On the Theory of Condensation Phase Transitions in Magnetic and Electrorheological Suspensions

Particle condensation in nonconducting electro- and magnetorheological suspensions under the action of external electric (magnetic) field was theoretically studied. It was shown that the phase separation of the particle system of the gas-liquid type is preceded by the formation of fairly long chain aggregates. Phase transition occurs as a condensation of these chains as a result of their polar electric (magnetic) interaction. This fact denotes the essential difference between the phase separation in the considered suspensions of polarizable particles from the phase transitions in ferro- and Seignette-electric fluids, i.e., colloidal suspensions of monodomain particles with permanent intrinsic moments, as well as from the transitions in molecular systems, where the condensation occurs in the ensemble of individual particles (molecules).     

Effect of magnetic field on phase transitions in solutions and melts of flexible polymers

The effect of the magnetic field on the phase diagrams of flexible-chain polymer–solvent systems is observed for the first time. Phase transitions in systems with the crystalline-phase separation (PE–o-xylene, PE–n-hexane, PE–chloroform, PE–o-dichlorobenzene, PEG–1,4-dioxane, PEG–toluene) and the amorphous demixing (PS–methyl acetate, PVA–ethanol, PDMS–butanone) are studied. The magnetic field increases the temperatures of crystallization of PE and PEG from solutions and melts but has no effect on phase transitions in PS, PVA, and PDMS solutions. The structures of polymer entities isolated from solutions and melts are studied. Under application of the magnetic field to PEG solutions, spherulites of substantially smaller sizes than those formed outside the field appear. The magnetic field increases the degree of crystallinity of PEG, but the degree of crystallinity and size of PE spherulites remain unchanged.     

Salting-out of isopropyl alcohol from aqueous solutions with potassium nitrate

The solubility of components and critical phenomena in a ternary system constituted by potassium nitrate, water, and isopropyl alcohol were studied by the visual-polythermic method in the temperature range 25–90°C. The formation temperature of the critical node of the monotectic equilibrium (critical solution—solid phase) and the solution compositions corresponding to the critical solubility points at different temperatures were determined. Isothermal solubility diagrams of the system were constructed, the previously suggested scheme of the topological transformation of the phase diagrams of ternary stratifying systems constituted by a salt and a binary solvent was confirmed, and the distribution coefficients of isopropyl alcohol at different temperatures were calculated.Translated from Zhurnal Prikladnoi Khimii, Vol. 77, No. 12, 2004, pp. 1945–1949.Original Russian Text Copyright © 2004 by Sinegubova, Ilin, Cherkasov, Kurskii, Tkachenko.     

Phase diagrams in the binary systems of tetracyanoethylene with mesitylene,durene and pentamethylbenzene

The phase diagrams of the binary systems of tetracyanoethylene (TCNE) with some methylbenzenes were determined by differential scanning calorimetry. In the durene-TCNE system a 11 complex was observed. The other two pairs of components form both 11 and 12 complexes. In all the systems, the complexes melted incongruently. Solid — solid phase transitions were found in the complexes in the pentamethylbenzene-TCNE system. The excess free energy of mixing of the liquid phase was estimated by fitting the modified van Laar equation to the measured liquidus lines. The enthalpy and the entropy of complex formation were used as the fitting parameters.

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Zusammenfassung Mittels DSC wurden die Phasendiagramme der binären Systeme aus Tetracyanoethylen (TCNE) mit einigen Methylbenzolen erstellt. Im System Duren-TCNE wurde ein 11 Komplex beobachtet. Die anderen beiden Komponentenpaare bilden sowohl 11 als auch 12 Komplexe. In allen Systemen schmelzen die Komplexe inkongruent. Im System Pentamethylbenzol-TCNE wurde für die Komplexe eine Fest-Fest-Phasenumwandlung gefunden. Durch Angleichen der modifizierten van Laar Gleichung an die gemessenen Liquidus-Kurven konnte die überschüssige freie Energie für das Mischens der flüssigen Phase geschätzt werden. Als Angleichparameter wurden Enthalpie und Entropie der Komplexbildung verwendet.

