The origin of and interactions between key thermodynamic anomalies are derived and analyzed, as are the interactions with the stability (or cavitation) limits. The conditions for interaction are derived from the underlying thermodynamic relations rather than using the morecommonly applied Taylor expansion method. As a result, we derive a general set of equations that govern the interactions between different lines of thermodynamic anomalies using standard manipulation of thermodynamic equations. The validity of the derivations is investigated by comparing them to numerical simulation data and previous Taylor expansion-based results. Simulations are performed using a modified Stillinger-Weber potential in which the balance of the two-and three-body interactions is varied and which serves to highlight the relationships between the various anomalies. The deeply supercooled regime is explored by employing replica exchange methods. The behavior of the anomalies is considered in terms of previously constructed thermodynamic "scenarios." Based on the newly uncovered interaction schemes, we propose a classification strategy for the thermodynamic anomalies (as first-or second-order) which could be extended to additional related anomalies.
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.
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...
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