Condensed-phase reaction paramete

As these examples have demonstrated, in particular for fast reactions, chemical kinetics can only be appropriately described if one takes into account dynamic 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 enviromnent 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 kmetics. 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. 

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). 

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). 

The SES and ESP approximations include the dynamics of solute degrees of freedom as fully as they would be treated in a gas-phase reaction, but these approximations do not address the full complexity of condensed-phase reactions because they do not allow the solvent to participate in the reaction coordinate. Methods that allow this are said to include nonequilibrium solvation. A variety of ways to include nonequilibrium solvation within the context of an implicit or reduced-degree-of-freedom bath are reviewed elsewhere [69]. Here we simply discuss one very general such NES method [76-78] based on collective solvent coordinates [71, 79]. In this method one replaces the solvent with one or more collective solvent coordinates, whose parameters are fit to bulk solvent properties or molecular dynamics simulations. Then one carries out calculations just as in the gas phase but with these extra one or more degrees of freedom. The advantage of this approach is its simplicity (although there are a few subtle technical details). 

Fig. 25 In-phase component of pressure-coupled response function for propellant-N (50 atm). Shaded region represents T-bumer measure-ments Horton and Price [35] NWC [36]. Model calculations are for quasi-steady model using parameters of Table 2. Condensed-phase reaction zone characteristic frequency is estimated to be // = 10,000 Hz quasi-steady assumption should be valid up to at least 3000 Hz.

Section 3 deals with reactions in which at least one of the reactants is an inorganic compound. Many of the processes considered also involve organic compounds, but autocatalytic oxidations and flames, polymerisation and reactions of metals themselves and of certain unstable ionic species, e.g. the solvated electron, are discussed in later sections. Where appropriate, the effects of low and high energy radiation are considered, as are gas and condensed phase systems but not fully heterogeneous processes or solid reactions. Rate parameters of individual elementary steps, as well as of overall reactions, are given if available. 

As discussed in Section 3.2.1, other explosion events can occur that impact process plant buildings, including condensed-phase explosions, uncontrolled chemical reactions, PV ruptures, and BLEVEs. Appendix A and Reference 5 describe the information needed and the methods available for calculating blast parameters from these events. 

The investigation of the chemical modification of dextran to determine the importance of various reaction parameters that may eventually allow the controlled synthesis of dextran-modified materials has began. The initial parameter chosen was reactant molar ratio, since this reaction variable has previously been found to greatly influence other interfacial condensations. Phase transfer catalysts, PTC s, have been successfully employed in the synthesis of various metal-containing polyethers and polyamines (for instance 26). Thus, the effect of various PTC s was also studied as a function of reactant molar ratio. 

Section 2 deals with reactions involving only one molecular reactant, i.e. decompositions, isomerisations and associated physical processes. Where appropriate, results from studies of such reactions in the gas phase and condensed phases and induced photochemically and by high energy radiation, as well as thermally, are considered. The effects of additives, e.g. inert gases, free radical scavengers, and of surfaces are, of course, included for many systems, but fully heterogeneous reactions, decompositions of solids such as salts or decomposition flames are discussed in later sections. Rate parameters of elementary processes involved, as well as of overall reactions, are given if available. 

Novozhilov (Ref 9) noted other instances where the instability criterion of Zel dovich is not satisfied. He also noted ZeTdovich s assertion that the form of the stability criterion may change if the variation in the surface temperature and the inertia of the reaction layer of the condensed phase are taken into account, and stability criteria obtained under the assumption that the chemical reaction zone in the condensed phase and all of the processes in the gas phase are without inertia. Novozhilov used a more general consideration of the problem to show that the stability region is determined by only two parameters Zel dovich s k and the partial derivative r of the surface temperature with respect to the initial temperature at constant pressure t=(dTi/(fro)p. Combustion is always stable if k 1, combustion is stable only when r >(k — l) /(k +1)... 

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