Non-reactive Models

Examples of the utility of simple models for providing atomic-level details of processes occurring in energetic materials are evident in a number of MD studies performed by Tsai and co-workers [106-108]. For instance, 

With the advent of first principles computational methods, highly scalable software and parallel computer architectures, more elaborate and accurate classical force fields than those discussed in the preceding section are being developed for predictions of physical and chemical properties of energetic solids. As indicated in section 2 of this chapter there are several 

In the development of the set of intermolecular potentials for the nitramine crystals Sorescu, Rice, and Thompson [112-115] have considered as the starting point the general principles of atom-atom potentials, proven to be successful in modeling a large number of organic crystals [120,123]. Particularly, it was assumed that intermolecular interactions can be separated into dispersive-repulsive interactions of van der Waals and electrostatic interactions. An additional simplification has been made by assuming that the intermolecular interactions depend only on the interatomic distances and that the same type of van der Waals potential parameters can be used for the same type of atoms, independent of their valence state. The non-electric interactions between molecules have been represented by Buckingham exp-6 functions, 

The atom-centered monopole charges have been determined by fitting the quantum mechanically derived electrostatic potential in the region 

Based on molecular packing calculations with and without symmetry constraints the lattice dimensions for RDX crystal have been reproduced to within 0.9% deviation relative to experimental results and with a very small translation and rotation (less than 1.1°) of the molecules inside the unit cell. Additionally, the lattice energy was found to be practically identical to the static lattice energy estimated based on the experimental enthalpy of sublimation (E AH S0M + 2RT). 

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Though a porous medium may be described adequately under non-reactive conditions by a smooth field type of diffusion model, such as one of the Feng and Stewart models, it does not necessarily follow that this will still be the case when a chemical reaction is catalysed at the solid surface. In these circumstances the smooth field assumption may not lead to appropriate expressions for concentration gradients, particularly in the smaller pores. Though the reason for this is quite simple, it appears to have been largely overlooked,... 

HGSystem offers the most rigorous treatments of HF source-term and dispersion analysis a ailable for a public domain code. It provides modeling capabilities to other chemical species with complex thermodynamic behavior. It treats aerosols and multi-component mixtures, spillage of a liquid non-reactive compound from a pressurized vessel, efficient simulations of time-dependent... 

HIWAY-ROADWAY are two models which compute die hourly concentrations of non-reactive pollutants downwind of roadways and predict pollutant concentrations within two hundred meters of a highway, respectively. 

The modeling of mass transport from the bulk fluid to the interface in capillary flow typically applies an empirical mass transfer coefficient approach. The mass transfer coefficient is defined in terms of the flux and driving force J = kc(cbuik-c). For non-reactive steady state laminar flow in a square conduit with constant molecular diffusion D, the mass balance in the fluid takes the form... 

If only partial screening is present, the fractal dimension takes a value somewhere between df and df. According to this model, a crosslinker deficiency, which leads to a more open structure and therefore a lower value of du increases the value of n. Dilution of the precursor with a non-reactive species has the same effect on the relaxation exponent. 

Despite these difficulties, the multi-environment conditional PDF model is still useful for describing simple non-isothermal reacting systems (such as the one-step reaction discussed in Section 5.5) that cannot be easily treated with the unconditional model. For the non-isothermal, one-step reaction, the reaction-progress variable Y in the (unreacted) feed stream is null, and the system is essentially non-reactive unless an ignition source is provided. Letting Foo(f) (see (5.179), p. 183) denote the fully reacted conditional progress variable, we can define a two-environment model based on the E-model 159... 

The model described in the previous sections is very complicated and therefore in Part I only isothermal studies will be reported. This limiting situation can be obtained by putting //, = 0 (i = 1,. ..,n) and setting the bulk temperatures equal to To in eq. (16b). In this paper the influence of multicomponent transport phenomena on the mass transfer rate between a gas/vapour and a liquid will be studied in detail for both non-reactive and reactive conditions. It should be stressed that the validity of the model developed in... 

The numerical jet model [9-11] is based on the numerical solution of the time-dependent, compressible flow conservation equations for total mass, energy, momentum, and chemical species number densities, with appropriate in-flow/outfiow open-boundary conditions and an ideal gas equation of state. In the reactive simulations, multispecies temperature-dependent diffusion and thermal conduction processes [11, 12] are calculated explicitly using central difference approximations and coupled to chemical kinetics and convection using timestep-splitting techniques [13]. Global models for hydrogen [14] and propane chemistry [15] have been used in the 3D, time-dependent reactive jet simulations. Extensive comparisons with laboratory experiments have been reported for non-reactive jets [9, 16] validation of the reactive/diffusive models is discussed in [14]. 

Ahmed FP, McLaughlin DP, Stanford SC, Stamford JA (2002) Maudsley reactive and non-reactive (MNRA) rats display hehavioral contrasts on exposure to an open field, the elevated plus maze or the dark-light shuttle hox. Abstract, FENS, Paris, France Ammassari-Teule A, Milhaud JM, Passino E, Restivo L, LassaUe JM (1999) Defective processing of contextual information may he involved in the poor performance of DBA/2 mice in spatial tasks. Behav Genet 29 283-289 Anisman H, Zalcman S, Shanks N, Zacharko RM (1991) Multisystem regulation of performance deficits induced hy stressors an animal model of depression. In Boulton AA, Baker GB, Martin-lverson MT (eds) Animal models in psychiatry, vol 2. Humana Press, Clifton, pp 1-59... 

