Bulk phase transitions

An ordering phase transition is characterized by a loss of symmetry the ordered phase has less symmetry than the disordered one. Hence, an ordering process leads to the coexistence of different domains of the same ordered phase. An interface forms whenever two such domains contact. The thermodynamic behavior of this interface is governed by different forces. The presence of the underlying lattice and the stability of the ordered domains tend to localize the interface and to reduce its width. On the other hand, thermal fluctuations favor an interfacial wandering and an increase of the interface width. The result of this competition depends strongly on the order of the bulk phase transition. 

Analysis of the results and comparison with the lipid phase transition observed iq the bulk lipid/water systems allows to conclude that the lowest temperature during heating at which measurable diffusion occurred correlates with the onset of formation of the lamellar Ln liquid crystalline phase of the given phospholipid. Therefore, the data support a correlation between the surface and bulk phase transitions. This was confirmed in recent studies where the lipid surface phase transition was successfully measured for the first time in foam film by independent means involving the detailed investigations of the temperature dependences of the W(C) curve for the foam film and its thickness. 

The inherently nonisothermal models that require temperature variations for oscillatory behavior fall into two groups. In both cases, the reaction is blocked and reactivated at different temperatures. The blockage is caused either by a surface blocking or by a bulk-phase transition of the catalyst. 

Fig. 6. General representations of heterogeneous oscillatory mechanisms, (a) Buffer-step model (b) coverage-dependent activation energy (c) empty-site model (d) Sales-TUrner-Maple model (e) Pt(lOO) phase transition model (f) Dagonnier model (g) blocking/ reactivation model (h) bulk-phase transition model.

For the remaining bulk-phase transition systems mentioned above, no model calculations or stability analyses have been performed, and the mechanisms are similar to the general scheme. Therefore these models will not be discussed in detail. 

In addition to the importance of the M41S materials for size- and shape-selective applications, these materials have been also regarded as a suitable mesoporous model adsorbent for testing theoretical predictions of pore condensation. Pore condensation represents a first order phase transition from a gas-like state to a liquid-like state of a pore fluid in presence of a bulk fluid reservoir, which occurs at a pressure p less than the saturation pressure po at gas-liquid coexistence of the bulk fluid [6,7]. In this sense pore condensation can be regarded as a shifted gas-liquid bulk phase transition due to confinement of a fluid to a pore. Recent work has shown that in fact the complete phase diagram of the confined fluid is shifted to lower temperature and higher mean density as compared with the bulk coexistence curve [e.g., 8,9]. 

Such a behavior, as measured by means of XPS, was reported previously for fcc-based Al-3%Ag alloy equilibrated between 550 and 770 K [82] (Fig. 19a). Below the bulk phase transition (680 K) hep-based Ag2Al-like... 

Fig. 19. The XPS bandwidth of the Ag 4d states in Al-3at.%Ag (top) and the Ag concentration (bottom), deduced from the emission intensity, as a function of temperature [82]. The bulk phase transition lies at 680 K.

Clusters, with their relatively short time scales, exhibit dynamic equilibrium between different phases, with passage between phases typically in the gigahertz range. This is how they exhibit phase coexistence [6, 7] within a temperature interval [15] rather than at a unique temperature (for a given pressure), typical of bulk phase transitions. Here we study the effect that width has on the detection of coexisting phases in the case of a discontinuous transition. 

Simulations of octahedral molecular clusters at constant temperature show two kinds of structural phase changes, a high-temperature discontinuous transformation analogous to a first-order bulk phase transition, and a lower-temperature continuous transformation, analogous to a second-order bulk phase transition. The former shows a band of temperatures within which the two phases coexist and hysteresis is likely to appear in cooling and heating cycles Fig. 10 the latter shows no evidence of coexistence of two phases. The width of the coexistence band depends on cluster size an empirical relation for that dependence has been inferred from the simulations. 

DTA Differential Thermal Analysis Specimen and reference sample Uniform heating Temperature difference Bulk - Phase transitions, cryslalllzallon 61... 

We consider the influence of sizes on the separation temperature. We start from the single-phase particle at high T (PQ in Figure 13.4) and then decrease T at fixed R and Co. As compared with the bulk phase transition temperature Tp, in... 

Measurements of full sets of sorption-thermodynamic data can be achieved reliably and rapidly with conqmterized control systems for high data accuracy. Correction for de(ad)sorption due to inherent tenperature changes during SIM experiments can be made. Sorption-saturation values of a system can be assessed if its isosteres coincide withcharacteristic bulk-phase transition curves, e.g., evaporation or sublimation curves. Phase transitions of the sorption phase can be observed directly from characteristic bending of isosteres. Sorption isotherms at any temperature and pressure that are physically meaningful, can be calculated from either concentration dependences of thermodynamic functions or directly from sets of isosteres. 

The corresponding relations between temperatures and monolayer film pressure of forms I and II in the case of monoelaidin is shown in Fig. 5.11. Monoelaidin, having a trans double bond, exhibit monolayers with liquid crystalline chains (form II) up to about 30 °C.The relation between the monolayer transitions and the corresponding bulk phase transition in the binary phase diagram of monoelaidin/water (Fig. 5.2 (b)) is thus very close. Monoolein shows only monolayers with liquid chains (form I) at all temperatures between 0 and 100 °C, which is in agreement with the phase diagram of monoolein/water shown in Fig. 5.2 (c). 

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