Eigenvalues of the boltzmann collision operator for binary gases: Relaxation of anisotropic distributions

The time eigenvalues of the Boltzmann collision operator for the hard-sphere cross section are calculated with a discrete ordinate method. The anisotropic part of the collision operator is considered in the present work. The approach to equilibrium of a gas initially non-maxwellian and anisotropic is considered.     

Matrix elements of the linear Boltzmann collision operator for systems of two components at different temperatures

Matrix elements of the linearized collision operators that arise in the linearization of the Boltzmann equations for a binary gas system are calculated. The collision operators employed here differ from those usually considered in that the Maxwell—Boltzmann distribution functions which appear are parametrized by two different temperatures, one for each component. The matrix representations of the isotropic portion of the collision operators are calculated with the Sonine polynomials as basis functions, and for the hard sphere cross section, recursion relations for the matrix elements are derived which permit their efficient numerical calculation. The dependene of a few matrix elements on the mass and temperature ratios of the two components is considered. In particular, the disparate mass limit is investigated and the range of validity of the Fokker—Planck operator as an approximation to the collision operator in this limit is briefly discussed.     

Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functions

The thermal Gaussian approximation (TGA) recently developed by Frantsuzov et al. [Chem. Phys. Lett. 381, 117 (2003)] has been demonstrated to be a practical way for approximating the Boltzmann operator exp(-betaH) for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the "forward-backward semiclassical dynamics" approximation developed by Shao and Makri [J. Phys. Chem. A 103, 7753 (1999); 103, 9749 (1999)]. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and calculation of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.     

Quantum-mechanical evaluation of the Boltzmann operator in correlation functions for large molecular systems: a multilayer multiconfiguration time-dependent Hartree approach

It is shown that the Boltzmann operator in time correlation functions for complex molecular systems can be evaluated in a numerically exact way employing the multilayer formulation of the multiconfiguration time-dependent Hartree theory in combination with Monte Carlo importance sampling techniques. The performance of the method is illustrated by selected applications to photoinduced intervalence electron transfer reactions in the condensed phase. Furthermore, the validity of approximate schemes to evaluate the Boltzmann is discussed.     

Density dependence of electron mobility in dense gases

The density (N) dependence of electron mobility (μ) in various dense gases (H₂, N₂, O₂, CO₂ and rare gases) has been calculated using a multiple-scattering approach. Deviation of the high density gas from its perfect gas behaviour has been taken into account through the temperature-dependent second virial coefficient. Multiple scattering of electrons leads to shifts in their kinetic energy and it also changes their distribution functions. This unified approach predicts both positive and negative effects. The positive (negative) effect entails on increase (decrease) of μ withN. We have assessed the available data on momentum transfer cross-sections by comparing the mobility at very low densities (Nμ)₀ with experimental results. The density dependence is studied by comparing the calculated ratioNμ)/Nμ)₀ with the observed values and other theoretical work. The Legler model which assumes a constant cross-section is inadequate for predicting the observed density dependence. We obtain good agreement with available experimental work for all the atomic and molecular species studied here.     

Adsorption of gases on binary and multicomponent semiconductors of the ZnSe-CdTe system

Adsorption of carbon monoxide(II) and oxygen on powders and nanofilms of solid solutions and binary compounds of the ZnSe-CdTe system was studied volumetrically, and by piezoquartz microweighing and IR spectroscopy of multiple disturbed complete internal reflections. The mechanisms and principles of adsorption were established in dependence on the conditions of the habitus of an experimental sample and the composition of the system’s semiconductors, based on an analysis of IR spectra; the thermodynamic and kinetic characteristics of adsorption; experimental dependences αp = f(T), αT = f(P), and αT = f(t); and the acid-base and other physicochemical characteristics of adsorbents and the electron nature of adsorbate molecules. Conclusions drawn earlier as to the retention of local active centers on the surface of a diamond-like semiconductor (which are responsible for adsorption and catalytic processes) upon a change in the habitus of a sample were confirmed. Certain features in the behavior of solid solutions (ZnSe) _x (CdTe)_{1 − x} were revealed alongside commonalities with binary compounds (ZnSe, CdTe), testifying to the presence of critical points on “adsorption characteristics-composition” diagrams. The most active adsorbents (with respect to CO and O₂) were discovered on the basis of these diagrams, which were used in creating highly sensitive and selective sensors.     

The pressure dependence of the mutual diffusion coefficients of binary mixtures of helium with ten other gases at 300 K: tests of Thorne's equation

The pressure dependences of the binary diffusion coefficients of ten systems containing helium have been measured at constant composition at 300 K. The results are compared with the Thorne—Enskog theory for moderately dense gases of rigid spheres, and a previously suggested empirical extension to the theory tested.     

