Thermodynamic Properties of Ternary Ionic Liquid Mixture Containing a Common Ion: Excess Molar Volumes,Excess Isentropic Compressibilities,Excess Molar Enthalpies and Excess Heat Capacities

In the present investigations, the excess molar volumes, \( V_{ijk}^{\text{E}} \), excess isentropic compressibilities, \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), and excess heat capacities, \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \), for ternary 1-butyl-2,3-dimethylimidazolium tetrafluoroborate (i) + 1-butyl-3-methylimidazolium tetrafluoroborate (j) + 1-ethyl-3-methylimidazolium tetrafluoroborate (k) mixture at (293.15, 298.15, 303.15 and 308.15) K and excess molar enthalpies, \( \left( {H^{\text{E}} } \right)_{ijk} \), of the same mixture at 298.15 K have been determined over entire composition range of x _i and x _j . Satisfactorily corrections for the excess properties \( V_{ijk}^{\text{E}} \), \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), \( \left( {H^{\text{E}} } \right)_{ijk} \) and \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \) have been obtained by fitting with the Redlich–Kister equation, and ternary adjustable parameters along with standard errors have also been estimated. The \( V_{ijk}^{\text{E}} \), \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), \( \left( {H^{\text{E}} } \right)_{ijk} \) and \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \) data have been further analyzed in terms of Graph Theory that deals with the topology of the molecules. It has also been observed that Graph Theory describes well \( V_{ijk}^{\text{E}} \), \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), \( \left( {H^{\text{E}} } \right)_{ijk} \) and \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \) values of the ternary mixture comprised of ionic liquids.     

Lego-like spheres and tori

Given a connected surface \({\mathbb {F}}^2\) with Euler characteristic \(\chi \) and three integers \(b>a\ge 1<k\), an \((\{a,b\};k)\)-\({\mathbb {F}}^2\) is a \({\mathbb {F}}^2\)-embedded graph, having vertices of degree only k and only a- and b-gonal faces. The main case are (geometric) fullerenes (5, 6; 3)-\({\mathbb {S}}^2\). By \(p_a\), \(p_b\) we denote the number of a-gonal, b-gonal faces. Call an \((\{a,b\};k)\)-map lego-admissible if either \(\frac{p_b}{p_a}\), or \(\frac{p_a}{p_b}\) is integer. Call it lego-like if it is either \(ab^f\)-lego map, or \(a^fb\)-lego map, i.e., the face-set is partitioned into \(\min (p_a,p_b)\) isomorphic clusters, legos, consisting either one a-gon and \(f=\frac{p_b}{p_a}\,b\)-gons, or, respectively, \(f=\frac{p_a}{p_b}\,a\)-gons and one b-gon; the case \(f=1\) we denote also by ab. Call a \((\{a,b\};k)\)-map elliptic, parabolic or hyperbolic if the curvature \(\kappa _b=1+\frac{b}{k}-\frac{b}{2}\) of b-gons is positive, zero or negative, respectively. There are 14 lego-like elliptic \((\{a,b\};k)\)-\({\mathbb {S}}^2\) with \((a,b)\ne (1,2)\). No \((\{1,3\};6)\)-\({\mathbb {S}}^2\) is lego-admissible. For other 7 families of parabolic \((\{a,b\};k)\)-\({\mathbb {S}}^2\), each lego-admissible sphere with \(p_a\le p_b\) is \(a^fb\) and an infinity (by Goldberg–Coxeter operation) of \(ab^f\)-spheres exist. The number of hyperbolic \(ab^f\,(\{a,b\};k)\)-\({\mathbb {S}}^2\) with \((a,b)\ne (1,3)\) is finite. Such \(a^f b\)-spheres with \(a\ge 3\) have \((a,k)=(3,4),(3,5),(4,3),(5,3)\) or (3, 3); their number is finite for each b, but infinite for each of 5 cases (a, k). Any lego-admissible \((\{a,b\};k)\)-\({\mathbb {S}}^2\) with \(p_b=2\le a\) is \(a^f b\). We list, explicitly or by parameters, lego-admissible \((\{a,b\};k)\)-maps among: hyperbolic spheres, spheres with \(a\in \{1,2\}\), spheres with \(p_b\in \{2,\frac{p_a}{2}\}\), Goldberg–Coxeter’s spheres and \((\{a,b\};k)\)-tori. We present extensive computer search of lego-like spheres: 7 parabolic (\(p_b\)-dependent) families, basic examples of all 5 hyperbolic \(a^fb\) (b-dependent) families with \(a\ge 3\), and lego-like \((\{a,b\};3)\)-tori.     

