Corresponding-states correlation for the compressed liquid density of metals

Applying the previous correlation for the saturated liquid density of metals, we have developed a corresponding-states correlation for the prediction of their compressed liquid densities. The correlation needs the values of the melting and boiling point parameters of metals plus an adjustable parameter, used to predict the saturated liquid densities. In this work, we have shown that by employing the Tait equation together with the previous correlation, for saturated liquid densities, it is possible to develop an accurate method for the prediction of the compressed liquid density of metals. The agreement of the predicted density values with the experimental ones for alkali metals, mercury, bismuth, tin, and lead over a wide range of temperatures, from melting point up to several hundred degrees above the boiling point, and pressures ranging from the vapor pressure up to 4000 bar, is quite good. From 821 data points examined for the aforementioned metals the average absolute deviation for the calculated densities compared with experiment is 0.72%. The correlation is also examined against a number of existing regularities for the liquid phase.     

A perturbed hard-sphere equation of state for liquid metals

A perturbed hard-sphere equation of state, developed previously for liquid alkali metals and liquid refractory metals, has been applied for PVT calculation of some pure liquid metals including alkaline earth metals, tin, lead, antimony, bismuth, and rubidium over a wide range of temperatures and pressures. Two temperature-dependent parameters appear in the equation of state, which are universal functions of the reduced temperature, i.e. two scale parameters are sufficient to calculate the temperature-dependent parameters. The scaling parameters can be easily obtained by employing a corresponding-states principle based on a Lennard-Jones potential energy function. Employing the present equation of state, the liquid densities of aforementioned metals at temperatures ranging from the melting point to 2000?K and at pressures ranging from vapour pressure up to 40,000?bar have been calculated and compared with experimental data. The average absolute deviation in predicted densities compared with experimental data is 1.54%.     

Equation of state for molten alkali metal alloys

Results on the density of binary and ternary alkali metal alloys of Cs–K, Na–K, Na–K–Cs, at temperatures from the freezing point up to several hundred degrees above the boiling point are presented. The theoretical equation of state is that of Ihm, Song, and Mason. The second virial coefficients, B(T), are calculated by using the corresponding states correlation of Boushehri and Mason. Calculation of the other two temperature-dependent parameters, α(T) and b(T), are performed by scaling rules with the latent heat of vaporization and the freezing point density as scaling constants. The results are within 5%.     

An extended saturated liquid density equation

The recently developed saturated liquid density correlation of Iglesias-Silva and Hall for halogenated paraffins is extended to other classes of compounds involving paraffins, cycloparaffins, olefins, diolefins, cyclic-olefins, aromatics, alcohols, ethers, liquefied inorganic gases, and others. The two adjustable parameters of the correlation are optimized and reported for 126 compounds. The average error for 5377 experimental data points was 0.27%. The correlation is extended to multicomponent mixtures. A set of mixing rules is proposed. The correlation with this set of mixing rules is used to predict the saturated liquid density of 86 multicomponent systems consisting of LNG, heavy hydrocarbons, CO₂, H₂S, alcohols and halogenated paraffins. The average of error for 1378 experimental data points was 1.03% with 0 bias with respect to experimental data. These values compare well with the values from well-known correlations. For polar compounds or multicomponent systems containing polar compounds, the computation of saturated liquid density by this correlation shows superiority with respect to the other correlations.     

Calculation of Conditional Equilibrium Constants of Reactions of Reduction of Titanium,Zirconium, and Hafnium Chlorides with Alkali Metals in a Melt of Their Chlorides

Equilibrium constants of the reactions of reduction of Ti, Zr, and Hf chlorides with metallic Li, Na, K, Rb, and Cs in their molten chlorides were calculated from published data.     

Investigation of the Stable Tetrahedron of the Quaternary Reciprocal System Na,K, Cs||F,Cl

The stable tetrahedron NaF–KF–KCl–CsCl of the quaternary reciprocal system Na, K, Cs||F, Cl was experimentally investigated by differential thermal analysis. The composition and melting point of the eutectic alloy were determined. The enthalpy of melting of the eutectic alloy was experimentally studied.     

Estimation of thermal conductivity of Na–K liquid metal alloy

For the first time the thermal conductivity of Na–K alloy has been computed using eight theoretical equations, already developed for binary liquid mixtures. The thermal conductivity values of Na–K alloy were obtained at three different temperatures (308,348,423) K, and at four different compositions of alloy. We have employed density and sound speed data for calculating λ alloy with the help of recently developed correlation. Density-Sound speed-thermal conductivity correlation gave excellent results.     

