Relaxation frequency, bulk water

In Eq. (1) Riu) is the longitudinal i = 1) or transverse i = 2) relaxation rate of the bulk water protons, corresponding to that measured for an analogous diamagnetic solution. In practice, Ri, coincides with the value determined for pure water under identical conditions of pH, temperature, and observation frequency. Clearly, the above relation strictly holds only for dilute solutions, in the absence of solute-solute interactions and of variations in viscosity. 

Figure 5. Median jump frequencies (Sr ) 1 for water adsorbed on NaX to saturation, for water on charcoal at saturation, and that expected for bulk water (from NMR relaxation times) dashed curve marked diff diffusion coefficients by magnetic field gradient technique normalized to (Sr) 1 by choice of jump distance of 2.7 A + dielectric relaxation times of Jansen...

Soil-Water Mixtures Figure 2 presents the dielectric spectra of clay-water mixtures (kaolinite and montmorillonite) after the influence of dc conductivity is removed. In addition to the orientational polarization of bulk water at 20GHz and adsorbed water at 10MHz, a low frequency polarization is observed at kHz to MHz frequencies. It should be noted that this low-frequency relaxation process cannot be generalized for all mineral-water... 

Halle et al. (1981) measured NMR relaxation for solutions of several proteins as a function of frequency and protein concentration. They estimated hydration by use of a two-state fast-exchange model with local anisotropy and with assumed values of the order parameter and several other variables. The hydration values ranged from 0.43 to 0.98 h for five proteins, corresponding approximately to a double layer of water about a protein. The correlation time for water reorientation was, averaged over the set of proteins, 20 psec, about eight times slower than that for bulk water. A slow correlation time of about 10 nsec was attributed to an ordering of water by protein at very high concentration. 

Beginning at the relaxation time of 8.3 ps of pure water at electrolyte concentration zero the addition of Bu NBr produces a relaxation process with the expected almost concentration-independent water relaxation time 8.5 ps (bulk water), the other with a strongly increasing relaxation time rj J indicating a water structure relaxing at much lower frequency, whereas Et NCl exhibits no split of the water relaxation time... 

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.)... 

Fig. 25. Frequency dependence of the water 2H longitudinal (circles) and transverse (filled squares) relaxation rates in an aqueous solution of bR solubilized in micelles of n-octyl-/)-D-glucoside at 4°C.The broken line refers to the relaxation rate of the bulk water, while the continuous curve results from a fit to the data of a biLorentzian function as described in the text.139 Reproduced with permission from Academic Press Ltd.

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. 

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 complex dielectric spectra of water/ChEOjo and water/ChEOi binary systems (at 5, 10, and 15 wt% water) were determined at 25 °C by time-domain reflectom-etry (frequency range of 0.1-20 GHz, [39]). The low-frequency process was assigned to the kinetics of the hydrophiUc layer of micelles, including the motion of hydrated oxyethylene chain and hydrated water. Additionally, the relaxation time of the high-frequency process was attributed to the cooperative rearrangement of the H-bond network of bulk water. Following various calculations, which are reported in the article, the effective hydration number of ethylene chain Zeo was estimated. 

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. 

One technique, Overhauser Dynamic Nuclear Polarization (ODNP), is based on the well-known chemical shift of water in NMR spectra. Ordinarily, the liquid water signal intensity is low however, intensity can be magnified 1000-fold by addition of a nitroxide spin label such as TEMPO. Precession of the unpaired electron in TEMPO at the Larmor frequency results in Nuclear Overhauser-mediated polarization of the protons in water. These get polarized within 15 A of the spin labels and then relax with a relaxation time determined by the local diffusivity, i.e. in bulk water, the diffusivity is high and so relaxation is rapid by contrast, in hydration layers, relaxation takes 10-fold longer than in bulk water. Next, the trick is to covalently tether spin labels to surfaces of interest and measure how relaxation rates in hydration layers change as adhesive proteins approach and locally dehydrate the surfaces. 

The equilibrium is dynamic in the way that a continual exchange of solute molecules takes place between the micelles and the bulk water. It has been shown previously (1) that the exchange process involving the alcohols propan-l-ol to hexan-l-ol and CTAB micelles is characterized by a single relaxation time in the ultrasonic frequency range 0.7 - 105 MHz. The dynamics of this process was described in terms of the kinetic principles previously... 

More recently, another intermediate timescale was explored by NMR relaxom-etry [102]. The spin-lattice relaxation times of water molecules were determined in the range of 20 ns to 20 ps by varying the magnetic field frequency from 10 kHz to 20 MHz and depending on the water content. This technique is well suited for the study of ionomer membranes because of its extreme sensitivity to water-polymer interactions, but it requires a structural and dynamic model to extract characteristic features. The effect of confinement is predominant in polyimides even at high water content (algebraic law with a slope of —0.5 characteristic of porous materials), whereas the diffusion quickly reaches a bulk behavior in Nafion (a plateau is observed at low magnetic fields). 

Paddison et al. performed high frequency (4 dielectric relaxation studies, in the Gig ertz range, of hydrated Nafion 117 for the purpose of understanding fundamental mechanisms, for example, water molecule rotation and other possible processes that are involved in charge transport. Pure, bulk, liquid water is known to exhibit a distinct dielectric relaxation in the range 10—100 GHz in the form of an e" versus /peak and a sharp drop in the real part of the dielectric permittivity at high / A network analyzer was used for data acquisition, and measurements were taken in reflection mode. 

Relaxation dispersion data for water on Cab-O-Sil, which is a monodis-perse silica fine particulate, are shown in Fig. 2 (45). The data are analyzed in terms of the model summarized schematically in Fig. 3. The y process characterizes the high frequency local motions of the liquid in the surface phase and defines the high field relaxation dispersion. There is little field dependence because the local motions are rapid. The p process defines the power-law region of the relaxation dispersion in this model and characterizes the molecular reorientations mediated by translational displacements on the length scale of the order of the monomer size, or the particle size. The a process represents averaging of molecular orientations by translational displacements on the order of the particle cluster size, which is limited to the long time or low frequency end by exchange with bulk or free water. This model has been discussed in a number of contexts and extended studies have been conducted (34,41,43). 

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