Volumetric Investigations on Molecular Interactions of Glycine/<Emphasis Type="SmallCaps">l</Emphasis>-alanine in Aqueous Citric Acid Solutions at Different Temperatures

Apparent molar volumes \((\phi_{V})\) of glycine/l-alanine in water and in aqueous citric acid (CA) solutions of varying concentrations, i.e. (0.05, 0.10, 0.20, 0.30, 0.40 and 0.50) mol·kg^?1 were determined from density measurements at temperatures T?=?(288.15, 298.15, 308.15, 310.15 and 318.15) K and at atmospheric pressure. Limiting partial molar volumes \((\phi_V^{\text{o}})\) and their corresponding partial molar volumes of transfer \((\Delta_{\text{tr}} \phi_{V} )\) have been calculated from the \(\phi_{V}\) data. The negative \(\Delta_{\text{tr}} \phi_{V}\) values obtained for glycine/l-alanine from water to aqueous CA solutions indicate the dominance of hydrophilic–hydrophobic/hydrophobic–hydrophilic and hydrophobic–hydrophobic interactions over ion/hydrophilic–dipolar interactions. Further, pair and triplet interaction coefficients, i.e. \((V_{\text{AB}} )\;{\text{and}}\; (V_{\text{ABB}} )\) along with hydration number \((n_{\text{H}} )\) have also been calculated. The effect of temperature on the volumetric properties of glycine/l-alanine in water and in aqueous CA solutions has been determined from the limiting partial molar expansibilities \((\partial \phi_{V}^{\text{o}} /\partial T)_{p}\) and their second-order derivative \((\partial^{2} \phi_{V}^{\text{o}} /\partial T^{2} )_{{P}}\). The apparent specific volumes \((\nu_{\phi} )\) for glycine and l-alanine tend to approach sweet taste behavior both in the presence of water and in aqueous CA solutions. The \(\nu_{\phi}\) values for glycine/l-alanine increase with increase in concentration of CA at all temperatures studied. This reveals that CA helps in enhancing the sweet taste behavior of glycine/l-alanine which also supports the dominance of hydrophobic–hydrophobic interactions.     

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 \((\chi_{{{ \exp } .}} )\).     

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.     

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.     

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.     

On the origins of intersecting potential energy surfaces

Techniques developed for investigating nonadiabatic processes in molecular systems are adapted to study the structure and properties of holomorphic and meromorphic functions of a complex variable, \(f(z)=\mathfrak {R}(f)+i\,\mathfrak {I}(f)\). The connection is that \(\mathfrak {R}(f)\) and \(\mathfrak {I}(f)\) are correlated two-dimensional scalar functions, interrelated by the Cauchy–Riemann equations. Exploiting this fact, it is demonstrated that \(\mathfrak {R}(f)\) and \(\mathfrak {I}(f)\) of f can be envisaged in Euclidean \({\mathbb {R}}^{3}\) space as a two-state set of constrained, intersecting two-dimensional potential energy surfaces (PESs), called the graph of f. Importantly, the analytic and algebraic properties of f dictate the geometric structure evinced in the graph of f. This parallels multi-state sets of higher-dimensional, constrained, intersecting PESs linked with correlated electronic eigenstates of the parameterized molecular Hamiltonian operator. In view of this association, the language and mathematical infrastructure devised by chemists for discussing and analyzing intersections in higher-dimensional PESs are suitably modified for f. Notably, an algorithm capable of optimizing roots and poles of f through analysis of the real, two-dimensional \(\mathfrak {R}(f)\) and \(\mathfrak {I}(f)\) functions is derived, which is based on intersection-adapted coordinate and constrained Lagrangian methodologies. As constrained, intersecting PESs are indispensible for conceptualizing and characterizing the physics governing nonadiabatic phenomena, f represents a foundational bridge to these more abstract constructions.     

