Revision of a multiparameter equation of state to improve the representation in the critical region: application to water

We have developed a crossover formalism for the thermodynamic surface of pure fluids, which can be applied to any multiparameter equation of state. This procedure has been used to incorporate scaling law behavior into a representation of the thermodynamic properties of water and steam developed by Pruss and Wagner (PW EOS) and adopted recently by the International Association for the Properties of Water and Steam. Our revision to this equation retains most of the functional form and coefficients of the PW EOS, but replaces two of the terms with a crossover representation of scaling law behavior. In order to develop this model, we first developed a new crossover formulation for steam in the critical region, and second, we have incorporated universal crossover functions into the original PW EOS. In the modified form, the PW equation of state reproduces the scaling laws down to dimensionless temperatures τ=10⁻⁷. Far from the critical point the equations practically coincide.     

A nonparametric scaling equation of state for liquids

A new nonparametric scaling equation of state is suggested. The equation correctly describes the p-ρ-T data and heat capacities of liquids close to the critical vaporization points. It was obtained with the use of the S spinodal and the mixing of scaling fields as a first approximation (asymmetric and nonasymptotic terms were ignored). The new equation was used to approximate the data on ⁴He, C₂H₄, and H₂O in the critical region. The results showed that it correctly described the critical behavior of thermodynamic functions, including isochoric heat capacity, not only in the asymptotic but also over a fairly wide density region at the critical point. The suggested equation of state describes the p-ρ-T data with the same error as the Schofield parametric equation of state. The new equation, however, better reproduces the behavior of heat capacities and is much simpler to use. As distinct from the Schofield equation, the new equation, like classic equations of state, allows the spinodal to be determined from the (?p/?v) _T = 0 condition at T < T _c .     

Modeling phase equilibria of alkanols with the simplified PC-SAFT equation of state and generalized pure compound parameters

The simplified PC-SAFT equation of state has been applied to liquid–liquid, vapor–liquid and solid–liquid equilibria for mixtures containing 1- or 2-alkanols with alkanes, aromatic hydrocarbons, CO₂ and water. For the alkanols we use generalized pure compound parameters. This means that two of the physical pure compound parameters, m (segment number) and σ (segment diameter), are obtained from linear extrapolations, since m and mσ³, increase linearly with respect to the molar mass, and moreover, the two association parameters (association energy and association volume) were assumed to be constant for all alkanols. Only the dispersion energy is fitted to experimental data. Thus it is possible to estimate parameters for several 1- and 2-alkanols. The final aim is to develop a group contribution approach for PC-SAFT which is suitable for complex compounds, considering that the motivation of this project is to obtain a thermodynamic model which can be used in the development of sophisticated products such as pharmaceuticals, polymers, detergents or food ingredients. One of the severe limitations in applying SAFT-type equations of state to these compounds is that the procedure for obtaining the pure compound parameters is usually based on fitting to saturated vapor pressure and liquid density data over an extended temperature range. However, such data are rarely available for complex compounds. To verify the new pure compound parameters, comparisons to ordinary optimized alkanol parameters, where all five pure compound parameters were fitted to experimental liquid density and vapor pressure data, were made. The results show that the new generalized alkanol parameters from this work perform at least as well as other alkanol parameter sets.     

Quenching of singlet oxygen by hindered amine light stabilisers. A flash photolytic study

Rate constants for the quenching of singlet oxygen (¹O₂, ¹δ_g) for a series of piperidines, piperidine-N-oxyl free radicals and some commercially used hindered amine light stabilisers (HALS) have been measured by a laser flash photolysis method. Quenching rate constants are in the order: piperidine-N-oxyl free radicals ≤ secondary piperidines < tertiary piperidines. For some commercial HALS, ¹O₂ quenching rate constants and the light protective effect towards polypropylene photo-oxidation have been compared. No correlation has been found between the stabilizing action and the quenching efficiency towards ¹O₂. The data obtained point to little contribution of singlet oxygen to the key steps of polyolefin photo-oxidation.     

