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.     

The Partial Molar Isothermal Compressions of the Nucleosides Adenosine,Cytidine, and Uridine in Aqueous Solution at <Emphasis Type="Italic">T</Emphasis> = (288.15 and 313.15) K

Sound speeds have been measured for aqueous solutions of the nucleosides adenosine, cytidine, and uridine at T = (288.15 and 313.15) K and at ambient pressure. The partial molar isentropic compressions at infinite dilution, \( K_{S,2}^{\text{o}} \), were derived from the speed of sound data. The partial molar heat capacities at infinite dilution, \( C_{p,2}^{\text{o}} \), for the three nucleosides at T = (288.15 and 313.15) K were also determined. These \( K_{S,2}^{\text{o}} \) and \( C_{p,2}^{\text{o}} \) results, along with partial molar isobaric expansions at infinite dilution, \( E_{2}^{\text{o}} = \, (\partial V_{2}^{\text{o}} /\partial T)_{p} \), that were derived using data from the literature, were used to evaluate the partial molar isothermal compressions at infinite dilution, \( K_{T,2}^{\text{o}} \{ K_{T,2}^{\text{o}} = - \, (\partial V_{2}^{\text{o}} /\partial p)_{T} \} \), for the nucleosides. The \( K_{T,2}^{\text{o}} \) results were rationalized in terms of nucleoside hydration and its temperature dependence.     

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.     

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.     

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.     

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 \( {\Delta_{\text{f}}^{} H}_{\text{m}}^{\text{o}} ({\text{C}}_{ 6} {\text{H}}_{ 4} {\text{NO}}_{2}^{-} \text{,aq}) = - \left( {603.2 \pm 1.2} \right)\;{\text{kJ}}{\cdot}{\text{mol}}^{-1} \).     

Physico-chemical Investigation of Mixed Micelle Formation Between Tetradecyltrimethylammonium Bromide and Dodecyltrimethylammonium Chloride in Water and Aqueous Solutions of Sodium Chloride

Conductometric measurements have been employed to gain a detailed insight into the interactions between two cationic surfactants, tetradecyltrimethylammonium bromide (TTAB) and dodecyltrimethylammonium chloride (DTAC), in water and in an aqueous solution of sodium chloride. The experimental data were analyzed according to Rubingh’s model within the framework of the pseudophase separation model. The evaluated values of critical micelle concentration (cmc) were found to be lower than their corresponding cmc ^id values, signifying attractive interactions involving both components in the solutions. The micellar mole fractions (\( X_{1}^{\text{Rub}} \)) of TTAB evaluated by Rubingh’s model were always larger than the ideal values (\( X_{1}^{\text{id}} \)), signifying the higher involvement of TTAB in mixed micelles of TTAB and DTAC. Activity coefficients (\( f_{ 1}^{\text{Rub}} \) and \( f_{ 2}^{\text{Rub}} \)) were always below one in all cases signifying synergism in the mixed micelles. All the outcomes point to synergism and attractive interactions in the mixed systems. Values of excess Gibbs energy were evaluated by employing Rubingh’s model (\( \Delta G_{\text{ex}}^{\text{Rub}} \)) and the \( \Delta G_{\text{ex}}^{\text{Rub}} \) values obtained are negative. The values of \( \Delta H_{\text{m}}^{\text{o}} \) and \( \Delta S_{\text{m}}^{\text{o}} \) reveal that hydrophobic interaction is expected to be the binding force between TTAB and DTAC in aqueous media at lower temperatures, while both hydrophobic interactions as well as exothermic interactions are involved at higher temperatures. The interaction forces between the surfactants were found to be enhanced in the presence of NaCl.     

