Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.

Saturated liquid densities of cryogenic liquids and refrigerants

The saturated liquid density, varrholr, data along the liquid vapour coexistence curve published in the literature for several cryogenic liquids, hydrocarbons and halocarbon refrigerants are fitted to a generalized equation of the following form varrholr = 1 + A(1 − Tr + B(1 − Tr)β The values of β, the index in phase density differences power law, have been obtained by means of two approaches namely statistical treatment of saturated fluid phase density difference data and the existence of a maximum in T(varrho1 − varrhov) along the saturation curve. Values of the constants A and B are determined utilizing the fact that Tvarrho1 has a maximum at a characteristic temperature T. Values of A, B and β are tabulated for Ne, Ar, Kr, Xe, N2, O2, methane, ethane, propane, iso-butane, n-butane, propylene, ethylene, CO2, water, ammonia, refrigerants-11, 12, 12B1, 13, 13B1, 14, 21, 22, 23, 32, 40, 113, 114, 115, 142b, 152a, 216, 245 and azeotropes R-500, 502, 503, 504. The average error of prediction is less than 2%.

Experimental and Computational Characterization of Alloy--Spinel--Corundum Equilibrium in the System Fe--Co--Al--O at 1873K

The three-phase equilibrium between alloy, spinel solid solution and alpha -Al sub 2 O sub 3 in the Fe--Co--Al--O system at 1873k was fully characterized as a function of alloy composition using both experimental and computational methods. The equilibrium oxygen content of the liquid alloy was measured by suction sampling and inert gas fusion analysis. The O potential corresponding to the three-phase equilibrium was determined by emf measurements on a solid state galvanic cell incorporating (Y sub 2 O sub 3 )ThO sub 2 as the solid electrolyte and Cr + Cr sub 2 O sub 3 as the reference electrode. The equilibrium composition of the spinel phase formed at the interface between the alloy and alumina crucible was measured by electron probe microanalysis (EPMA). The experimental results were compared with the values computed using a thermodynamic model. The model used values for standard Gibbs energies of formation of pure end-member spinels and Gibbs energies of solution of gaseous O in liquid Fe and cobalt available in the literature. The activity--composition relationship in the spinel solid solution was computed using a cation distribution model. The variation of the activity coefficient of O with alloy composition in the Fe--Co--O system was estimated using both the quasichemical model of Jacob and Alcock and Wagner's model along with the correlations of Chiang and Chang and Kuo and Chang. The computed results of spinel composition and O potential are in excellent agreement with the experimental data. Graphs. 29 ref.--AA

Characterization of Alloy-Spinel-Corundum Equilibrium in the System Fe-Ni-Al-O

The three phase equilibrium between alloy, spinel solid solution and α-alumina in the Fe-Ni-Al-O system has been fully characterized at 1823K as a function of alloy composition using both experimental and computational methods. The oxygen potential was measured using a solid state cell incorporating yttria-doped thoria as the electrolyte and Cr+ Cr2O3 as the reference electrode. Oxygen concentration of the alloy was determined by an inert gas fusion technique. The composition of the spinel solid solution, formed at the interface between the alloy and an alumina crucible, was determined by EPMA. The variation of the oxygen concentration and potential and composition of the spinel solid solution with mole fraction of nickel in the alloy have been computed using activities in binary Fe-Ni system, free energies of formation of end member spinels FeO•(1+x)Al2O3 and NiO•(1+x)Al2O3 and free energies of solution of oxygen in liquid iron and nickel, available in the literature. Activities in the spinel solid solution were computed using a cation distribution model. The variation of the activity coefficient of oxygen with alloy composition in Fe-Ni-O system was calculated using both the quasichemical model of Jacob and Alcock and the Wagner's model, with the correlation of Chiang and Chang. The computed results for the oxygen potential and the composition of the spinel solid solution are in good agreement with the measurements. The measured oxygen concentration lies between the values computed using models of Wagner and Jacob and Alcock. The results of the study indicate that the deoxidation hyper-surface in multicomponent systems can be computed with useful accuracy using data for end member systems and thermodynamic models.