Correlation for prediction of interfacial tensions of pure alkane,naphthenic and aromatic compounds between their freezing and critical points

A simple equation has been developed for predicting the interfacial tensions of pure alkanes, aliphatic and aromatic hydrocarbons between their freezing and critical points. The equation has the form

and represents the interfacial tension using a generalized correlation developed by Sivaraman et al. (1984) for predicting the latent heats of vaporization of normal fluids and coal-liquid model compounds. Here σ^* is the reduced dimensionless interfacial tension, and L^*₍₀₎ and L^*₍₁₎ are the reduced dimensionless latent heats of vaporization; A and N are system-independent constants. Subsequent tests of this correlation in predicting interfacial tension over a broad domain of reduced temperatures for a large number of different types of compounds have confirmed the validity of our approach. The percentage deviations in interfacial tension are in the range? 3.87 to 5.99 in the range of reduced temperatures 0.03 < ? = (T_c ? T)/T_c < 0.55.     

The diffusion of oxygen and ion transport in lanthanum cobaltite LaCoO<Subscript>3-δ</Subscript>

The chemical diffusion coefficient of oxygen vacancies and oxygen ion conductivity in lanthanum cobaltite LaCoO₃ were determined by the polarization method as functions of oxygen partial pressure \(p_{O_2 } \) (atm) and temperature T(K) over the ranges ?4 ≤ log \(p_{O_2 } \) ≤ 0 and 1173 K ≤ T ≤ 1323 K. The mobilities (cm²/(V s)) of oxygen vacancies calculated over the temperature range studied satisfy the inequalities 1.8 × 10^?5 ≤ \(v_{v_0 } \) ≤ 3.4 × 10^?5. The transfer numbers of oxygen vacancies were calculated. These numbers change depending on oxygen partial pressure over the range 5 × 10^?7 ≤ t ₀ ≤ 1 × 10^?5. The activation energy of self-diffusion of oxygen vacancies was found to be E _a= 104 ± 10 kJ/mol (1.1 ± 0.1 eV).     

Rubber elasticity in the range of small uniaxial tensions and compressions. Results for poly(dimethylsiloxane)

Results of uniaxial tension and compression experiments are reported on crosslinked polydimethylsiloxane (PDMS) networks in the unswollen state over the range 0.5 < α^?1 < 1.2 where α is the extension ratio. Curves representing the reduced force [f] = f(V⁰/V)^1/3(α – α^?2)^?1 plotted against α^?1 can be approximated by straight lines for 0.5 < α^?1 < 0.9, in agreement with the phenomenological Mooney equation. As α^?1 approaches 1, however, they tend to level off and continue into the α^?1 > 1 region with decreasing slope. These results are in agreement with the predictions of recent elasticity theories that incorporate the effect of junction-chain entanglements in the elastic free energy.     

Mass and Ion Transport in Ketones and Ketone Electrolytes: Comparison with Acetate Systems

Self-diffusion coefficient measurements were performed for pure n-alkyl ketone liquids using the pulsed field gradient NMR spin-echo technique. Ionic conductivities and dielectric constants of 0.0055 mol·L^?1 tetrabutylammonium trifluoromethanesulfonate in 2-pentanone, 2-hexanone, 2-heptanone, 2-octanone, 2-nonanone, and 2-decanone were also measured. The temperature-dependent conductivities and diffusion coefficients over the range 5–80 °C can be described using the compensated Arrhenius formalism. Compensated Arrhenius equation plots were used to calculate the average activation energy for both sets of data. The average activation energy from conductivity data is approximately equal to that from diffusion data. The data for the pure ketones and ketone-based electrolytes are compared with analogous data for pure n-alkyl acetates and n-alkyl acetate-based electrolytes.     

Equation of state molecular parameters for a theory of pure r-mer fluids in the liquid phase

Costas, M. and Sanctuary, B.C., 1984. Equation of state molecular parameters for a theory of pure r-mer fluids in the liquid phase. Fluid Phase Equilibria, 18: 47–60.Equation of state parameters for a theory of pure r-mers (Costas and Sanctuary, 1981) are presented for sixty common substances. The equation of state is tested for its ability to reproduce and predict thermodynamic data in the liquid phase. The theory has only two adjustable parameters: ν^*, the close-packed volume of the r-mer, and ?^* = z?/2, where ? is the nonbonded mer-mer attractive interaction energy and z is the lattice coordination number, set to be a constant equal to 12. The number of r-mers per molecule, r, is also fixed for a given liquid to be equal to the number of atoms in the molecule other than hydrogen. The fitting proceduce is fast and simple. The adjustment only involves the use of widely available density data. Comparisons between experimental and calculated first- and second-order thermodynamic properties are shown for several substances. A comparison with the equation of state due to Jain and Simha (1981) for PVT data for n-dodecane is presented. The theory qualifies as a useful tool, especially in engineering applications, for estimating thermodynamic properties in the liquid phase.     