Solvent extraction of calcium and strontium into nitrobenzene by using synergistic mixture of hydrogen dicarbollylcobaltate and diphenyl-<Emphasis Type="Italic">N</Emphasis>-butylcarbamoylmethyl phosphine oxide

Extraction of microamounts of calcium and strontium by a nitrobenzene solution of hydrogen dicarbollylcobaltate (H⁺B^?) in the presence of diphenyl-N-butylcarbamoylmethyl phosphine oxide (DPBCMPO, L) has been investigated. The equilibrium data have been explained assuming that the species HL⁺, \( {\text{HL}}_{2}^{ + } \), \( {\text{ML}}_{2}^{2 + } \), \( {\text{ML}}_{3}^{2 + } \) and \( {\text{ML}}_{4}^{2 + } \) (M²⁺ = Ca²⁺, Sr²⁺) are extracted into the organic phase. The values of extraction and stability constants of the cationic complexes in nitrobenzene saturated with water have been determined. In the considered nitrobenzene medium, it was found that the stability of the \( {\text{SrL}}_{2,{\text{org}}}^{2 + } \) complex is somewhat higher than that of species \( {\text{CaL}}_{2,{\text{org}}}^{2 + } \), while the stability constants of the remaining strontium complexes \( {\text{SrL}}_{3,{\text{org}}}^{2 + } \) and \( {\text{SrL}}_{4,{\text{org}}}^{2 + } \) are smaller than those of the corresponding complex species \( {\text{CaL}}_{n}^{2 + } \) (n = 3, 4).     

Additional Aspects of Complexation of Gold(I) with Thiomalate

Some equilibria involving gold(I) thiomalate (mercaptosuccinate, TM) complexes have been studied in the aqueous solution at 25 °C and I?=?0.2 mol·L^?1 (NaCl). In the acidic region, the oxidation of TM by \( {\text{AuCl}}_{4}^{ - } \) proceeds with the formation of sulfinic acid, and gold(III) is reduced to gold(I). The interaction of gold(I) with TM at n_TM/n_Au?≤?1 leads to the formation of highly stable cyclic polymeric complexes \( {\text{Au}}_{m} \left( {\text{TM}} \right)_{m}^{*} \) with various degrees of protonation depending on pH. In general, the results agree with the tetrameric form of this complex proposed in the literature. At n_TM/n_Au?>?1, the processes of opening the cyclic structure, depolymerization and the formation of \( {\text{Au}}\left( {\text{TM}} \right)_{2}^{*} \) occur: \( {\text{Au}}_{4} ( {\text{TM)}}_{4}^{8 - } + {\text{TM}}^{3 - } \rightleftharpoons {\text{Au}}_{ 4} ( {\text{TM)}}_{5}^{11 - } \), log₁₀ K₄₅?=?10.1?±?0.5; 0.25 \( {\text{Au}}_{4} ( {\text{TM)}}_{4}^{8 - } + {\text{TM}}^{3 - } \rightleftharpoons {\text{Au(TM)}}_{2}^{5 - } \), log₁₀ K₁₂?=?4.9?±?0.2. The standard potential of \( {\text{Au(TM)}}_{2}^{5 - } \) is \( E_{1/0}^{ \circ } = -0. 2 5 5\pm 0.0 30{\text{ V}} \). The numerous protonation processes of complexes at pH?<?7 were described with the use of effective functions.     

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 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.     

Density and Viscosity of a Ternary $$ x_{1} $$ 1-He xene(1) + $$ x_{2} $$ x2 1-Octene(2) + (1 − − x2) 1-Decene(3) Mi xture at High Temperatures and High Pressures

The density and viscosity of a ternary 1-hexene(1) + 1-octene(2) +1-decene(3) mixture (\( w_{1} = w_{2} = w_{3} = 0.333 \) weight fractions or \( x_{1} = 0.4257 \),\( x_{2} = 0.3190 \), \( x_{3} = 0.2553 \) mole fractions of 1-hexene, 1-octene, and 1-decene, respectively) have been simultaneously measured over the temperature range from (298 to 471) K and at pressures up to 196 MPa using a combined method of hydrostatic weighing and falling-body techniques, respectively. The combined expanded uncertainties of the density, pressure, temperature, concentration, and viscosity measurements at the 95% confidence level with a coverage factor of k = 2 are estimated to be (0.15 to 0.30)%, 0.05%, 0.02 K, 0.005 mol%, and (1.5 to 2.0)%, respectively. The measured densities and viscosities were used to calculate the excess molar volumes and viscosity differences. The excess molar properties (\( G_{\text{m}}^{\text{E}} , \, H_{\text{m}}^{\text{E}} , \, S_{\text{m}}^{\text{E}} \) and \( C_{\text{pm}}^{\text{E}} \)) and their pressure derivatives as a function of temperature and pressure have been calculated using the derived excess molar volumes. The measured viscosities were used to develop a theoretically based viscosity correlation model (Arrhenius–Andrade type equation) for the mixture.     

