Non-equilibrium simulations of thermally induced electric fields in water

Abstract

Using non-equilibrium molecular dynamics simulations, it has been recently demonstrated that water molecules align in response to an imposed temperature gradient, resulting in an effective electric field. Here, we investigate how thermally induced fields depend on the underlying treatment of long-ranged interactions. For the short-ranged Wolf method and Ewald summation, we find the peak strength of the field to range between 2 × 10 7 and 5 × 10 7 V/m for a temperature gradient of 5.2 K/Å. Our value for the Wolf method is therefore an order of magnitude lower than the literature value [J. Chem. Phys. 139, 014504 (2013) and 143, 036101 (2015)]. We show that this discrepancy can be traced back to the use of an incorrect kernel in the calculation of the electrostatic field. More seriously, we find that the Wolf method fails to predict correct molecular orientations, resulting in dipole densities with opposite sign to those computed using Ewald summation. By considering two different multipole expansions, we show that, for inhomogeneous polarisations, the quadrupole contribution can be significant and even outweigh the dipole contribution to the field. Finally, we propose a more accurate way of calculating the electrostatic potential and the field. In particular, we show that averaging the microscopic field analytically to obtain the macroscopic Maxwell field reduces the error bars by up to an order of magnitude. As a consequence, the simulation times required to reach a given statistical accuracy decrease by up to two orders of magnitude.

Theoretical Prediction of Thermal Polarization

“…As pointed out in Ref. 8, the piecewise constant profile for cos θ is established fairly quickly, but because there is no energetic penalty for having a net dipole moment with tinfoil boundary conditions, long simulation times may be required for cos θ to be centred around zero perfectly. Since the constant term (1/L) ∫ L cos θ(z) dz is very small and must vanish by symmetry for an infinitely long run, we are justified in subtracting it from the sampled profile cos θ(z) to reduce the computational cost.…”

“…S1). We compare simulation results to the theoretical estimates obtained with Eqs (5) and (8) (Fig. 3).…”

“…To benchmark the predictions of this equation against simulation results, we ran non-equilibrium molecular dynamics (NEMD) simulations of an off-centre Stockmayer fluid in a quasione-dimensional geometry. We imposed temperature and density gradients by simulating a hot and a cold reservoir orthogonal to the z axis [8], so that all thermodynamic driving forces varied only along z. Following the approach of Daub et al [9], we disentangled the effects of the two gradients by applying a body force to each particle.…”

“…Finally, we demonstrated that very reasonable predictions can be obtained solely based on the LJ EOS and the non-equilibrium density and temperature profiles. In future work, it will be interesting to see whether our theory can be extended to water, where quadrupolar interactions are known to play an important role in thermal polarisation [8,17].…”

Microscopic analysis of thermo-orientation in systems of off-centre Lennard-Jones particles

“…8 is that the various terms in our Eq. (15) are all identified as forces (acting along the direction, which is the direction of ). In particular, = · ∇ and = ( / ) · ∇ are referred to as 'ideal forces'.…”