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Integral Equation Prediction of the Structure of Alternating Copolymer Nanocomposites near a Substrate.

The packing structure and phase behavior of polymer-nanoparticle mixtures under confinement play an important role in developing strategies for rational design of nanomaterials. However, understanding the microscopic dispersion and aggregation mechanism of polymer nanocomposites is a great challenge through experimental techniques. In this work, the microscopic structure of alternating copolymer nanocomposites (ACNs) near a substrate is investigated systematically through extension of the inhomogeneous polymer reference interaction site model (PRISM) theory. In order to characterize the flexibility and internal chain stiffness of copolymers, a semiflexible chain model is introduced to describe the intramolecular correlations between different monomers. Based on the bridge functionals derived from the fluids density functional theory, the modified hypernetted chain closure is integrated with the PRISM equation to form a full theoretical framework to capture the density distributions of ACNs. The influence of the particle volume fraction, nanoparticle diameter, and adsorption strengths between different interaction sites on the packing structure of ACNs under confinement is analyzed and discussed in detail. With the increase of the particle volume fraction, the size asymmetry between nanoparticles and copolymer monomers can greatly influence the density profiles of ACNs near a substrate. Increasing the nanoparticle diameter, the density distribution of nanoparticles experiences a process from absorbing onto the solid surface to segregating from the wall to larger distances. With increasing the adsorption strength between copolymers and nanoparticles, the density distribution of nanoparticles decreases, which is similar to the case of nanoparticles containing attractive interactions. All these characteristics of ACNs show that the current inhomogeneous PRISM theory can give a detailed description of the packing behavior of different segments. Predictive approaches could be desired and developed for design control of alternating copolymer nanocomposites under confinement.