Blinded predictions of distribution coefficients in the SAMPL5 challenge

In the context of the SAMPL5 challenge water-cyclohexane distribution coefficients for 53 drug-like molecules were predicted. Four different models based on molecular dynamics free energy calculations were tested. All models initially assumed only one chemical state present in aqueous or organic phases. Model A is based on results from an alchemical annihilation scheme; model B adds a long range correction for the Lennard Jones potentials to model A; model C adds charging free energy corrections; model D applies the charging correction from model C to ionizable species only. Model A and B perform better in terms of mean-unsigned error (\(\hbox {MUE}=6.79<6.87<6.95 \log\) D units ? 95 % confidence interval) and determination coefficient \((\hbox {R}^2 = 0.26< 0.27< 0.28)\), while charging corrections lead to poorer results with model D (\(\hbox {MUE}=12.8<12.63<12.98\) and \(\hbox {R}^2 = 0.16<0.17<0.18\)). Because overall errors were large, a retrospective analysis that allowed co-existence of ionisable and neutral species of a molecule in aqueous phase was investigated. This considerably reduced systematic errors (\(\hbox {MUE}=1.87<1.97<2.07\) and \(\hbox {R}^2 = 0.35<0.40<0.45\)). Overall accurate \(\log D\) predictions for drug-like molecules that may adopt multiple tautomers and charge states proved difficult, indicating a need for methodological advances to enable satisfactory treatment by explicit-solvent molecular simulations.     

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.     

Interaction Between an Active Pharmaceutical Ingredient Ionic Liquid Benzalkonium Salicylate and Small Biomolecules in Aqueous Solution: UV Absorption,Conductivity, and Volumetric Study

UV absorption spectroscopy, electrical conductivity and density experiments have been used to investigate the interactions of some small biomolecules (amino acids/dipeptides) with an active pharmaceutical ingredient in ionic liquid form (API-IL), benzalkonium salicylate (BaSal), in aqueous solution. A number of useful parameters, such as critical micellar concentration (cmc), aggregation number (N_agg) and limiting molar conductivity (Λ₀) of BaSal, standard partial molar volumes (\(V_{2,\phi }^{ \circ }\)), corresponding volumes of transfer from water to aqueous BaSal solutions (Δ_trV^o), standard partial molar expansibilities (\(E_{\phi }^{ \circ }\)), hydration number (n_H) of small biomolecules, as well as the binding constants (K_b) for small biomolecule–BaSal complexes have been evaluated. The dependence of the properties on concentration, temperature and alkyl chain length of amino acids/dipeptides is examined. The results are used to identify the solute–solvent physicochemical interactions occurring in the studied systems.     

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.     

Aromaticity of Bare Iridium Trimers and Ir3M0/+ and $$\rm{Ir}_3M_2^{+/3+}$$ (M = Li,Na, K,and Be,Ca) Bimetallic Clusters

The structural stabilities, bonding nature, electronic properties, and aromaticity of bare iridium trimers \(\rm{Ir}_3^{+/-}\) with different geometries and spin multiplicities are studied at the DFT/B3LYP level of theory. The ground state of the \(\rm{Ir}_3^{+}\) cation is found to be the ³A₂ (C_2v) triplet state and the ground state of the \(\rm{Ir}_3^{-}\) anion the ⁵A₂ (C_2v) quintet state. A detailed molecular orbital (MO) analysis indicates that the ground-state \(\rm{Ir}_3^{+}\) ion (C_2v, ³A₂) possesses double (σ and partial δ) aromaticity as well as the ground-state \(\rm{Ir}_3^{-}\) ion (C_2v, ⁵A₂). The multiple d-orbital aromaticity is responsible for the totally delocalized three-center metal-metal bond of the triangular Ir₃ framework. \(\rm{Ir}_3^{-}\) (C_2v, ¹A₁) structure motif is perfectly preserved in pyramidal Ir₃M^0/+ (C_s, ¹A′) and bipyramidal \(\rm{Ir}_3M_2^{+/3+}\) (C_2v, ¹A₁) (M = Li, Na, K and Be, Ca) bimetallic clusters which also possess the corresponding d-orbital aromatic characters.     

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

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.     

