Water dielectric function

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]. 

Macroscopic models have been developed that describe the protein and the water as macroscopic dielectric materials. In their simplest form these models use a distance-independent dielectric function, i.e. a simple Coulomb interaction. Others may apply a distance-dependent dielectric function. The more detailed implementatiorrs include a descriptions of the protein-solvent botmdary in terms of solvent accessibihty and ionic-strength effects (Gilson and Honig, 1988). 

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 c" for ice is taken partly from Irvine and Pollack (1968) and partly from an unpublished compilation of the optical constants of ice, from far ultraviolet to radio wavelengths, by Stephen Warren (to be submitted to Applied Optics).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

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). 

Fig. 6 The Cole-Cole plot of the contribution from water to the frequency dependent dielectric function. The reduced real part [c (u )] is plotted against the reduced imaginary part (c (u>)]. Note the non-Debye character in the micellar solution.

A high content of linolenate in the thylakoid membranes would, most probably, make them more fluid and also provide a medium of low dielectric constant. In this medium, the electron-transport chains that are inhibited by water can function well.384-386 It was found that photoreduction of cytochrome C is increased by the addition of MGDG and DGDG.387 A complex that contained 12% of manganese, DGDG, and a flavine was isolated from a variety of leaves388 this was found to have a high redox potential, and thus, it may participate as an oxidizer. 

The first term, which contains the the static dielectric permittivities of the three media , 2, and 3, represents the Keesom plus the Debye energy. It plays an important role for forces in water since water molecules have a strong dipole moment. Usually, however, the second term dominates in Eq. (6.23). The dielectric permittivity is not a constant but it depends on the frequency of the electric field. The static dielectric permittivities are the values of this dielectric function at zero frequency. 1 iv), 2 iv), and 3(iv) are the dielectric permittivities at imaginary frequencies iv, and v = 2 KksT/h = 3.9 x 1013 Hz at 25°C. This corresponds to a wavelength of 760 nm, which is the optical regime of the spectrum. The energy is in the order of electronic states of the outer electrons. 

Figure 1.12 Dielectric function s 1 (k) for bulk water calculated with the RISM method (dashed line) and for MD simulations (solid line) [35].

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. 

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