Tricritical Endpoint Research Articles

Origin of Three Coexisting Phases in a Microemulsion System

Phase behavior in a NaCl/water/sodium octyl sulfonate (R 8SO 3Na)/hexanol/isooctane system was systematically investigated at constant pressure. Three-phase body containing water, surfactant (middle-phase microemulsion, D), and oil phases appears at a tricritical point at higher temperatures, whereas it appears via a four-phase region at lower temperatures. The four-phase body is formed by overlapping the three-phase body and another three-phase body including another surfactant phase (D′). We have investigated how the tricritical point or the four-phase body is produced from systems of fewer components. The effects of temperature and other variables on the tricritical point and the four-phase body are discussed. A possible explanation for the origin of the three-phase body (the existence of a tricritical endpoint) is given.

Comparison of Centocor CA 125 II TM with the Biomira Truquant OV TM and Biomira Truquant OV2 TM assays for the determination of CA125

The p(T) projections of the critical curves and of the (liquid + liquid + gas) (llg) three-phase curves for 23 binary mixtures of (an n-alkane + water) with alkane-carbon numbers i = 1 to 12 and i = 14, 16, 18, 20, 24, 25, 26, 28, 30, 32, and 36 were measured. The shape of the critical curves of the mixtures changes systematically with i. All critical curves are interrupted and show (gas + gas) equilibria of the second kind. The llg curves are at higher pressures than the vapour pressures of the pure substances, and all end in a (liquid + gas) upper critical end point (lg-UCEP). Up to the mixtures i = 25, along the p(T) projection of the llg lines up to the lg-UCEP, the alkane-rich liquid phase is lighter than the water-rich liquid phase. The consequence is that the critical curve starting from the lg-UCEP ends in the critical point of the alkane. As from i = 28, a barotropic phase reversal of the two liquid phases occurs on the llg curve before the UCEP is reached, so that, at the UCEP, the now lighter water-rich liquid phase becomes identical with the gas phase and the critical curve starting from the UCEP runs to the critical point of water. For a defined pseudo-binary mixture of (alkane mixture + water) with a fictitious alkane-carbon number between i = 26 and i = 28, this barotropic effect must occur directly at the UCEP. This means that all three phases here become simultaneously identical at the UCEP and the llg curve thus ends in a tricritical end point TCEP, a phase behaviour which has hitherto not been known. The three branches of the critical curve, viz. the high-pressure branch l1l2 and the two branches l1g and l2g, which start from the critical point of water or the alkane mixture, respectively, end in this tricritical end point TCEP. At TCEP the three-phase line and the three branches of the critical curve (l1l2, l1g, and l2g) have the same slope. The TCEP occurs in the border-line case between the two sub-classes a and b of phase-behaviour type III (classification according to van Konynenburg and Scott). In sub-class IIIa the critical curve starting at the UCEP ends at the critical point of the n-alkane and in sub-class IIIb at the critical point of water. For mixtures with i = 1 to i = 26, the high-pressure branch of the critical curve starting from the critical point of water runs first to lower temperatures and, with increasing pressures, via a temperature minimum back to higher temperatures. For all mixtures with i = 7 to i = 26 this branch of the critical curve additionally also passes through a pressure minimum between the critical point of water and the temperature minimum. All mixtures with i ⩾ 28 have a high-pressure high-temperature branch of the critical curve which, starting from the critical point of the alkane, first runs via a pressure maximum and pressure minimum to lower temperatures and finally, after passing through a temperature minimum, rises again. The phenomenological relations in phase behaviour on transition from type II to type III and from type IIIa to type IIIb with the characteristic intermediate stages are presented schematically with the aid of the p(T) projections of their critical curves.

Phase equilibria in alloys displaying diffusional and displacive characteristics

The characteristics of phase equilibria and their representation by means of phase diagrams are examined for simple systems that can undergo both diffusive and displacive phase transitions. The displacive and diffusional transitions are modeled using a simple shear and miscibility gap with a consolute critical point, respectively. Under certain conditions, both the displacive and diffusional transitions can be graphically represented using free energy-concentration diagrams with accompanying common-tangent construction. The displacive transition can lead to tricritical points and critical end points in a temperature-concentration phase diagram. It is also shown that martensite start and finish temperatures can be equilibrium features of a phase diagram under certain mechanical loading conditions and that surface relief effects can also result from a purely diffusional phase transition.

