Rotational Energy Relaxation Research Articles

Determination of the rotational relaxation cross section of carbon dioxide from spectral measurements

The pressure-induced transformation of the spectrum of the Q branch of the ν1 mode (1388 cm−1) of CO2 molecules is quantitatively interpreted. The contributions to the width of the spectrum from three relaxation mechanisms—vibrational dephasing, rotational relaxation, and the Doppler effect—are taken into account. From the fitting of the calculated and measured spectra of the Q branch, the effective cross section of the rotational energy relaxation is determined.

Nonequilibrium Bhatnagar–Gross–Krook model for nitrogen shock structure

This Brief Communication is about the study of diatomic gas shock structure based on the nonequilibrium gas-kinetic Bhatnagar–Gross–Krook (BGK) model, where an additional rotational energy relaxation equation is added. The BGK Navier–Stokes flow solver is extended to solve the nonequilibrium gas kinetic model. The numerical solutions are compared with the experiment measurements and direct simulation Monte Carlo solutions.

Time-domain investigation of OH ground-state energy transfer using picosecond two-color polarization spectroscopy

Two-color polarization spectroscopy was used to investigate rotational energy transfer (RET) and relaxation of orientation and alignment in the ground electronic state of OH in an atmospheric-pressure methane–air flame. Two independently tunable lasers produced nearly transform-limited infrared and ultraviolet pulses of 50 ps duration. The infrared laser excited rovibrational transitions, and delayed ultraviolet pulses probed electronic transitions from either the directly pumped or collisionally populated states. Alignment and orientation relaxation times were measured for individual rotational levels in OH X 2 Π 3/2(v=1) , and the feasibility of time-domain investigation of state-to-state energy transfer processes was demonstrated.

Variable sphere molecular model for inverse power law and Lennard-Jones potentials in Monte Carlo simulations

The variable sphere (VS) molecular model for the Monte Carlo simulation of rarefied gas flow is introduced to provide consistency for diffusion and viscosity cross-sections with those of any realistic intermolecular potential. It is then applied to the inverse power law (IPL) and Lennard-Jones (LJ) potentials. The VS model has a much simpler scattering law than either the variable hard sphere (VHS) or variable soft sphere (VSS) models; also, it has almost the same computational efficiency as the VHS and VSS models. A simulation of velocity relaxation in a homogeneous space and two comparative simulations of molecular diffusion in a homogeneous heat-bath gas and normal shock wave structure in a monatomic gas are made to examine VS model validity. The relaxation to a Maxwellian distribution function and equipartition between all degrees of freedom are well established; good agreement is shown in the molecular diffusion and shock wave structure between the VS model and the IPL and LJ potentials. The VS model is combined with the statistical inelastic cross-section (SICS) model and applied to simulation of translational and rotational energy relaxation in a homogeneous space. The VS model shows the relaxation of Maxwellian and Boltzmann distribution functions and equipartition between all degrees of freedom. Comparative calculation between the VS model with the SICS (VS-SICS) model and the VSS model with the SICS (VSS-SICS) model is made for rotational relaxation in a nitrogen normal shock wave. Good agreement is shown in the shock wave structure and rotational energy distribution function between the VS-SICS model and the VSS-SICS model. This study demonstrates that diffusion and viscosity cross-sections, rather than the scattering law of each molecular collision, affect macroscopic transport phenomena.

Rotational energy relaxation of polar diatomic molecules diluted in simple liquids

The rotational energy relaxation (T1 processes) of polar diatomic molecules diluted in nonpolar liquids is analyzed by means of a non-Markovian theory for the energy time autocorrelation function that does not require the usual population-coherence decoupling approximation. Non-Markovian rate equations are obtained in terms of two-time conditional probabilities and the involved transition rates are calculated in terms of quantum time correlation functions associated to the solute–solvent interaction. Alternative time scales for the discrete rotational levels have been introduced and compared with previous definitions. The usual long time, Markovian limit is recovered. The theory is applied to the study of the rotational energy relaxation of HCl in liquid SF6.

Rotational energy relaxation in CH4 and CH4-He, Ar collisions calculated from coherent and stimulated Raman spectroscopy data

Theoretical treatment of the evolution of the methane Q branch contour with pressure is given in the framework of a quantum model of rotational relaxation with allowance for the tetra-hedral symmetry of rotational levels. The results obtained are compared in detail with available experimental data. As a result, rotational energy relaxation cross-sections for methane and its mixtures with helium and argon have been determined.

