Critical Constants Research Articles

Molecular Dynamics Simulation of Liquid-Vapor Coexistence Curves of Metals

A Molecular dynamics implementation of Gibbs ensemble method is applied to determine liquid-vapor coexistence curves of metals using embedded atom model potentials. As an application of the code we developed, the liquid-vapor coexistence curves of Aluminum and Copper are simulated using Cai and Ye potential. The critical constants obtained were found to be slightly lower than the range of experimental results. The results show that the potentials parameters obtained by fitting to low temperature solid properties are not adequate to accurately determine the liquid-vapor phase diagram.

Critical properties of some tetraalkoxysilanes and tetraalkoxytitaniums with branched alkyl radicals

The critical pressures and the critical temperatures of tetraisopropoxytitanium, tetra-tert-butoxytitanium, and tetraisopropoxysilane have been measured. The decomposition of the substances studied begins at temperatures below their critical ones. A pulse-heating method which allows measuring the critical properties of thermally unstable compounds has been used. The times of heating from the beginning of a pulse to the moment of reaching the critical temperature were from 0.03 to 1ms. The short residence times provided little degradation of the substances in the course of the experiments. The critical constants of tetraalkoxytitaniums and tetraalkoxysilanes with branched and straight alkyl chains have been compared. The experimental critical constants of tetraalkoxytitaniums and tetraalkoxysilanes have also been compared with those calculated using various group-contribution methods.

Exact simultaneous confidence intervals for a finite set of contrasts of three, four or five generally correlated normal means

The construction of a set of simultaneous confidence intervals for any finite number of contrasts of p generally correlated normal means is considered. It is shown that the simultaneous confidence level can be expressed as a (p−2)-dimensional integral for a general p≥3. This expression allows one to compute quickly and accurately, by using numerical quadrature, the required critical constants and multiplicity adjusted p-values for at least p=3, 4 and 5, involving only one-, two- and three-dimensional integrals, respectively. Real data examples from a drug stability study and a dose response study are used to illustrate the method.

Systematic prediction of critical point coordinates from molecular parameters of equations of state and interaction potentials

We compare the accuracy of three types of models for prediction of experimental values of the critical volume V C, temperature T C and pressure P C of 15 fluids. These models (van der Waals equations of state, two-body Lennard-Jones and Approximate Non-Conformal potentials, and effective potentials including three-body-force effects) can be regarded as systematic improvements on the description of molecular interactions. We begin by introducing experimentally-defined parameters that characterize the mean molecular-scale energy E, volume β and energy density ξ for each fluid, showing that the experimental critical coordinates are linear functions of these mean molecular parameters. Then we use parametrizations for the fluids considered, reported in the literature, to calculate the critical coordinates for each of the models to be compared. All these models give a qualitatively-correct linear dependency of the critical coordinates with the characteristic molecular parameters, but only the introduction of three-body forces and non-conformal interactions result in quantitatively-correct predictions: both the van der Waals equations and the two-body Lennard-Jones models overestimate V C and underestimate T C and P C. The ability to predict accurately the critical constants can be useful for providing insight into basic molecular interactions, guiding experimental determination of phase diagrams, and characterizing fluids for chemical engineering applications.

High-Pressure Phase Behavior of Heptadecafluoro-1-decene and Nonafluoro-1-hexene in Supercritical Carbon Dioxide

High-pressure phase behavior measurements of (CO2 + heptadecafluoro-1-decene) and (CO2 + nonafluoro-1-hexene) binary mixture systems were carried out using a variable volume view cell. The experimental range of temperature and pressure are from 313.2 K to 343.2 K and up to 15 MPa, respectively. The correlation was performed using the Peng–Robinson equation of state and the van der Waals one-fluid mixing rule. The critical constants, Tc and Pc, were estimated by the several group contribution methods. The acentric factor was estimated by the Lee–Kesler method.

Experimental evidence of synchronization of time-varying dynamical network

We investigate synchronization of time varying networks and stability conditions. We derive interesting relations between the critical coupling constants for synchronization and switching times for time-varying and time average networks. The relations are based on the additive property of Lyapunov exponents and are verified experimentally in electronic circuit.

