The Static Dielectric Constant of Water

The effective value of in Eq. (28) may be calculated using various assumptions. Kirkwood72 proposed that for associated liquids is pA2(l + riofy), where fv is the electrostatic radial distribution function 

The radial distribution function was obtained by Pople,103 c.f., Harris and Alder,110 Haggis, Hasted, and Buchanan.111 Pople showed that Kirkwood s assumption of complete hydrogen bonding in the first shell with none in the second was oversimplified. The first shell dipoles are bonded to the second via bent hydrogen bonds of bending 

33 l(cos52.25Lexp + g/kT)21. Pople found the effect of each shell on the static dielectric constant using the tij values from the radial distribution function. With g/kT = 10 at 273 K, the relative contributions of the first, second, and third shells were found to be 1.20, 0.33, and 0.07, and the temperature dependence of the dielectric constant showed good agreement between theory and experiment.103 

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According to the Kirkwood theory of polar dielectrics, simple relations (23) between molecular dipole moment vectors and the mean-square total dipole moment of water clusters can be used to compute the static dielectric constant of water. As the normalized mean-square total dipole moment increases towards unity, theory predicts decreases in the static dielectric constant. Since MD results indicate that the mean-square total dipole moment of interfacial water is greater than that for bulk water (48), the static dielectric... 

Finally, the static dielectric constant of water was of particular interest to us because it controls the solvent behaviour of water and the ionic dissociation of dissolved salts. Fig. 3 shows our results for the behaviour of the dielectric constant up to 1000 and to a density of 1 g cm derived from static measurements up to 550 C and 5000 bar [36,37] and from model calculations at higher temperatures [38,39]. 

Wasserman E, Wood B, Brodholt J (1995) The static dielectric constant of water at pressures up to 20 kbar and temperatures to 1273 K Experiment, simulations, and empirical equations. Geochim Cosmochim Acta 59 1-6... 

By setting the appropriate pressure and temperature conditions one can tune solvation properties to affect reaction rates and chemical equilibria. For example, as illustrated in Figure 15.1, by changing state parameters one can reduce the static dielectric constant of water to a value characteristic for low-polar solvents. Supercritical water (SW) may substitute toxic organic solvents, such as acetone ( 25 = 20.7) or benzene ( 25 = 2.3). In contrast to ambient water, supercritical fluid is a poor solvent for ionic species but is well miscible with hydrocarbons and gases. 

Uematsu, M. Harder, W. French, E. U. "The Static Dielectric Constant of Water to 550 C and 5 kbar". Report of the "international Association on the Properties of Steam" (TAPS) Sept. 1976. 

In principle. In practice, this is not so easy a case in point are lhe attempts to correctly calculate the static dielectric constant of water using its molecular dipole moment. 

Fernandez, D.P., Mulev, Y., Goodwin, A.R.H., and Levelt Sengers, J.M.H. (1995) A database for the static dielectric constant of water and steam. J. Phys, Chem. 

The addition of salts modifies the composition of the layer of charges at the micellar interface of ionic surfactants, reducing the static dielectric constant of the system [129,130]. Moreover, addition of an electrolyte (NaCl or CaCli) to water-containing AOT-reversed micelles leads to a marked decrease in the maximal solubihty of water, in the viscosity, and in the electrical birefringence relaxation time [131],... 

Characteristic frequencies may be found from dielectric permittivity data or, even better, from conductivity data. The earlier data by Herrick et al. (6) suggest that there is no apparent difference between the relaxation frequency of tissue water and that of the pure liquid (7). However, these data extend only to 8.5 GHz, one-third the relaxation frequency of pure water at 37°C (25 GHz), so small discrepancies might not have been uncovered. We have recently completed measurements on muscle at 37°C and 1°C (where the pure water relaxation frequency is 9 GHz), up to 17 GHz. The dielectric properties of the tissue above 1 GHz show a Debye relaxation at the expected frequency of 9 GHz (8 ) (Figure 3). The static dielectric constant of tissue water as determined at 100 MHz compares with that of free water if allowance is made for the fraction occupied by biological macromolecules and their small amount of bound water (1, 9). 

It is now well understood that the static dielectric constant of liquid water is highly correlated with the mean dipole moment in the liquid, and that a dipole moment near 2.6 D is necessary to reproduce water s dielectric constant of s = 78 T5,i85,i96 holds for both polarizable and nonpolarizable models. Polarizable models, however, do a better job of modeling the frequency-dependent dielectric constant than do nonpolarizable models. Certain features of the dielectric spectrum are inaccessible to nonpolarizable models, including a peak that depends on translation-induced polarization response, and an optical dielectric constant that differs from unity. The dipole moment of 2.6 D should be considered as an optimal value for typical (i.e.. 

Waals envelope of the solvent. This projection can be expressed in terms of a response function, whose kernel contains a damping factor (the dielectric constant ) very near to the optical dielectric constant of water, eopt, when the water molecules are held fixed, or rapidly increasing towards the static dielectric constant, when water molecular motions are allowed and their number in the cluster increases. This is the origin of our PCM model (more details can be found in Tomasi, 1982). Surely, similar considerations spurred Rivail and coworkers to elaborate their SCRF method (Rivail and Rinaldi, 1976). An additional contribution to the formulation of today continuum models came from the nice analysis given by Kolos (Kolos, 1979 dementi et al., 1980) of the importance of dispersion contributions. 

The static dielectric constant of superheated water was measured by the relative noncontact bridge method. " The glass measuring cell was relieved of pressure. Measurements were made in the range from 423 to 573 K along isotherms with an interval of 10 K. Within the measurement error the static dielectric constant of superheated water remains unchanged along the isotherms. 

All the calculations have been performed at SCF level with a basis set equal to the Dunning/Huzinaga valence double-zeta. All the calculations in solution have been performed using the lEF version of the PCM method and they refer to a medium having dielectric constant e = 78.5 corresponding to the static dielectric constants of liquid water at 298 K. 

Hamelin J, Mehl JB, Moldover MR. 1998. The static dielectric constant of liquid water between 274 and 418 K near the saturated vapor pressure. Int. J. Thermophys. 19 1359-1380. 

The dielectric spectra of aqueous protein solutions exhibit anomalous dielectric increments where the value of the static dielectric constant of the solution is significantly larger than that of pure water. A typical experimental result illustrating the dielectric increment is shown in Figure 8.3, where the real part of the frequency-dependent dielectric constant of myoglobin is evident. Both the increment at zero frequency and the overall shape of this curve have drawn a lot of attention. 

In the colloidal domain, most of the authors are getting on together for attributing the I potential of air bubbles immersed in water to specific adsorption of hydroxide ions at the air-water interface. An attempt to explain this specific adsorption is based on the fact that the static dielectric constant of the interfacial region between air and water is less than that of the adjacent aqueous phase [51]. Work is therefore required to transfer an ion from the aqueous phase into the interfacial region. This work is positive and thus unfavorable for ion adsorption as it is greater for smaller ions than for larger ones, hydroxide ions would be adsorbed in preference to smaller hydrated protons. 

Fig. 6 Potential of mean force between a sodium ion and a chloride ion at infinite dilution in water at 298 K obtained from atomistic simulations with the SPC/E water model (red curve). (Adapted from [75]). The dashed curve shows the Coulomb potential - e lAneocr with a = 71 the static dielectric constant of SPC/E water...

Figure 15.1 Static dielectric constant of water as function of temperature calculated for the isobar P—25 MPa using the empirical equation proposed to correlate the measured values with temperature and density of water. Inset shows ambient values of the static dielectric constant of selected organic solvents.

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