Points Of Binary Mixtures Research Articles

Method for prediction of liquid-vapor critical points in binary mixtures: geometrical-EOS model

A new method for predicting the Liquid- Vapor critical point of binary mixture, is presented, which is based in geometrical distances. Actually, the method is based on the minimization of the distance between the experimental and calculated values of the critical temperatures and critical pressures. The SRK and PR equations of state along with classical mixing rules of van der Waals were used as thermodynamic models to calculate the critical point of a given mixture. The proposed method requires that the mixture parameters a, b, and the covolume ε = b/v of each equation of state be determined at each iteration by solving the resulting cubic equation. For nine binary mixtures containing: hydrocarbon derivatives, carbon dioxide and alcohols are studied. The AARE of the calculated values is about 0.86% for critical temperature and 2.07% for critical pressure. Good agreements are found between the calculated results and experimental data. The technique is a general purpose one and can be applied in connection with other thermodynamic models.

Boiling Point Measurement of Gamma-valerolactone/water and Gamma-valeroctone/ethanol Mixtures at Different Concentrations and Pressures

Gamma-valerolactone (GVL) is used in green technology to produce chemicals and biofuels. Separation of GVL from mixtures within a process is a recurring challenge in chemical plants. Experimental boiling point determination containing its mixtures is fundamental as a preliminary stage of vapor-liquid equilibrium studies. The boiling point of binary mixtures of GVL/water and GVL/ethanol were measured at five compositions each, and range pressure from about 7.0 ?????? to 91.0 ?????? (±0.8??????). Experiments were carried out to determine the boiling point using a simplified ebulliometer. The experimental data were correlated with the Non-Random Two Liquid (NRTL) model. The correlated parameters of the NRTL model were used to calculate the vapor-liquid equilibrium of the mixture using the methodology of Gibbs energy minimization with ideal vapor phase.Key Words: Gamma-valerolactone, Boiling point, NRTL.

Prediction method of both azeotropic and critical points of the binary refrigerant mixtures

The prediction of the azeotropic point and the determination of the critical point inbinary mixtures is very important in refrigerating industry. In this task, a simple method ispresented in order to predict and determine both azeotropic and critical points. Our methodemploys experimental data and a thermodynamic model. 1,1,1,2‐tetrafluoroethane (R134a) in themixture presents the possibility of inventing the azeotropic and critical properties. The mixturesstudied in this work are: Cyclopropane (RC270), Propylene (R1270), Hexafluoroethane (R116) andCarbon dioxide (R744) based on 1,1,1,2‐tetrafluoroethane (R134a). The model consists of thePeng–Robinson equation of state (EoS), the Mathias–Copeman alph a function and the Wong‐Sandler mixing rules involving the NRTL model. The results proved that there is a good agreementbetween the predicted values and the experimental data. The presented methods are able topredict the azeotropic and determine critical positions.

Vapor–Liquid Equilibria of the Binary System 1,5-Hexadiene + Allyl Chloride

Knowledge of accurate vapor–liquid equilibrium data for mixtures of allyl chloride and 1,5-hexadiene is important for several industrial purposes. The bubble points of binary mixtures of allyl chlo...

An apparent critical point in binary mixtures of nitrotoluene with alkanes: Experimental and simulation study

We report an experimental and simulation study of binary mixtures of o- and m-nitrotoluene with decane and hexadecane. Mixtures of o-nitrotoluene with alkanes form a classical critical mixtures, but m-nitrotoluene / n - alkane mixtures show an apparent critical point, which lies in a metastable, experimentally inaccessible state, below the melting point, affecting physical and chemical properties of this systems in the stable liquid phase. The presence of the apparent critical point in this mixture has been experimentally observed by Nonlinear Dielectric Effect (NDE) measurements as an anomalous increase in the NDE values typical of critical concentrations. The phase diagram of this mixture shows evidence that the system freezes in the homogenous phase and its melting point is higher than its critical temperature [1-3]. For such a system, we performed Monte Carlo simulations aimed at analysing the kind of phase transitions observed, and the conditions of their occurrence in a nonpolar/dipolar mixture. We perform studies for classical critical systems of o-nitrotoluene with decane and hexadecane The enthalpy, configurational energy and radial distribution function have been estimated by the MC simulation method in the NPT system. Immiscibility conditions according to Schoen and Hoheisel [4] approach are also discussed.

