Rotational Relaxation Processes Research Articles

Experimental study of rotational relaxation for D2(1,12) in collisions with N2.

The rotational relaxation behavior of D2(1,12) in a D2-N2 mixture was investigated using coherent anti-Stokes Raman scattering (CARS) technique. The rovibrational level v = 1 and J = 12 of D2 was selectively excited through stimulated Raman pumping while monitoring the temporal evolution of population for D2(1, J ≤ 12) molecules using time-resolved CARS spectroscopy. The results demonstrate that the rotational relaxation processes of D2(1,12) encompass both multi-quantum relaxation and continuous single-quantum relaxation. When α, the molar ratio of N2, is less than 0.5, D2(1,12) predominantly undergoes a single quantum relaxation process transition. However, when α ≥ 0.5, the multi-quantum relaxation mechanism gradually predominates. The total rotational relaxation rate coefficients of D2(1,12) collisions with N2 and D2 at 295K were determined to be 3.974 × 10-14 and 1.179 × 10-14cm3s-1, respectively. The temperature dependence of rotational relaxation rate of D2(1,12) was investigated within the temperature range of 295-453K. With increasing temperature, the dominant relaxation process exhibited an accelerated behavior, while the minor relaxation process remained largely unaffected. The rotational temperature of the D2molecule at various N2 molar ratios was determined through the utilization of Boltzmann plots. The rotational temperature undergoes a rapid decline within 2 μs, corresponding to the near-resonant rotation-vibration relaxation process of D2(1,12) collisions with N2. The system reaches a quasi-equilibrium state when the delay time is 3 μs. The findings of this study can serve as a valuable empirical basis for further validation of the kinetic theory and simulation.

Synthesis of Subporphyrin Free Bases.

BIII subporphyrins are the legitimate ring-contracted porphyrins consisting of three pyrroles and three meso-carbons and their chemistry has been extensively developed since the first synthesis in 2006. However, subporphyrin free bases have never been synthesized, despite tremendous attempts to remove the BIII ion. Here we report that Suzuki-Miyaura coupling between α,α'-diborylated tripyrrane 1 and tetrabromide 5 gave subporphyrin free bases 6, 6 A, and free base dimer 7 in 6 %, 4 %, and 2 % yields as the first examples. Subporphyrin free bases exhibit curved bowl-like structures and distinct 14π-aromaticity. Steady-state and time-resolved spectroscopy revealed that the excited-state behaviors of the subporphyrin free bases are comparable with those of the corresponding BIII subporphyrins. Rotational relaxation processes in the excited states have been revealed, which enhance the electronic interactions with the meso-aryl substituents and between the two subporphyrins.

Synthesis of Subporphyrin Free Bases

AbstractBIII subporphyrins are the legitimate ring‐contracted porphyrins consisting of three pyrroles and three meso‐carbons and their chemistry has been extensively developed since the first synthesis in 2006. However, subporphyrin free bases have never been synthesized, despite tremendous attempts to remove the BIII ion. Here we report that Suzuki–Miyaura coupling between α,α′‐diborylated tripyrrane 1 and tetrabromide 5 gave subporphyrin free bases 6, 6 A, and free base dimer 7 in 6 %, 4 %, and 2 % yields as the first examples. Subporphyrin free bases exhibit curved bowl‐like structures and distinct 14π‐aromaticity. Steady‐state and time‐resolved spectroscopy revealed that the excited‐state behaviors of the subporphyrin free bases are comparable with those of the corresponding BIII subporphyrins. Rotational relaxation processes in the excited states have been revealed, which enhance the electronic interactions with the meso‐aryl substituents and between the two subporphyrins.

