Abstract
To calculate the formation energy of a binary mixture droplet out of the gas phase in classical ‘heteromolecular’ nucleation theory, one has to take into account that the concentration of the solution near the droplet surface can be different from the composition in the droplet interior (‘surface enrichment’, Gibbs adsorption equation). This problem is solved in a simple picture where the composition varies spatially but where one has a sharp liquid-gas surface. In a material independent continuum theory, the variation of the composition is assumed to give a free energy contribution proportional to the square of the concentration gradient. This treatment of the surface enrichment gives a formation energy contribution smaller (for large droplets) by a factor 1 −1/√3 than previous theories (Döring and Neumann, 1940; Stauffer and Kiang, 1974), which therefore overestimated the surface enrichment for large droplets. This continuum theory is tested by Monte Carlo methods on a particularly symmetric mixture, the magnetic spin 1/2 Ising model. Here up-spins are identified with one type of molecule and down spins with another type. Reasonable agreement with the continuum theory is found, even for parameter ranges where the assumptions of the continuum theory are no longer valid. The results show clearly a strong but smooth variation of the concentration within the droplet. They constitute to our knowledge the first computer simulations of mixture microclusters.
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References
Abraham, F. F.: 1974, Homogeneous Nucleation Theory. Academic Press, London/New York.
Binder, K.: 1974, Thin Solid Films 20, 367.
Binder, K.: 1975, in C. Domb, and M. S. Green (eds.), Phase Transitions and Critical Phenomena, Vol. 5. Academic Press, London/New York.
Binder, K. and Hohenberg, P. C.: 1974, Phys. Rev. B9, 2194.
Binder, K., Rauch, H., and Wildpaner, V.: 1970, J. Phys. Chem. Solids 31, 391.
Binder, K., Rauch, H., and Wildpaner, V.: 1974, Moscow Magnetism Conference 1973, to be published.
Cox, R. A.: 1974: Tellus 26, 235.
Chu, B.: 1972, Ber. Bunsenges. 76, 202.
Döring, W. and Neumann, K.: 1940, Z. Physik. Chem. A186; 193; 203.
Doyle, G. J.: 1961, J. Chem. Phys. 35, 795.
Englert-Chwoles, A. and Prigogine, I.: 1958, Nuovo Cim. Suppl. 9, 347.
Eyring, H. and Jhon, M. S.: 1969, Significant Liquid Structures, Wiley, New York.
Fisk, S. and Widom, B.: 1969, J. Chem. Phys. 50, 3219.
Flood, H.: 1934. Z. Physik. Chem. A170, 286.
Guggenheim, E. A.: 1952, Mixtures, Clarendon Press, Oxford.
Kadanoff, L. P., Götze, W., Hambler, D., Hecht, R., Lewis, E. A. S., Palciauskas, V., Rayl, M., Swift, J., Aspnes, D., and Kane, J.: 1967, Rev. Mod. Phys. 39, 395.
Kiang, C. S., Stauffer, D., Mohnen, V. A., Bricard, J., and Vigla, D.: 1973, Atmos. Envir. 7, 1279.
Kiang, C. S. and Stauffer, D.: 1974, Faraday Symp. Chem. Soc. 7, 26.
Kim, S. W., Eyring, H., and Lee, Y. T.: 1969, J. Chem. Phys. 51, 3967.
Langer, J. S. and Turski, L. A.: 1973, Phys. Rev. A8, 3230.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E.: 1953, J. Chem. Phys. 21, 1087.
Müller-Krumbhaar, H. and Binder, K.: 1973, J. Stat. Phys. 8, 1.
Rusanov, A. I.: 1971, in J. F. Danielli, M. D. Rosenberg, and D. A. Cadenhead (eds.), Progress in Surface and Membrane Science, Vol. 4, Academic Press, London/New York.
Sarkies, K. W. and Frankel, N. E.: 1971, J. Chem. Phys, 54, 433 and preprint.
Stauffer, D. and Kiang, C. S.: 1974, Icarus 21, 129.
Thomas, S.: 1974, Appl. Phys. Letters 24, 1.
Tolman, R. C.: 1949, J. Chem. Phys. 17, 333.
Wildpaner, V.: 1974, Z. Physik 270, 215.
Wu, E. S. and Webb, W. W.: 1973, Phys. Rev. A8, 2065 and 2077.
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After October 1, 1978 at Institute for Theoretical Physics, University, D-66 Saarbrücken 15, F.R.G.
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Stauffer, D., Binder, K. & Wildpaner, V. Structure of binary solution droplets: Continuum theory and Monte Carlo simulation. Water, Air, and Soil Pollution 3, 515–525 (1974). https://doi.org/10.1007/BF00341005
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DOI: https://doi.org/10.1007/BF00341005