Dissociation Behavior of <Emphasis Type="SmallCaps">l</Emphasis>(+)-Lactic Acid in Aqueous Solutions of (1-Alkyl-4-methylpyridinium bromide + Poly (ethyleneglycol)) at <Emphasis Type="Italic">T</Emphasis> = (288.15–318.15) K

The effect of 1-alkyl-4-methylpyridinium based ionic liquids on the conductivity behavior of l(+)-lactic acid (LaH) was studied in Poly(ethylene glycol) (PEG) aqueous solutions. The molar conductivities of LaH in the aqueous solutions of PEG, (PEG + 1-hexyl-4-methylpyridinium bromide) and (PEG + 1-octyl-4-methylpyridinium bromide) were measured over the temperature ranges of 288.15–318.15 K. The molar conductivity data were analyzed by applying the Quint–Viallard (QV) conductivity equation to determine the limiting molar conductivities (Λ ⁰) and dissociation constants (\( K_{\text{D}} \)). The results show that the values of limiting molar conductivity increased as the temperature increased, which indicates that the dissociation process is endothermic. The \( K_{\text{D}} \) values were also used to calculate the dissociation standard thermodynamic functions (\( \Delta G_{\text{D}}^{0} \), \( \Delta S_{\text{D}}^{0} \) and \( \Delta H_{\text{D}}^{0} \)). The results revealed that the dissociation process of LaH is controlled by entropy at all temperatures.     

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.     

Imidazolium-Based Ionic Liquids Containing the Trifluoroacetate Anion: Thermodynamic Study

New experimental vapor pressures and vaporization enthalpies of the ionic liquids \( [ {\text{C}}_{2} {\text{mim][CF}}_{3} {\text{CO}}_{2} ] \) and \( [ {\text{C}}_{4} {\text{mim][CF}}_{3} {\text{CO}}_{2} ] \) have been measured by the QCM method. The solution enthalpies of these ionic liquids were measured by using high-precision solution calorimetry and were used for calculation the aqueous enthalpy of formation \( \Delta_{\text{f}} H_{\text{m}}^{ \circ } ({\text{CF}}_{ 3} {\text{CO}}_{2}^{ - } ,_{{}} {\text{aq}}) \) of the anion for combination with quantum-chemical results. The solubility parameters of the ILs under study have been derived from experimental \( \Delta_{\text{l}}^{\text{g}} H_{\text{m}}^{ \circ } \)(298.15 K) values and were used for estimation of miscibility of some common solutes with \( [ {\text{C}}_{n} {\text{mim][CF}}_{3} {\text{CO}}_{2} ] \).     

The Study of Intermolecular Interactions for <Emphasis Type="SmallCaps">dl</Emphasis>-Alanine and Glycine in Aqueous <Emphasis Type="SmallCaps">l</Emphasis>(+)-Arabinose Solutions at Different Temperatures and Ambient Pressure,Using the Volumetric Approach

Density measurements are used to calculate the apparent molar volumes V_φ, limiting apparent molar volumes \(V_{\varphi }^{0}\), limiting apparent molar volumes of transfer, \(\Delta_{\text{t}} V_{\varphi }^{0}\), limiting apparent molar expansibilities, \(E_{\varphi }^{0}\), and hydration numbers n_H, for dl-alanine and glycine in aqueous solutions of l(+)-arabinose at T?=?293.15 to 313.15 K. To obtain the limiting apparent molar volume, the V_φ values are extrapolated to zero molality using the linear form of the Redlich–Meyer equation. Also, the limiting apparent molar volumes of transfer, \(\Delta_{\text{t}} V_{\varphi }^{0}\), for the amino acids, from water to aqueous l(+)-arabinose solutions, are calculated from the \(V_{\varphi }^{0}\) values. The limiting apparent molar expansibility, \(E_{\varphi }^{0}\), values have been obtained from the first derivative of limiting apparent molar volumes with respect to temperature. Also the hydration number, n_H, for both amino acids in the ternary solutions are estimated. Possible solute–solvent interactions in the studied ternary systems are discussed.     

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.     

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.     

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.     

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.