Activation parameters volumes

Activation energy Activation of cellulose Activation parameters Activation volume Activators... 

The two-dimensional carrier confinement in the wells formed by the conduction and valence band discontinuities changes many basic semiconductor parameters. The parameter important in the laser is the density of states in the conduction and valence bands. The density of states is gready reduced in quantum well lasers (11,12). This makes it easier to achieve population inversion and thus results in a corresponding reduction in the threshold carrier density. Indeed, quantum well lasers are characterized by threshold current densities as low as 100-150 A/cm, dramatically lower than for conventional lasers. In the quantum well lasers, carriers are confined to the wells which occupy only a small fraction of the active layer volume. The internal loss owing to absorption induced by the high carrier density is very low, as Httie as 2 cm . The output efficiency of such lasers shows almost no dependence on the cavity length, a feature usehil in the preparation of high power lasers. 

The dependence of the rate constant on pressure provides another activation parameter of mechanistic utility. From thermodynamics we have (dGldP)T = V, where V is the molar volume (partial molar volume in solutions). We define the free energy of activation by AG = G — SGr. where SGr is the sum of the molar free energies of the reactants. Thus, we obtain... 

Table 7.1 Debye-Hiickel parameters for the activity coefficient, volume, enthalpy, and...

In the [Fe(pyimH)2](BPh4)2 and [Fe(pybimH)2](BPh4)2 complexes of the bidentate ligands pyimH = 2-(2 -pyridyl)imidazole and pybimH = 2-(2 -pyridyl)benzimidazole a significant solvent dependence of molar volumes and activation parameters was observed [90, 91], cf. Table 4. On the other hand, the activation volume for the T2 conversion AF l i solvent independent or... 

Kinetics and activation parameters for NO reactions with a series of iron(II) aminocarboxylato complexes have been obtained (Table II) in aqueous solution (31). Rate constants for these reactions ranged from 105 to 108M-1s-1 for the series of iron(II) complexes studied. The reactions of NO with Fen(edta) (edta = ethylenediaminetetraacetate) and Fen(Hedtra) (Hedtra = hydroxyethylenediaminetriacetate) yielded activation volumes of +4.1 and +2.8 cm3 mol-1, respectively and were assigned to a dissociative interchange (Id) mechanism (31b). All of the iron(II) aminocarboxylato complexes studied followed a similar pattern with the exception of the Fen(nta) (Nta = nitriloacetic acid) complex which gave a AV value of —1.5 cm3 mol-1. The reaction of this complex with... 

NO was proposed to occur through an associative interchange mechanism (Ia). A recent study of the formation of [Fe(H20)5(N0)]2+ from aquated ferrous ion (30) resulted in activation parameters similar to those for chelated ferrous ion (Table II). The small and positive activation volumes were used to assign the reaction mechanism as dissociative interchange in character. 

In two earlier studies (106, 107), the oxidation of two Schiff base complexes were studied at room temperature, but in these cases only activation parameters for the overall process could be obtained since it was not possible to detect the formation of an intermediate species which could be attributed to a peroxo species. Nevertheless, the kinetic measurements provided indirect evidence for the existence of this intermediate. In both studies negative values for the activation entropies and the activation volumes were obtained. The oxidation of [Cu2(H-BPB-H)(CH3CN)2](PF6)2 (H-BPB-H = l,3-bis[iV-(2-pyridylethyl)-formidoyl]benzene) is accompanied by an activation entropy of -53 11 J K-1 mol-1 and an activation volume of -9.5 0.5 cm3 mol-1. In... 

Valuable information on mechanisms has been obtained from data on solvent exchange (4.4).The rate law, one of the most used mechanistic tools, is not useful in this instance, unfortunately, since the concentration of one of the reactants, the solvent, is invariant. Sometimes the exchange can be examined in a neutral solvent, although this is difficult to find. The reactants and products are however identical in (4.4), there is no free energy of reaction to overcome, and the activation parameters have been used exclusively, with great effect, to assign mechanism. This applies particularly to volumes of activation, since solvation differences are approximately zero and the observed volume of activation can be equated with the intrinsic one (Sec. 2.3.3). 