Freezing of a colloidal liquid subject to shear flow

A nonequilibrium generalization of the density-functional theory of freezing is proposed to investigate the shear-induced first-order phase transition in colloidal suspensions. It is assumed that the main effect of a steady shear is to break the symmetry of the structure factor of the liquid and that for small shear rate, the phenomenon of a shear-induced order-disorder transition may be viewed as an equilibrium phase transition. The theory predicts that the effective density at which freezing takes place increases with shear rate. The solid (which is assumed to be a bcc lattice) formed upon freezing is distorted and specifically there is less order in one plane compared with the order in the other two perpendicular planes. It is shown that there exists a critical shear rate above which the colloidal liquid does not undergo a transition to an ordered (or partially ordered) state no matter how large the density is. Conversely, above the critical shear rate an initially formed bcc solid always melts into an amorphous or liquidlike state. Several of these predictions are in qualitative agreement with the light-scattering experiments of Ackerson and Clark. The limitations as well as possible extensions of the theory are also discussed.

Volume effects and associations in liquid alloys

The regular associated solution model for binary systems has been modified by incorporating the size of the complex as an explicit variable. The thermodynamic properties of the liquid alloy and the interactions between theA ?B type of complex and the unassociated atoms in anA-B binary have been evaluated as a function of relative size of the complex using the activity coefficients at infinite dilution and activity data at one other composition in the binary. The computational procedure adopted for determining the concentration of clusters and interaction energies in the associated liquid is similar to that proposed by Lele and Rao. The analysis has been applied to the thermodynamic mixing functions of liquid Al-Ca alloys believed to contain Al2Ca associates. It is found that the size of the cluster significantly affects the interaction energies between the complex and the unassociated atoms, while the equilibrium constant and enthalpy change for the association reaction exhibit only minor variation, when the equations are fitted to experimental data. The interaction energy between unassociated free atoms remains virtually unaltered as the size of the complex is varied between extreme values. Accurate data on free energy, enthalpy, and volume of mixing at the same temperature on alloy systems with compound forming tendency would permit a rigorous test of the proposed model.

Modelling of a batch sonochemical reactor

Ultrasonication of aqueous KI solution is known to yield I2 due to reaction of iodide ions with hydroxyl radicals, which in turn are generated due to cavitation. Based on this conceptual framework, a model has been developed to predict the rate of iodine formation for KI solutions of various concentrations under different gas atmospheres. The model follows the growth and collapse of a gas-vapour cavity using the Rayleigh-Plesset bubble dynamics equation. The bubble is assumed to behave isothermally during its growth phase and a part of the collapse phase. Thereafter it is assumed to collapse adiabatically, yielding high temperatures and pressures. Thermodynamic equilibrium is assumed in the bubble at the end of collapse phase. The contents of the bubble are assumed to mix with the liquid, and the reactor contents are assumed to be well stirred. The model has been verified by conducting experiments with KI solutions of different concentrations and using different gas atmospheres. The model not only explains these results but also the existence of a maximum when Ar-O2 mixtures of different compositions are employed.

Gas-liquid nucleation at large metastability: unusual features and a new formalism

