The assumptions inherent in the derivation of the Hertz-Knudsen equation are (1) the vapor phase does not have a net motion (2) the bulk liquid temperature and corresponding vapor pressure determine the absolute rate of vaporization (3) the bulk vapor phase temperature and pressure determine the absolute rate of condensation (4) the gas-liquid interface is stationary and (5) the vapor phase acts as an ideal gas. The first assumption is rigorously valid only at equilibrium. For nonequilibrium conditions there will be a net motion of the vapor phase due to mass transfer across the vapor-liquid interface. The derivation of the expression for the absolute rate of condensation has been modified by Schrage (S2) to account for net motion in the vapor phase. The modified expression is [Pg.355]

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. [Pg.371]

Equation 1 relates the force fields describing the motions of the molecule in the condensed and in the gaseous phase with the activity ratio. These fields are different owing to the effect of the intermolecular forces which are operative in the condensed phase. The intermolecular forces are exclusively solute-solute forces in the pure state (where the ratio P /P reduces to the vapor pressure isotope effect, VPIE), [Pg.100]

Because processes of interest to us take place in condensed phases, we can usually exclude rotational levels from our discussion gas phase rotational motions become in the condensed phase librations and intermolecular vibrations associated with the molecular motion in its solvent cage. [Pg.643]

The theoretical analysis of experimentally observed VPIE data has furnished information, among others, (1) about the details of the intermolecular interactions in the liquid phase, (2) on the vibrational coupling between internal vibrations and molecular translations and/or rotations, which occurs in the condensed phase, (3) on the density dependence of the force constants, which govern the external molecular motions and internal vibrations in the liquid, (4) on changes in vibrational anharmonicity, which occur on condensation, as well as (5) on the magnitude of the dielectric correction to IR absorption peaks in condensed phases. [Pg.711]

Abstract. In this chapter we discuss approaches to solving quantum dynamics in the condensed phase based on the quantum-classical Liouville method. Several representations of the quantum-classical Liouville equation (QCLE) of motion have been investigated and subsequently simulated. We discuss the benefits and limitations of these approaches. By making further approximations to the QCLE, we show that standard approaches to this problem, i.e., mean-field and surface-hopping methods, can be derived. The computation of transport coefficients, such as chemical rate constants, represent an important class of problems where the QCL method is applicable. We present a general quantum-classical expression for a time-dependent transport coefficient which incorporates the full system s initial quantum equilibrium structure. As an example of the formalism, the computation of a reaction rate coefficient for a simple reactive model is presented. These results are compared to illuminate the similarities and differences between various approaches discussed in this chapter. [Pg.383]

For intramolecular vibrations, each site was considered independently. However, the reorganizations in the surrounding solvent are necessarily properties of both sites since some of the solvent molecules involved are shared between reactants. The critical motions in the solvent are reorientations of the solvent dipoles. These motions are closely related to rotations of molecules in the gas phase but are necessarily collective in nature because of molecule—molecule interactions in the condensed phase of the solution. They have been treated theoretically as vibrations by analogy with lattice vibrations of phonons which occur in the solid state.32,33 [Pg.339]

We show how the quantum-classical evolution equations of motion can be obtained as an approximation to the full quantum evolution and point out some of the difficulties that arise because of the lack of a Lie algebraic structure. The computation of transport properties is discussed from two different perspectives. Transport coefficient formulas may be derived by starting from an approximate quantum-classical description of the system. Alternatively, the exact quantum transport coefficients may be taken as the starting point of the computation with quantum-classical approximations made only to the dynamics while retaining the full quantum equilibrium structure. The utility of quantum-classical Liouville methods is illustrated by considering the computation of the rate constants of quantum chemical reactions in the condensed phase. [Pg.521]

While in the frequency domain all the spectroscopic information regarding vibrational frequencies and relaxation processes is obtained from the positions and widths of the Raman resonances, in the time domain this information is obtained from coherent oscillations and the decay of the time-dependent CARS signal, respectively. In principle, time- and frequency-domain experiments are related to each other by Fourier transform and carry the same information. However, in contrast to the driven motion of molecular vibrations in frequency-multiplexed CARS detection, time-resolved CARS allows recording the Raman free induction decay (RFID) with the decay time T2, i.e., the free evolution of the molecular system is observed. While the non-resonant contribution dephases instantaneously, the resonant contribution of RFID decays within hundreds of femtoseconds in the condensed phase. Time-resolved CARS with femtosecond excitation, therefore, allows the separation of nonresonant and vibrationally resonant signals [151]. [Pg.135]

© 2019 chempedia.info