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We wish to thank M. Dankowski for his help in connecting the DSC apparatus to the microcomputer.     

Theory of phase diagrams described by thermodynamic potentials with T d symmetry

Phase diagrams of crystals induced by irreducible representations with symmetry group \(L = \bar 43m\) (T _d ) are constructed within the phenomenological theory of second-order phase transitions. A model of the Landau thermodynamic potential is studied, state equations of all symmetry-conditioned phases are obtained, and general conditions for their thermodynamic stability are formulated. Equations for the boundaries of phase areas and lines of phase transitions are obtained for the fourth order of expansion of the potential via components of the order parameter. Some types of the collapse of the multicritical point of the phase diagram for the eighth order of potential expansion are studied using computer calculations. The possible existence of phase diagrams that contain one or more triple points and areas of existence of three and four phases is shown for the first time for the potentials with the above symmetry. Examples are given of crystals that undergo phase transitions in the considered symmetry of the order parameter.     

Zustandsdiagramme binärer Phospholipidmischungen

The transition curves were calculated on the basis of two types of ideal phase diagrams:

miscibility in the liquid phase and immiscibility in the solid phase;

complete miscibility in both liquid and solid phases.

A comparison was made of the theoretical curves with observed transition curves.     

Solvent-generated HPLC systems with β-cyclodextrin derivatives as chiral additives

It is shown that enantioselective solvent-generated liquid-liquid and liquid-solid Chromatographic systems with -cyclodextrin derivatives can be realized. The liquid-liquid systems are based on ternary solvent systems of limited miscibility, containing chiral additives; the chiral stationary phase is spontaneously generated on the porous microparticulate silica used as a solid support. In the solvent-generated adsorption systems a very small proportion of -cyclodextrin derivatives is added to the mobile phase. These components act as column activators, since they are strongly adsorbed on the RP solid support where they form new stereoselective adsorption sites. It is demonstrated that dynamically generated systems with -cyclodextrin derivatives as chiral agents are powerful and versatile tools for enantioseparation of different types of compounds. This technique creates not only a new type of selectivity but also leads to very stable and reproducible Chromatographic columns.Dedicated to Professor J. F. K. Huber on the occasion of his 65th birthday     

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.     

To the Theory of the Aggregation of Polydisperse Colloids

Particle aggregation in polydisperse colloids is studied theoretically. It is assumed that the aggregation follows phase transition scenario with the formation of dense uniform colloidal phases. Bidisperse model corresponding to the system of relatively large and small particles is considered. Van der Waals attraction between large particles and the action of relevant entropy forces due to the presence of depleted layers of small particles are taken into account. The diagrams of equilibrium phase transitions of gas–liquid and gas–solid types occurring in the ensemble of large particles are constructed. The influence of size and concentration of small particles on the pattern and structure of phase diagrams is studied. It is shown that an increase in the concentration of small particles leads, on the one hand, to a rise of phase transition temperature and, on the other hand, to an increase in the threshold concentration of large particles.     

Estimation of the Thermodynamic Quality of Alkylbenzenes with Respect to Low Density Polyethylene

The original optical method was used for the first time to obtain complete diagrams of the state of mixtures of low-density polyethylene with o-xylene and ethylbenzene. The diagrams are of the type describing the phase state of systems partially crystalline polymer–good solvent. In contrast to the diagrams described in the literature, the diagrams described here contain an additional boundary curve for the solubility of the liquid in the polymer. Using the coordinates of the intersection of this line with the curve of complete amorphization of the polymer, five alkyl benzenes were ranked according to their thermodynamic affinity to low-density polyethylene.     

Berthollide formation conditions

Possible routes to generate berthollide phases are considered, specifically, via the separation of part of a component-based solid solution due to morphotropic transitions and as a result of the intersection of the binodal line with the solidus curve. Particular example phase diagrams are given for binary systems containing berthollides. Experimental data on berthollide phase formation in systems of MF₂-RF₃ and NaF-RF₃ (where R stands for rare-earth elements) are summed up.     