Crystallization study of Se<Subscript>86</Subscript>Sb<Subscript>14</Subscript> glass

The present study concerns with high-accuracy determination of crystallization activation energy (\(E_{\text{c}}\)), the frequency factor (\(k_{0}\)), the kinetic exponent (n) for Se₈₆Sb₁₄ glass. Different three methods have been used to investigate the \(E_{\text{c}} \,{\text{and}}\,k_{0 }\) values. It was found that the deduced value of k ₀ based on Kissinger’s method is too small compared with the others. Therefore, it can’t be used to investigate k ₀ value. Where \(E_{\text{c}} \,{\text{and}}\,k_{0}\) values are already known, the overall reaction rate \(k = k_{0 } { \exp }\left( { - E_{\text{c}} /\left( {R \cdot T} \right)} \right)\) at any temperature can be calculated. Now, Avrami’s equation (\(\chi = 1 - { \exp }\left( { - \left( {kt} \right)^{\text{n}} } \right)\)) contains only one unknown which is the kinetic exponent (n). This method enables us to determine n value without any approximations. The values’ crystallization fraction \((\chi_{\text{th}} )\) that theoretically calculated is the same as that experimentally investigated \((\chi_{{{ \exp } .}} )\).     

The mass renormalization for the translational Brownian motion

The damped harmonic oscillator is modeled as a local mode X with mass m and frequency \(\omega _{0}\) immersed in a phonon bath with spectral density function \(j_{0}(\omega \)). This function behaves as \(\omega ^{s}\, (s= 1,2,3,\ldots )\) when \(\omega \rightarrow 0\). The limit \(\omega _{0} = 0\) represents translational (free) Brownian motion. The earlier work (Hakim and Ambegaokar in Phys Rev A 32:423, 1985) concluded that the so defined limit transition is prohibited for spectral densities with \(s<2\). In the present study we demonstrate that a specially constructed preliminary excitation changing the original bath spectrum as \(j_{0}(\omega ) \rightarrow j(\omega )\) allows for treating the free damped motion of X with no restriction for the initial spectrum dimensionality. This procedure validates the finite mass renormalization (i.e. \(m\rightarrow M\) when \(\omega _{0}\rightarrow 0)\) for the conventional bath spectra with \(s=1,2\). We show that the new spectral density \(j(\omega )\) represents the momentum bilinear interaction between mode X and the environmental modes, whereas the conventional function \(j_{0}(\omega )\) is inherent to the case of bilinear coordinate interaction in terms of the same variables. The translational damping kernel is derived based on the new spectral density.     

The Study of Solute–Solvent Interactions in 1-Butyl-3-Methylimidazolium Hexafluorophosphate + 2-Pyrrolidone from Volumetric,Acoustic, Optical and Spectral Properties

The density (ρ), speed of sound (u) and refractive index (n_D) of [Bmim][PF₆], 2-pyrrolidone and their binary mixtures were measured over the whole composition range as a function of temperature between (303.15 and 323.15)?K at atmospheric pressure. Experimental values were used to calculate the excess molar volumes \( \left( {V_{m}^{\text{E}} } \right) \), excess partial molar volumes \( \left( {\overline{V}_{m}^{\text{E}} } \right) \), partial molar volumes at infinite dilution \( \left( {\overline{V}_{m}^{{{\text{E}},\infty }} } \right) \), excess values of isentropic compressibility \( \left( {\kappa_{S}^{\text{E}} } \right) \), free length \( \left( {L_{\text{f}}^{\text{E}} } \right) \) and speeds of sound \( \left( {u^{\text{E}} } \right) \) for the binary mixtures. The calculated properties are discussed in terms of molecular interactions between the components of the mixtures. The results reveal that interactions between unlike molecules take place, particularly through intermolecular hydrogen bond formation between the C₂–H of [Bmim][PF₆] and the carbonyl group of pyrrolidin-2-one. An excellent correlation between thermodynamic and IR spectroscopic measurements was observed. The observations were further supported by the Prigogine–Flory–Patterson (PFP) theory of excess molar volume.     

