Accuracy, Transferability, and Efficiency of Coarse-Grained Models of Molecular Liquids.

Coarse-graining (CG) approaches are becoming essential tools in the study of complex systems because they can considerably speed up computer simulations, with the promise of determining properties in a range of length scales and time scales never before possible. While much progress in this field has been achieved in recent years, application of CG methods is still inhibited by the limited understanding of a number of conceptual points that need to be resolved to open up the field of CG to a wide range of applications in material science and biology. In this paper, we present some of the key findings that emerged from the development of the integral equation theory of coarse-graining (IECG), which addresses some of the fundamental questions in coarse-graining. Although the IECG method pertains to the CG of polymer liquids, and specifically homopolymer melts are illustrated here, many of the results that emerge from the study of the IECG approach are general and apply to the CG of any molecular liquid. Through this method, we developed a formal relation between the statistical mechanics of CG and a number of predicted physical properties. On the basis of the theory of liquids, the IECG affords the analytical solution of the intermolecular potential for macromolecules represented by a Markov chain of CG sites, thus providing a transparent tool for analysis of the properties in coarse-graining. We identify three key requirements that render a CG model useful: accuracy, transferability, and computational efficiency. When these three requirements are fulfilled, the CG model becomes widely applicable and useful for studying regions in the phase space that are not covered by atomistic simulations. In the process, the IECG answers formally a number of relevant questions on how structural, thermodynamic, and dynamical properties are modified during coarse-graining. It sheds light upon how the level of CG affects the shape of the CG potential and how, in turn, the shape of the potential affects the physical properties. It tests the validity of selecting the potential-of-mean force as the effective pairwise CG potential and the role of higher-order many-body corrections to the pairwise potential to recover structural and thermodynamic consistency of the CG model. Because the IECG theory can be analytically formalized, it does not suffer from the problem of transferability and, in the canonical ensemble, leads to consistent pair distribution functions, pressure, isothermal compressibility, and excess free energy at variable levels of CG from the atomistic to the ultra-CG model, where macromolecules are represented as interpenetrable soft spheres.

Theoretical reconstruction of realistic dynamics of highly coarse-grained cis-1,4-polybutadiene melts.

The theory to reconstruct the atomistic-level chain diffusion from the accelerated dynamics that is measured in mesoscale simulations of the coarse-grained system, is applied here to the dynamics of cis-1,4-polybutadiene melts where each chain is described as a soft interacting colloidal particle. The rescaling formalism accounts for the corrections in the dynamics due to the change in entropy and the change in friction that are a consequence of the coarse-graining procedure. By including these two corrections the dynamics is rescaled to reproduce the realistic dynamics of the system described at the atomistic level. The rescaled diffusion coefficient obtained from mesoscale simulations of coarse-grained cis-1,4-polybutadiene melts shows good agreement with data from united atom simulations performed by Tsolou et al. [Macromolecules 38, 1478 (2005)]. The derived monomer friction coefficient is used as an input to the theory for cooperative dynamics that describes the internal dynamics of a polymer moving in a transient regions of slow cooperative motion in a liquid of macromolecules. Theoretically predicted time correlation functions show good agreement with simulations in the whole range of length and time scales in which data are available.

Thermodynamic consistency in variable-level coarse graining of polymeric liquids.

Numerically optimized reduced descriptions of macromolecular liquids often present thermodynamic inconsistency with atomistic level descriptions even if the total correlation function, i.e. the structure, appears to be in agreement. An analytical expression for the effective potential between a pair of coarse-grained units is derived starting from the first-principles Ornstein-Zernike equation, for a polymer liquid where each chain is represented as a collection of interpenetrating blobs, with a variable number of blobs, n(b), of size N(b). The potential is characterized by a long tail, slowly decaying with characteristic scaling exponent of N(b)(1/4). This general result applies to any coarse-grained model of polymer melts with units larger than the persistence length, highlighting the importance of the long, repulsive, potential tail for the model to correctly predict both structural and thermodynamic properties of the macromolecular liquid.

Analytical rescaling of polymer dynamics from mesoscale simulations.

We present a theoretical approach to scale the artificially fast dynamics of simulated coarse-grained polymer liquids down to its realistic value. As coarse graining affects entropy and dissipation, two factors enter the rescaling: inclusion of intramolecular vibrational degrees of freedom and rescaling of the friction coefficient. Because our approach is analytical, it is general and transferable. Translational and rotational diffusion of unentangled and entangled polyethylene melts, predicted from mesoscale simulations of coarse-grained polymer melts using our rescaling procedure, are in quantitative agreement with united-atom simulations and with experiments.

Multiscale modeling of coarse-grained macromolecular liquids.

A first-principle multiscale modeling approach is presented, which is derived from the solution of the Ornstein-Zernike equation for the coarse-grained representation of polymer liquids. The approach is analytical, and for this reason is transferable. It is here applied to determine the structure of several polymeric systems, which have different parameter values, such as molecular length, monomeric structure, local flexibility, and thermodynamic conditions. When the pair distribution function obtained from this procedure is compared with the results from a full atomistic simulation, it shows quantitative agreement. Moreover, the multiscale procedure accurately captures both large and local scale properties while remaining computationally advantageous.