Vibrational Relaxation Time Research Articles

Quartz-Enhanced Photoacoustic Spectroscopy (QEPAS) Detection of the ν7 Band of Ethylene at Low Pressure with CO2 Interference Analysis.

Ethylene (C2H4) was detected using quartz-enhanced photoacoustic spectroscopy (QEPAS) at 10.5 µm with a continuous wave, distributed-feedback quantum cascade laser as the light source. The QEPAS sensor was operated at low pressures (≤200 torr) to eliminate the cross-talk spectral interference between C2H4 and CO2, a major interfering species in practical applications. The sensor was calibrated to show a good linear response to C2H4 concentration and the Allan deviation analysis demonstrated a minimum detection limit of 8 ppb at an integration time of 90 s. Although no spectral overlap between C2H4 and CO2 was confirmed at the pressure ≤200 torr by the direct absorption measurement using a 28-m multipass cell, we observed the apparent influence of the CO2 addition to the C2H4/N2 mixture on the photoacoustic signal of C2H4. An energy transfer model involving the vibration-vibration (VV) and vibration-translation (VT) transitions in the C2H4-CO2-N2 system was constructed to interpret the experimental data. Additionally, the vibrational relaxation times of C2H4 were obtained based on the QEPAS technique and the energy transfer model, which were in good agreement with the previous studies.

Molecular Tuning of the Vibrational Thermal Transport Mechanisms in Fullerene Derivative Solutions.

Control over the thermal conductance from excited molecules into an external environment is essential for the development of customized photothermal therapies and chemical processes. This control could be achieved through molecule tuning of the chemical moieties in fullerene derivatives. For example, the thermal transport properties in the fullerene derivatives indene-C60 monoadduct (ICMA), indene-C60 bisadduct (ICBA), [6,6]-phenyl C61 butyric acid methyl ester (PCBM), [6,6]-phenyl C61 butyric acid butyl ester (PCBB), and [6,6]-phenyl C61 butyric acid octyl ester (PCBO) could be tuned by choosing a functional group such that its intrinsic vibrational density of states bridge that of the parent molecule and a liquid. However, this effect has never been experimentally realized for molecular interfaces in liquid suspensions. Using the pump-probe technique time domain thermotransmittance, we measure the vibrational relaxation times of photoexcited fullerene derivatives in solutions and calculate an effective thermal boundary conductance from the opto-thermally excited molecule into the liquid. We relate the thermal boundary conductance to the vibrational modes of the functional groups using density of states calculations from molecular dynamics. Our findings indicate that the attachment of an ester group to a C60 molecule, such as in PCBM, PCBB, and PCBO, provides low-frequency modes which facilitate thermal coupling with the liquid. This offers a channel for heat flow in addition to direct coupling between the buckyball and the liquid. In contrast, the attachment of indene rings to C60 does not supply the same low-frequency modes and, thus, does not generate the same enhancement in thermal boundary conductance. Understanding how chemical functionalization of C60 affects the vibrational thermal transport in molecule/liquid systems allows the thermal boundary conductance to be manipulated and adapted for medical and chemical applications.

Free-Energy-Gap Law for Ultrafast Charge Recombination of Ion Pairs Formed by Intramolecular Photoinduced Electron Transfer.

In this article, regularities of ultrafast charge recombination (CR) kinetics in photoinduced intramolecular electron transfer in polar solvents are studied. The kinetics of charge separation and ensuing ultrafast CR are simulated within the framework of the multichannel stochastic model. This model accounts for the reorganization of both the solvent and a number of intramolecular high-frequency vibrational modes. The solvent relaxation is described in terms of two relaxation modes. For ultrafast CR, the free-energy-gap law strongly depends on the parameters: the electronic coupling, reorganization energy of intramolecular high-frequency vibrational modes, and the vibrational and solvent relaxation times. The semilog dependence of the CR rate constant on the free-energy gap varies from a parabolic shape to a nearly linear one with increasing the electronic coupling and decreasing the vibrational relaxation time. The dynamic solvent effect in CR is predicted to be large in the area of strong exergonicity and small in the area of weak exergonicity. This regularity is opposite to that observed for the thermal reactions.

