Condensed phase processes

The general approach is illustrated in detail for the case of aqueous ferrous and ferric ions, and the calculated rate constant and activation parameters are found to be in good agreement with the available experimental data. The formalisms we have employed in studying such complicated condensed phase processes necessarily rely on numerous approximations. Furthermore, some empirical data have been used in characterizing the solvated ions. We emphasize, nevertheless, that (1) none of the parameters were obtained from kinetic data, and (2) this is, as far as we are aware, the first such theoretical determination to be based on fully Ab initio electronic matrix elements, obtained from large scale molecular orbital (MO) calculations. A molecular orbital study of the analogous hexaaquo chromium system has been carried out by Hush, but the calculations were of an approximate, semi-empirical nature, based in part on experi-... 

Electrodeposition is by its nature a condensed phase process, whereas most studies of ALE have been performed using gas phase or vacuum methodologies, CVD or MBE. A solution phase deposition methodology related to ALE has been developed in France by Nicolau et al. [27-32] (Fig. 2), in which adsorbed layers of elements are formed by rinsing a substrate in aqueous solutions containing ionic precursor for the desired elements, sequentially, in a cycle. After exposure to each precursor, the substrate is copiously rinsed and then transferred to a solution containing the precursor for the next element. The method is referred to as successive ionic layer adsorption and reaction (SILAR). Reactivity in SILAR appears to be controlled by the rinsing procedure, solution composition, pH, and specifically... 

This paper provides an example of how accurate continuum models can open the door to the modeling of condensed-phase processes where solvation free energies have a very large influence on reaction energetics. It additionally offers a case study of how to first choose a model on the basis of experimental/tlieoretical comparisons over a relevant data set, and then apply tliat model with a greater expectation for its utility. The generality of this approach to other (equilibrium) electrochemical reactions seems promising. 

In quantum-classical Liouville (QCL) dynamics the partition of the system into bath and subsystem is motivated by the observation that for many condensed phase processes it is essential to account for the quantum mechanical character of only a few light (characteristic mass m) degrees of freedom the remaining heavy (characteristic mass M) degrees of freedom may be treated classically to a high degree of accuracy. 

Eq. (28) are used initially for obtaining the kinetic equations for condensed phase processes. Let us discuss a fairly general case for the theory of surface processes and assume the lattice to be inhomogeneous and the radius of the adspecies interaction pair potential to be equal to R (R> 1). 

M.A. Schroeder, R.A. Fifer, M.S. Miller, R.A. Pesce-Rodriguez, C.J.S. McNesby, G. Singh Condensed-phase Processes During Combustion of Solid Gun Propellants. I. Nitrate Ester Propellants, Combust. Flame, 126 (2001) 1569-1576 II. 1577-1598. 

While ab initio molecular dynamics simulations of condensed phase system hold great promise for accurate modeling of condensed phase processes, we anticipate that their use in large-scale simulations of reactions of energetic materials will not be feasible for several years. Therefore, until the computational limitations are eased, then molecular dynamics simulations of energetic materials in the condensed phase will be restricted to classical descriptions of reactions. 

COMBINED QM/MM METHODS FOR THE SIMULATION OF CONDENSED PHASE PROCESSES USING AN APPROXIMATE DFT APPROACH... 

QMZMM Methods for Simulation of Condensed Phase Processes... 

We feel that the erratic deflagration behavior of pure hydrazine perchlorate is attributable to the presence or absence of small amounts of impurities that catalyzed the condensed phase process, which implies that when the condensed phase process did not occur, deflagration would not propagate. The function of the fuels then would be to allow exothermic oxidation-reduction reactions to occur in the condensed phase... 

With adiabatic combustion, departure from a complete control of m by the gas-phase reaction can occur only if the derivation of equation (5-75) becomes invalid. There are two ways in which this can happen essentially, the value of m calculated on the basis of gas-phase control may become either too low or too high to be consistent with all aspects of the problem. If the gas-phase reaction is the only rate process—for example, if the condensed phase is inert and maintains interfacial equilibrium—then m may become arbitrarily small without encountering an inconsistency. However, if a finite-rate process occurs at the interface or in the condensed phase, then a difficulty arises if the value of m calculated with gas-phase control is decreased below a critical value. To see this, consider equation (6) or equation (29). As the value of m obtained from the gas-phase analysis decreases (for example, as a consequence of a decreased reaction rate in the gas), the interface temperature 7], calculated from equation (6) or equation (29), also decreases. According to equation (37), this decreases t. Eventually, at a sufficiently low value of m, the calculated value of T- corresponds to Tj- = 0, As this condition is approached, the gas-phase solution approaches one in which dT/dx = 0 at x = 0, and the reaction zone moves to an infinite distance from the interface. The interface thus becomes adiabatic, and the gas-phase processes are separated from the interface and condensed-phase processes. 

When compared with reactions in the gas phase, the theory of condensed phase processes meets the additional difficulty of having to deal with solvent interactions, but the detailed understanding of their effects is crudal in many... 

Numerical simulations have become a central tool in studies of condensed phase processes. The science, technique, and art of this tool are subjects of several excellent texts. Here we assume that important problems such as choosing a... 

Unlike the condensed phase process, for which the large activation energy, thermal decomposition mechanism EJRT 1) has been established by a large amount of evidence, a similar consensus has not developed for the gas phase. A range of activation energies for the gas phase from very large (Eg/RT 1) to very small Eg/RT 1) can be reasonably postulated. Since the interpretation of the reaction equation depends on the value of Eg, mechanistic interpretation will come later in connection with solutions corresponding to various values of Eg that have been obtained. 

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