Thermochemical Properties of Dissolution of Nicotinic Acid C<Subscript>6</Subscript>H<Subscript>5</Subscript>NO<Subscript>2</Subscript>(s) in Aqueous Solution

Nicotinic acid (also known as niacin) was recrystallized from anhydrous ethanol. X-ray crystallography was applied to characterize its crystal structure. The crystal belongs to the monoclinic system, space group P2₍₁₎/c. The crystal cell parameters are a = 0.71401(4) nm, b = 1.16195(7) nm, c = 0.71974(6) nm, α = 90°, β = 113.514(3)°, γ = 90° and Z = 4. Molar enthalpies of dissolution of the compound, at different molalities m/(mol·kg^?1) were measured with an isoperibol solution–reaction calorimeter at T = 298.15 K. The molar enthalpy of solution at infinite dilution was calculated, according to Pitzer’s electrolyte solution model and found to be \( \Delta_{\text{sol}} H_{m}^{\infty } = ( 2 7. 3 \pm 0. 2) \) kJ·mol^?1 and Pitzer’s parameters (\( \beta_{{\text{MX}}}^{{\text{(0)}L}} \), \( \beta_{{\text{MX}}}^{{\text{(1)}L}} \) and \( C_{{\text{MX}}}^{\phi L} \)) were obtained. The values of apparent relative molar enthalpies (\( {}^{\phi }L \)) and relative partial molar enthalpies (\( \overline{{L_{2} }} \) and \( \overline{{L_{1} }} \)) of the solute and the solvent at different molalities were derived from the experimental enthalpy of dissolution values of the compound. Also, the standard molar enthalpy of formation of the anion \( {\text{C}}_{ 6} {\text{H}}_{ 4} \text{NO}_{2}^{-} \) in aqueous solution was calculated to be \( {\Delta_{\text{f}}^{} H}_{\text{m}}^{\text{o}} ({\text{C}}_{ 6} {\text{H}}_{ 4} {\text{NO}}_{2}^{-} \text{,aq}) = - \left( {603.2 \pm 1.2} \right)\;{\text{kJ}}{\cdot}{\text{mol}}^{-1} \).     

Volumetric,Acoustic and Transport Properties of Metformin Hydrochloride Drug in Aqueous <Emphasis Type="SmallCaps">d</Emphasis>-Glucose Solutions at <Emphasis Type="Italic">T</Emphasis> = (298.15–318.15) K

Apparent molar volumes, apparent molar adiabatic compressibilities and viscosity B-coefficients for metformin hydrochloride in aqueous d-glucose solutions were determined from solution densities, sound velocities and viscosities measured at T = (298.15–318.15) K and at pressure p = 101 kPa as a function of the metformin hydrochloride concentrations. The standard partial molar volumes (\( \phi_{V}^{0} \)) and slopes (\( S_{V}^{*} \)) obtained from the Masson equation were interpreted in terms of solute–solvent and solute–solute interactions, respectively. Solution viscosities were analyzed using the Jones–Dole equation and the viscosity A and B coefficients discussed in terms of solute–solute and solute–solvent interactions, respectively. Adiabatic compressibility (\( \beta_{s} \)) and apparent molar adiabatic compressibility (\( \phi_{\kappa }^{{}} \)), limiting apparent molar adiabatic compressibility (\( \phi_{\kappa }^{0} \)) and experimental slopes (\( S_{\kappa }^{*} \)) were determined from sound velocity data. The standard volume of transfer (\( \Delta_{t} \phi_{V}^{0} \)), viscosity B-coefficients of transfer (\( \Delta_{t} B \)) and limiting apparent molar adiabatic compressibility of transfer (\( \Delta_{t} \phi_{\kappa }^{0} \)) of metformin hydrochloride from water to aqueous glucose solutions were derived to understand various interactions in the ternary solutions. The activation parameters of viscous flow for the studied solutions were calculated using transition state theory. Hepler’s coefficient \( (d\phi /dT)_{p} \) indicated the structure making ability of metformin hydrochloride in the ternary solutions.     

