Multiresolution coarse-graining of polymer models

Ahmed Ismail, Massachusetts Institute of Technology

Polymers are quintessential examples of the need for simulations at multiple scales: at one end, we can study short chains using quantum chemistry methods; yet polymers can have relaxation times on the order of seconds or longer, and molecular weights of 106 or more. Even with modern computational resources, simulating behavior at long times or for long chains is still prohibitively expensive. While many approaches have been developed for studying such systems, many of these are specific to particular polymer chemistries, or fundamentally change the basic model of the system on an ad hoc basis. We propose a new algorithm for studying coarse-grained polymer models represented as interacting lattice random walks.

We have introduced the wavelet-accelerated Monte Carlo (WAMC) algorithm for hierarchical studies of lattice models, and demonstrated its usefulness in studying Ising models [J. Chem. Phys., 118, 4414 (2003) and 118, 4424 (2003)]. In the present work, we extend the basic ideas developed to interacting lattice random walks. These walks can incorporate many of the same interactions as traditional “off-lattice” polymer models: excluded volume, stiffness, and non-bonded pair interactions. Coarse-graining the chain using the wavelet transform leads to each segment of the chain being replaced by a bead located at the center of mass of the segment. Interactions along the contour – such as stiffness potentials – are directly handled as well and incorporated as an internal configuration energy. Non-bonded interactions, such as excluded volume and non-bonded pair interactions, must be handled differently; we discuss possible approaches for handling these terms hierarchically within the WAMC framework. We present the details of the implementation of this algorithm, its performance for basic thermodynamic properties, as well as its connections to other effective coarse-grained models such as freely-jointed and Gaussian chains.

Abstract Author(s): Ahmed E. Ismail, George Stephanopoulos, and Gregory C. Rutledge<br />Department of Chemical Engineering, MIT