Water relaxation, temperature dependence

Fig. 12.1 Illustration of the temperature sensitivity of 15N relaxation parameters, Rlf R2t and NOE, as indicated. Shown are the relative deviations in these relaxation parameters from their values at 25 °C as a function of temperature in the range of + 3 °C. The expected variations in / ] and R2 due to temperature deviations of as little as +1 °C are already greater than the typical level of experimental precision ( % ) of these measurements (indicated by the dashed horizontal lines). For simplicity, only temperature variation of the overall tumbling time of the molecule (due to temperature dependence of the viscosity of water) is taken into account the effect of temperature variations on local dynamics is not considered here.

The temperature dependence of the MRD profile for the protein-water systems where the protein is magnetically a solid, is remarkably weak. The relaxation rate is proportional to IjT, which is consistent with Eq. (4) that was derived on the assumption that the relaxation process is a direct spin-phonon coupling rather than an indirect or Raman process. If it were a Raman process, there would be no magnetic field dependence of the relaxation rate therefore, the temperature dependence provides good evidence in support of the theoretical foundations of Eq. (6). 

This study is similar to those previously done by Derbyshire and Duff (20) and Nystrom et al. (21) who studied water swellable gels. However, in the first of these, the use of proton NMR complicated the relaxation data because of proton-proton coupling. Furthermore, their study focused on the freezing (or non-freezing) of water which also complicated matters. In the present study, we are always well above the freezing point of toluene so that one need not worry about the freezing of the solvent. The study by Nystrom et al. (21) used deuterium NMR of D2O, but an unusual temperature dependence was observed, possibly due to the exchange of the protons or deuterons. Our present data are not complicated... 

Figure 4. Temperature dependence of the longitudinal relaxation time of water in the water-NaLS system.

Fig. 14. Temperature dependence of the scattered intensity, I, and the relaxation rate, T, for 2.5% polyacrylamide gel in water. Here T is divided by the square of the scattering vector, q2...

Figure 3. Temperature dependence of proton relaxation time Ti of water in NaPtY. Pore filling factor 6 0.8. Pretreatment procedure for 20 hours at 100° Ifi0°C. For comparison the results for NaY without platinum are also plotted.

An Arrhenius-type analysis of temperature dependence can be used to calculate the enthalpy and entropy of activation for the relaxation process. For liquid water, the enthalpy of activation is 19 kjmol-1, which corresponds approximately to the energy required to break one hydrogen bond. For ice, the equivalent enthalpy is 54 kj mol-1,... 

When the viscosity of the solution increases by using ethyleneglycol or glycerol water mixtures as solvent, the rotational correlation time increases. This determines (1) higher relaxivity values at low frequencies (2) a shift toward lower frequencies of the a>s dispersion (3) the appearance of a second dispersion (ascribed to the a>i dispersion) at high fields. Temperature dependence studies show that the observed rates are not controlled by exchange, but arise from variation of the rotational correlation time. 

Returning to our problem, we remark that the temperature dependences of such parameters as, for example, the Debye relaxation time td(7 ) (which determines the low-frequency dielectric spectra), or the static permittivity s are fortunately known, at least for ordinary water [17], As for the reorientation time dependence t(T), it should probably correlate with in(T), since the following relation (based on the Debye relaxation theory) was suggested in GT, p. 360, and in VIG, p. 512 ... 

The dielectric relaxation properties in a sodium bis(2-ethylhexyl) sulfosuc-cinate (AOT)-water-decane microemulsion near the percolation temperature threshold have been investigated in a broad temperature region [47,143,147]. The dielectric measurements of ionic microemulsions were carried out using the TDS in a time window with a total time interval of 1 ps. It was found that the system exhibits a complex nonexponential relaxation behavior that is strongly temperature-dependent (Figure 8). 

Therefore, the observed process (I) could be related to the cooperative dynamics of glycerol in the supercooled phase, while process (II) is most likely related to the crystalline phase of glycerol and is the result, similar to water, of the mobility of defects in the crystalline lattice [200]. The temperature dependence of the relaxation time for dehydrated glycerol is compared in Fig. 23 with those for the usual behavior of glycerol, which has absorbed some water from the atmosphere. 

The typical results of recent BDS studies of glycerol-water mixtures of 75 mol% of glycerol at different temperatures are presented in Fig. 25 [208]. Figure 26 shows that the temperature dependencies of the main relaxation... 

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