Chemical applications of group theory and topology

The following procedure is described for investigating the qualitative dynamics of simple chemical systems: 1) A so-called influence diagram is generated representing the relationships between the reference reactants (phase-determining intermediates); 2) This influence diagram is used to generate a truth table indicating possible transitions between state vectors representing the signs of the time derivatives of of the reference reactant concentrations; 3) The truth table is used to determine a state transition diagram representing the flow topology around unstable equilibrium points; 4) The characteristic equation of the adjacency matrix of the influence diagram is solved in order to determine the presence of such unstable equilibrium points. The two types of qualitative dynamics possible for chemical systems containing two reference reactants and one feedback circuit are bifurcation between two attracting regions (bistability) and limit cycle oscillation. However, in two reference reactant systems oscillation requires an additional self-activating loop to generate the unstable equilibrium point required for its realization. Bistability and limit cycle oscillation are also two of the possible types of qualitative dynamics for chemical systems containing three reference reactants. However, chemical systems with three reference reactants and two or more feedback circuits can also contain interlocking limit cycles, which can lead to toroidal oscillations or chaos. The influence diagrams are given for the systems exhibiting these various types of dynamic behavior along with a summary of the important properties of all 729 possible influences for simple chemical systems containing three reference reactants.     

Thermodynamic Analysis of Phase Equilibria in the System Cyclohexane—Methanol

The phase diagram of cyclohexane-methanol was thermodynamically modeledin the range of 150 T/K 360 and at a pressure of 1 bar on the basis ofavailable experimental data. The Gibbs energy functions of four pure solid andtwo mixture phases were taken into consideration. The liquid phase was describedby a model based on mole fraction statistics and the simplified assumption ofmethanol tetramers mixed with cyclohexane monomers. The gas phase was treatedas a nonideal mixture with a Gibbs energy modeled on the basis of the virialcoefficient formalism considering only monomers. The Gibbs energies of the twosolid modifications of pure methanol, as well as pure cyclohexane, were fixedusing literature data. The pressure dependence of the Gibbs energies of the liquidand solid phases were neglected. The complete T-x phase diagram includinggas/liquid equilibria as well as p-x phase diagrams in the range of 20 and 55°C werecalculated. Experimental and calculated data were found to agree reasonably well.     

Phase equilibria and structures in ternary systems of a cationic surfactant (C16 TABr or (C16 TA)2SO4), alcohol,and water

The dependence of alcohol chain length on the isothermal phase behavior of the ternary systems hexadecylrrimethylammonium bromide/alcohol/water has been investigated. A liquid crystalline phase (the normal hexagonal one) occurs in the phase diagrams along the surfactant/water axis and this phase extends in the interior of the diagrams.When the alcohol is methanol, ethanol or butanol, there is in the ternary phase diagram a continuous solution region from the water to the alcoholic corner, and in the butanol case, in addition, a small region of lamellar liquid crystalline phase in the interior of the diagram. When the alcohol chain length is increased, the continuous solution region is divided into two subregions, an aqueousL ₁ and an alcoholicL ₂. The lamellar phase occupies the center of the phase diagrams and has the capability to incorporate large amounts of water under one-dimensional swelling. On the alcoholic side of the lamellar phase occur a reversed hexagonal liquid crystalline phase and a cubic liquid crystalline phase in the octanolic system; in the decanolic system the cubic phase is missing, but instead another liquid crystalline phase, presumably with rod-structure, occurs in addition to the reversed hexagonal phase.In a decanolic system where the monovalent bromide ion is replaced by the divalent sulphate ion there are the same solution regionsL ₁ andL ₂, and phase regions with liquid crystalline normal hexagonal and lamellar structures. The lamellar phase has lost much of its capability of incorporating water. That is in analogy with the conditions in anionic systems where the counterion charge has been increased. There is no reversed hexagonal phase, but on the alcoholic side of the lamellar phase, there is the same foreign liquid crystalline phase with a presumed rod-structure as in the monovalent system.     

