Isotope effect on the thermodynamic quantities of gaseous uranium hexafluoride

1976 ◽  
Vol 54 (1) ◽  
pp. 160-165 ◽  
Author(s):  
Jan Bron
Keyword(s):  
Partition Function ◽  
Quantum Correction ◽  
Isotope Effects ◽  
Uranium Atom ◽  
Uranium Hexafluoride ◽  
Thermodynamic Quantities ◽  
Heavy Isotope ◽  
Statistical Mechanical ◽  
Lower Temperature ◽  
The Masses

For gaseous UF6 changes in the thermodynamic quantifies ΔG (= ΔA), ΔH (= ΔU), ΔCp (= ΔCv), and ΔS upon isotopic substitution can be determined by using the spectroscopically determined geometry and force field. The differences ΔG etc. are defined as (G238 – Gx), where 238 and x (x = 235, 234, 233, and 232) are the masses of the central uranium atom. The changes in the thermodynamic quantities are related to the logarithm of the partition function ratio of the UF6 species compared. The logarithm of the partition function ratio can be conveniently expressed as a series in temperature and hence, by using statistical mechanical relationships, the changes in thermodynamic quantities can be expressed as a series in temperature.Since these changes form examples of heavy isotope effects the validity and utility of the first quantum correction can be investigated. Uncertainties and trends in the magnitudes of the differences in the thermodynamic quantities due to uncertainties or changes in spectroscopic parameters are discussed by means of the first quantum correction. It has been found that the first quantum correction has little quantitative value in the lower temperature region, but it can be used in that range to explain some observed trends in the isotope effects. Some of the conclusions can also be applied to kinetic and equilibrium heavy isotope effects.

THE EXACT SOLUTION OF SOME LATTICE STATISTICS MODELS WITH FOUR STATES PER SITE

1964 ◽  
Vol 42 (8) ◽  
pp. 1564-1572 ◽  
Author(s):  
D. D. Betts
Keyword(s):  
Partition Function ◽  
Nearest Neighbor ◽  
Quaternary Alloy ◽  
Interesting Property ◽  
Two Dimensions ◽  
Lattice Statistics ◽  
Critical Temperatures ◽  
Different Types ◽  
Interacting Systems ◽  
Statistical Mechanical

Statistical mechanical ensembles of interacting systems localized at the sites of a regular lattice and each having four possible states are considered. A set of lattice functions is introduced which permits a considerable simplification of the partition function for general nearest-neighbor interactions. The particular case of the Potts four-state ferromagnet model is solved exactly in two dimensions. The order–disorder problem for a certain quaternary alloy model is also solved exactly on a square net. The quaternary alloy model has the interesting property that it has two critical temperatures and exhibits two different types of long-range order. The partition function for the spin-3/2 Ising model on a square net is expressed in terms of graphs without odd vertices, but has not been solved exactly.

The Importance of Anharmonicity of The Vibrational Excited States in Chemical Kinetics

1975 ◽  
Vol 53 (20) ◽  
pp. 3069-3074 ◽  
Author(s):  
Jan Bron
Keyword(s):  
Transition State ◽  
Excited States ◽  
Isotope Effects ◽  
Kinetic Isotope Effects ◽  
Vibrational States ◽  
Vibrational Anharmonicity ◽  
Kinetic Isotope ◽  
Large Correction ◽  
Lower Temperature ◽  
Lower Temperature Region

The corrections to rate constants for an harmonicity of vibrational excited states have been evaluated over the temperature range of 200–1100 K. The reaction O2 + X, where X is H or D, has been chosen as the model system. Only the influence of vibrational anharmonicity of the triatomic transition state has been determined. Two geometric shapes for the transition state, bent and isosceles configurations, have been investigated in detail by the bond order method.It is found that the correction can be large, depending upon the geometry and force field of the transition state and the temperature. The magnitude of the correction for anharmonicity of the vibrational excited states depends mainly, at a particular temperature, on the strength of the O—X bond in the transition state. In the case of a large correction, anharmonicity may lead to a nonlinear Arrhenius plot.Because of cancellation effects, the correction for anharmonicity of the excited vibrational states in kinetic isotope effects can be ignored in the lower temperature region. It has also been found that anharmonicity of the vibrational groundstate can explain unexpected large isotope effects.