Generalized theory of capillarity for axisymmetric menisci

A high-curvature generalization of the Laplace equation of capillarity and the Young equation of capillarity (including line tension) is developed for an axisymmetric solid-liquid-fluid system. The most general expressions for the Laplace and Young equations do not assume a particular form for the specific surface free energy. However, when a particular form, i.e., ω^(A) = γ^(A)_∞+ C_JJ+ C_kK, which is related to Gibbs' expression for a highly curved menisci,¹ is assumed to hold for the specific surface free energy then we are able to recover the expected simplified form of the Laplace equation. The corresponding high-curvature Young equation includes a couple which balances the surface moments at the contact line. Unfortunately, the effect of this couple could be confused with the effect of line tension in experiments which attempt to measure the dependence of the contact angle on the contact line radius.     

Electron stimulated desorption: A critical review

A critical review of the literature in the field of electron stimulated desorption is presented. The material is covered through December 1976. The literature on electron-induced ion desorption using bombarding electrons with energy <200 eV has been reviewed in detail several times. This review, therefore, concentrates on electron-induced desorption of ground state and excited state neutrals and the effect of electron bombarding energy in the energy range above several hundred eV. There is general agreement that ESD involves the direct interaction of the bombarding electron with the adsorbed species. Electronic transitions to anti-bonding modes result in the desorption of neutrals, excited state and ionic species. The cross sections are atomic in nature and vary from 10^-15 cm² to <10^-20 cm². The interactions and cross sections are relatively independent of the substrate material. The largest cross sections occur for weakly bound molecular species. Although there is agreement on the qualitative character of the interaction, there is very poor agreement on the quantitative cross section values. Very little information exists at all on direct measurements of neutral desorption and the effect of bombarding electron energy in the energy range above 500 eV.The material on neutral desorption is divided into three parts, namely experiments involving total pressure measurements, partial pressure measurements, and detection of desorbing excited state neutrals. The following section considers high energy data, independent of type of desorbing particle. Finally, new data concerning ion angular distributions in ESD is discussed.     

An equation of state for gases and liquids

We present an equation of state that can represent within experimental error most individual sets of published PVT data for most fluids, whether in the range of vapor at moderate pressures, or compressed liquids, or gases at very high temperatures and densities, any region in fact except the vicinity of the critical point. In terms of pressure the equation is P = DRT [1 + (D/T) (c₁T + c₂D - 1) / (c₃ + c₄T^{$\text{sol1}\text{2}$} + c₅D + c₆D²)] where D = 1/V, the density in mole 1^?1. The coefficients are readily determined by a least squares fit of the data. An additional term is sometimes needed if the D range is very wide, say several times D_c. Different fluids can be simultaneously represented over a limited range, such as the compressed liquid region, by a single reduced form of the equation in which all but three of the constants are the same for all, and these three (a reducing T, 1/c₁, a reducing D, 1 / c₂, and a dimensionless parameter) are characteristic of each individual fluid. The equation can also simultaneously represent many data sets for a single fluid from many labs and covering various T and D ranges. From this, a consistent representation of its thermodynamic properties can be derived.     

Quintic equation of state for pure substances in sub- and supercritical range

A new quintic equation of state (EOS) for pure substances and mixtures is proposed. The equation is based on critical parameters and one saturation point. The proposed Q5EOS is a generalisation of many cubic equations of state. Equation Q5 has five parameters, four of which are temperature-independent. The temperature-dependent parameter a is expressed by a relation based on a simple power function. Parameters defining this function can be calculated from saturation data, Boyle temperature and supercritical data.     

