Isothermic processes phase transitions

In current industrial practice, reactive processing carried out in non-isothermal conditions, for both inherent and other reasons, such as changes in temperature at the surface of an article during the process cycle. Inherent reasons are the existence of inner heat sources, which can be of chemical origin (enthalpy of reaction), heat of phase transition from crystallization of a newly formed polymer or heat dissipated due to the flow of a reactive mass. 

The process of catalyst oxidation and reduction can be treated as a reversible phase transition [136]. It is to this process that the authors of recent investigations [37, 47-49, 85] ascribe critical effects. When studying kinetic self-oscillations in the oxidation of hydrogen over nickel [37] and measuring CPD, the authors established that the reaction performance oscillates between the states in which oxygen is adsorbed either on the reduced or on the oxidized nickel surface. Vayenas et al. [47-49], by using direct measurements of the electrochemical activity of 02 adsorbed on Pt, showed that the isothermal self-oscillations of the ethylene oxidation rate over Pt are due to the periodic formation and decomposition of subsurface Pt oxides. A mathemati-... 

The hydrogenation and dehydrogenation processes of the obtained composites were studied. These composites were found to interact with hydrogen much faster than initial mixtures of the powders. The desorption isotherms (Fig. 5) obtained at temperatures 523-573 K demonstrate 2 plateaus, which are correspond to the phase transitions in the systems Mg2Ni-Fl2 and Mg-H2 (isotherms for the systems La(Mm)Ni5-Fl2 and La(Mm)-H2 are not revealed because of their small quantity). 

For a reversible isothermal process the entropy change of the phase transition follows from q, via to AS = q/T. By way of illustration, values for q and AS thus... 

In the case of a localized 1/n adsorption, which is observed in many Me UPD systems at relatively high AE or low F (formation of expanded Meads superlattice structures, cf. Section 3.4), the adsorption process can be described by the so-called hard-core lattice gas models using different analytical approximations or Monte Carlo simulations [3.214, 3.262-3.264]. Monte Carlo simulation for 1/2 adsorption on a square lattice is dealt in Section 8.4. Adsorption isotherms become asymmetrical with respect to AE and are affected by the structures of the Meads overlayer and S even in the absence of lateral Meads interactions [3.214, 3.262-3.264]. Furthermore, the critical interaction parameter for a first order phase transition, coc, which is related to the critical temperature, Tc, increases in comparison to the 1/1 adsorption. 

Bewick and Thomas [3.110-3.114, 3.270] measured electrochemically and by optical means different Me UPD systems Ag(A 0/Pb, H, ClOd", acetate and citrate, CnQikt)/ h H C104, acetate, and AgQikt)m SOd with Qikt) = (111), (100), and (110). Potentiostatic pulse measurements showed non-monotonous current transients for Ag(lll) substrates which are attributed to a first order phase transition. As an example, a current transient in the system Pig hkt)/Vf, H, SOd is shown in Fig. 3.46. In the case of Ag(lOO) and Ag(llO) substrates, higher order phase transitions were supposed. Clear evidence of a participation of 2D nucleation and growth steps in the 2D Meads phase formation process was found in the system Cu(lll)/Pb H", ClOd", acetate [3.270]. Non-monotonous current transients and a discontinuity in the q(lsE,fi) isotherm were observed (Fig. 3.13). 

Experimental results recently obtained in the systems Au(/zifeO/X and Ag(hkl)/X with X" = Cr, Br, J as well as in the system AuQikl)/uraci e did not give clear evidence of phase transitions of higher order in 2D phase formation processes. Isotherms, transients, and X-ray scattering data were found not to be self-consistent. Furthermore, the interpretation of the data is not in full agreement with modern phase transition theories. 

It is easy to calculate entropy changes for isothermal processes, because T is constant and comes outside the integral to give AS = q ev/T. A specific example is the isothermal compression or expansion of an ideal gas, for which AS = nR InlVf/V ). A second example is any phase transition at constant pressure for which q, y = The entropy change is then AS ang =... 

Herein, we expand on the discussion of our recently observed isothermal amorphous-amorphous-amorphous transition sequence. We achieved to compress LDA in an isothermal, dilatometric experiment at 125 K in a stepwise fashion via HDA to VHDA. However, we can not distinguish if this stepwise process is a kinetically controlled continuous process or if both steps are true phase transitions (of first or higher order). We want to emphasize that the main focus here is to investigate transitions between different amorphous states at elevated pressures rather than the annealing effects observed at 1 bar. The vast majority of computational studies shows qualitatively similar features in the metastable phase diagram of amorphous water (cf. e.g. Fig.l in ref. 39) at elevated pressures the thermodynamic equilibrium line between HDA and LDA can be reversibly crossed, whereas by heating at 1 bar the spinodal is irreversibly crossed. These two fundamentally different mechanisms need to be scrutinized separately. 

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