Peter A. Beckmann

Spectral densities and nuclear spin relaxation in solids

Abstract We investigate the properties of ten spectral densities relevant for nuclear spin relaxation studies in solids. This is preceded by a brief review of nuclear spin relaxation in solids which includes a discussion of the appropriate spin-dependent interactions and the various relaxation rates which can be measured. Also, the link between nuclear spin relaxation and dielectric relaxation is discussed. Where possible and/or appropriate each of the spectral densities is expressed as a continuous distribution of Bloembergen-Purcell-Pound (or Debye) spectral densities 2ξ /(1 + ξ 2 ω 2 ) for nuclear Larmor angular frequency ω and correlation time ξ. The spectral densities are named after their originators or the shape of the distributions of correlation times or both and are (1) Bloembergen-Purcell-Pound or δ-function, (2) Havriliak-Negami, (3) Cole-Cole, (4) Davidson-Cole, (5) Fang, (6) Fuoss-Kirkwood, (7) Bryn Mawr, (8) Wagner or log-Gaussian, (9) log-Lorentzian, and (10) Frohlich or energy box. The Havriliak-Negami spectral density is related to the Dissado-Hill theory for dielectric relaxation. The spectral densities are expressed in a way which makes them easy to compare with each other and with experimental data. Many plots of the distributions of correlation times and of the spectral densities vs. various correlation times characterizing the distributions are given.

Nuclear spin-lattice relaxation rates in liquid crystals

The spin-lattice relaxation rates R (i) have been measured for the deuterons in 4-n-pentyl-d11-4′-cyanobiphenyl-d4 (5CB-d15) and 4-n-pentyl-d1-4′-cyanobiphenyl (5CB-d1) at 30·7 MHz and over the temperature range 257 to 400 K which includes the nematic-isotropic transition, T NI, at 308 K. Both samples display a small biphasic region because of the presence of a low concentration of an unknown impurity. The variation of both quadrupolar splittings and R (i) values have been carefully measured at 0·1 K intervals close to and in this interesting region. A discontinuity in the relaxation rate of the deuteron at the first position in the alkyl chain has been detected at T NI. The observed discontinuity is in good agreement with the change in R (i) predicted to occur because of the onset of long range orientational order at this temperature. There are regions of temperature in both phases where in R (i) varies linearly with T -1 and from which apparent activation energies can be determined for C-D bond reorient...

Molecular dynamics in a liquid crystal: Measurement of spectral densities at several sites in the nematogen 4-n-pentyl-4′-cyanobiphenyl

Experiments are described for determining the auto-correlation spectral densities J 1(ω0) and J 2(2ω0) for deuterons at each position in the alkyl chain and in one aromatic ring of the nematogen 4-n-pentyl-d11-4′-cyano-2,3,5,6-d4-biphenyl (5CB-d15). The experiments involve selective population inversions followed by non-selective monitoring of the spectrum. The efficiency of the method is compared with that of the Jeener-Broekaert sequence. The results are discussed in terms of models for the molecular motion which treat the molecules either as rigid, cylindrically symmetric rods, or which assume that the internal modes of molecular motion are fast enough to be decoupled from the overall molecular rotations. Both models fail to explain the dependence of the ratio J 1(ω0)/J 2(2ω0) on position in the molecule. It is suggested that the variation of the ratio of spectral densities with position reflects the importance of both internal modes of molecular motion, which affects both J 1(ω0) and J 2(2ω0) and dire...

Methyl reorientation in methylphenanthrenes. I. Solid state proton spin–lattice relaxation in the 3‐methyl, 9‐methyl, and 3,9‐dimethyl systems

We have investigated the dynamics of methyl group reorientation in solid methyl‐substituted phenanthrenes. The temperature dependence of the proton spin–lattice relaxation rates has been measured in polycrystalline 3‐methylphenanthrene (3‐MP), 9‐methylphenanthrene (9‐MP), and 3,9‐dimethylphenanthrene (3,9‐DMP) at Larmor frequencies of 8.50, 22.5, and 53.0 MHz. The data are interpreted using a Davidson–Cole spectral density which implies either that the correlation functions for intramolecular reorientation are nonexponential or that there is a distribution of exponential correlation times. Comparing the fitted parameters that characterize the relaxation data for the three molecules shows that the individual contributions to the relaxation rate from the 3‐ and 9‐methyls in 3,9‐DMP can be separated and that the parameters specifying each are similar to the equivalent group in the two single methylphenanthrenes. The 9‐methyl group is characterized by effective activation energies of 10.6±0.6 and 12.5±0.9 kJ/...

The Relationship between 207Pb NMR Chemical Shift and Solid-State Structure in Pb(II) Compounds

The analysis of heavy-metal solids with NMR spectroscopy provides a means of investigating the electronic environment through the dependence of the chemical shift on structure. We have investigated the relation of the 207Pb NMR isotropic chemical shift, span, and skew of a series of solid Pb(II) compounds to lattice parameters. Complementary relativistic spin-orbit density functional calculations on clusters such as PbI64- that model the local environment in the dihalides show a dependence of NMR properties on the local structure in good agreement with experimental results.