An apparent critical point in binary mixtures of m-nitrotoluene with n-alkanes; experimental and simulation study

We report a simulation study of the system m-nitrotoluene–n-decane, showing an apparent critical point, which lies in their metastable, experimentally inaccessible state, below their melting point, affecting physical and chemical properties of this systems in the stable liquid phase. The presence of the apparent critical point in this mixture has been experimentally observed by the non-linear dielectric effect (NDE) as an anomalous increase in the NDE values typical of critical concentrations. The phase diagrams of this mixture have evidenced that the system freezes in the homogenous phase and its melting point is higher than its critical temperature [M. Śliwińska-Bartkowiak, B. Szurkowski, T. Hilczer, Chem. Phys. Lett. 94 (1983) 609, M. Śliwińska-Bartkowiak, Ber. Bunsengess. Phys. Chem. 94 (1990) 64, M. Śliwińska-Bartkowiak, Phys. Lett. A 128 (1988) 84]. For such a system, we performed Monte Carlo simulations aimed at analyzing the kind of phase transition observed, and their conditions of their occurrence in a Lennard-Jones mixture. The enthalpy, configurational energy and radial distribution function have been estimated by the MC simulation method in the NPT system. Immiscibility conditions according to Hoheisel [M. Schoen, C. Hoheisel, Mol. Phys. 57 (1986) 65] approach have also been discussed.

An apparent critical point in binary mixtures: Experimental and simulation study

We report the experimental and simulation studies for the system of nitrobenzene-cyclododecane, showing an apparent critical point, which lies in their metastable, experimentally inaccessible state, below their melting point, affecting physical and chemical properties of this system in the stable liquid phase. The nonlinear dielectric effect (NDE) was measured in the mixture of nitrobenzene with cyclododecane. The mixture has been found to show an apparent critical point which lies below the melting point, manifested as anomalous NDE behavior in the vicinity of the critical concentrations in the stable liquid phase. The melting temperature of this system was estimated using the differential scanning calorimetry method. For such a system, we also performed Monte Carlo (MC) simulations that aimed to analyze the kinds of phase transitions observed and the conditions of their occurrence in Lennard-Jones mixture. The enthalpy, configurational energy, and radial distribution function have been estimated by the MC simulation method in the N-P-T system. Immiscibility conditions according to the approach by Schoen and Hoheisel [Mol. Phys. 57, 65 (1986)] are also discussed.

06/00927 Novel approach for the calculation of critical points in binary mixtures using global optimization: Freitas, L. et al. Fluid Phase Equilibria, 2005, 225, 29–37.

06/00927 Novel approach for the calculation of critical points in binary mixtures using global optimization: Freitas, L. et al. Fluid Phase Equilibria, 2005, 225, 29–37.

Griffiths-Wheeler geometrical picture of critical phenomena: Experimental testing for liquid-liquid critical points

An experimental approach to the verification of specific relations between thermodynamic properties as predicted from the Griffiths-Wheeler theory of critical phenomena in multicomponent systems is developed for the particular case of ordinary liquid-liquid critical points of binary mixtures. Densities rho(T) , isobaric heat capacities per unit volume C(p)(T) , and previously reported values of the slope of the critical line (dT/dp)c for five critical mixtures are used to check the thermodynamic consistency of C(p) and rho near the critical point. An appropriate treatment of rho (T) data is found to provide the key solution to this issue. In addition, various alternative treatments for C(p)(T) data provide values for both the critical exponent alpha and the ratio between the critical amplitudes of the heat capacity A+/A- that are in agreement with their widely accepted counterparts, whereas two-scale-factor universality is successfully verified in one of the systems studied.

Behavior of the layer compression elastic modulus near, above, and below a smectic C?hexatic I critical point in binary mixtures

We present the first study of the layer compression modulus B carried out near, above and below the Smectic C-Hexatic I critical point in racemic mixtures of methylbutyl phenyl octylbiphenyl-carboxylate (8SI) and the octyloxy biphenyl analog (8OSI), at frequencies ranging from 0.2 Hz to 2 x 10(3) Hz. The behavior of B as a function of temperature shows a progressive evolution from a first order transition in 8SI to a continuous supercritical behavior in 8OSI. The latter is characterized by an increase in B, which appears above the transition, and which is followed by a leveling off when the temperature is decreased towards the transition. It is proposed that this behavior stems from the relaxation of the hexatic domains which are frozen in the frequency range studied. For the supercritical and near-critical compounds, B exhibits a small dip near the transition temperature, which is visible in the low frequency range only, indicating that the dynamics associated with the critical point is very slow. We also report measurements in the Crystal-J phase of the pure compounds, and show that 8SI behaves mechanically as a hexatic phase and 8OSI as a soft crystal phase.

