S. A. Egorov

A THEORY OF VIBRATIONAL ENERGY RELAXATION IN LIQUIDS

A microscopic statistical mechanical theory of the vibrational energy relaxation of a diatomic solute in an atomic solvent is presented. The diatomic is treated as a breathing Lennard‐Jones sphere. The relaxation rate is obtained from the Fourier transform of the force–force time‐correlation function. The latter is expanded in powers of time (up to t4), and expressions for the expansion coefficients are derived using equilibrium statistical mechanics. These coefficients are used to determine the parameters of an analytic ansatz for this correlation function, which can be evaluated at all times (and thus can be Fourier transformed). The resulting theory for the time‐correlation function is compared to numerical results from a molecular dynamics simulation. Theoretical results for the vibrational relaxation rate are compared to experiments on I2 in Xe over a wide range of densities and temperatures.

Semiclassical approximations to quantum time correlation functions

Abstract Over the last 40 years several ad hoc semiclassical approaches have been developed in order to obtain approximate quantum time correlation functions, using as input only the corresponding classical time correlation functions. The accuracy of these approaches has been tested for several exactly solvable gas-phase models. In this paper we test the accuracy of these approaches by comparing to an exactly solvable many-body condensed-phase model. We show that in the frequency domain the Egelstaff approach is the most accurate, especially at high frequencies, while in the time domain one of the other approaches is more accurate.

Vibrational energy relaxation of polyatomic solutes in simple liquids and supercritical fluids

A microscopic statistical mechanical theory of vibrational energy relaxation rates for polyatomic solutes in simple solvents is presented. The theory is based on a model of a spherical solute present at infinite dilution in a fluid of spherical solvent particles, and the solute–solvent interaction potential depends on the vibrational coordinates of the solute. The theory is applied to study the experimentally observed anomalous density and temperature dependence of vibrational relaxation rates in supercritical fluids in the vicinity of the critical point. A quantitative comparison of the theory with experiment is presented, and the agreement is satisfactory.

Spherical polymer brushes under good solvent conditions: Molecular dynamics results compared to density functional theory

A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions by molecular dynamics methods and density functional theory. With increasing chain length, the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretical tools are presented. Finally, a brief discussion of the experiment is given.

Interactions between colloidal particles in polymer solutions: A density functional theory study

We present a density functional theory study of colloidal interactions in a concentrated polymer solution. The colloids are modeled as hard spheres and polymers are modeled as freely jointed tangent hard sphere chains. Our theoretical results for the polymer-mediated mean force between two dilute colloids are compared with recent simulation data for this model. Theory is shown to be in good agreement with simulation. We compute the colloid-colloid potential of mean force and the second virial coefficient, and analyze the behavior of these quantities as a function of the polymer solution density, the polymer chain length, and the colloid/polymer bead size ratio.

Nonradiative relaxation processes in condensed phases: Quantum versus classical baths

We consider the problem of calculating the nonradiative multiphonon transition rate between two electronic states of an impurity embedded in a condensed-phase environment, where all the nuclear degrees of freedom of the bath are taken in the harmonic approximation, and the two electronic states are coupled to the bath diagonally and off-diagonally. The diagonal coupling term includes displacements of the equilibrium positions of the bath modes, the frequency shifts, and Duschinsky rotations of the bath modes between the two electronic states. We consider two forms of the off-diagonal coupling term—the first assumes that this term is independent of the nuclear degrees of freedom, and thus the coupling between the two diabatic electronic states is taken to be a constant; the second is based on the Born–Oppenheimer method in which the off-diagonal coupling term between the two adiabatic electronic states is taken to be a function of the bath momenta operators. This general model is used to examine the accura...

ON THE THEORY OF MULTIPHONON RELAXATION RATES IN SOLIDS

A theory of multiphonon relaxation for electronically or vibrationally excited impurities in crystals is developed. Two alternative approaches within the static‐coupling scheme are presented and their relative importance is discussed. For each approach a closed‐form analytical expression for the relaxation rate is given as a function of energy gap and temperature. We consider relaxation either by optical or acoustic phonons. From the analytical expressions we derive approximate energy gap laws for the zero‐temperature rates, and discuss the origin and applicability of a popular phenomenological assumption for the rate’s temperature dependence. The predictions of the theory are compared with energy gap‐ and temperature‐dependent experimental data for various electronic transitions of rare‐earth impurities in YAlO3.

Vibrational energy relaxation in liquid oxygen

Abstract We consider theoretically the relaxation from the first excited vibrational state to the ground state of oxygen molecules in neat liquid oxygen. The relaxation rate constant is related in the usual way to the Fourier transform of a certain quantum mechanical force-force time-correlation function. A result from Egelstaff allows one instead to relate the rate constant (approximately) to the Fourier transform of a classical force-force time-correlation function. This Fourier transform is then evaluated approximately by calculating three equilibrium averages from a classical molecular dynamics simulation. Our results for the relaxation times (at two different temperatures) are within a factor of 5 of the experimental relaxation times, which are in the ms range.

Anomalous nanoparticle diffusion in polymer solutions and melts: a mode-coupling theory study.

Mode-coupling theory is employed to study diffusion of nanoparticles in polymer melts and solutions. Theoretical results are directly compared with molecular dynamics simulation data for a similar model. The theory correctly reproduces the effects of the nanoparticle size, mass, particle-polymer interaction strength, and polymer chain length on the nanoparticle diffusion coefficient. In accord with earlier experimental, simulation, and theoretical work, it is found that when the polymer radius of gyration exceeds the nanoparticle radius, the Stokes-Einstein relation underestimates the particle diffusion coefficient by as much as an order of magnitude. Within the mode-coupling theory framework, a microscopic interpretation of this phenomenon is given, whereby the total diffusion coefficient is decomposed into microscopic and hydrodynamic contributions, with the former dominant in the small particle limit, and the latter dominant in the large particle limit. This interpretation is in agreement with previous mode-coupling theory studies of anomalous diffusion of solutes in simple dense fluids.

Local density enhancement in dilute supercritical solutions

Abstract We study the structure around a dilute Lennard-Jones (LJ) solute in a supercritical LJ fluid using integral equation theories and Monte Carlo simulation. We show that the Percus–Yevick approximation can be seriously in error in the near-critical region. The solutes coordination number as a function of the solvent density can be nearly linear, or quite non-linear, depending on the solute–solvent interaction. These results are rationalized as a crossover from a low-density energy-dominated regime to a high-density entropy-(packing-) dominated regime, and are discussed within the context of the local density enhancement concept.