Some Observations on the Theory of Dielectric Relaxation in Associated Liquids

Abstract

The theory of a b s o l~~t e rcaction rates is esamined for the case of relasation it1 associated polar liquids where the activatiori process is probably an excitation of a librational motion to one of complete rotation over a rotatioilal potential energy barrier. The rotational barriers in water are calculated using the point-charge model of the water quadrupole and the eifect of thermal bond bending is csamiiied. The esperiineiital heats of activation for dielectric relaxation in water and deuterium oside are cliscussed and their temperature dependence examined; the heat capacity change for rotational activation is derived. Isotopic effects in the heats of activation, the relaxation times, and frequency factors are discussed. A qualitative explanation is sought for the homogeneity of relasation times in water; rotatioil of water molecules in the fields of the hvdroxoni~~m and hvdroside ions Dresent in water mav account for the narrow distribution of ;elasation times observeti cxpcr~mentally. This ineihanis~n is shown t c be consistent with other theoretically derived quantities and with the mechanism of proton mobility in watcr. A different mechanism is indicated in ice, where the proton concentration is lower, but in ice containing estra protons, the mechanism probably reverts to that existing in water. INTRODUCTIONAlthough it appears that a number of substances, e.g. H2S, hydrogen halides, N2, 0 2 , CHI, and certain ammonium salts exhibit rotation-libration transitions (1) as indicated by changes of the specific heat (2, 3) and dielectric constant (4, 5) over a relatively narrow range of temperatures, a free rotation model for treatment of dielectric relaxation behavior is in general inapplicable to more polar associated condensed phases, e.g. water and the alcohols. In such systems the molecules execute librational oscillations rather than rotational motion except upoil activation when a temporary librationrotation transition is indicated, the frequency of which is inversely related to the relaxation time as determined from dielectric dispersion or absorption conductance studies. In the theory of absolute reaction rates as applied to ordinary chemical reactions, the passage of the reacting particle over the potential-energy barrier has been regarded as a transition of one vibrational mode into a linear translational one along the reaction coordinate. Extraction of the partition function for this motion from the total partition function for the activated state, followed by multiplication by the classical average linear velocity of the particle along the reaction co-ordinate, leads to the familiar rate expression for the rate constant of the process. I t has usually been assumed (6, 7) without proof that the same expression holds for a libration-rotation activation in dielectric relaxation. I t is of interest to show that a formal treatment of rotational instead of the translational activation leads to the same absolute rate equation.For an activation of, for example, a diatomic molecule A from librational to...

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