Interfacial structure, surface enrichment, interdiffusion, spinodal decomposition

6 Interfacial structure, surface enrichment, interdiffusion, spinodal decomposition 

For simulating bulk properties of materials, one uses periodic boundary conditions in all three spatial directions throughout. However, other boundary conditions are needed for simulating interfacial and surface phenomena. 

In models of Ising ferromagnets a common method to stabilize one interface between spin-up and spin-down phases is the use of antiperiodic boundary conditions in one direction of the system, r(f - - L ez) = — r ri), where is a unit vector in the z-direction (perpendicular to the interface that is stabilized), and L is the linear dimension of the system perpendicular to the interface. In the x,y-directions parallel to the interface, where one then uses linear dimensions which may be chosen different from Li, standard periodic boundary conditions are used ( t(g + = cr(fv) if x is 

This method can be straightforwardly generalized to lattice models of symmetrical polymer mixtures an A-chain part of which leaves the box through the boundary at z = Lx re-enters the system at z = 1 as a B-chain, etc. Comparing such a simulation with a simulation with standard periodic boundary conditions in all directions for the same Ly x Ly x Lx geometry, one can obtain excess properties due to the interface, such as the inter- 

Cifra et a/. use a wall-monomer interaction = wb but consider different volume fractions (f A b the bulk of their thin film system, carrying out the simulation in the canonical ensemble, while the data of Fig. 7.21(b) are obtained from semi-grand-canonical techniques. The simulation by Cifra et a/. is of great interest as a first step towards the modeling of the situation used in experiment, where one normally has two inequivalent interfaces one is the interface between the thin film of the polymer blend and an adsorbing substrate, and the other is an interface between the film and vacuum or air, respectively. Cifra et a/. achieve this 

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