Kinetics condensed-phase reactions

MPa, which has been observed in HMX combustion data, whereas the 1 model does not. The reason is that as pressure drops below 1 MPa, the burning rate for Eg 1 becomes increasingly sensitive to condensed phase reaction kinetics and does so in a continuous fashion. One trend that is obscured by using non-dimensional variables as presented here is that dimensional temperature sensitivity Gp = k/ T - Tg) is also sensitive to radiant flux qr in the range of... 

A logical next step is to incorporate these numerical models into combustion simulations. Ultimately, though, it will be necessary to develop new kinetic paradigms for condensed phase reaction kinetics that are firmly grounded in the underlying molecular properties. 

As these examples have demonstrated, in particular for fast reactions, chemical kinetics can only be appropriately described if one takes into account d3mamic effects, though in practice it may prove extremely difficult to separate and identify different phenomena. It seems that more experiments under systematically controlled variation of solvent environment parameters are needed, in conjunction with numerical simulations that as closely as possible mimic the experimental conditions to improve our understanding of condensed-phase reaction kinetics. The theoretical tools that are available to do so are covered in more depth in other chapters of this encyclopedia and also in comprehensive reviews [6, 118. 119]. 

Experimental determination of Ay for a reaction requires the rate constant k to be determined at different pressures, k is obtained as a fit parameter by the reproduction of the experimental kinetic data with a suitable model. The data are the concentration of the reactants or of the products, or any other coordinate representing their concentration, as a function of time. The choice of a kinetic model for a solid-state chemical reaction is not trivial because many steps, having comparable rates, may be involved in making the kinetic law the superposition of the kinetics of all the different, and often unknown, processes. The evolution of the reaction should be analyzed considering all the fundamental aspects of condensed phase reactions and, in particular, beside the strictly chemical transformations, also the diffusion (transport of matter to and from the reaction center) and the nucleation processes. 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

The FDS5 pyrolysis model is used here to qualitatively illustrate the complexity associated with material property estimation. Each condensed-phase species (i.e., virgin wood, char, ash, etc.) must be characterized in terms of its bulk density, thermal properties (thermal conductivity and specific heat capacity, both of which are usually temperature-dependent), emissivity, and in-depth radiation absorption coefficient. Similarly, each condensed-phase reaction must be quantified through specification of its kinetic triplet (preexponential factor, activation energy, reaction order), heat of reaction, and the reactant/product species. For a simple charring material with temperature-invariant thermal properties that degrades by a single-step first order reaction, this amounts to -11 parameters that must be specified (two kinetic parameters, one heat of reaction, two thermal conductivities, two specific heat capacities, two emissivities, and two in-depth radiation absorption coefficients). 

The development of environmentally acceptable incineration technologies for the disposal of hazardous wastes is dependent on an understanding of the roles of (1) atomization or method of introduction of the waste materials, (2) evaporation and condensed-phase reactions of the waste droplets in the incinerator environment, (3) turbulent mixing in the incinerator, (4) kinetics of the thermal degradation and oxidation of the chemical species in question, and (5) heat transfer in the incinerator. 

Experiments aimed at probing solvent dynamical effects in electrochemical kinetics, as in homogeneous electron transfer, are only of very recent origin, fueled in part by a renaissance of theoretical activity in condensed-phase reaction dynamics [47] (Sect. 3.3.1). It has been noted that solvent-dependent rate constants can sometimes be correlated with the medium viscosity, t] [101]. While such behavior may also signal the onset of diffusion-rather than electron-transfer control, if the latter circumstances prevail this finding suggests that the frequency factor is controlled by solvent dynamics since td and hence rL [eqn. (23), Sect. 3.3.1] is often roughly proportional to... 

Chemical means include 1) modification of polymer morphology and structure modification of composition and relative amounts of material components, causing a variation of condensed- and gas-phase reaction kinetics and mechanisms, at their interface 2) affecting the flame with various chemical agents (gas-phase combustion inhibitors). 

Condensed phase reactions are necessarily influenced by their environment. Reactant-reactant, solvent-solvent, and solvent-reactant intermolecular forces always affect, to some degree, the course of imimolecular processes in solution. This makes the rates of these reactions far less predictable by a priori considerations, and renders critical evaluation of solution kinetics very difficult. Nevertheless, the results can be broadly related to theory and extreme contradictions in the data can often be pinpointed. The primary value of the solution kinetics is, then, found in the assignment of the most reasonable mechanism and the relationship between structure and relative reactivity in a series of compounds. 

Independently of the adopted approach for the mechanism formulation, the estimation of the rate constants for all the reaction classes involved in the pyrolysis process of PE, PP, PS and PVC is of critical importance in model development. As already mentioned, the kinetic parameters of the condensed-phase reactions are directly derived from the rate parameters of the analogous gas-phase reactions, properly corrected to take into account transposition in the liquid phase (e.g., Section II.D). 

T. D. (2004) Ensemble-averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed-phase reactions,... 

B. In their analytical model, WSB used zero-order reaction kinetics for the first reaction and obtained the steady state solution to the resulting set of algebraic equations by iteration using both reactions. However, our model starts from igniting the pure HMX solid by a constant (simulated laser) heat flux, and we have experimented with different types of kinetics for the first (condensed phase) reaction. This strategy allows us to represent the solid-gas interface as a structured region in one dimension, as opposed to a discontinuous boundary. 

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