Rotational energy relaxation of individual rotational states in liquids

The manner in which most molecules reorient in liquids bears little resemblance to the process in the gas phase. For small-moment-of-inertia species such as the hydrides, however, the observation of discrete spectroscopic lines corresponding to individual isolated-molecule quantum transitions suggests that one is actually seeing single-molecule dynamics perturbed only weakly by the environment—just as one sees with solution-phase vibrational behavior. We examine here the degree to which such individual rotational quantum states remain well defined in liquids by considering the rates of discrete energy-level-to-energy-level transitions in solution. For rotational quantum states that do preserve their free-rotor character in a liquid, we find that the transition rate between angular momentum states obeys a rotational Landau–Teller relation strikingly similar to the analogous expression for vibration: the rate is proportional to the liquid’s rotational friction evaluated at the transition frequency. Subsequent evaluation of this friction by classical linearized instantaneous-normal-mode theory suggests that we can understand this relationship by regarding the relaxation as a kind of resonant energy transfer between the solute and the solution modes. On specializing to the particular cases of H2 and D2 in Ar(l), we find that the most critical modes are those that move the light solute’s center of mass with respect to a single nearby solvent. This observation, in turn, suggests a generalization of instantaneous-normal-mode ideas that transcends both linear coupling and harmonic dynamics: an instantaneous-pair theory for the relaxation of higher-lying levels. By employing a linearized instantaneous-normal-mode theory of relaxation within the liquid band and an instantaneous-pair theory for higher-frequency relaxation, we find that the resonant-transfer paradigm is reasonably successful in reproducing molecular dynamics results spanning a wide range of different rotational states.

Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy

We investigate the free cooling of inelastic rough spheres in the presence of Coulomb friction. Depending on the coefficients of normal restitution e and Coulomb friction μ, we find qualitatively different asymptotic states. For nearly complete normal restitution (e close to 1) and large μ, friction does not change the cooling properties qualitatively compared to a constant coefficient of tangential restitution. In particular, the asymptotic state is characterized by a constant ratio of rotational and translational energies, both decaying according to Haff's law. However, for small e and small μ, the dissipation of rotational energy is suppressed, so that the asymptotic state is characterized by constant rotational energy while the translational energy continues to decay as predicted by Haff's law. Introducing either surface roughness for grazing collisions or cohesion forces for collisions with vanishing normal load, causes the rotational energy to decay according to Haff's law again in the asymptotic long-time limit with, however, an intermediate regime of approximately constant rotational energy.

Rotational relaxation time in CO free jets

The electron beam fluorescence technique was applied to measure the rotational energy relaxation cross-sections in carbon monoxide free jets. The data were obtained in the low temperature region from 20 to 200 K and compared with the results of ultrasound, thermal conductivity, free jet and line broadening experiments. The overall scatter of the experimental data runs to one order of magnitude, and their temperature dependence differs. This fact calls for further theoretical and experimental investigations of rotational relaxation rates in carbon monoxide.

Measurement of rotational relaxation in the ground state of methane perturbed by argon at low temperature

Relaxation processes at low temperature in methane perturbed by argon have been investigated on the basis of new measurements. Diode laser absorption spectra of methane in the region of the dyad ν 2/ ν 4 in supersonic expansions have been recorded. The time of relaxation of the ground state mean rotational energy was derived from the observed dependences of the rotational temperature on the concentration in the jet. A semi-classical model was used to calculate the state-to-state relaxation rate constants at room temperature. The evaluation of the time of relaxation of the mean rotational energy using semi-empirical temperature dependence laws is presented and discussed.

The influence of rotational and vibrational energy relaxation on boundary-layer stability