Experimental investigations on rotation–vibration energy transfer in H2–N2 collisions

We investigated the rotational–vibrational impact energy transfer processes in a H2–N2 gas mixture system. The stimulated Raman pumping technique was used to excite H2 molecules to the (1, 7) high rotational states. The population of the H2(1, 7) level was verified by the coherent anti-Stokes Raman (CARS) spectra, the total pressure of the mixture was maintained at 500 Torr and nitrogen with different molar ratios was filled in the sample cell. The collisional deactivation rate coefficients of the excited state H2(1, 7) with H2 and N2 were obtained by fitting the experimental data with the Stern–Volmer equation. The multi-quantum near-resonant rotational relaxation process of H2(1, 7) colliding with N2 was confirmed by the time-resolved CARS profile measurements of H2(v = 1, J = 7, 5, 3) after the excitation of H2(1, 7). The results can provide data reference for atomic and molecular physics, atomic and molecular collisions, rotation and vibration excitation calculation, etc.

Molecular simulation of Rayleigh-Brillouin scattering in binary gas mixtures and extraction of the rotational relaxation numbers.

Rayleigh-Brillouin scattering (RBS) in gases has received considerable attention due to its applications in LIDAR (light detection and ranging) remote sensing and gas property measurements. In most cases, the RBS spectra in the kinetic regime are calculated based on kinetic model equations, which are difficult to be applied to complex gas mixtures. In this work, we employ two widely used molecular simulation methods, i.e., direct simulation Monte Carlo (DSMC) and molecular dynamics (MD), to calculate the spontaneous RBS spectra of binary gas mixtures. We validate these two methods by comparing the simulation results for mixtures of argon and helium with the experimental results. Then we extend the RBS calculations to gas mixtures involving polyatomic gases. The rotational relaxation numbers specific to each species pair in DSMC are determined by fitting the DSMC spectra to the MD spectra. Our results show that all the rotational relaxation numbers for air composed of N_{2} and O_{2} increase with temperature in the range of 300-750 K. We further calculate the RBS spectra for binary mixtures composed of N_{2} and one noble monatomic gas, and the simulation results show that the rotational relaxation of N_{2} is greatly affected by the mass of the noble gas atoms. This work demonstrates that RBS is a promising and alternative way to study the rotational relaxation process in gas mixtures.

A detailed multiscale study of rotational–translational relaxation process of diatomic molecules

This article continues our cycle devoted to comprehensive investigation of the diatomic molecule collision process. In this paper, we focus particularly on the in-depth study of the rotational–translational (R–T) energy exchange process and Borgnakke–Larsen (BL) energy exchange model used in the direct simulation Monte Carlo method. The present study, which was performed on several levels of description (molecular, microscopic, and macroscopic), is based mainly on the highly detailed dataset (around 1011 configurations) of binary N2–N2 collisions, obtained via the classical trajectory calculation (CTC) method. This dataset, along with the explicit mathematical representation of the Borgnakke–Larsen model derived in the present paper, allowed us to obtain new results regarding the R–T energy exchange process: (1) we present an ab initio method to derive physically accurate expressions for inelastic collision probability pr in the BL model directly from CTC data; (2) we present a new two-parametric model for pr and compared it to the previously known models, including the recent nonequilibrium-direction-dependent model of Zhang et al. [“Nonequilibrium-direction-dependent rotational energy model for use in continuum and stochastic molecular simulation,” AIAA J. 52(3), 604 (2014)]; (3) it showed that apart from the well-known dependence of the rotational relaxation rate on “direction to equilibrium” (ratio between translational and rotational temperatures), on molecular scale, rotationally over-excited molecule pairs demonstrate almost zero energy transfer to the translational energy mode (even in the case of very significant discrepancies between translational and rotational energies); (4) it was also shown that the Borgnakke–Larsen approach itself may require reassessment since it fails to give a proper description of distribution of post-collision energies. Throughout this paper, we also tried to put together and analyze the existing works studying the rotational relaxation process and estimating the rotational collision number Zrot by performing reviews and assessment of (1) numerical approaches to simulate non-equilibrium problems, (2) models for inelastic collision probabilities pr, (3) approaches to estimate Zrot, and (4) intermolecular potentials used for molecular dynamics and CTC simulations. The corresponding conclusions are given in this paper.

Rotational relaxation model for nitrogen and its application in free jet expansion problem

This paper studies a rotational relaxation process in nitrogen. A series of more than 200 × 106 classical trajectory calculations (CTCs) of collisions of nitrogen molecules were carried out. Based on the CTC results, a collision model accounting for rotational relaxation was proposed and used for three-dimensional event-driven molecular dynamics simulation of a free jet expansion. It was shown that the collision model parameterized by the CTCs can produce results in good agreement with the existing experimental measurements.

