Single chain in mean field simulations: Quasi-instantaneous field approximation and quantitative comparison with Monte Carlo simulations

Abstract

The description of fluctuations by single chain in mean field (SCMF) simulations is discussed and the results of this particle-based self-consistent field technique are quantitatively compared to Monte Carlo simulations of the same discretized Edwards-Hamiltonian providing exact reference data. In SCMF simulations one studies a large ensemble of noninteracting molecules subjected to real, external fields by Monte Carlo simulations. The external fields approximate nonbonded, instantaneous interactions between molecules. In the self-consistent mean field theory the external fields are static and fluctuation effects are ignored. In SCMF simulations, the external fields fluctuate since they are frequently recalculated from the instantaneous density distribution of the ensemble of molecules. In the limit of infinitely high density or instantaneous update of the external fields, the SCMF simulation method accurately describes long-wavelength fluctuations. At high but finite updating frequency the accuracy depends on the discretization of the model. The accuracy is illustrated by studying the single chain structure and intermolecular correlations in polymer melts, and fluctuation effects on the order-disorder transition of symmetric diblock copolymers.

Kinetics of directed self-assembly of block copolymers on chemically patterned substrates

“…The Single-Chain-in-Mean-Field algorithm is the Monte-Carlo analog of multipletime step algorithm in molecular dynamics simulations [32] and temporarily replaces the weak, non-bonded forces by external, fluctuating fields that are recomputed from the instantaneous microscopic densities, Eq. (3), after each SMC sweep over all segments [22,29,33]. This quasiinstantaneous approximation of the pairwise interactions is accurate and quantitatively describes composition fluctuations.…”

“…We use Smart Monte-Carlo (SMC) updates [28] in conjunction with the Single-Chain-inMean-Field algorithm [29]. The former scheme biases the proposed, local, random displacements of coarse-grained segments according to the strong bonded forces.…”

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

“…The paper of Laradji et al was pioneering in introducing the concept of conducting particle-based simulations with interactions described via collective variables and also two ways of calculating these collective variables: grid-based and continuum weighting-function-based. A clearer discussion of this point is found in studies of brushes in poor solvent by Soga et al 32 Later, Daoulas and Müller 33 and Detcheverry et al 34 have extensively used this methodology to study a wide range of polymeric systems. This technique has been very successful in describing the self-assembly and the ordering of block copolymers on patterned substrates encountered in processes such as nanolithography.…”

A multiscale modeling study of loss processes in block-copolymer-based solar cell nanodevices

“…22,32,33 Methods going beyond the MF level have been introduced recently and may be used for computing the structural-dynamical characteristics of polymer-solvent systems with strong repulsive interactions between monomers, which may arise, e.g., in cases where the polymers possess polar or ionic groups in the semi-dilute or dilute concentration regime. 22,[33][34][35][36] In a recent work, 5 we have extended the range of application of the field-theoretic methods mentioned previously, to investigate the loss processes of charge carriers and excitons in defect structures of nanostructured polymer solar cells. This approach is based on combining either the timedependent Ginzburg-Landau method or the SCFT method, to generate morphologies of different scale of phase separation and degree of defect formation, with a first reaction (FR)-type dynamic Monte Carlo (DMC) method, to simulate the elementary photovoltaic processes involving the charge carriers and excitons within a particle description.…”