Irreversible transformation

Irreversible transformations are those in which reactants do not reform from products upon cooling. Generally one of the reactants is in a metastable state, and only requires thermal agitation or the presence of a catalyst to initiate the transformation. Examples would be combustion of a fossil fuel or glass devitrification. Power-compensated DSC has a distinct advantage over heat-flux DSC in determining the kinetics of transformation from metastable phases. In these type of reactions, 

11 Implied in this discussion is that the exothermic deviation of the trace (in the temperature region where liquid and solid are in equilibrium) should follow the slope of the liquidus line Thus, it is conceivable that the shape of the liquidus line can be predicted from the shape of a single DTA cooling trace of a strategic (e.g. 59 mol% AI2O3) composition. 

Under slower heating rates in heat-flux DSC, the deviation of sample temperature from the setpoint during a self-feeding reaction may be maintained adequately small so as to be neglected. If the furnace feedback control is set to act based on the temperature of the sample (that is the sample temperature thermocouple is the control thermocouple), then the control system may be able to allow the transforming sample to heat itself at a constant rate, and the heat input from the furnace will retreat as needed. 

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Irreversible transformations, from more disordered toward more ordered modifications of a given form have been, for instance, observed for the a form of i-PP [39,40,43,44] (see Sect. 2.4), as well as for the most common form of i-PS [74], In these cases the transitions occur by recrystallization processes in the respective melting regions. 

P. Hinsinger, F. Elsass, B. Jaillard, and M. Robert, Root-induced irreversible transformation of a trioctahedral mica in the rhizosphere of rape. J. Soil Sci. 44 535 (1993). 

Let us consider a simple, irreversible transformation of S to P. If we have some experimental means of quantifying the concentration of S and/or of P, we can define the velocity of the reaction in terms of the change in [.S ] or [P] as a function of time. Figure Al.l illustrates a typical time course, or progress curve for such a reaction in terms of [.S] and P. As described in Chapter 2, we can focus our attention on the very early portion of such a progress curve, where the concentrations of [5] and P vary linearly with time. From this portion of the curve we can define an initial... 

Logical Structures. When a synthetic organic chemical is released into an aquatic system, the entire array of transport, transfer, and transformation processes begins at once to act on the chemical. Transport from the point of entry into the bulk of the system takes place by advection and by turbulent dispersion. Transfers to sorbed forms and irreversible transformation processes proceed simultaneously with the transport of the chemical. After the elapse of sufficient time, the chemical comes to be distributed throughout the system, with relatively smooth concentration gradients resulting from dilution, speciation, and... 

Simple Parallel Reactions. The simplest types of parallel reactions involve the irreversible transformation of a single reactant into two or more product species through reaction paths that have the same dependence on reactant concentrations. The introduction of more than a single reactant species, of reversibility, and of parallel paths that differ in their reaction orders can complicate the analysis considerably. However, under certain conditions, it is still possible to derive useful mathematical relations to characterize the behavior of these systems. A variety of interesting cases are described in the following subsections. 

Geissler, P. L. Dellago, C., Equilibrium time correlation functions from irreversible transformations in trajectory space, J. Phys. Chem. B 2004,108, 6667-6672... 

Except for those catalysts subjected to the previously mentioned conditions, which lead to irreversible transformation of the active phase and/or the support material, the HDT catalysts are regenerable [37], Through a systematic and careful procedure, the spent catalyst is unloaded from the reactor and regenerated by specialized companies. The possibility of in situ regeneration is also commercially offered and the decision, on which method would be used, is typically based on economical considerations [38],... 

The extent to which the ion-radical pair suffers a subsequent (irreversible) transformation (with rate constant k characteristic of highly reactive cation radicals and anion radicals) that is faster than the reverse or back electron transfer (/cBET) then represents the basis for the electron-transfer paradigm that drives the coupled EDA/CT equilibria forward onto products (P)20 (equation 8). 

The same analysis may also be applied when B is a secondary radical formed upon fast and irreversible transformation of a primary radical, B1... 

Quantitative predictions about the heats of formation of hydrides of intermetallic compounds have been discussed by Shilov etal. (1989) they studied reversible and irreversible transformations in intermetallic compound-hydrogen systems and observed that four basic types of PIT diagrams exist for these systems. 

