Debye frequency, hydrogen bonds

All protic solvents undergo multiple relaxation processes due to the presence of hydrogen bonding. In the case of water and formamide (F), the data can be described in terms of two Debye relaxations. For the alcohols and A-methyl-formamide (NMF), three Debye relaxations are required for the description. In all of these solvents, the low-frequency process involves the cooperative motion of hydrogen-bonded clusters. In the case of water and the alcohols the high-frequency process involves the formation and breaking of hydrogen bonds. The intermediate process in the alcohols is ascribed to rotational diffusion of monomers. Studies of dielectric relaxation in these systems have been carried out for the -alkyl alcohols up to dodecanol [8]. Values of the relaxation parameters for water and the lower alcohols are summarized in table 4.5. 

Table 5.3 shows that AV (calc) agrees with the experimentally observed to within the experimental uncertainty for the Debye solvents acetone and acetonitrile, and comes surprisingly close for methanol which, because intermolecular hydrogen-bonding contributes several frequencies to the apparent tl, is not considered to be a Debye liquid. Unfortunately, there are insufficient data for application of Eq. (5.23) to the Ru(hfac)3 electrode reaction in propylene carbonate, which is also regarded as a non-Debye liquid. In any event, the implication is that the fifty-percent rule applies to volumes of activation for electrode reactions but its effect is swamped by solvent dynamical contributions. 

Perl (93) has made measurements of 1-propanol solutions with water added to mole fraction 0.75 at 25< C at frequencies from 10 MHz to 5 or 106Hz. These showed a principal Debye relaxation with times from 320 ps for pure alcohol to 48 ps for the water rich solution, roughly as expected, and also a smaller but increasing higher frequency relaxation with time T2 of approximately 20 ps at all concentrations. This is very nearly the value found by Garg and Smyth for the secondary relaxation of neat 1-propanol. This result suggests some sort of conformational motions in hydrogen bonded networks of the two species, as will be discussed elsewhere (93). 

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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