Hyung Kyu Shin

Dependence of the Probabilities of Vibrational De‐Excitation on Interaction Potentials

Using the WKB semiclassical approximation, the dependence of the probability of vibrational de‐excittion on the assumed form of the interaction potential is discussed. The asymptotic results show that the Morse and Lennard‐Jones potentials have, respectively, two and three correction terms in the exponential part. The magnitudes of the correction terms are important compared to the leading term. The exact form of the leading term is also dependent upon the interaction potential.

Inelastic Molecular Collisions with a Lennard‐Jones (12–6) Interaction Energy

Vibrational energy transfer is discussed for a Lennard‐Jones intermolecular interaction energy by use of the WKB semiclassical wavefunctions, from the point of view of the effect of an attractive term in the interaction energy. The effect is found to be very important in controlling the over‐all magnitude of the de‐excitation probability per unit time. An expression for fitting a Lennard‐Jones potential to an exponential potential is derived by comparing the leading terms in the exponent of the perturbation integral.

Approximate Expression for the Tunneling Correction

By using an approximate method, the tunneling‐correction factor for the unsymmetrical Eckart potential function and its temperature dependence are formulated in forms which are capable of simple numerical calculations. The method is designed to evaluate the integral which includes a violently changing exponent. The result is compared with Johnstons results obtained by electronic computation; the agreement is good in chemically interesting cases.

Diffusion of liquids in unsaturated paper

SummaryThe flow of liquids in porous media such as paper can be described by the parabolic diffusion equation divD gradw=∂w/∂t when the only driving forces are capillary in nature. This equation can be extended to include other forces, such as gravitational, by writing the diffusion equation in terms of a free energy or potential gradient.Experimental data are obtained for one-dimensional flow in paper from which the diffusion coefficientD(w) is evaluated. Flow is then described in terms of an interconnected capillary pore model. It is shown that flow through this model obeys the diffusion equation. A theoretical derivation of the diffusion coefficient for flow in paper, based on a pore size determination by a static method, gives the correct form forD(w) but gives values ofD(w) considerably larger than found experimentally.This discrepancy is attributed to the approximation used in treating pore geometry. Comparison of the rate of flow through a more realistic model of paper involving a three-dimensional stack of rods shows the importance of considering pore geometry.ZusammenfassungDas Fließ en von Flüssigkeiten in porigen Medien wie Papier kann durch eine parabolische Diffusionsgleichung divD gradw=∂w/∂t beschrieben werden, wenn die einzige treibende Kraft kapillarer Natur ist. Diese Gleichung läß t sich erweitern, um andere Kräfte wie die Gravitation einzuschließ en, wenn man die Diffusionsgleichung in Termen der freien Energie oder der Potentialgradienten schreibt.Experimentelle Daten werden aus eindimensionalem Fließ en in Papier erhalten, von dem der DiffusionskoeffizientD(w) ausgewertet ist. Der Fluß wird dann in Termen des Verbundkapillarenmodells beschrieben. Es wird gezeigt, daß der Fluß durch dieses Modell einer Diffusionsgleichung gehorcht. Eine theoretische Ableitung des Diffusionskoeffizienten für den Fluß in Papier, begründet auf die Bestimmung der Porengröße durch eine statische Methode, gibt korrekt dieForm vonD(w) wieder, ergibt jedoch fürD(w) Werte beträchtlich größer als die experimentell gefundenen.Diese Diskrepanz wird der Näherung zugeschrieben, die bei Behandlung der Porengeometrie angewendet wird. Vergleich von Geschwindigkeit und Fluß durch ein der Wirklichkeit mehr entsprechendes Modell des Papiers, das einem dreidimensionalen Ineinanderstecken von Stäbchen entspricht, zeigt die Bedeutung der Betrachtung der Porengeometrie.

On the Hydrogen—Bromine Reaction Rate in a Nonsteady State

The deviations of atom concentrations and over‐all rate from steady‐state conditions for the H2–Br2 reaction are evaluated as functions of the extent of reaction in a temperature range 1000°—1600°K. Both the concentration and rate deviations are serious at 1400°—1600°K. The major source of the nonsteady state deviation in rate is the reaction k5[H][Br2] and the regenerating cycle proceeds in nonsteady state except at the later stage of the reaction. A previously obtained result that two atom concentration deviations e1 and e2 are nearly identical is equivalent to the condition that the rate of change of the H‐atom concentration vanishes. At elevated temperatures, analysis of the atom concentration deviations alone does not give sufficient information for the evaluation of the steady‐state hypothesis; the over‐all rate deviation must be obtained to answer the question of steady‐state validity.

STEADY-STATE DEPARTURE IN ENZYME REACTIONS

A method is described for calculating the departure from steady-state conditions in enzyme reactions. This provides an immediate and simple criterion for the validity of the steady-state approximation. Several variations of the general method, differing in the degree of simplicity and in the treatment of initial transients, are formulated and discussed. These methods are applied to the general case of an enzyme reaction following the Michaelis–Menten mechanism. Specific applications are made using the data of Chance and Gutfreund. While in these specific cases the steady-state concentration of intermediate is reasonably accurate, the extent of reaction may easily vary from that calculated by means of the steady state.