Effect of combining rules for cubic equations of state on the prediction of double retrograde vaporization

In this work, the phenomenon of double retrograde vaporization (DRV) is simulated using the Peng–Robinson equation of state with the classical mixing rules and several combining rules for the cross-energy and cross-co-volume parameters. The binary interaction parameters are set equal to zero in all cases, i.e., the calculations are entirely predictive. An interesting conclusion is that the predictions using the classical combining rules (geometric mean rule for a_ij and arithmetic mean rule for b_ij) provide the best agreement with the experimental data for all the systems tested: methane + n-butane, methane + n-pentane, ethane + limonene, and ethane + linalool. Another interesting observation is that several combining rules for b_ij, other than the arithmetic mean rule, predict the existence of three phases in equilibrium in a very narrow temperature range close to the critical temperature of methane in the methane + n-pentane system, even though, literature data indicates that n-hexane is the first n-alkane to present partial liquid phase immiscibility with methane.     

THE SOLID STATE REACTIONS AND TRANSITIONS IN HIGH POLYMERIC SYSTEMS Ⅲ. THE BULK CRYSTALLIZATION OF LANTHANIDECATALYTICALLY POLYMERIZED POLYDIENES

For the mechanism of isothermal bulk crystallization of high polymers, beside the nucleation and growth steps, the unimpingement of growing crystal aggregates should be taken into account for the modification of the Avrami equation. Starting from Poisson distribution function of growing crystal aggregates, the probability of the unimpinging ones should be P(0)+P(1), then the Q-modified Avrami equation thus derived can be expressed aswhere V0 represents the volume fraction of crystal aggregates at crystallization time t at a given temperature, while the exponent n on t relates to the mode of nucleation and growth, and K_q is the corresponding shape factor. This Q-modified one is verified satisfactory by the isothermal bulk crystallization of lanthanidecatalytically polymerized polybutadiene (Ln-PB), polyisoprene (Ln-PIR) and their copolymers (LnPB/IR). Furthermore, the proposed mechanism is well identified by the change of morphological state during the course of crystallization of the corresponding east film of Ln-PB TR (92/8) at-60°(Fig. 1).Upon examination of the influence of the number of entanglement on crystallization rate, it reveals the existence of two stages of entanglementation, the primary and the secondary ones (Fig. 19)The equation for dependence of molecular weight and entanglement on bulk crystallization rate has been derived as Eq. 13 or 18 for Ln-PB, and verified by the experimental rate data of well fractionated Ln-PB samples crystallized at -9.1 to -15℃(Fig.20).     

Spherical models with a Gates-Penrose-type phase transition

Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U (r)=q(r)+(r), in the limit0, where the Fourier transform (p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.     

Applicability of polymer theories to the thermodynamics of proteins at the air/water interface: example of β-lactoglobulin

Knowledge of the equation of state of adsorbed or deposited layers of proteins at the air/water interface is of fundamental interest in the understanding of the surface activity of these molecules. Using scaling laws of current polymer theories, it has been shown that the equation of state of the interfacial layer in the semi-dilute regime should relate the surface pressure to the surface concentration through a power law. The exponent of this power law should reflect the quality of the solvent and the conformation of the adsorbed polypeptide chain. In the case of β-lactoglobulin layers, in the range of surface concentrations that should correspond to the semi-dilute regime, the relationship between surface pressure and surface concentration is expressed as a power law. The exponent of this power law is strongly influenced by the nature of the aqueous substrate and by the net charge of the protein molecule. The use of scaling laws gives a coherent view of the expansion of the polypeptide chain in the interfacial layer and of the relationship between surface concentration and surface pressure in the semi-dilute regime. This result favours a strong similarity between β-lactoglobulin and a polymer chain in the interfacial layer. It is concluded that current theories of polymer adsorption could be applied to interfacial protein layers.     

