Molecular Internal Energy Research Articles

Anisotropic Solvent Structuring in Aqueous Sugar Solutions

The details of solution structure have proven difficult to probe experimentally, but computer simulations allow solvent structuring to be examined directly. We report here molecular dynamics (MD) simulations of a series of pentose sugars in solution, describe in detail the three-dimensional structuring which these molecules impose on water, and relate this structuring to the solute molecular topologies. Well-defined first and second solvation shells are observed around the sugar molecules with specific locations determined by the arrangement of functional groups within each solute. Calculated molecular internal energies and solvent interaction energies generally correspond qualitatively with earlier models of sugar energetics based on stability factors. However, pairs of axial hydroxyl groups on the same side of a sugar ring were found to be disfavored by solvation energy, not by internal energy, which is actually more favorable due to intramolecular hydrogen bonding, in accord with both quantum mechanical calculations and a crystal structure for a related molecule determined by diffraction. A single axial hydroxyl group could be favored or disfavored energetically by hydration, depending on the particular circumstance.

Reinvestigation of the photodissociation kinetics of m-iodotoluene molecular ion

Photodissociation kinetics of the m-iodotoluene molecular ion has been investigated on a nanosecond time scale by mass-analyzed ion kinetic energy spectrometry. Photodissociation rate constants have been determined at molecular ion internal energies of 3.7–4.3 eV. The influence of the collisional relaxation of the molecular ion occurring in the ion source on the rate constant has been corrected, which was not considered in the previous photodissociation experiment. The kinetic energy release distributions (KERDs) determined from the ion kinetic energy profiles are composite due to the participation of two competing reaction channels, one leading to the formation of m-tolyl ion and the other to tropylium ion. By separating these bimodal KERDs, the branching ratios for the two channels have been obtained. From the overall rate constants and the branching ratios, rate constants for each channel have been determined on a nanosecond time scale. It has been found that the rate-energy data for each channel can be explained adequately by the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The production of m-tolyl ion proceeds via a loose transition state while that of tropylium ion proceeds via a tight transition state. Refined experimental data together with the microsecond data reported by Lin and Dunbar have been found to be essential to arrive at the correct mechanistic pictures for these reactions

Transport properties of nonequilibrium polyatomic gas mixtures

It is shown that the well-known Hirschfelder-Euken correction to the thermal conductivity of a polyatomic gas mixture given by the first approximation in Sonine polynomials can be less than the corresponding exact value (for a Lorentz mixture of light and heavy molecules interacting in accordance with Coulomb's law) by a factor of 3.4. Fairly high accuracy is achieved in the second approximation in Sonine polynomials. Within the framework of the latter, similar corrections to the nonequilibrium heat and diffusion fluxes are found. On the basis of the generalized Chapman-Enskog method a more general case is studied. In this case some of the nonelastic collision integrals is also taken into account in calculating the transport coefficients. The transport coefficients are either represented in terms of the well-known formulas for fast and retarded internal molecular energy exchange or convenient approximate expressions are obtained.

Relaxational hydrodynamics from the Boltzmann equation

Abstract In hydrodynamics of polyatomic gases one usually assumes a proportionality between the viscous part of the scalar pressure and the instantaneous value of the divergence of the flow velocity: Π =−ηv∇·v/ However, in fast phenomena such as ultrasound propagation, collisional relaxation of internal (e.g. rotational) molecular energy must be taken into account whenever the respective relaxation time significantly exceeds the mean time of free flight. A system of hydrodynamic equations generalized in this sense has been worked out by Kohler and Vestner in two-temperature language via the moment method, and is rederived here by the Chapman-Enskog procedure. The system can be reduced to four equations for the functions v, T, p, Π, the last one involving a relaxation term τd″dΠ/dt with τ″ = 3cvηv/2crotp. The analysis of sound absorption and dispersion serves as an example of application.

A detailed evaluation of the heating efficiency in the middle atmosphere

The conversion to heat of solar ultraviolet radiation absorbed by ozone and molecular oxygen in the terrestrial mesosphere and lower thermosphere occurs through a series of complex processes. Upon photolysis of the O3 or O2, significant amounts of chemical potential energy and atomic and molecular internal energy are generated. The disposition of the internal energy largely determines the rate at which the atmosphere is heated. In addition, the chemical energy is released subsequent to exothermic chemical reactions which may occur long after and far away from the location of photon deposition. Energy may be lost from the atmosphere by airglow from excited photolysis products or by chemiluminescent emission from product species of exothermic chemical reactions. In this paper we examine the role of airglow losses in reducing the efficiency of solar heating in the Hartley, Huggins, and Chappuis bands of ozone and in the Herzberg, Ly α, Schumann‐Runge continuum, and Schumann‐Runge bands of molecular oxygen. We also examine the role of heating due to seven chemical reactions and calculate the efficiencies for those reactions with significant chemiluminescent loss. Parameterizations of the heating efficiency that are readily applicable to numerical models are given for those processes with nonunit efficiencies. Results from the calculation of heating rates for individual processes indicate that the reaction of atomic hydrogen and ozone is potentially the largest single source of heat in the vicinity of the mesopause. However, significant improvement is still needed in the knowledge of the quenching and chemical reaction rates of vibrationally excited OH before the efficiency of this reaction can be confidently calculated. Our calculations also indicate that even under strong quenching, most of the OH is in vibrationally excited form above 85–90 km. Finally, the bulk heating efficiency due to the combination of solar and chemical heating is calculated. The calculated bulk efficiencies demonstrate that airglow and chemiluminescent emission significantly reduce the amount of energy available for heat throughout the mesosphere and lower thermosphere.

