Coarse-grained interactions in polymer melts: a variational approach

We investigate the modeling of a polymer melt on large length scale by averaging out fast fluctuating degrees of freedom in the microscopic model. We determine pair interactions in the coarse-grained system that give the best representation of the fine-grained system in a variational sense. Starting from the Gibbs-Bogoliubov inequality we derive a correction to a trial potential that minimizes the variational free energy of the coarse-grained system. By applying this correction repeatedly, pair interactions that are optimal in variational sense are obtained self-consistently. To calculate the potential of mean force in the polymer system, we consult the replica approach. The effective potential results in a radial distribution function for the coarse-grained sites that is less structured than that of the microscopic system. We also found that the soft effective interaction is unable to reproduce the virial distribution of the fine-grained system.

[1]  C. Harris,et al.  Generalized Brownian dynamics. I - Numerical integration of the generalized Langevin equation through autoregressive modeling of the memory function. II - Vibrational relaxation of diatomic molecules in solution , 1990 .

[2]  A. Jansen,et al.  Dynamics of molecular crystals , 1986 .

[3]  L. Brusch,et al.  A new simple version of the replica method , 1999 .

[4]  Reinier L. C. Akkermans,et al.  A structure-based coarse-grained model for polymer melts , 2001 .

[5]  Michel Mareschal,et al.  Microscopic simulations of complex hydrodynamic phenomena , 1993 .

[6]  Reinier L. C. Akkermans,et al.  Coarse-grained dynamics of one chain in a polymer melt , 2000 .

[7]  Hansen,et al.  Can polymer coils Be modeled as "Soft colloids"? , 2000, Physical review letters.

[8]  Harold L. Friedman,et al.  Brownian dynamics: Its application to ionic solutions , 1977 .

[9]  A. Lyubartsev,et al.  Calculation of effective interaction potentials from radial distribution functions: A reverse Monte Carlo approach. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  L. Reatto.  The inference of interatomic forces from structural data on liquids , 1988 .

[11]  Sam F. Edwards,et al.  The theory of rubber elasticity , 1976, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[12]  Kurt Kremer,et al.  Bridging the Gap Between Atomistic and Coarse-Grained Models of Polymers: Status and Perspectives , 2000 .

[13]  I. R. Mcdonald,et al.  Theory of simple liquids , 1998 .

[14]  Giovanni Ciccotti,et al.  Molecular dynamics simulation of rigid molecules , 1986 .

[15]  Reinier L C Akkermans,et al.  Molecular dynamics of polymer growth , 1998 .

[16]  W. Briels,et al.  THE CALCULATION OF FREE-ENERGY DIFFERENCES BY CONSTRAINED MOLECULAR-DYNAMICS SIMULATIONS , 1998 .

[17]  Weis,et al.  Iterative predictor-corrector method for extraction of the pair interaction from structural data for dense classical liquids. , 1986, Physical review. A, General physics.

[18]  R. L. Henderson.  A uniqueness theorem for fluid pair correlation functions , 1974 .

[19]  Yitzhak Rabin,et al.  Statistical physics of polymer gels , 1996 .

[20]  J. Koelman,et al.  Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics , 1992 .

[21]  H. C. Andersen,et al.  Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids , 1971 .