1:128 (1961); G. Wilemski and M. Fixman,J. Chem. Phys. 58:4009 (1973); B. U. Felderhof and J. M. Deutsch,J. Chem. Phys. 64:4551 (1976); J. M. Deutch, B. U. Felderhof, and M. J. Saxton,J. Chem. Phys. 64:4559 (1976).
M. S. Jhon and J. S. Dahler,J. Chem. Phys. 68:812 (1978).
D. Forster,Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions (W. A. Benjamin, New York, 1976).
R. D. Mosteller and J. J. Duderstadt,J. Stat. Phys. 9:197 (1973);11:409 (1974).
A. Z. Akcasu,Phys. Rev. A 7:182 (1973); G. F. Mazenko,Phys. Rev. A 7:222 (1973).
M. Tokuyama and H. Mori,Prog. Theor. Phys. 55:411 (1976); N. Hashitsume, F. Shibata, and M. Shingu,J. Stat. Phys. 11:155 (1977); F. Shibata, Y. Takahashi, and N. Hashitsume,J. Stat. Phys. 11:171 (1977).
K. S. J. Nordholm and R. Zwanzig,J. Stat. Phys. 13:347 (1975); K. S. J. Nordholm Thesis, Univ. of Maryland (1974); H. Grabert,Z. Phys. B 26:79 (1977).
M. S. Jhon, R. C. Desai, and J. S. Dahler,J. Chem. Phys. 68:5615 (1978).
N. Szabo,J. Phys. C. Solid State Phys. 5:L241 (1973); R. Evans, B. L. Gyorffy, N. Szabo, and J. M. Ziman, inThe Properties of Liquid Metals (Proc. 2nd Int. Conf., Tokyo, 1972) (Taylor and Frances, London, 1973), p. 319; J. S. Rousseau, J. C. Stoddert, and N. H. March, inThe Properties of Liquid Metals (Proc. 2nd Int. Conf., Tokyo, 1972) (Taylor and Frances, London, 1973), p. 249; L. E. Ballentine and W. J. Heaney,J. Phys. C. Solid State Phys. 7:1985 (1974).
I. M. Glazman and Ju. I. Ljubic,Finite-Dimensional Linear Analysis (The MIT Press, Cambridge, Mass., 1974), Chapter 10.
R. A. Ferrell,Phys. Rev. Lett. 24:1169 (1970).
D. Bedeaux and P. Mazur,Physica 73:431 (1974).
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This research was supported by a grant from the National Science Foundation.
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Jhon, M.S., Dahler, J.S. A mode-mode coupling theory of chemical reaction in a dense fluid. J Stat Phys 20, 3–18 (1979). https://doi.org/10.1007/BF01013743
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DOI: https://doi.org/10.1007/BF01013743