Daniel Kivelson

Theory of ESR Linewidths of Free Radicals

A theory of ESR linewidths for substances in which the magnetic anisotropy is small and for which the orbital magnetism has been essentially quenched is developed. Nuclear quadrupole moments, zero field splittings, anisotropic Zeeman terms, and intramolecular electron‐nuclear dipolar interactions, as well as motional and exchange effects are considered in the strong field case. The theory is developed in a manner that is particularly adaptable to the study of liquids but it is also applied to crystals since the resulting equations, though only applicable for small anisotropies, are particularly simple. The theory provides an extension of previous theories on ESR spectra in liquids. Several applications of the theory are discussed with particular emphasis on V4+ chelates. The theory of exchange in liquids, a phenomenon which is complicated by the noncommutivity of the motional and exchange Hamiltonians is considered in special detail. It is shown that this theory can be used to explain Haussers results—th...

ESR Linewidths in Solution. I. Experiments on Anisotropic and Spin—Rotational Effects

The linewidths of the hyperfine components of the ESR spectra of vanadyl acetylacetonate in liquid toluene have been measured as a function of concentration, temperature, and applied field. The g‐tensor and hyperfine‐tensor components have been determined and used, along with the spectral data, to determine the Debye rotational correlation time τR. This analysis agrees very well with the experimental observations. A residual linewidth, not dependent upon the above mechanism, and independent of nuclear quantum number and applied field, has been studied and found to vary as T/η, where η is the viscosity. This residual linewidth is ascribed to a spin—rotational interaction.

ESR Linewidths in Solution. II. Analysis of Spin—Rotational Relaxation Data

In Part I of this series the residual linewidths for vanadyl acetylacetonate in toluene were found to be proportional to (T/η), where η is the viscosity, and independent of applied field. Since the solutions are dilute, spin exchange is not important. The residual linewidth is attributed to a spin—rotational relaxation mechanism, and calculations based on a perturbation theory of spin—rotational interactions and Hubbards theory of spin—rotational relaxation yield results in reasonably good agreement with experiment. This relaxation mechanism is probably significant for many dilute S = ½ systems in liquids. For systems with weak anisotropic intermolecular interactions, e.g. ClO2 in CCl4, the correlation time τω for angular momentum and the spin—rotational contribution to the linewidth appear to be larger than those predicted by Hubbards theory.

A thermodynamic theory of supercooled liquids

A novel thermodynamic theory of the properties of supercooled liquids as they get glassy is presented. It is based on the postulated existence of a narrowly avoided thermodynamic phase transition at a temperature T∗ ⩾ Tm, where Tm is the melting point, and the “avoidance” is due to geometric frustration. We show that as a consequence two large emergent length scales develop at temperatures less than T∗, and we also show that this picture is consistent with appropriate statistical mechanical models. A theoretical expression is obtained which permits collapse of the viscosity versus temperature of all known glass-formers onto a single master-curve.

BREAKDOWN OF THE STOKES-EINSTEIN RELATION IN SUPERCOOLED LIQUIDS

The Stokes–Einstein and Stokes–Einstein–Debye relations hold well in nonsupercooled liquids; however, sizeable deviations from the former appear in supercooled liquids, leading to a ‘‘decoupling’’ of translational diffusion from viscosity and reorientational relaxation. We attribute this breakdown and this ‘‘decoupling’’ to the existence of structured domains in the supercooled liquid.

ESR Linewidths in Solution. V. Studies of Spin–Rotational Effects Not Described by Rotational Diffusion Theory

We have measured the ESR linewidths of ClO2 as a function of temperature in a number of solvents. The dominant spin relaxation mechanism is the motional modulation of the spin–rotational interaction; therefore, the measurements yield the autocorrelation times for angular momentum. The experimental data can be correlated with the aid of the relation τJα−1 = (8πr03ηκ / Iα) + Δα2[τJβτJγ / (τJβ + τJγ)], where τJα is the autocorrelation time for the component of angular momentum along the αth molecular axis (α = x, y,z), Iα is the moment of inertia about the αth axis, η is the coefficient of viscosity for the solvent, r0 is a translational hydrodynamic radius which is determined experimentally by means of diffusion experiments, Δα is the frequency of precession of the αth component of angular momentum, a frequency which vanishes for spherical tops and linear molecules and can be calculated entirely in terms of known components of the moment of inertia, and κ is an adjustable parameter which is assumed to be in...

