Polymers can be theoretically and computationally described by models pertaining to different length scales and corresponding time scales. These models have traditionally been used independently of each other. Recently, considerable progress has been made in systematically linking models of different scales. This Review focuses on the generation of lattice and off-lattice coarse-grained polymer models, whose "monomers" correspond to roughly a chemical repeat unit, from chemically detailed atomistic simulations of the same polymers. Computational methods are described as well as applications to polymers in the melt and in solution. The success of multiscale simulations in solving real-world polymer problems that could not be solved in any other way suggests that they will have an important role to play in the future.

Coarse-graining in polymer simulation: from the atomistic to the mesoscopic scale and back.

The dissipative particle dynamics (DPD) simulation method has been used to study mesophase formation of linear (AmBn) diblock copolymer melts. The polymers are represented by relatively short strings of soft spheres, connected by harmonic springs. These melts spontaneously form a mesocopically ordered structure, depending on the length ratio of the two blocks and on the Flory–Huggins χ-parameter. The main emphasis here is on validation of the method and model by comparing the predicted equilibrium phases to existing mean-field theory and to experimental results. The real strength of the DPD method, however, lies in its capability to predict the dynamical pathway along which a block copolymer melt finds its equilibrium structure after a temperature quench. The present work has led to the following results: (1) As the polymer becomes more asymmetric, we qualitatively find the order of the equilibrium structures as lamellar, perforated lamellar, hexagonal rods, micelles. Qualitatively this is in agreement wi...

Dynamic simulation of diblock copolymer microphase separation

We review a class of new computer simulation methods for polymeric fluids and other soft condensed matter systems that are based on an underlying field-theoretic description. These methods, while still in an early stage of development, show considerable promise for studying the equilibrium properties of many-component systems capable of intricate self-assembly, such as solutions and blends containing block and graft copolymers. Field-theoretic simulation methods also provide a great deal of flexibility in model building and coarse graining, and appear to be particularly well suited to treat systems with soft, long-range interactions, such as polyelectrolytes. We attempt to connect various related theoretical approaches, such as self-consistent field theory and dynamic density functional theory, within a common framework.

Field-Theoretic Computer Simulation Methods for Polymers and Complex Fluids

Multiscale modeling and simulation of polymer nanocomposites

Ionic liquids (ILs) offer a wide range of promising applications because of their much enhanced properties. However, further development of such materials depends on the fundamental understanding of their hierarchical structures and behaviors, which requires multiscale strategies to provide coupling among various length scales. In this review, we first introduce the structures and properties of these typical ILs. Then, we introduce the multiscale modeling methods that have been applied to the ILs, covering from molecular scale (QM/MM), to mesoscale (CG, DPD), to macroscale (CFD for unit scale and thermodynamics COSMO-RS model and environmental assessment GD method for process scale). In the following section, we discuss in some detail their applications to the four scales of ILs, including molecular scale structures, mesoscale aggregates and dynamics, and unit scale reactor design and process design and optimization of typical IL applications. Finally, we address the concluding remarks of multiscale strat...

Multiscale Studies on Ionic Liquids

In this paper we discuss a new generalized time-dependent Ginzburg-Landau theory for the numerical calculation of polymer phase separation kinetics in 3D. The thermodynamic forces are obtained by a mean-field density functional method, using a Gaussian chain as a molecular model. The method is especially aimed at describing the formation kinetics of the irregular morphologies which are typical for many industrial systems. As proof of concept we present the formation of irregular morphologies in quenched symmetric and asymmetric block copolymer melts.

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The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts

We describe a new class of phenomenological mesoscopic models to simulate the phase separation dynamics in three dimensional complex liquids, based on dynamic density functional methods. These models are generalizations of time-dependent Ginzburg–Landau models and contain a molecular description of the liquids in the free energy functional. Possible applications are in process industries (HIPS, paints, detergents, surfactants,…), petroleum industries (oil recovery), pharmaceutical industries (drug delivery) and consumer product industries (food processing, cosmetics). We show the results of the simulation of the microphase behaviour of aqueous PL64 solutions. The work described here was mainly done within ESPRIT research projects funded by the European Union.

O. A. Evers

Papers

The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts

The MesoDyn project: software for mesoscale chemical engineering

Simple numerical quadrature rules for Gaussian chain polymer density functional calculations in 3D and implementation on parallel platforms