An equation of state contribution for dipolar and quadrupolar square-well fluids

A dipolar–quadrupolar contribution to the residual Helmholtz energy for a polar square well (a square well plus either a point dipole or a point quadrupole) fluid is developed based on the Padé approximation. Taking the square well system as reference, the contribution is formulated using an expansion for radial distribution function of the reference system. In addition to square well potential parameters the contribution depends only on dipole and quadrupole moments. This term is added as perturbation to a generalized equation of state for square well fluids. The results are then compared with the available simulation data in the literature. With the new equation obtained, it was possible to predict liquid–vapour equilibrium properties and critical properties of polar square well fluids more accurately than with available perturbation theories for multipolar square well systems. Application of the equation of state to a real dipolar (water) and a real quadrupolar (carbon dioxide) fluid indicated that the polar contribution greatly improved the predictions of saturation properties. Accurate prediction of critical properties for polar square well fluids remains as a challenge. This work can be useful in the development of better equations of state.     

Lattice density functional theory for confined Ising fluids: comparison between different functional approximations in slit pore

ABSTRACT

In this paper, Lafuente and Cuesta's cluster density functional theory (CDFT) and lattice mean field approximation (LMFA) are formulated and compared within the framework of lattice density functional theory (LDFT). As a comparison, an LDFT based on our previous work on nonrandom correction to LMFA is also developed, where local density approximation is adopted on the correction. The numerical results of density distributions of an Ising fluid confined in a slit pore obtained from Monte Carlo simulation are used to check these functional approximations. Due to rational treatment on the coupling between site-excluding entropic effect and contact-attracting enthalpic effect by CDFT with Bethe-Peierls approximation (named as BPA-CDFT for short), the improvement of BPA-CDFT beyond LMFA is checked as expected. And it is interesting that our LDFT has a comparative accuracy with BPA-CDFT. Apparent differences between the profiles such as solvation force, excess adsorption quantity and interfacial tension from LMFA and non-LMFAs are found in our calculations. We also discuss some possible theoretical extensions of BPA-CDFT.     

19F-decoupling of half-integer spin quadrupolar nuclei in solid-state NMR: application of frequency-swept decoupling methods

In solid-state NMR studies of minerals and ion conductors, quadrupolar nuclei like ⁷Li, ²³Na or ¹³³Cs are frequently situated in close proximity to fluorine, so that application of ¹⁹F decoupling is beneficial for spectral resolution. Here, we compare the decoupling efficiency of various multi-pulse decoupling sequences by acquiring ¹⁹F-decoupled ²³Na-NMR spectra of cryolite (Na₃AlF₆). Whereas the MAS spectrum is only marginally affected by application of ¹⁹F decoupling, the 3Q-filtered ²³Na signal is very sensitive to it, as the de-phasing caused by the dipolar interaction between sodium and fluorine is three-fold magnified. Experimentally, we find that at moderate MAS speeds, the decoupling efficiencies of the frequency-swept decoupling schemes SW_f-TPPM and SW_f-SPINAL are significantly better than the conventional TPPM and SPINAL sequences. The frequency-swept sequences are therefore the methods of choice for efficient decoupling of quadrupolar nuclei with half-integer spin from fluorine.     

Two-dimensional one pulse MAS of half-integer quadrupolar nuclei

We show that the two-dimensional one pulse (TOP) representation of magic-angle spinning nuclear magnetic resonance data of half-integer quadrupolar nuclei has significant advantages over the conventional one-dimensional spectrum. The TOP spectrum, which correlates NMR frequency to spinning sideband order, provides a rapid determination of the number of sites as well as the size of the their quadrupolar coupling. Additionally, synchronous acquisition spectra of the central and satellite transition resonances can be separated by different projections of the TOP spectrum, with higher resolution spectra often found in the satellite transitions projection. A previously perceived problem of centerband aliasing in TOP can be eliminated with an algorithm that uses larger subspectral widths and the sideband order dimension to distinguish centerbands from sidebands.     

Measurement of J-couplings between spin-(1/2) and quadrupolar nuclei by frequency selective solid-state NMR

We report a REDOR-based scheme for the measurement of heteronuclear J-couplings in solid samples with well defined structure, containing spin-12 and quadrupolar nuclei, which can be used with selective RF irradiation to target a specific spin pair, and which provides direct information about the number of coupled spins.     

High resolution heteronuclear correlation NMR spectroscopy between quadrupolar nuclei and protons in the solid state

A high resolution two-dimensional solid state NMR experiment is presented that correlates half-integer quadrupolar spins with protons. In this experiment the quadrupolar nuclei evolve during t1 under a split-t1, FAM-enhanced MQMAS pulse scheme. After each t1 period ending at the MQMAS echo position, single quantum magnetization is transferred, via a cross polarization process in the mixing time, from the quadrupolar nuclei to the protons. High-resolution proton signals are then detected in the t2 time domain during wPMLG5* homonuclear decoupling. The experiment has been demonstrated on a powder sample of sodium citrate and 23Na-1H 2D correlation spectra have been obtained. From the HETCOR spectra and the regular MQMAS spectrum, the three crystallographically inequivalent Na+ sites in the asymmetric unit were assigned. This MQMAS-wPMLG HETCOR pulse sequence can be used for spectral editing of half-integer quadrupolar nuclei coupled to protons.     