Densities,Ultrasonic Velocities,Excess Properties and IR Spectra of Binary Liquid Mixtures of Organic Esters (Ethyl Lactate,Some Organic Carbonates)

Organic esters of carbonic acid {dimethyl carbonate (DMC)/diethyl carbonate (DEC)/propylene carbonate (PC)}, in combination with a lactate ester {ethyl lactate (EL)}, with green chemistry characteristics were chosen for the present study of molecular interactions in binary liquid mixtures. Densities (ρ) and ultrasonic velocities (U) of the pure solvents and liquid mixtures were measured experimentally over the entire composition range at temperatures (303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure. The experimental data was used to calculate thermodynamic and acoustic parameters \( V_{\text{m}}^{\text{E}} \), \( \kappa_{S}^{\text{E}} \), \( L_{\text{f}}^{\text{E}} \), \( \bar{V}_{\text{m,1}}^{{}} \), \( \bar{V}_{\text{m,2}}^{{}} \), \( \bar{V}_{\text{m,1}}^{\text{E}} \), \( \bar{V}_{\text{m,2}}^{\text{E}} \), \( \bar{V}_{ 1}^{\text{E,0}} \) and \( \bar{V}_{ 2}^{\text{E,0}} \) and the excess functions were fitted with the Redlich–Kister polynomial equation to obtain the binary solution coefficients and the standard deviations. It was observed that the values of \( V_{\text{m}}^{\text{E}} \), \( \kappa_{S}^{\text{E}} \) and \( L_{\text{f}}^{\text{E}} \) are positive for the mixtures of (EL + DMC/DEC) and negative for those of (EL + PC) over the entire range of composition and temperature. The positive values of \( V_{\text{m}}^{\text{E}} \), \( \kappa_{S}^{\text{E}} \) and \( L_{\text{f}}^{\text{E}} \) indicate the action of dispersion forces between the component molecules of (EL + DMC/DEC) mixtures whereas negative values for the mixture (EL + PC) suggest the existence of strong specific interactions between the component molecules, probably resulting from chemical and structural contributions. The excess properties have also been analyzed by using the reduced (\( Y^{\text{E}} /x_{1} x_{2} \)) excess function approach and the results are found to be in agreement with those from the corresponding \( Y^{\text{E}} \)(= \( V_{\text{m}}^{\text{E}} \), \( \kappa_{S}^{\text{E}} \) and \( L_{\text{f}}^{\text{E}} \)) values. This is further supported by FTIR spectral analysis.     

Methodology to determine the apparent specific heat capacity of metal hydroxides for thermochemical energy storage

Thermochemical energy storage uses reversible thermochemical reactions to store and release heat, representing a promising technology for energy conservation and utilizing fluctuating renewable energy sources and waste heat. Many recent studies have focused on determination of the enthalpy of reaction of possible thermochemical materials (TCM) based on thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). So far, comparatively few attempts have been made to characterize the apparent specific heat capacity at constant pressure \(c_{\text{p}}^{\text{app}} \left( T \right)\) of the investigated TCM. The purpose of this study is to outline a measurement and analysis procedure to evaluate \(c_{\text{p}}^{\text{app}} \left( T \right)\) of powdery TCM. The procedure is presented focusing on two metal hydroxides Ca(OH)₂ and Mg(OH)₂. Preliminary TGA experiments were conducted to identify reaction-free temperature intervals and mass change. Starting from the metal hydroxide, subsequent DSC experiments with two consecutive heating and cooling cycles were carried out to determine \(c_{\text{p}}^{\text{app}} \left( T \right)\) of the initial hydroxide and the oxide product. Three separate DSC runs for each candidate enable an evaluation of measurement uncertainty, and \(c_{\text{p}}^{\text{app}} \left( T \right)\) results were compared to available literature data. Preliminary TGA experiments have shown that the applied heating rate β has a strong effect on the measured dehydration reaction. This result influences the consecutive \(c_{\text{p}}^{\text{app}} \left( T \right)\) interpretation of the metal hydroxides. Analysis of the measured \(c_{\text{p}}^{\text{app}} \left( T \right)\) data compared to literature show good agreement for both metal hydroxides and oxides. Overlapping endotherm effects, which are not part of \(c_{\text{p}} \left( T \right)\), have to be considered for further thermal conductivity calculations.     