We investigate the influence of rotational and vibrational energy relaxation on the stability of laminar boundary layers in supersonic flows by numerically solving the linearized equations of motion for a flow in thermal non-equilibrium. We model air as a mixture of nitrogen, oxygen and carbon dioxide, and derive accurate models for the relaxation rates from published experimental data in the field of physical chemistry. The influence of rotational relaxation is to dampen high-frequency instabilities, consistent with the well known damping effect of rotational relaxation on acoustical waves. The influence of rotational relaxation can be modelled with acceptable accuracy through the use of the bulk-viscosity approximation when the bulk viscosity is computed with a formula described herein. Vibrational relaxation affects the growth of disturbances by changing the characteristics of the laminar mean flow. The influence is strongest when the flow field contains a region at, or near, stagnation conditions, followed by a rapid expansion, such as inside wind tunnels and around bodies with a blunt leading edge, whereby the rapid expansion causes the internal energy to freeze in a distribution out of equilibrium. For flows at Mach 4.5 and stagnation temperature of 1000 K, the total amplification exhibited by boundary-layer disturbances over a sharp flat plate in wind-tunnel flows can reach a value that is fifty times as high as the value computed under the assumption of thermal equilibrium. The difference in amplification can be twice as high in the case of a blunt flat plate at atmospheric flight conditions.

Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy

We study the exchange of kinetic energy between translational and rotational degrees of freedom for inelastic collisions of rough spheres. Even if equipartition holds in the initial state it is immediately destroyed by collisions. The simplest generalisation of the homogeneous cooling state allows for two temperatures, characterizing translational and rotational degrees of freedom separately. For times larger than a crossover frequency, which is determined by the Enskog frequency and the initial temperature, both energies decay algebraically like $t^{-2}$ with a fixed ratio of amplitudes, different from one.

Relaxation of rotational energy in supersonic gas-dynamic jet expansion into vacuum

Relaxation of rotational energy in supersonic gas-dynamic jet expansion into vacuum

Orthogonal transformations in the line space and modelling of rotational relaxation in the Raman spectra of linear tops

Collisional relaxation of linear tops is considered for molecular tensor quantities time-conserved in the ideal gas (angular momentum and its products). By introducing new bases in the line space (the associated Laguerre polynomials of a discrete variable), a simpler description of relaxation is attained. In the Markov limit, the relevant time autocorrelations are shown to decay slower than given by the mono-exponential law; a formula is derived for the correction. Using perturbation theory (PT), a general 4-state, non-Markovian expression for the relaxation matrix Γ is found and analyzed. Based on this expression, a new model of Γ is proposed and used to calculate the collisional cross sections characterizing depolarized Rayleigh scattering and rotational energy relaxation in nitrogen. Though on the rotational momentum scale the validity domains of the PT high Js) and the infinite-order sudden approximation (low Js) complement each other, the structures of the expressions for the Γ matrix elements given by both approaches appear to have much in common.

Temperature dependence of rotationally inelastic rate constants fitting laws

The recently developed quasiclassical ECS-E fitting law has been employed to study the temperature dependence of rotational energy relaxation rates. By comparing the rotational energy relaxation cross-sections given by the phenomenological and microscopic approaches, we have derived the relationship between the intermolecular potential parameters and three independent parameters of the model, thus deriving the temperature-dependent form of the quasiclassical ECS-E law. The ability of our model to predict the temperature dependence of the energy relaxation cross-section and the widths of the Raman Q-branch isolated lines has been tested with nitrogen as an example. The method for the determination of anisotropy parameters of the potential (in the form of a non-spherical Morse potential) has been suggested, on the condition that numerical values of the model parameters are determined through an inversion-fitting procedure from the Q(j)-line-broadening coefficients. The primary advantage of our approach is the possibility of calculating rotational relaxation rates from the given form of the interaction potential. This possibility is illustrated by the calculation of the argon-broadening coefficients for nitrogen Q-branch lines and the rotational energy relaxation cross-section for this system.

Anisotropy Measurements of Solvated HgI2Dissociation: Transition State and Fragment Rotational Dynamics

Pump−probe anisotropy measurements of HgI2 photodissociation in ethanol were carried out. The reactive motion from electronically excited HgI2 toward HgI and I is clearly evident in the signal. The subsequent randomization of the HgI orientational distribution occurs in the biphasic manner typical for some other diatomic molecules, with a 500-fs component that has an inertial motion contribution and a slow (8−10-ps) diffusive component. Interpretations of these regions were assisted by molecular dynamics simulations, which also were used to show that the rotational energy relaxation would be very fast in this system. The magnitudes of the anisotropies at different pump wavelengths show that the near-UV absorption of HgI2 involves overlapping 1Σ+ → 1Σ- and 1Σ+ → 1Π transitions, consistent with magnetic circular dichroism (MCD) measurements. The anisotropy decay shows oscillations which are proposed to arise from oscillations in the volume and moment of inertia as the vibrational wavepacket moves in the anharmonic HgI potential.