Charakterisierung der Mischbarkeitseigenschaften binärer Monoschichten durch Messung der Gleichgewichtsspreitungsdrucke

1. The equilibrium spreading pressures were studied as a function of composition of the following binary systems by use of the Wilhelmy-method atT=295 K on aqueous substrate:

octadecyldiethylphosphine oxide/1-hexadecanol (I)

octadecyldiethylphosphine oxide/1-eicosanol (II)

octadecyldiethylphosphine oxide/stearic acid (III)

1. The equilibrium spreading pressures of the pure components of the systems I und II, respectively, decrease due to addition of the corresponding components of mixture. A minimum occurs at the mole fractionx=0,50. The equilibrium spreading pressures of mixtures of system III rise with increasing mole fraction of octadecyldiethylphosphine oxide.
2. The three spreading diagrams are based on one general type. The phase rule is applied and shows that the components of the 3 systems must be immiscible in the monolayer but miscible in the bulk phase.

     

Ternary Polymer Solutions with Hydrogen Bonds, 2

Experimental ternary phase diagrams for ternary systems CHL/PS‐MAA/PVPy with diverse MAA contents have been determined by GPC. The presence of MAA in the copolymers gives rise to specific interactions, by hydrogen bond formation between both polymeric components, so strong that the isotherm for the system with the highest MAA content so far studied, CHL/PS‐MAA(8%)/PVPy, is representative of a complex coacervation situation. By applying the theoretical background deduced by coupling the Flory‐Huggins lattice model to the AET developed for ternary polymeric systems SPP with specific intermolecular interactions (via hydrogen bonds), free energy surfaces for the CHL/PS‐MAA/PVPy systems are constructed. From these plots theoretical ternary phase diagrams are deduced and a fair agreement with those obtained experimentally is observed.

     

The solid-liquid phase diagrams of binary mixtures of even saturated fatty alcohols

This study is part of a work developed in the author's research group on the solid-liquid equilibrium of fatty substances. The phase diagrams of the following fatty alcohol systems were determined by differential scanning calorimetry (DSC): 1-octanol + 1-dodecanol, 1-octanol + 1-tetradecanol, 1-decanol + 1-tetradecanol, 1-decanol + 1-hexadecanol and 1-dodecanol + 1-octadecanol. The liquidus lines of three of these systems were previously reported in the literature but the other two systems were never published. Moreover other transitions, in addition to the eutectic temperature, were also detected in all the systems. A region of solid solution at the extreme left of the phase diagrams was observed for all the binary mixtures. Polarized light microscopy was used to complement the characterization of the systems for a full grasp of the phase diagrams. The solid-liquid equilibrium was modeled using the Margules 2-suffix, Margules 3-suffix, NRTL and UNIFAC Dortmund equations.     

Magnetic phase transitions in nanostructures induced by shear stress under high pressure

Magnetic phase transitions of the first and second order were revealed by Mössbauer spectroscopy in nanosystems of - and -ferric oxides and metallic europium subjected to shear stress (240°) under high pressure (20 kbar). For - and -ferric oxide nanoclusters, the Curie (Neel) points decreased to 300 K, whereas for nanostructured europium the Neel point increased from 90 to 100 K. The thermodynamic model of magnetic phase transitions predicting a change in the character of magnetic phase transitions and a decrease (increase) in the critical Neel (Curie) points in nanoclusters was developed. The type of magnetic phase transitions and the change in the critical points were caused by defects in nanoclusters, whose maximum concentration was observed for the clusters with the 20—50 nm size range.     

Phase diagrams with critical and tricritical liquid phase solution points in a ternary system

Critical phenomena of liquid phase stratification in ternary systems are considered. Models of the T-x ₁-x ₂ phase diagrams with critical and tricritical liquid solution points and isothermal diagrams over the corresponding interinvariant intervals are given.