Calculation of phase diagrams not requiring the derivatives of the Gibbs energy demonstrated for a mixture of two homopolymers with the corresponding copolymer

A method is presented which allows the calculation of phase diagrams (spinodal, binodal and tie lines) on the basis of the Gibbs energy of mixing ΔG. No derivatives of ΔG with respect to the composition variables are required. This method is particularly useful in cases where the composition dependence of ΔG is very complex and no analytical representation of the derivatives can be given. The method is applied to a ternary mixture of two homopolymers with a copolymer consisting of the same monomers. The sequence distribution of the copolymer is kept constant between random and purely alternating, and phase diagrams are calculated for different chemical compositions of the copolymer. The complex phase separation behavior resulting for a 1 : 1 copolymer becomes much simpler as one monomeric unit starts to predominate in the copolymer.     

Calculation of critical points not requiring the derivatives of the Gibbs energy demonstrated for a mixture of two homopolymers with the corresponding copolymer

The method for the calculation of phase diagrams (spinodal, binodal and tie lines) exclusively on the basis of the Gibbs energy of mixing, ΔG, with no need of calculating its derivatives with respect to the composition variables was extended to determine the critical conditions and the condition of the stability of the critical points. The method is applied to a ternary mixture of two homopolymers with a copolymer consisting of the same monomers. The sequence distribution of the copolymer is kept constant between random and purely alternating, and phase diagrams are calculated for different chemical compositions of the copolymer. Three critical lines were found within a very small interval of the copolymer composition.     

Calcul des diagrammes de fusion de melanges ternaires. Technique numerique et application au systeme NaCl-CaCl2-MgCl2

An efficient numerical method for the calculation of the ternary phase diagrams is presented. The results obtained with the NaCl-CaCl₂-MgCl₂ ternary system are given.     

Phase equilibria of poly(ɛ-caprolactone)-<Emphasis Type="Italic">co</Emphasis>-poly(acryl methacrylate)-methylene chloride systems and the phase structure of polymer binary mixtures

Isothermal cross sections of amorphous separation diagrams of the ternary systems poly(ɛ-caprolactone)-co-poly(acryl methacrylate) Eudragite RS-methylene chloride and poly(ɛ-caprolactone)-co-poly(acryl methacrylate) Eudragite E-methylene chloride are obtained via the experimental methods of turbidity points and analytical transmission electron microscopy and the calculation semi-empirical method of constructing boundary lines of phase diagrams. It is shown that the composition of copoly(acryl methacrylate) affects the length of the solubility region in the ternary phase diagram and the character of the anisotropy of films prepared via solvent evaporation. The determination of coordinates of figurative points corresponding to the completion of phase separation shows that the mechanism of phase separation for both systems is of the spinodal type. The specific orientation of polycaprolactone crystallites during film preparation from the poly(ɛ-caprolactone)-Eudragite RS mixture is determined by the morphology of the film formed during solvent evaporation and the phase composition.     

Computer-assisted optimization of selectivity (mobile phase,pH, and ion concentration) in high-perfomance liquid chromatography

A computer-assisted method is presented for optimization of mobile phase composition in reverse-phase and normal-phase HPLC. The method is based on window diagrams, but only three preliminary tests are required. The method is successfully applied to two examples and there is good agreement between predicted and experimental results. Optimal values for ion concentration and pH in ion chromatography from a published optimization method are compared to values calculated using the computer-assisted method presented in this paper. The same results are obtained, but the method presented here is simpler and faster than previously published one.     

Phase-Separation Phenomena of Copolymer Solutions and Fractionation of Copolymers by Chemical Composition

Precipitation temperature-total polymer concentration diagrams for toluene solutions of two styrene-acrylonitrile copolymers different in chemical composition and their mixtures were determined and then triangular phase diagrams of this system were constructed from these diagrams. It is speculated from the triangular phase diagrams and experimentally shown that the copolymer may be effectively fractionated by chemical composition in this system.     

PTX phase equilibrium study of new solid solution systems,Cd1−xMxS (M = Mg,Ca, Sr)

Pressure, temperature, and composition phase equilibrium diagrams of new solid solution systems of the Cd_1?xM_xS (M = Mg, Ca, Sr) type were investigated using the quenching method. The stable region for the rock-salt-type phase is widely extended toward the high-temperature/low-pressure region by substituting 10–20 mole% of Cd with Ca or Sr. Temperature and composition phase diagrams for each solid solution system were obtained at 2 GPa. The rock-salt-type phase stability is discussed in view of these phase relations.     