State-to-state chemical kinetic mechanism for HF chemical lasers

State-to-state rotational relaxation processes play a critical role in predicting rotational nonequilibrium, which can significantly affect total laser power and spectral distribution. In this paper, the state-to-state rotational relaxation rate coefficients for the pumping reaction of F + H2, the rotational energy transfer processes of HF(υ, j = 0–10) + HF(υ′, j′ = 0–10) and HF(υ, j = 0–10) + H2 are calculated. Subsequently, a detailed state-to-state chemical kinetic mechanism is constructed including 61 species and 124,482 elementary reactions for HF chemical lasers. All of these rotational relaxation rate coefficients have been expressed with Arrhenius-like formulas. A comparison of the Boltzmann distribution model with the detailed state-to-state chemical mechanism has been analysed and discussed. These results show that rotational nonequilibrium processes can significantly affect the distribution of ro-vibrational excited HF molecules. The rotational distributions of HF(υ = 0–2, j) are far from equilibrium distribution. Conversely, the distributions of HF(υ = 3, 4, j) seem to be a Boltzmann distribution. These results indicate that numerical models must include the rotational nonequilibrium processes and numerical models using a Boltzmann distribution for the rotational populations cannot predict performance of real HF chemical lasers.

Decoupling Multiple Rotational Relaxations of Hydrogen to Detect Gas Mixtures

Decoupling multiple acoustic relaxations in multi-component gas mixtures is an effective method to acquire acoustic relaxation characteristic of gas molecules, which can be used to determine gas composition. However, decoupling multiple rotational relaxations of hydrogen still remains challenge. In this paper, we present the decoupling model of hydrogen and decouple the multiple rotational relaxation into the group of single-relaxation ones. Based on this model, the whole rotational relaxation process of hydrogen can be simplified as a few decoupled single rotational relaxation processes. The decoupled results of the effective specific heat, the absorption spectrum and the acoustic velocity dispersion agree with the experimental data, which validates our decoupling model. Furthermore, the proposed decoupling rotational relaxation model can be combined with the existing decoupling vibration model to detect gas mixture. Applications in the detection of gas mixtures including N 2 , CO 2 , O 2 and H 2 are provided. Compared with existing gas sensing method ignoring rotational relaxation, our detection result of gas mixtures H 2 - O 2 - H 2 O is more convincing since the proposed decoupling model contains significant rotational relaxation of hydrogen. Therefore, the proposed decoupling model not only reveals the mechanism of multiple rotational relaxations of hydrogen, but also provides the new method to detect hydrogen gas mixtures.

Microscopic origin of the logarithmic relaxation in molecular glass-forming liquids

Logarithmic relaxation is a unique relaxation process exhibited by a few molecular liquids and biomolecules. However, the microscopic origin of logarithmic relaxation is still unclear. To understand the origin of this process, we studied two liquids that exhibit logarithmic relaxation in a dissolved state using quasielastic neutron scattering (QENS) and depolarized dynamic light scattering (DDLS). Although the intermolecular potential of the liquids is drastically different in the dissolved state from the bulk liquids, we observed that the logarithmic relaxation still persists. Our results indicate that the intermolecular potential does not play a role in determining the logarithmic relaxation process. The coupling of rotational and translational relaxation processes could be the origin of the logarithmic relaxation process exhibited by the molecular liquids.

Effect of Urea on Solvation Dynamics and Rotational Relaxation of Coumarin 480 in Aqueous Micelles of Cationic Gemini Surfactants with Different Spacer Groups.