Nucleation at large metastability is still largely an unsolved problem, even though it is a problem of tremendous current interest, with wide-ranging practical value, from atmospheric research to materials science. It is now well accepted that the classical nucleation theory (CNT) fails to provide a qualitative picture and gives incorrect quantitative values for such quantities as activation-free energy barrier and supersaturation dependence of nucleation rate, especially at large metastability. In this paper, we present an alternative formalism to treat nucleation at large supersaturation by introducing an extended set of order parameters in terms of the kth largest liquid-like clusters, where k = 1 is the largest cluster in the system, k = 2 is the second largest cluster and so on. At low supersaturation, the size of the largest liquid-like cluster acts as a suitable order parameter. At large supersaturation, the free energy barrier for the largest liquid-like cluster disappears. We identify this supersaturation as the one at the onset of kinetic spinodal. The kinetic spinodal is system-size-dependent. Beyond kinetic spinodal many clusters grow simultaneously and competitively and hence the nucleation and growth become collective. In order to describe collective growth, we need to consider the full set of order parameters. We derive an analytic expression for the free energy of formation of the kth largest cluster. The expression predicts that, at large metastability (beyond kinetic spinodal), the barrier of growth for several largest liquid-like clusters disappears, and all these clusters grow simultaneously. The approach to the critical size occurs by barrierless diffusion in the cluster size space. The expression for the rate of barrier crossing predicts weaker supersaturation dependence than what is predicted by CNT at large metastability. Such a crossover behavior has indeed been observed in recent experiments (but eluded an explanation till now). In order to understand the large numerical discrepancy between simulation predictions and experimental results, we carried out a study of the dependence on the range of intermolecular interactions of both the surface tension of an equilibrium planar gas-liquid interface and the free energy barrier of nucleation. Both are found to depend significantly on the range of interaction for the Lennard-Jones potential, both in two and three dimensions. The value of surface tension and also the free energy difference between the gas and the liquid phase increase significantly and converge only when the range of interaction is extended beyond 6-7 molecular diameters. We find, with the full range of interaction potential, that the surface tension shows only a weak dependence on supersaturation, so the reason for the breakdown of CNT (with simulated values of surface tension and free energy gap) cannot be attributed to the supersaturation dependence of surface tension. This remains an unsettled issue at present because of the use of the value of surface tension obtained at coexistence.

Solubility and activity of oxygen in liquid gallium and gallium copper alloys

The solubility of oxygen in liquid gallium in the temperature range 775 –1125 °C and in liquid gallium-copper alloys at 1100 °C, in equilibrium with β-Ga2O3, has been measured by an isopiestic equilibrium technique. The solubility of oxygen in pure gallium is given by the equation log (at.% O) = −7380/T + 4.264 (±0.03) Using recently measured values for the standard free energy of formation of β-Ga2O3 and assuming that oxygen obeys Sievert's law up to the saturation limit, the standard free energy of solution of oxygen in liquid gallium may be calculated : View the MathML sourceΔ°298 = −52 680 + 6.53T (±200) cal where the standard state for dissolved oxygen is an infinitely dilute solution in which the activity is equal to atomic per cent. The effect of copper on the activity of oxygen dissolved in liquid gallium is found to be in good agreement with that predicted by a recent quasichemical model in which it was assumed that each oxygen is interstitially coordinated to four metal atoms and that the nearest neighbour metal atoms lose approximately half their metallic cohesive energies.

Solubility and activity of oxygen in liquid indium and copper indium alloys

The solubility of oxygen in liquid indium in the temperature range 650–820 °C and in liquid copper-indium alloys at 1100 °C in equilibrium with indium sesquioxide has been measured by a phase equilibration technique. The solubility of oxygen in pure indium is given by the relation log(at.% O) = −4726/T + 3.73 (±0.08) Using the recently measured values for the standard free energy of formation of In2O3 and assuming that oxygen obeys Sievert's law up to saturation, the standard free energy of solution of molecular oxygen in liquid indium is calculated as View the MathML sourceΔG°= −51 440 + 8.07 T (±500) cal where the standard state for dissolved oxygen is an infinitely dilute solution in which activity is equal to atomic per cent. The effect of indium additions on the activity coefficient of oxygen dissolved in liquid copper was measured by a solid oxide galvanic cell. The interaction parameter ϵ0In is given by View the MathML source The experimentally determined variation of the activity coefficient of oxygen in dilute solution in Cu-In alloys is in fair agreement with that predicted by a quasichemical model in which each oxygen atom is assumed to be interstitially coordinated to four metal atoms and the nearest neighbour metal atoms are assumed to lose approximately half their metallic cohesive energies.