Investigation of the mechanism of nicotine demethylation in Nicotiana through 2H and 15N heavy isotope effects: Implication of cytochrome P450 oxidase and hydroxyl ion transfer

2007 ◽  
Vol 458 (2) ◽  
pp. 175-183 ◽  
Author(s):  
Roland Molinié ◽  
Renata A. Kwiecień ◽  
Piotr Paneth ◽  
Wilfried Hatton ◽  
Jacques Lebreton ◽  
...  
Keyword(s):  
Cytochrome P450 ◽  
Isotope Effects ◽  
Ion Transfer ◽  
Heavy Isotope ◽  
Hydroxyl Ion

THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

Takahasi Nearest-Neighbour Gas Revisited III; Lennard-Jones Gases

2013 ◽  
Vol 68 (12) ◽  
pp. 773-776
Author(s):  
Akira Matsumoto
Keyword(s):  
Virial Coefficient ◽  
Analytical Formula ◽  
Second Virial Coefficient ◽  
Thermodynamic Quantities ◽  
Inflexion Point ◽  
Lennard Jones ◽  
First Order Phase Transition ◽  
Higher Temperature ◽  
Lower Temperature ◽  
First Order Phase

Some thermodynamic quantities for the Lennard-Jones (12,6) potential are expressed as analytical formula at an isobaric process. The parameters of Lennard-Jones gases for 18 substances are obtained by the second virial coefficient data. Also some thermodynamic quantities for benzene are calculated numerically and drawn graphically. The inflexion point of the length L which depends on temperature T and pressure P corresponds physically to a boiling point. L indicates the liquid phase from lower temperature to the inflexion point and the gaseous phase from the inflexion point to higher temperature. The boiling temperatures indicate reasonable values comparing with experimental data. The behaviour of L suggests a chance of a first-order phase transition in one dimension.

scholarly journals Annihilating random walks and perfect matchings of planar graphs

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Massimiliano Mattera
Keyword(s):  
Partition Function ◽  
Random Walks ◽  
Mechanical Model ◽  
Planar Graphs ◽  
Perfect Matchings ◽  
Statistical Mechanical Model ◽  
International Audience ◽  
Statistical Mechanical ◽  
Annihilating Random Walks

International audience We study annihilating random walks on $\mathbb{Z}$ using techniques of P.W. Kasteleyn and $R$. Kenyonon perfect matchings of planar graphs. We obtain the asymptotic of the density of remaining particles and the partition function of the underlying statistical mechanical model.

Theory of Unimolecular Decomposition— The Statistical Approach

1996 ◽  
Author(s):  
Tomas Baer ◽  
William L. Hase
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Density Of States ◽  
Quantum Statistical Mechanics ◽  
Thermodynamic Quantities ◽  
Unimolecular Decomposition ◽  
Thermal Systems ◽  
System P ◽  
Quantum Statistical ◽  
Basic Ideas

The partition function and the sum or density of states are functions which are to statistical mechanics what the wave function is to quantum mechanics. Once they are known, all of the thermodynamic quantities of interest can be calculated. It is instructive to compare these two functions because they are closely related. Both provide a measure of the number of states in a system. The partition function is a quantity that is appropriate for thermal systems at a given temperature (canonical ensemble), whereas the sum and density of states are equivalent functions for systems at constant energy (microcanonical ensemble). In order to lay the groundwork for an understanding of these two functions as well as a number of other topics in the theory of unimolecular reactions, it is essential to review some basic ideas from classical and quantum statistical mechanics. As discussed in chapter 2, the classical Hamiltonian, H(p,q), is the total energy of the system expressed in terms of the momenta (p) and positions (q) of the atoms in the system.

scholarly journals MD-Simulation of Molten (Li, K)Cl at the Eutectic Composition. Self-Exchange Velocities of Li- and K-Isotopes near the Cl--Ions

1987 ◽  
Vol 42 (1) ◽  
pp. 21-28 ◽  
Author(s):  
Isao Okada
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulation ◽  
Md Simulation ◽  
Eutectic Composition ◽  
Isotope Effects ◽  
Dynamics Simulation ◽  
Atomic Masses ◽  
The Masses ◽  
Oscillating Motion

Molecular dynamics simulation (MD) has been done for a molten (Li, K)Cl mixture of the eutectic composition at about 700 K, 950 K and 1100 K and, for comparison, also for pure LiCl and KCl at about 950 K and 1100 K The atomic masses of half the Li+ and K+ ions have been set at 6.941 and 39.098, respectively. Self-exchange velocities (SEV’s) of these cations have been calculated. The Chemla effect is reflected by the SEV’s. The isotope effects of the SEV’s in the mixture increase slightly with temperature. The motions of the cations with respect to the adjacent CI- are classified into four modes: (1) an oscillating motion, (2) a leaving motion, (3) a wandering motion and (4) a coming-back motion. It is found that the velocity of the leaving motion is dependent only on the masses and the temperature, and independent of the kind of cations and the composition.

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