Dielectric constant water, frequency dependence

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

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. 

The high dielectric constant of water, as well as that of ice, is not connected with this since it is as high as this for both H20 and DaO. In ice, as well as in heavy ice, it appears from the frequency- and temperature-dependence of the dielectric constant that the activation energy, associated with the orientation of the dipoles in an alternating electric field, is equal to 13.2 kcal/mole (Cole) which therefore points to the rupture of several hydrogen bonds. 

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.. 

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.)... 

The conducting properties of a liquid in a porous medium can provide information on the pore geometry and the pore surface area [17]. Indeed, both the motion of free carriers and the polarization of the pore interfaces contribute to the total conductivity. Polymer foams are three-dimensional solids with an ultramacropore network, through which ionic species can migrate depending on the network structure. Based on previous works on water-saturated rocks and glasses, we have extracted information about the three-dimensional structure of the freeze-dried foams from the dielectric response. Let be d and the dielectric constant and the conductivity, respectively. Dielectric properties are usually expressed by the frequency-dependent real and imaginary components of the complex dielectric permittivity ... 

Equations (92) and (93) show that the presence of a solvent medium other than a free space much reduces the magnitude of van der Waals interactions. In addition, the interaction between two dissimilar molecules can be attractive or repulsive depending on refractive index values. Repulsive van der Waals interactions occur when n3 is intermediate between nx and n2, in Equation (92). However, the interaction between identical molecules in a solvent is always attractive due to the square factor in Equation (93). Another important result is that the smaller the n - nj) difference, the smaller the attraction will be between two molecules (1) in solvent (3) that is the solute molecules will prefer to separate out in the solvent phase which corresponds to the well-known like dissolves like rule. However there are some important exceptions to the above explanation, such as the immiscibility of alkane hydrocarbons in water. Alkanes have nx = 1.30-1.36 up to 5 carbon atoms, and water has a refractive index of n = 1.33, and very high solubility may be expected from Equation (93) since the van der Waals attraction of two alkane molecules in water is very small. Nevertheless, when two alkane molecules approach each other in water, their entropy increases significantly because of the very high difference in their dielectric constants and also the zero-adsorption frequency contribution consequently alkane molecules associate in water (or vice versa). This behavior is not adequately understood. 

We demonstrate for ice and water the frequency dependence s (v) of the dielectric constant calculated in the far-IR region (Fig. 22a). In Fig 22b the Cole-Cole diagram s"[s (v)] is also shown in this region. The theoretical dependences agrees reasonably with the experimental ones. The latter, shown by open circles, are obtained from data of Warren [49] and Downing and Williams [22]. 

Figure 22 Frequency dependence of dielectric constant e in the far-IR region, calculated for ice at —7°C (a) and for water at 27°C (c) and the relevant Cole-Cole diagrams pertinent to ice (b) and water (d). Open circles refer to the experimental data by Warren [49] and Downing and Williams [22]. Notation V, T, L refer, respectively to the V-, T-, and L-bands.

Figure 37 Frequency dependences of the loss factor (a) and of the dielectric constant (b) calculated (solid curve) and measured (open circles) in water, (c) Contributions to loss due to libration of a permanent dipole in the hat well (1), vibration of a nonrigid dipole along the H bond (2), reorientation of polar molecules about this bond (3), and transverse vibration of a nonrigid dipole with respect to the H bond (4). Temperature 300 K.

THE SOLVATION FORCE. The electrostatic and van der Waals disj>ersion forces retain the common attribute of depending on the nature of liquid water in the aqueous solution phase only through the macroscopic dielectric constant. In the case of the electrostatic force as exemplified in Eq. 6.16, the only dependence on the properties of liquid water comes through the parameter k, which, as shown in connection with Eq. 5.11, is a function of the bulk (zcro>frequency) dielectric constant, D. Similarly, for... 

Let us first discuss estimates fi om DR measurements that provide several important pieces of information. These experiments measure the frequency-dependent dielectric constant and provide a measure of a liquid s polarization response at different frequencies. In bulk water, we have two dominant regions. The low-frequency dispersion gives us the well-known Debye relaxation time, Tq, which is equal to 8.3 ps. There is a second prominent dispersion in the high-frequency side with relaxation time constant less than Ips which contains combined contributions from low-frequency intermolecular vibrations and libra-tion. Aqueous protein solutions exhibit at least two more dispersions, (i) A new dispersion at intermediate frequencies, called, d dispersion, which appears at a timescale of about 50 ps in the dielectric spectrum, seems to be present in most protein solutions. This additional dispersion is attributed to water in the hydration layer, (ii) Another dispersion is present at very low frequencies and is attributed to the rotation of the protein. 

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. 

Dielectric relaxation results are proven to be the most definitive to infer the distinctly different dynamic behavior of the hydration layer compared to bulk water. However, it is also important to understand the contributions that give rise to such an anomalous spectrum in the protein hydration layer, and in this context MD simulation has proven to be useful. The calculated frequency-dependent dielectric properties of an ubiquitin solution showed a significant dielectric increment for the static dielectric constant at low frequencies but a decrement at high frequencies [8]. When the overall dielectric response was decomposed into protein-protein, water-water, and water-protein cross-terms, the most important contribution was found to arise from the self-term of water. The simulations beautifully captured the bimodal shape of the dielectric response function, as often observed in experiments. 

The field s strength and its frequency are fixed by the eqnip-ment, whereas the other parameters are material-dependent As the dielectric constant of water is over an order of magnitude greater than the woody materials, moisture is preferentially heated, a process that leads to a more uniformly moist product with time. This feature is one of the attractions of the technique, for example, in moisture leveling in the mannfac-ture of plywood to avoid delamination during subsequent hot pressing (Schiffmann, 1995). 

The dielectric properties of water and other polar substances are measured by the relative dielectric constant, e, valid in a static electric field. For a propagating EM field, the dielectric constant depends on the frequency of the radiation, for the reasons just given. At light frequencies, the oscillation of dipoles or the vibrations of nuclei are unimportant. Then, as follows from Maxwell s equations, the dielectric constant for a substance is equal to the square of the refractive index (not proven) ... 

Whether CT is possible depends on the polarity of the solvent, as measured by the dielectric constant. There are essentially two important dielectric constants one for slow processes or the static dielectric constant (Cj) and the other for very fast processes (faster than any reorganization process), referred to as or the dielectric constant at infinite frequency. of a compound can be obtained by measuring the capacitance of a condensator where the compound is used as a dielectricum. is obtained by measuring molecular polarizability. The higher the frequency of the applied electric field, the slower are the motions in the medium to follow the variations in the field. For example, a water molecule has a certain rotation time and when the field frequency is too fast, the water molecule no longer moves with the field. When the frequencies applied correspond to UV frequencies, (for all practical purposes) is measured. One may show that = n, where n is the refractive index. 

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