Generalized approach to global renormalization-group theory for fluids

The global renormalization-group theory (GRGT) for fluids is derived starting with the square-gradient approximation for the Helmholtz free energy functional such that any mean-field free energy density and direct correlation function can be employed. The new derivation uses Wilson's functions for representing density fluctuations, thereby relaxing the assumption of cosine variation of density fluctuations used in earlier approaches. The generality of the present approach is shown by deriving the relationships to the earlier developments. A qualitative way to infer the free parameters in the present form of GRGT is also suggested. The new theory is applied to square-well fluids of ranges 1.5 and 3.0 (in units of hard-sphere diameter) and Lennard-Jones fluids. It is shown that the present theory produces a flat isotherm in the two-phase region. Thus the theory accounts for fluctuations at all length scales and avoids the use of Maxwell's construction. An analysis of the liquid-vapor phase diagrams and the critical constants obtained for different potentials shows that, with a mean-field free energy density that is accurate away from the critical region and an appropriate coarse graining length for the mean-field theory, GRGT can provide results in good agreement with the simulation and experimental results.

Simultaneous selection of treatments better and worse than the best and worst controls

In this paper, we consider p(p≥2) and q(q≥2) independent treatment and control populations respectively, such that an appropriate probability model for the data from ith(jth) treatment (control) population is a member of absolutely continuous location and scale family of distributions which have common scale parameter and possibly differ in location parameters. For example, there may be p newly invented drugs/varieties of seeds/components which have to compete with their existing q standard competitors in terms of their average responses. A newly invented drug/variety of seed/component is said to be good (bad) if the distance of its average response from the largest (smallest) average response of q control populations is more (less) than δ1(δ2) units, where δ1 and δ2 are positive constants to be specified by the experimenter. In this setting a selection procedure is proposed to select simultaneously two subsets SU and SL of the p treatment populations such that the subset SU contains all the good treatments and the subset SL contains all the bad treatments with probability at least P∗, where P∗ is a pre-assigned value. The proposed procedure was applied to normal and two parameters exponential probability models separately and the relevant selection constants have been tabulated. The implementation of the proposed methodology is demonstrated through a numerical example based on real life data. The authenticity of numerically computed critical constants have been verified through simulation. Further, if we define the ith treatment population as bad (good) if the distance of its average response from the largest (smallest) average response of q control populations is less (more) than δ3(δ4) units, where δ3 and δ4 are to be specified by the experimenter such that δ4>δ3>0, then we have proposed a simultaneous selection procedure to select SU and SL and a sample size is determined so that the probability of omitting a good (bad) treatment population from SU(SL) or selecting a bad (good) treatment population in SU(SL) is at most 1−P∗.

Robust half-metallicity of AlCoN and AlNiN

Theoretical investigations of Al1-xCoxN and Al1-xNixN (x = 0.25) in the zinc blende phase are presented. The robustness of half metallicity of these compounds with correlation to their lattice compressions is discussed. The results show that both compounds retain their half-metallic nature (conductor for spin up state and semiconductor for spin down state) with their lattice compressions up to certain critical lattice constants. Abrupt changes in the electronic and magnetic properties are observed at these robust transition lattice constants (RTLCs). These compounds lose their integer magnetic moments of 4μβ for Al1-xCoxN and 3 μβ for Al1-xNixN at RTLCs. The calculated RTLC for Al0.75Co0.25N is 4.4 A and for Al0.75Ni0.25N is 4.2 A. The possible compression in the lattice constants from their relaxed states while maintaining their half-metallic nature is up to 4% for both compounds. © 2012 Wiley Periodicals, Inc.

A Note on Testing Homogeneity of Several Exponential Location Parameters

In this article, the problems of testing homogeneity of several exponential location parameters against simple and tree ordered alternatives are considered separately. Test procedures for both the alternatives are proposed using restricted maximum likelihood estimators (RMLE) of exponential location parameters under the respective orderings. Critical constants for the implementation of the proposed procedures are tabulated. Power comparison of the proposed test procedure under the simple ordered alternative with the procedure of Chen (1982) and of Dhawan and Gill (1999) is carried out using Monte-Carlo simulation.

