Calculation Of Binary Phase Diagrams Research Articles

Prediction of polymer-solvent miscibility properties using the force field based quasi-chemical method PAC-MAC

We present a modification to the recently developed Pair Configuration to Molecular Activity Coefficient (PAC-MAC) method in order to obtain miscibility properties of multicomponent mixtures containing polymers. PAC-MAC is a force field based quasi-chemical method originally used for rapid calculation of binary phase diagrams of small molecules. A comparison with an experimental database, containing 779 Flory Huggins χ-interaction parameters of polymer solutions, results in a correlation coefficient of 0.837 and a total root mean squared error (RMSE) of 0.593. The highest accuracy is obtained for solutions containing polystyrenes (RMSE = 0.212) or polyacrylates (RMSE = 0.308). PAC-MAC and the competitive COSMO-RS model show comparable accuracy in the prediction of solvent activities, even though PAC-MAC only uses atomic point charges instead of a quantum mechanically calculated charge distribution. PAC-MAC is a quick method for obtaining a rough indication of the mixing free energy.

Extensive Accuracy Test of the Force-Field-Based Quasichemical Method PAC–MAC

We present a comprehensive evaluation of the recently developed pair configuration to molecular activity coefficient (PAC–MAC) method. PAC–MAC is a force-field-based quasichemical method for rapid calculation of binary phase diagrams. The accuracy of the method is tested by comparing the calculated excess mixing free energy with experimental data for 1092 binary mixtures. The root mean squared error (RMSE) is shown to be 0.15 kBT. Furthermore, a comparison with UNIFAC and molecular simulations is performed. UNIFAC shows a significantly higher accuracy (RMSE: 0.07 kBT), whereas molecular simulations lead to comparable results. The accuracy of both molecular simulations as well as PAC–MAC depends highly on the used force field. The binary parameters of UNIFAC are optimized using experimental miscibility data, whereas the force field parameters are not. Therefore, a better performance of UNIFAC is expected. A concise data set shows the capacity of PAC–MAC in predicting results obtained using Monte Carlo simu...

Predicting the enthalpies of melting and vaporization for pure components

A mathematical model of the melting and vaporization enthalpies of organic components based on the theory of thermodynamic similarity is proposed. In this empirical model, the phase transition enthalpy for the homological series of n-alkanes, carboxylic acids, n-alcohols, glycols, and glycol ethers is presented as a function of the molecular mass, the number of carbon atoms in a molecule, and the normal transition temperature. The model also uses a critical or triple point temperature. It is shown that the results from predicting the melting and vaporization enthalpies enable the calculation of binary phase diagrams.

Thermodynamic assessments of binary phase diagrams in organic and polymeric systems

The Sanchez–Lacombe (SL) model and the Flory–Huggins model were used for the calculation of binary phase diagrams in organic and polymer systems, respectively. The thermodynamic parameters of the liquid and gas phases in acetone–carbon disulfide (CS 2), butane–heptane, cyclohexane–aniline systems, and liquid phases in polystyrene–polybutadiene and polystyrene–bisphenol A poly-carbonate systems were optimized, based on the experimental data. The calculated results with various pressures are in good agreement with the experimental data. It is hoped that this method will be widely applied in the prediction of binary phase diagrams in organic and polymer systems.

PhDi—Software package for calculation of binary phase diagrams

A new algorithm for the calculation of phase diagrams based on the method of convex hulls is presented. The computer program and database for thermodynamic modeling of binary systems are described and examples of calculated phase diagrams are given.

Some special features of design of binary phase diagrams in an approximation of regular solutions

We have suggested a method for calculating the phase equilibrium in phase diagrams of binary systems where the interaction parameters of the two phases differ considerably. The method can be recommended as a base variant for similar cases. The program realizing the method also envisages the calculation of stratification of phases in equilibrium and the calculation of binary phase diagrams with an intermediate phase. It is possible to determine the interaction parameters from the appropriate experimental data.

Calculation of binary phase diagrams of refractory metals, Ta, W, Tc, and Re, with liquid metals, Am, Cm, and Bk, using a regular solution theory modification

The binary phase diagrams of several refractory metals such as Ta, W, Tc, and Re with three low melting metals Am, Cm, and Bk were calculated by the modified regular solution theory. Although there are several parameters that can influence the predictions of the phase diagrams, in this present study they were limited to the internal pressure difference. The internal pressure parameters of solid metals were calculated from the internal parameters of liquid metals. The phase boundaries are then calculated from the modified regular solution theory. A HP-41C program was applied to solve the analytical equations for solubilities and then the solubilities were transferred to analytical equation formats by the Chebyshev Polynomials program. Thus, the phase boundaries can be easily obtained as a function of temperature.

General algorithm, its mathematical basis and computer autonomic program for calculation of phase diagrams of binary systems, containing p disordered phases of variable and q phases of constant compositions at (p,q) ≤ 10

The method of thermodynamic calculation of binary phase diagrams (2PD), containing p disordered phases of variable composition and q phases of constant composition for case (p,q) ≤ 10 was constructed in this paper. In this method 1) the definition of all possible solutions of phase equilibrium equations system (PEES) was realized; 2) the — separation of PEES' roots or tie-line's ends at (T,P) = const was conducted; 3) the original algorithm for calculation of PEES' roots was constructed and programmed and theorems about this algorithm convergence and about behaviour of this convergence were formulated and — proved; 4) the algorithm for autonomic selection of thermodynamically stable tie- lines was constructed and thereby calculating process T-x phase diagrams was automated. Some examples of using this method for calculation of binary phase diagrams for Cr-W, Ni-H, Ni-Al and Ni-Cr are reported here.

Numerical techniques for the calculation of binary phase diagrams

Numerical techniques are presented for the calculation of binary phase diagrams. Most compositions are obtained directly through a Taylor series expansion of the composition with respect to temperature. The series is limited to the second order term and analytic expressions of the slopes and curvatures of phase boundaries have been developed for its use. A Newton-Raphson iteration technique tests the convergence of the results. The method is efficient and accommodates various formalisms for the free energy functions. The series is not applicable to very dilute solutions of a component, near the critical point of a miscibility gap or in the vicinity of the congruent transformation point of a compound; in these cases, alternate equations have been derived.

Numerical techniques for the calculation of binary phase diagrams

Numerical techniques for the calculation of binary phase diagrams