Rotational Relaxation Research Articles

Energy‐corrected sudden modeling of the non‐Markovian rotational relaxation matrix for high‐pressure Raman spectra of pure nitrogen

AbstractThe general expression derived previously (A.P. Kouzov, J.V. Buldyreva, A.V. Sokolov, J. Chem. Phys. 149, 044305 (2018)) for the frequency‐dependent rotational relaxation matrix describing collisions of linear molecules is put into an energy‐corrected‐sudden (ECS) form convenient for spectra modeling. The translational interaction spectral functions characterizing the intracollisional dynamics and determining the relaxation matrix elements are factorized into a frequency‐dependent and an anisotropy ranks‐dependent parts. The particular case of isotropic Raman Q‐branch enables to establish connections of these parts with the adiabaticity factor accounting for the molecular rotation during the collision and the bimolecular relaxation rates, respectively. Analyses of these rates allow suggesting their realistic exponential‐polynomial model representations with a few adjustable parameters determined from fits on experimentally available line widths. Thanks to the universal character of the non‐Markovian approach, the same parameters enable realistic computations of anisotropic Raman spectra up to very far spectral wings and without any additional parameter with respect to the Markovian ECS.

Computer Simulations of Dynamic Response of Ferrofluids on an Alternating Magnetic Field with High Amplitude

The response of ferrofluids to a high-amplitude AC magnetic field is important for several applications including magnetic hyperthermia and biodetection. In computer simulations of the dynamic susceptibility of a ferrofluid outside the linear response region, there are several problems associated with the fact that an increase in the frequency of the AC field leads to the appearance of additional computational errors, which can even lead to unphysical results. In this article, we study the dependence of the computational error arising in the computer simulation of the dynamic susceptibility on the input parameters of the numerical algorithm: the length of the time step, the total number of computer simulation periods, and averaging period. Computer simulation is carried out using the Langevin dynamics method and takes Brownian rotational relaxation of magnetic particles and interparticle interactions into account. The reference theory [Yoshida T.; Enpuku K. Jap. J. Ap. Phys. 2009] is used to estimate computational error. As a result, we give practical recommendations for choosing the optimal input parameters of the numerical algorithm, which make it possible to obtain reliable results of the dynamic susceptibility of a ferrofluid in a high-amplitude AC field in a wide frequency range.

Theoretical modelling of a rotating mirror Q switched CW CO laser

Theoretical model for a rotating mirror Q switched CW CO laser is presented. It considers 36 vibration levels including the ground level of CO molecule. Lasing on 20 rotational lines in 18 vibration bands is considered. The lasing on these lines takes place between the rotational sublevels associated with each vibration level. Hence one is required to develop the rate equations for the 36 vibration levels, 397 rotational sublevels and also the equations for the photon densities associated with the360 lasing lines. These equations include the varying loss experienced by the lasing mode as it traverses the gain medium due to rotation of the mirror. The discharge has a thermal gradient. To take this into account we divide the gain medium into two zones, a central one matching with the laser mode and the rest of the discharge zone as the second zone. The two zones are assigned two temperatures as per the calculated average temperatures in these two zones. The calculations of how the above variables vary with time are carried out with the help of a fourth order Runge Kutta routine in the two zones separately. For each time step the model also calculates the intersection areas of the laser mode with the two zones. The actual power profiles of all the individual lasing lines are obtained by combining their powers in these two zones and the corresponding intersection areas. An important application of this laser in additional frequency generation in nonlinear crystals, require time synchronisation among interacting pulses. Our results show that in each vibration band about 12 to –13 lines operate, but only 3 to –4 among them are strong and are well synchronised in time. Their growth is determined by cascade lasing, higher gain coefficient compared to their neighbours and preference of their growth due to rotational relaxation. The results at operation of the rotating mirror at100 Hz, shows that about 222 lines operate and about 65 lines shows this synchronisation property. The results have been validated with experimental data available in the literature.

Pressure Effects on the Relaxation of an Excited Ethane Molecule in High-Pressure Bath Gases.