Development of a two-dimensional binning model for N2–N relaxation in hypersonic shock conditions

A high fidelity internal energy relaxation model for N2–N suitable for use in direct simulation Monte Carlo (DSMC) modeling of chemically reacting flows is proposed. A novel two-dimensional binning approach with variable bin energy resolutions in the rotational and vibrational modes is developed for treating the internal mode of N2. Both bin-to-bin and state-specific relaxation cross sections are obtained using the molecular dynamics/quasi-classical trajectory (MD/QCT) method with two potential energy surfaces as well as the state-specific database of Jaffe et al. The MD/QCT simulations of inelastic energy exchange between N2 and N show that there is a strong forward-preferential scattering behavior at high collision velocities. The 99 bin model is used in homogeneous DSMC relaxation simulations and is found to be able to recover the state-specific master equation results of Panesi et al. when the Jaffe state-specific cross sections are used. Rotational relaxation energy profiles and relaxation times obtained using the ReaxFF and Jaffe potential energy surfaces (PESs) are in general agreement but there are larger differences between the vibrational relaxation times. These differences become smaller as the translational temperature increases because the difference in the PES energy barrier becomes less important.

Thermal relaxation of molecular oxygen in collisions with nitrogen atoms

Investigation of O2-N collisions is performed by means of the quasi-classical trajectory method on the two lowest ab initio potential energy surfaces at temperatures relevant to hypersonic flows. A complete set of bound-bound and bound-free transition rates is obtained for each precollisional rovibrational state. Special attention is paid to the vibrational and rotational relaxations of oxygen as a result of chemically non-reactive interaction with nitrogen atoms. The vibrational relaxation of oxygen partially occurs via the formation of an intermediate NO2 complex. The efficient energy randomization results in rapid vibrational relaxation at low temperatures, compared to other molecular systems with a purely repulsive potential. The vibrational relaxation time, computed by means of master equation studies, is nearly an order of magnitude lower than the relaxation time in N2-O collisions. The rotational nonequilibrium starts to play a significant effect at translational temperatures above 8000 K. The present work provides convenient relations for the vibrational and rotational relaxation times as well as for the quasi-steady dissociation rate coefficient and thus fills a gap in data due to a lack of experimental measurements for this system.

A network approach to unravel correlated ion pair dynamics in protic ionic liquids. The case of triethylammonium nitrate

The intermolecular interactions in the title compound are investigated using self-consistent charge density functional based tight binding molecular dynamics. Emphasis is put on the analysis of correlated motions of ion pairs using ideas of network theory. At equilibrium such correlations are not very pronounced on average. However, there exist sizable local correlations for cases where two cations share the same anion via two NHO-hydrogen bonds. The effect of an external perturbation, which artificially introduces a sudden local heating of an NH-bond, is investigated using nonequilibrium molecular dynamics. Here, it is found that the average NH bond vibrational relaxation time is about 5.3ps. This energy redistribution is rather nonspecific with respect to the ion pairs and does not lead to long-range correlations spreading from the initially excited ion pair.

