Mean spherical approximation-mass action law theory of equilibrium and conductance in ionic solutions

An improved Bjerrum theory obtained by combining the mean spherical approximation with the mass action law (MSA&MAL) is used to calculate the fraction of ions unpaired over the full range of states of a primitive model electrolyte. It is combined with a new theory for the electrical conductance of the primitive model under the MSA to yield the conductance of an electrolyte over a wide range of concentrations and Bjerrum parameters with only two parameters A_o and R, the distance of closest approach, adjusted to fit the conductivity data. The theory fits the data for aqueous alkali halides over a wide concentration range with A_o values in good agreement with those deduced by more conventional theories and with reasonable small ion pairing constants deduced from the data. It fits the data for LiBr in octanol without the need for invoking triple ion formation. It leads to reasonable predictions for the conductance curves for 1:1 electrolytes even up to the molar region for solvents with dielectric constant from 10 to 80.     

Comparison between Gibbs free energy minimization and mass action law for a multitemperature plasma with application to nitrogen

This paper gives all the necessary physical equations to determine the composition and the thermodynamic properties in a multitemperature plasma utilizing two different methods: the first method is based on Gibbs free energy minimization and the second is based on the resolution of the mass action law. The lowering terms of the ionization potential and thermodynamic properties are given for a multitemperature plasma using the Debye-Hückel approximation. Numerical application is made to a nitrogen plasma.     

Long-range-corrected hybrids using a range-separated Perdew-Burke-Ernzerhof functional and random phase approximation correlation

We build on methods combining a short-range density functional approximation with a long-range random phase approximation [B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 130, 081105 (2009)] or second-order screened exchange [J. Paier et al., J. Chem. Phys. 132, 094103 (2010)] by replacing the range-separated local density approximation functional with a range-separated generalized gradient approximation functional in the short range. We present benchmark results that show a marked improvement in the thermodynamic tests over the previous local density approximation-based methods while retaining those methods' excellent performance in van der Waals interactions.     

胶束电动力学毛细管色谱中有机调节剂对溶质容量因子的影响

将质量作用定律应用于胶束电动力学毛细管色谱中溶质、有机添加剂和胶束之间的相互作用研究,得到了溶质容是因子与各过程平衡常数及有机添加剂、表面活性剂浓度的关系的数学表达式。进一步分析表明,研究调节剂在胶束中可能有一定的溶解度,但这一过程对于胶束在电泳过程中的迁移速度几乎没有影响;有机添加剂对溶质容量因子的影响主要反映为其对表面活性剂临界胶束浓度的影响,在一级调节剂浓度不变的情况下,溶质容基因子与表面活性剂浓度之间满足很好的线性关系。     

Remarks on the correlation function implied by the Bjerrum theory of ion pairing

The Friedman theory of correlation functions implied by the Bjerrum theory is generalized by taking into account additional terms and by improving the basic expression for the free energy. By combining the mean spherical approximation (MSA) and the mass action law (MAL) good agreement with HNC and MC data is reached.     

Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo

Improvements beyond the primitive approximation in the path integral Monte Carlo method are explored both in a model problem and in real systems. Two different strategies are studied: The Richardson extrapolation on top of the path integral Monte Carlo data and the Takahashi-Imada action. The Richardson extrapolation, mainly combined with the primitive action, always reduces the number-of-beads dependence, helps in determining the approach to the dominant power law behavior, and all without additional computational cost. The Takahashi-Imada action has been tested in two hard-core interacting quantum liquids at low temperature. The results obtained show that the fourth-order behavior near the asymptote is conserved, and that the use of this improved action reduces the computing time with respect to the primitive approximation.     

Improvement on macroscopic compressibility approximation and beyond

A numerical procedure is proposed to extend the thermodynamic perturbation expansion (TPE) to a higher order. It is shown that the present second order term is superior to that due to a macroscopic compressibility approximation (MCA), a local compressibility approximation, and a superposition approximation by Barker and Henderson [Rev. Mod. Phys. 48, 587 (1976)]. Extensive model calculation and comparison with simulation data available in literature and supplied in the present report indicate that the present third order TPE is superior to a previous second order TPE based on the MCA, two previous perturbation theories, which are respectively based on an analytical mean spherical approximation for an Ornstein-Zernike equation, and an assumed explicit functional form for the Laplace transform of radial distribution function multiplied by radial distance, and a recent generalized van der Waals theory. The present critical temperature for a hard core attractive Yukawa fluid of varying range is in very good agreement with that due to a hierarchical reference theory. The present third order TPE is computationally far more modest than the self-consistent integral equation theory, and therefore is a viable alternative to use of the latter.     