We use molecular dynamics to calculate the rotational and vibrational energy relaxation of C2H6 in Ar, Kr, and Xe bath gases over a pressure range of 10-400 atm and at temperatures of 300 and 800 K. The C2H6 is instantaneously excited by 80 kcal/mol randomly distributed into both vibrational and rotational modes. The computed relaxation rates show little sensitivity to the identity of the noble gas in the bath. Vibrational relaxation rates show a nonlinear pressure dependence at 300 K. At 800 K the reduced range of bath gas densities covered by the range of pressures does not yet show any nonlinearity in the pressure dependence. Rotational relaxation is characterized with two relaxation rates. The slower rate is comparable to the vibrational relaxation rate. The faster rate has a linear pressure dependence at 300 K but an irregular, nonlinear pressure dependence at 800 K. To understand this, a model was developed based on approximating the periodic box used in the molecular dynamics simulations by an equal-volume collection of cubes where each cube is sized to allow only single occupancy by the noble gas or the molecule. Combinatorial statistics then leads to a pressure- and temperature-dependent analytic distribution of the bath gas species the molecule encounters in a collision. This distribution, the dissociation energy of molecule/bath gas complexes and bath gas clusters, and the computed energy release per collision combine to show that only at 300 K is the energy release sufficient to dissociate likely complexes and clusters. This suggests that persistent and pressure-dependent clusters and complexes at 800 K may be responsible for the nonlinear pressure dependence of rotational relaxation.

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.

Structure and dynamics of liquid linear and cyclic alkanes: A molecular dynamics study

Small linear alkanes, pentane and hexane, and their cyclic counterparts, cyclopentane and cyclohexane, have been examined via molecular dynamics simulations. We assess the thermodynamic, structural and dynamic behavior of said liquids, paying particular attention to dynamic properties such as diffusion coefficients, vibrational spectra, rotational correlation functions and relaxation times. The study gives an insight into the overall behavior of small alkanes, accentuating the nuances imposed by the difference in molecular shape. This is particularly relevant when considering the widespread use of these liquids as solvents.

The protein hydration layer in high glucose concentration: Dynamical responses in folded and intrinsically disordered dimeric states

This exposition reveals the effect of glucose as a molecular crowder on the solvent environment in proximity of the protein surface in putative folded (Ubiquitin) and intrinsically disordered (dimeric Amyloid beta) states. Atomistic simulations reveal markedly higher structural perturbation in the disordered systems due to crowding effects, while the folded state retains overall structural fidelity. Key hydrophobic contacts in the disordered dimer are lost. However, glucose induced crowding results in elevated hydration on surfaces of both protein systems. Despite evident differences in their structural responses, the hydration layer of both the folded and disordered states display a distinct enhancement in lifetimes of mean residence and rotational relaxation under the hyperglycemic conditions. The results are crucial in the light of emergent co-solvent induced biological phenomena in crowded media.

Nonlinear response of a dilute ferrofluid to an alternating magnetic field

The response of dilute monodisperse ferrofluid to alternating magnetic field is studied theoretically. Brownian rotational relaxation of magnetic nanoparticles is taken into account. Susceptibilities of magnetization harmonics are calculated in a wide range of field amplitudes and frequencies via three common approaches: the Fokker-Planck equation for the one-particle orientation distribution function, the Martsenyuk-Raikher-Shliomis effective field method and the Langevin dynamics simulation which is based on direct numerical integration of particles’ stochastic equations of motion. A comparison of these approaches revealed that all of them are able to describe accurately the behavior of the fundamental magnetization harmonic in a broad range of field parameters. But in the case of high-order harmonics, shortcomings of Langevin dynamics and the effective field method manifest themselves. Due to strong random fluctuations of the system magnetization, Langevin dynamics fails to produce reliable results in the weak-field limit, i.e. when the characteristic magnetic energy scale is lower than the system thermal energy. The Martsenyuk-Raikher-Shliomis equation gives a large systematic error for high-order harmonics if the field period is comparable with (or smaller than) the Brownian relaxation time.

Photodynamics of biological active flavin in the presence of zwitterionic surfactants

In the flavin family of photoactive biomolecules, lumichrome (LM) is a very important compound. It contains a tri-cyclic structure with methyl groups at two sides. It formed by the partial decomposition and biodegradation of riboflavin in both acidic as well as in neutral medium. Herein, we have studied the photophysical properties of LM in the presence of two zwitterionic surfactants, namely dodecyldimethyl(3-sulfopropyl) ammonium hydroxide inner salt (DSB), and tetradecyldimethyl(3-sulfopropyl) ammonium hydroxide inner salt (TSB), having the same head group but a different tail part. We have used steady-state absorption, fluorescence emission, and time-resolved fluorescence emission measurements. We observed that in the presence of zwitterionic surfactant aggregates LM shows excitation and emission wavelength dependent emission properties, which demonstrate the structural changes that take place from one form to another prototropic form of LM molecule. The higher rotational relaxation time of LM in the case of DSB compared to TSB demonstrated that LM is facing more rigid environment in DSB micelles compared to TSB micelles.