Sequential Preparation of Series of Ternary Solutions

For ternary (and more general multicomponent) liquid-phase systems, solution preparation is a necessary step in measuring thermodynamic and transport property data and in identifying compositions useful in specific applications. We consider a ternary system comprised of liquid components A, B, and C (typically, nonelectrolytes), fully miscible over the entire range of composition. Achieving uniform coverage of the ternary triangle of compositions, with mass fraction increments of \( {1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-0pt} N} \) corresponding to mass fractions of \( w_{\text{A}} = {m \mathord{\left/ {\vphantom {m N}} \right. \kern-0pt} N} \), \( w_{\text{B}} = {n \mathord{\left/ {\vphantom {n N}} \right. \kern-0pt} N} \), \( w_{\text{C}} = 1 - w_{\text{A}} - w_{\text{B}} \), for \( 0 \le m \le N \) and \( 0 \le m + n \le N \), requires preparation of \( {{(N + 1)(N + 2)} \mathord{\left/ {\vphantom {{(N + 1)(N + 2)} 2}} \right. \kern-0pt} 2} \) solutions. If the minimum quantity required for each composition is characterized in terms of a volume, as for, say, viscometry, then the volume required, if each solution is prepared directly from pure components, will grow with N more rapidly than quadratically. We develop an approach that mixes previously prepared solutions to make new compositions, and substantially reduces the amount of material needed. We illustrate this approach in detail when the components are liquids with the same density, miscible in all compositions, with no volume change on mixing, and each solution can be fully recovered to prepare subsequent solutions. For \( N = 10 \), only nine units are required, compared to 66 units for the conventional approach, while the number of weighings is reduced by 55%. Modifications to deal with cases in which the pure components have different densities, some material is not recovered after measurement, and the components have different costs, are discussed.     

On the structure of discrete spectrum of a non-selfadjoint system of differential equations with integral boundary condition

In this paper, we investigated the spectrum of the operator \(L(\lambda )\) generated in Hilbert Space of vector-valued functions \(L_{2}(\mathbb {R}_{+},C_{2})\) by the system

$$\begin{aligned} iy_{1}^{'}(x,\lambda )+q_{1}(x)y_{2}(x,\lambda )&=\lambda y_{1}(x,\lambda )\\ -iy_{2}^{'}(x,\lambda )+q_{2}(x)y_{1}(x,\lambda )&=\lambda y_{2}(x,\lambda ),x\in \mathbb {R}_{+}:=(0,\infty ), \end{aligned}$$

and the integral boundary condition of the type

$$\begin{aligned} \int _{0}^{\infty }K(x,t)y(t,\lambda ){\mathrm {dt}}+\alpha y_{2}(0,\lambda )-\beta y_{1}(0,\lambda )=0 \end{aligned}$$

where \(\lambda \) is a complex parameter, \(q_{i},\,i=1,2\) are complex-valued functions and \(\alpha ,\beta \in \mathbb {C}\). K(x, t) is vector fuction such that \(K(x,t)=(K_{1}(x,t),K_{2}(x,t)),\,K_{i}(x,t)\in L_{1}(0,\infty )\cap L_{2}(0,\lambda ),\,i=1,2\). Under the condition

$$\begin{aligned} \left| q_{i}(x)\right| \le ce^{-\varepsilon \sqrt{x}},c>0,\varepsilon >0,i=1,2 \end{aligned}$$

we proved that \(L(\lambda )\) has a finite number of eigenvalues and spectral singularities with finite multiplicities.

     

Thermo Physical and Spectroscopic Properties of Binary Liquid Systems: Ethanoic Acid/Propanoic Acid/Butanoic Acid with 2-Methylaniline