Volumetric profile of polymer melts from the ISM equation of state

Knowledge of the volumetric or pressure–volume–temperature (PVT) profile of molten polymers is important for both engineering and polymer physics. Ihm–Song–Mason (ISM) equation of state (EOS) has been employed to predict the volumetric properties of 12 molten polymers. The significance of the present paper is three temperature-dependent parameters of the ISM EOS to be determined using corresponding states correlations based on the molecular scaling constants, dispersive energy parameters between segments/monomers (ε) and segment diameter (σ) rather than bulk properties, e.g. the liquid density and temperature both at normal boiling point. The ability of the ISM EOS has been evaluated by comparing the results with 1390 literature datapoints for the specific volumes over the temperature range from 293 to 603.5 K and pressure range from 0.1 to 200 MPa. The average absolute deviation (AAD) of the calculated specific volumes from literature data was found to be 0.52%. The isothermal compressibility coefficients, κ_T values of molten polymers have also been predicted using the ISM EOS. From 684 datapoints examined, the AAD of estimated κ_T was equal to 7.55%. Our calculations on the volumetric and thermodynamic properties of studied polymers reproduce the literature data with reasonably good accuracy.     

Surface tensions of inorganic multicomponent aqueous electrolyte solutions and melts

A semiempirical model is presented that predicts surface tensions (σ) of aqueous electrolyte solutions and their mixtures, for concentrations ranging from infinitely dilute solution to molten salt. The model requires, at most, only two temperature-dependent terms to represent surface tensions of either pure aqueous solutions, or aqueous or molten mixtures, over the entire composition range. A relationship was found for the coefficients of the equation σ = c(1) + c(2)T (where T (K) is temperature) for molten salts in terms of ion valency and radius, melting temperature, and salt molar volume. Hypothetical liquid surface tensions can thus be estimated for electrolytes for which there are no data, or which do not exist in molten form. Surface tensions of molten (single) salts, when extrapolated to normal temperatures, were found to be consistent with data for aqueous solutions. This allowed surface tensions of very concentrated, supersaturated, aqueous solutions to be estimated. The model has been applied to the following single electrolytes over the entire concentration range, using data for aqueous solutions over the temperature range 233-523 K, and extrapolated surface tensions of molten salts and pure liquid electrolytes: HCl, HNO(3), H(2)SO(4), NaCl, NaNO(3), Na(2)SO(4), NaHSO(4), Na(2)CO(3), NaHCO(3), NaOH, NH(4)Cl, NH(4)NO(3), (NH(4))(2)SO(4), NH(4)HCO(3), NH(4)OH, KCl, KNO(3), K(2)SO(4), K(2)CO(3), KHCO(3), KOH, CaCl(2), Ca(NO(3))(2), MgCl(2), Mg(NO(3))(2), and MgSO(4). The average absolute percentage error between calculated and experimental surface tensions is 0.80% (for 2389 data points). The model extrapolates smoothly to temperatures as low as 150 K. Also, the model successfully predicts surface tensions of ternary aqueous mixtures; the effect of salt-salt interactions in these calculations was explored.     

Theoretical investigation of the viscosity of some liquid metals and alloys

The viscosities of some liquid metals and liquid binary alloys have been determined using the theoretical model developed by Morioka et al. (Z. Metallkd. 93, 4 (2002)). The model was applied successfully to the liquid mono-component metals Hg and Na and to the liquid binary alloys Hg–Na, Ag–Cu, Bi–Sn and Ag–Sb. The model successfully described the temperature dependence of viscosity for Hg and Na for a wide range of temperatures. The values of the adjustable parameters k and z were obtained for Hg and Na. For the liquid binary alloys, calculations were done at a particular temperature for each alloy and our results show that for Hg–Na and Ag–Cu there are both qualitative and quantitative agreements between calculated and experimental viscosity data. However, Bi–Sn and Ag–Sb manifested significant levels of quantitative discrepancies between calculated and experimental viscosity data.     

Temperature dependence of electric conductivity of molten binary mixtures of alkali and rare-earth metals chlorides

The temperature dependences of the specific and molar electric conductances of CeCl₃-MCl and LnCl₃-KCl (M=Li, Na, K, and Cs; Ln=Er and Yb) molten binary mixtures of various compositions were studied. The size of the cations of alkali and rare-earth metals was demonstrated to affect the intensity of the interactions of the components of the systems. Deviations of the molar conductance isotherms from additivity and dependence of the isotherms on the ratio between the mixture components were explained by the formation of complexes in the melts.     

Accurate viscosity modeling of liquid metals based on friction theory and PC-SAFT equation of state

Values of the viscosities of liquid metals are important in the prediction of fluid flow in many metallurgical manufacturing processes. In this work the friction theory (f-theory) for viscosity modeling is used in conjunction with PC-SAFT equation of state for describing the viscosity behavior of liquid metals (Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Hg, In, Ag, Ni, Au, Al). This f-theory model has been shown to provide satisfactory results for the modeling of the viscosity of liquid metals over wide range of temperature. The average deviation is 1.10%.     