An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases

The most widely used technique for performing phase equilibria calculations is the K-value method (equality of chemical potentials). This paper proposes a more efficient algorithm to achieve the results that includes Gibbs minimization when we know the number of phases. Using the orthogonal derivatives, the tangent plane equation and mass balances, it is possible to reduce the Gibbs minimization procedure to the task of finding the solution of a system of non-linear equations. Such an operation is easier and faster than finding tangents or areas, and appears to converge as fast as the K-value method. Examples illustrate application of the new technique to two and three phases in equilibrium for binary and ternary mixtures.     

Mutual Solubilities of Water and Alkanes

Summary.  The evaluation of mutual solubility data for systems water with n-alkanes, isoalkanes, and cycloalkanes along the three phase line is reported and a formula for the prediction of solubility of alkanes in water is developed. Then a cubic equation of state with an added term, which accounts for hydrogen bonding is used for correlation of liquid–liquid equilibrium data and for prediction of solubility of water in hydrocarbons using alkane in water solubility data. Comparison of the predicted and experimental solubilities is performed using all accessible experimental data. With this approach it is possible to predict the solubilities of water in alkanes with good accuracy over the temperature range up to about 20 K below critical temperature. Solubility of alkanes in water can also be calculated using experimental data for solubility of water in alkanes but results of these calculations are more sensitive to experimental errors of the data. Corresponding author: E-mail: macz@ichf.edu.pl Received August 5, 2002; accepted (revised) September 13, 2002 Published online March 13, 2003 RID="a" ID="a" Dedicated to Prof. Dr. H. Gamsj?ger on the occasion of his 70^th birthday anniversary     

The investigation of the (p,ρ,T) and (ps,ρs,Ts) properties of {(1−x)CH3OH + xLiBr} for the application in absorption refrigeration machines and heat pumps

The (p,ρ,T) and (p_s,ρ_s,T_s) properties of {(1−x)CH₃OH + xLiBr} over a wide range of state parameters are reported for the first time. The experiments were carried out in a constant volume piezometer over a temperature range from 298.15 K to 398.15 K, at 0.08421, 0.13617, 0.19692, 0.23133 and 0.26891 mole fractions and from atmospheric pressure up to 60 MPa. The experimental uncertainties are ΔT=±3 mK for temperature, Δp=±5·10⁻² MPa for high pressure and Δp=±5·10⁻⁴ MPa for atmospheric pressure, Δρ=±3·10⁻² kg · m⁻³ for density. An equation of state was derived for correlation of the experimental data of the solutions.     

Shock-wave equation-of-state studies at Los Alamos

A history of the shock-wave equation-of-state (EOS) studies at Los Alamos is given. Particular emphasis is placed on the pioneering research in the 1950s where many of the experimental techniques and methods of analysis were developed, which we now take for granted. A brief review of shock-wave physics is given, which illustrates important hydrodynamic and thermodynamic concepts. Recent studies on the EOS of Ti are presented with emphasis on the-to- phase transition. VISAR wave profiles for polycrystalline Ni and singlecrystal Ni are presented to determine the strengths of these materials under pressure. Low-density polystyrene foam Hugoniot experiments are described and results analyzed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Evaluation of the parameters of the Bender equation of state for low acentric factor fluids and carbon dioxide

Volumetric properties of several low acentric factor fluids (Ar, CH₄, C₂H₆, Kr, N₂, Ne, O₂, Xe) as well as CO₂ are modeled using the Bender equation of state. This equation is a linear function of 19 adjustable parameters, which are evaluated from properties data, using a linear numerical procedure. The validity of the EOS is tested by calculating the Joule-Thomson inversion curve. A simple model is in particular used to correlate the inversion properties predicted by the Bender equation, expressed in term of reduced pressure as a function of reduced temperatures ranging from 0.8 to 6. The simple correlation reproduces accurately the used data. We employ data on state behaviour ρ(P,T) of homogeneous fluid phases, vapour-liquid equilibrium, second virial coefficient and the coordinates of the critical point.