Monte Carlo Simulation of Phase Equilibria for Random Copolymers

Assembly of copolymer blend on nanopatterned surfaces: a molecular simulation study

We report a molecular simulation study on the assembly of an (A7B5)5/A7B5 copolymer blend on nanopatterned surfaces. The density distributions, anisotropic radii of gyration, and conformations of both copolymers are quantitatively characterized. As the width of stripes on the surface decreases, the shape and thickness of the assembled film are found to be in qualitative agreement with those from experiments. The simulation results indicate that the shape and conformation of ordered film can be modulated by tuning the adsorption energy between the surface and the polymer or by adjusting the width of the stripes on the surface. We can regulate the width of the stripes to obtain a desired polymer conformation without altering the assembled film. In remarkable contrast to the pure copolymer, the radii of gyration of the blend in three directions are consistently smaller. The simulation reveals that the addition of a short chain during assembly is of central importance in restructuring the conformations of the long chain.

Recognition of multiblock copolymers on nanopatterned surfaces: insight from molecular simulations

The recognition of multiblock copolymers on nanopatterned surfaces has been investigated by molecular simulations. All the copolymers (AnB12-n)5 are composed of 60 square-well segments, but with various architectures by changing n. Segment density profiles, radii of gyration, pattern transfer parameters, and three adsorption conformations (tail, loop, and train) are examined quantitatively. It is found that the copolymer can recognize the adsorbing stripes on surface and the surface vicinity. The recognition affinity becomes stronger with increasing the stripe width, the adsorption strength, and the number of adsorbing segments in copolymer chain. From surface to bulk phase, the shape of copolymer changes from elongated to elliptical, and finally to globular. Among the three adsorption conformations, tail has the greatest average size while train has the smallest. With the increased number of nonadsorbing segments, the average size shows an increase in tail but a decrease in train.

Integral equation theory of random copolymer melts: Self-consistent treatment of intramolecular and intermolecular correlations

A self-consistent integral equation theory is presented for the conformational properties and spinodal lines of random copolymer melts. The theory combines field-theoretic methods with the polymer reference interaction site model (PRISM) theory. The many-chain problem is replaced by a single chain where the sites interact via a bare plus a self-consistently determined medium-induced potential, and the conformational properties are obtained using a variational method. The theoretical prediction for the spinodal line is qualitatively similar to that of non-self-consistent PRISM theory. The theory predicts macroscopic phase separation for all values of the monomer correlation strength, lambda. The inverse spinodal temperature is a nonmonotonic function of lambda with a maximum at lambda(max). For large values of lambda( approximately 1), the values of spinodal temperatures are almost identical to those of non-self-consistent PRISM theory. For low values of lambda, however, the theory predicts higher values for spinodal temperatures than non-self-consistent PRISM theory. The theory predicts significant changes in the mean-square end-to-end distance as the temperature is decreased.

Stationary dynamics approach to analytical approximations for polymer coexistence curves

Phase separation in polymer blends is an important process. However, the compositions of the coexisting phases can only be predicted by numerical methods. We provide simple analytical expressions which serve as good approximations for the compositions after phase separation of binary homopolymer blends. These approximations are obtained by a stationary dynamics approach: we calculate the compositions of two polymer mixtures such that the stationary diffusion between these distinguishable mixtures vanishes. For the diffusion equations we employ composition-dependent diffusion coefficients, as derived according to the slow- and fast-mode theory from the Flory-Huggins free energy. The analytical results are in good agreement with exact (numerically calculated) binodal compositions. Our coexistence curves are more accurate than some conventional approximations. Another advantage of the stationary dynamics approach is that it is not only applicable to binary polymer blends or polymer solutions, but also to symmetrical multicomponent blends. The same diffusion coefficients may be used to obtain the exact spinodal compositions in multicomponent systems.