Anisotropic diffusion of membrane proteins at experimental timescales.

Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT trajectories can reveal deviations from ideal Brownian behavior. Among others, this includes confinement effects and anomalous diffusion, which are manifestations of both the nanoscale structure of the underlying membrane and the structure of the diffuser. With the rapid increase in temporal and spatial resolution of experimental methods, a new aspect of the motion of the particle, namely, anisotropic diffusion, might become relevant. This aspect that so far received only little attention is the anisotropy of the diffusive motion and may soon provide an additional proxy to the structure and topology of biomembranes. Unfortunately, the theoretical framework for detecting and interpreting anisotropy effects is currently scattered and incomplete. Here, we provide a computational method to evaluate the degree of anisotropy directly from molecular dynamics simulations and also point out a way to compare the obtained results with those available from SPT experiments. In order to probe the effects of anisotropic diffusion, we performed coarse-grained molecular dynamics simulations of peripheral and integral membrane proteins in flat and curved bilayers. In agreement with the theoretical basis, our computational results indicate that anisotropy can persist up to the rotational relaxation time [τ=(2Dr)-1], after which isotropic diffusion is observed. Moreover, the underlying topology of the membrane bilayer can couple with the geometry of the particle, thus extending the spatiotemporal domain over which this type of motion can be detected.

An insight into the dissolution of cellulose in 1-butyl-3-methylimidazolium chloride-DMSO binary Mixture: Exploring the dynamics of rhodamine 6G and fluorescein

The change in the interaction of solute and the ionic liquid-DMSO mixture with the extent of dissolution of cellulose is investigated through fluorescence spectroscopic studies. This study aims to provide an insight into the dissolution of cellulose in ionic liquid-DMSO mixtures in terms of photophysical aspects. Although the rheology and viscoelastic properties of ionic liquid-DMSO-cellulose mixtures are well studied in the early literature, there is a lack of photophysical investigation. For this reason, we have taken two oppositely charged but structurally similar solutes, fluorescein sodium salt (Fl-Na) and rhodamine 6G (R6G), to investigate their rotational and translational dynamics in the mixture. Analysis of the time-resolved fluorescence anisotropy data using the Stokes-Einstein-Debye (SED) theory suggests that the rotational relaxation times of the solutes follow near stick hydrodynamics in absence of cellulose. The solutes experienced a strong interaction in pure DMSO and with the increasing concentration of BmimCl, the specific interaction between the solvent and the solute decreases as indicated in decreasing Cobs values. While in presence of cellulose, the solutes follow near slip hydrodynamics in low BmimCl concentration but at higher concentration, the specific interaction increases. From the temperature-dependent anisotropy, we have observed that both R6G and Fl-Na follows the super-stick trend, and with increasing temperature specific interaction between the solute and solvent increases. On the other hand, in presence of cellulose, their rotational reorientation times appear close to the slip boundary condition at low temperature, and with increasing temperature, it approaches close to the stick boundary. Fluorescence Correlation Spectroscopy (FCS) indicates the presence of structural heterogeneity in the BmimCl-DMSO mixture formed due to the segregation of the hydrophobic chain of the ionic liquid. Therefore, the experimental results of this work suggest that the dissolution of cellulose modulates the dynamics of the solutes in ionic liquid–DMSO mixtures.

Hydration of a small protein under carbon nanotube confinement: Adsorbed substates induce selective separation of the dynamical response

The co-involvement of biological molecules and nanomaterials has increasingly come to the fore in modern-day applications. While the "bio-nano" (BN) interface presents physico-chemical characteristics that are manifestly different from those observed in isotropic bulk conditions, the underlying molecular reasons remain little understood; this is especially true of anomalies in interfacial hydration. In this paper, we leverage atomistic simulations to study differential adsorption characteristics of a small protein on the inner (concave) surface of a single-walled carbon nanotube whose diameter exceeds dimensions conducive to single-file water movement. Our findings indicate that the extent of adsorption is decided by the degree of foldedness of the protein conformational substate. Importantly, we find that partially folded substates, but not the natively folded one, induce reorganization of the protein hydration layer into an inner layer water closer to the nanotube axis and an outer layer water in the interstitial space near the nanotube walls. Further analyses reveal sharp dynamical differences between water molecules in the two layers as observed in the onset of increased heterogeneity in rotational relaxation and the enhanced deviation from Fickian behavior. The vibrational density of states reveals that the dynamical distinctions are correlated with differences in crucial bands in the power spectra. The current results set the stage for further systematic studies of various BN interfaces vis-à-vis control of hydration properties.

