Phase Transition Type

Approximately twenty different lipid systems have been examined by the method of TRXRD. The list includes single lipid species as well as binary lipid, lipid-small molecule and lipid-protein mixtures and isolated membranes and membrane lipid extracts (Table 1). A total of thirty, nominally distinct phase transition types are described in the table. The actual number of disparate phase transitions is expected to be less than this because of redundancies arising from an inadequate nomenclature and/or incomplete phase characterization. 

As already demonstrated, for relatively recent sedimentary rocks and weathering crusts (20-200 Ma), the characteristic sequence of silica transformation is silica gel —> opal-A —> opal-CT —> chalcedony —> quartz. This is a well studied, polymorphous transformation of the solid phase transition type (a-cristobalite —> a-quartz) (Plyusnina 1983,1986,1990). One aspect of the solid phase transformations is the gradual transition of one silica phase to another and the gradual transformation of morphological features down the stratigraphic column with increasing burial depth and age (similarly in weathering crusts). The observed sequential cristobalite-quartz ratio would be unlikely to occur in rocks with repeated dissolution and crystallization from solution (Plyusnina 1983). 

Molten eutectic salts (NaOH-NaNOs, NaCl-KCl-MgCl2 etc.) Organic solid-liquid phase transition type Paraffin wax (n-decane etc.)... 

Fig. 1.16 Some ferroelectric compounds and their phase transition types and temperatures. Different thermal expansion of calcium barium niobate in [hfcO] and [001] direction. Cracking along [hkO) faces In potassium lithium niobate caused by crossing the phase transition temperature at about 450°C.

The surfactant HLB, where increasing the HLB results in the phase transitions type 2 to type 3 to type 1... 

Fuerstenau and Healy [100] and to Gaudin and Fuerstenau [101] that some type of near phase transition can occur in the adsorbed film of surfactant. They proposed, in fact, that surface micelle formation set in, reminiscent of Langmuir s explanation of intermediate type film on liquid substrates (Section IV-6). 

The initial classification of phase transitions made by Ehrenfest (1933) was extended and clarified by Pippard [1], who illustrated the distmctions with schematic heat capacity curves. Pippard distinguished different kinds of second- and third-order transitions and examples of some of his second-order transitions will appear in subsequent sections some of his types are unknown experimentally. Theoretical models exist for third-order transitions, but whether tiiese have ever been found is unclear. 

Flere we discuss the exploration of phase diagrams, and the location of phase transitions. See also [128. 129. 130. 131] and [22, chapters 8-14]. Very roughly we classify phase transitions into two types first-order and continuous. The fact that we are dealing with a finite-sized system must be borne in mind, in either case. 

Micellization is a second-order or continuous type phase transition. Therefore, one observes continuous changes over the course of micelle fonnation. Many experimental teclmiques are particularly well suited for examining properties of micelles and micellar solutions. Important micellar properties include micelle size and aggregation number, self-diffusion coefficient, molecular packing of surfactant in the micelle, extent of surfactant ionization and counterion binding affinity, micelle collision rates, and many others. 

Type-n structures are formally the out-of-phase transition states between two type-I structures, even if there is no measurable banier. 

On the other hand, the formation of the high pressure phase is preceded by the passage of the first plastic wave. Its shock front is a surface on which point, linear and two-dimensional defects, which become crystallization centers at super-critical pressures, are produced in abundance. Apparently, the phase transitions in shock waves are always similar in type to martensite transitions. The rapid transition of one type of lattice into another is facilitated by nondilTusion martensite rearrangements they are based on the cooperative motion of many atoms to small distances. ... 

Another example of phase transitions in two-dimensional systems with purely repulsive interaction is a system of hard discs (of diameter d) with particles of type A and particles of type B in volume V and interaction potential U U ri2) = oo for < 4,51 and zero otherwise, is the distance of two particles, j l, A, B] are their species and = d B = d, AB = d A- A/2). The total number of particles N = N A- Nb and the total volume V is fixed and thus the average density p = p d = Nd /V. Due to the additional repulsion between A and B type particles one can expect a phase separation into an -rich and a 5-rich fluid phase for large values of A > Ac. In a Gibbs ensemble Monte Carlo (GEMC) [192] simulation a system is simulated in two boxes with periodic boundary conditions, particles can be exchanged between the boxes and the volume of both boxes can... 

There have been other promising lines along which the theory of quenched-annealed systems has progressed recently. One of them, worth discussing in more detail, is the adsorption of fluids in inhomogeneous, i.e. geometrically restricted, quenched media [31,32]. In this area one encounters severe methodological and technical difficulties. At the moment, a set of results has been obtained at the level of a hard sphere type model adsorbed in sht-like pores with quenched distribution of hard sphere obstacles [33]. However, the problem of phase transitions has remained out of the question so far. 

However, we also need to discuss how the attractive interactions between species can be included in the theory of partly quenched systems. These interactions comprise an intrinsic feature of realistic models for partially quenched fluid systems. In particular, the model for adsorption of methane in xerosilica gel of Kaminsky and Monson [41] is characterized by very strong attraction between matrix obstacles and fluid species. Besides, the fluid particles attract each other via the Lennard-Lones potential. Both types of attraction (the fluid-matrix and fluid-fluid) must be included to gain profound insight into the phase transitions in partly quenched media. The approach of Ford and Glandt to obtain the chemical potential utilizing... 

E. V. Albano. Monte Carlo simulation of a bimolecular reaction of the type A-t- (1/2) B2 —> AB. The influence of A-desorption on kinetic phase transitions. Appl Phys A 55 226-230, 1992. 

Models of a second type (Sec. IV) restrict themselves to a few very basic ingredients, e.g., the repulsion between oil and water and the orientation of the amphiphiles. They are less versatile than chain models and have to be specified in view of the particular problem one has in mind. On the other hand, they allow an efficient study of structures on intermediate length and time scales, while still establishing a connection with microscopic properties of the materials. Hence, they bridge between the microscopic approaches and the more phenomenological treatments which will be described below. Various microscopic models of this type have been constructed and used to study phase transitions in the bulk of amphiphihc systems, internal phase transitions in monolayers and bilayers, interfacial properties, and dynamical aspects such as the kinetics of phase separation between water and oil in the presence of amphiphiles. 

Pressure-induced phase transitions in the titanium dioxide system provide an understanding of crystal structure and mineral stability in planets interior and thus are of major geophysical interest. Moderate pressures transform either of the three stable polymorphs into the a-Pb02 (columbite)-type structure, while further pressure increase creates the monoclinic baddeleyite-type structure. Recent high-pressure studies indicate that columbite can be formed only within a limited range of pressures/temperatures, although it is a metastable phase that can be preserved unchanged for years after pressure release Combined Raman spectroscopy and X-ray diffraction studies 6-8,10 ave established that rutile transforms to columbite structure at 10 GPa, while anatase and brookite transform to columbite at approximately 4-5 GPa. 

When 0.4 < x < 0.53, an orthorhombic phase is observed in the AgxNb02+xFi.x system. This phase undergoes a phase transition at 900°C that leads to the formation of a tetragonal phase, which crystallizes in a tetragonal tungsten bronze-type structure with cell parameters a = 12.343 and c = 3.905 A. When 0.82 < x < 1, solid solutions based on AgNb03 were found, which crystallize in a perovskite-type structure. 

The function of I2g> (T) in the vicinity of the phase transition to centrosymmetric conditions usually has a linear character. Such behavior corresponds to ferroelectrics that undergo type II phase transitions and for which the SHG signal, l2Curie temperature is described by the Curie - Weiss Equation ... 

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