Reaction condensed phase

In the sections below a brief overview of static solvent influences is given in A3.6.2, while in A3.6.3 the focus is on the effect of transport phenomena on reaction rates, i.e. diflfiision control and the influence of friction on intramolecular motion. In A3.6.4 some special topics are addressed that involve the superposition of static and transport contributions as well as some aspects of dynamic solvent effects that seem relevant to understanding the solvent influence on reaction rate coefficients observed in homologous solvent series and compressed solution. More comprehensive accounts of dynamics of condensed-phase reactions can be found in chapter A3.8. chapter A3.13. chapter B3.3. chapter C3.1. chapter C3.2 and chapter C3.5. 

Kramers solution of the barrier crossing problem [45] is discussed at length in chapter A3.8 dealing with condensed-phase reaction dynamics. As the starting point to derive its simplest version one may use the Langevin equation, a stochastic differential equation for the time evolution of a slow variable, the reaction coordinate r, subject to a rapidly statistically fluctuating force F caused by microscopic solute-solvent interactions under the influence of an external force field generated by the PES F for the reaction... 

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],... 

Grote R F and Hynes J T 1981 Reactive modes in condensed phase reactions J. Chem. Phys. 74 4465... 

The Beckstead-Derr-Price model (Fig. 1) considers both the gas-phase and condensed-phase reactions. It assumes heat release from the condensed phase, an oxidizer flame, a primary diffusion flame between the fuel and oxidizer decomposition products, and a final diffusion flame between the fuel decomposition products and the products of the oxidizer flame. Examination of the physical phenomena reveals an irregular surface on top of the unheated bulk of the propellant that consists of the binder undergoing pyrolysis, decomposing oxidizer particles, and an agglomeration of metallic particles. The oxidizer and fuel decomposition products mix and react exothermically in the three-dimensional zone above the surface for a distance that depends on the propellant composition, its microstmcture, and the ambient pressure and gas velocity. If aluminum is present, additional heat is subsequently produced at a comparatively large distance from the surface. Only small aluminum particles ignite and bum close enough to the surface to influence the propellant bum rate. The temperature of the surface is ca 500 to 1000°C compared to ca 300°C for double-base propellants. 

Alternate expressions can also be written for equilibrium constants in condensed phase reactions. For example, for the reaction... 

Chymotrypsin, 170,171, 172, 173 Classical partition functions, 42,44,77 Classical trajectories, 78, 81 Cobalt, as cofactor for carboxypeptidase A, 204-205. See also Enzyme cofactors Condensed-phase reactions, 42-46, 215 Configuration interaction treatment, 14,30 Conformational analysis, 111-117,209 Conjugated gradient methods, 115-116. See also Energy minimization methods Consistent force field approach, 113 Coulomb integrals, 16, 27 Coulomb interactions, in macromolecules, 109, 123-126... 

Both the 12C/13C primary KIE and the 14N/15N secondary KIE have been determined (Table 4-2) [19, 20], with the immediate adjacent atoms about the isotopic substitution site quantized as well. To our knowledge, we are not aware of any such simulations prior to our work for a condensed phase reaction with converged secondary heavy isotope effects. This demonstrates the applicability and accuracy of the PI-FEP/UM method. 

A variety of experimental methods has been used to study the thermal chemistry of the unsaturated iron fragments produced by photolysis. For example, regeneration of 1Fe(CO)s was observed upon heating low-temperature matrices in which Fe(CO)5 had been photolyzed (35). These condensed-phase reactions are rather complex, as in some cases, components of the inert matrix may form adducts Fe(C0)4L or Fe(CO)sL (L = N2, Xe, CH4), so that the reaction observed is not simply CO addition to an unsaturated iron tetracarbonyl fragment. The same reactions were studied in the gas phase, using flash... 

The discussion of potential energy surfaces thus far has implicitly assumed that gas-phase reactions are in focus. For condensed-phase reaction dynamics, where thermal fluctuations have a significant and intrinsic role, the situation is much more unsettled. The reader is referred to the list of challenges to condensed-phase electronic structure theory recently made by Truhlar, who asks if condensed-phase electronic structure may be "... not only waiting for its Hylleraas, but even waiting for its Schrodinger [112] The development of liquid-phase dynamics will surely continue to be an intense area of research through the foreseeable future. 

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. 

A schematic representation of the combustion wave structure of a typical energetic material is shown in Fig. 3.9 and the heat transfer process as a function of the burning distance and temperature is shown in Fig. 3.10. In zone I (solid-phase zone or condensed-phase zone), no chemical reactions occur and the temperature increases from the initial temperature (Tq) to the decomposition temperature (T ). In zone II (condensed-phase reaction zone), in which there is a phase change from solid to liquid and/or to gas and reactive gaseous species are formed in endothermic or exothermic reactions, the temperature increases from T to the burning surface temperature (Tf In zone III (gas-phase reaction zone), in which exothermic gas-phase reactions occur, the temperature increases rapidly from Tj to the flame temperature (Tg). 

The combustion wave of HMX is divided into three zones crystallized solid phase (zone 1), solid and/or liquid condensed phase (zone 11), and gas phase (zone 111). A schematic representation of the heat transfer process in the combustion wave is shown in Fig. 5.5. In zone 1, the temperature increases from the initial value Tq to the decomposition temperature T without reaction. In zone 11, the temperature increases from T to the burning surface temperature Tj (interface of the condensed phase and the gas phase). In zone 111, the temperature increases rapidly from to the luminous flame temperature (that of the flame sheet shown in Fig. 5.4). Since the condensed-phase reaction zone is very thin (-0.1 mm), is approximately equal to T . 

The combustion wave of GAP copolymer is divided into three zones zone I is a non-reactive heat-conduction zone, zone II is a condensed-phase reaction zone. 

The condensed-phase reaction zone of a burning-interrupted BAMO copolymer is identified by infrared (IR) spectral analysis. In the non-heated zone, the absorption of the N3 bond, along with the absorptions of the C-O, C-H, and N-H bonds. 

The soUd-phase reaction zone is also termed the subsurface reaction zone or condensed-phase reaction zone . As the dark zone reaction represents an induction zone ahead of the flame zone, the dark zone is also termed the preparation zone when it produces a luminous flame. Since the flame zone is luminous, it is also termed the luminous flame zone . 

The combustion wave of an HMX composite propellant consists of successive re-achon zones the condensed-phase reachon zone, a first-stage reaction zone, a second-stage reaction zone, and the luminous flame zone. The combustion wave structure and temperature distribution for an HMX propellant are shown in Fig. 7.47. In the condensed-phase reaction zone, HMX particles melt together with the polymeric binder HTPE and form an energetic liquid mixture that covers the burning surface of the propellant. In the first-stage reaction zone, a rapid exother-... 

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