Rotational Relaxation Processes Research Articles

Rotational relaxation of nitrogen in ternary mixtures N2–CO2–H2O: Consequences in coherent anti-Stokes Raman spectroscopy thermometry

The influence of CO2 and H2O on the rotational relaxation processes of N2 in ternary mixtures N2–CO2–H2O is investigated. The efficiency of these perturbers is responsible for significant modifications of the state-to-state relaxation rates and broadening coefficients. Flame data are well reproduced by taking into account these modifications. The role of these minor species in the determination of temperatures in premixed flames is analyzed. The present relaxation model allows us to understand why the discrepancy between observed and calculated coherent anti-Stokes Raman spectroscopy (CARS) spectra in flames is sometimes resolved by empirically adding a dephasing component to pure nitrogen linewidths. Moreover, this model improves the accuracy of CARS temperature measurements.

Theory of pulsed dye lasers including dye-molecule rotational relaxation.

In this paper a phenomenological semiclassical theory of pulsed-laser-pumped dye-laser light amplifiers is presented. The theory accounts for the broadband radiation absorption and emission characteristics of dye molecules in liquid solvents. Dye-molecule fluorescence, vibrational, rotational, and electric polarization relaxation processes are represented by phenomenological relaxation rates. In general, it is found that due to dye-molecule rotational relaxation the laser-pumped dye medium is optically anisotropic. The pump- and dye-laser beams propagate through the dye medium as essentially transverse electromagnetic waves whose amplitude and polarization state changes. The theory is applicable to pulse durations \ensuremath{\tau}\ensuremath{\lesssim}10--100 ns including the ultrashort pulse regime. The regime \ensuremath{\tau}\ensuremath{\gtrsim}1 ps in which the pump- and dye-laser pulse lengths are long compared to the dye-molecule vibrational and electric polarization relaxation times is considered in detail. Amplification of partially polarized quasimonochromatic light is described by a self-consistent set of equations for the components of the pump- and dye-laser light coherency matrices and the orientation populations of the lowest vibronic levels of the dye molecule's ${\mathit{S}}_{0}$ and ${\mathit{S}}_{1}$ electronic states.The interaction of the pump- and dye-laser beams with the dye molecules is characterized by complex electric susceptibility tensors. Kramers-Kronig or Hilbert transform relations are found that permit dye-molecule absorption and emission cross sections to be used to calculate the pump- and dye-laser susceptibility tensors. All the physical parameters in the theory may be determined by conventional experimental techniques. When the dye-molecule rotational relaxation rate ${\ensuremath{\gamma}}_{\mathit{R}}$ is much larger than the fluorescence rate ${\ensuremath{\gamma}}_{\mathit{F}}$, ${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}1}$, and the pump-laser absorption and dye-laser stimulated emission rates, then the dye-molecule electric susceptibility tensors are diagonal. The laser-pumped dye-laser medium is optically isotropic. When these conditions do not hold the medium is optically anisotropic and coherency matrices may be used to describe the propagation of the pump- and dye-laser beams. This procedure is illustrated for the case of transversely pumped dye lasers. In the small-signal regime analytic solutions for the dye-laser-light coherency matrix components are developed for arbitrary initial polarization state, pulse duration, and ${\ensuremath{\gamma}}_{\mathit{F}}$/${\ensuremath{\gamma}}_{\mathit{R}}$. In the large-signal regime numerical solutions are obtained for the amplification of short, (\ensuremath{\tau}${\ensuremath{\gamma}}_{\mathit{F}}$,\ensuremath{\tau}${\ensuremath{\gamma}}_{\mathit{R}}$)\ensuremath{\ll}1, and quasi-steady-state (\ensuremath{\tau}${\ensuremath{\gamma}}_{\mathit{F}}$,\ensuremath{\tau}${\ensuremath{\gamma}}_{\mathit{R}}$)\ensuremath{\gg}1, pulses for arbitrary values of ${\ensuremath{\gamma}}_{\mathit{F}}$/${\ensuremath{\gamma}}_{\mathit{R}}$ when the pump- and dye-laser polarizations are parallel. In general, it is found that for a wide range of physical conditions of interest dye-molecule rotational relaxation is important, and significant changes in the amplification characteristics of the medium, i.e., the rate of amplification, amplification efficiency, and polarization state of the light, will occur.

