The vanishing limit of the square-well fluid: the adhesive hard-sphere model as a reference system

We report a simulation study of the gas-liquid critical point for the square-well potential, for values of well width delta as small as 0.005 times the particle diameter sigma. For small delta, the reduced second virial coefficient at the critical point B2*c is found to depend linearly on delta. The observed weak linear dependence is not sufficient to produce any significant observable effect if the critical temperature Tc is estimated via a constant B2*c assumption, due to the highly nonlinear transformation between B2*c and Tc. This explains the previously observed validity of the law of corresponding states. The critical density rho c is also found to be constant when measured in units of the cube of the average distance between two bonded particles (1+0.5 delta)sigma. The possibility of describing the delta-->0 dependence with precise functional forms provides improved accurate estimates of the critical parameters of the adhesive hard-sphere model.     

Molecular structure of 3-aminobenzoic acid complexes with alkali metals

The vibration (FT-IR, FT-Raman), electronic (UV-Vis) and NMR (1H and 13C) spectra for 3-aminobenzoic acid and its alkali metal salts were recorded. The influence of lithium, sodium, potassium, rubidium and cesium on the electronic system of the 3-aminobenzoic acid was studied. The assignment of the vibration spectra was done. Characteristic shifts of band wavenumbers and changes in band intensities along the metal series were observed. Good correlation between the wavenumbers of the vibrational bands in the IR and Raman spectra for 3-aminobenzoates and ionic potential, electronegativity, atomic mass and affinity of metal cations were found. The chemical shifts of protons (1H NMR) and carbons (13C NMR) in the series of studied alkali metals were also observed. Optimized geometrical structures of studied compounds were calculated by ab initio and density functional methods.     

Corresponding states theory and thermodynamic properties of liquid alkali metals

According to phenomenological scaling and the law of corresponding states, reduced coordinates F ^*-T ^*, where F* represents the reduced thermodynamic properties (enthalpy of vaporization, speed of sound, surface tension, saturated liquid density) and T ^* is the reduced temperature, are introduced for the prediction of the thermodynamic properties of alkali metals. Values of the thermodynamic properties from the melting point up to boiling point are correlated. It has been shown that the correlation between reduced thermodynamic properties, as well as with the reduced temperature, can be expressed as a unique straight-line plot with a linear correlation coefficient of 0.9998. The proposed correlation has a simple form for easy calculation, requires only the melting and boiling point parameters, which are usually easy to acquire, and can predict the thermodynamic properties from the melting temperature up to the boiling temperature accurately.     

New fluorochromatouranylates of alkali metals: Synthesis and structure

Four new fluorochromatouranylates, namely, K[UO₂(CrO₄)F] · 1.5H₂O (I), Rb[UO₂(CrO₄)F] · 1.5H₂O (II), Rb[UO₂(CrO₄)F] · 0.5H₂O (III), and Cs[UO₂(CrO₄)F] · 0.5H₂O (IV), have been synthesized, and their crystallographic characteristics have been determined. All the compounds crystallize in monoclinic system, space group P2₁/c, with the unit cell parameters a = 13.1744(5) Å, b = 9.4598(3) Å, c = 13.0710(4) Å, β = 103.746(1)°, Z = 4, R = 0.0235 (I); a = 13.5902(7) Å, b = 9.5022(4) Å, c = 13.2271(6) Å, β = 102.914(2)°, Z = 4, R = 0.0247 (II); a = 24.7724(8) Å, b = 12.6671(4) Å, c = 9.4464(3) Å, β = 97.661(1)°, Z = 8, R = 0.0448 (III); a = 25.725(1) Å, b = 12.8261(5) Å, c = 9.4929(4) β = 97.208(1)°, Z = 8 (IV). The pairs of compounds I and II and compounds III and IV are isostructural. Crystals of compounds I–III have been subjected to complete X-ray diffraction study. It has been established that the structures of compounds I–III are built of [UO₂(CrO₄)F] _n ^n? layers, which are parallel to the (100) plane and linked into a framework by alkali-metal cations located between layers, together with water molecules. The effect of topological and geometric isomerism on the structural features of 34 known uranyl compounds of the AT³M² crystallochemical group, to which the studied compounds I–III also belong, is discussed.     

Alternative reference system in the thermodynamics of solid elastic electrodes

Basic quantities in the thermodynamics of the solid elastic electrode are the surface tension tensor g _mn and the work needed for the formation of the surface (interface) γ. It is scarcely mentioned explicitly anywhere that these intensive (specific) quantities are related to the surface of the elastically deformed electrode. On the other hand, in the thermodynamics of the volume elasticity, the free energy density of the deformed solid is related to the volume of the undeformed solid. In this paper, we introduce equivalently the undeformed surface of the solid elastic electrode as reference for both the surface tension tensor and the work of formation of the surface. Generalizing the analysis of two model systems, we deduce the corresponding alternative form of the Shuttleworth equation, where the two quantities appear as generalized force and generalized potential, and discuss consequences for the formulation of the differential of the surface excess of the internal energy.Dedicated to the memory of W. Schwabe     