The Auxiliary Field Method in Quantum Mechanics

The auxiliary field method is a new technique to obtain closed formulae for the solutions of eigenequations in quantum mechanics. The idea is to replace a Hamiltonian $H$ for which analytical solutions are not known by another one $\tilde H$, including one or more auxiliary fields. For instance, a potential $V(r)$ not solvable is replaced by another one $P(r)$ more familiar, or a semirelativistic kinetic part is replaced by an equivalent nonrelativistic one. The approximation comes from the replacement of the auxiliary fields by pure real constants. The approximant solutions for $H$, eigenvalues and eigenfunctions, are then obtained by the solutions of $\tilde H$ in which the auxiliary parameters are eliminated by an extremization procedure for the eigenenergies. If $H=T(\bm p)+V(r)$ and if $P(r)$ is a power law, the approximate eigenvalues can be written $T(p_0)+V(r_0)$, where the mean impulsion $p_0$ is a function of the mean distance $r_0$ and where $r_0$ is determined by an equation which is linked to the generalized virial theorem. The general properties of the method are studied and the connections with the envelope theory presented. This method is first applied to nonrelativistic and semirelativistic two-body systems, with a great variety of potentials. Closed formulae are produced for energies, eigenstates, various observables and critical constants, with sometimes a very good accuracy. The method is then used to solve nonrelativistic and semirelativistic many-body systems with one-body and two-body interactions. For such cases, analytical solutions can only be obtained for systems of identical particles, but several systems of interest for atomic and hadronic physics are studied. General results concerning the many-body critical constants are presented, as well as duality relations existing between approximate and exact eigenvalues.

Analyzing surface tension in higher alkanes and their CO2 mixtures

We have used polymer density functional theory to study the surface tension behavior of heavy hydrocarbons and their binary mixtures with CO2, for which very limited data is available in the literature. Dodecane (C12H26), tertacosane (C24H50), and hexatriacontane (C36H74), and their CO2 binary mixtures have been studied over a wide range of temperature (313–423K) and pressure (ambient to 30MPa) conditions representative of typical petroleum reservoirs. We have compared three parameterization schemes and showed that parameterization using critical constants gives surface tension results that are in very good agreement with the available experimental data. The most significant result from this study is the double crossover behavior in the surface tension of the alkane–CO2 binary mixtures, resulting from the simultaneous changes in liquid density and CO2 solubility.

High-pressure phase behavior of tri-ethylene glycol dimethacrylate and tetra-ethylene glycol dimethacrylate in supercritical carbon dioxide

In this study, high-pressure phase behavior data, the pressure-composition (P-x) isotherms for the CO2+T3EGDMA and CO2+T4EGDMA binary mixture system, were measured using the static method with a variable-volume view cell at temperatures ranging from 313.2 to 363.2K. The experimental data correlation was performed using the Peng–Robinson Equation of State (PR-EOS) and the van der Waals one-fluid mixing rule. The critical constants for the PR-EOS were estimated using the several group contributions. The acentric factor was estimated using the Lee–Kesler method. The Joback method shows the better correlation results than the others.

Hermite–Pade´ approach to thermal stability of reacting masses in a slab with asymmetric convective cooling

In this paper, the thermal stability of combustible materials uniformly distributed in a slab under Bimolecular, Arrhenius and Sensitised exothermic reactions is investigated. The slab surfaces are assumed to exchange heat asymmetrically with the ambient following Newton's cooling law. Using a perturbation method coupled with a special type of Hermite–Pade´ approximation technique, the governing non-linear differential equation is tackled analytically. The important properties of the temperature field including thermal criticality conditions are obtained. These critical constants for thermal stability of the slab are represented by turning point on the bifurcation diagram and may be significant to the service-worthiness of industrial products, to the life span of structures, as well as to public safety.

The range statistic and procedures to select the best systems

This paper investigates the hypothesis testing of equivalence of mean of multiple systems using the range statistic. The procedure allows unequal variances among systems. Equivalence testing has many applications in screening for new product development. First, the required sample sizes for equivalence testing at a specified confidence are derived. We then develop an indifference-zone procedure to select only the best systems. For a specified confidence level P*, the selected subset is guaranteed to contain all the best systems and none of the systems that deviate more than a specified amount from the best systems. A table of critical constants is provided for implementing the procedure. An experimental performance evaluation demonstrates the validity and efficiency of the procedure.