If one of the substituents R1 or R2 is hydrogen, then the interconversion of the endo-and exo-isomers (101 and 103) is accompanied by an irreversible transformation into l//-2-benzazepines 104 (equation 36). Otherwise (i.e. when R1, R2 / H) the rearrangement of compounds 101 is slower and leads to formation of 5//-2-benzazepine system 102 (equation 35)52. 

A clue to the direction that needs to be followed to reach a criterion of spontaneity can be obtained by noticing in Table 5.1 that Q and Ware equal to zero for the reversible cycle but are not zero for the irreversible cycle. In other words, it is changes in the surroundings as well as changes in the system that must be considered in distinguishing a reversible from an irreversible transformation. Evidently, then, we need to find a... 

We may contrast this result for A totai with that for Al/totai for an ideal gas, as mentioned in Section 5.1. In the irreversible expansion of an ideal gas, Allgys = 0 the surroundings undergo no change of state (Q and W are both equal to zero), and hence, A /total = 0- ff we consider the reversible expansion of the ideal gas, AUsys is also equal to zero and AUsun is equal to zero because Q = —W, so again A /total = 0- Clearly, in contrast to AS, AU does not discriminate between a reversible and an irreversible transformation. 

THL.l. 1. Prigogine, Moderation et transformation irreversibles des systemes ouverts (Moderation and irreversible transformation in open systems). Bull. Cl. Sci. Acad. Roy. Belg. 31, 600-606 (1945). 

In addition to simple electron transfers in which no chemical bond is either broken or formed, numerous organic reactions, previously formulated by movements of electron pairs, are now understood as processes in which an initial electron transfer from a nucleophile (reductant) to an electrophile (oxidant) produces a radical ion pair, which leads to the final products via the follow-up steps involving cleavage and formation of chemical bonds [11-23], The follow-up steps are usually sufficiendy rapid to render the initial electron transfer the rate-determining step in an overall irreversible transformation [24], In such a case, the overall reactivity is determined by the initial electron-transfer step, which can also be well designed based on the redox potentials and the reorganization energies of a nucleophile (reductant) and an electrophile (oxidant). 

Figure 5.3. Connections among r- and p-space densities, density matrices, and form factors. Two-headed arrows signify reversible transformations single-barbed arrows signify irreversible transformations. A Fourier transform is denoted by JF.

The reaction in alcoholic medium of a /3-diketone, a base and VOCl2 in 1 2 1 molar ratios leads to compounds [VO(alkoxy)(/8-diketonato)]2.553 This is an interesting result since [VO(/3-diketonato)2] form if the reaction with the same species is carried out in molar ratios of 2 2 1 or 1 1 1. Therefore, the stoichiometry in which the reagents are mixed will drive the reaction towards one product or the other. This behaviour was rationalized assuming Scheme 16 where an intermediate [VO(OH)L] (not isolated) forms and is irreversibly transformed to the corresponding [VO(OR)L] compound. 

Engel (1883) and Linck 1 (1899) stated that amorphous arsenic is transformed at 360° C., irreversibly and with considerable development of heat, into metallic arsenic Erdmann and Reppert gave 303° C. as the transformation temperature, while Jolibois 2 and Gaubeau 3 determined the point of irreversible transformation both of the brown and grey varieties to be 270° to 280° C. Erdmann gave the transition point between the brown form and the grey form as 180° C., but such a critical point has not been substantiated. Jolibois asserted that his thermal observations admitted only two allotropes, the ordinary grey... 

The Cope rearrangement of fluorine-containing hexa-1,5-dienes has been studied extensively by Dolbier and co-workers.3-5 In contrast to the acceleration obtained in the oxy-Cope rearrangement (i.e.. the irreversible transformation of 3-hydroxy-l,5-dienes to the corresponding 6-oxoalkenes). substitution of fluorine at positions 1 or 3 has very little influence on the kinetic system shown below, and is comparable to 3-methyl substitution.4 Temperatures between 236 and 278 C were required for the kinetic studies of 1 and 2. 

The y phase of bismuth molybdate underwent a reversible transformation to the metastable tetragonal y" modification. This metastable modification was observed in the temperature range of 520° to 550°C and underwent an irreversible transformation to the y modification which readily formed at 700°C. The results indicated that the y modification corresponds to that reported by Blasse (83). However, refinement of the crystal data utilizing a single crystal revealed that this y modification was orthorhombic with lattice parameters a = 15.99 A, b = 15.92 A, and c = 17.43 A. An additional observation was the reversible transformation of the y modification to y at 900°C. 

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