Dielectric function of water

The Debye equations (9.42) are particularly important in interpreting the large dielectric functions of polar liquids one example is water, the most common liquid on our planet. In Fig. 9.15 measured values of the dielectric functions of water at microwave frequencies are compared with the Debye theory. The parameters tod, e0v, and r were chosen to give the best fit to the experimental data r = 0.8 X 10 -11 sec follows immediately from the frequency at which e" is a maximum e0d — e0v is 2e"ax. 

Figure 9.15 Dielectric function of water at room temperature calculated from the Debye relaxation model with r = 0.8 X 10 11 sec, eQcl = 77.5, and e0l, = 5.27. Data were obtained from three sources Grant et al. (1957), Cook (1952), and Lane and Saxton (1952).

Figure 10.3 Dielectric functions of water (Hale and Querry, 1973). c" for ice is taken partly from Irvine and Pollack (1968) and partly from an unpublished compilation of the optical constants of ice, from far ultraviolet to radio wavelengths, by Stephen Warren (to be submitted to Applied Optics).

If the structure of water depends on distance from a surface, so must its physical properties, including its dielectric function. We noted in Section 9.5 that at microwave frequencies the dielectric function of water changes markedly when the molecules are immobilized upon freezing as a consequence, the relaxation frequency of ice is much less than that of liquid water. Water irrotationally bound to surfaces is therefore expected to have a relaxation frequency between that of water and ice. 

P. A. Bopp, A. A. Kornyshev and G. Sutmann, Frequency and wave-vector dependent dielectric function of water collective modes and relaxation spectra, J. Chem. Phys., 109 (1998) 1939-58. 

For weak electrolytes, at small concentrations, the electrical conductivity is almost proportional to the electrolyte concentration. For higher concentrations, the degree of dissociation decreases. Consequently, the electrical conductivity reaches a maximum as a function of the electrolyte concentration. For strong electrolytes this maximum also exists, because when the electrolyte concentration is increased, the ionic interaction becomes stronger. This is illustrated for a NaOH solution in Fig. 3.6. In this figure the influence of the electrolyte temperature on the conductivity can be seen. The temperature mainly influences the viscosity of the electrolyte, which influences the drift velocity of the ions. Other effects are the changes in the dielectric function of water and the degree of dissociation of the electrolyte. 

In Fig. 4.24, we plot the experimental free energies W(l, 1) as a function of the proton-proton distance Rjfu. We also plot the theoretical curve for the Coulombic interaction between the two protons, as modified by the macroscopic dielectric constant of water D = 78.54. It is clear that the values of W(l, 1) for the larger molecules follow closely the theoretical curve with a fixed value of D. Large... 

Figure 8.3 Dielectric constant of water as a function of P and T conditions. Reprinted from T. M. Seward, Physics and Chemistry of Earth, 13, 113-132, copyright 1981, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

Nevertheless, certain collective excitations can occur in the condensed phase. These may be brought about by longitudinal coulombic interaction (plasmons in thin films) or by transverse interaction, as in the 7-eV excitation in condensed benzene, which is believed to be an exciton [12]. Special conditions must be satisfied by the real and imaginary parts of the dielectric function of the condensed phase for collective excitations to occur. After analyzing these factors, it has been concluded that in most ordinary liquids such as water, collective excitations would not result by interaction of fast charged particles [13,14]. 

Water molecules are oriented at the surfaces of macromolecules as well as at solid surfaces. For example, Bernal (1965) refers to a regular formation of ice surrounding most protein molecules, although by ice he does not mean free water ice. Bound water in hydration shells surrounding macromolecules in aqueous solutions is sometimes denoted as lattice-ordered or ice-like and has been taken into account in interpreting the dielectric functions of such solutions (Buchanan et al., 1952 Jacobson, 1955 Pennock and Schwan, 1969). 

The great solvent power of water, especially for ionic compounds, is due to its dielectric constant. If this were only, say 10, instead of the actual 80, it would mean that water could dissolve only a trace of sodium chloride. This solvent action of water., naturally. plays an important role in geology. In biology, water functions as a means of conveying salts and other substances which circulate in the bodies of animals and plants. It is outside the scope of this book to discuss any further the function of water on this planet, a subject which could fill many volumes. It is important in this context that we now know water molecules to possess a dipole moment and to discover whether perhaps this fact can provide an explanation of the unique properties of water. 

There are numerous properties of materials which can be used as measures of composition, e.g. preferential adsorption of components (as in chromatography), absorption of electromagnetic waves (infra-red, ultra-violet, etc.), refractive index, pH, density, etc. In many cases, however, the property will not give a unique result if there are more than two components, e.g. there may be a number of different compositions of a particular ternary liquid mixture which will have the same refractive index or will exhibit the same infra-red radiation absorption characteristics. Other difficulties can make a particular physical property unsuitable as a measure of composition for a particular system, e.g. the dielectric constant cannot be used if water is present as the dielectric constant of water is very much greater than that of most other liquids. Instruments containing optical systems (e.g. refractometers) and/or electromechanical feedback systems (e.g. some infra-red analysers) can be sensitive to mechanical vibration. In cases where it is not practicable to measure composition directly, then indirect or inferential means of obtaining a measurement which itself is a function of composition may be employed (e.g. the use of boiling temperature in a distillation column as a measure of the liquid composition—see Section 7.3.1). 

A numerical tabulation of recent data for water is given in R. R. Dagastine, D. C. Prieve, and L. R. White, "The dielectric function for water and its application to van der Waals forces," J. Colloid Interface Sci., 231, 351-8 (2000). The tabulation, at http //www.cheme.cmu.edu/jcis/, gives e(i n) for at room temperature together with a suggested procedure to compute s(i n) at other temperatures. This site also presents data tables for several other materials. 

Fig. 11. Hydration dependence of dielectric response at 25 GHz. Dielectric constant (e ) and loss (s") of packed lysozyme powder as a function of water content. Frequency, 25 GHz temperature, 25°C. (From Harvey and Hoekstra, 1972.)... 

Figure 3. The Dielectric Constant of Water as a Function of Temperature. 

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. 

Until the last 30 or 40 years, relatively little effort had been made to elucidate in any detail the structure and function of water in cells. Fortunately, however, the situation is changing, and a growing body of evidence already suggests that at least some of the water in cells differs in its properties (such as density, viscosity, dielectric behavior, and heat capacity) from the ordinary bulk liquid. The lack of suitable measurement techniques has hampered the attainment of a more definitive description of intracellular water, nonetheless, much about it now appears within our grasp. 

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