Memory effects on the rotational relaxation of diatomic polar molecules in non-polar liquids

A quantum study of the rotational energy relaxation ( T 1) and dephasing ( T 2) processes for diatomic polar molecules in a non-polar liquid host is given without invoking the Markovian hypothesis. The study is based on a model consisting of a rigid rotor stochastically coupled to a thermal bath. The time evolution of the reduced density operator of the rotor is described by a master equation with time-dependent matrix coefficients, which contains all information about the time dependence of the T 1 and T 2 rotational relaxation processes. Explicit expressions for the times characterizing these processes are derived on the basis of a quantum treatment for the time autocorrelation functions (TAF) of the rotor-bath interaction Hamiltonian. A numerical application for HCl in liquid Ar is also reported.

Collision‐Induced Intersystem Crossing in CH2 (ã 1A1): A Quantitative Analysis Using the Mixed‐State Model

AbstractThe mechanism of collision‐induced intersystem crossing (ISC) in CH2 from the ã 1A1 first excited singlet to the X̃ 3B1, triplet ground electronic state, CH2 (ã) + M → CH2 (X̃) + M, is investigated. Collisional ISC rate constants are calculated for four selected collider gases, M = He, Ar, N2, and CH4, using the “mixed‐state” model of Freed and Gelbart. The most important triplet‐perturbed rotational levels in the ã‐state are identified from the spectroscopic data reported in the literature. The rates of rotational relaxation processes, which according to the model effectively govern the collision‐induced ISC, are determined by studying the collision broadening of CH2 (X̃) Far Infrared Laser Magnetic Resonance (FIR‐LMR) transitions. The collisional ISC rate constants for CH2 in the ortho nuclear spin modification are calculated to be kISC = 1.4 · 1012, 4.0 · 1012, 7.8 · 1012, and 6.6 · 1012 cm3/mol · s for M = He, Ar, N2, and CH4, respectively. The results are in good agreement with published experimental rate constants.

Study of processes of translational, rotational, and vibrational relaxation based on CARS spectra line shapes

This paper reviews the various physico-chemical processes responsible for actual linewidths encountered in high-resolution coherent anti-Stokes Raman spectroscopy (CARS). Most of the experimental data are based on linewidth measurements using a pulseamplified CARS spectrometer with an emission bandwidth (FWHM) of 2×10−3 cm−1. Detailed rotational and vibrational relaxation constants have been obtained from the analysis of theQ-branch profiles of C2H2, N2, CH4, and SiH4.

Cross sections for translational and rotational relaxation in Li/Li 2 and Na/Na 2 molecular beams

Translational and rotational relaxation processes in alkali monomer-dimer free-jet expansions are investigated both theoretically and experimentally. Based on a sudden-freeze model, simple formulas are derived for the extraction of effective translational relaxation cross sections from terminal Mach numbers and effective rotational relaxation cross sections from measured terminal rotational populations. These formulas are verified in a state-resolved laser-molecular beam study. The magnitude of the rotational cross section is found to be strongly state dependent and to be essentially the same for Na 2 and Li 2. The terminal dimer velocity exceeds that for the monomers in Na/Na 2 but not in Li/Li 2. An earlier sudden-freeze analysis for rare gases is used to correlate terminal dimer mole fractions measured for Li/Li 2 beams with dimensionless parameters. From this correlation and applying energy conservation to the measured terminal velocities we found that at least 60% of the binding energy released in dimer formation in Li/Li 2 beams resides terminally in internal degrees of freedom.