The pressure dependence of the mutual diffusion coefficients of binary mixtures of helium and six other gases at 300 K: tests of Thorne's equation

A Loschmidt cell has been used to measure the pressure dependence, at constant composition and temperature, for six systems consisting of binary mixtures of helium. The results are compared with the Thorne—Enskog theory for moderately dense gases of rigid spheres, and an extension to the theory suggested.     

Concentration dependence of the boiling point of binary equidistant solutions

A concentration dependence of the boiling point of binary equidistant mixtures in isobaric conditions was revealed. The dependence is a solution to a second-order inhomogeneous difference equation describing the autoregression properties of solutions.     

Velocity dependence of collision broadening cross sections in NH3

The velocity dependence of collision broadening cross sections for both self-broadening and Xe broadening of an infrared transition in NH₃ has been studied by measuring laser saturation resonance linewidths for molecules with specified velocities along the laser propagation direction. For self-broadening, the velocity dependence is in accord with inelastic collisions due to a predominantly dipole-dipole interaction potential, with smaller contributions due to shorter range forces, whereas for Xe broadening, the magnitude and velocity dependence of the collision broadening cross section is in better agreement with velocity changing collisions in the pressure range studied.     

Mass dependence of mutual diffusion coefficient: computer simulation study

Molecular dynamic computer simulations are performed to study the mass dependence of mutual diffusion coefficient in an isotopic, equimolar binary system. The particles of the system are assumed to be interacting via Lennard-Jones potential. The self- and mutual diffusion coefficients are calculated from the time dependence of the mean square displacement and from the velocity correlation function using the Green–Kubo formula. The study has been carried out at different densities and temperatures. Like the self-diffusion coefficient, the mutual diffusion coefficient is also found to be weakly dependent on the mass ratio. Our study also shows that the temperature of the system has a negligible effect on the mass dependence of the diffusion coefficients.     

Unusual behavior of CMC for binary mixtures of alkyltrimethylammonium bromides: dependence on chain length difference

The critical micelle concentrations (CMC) of binary mixtures of alkyltrimethylammonium bromides (CnTAB) were measured by a conductivity method. The CMCs of C12TAB-C14TAB and C14TAB-C16TAB systems exhibit the usual behavior, namely a monotonic decrease of the CMC with the mole fraction of the longer chain surfactant. However, the CMC behaviors of C10TAB-C16TAB, C11TAB-C16TAB, C12TAB-C16TAB, and C11TAB-C14TAB are unusual. The behaviors of the CMCs with mole fraction for these systems consist of three regions, of which the first is characterized by a very small decrease of the CMC in the range of low mole fraction, followed by a second where there is an abrupt decrease of the CMC, and a third where the CMCs exhibit their usual behavior. The molecular interaction parameter omega is almost equal to zero for mixtures that have the usual CMC behavior, but is small and positive for those systems with unusual CMCs. We infer that for very low mole fractions of C16TAB, the C16TA ion in the C12TAB-C16TAB system penetrates imperfectly into the micelle and its two methylene groups exist outside the micelle.     

Negative collision energy dependence of Br formation in the OH + HBr reaction

The reaction between HBr and OH leading to H(2)O and Br in its ground state is studied by means of a crossed molecular beam experiment for a collision energy varying from 0.05 to 0.26 eV, the initial OH being selected in the state |JOmega> = |3/2 3/2> by an electrostatic hexapole field. The reaction cross-section is found to decrease with increasing collision energy. This negative dependence suggests that there is no barrier on the potential energy surface for the formation pathway considered. The experimental results are compared with the previously reported quantum scattering calculations of Clary et al. (D. C. Clary, G. Nyman and R. Hernandez, J. Phys. Chem., 1994, 101, 3704), and briefly discussed in the light of skewed potential energy surfaces associated with heavy-light-heavy type reactions.     

Quantum-state-resolved CO2 scattering dynamics at the gas-liquid interface: incident collision energy and liquid dependence

Quantum-state-resolved dynamics at the gas-liquid interface are probed by colliding supersonically cooled molecular beams of CO(2) with freshly formed liquid surfaces in a vacuum. Translational, rotational, and vibrational state distributions of both incident and scattered fluxes are measured by high-resolution direct infrared absorption spectroscopy and laser dopplerimetry in the 00(0)0 and 01(1)0 rovibrational manifolds of CO(2) in the asymmetric stretch manifold. The present studies investigate the role of incident molecular beam energy (E(inc) = 1.6(1), 4.7(2), 7.7(2), and 10.6(8) kcal/mol) on these distributions for a series of perfluorinated, hydrocarbon, and hydrogen-bonded liquids. Boltzmann analysis of the internal quantum-state populations provide evidence for nonthermal scattering dynamics, as confirmed by Dopplerimetry on the absorption profiles. The data provide quantum-state-resolved support for a dual channel picture of the scattering process, consisting of either prompt impulsive scattering (IS) or longer duration trapping-desorption (TD) events, with the fraction observed in each channel dependent on incident kinetic energy and the physical properties of the liquid surface. The clear evidence that internal CO(2) rotational populations arising from the IS channel can be adequately described by a Boltzmann temperature (albeit with E(IS) > RT(S)) is consistent with previous gas-solid scattering studies and suggests that even nominally "prompt" IS events reflect both single (i.e. direct) and multiple impulsive interactions with the liquid interface.     

