## Coarse-grained simulation of liquid crystals

By: Douglas Cleaver

From: Sheffield Hallam University, Sheffield, United Kingdom

At: Complexo Interdisciplinar, Anfiteatro

[2009-01-22]

Numerous complex fluid systems exhibit orientational anisotropy at a supra-molecular length-scale which then affects their overall material or processing properties. In many such systems, e.g. polymer melts, this anisotropy has finite range but manifests itself at a macroscopic level through some non-Newtonian or viscoelastic behaviour. In others, most obviously thermotropic liquid crystals (LCs), the orientational anisotropy extends throughout the system. We present here a study that relates to the development of novel mesoscopic off-lattice simulation techniques for ordered fluids, in particular thermotropic LCs, which can be applied in both static and flow regimes. First we consider Dissipative particle dynamics (DPD) as a method of choice due to its simplicity and popularity. DPD [1, 2] is a promising mesoscopic simulation technique which, over the last decade, has become a popular method for simulating dynamical and rheological properties of both simple and complex fluids. Recently Ellero et al [3], following ten Bosch [4], have investigated the behaviour of DPD particles invested with an additional vector degree of freedom, culminating in the development of a fluid particle model for viscoelastic flows. We have extended the ideas of Ellero et al by associating a traceless, symmetric, order tensor, Q, with each DPD particle. Microscopically, these order tensors convey information about the state of orientational ordering of the molecules which are assumed to be represented by each DPD particle. The DPD scheme can be further generalised by incorporating Q-tensor dependence in the forces. We have also considered a top-down approach by using mesh-free methods. In this, we have taken a continuum description of LCs and, through appropriate discretisation, determined the interaction terms between particles that are required to yield a consistent description at the mesoscale. This approach follows the general methodologies of Modified Smoothed Particle Hydrodynamics (MSPH) [5, 6] which allows one to solve partial differential equations on a set of randomly distributed interpolation points.

### References:

[1] P. J. Hoogerbrugge and J. M. V. A. Koelman, Europhysics Letters, 19, 155
(1992)

[2] P. Espanol and P. B. Warren, Europhysics Letters, 30, 191 (1995)

[3] M. Ellero, P. Espanol, E.G. Flekkoy, Physical Review E, 68, 041504 (2003)

[4] B.I.M. ten Bosch, Journal of Non-Newtonian Fluid Mechanics, 83, 231 (1999)

[5] Liu, M. B., Xie, W. P. and Liu, G. R. Applied mathematical modelling, 29
(12), 1252-1270 (2005)

[6] Zhang, G. M. and Batra, R. C. Computational mechanics, 34 (2), 137-146 (2004)