Insertion thermodynamics

M—H bond dissociation energies, 1, 287 photochemistry, 1, 251 single crystal neutron diffraction, 1, 578 stability toward disproportionation, 1, 301 Metal—hydrogen bonds bond dissociation energy in 1,2-dichloroethane, 1, 289 stable metal hydrides in acetonitrile, 1, 287 thermochemical cycle, 1, 286 in THF and dichloromethane, 1, 289 olefin insertion thermodynamics, 1, 629 in Zr(IV) bis-Cp complexes, 4, 878 Metal—hydrogen hydricity data, 1, 292... 

What has been developed within the last 20 years is the computation of thermodynamic properties including free energy and entropy [12, 13, 14]. But the ground work for free energy perturbation was done by Valleau and Torrie in 1977 [15], for particle insertion by Widom in 1963 and 1982 [16, 17] and for umbrella sampling by Torrie and Valleau in 1974 and 1977 [18, 19]. These methods were primarily developed for use with Monte Carlo simulations continuous thermodynamic integration in MD was first described in 1986 [20]. 

In calculations of pore size from the Type IV isotherm by use of the Kelvin equation, the region of the isotherm involved is the hysteresis loop, since it is here that capillary condensation is occurring. Consequently there are two values of relative pressure for a given uptake, and the question presents itself as to what is the significance of each of the two values of r which would result from insertion of the two different values of relative pressure into Equation (3.20). Any answer to this question calls for a discussion of the origin of hysteresis, and this must be based on actual models of pore shape, since a purely thermodynamic approach cannot account for two positions of apparent equilibrium. 

The molecular features of covalent hydration are also present in the dihydroxy series, i.e., in pteridine-2,6-dione (30) and in pteridine-4,6-dione. The latter compound is hydrated only at the C(7)—N(8) double bond, whereas (30) forms two hydrated species, 7-hydroxy-7,8-dihydro- (29) and 4-hydroxy-3,4-dihydro-pteridin-2,6-dione (31) (equation 8). Structure (29) is thermodynamically the more stable substance (31) is formed more rapidly in solution but disappears slowly with time (63JCS5151). Insertion of a 4-methyl group greatly reduces the extent of 3,4- in favour of 7,8-hydration by a blocking effect . 

At the beginning of the century, nobody knew that a small proportion of atoms in a crystal are routinely missing, even less that this was not a mailer of accident but of thermodynamic equilibrium. The recognition in the 1920s that such vacancies had to exist in equilibrium was due to a school of statistical thermodynamicians such as the Russian Frenkel and the Germans Jost, Wagner and Schollky. That, moreover, as we know now, is only one kind of point defect an atom removed for whatever reason from its lattice site can be inserted into a small gap in the crystal structure, and then it becomes an interstitial . Moreover, in insulating crystals a point defect is apt to be associated with a local excess or deficiency of electrons. 

Figure 2. Reactions that occur in lead-acid batteries versus electrode potential (thermodynamic situation). Their equilibrium potentials are inserted as boxed numbers. Equilibrium potentials of the charge-discharge reactions (Pb/PbS04 and PhS04/Pb02) are represented by hatched columns, to indicate their dependence on acid concentration. The inserted equilibrium potentials (-0.32 and +l. 75 V) of the charge discharge reactions correspond to an acid density of 1.23 gem 3.

The thermodynamic properties of to-potactic insertion reaction materials with selective equilibrium are quite different from those of materials in which complete equilibrium can be assumed, and reconstitution reactions take place. Instead of flat plateaus related to polyphase equilibria, the composition-dependence of the potential generally has a flat S-type form. 

From a thermodynamic point of view, apart from charge density and specific charge, the redox potential of lithium insertion into/removal from the electrode materials has to be considered also. For instance, the redox potential of many Li alloys is between -0.3 and -1.0 V vs. Li/Li+, whereas it is only -0.1 V vs. 

The general catalytic cycle for the coupling of aryl-alkenyl halides with alkenes is shown in Fig. 9.6. The first step in this catalytic cycle is the oxidative addition of aryl-alkenyl halides to Pd(0). The activity of the aryl-alkenyl halides still follows the order RI > ROTf > RBr > RC1. The olefin coordinates to the Pd(II) species. The coordinated olefin inserts into Pd—R bond in a syn fashion, p-Hydrogen elimination can occur only after an internal rotation around the former double bond, as it requires at least one /I-hydrogen to be oriented syn perpendicular with respect to the halopalladium residue. The subsequent syn elimination yields an alkene and a hydridopalladium halide. This process is, however, reversible, and therefore, the thermodynamically more stable (E)-alkene is generally obtained. Reductive elimination of HX from the hydridopalladium halide in the presence of a base regenerates the catalytically active Pd(0), which can reenter the catalytic cycle. The oxidative addition has frequently assumed to be the rate-determining step. 

