Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system

Abstract

Abstract:The structure of a polystyrene matrix filled with tightly cross-linked polystyrene nanoparticles, forming an athermal nanocomposite system, is investigated by means of a Monte Carlo sampling formalism. The polymer chains are represented as random walks and the system is described through a coarse grained Hamiltonian. This approach is related to self-consistent-field theory but does not invoke a saddle point approximation and is suitable for treating large three-dimensional systems. The local structure of the polymer matrix in the vicinity of the nanoparticles is found to be different in many ways from that of the corresponding bulk, both at the segment and the chain level. The local polymer density profile near to the particle displays a maximum and the bonds develop considerable orientation parallel to the nanoparticle surface. The depletion layer thickness is also analyzed. The chains orient with their longest dimension parallel to the surface of the particles. Their intrinsic shape, as characterized by spans and principal moments of inertia, is found to be a strong function of position relative to the interface. The dispersion of many nanoparticles in the polymeric matrix leads to extension of the chains when their size is similar to the radius of the dispersed particles.

Structure of Polymer Layers Grafted to Nanoparticles in Silica–Polystyrene Nanocomposites

“…We provide here some details on the FOMC model, which was introduced in ref 41. The configurational partition function on which the Monte Carlo sampling is based is expressed as a functional integral over the paths of all chains and as an integral over all nanoparticle positions and orientations.…”

“…The summation extends over all free and grafted segments of the system, excluding only the interaction between the segments which are directly connected to a particle and the particle itself. The interaction of a polymeric segment and a nanoparticle can be calculated using eqs 11-13 of ref 41, which are restated in the Supporting Information to the present paper, with suitable Hamaker constants for the polymer and the particle. The Hamaker constant governing the interaction between two spherical bodies can be calculated as 45 …”

“…Rigid displacements and rotations of the chains, mirroring transformations through planes passing through the chain centers of mass, and exchanges of entire chains keeping their center of mass positions fixed, are used. 52 In addition, the internal conformations of chains are sampled using flips of internal segments, 41 end segment rotations, 41 reptation 53 and pivot 54 moves. Grafted chains equilibrate only through flip, end rotation and pivot moves, which keep their grafted end constrained.…”

“…The analysis is based on a coarse-grained Monte Carlo simulation method which has already been applied to a complex three-dimensional polymer-polymer nanocomposite system. 41 Although the level of description is coase-grained (e.g., employing freely-jointed chains to represent the matrix), the approach developed aims at predicting the behavior of a nanocomposite with specific chemistry quantitatively, in contrast to previous coarse-grained simulations. A main characteristic of the method is that it treats polymer-polymer and polymer-particle interactions in a different manner: the former are accounted for through a suitable functional of the local polymer density, while the latter are described directly by an explicit interaction potential.…”

Statistical Properties of a Polymer Chain in the Environment with Low Concentration of Nanoparticles

“…The existence of NPs can change the dynamics of polymers and therefore shifts the glass transition temperature [14] and slows down the diffusion of polymer chains [15]. Recently, the dynamics of polymer melts and concentrated polymer solutions have been studied intensively by experiments [16,17], theory and computer simulations [18][19][20][21]. It was found that the properties of polymers would be influenced by many parameters, such as size, shape, and concentration of NPs and interaction strength between polymer and NP [10].…”