Radiation of molecules in Benešov bolide spectra

We analyzed molecular radiation in the spectra of the very bright Benešov bolide. The Benešov bolide appeared over the Czech Republic on May 7, 1991 and reached an absolute magnitude of –19.5. It was caused by a meteoroid larger than 1m. Small meteorites of various mineralogical types were recovered recently (Spurný et al. [2014] Astron. Astrophys., 570, A39, 14 p.). The spectrum of the bolide, recorded on two photographic plates, is probably the richest meteor spectrum ever obtained. It contains hundreds of atomic emission lines, continuous radiation and molecular bands, and covers the whole bolide trajectory from the altitude of 90–20km. In this paper we focus on identification and analysis of molecular bands. The identification of FeO, CaO, AlO, and MgO, reported earlier (Borovička and Spurný [1996] Icarus, 121, 484–510) was confirmed. In addition, radiation of N2 was probably detected. The oxides were best seen in the wake and in the radiating cloud left at the position of the bolide flare at the altitude of 24.5km. Trace of N2 was seen only in the meteor at lower altitudes. FeO bands are present in the spectra from the highest altitudes. We suppose that FeO was ablated directly in molecular form at high altitudes. CaO was first detected just below 50km and its intensity, relatively to FeO, strongly increased toward lower altitudes. AlO, which is similarly refractive as CaO, behaved as FeO rather than CaO at lower altitudes. MgO was observed only in the radiating cloud. The spectrum of the cloud is unique because it contains almost no atomic lines. We compared the data with theoretical calculations of the presence of molecules in the mixture of meteoric vapors and air at various altitudes and temperatures. CN and TiO were not found. The upper limit of CN is in agreement with theory for ordinary chondrite meteoroid. Most of carbon should be in fact present in the form of CO, but CO bands are too weak to be detected. The non-detection of TiO can be explained by the fact that temperature in the wake and the cloud was lower than needed for the presence of TiO bands. However, AlO was found to be about 40 times more abundant than MgO, although comparable abundances are expected. The explanation may be that the abundances are in fact comparable but there are non-equilibrium conditions in the radiating cloud with the excitation temperature of MgO lower than that of AlO. The difference may be caused by higher ablation temperature of Al. Another non-equilibrium effect is the observed difference between the rotational (∼1000K) and vibrational (∼3000K) temperature of AlO molecules. This can be explained by short hydrodynamic timescale and the fact that vibrational relaxation time is significantly longer than rotational relaxation time. The vibrational temperature therefore could not decrease so quickly during the cooling and expansion of the cloud because of insufficient number of collisions. FeO and CaO could not be analyzed in detail, because their molecular constants, especially transition probabilities, are not well known. The increase of the CaO/FeO ratio with decreasing altitude could be, nevertheless, explained in scope of equilibrium chemistry.

Quantum and quasi-classical collisional dynamics of O2-Ar at high temperatures.

A hypersonic vehicle traveling at a high speed disrupts the distribution of internal states in the ambient flow and introduces a nonequilibrium distribution in the post-shock conditions. We investigate the vibrational relaxation in diatom-atom collisions in the range of temperatures between 1000 and 10 000 K by comparing results of extensive fully quantum-mechanical and quasi-classical simulations with available experimental data. The present paper simulates the interaction of molecular oxygen with argon as the first step in developing the aerothermodynamics models based on first principles. We devise a routine to standardize such calculations also for other scattering systems. Our results demonstrate very good agreement of vibrational relaxation time, derived from quantum-mechanical calculations with the experimental measurements conducted in shock tube facilities. At the same time, the quasi-classical simulations fail to accurately predict rates of vibrationally inelastic transitions at temperatures lower than 3000 K. This observation and the computational cost of adopted methods suggest that the next generation of high fidelity thermochemical models should be a combination of quantum and quasi-classical approaches.

Quantum Interference in the Vibrational Relaxation of the O-H Stretch Overtone of Liquid H2O.

Using femtosecond two-color infrared pump-probe spectroscopy, we study the vibrational relaxation of the O-H stretch vibrations of liquid H2O after excitation of the overtone transition. The overtone transition has its maximum at 6900 cm(-1) (1.45 μm), which is a relatively high frequency in view of the central frequency of 3400 cm(-1) of the fundamental transition. The excitation of the overtone leads to a transient induced absorption of two-exciton states of the O-H stretch vibrations. When the overtone excitation frequency is tuned from 6600 to 7200 cm(-1), the vibrational relaxation time constant of the two-exciton states increases from 400 ± 50 fs to 540 ± 40 fs. These values define a limited range of relatively long relaxation time constants compared to the range of relaxation time constants of 250-550 fs that we recently observed for the one-exciton O-H stretch vibrational state of liquid H2O ( S. T. van der Post et al., Nature Comm. 2015 , 6 , 8384 ). We explain the high central frequency and the limited range of relatively long relaxation time constants of the overtone transition from the destructive quantum interference of the mechanical and electrical anharmonic contributions to the overtone transition probability. As a result of this destructive interference, the overtone transition of liquid H2O is dominated by molecules of which the O-H groups donate relatively weak hydrogen bonds to other H2O molecules.