Novel approach for the calculation of critical points in binary mixtures using global optimization

Critical point calculations in binary mixtures is a very important subject in phase equilibria study. A robust method for this task is certainly a powerful tool for calculation of critical loci. These critical diagrams are, usually, employed in the characterization of the behavior in two-component systems. In this paper, a new methodology for critical point calculation in binary systems, via global optimization, is presented. This approach is a particular case of the recently proposed formulation in chemical engineering literature by Henderson et al. [N. Henderson, L. Freitas, G.M. Platt, Prediction of critical points: a new methodology using global optimization, AIChE J. 50 (2004) 1300]. This novel methodology provides a robust algorithm, which does not involve derivatives of the objective function and is insensitive to the initial guesses. We obtain results for six binary systems and perform comparisons among experimental data (for systems n-butane/carbon dioxide, ethane/propane and ethane/n-butane). We also present new calculations for systems methane/hydrogen sulfide, carbon dioxide/n-octane and carbon dioxide/n-hexadecane, and showing a detailed analysis of the critical phenomena for the system methane/hydrogen sulfide. We detected that this last system can exhibits up to three critical points, for some compositions. The results illustrate the capability of the simulated annealing algorithm to find several critical points for binary systems.

Properties of the liquid-liquid coexistence curves with several critical points

The thermodynamic analysis of the coexistence curves with any number of critical points in binary mixtures at constant pressure was carried out in the framework of the regular-mixing theory. We proposed a universal temperature dependence of the general energy interaction parameter both for one and for several critical points. An evolution of multicritical point coexistence curves was analyzed and a unified consideration of the boundaries of liquid-liquid and vapor-liquid equilibria was fulfilled. As a result, new properties of the multicritical point coexistence curves were derived and new phase transitions were theoretically predicted. The relationships between conjugate phase separation temperatures were applied to calculate a pressure dependence of mutual solubility of the 2-butanol/water mixtures as a system with three critical points. Moreover, the generalized reduced temperature for the systems with several critical points was introduced to compare scaling and regular-mixing approaches to the quantitative description of the published experimental data on coexistence curves with two critical points.

PSRK Prediction of Critical Points in Binary Mixtures Containing Alkanes or Cycloalkanes.

PSRK Prediction of Critical Points in Binary Mixtures Containing Alkanes or Cycloalkanes.

Critical temperature and concentration versus molecular weight in polymer blends: Conformations, fluctuations, and the Ginzburg criterion

We use the field-theoretical methods to derive the self-consistent one-loop equations (Hartree approximation) for the location of the critical point in binary mixtures of polymers. The small parameter in the loop expansion is the inverse of the square root of the number of segments (monomers) in a polymer chain 1/√N. Both the ideal chain conformation and fluctuation corrections to the Flory–Huggins mean field result are taken into account. For symmetric mixtures, the critical temperature Tc is shown to deviate from its mean field value (∼N) as √N, while the critical concentration remains unchanged in comparison to its mean field value φ̄c=1/2. Since the fluctuations tend to disorder the system, the real value of the critical temperature is lower than its mean field value. For asymmetric A,B mixture (NA≳NB), the critical concentration of A monomers φ̄c is shown to be larger than its mean field value. In the limit of NA→∞, the critical temperature attains its mean field value, even for finite NB. However, we estimate that for NA=NB∼104, the correction to the Flory–Huggins parameter at the critical point may still be of the order of 10%, although it depends on the details of the system. The explicit formulas for Tc and φ̄c as functions of NA and NB are given. The role of the upper wave vector cutoff in these formulas is emphasized and its proper estimate is given. The loop expansion, viewed as an expansion in a small parameter, is correct as long as both NA and NB are much larger than unity and breaks down when any of these quantities becomes of the order of unity. The calculation of the Ginzburg region in the temperature-concentration plane is also given. It is based on the analysis of the scattering intensity. The comparison with the earlier estimates of the Ginzburg criterion (for temperature) is made.