The stability of liquid water is due in large part to the ability of water molecules to form hydrogen bonds with one another. Such bonds tend to stabilize the molecules in a pattern where the hydrogens of one water molecule are adjacent to oxygens of other water molecules. When chemical species dissolve, they must insert themselves into this matrix, and in the process break some of the bonds that exist between the water molecules. If a substance can form strong bonds with water, its dissolution will be thermodynamically favored, i.e., it will be highly soluble. Similarly, dissolution of a molecule that breaks water-to-water bonds and replaces these with weaker water-to-solute bonds will be energetically im-favorable, i.e., it will be relatively insoluble. These principles are presented schematically in Fig. 15-1. 

The thermodynamic properties of magnesium make it a natural choice for use as an anode material in rechargeable batteries, as it may provide a considerably higher energy density than the commonly used lead-acid and nickel-cadmium systems, while in contrast to Pb and Cd, magnesium is inexpensive, environmentally friendly, and safe to handle. However, the development of Mg-ion batteries has so far been limited by the kinetics of Mg " " diffusion and the lack of suitable electrolytes. Actually, in spite of an expected general similarity between the processes of Li and Mg ion insertion into inorganic host materials, most of the compounds that exhibit fast and reversible Li ion insertion perform very poorly in Mg " ions. Hence, there... 

Lattice Vacancies and Interstitials Defects such as lattice vacancies and interstitials fall into two main categories intrinsic defects, which are present in pure crystal at thermodynamic equilibrium, and extrinsic defects, which are created when a foreign atom is inserted into the lattice. 

Figure 4.11 Optimized structures of CH cO species, as indicated, over aqueous-solvated Pt(lll) as determined by DFT in Cao et al. [2005]. Horizontal and vertical arrows indicate C—H and O—H cleavage steps, respectively. Reaction energies are included for the aqueous phase [Cao et al., 2005] and the vapor phase (in parentheses) [Desai et al., 2002]. The thermodynamically preferred aqueous phase pathway is indicated by bold arrows (in blue). (See color insert.)...

The electrochemical intercalation/insertion is not a special property of graphite. It is apparent also with many other host/guest pairs, provided that the host lattice is a thermodynamically or kinetically stable system of interconnected vacant lattice sites for transport and location of guest species. Particularly useful are host lattices of inorganic oxides and sulphides with layer or chain-type structures. Figure 5.30 presents an example of the cathodic insertion of Li+ into the TiS2 host lattice, which is practically important in lithium batteries. 

One common feature of all M + hydrocarbon systems mentioned in Sec. 1.2.2 is that none of the products resulted from cleavage of a C-C bond. This is a result of several factors. First, C-H bonds are less directional than C-C bonds (Sec. 1.1), allowing for multicentered bonding at the transition state, which tends to lower the barrier for C-H insertion relative to C-C insertion.2,18,22 Second, since M-H bonds are usually stronger than M-C bonds, intermediates resulting from insertion into a C-H bond are usually thermodynamically favored.141 Third, there are typically more C-H bonds in hydrocarbons than C-C bonds, so C-H insertion is also statistically favored. Finally, C-H bonds are more accessible to an incoming metal atom and are therefore more susceptible to insertion. 

Complexation of Cd with a series of polyamine macrocycles, but also related open-chain polyamines, comprising or attached to the 2,2 -bipyridine (bipy) and 1,10-phenanthroline (phen) moieties, has been studied by combined UV/vis spectrometry and potentiometry.24 Formation constants and distribution diagrams of the species present have been evaluated. As a result the thermodynamic stabilities, i.e., the formation constants, are lower for the bipy- and phen-contain-ing ligands than those for Cd complexes with aliphatic oligoaza macrocycles containing the same number of N donors. The probable reason is loss of flexibility of the ligands caused by the size and stiffness of the inserted heteroaromatic moieties. 

Thus, for a hydrophobic solute is determined by quantifying the probability po of successfully inserting a hard-core solute of the same size and shape into equilibrium configurations of water, as illustrated in Figure 4. A virtue of this approach is that the thermodynamics of hydrophobic hydration characterized by is determined from the properties of pure water alone. The solute enters only through its molecular size and shape (see Fig. 4). 

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