Non-equilibrium molecular dynamics studies of fluids in a thermal gradient
Frank R ¨omer et al.a
Department of Chemistry, Imperial College London, London SW7 2AZ, UK f.romer@imperial.ac.uk
(Dated: July 18, 2012)
I. INTRODUCTION
Thermal gradients are responsible for a wide range of non equilibrium effects, heat transport, electron transport (thermoelectricity) [1], mass transport in suspensions (thermophoresis) [2–5], mass separation in liquid mixtures [6–8] and nucleation and growth of colloidal crystals [9]. In our studies we are more focused on heat transport and the implications of the thermophoretic force.
A fundamental understanding of the mechanisms of heat transport on a molecular level is vital to design high performance fluids with applications in heat management problems. With the miniaturisation of electronic components, which can have dimensions of tens of nanometers, scientists and engineers face new challenges in the design of fluids that can efficiently transport the heat dissipated. Hence, it is important to understand the microscopic mechanisms determining the heat transfer of fluids, and how the transfer depends on the presence of additives.
The mass transport and separation in mixtures or solutions induced by a thermal gradient, the Ludwig- Soret [12, 13] effect, also plays an important role in applications and industrial processes, e.g. CVD, fractionation of suspensions and isotope separation. It is involved in degradation of functional materials [15], thermodynamics of seawater [16], DNA replication [17] and pattern formation in polymer blends [18]. Unfortunately there is no full microscopic interpretation of the Ludwig-Soret effect available [14]
till yet.
II. METHOD
Computer simulations offer the opportunity to study such processes at a molecular level and enable the computation of properties that are experimentally hard to obtain or not directly accessible. To study the response of a fluid to a thermal gradient we utilized boundary driven non equilibrium molecular dynamics (NEMD) simulations [10, 11]. The temperature gradient is induced by thermostating different regions in the simulation box. Figure 1 shows a sketch of our simulation box, with the thermostating layers at the edges (hot region) and the centre of the box (cold region), which render a cell that is fully periodic. To obtain data we divide the box in 120 layers along the main axis (thermal gradient) of the symmetric oblong simulation box. The thermalized layers as well as the next four nearby are always ignored for evaluation. In order to improve the statistics, the profile, which includes two temperature gradients, is folded around the two central (cold) layers.
FIG. 1. Sketch of the simulation set up (left) employed in this work, and the resulting temperature profile (right).
The cold layer is located in the center of the simulation cell and the hot layers at the edges of the cell.
aThis work is naturally not the fruit of my efforts alone, but also benefited from the collaboration and contributions of:
F. Bresme, J. Muscatello, S. Serapian, D. Bedeaux and J.M. Rubi.
III. RESULTS
We start our investigations with a theoretical model, diatomic molecules consisting of two tangent spheres connected by a rigid bond. The interaction between the particles is soft repulsive: Uij = 4ǫ(σij/r)12withσij = (σi+σj)/2. To study the impact of the molecular anisotropy on the response to the thermal gradient we varied the diameter ratio of the two sites in the interval,σ2 /σ1 = 1, 3/4,2/3, 1/2 and 1/3 and the mass ratio. In order to compare the results between the different fluids we fixed the average packing fraction.
We could show [19] that these diatomic fluids adopt a preferred orientation as a response to a tem- perature gradient. We find that the magnitude of this thermomolecular orientation (TMO) effect is proportional to the strength of the temperature gradient and the degree of molecular anisotropy. By com- paring with simulations of corresponding binary mixtures, we show that the preferred orientation of the diatomic molecules follows the same trends observed in the Soret effect of binary mixtures. Moreover, we were able to establish a correlation between the TMO effect and the Soret effect.
Further on, we investigated [20] a more realistic model, a two centre Lennard-Jones (2CLJ) molecule with overlapping sites and with a flexible bond modelled by a harmonic potential. Again we varied the diameter ratio of the two sites. Here we could verify the TMO as well as the correlation between the TMO effect and the Soret effect. We have investigated the dependence of the thermal thermal conduc- tivity and heat transfer mechanism with the molecular geometry. Comparing the different models at the same thermodynamic state with respect to the critical point, we find that the thermal conductivity decreases with molecular anisotropy. It shows that the contribution of the different sites to the heat flux is linear proportional to the ratio of exposed surface of each site in the molecule. Surprisingly, the con- tribution of the flexible bond to the heat flux found to be negligible as compared with the intermolecular contributions.
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