Laser double-resonance mesurements of rotational relaxation rates of HF( J=13) with rare gases, H2, and D2

Rotational relaxation rates for HF(v=0, J=13) colliding with rare gases (He, Ne, Ar, Kr, Xe), H2, and D2 are measured using a transient-absorption double-resonance technique. The relaxation rate constants with rare gases (rotation-to-translation, R–T) decrease dramatically through the series He–Ne–Ar, then increase substantially through the series Ar–Kr–Xe, revealing the increased effectiveness of either highly impulsive or highly attractive collisions. Rate constants at 298 K are: (He), 1.3±0.2×10−11; (Ne), 2.2±0.4×10−12; (Ar), 9.3±0.9×10−13; (Kr), 4.4±0.5×10−12; (Xe), 6.2±0.6×10−12 cm3 molecule−1 s−1. The fact that the rate constants with hydrogen (1.1±0.2×10−10 cm3 molecule−1 s−1) and deuterium (1.2±0.2×10−10 cm3/molecule−1 s−1) are ten times faster than with helium underscores the importance of rotation-to-rotation (R–R) transfer in the rotational relaxation process. The decrease in rates from He to Ar can be understood by an impulsive-type model, analogous to the Schwartz, Slawsky, and Herzfeld (SSH) treatment of vibration-to-translation transfer. However, the increasing trend from Ar to Xe, while clearly due to the increasing magnitude of the attractive interaction, is not easily modeled.

Influence of a buffer gas on multiphoton dissociation of molecules in the radiation field of a pulsed CO2laser

An experimental study was made of the influence of a buffer gas (argon) on the yield and isotopic selectivity of the dissociation of the CF2Cl2, CF2HCl, and CF3Cl molecules by pulsed CO2 laser radiation. The dependences obtained were analyzed taking into account the processes of rotational and VT relaxation, and collisional line broadening. A correlation was discovered between the characteristic features of the influence of the buffer gas on the dissociation of the molecules and the existence of lf molecular vibrations in them. A suggestion was put forward of the existence of a broad component in the spectrum of the lines due to transitions in the polyatomic molecules. It was concluded that collisional line broadening is the principal factor responsible for increasing the dissociation yield of the molecules when a buffer gas is added.

A two-state stochastic model for the dynamics of constrained water in reversed micelles

Translational diffusion leads the tagged water molecule to explore regions of the reversed micelle with a varying degree of space hindrance, thereby modulating the rotational relaxation process. A two-state modulation is shown to result in satisfactory agreement with the NMR experimental data on the rotational correlation time as a function of the micelle radius.

Short-pulse, multiline energy extraction from a transversely excited atmospheric CO2 laser amplifier

Data are presented on the energy extraction from a transversely excited atmospheric CO2 laser amplifier by a 1.1-ns pulse consisting of an adjustable number of lines which are generated by a multiline oscillator of a new design. An increase in energy extraction of 95% with respect to single-line extraction was achieved with a pulse consisting of up to six lines in the 10.6-μm branch. Energy extraction at a fixed number of lines was not very sensitive to their spectral distribution. We observed a maximum increase of about 8% when the lines were spread over the 00°1–10°0 vibrational band. This indicates a slight preference for small Δj values in the rotational relaxation processes.

A comparison of the complete and truncated versions of the polar wander equations

We give a theoretical development of a uniformly valid solution for describing the polar motions of a layered viscoelastic earth. Such solutions require the usage of two classes of eigenspectra to describe the processes of rotational deformation and viscous relaxation. One set consisting of real eigenvalue describes the isostatic relaxation of the mantle by viscous creep. The second one governs the readjustment of the rotational axis of the viscoelastic earth, and the eigenspectrum is complex valued. These solutions are capable of describing rotational phenomena ranging from Chandler wobble excitation to long‐term polar drift. A comparative study is conducted between the complete solution for polar wander and one in which a number of the rotational modes has been truncated. For a four‐layer model consisting of an elastic lithosphere, a two‐layer, adiabatically stratified viscoelastic mantle, and an inviscid core, such a comparison shows that at most a 30% difference exists in the viscosity solutions of the lower mantle, which are obtained by fitting the theoretical predictions to the observed polar wander data. Although the polar speeds from the various models can vary by as much as a factor of 2, the differences in the inverted viscosity solutions are sharply reduced upon fitting the calculations with the actual data for the time window, between 5 and 7×103 years, which characterizes the hiatus between the termination time of the deglaciation period and today. The averaged polar drift from typical glacial cycles in the Pleistocene shows an initial magnitude of 0(1°/m.y., which after a few million years decays to a steady state value of a few tenths of a degree per million years.

