Ortho-para Hydrogen Mixtures Research Articles

Nuclear Magnetic Resonance Spectroscopy

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Orientational Glasses: NMR and Electric Susceptibility Studies

We review the results of a wide range of nuclear magnetic resonance (NMR)measurements of the local order parameters and the molecular dynamics of solid ortho-para hydrogen mixtures and solid nitrogen-argon mixtures that form novel molecular orientational glass states at low temperatures. From the NMR measurements, the distribution of the order parameters can be deduced and, in terms of simple models, used to analyze the thermodynamic measurements of the heat capacities of these systems. In addition, studies of the dielectric susceptibilities of the nitrogen-argon mixtures are reviewed in terms of replica symmetry breaking analogous to that observed for spin glass states. It is shown that this wide set of experimental results is consistent with orientation or quadrupolar glass ordering of the orientational degrees of freedom.

Cluster relaxation dynamics in liquids and solids near the glass-transformation temperature

The structural relaxation in glass-forming materials is studied near the glass transformation temperature Tg indicated by the heat capacity maximum. The late-time asymptote of the Kohlrausch–Williams–Watts form of the relaxation function is rationalized via the mesoscopic-scale correlated regions in terms of the Debye-type clusters following the dynamic scaling law. It is repeatedly shown that regardless of underlying microscopic realizations in glass formers with site disorder the structural relaxation is driven by local random fields, described via the directed random walks model. The relaxation space dimension ds=3 at Tg is suggested for relaxing units of fractal dimension df=5∕2 for quadrupolar-glass clusters in ortho–parahydrogen mixtures, that is compared with entangled-chain clusters in polymers (df=1) and solid-like clusters relaxing in supercooled molecular liquids (with ds=6 and df=3). The relaxation dynamics of orientational-glass clusters in plastic crystals is attributed to the model of continuous-time random walks in space ds=6. As a by-product, the expansivity in polymers, molecular liquids, and networks is predicted.

Quadrupolar glass state in para-hydrogen and ortho-deuterium under pressure

The main features of the possible quadrupolar glass state in ortho-deuterium and para-hydrogen under high pressure are predicted and considered in replica-symmetric approximation in analogy with glassy behavior of diluted ortho-hydrogen at low pressures. The quadrupolar model with J=2 is suggested. The orientational order and glass regime grow continuously on cooling, as is the case with ortho-para hydrogen mixtures at zero pressure.

The Orientational Ordering of Molecular Hydrogen in 2D

The orientational ordering of ortho-hydrogen molecules on a triangular lattice is calculated as a function of ortho concentration using the method of restricted traces. The calculated temperatures for the transitions from the disordered phase to the long range pinwheel ordered phase show a strong concentration dependence with a critical concentration Xc=73% below which the long range ordering is not realized in this model. The results are consistent with recent NMR studies of ortho-para hydrogen mixtures adsorbed as a commensurate \(\sqrt 3 \)×\(\sqrt 3 \) structure on hexagonal boron nitride for which Xc=69±4%. The values of the observed transition temperatures can only be understood if there is a large renormalization of the effective quadrupolar interaction constant in 2D.

Intrinsic–Field Cooperative Freezing into Orientational Glass–Phase in Solid Hydrogen. Theory and Experiment

We report on the mechanism of orientational freezing in ortho–para–hydrogen mixtures. We argue that instead of the Zeeman–type uncorrelated intrinsic field, which dominats at high temperatures, the molecular ordering field, strongly correlated by the reaction Onsager–type field, drives the cooperative short–range ordering into the glass–like states. This mechanism is in accord with the observed unsaturated orientational order caused by moderation of the ordering field

Orientational quadrupolar glass in ortho-para hydrogen mixtures. II. Comparison with experiment

A comparative analysis of experimental data on the orientational order parameter, heat capacity and Gruneisen parameter with those predicted by the mean-field microscopic theory given in the accompanying paper is carried out. The orientation-motion freezing mechanisms driven by the strain, quadrupolar and reaction fields are identified. It is proved that within the quadrupolar glass (QG) phase the random-site effects dominate over random-bond dilution effects. The entry to the QG phase is characterized by the freezing temperature, at which the total intrinsic field disappears. The QG ground-state distribution function known from NMR spectroscopy is proposed.

