Fluctuations of local electric field and dipole moments in water between metal walls

Abstract

We examine the thermal fluctuations of the local electric field E loc k and the dipole moment µ k in liquid water at T = 298 K between metal walls in electric field applied in the perpendicular direction. We use analytic theory and molecular dynamics simulation. In this situation, there is a global electrostatic coupling between the surface charges on the walls and the polarization in the bulk. Then, the correlation function of the polarization density pz(r) along the applied field contains a homogeneous part inversely proportional to the cell volume V . Accounting for the longrange dipolar interaction, we derive the Kirkwood-Fröhlich formula for the polarization fluctuations when the specimen volume v is much smaller than V . However, for not small v/V , the homogeneous part comes into play in dielectric relations. We also calculate the distribution of E loc k in applied field. As a unique feature of water, its magnitude |E loc k | obeys a Gaussian distribution with a large mean value E0 ∼ = 17 V/nm, which arises mainly from the surrounding hydrogen-bonded molecules. Since |µ k |E0 ∼ 30kBT , µ k becomes mostly parallel to E loc k . As a result, the orientation distributions of these two vectors nearly coincide, assuming the classical exponential form. In dynamics, the component of µ k (t) parallel to E loc k (t) changes on the timescale of the hydrogen bonds ∼ 5 ps, while its smaller perpendicular component undergoes librational motions on timescales of 0.01 ps.

Microscopic dynamics of charge separation at the aqueous electrochemical interface

“…These fluctuations mimic the electrostatic contributions of image charges and are consistent with a textbook description of a metal in that they obey the Johnson-Nyquist relation (29). As found in other studies (30)(31)(32), this description of the electrostatic environment results in an electrostatic potential that is rapidly varying near the electrode, but homogeneous in the bulk, with concomitant Gaussian electric field fluctuations (24). Other electronic degrees of freedom, such as those that determine the details of water-platinum binding, are described implicitly by using empirical interaction potentials.…”

Power-law electrokinetic behavior as a direct probe of effective surface viscosity

“…At hydrophobic surfaces, however, a depletion layer and a finite slip length are observed, indicating a decreased effective viscosity [4,5,6,7,8,9,19,20,21]. The interfacial dielectric profile of water has been studied using molecular dynamics (MD) simulations [4,5,6,7,8,19,20,21,22,23,24,25,26], revealing a highly inhomogeneous and oscillating profile near the interface [22,23]. Whereas an effective interfacial dielectric constant can be readily obtained from capacitance measurements, experimental determination of the interfacial viscosity has been controversial [27,28,29].…”

Ferroelectric glass of spheroidal dipoles with impurities: polar nanoregions, response to applied electric field, and ergodicity breakdown

“…As can be seen in Figs.9 and 10(b), the dipoles next to the walls are parallel or antiparallel to the z axis (along [111]), whose distances from the walls are about 0.5. This is due to their interaction with the image dipoles in the walls (see Appendix A) 69,71,72 . For ∆Φ = 0, these two orientations appear equally on the average due to the toptail symmetry of our spheroidal dipoles.…”

“…The numerical calculations were preformed on CRAY XC40 at YITP in Kyoto University and on SGI ICE XA/UV at ISSP in the University of Tokyo. Appendix A: Electrostatics of dipole systems Here, we explain the electrostatics of dipoles between metal walls in applied field [68][69][70][71][72] . The electric potential due to the image dipoles is equivalent to that due to the surface charge densities, written as σ 0 (x, y) at z = 0 and σ H (x, y) at z = H. Without adsorption and ionization on the surfaces, the dipole centers are somewhat away from the walls (see the comment below Eq.…”

“…On the other hand, we investigate general aspects of ferroelectric glass with a simple molecular model. In electrostatics, we use an Ewald scheme includ-ing image dipoles and applied electric field 68,69 , which has been used to study water between electrodes [70][71][72] . To prepare a mixed crystal, we cool a liquid mixture from high T ; then, our impurity distribution at low T is naturally formed during crystallization 57,58 .…”