In this paper, we present detailed experimental and theoretical studies of the femtosecond dynamics of microscopic friction. The real-time rotational motion of a well-defined system of diatomic solute in monatomic solvent has been studied for two solvents ranging from gas to liquid densities. Both coherent inertial and diffusive limits of the motion and all stages in the transition between these two regimes are observed in detail. The transient anisotropies over the entire range of experimental densities and solvents are well-represented by the J-coherence bimolecular collision model presented here. This stochastic hard-sphere collision model explicitly relates the physical properties of the solvent to the anisotropy and the coefficient of rotational friction, permitting calculation of the transient anisotropy from the Enskog hard-sphere collision frequency. Friction coefficients obtained from J-coherence analysis of experimental anisotropies were compared with those from Gordon J-diffusion, and Langevin−...

Femtosecond dynamics of solvation : microscopic friction and coherent motion in dense fluids

In a microscopic theory for the dynamics of a classical hard sphere fluid a kinetic equation is derived and solved approximately. Besides incorrelated binary collisions which are already included in the generalised Enskog theory, the theory also describes correlated collisions by a mode-coupling approximation. This results in a closed set of non-linear equations for the correlation functions of density, longitudinal and transverse current density and energy density to be solved numerically. The only input required is the density. All existing sum rules of these correlation functions are fulfilled. The theory includes the free particle limit, the exact thermodynamics and a proper hydrodynamic limit yielding corrections to the Enskog transport coefficients.

https://iopscience.iop.org/article/10.1088/0022-3719/15/13/011/pdf

Dynamics of a classical hard-sphere gas I. Formal theory

Based on a microscopic approach we present results for the changes in thermodynamic derivatives at the glass transition. These changes are expressed in terms of correlation functions of the frozen out microscopic pressure and energy fluctuations. Quantitative results for the discontinuities as well as the Prigogine–Defay ratio are obtained within a simple model and agrees quite well with experimental results. A generalized order parameter is identified in terms of a correlation function, describing the frozen in local structure of the glass.

Changes of thermodynamic quantities at the glass transition

Kinetic theory of single-particle motion in a fluid

The kinetic theory of chemical reactions in dense fluids is extended to calculate the dynamics of a reactive pair of particles. Given an initial pair distribution, the probability that the pair of particles will remain unreacted is calculated. Explicit solutions are obtained by taking into account repeated ring events and the results are shown to be a generalization of Fick’s law calculations for this problem. Other classes of dynamical events which lead to a coupling of the diffusive motion of the pair are examined in a more formal way and their physical significance is discussed. The applicability of the theory to the analysis of recombination reactions in liquids is discussed.

Kinetic theory of reactive pair dynamics in liquids

We present a renormalized kinetic theory for tagged particle motion in a rough sphere fluid which includes the effects of correlated collisions The kinetic theory is a generalization of a recent theory for monatomic fluids by Mazenko The correlated collisions create slowly decaying memory in the linear (ψv) and angular (ψω) velocity correlation functions on account of the coupling of the test particle density fluctuations to various moments of the full phase space density correlation function (These moments are connected with the conserved variables in the system) We use the theory to study ψv and ψω and compare the results with recent molecular dynamics experiments of O’Dell and Berne The kinetic theory yields the correct long time power law decay for both ψv and ψω without imposing any wave vector cutoff characteristic of the hydrodynamic theories It also yields useful new insights into various mode couplings responsible for the behavior of ψv and ψω at small and intermediate times The qualitativ

Kinetic theory of rough sphere fluids: Linear and angular velocity correlation functions

We construct a kinetic equation for the phase space density correlation function (PSDCF) in a rough sphere fluid (at the generalized Enskog level) which is valid for arbitrary wave number and frequency. The kinetic equation yields the first two kinetic sum rules exactly; also the density–density correlation function implied by it has the correct first four sum rules exactly. We use the short time behavior of PSDCF and the generalized hydrodynamics approach to construct approximate interpolation formulas for a variety of space–time dependent correlation functions related to conserved variables in the fluid. The coupling of modes described by these correlation functions to the test particle density fluctuations is responsible for the known asymptotic power law decay in the linear and angular velocity correlation functions. As a by‐product of this study, we also obtain expressions for various (bare) transport coefficients in a dense rough sphere fluid.

Kinetic theory of rough sphere fluids: Density fluctuations

Kinetic theory of rough sphere fluids: Matrix elements

Dynamical correlations in rough sphere fluids

The effect of a magnetic field on the time‐dependent correlation functions appropriate to the thermal conductivity and self‐diffusion in a dilute molecular gas is investigated. For the thermal conductivity and the energy current correlations, calculations are made for the rough sphere interaction as well as for nitrogen gas. For the calculation of the velocity correlation function, the rough sphere model is used to study the effects due to correlations arising from terms odd in angular momentum. The qualitative similarity that is found in various diagonal correlation functions and in the oscillating structure that is found in many transverse correlation functions is discussed.

Magnetic field dependence of thermal correlations in molecular gases

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