Does the quadrupolar glass indicate a new type of spin glass?

We discuss the problem of ordering random-bond and disordering random-field effects in the quadrupolar orientational glass. Molecular field estimation, improved by configurational and thermal fluctuations, is given in the framework of the short-range vector model for site-diluted ortho-para hydrogen mixtures. We conclude that quadrupolar glass orientational ordering critically depends on the random-bond effects and is driven by strong correlated molecular and reaction fields.

Vibrational Raman spectra of hydrogen and deuterium mixtures at high pressures.

Room-temperature mixtures of hydrogen and deuterium in the fluid and solid states have been studied to 60.5 GPa (605 kbar). Raman-scattering measurements performed on these mixtures showed substantial deviations in the pressure dependence of the vibrational stretching frequencies of the molecules as compared with spectra from monomolecular hydrogenic samples. Most notably, the maximum in the vibron-frequency shift occurs at higher pressures. These observations are explained in terms of the coupling interaction between identical molecules, the same interaction that governs the ${\mathit{Q}}_{1}$(0) and ${\mathit{Q}}_{1}$(1) frequency shifts in ortho-para hydrogen mixtures.

Long-time relaxation behavior in orientational glasses

The long-time relaxation observed in the orientational glass phase of solid ortho-parahydrogen mixtures is related to the low-temperature specific heat using a simple unified model. The use of stimulated spin echoes to study slow molecular motions is discussed in detail. The analysis is based on the domination of low-energy large-scale cluster excitations in the relaxation processes as introduced in Fisher and Huse's recent picture of the low-temperature behavior of short-range spin glasses.

Low-frequency dynamics of orientational glasses.

We provide a unified explanation of the low-frequency relaxation and the low-temperature specific heat of the orientational-glass plase of solid ortho-para hydrogen mixtures. The analysis is based on Fisher and Huse's recent picture of the short-range spin glasses and the domination of the long-term relaxation by low-energy large-scale-cluster excitations.

Orientational order–disorder transitions in solid hydrogen

We discuss the orientational ordering in solid ortho–para hydrogen mixtures. Following a brief sketch of the properties of the ortho and para hydrogen modifications and the long-range ordering of an assembly of J = 1 quantum rotors (ortho-H2), we consider the nature of the purely local ordering seen in random dilute ortho–para mixtures. Measurements of the quasi-static glass order parameter and the mean correlation time for the molecular alignments are interpreted in terms of a rapid but continuous freezing of the orientational fluctuations.

Orientational ordering in solid hydrogen

The orientational ordering in solid ortho–para hydrogen mixtures is reviewed with emphasis on dilute mixtures for which a glass-like freezing of the randomly distributed quantum rotators is observed. The interpretation of the various nuclear magnetic resonance experiments used to monitor the relevant order parameters is discussed, and a summary is given of the current consensus and outstanding problems concerning the nature of the ordering in random dilute mixtures.

Comparison of local ordering of orthohydrogen molecules above and below the percolation threshold in solid ortho-para mixtures

We report measurements of the local orientational ordering in solid ortho-para hydrogen mixtures for ortho concentrations near the site percolation threshold. The results indicate a weak collective ordering for concentrations above percolation which is absent for low concentrations.

Non-exponential relaxation of nuclear magnetization in solid ortho-para hydrogen mixtures

We report calculations of the decay of the nuclear magnetization of different isochromats in the NMR absorption spectrum of solid mixtures of ortho-para hydrogen. The calculated decays show significant departures from exponential recovery and are in good overall agreement with experimental results reported elsewhere. A slowly component, characteristic of the quadrupolar glass phase is predicted at long times.