The present work highlights the effect of urea on solvation dynamics and the rotational relaxation of Coumarin 480 (C-480) in the Stern layer of aqueous micelles of cationic gemini surfactants, 12-4(OH)n-12 (n = 0, 1, 2). UV–visible absorption, steady-state fluorescence and fluorescence anisotropy, time-resolved fluorescence and fluorescence anisotropy, and dynamic light scattering measurements have been carried out for this study. The formation of micelles becomes disfavored in the presence of urea at high concentration. Solvation dynamics is bimodal in nature with fast solvation as a major component. The average solvation time increases, reaches a maximum, and then decreases with increasing concentration of urea because the degree of counterion dissociation also follows the same order with the addition of urea in the micellar solution. With increased degree of counterion dissociation, the extent of clustering of water molecules is increased, resulting in slower solvation process. The −OH group present in the spacer group of gemini surfactant controls the rate of solvation by shielding the water molecules from the probe molecules forming hydrogen bond. The microviscosity of micelles is decreased with increasing concentration of urea, as a result of which the rotational relaxation process becomes faster. In the presence of the −OH group in the spacer group, the microviscosity of micelles is enhanced, resulting in longer rotational relaxation time. Rotational relaxation process is bimodal in nature with the major contribution from the fast component to the fluorescence depolarization. Slow rotational relaxation is mainly due to the lateral diffusion of C-480 molecules along the surface of the micelle. The tumbling motion of the micelle as a whole is much slower than the lateral diffusion of C-480. Wobbling motion of C-480 becomes faster with increasing concentration of urea as a result of decreased microviscosity of micelles. The alignment of C-480 molecules in micelles might change with changing microviscosity.

Rotational Dynamics of Solutes with Multiple Single Bond Axes Studied by Infrared Pump-Probe Spectroscopy.

To investigate the relationship between the structural degrees of freedom around a vibrational probe and the rotational relaxation process of a solute in solution, we studied the anisotropy decays of three different N3-derivatized amino acids in primary alcohol solutions. By performing polarization-controlled IR pump-probe measurements, we reveal that the anisotropy decays of the vibrational probe molecules in 1-alcohol solutions possess two decay components, at subpicosecond and picosecond time scales. On the basis of results showing that the fast relaxation component is insensitive to the vibrational probe molecule, we suggest that the anisotropy decay of the N3 group on a subpicosecond time scale results from a local, small-amplitude fluctuation of the flexible vibrational probe, which does not depend on the details of its molecular structure. However, the slow relaxation component depends on the solute: with longer alkyl chains attached to the N3 group, the anisotropy decay of the slow component is faster. Consequently, we conclude that the slow relaxation component corresponds to the reorientational motion of the N3 group correlated with other intramolecular rotational motions (e.g., rotational motions of the neighboring alkyl chain). Our experimental results provide important insight into understanding the rotational dynamics of solutes with multiple single bond axes in solution.

Activated barrier crossing dynamics of a Janus particle carrying cargo.

We numerically study the escape kinetics of a self-propelled Janus particle, carrying a cargo, from a meta-stable state. We assume that the cargo is attached to the Janus particle by a flexible harmonic spring. We take into account the effect of the velocity field created in the fluid due to movements of the dimer's components, by considering a space-dependent diffusion tensor (Oseen tensor). Our simulation results show that the synchronization between barrier crossing events and the rotational relaxation process can enhance the escape rate to a large extent. Also, the load carrying capability of a Janus particle is largely controlled by its rotational dynamics and self-propulsion velocity. Moreover, the hydrodynamic interaction, conspicuously, enhances the escape rate of the Janus-cargo dimer. The most important features in escape kinetics have been justified based on analytic arguments.