Temporal Behavior of the Pump Pulses, Residual Pump Pulses, and THz Pulses for D2O Gas Pumped by a TEA CO2 Laser

Temporal behavior of the pump pulses, residual pump pulses, and THz pulses for optically pumped D2O gas molecules was investigated by using a tunable TEA CO2 laser as the pumping source. The pulse profiles of pump laser pulses, residual pump pulses, and the THz output pulses were measured, simultaneously, at several different gas pressures. For THz pulse, the pulse delay between the THz pulse and the pump pulse was observed and the delay time was observed to increase from 40 to 70 ns with an increase in gas pressure from 500 to 1700 Pa. Both THz pulse broadening and compression were observed, and the pulse broadening effect transformed to the compression effect with increasing the gas pressure. For the residual pump pulse, the full width at half maximum (FWHM) of the main pulse decreased with increasing gas pressure, and the main pulse disappeared at high gas pressures. The secondary pulses were observed at high gas pressure, and the time intervals of about 518 and 435 ns were observed between the THz output pulse and the secondary residual pump pulse at the pressure of 1400 Pa and 1700 Pa, from which the vibrational relaxation time constants of about 5.45 and 5.55 μs Torr were obtained.

Mutual effect of vibrational relaxation and chemical reactions in viscous multitemperature flows.

We study coupling of vibrational relaxation and chemical reactions in nonequilibrium viscous multitemperature flows. A general theoretical model is proposed on the basis of the Chapman-Enskog method modified for strongly nonequilibrium reacting flows; the model differs from models commonly used in computational fluid dynamics since it is able to capture additional cross-coupling terms arising in viscous flow due to compressibility and mutual influence of all nonequilibrium processes occurring in a mixture. The set of fluid dynamic equations is derived starting from the Boltzmann equation; the relaxation terms in these equations are described using the kinetic transport theory formalism. Reaction and relaxation rates depend on the distribution function and thus differ in the zero-order and first-order approximations of the Chapman-Enskog method. An algorithm for the calculation of multitemperature reaction and relaxation rates in both inviscid and viscous flows is proposed for the harmonic oscillator model. This algorithm is applied to estimate the mutual effect of vibrational relaxation and dissociation in binary mixtures of N(2) and N, and O(2) and O, under various nonequilibrium conditions. It is shown that modification of the Landau-Teller expression for the VT relaxation term works rather well in nitrogen, whereas it fails to predict correctly the relaxation rate in oxygen at high temperatures. In oxygen (in contrast to nitrogen), the first-order cross effects of dissociation and VT relaxation are found to be significant. A method for calculation of vibrational relaxation time based on the kinetic theory definition is suggested. Two-temperature dissociation rate coefficients are calculated in the zero- and first-order approximations and compared to other models.

Effect of Intramolecular High-Frequency Vibrational Mode Excitation on Ultrafast Photoinduced Charge Transfer and Charge Recombination Kinetics.

A model of photoinduced ultrafast charge separation and ensuing charge recombination into the ground state has been developed. The model includes explicit description of the formation and evolution of nonequilibrium state of both the intramolecular vibrations and the surrounding medium. An effect of the high-frequency intramolecular vibrational mode excitation by a pumping pulse on ultrafast charge separation and charge recombination kinetics has been investigated. Simulations, in accord with experiment, have shown that the effect may be both positive (the vibrational mode excitation increases the charge-transfer rate constant) and negative (opposite trend). The effect on charge separation kinetics is predicted to be bigger than that on the charge recombination rate but nevertheless the last is large enough to be observable. The amplitude of both effects falls with decreasing vibrational relaxation time constant, but the effects are expected to be observable up to the time constants as short as 200 fs. Physical interpretation of the effects has been presented. Comparisons with the experimental data have shown that the simulations, in whole, provide results close to that obtained in the experiment. The reasons of the deviations have been discussed.

Electron-vibration relaxation in oxygen plasmas

An ideal chemical reactor model is used to study the vibrational relaxation of oxygen molecules in their ground electronic state, X3Σg-, in presence of free electrons. The model accounts for vibrational non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules. The vibrational levels of the molecules are treated as separate species, allowing for non-Boltzmann distributions of their population. The electron and vibrational temperatures are varied in the range [0–20,000]K. Numerical results show a fast energy transfer between oxygen molecules and free electron, which causes strong deviation of the vibrational distribution function from Boltzmann distribution, both in heating and cooling conditions. Comparison with Landau–Teller model is considered showing a good agreement for electron temperature range [2000–12,000]K. Finally analytical fit of the vibrational relaxation time is given.

Rovibrational energy transfer and dissociation in O2-O collisions.

