Transition temperature pressure dependence

The Gibbs-DiMarzio approach, as has been stated, rests on the existence of a true second-order thermodynamic transition at a temperature T2 below the observed Tg. The pressure dependence of T2 can thus be obtained by the methods of equilibrium thermodynamics. For a first-order phase transition, the pressure dependence of the transition temperature is given by the Clapeyron equation... 

For crude oil systems, the mutiphase behavior is complicated. At moderate temperatures <90 °C the system appears to move towards a II( —) state as the temperature is increased. At higher temperatures, the system will move towards the II( +) state. For a given system, the phase transition temperatures are dependent on pressure. 

Zhu L, Chen W, Hase W L and Kaiser E W 1993 Comparison of models for treating angular momentum in RRKM calculations with vibrator transition states. Pressure and temperature dependence of CI+C2H2 association J. Phys. Chem. 97 311-22... 

The extent of decarboxylation primarily depends on temperature, pressure, and the stabihty of the incipient R- radical. The more stable the R- radical, the faster and more extensive the decarboxylation. With many diacyl peroxides, decarboxylation and oxygen—oxygen bond scission occur simultaneously in the transition state. Acyloxy radicals are known to form initially only from diacetyl peroxide and from dibenzoyl peroxides (because of the relative instabihties of the corresponding methyl and phenyl radicals formed upon decarboxylation). Diacyl peroxides derived from non-a-branched carboxyhc acids, eg, dilauroyl peroxide, may also initially form acyloxy radical pairs however, these acyloxy radicals decarboxylate very rapidly and the initiating radicals are expected to be alkyl radicals. Diacyl peroxides are also susceptible to induced decompositions ... 

The last phase transition is to the soHd state, where molecules have both positional and orientational order. If further pressure is appHed on the monolayer, it collapses, owiag to mechanical iastabiHty and a sharp decrease ia the pressure is observed. This coUapse-pressure depends on the temperature, the pH of the subphase, and the speed with which the barrier is moved. 

A second general criterion for pressure sensitivity is that the glass transition temperature of the adhesive be below the use temperature, which is usually room temperature. Broadly speaking, the To will be about 30-70°C below room temperature, depending on the base polymer and any added modifiers. 

The question arises as to how useful atomistic models may be in predicting the phase behaviour of real liquid crystal molecules. There is some evidence that atomistic models may be quite promising in this respect. For instance, in constant pressure simulations of CCH5 [25, 26] stable nematic and isotropic phases are seen at the right temperatures, even though the simulations of up to 700 ps are too short to observe spontaneous formation of the nematic phase from the isotropic liquid. However, at the present time one must conclude that atomistic models can only be expected to provide qualitative data about individual systems rather than quantitative predictions of phase transition temperatures. Such predictions must await simulations on larger systems, where the system size dependency has been eliminated, and where constant... 

For a polymorphic drug, the polymorph obtained depends on the physical conditions, such as temperature, pressure, solvent, and the rate of desupersaturation. For a solvated drug, in addition to these conditions, the thermodynamic activity of the solvating solvent may also determine the solvate obtained. However, kinetic factors may sufficiently retard the crystallization of a stable form or the solid-state transition to the stable form that an unstable form may be rendered metastable. 

Fig. 8 Temperature dependence of din f>/d(T 1), i.e., slope of the Arrhenius plot as a function of temperature for (a) (EDT-TTFBr2)FeBr4 at various pressures - the data for 0, 5.8 and 10.1 kbar are vertically shifted up by 60, 40 and 20 K, respectively, for clarity (b) (EDO-TTFBr2)2GaCl4 and (EDO-TTFBr2)2FeCl4 at 11 kbar. TMl and TN are the metal-insulator transition temperature and the Neel temperature, respectively, hi (b) the metal-insulator transition is observed as two separate peaks...

Somewhat unusual pressure dependence of the nature of the spin transition curve has been found for chain-like SCO systems containing substituted bridging triazole ligands [163, 164]. Although the transition is displaced to higher temperatures with increase in pressure, the shape of the transition curve, unusually, is effectively constant, i.e. there is no significant change in the hysteresis width and the transition remains virtually complete. This has been taken to indicate that the cooperativity associated with the transitions in these and related systems is confined within the iron(II) triazole chains. 

The influence of pressure has also been used to tune the ST properties of these ID chain compounds. Application of hydrostatic pressure ( 6 kbar) on [Fe(hyptrz)3] (4-chlorophenylsulfonate)2 H20 (hyptrz=4-(3 -hydroxypro-pyl)-l,2,4-triazole) provokes a parallel shift of the ST curves upwards to room temperature (Fig. 5) [41]. The steepness of the ST curves along with the hysteresis width remain practically constant. This lends support to the assertion that cooperative interactions are confined within the Fe(II) triazole chain. Thus a change in external pressure has an effect on the SCO behaviour comparable to a change in internal electrostatic pressure due to anion-cation interactions (e.g. changing the counter-anion). Both lead to considerable shifts in transition temperatures without significant influence on the hysteresis width. Several theoretical models have been developed to predict such SCO behaviour of ID chain compounds under pressure [50-52]. Figure 5 (bottom) also shows the pressure dependence of the LS fraction, yLS, of... 

The temperature at which a phase transition occurs is dependent on pressure (Figure 7). At atmospheric pressure (1 atm) the solid-to-liquid phase transition occurs at 0 °C and the liquid-to-gas phase transition occurs at 100 °C. If we increase the pressure, say to 100 atm, the solid-to-liquid phase transition occurs at a temperature slightly less than 0°C (—0.74°C) however, the liquid-to-gas phase transition occurs at a much greater temperature (312°C). If we decrease the pressure, say to 0.1 atm, the solid-to-liquid phase transition occurs at a temperature slightly greater than 0°C (0.004 °C) and the liquid-to-gas phase transition occurs at a lower temperature (46 °C). If we decrease the pressure further to below the triple point, there is no solid-to-liquid phase transition rather, the solid-to-gas phase transition occurs directly. At a pressure of 0.001 atm, the sublimation temperature is — 20.16°C. 

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