The viscosity increases approximately as and drere is, of course, no vestige of die activation energy which characterizes die transport properties of condensed phases. [Pg.110]

The theory is closely related to the theory of the quantum effect upon volumes and energies of condensed phases. De Boer and Blaisse showed that by use of quantum-mechanical cell theory a relation between the reduced volume Fq at 0 K and the reduced energy o at 0 K can be derived. These quantities are defined by [Pg.233]

The observations of vibrational coherence in optically initiated reactions described above clearly show that the standard assumption of condensed-phase rate theories—that there is a clear time scale separation between vibrational dephasing and the nonadiabatic transition—is clearly violated in these cases. The observation of vibrational beats has generally been taken to imply that vibrational energy relaxation is slow. This viewpoint is based on the optical Bloch equations applied to two-level systems. In this model, the total dephasing rate is given by [Pg.148]

Although the traditional approach of transition structure determination and reaction path following is perfectly suited for gas phase reactions, which can also provide major insight into the mechanism of condensed phase reactions, (14-16) it is also important to specifically consider the fluctuation and collective solvent motions accompanying the chemical transformation in solution.(17, 18) One approach that has been used to address this problem is the use of an energy-gap reaction coordinate, A. - [Pg.248]

A liquid does not have a fixed shape, so the surface area of a liquid can be easily changed. (The surface area of solids can also be changed by processes such as grinding. However, this requires a considerable amount of energy.) In condensed phases, molecules on the surface have a different environment from molecules in the bulk therefore, a measure of the surface area is necessary to completely define the state of the system. In Chapter 11, we will discuss surface effect in liquids by use of the surface tension, y, which is the extra energy per unit [Pg.40]

Equations (1) and (4) or other variations of the 12-6 power law are often called the Lennard-Jones potential. The numerical values of the constants in the Lennard-Jones potential may be obtained from studies of the compressibility of condensed phases, the virial coefficients of gases, and by other methods. A summary of these methods and other expressions for the molecular interaction energy can be found in the book by Moelwyn-Hughes (1964). [Pg.470]

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 [Pg.2243]

R.C. Oliver et al, USDeptCom, Office Tech-Serv ..AD 265822,(1961) CA 60, 10466 (1969) Metal additives for solid proplnts formulas for calculating specific impulse and other proplnt performance parameters are given. A mathematical treatment of the free-energy minimization procedure for equilibrium compn calcns is provided. The treatment is extended to include ionized species and mixing of condensed phases. Sources and techniques for thermodynamic-property calcns are also discussed [Pg.946]

On several occasions, the reader will notice a direct connection between the topics covered in the book and other, related areas of statistical mechanics, such as the methodology of computer simulations, nonequilibrium dynamics or chemical kinetics. This is hardly a surprise because free energy calculations are at the nexus of statistical mechanics of condensed phases. [Pg.525]

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