Taikyue Ree

A perturbation theory of classical equilibrium fluids

A new perturbation theory which is reliable over a wide fluid region is presented. The new theory reduces to the theory of Weeks, Chandler, and Anderson at densities near or below the triple point density of a simple fluid but it can also accurately predict thermodynamic properties at higher densities near the freezing line of the fluid. This is done by employing an optimized reference potential whose repulsive range decreases with increase in density. Thermodynamic properties for Lennard‐Jones, exponential‐6, and inverse nth‐power (n=12, 9, 6, and 4) potentials have been calculated from the new theory. Comparison of the calculated data with available Monte Carlo simulations and additional simulations carried out in this work shows that the theory gives excellent thermodynamic results for these systems. The present theory also gives a physically reasonable hard‐sphere diameter over the entire fluid range.

A perturbation theory of classical solids

We have developed a new perturbation theory that extends our earlier perturbation theory of fluids to solids and that is reliable over a wide solid region. Characteristic features of this new theory are the use of an optimized reference potential whose repulsive range shrinks with density and its ability to deal with both harmonic and anharmonic thermodynamic properties on equal footing. Thermodynamic properties of face‐centered‐cubic crystals are computed from the new theory for the Lennard‐Jones system, the exponential‐6 system, and the inverse nth‐power (n=12, 9, 6, and 4) systems. Monte Carlo simulations are also performed to supplement available data. A comparison of theory and computer simulation shows excellent agreement, except for the softest repulsive system (n=4). The agreement extends from an anharmonic region near the melting line to a harmonic region, where the hard‐sphere reference system achieves close to 92% of the close‐packed density. Beyond this region errors in the analytic fits to th...

Hard‐sphere radial distribution functions for face‐centered cubic and hexagonal close‐packed phases: Representation and use in a solid‐state perturbation theory

The hard‐sphere radial distribution functions, gHS(r/d,η), for the face‐centered cubic and hexagonal close‐packed phases have been computed by the Monte Carlo method at nine values of the packing fraction, η[=(π/6)ρd3], ranging from 4% below the melting density to 99% of the close‐packed density. The Monte Carlo data are used to improve available analytic expressions for gHS(r/d,η). By utilizing the new gHS(r/d,η) in the Henderson and Grundke method [J. Chem. Phys. 63, 601 (1975)], we next derive an expression for yHS(r/d,η) [=gHS(r/d)exp{βVHS(r)}] inside the hard‐sphere diameter, d. These expressions are employed in a solid‐state perturbation theory [J. Chem. Phys. 84, 4547 (1986)] to compute solid‐state and melting properties of the Lennard‐Jones and inverse‐power potentials. Results are in close agreement with Monte Carlo and lattice‐dynamics calculations performed in this and previous work. The new gHS(r/d,η) shows a reasonable thermodynamic consistency as required by the Ornstein–Zernike relation. As...

High-pressure equations of state of krypton and xenon by a statistical mechanical theory

We present statistical mechanical calculations for krypton and xenon, employing accurate pair potentials with and without condensed‐phase modifications. A unique feature of the present work is that solid‐ and fluid‐phase thermodynamic properties are both computed within a single framework, using our recently developed hard‐sphere perturbation theory. Results are applied to analyze experimental fluid, solid, and fluid–solid transition data, ranging up to 2×106 atmospheres at several temperatures. Effective pair potentials for both krypton and xenon, inferred from the analysis, contain short‐ and long‐range modifications to the pair potential of Aziz and Slaman. The long‐range correction is repulsive and originates from the well‐known Axilrod–Teller three‐body potential, while the short‐range correction is attractive and is needed for describing high‐compression data. Experimental isotherms above 50 GPa for xenon require a further softening of the short‐range repulsion from Barker’s correction (obtained fro...

Phase diagram of a Lennard‐Jones solid

A phase diagram of a Lennard‐Jones solid at kT/e≥0.8 is constructed by our recent perturbation theory. It shows the stability of the face‐centered‐cubic phase except within a small pressure and temperature domain, where the hexagonal‐close packed phase may occur. The theory predicts anharmonic contributions to the Helmholtz free energy (important to the crystal stability) in good agreement with Monte Carlo data.

An algebraic approach to vibrational transitions in the forced Morse oscillator

Abstract An expression for the probability of vibrational transitions in the Morse oscillator has been derived by use of the anharmonic commutation relations in an approximate solution of the Schrodinger equation of motion. The inclusion of the oscillator anharmonicity leads to a complicated probability expression, but in the weak-coupling limit the expression reduces to an anharmonic scaling relation of P ν→ν+1 /(ν + 1) (1 − ν x 0 ) P 0→1 = 1, where x 0 is the anharmonicity parameter. For H 2 + He, this relation appears to hold well up to collision energies of ≈1.5 vibrational quanta.

Exact classical calculations of vibrational energy transfer in a Morse oscillator

Exact energy transfer in the collinear collision of a Morse oscillator with a particle is calculated from the numerical integration of the classical equations of motion over a wide range of collision energies. The exact classical energy transfer values are compared with those of the harmonic oscillator case for several different types of collisions. Except for the collisions involving a heavy homonuclear diatomic molecule and a light incident particle, the Morse energy transfer values are seriously different from the harmonic case. The time dependence of energy transfer during the collision especially at high collision energies is studied in detail to obtain information on the occurrence of multiple impacts in each collision. The deviation of the harmonic energy transfer from the Morse values is discussed in terms of the impact multiplicity.

On the mechanism of spiking and bursting in excitable cells

A mathematical model previously developed to explain beta-cell membrane potential oscillations has been modified to accommodate the external variation of K+, Na+ and Ca2+ concentrations. Our model, which is applicable to excitable cells, incorporates the barrier kinetics. Hodgkin-Huxley-type gating mechanism, and an electrogenic Na+-K+ pump. Numerical solutions of our model are in agreement with many of the experimental results reported in the literature on excitable cells.

Vibration--vibration energy exchange in iodine molecules

Vibration–vibration energy exchange probabilities between iodine molecules (X 1Σ+g) have been calculated by use of the solution of the time‐dependent Schrodinger equation. The interaction potential is constructed by summing four orientation averaged atom–atom interactions. One‐quantum probabilities Pv,0v−1,1(T) for v−1,1→v,0 are found to be very large in a temperature range of 100–3000 K. At lower temperatures, the approximate linear relation pv,0v−1,1(T)≂vP1,00,1(T) holds. When v is small, the probability increases linearly with temperature. Multiquantum transitions v,0→v−n,n with n≳1 are found to be negligible near room temperature, but they become quite efficient at higher temperatures. Energy exchange probabilities are formulated in infinite order and their reduction to first‐order expressions are discussed in detail. The effects of molecular attraction are also discussed.

Dependence of bond dissociation on initial vibrational phase in the He + I2 system

Abstract The dependence of the dissociation of an excited I2 in the HE + I2 system on initial vibrational phase has been explored using classical trajectory methods, with particular emphasis on those features of the trajectories responsible for the lower and upper limit of dissociative phase range. The presence of the regions of initial vibrational phase leading to dissociation and nondissociation is analyzed in detail. In the dissociative phase region, the lower limit is characterized by trajectories associated with a long dissociation time, while the upper limit represents an abrupt change in the vibrational energy transfer characteristics of I2.