Kinetic Studies on Intramolecular Excimer Formation in Dinaphthylalkanes

Abstract Various dinaphthylalkanes in which two naphthyl groups are separated by three carbon atoms were prepared, and intramolecular excimer formation was investigated. All rate constants in Förster’s kinetics were determined by the steady state and time-resolved fluorescence measurements. A large difference in the association rate constant was observed with variation of molecular structure. The results suggest that intramolecular excimer formation is directly controlled by the rotational relaxation processes of the molecules from their neighboring conformations to the excimer conformation. A large formation rate (7.9×108 s−1 at 25 °C) was observed for meso-2,4-dinaphthylpentane, the rate for the racemo isomer being found to be one tenth of that for the meso isomer. This indicates that the isotactic sequence in vinyl aromatic polymers plays an important role in the intramolecular excimer formation.

Picosecond relaxation processes in liquids

Recently there have been a number of important experimental and theoretical developments that focus on the dynamics of rotational and vibrational relaxation processes of molecules in liquids. This marks the emergence of a microscopic description of the forces that govern the structure of fluids. Ultra-short laser pulses permit us to observe directly the consequences of these molecular interactions by probing several causally related phenomena, namely electron localization, fluorescence depolarization and optical Kerr rotation in polar liquids. I present recent results from the picosecond laser spectroscopy of relaxation processes in liquids, and discuss their implications in terms of the influence of the molecular motion on reaction dynamics in liquids in general and on electron transfer processes specifically.

Critically evaluated rate constants for gaseous reactions of several electronically excited species

An extensive evaluation is presented of the available gas phase chemical kinetic rate constants for the interactions of the low lying electronic states of several atoms and molecules with numerous collision partners. These include the following excited states: C(21D2,21S0), N(22D3/2,5/2,22P1/2,3/2), P(32D3/2,5/2,32P1/2,3/2,), S(31D2,31S0). Se(43P0,41D2,41S0), Te(53P1,0,51D2,51S0), CO(a3Π,a′3Σ+,d3Δ,e3Σ−,A1Π), CS(a3Π,A1Π), OH(A2Σ+), OD(A2Σ+), O2(c1Σu−,C3Δu,A3Σu+,B3 Σu−), and S2(a1Δg,b1Σg+,A3Σu+, B3Σu−). Wherever possible, recommended values are suggested. Much of the data refers only to room temperature. To facilitate the evaluation, collision-free radiative lifetimes often have been required. These also have been evaluated and are presented. The mechanisms of the interactions and the various potential kinetic channels are discussed. These include such processes as chemical reactions, electronic quenching to the ground electronic state, electronic cross relaxation to an adjacent excited state, and for molecules, vibrational and rotational relaxation processes within the excited state. A complete coverage of the literature published prior to 1978 has been attempted.

Self-broadening of the absorption lines of the fundamental vibration-rotation band of HF molecules and processes of rotational relaxation

Self-broadening of the absorption lines of the fundamental vibration-rotation band of HF molecules and processes of rotational relaxation

Primary products of multiphoton dissociation of the C2H4 molecule in an intense IR field

A systematic investigation of C2H4 dissociation in an intense IR field with formation of C2 radicals has been carried out by the laser induced fluorescence method. It has been found out that C2 radicals are formed at ethylene pressures less than 0.1 torr without collisions and in the sense are the primary products of dissociation. The role of collisions at pressures of 0.1–4 torr can be explained by a rotational relaxation process at low vibrational levels of the C2H4 molecule. The rotational relaxation time has been experimentally estimated to be 20 ns torr. Various possible mechanisms of C2 radical formation are discussed.