Acoustic rotational relaxation of hydrogen around normal temperture

Hydrogen is an important energy carrier, and it is widely used due to its extraordinary advantages, such as high heat, clean fuel, being large-scale and renewable. The detection of hydrogen is essential in practical application. Therefore, many researches have focused on monitoring the hydrogen concentration over the past years. Acoustic relaxation theory based on molecular relaxation process is a very promising method of detecting hydrogen gas. However, the existing acoustic relaxation models for gas detection are developed from the vibrational relaxation of gas molecules, and thus they are not applicable for hydrogen and its mixture. In this paper, we present a model for the rotational relaxation process of hydrogen. Firstly, the molecular relaxation process of hydrogen is different from those of other gases due to its large spacing of rotational energy-level and special molecular physical structure. Acoustic relaxation process of hydrogen is mostly determined by the molecular rotational relaxation. Hydrogen molecule is made up of one quarter of para-hydrogen and three quarters of ortho-hydrogen at normal temperature. There is three-rotational-level model for hydrogen rotational relaxation, such as rotational level in states with J=0, 2, 4 (J is rotational quantum-number) for para-hydrogen and J=1, 3, 5 for ortho-hydrogen. Secondly, we introduce effective specific heat into one-mode rotational relaxation at constant pressure, and then extend it to multi-mode rotational relaxation. Upon periodic perturbation of acoustic waves, the temperature and the number of molecules in each rotational level change periodically in the relaxation process. On the basis, we obtain the relaxation equations in a matrix form and calculate effective specific heat at constant pressure for rotational relaxation process. With the relationship between the complex wave number and the effective thermodynamics acoustic speed, we calculate the frequency-dependent acoustic speed and relaxation absorption, and then discuss the difference between the rotational relaxation and the vibrational relaxation. Thirdly, we compare the predicted acoustic speed and absorption spectrum with their corresponding experimental data and investigate the influences of rotational characteristics on absorption spectra in hydrogen and its mixtures. The simulation results show that acoustic speed and relaxation absorption curves calculated by the proposed model are in good agreement with their corresponding experimental data. The model is not only applicable to pure hydrogen gas but also can be used to obtain the acoustic relaxation spectra of gas mixtures with multiple vibrational modes. This model provides a theoretical foundation for the acoustic detecting of hydrogen gas mixtures.

Rational extended thermodynamics of a rarefied polyatomic gas with molecular relaxation processes.

We present a more refined version of rational extended thermodynamics of rarefied polyatomic gases in which molecular rotational and vibrational relaxation processes are treated individually. In this case, we need a triple hierarchy of the moment system and the system of balance equations is closed via the maximum entropy principle. Three different types of the production terms in the system, which are suggested by a generalized BGK-type collision term in the Boltzmann equation, are adopted. In particular, the rational extended thermodynamic theory with seven independent fields (ET_{7}) is analyzed in detail. Finally, the dispersion relation of ultrasonic wave derived from the ET_{7} theory is confirmed by the experimental data for CO_{2},Cl_{2}, and Br_{2} gases.

Effect of Hydrophobicity of Tails and Hydrophilicity of Spacer Group of Cationic Gemini Surfactants on Solvation Dynamics and Rotational Relaxation of Coumarin 480 in Aqueous Micelles.

Solvation dynamics and rotational relaxation of coumarin 480 in aqueous micelles of cationic gemini surfactants with diethyl ether (EE) spacer group (m–EE–m) and tails with varying tail lengths (m = 12, 14, and 16) have been studied. Studies have been carried out by measuring UV–visible absorption, steady-state fluorescence and fluorescence anisotropy, time-resolved fluorescence and fluorescence anisotropy, 1H NMR spectroscopy, and dynamic light scattering. Effects of hydrocarbon tail length and hydrophilicity of spacer group on solvation dynamics and rotational relaxation processes at inner side of the Stern layer of micelles have been studied. With increasing hydrophobicity of tails of surfactants, water molecules in the Stern layer become progressively more rigid, resulting in a decrease in the rate of solvation process with slow solvation as a major component. With increasing hydrophilicity of the spacer group of gemini surfactant, the extent of free water molecules is decreased, thereby making the duration of the solvation process longer. Solvation times in the micelles of gemini surfactants with hydrophilic spacer are almost 4 times longer compared to those in the micelles of their conventional counterpart. Rotational relaxation time increases with increasing tail length of surfactant as a result of increasing microviscosity of micelles with fast relaxation as a major component. With increasing hydrophilicity of the spacer group, the anisotropy decay becomes slower due to the formation of more compact micelles. Rotational relaxation in gemini micelles is also slower compared to that in their conventional counterpart. The anisotropy decay is found to be biexponential with lateral diffusion of the probe along the surface of the micelle as a slow component. Rotational motion of micelle as a whole is a very slow process, and the motion becomes further slower with increasing size of the micelle. The time constants for wobbling motion and lateral diffusion of the probe become longer with increasing microviscosity of micelles.

Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles

We investigate the collective behavior of self-propelled particles (SPPs) undergoing competitive processes of pattern formation and rotational relaxation of their self-propulsion velocities. In full accordance with previous work, we observe transitions between different steady states of the SPPs caused by the intricate interplay among the involved effects of pattern formation, orientational order, and coupling between the SPP density and orientation fields. Based on rigorous analytical and numerical calculations, we prove that the rate of the orientational relaxation of the SPP velocity field is the main factor determining the steady states of the SPP system. Further, we determine the boundaries between domains in the parameter plane that delineate qualitatively different resting and moving states. In addition, we analytically calculate the collective velocity of the SPPs and show that it perfectly agrees with our numerical results. We quantitatively demonstrate that does not vanish upon approaching the transition boundary between the moving pattern and homogeneous steady states.

Direct simulation Monte Carlo modeling of relaxation processes in polyatomic gases

Relaxation processes of polyatomic molecules are modeled and implemented in an in-house Direct Simulation Monte Carlo code in order to enable the simulation of atmospheric entry maneuvers at Mars and Saturn’s Titan. The description of rotational and vibrational relaxation processes is derived from basic quantum-mechanics using a rigid rotator and a simple harmonic oscillator, respectively. Strategies regarding the vibrational relaxation process are investigated, where good agreement for the relaxation time according to the Landau-Teller expression is found for both methods, the established prohibiting double relaxation method and the new proposed multi-mode relaxation. Differences and applications areas of these two methods are discussed. Consequently, two numerical methods used for sampling of energy values from multi-dimensional distribution functions are compared. The proposed random-walk Metropolis algorithm enables the efficient treatment of multiple vibrational modes within a time step with reasonable computational effort. The implemented model is verified and validated by means of simple reservoir simulations and the comparison to experimental measurements of a hypersonic, carbon-dioxide flow around a flat-faced cylinder.

Solvation dynamics and rotational relaxation of coumarin 153 in mixed micelles of Triton X-100 and cationic gemini surfactants: effect of composition and spacer chain length of gemini surfactants.

Solvation dynamics and rotational relaxation of coumarin 153 (C-153) in mixed micelles of non-ionic surfactant, Triton X-100 and a series of cationic gemini surfactants, 12-s-12, 2Br with varying polymethylene spacer chain length (s = 3, 6, 8, 12) at different bulk mole fractions of a surfactant were studied. Studies were carried out by means of UV-Vis absorption, steady-state fluorescence and fluorescence anisotropy, time-resolved fluorescence and fluorescence anisotropy, and dynamic light scattering measurements. While micropolarity of the environment around C-153 in mixed micelles increased, the microviscosity decreased with increasing amount of a gemini surfactant. This is because the thickness of the Stern layer of micelles increases as a result of greater extent of penetration of water molecules. Solvation dynamics and rotational relaxation of C-153 become faster with increasing mole fraction of a gemini surfactant in the mixed micelles. Increasing the thickness of the Stern layer leads to an increase in the number of water molecules hydrogen bonded among themselves, resulting in an increase in polarity and microfluidity of the environment. At a given bulk mole fraction of a surfactant, the microviscosity of micelles decreases with increasing the spacer chain length of the gemini surfactant resulting in an increase in the rate of the rotational relaxation process. However, at a given bulk mole fraction of a surfactant, solvation dynamics becomes slower with increasing spacer chain length from s = 3 to 8 because of the increasing degree of counter ion dissociation. The slow rotational relaxation process is mainly due to the lateral diffusion of C-153 along the surface of the micelles. Rotationalmotion of the micelle as a whole is much slower than the lateral diffusion of C-153.

Rotational relaxation processes in free-standing thin SmC films

A theoretical description of the process of reorientation of the c-director and the tangential component of the velocity vector in a hybrid-oriented SmC film stretched between the rotating inner and rest outer frames has been proposed. Within the framework of the nonlinear generalization of the classical Ericksen–Leslie theory for the case of smectic phases, it has been shown that the magnitude and character of the reorientation of the c-director field and the formation of hydrodynamic flows in SmC films are strongly affected by the curvature and direction of rotation of the inner frame.