Vapor–liquid equilibrium of carbon dioxide with diethyl methylmalonate,diethyl ethylmalonate and diethyl n-butylmalonate at elevated pressures

Vapor–liquid equilibrium (VLE) data for binary mixtures of CO₂ with homologous esters of diethyl methylmalonate, diethyl ethylmalonate, and diethyl n-butylmalonate at 308.2, 318.2, and 328.2 K, respectively, over the pressure range 1.4–8.4 MPa were measured using a semi-flow apparatus. New gas solubility data for CO₂ in esters are presented, and the Henry’s law constants for CO₂ in these esters are evaluated by employing the Krichevsky–Ilinskaya (KI) equation. The VLE data were also correlated using the Soave–Redlich–Kwong and the Peng–Robinson equations of state (EOSs) with various types of mixing rules. It is shown that EOS with both the van der Waals mixing rules and the two adjustable parameters yield satisfactory correlation results.     

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.     

Vapor–liquid equilibria of the binary mixtures formed by nitromethane with five alkyl alkanoates at 101.3 kPa

Vapor–liquid equilibria were measured at 101.3 kPa, in a range of temperatures from 350.28 to 374.69 K, for five binary mixtures formed by nitromethane with ethyl acetate, propyl acetate, isopropyl acetate, methyl propionate, and ethyl propionate. Calculations of nonideality of the vapor phase were made with Soave–Redlich–Kwong equation of state. Thermodynamic consistency of data was tested via Herington analysis. Two systems show minimum boiling azeotropes. The experimental VLE data were reduced and binary parameters for four liquid models, such as van Laar, Wilson, NRTL and UNIQUAC, were fitted. A comparison of model performances was made by using the criterion of average absolute deviations in boiling point and in vapor-phase composition.     

Surface Tension of Liquid Organic Acids: An Artificial Neural Network Model

An artificial neural network model is proposed for the surface tension of liquid organic fatty acids covering a wide temperature range. A set of 2051 data collected for 98 acids (including carboxylic, aliphatic, and polyfunctional) was considered for the training, testing, and prediction of the resulting network model. Different architectures were explored, with the final choice giving the best results, in which the input layer has the reduced temperature (temperature divided by the critical point temperature), boiling temperature, and acentric factor as an independent variable, a 41-neuron hidden layer, and an output layer consisting of one neuron. The overall absolute percentage deviation is 1.33%, and the maximum percentage deviation is 14.53%. These results constitute a major improvement over the accuracy obtained using corresponding-states correlations from the literature.     

Preparation of high purity alkali metals by near melting point segregation

Pure alkali metal preparation is a complex problem: in most available commercial samples, all of them are simultaneously present. Conventional separation techniques are not always effective enough to reach parts per million total impurity levels. However, near the melting point, superficial segregation occurs. A zone melting derived technique coupled with a specifically developed solvent extraction process allows the total impurity content of sodium to be lowered below a few parts per million. The described thermal process, although using chemical reactions, is purely physically steered: it purifies as well potassium containing sodium as sodium containing potassium. 4 alkali metals are considered: Li, Na; K, and Cs.     

Surface tension of pure liquid lanthanide and early actinide metals

A systematic theoretical study of the surface tension of liquid rare earth metals and early actinides is performed. An equation, based on the theoretical considerations suggested by Eyring, enables one to calculate the surface tension of elementary substances in a wide temperature range from melting to boiling points. The results of temperature-dependent surface tension calculations of a pure liquid terbium (1629–1880?K) are fitted as γ?=?845?0.1 (T???T _m) (mJ?m²), where the surface tension decreases linearly with temperature. The surface tension was also calculated, at melting points, for all the liquid rare earth metals from La to Lu and for the first six metals of the actinide series from Ac to Pu. It is observed that the lanthanides may be divided into three groups in accordance with their electronic structure. Mostly, the calculated results agree well with available experimental data.     

Determination of alkali metals in control and AD brain samples by different techniques

Several metals are suspected or known to be involved in neurological disorders such as Alzheimer's disease (AD), therefore, elemental distribution studies have received intense attention for years. The present work focuses on a group of lesser studied elements in this context, alkali metals.Previously, an adequate neutron activation analysis (NAA) method has been developed and applied successfully for the determination of Na, K, Rb and Cs in brain samples of control subjects. This work has been extended to include AD patients, so that average values, distribution patterns and interpersonal variability could be compared and possible correlation between control and AD data could be studied.Despite the merits of the technique, its drawbacks are evident. Therefore, applicability of rapid spectrochemical methods as alternatives has been investigated. ICP-AES has been used for analysis of Li, Na and K. No interferences were observed, but ultrasonic nebulisation was needed for Li quantification. Rb and Cs were measured by ICP-MS with In as internal standard. Agreement between different techniques is found to be good for Na, K and Rb, while Cs values show somewhat higher differences.     

Solubility of nitrogen and ethylene in molten,low-density polyethylene to 69 atmospheres

Statistical mechanical correlations of ethylene and nitrogen solubility in molten, low-density polyethylene at several temperatures and at pressures to 69 atm are presented. The solubilities are taken from data previously published by us and by other workers. The data are modeled with a corresponding-states solution analysis applicable to mixtures of high-and low-density fluids. The model is based on a simple variation of the Flory and Prigogine corresponding-states theories. Gas sorption data are modeled well within experimental precision.