Ternary phase diagrams of DNTF and TNAZ and their eutectics

The eutectic ternary phase diagrams of some typical volatilizable energetic materials have been investigated by high pressure differential scanning calorimeter (PDSC). The ternary H–X phase diagrams for TNT/TNAZ/DNTF (TTD) and TNAZ/DNTF/RDX (TDR) systems were constructed by the correlation of the apparent fusion heat with the composition (H–X method). And, the ternary T–X phase diagrams (the temperature dependence on composition) for the two ternary systems were constructed by calculating from the data of the five T–X binary phase diagrams. The eutectic compositions (mol%) of TTD and TDR ternary systems were obtained to be 52.3/27.3/20.4 (H–X method), 53.2/25.8/21.0 (T–X method) and 54.9/39.6/5.5 (H–X method), 55.1/42.2/2.7 (T–X method), respectively. The eutectic temperatures of the ternary systems were obtained by PDSC determination and T–X method calculation to be 76.5 and 76.7 °C, 47.5 and 50.2 °C, respectively. It is shown that the results obtained by two methods are in agreement and the error in measuring or calculating eutectic compositions and temperatures for the two ternary systems are within allowable ranges of ±3 mol% and ±3 °C, respectively. Moreover, by means of constructing two ternary H–X phase diagrams with different fixed composition of a component and comparing the apparent fusion heat of eutectics with calculated one, the results obtained from H–X method for TTD system were proved. The results showed that the gasification or volatilization of easy volatile materials could be efficiently restrained by high pressure atmosphere, and the perfectly and ideally H–X ternary phase diagrams can be constructed. In comparison with T–X method, H–X method has as a virtue of being quick and simple, especially on constructing ternary phase diagram.     

Fluid phase stability and equilibrium calculations in binary mixtures: Part II: Application to single-point calculations and the construction of phase diagrams

The methodology presented in Part I of this work is applied to a large number of pressure–temperature flash calculations, and to the automated construction of constant temperature pressure–composition phase diagrams, and constant pressure temperature–composition phase diagrams for binary mixtures modeled with an augmented van der Waals equation of state. An automated prototype implementation of the algorithm is developed for this purpose. We follow the classification of Scott and van Konynenburg [R.L. Scott, P.H. van Konynenburg, Discuss. Faraday Soc. 49 (1970) 87] and present phase diagrams corresponding to non-azeotropic mixtures of the five main types of fluid phase behavior (I–V), studying in detail representative diagrams at constant pressure and constant temperature. Special attention is given to the solution of numerically problematic equilibrium regions, such as those close to three-phase equilibria where metastable and unstable critical points can also be found. Of the order of 10⁴ flash calculations at varying temperatures and pressures, and for different intermolecular parameters of the components in the mixture, have been carried out. The algorithm provides the correct stable equilibrium state for all of the points considered. Despite the fact that our implementation is not optimised for performance, we find that the algorithm identifies the stable solution in difficult regions of the phase space without any penalty in terms of computational time, when compared to simpler regions.     

The Fractionation of Copolymers by Chemical Composition

Abstract

Phase diagrams for the system of methyl ethyl ketone, cyclo-hexane, and styrene-acrylonitrile copolymer were determined. The phase diagrams indicate that the copolymer may be fractionated by chemical composition in this system. Discussions of the thermodynamics are also presented, to show that copolymers can effectively be fractionated into fractions of different compositions if a system can be found in which the difference between the Flory interaction parameters (x parameters) of two constituents of the copolymer with solvent is sufficiently large. Theoretically, the fractionation of copolymer must always occur to a certain extent, depending both on chemical composition and molecular weight. The composition fractionation results of styrene-acrylonitrile copolymers are given to confirm the discussions.     

Speciation fingerprints of binary mixtures by optimized repeated two-phase separation

A method for determination of the composition of binary mixtures of a metal or radionuclide species by optimized repeated two-phase separations (SORTS) was proposed and theoretically substantiated. Its principle consists in repeated equilibration of two immiscible phases, one being the original liquid or solid matrix with minimal adjustment of its composition and varying the phase ratio (separation stage cut) as the optimized parameter. The batch separation technique may consist in the repeated solvent extraction or aqueous biphasic distribution, or in the replicate equilibration with solvent or leaching solution. Results of SORTS can be presented e.g. by Tukey box diagrams as the characteristic fingerprints of original species composition.     