Structural changes induced by energetic heavy-ion bombardment in BaFe12O19: HREM investigation for low irradiation doses

Monocrystalline and polycrystalline samples of hexaferrite BaFe₁₂O₁₉ irradiated with argon and krypton ion beams of 44 and 35 MeV per nucleon, respectively, have been investigated by HREM for doses close to 2 × 10¹³ and 2 × 10¹² ions · cm⁻². Electron microscopy examinations of the samples placed in the low energy range (0 ≤ E < 0.6 GeV for Ar and 0 ≤ E < 0.9 GeV for Kr) show several characteristic, morphologic, and crystallographic features involving numerous fractures, important bendings of the crystals, and extensive disorder leading to the loss of periodicity in the c direction. Typical induced defects have been observed and are believed to be associated with displacement cascades created by the primary ejected ions.     

A new equation of state for polar and nonpolar pure fluids

Chung, T.H., Khan, M.M., Lee, L.L. and Starling, K.E., 1984. A new equation of state for polar and nonpolar pure fluids. Fluid Phase Equilibria, 17: 351–372A new equation of state based on the concept of perturbation theory and the hard-convex-body equation of state has been developed successfully for nonpolar compounds. The equation can predict the thermodynamic properties (density, enthalpy departure and vapor pressure) of a wide range of pure fluids from small, spherical (argon-like) molecules to large, structurally complex molecules. For nonpolar compounds, the equation employs three parameters: the shape, size and energy parameters. For normal paraffins, the size parameter (hard-core volume) is related to the measurable van der Waals volume given by Bondi. For most other compounds, it is related to the critical volume. The shape-parameter values reflect the structure and degree of acentricity of the compound of interest. The equation has been extended to polar and associating compounds by using the mean-potential model. For polar compounds, a fourth parameter is required. The equation has been tested extensively for polar (dipolar and quadrupolar) and hydrogen-bonding compounds. The applicability of this equation for such a wide variety of substances provides an important first step in the development of a composition-dependent equation of state for mixtures.     

Preparation and properties of La1−xCaxCoO3 (0,2 ≤ x ≤ 0,6)

The preparatory conditions for the oxide compositions La_1?xCa_xCoO_3?δ have been determined along with their crystallographic, thermochemical, and electrical properties. Single phase solid solutions of the perovskite structure form atx < 0.6. It has been established that the compounds obtained in the open air atmosphere are oxygen deficient, the deficit increasing withx and temperature. The specific resistivity atx = 0.2–0.6 is (1–2)·10^?3 ohm·cm; it increases with the concentration of oxygen vacancies. At 0.3 ≤ x ≤ 0.6 thep-type conductivity is metallic in character with low temperature resistivity coefficients of the order (1–5)·10^?4 K^?1 in the interval 20–700°C.     

Transition of the electronic response from molecular-like to jellium-like in cold,small sodium clusters

Absolute photoabsorption cross sections for Na _n ⁺ (2≤n≤21) were measured in the visible energy range. The cluster ions were produced in a gas aggregation source and thus have a canonical distribution of internal energy corresponding to a temperature of ～ 105 K. The spectra for n≤9 and 11 exhibit between two and six absorption lines, and are in qualitative agreement with ab inito quantum chemical calculations. For n=15 and 21, the position of the resonances can be explained as excitations of a nearly free electron gas in a spheroidal container. An evolution is thus observed from molecular-like transitions to a giant collective resonance of the electron cloud. The integrated oscillator strength is 0.95 per 3s-electron in the energy range covered for n≥4, showing that the main excitations of the valence electrons have been found.     

The collective response of deformed sodium clusters

We employ the structure-averaged jellium model (SAJM) to obtain the selfconsistent LDA Kohn-Sham ground state of axially deformed sodium clusters with broken leftright symmetry, and calculate the dipole-response of the low-energy isomers using the local RPA (LRPA) scheme in the range 7 < Z ≤ 59. We choose the multipole operators r ^P Y _LM (p=1,...,10; L=1,...,4, M=0,1) as coupled intrinsic modes of the electron system. The collective spectra are compared with recent measurements of the dipole absorption cross section performed by Meibom et al., and we find very good agreement of the positions and strengths of the leading collective modes in the measured range 47 < Z ≤ 59.