Densities (ρ), speeds of sound (u), and viscosities (η) are reported for binary mixtures of 2-methylaniline with carboxylic acids (ethanoic acid, propanoic acid and butanoic acid) over the entire composition range of mole fraction at T?=?(303.15–318.15) K and at atmospheric pressure (0.1 MPa). The excess properties such as excess molar volume (V _m ^E ), excess isentropic compressibility (κ _S ^E ) and excess Gibbs energy of activation of viscous flow (G^*E) are calculated from the experimental densities, speeds of sound and viscosities. Excess properties are correlated using the Redlich–Kister polynomial equation. The partial molar volumes, \( \bar{V}_{\text{m,1}} \) and \( \bar{V}_{\text{m,2}} \), partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}} \) and \( \bar{K}_{\text{s,m,2}} \), excess partial molar volumes, \( \bar{V}_{\text{m,1}}^{\text{E}} \) and \( \bar{V}_{\text{m,2}}^{\text{E}} \), and excess partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}}^{\text{E}} \) and \( \bar{K}_{\text{s,m,2}}^{\text{E}} \), over whole composition range, partial molar volumes, \( \bar{V}_{\text{m,1}}^{ \circ } \) and \( \bar{V}_{\text{m,2}}^{ \circ } \), partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}}^{ \circ } \) and \( \bar{K}_{\text{s,m,2}}^{ \circ } \), excess partial molar volumes, \( \bar{V}_{\text{m,1}}^{{ \circ {\text{E}}}} \) and \( \bar{V}_{{{\text{m}},2}}^{{ \circ {\text{E}}}} \), and excess partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}}^{{ \circ {\text{E}}}} \) and \( \bar{K}_{\text{s,m,2}}^{{ \circ {\text{E}}}} \), of the components at infinite dilution have also been calculated from the analytically obtained Redlich–Kister polynomials. The excess molar volume V^E results are analyzed using the Prigogine–Flory–Patterson theory. Analysis of each of the three contributions viz. interactional V^E(int.), free volume V^E(fv.) and characteristic pressure p* to V^E showed that the interactional contributions are positive for all systems while the free volume and characteristic pressure p* contributions are negative for all the binary mixtures. The results are analyzed in terms of attractive forces between 2-methylaniline and carboxylic acids molecules. Good agreement is obtained between excess quantities and spectroscopic data.     

Experimental Investigation on the Effect of a Microsecond Pulse and a Nanosecond Pulse on NO Removal Using a Pulsed DBD with Catalytic Materials

In this study, an experimental investigation of the removal of NO from an atmospheric air stream has been carried out with a non-thermal plasma dielectric barrier discharge reactor filled with different catalytic materials. TiO\(_2\), CuO–MnO\(_2\)–TiO\(_2\), CuO–MnO\(_2\)–Al\(_2\)O\(_3\) catalysts were used to study the synergy between the plasma and the catalysts. The NO\(_\mathrm{{x}}\) removal efficiency and by-products formation were studied as a function of energy density, pulse rise time and width using a plasma catalytic configuration. It was observed that the shorter pulses are more efficient for NO\(_\mathrm{{x}}\) removal but at the expense of higher by-products formation such as N\(_2\)O and O\(_3\). A comparison has been made between an in-plasma catalytic configuration and a post-plasma catalytic configuration. Among all the three catalysts that were studied, CuO–MnO\(_2\)–TiO\(_2\) catalyst showed the best performance with respect to the removal efficiency as well as the by-products formation in both the in-plasma and the post-plasma catalytic configuration. In general, the post-plasma configuration showed better results with respect to low by-products formation.     

Deposition Morphology and Magnetism of Co,Pt Adatoms and Small CoPt Adclusters on Ni(100) Substrate

Theoretical calculations of Co\(_{n-x}\)Pt\(_x\) (n = 1–3; \(x \le n\)) clusters on Ni(100) surface for their spin and orbital magnetic moments, as well as the magnetic anisotropy energy (MAE), are performed by using the density-functional theory (DFT) method including a self-consistent treatment of spin–orbit coupling (SOC). The results reveal that the ferromagnetic Co atoms in intra Co\(_{n-x}\)Pt\(_x\) adclusters couple ferromagnetically to their underlayer Ni atoms. The predominant inter-interactions between Co adatoms and Ni surface with the partly filled 3d band, together with the secondary intra-interactions between Co adatoms and Pt adatoms with fully filled 5d band, lead to a strongly quenched orbital moment (\(\mu _{\mathrm{{orb}}}^{\mathrm{{Co}}}\) = 0.18–0.14 \(\mu _B\); \(\mu _{\mathrm{{orb}}}^{\mathrm{{Pt}}} \approx \) 0.24–0.19 \(\mu _B\)) but a less quenched spin moment (\(\mu _{\mathrm{{spin}}}^{\mathrm{{Co}}} \approx \) 2.0 \(\mu _B\); \(\mu _{\mathrm{{spin}}}^{\mathrm{{Pt}}} \approx \) 0.35 \( \mu _B\)). The MAEs of CoPt adclusters exhibit a strong dependence on alloying effect rather than size effect, which is direly proportional to SOC strength and orbital moment anisotropy. The oxidations of CoPt clusters always reduce orbital magnetic moments and consequently decrease the corresponding MAEs.     