High-pressure phase behavior of propyl lactate and butyl lactate in supercritical carbon dioxide

Lactate esters synthesized with lactic acid and ester are used as solvents and reactants in various industries, including agricultural chemistry, pharmaceuticals, electronics, and fine chemicals. Among lactate esters, high purity propyl lactate and butyl lactate are used to produce fine chemicals and in the synthesis of chiral intermediates for use in pesticides and drugs. However, distillation for the removal of propyl lactate and butyl lactate alters or degenerates products due the high boiling points of these two lactate esters. This problem can be solved by supercritical fluid extraction (SCFE) at lower temperatures. SCFE process requires high-pressure phase behavior data on CO 2 and lactates for its design and operation. In this study, high-pressure phase behavior of propyl lactate and butyl lactate in CO 2 was measured from (323.2 to 363.2) K using a variable-volume view cell apparatus. Experimental data were well correlated by the Peng–Robinson equation of state using the van der Waals one-fluid mixing rules. The critical constants were estimated by the Joback method, the Constantinou–Gani method, and the Nannoolal–Rarey method. Acentric factor was estimated by the Lee–Kesler method.

Thermodynamic properties of the freely jointed tangent homonuclear Yukawa chain fluid

Recently, a simple analytical expression for the first coordination shell (1 ≤ x ≤ 2) of the average site–site intermolecular radial distribution function (ASSIRDF) of the freely jointed tangent hard sphere chain (FJTHSC) fluid has been proposed. This expression was used in the framework of the second-order Barker–Henderson perturbation theory together with the site–site intermolecular hard-core Yukawa potential in order to obtain an equation of state (EOS) for the freely jointed tangent Yukawa chain (FJTYC) fluid. The derived EOS was used for calculating the thermodynamic properties of the FJTYC fluid, with the attraction of variable range, such as compressibility factor, vapor–liquid equilibria and critical constants. The calculated compressibility factors, above the critical temperature, were compared with the available simulation data and the results of the well-known theories for a wide range of densities, temperatures and different values of attractive ranges. The overall agreement was good and the accuracy of the results could compete with the accuracy of those obtained using very famous theories and equations of state in the literature such as the statistical associate fluid theory with the interaction of variable range (SAFT-VR).

High-Pressure Phase Behavior of Binary Mixtures of Octafluoropentyl Acrylate and Octafluoropentyl Methacrylate in Supercritical Carbon Dioxide

Pressure–composition isotherms are obtained for the carbon dioxide + 2,2,3,3,4,4,5,5-octafluoropentyl acrylate (OFPA) and carbon dioxide + 2,2,3,3,4,4,5,5-octafluoropentyl methacrylate (OFPMA) systems using a static apparatus at a temperature range from (313.2 to 393.2) K and pressures up to 17.86 MPa. The solubility of OFPA and OFPMA for the (carbon dioxide + OFPA) and (carbon dioxide + OFPMA) systems increases as the temperature increases at constant pressure. Liquid–liquid–vapor equilibria for the (carbon dioxide + OFPA) and (carbon dioxide + OFPMA) systems were not observed at these conditions. We determined new parameters for the critical constants by using the Joback, modified Joback, and Constantinou–Gani group contribution methods. The acentric factor was determined by using Ambrose and Walton's method. Using these parameters, the experimental results for (carbon dioxide + OFPA) and (carbon dioxide + OFPMA) systems are correlated with the Peng–Robinson equation of state (EOS) using a van der Waals...

Phase Coexistence and a Critical Point in Ultracold Neutral Plasmas

We show the existence of the liquid-vapor phase coexistence and a critical point for strongly coupled ions in ultracold neutral (UCN) plasmas. Expressions for the free energy of UCN plasmas and an equation of state for the ions are obtained in the mean field approximation. A van der Waals-like isotherm shows the existence of a critical point in UCN plasmas. Depending on the ion temperature, the ions are shown to exist in a mixed vapor-liquid phase for a range of the ion Coulomb coupling parameter Γ(i) (defined by the ratio between the ion interaction and the ion kinetic energies), and in a strongly coupled liquid state for values of Γ(i) above this range. The estimates of critical constants show that it may be possible to observe these phenomena in the present day UCN plasmas.

Development of a new model for biodiesel viscosity prediction based on the principle of corresponding state

A new model for predicting the viscosities of biodiesel is presented in this work. This model is based on the principle of corresponding states, using one- and two-reference fluids. For the critical constants of methyl esters, the Marrero–Gani method was used. For biodiesels, Lee–Kesler’s mixing rules were used for critical constants calculations. The two models studied in this work were compared with Ceriani et al. [5], Yuan [6], and Revised Yuan [7] models. A set of data on biodiesel viscosity was used in this work, consisting of 31 pure biodiesels and 4 mixtures of biodiesel (totalizing 193 experimental data). The best result was found using a two-reference-fluids model, methyl laurate (C12:0) and methyl oleate (C18:1), with a global average relative deviation of 6.66%.