Molecular dynamics of half-integer quadrupolar nuclei studied by QCPMG solid-state NMR experiments on static and rotating samples. Theory and simulations

Simulations of QCPMG NMR type experiments have been used to explore dynamic processes of half-integer quadrupolar nuclei in solids. By setting up a theoretical approach that is well suited for efficient numerical simulations the QCPMG type experiments have been analyzed regarding the effect of the magnitude of the EFG- and CSA-tensors, the spin-quantum number, different dynamical processes and MAS. Compared to the QE experiment the QCPMG experiment offers not only intensity gain by an order of magnitude and changes in overall lineshape as a function of the kinetic rate constant but the lineshape of the individual spin-echo sidebands is also very sensitive towards dynamics. Hereby a visual identification of the dynamics is obtained. In common for all the simulations the spin-echo sidebands are narrow in the slow (k< or =10(2) Hz) and the fast (k> or =10(7) Hz) dynamic regime whereas they are broadened in the intermediate regime 10(3)< or =k< or =10(7) Hz. The maximum intensity of the spin-echo sidebands for two-site jumps is highly dependent on the type of anisotropic interactions involved and the type of QCPMG experiment. Hence, in the fast limit the maximum intensity was 140% of the initial intensity when significant CSA was present or under the QCPMG-MAS experiment compared to 89 or 71% for the static experiment influenced by the quadrupolar interaction only. For 3-, 4-, and 6-site jumps the maximum intensity in the fast limit reached up to 339% of the intensity in the static limit.     

Multiple-quantum magic-angle spinning NMR with cross-polarization: Spectral editing of high-resolution spectra of quadrupolar nuclei

An experiment is presented that combines the multiple-quantum magic-angle spinning (MQMAS) technique with cross-polarization (CP). As a preliminary test of this new method, we measured and compared the ²⁷Al 3QMAS and ¹⁹F → ²⁷A1 CP 3QMAS spectra of a fluorinated AlPO₄ aluminophosphate. Complete discrimination between the fluorinated and nonfluorinated Al sites was easily achieved, which demonstrates the usefulness of CP MQMAS for spectral editing. Future applications of this experiment will include other spin pairs and heteronuclear correlation NMR spectroscopy.     

Double-quantum homonuclear NMR correlation spectroscopy of quadrupolar nuclei subjected to magic-angle spinning and high magnetic field

We present a new application of the symmetry-based dipolar recoupling scheme, for exciting directly double-quantum (2Q) coherences between the central transition of homonuclear half-integer quadrupolar nuclei. With respect to previously published 2Q-recoupling methods (M. Eden, D. Zhou, J. Yu, Chem. Phys. Lett. 431 (2006) 397), the sequence is used without π/2 bracketing pulses and with an original super-cycling. This leads to an improved efficiency (a factor of two for spin-5/2) and to a much higher robustness to radio-frequency field inhomogeneity and resonance offset. The 2Q-coherence excitation performances are demonstrated experimentally by ²⁷Al NMR experiments on the aluminophosphates berlinite, VPI5, AlPO₄-14, and AlPO₄-CJ3. The two-dimensional 2Q–1Q correlation experiments incorporating these recoupling sequences allow the observation of 2Q cross-peaks between central transitions, even at high magnetic field where the difference in offset between octahedral and tetrahedral ²⁷Al sites exceeds 10 kHz.     

An alternative construction of the Percus-Yevick equation based on the equilibrium BBGKY hierarchy

The existing derivations of the Percus-Yevick equation are not readily extendable into the nonequilibrium domain. In particular, the elegant Percus functional construction relies on a test particle theorem which lacks an exact nonequilibrium generalization. We propose here a new construction which utilizes some elementary ideas of functional expansions together with the equilibrium BBGKY hierarchy of equations. Also, we feel this new construction provides fresh insight into the physical basis of the equilibrium Percus-Yevick equation.This research was supported in part by a grant from the Faculty Research Award Program of the City University of New York.     

Density functional approximations for classical fluids with long-range interactions

Density functional approximations for systems interacting via long-range forces are revisited. The theory is illustrated with examples of one-component plasmas in two and three dimensions.Dedicated to Philippe Choquard, Coulomb fluid expert.     

