Numerical evidence for thermally induced monopoles

Abstract

Electric charges are conserved. The same would be expected to hold for magnetic charges, yet magnetic monopoles have never been observed. It is therefore surprising that the laws of nonequilibrium thermodynamics, combined with Maxwell's equations, suggest that colloidal particles heated or cooled in certain polar or paramagnetic solvents may behave as if they carry an electric/magnetic charge. Here, we present numerical simulations that show that the field distribution around a pair of such heated/cooled colloidal particles agrees quantitatively with the theoretical predictions for a pair of oppositely charged electric or magnetic monopoles. However, in other respects, the nonequilibrium colloidal particles do not behave as monopoles: They cannot be moved by a homogeneous applied field. The numerical evidence for the monopole-like fields around heated/cooled colloidal particles is crucial because the experimental and numerical determination of forces between such colloidal particles would be complicated by the presence of other effects, such as thermophoresis.soft matter | molecular simulation | colloids | monopoles | nonequilibrium thermodynamics T he existence of quasi-monopoles in a system of heated or cooled colloidal particles in a polar or paramagnetic fluid follows directly from nonequilibrium thermodynamics, combined with the equations of electro/magneto-statics (1). Although suggested theoretically, they have thus far not been studied experimentally. This paper provides numerical evidence indicating that the predicted effects are real and robust. In what follows, we consider the case of thermally induced quasi-monopoles in a dipolar liquid, but all our results also apply to paramagnetic liquids. It has been shown that a thermal gradient will create an electric field in a liquid of dipolar molecules with sufficiently low symmetry (2, 3). In the absence of any external electric field, a heated or cooled colloidal particle placed in such a liquid will generate an electric field according to the phenomenological relation (2, 4, 5)where T (r) is the temperature and S TP the thermo-polarization coefficient, with a magnitude that is not known a priori. For water near room temperature, S TP has been estimated to be S TP ≈ 0.1 mV/K (4, 6). Let us next consider the electric polarization around a heated (or cooled) colloidal particle, for brevity also referred to simply as a colloid. We note that the sole function of the colloid is to generate a temperature gradient field in the solvent, which in turn couples to the electric field via Eq. 1. Other heat sources (sinks) would lead to the same effect. In steady state the temperature profile at a distance r from the center of an isolated, spherical colloid of radius R satisfiesand hencewhere T∞ is the temperature in the bulk liquid andr the radially outward-pointing unit vector. Note that E TP decays as 1/r 2 . Using Gauss's theorem, we can then writewhere 0 is the dielectric permittivity of a vacuum. In words, the flux through a closed surface around a neutral colloi...

Theoretical Prediction of Thermal Polarization

“…This 'thermo-polarisation' (TP) effect is closely related to the thermo-orientation effect in non-polar fluids [5,6]. The existence of the TP effect has been verified numerically for a range of different models of water [4,7,8], polar dumbbell molecules [5,9], and an off-centre Stockmayer model for which the induced TP field is equivalent to one generated by a Coulomb charge [10].…”

“…In this Letter, we propose a mean-field approach to predict the thermally induced alignment of an off-centre Stockmayer liquid without the need for any fitting parameters. In this particularly simple model of a polar fluid [10], the original Stockmayer potential [11] is modified by displacing the Lennard-Jones (LJ) site from the position of the dipole p, which continues to be located at the centre of mass. Such asymmetry is required to produce forces that reorientate molecules in thermal gradients.…”

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

“…(18) does hold; the LEP assumption is that it remains true away from equilibrium. Combining Eqs (14), (17) and (18) yields Eq. (12).…”

“…which measures the correlation between the interparticle force and the orientation. The LEP predictions [Eqs (17) and (18)] are that…”

“…If the molecules in the fluid are polar, such a spontaneous orientation results in an emergence of electrical polarisation, or 'thermopolarisation', as found in computer simulations of water [11][12][13][14][15] and other fluids. 7,8,16,17 Thermopolarisation and thermoorientation effects are thought to have a common origin; 5,7,8 in the following, we consider non-polar molecules without any electrostatic interactions, so our analysis is restricted to the thermo-orientation effect. However, we anticipate the principles described here can also be applied to thermopolarisation.…”