Solubility and activity of oxygen in liquid germanium and germanium copper alloys

The solubility of oxygen in liquid germanium in the temperature range 1233 to 1397 K, and in liquid germanium-copper alloys at 1373 K, in equilibrium with GeO2 has been measured by the phase equilibration technique. The solubility of oxygen in pure germanium is given by the relation R470 log(at. pct 0)=-6470/T+4.24 (±0.07). The standard free energy of solution of oxygen in liquid germanium is calculated from the saturation solubility, and recently measured values for the free energy of formation of GeO2, assuming that oxygen obeys Sievert’s law up to the saturation limit. For the reaction, 1/2 O2(g)→ OGe ΔG° =-39,000 + 3.21T (±500) cal = -163,200 + 13.43T (±2100) J. where the standard state for dissolved oxygen is that which makes the value of activity equal to the concentration (in at. pct), in the limit, as concentration approaches zero. The effect of copper on the activity of oxygen dissolved in liquid germanium is found to be in good agreement with that predicted by a quasichemical model in which each oxygen was assumed to be bonded to four metal atoms and the nearest neighbor metal atoms to an oxygen atom are assumed to lose approximately half of their metallic bonds.

Vapor pressure of liquid metals and alloys

The Gibbs-Bogoliubov formalism in conjunction with the pseudopotential theory is applied to the calculation of the vapour pressure of eight liquid metals from Groups I to IV of the periodic table and of alloys (Na-K). The calculated vapour pressure of the elements and their temperature dependencies, the partial pressures, activities and boiling points of the alloys are all found to be in reasonable agreement with measured data.

Solubility and activity of oxygen in liquid antimony

The solubility limit of oxygen in liquid antimony has been measured by a novel isopiestic technique in the temperature range 995--1175 deg K. The results can be expressed by the equation log c = --5500/T + 3.754 ( plus/minus 0.04) with c in at.% O and T in deg K. The oxygen potential over Sb + O alloys equilibrium with Sb2O3 has been measured by a solid state cell using a fully stabilized CaO.ZrO2 electrolyte. The cell was designed to contain the Sb + Sb2O3 mixture in a closed volume, that the vaporization of the oxide can be minimized and true equilibrium attained. The Gibbs free energy of the reaction 2 Sb(s) + 3/2 O2 = Sb2O3(s) is Delta G deg = --719560 + 274.51 T( plus/minus 500) and Sb(l) + 3/2 O2 = Sb2O3(l), Delta G deg = --704711 + ( plus/minus 500) ( Delta G deg in J/mole, T in deg K). The combination of these results with Sieverts' law yields the standard free energy of solution of oxygen in liquid antimony according to the reaction 1/2 O2 = \O\Sb,at.% as Delta G deg = --129620 + 14.23 T ( plus/minus 950). The standard enthalopy and entropy of the solution of oxygen in Sb are compared with values for other metal- oyxgen systems, and with the standard enthalpies of formation of corresponding oxides. The resulting correlations permit the estimation of the standard free energy of solution of oxygen in pure metals for which experimental information is lacking. 24 ref.--AA

Solubility and activity of oxygen in liquid manganese

The oxygen concentration of liquid manganese in equilibrium with MnAl2+2xO4+3x and α−Al2O3 has been determined in the temperature range 1520 to 1875 K. The oxygen content of quenched samples, wrapped in oxygen-free nickel foil, was determined by an inert gas fusion technique. The results are combined with accurate data now available on the Gibbs energies of formation of MnO and Al2O3−saturated MnAl2+2xO4+3x to derive the oxygen content of liquid manganese in equilibrium with MnO and the Gibbs energy of solution of diatomic oxygen gas in liquid manganese. The enthalpy and entropy of solution of oxygen in manganese are compared with similar data on other metal-oxygen systems.

A galvanic sensor for SO3/SO2 based on CaF2/CaSO4 couple

Measurements on the solid state cell, View the MathML source using single crystal CaF2 as the solid electrolyte and CaSO4 as an auxiliary electrode, indicate that the EMF is in agreement with that predicted by the Nernst equation when equilibrium is assumed in the gas phase near the electrodes. The cell can be used to measure the View the MathML source content of gases at temperatures near 1200 K, where approximately 2 h ate required to obtain a steady EMF, without the use of catalysts to improve the kinetics of exchange reaction in the auxiliary electrode. For most applications, the cell EMF will be affected by the presence of water vapour in the gas phase. The cell is well suited for thermodynamic measurements on sulfates, pyrosulfates and their solid and liquid solutions.