Transport selectivity of carbonate and chloride ions througha strongly alkaline anion-exchange membrane before and after its modification with sodium alginate

The transport selectivity of carbonate ions relative to chloride ions \(\left( {P_{Cl^ - }^{CO_3^{2 - } } } \right)\) through an anion-exchange membrane during electrodialysis is investigated before and after the membrane was modified by the electrolytic precipitation of sodium alginate on its surface, as well as by pretreating the membrane in a solution of sodium alginate. It is established that the experimental value of \(P_{Cl^ - }^{CO_3^{2 - } } \) is appreciably smaller than the calculated value for the unmodified membrane at low values of current density. At large currents the calculated value of \(P_{Cl^ - }^{CO_3^{2 - } } \) is 0.83, and the experimental value is 0.64. During electrodialysis of the working solution, which contains sodium alginate at a concentration of 1–2 g l^?1, \(P_{Cl^ - }^{CO_3^{2 - } } \) decreases by 2–3 times in the current-density range 0.25–1 A dm^?2. Pretreatment of the membrane in a solution of sodium alginate having a concentration of 10 g l^?1 for 72 h decreases \(P_{Cl^ - }^{CO_3^{2 - } } \) from 0.50 (unmodified membrane) to 0.35.     

Densities and Speeds of Sound of Binary Liquid Mixtures of 1,4-Butanediol with 2-Methoxyethanol and 2-Propoxyethanol at <Emphasis Type="Italic">T</Emphasis> = (303.15, 308.15, 313.15 and 318.15) K

Densities, ρ, and speeds of sound, u, for the binary liquid mixtures of 1,4-butanediol (1,4-BD) + 2-alkoxyethanols {2-methoxyethanol (2-ME), or 2-propoxyethanol (2-PE)} over the whole composition range have been measured at T = (303.15, 308.15, 313.15 and 318.15) K, and at atmospheric pressure (p = 0.1 kPa). Experimental data for the densities and speeds of sound have been used to derive the quantities like excess molar volume, \( V_{\text{m}}^{\text{E}} \), excess isentropic compressibility, \( \kappa_{S}^{\text{E}} \), excess molar isentropic compressibility, \( K_{{S,{\text{m}}}}^{\text{E}} \), excess speed of sound, \( u^{\text{E}} \), and excess isobaric thermal expansion \( \alpha_{p}^{\text{E}} \). These excess parameters were correlated by Redlich–Kister polynomials. Excess partial molar volumes (\( \bar{V}_{\text{m,1}}^{\text{E}} \) and \( \bar{V}_{\text{m,2}}^{\text{E}} \)) and their limiting values at infinite dilution (\( \bar{V}_{\text{m,1}}^{{ 0 {\text{E}}}} \) and \( {\bar{\text{V}}}_{\text{m,2}}^{{ 0 {\text{E}}}} \)) have been calculated from the experimental density measurements and were analytically obtained using the Redlich–Kister polynomials. The results are discussed in terms of intermolecular interactions and their dependence on composition and temperature.     

Ab initio investigation of the lower-energy candidate structures for (H<Subscript>2</Subscript>O)<Subscript>10</Subscript><Superscript>+</Superscript> water cluster

Low-lying structures of water cationic clusters and the compounds with the OH radical have become a hot topic in recent years. We here investigate the cluster \( {\left({\mathrm{H}}_2\mathrm{O}\right)}_{10}^{+} \) and calculate its ideal structures by the quantum chemical calculation together with the particle swarm optimization method. We analyzed the properties of the obtained lower-energy isomers of \( {\left({\mathrm{H}}_2\mathrm{O}\right)}_{10}^{+} \). Their energies are further re-optimized and demonstrated at three different methods with two basis sets. Based on our numerical calculations, a new cage-like structure of \( {\left({\mathrm{H}}_2\mathrm{O}\right)}_{10}^{+} \) with the lowest energy is obtained at MP2/aug-cc-pVDZ level. Our results showed the comparison of energy order at different conditions and demonstrated the influence of temperature on the relative Gibbs energy and IR spectra. Moreover, we also contained the molecule orbitals to discuss the stability of these representative isomers.     