Temperature-dependent rotationally inelastic collisions of OH− and He

We have studied the fundamental rotational relaxation and excitation collision of OH- J=0 <-> 1 with helium at different collision energies. Using state-selected photodetachment in a cryogenic ion trap, the collisional excitation of the first excited rotational state of OH- has been investigated and absolute inelastic collision rate coefficients have been extracted for collision temperatures between 20 and 35 K. The rates are compared with accurate quantum scattering calculations for three different potential energy surfaces. Good agreement is found within the experimental accuracy, but the experimental trend of increasing collision rates with temperature is only in part reflected in the calculations.

Visualization of Acoustic Energy Absorption in Confined Aqueous Solutions by PNIPAM Microgels: Effects of Bulk Viscosity.

Ultrasound propagation in liquids is highly influenced by its attenuation due to viscous damping. The dissipated energy will be partially absorbed by the liquid due to its dynamic viscosity as well as its bulk viscosity. The former results in the generation of a flow that is called acoustic streaming, and the latter is associated with the vibrational and rotational relaxation of liquid molecules. Measuring the ultrasonic wave attenuation due to the bulk viscosity is presented as a novel method in this article. Poly(N-isopropylacrylamide) (PNIPAM) microgels, which are soluble in several solvents such as water, were used as acousto-responsive markers in water, which upon absorption of ultrasonic energy undergo a volume phase transition due to the breakage of their hydrogen bonds. Thus, they become insoluble in water, and due to shrinking, their optical density increases. As a result, their agglomeration can be seen as a turbid medium. We managed to visualize the ultrasonic energy absorption due to the bulk viscosity using the turbidity since the excess acoustic energy on top of the absorbed energy for the translational motion of liquid is spent to break the hydrogen bonds between PNIPAM and water. In addition, to quantify the turbidity phenomenon, the total energy required for breaking hydrogen bonds in the solution is calculated, and its evolution, according to the input power intensity, is quantified by image processing. The effect of viscosity by changing the microgel concentration was investigated, and it is shown that an increasing microgel concentration increases the acoustic energy absorption rate much greater than its dynamic viscosity. Therefore, the bulk viscosity, as the responsible parameter for this increase, is measured directly from the energy of broken hydrogen bonds. The results show that at low solution concentration (0.2 wt %) the bulk viscosity is in the same order of magnitude as its dynamic viscosity. Increasing the concentrations to 1 and 5 wt % increases the bulk viscosity and consequently the structural relaxation time by 1 and 2 orders of magnitude, respectively.

Ab initio simulation of hypersonic flows past a cylinder based on accurate potential energy surfaces

For the first time in the literature, we present 2D simulations of hypersonic flows around a cylinder obtained from accurate ab initio potential energy surfaces (PESs). We compare results obtained from a low fidelity (empirical) and a high fidelity (ab initio) PES, thus demonstrating the impact of PES accuracy on the entire aerothermodynamic field around the body. We observe that the empirical PES is not adequate to accurately reproduce rotational and vibrational relaxation in the hypersonic flow, both in the compression and expansion regions of the flow field. This approach, enabled by advancements in large-scale computing, paves the way to the direct simulation of hypersonic flows where the only modeling input is the PES that describes molecular interactions between the various air constituents. Such flow field simulations provide benchmark solutions for the validation of reduced-order models.