Supercooled liquids and the glass transition: Temperature as the control variable

It has long been appreciated that both temperature and density play roles in determining the extremely super-Arrhenius, low-temperature behavior of the viscosity and long α-relaxation times that characterize fragile supercooled liquids. But what has not been generally appreciated, and what we believe we have established (by focusing on a model-free analysis in terms of temperature and density, rather than upon temperature and pressure) is that over the range of densities and temperatures spanned by the experiments carried out at 1 atm pressure, temperature is the dominant control variable. This information is essential input to the formulation of a theory or model of the long-time dynamics of low-temperature fragile liquids, and it suggests a focus on activated dynamics rather than on free volume. This work indicates that, except possibly at very high densities (very high pressures), the glass transition is not a result of congestion due to a lack of free volume.

Unified Theory of Orientational Relaxation

A mathematically simple model for orientational relaxation in liquids is presented. This theory, expressed in terms of Moris formalism for generalized hydrodynamics, is developed with three orientational variables interrelated by three coupled linear transport equations. The three variables are D,dD/dt, and d2D/dt2, where D is a relevant Wigner rotational transformation function. In appropriate limits the theory reduces to that for rotational diffusion, gas‐like extended rotational diffusion (GLED) and solid‐like oscillatory rotations (SLOR) or cell model motions. This theory, which we call the pseudo‐GLED‐SLOR theory, therefore gives a unified picture, encompassing all limits, of molecular rotations in liquids. The assumptions, and consequently the results, differ slightly from those usually introduced in the GLED and SLOR theories; the various limiting forms of molecular reorientation are obtained in the present theory via restrictions on the quantities, D,dD/dt, d2D/dt2, and d3D/dt3, whereas the usual...

Spin Exchange in Solutions of di‐Tertiary‐Butyl Nitroxide

The ESR linewidths of dilute solution of di‐tertiary‐butyl nitroxide (DTBN) in n‐pentane and propane have been studied. Corrections have been made for (1) spin‐rotational effects, (2) the variation of concentration with temperature, (3) the line‐shape distortion of overlapping “strongly exchanging” lines, (4) the exchange narrowing of inhomogeneous linewidth contributions arising from proton extra hyperfine splitting, and (5) the temperature dependence of the diffusional step length λ. Existing theories of spin exchange appear adequate to explain the low‐concentration data; at high concentration it is not possible to make all the corrections discussed above and the comparison of theory and experiment is not meaningful. In n‐pentane we found that (zT/z).Jλ02 = 5×1012 A2 sec−1 and JzT = 4.9×1011 sec−1, where J is minus two times the exchange integral, λ0 is the diffusional step length at the freezing point, zT is the mean total number of molecular nearest neighbors, and z is the number of new radical neares...

Theory of k‐Independent Depolarized Rayleigh Wing Scattering in Liquids Composed of Anisotropic Molecules

A discussion is presented of the k‐independent factors that contribute to the depolarized Rayleigh wing scattering in liquids composed of anisotropic molecules. The spectrum consists of a sharp line (several tenths cm−1) and a broad line (several cm−1 or tens of cm−1). It is suggested that the spectrum arises from at least two separate processes, each of which induces fluctuations in off diagonal elements of the dielectric tensor: molecular reorientation, which is a relatively slow process, and some form of intermolecular interaction, which is a rapid process. The autocorrelation functions for the slow and rapid processes account in large part for the sharp and broad lines, respectively; however, the heretofore neglected cross correlation function between the slow and rapid processes may contribute significantly to the spectrum, particularly to the sharp line which may be appreciably reduced in intensity due to the cross correlation. This reduction in sharp line intensity suggests that the difference betw...