Energy Conversion Efficiency in Low- and Atmospheric-Pressure Plasma Polymerization Processes,Part II: HMDSO

For at least forty years, there has been an interest to correlate the structure of plasma polymer coatings with fabrication parameters during deposition, most particularly with the energy input per monomer molecule, \( E_{\text{m}} \). In our two laboratories, we have developed methods for measuring \( E_{\text{m}} \) (or somewhat equivalent activation energy, \( E_{\text{a}} \)) in low- (LP) and atmospheric-pressure (AP) discharge plasmas. We earlier proposed energy conversion efficiency, ECE, as a new parameter which permits direct comparison of LP and AP experiments. This is done here for the case of a much-studied organosilicon precursor (monomer), hexamethyl-disiloxane. “Critical” \( E_{\text{m}} \) (or \( E_{\text{a}} \)) values that demarcate ECE regimes separating different fragmentation/reaction mechanisms are found to agree remarkably well, and to correlate with specific mechanisms. Furthermore, deposition rates, and structural (for example, “organic/inorganic” content ratio) characteristics are seen to display very similar behaviors, despite additional drastically differing fabrication conditions like pure or highly diluted (in Ar carrier gas) monomer feed in the LP and AP cases, respectively.     

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.     

Measurement and Calculation the Excess Molar Properties of Binary Mixtures Containing Isobutanol, 1-Amino-2-Propanol,and 1-Propanol at Temperatures of (293.15 to 333.15) K

Densities, ρ, and viscosities, η, of pure isobutanol, 1-amino-2-propanol, and 1-propanol, along with their binary mixtures of {x ₁isobutanol + x ₂1-propanol}, {x ₁1-amino-2-propanol + x ₂1-propanol}, and {x ₁1-amino-2-propanol + x ₂isobutanol} were measured over the entire composition range and at temperatures (293.15–333.15) K at ambient pressure (81.5 kPa). Excess molar properties such as the excess molar volume, V _m ^E , partial molar volumes, \( \bar{V}_{1} \) and \( \bar{V}_{2} \), excess partial molar volumes, \( \bar{V}_{1}^{\text{E}} \) and \( \bar{V}_{2}^{\text{E}} \), thermal expansion coefficient, α, excess thermal expansion coefficient, α ^E, viscosity deviation, Δη, and the excess Gibbs energy of activation, ?G ^E*, for the binary mixtures were calculated from the experimental values of densities and viscosities. The excess values of the binary mixtures are negative in the entire composition range and at all temperatures, and increase with increasing temperature. Viscosity deviations, Δη, are negative over the entire composition range and decrease with increasing temperature. The viscosities of the mixtures were correlated by the models of McAllister, Heric, Hind, Katti, and Nissan. The obtained data were correlated by Redlich–Kister equation and the fitting parameters and standard deviations were determined.     

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 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.     

On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)

In our recent works (R. Szmytkowski, J. Phys. A 39:15147, 2006; corrigendum: 40:7819, 2007; addendum: 40:14887, 2007), we have investigated the derivative of the Legendre function of the first kind, P _ν(z), with respect to its degree ν. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, \({P_{\nu}^{\pm m}(z)}\), with respect to the degree ν, for \({m \in \mathbb{N}}\). At first, we establish several contour-integral representations of \({\partial P_{\nu}^{\pm m}(z)/\partial\nu}\). They are then used to derive Rodrigues-type formulas for \({[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}}\) with \({n \in \mathbb{N}}\). Next, some closed-form expressions for \({[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}}\) are obtained. These results are applied to find several representations, both explicit and of the Rodrigues type, for the associated Legendre function of the second kind of integer degree and order, \({Q_{n}^{\pm m}(z)}\); the explicit representations are suitable for use for numerical purposes in various regions of the complex z-plane. Finally, the derivatives \({[\partial^{2}P_{\nu}^{m}(z)/\partial\nu^{2}]_{\nu=n}, [\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=n}}\) and \({[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=-n-1}}\), all with m > n, are evaluated in terms of \({[\partial P_{\nu}^{-m}(\pm z)/\partial\nu]_{\nu=n}}\). The present paper is a complementary to a recent one (R. Szmytkowski, J. Math. Chem 46:231, 2009), in which the derivative \({\partial P_{n}^{\mu}(z)/\partial\mu}\) has been investigated.