Rotational Dynamics of Water at the Phospholipid Bilayer Depending on the Head Groups Studied by Molecular Dynamics Simulations

Hydration states are a crucial factor that affect the self-assembly and properties of soft materials and biomolecules. Although previous experiments have revealed that the hydration state strongly depends on the chemical structure of lipid molecules, the mechanisms at the molecular level remain unknown. Classical and density-functional tight-binding (DFTB) molecular dynamics (MD) simulations are employed to determine the mechanisms underlying dissimilar water dynamics between lipid membranes with phosphatidylcholine (PC) and phosphatidylethanolamine (PE) head groups. The classical MD simulation shows that rotational relaxations of water are faster on the PE lipid than on the PC lipid, which is consistent with a previous experimental study using terahertz spectroscopy. Furthermore, DFTB-MD simulation of N(CH3)4+ and NH4+ ions, which correspond to the different head groups in PC and PE, respectively, shows qualitative agreement with the classical MD simulation. Remarkably, the PE lipids and the NH4+ ions break hydrogen bonds between water molecules in the secondary hydration shell. In contrast, the PC lipids and the N(CH3)4+ ions bind water molecules weakly in both the primary and secondary hydration shells and increase hydrogen bonds between water. Our atomistic simulations show that these changes in the hydrogen-bond network of water molecules cause the different rotational relaxation of water molecules between the two lipids.

A close coupling study of the bending relaxation of H2O by collision with He.

We present a close coupling study of the bending relaxation of H2O by collision with He, taking explicitly into account the bending-rotation coupling within the rigid-bender close-coupling method. A 4D potential energy surface is developed based on a large grid of ab initio points calculated at the coupled-cluster single double triple level of theory. The bound states energies of the He-H2O complex are computed and found to be in excellent agreement with previous theoretical calculations. The dynamics results also compare very well with the rigid-rotor results available in the Basecol database and with experimental data for both rotational transitions and bending relaxation. The bending-rotation coupling is also demonstrated to be very efficient in increasing bending relaxation when the rotational excitation of H2O increases.

Plane wave propagation in dual-phase-lag generalized thermoelastic transversely isotropic structure with rotation effect

The aim of this work is to investigate the influence of rotation and dual-phase-lag (DPL) theory of generalized thermoelasticity on the reflection of plane waves in a transversely isotropic thermoelastic half-space. It is supposed that the elastic half-space rotates with steady angular velocity. Since the basic equations were solved in a two-dimensional space, so three types of quasi-plane waves are found based on the three of velocities of plane waves. The amplitude ratios and their coefficients of these diverse plane waves according to a suitable boundary conditions are obtained analytically. The impact of incident angle, rotation and thermal relaxation times of DPL theory are computed numerically for a specific material and represented graphically.

Prediction of shock standoff distance with modified rotational relaxation time of air mixture

The rotational relaxation time of an air mixture is modified as an approach to improve accuracy when predicting hypersonic shock standoff distance. A novel atomistic quasi-classical trajectory (QCT) method with a modified approach is devised to drastically reduce computational cost, and rigorously model the rotational relaxation time of N2 in N2–N and N2–N2 collisions. The calculated full sets of rotational state-to-state transition rates obtained by the QCT method are fed into the rotational state-resolved master equations to determine the rotational relaxation time of N2. Clear discrepancies are observed when the present rotational relaxation time is compared with existing empirical data for N2. The existing empirical model is utilized to determine the rotational relaxation time of other atmospheric gas species. Then the present set of rotational relaxation times for the air mixture is employed to predict the hypersonic shock standoff distance over a blunt body of the ground and flight experiments. Compared with the results from the two-temperature model, the rotational nonequilibrium enlarges the hypersonic shock standoff distance. This increase in shock standoff distance by the rotational nonequilibrium is attributed to the delay in chemical reactions inside the shock layers. The accuracy of the predicted measured shock standoff distance is improved by considering the present rotational relaxation time of the air mixture.

Improvement and determination of higher-order centrifugal distortion constants of the [formula omitted] electronic transition of NO

The highly rotationally excited states in the A2Σ+-X2ΠΩ band of NO were investigated by laser-induced fluorescence and multi-photon ionization spectroscopy. The rotational states with J up to 80.5 were prepared by CH3ONO photodissociation in the S1 and S2 excited states for spectroscopic measurements. In total, 3890 lines of nine vibronic bands were analyzed. The observed line positions deviated from the values calculated using the previous molecular constants as J increased in the J > 50.5 region. The sextet-order centrifugal distortion constants were determined for the A2Σ+and X2ΠΩ states so that the transition frequencies associated with the high-J states could reproduce the observed results within the experimental accuracy. The band origin values, whose errors have been discussed in previous studies, were refined in the present analysis. The experimental condition to suppress the rotational relaxation of the high-J states was examined, enabling us to determine the higher-order centrifugal distortion constants.