Solvent dependence of charge-transfer transitions in binary aqueous mixtures

Summary Charge-transfer transitions of Ru(bipy) ₃ ²⁺ , Fe(bipy) ₃ ²⁺ , Fe(CN) ₆ ^3- , and free bipy (bipy=2,2-bipyridine) are solvent dependent. Evidence is presented that dielectric continuum theory provides a reasonable basis for interpreting medium effects on the electronic transition energies in binary solvent mixtures as well as in pure solvents.     

On the pressure dependence of the muon spin polarization in mixtures of noble gases

In muon spin rotation (μSR) experiments, where spin-polarized positive muons are stopped in condensed matter, three magnetically distinguishable chemical environments can be observed. That is, the Larmor frequencies associated with diamagnetic environments and two types of paramagnetic environments (muonium and radicals) can be resolved. The chemical identities of the latter two are distinct since their Larmor frequencies are distinct, whereas the chemical identities of the possible diamagnetic species are not determined by the Larmor frequency since chemical shifts can not be resolved in μSR experiments. However, two different diamagnetic species have been observed in experiments performed on mixtures of noble gases. Their distinction arises through different thermal rate constants that lead to “fast” and “slow” relaxing components of the diamagnetic signal. The pressure dependencies of the amplitudes associated with these components are related to the stopping dynamics of muons in noble gas targets. A set of coupled rate equations for muon spin dynamics, based upon quantal Boltzmann equations, have been developed to describe this process in single component gases. This theory is now extended to mixtures. In particular, the dynamics of the muon spin is generated by the muonium hyperfine interaction and by time dependent rate constants for the various chemical species that are assumed to be present, namely, muonium and three diamagnetic species. Radicals have not yet been observed in low pressure gases. The coupled quantal rate equations are solved for two models of the stopping dynamics wherein the rates are taken as square box functions of time.     

The dependence of collision induced fragmentation pattern on the internal energy of the precursor ion

A Method is presented whereby product organic ions formed as the result of fragmentation of metastable ions can be selected on the basis of their internal energies. The method requires requires angular collimation of the beam of reactant ions issuing from the ion source and that the fragmentation of the metastable ions is studied in the first field free region of a reversed geometry double focusing mass spectrometer. The product ions that make up the metastable peak are allowed to fall on the intermediate resolving slit and, by adjusting the magnet current over a small range, ions contained in different regions of the peak can be allowed into the second field free region. It is shown that the position of an ion within the metastable peak correlates with its internal energy, ions near the edges of the peak being the least excited. The ions entering the second field free region can be investigated by collisional activation. This has been done for molecular ions of p-chlorophenol, methylbenzoate, benzaldehyde, m-chlorotoluene and n-butane. The in which the collision induced fragmentation pattern varies with internal energy of the ions is illustrated.     

Mole fraction dependence of physical properties for a binary cyanobiphenyl liquid crystal system

The physical properties of a binary liquid crystal system were investigated, namely the transition temperatures, birefringence and viscoelastic constants measured by using thermal optical microscopy, differential scanning calorimetry and light scattering techniques with coherent laser light beams. These properties were sometimes found to exhibit linear dependence on the mole fractions of the components. Our results indicate that a required property is obtainable by the regulation of the molar ratio as if the length of the alkyl chain connected with a cyanobiphenyl core group were variable; i.e. the apparent chain length could be controlled.     

Determination of the concentration dependence of polyelectrolyte diffusion coefficients by application of the Boltzmann gradient method

The concentration dependence of a polyelectrolyte diffusion coefficient in aqueous low salt solution (KCl, 1 mM) is determined from a single dynamic gradient experiment. The Boltzmann method is applied to calculate the diffusion coefficient. A special diffusion cell is constructed that minimizes aberrations in the optical detection of the polyion concentration profile. Bovine serum albumin (BSA) is chosen as a model polyion. To get information about the diffusion process down to very small polyion concentrations, the BSA molecule is fluorescently labeled. The fluorescence intensity is used as a measure of the polyion concentration. The change of the polyion net charge caused by labeling is discussed. The cell is illuminated by an LED, and the fluorescence intensity profile is detected by a CCD camera. Experiments at 5 and 17 degrees C show that the diffusion coefficient of labeled BSA remains constant in the very low polyion concentration range below a threshold of about 1.5 g/l. This is in contradiction to the linear concentration dependence of polyion diffusion coefficients at very low concentrations often postulated in the literature without reference to direct experimental evidence. Our finding is confirmed by dynamic light scattering experiments published recently. An explanation for this behavior based on a modified Donnan osmotic compressibility approach is given.