Abstract
Extensive Monte Carlo calculations are used to study the still not well understood process of phase separation in binary systems. The results show that for a separation dominated by long-wavelength fluctuations a mean-field description holds in certain concentration regions. This, however, is only true for short times after the system has been brought into a non-equilibrium state. A crucial parameter is the interaction range. It determines the region and the time where the mean field description is valid. At later times the structure factor exhibits dynamical scaling. Scaling is also investigated for the metastable states. The results are applicable to polymer blends with long chains or binary alloys with long-range forces.
Similar content being viewed by others
References
Waals, J.D. van der: Dissertation Leiden 1873
Lebowitz, J.L., Penrose, O.: J. Math. Phys.7, 98 (1966)
Penrose, O., Lebowitz, J.L.: In: Studies in statistical mechanics, Lebowitz, J.L., Montroll E.W., eds. Vol. 7. Amsterdam: North Holland 1979
Becker, R., Döring, W.: Ann. Phys. (Leipzig)24, 719 (1935)
Döring, W.: Z. Phys. Chem.36, 317 (1937)
Cahn, J.W., Hilliard, J.E.: J. Chem. Phys.28, 258 (1958)
Cahn, J.W., Hilliard, J.E.: J. Chem. Phys.31, 688 (1959)
Zezzlemoyer, A.C. (ed.): Nucleation I. New York: Dekker 1969
Cahn, J.W.: Acta Metall.9, 795 (1961)
Cahn, J.W.: J. Chem. Phys.42, 93 (1965)
Cahn, J.W.: Trans. Am. Inst. Min. Metall. Pet. Eng.166, 242 (1968)
Hilliard, J.E.: In: Phase transitions, Aaronsen, H.I. (ed.). Cleveland: American Society for Metals 1970
Cook, H.E.: Acta Metall.18, 297 (1970)
Fisher, M.E.: Physica3, 255 (1967)
Langer, J.S.: Ann. Phys. (NY)41, 108 (1967)
Langer, J.S.: Physica73, 61 (1974)
Binder, K.: Phys. Rev. B8, 3423 (1973)
Binder, K., Müller-Krumbhaar, H.: Phys. Rev. B9, 2328 (1974);
Binder, K.: Ann. Phys.98, 390 (1976)
Chu, B., Schoenes, F.J., Fisher, M.E.: Phys. Rev.185, 219 (1969)
Binder, K., Billotet, C., Mirold, P.: Z. Phys. B — Condensed Matter and Quanta30, 183 (1978)
Heermann, D.W., Klein, W., Stauffer, D.: Phys. Rev. Lett.49, 1262 (1982)
Heermann, D.W.: Phys. Rev. Lett.52, 1126 (1984)
Heermann, D.W., Coniglio, A., Klein, W., Stauffer, D.: J. Stat. Phys.36, 447 (1984)
Snyder, H.L., Meakin, P., Reich, S.: Macromolecules16, 757 (1983)
Binder, K.: Phys. Rev. A29, 341 (1984)
Gunton, J.D., San Miguel, M., Sahni, P.S.: In: Phase transitions and critical phenomena. Domb, C., Lebowitz, J.L. (eds.), Vol. 8. New York: Academic Press 1983
Langer, J.S.: Ann. Phys. (NY)65, 53 (1971)
Flory, P.J.: Principles of polymer chemistry. Ithaca: Cornell University Press 1967
Ornstein, L.S., Zernike, F.: Proc. K. Ned. Akad. Wet.17, 793 (1914)
See, for example, the review on liquid mixtures by Goldburg, W.I.: In: Scattering techniques applied to supramolecular and nonequilibrium systems. Sow-Hsin Chen et al. (eds.). New York: Plenum 1981
For a review on small-angle scattering experiments on Al−Zn alloys, see Gerold, V., Kostzro, G.: J. Appl. Crystallogr.11, 376 (1978)
Marro, J., Bortz, A.B., Kalos, M.H., Lebowitz, J.L.: Phys. Rev. B12, 2000 (1975)
Sur, A., Lebowitz, J.L., Marro, J., Kalos, M.H.: Phys. Rev. B15, 3014 (1977)
Khachaturyan, A.G.: Theory of phase transitions and the structure of solid solutions. Moskau: Nauka 1974
Skripov, V.P., Skripov, A.V.: Sov. Phys. Usp.22, 389 (1979)
Parashinskii, A.Z., Pokiovski, V.L.: In: Fluctuation theory of phase transitions. Moskau: Nauka 1975
Binder, K.: J. Chem. Phys.79, 6387 (1983)
Cahn, J.W.: Acta Metall.14, 1685 (1966)
Brout, R.: Phys. Rev.115, 824 (1959)
Grant, M., San Miguel, M., Vinals, J., Gunton, J.D.: Preprint
Marro, J., Valles, J.L.: Phys. Lett. A95, 443 (1983)
Marro, J., Valles, J.L., Sancho, J.M.: In: Proc. of the International Conference on phase transitions in solids, Maleme Crete 1983
Singhal, S.P., Herman, H., Kostzro, G.: J. Appl. Crystallogr.11, 572 (1978)
Agarwal, S., Herman, H.: Scr. Metall.7, 503 (1973)
Chou, Y.C., Goldburg, W.I.: Phys. Rev. A20, 2015 (1979)
Marro, J., Lebowitz, J.L., Kalos, M.H.: Phys. Rev. Lett43, 282 (1979)
Lebowitz, J.L., Marro, J., Kalos, M.H.: Acta Metall.30, 297 (1982)
Marro, J., Bortz, A.B., Kalos, M.H., Lebowitz, J.L.: Phys. Rev. b12, 2000 (1975)
Abraham, D.F., Koch, S.W., Desai, R.C.: Phys. Rev. Lett.49, 923 (1982)
Langer, J.S., Bar-on, M., Miller, H.D.: Phys. Rev. A11, 1417 (1975)
Binder, K., Billotet, C., Mirold, P.: Z. Phys. B — Condensed Matter and Quanta30, 313 (1978)
Furukawå, H.: Phys. Rev. Lett.43, 136 (1979)
Snyder, H.L., Meakin, P.: J. Chem. Phys.79, 5588 (1983)
Lifshitz, I.M., Slyozov, V.V.: J. Phys. Chem. Solids13, 35 (1961)
Wagner, C.: Z. Elektrochem.65, 581 (1961)
Heermann, D.W.: Z. Phys. B — Condensed Matter55, 309 (1984)
Binder, K., Stauffer, D.: Phys. Rev. Lett.33, 1006 (1974)
Binder, K.: Phys. Rev. B15, 4425 (1977)
Knobler, C.M., Wong, W.C.: J. Phys. Chem.85, 1972 (1981)
Kawasaki, K., Yalabik, M.C., Gunton, J.D.: Phys. Rev. A17, 455 (1978)
Heermann, D.W., Binder, K.: (to be published)
Binder, K., Heermann, D.W.: In: Proceedings of the NATO Conference Geilo, Norway 1985
Heermann, D.W.: (to be published)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heermann, D.W. Scaling and mean-field-like behaviour in phase separation processes. Z. Physik B - Condensed Matter 61, 311–323 (1985). https://doi.org/10.1007/BF01317798
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01317798