The activation parameters for the cation-independent pathway ( o) can be accounted for by a modified semiclassical Marcus-Hush theory. Lower enthalpies, and more positive volumes of activation are noted for the M +-catalyzed pathway. - ... 

Activation parameters have been determined for eliminative thermal decomposition of hexahydro-l,3,5-trinitro-l,3,5-triazine and related compounds, under high pressure in dilute solution." The negative activation volumes, low enthalpies of activation. 

Table V summarizes rate constants, and activation volumes for water exchange on [M(0H)(H20)5] together with those of [M(H20)6] . Accuracy of exchange rate constants /jqh and its activation parameters AH and AS relies on the knowledge of AHj , and ASa° (39,52). The hydrolysis of aqueous M " " ions is complicated by oligomerization and ranges of hydrolysis constants have been reported for example for Al (91,92) and Ga (93-95). As a general trend a strong increase in the lability of the coordinated water molecules is observed for the hydrolyzed species when compared to the hexa-aqua ions. Even at very low pH, where the mole fraction of the hydrolyzed species is extremely small, the water exchange observed by NMR on the bulk water can be dominated by the fast exchange on [M(0H)(H20)5] and not by the much slower exchange on...

Experiments cannot tell us what transition states look like. The fact is that transition states cannot even be detected experimentally let alone characterized, at least not directly. While measured activation energies relate to the energies of transition states above reactants, and while activation entropies and activation volumes, as well as kinetic isotope effects, may be invoked to imply some aspects of transition-state structure, no experiment can actually provide direct information about the detailed geometries and/or other physical properties of transition states. Quite simply, transition states do not exist in terms of a stable population of molecules on which experimental measurements may be made. Experimental activation parameters provide some guide, but tell us little detail about what actually transpires in going from reactants to products. 

The amount of water in the reaction mixture can be quantified in different ways. The most common way is to nse the water concentration (in mol/1 or % by volume). However, the water concentration does not give much information on the key parameter enzyme hydration. In order to have a parameter which is better correlated with enzyme hydration, researchers have started to nse the water activity to quantify the amount of water in non-conventional reaction media (Hailing, 1984 Bell et al, 1995). For a detailed description of the term activity (thermodynamic activity), please look in a textbook in physical chemistiy. Activities are often very nselul when studying chemical equilibria and chemical reactions of all kinds, but since they are often difficult to measure they are not used as mnch as concentrations. Normally, the water activity is defined so that it is 1.0 in pure water and 0.0 in a completely dry system. Thus, dilute aqueous solutions have water activities close to 1 while non-conventional media are found in the whole range of water activities between 0 and 1. There is a good correlation between the water activity and enzyme hydration and thns enzyme activity. An advantage with the activity parameter is that the activity of a component is the same in all phases at eqnihbrium. The water activity is most conveniently measnred in the gas phase with a special sensor. The water activity in a liqnid phase can thns be measured in the gas phase above the liquid after equilibration. 

The nature of the active species in the anionic polymerization of non-polar monomers, e. g. styrene, has been disclosed to a high degree. The kinetic measurements showed, that the polymerization proceeds in an ideal way, without side-reactions, and that the active species exist in the form of free ions, solvent-sparated and contact ion pairs, which are in a dynamic equilibrium (l -4). For these three species the rate constants and activation parameters (including the activation volumes), as well as the rate constants and equilibrium constants of interconversion have been determined (4-7.) Moreover, it could be shown by many different methods (e. g. conductivity and spectroscopic methods) that the concept of solvent-separated ion pairs can be applied to many ionic compounds in non-aqueous polar solvents (8). 

Activation parameters that have been measured for Aal1 reactions are generally consistent with a unimolecular rate-determining step. The volume of activation for the hydrolysis of f-butyl acetate in 0.01 M HCI at 60°C is zero, within experimental error70. No significant change in rate is observed from atmospheric pressure up to 2 kbar, although this increase in pressure almost doubles the rate of hydrolysis of ethyl acetate in 0.1 M HCI at 35°C. 

---