Use of the Wilson equation to calculate solid-liquid phase equilibria in binary and ternary systems

Generalized formulation is presented for calculating simple eutectic type solid-liquid phase diagrams for binary and ternary systems by using the Wilson equation for molar excess Gibbs energy in the liquid phase. The liquidus surface and eutectic points of molten salt mixtures with a common ion were calculated and compared with experimental values. The average error in the estimation of ternary eutectic composition was ± 0.013 (mole fraction) for the two ternary systems tested. The agreement was generally better than that obtained with the regular solution approximation.     

不同压力下碳氢体系低压金刚石的非平衡定态系列相图

系统压力是低压金刚石薄膜生长实验中重要的实验参数，如果采用合理的计算方法定量化地预测出压力对金刚石薄膜生长条件的影响，则可以直接用于指导其实验研究。本文报道根据非平衡热力学耦合理论模型绘制了C-H体系金刚石生长投影相图，经与大量实验结果比较相一致，并系统地计算了压力变化的碳氢体系金刚石生长非平衡定态截面相图，得到了金刚石生长区随压力变化的规律。计算得到的相图与经典平衡相图有本质不同，均有金刚石生长区，因而可以合理解决金刚石低压下连续生长而石墨被腐蚀与经典平衡热力学之间的矛盾。本文的计算结果可以为金刚石生长实验提供定量化的压力条件的选择和优化实验条件。     

Reverse Schreinemakers Method for Experimental Analysis of Mixed-Solvent Electrolyte Systems

A method based on Schreinemakers’s tie-line theory of 1893 is derived for determining the composition and phase amounts in solubility experiments for multi-solvent electrolyte systems. The method uses the lever rule in reverse compared to Schreinemakers’s wet residue method, and is therefore called the reverse Schreinemakers (RS) method. The method is based on simple mass balance principles similar to the wet residues method. It allows for accurate determination of the mixed-solvent phase composition even though part of the solvent may precipitate as complexes between solvent and salt. Discrepancies from determining the composition of salt mixtures by pH titration are discussed, and the derived method significantly improves the obtained result from titration. Furthermore, the method reduces the required experimental work needed for analysis of phase composition. The method is applicable to multi-solvent systems and may be used for the determination of solid-phase compositions, similar to Schreinemakers’s original “rest” method. An example calculation is presented for the Na₂CO₃-NaHCO₃-MEG-H₂O system.     

Phase equilibria in ternary polymer blends

The phase states and rheological properties of blends of three polymers??polystyrene, poly(methyl methacrylate), and the styrene-acrylonitrile copolymer??in the common solvent chloroform are studied. The phase diagrams are constructed and the positions of spinodals are determined via the method of turbidity points. The effect of the third polymer on the compatibility of the binary blend obeys Prigogine??s rule; that is, it is determined by the solubility of the added polymer in the first two components. The extremum composition dependence of rheological properties of ternary polymer systems in the vicinity of the separation point (the metastable region) is found. Through the method of convex-shell construction, the phase diagrams are calculated.     

Structural Features of Solid Phases and Topology of Phase Diagrams

The paper considers model phase diagrams of binary and ternary systems involving transformations (transitions) of phase equilibria. The relationship between the type of structural solidstate transformation and the type of phase diagram is shown. Topological series of phase diagrams of systems with continuous and limited types of solid solutions are considered, including phase diagrams with polymorphic transitions between intermediate solid phases of variable composition.     

Analytical expressions to calculate relative amounts of phases in a three-component phase diagram

The relative amounts of different phases in multiphase regions in the common three-component phase diagrams are usually estimated graphically using geometrical features of the diagram. The present contribution introduces algebraic expressions for the lines in the diagram, which allow these numbers to be calculated directly from the experimental results. The method is an extension of the classical methods, which were translated into convenient computer programs [Laughlin, R. G. The Aqueous Phase Behavior of Surfactants; Academic Press: New York, 1994] to calculate the amount of different phases for individual compositions. The introduction of analytical geometry allows simplified expressions to be used for the calculations and the amounts to be presented as continuous functions of the total composition.     

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.     

Experimental investigation and thermodynamic prediction of the Al–Ge–Zn phase diagram

The knowledge of the phase diagram of the Al?CGe?CZn ternary system is of importance in the development of high temperature soldering materials. In this study, the phase diagram of the Al?CGe?CZn ternary system was calculated by the calculation of phase diagrams method using binary thermodynamic parameters included in the COST MP0602 thermodynamic database. Chosen alloys with compositions along two vertical sections with molar ratio Al/Ge?=?3/1 and 1/3 were measured using DTA (differential thermal analysis). The experimentally determined phase transition temperatures from this work and phase equilibria data from literature were compared with calculation results and good mutual agreement was noticed.