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.     

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.     

Assessing protein–ligand binding modes with computational tools: the case of PDE4B

In a first step in the discovery of novel potent inhibitor structures for the PDE4B family with limited side effects, we present a protocol to rank newly designed molecules through the estimation of their IC\(_{50}\) values. Our protocol is based on reproducing the linear relationship between the logarithm of experimental IC\(_{50}\) values [\(\log\)(IC\(_{50}\))] and their calculated binding free energies (\(\Delta G_\mathrm{binding}\)). From 13 known PDE4B inhibitors, we show here that (1) binding free energies obtained after a docking process by AutoDock are not accurate enough to reproduce this linear relationship; (2) MM-GB/SA post-processing of molecular dynamics (MD) trajectories of the top ranked AutoDock pose improves the linear relationship; (3) by taking into account all representative structures obtained by AutoDock and by averaging MM-GB/SA computations on a series of 40 independent MD trajectories, a linear relationship between \(\log\)(IC\(_{50}\)) and the lowest \(\Delta G_\mathrm{binding}\) is achieved with \(R^2=0.944\).     

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.     

Thermal analysis of earlywood and latewood of larch (<Emphasis Type="Italic">Larix gmelinii</Emphasis> (Rupr.) Rupr.) found along the Polar tree line

This work introduces a new method of calculations depending on the essential assumptions of the kinetic methods, with the least amount of approximations to find the apparent kinetic parameters calculated for the crystallization of the Se₉₀Te₁₀ powders with heterogeneous particle sizes and shapes under non-isothermal conditions. The apparent kinetic parameters calculated by the new method are compared with that calculated blindly by applying Málek’s method, ignoring its applicability condition of invariant activation energy. The new method is based on the assumption that the kinetic function \(f\left( \alpha \right)\) parameters are independent of the heating rate \(\beta\) and time \(t\), and the fitting temperature function is assumed to be in the approximated form \(K\left( T \right) = K\left( {t,\beta } \right) = ct^{\text{r}} \beta^{\text{s}}\). The exponents \(r\) and \(s\) are calculated isoconversionally, while the constant \(c\) and the kinetic function \(f\left( \alpha \right)\) parameters are calculated by a curve fitting method using a generalized form of the ?esták and Berggren function, considering the steadily and logarithmic acceleration and deceleration of the curve. According to the data in this work, the fitting temperature function can be roughly approximated to the form \(K\left( T \right) \approx c/t\) which work in with the physical dimensions of the rate constant. Moreover, the Arrhenian and the non-Arrhenian parameters, which describe the fitting temperature function \(K\left( T \right)\), are calculated isoconversionally. The deduced parameters work harmonically together to perfectly fit the experimental and the true 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.     

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.     

Structural,Energetic, and Magnetic Properties of Ag$$_{}$$Rh$$_{m}$$m and Ag$$_{m}$$mRh$$_{}$$ Clusters with $$n \le 20$$n≤20 and $$m=0,1$$m=0,1

At first, a genetic algorithm in combination with either the parametrized density-functional tight-binding method or a Gupta-potential is used to determine the putative global minimum energy structures of mixed Ag\(_{n-m}\)Rh\(_{m}\) and Ag\(_{m}\)Rh\(_{n-m}\) clusters with \(n\le 20\) and \(m=0,1\). Subsequently, the resulting structures are re-optimized with a first-principles method. The results demonstrate that the exchange of a single silver atom by rhodium leads to compact core-shell-like structures with structural motifs well known from the Lennard-Jones system. For the systems of the present study, AgRh\(_{n-1}\) clusters retain their cube-based structural motif and the silver atoms typically avoid the corner positions within a cube if possible. Population analysis of both cluster systems shows that the total magnetic moment is mainly due to unpaired electrons on the rhodium atoms with a small ferro-magnetic contribution of the silver host in Ag\(_{n-1}\)Rh and virtually no contribution to the total magnetic moment from the single silver atom in AgRh\(_{n-1}\) clusters.     

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.     

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.     

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.     

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.     

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.     

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.     

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).     

On the dissolution state of cellulose in cold alkali solutions

We have characterized the dissolved state of microcrystalline cellulose (MCC) in cold alkali [2.0 M NaOH(aq)] solutions using a combination of small angle X-ray (SAXS) and static light scattering (SLS), \(^1\)H NMR, NMR self-diffusion, and rheology experiments. NMR and SAXS data demonstrate that the cellulose is fully molecularly dissolved. SLS, however, shows the presence of large concentration fluctuations in the solution, consistent with significant attractive cellulose-cellulose interactions. The scattering data are consistent with fractal cellulose aggregates of micrometre size having a mass fractal dimension \(D\sim 1.5\). At 25\(\,^{\circ }\mathrm {C}\) the solution structure remains unchanged on the time scale of weeks. However, upon heating the solutions above 35\(\,^{\circ }\mathrm {C}\) additional aggregation occurs on the time scale of minutes. Decreasing or increasing the NaOH concentration away from the “optimum” 2 M also leads to additional aggregation. This is seen as an increase of the SAXS intensity at lower q values. Addition of urea (1.8 and 3.6 M, respectively) does not significantly influence the solution structure. With these examples, we will discuss how scattering methods can be used to assess the quality of solvents for cellulose.     

Analytical evaluation of zero-pressure Joule–Thomson coefficient using second virial coefficient and its application

In this paper, we present an analytical procedure to evaluate the zero-pressure Joule–Thomson coefficient using the second virial coefficient over the Lennard-Jones (12-6) potential. The analytical expressions are derived for the first and second derivatives of the second virial coefficient. The proposed formulae guarantee the accurate and fast calculation of the Joule–Thomson coefficient. As an example of application, the analytical expression obtained is used to calculate results for the molecules He, Xe, \(N_2 \), \(H_2 \), \(O_2 \), \({\textit{CO}}\), \(C_2 H_4 \), \(C_3 H_8 \) and \(C_5 H_{12} \). The results obtained by the present analytical expression are found to be in good agreement with the data in the literature. The calculation of results will help to estimate the Joule–Thomson coefficient with sufficient reliability and to determine the interaction potentials.     

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.     

Solubility Thermodynamics of CyMe$$_{}$$-BTBP in Various Diluents Mixed with TBP

The two organic ligands 6,6′-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydrobenzo[1,2,4]triazin-3-yl)[2,2′]bipyridine (CyMe\(_{4}\)-BTBP) and tri-butyl phosphate (TBP) have previously been investigated in different diluents for use within recycling of used nuclear fuel through solvent extraction. The thermodynamic parameters, \(K_{\mathrm{S}}\), \(\Delta C_{p}\), \(\Delta H^{0}\) and \(\Delta S^{0}\), of the CyMe\(_{4}\)-BTBP solubility in three diluents (cyclohexanone, octanol and phenyl trifluoromethyl sulfone) mixed with TBP have been studied at 288, 298 and 308 K, both as pristine solutions and pre-equilibrated with 4 mol\(\cdot \)L\(^{-1}\) nitric acid. In addition, the amount of acid in the organic phase and density change after pre-equilibration have been measured. The solubility of CyMe\(_{4}\)-BTBP increases with an increased temperature in all systems, especially after acid pre-equilibration. This increased CyMe\(_{4}\)-BTBP solubility after pre-equilibration could be explained by acid dissolution into the solvent. Comparing the \(\Delta H^{0}\) and \(\Delta S^{0}\) calculated using \(\Delta C_{p}\) with the same parameters derived from a linear fit indicates temperature independence of all three thermodynamic systems. The change in enthalpy is positive in all solutions.