Electric field induced transitions in water clusters

doi:10.1016/S0166-1280(02)00111-2

Journal of Molecular Structure: THEOCHEM

Volume 593, Issues 1–3, 27 September 2002, Pages 19-32

https://doi.org/10.1016/S0166-1280(02)00111-2 Get rights and content

Abstract

The influence of an external uniform electrostatic field on the internal energy and polarization of a medium-sized water cluster, consisting of 40 molecules is studied at four temperatures: 150, 170, 200, and 240 K, by means of the Monte Carlo method. The external field is slowly varied in the 0.5×10⁷–7×10⁷ V/cm range. The system shows an abrupt change of its properties at some critical value of the field, E_tr, where a transition from a normal (solid-like or liquid-like) to a superpolarized cluster state is observed. This process has the character of a first-order phase transition and is accompanied by the absorption of heat. For intermediate field strengths, polarization has been found to increase with increasing temperature, an effect, which through a simple analytical model has been shown to be the result of the interplay between the strength of the attractive water–water interactions and the strength of the external field. Also E_tr has been found to decrease with increasing temperature, in contrast to the behavior dictated by the Clausius–Clayperon equation for field-induced transitions between equilibrium states.

Introduction

Present work is a continuation of previous studies [1], [2] regarding the influence of uniform and static external electric fields, in the 0.5×10⁷–10⁸ V/cm range on the structure and dynamics of small water clusters. From Monte Carlo (MC) calculations [1] at a few selective fields and by employing the ST2 potential model, it was found that weak electric fields do not considerably affect the melting temperature (T_m) of the cluster, which, however, becomes suppressed for stronger ones at conditions of polarization saturation of the cluster. Electric fields, in general, tend to the weakening or destruction of the hydrogen-bonding network of water. This is manifested primarily into the dielectric constant of the bulk, which from experimental [3] and theoretical studies [4], [5] has been found to be a monotonically decreasing function of the applied external field, provided that external fields are larger than about 10⁶ V/cm. Another evidence comes from the smearing off of the structure of the g_HH(r) correlation function of bulk water under the application of fields of about 10⁸ V/cm, as it has been shown in calculations by Watts [6]. This effect was attributed to the enhancement of the free rotation of the hydrogen atoms of a water molecule about the direction of the applied field. The decrease of the hydrogen bond strength in the liquid as a result of the applied field has been reported in calculations by Heinzinger and Kiselev [7].

Our MC calculations [1] and specifically the behavior of the longitudinal and transverse components of the susceptibility tensor as a function of temperature and for selective electric fields in the weak and strong regime have shown that there is an overall enhancement of the reorientational motions of water molecules in the cluster. Longitudinal components can be associated with the tumbling molecular motions with respect to the field axis, whereas transverse components with both tumbling and spinning motions (about the field axis). Thus at temperatures below T_m, both weak and strong fields induce an enhancement of spinning, but not of tumbling motions, whereas for temperatures above T_m, tumbling motions are predominantly enhanced compared with the spinning ones. Finally, for strong enough fields, tumbling motions are completely suppressed due to electrofreezing [8], [9], [10], [11].

In a subsequent molecular dynamics (MD) investigation [2] at $T=200 K$ of the translational and reorientational dynamics of a water cluster as a function of the external field, and by employing the TIP4P model for water–water interactions it was shown that the application of an external field in the 10⁷ V/cm range results into the enhancement of the reorientational decay rates of the molecular intrinsic axes and of the self-diffusion coefficients. On the other hand, strong enough fields in the 10⁸ V/cm range result to the suppression of both translational and rotational diffusion of the molecules. This was attributed to cluster restructuring, namely, to the appearance of configurations reminiscent of a proton-ordered lattice found also in bulk [8], [9], [10].

Reorientational relaxation in Ref. [2] has been found to obey a stretched exponential behavior of the Kohlrausch–Williams–Watts (KWW) type [12], where a correspondence between the electric field dependence of the β-exponent and molecular cooperativity has been established. We have found that an enhanced cooperativity of the molecular spinning and (independently) of the tumbling motions is required for the dipole alignment along the field, but after this has been facilitated to a considerable degree, cooperativity is required only in the molecular tumbling motions in order for the quasi-cubic ice structure to be obtained. After a certain field value, molecules are found to spin independently of each other (β=1) due to the complete destruction of the lateral (transverse to the field) hydrogen bonding network.

