### Multiresolution modeling of polymers using wavelet-accelerated Monte Carlo

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Ahmed Ismail, Massachusetts Institute of Technology
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The need for novel approaches to model polymers remains unabated even with the enormous increases in computational power of the last few years. While many multiscale approaches have been designed to study polymers, most of these are designed with very specific length or time scales in mind. Thus, interesting physical phenomena that occur in so-called ‘mesoscales’ between the microscopic and macroscopic scales generally studied cannot be elucidated by such means.

We have previously introduced the wavelet-accelerated Monte Carlo (WAMC) algorithm as a means of coarse-graining lattice systems. Although its initial application was to Ising lattices [*J. Chem. Phys.*, 118, 4414 and 4424 (2003)], the underlying principles can be readily extended to study polymer chains. The principal advantages of the WAMC methodology are flexibility and computational efficiency. The inherent flexibility of the model allows us to study polymer chains at any desired degree of resolution. Furthermore, the existence of scaling laws, readily obtained through simulations at different levels of resolution and for chains of different lengths, can be used to ‘map’ results to resolutions that have not been directly simulated.

Impressive gains can also be made in simulation efficiency: the hierarchical nature of the WAMC algorithm means that chain lengths which are normally impossible to simulate atomistically are readily handled. This is possible because, for the WAMC algorithm, both the time required to generate a new configuration and the number of configurations needed between decorrelated states depends only on the number of coarse-grained variables being simulated at any one time.

We present the details of the implementation of the WAMC algorithm for polymer chains, its performance for basic structural 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