Integral Equation Prediction of Surface-Induced Layering Transition of Polymer Nanocomposites

Abstract

The polymer reference interaction site model (PRISM) integral equation for inhomogenous polymers was applied to investigate layering transitions of nanoparticle/polymer blends near solid surfaces. The equation has the advantage over other theoretical approaches in describing the chemical and morphologic details of polymers. Construction of a novel bridge function derived from a free-energy functional allowed the PRISM equation to be solved with a modified hypernetted chain approximation. Tested by the density functional theory as well as molecular simulations, the equation is quantitatively reliable for the inhomogeneous blends containing flexible or semiflexible polymer chains. Accordingly, the effects of particle size, the attractive interaction strength between particles and polymer monomers, and the stiffness of polymer chains on the layering transitions were investigated to decipher the contribution of the packing and configurational entropies.

Novel Synthesis of CdSe Quantum Dots in a Confined Space by Using a High Internal Phase Emulsion and Their Application in Fluorescent Labeling

“…Based on the above experimental results, the generation mechanism of QDs in HIPE was proposed (Figure ). Attributed to the existence of surface (or interface), the actual dispersion of materials in reactor was un‐even, and would be enriched on the surface ,a), for example, the aggregation of materials on the surface of glass tube could be totally ignored because of the giant difference between the dimension of macroscopic‐scale tube and the nano‐scale aggregated layer, and the materials could be considered to be dispersed uniformly.…”

pyPRISM: A Computational Tool for Liquid-State Theory Calculations of Macromolecular Materials

“…PRISM has also greatly expanded our understanding of the structure and miscibility behavior of polymer nanocomposites ,− and polymer–colloid suspensions. − For the latter, novel polymer physics-guided closures have been formulated and widely applied. For both these systems, it is of primary interest to understand the spatial structure and phase separation of the particle (filler or colloid) and how polymers statistically organize around the particle.…”

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

“…Up to now, although the structure and properties of PNCs have been extensively investigated in the limit of bulk systems, the effect of substrates or confinement on the structure and phase behavior of PNCs is seldom discussed . The technological developments of PNCs show that phase behavior with layering transition and the interactions between nanoparticles and polymers is impacted by substrate or nanoscale channels. − Self-healing surfaces, switchable catalysts, and polymeric materials designs , are also correlated with the structure, thermodynamics, and phase behavior of nanoparticle–polymer mixtures near the solid surface . It is pointed out that the surface-induced layering transition of PNCs can be greatly affected by the packing entropy of nanoparticles and the configurational entropy of polymer chains. ,,, The chemical and physical parameters of the monomer-particle correlations, interactions between the surface and PNCs, and the molecular structure of polymer chains play significant roles in the spatial organization of nanoparticles near a substrate. , The influence of the dispersion state of nanoparticles on the structure and phase behavior of PNCs indicates that systematical understanding the combination effects of these factors is quite necessary and helpful for new materials design and applications …”

“…Although experimental and simulation work has been performed to investigate the morphology of CPNs near a substrate, − the influence of parameters of interaction and chemistry on the microscopic dispersion and aggregation mechanism of alternating copolymer nanocomposites (ACNs) is still poorly understood; and experimental techniques become difficult in separating the different contributions from different components, and molecular dynamics (MD) simulation also has the problem of being computationally intensive in simulating asymmetric PNCs under confinement. ,,, Meanwhile, the polymer reference interaction site model (PRISM) ,,,− ,,,,− theory has been widely used to investigate the structure and properties of polymer melts, solutions, blends, and copolymers. It has also been extended to model the structure, effective interactions, and phase separation of PNCs and give some quantitative predictions with small angle scattering experiments in some realistic PNCs systems. ,− Moreover, by constructing a local bridge functional obtained from the density functional theory (DFT) in the traditional approximate closure equation, , the inhomogeneous PRISM theory was further extended to describe the structure and properties of inhomogeneous systems with a quantitative description of density distributions of nanoparticle/polymer blends, real polymer systems, and microphase separation behavior of polymers near a substrate. ,,,− Therefore, the modified inhomogeneous PRISM theory provides us with a desirable theoretical tool to investigate the structure and density profiles of PNCs near a substrate . Although the impact of monomer sequence, composition, and chemical heterogeneity on copolymer-mediated effective interactions between nanoparticles, effect of copolymer sequence on structure and relaxation times near a nanoparticle surface, and effective interactions and spatial dispersion of nanoparticles in multiblock copolymer melts have been systematically investigated by the ...…”

“…In this work, the modified inhomogeneous PRISM theory , is further extended to investigate the surface-induced density profiles and packing structures of ACNs near the solid surface. The effects of the particle volume fraction, nanoparticle diameter, potential interaction between nanoparticles and copolymer sites, and nanoparticle–nanoparticle interaction on the interfacial structure of ACNs near the solid wall are systematically discussed and analyzed.…”