Correlation functions in the quadrupolar glass phase of solid hydrogen

A precise description of the molecular order parameters and their correlation functions that determine the NMR line shapes, damping of spin echoes, and the longitudinal nuclear relaxation in solid ortho-para hydrogen mixtures is given and the effects of fluctuations of the order parameters on the NMR measurements are discussed. This formalism is used to make precise definitions of terms such as freezing, dynamic gel, formation, etc., that have been used in the literature to describe the NMR results. An operational definition of a quadrupolar glass is given in terms of the correlation functions and the different NMR techniques are analyzed to show what properties of the correlation functions can be deduced in each case. The time scale of the variations of the correlation functions probed by the different experiments is discussed in detail.

Nuclear Spin Relaxation of Hydrogen in a Solid Argon Matrix

${T}_{1}$ and ${T}_{2}$ data at 5.5 K measured at 33 MHz are reported for solid matrices of normal hydrogen in argon with hydrogen mole fraction $0.004lxl0.33$. The results are interpreted in terms of a theory developed by Ebner and Myles in their study of solid ortho-para hydrogen mixtures. The crystal field consistent with the data is estimated to be 0.2 K. The ${T}_{2}$'s, taken from the far-infrared detectors, are smaller than those predicted.

Molecular interactions in the condensed phases of ortho-para hydrogen mixtures

Because mixtures containing arbitrary ratios of ortho ($J=1$) and para ($J=0$) concentrations can be prepared, the condensed phases of hydrogen afford a unique opportunity to study interactions between isotropic and anisotropic molecules which are chemically identical. Detailed measurements are reported here of the rotational Raman spectra in the liquid and solid phases of ortho-para hydrogen mixtures, with para concentrations between 25% and 96% at temperatures between 10 and 23\ifmmode^\circ\else\textdegree\fi{}K. Changes in the configuration and dynamics of the molecular environment with temperature and ortho concentration are clearly reflected in the rotational Raman line shapes. Logarithmically recorded spectra, covering an intensity dynamic range of typically ${10}^{4}$, reveal two relatively independent types of interaction which respectively govern the near (30 ${\mathrm{cm}}^{\ensuremath{-}1}$) and far (>30 ${\mathrm{cm}}^{\ensuremath{-}1}$) wings. Quantum calculations of the low-frequency mechanism, electric quadrupole-quadrupole molecular pair interactions, are presented. They are found to produce values for the second frequency moments for all three ($J=1\ensuremath{\rightarrow}1$, $J=1\ensuremath{\rightarrow}3$, and $J=0\ensuremath{\rightarrow}2$) rotational transitions which agree well both in absolute magnitude and in concentration dependence with experimental observations. The far wings in the solid spectra consist of phonon sidebands whose structure is in good agreement with the phonon density of states previously observed by neutron scattering. In the liquid mixtures the far-wing line shapes are insensitive to temperature or concentration variation and are very similar to the solid wings.

Viscosity of ortho and para hydrogen mixtures

The viscosity of ortho-para hydrogen mixtures below 25 K is investigated for a model interaction chosen with an isotropic component that reproduces the high temperature viscosity and virial coefficient data and an anisotropic component inferred from rotation relaxation measurements. The T-matrix elements were calculated with a fast modification of the Numerov method and a close-coupled approximation adapted from the Arthurs-Dalgarno formalism. The model in itself could not explain the viscosity experiments of Becker and Stehl, but, when supplemented by dispersion forces dependent on the rotational state, proved to be satisfactory.

Rotational transitions and thermal diffusion in ortho and para hydrogen

The principal contributors to thermal diffusion in ortho-para hydrogen mixtures are identified as the ( 0→2 2→0) rotational transitions. The effects of rotation energy dependent interaction potentials and resonances with bound states were found to be minor.