The order parameter and crossovers at the critical points of binary mixtures

The long-standing problem of determining the order parameter of the lines of critical points in binary mixtures is addressed and solved within the framework of the hierarchical reference theory of fluids which has already proven successful in one-component systems. An exact relation is given, expressing the order parameter in terms of easily accessible experimental data, like the partial molar volumes. The competition between two fixed points is identified as the mechanism leading to the strong corrections to scaling seen experimentally.

Calculation of critical lines in binary mixtures with the simplified perturbed hard chain theory

Abstract Pelt, A. van, Peters, C.J. and Swaan Arons, J. de, 1993. Calculation of critical lines in binary mixtures with the simplified perturbed hard chain theory. Fluid Phase Equilibria , 84: 23-47. In this paper it is shown that the simplified perturbed hard chain (SPHCT) equation of state is able to describe critical lines in binary hydrocarbon mixtures with good accuracy, as long as the size ratio of the unlike molecules is less than two. To perform the calculations of critical points in binary mixtures a modified Hicks-Young algorithm is used. The Hicks-Young algorithm and its modifications are extensively discussed in this paper. For many hydrocarbon mixtures binary interaction coefficient values ( k 12 ) were evaluated from critical data. This systematic investigation of critical curves in binary hydrocarbon mixtures is a continuation of our previous investigations (van Pelt, A., Peters, C.J., and de Swaan Arons, J., 1992. Fluid Phase Equilibria, 74: 67-83) in which the SPHCT equation of state was used to describe the saturated vapour pressures in the critical region of pure components.

Experimental study of the electric-field-induced smectic A-ferroelectric smectic C critical point in binary mixtures: Approach to tricritical behavior

A system of binary mixtures of two liquid crystal compounds is prepared possessing a tricritical point in the smectic A-ferroelectric smectic C transition line in the temperature-composition plane. In several mixtures with different distinctness of the first-order nature of the transition the approximate coordinates of the electric-field-induced critical point, at which the first-order transition vanishes, are determined by measurements of the electric displacement. The critical field strength and the temperature difference between the transition at zero field and the critical point shrink to zero as the tricritical point is approached. This is the first study of the wing critical points of a tricritical point in liquid crystal phase transitions.

On the Calculation of Liquid-Liquid Equilibria near an upper Critical Mixing Point in Binary Mixtures

Article On the Calculation of Liquid-Liquid Equilibria near an upper Critical Mixing Point in Binary Mixtures was published on January 1, 1987 in the journal Zeitschrift für Physikalische Chemie (volume 268O, issue 1).

Anomalous mixing times in turbulent binary mixtures at high Prandtl number

A theory of turbulent binary fluid mixtures is applied to situations where the diffusive Prandtl number, $P=\frac{\ensuremath{\nu}}{D}$, far exceeds the Reynolds number $R$. This regime is accessible just above the consolute point in binary mixtures, where Prandtl numbers in excess of ${10}^{6}$ have been observed. We find that sizable large-scale inhomogeneities are mixed to uniformity quite slowly, in a time of order $\ensuremath{\tau}=\frac{{t}_{0}P}{R}$, where ${t}_{0}$ is a characteristic stirring time. The spectrum of concentration fluctuations rapidly acquires a peak at wave vector ${k}^{*}\ensuremath{\sim}{k}_{0}R$, where ${k}_{0}^{\ensuremath{-}1}$ is the scale of the initial inhomogeneity. Mixing times of ten minutes or more are possible.

On the Application of Neutron Small Angle Scattering to the Study of Fluctuations Near the Liquid-liquid Critical Point in Binary Mixtures

A comparative survey is made of the neutron and light scattering techniques as applied to structural investigations in the vicinity of critical points in fluids. For neutron scattering as applied to fluctuations in binary mixtures, some criteria for a good contrast in order to optimize the scattering parameters such as the isotopic composition or the concentration are considered. This leads us to show how to write the partial structure factors in binary mixtures in order to remove the coupling between concentration and density fluctuations artificially introduced bv Bhatia and Thornton when the components are of different size. Finally, the amplitudes of the concentration fluctuations near a critical point are discussed.