Organisers

• Vladimir Lobaskin (University College Dublin, Ireland)
• Mikko Karttunen (Dept. of Applied Mathematics, The University of Western Ontario, Canada)
• Pep Español (Universidad Nacional de Educación a Distancia, Madrid, Spain)

Supports

   CECAM

Science Foundation Ireland

Description

A variety of mesoscale simulation techniques has been developed over the last decades. The central idea of the methods like dissipative particle dynamics, smooth particle hydrodynamics, lattice Boltzmann, or multiparticle collision dynamics (stochastic rotation dynamics) is the replacement of complete set of molecules in a complex fluid by a smaller number of particles possessing the same properties as the initial set. In addition to reducing the number of degrees of freedom, this replacement allows one to avoid direct modelling of fast motions and, therefore, the need for small time steps in simulations. While the systematic coarse-graining methods based on rigorous statistical mechanics exist for static properties, the mesoscale methods for complex fluids often lose the connection to the original microscopic description. Different approaches exists to set up the parameters of coarse-grained system based on matching (i) equilibrium properties of the original fluid (density, pressure, size of hydration layer, surface tension, contact angle), (ii) dynamic properties (viscosity, friction coefficients, molecular relaxation times). The practice shows, however, that fixing the static properties does not guarantee the accuracy of the resulting dynamic behaviour.

We believe that there is a need of methodological advances in order to compute out of atomistic simulations the different reversible (effective potentials, equations of state, surface tension) and irreversible parts (frictions, viscosities, relaxation times) of the coarse-grained dynamic equations. The main obstacle in achieving this goal is the need of dealing with functions of many variables. Pair-wise assumptions seem to be the easiest solution, but may be there are other possibilities.

Attempts to bridge the timescales to microsecond and longer regimes have been made using various mesoscale methods, such as lattice-Boltzmann methods [1-4], particle based off-lattice methods such as dissipative particle dynamics [5-8], multi-particle-collision (or stochastic rotational) dynamics (MPCD) [9-12], and Brownian dynamics of stokeslets with hydrodynamics based on the Green function formalism [13-14]. On the basis of these techniques a few hybrid schemes were developed and used to study phenomenology of non-equilibrium processes, dynamic scaling, etc. The DPD approach has been successfully used for modelling surfactant self-assembly, including aggregation of phospholipids. The MPCD approach was applied for modelling dynamics of long polymer chains near obstacles, shear driven dynamics of star polymers, vesicles, and red blood cells, colloidal sedimentation [15]. The lattice Boltzmann method was applied to model flow in narrow channels, past rough surfaces, and surfaces with complex boundary conditions including partial slippage [16]. A few quantitative studies addressed dynamics of disperse systems: colloidal dispersions or polymer solutions where, however, only one or two types of particles with a single interaction potential were involved [15,17,18]. A recent themed issue in Phys.Chem.Chem.Phys  [19] offers a general view of the state of the art on Coarse-grained modeling of soft condensed matter. 

From a theoretical point of view, coarse-graining has a solid foundation in what is also known as non-equilibrium statistical mechanics with a clear treatment of both static and dynamic properties, the latter in the form of Green-Kubo expressions [20,21]. While the framework is well established, its practical implementation has only been successfully addressed for static properties. Just recently dynamic properties are being considered in a systematic way [22,23] 

Scientific Objectives

Our goal is to discuss and develop systematic procedures for constructing coarse-grained descriptions of complex fluids that would allow to preserve the ratios between various timescales, establish the connection to microscopic parameters, and enable one to trace back absolute times from mesoscale simulations and thus to achieve a quantitative description of their dynamic properties.

These are some of the questions that we would like the participants to address in particular:

Selection of variables

The theory of coarse-graining assumes that we all know what are the variables that define our level of description. They are the slow variables. Hydrodynamic variables are always a good candidate because at low wavenumber they are definitely slow. But as we enter more detailed levels in order to achieve molecular specificity, we no longer have a guide for the selection of variables. Centers of mass probably move slower that "the rest" but, are they the best candidates? What about "modes"?  This questions clearly point at the need of finding systematic ways of identifying good coarse-variables. Do we have a theory, or methods, for the systematic detection of the good coarse variables?

Systematic construction of the model

Given that the structure of the coarse-grained equations is clear, the remaining problem is "just" to compute the building blocks of the equations. These blocks are functions of (all) the selected coarse-variables. Is it always better to compute them from atomistic simulations? How to do that? How to deal with the fact that they are functions of highly dimensional spaces? On the other hand, are there systematic ways of inputting macroscopic information into the building blocks of a coarse model?

Transitivity

Ideally, we would like to have coarse-descriptions such that if we further coarsen the system we get correct results. For example, imagine that we coarsen a fluid made of complex molecules with the centers of mass (CoM) of the molecules, and we have effective potentials and frictions between the centers of mass. We may be even proud that we can achieve reasonable agreement with the radial distribution function and the velocity autocorrelation functions of the CoM computed atomistically. How can we achieve, in addition, that the viscosity, which is a property of the even coarser hydrodynamic level is the correct one (the one that you can in principle compute also from atomistic simulations)? Or, at the coarsest possible level, which is that of macroscopic thermodynamics, how do we ensure that the thermodynamic behaviour of the coarse-grained system is the same as that of the atomistic one?

In other words, is it possible to have coarse-grained models that are transitive in this sense?

References

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23. C. Hijon, P. Español, E. vanden Eijnden, R. Delgado-Buscalioni, Faraday Discuss. 144, ?? (2010), in press