Condensed Phase Model

Molecular dynamics simulations are attractive because they can provide not only quantitative information about rates and pathways of reactions, but also valuable insight into the details of ho y the chemistry occurs. Furthermore, a dynamical treatment is required if the statistical assumption is not valid. Yet another reason for interest in explicit atomic-level simulations of the gas-phase reactions is that they contribute to the formulation of condensed-phase models and, of course, are needed if one is to include the initial stages of the vapor-phase chemistry in the simulations of the decomposition of energetic materials. These and other motivations have lead to a lot of efforts to develop realistic atomic-level models that can be used in MD simulations of the decomposition of gas-phase energetic molecules. 

The above discussion neglects polarization effects. In part, these are taken into account by the empirical scaling procedures (e.g., the dipole moment of the water molecule in condensed-phase models is chosen to be larger than the gas-phase value).12 Internal charge rearrangements due to conformational... 

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

Many of the condensed phase effects mentioned above have been studied computationally using the PI-QTST approach outlined in die first part of the last section. One such study 48 has focused on the model synnnetric... 

The tenn represents an externally applied potential field or the effects of the container walls it is usually dropped for fiilly periodic simulations of bulk systems. Also, it is usual to neglect v - and higher tenns (which m reality might be of order 10% of the total energy in condensed phases) and concentrate on For brevity henceforth we will just call this v(r). There is an extensive literature on the way these potentials are detennined experimentally, or modelled... 

The most important molecular interactions of all are those that take place in liquid water. For many years, chemists have worked to model liquid water, using molecular dynamics and Monte Carlo simulations. Until relatively recently, however, all such work was done using effective potentials [4T], designed to reproduce the condensed-phase properties but with no serious claim to represent the tme interactions between a pair of water molecules. 

The first molecular dynamics simulation of a condensed phase system was performed by Alder and Wainwright in 1957 using a hard-sphere model [Alder and Wainwright 1957]. In this model, the spheres move at constant velocity in straight lines between collisions. All collisions are perfectly elastic and occur when the separation between the centres of... 

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. 

Proper condensed phase simulations require that the non-bond interactions between different portions of the system under study be properly balanced. In biomolecular simulations this balance must occur between the solvent-solvent (e.g., water-water), solvent-solute (e.g., water-protein), and solute-solute (e.g., protein intramolecular) interactions [18,21]. Having such a balance is essential for proper partitioning of molecules or parts of molecules in different environments. For example, if the solvent-solute interaction of a glutamine side chain were overestimated, there would be a tendency for the side chain to move into and interact with the solvent. The first step in obtaining this balance is the treatment of the solvent-solvent interactions. The majority of biomolecular simulations are performed using the TIP3P [81] and SPC/E [82] water models. 

Specification of. S SkCG, CO) requires models for the diffusive motions. Neutron scattering experiments on lipid bilayers and other disordered, condensed phase systems are often interpreted in terms of diffusive motions that give rise to an elastic line with a Q-dependent amplitude and a series of Lorentzian quasielastic lines with Q-dependent amplitudes and widths, i.e.. 

The low-temperature chemistry evolved from the macroscopic description of a variety of chemical conversions in the condensed phase to microscopic models, merging with the general trend of present-day rate theory to include quantum effects and to work out a consistent quantal description of chemical reactions. Even though for unbound reactant and product states, i.e., for a gas-phase situation, the use of scattering theory allows one to introduce a formally exact concept of the rate constant as expressed via the flux-flux or related correlation functions, the applicability of this formulation to bound potential energy surfaces still remains an open question. 

Simulations of monolayers have focused on internal phase transitions, e.g., between the expanded phase and the condensed phases, between different tilted phases, etc. These phenomena cannot be reproduced by models with purely repulsive interactions. Therefore, Haas et al. [148,149] represent the amphiphiles as stiff Lennard-Jones chains, with one end (the head bead) confined to move in a plane. In later versions of the model [150-152], the head bead interactions differ from those of the tail beads they are taken to be purely repulsive, and the head size is variable. 

FIG. 8 Phase diagram of a Langmuir monolayer in a model of grafted stiff Lennard-Jones chains. LE denotes a disordered expanded phase, LC-U a condensed phase with untilted chains, LC-NN and LC-NNN condensed phases with collective tilt towards nearest neighbors and next-nearest neighbors, respectively, and LC-mod a phase which has a superstructure and an intermediate direction of tilt. (From Stadler and Schmid [151].)... 

---