A set of state-specific transition rates for each rovibrational level is generated for the O2(X(3)Σ(g)(-))-O(3)P system using the quasi-classical trajectory method at temperatures observed in hypersonic flows. A system of master equations describes the relaxation of the rovibrational ensemble to thermal equilibrium under ideal heat bath conditions at a constant translational temperature. Vibrational and rotational relaxation times, obtained from the average internal energies, exhibit a pattern inherent in a chemically reactive collisional pair. An intrinsic feature of the O3 molecular system with a large attractive potential is a weak temperature dependence of the rovibrational transition rates. For this reason, the quasi-steady vibrational and rotational temperatures experience a maximum at increasing translational temperature. The energy rate coefficients, that characterize the average loss of internal energy due to dissociation, quickly diminish at high temperatures, compared to other molecular systems.

Deconstructing the Heterogeneity of Surface-Bound Catalysts: Rutile Surface Structure Affects Molecular Properties

Catalytic interfaces involving surface-bound molecular catalysts often exhibit a large structural heterogeneity from uncontrolled variation in surface morphology. Conventional spectroscopic techniques typically average over these different structural motifs within the sample, making it difficult to link the underlying surface morphology to the properties of the immobilized catalyst. Here we present the first direct comparison of the vibrational dynamics of a CO2 reduction catalyst bound to two different single-crystalline TiO2 surfaces, rutile (001) and (110), probed with transient surface-specific sum-frequency generation spectroscopy. We find that the change in surface structure between crystallographic faces alters both the vibrational frequency and relaxation time of the symmetric carbonyl stretching mode of the catalyst, with (001) displaying a lower frequency and longer relaxation time. This results from a change in the catalyst electronic structure and indicates that the molecular properties of the catalyst, likely including the catalytic properties, depend on the specific TiO2 surface to which it is bound. The comparison of the molecular properties on these two single crystal surfaces is an essential step toward understanding how semiconductor surface structure influences catalyst behavior and identifying optimal surface structures for improved catalytic performance.

Master Equation Study of Vibrational and Rotational Relaxations of Oxygen

Transition rates in collisions for each vibrational and rovibrational state are generated by means of the quasi-classical trajectory method using potential energy surfaces of different fidelities. The first potential energy surface, obtained via the double many-body expansion method, is adopted to obtain vibrational transition rates assuming transrotational equilibrium. The trajectory simulation on a simpler potential surface, based on the two-body pairwise interaction, generates a complete set of rates for each internal state. Vibrational and rotational relaxations of oxygen in a heat bath of parent atoms are modeled by a system of master equations at translational temperatures between 1000 and 20,000 K. It is shown that the vibrational relaxation becomes less efficient at high temperatures, in contrast with the conventional equation for relaxation time proposed by Millikan and White (“Systematics of Vibrational Relaxation,” Journal of Chemical Physics, Vol. null, No. null, 1963, Paper 3209). Rotational and vibrational relaxation times are the same order of magnitude in the range of temperatures observed in hypersonic flows. The excitation of the vibrational mode in collisions under typical postshock conditions occurs earlier than in other molecular systems. The exchange channel plays an important role in the internal energy randomization.

Excited states of the high-frequency vibrational modes and kinetics of ultrafast photoinduced electron transfer

The effect of the carrier frequency of the exciting laser pulse on the kinetics of intramolecular photoinduced charge transfer in the multi-channel stochastic model is studied. It is shown that the population of different states of high-frequency intramolecular modes upon varying the frequency of the excitation pulse can considerably alter the rate constant of ultrafast charge transfer. It is found that a negative vibrational spectral effect is expected in the vicinity of a barrier-free area (the rate constant of photoinduced charge transfer decreases along with the carrier frequency of the excitation pulse), while a positive effect is predicted in areas of high and low exergonicity (an inverse dependence). It is concluded that the value of the spectral effect falls along with the time of vibrational relaxation. For ultrafast photo-induced charge transfer, however, it remains considerable up to relaxation times of 100 fs.

