Research School of Chemistry **Machine** VP, CM

**Co-Investigator** Peter J Daivis

Research School of Chemistry

**Transport Processes in Liquids of Flexible Chain Molecules/Molecular
Dynamics on the CM-5**

The object of these two projects is to provide an understanding of the microscopic processes underlying transport phenomena in complex liquids. We develop and use both equilibrium and non-equilibrium molecular dynamics simulation methods that can be applied to simple or complex liquids. The model system that we most commonly use for our studies of complex liquids is the homologous series of n-alkanes. These molecules represent the simplest examples of non-rigid molecules for which an extensive body of experimental data exists.

**What are the basic questions addressed?**

How are macroscopic properties such as the self diffusion coefficient, viscosity and thermal conductivity related to microscopic processes occurring in non-equilibrium alkane liquids?

**What are the results to date and the future of the work?**

The thermal conductivity tensor of shearing liquid butane has been studied by non-equilibrium molecular dynamics methods. We have found that the effect of shear on the thermal conductivity tensor is calculable by our methods, but it is too small to be measured experimentally at the accessible strain rates. The effect is known to be measurable for polymer melts, but simulation of such systems will be difficult due to the huge computer power required.

We have completed a study in which the linear thermal conductivity of liquid butane has been calculated by non-equilibrium methods using two different molecular models. The first model was the Ryckaert-Bellemans model, a well known united atom model, and the second was a more realistic model called the anisotropic united atom model, which has several improvements over the Ryckaert-Bellemans model. We found that the new model gives better agreement with experiment at high temperatures, but it is significantly more difficult to simulate at low temperatures due to very slow structural relaxations not present in the Ryckaert-Bellemans model.

Using the CM-5, we have been able to generate very accurate velocity, stress and heat flux autocorrelation functions for the Ryckaert-Bellemans model of liquid butane. These correlation functions have allowed us to compute definitive values for the self diffusion coefficient, viscosity and thermal conductivity, and have allowed us to critically discuss the scattered values of these transport coefficients so far published in the literature.

There has recently been some discussion in the literature about the use of Einstein relations for the computation of collective transport coefficients such as the viscosity. Although it is known that Einstein relations for collective transport coefficients, in their standard form, are not compatible with the periodic boundary conditions usually used in molecular dynamics simulations, we have found that it is possible to use the non-zero wavevector forms of these equations for computation.

Future work will include extension of our simulation techniques to simpler models of chain molecules suitable for studies of long polymers, continuing studies of coupled transport phenomena in non-equilibrium systems and further development of our work on Einstein relations in periodic boundary conditions

**What computational techniques are used and why is a supercomputer
required?**

Our simulation methods employ well vectorized molecular dynamics code (typically >90% vectorization) on the VP to simulate various models of alkane liquids. Although the simpler simulations can now be performed on workstations, our more demanding work on the anisotropic united atom models requires supercomputers for timely production runs. The computation of correlation functions on the CM-5 has been greatly expedited by the introduction of the cloning method, which uses ensemble averaging over independent initial conditions in addition to time averaging. The superior speed of convergence of correlation functions calculated in this way has been a major aid to our understanding of the relations between Einstein and correlation function expressions for transport coefficients. We intend to make substantial improvements to our CM-5 code in the near future to enable simulations of large polymeric systems.

**Publications**

*Non-equilibrium molecular dynamics calculation of thermal
conductivity of flexible molecules: butane*, P J Daivis and D J Evans, Mol.
Phys. **81,** 1289-1295 (1994).

*Thermal conductivity of a shearing molecular fluid,* P J Daivis and D J
Evans, Int. J. Thermophys., accepted for publication.

*Temperature dependence of the thermal conductivity for two models of liquid
butane*, P J Daivis and D J Evans, Chem. Phys., accepted for publication.

*Transport coefficients of liquid butane near the boiling point by
equilibrium molecular dynamics*, P J Daivis and D J Evans, J. Chem. Phys.,
submitted for publication.

*Einstein relations and the wavevector and frequency dependent transport
coefficients*, P J Daivis and D J Evans, Phys. Rev. E., submitted for
publication.