Abstract
We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density ρc is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields γ=2ν=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields ρc∼L −2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length ξ∼(δρ/ρ c )−v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from ρc be no larger thanδρ∼L −2. Otherwise, crossover behavior will be observed.
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References
D. Stauffer,Introduction to Percolation Theory (Taylor & Francis, London, 1985); D. Stauffer, inPercolation, Structures and Processes, G. Deutscher, R. Zallen, and J. Adler, eds. (Adam Hilger, Bristol, England, 1983).
A. Coniglio, U. De Angelis, and A. Forlani,J. Phys. A 10:1123 (1977).
Y. C. Chiew and E. D. Glandt,J. Phys. A 16:2599 (1983).
Y. C. Chiew and G. Stell,J. Chem. Phys. 90:4956 (1989); G. Stell,J. Phys. A 17:L859 (1984).
T. DeSimone, S. Demoulini, and R. M. Strati,J. Chem. Phys. 85:391 (1986).
J. Xu and G. Stell,J. Chem. Phys. 89:1101 (1988).
Y. C. Chiew, G. Stell, and E. D. Glandt,J. Chem. Phys. 83:761 (1985).
J. K. Percus and G. J. Yevick,Phys. Rev. 110:1 (1958); J. K. Percus, inEquilibrium Theory of Classical Fluids, H. L. Frisch and J. L. Lebowitz, eds. (Benjamin, New York, 1964).
E. M. Waisman,Mol. Phys. 25:45 (1973).
S. A. Safran, I. Webman, and G. S. Grest,Phys. Rev. Lett. 55:1896 (1985).
J. G. Saven, J. L. Skinner, and J. R. Wright,J. Chem. Phys. (1991).
M. Lupkowski and P. A. Monson,J. Chem. Phys. 89:3300 (1988).
D. Laria and F. Vericat,Phys. Rev. B 40:353 (1989).
D. Chandler, inStudies in Statistical Mechanics VIII, E. W. Montroll and J. L. Lebowitz, eds. (North-Holland, Amsterdam, 1982), p. 275; and P. A. Monson and G. P. Morriss,Adv. Chem. Phys. 77:451 (1990).
D. Chandler, J. D. Weeks, and H. C. Andersen,Science 220:787 (1983).
I. Balberg, N. Binenbaum, and N. Wagner,Phys. Rev. Lett. 52:1465 (1984); I. Balberg, C. H. Anderson, S. Alexander, and N. Wagner,Phys. Rev. B 30:3833 (1984); A. L. R. Bug, S. A. Safran, and I. Webman,Phys. Rev. B 33:4716 (1986).
T. L. Hill,J. Chem. Phys. 23:617 (1955); T. L. Hill,Introduction to Statistical Thermodynamics (Addison-Wesley, Reading, Massachusetts, 1960).
B. M. Ladanyi and D. Chandler,J. Chem. Phys. 62:4308 (1975).
D. Chandler and L. R. Pratt,J. Chem. Phys. 65:2925 (1976); L. R. Pratt and D. Chandler,J. Chem. Phys. 66:147 (1977).
D. Chandler and H. C. Andersen,J. Chem. Phys. 57:1930 (1972).
D. Chandler,Mol. Phys. 31:1213 (1976).
L. J. Lowden, RISM, RISMGR, RISMSK: Program Number QCPE 306, Quantum Chemistry Program Exchange, Indiana University, Bloomington, Indiana 47401.
D. Chandler, Y. Singh, and D. M. Richardson,J. Chem. Phys. 81:1975 (1984); D. Chandler,Chem. Phys. Lett. 139:108 (1987).
K. S. Schweizer and J. G. Curro,Chem. Phys. 149:105 (1990), and references cited therein.
F. Hirata and R. M. Levy,J. Phys. Chem. 93:479 (1989).
I. Balberg and N. Binenbaum,Phys. Rev. A 35:5174 (1987).
D. M. Bigg,Polym. Eng. Sci. 19:1188 (1979).
I. Balberg,Phil. Mag. 56:991 (1987).
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Leung, K., Chandler, D. Theory of percolation in fluids of long molecules. J Stat Phys 63, 837–856 (1991). https://doi.org/10.1007/BF01029986
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DOI: https://doi.org/10.1007/BF01029986