Signal enhancement in 5QMAS spectra of spin-5/2 quadrupolar nuclei

5QMAS experiments on spin-5/2 systems display a low sensitivity compared with their 3QMAS counterparts. Nevertheless, the superior resolution of 5QMAS over 3QMAS makes these experiments a favorable choice for many materials. We report an enhancement scheme for the 5QMAS experiment, using an improved five-quantum excitation pulse scheme combined with a FAM-II conversion pulse. The results are verified experimentally on a polycrystalline sample of gamma-(27)Al(2)O(3), showing an enhancement factor of 2.4 over the simple two-pulse (CW) 5QMAS scheme. Numerical computations of the efficiency parameter epsilon support these results.     

On a Raychaudhuri equation for hot gravitating fluids

We generalise the Raychaudhuri equation for the evolution of a self gravitating fluid to include an Abelian and non-Abelian hybrid magneto fluid at a finite temperature. The aim is to utilise this equation for investigating the dynamics of astrophysical high temperature Abelian and non-Abelian plasmas.      

电流变液系统流动的渐近估计

根据电流变液中球形颗粒的运动模型，研究了颗粒质量很小时，电流变液中颗粒运动的渐近状态，利用微分不等式理论，给出了相应运动的渐近估计. 关键词： 电流变液 微分不等式理论 渐近估计     

光电耦合器电离辐射损伤电流传输比1/f噪声表征

在研究光电耦合器电离辐射损伤机理基础上,分别建立光电耦合器电离辐射损伤电流传输比(CTR)表征模型和1/f噪声表征模型.结果表明CTR退化和噪声增加都归因于辐射后光敏三极管集电结和发射结处SiO₂/Si界面缺陷增多.根据CTR退化和噪声变化分别与辐射剂量的关系,建立起噪声变化与CTR退化之间的关系,辐照实验对表征模型正确性进行了验证.运用噪声变化与辐射剂量的关系,通过低剂量辐照实验可以预测高剂量辐射后光电耦合器退化程度,故可用于评价光电耦合器抗辐射能力. 关键词： f噪声')" href="#">1/f噪声 光电耦合器 缺陷 模型     

Adsorption isotherms for fluids with strong interparticle repulsions

We derive adsorption isotherms for an adsorbate of hard-sphere particles with sticky interactions at any fluid density being adsorbed onto a plane, sticky surface. The theory is based on the Percus-Yevick theory for bulk fluids and explicitly includes the equilibrium between the adsorbed fluid and the bulk adsorbate. The theory predicts a surface condensation at low temperatures and low bulk densities in good agreement with surface condensations found in experimental studies of adsorption of gases onto graphite. An approximate law of corresponding states for these transitions is developed. At higher bulk densities and room temperatures, the adsorption isotherms can show a maximum, in accord with recent experimental work.Supported by the Australian Research Grants Commission.     

Influence of sodium ion dynamics on the 23Na quadrupolar interaction in sodalite: a high-temperature 23Na MAS NMR study

High-temperature ²³Na MAS NMR experiments up to 873 K for a number of different sodalites (Na₈[AlSiO₄]₆(NO₃)₂, Na₈[AlSiO₄]₆(NO₂)₂, Na₈[AlSiO₄]₆I₂, Na_7.9[AlSiO₄]₆(SCN)_7.9 · 0.5H₂O, Na₈[AlGeO₄]₆(NO₃)₂, and Na₇[AlSiO₄]₆(H₃O₂) · 4H₂O) were carried out. The spectra of the first five sodalites consist of a quadrupolar MAS pattern with different quadrupolar coupling constants. The quadrupolar interaction for the thiocyanate sodalite, the nitrate aluminosilicate, and germanate sodalite decreases strongly passing a coalescence state on heating, while the quadrupolar interaction of the iodide and nitrite sample shows nearly no change. The basic hydrosodalite shows an asymmetric lineshape at room temperature and, between 350 and 370 K, a second line due to the evaporation of cage-water emerges. The linewidth increases with rising temperature. The temperature dependence of the quadrupolar interaction seems to be a function of the sodalite β-cage expansion. Two conceivable jump mechanisms are proposed for a tetrahedral two-site jump between occupied and unoccupied tetrahedral sites.     

A simple and accurate equation of state for hard-disk fluids

A long-standing problem for hard-disk fluids is to find a simple and accurate equation of state. By observing the known updated virial coefficients from up to , we obtain an accurate empirical formula, with errors less than 0.5%. We further assume that the empirical formula is valid for all the virial coefficients. Using this assumption, we obtain a simple and accurate equation of state. In the density range 0<ρa²≤0.83, the predicted pressures are in good agreement with the simulation results. For 0<ρa²≤0.70, the errors are less than 0.007%. Even at ρa²=0.83, the error is only 0.5%.     

Fortran codes for the correlation functions of hard sphere fluids

Our Fortran codes for hard sphere fluids and their mixtures for the correlation functions that arise from the Percus–Yevick theory and the Verlet–Weis semi-empirical correction have proven useful during a period of nearly four decades and continue to be useful. In order to make these codes even more widely available, a brief summary is presented here and listings of these codes are given in the electronically accessible Supplementary Material to this paper.