The thermal conductivity of pure polyatomic gases at moderate pressure

Based on the binary collisions of molecules, the kinetic theory of pure gases is valid for all pressures the higher the temperature increases. The mechanism of relaxation in the molecular internal energy exchange and the peculiar behaviour of polar gases are empirically taken into account through the reduced Planck constant (the de Boer parameter) to give an expression of the thermal conductivity.

Thermal Diffusion in a Lorentz Gas

Regarding an isotropic Lorentz gas, thermal transport properties are discussed at the most elementary level. Lorentz's original equations for heat and matter flows are reformulated in terms of kinetic quantities of dilute gases to clarify the nature of transport coefficients from the viewpoint of linear nonequilibrium thermodynamics including the Onsager reciprocal theorem. Especially referring to thermal diffusion properties of the Lorentz gas, Lorentz's transport equations are studied by using the transported internal energy E ** and the internal energy of transport E * which are connected with E ** = E * +\bar E , where \bar E is the partial molecular internal energy. In this case, E * = k T /2 and \bar E =(3/2) k T , and hence E ** =2 k T , using the Boltzmann constant k and the temperature T . A special case, E * being a constant activation energy of usual diffusion, is briefly discussed.

How Robust are Bottlenecks to Unimolecular Fragmentation?

AbstractSome properties of classical mechanical phase space resonances that serve as bottlenecks to the redistribution of internal molecular energy are investigated. Resonances of a two degree of freedom model van der Waals (vdW) molecule are subjected to a linear harmonic perturbation from an additional degree of freedom. The resulting effects on the phase portrait of the subsystem appear to be independent of the frequency of the third oscillator but relatively small coupling critically affects most quasi‐periodic resonances. The approximate separatrix in the vdW degree of freedom is used as a dividing surface in an analysis of the vdW molecule fragmentation rate. The influence on the separatrix of coupling to a third oscillator supports the validity of the two degree of freedom model for systems with small to moderate coupling. The golden mean resonance remains the most robust resonance of the two degree of freedom phase portrait even when the third oscillator coupling is nonzero, an observation which supports the recognition of golden mean resonances as the main intramolecular bottlenecks.

Ionic dissociation of methanol studied by photoelectron–photoion coincidence spectroscopy

Ionic dissociation of methanol has been investigated by means of photoelectron–photoion coincidence spectroscopy. Breakdown curves and average kinetic energies released in the fragmentations were obtained as a function of molecular ion internal energy. In the CH2OH+ formation about 45% of the excess energy available for the dissociation is converted into translational energy of products. In contrast, the average translational energies released in the formation of CH3+ and HCO+ ions are 0.4 and 2.5 eV, respectively, and these values remain constant irrespective of the excess internal energy over the excited states of ions, 6a′−1, 1a″−1, and 5a′−1. All results including the breakdown curves reveal that the statistical theories of unimolecular decomposition can not give a satisfactory interpretation to mass spectra of methanol. Alternative mechanisms are discussed to account for the observations.

Transport properties in dilute gases: an approach using time-correlation functions. Part 1.—Viscosity and thermal conductivity of gases and gas mixtures in which the exchange of molecular internal energy is slow

Equations for the viscosity and thermal conductivity are derived, using the method of time-correlation functions, for dilute single gases and gas mixtures which may contain polyatomic molecules, but in which the rate of exchange of internal molecular energy is slow. The treatment follows that of H. Mori, who showed that the assumption of an exponential form for the time-correlation functions leads to expressions for the viscosity and thermal conductivity of a single monatomic gas that are identical with those of the Chapman–Enskog first approximations. In the present analysis, time-correlation functions have to be considered in general to be sums of exponential decays which are justified on the basis of the first-collision approximation of Reissner and Steele. For many systems considered, familiar equations are obtained, e.g., Chapman–Enskog first approximations and the modified Eucken and Hirschfelder–Eucken equations. For viscosity and for the translational contribution to thermal conductivity in mixtures, however, simpler (though less correct) equations than the Chapman–Enskog approximations are obtained: in the case of thermal conductivity a new equation is derived and tested. Though less rigorous than the traditional methods, the derivations are simpler and more easily understood in physical terms (provided the expressions for the transport properties in terms of time-correlation functions are accepted as a starting point) and therefore the approach offers some advantages.