Fluid mixtures at high pressures IX. Phase separation and critical phenomena in 23 ( n-alkane + water) mixtures

The p( T) projections of the critical curves and of the (liquid + liquid + gas) (llg) three-phase curves for 23 binary mixtures of (an n-alkane + water) with alkane-carbon numbers i = 1 to 12 and i = 14, 16, 18, 20, 24, 25, 26, 28, 30, 32, and 36 were measured. The shape of the critical curves of the mixtures changes systematically with i. All critical curves are interrupted and show (gas + gas) equilibria of the second kind. The llg curves are at higher pressures than the vapour pressures of the pure substances, and all end in a (liquid + gas) upper critical end point (lg-UCEP). Up to the mixtures i = 25, along the p( T) projection of the llg lines up to the lg-UCEP, the alkane-rich liquid phase is lighter than the water-rich liquid phase. The consequence is that the critical curve starting from the lg-UCEP ends in the critical point of the alkane. As from i = 28, a barotropic phase reversal of the two liquid phases occurs on the llg curve before the UCEP is reached, so that, at the UCEP, the now lighter water-rich liquid phase becomes identical with the gas phase and the critical curve starting from the UCEP runs to the critical point of water. For a defined pseudo-binary mixture of (alkane mixture + water) with a fictitious alkane-carbon number between i = 26 and i = 28, this barotropic effect must occur directly at the UCEP. This means that all three phases here become simultaneously identical at the UCEP and the llg curve thus ends in a tricritical end point TCEP, a phase behaviour which has hitherto not been known. The three branches of the critical curve, viz. the high-pressure branch l 1l 2 and the two branches l 1g and l 2g, which start from the critical point of water or the alkane mixture, respectively, end in this tricritical end point TCEP. At TCEP the three-phase line and the three branches of the critical curve (l 1l 2, l 1g, and l 2g) have the same slope. The TCEP occurs in the border-line case between the two sub-classes a and b of phase-behaviour type III (classification according to van Konynenburg and Scott). In sub-class IIIa the critical curve starting at the UCEP ends at the critical point of the n-alkane and in sub-class IIIb at the critical point of water. For mixtures with i = 1 to i = 26, the high-pressure branch of the critical curve starting from the critical point of water runs first to lower temperatures and, with increasing pressures, via a temperature minimum back to higher temperatures. For all mixtures with i = 7 to i = 26 this branch of the critical curve additionally also passes through a pressure minimum between the critical point of water and the temperature minimum. All mixtures with i ⩾ 28 have a high-pressure high-temperature branch of the critical curve which, starting from the critical point of the alkane, first runs via a pressure maximum and pressure minimum to lower temperatures and finally, after passing through a temperature minimum, rises again. The phenomenological relations in phase behaviour on transition from type II to type III and from type IIIa to type IIIb with the characteristic intermediate stages are presented schematically with the aid of the p( T) projections of their critical curves.

Fluctuation-induced first-order transitions and symmetry-breaking fields: Then=3-component cubic model

The effects of an off-diagonal quadratic symmetry-breaking field, $g$, on a three-component ($n=3$) cubic model with no accessible fixed points are studied. It is shown that this perturbation induces a crossover from first-order to continuous transition. Depending upon the initial values of the parameters characterizing the model, two types of ($g,T$) phase diagrams are possible, both of which are rather complex, exhibiting tricritical, critical, and critical end points. The ($g,T$) phase diagrams are studied using large-$g$ expansion, mean-field theory, and renormalization-group analysis. A universal amplitude ratio associated with the critical end points is calculated to leading (zeroth) order in $\ensuremath{\epsilon}=4\ensuremath{-}d$. The phase diagrams are predicted to be realizable in certain $n=3$ cubic crystals undergoing structural phase transitions, such as BaTi${\mathrm{O}}_{3}$, RbCa${\mathrm{F}}_{3}$, and KMn${\mathrm{F}}_{3}$.