Diffusion Wavelet Decomposition for Coarse-Graining of Polymer Chains
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Diffusion Wavelet Decomposition for Coarse-Graining of Polymer Chains B. Christopher Rinderspacher,1 Jaydeep P. Bardhan,2 and Ahmed E. Ismail3 1 Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA 2 Dept. of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115 3 Dept. of Mechanical Engineering, RWTH Aachen University, Aachen, Germany ABSTRACT Here we present an alternative approach to coarse graining, based on the multiresolution diffusion-wavelet approach to operator compression, which does not require explicit atomisticto-coarse-grained mappings. Our diffusion-wavelet method takes as input the topology and sparsity of the molecular bonding structure of a system, and returns as output a hierarchical set of degrees of freedom (DoFs) of system-specific coarse-grained variables. Importantly, the hierarchical compression provides a clear framework for modeling at many model scales (levels), beyond the common two-level CG representation. Our results show that the resulting hierarchy separates localized modes, such as a single C-C vibrational mode, from larger-scale motions, e.g., long-range concerted backbone vibrational modes. Our approach correctly captures small-scale chemical features, such as cellulose ring structures, and alkane side chains or CH2 units, as well as large-scale features of the backbone. In particular, the new method’s finest-scale modes describe DoFs similar to united atom models and other chemically-defined CG models. Modes at coarser levels describe increasingly large connected portions of the target polymers. For polyethylene and polystyrene, spatial coordinates and their associated forces were compressed by up to two orders of magnitude. The compression in forces is of particular interest as this allows larger timesteps as well as reducing the number of DoFs. INTRODUCTION Many problems in materials design involve optimizing semi-crystalline polymeric materials with respect to their dynamical behavior or non-equilibrium properties. These problems pose substantial modeling challenges that do not afflict crystalline or amorphous materials. First, length scales on the order of 10 μm are required to model many semi-crystalline materials as well as rare-event phenomena involving low-to-medium defect concentrations (for example, aggregation, crack initiation, and strain-induced crystallization). This scale exceeds current computational resources for molecular-dynamics (MD) simulations by a factor of 1000. Ultrahigh-molecular-weight polyethylene (UHMWPE) offers a classic example of the scale challenge: despite its simple chemical makeup CnH2n+2 , as a material with n ≫ 100,000 it exhibits large regions of disorder that coexist with crystalline regions. Compounding the challenge, fully atomic detail is required for performance-determining phenomena such as vacancies, dislocations, and crack tips; consequently, MD simulations represent the state of the art for computational design of materials from first principles. In contrast, for crystalline materials one may u
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