Z. Phys. B - Condensed Matter 61, 311-323 (1985) Condensed Ze. c.r,. Matter for Physik B 9 Springer-Verlag 1985 Scaling and Mean-Field-Like Behaviour in Phase Separation Processes Dieter W. Heermann Institut ffir Physik, Johannes-Gutenberg-Universit~it, Mainz, Federal Republic of Germany and Institut ftir Festktirperforschung, Kernforschungsanlage Jiilich, Federal Republic of Germany Received June 4, 1985 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. 1. Introduction Consider a binary (A, B)-mixture such as a binary alloy or a polymer blend with a miscibility gap. A fast quench from a homogeneous thermal equilib- rium state to a state inside the miscibility gap is performed. This renders the system thermally unsta- ble and it evolves towards a stable equilibrium state, where the two phases, one A- and the other B-rich coexist (c.f. Fig. 1). The evolution is poorly understood for systems with short-range interaction. On the other hand, systems with infinite-range interaction, i.e., mean-field [1-3] are well understood. In mean-field theory two re- gions have to be distinguished into which a quench is performed: the metastable and the spinodal region. In the metastable region the initial evolution takes place by localized fluctuations [4 8], whereas in the spinodal region it takes place by delocalized long- wavelength fluctuations [9-13]. The metastable and the spinodal region are separated by the spinodal. Theoretical considerations [14-17], Monte Carlo calculations [18] as well as experiments [19] in- dicated that the above division into metastable and intrinsically unstable states are an artifact of the mean-field theory. The spinodal singularity is roun- ded [17-20] and there is a gradual transition from the metastable to the spinodal region. The cited rt ONE-PHASE REGION / i I TWO -PHASE REGION C Fig. 1. Shown is a schematicat phase diagram of a binary system. The full line represents the coexistence curve and the broken curve the spinodal. The spinodal separates the metastable from the spinodal region. Indicated is a fast quench from a thermody- namic equilibrium state to a non-equilibrium state in the metasta- ble region. The system then evolves towards coexistence Monte Carlo work was done for models with short- range interaction. Recent studies [21-23] on models with medium- and long-range interaction indicated