Remarks on triple ion formation. Interpretation of conductance data

It is shown that it is possible to fit conductance data in solvents of low dielectric constant without the additional assumption of triple ion formation. With the aid of two new conductance equations, which incoporate in different ways a mass action law for ion pairing but not for ion triplets, we can account for the conductivity data for the systems LiBr in octanol and NaI in butanol. One of the equations incorporates the mean spherical approximation.     

Determination of Hydrogen Single Ion Activity Coefficients in Aqueous HCl Solutions at 25°C

The single ion activity coefficients of hydrogen and chloride ions in aqueous HCl solutions have been estimated at 25°C at concentrations up to 1 mol-kg^–1, using potentiometric measurements with ion-selective electrodes and appropriate calibration procedures. Two methods are described for an internal calibration of the electrodes in the extended Debye–Hückel concentration range. The results are compared to the conventional pH calibration with external buffer solutions. Since the latter calibration method does not account for the liquid junction potential E _J which arises at the reference electrode, the resulting activity coefficients are quite different in HCl solutions of higher concentration. These differences between internal and external calibration decrease significantly, when a correction for E _J is introduced into the conventional pH calibration. Hence, in solutions of higher ionic strength the accuracy of the conventional pH electrode calibration using buffer solutions is very limited, when exact H⁺ activities are required. The consistency of the results indicates that the liquid junction potentials in the examined systems calculated by the Henderson/Bates approximation are of reasonable precision.     

Stability of Anionic Complexes in Halide Melts of Bivalent Metals

The effect of volume variation at the possible dissociation equilibria of (MX₄)^2– anionic complexes in halide melts of bivalent metals are analyzed in terms of the mean-sphere approximation (MSA) of the statistical theory. Within the framework of the simplified model of charged hard spheres of different diameters and valences, the complete system of equilibrium equations is obtained, i.e., equations of the law of mass action and equations of state. This system makes possible self-correlated calculations of both the equilibrium concentration of autocomplexes and the melt density. It is shown that the simplest approximation of the complex diameter as the treble diameter of simple ions overestimates the effects of volume variations when considering dissociation. Taking into account the superposition of spheres makes it possible to describe the smoother volume variations with the temperature.     

The surface charge density/surface potential relationship and the Poisson-Boltzmann equation

A procedure is described which provides an approximate analytic expression for the relationship between the surface charge density and the surface potential of a spherical or cylindrical colloidal particle in a general type of electrolyte. The first approximation is found and the approximation error is given. Also derived are the fourth approximation for a symmetric z-z type electrolyte and the second approximation for a symmetric z-z, 2z-2z type electrolyte.     

Calibration function for the orbitrap FTMS accounting for the space charge effect

Ion storage in an electrostatic trap has been implemented with the introduction of the Orbitrap Fourier transform mass spectrometer (FTMS), which demonstrates performance similar to high-field ion cyclotron resonance MS. High mass spectral characteristics resulted in rapid acceptance of the Orbitrap FTMS for Life Sciences applications. The basics of Orbitrap operation are well documented; however, like in any ion trap MS technology, its performance is limited by interactions between the ion clouds. These interactions result in ion cloud couplings, systematic errors in measured masses, interference between ion clouds of different size yet with close m/z ratios, etc. In this work, we have characterized the space-charge effect on the measured frequency for the Orbitrap FTMS, looking for the possibility to achieve sub-ppm levels of mass measurement accuracy (MMA) for peptides in a wide range of total ion population. As a result of this characterization, we proposed an m/z calibration law for the Orbitrap FTMS that accounts for the total ion population present in the trap during a data acquisition event. Using this law, we were able to achieve a zero-space charge MMA limit of 80 ppb for the commercial Orbitrap FTMS system and sub-ppm level of MMA over a wide range of total ion populations with the automatic gain control values varying from 10 to 10⁷.     

Atomic Absorption Spectrophotometric Determination of Copper (I) after Adsorption of its 4′-(p-Methoxyphenyl)-2, 2′:6′, 2″-Terpyridine Tetraphenylborate Ion-Associated Complex on Microcrystalline Naphthalene

A new atomic absorption spectrophotometric method has been developed for the trace determination of copper after adsorption of its 4′-(p-methoxyphenyl)-2, 2′:6′,2″-terpyridine tetraphenylborate ion-associated complex on microcrystalline naphthalene. This complex is adsorbed on microcrystalline naphthalene in the pH range 0.5-11.0 by shaking for a few seconds. The solid mass so formed is separated by filtration, dissolved in dimethylformamide and the absorbance is measured at 324.7 nm. Beer's law is obeyed in the concentration range 5.0-60.0 μg of copper in 10 ml of the final dimethylformamide solution. The replicate determinations of a sample containing 30 μg of copper gave a mean absorbance of 0.171 with a standard deviation of 0.0019 and a relative standard deviation of 1.11%. The method has been applied to the determination of copper in certain standard reference materials.     

