Single-Chain-in-Mean-Field Simulations

Partide-based SCF schemes like single chain in mean field -simulations [96] avoid the use of an Onsager coefficient and are applicable to systems with strong spatial inhomogeneities... 

Single-Chain-in-Mean-Field Simulations and Grid-Based Monte Carlo Simulation of the Field-Theoretic Hamiltonian... 

Hybrid particle-field models combine single-cbain simulations with an appropriate field-theoretical approach. The corresponding class of multiscale techniques includes the single-chain-in-mean-field (SCMF) method, the theoretically informed coarse-grain (TICG) simulation scheme, self-consistent Brownian dynamics (SCBD), and the MD-SCF method, in which self-consistent field theory (SOFT) and particle-based MD are combined. 

Single-chain-in-mean-field (SCMF) simulation [40-42, 86] is an approximate, computational method that retains the computational advantage of self-consistent field theory but additionally includes fluctuation effects because, in contrast to self-consistent theory, SCMF simulations aim at preserving the instantaneous description of the fluctuating interactions of a segment with its environment. In this partide-based simulation technique, one studies an ensemble of molecules in fluctuating, real, external fields. The explicit particle coordinates are the degrees of freedom and not the collective variables, densities and fields. 

Figure 17 Illustration of DSA simulations of chemical epitaxy (left two columns) or graphoepitaxy (right columns). The top row shows straight or wavy chemical patterns ortopographical walls on a simulated substrate. Green regions are selective for the A block (red) and yellow regions selective forthe B block (blue) of a model block copolymer, while gray surfaces are neutral. DSA of a disordered thin film of symmetric AB diblock copolymer was simulated in the presence of each substrate pattern using single chain in mean-field Monte Carlo to produce the self-assembled structures in the bottom row.

In the case of general chain architectures, however, the mean fleld problem of a single chain in an external fleld cannot be cast in the form of a modified diflusion equation, and the density that a single chain creates in the external field and the concomitant single-chain partition function have to be estimated by partial enumeration [30-34], This methodology has been successfully applied to study the packing of short hydrocarbon chains in the hydrophobic interior of lipid bilayers [31,32,34] and polymer brushes [33] and to quantitatively compare the results of Monte Carlo simulations to the predictions of the mean field theory without adjustable parameters [30], The latter application is illustrated in Figure 5.2. 

There has been considerable interest in the simulation of lipid bilayers due to their biological importance. Early calculations on amphiphilic assemblies were limited by the computing power available, and so relatively simple models were employed. One of the most important of these is the mean field approach of Marcelja [Marcelja 1973, 1974], in which the interaction of a single hydrocarbon chain with its neighbours is represented by two additional contributions to the energy function. The energy of a chain in the mean field is given by ... 

In what follows, we use simple mean-field theories to predict polymer phase diagrams and then use numerical simulations to study the kinetics of polymer crystallization behaviors and the morphologies of the resulting polymer crystals. More specifically, in the molecular driving forces for the crystallization of statistical copolymers, the distinction of comonomer sequences from monomer sequences can be represented by the absence (presence) of parallel attractions. We also devote considerable attention to the study of the free-energy landscape of single-chain homopolymer crystallites. For readers interested in the computational techniques that we used, we provide a detailed description in the Appendix. ... 

The SD method, in which no explicit solvent is included, is an efficient means for simulating the conformational behavior of single chains under good solvent conditions. However, it does not provide a correct description of the chain dynamics because of the lack of hydrodynamic interactions. As a chain monomer moves in solution, it exerts a force on the solvent tha changes the velocity field from its undisturbed value. The... 

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