The conclusions drawn so far from our MC and MD studies, despite the different methods and the potential models used are that external electric fields in the 10⁷ V/cm range result in the enhancement of the molecular reorientational rates and to the weakening of the hydrogen bonding pattern in the cluster. This fact is expected to alter drastically the solvation and reactive properties of the medium compared to the zero-field case. In a sense, water clusters can be considered to play the role of large defects that can appear locally on the surface of an ice microcrystal, like those existing in the polar stratosphere and which are known to play a dominant role in the ozone depletion process [13], [14] by catalysing some key reactions involving chlorine containing compounds. Such local defects are expected to be under the influence of strong electric fields because of the accumulation of adsorbed ions and solvent separated ion pairs, or because of local distortions in the distribution of charge close to microscopic lattice point defects and fractures. Therefore, polar molecules or ions from the overlying vapor are selectively drawn to these areas of the ice surface. Present as well as our previous studies [1], [2] are expected to contribute from another perspective to the elucidation of the mechanisms that influence the uptake of these compounds from roughened, non-ideal ice surfaces, as recent experiments [15] and simulations [16] actually show.

The MD examination [2] (at a single temperature $T=200 K$ ), of certain static and dynamic quantities as a function of the external field has shown that at a particular field strength (transition field) these quantities display a discontinuous jump in their values. Whether this behavior is related to a phase transition and in which way the transition field behaves with respect to temperature changes is the scope of the present work. Here we adopt the MC method and the ST2 potential, and we examine the variation of internal energy and polarization of a water cluster with N=40 water molecules, as a function of the external field at four distinct temperatures, below and above the melting temperature of the cluster at E=0.

The organization of the paper is as follows. Section 2 presents the computational procedure. Section 3.1 considers the cluster melting at zero field, whereas 3.2 Effect of an external electric field on polarization, 3.3 Effect of an external electric field on cluster energy, the variation of cluster polarization and internal energy, respectively, with respect to the external field. Section 4 concludes.

Section snippets

Computational procedure

The total energy of the system consists of four terms $U=U_{pair}^{w–w} +U^{w–field} +U_{pol}^{w–field} +U_{ind}^{w–w}$ where U_pair^w–w accounts for the pairwise water–water interactions. For this purpose, the ST2 [17], [18], [19], [20] potential model has been employed. In the five centered Rahman and Stillinger ST2 potential, four equal in magnitude charges of q=1.132062×10⁻¹⁰ CGS units are placed on the vertices of a tetrahedron. The two positive and negative charges are located at a distance of 1.0 and 0.8 Å,

Cluster melting at E=0

First of all, we calculated the change of cluster internal energy as a function of temperature (caloric curve) at zero field. This is shown in Fig. 1(a). The change of slope at about $T=208 K$ gives an identification of the melting temperature of the cluster. Heat capacity shows a maximum as well, at the same temperature and is displayed in Fig. 1(b). Within statistical error, similar results have been obtained in our previous work [1] for a larger cluster (N=64). In fact, melting temperature

Conclusion

It has been demonstrated that unlike atom–atom correlation functions, angle correlations between dipoles 〈cos ξ〉, as a function of their distance R are an unambiguous indicator of the phase state of the system. For a cluster in the solid-like state and E=0, 〈cos ξ〉 displays a strong oscillatory character, which is destroyed when the system, on melting, is found in the liquid-like state. A similar picture emerges with the application of a strong electric field, where angular correlations, being

Acknowledgements

Financial support by the INTAS99-01162 grant is gratefully acknowledged.

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Electric field induced transitions in water clusters

Abstract

Introduction

Section snippets

Computational procedure

Cluster melting at E=0

Conclusion

Acknowledgements

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Chem. Phys.

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J. Phys. Chem.

J. Chem. Phys.

J. Am. Chem. Soc.

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev. B

Trans. Faraday Soc.

Science

J. Geophys. Res.

J. Phys. Chem. A

J. Chem. Soc., Faraday Trans.