Debye relaxation liquid water

In our early work33 [50] the constant field model was applied to liquid water, where the harmonic law of particles motion, corresponding to a parabolic potential, was actually employed in the final calculations of the complex permittivity. In this work, qualitative description of only the libration band was obtained, while neither the R-band nor the low-frequency (Debye) relaxation band was described. Moreover, the fitted mean lifetime x of the dipoles, moving in the potential well, is unreasonably short ( ().02 ps)—that is, about an order of magnitude less than in more accurate calculations, which will be made here. 

As a second example, we consider liquid fluoromethane CH3F, which is a typical strongly absorbing nonassociated liquid. For our study we choose the temperature T 133 K near the triple point, which is equal to 131 K. The relevant experimental data [43] were summarized in Table IV. As we see in Table VIII, which presents the fitted parameters of the model, the angle p is rather small. At this temperature the density p of the liquid, the maximum dielectric loss and the Debye relaxation time rD are substantially larger than they would be, for example, near the critical temperature (at 293 K). At such small (5 the theory given here for the hat-curved model holds. For calculation of the complex permittivity s (v) and absorption a(v), we use the same formulas as for water. 

Figure 1. Debye-type relaxation spectra for liquid water, adsorbed water, ice, and hydrate. Solid lines correspond to real relative permittivity n and dotted lines represent imaginary permittivity k [3, 5, 11, 10].

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). 

Since the reduced spectrum x"( ) clearly shows the low-ftequency Raman modes, we introduced a simple model to analyze the spectral profile of x"(.v) for obtaining the quantitative information. The model is composed of two damped harmonic oscillator modes and one Debye type relaxation mode (liquid water) or one Cole-Cole type relaxation mode (aqueous solution). Cole-Cole type relaxation is usually adopted in analyzing the dielectric relaxation. The formula of Cole-Cole type relaxation is represented as ... 

Pure liquids - water and alcohols Water and peroxides (HO-OH) represent a limiting state of such interactions. In the liquids state, water molecules associate by hydrogen-bond formation. Despite its apparently complex molecular structure, because of its strong association, water closely followed simple Debye relaxation (at 25 °C sr = 78.2, ooj = 5.5, t = 6.8 x 10 s, and h = 0.02, the Cole-Cole term). 

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 relaxation time can be deduced from the Debye-like drcular arc. A plot of T values versus the inverse of temperature (10 /r) (Fig. 25.4) allows a measure of activation energy (Fig. 25.5). The separation of domains already discussed above is clearly visible, from fast reorientational motions of dipolar polyatomic ions such as HX04 and HjO" to slow reorientation of NH4 ions. Motions of water molecules cover a broad region they are slow in gel, medium in superionic materials (e.g. HUP) and fast in liquid water. 

The dielectric response of water can be described by a Debye model including two relaxation times, a slow (x ) and a fast (x ), which are related to the collective reorientation of the hydrogen bonded liquid and the fast reorientation of a single water molecule, respectively [139,140]. According to this treatment, the solvent is modeled as a structureless fluid with a frequency-dependent dielectric constant e(m). In the case of water, e(m) is generally expressed in the Debye form ... 

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