The Condensed Phase

Here a°(c) is the standard state chemical potential of condensed fluid in equilibrium with the vapor at the vapor pressure P, and the temperature of the measurement. 

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There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

Harris A L, Berg M and Harris C B 1986 Studies of chemical reactivity in the condensed phase. I. The dynamics of iodine photodissociation and recombination on a picosecond time scale and comparison to theories for chemical reactions in solution J. Chem. Phys. 84 788... 

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... 

Of great interest to physical chemists and chemical physicists are the broadening mechanisms of Raman lines in the condensed phase. Characterization of tliese mechanisms provides infomiation about the microscopic dynamical behaviour of material. The line broadening is due to the interaction between the Raman active chromophore and its environment. 

Applications of ultrafast spectroscopy to chemical dynamics, especially in the condensed phase and in proteins. 

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. 

Much of chemistry occurs in the condensed phase solution phase ET reactions have been a major focus for theory and experiment for the last 50 years. Experiments, and quantitative theories, have probed how reaction-free energy, solvent polarity, donor-acceptor distance, bridging stmctures, solvent relaxation, and vibronic coupling influence ET kinetics. Important connections have also been drawn between optical charge transfer transitions and thennal ET. 

While the classical approach to simulation of slow activated events, as described above, has received extensive attention in the literature and the methods are in general well established, the methods for quantum-dynamical simulation of reactive processes in complex systems in the condensed phase are still under development. We briefly consider electron and proton quantum dynamics. 

Bash, P.A., Field, M.J.,Karplus, M. Free energy perturbation method for chemical reactions in the condensed phase A dynamical approach baaed on a combined quantum and molecular dynamics potential. J. Am. Chem. Soc. 109 (1987) 8092-8094. 

Numerous mathematical formulas relating the temperature and pressure of the gas phase in equilibrium with the condensed phase have been proposed. The Antoine equation (Eq. 1) gives good correlation with experimental values. Equation 2 is simpler and is often suitable over restricted temperature ranges. In these equations, and the derived differential coefficients for use in the Hag-genmacher and Clausius-Clapeyron equations, the p term is the vapor pressure of the compound in pounds per square inch (psi), the t term is the temperature in degrees Celsius, and the T term is the absolute temperature in kelvins (r°C -I- 273.15). 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

The Clapeyron equation expresses the dynamic equilibrium existing between the vapor and the condensed phase of a pure substance ... 

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. 

Either mechanism can be used to describe how antimony—halogen systems operate in both the condensed and vapor phases. In the condensed phase a chat that is formed during the reaction of the polymer, antimony trioxide, and the halogen reduces the rate of decomposition of the polymer therefore, less fuel is available for the flame (16). 

Phosphoms-containing additives can act in some cases by catalyzing thermal breakdown of the polymer melt, reducing viscosity and favoring the flow or drip of molten polymer from the combustion zone (25). On the other hand, red phosphoms [7723-14-0] has been shown to retard the nonoxidative pyrolysis of polyethylene (a radical scission). For that reason, the scavenging of radicals in the condensed phase has been proposed as one of several modes of action of red phosphoms (26). 

The system of primary interest, then, is that of a condensable vapor moving between a Hquid phase, usually pure, and a vapor phase in which other components are present. Some of the gas-phase components may be noncondensable. A simple example would be water vapor moving through air to condense on a cold surface. Here the condensed phase, characterized by T and P, exists pure. The vapor-phase description requiresjy, the mole fraction, as weU as T and P. The nomenclature used in the description of vapor-inert gas systems is given in Table 1. 

Units and Concentration. In the gaseous as well as the condensed phases, molecular concentration by molecular species is of prime importance. By convention, total pressure in a MaxweUian gas is used as though it indicates the quaUty of the vacuum and as though MaxweUian gases were the rule rather than the exception (12). In general, in dynamic systems, gas pressure (or its partial pressure components) is neither isotropic nor an adequate indicator of molecular significance. 

Partial Concentration. The sum of the partial concentrations (pressures) in a free molecular gas is equal to the total concentration (pressure). However, all gaseous components, at the same partial pressure or absolute pressure or ratios thereof, are not likely to have the same significance to any or all vacuum appHcations. The significance of the condensed-phase concentrations must therefore be considered. 

Molecular transport concerns the mass motion of molecules in condensed and gaseous phases. The mass motions are driven primarily by temperature. As time progresses, the initial mass motion results in concentration gradients. In the condensed phase, dow along concentration gradients is described by Fick s law. 

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