Ionic microgels as model systems for colloids with an ultrasoft electrosteric repulsion: structure and thermodynamics

We present a theoretical analysis of the structural properties and phase behavior of spherical, loosely cross-linked ionic microgels that possess a low monomer concentration. The analysis is based on the recently derived effective interaction potential between such particles [A. R. Denton, Phys. Rev. E 67, 011804 (2003)]. By employing standard tools from the theory of the liquid state, we quantitatively analyze the pair correlations in the fluid and find anomalous behavior above the overlap concentration, similar to the cases of star-branched neutral and charged polymers. We also employ an evolutionary algorithm in order to predict the crystalline phases of the system without any a priori assumptions regarding their symmetry class. A very rich phase diagram is obtained, featuring two reentrant melting transitions and a number of unusual crystal structures. At high densities, both the Hansen-Verlet freezing criterion [J.-P. Hansen and L. Verlet, Phys. Rev. 184, 151 (1969)] and the Lindemann melting criterion [F. A. Lindemann, Phys. Z. 11, 609 (1910)] lose their validity. The topology of the phase diagram is altered when the steric interactions between the polymer segments become strong enough, in which case the lower-density reentrant melting disappears and the region of stability of the fluid is split into two disconnected domains, separated by intervening fcc and bcc regions.     

Theoretical model of the alkali metals interferences in flame emission spectrometry

The theoretical relationship between the analytical emission signal and the concentrations of the alkali metals in a sample has been formulated. The determination of potassium in the presence of sodium in the air-acetylene flame has been considered as an example. The following processes proceeding in the flame, proved to be important in the examination of interferences: ionization of K, Na and the flame components, as well as the formation of compounds between K and the species of the flame gas. The results of the calculations are in good agreement with the results obtained experimentally.A formulation of the simplified mathematical models of the interferences (matrix effect), which are of practical importance, is suggested. Only the most significant processes are taken into account in the formulation of the model. Some parameters in the model are obtained empirically by the fitting procedure.     

Influence of alkaline earth metals on molecular structure of 3-nitrobenzoic acid in comparison with alkali metals effect

The influence of beryllium, magnesium, calcium, strontium and barium cations on the electronic system of 3-nitrobenzoic acid was studied in comparison with studied earlier alkali metal ions [1]. The vibrational FT-IR (in KBr and ATR techniques) and ¹H and ¹³C NMR spectra were recorded for 3-nitrobenzoic acid and its salts. Characteristic shifts in IR and NMR spectra along 3-nitrobenzoates of divalent metal series Mg → Ba were compared with series of univalent metal Li → Cs salts. Good correlations between the wavenumbers of the vibrational bands in the IR spectra for 3-nitrobenzoates and ionic potential, electronegativity, inverse of atomic mass, atomic radius and ionization energy of metals were found for alkaline earth metals as well as for alkali metals. The density functional (DFT) hybrid method B3LYP with two basis sets: 6-311++G** and LANL2DZ were used to calculate optimized geometrical structures of studied compounds. The theoretical wavenumbers and intensities of IR spectra as well as chemical shifts in NMR spectra were obtained. Geometric aromaticity indices, atomic charges, dipole moments and energies were also calculated. The calculated parameters were compared to experimental characteristic of studied compounds.     

Liquid–liquid equilibrium calculation in binary water + nonionic surfactant CiEj systems with a new mass-action law model based on continuous thermodynamics

A systematic study of the LLE for a number of aqueous solutions of n-alkyl polyglycol ethers (C_iE_j) with tail length i from 4 to 12 and head length j from 1 to 6 is presented. For calculation a new thermodynamic model was developed basing on the mass-action law and continuous thermodynamics. Besides the micellization the self association of water is taken into account. The resulting polydisperse mixture of micelles and water associates is described by two continuous aggregation-size distribution functions depending on temperature and surfactant concentration. The Gibbs energy of the mixture is calculated by the Flory-Huggins theory with a temparature dependent parameter χ. The model is applied to 13 water + C_iE_j systems with LCST behavior and to the three systems water + C₄E₁, water + C₁₀E₄ and water + C₁₀E₅ with closed-loop miscibility gaps. For the former 13 systems four parameters were fitted to the experimental equilibrium data. For the systems with closed-loop miscibility gaps two additional parameters were necessary, due two the more extended temperature range. The agreement between calculated and experimental data is very good for nearly all systems of both types.     

Network computing: the Hartree-Fock calculation as a model

Distributed computation over local and wide-area networks is gaining importance and may soon become the primary means in high performance computing. The development in all areas of scientific computing is closely coupled with the development of efficient application software that fully utilizes the power of the modern computer resources. In numerical quantum chemistry, the adaptation of method and program development to parallel and distributed-parallel computing has shown remarkable results. The contributions of Jan Alml?f in this area of research are briefly reviewed in this paper. The integral-direct Hartree-Fock calculation (zeroth, first and second derivatives) will be used as a model to investigate network-computing techniques and paradigms. Received: 2 February 1997 / Accepted: 24 March 1997