NMR chemical shift and J coupling parameterization and quantum mechanical reference spectrum simulation for selected nerve agent degradation products in aqueous conditions

The spectral parameters of selected nerve agent degradation products relevant to the Chemical Weapons Convention, namely, ethyl methylphosphonate, isopropyl methylphosphonate, pinacolyl methylphosphonate and methylphosphonic acid, were studied in wide range of pH conditions and selected temperatures. The pH and temperature dependence of chemical shifts and J couplings was parameterized using Henderson–Hasselbalch‐based functions. The obtained parameters allowed calculation of precise chemical shifts and J coupling constants in arbitrary pH conditions and typical measurement temperatures, thus facilitating quantum mechanical simulation of reference spectra in the chosen magnetic field strength for chemical verification. Copyright © 2017 John Wiley & Sons, Ltd.     

ACTION SPECTRA FOR THE trans TO cis PHOTOISOMERISATION OF UROCANIC ACID in vitro and IN MOUSE SKIN

Urocanic acid (UCA) is a major UV chromophore in the upper layers of the skin where it is found predominantly as the trans isomer. UV irradiation induces photoisomerisation of trans-UCA to cis-UCA which has been shown to mimic some of the immunosuppressive properties of UV exposure. We examined the wavelength dependence for trans-UCA to cis-UCA photoisomerisation in vitro and in mouse skin in vivo over the spectral range270–340 nm. The resulting action spectra were very similar with maximal effectiveness at300–315 nm and equal activity at 270 nm and325–330 nm, demonstrating that UVA-II radiation (320–340nm) is efficient at UCA photoisomerisation. These action spectra differed markedly from the trans-UCA absorption spectrum in vitro and also the reported action spectrum for UV suppression of contact hypersensitivity in mice. These findings suggest that the relationship between cis-UCA formation in skin and UV-induced immunosuppression may be complex.     

Conventional residual liquid junction potentials in dilute solutions

Conventional residual liquid junction potentials were measured between NBS 1:1 phosphate buffer and various dilute solutions with ionic strengths of 1-100 mmol kg^?1, using 3.5 mol kg^?1 potassium chloride as the bridge electrolyte. All junctions were of the free-diffusion type, formed within a 1-mm capillary. The conventional residual junction potential was indistinguishable from zero (± 0.5 mV), for dilute solutions of primary reference standards, for which calculations based on the Henderson equation predict values of 0.8–1.3 mV. Solutions of Tris-HCl (20–100 mmol kg^?1) and dilute HCl (1–50 mmol kg^?1) had appreciable conventional residual liquid junction potentials (1.1–3.3 mV). The experimental values for dilute HCl solutions compare favourably with those calculated with the Henderson equation. These results suggest that the pH of hard waters, measured using the NBS pH scale, will be a good approximation (within 0.01 pH) to pa_H, so that pH can be interpreted in terms of the activity of the hydrogen ions. Further measurements are required to ascertain whether this approximation is true for soft and acidic waters.     

On the stability of (MX6)3− complexes in halide melts of three-valent metals

ABSTRACT

The effects of volume change at dissociation equilibrium of possible anion complexes of the (MX₆)^3? type in halide melts of trivalent metals MX3 within the statistical thermodynamics based on the MSA approximation were analysed. With the help of a simplified Akdeniz–Tosi model of a mixture of charged hard spheres of different diameters and valencies, we obtained the full system of equilibrium equations including the mass action law (MAL) and the equation of state (EoS). It was shown that the simplest approximation of the complex diameter as a tripled diameter of simple ions leads to a significant overestimation of the effects of volume changes at dissociation. It was found that the complex dissociation should be accompanied by a significant increase in density in a narrow temperature interval. It can be associated with the specific manifestation of electrolytic dissociation in the case of the trivalent metal halides’ auto-complexation.     

Calculating thermodynamic properties from perturbation theory: Part III. The mixtures of square-well chain fluid

A completely analytic perturbation theory has been developed to calculate the Helmholtz energy, compressibility factor, internal energy and constant-volume heat capacity for square-well chain fluid mixtures. This theory is based on the improved Barker–Henderson macroscopic compressibility (mc) approximation proposed by Zhang, the first-order perturbation theory of Wertheim in which Zhang’s analytic monomer radial distribution function as the function of temperature and monomer density is used, and a simple mixing rule similar to that of Hino–Prausnitz. The validity of the perturbation theory is evaluated by comparing the calculated compressibility factor, internal energy and constant-volume heat capacity for the freely jointed square-well chain mixtures from the theory to MC simulation data. The results show that the theory predicts results in good agreement with simulation results.