State-to-state rate constants and rotational relaxation time in nitrogen

Abstract A recently developed ‘quasiclassical ECS-E’ fitting law for rotational transition rates has been used for a detailed comparison of theoretical and experimental data on rotational energy relaxation in nitrogen. A wide range of data on line broadening coefficients, ultrasonic absorption, population kinetics of isolated rotational levels exposed to laser pumping and population kinetics in a free jet has been analysed in order to refine the effective intermolecular parameters of the model thus providing a temperature-dependent form of the fitting law from 35 up to 1500 K.

Rotational Relaxation in Fluid Nitrogen: An Ambiguity in the Interpretation of the Q-Branch Collapse?

A molecular dynamics simulation of nitrogen at 295 K and at densities ranging from 400 to 1000 amagat has been carried out. Relaxation times which give the rotational contribution to isotropic Raman Q-branch half-widths have been determined from the simulations. A comparison of these simulations with experiment leads to the conclusions that (1) extreme motional narrowing theory is applicable to the calculation of bandwidths for densities not less than 700 amagat; (2) the nonlinear density dependence of rotational energy relaxation times should be incorporated in the scaling laws to obtain dependable calculations of bandwidths; (3) by rescaling molecular dynamics results of Levesque et al. (J. Chem. Phys. 1980, 72, 2744) for liquid nitrogen we show that negative rotational relaxation−vibrational dephasing cross correlation is not negligible for fluid nitrogen at high density and 295 K; and (4) calculations of the collision frequency for a model ensemble of hard spheres with density-dependent diameters (Ben-Amotz, D.; Hershbach, D. R. J. Phys. Chem. 1993, 97, 2295) yield good estimates for the density dependence of the simulated relaxation times.

Rotational energy relaxation of symmetric top molecules by collisions with atoms

Abstract The infinite-order sudden approximation has been used to calculate the effective cross sections for R-T energy transfer (σE) of symmetric top molecules by collisions with atoms. In a final form σE is expressed via 〈ΔE2〉 (the mean-square change in rotational energy), which is analytically expressed through the partial phase shifts. A quadratic dependence of σE on phase shifts derived in the present study indicates a very high sensitivity of σE to the details of the anisotropic potential. Within the developed formalism, spherical and linear molecules are treated as the limiting cases. Detailed comparisons between the IOSA values and semiclassical sudden calculations are carried out for rare-gas-SF6 mixtures.

Collisional effects in Q branch coherent anti-Stokes Raman spectra of N2 and O2 at high pressure and high temperature

A temperature and pressure dependent study of coherent anti-Stokes Raman scattering (CARS) Q branch spectra of molecular nitrogen and oxygen has been conducted. Spectra at pressures up to 250 MPa and in the temperature range 298 K<T<850 K have been obtained using a scanning CARS apparatus. The full-width at half-maximum (FWHM) as well as peak position of collapsed Q branch profiles were measured. Measurements also have been made in synthetic air and in mixtures with argon. A detailed comparison of Q branch CARS band shapes with theoretical models of quantum mechanical and quasiclassical origin has been performed. On the one hand existing scaling laws like the modified energy gap (MEG), energy corrected sudden (exponential) polynomial energy gap [ECS-(E)P], polynomial energy gap (PEG), and statistical polynomial energy gap (SPEG) laws that give analytical expressions for rotational relaxation rates are used in a CARS code to calculate half-widths of the collapsed Q branch of nitrogen and oxygen. Many of these models show significant deviations from experimental results in the high pressure regime investigated here. For nitrogen the PEG-law, although not very suitable at lower densities, at room temperature reasonably reproduces the half-widths in the high pressure regime. The same is true for the ECS-EP law at low and high temperatures, whereas the SPEG-law only gives reasonable results at high temperature. For oxygen only the MEG and ECS-EP laws (at room temperature) give half-widths that are within the error limits of the measurement. On the other hand, within experimental error frequency shifts and half-widths of N2 and O2 CARS-spectra are well described by the classical approach throughout the density range. It is found that dephasing contributions to the density induced spectral shift cannot be neglected at room temperature but are less important at higher temperatures. In comparison to experimental data the quasiclassical model provides physical interpretation of temperature dependent cross sections for rotational energy relaxation processes in nitrogen and oxygen at high densities.