Transport properties in dilute gases: an approach using time-correlation functions. Part 2.—Viscosity and thermal conductivity of gases and gas mixtures in which the exchange of molecular internal energy is significant

Transport properties in dilute gases: an approach using time-correlation functions. Part 2.—Viscosity and thermal conductivity of gases and gas mixtures in which the exchange of molecular internal energy is significant

A bactracking algorithm for exact counting of internal molecular energy levels

An algorithm is described for counting exactly internal molecular energy levels. Difficulties in the concept of the density of states are reinvestigated. The influence of anharmonicity is shortly discussed and it is shown that reliable densities can only be obtained for low energies if anharmonicity constants are used.

High-speed leading edge problem

The sharp leading edge problem has been studied for both monatomic and diatomic gases using the Boltzmann equation with the Bhatnagar-Gross-Krook type models as the governing equation and the discrete ordinate method with a closed-boundary value approach as a tool. Plate length relative to the freestream mean free path is taken to be 52. The gas-surface interaction law is assumed to be diffuse reflection. The local distribution functions of molecular velocities and internal energies (for the diatomic gas) for the entire flow field have been calculated for M ∞ = 6.1; thus, the complete flow field has been determined for Tw/T0 = 0.11 and 0.18. Comparisons are made between the calculated results and experimental data. It should be pointed out that the present theory provides a technique to calculate not only gasdynamic variables such as density, flow velocity, pressure, and temperature, but also the nonequilibrium distributions of molecular velocities and internal energies that are very useful in the determination of nonequilibrium radiation intensities.

Nonequilibrium Effects in Recombination-Dissociation Kinetics II

The selfconsistent theory of recombination-dissociation kinetics developed in an earlier article is derived in a more rigorous manner. A noniterative solution is obtained for the resulting equations describing the nonequilibrium distribution of the internal molecular energy levels. This method of solving these equations also leads to a number of interesting mathematical and physical insights about the importance of nonequilibrium effects in recombination-dissociation kinetics. Implicit in these equations is a method for calculating the vibrational relaxation times for both recombination and dissociation reactions. These same equations also arise in calculating the rate constant for a nontrivial model of a dissociating diatomic molecule. The mathematical techniques used to derive this information also allows us to show that the selfconsistent theory is really a generalization of the conventional steady-state approximation and a special case of a projection operator formalism for solving problems in nonequilibrium statistical mechanics.

Theory of transport properties of gases

Kinetic theory of transport properties of dilute gases, relating it to flames processes, noting assumptions of chapman-enksog theory, discussing real and dusty gases as well as rocket exhausts

Phenomenological Theory of the Molecular Absorption and Dispersion of Sound in Fluids and the Relation between the Relaxation Time of the Internal Energy and the Relaxation Time of the Internal Specific Heat

Molecular absorption and dispersion formulas applicable for both liquids and gases have been derived in a phenomenological manner. It was pointed out that the relaxation time of the molecular internal energy τ must be distinguished from the relaxation time of the internal specific heat β and the relation between these two quantities was discussed in detail. The relaxation time τ has the advantage of making the dispersion formula simpler and directly comparable with the dispersion formulas in other cases, such as the relaxation of shear viscosity. The relaxation time β on the other hand, is more closely related with the collision excitation probability of the molecules than τ.

Molecular Amplification and Generation of Microwaves

This paper is a general introduction to the field of amplification and generation of microwaves using molecular rather than electronic processes. The basic physical properties of molecular systems as related to amplification are reviewed. The properties of molecular amplifiers, such as gain, bandwidth, saturation power, and noise figure are discussed, and several specific types of amplifiers are described. These include the molecular-beam Maser, the "hot-grid cell," amplifiers excited by rf pulses and by "adiabatic fast passage," and amplifiers based on multilevel molecular internal energy systems, including "optically pumped" amplifiers. Molecular amplifiers may add very little noise to the signal to be amplified: noise figures under one db can be obtained. With suitable feedback, such amplifiers become oscillators of extremely high spectral purity. High gains can be achieved using regeneration, but bandwidths are relatively small. These range from the order of tens of kilocycles for amplifiers using a gaseous molecular system, to megacycles, using solids. Molecular amplifiers saturate at low input powers, of the order of microwatts. Variations of the devices discussed may provide a means of generating millimeter and submillimeter waves.

Internal Molecular Energy of Atomic Vibration

Internal Molecular Energy of Atomic Vibration

Internal Molecular Energy of Atomic Vibration

Internal Molecular Energy of Atomic Vibration