Algorithm for reconstructing vibrational relaxation times in excitable gases by two-frequency acoustic measurements

Vibrational relaxation time is a parameter describing the macroscopic behavior of vibrational energy transition rate between molecular internal degrees of freedom (DOF) and external DOF in excitable gas, which determines the relaxation frequency of the maximum point in acoustic absorption spectrum. To measure the vibrational relaxation time, the traditional methods are used to obtain the acoustic absorption spectra by changing the ambient pressure at several operating frequencies. However, these traditional methods are not suitable for real-time measurement due to the complexity of equipment implementation and the non-ideality of test gas under high pressure. In order to solve those problems, we have developed an algorithm [2013 Meas. Sci. Technol. 24 055002] to capture the primary vibrational relaxation processes only based on the measurements of sound absorption and sound speed at two operating frequencies and a single pressure. But the algorithm only can reconstruct the absorption maximum and it cannot capture the relaxation time with high precision. To measure the frequency dependence of the complex effective specific heat of the relaxing gas, an algorithm synthesizing relaxation processes is given by Petculescu and Lueptow [2005 Phys. Rev. Lett. 94 238301]. In its derivation process, relaxational angular frequency was set to be the inverse ratio to relaxation time. However, the relaxational angular frequency was measured in the adiabatic process of transmission thermodynamic, while the relaxation time was obtained in the thermodynamic isothermal process, the derivation confused the two thermodynamic processes, making the algorithm unable to capture the relaxation frequency with high precision. In order to estimate the relaxation time with higher accuracy, in this paper we first obtain the theoretical relationship among the relaxation times under the three types of thermodynamics conditions, i. e., isothermal, adiabatic constant pressure and adiabatic constant volume. Then we correct the relaxation time derivation and propose our corrected algorithm to reconstruct the relaxation frequencies and relaxation times under the conditions of isothermal, adiabatic constant pressure and adiabatic constant volume. In experiments and simulations, the relaxation times and relaxation frequencies reconstructed by our corrected algorithm for various gas compositions including carbon dioxide, methane, chlorine, nitrogen, and oxygen around room temperature are consistent with the experimental data.

Oxygen Vibrational Relaxation Times: Shock Tube/Laser Absorption Measurements

The vibrational relaxation times of oxygen were measured using laser absorption spectroscopy behind incident and reflected shocks in a shock tube. The Bethe–Teller equation was used to model the vibrational relaxation, which (along with the shock jump relations) was used to model the gas dynamics conditions throughout the nonequilibrium relaxation process. The absorbance was modeled based on these gas dynamics conditions while adjusting the vibrational relaxation time to fit the model to the measured oxygen absorbance time history at wavelengths 210–230 nm in the Schumann–Runge system. Undiluted oxygen was studied behind incident shocks at initial postshock translational/rotational temperatures from 1000 to 3300 K and pressures from 0.05 to 0.7 atm, while a mixture of 2% oxygen in argon was studied behind incident and reflected shocks at initial translational/rotational temperatures from 1000 to 4000 K and pressures from 0.2 to 1 atm. Good agreement was found with prior experimental work by White and Millikan, Losev and Generalov, and Camac; however, the current relaxation time data have less scatter and reduced uncertainty. The current results are also in excellent agreement with the well-known relaxation time recommendations of Millikan and White.

Numerical study on wall pressure over cone region of blunt-nosed body in high enthalpy shock tunnel HIEST

A cause of an overestimation of the computed surface pressure on a blunted cone in high-temperature hypersonic flow is explored. The overestimation was observed in a free-piston shock tunnel at the stagnation of H0=15.6 and 10.1 MJ/kg. The sensitivity analysis reveals that a reduction of the upstream translational temperature in the range of 100 to 300 K substantially improves the agreement of the surface pressure with the measured data. As the cause of the lower upstream translational temperature, radiative cooling effect is included in the thermochemical nonequilibrium calculation in the nozzle, the translational temperature at the nozzle exit is reduced to about 250 K. Using the obtained flow variables as the upstream boundary condition, the computed pressure agrees quite well with the experimental data. In order to clarify whether other variables such as translational–vibrational relaxation time, chemical reaction rates, and upstream chemical composition could be the cause of the discrepancy, uncertainty quantification is employed. It is shown that these parameters of the thermochemical model and upstream chemical composition have minor effect on the agreement of surface pressure. It is concluded that the observed discrepancy in the surface pressure is due to radiative cooling effect of high temperature gas in the nozzle region.