1H nuclear magnetic resonance spin-lattice relaxation, 13C magic-angle-spinning nuclear magnetic resonance spectroscopy, differential scanning calorimetry, and x-ray diffraction of two polymorphs of 2,6-di-tert-butylnaphthalene

Polymorphism, the presence of structurally distinct solid phases of the same chemical species, affords a unique opportunity to evaluate the structural consequences of intermolecular forces. The study of two polymorphs of 2,6-di-tert-butylnaphthalene by single-crystal x-ray diffraction, differential scanning calorimetry (DSC), 13C magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy, and 1H NMR spin-lattice relaxation provides a picture of the differences in structure and dynamics in these materials. The subtle differences in structure, observed with x-ray diffraction and chemical shifts, strikingly affect the dynamics, as reflected in the relaxation measurements. We analyze the dynamics in terms of both discrete sums and continuous distributions of Poisson processes.

Solid State Proton Spin Relaxation in Ethylbenzenes: Methyl Reorientation Barriers and Molecular Structure

We have investigated the dynamics of the ethyl groups and their constituent methyl groups in polycrystalline ethylbenzene (EB), 1,2‐diethylbenzene (1,2‐DEB), 1,3‐DEB, and 1,4‐DEB using the solid state proton spin relaxation (SSPSR) technique. The temperature and Larmor frequency dependence of the Zeeman spin‐lattice relaxation rate is reported and interpreted in terms of the molecular dynamics. We determine that only the methyl groups are reorienting on the nuclear magnetic resonance time scale. The observed barrier of about 12 kJ/mol for methyl group reorientation in the solid samples of EB, 1,2‐DEB, and 1,3‐DEB is consistent with that of the isolated molecule, implying that in the solid state, intermolecular electrostatic interactions play a minor role in determining the barrier. The lower barrier of 9.3±0.2 kJ/mol for the more symmetric 1,4‐DEB suggests that the crystal structure is such that the minimum in the anisotropic part of the intramolecular potential is raised by the intermolecular interaction...

Proton spin-lattice relaxation and methyl group rotation

Abstract Proton spin-lattice relaxation times have been measured at 16, 31, and 59 MHz in 4-methyl-2,6-ditertiarybutyl phenol between 80 K and its melting point, 340 K. The variation of T 1 with temperature shows too distinct minima. The lower-temperature minimum has been analyzed in terms of relaxation by reorientation of four of the six t-butyl methyl groups with an average apparent activation energy of about 2.4 kcal mole −1 (104 meV molecule −1 ). The higher-temperature minimum has been analyzed in terms of relaxation by reorientation of the t-butyl groups about their C 3 axes with four of the six t-butyl methyl groups reorienting very rapidly, and the remaining two reorienting with correlation time similar to that of the t-butyl group. The activation energy for the higher-temperature minimum is 5.76 kcal mole −1 (250 meV molecule −1 ). Steric potential calculations are used to add weight to these assignments, and a number of peculiarities displayed by the lower-temperature minimum are discussed.

Methyl and Tert-Butyl Reorientation and Distributions of Activation Energies in Molecular Solids: A Nuclear Spin-Relaxation Study in 2,4- and 2,5-Di-Tert-Butylhydroxybenzene

We have measured proton Zeeman relaxation rates R in the 2,4‐ and 2,5‐isomers of di‐tert‐butylhydroxybenzene (DTHB) in the solid state. R was measured as a function of temperature T at proton Larmor frequencies of ω/2π=8.50, 22.5, and 53.0 MHz. The T ranges were from 78 K to just below the melting points of 2,4‐ and 2,5‐DTHB, 385 and 323 K, respectively. The 2,5‐DTHB R vs T and ω can be interpreted qualitatively in terms of three Bloembergen–Purcell–Pound (BPP) spectral densities, one for each of the three types of rotors in the molecule. The quantitative agreement is poor but a good fit is obtained using either a Davidson–Cole (DC) or Frolich spectral density, still preserving the three rotor types. The implications of this are discussed. The BPP and DC spectral densities fail completely in interpreting R vs T and ω for 2,4‐DTHB whereas good quantitative fits are obtained using a Frolich spectral density. The distributions of activation energies characterizing the three rotor types are so wide for the Fr...

The Haupt effect: coupled rotational and dipolar relaxation of methyl groups

A theory is described for the dynamic proton dipolar polarization observed by Haupt (1972) in 4-methylpyridine following a sudden temperature change. The theory differs from that of Haupt in assuming that transitions which change the rotational quantum number of the 4-methyl group by +or-3 occur very rapidly, maintaining thermal equilibrium within each of the three subsets of rotational levels corresponding to the three methyl group proton spin symmetry species A, Ea and Eb. The difference of A and E species populations approaches the new equilibrium value slowly and exponentially, following the temperature jump, and generates dipolar polarization in the process. Transitions between Ea and Eb species lead to destruction of the polarization, whose evolution from zero due to these competing processes has the simple form C(exp(-at)-exp(-bt)). This is checked by a modified version of Haupts experiment in which the initial temperature jump is followed by a later burst of RF pulses which reduces the dipolar polarization to zero.