Properties relaxation frequency, bulk

Physical Mechanisms. The simplest interpretation of these results is that the transport coefficients, other than the thermal conductivity, of the water are decreased by the hydration interaction. The changes in these transport properties are correlated the microemulsion with compositional phase volume 0.4 (i.e. 60% water) exhibits a mean dielectric relaxation frequency one-half that of the pure liquid water, and ionic conductivity and water selfdiffusion coefficient one half that of the bulk liquid. In bulk solutions, the dielectric relaxation frequency, ionic conductivity, and self-diffusion coefficient are all inversely proportional to the viscosity there is no such relation for the thermal conductivity. The transport properties of the microemulsions thus vary as expected from simple changes in "viscosity" of the aqueous phase. (This is quite different from the bulk viscosity of the microemulsion.)... 

There is a duality in the electrical properties of tissue. Tissue may be regarded as a conductor or a dielectric. In frequencies of 100 kHz or less, most tissues are predominantly electrolytic conductors. Therefore, we start Chapter 2 with a look at electrolytes. Bulk electrolyte continuity is broken in two important ways by electrode metal plates and by cell membranes. This break in continuity introduces capacitive current flow segments. At the electrodes, electric double layers are formed in the electrolyte the cell interiors are guarded by membranes. With high-resolution techniques, it is possible to extract important capacitive (i.e., dielectric) properties even at low frequencies, such as 10 Hz. At higher frequencies, such as 50 kHz, the dielectric properties of tissue (discussed in Chapter 3) may dominate. At the highest frequencies, tissue properties become more and more equal to that of water. Pure water has a characteristic relaxation frequency of approximately 18 GHz. 

Three groups of phenomena affect the frequency-dependence of ultrasonic wave propagation classical processes, relaxation, and scattering, of which scattering is likely to dominate in foodstuffs due to their particulate nature. The two classical thermal processes are radiation and conduction of heat away from regions of the material, which are locally compressed due to the passage of a wave they can lead to attenuation but the effect is negligible in liquid materials (Herzfield and Litovitz, 1959 Bhatia, 1967). The third classical process is due to shear and bulk viscosity effects. Attenuation in water approximates to a dependence on the square of the frequency and because of this it is common to express the attenuation in more complex liquids as a()/o or a(f)jf2 in order to detect, or differentiate from, water-like properties. 

Shablakh et al. (1984) investigated the dielectric properties of bovine serum albumin and lysozyme at different hydration levels, at low frequency. Besides a relaxation attributed to the electrode—sample interface, they detected a further bulk relaxation that can be confused with a d.c. conduction effect. The latter relaxation was explained by a model of nonconductive long-range charge displacement within a partially connected water structure adsorbed on the protein surface. This model has nonconventional features that differ from the assumptions of other more widely accepted models based on Debye relaxations. 

Because of the very small effects expected and, consequently, the immense experimental difficulties involved in measuring them, techniques are not yet well developed which make use of these properties. The bulk of the work has made use of the disturbing influence of high-frequency sound-waves on reacting solutions, and the remainder of this section will discuss briefly the application of acoustical methods to the study of chemical relaxation. 

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 application of nuclear magnetic resonance spectroscopy within the food sector has, imtil recently, focussed primarily on the use of time domain (TD) techniques. These enable the quantitative measurement of bulk properties such as water and fat content in whole foods. The measurement relies on the intrinsic relaxation properties of the proton nucleus when a radio frequency pulse is applied to a sample placed in a magnetic field. The differential between the relaxation properties of major food components allows the proportion of these components to be estimated by reference to a calibration safes. This form of NMR spectroscopy is routinely applied for quality and composition checks and is often undertaken in situ as the instrumentation is both inexpensive and robust... 

Similar property distributions occur throughout the frequency spectrum. The classical example for dielectric liquids at high frequencies is the bulk relaxation of dipoles present in a pseudoviscous liquid. Such behavior was represented by Cole and Cole [1941] by a modification of the Debye expression for the complex dielectric constant and was the first distribution involving the important constant phase element, the CPE, defined in Section 2.1.2.3. In normalized form the complex dielectric constant for the Cole-Cole distribution may be written... 

Here all the dielectric polarisation has been subsumed in e and the SCP manifested in p. Thus the bulk dielectric properties of the material are accounted for by the intensive quantity e which will here be taken, as usual, independent of p and E. The present work will, for simplicity, deal with a homogeneous, isotropic material, usually in a one-dimensional approximation. It will be assumed that all frequency dispersions associated with e occur appreciably above all SCP frequencies of interest. This criterion requires that the lowest-frequency dielectric dispersion region occurs appreciably above the radial frequency, = tj), associated with the dielectric relaxation time of the bulk material. 

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