Rotational relaxation of molecular nitrogen in a freely expanding jet

In connection with the assumption about the possibility of producing a gasdynamic laser at rotational transitions of diatomic molecules (1, 2] and a gasdynamic condense-laser by using the phenomenon of condensation to produce the population inversion [3–5], a quantitative description of the kinetics of the rotational relaxation of the simplest diatomic molecules is necessary. In contrast to the traditional approach in gasdynamics and the theory of transport processes, when one parameter (the rotational relaxation time) is used in the description of rotational relaxation, a substantially more detailed description at the population level of the individual rotational states is required in solving spectroscopy and laser physics problems. This paper is devoted to a theoretical and experimental investigation of the rotational relaxation of nitrogen in a free, low density jet under conditions when a substantial nonequilibrium holds in the rotational level populations. On the basis of representations developed earlier [1, 6], a model is constructed for a relaxing gas which yields the magnitude of the population of individual rotational levels. The selection of a molecular nitrogen free jet as a subject for investigation is explained by the fact that the gasdynamics of such a flow has been studied well [7]. Moreover, at this time diagnostic methods have been developed to determine the molecule concentrations at many (k≤20) rotational levels [8]; hence, a jet is a good object on which a detailed comparison between theory and experiment can be made, as is done in this paper. Separation of the translational and rotational relaxation processes is allowed in the theoretical description of the flow with relaxation studied in this paper on the basis of the fact that the buildup of a Maxwell molecule velocity distribution because of elastic collisions occurs more rapidly than the redistribution of molecules at the rotational levels because of inelastic collisions. Such an approach is apparently valid for molecular hydrogen with a large value of the rotational quantum [9]. A model with separation of the processes is hypothetical for nitrogen molecules whose rotational constant is ≈ 1/20 that for hydrogen, and is confirmed in this paper by comparing computations with experiment. It is hence assumed that rotational relaxation proceeds in an N2 molecule stream with a known temperature, density, and velocity distribution obtained from measurements.

Application of single vibronic level spectroscopy to the study of relaxation processes in glyoxal vapour

Abstract Detailed information about vibrational and rotational processes in the excited singlet state can be obtained from the emission spectrum originating from different, selectively excited levels by means of time-integrated and time-resolved measurements. As an example, recently obtained results of a high resolution study of the single vibronic level fluorescence of glyoxal vapour ( C H O C H O) are presented. At low pressures the effect of one single collision has been measured. A strong propensity for single vibrational quantum changes is apparent in all measurements. The cross section of these processes is of the order of the gas kinetic value. Direct information about the dominant routes of vibrational energy degradation was obtained from time-resolved measurements and from the structure growth in the fluorescence spectrum as a function of the pressure. Addition of foreign gases (propane, CO 2 , N 2 , CO and Ar) has little influence on the branching ratios of the different relaxation routes. V-T transfer appears to be a leading mechanism. The main feature of the rotational relaxation process in the vibrationless S 1 state of glyoxal, is a fast equilibration, the relaxation is not restricted to small changes of the rotational quantum number K.

Information theory and bulk rotational or vibrational relaxation processes

The possible occurrence in bulk relaxation of pure-exponential, near-exponential, and non-exponential decay of the total energy is examined in terms of the normal-mode and information-theoretic approaches. Experimental tests are suggested for the identification of pure-exponential decay caused by adherence to the 'sum rule', and of near-exponential decay. In the case of near-exponential decay (as opposed to pure-exponential decay), it is not possible to derive reliable state-to-state rate constants by invoking approximate adherence to the sum rule.

Vib–rotational energy distributions and relaxation processes in pulsed HF chemical lasers

The rate equations governing the temporal evolution of photon densities and level populations in pulsed F+H2→HF+H chemical lasers are solved for different initial conditions. The rate equations are solved simultaneously for all relevant vibrational–rotational levels and vibrational–rotational P-branch transitions. Rotational equilibrium is not assumed. Approximate expressions for the detailed state-to-state rate constants corresponding to the various energy transfer processes (V–V, V–R,T, R–R,T) coupling the vib–rotational levels are formulated on the basis of experimental data, approximate theories, and qualitative considerations. The main findings are as follows: At low pressures, R–T transfer cannot compete with the stimulated emission, and the laser output largely reflects the nonequilibrium energy distribution in the pumping reaction. The various transitions reach threshold and decay almost independently and simultaneous lasing on several lines takes place. When a buffer gas is added in excess to the reacting mixture, the enhanced rotational relaxation leads to nearly single-line operation and to the J shift in lasing. Laser efficiency is higher at high inert gas pressures owing to a better extraction of the internal energy from partially inverted populations. V–V exchange enhances lasing from upper vibrational levels but reduces the total pulse intensity. V–R,T processes reduce the efficiency but do not substantially modify the spectral output distribution. The photon yield ranges between 0.4 and 1.4 photons/HF molecule depending on the initial conditions. Comparison with experimental data, when available, is fair.