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Mesoscopic Simulations

Coarse-graining is currently one of the most active areas of research in computational soft condensed matter physics. Elimination of superfluous degrees of freedom in a systematic and rigorous way can lead to enormous simplification of computational problems, bringing previously impossible computations into the realm of possibility. Computational techniques such as Brownian Dynamics have been used for many years to efficiently simulate the motion of dilute polymer and colloidal solutions by representing the effect of the solvent on a suspended particle as a drag force plus a random force. This is a very commonly used form of coarse-graining, in which the solvent need not be considered in all its atomic detail, but is instead represented by macroscopic or mesoscopic parameters.

Simulations of concentrated polymer and colloidal solutions on the other hand, require the computation of complicated many-body hydrodynamic interactions rather than a simple single-particle drag force. In dilute solutions, only two-body hydrodynamic interactions are required, and analytical results for the dynamic properties of dilute polymer solutions are readily available. These analytical results, which include the effects of excluded- volume and hydrodynamic interactions up to the level of pair interactions, have recently been shown to agree very well with the results of Brownian Dynamics simulations and experimental results when both are extrapolated to certain limits. This agreement confirms the validity of many of the assumptions that are made in developing the coarse-grained theory of dilute polymer solutions.

However, as the concentration is increased, two issues with regard to carrying out Brownian dynamics simuations arise. Firstly, it is presently not known if Brownian simulations will give results that agree with experimental results. This is where direct molecular simulation can provide important insights into theories of coarse-graining. By explicitly simulating both the solvent and the solute, molecular dynamics simulations provide data from which the correct hydrodynamic interactions emerge with no additional assumptions. The disadvantage of molecular dynamics is of course the enormous computational task of simulating both the solvent and the solute in atomic detail. However, recent advances have shown that although this task is difficult, it is not impossible. This makes a direct comparison between atomistically detailed simulations and Brownian Dynamics (BD) possible. The second issue with regard to BD is its computational intensity, which scales in a naive implementation as O(N³), where N is the number of particles. This computational intensity makes it impossible to simulate many particle systems. It is here that it might be advantageous to use other "mesoscopic" simulation techniques such as the lattice Boltzmann technique. At the present moment no detailed comparisons exist between different mescoscopic simulation techniques that help one decide the circumstances under which one would choose one technique over another.

In our work, we aim to generate a set of highly precise reference data for the static and dynamic properties of semidilute polymer solutions by Molecular dynamics, Brownian Dynamics and lattice Boltzmann techniques. New, efficient algorithms will be used to enable us to study long chain polymers in semidilute solutions, and new techniques for computing many-body hydrodynamic interactions will be implemented. These results will then serve as benchmarks that will enable one to make a rational choice of the appropriate simulation technique to be used, that is best tailored for the situation at hand.

Collaborators

1. B. Duenweg, Max Planck Institute for Polymer Research
2. R. Varley, CSIRO
3. P. Daivis, RMIT
2. B. Todd, Swinburne University

Funding

1. Engineering Faculty Grants Scheme, Monash University
2. Monash-CSIRO Collaborative Research Support Scheme
3. Victorian Partnership for Advanced Computing e-Research Program Grants Scheme

Conference Presentations and Publications on this topic

1. T. T. Pham, U. D. Schiller, J. R. Prakash and B. Duenweg, Implicit and explicit solvent models for the simulation of a single polymer chain in solution: Lattice Boltzmann vs Brownian dynamics, reprint (2008).


1. T. T. Pham, U. D. Schiller, J. R. Prakash and B. Duenweg, Implicit and explicit solvent models for the simulation of a single polymer chain in solution: Lattice Boltzmann vs Brownian dynamics, Seventh Liquid Matter Conference, Sweden, 27 June - 1 July, 2008.