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

Abstract

We examine the thermal fluctuations of the local electric field $E_k^{\mathrm{loc}}$ and the dipole moment ${\mu }_k$ 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 $p_z(r)$ along the applied field contains a homogeneous part inversely proportional to the cell volume $V$. Accounting for the long-range dipolar interaction, we derive the Kirkwood-Fr$\ddot{\mathrm{o}}$hlich 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 $E_k^{\mathrm{loc}}$ in applied field. As a unique feature of water, its magnitude $|E_k^{\mathrm{loc}}|$ obeys a Gaussian distribution with a large mean value $E_0\cong 17$V$/$nm, which arises mainly from the surrounding hydrogen-bonded molecules. Since $|{\mu }_k|E_0\sim 30k_{\mathrm{B}}T$, ${\mu }_k$ becomes mostly parallel to $E_k^{\mathrm{loc}}$. As a result, the orientation distributions of these two vectors nearly coincide, assuming the classical exponential form. In dynamics, the component of ${\mu }_k(t)$ parallel to $E_k^{\mathrm{loc}}(t)$ changes on the timescale of the hydrogen bonds $\sim 5$ ps, while its smaller perpendicular component undergoes librational motions on timescales of 0.01 ps.

17 pages, 15 figures. Accepted in J. Chem. Phys

References in corpus (2)

• Polar nanoregions in water - a study of the dielectric properties of TIP4P/2005, TIP4P/2005f and TTM3F
• Molecular Dynamics Simulation of Water between Metal Walls under Electric Field: Dielectric Response and Dynamics after Field Reversal

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