Lattice calculations surface segregation

In this review, we introduce another approach to study the multiscale structures of polymer materials based on a lattice model. We first show the development of a Helmholtz energy model of mixing for polymers based on close-packed lattice model by combining molecular simulation with statistical mechanics. Then, holes are introduced to account for the effect of pressure. Combined with WDA, this model of Helmholtz energy is further applied to develop a new lattice DFT to calculate the adsorption of polymers at solid-liquid interface. Finally, we develop a framework based on the strong segregation limit (SSL) theory to predict the morphologies of micro-phase separation of diblock copolymers confined in curved surfaces. 

Fig.6. The B2(110) surface average (solid lines) and sub-lattice (dotted lines) concentrations of the segregant in AB model alloy as a function of reduced temperature calculated in the FCEM approximation for different segregation/order factors r (indicated near the plots). The difference in sub-lattice concentrations corresponds to the surface LRO parameter that vanishes at the surface transition temperature Tg that coincides with the bulk transition temperature T independently of r.

Fig. 11. Surface tension for amine-terminated PDMS (squares) as a function of l/Afn-The two thicker lines represent predictions from the lattice model calculations, assuming various group additivity expressions to calculate the surface interaction parameter. The two thinner lines are predictions that neglect end group segregation effects. From Ref. 7.

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