Studies On The Interactions In The Systems Of Polymer Brushes By Self-Consistent-Field Theory

End-grafting polymers onto particle surfaces has always been a spotlight in both experimental and theoretical researches for its extensive applications in stabilizing particle dispersion systems, improving biocompatibility of materials, and modifying wetting properties of surfaces, etc. In the field of polymer brushes, the hypothesis of lateral homogeneity of grafting density, which has perfectly explained the behaviors of liquid brushes with mobile grafting sites, however, fails to apply to systems where the size of particles being of the same order as that of the grafting polymers. It becomes even more debatable for real situations in which the polymer brushes bear closer resemblance to a solid brush, where the grafting sites are immobile. To clarify these issues, we develop self-consistent field theory (SCFT) for polymer brushes to address both the liquid and solid cases.We first explore the interaction between a planar brush and a cylindrical particle by the modified SCFT, and the influences of particle shape, particle size and grafting parameters on the interaction are discussed. In the absence of enthalpy effects, the following results are obtained: (1) At intermediate distance, a maximum appears on the force-distance curve of all the liquid brush/particle system, however, for the solid brush/particle system the presence of the maximum point relies on the parameters chosen; (2) If the particle is far away from the grafting surface, the interactions between the particle and polymer brush are similar in both cases; (3) The inflexion and maximum on the force-distance plots indicate the structural characteristics of these polymer brushes.We also study the interaction between two identical spherical brushes in a polymer melt and investigate the effects of grafting density, particle size, length of melt chains, and the mobility of the grafting sites. The results are shown as follows: (1) The structure of the spherical brushes is so susceptible to particle radius, grafting density, and the length of the melt chains that increasing these parameters will lead to a structure transition from a "wet" to "dry" brush; (2) The pairwise interactions vary from repulsive at short distance to attractive at long distance, according to different particle radius, grafting density, and the length of melt chains; (3) The attractive force between spherical brushes is a consequence of entropy increase when moving the melt chains from limited proximity of brushes to free the bulk space; (4) The differencesbetween solid and liquid brushes are unnoticeable when the two spherical brushes are not closely located. However, as the separation is decreased, the repulsion between solid brushes becomes relatively stronger than that between liquid ones.Due to the bridging role in polymer physics and nano-particle physics played by star polymers, which can be viewed as high-curvatured spherical polymer brushes, we extend our research to the interactions between regular star polymers in athermal solvents, and calculate the effective two-body interaction potential. We find the results in agreement with those of scaling theories and other particle-based simulations. For the triplet potential among three aligned bodies, the weak interaction confirms the rationality of particle-based simulations which only involve pair-wise potentials.