Although the kinetic rate and energy partitioning are qualitatively consistent with a pure ER process, other aspects of the experiments and most of the theory (see discussion below) imply that the abstraction is more properly described as a combination of ER and HA reactions. The large a for abstraction is inconsistent with theoretical studies of a pure ER process as this requires a direct hit of the incoming H(D) with the adsorbed D(H) [380,381]. There is also no way to reconcile formation of homonuclear products with a pure ER process. In addition, similar kinetic experiments on other metals, e.g., Ni(100) [146], Pt(lll) [147,382], etc., are not even in qualitative agreement with the simple ER rate law above. In those cases, it is necessary to develop more sophisticated HA kinetic mechanisms to describe the kinetics experiments [383-385]. The key parameter of these kinetic models is the ratio of reaction to non-reactive trapping, pr/ps. For pr/ p, = 1, the HA kinetics looks very much like the simple ER case, and this is the reason H(D) + D(H)/Cu(lll) has such simple kinetics. 

Thus, the hydroxyl group fulfills a dual role (l) due to formation of the EHn complex it significantly activates the epoxy ring and, (2) upon formation of the non-reactive A Hn complexes, the reaction rate decreases as a result of a drop in the concentration of the primary and secondary amines and free hydroxyl groups not entering the A Hn complex which catalyzes the reaction. The latter factor has a greater effect on the rate drop than the former, which is confirmed by a direct experiment14,44>. Addition of a model secondary alcohol, e.g. cyclohexanol, increases not only the reaction rate but also the conversion at which the reaction becomes be sharply inhibited. 

Non-linearities arising from non-reactive interactions between adsorbed species will not be our main concern. In this section we return to variations of the Langmuir-Hinshelwood model, so the adsorption and desorption processes are not dependent on the surface coverage. We are now interested in establishing which properties of the chemical reaction step (12.2) may lead to multiplicity of stationary states. In particular we will investigate situations where the reaction step requires the involvement of additional vacant sites. Thus the reaction step can be represented in the general form... 

Application of the principle of stereoelectronic control predicts that the first tetrahedral intermediate must have conformation 21 rather than 23. As a result, the non-reactivity of the above two peptide substrates can be readily explained. In these two substrates, the amide nitrogen carries an extra alkyl substituent and molecular models show that this extra... 

Fig.12.4a-d. RADACK procedure a B-DNA represented in a space-filling model b the reactive atoms only c the same atoms but with sizes according to their OH cross-section d with the non-reactive atoms re-added according to Begusova et al. (2001b, with permission)... 

Simulation of frank SSBs and base damage as expressed by ALS has been achieved with the RADACK (RADiation attACK) procedure (Begusova et al. 2001b). This takes into account that the various nucleobases and the hydrogens of the sugar moiety react with different rate constants. The effect is shown in Fig. 12.4, where B-DNA is represented in a space-filling model with only the reactive atoms represented, with the same atoms but with sizes according to their OH cross-section or with the non-reactive atoms re-added. It is the last structure that- OH "encounters" in the RADACK procedure. 

Fig. 4.23 also indicates a slight decrease of the signal plateau which, at a first glance, was unexpected. In the following, a reactive dispersion model given in ref. [37] is applied to deduce rate constants for different reaction temperatures. A trapezoidal response function will be used. The temperature-dependent diffusion coefficient was calculated according to a prescription by Hirschfelder (e.g., [80], p. 68 or [79], p. 104] derived from the Chapman-Enskog theory. For the dimensionless formulation, the equation is divided by M/A (with M the injected mass and A the cross-section area). This analytical function is compared in Fig. 4.24 with the experimental values for three different temperatures. The qualitative behavior of the measured pulses is well met especially the observed decrease of the plateau is reproduced. The overall fit is less accurate than for the non-reactive case but is sufficient to now evaluate the rate constant. 

For the non-reactive tracer tests, a solution containing KI was introduced to the bottom of the column (up-flow mode) using a Rainin Model SD-200 solvent delivery pump. The first non-reactive tracer test was performed after complete water saturation of a column. PCE was then introduced into the bottom of the column using a Harvard Apparatus Model 22 syringe pump at a flow rate of 0.33 mL/min. When approximately 70% of the pore volume... 

Figure 3.90 In contrast to the (non-reactive) Taylor model, the tracer gas speed for a reacting gas is unequal to the carrier gas speed. This fact can be derived from the exponential term in the solution of the concentration of the tracer gas cA at the channel exit [38].

The above analytical solution was expanded to three dimensions. In such a way, the reactor geometry or the channel can be designed. An appropriate simplified model, given in [38], can be derived from the diffusion equation. Appropriate boundary conditions at the channel walls account for the heterogeneous wall reaction. The concentration of a species A which reacts at the channel wall irreversibly to a species B was given as a function of the lateral channel dimensions y and z and the axial channel dimension xv For an inert gas and for y and z equal to zero (coordinate center indicated in Figure 3.94), Eq. (3.13) reduces to the solution of a non-reactive fluid given above ... 

The third chapter focuses on the modelization of solvent effects on ground state chemical reactivity and excited state reactive and non-reactive processes. 

A description of the method of molecular dynamics simulations and its applications to energetic materials research is provided. We present an overview of the development of both reactive and non-reactive interaction potentials used to describe the energetic materials in different phases. Limitations as well as performances of the current models are indicated, including recent advances in reactive model development. Applications of the method to both gas and condensed phases of energetic materials are given to illustrate current capabilities. 

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