CN (<Emphasis Type="Italic">B</Emphasis><Superscript>2</Superscript>Σ<Superscript>+</Superscript> → <Emphasis Type="Italic">X</Emphasis><Superscript>2</Superscript>Σ<Superscript>+</Superscript>) Violet System in a Cold Atmospheric-Pressure Argon Plasma Jet

\( {\text{CN}} (B^{2}\Sigma ^{ + } \to X^{2}\Sigma ^{ + } ) \) violet system was investigated using optical emission spectroscopy in a non-equilibrium microwave atmospheric-pressure plasma jet in argon expanding in air. From the analysis of the emission spectra of the discharge in the range of 380 and 400 nm, the violet system of CN was found to be overlapped with the \( {\text{N}}_{2}^{ + } \left( {B^{2}\Sigma _{u}^{ + } , v = 1 \to X^{2}\Sigma _{g}^{ + } , v = 1} \right) \) and \( {\text{N}}_{2} \left( {C^{3}\Pi _{u} \to B^{3}\Pi _{g} } \right) \) bands, sequence \( \Delta \upsilon = - \;3 \). A numerical disentangle technique, developed in this work, permitted to obtain a well resolved violet system from the different systems observed, namely the nitrogen First Negative and the Second Positive systems. The \( {\text{CN}} (B^{2}\Sigma ^{ + } \to X^{2}\Sigma ^{ + } ) \) band head intensity was determined and analysed as function of discharge powers between 30 and 150 W and fluxes between 2.5 and 10.0 slm. With aid of this numerical approach it was also possible to obtain the rotational temperature, from (1600 ± 100) to (2300 ± 100) K and vibrational temperature between (9000 ± 800) and (14,000 ± 800) K along the plasma jet. The kinetics of \( {\text{CN}} (B^{2}\Sigma ^{ + } ) \) state was analysed as well.     

Thermodynamic Study on the Protonation and Na<Superscript>+</Superscript>, Ca<Superscript>2+</Superscript>, Mg<Superscript>2+</Superscript>-Complexation of a Biodegradable Chelant (HEIDA) at Different Ionic Strengths and Temperatures

A potentiometric method has been used for the determination of the protonation constants of N-(2-hydroxyethyl)iminodiacetic acid (HEIDA or L) at various temperatures 283.15?≤?T/K?≤?383.15 and different ionic strengths of NaCl_(aq), 0.12?≤?I/mol·kg^?1?≤?4.84. Ionic strength dependence parameters were calculated using a Debye–Hückel type equation, Specific Ion Interaction Theory and Pitzer equations. Protonation constants at infinite dilution calculated by the SIT model are \( \log_{10} \left( {{}^{T}K_{1}^{\text{H}} } \right) = 8.998 \pm 0.008 \) (amino group), \( \log_{10} \left( {{}^{T}K_{2}^{\text{H}} } \right) = 2.515 \pm 0.009 \) and \( \log_{10} \left( {{}^{T}K_{3}^{\text{H}} } \right) = 1.06 \pm 0.002 \) (carboxylic groups). The formation constants of HEIDA complexes with sodium, calcium and magnesium were determined. In the first case, the formation of a weak complex species, NaL, was found and the stability constant value at infinite dilution is log₁₀K_NaL?=?0.78?±?0.23. For Ca²⁺ and Mg²⁺, the CaL, CaHL, CaL₂ and MgL species were found, respectively. The calculated stability constants for the calcium complexes at T?=?298.15 K and I?=?0.150 mol·dm^?3 are: log₁₀β_CaL?=?4.92?±?0.01, log₁₀β_CaHL?=?11.11?±?0.02 and \( \log_{10} \beta_{\text{Ca{L}}_{2}} \)?=?7.84?±?0.03, while for the magnesium complex (at I?=?0.176 mol·dm^?3): log₁₀β_MgL?=?2.928?±?0.006. Protonation thermodynamic functions have also been calculated and interpreted.     

Extending the McClelland formula for total $$\pi $$-electron energy

The McClelland formula, based on the upper bound \(\sqrt{2mn}\), is capable of reproducing over 99.5% of the total \(\pi \)-electron energy (\(E_\pi \)) of a conjugated hydrocarbon, whose molecules possess n carbon atoms and m carbon–carbon bonds. Its weak point is that it predicts equal \(E_\pi \)-values for all isomers. We now show how this failure can be overcome, offering a general strategy for extending McClelland’s formula. By means of one of these extensions, \(E_\pi \) is related with the energy of the highest occupied molecular orbital, and the error of the new formula is diminished by more than \(50\%\) relative to the standard McClelland approximation.