A systematic study of Rayleigh-Brillouin scattering in air, N2 and O2 gases

Spontaneous Rayleigh-Brillouin scattering experiments in air, N2 and O2 have been performed for a wide range of temperatures and pressures at a wavelength of 403 nm and at a 90 degrees scattering angle. Measurements of the Rayleigh-Brillouin spectral scattering profile were conducted at high signal-to-noise ratio for all three species, yielding high-quality spectra unambiguously showing the small differences between scattering in air, and its constituents N2 and O2. Comparison of the experimental spectra with calculations using the Tenti S6 model, developed in 1970s based on linearized kinetic equations for molecular gases, demonstrates that this model is valid to high accuracy. After previous measurements performed at 366 nm, the Tenti S6 model is here verified for a second wavelength of 403 nm. Values for the bulk viscosity for the gases are derived by optimizing the model to the measurements. It is verified that the bulk viscosity parameters obtained from previous experiments at 366 nm, are valid for wavelengths of 403 nm. Also for air, which is treated as a single-component gas with effective gas transport coefficients, the Tenti S6 treatment is validated for 403 nm as for the previously used wavelength of 366 nm, yielding an accurate model description of the scattering profiles for a range of temperatures and pressures, including those of relevance for atmospheric studies. It is concluded that the Tenti S6 model, further verified in the present study, is applicable to LIDAR applications for exploring the wind velocity and the temperature profile distributions of the Earth's atmosphere. Based on the present findings, predictions can be made on the spectral profiles for a typical LIDAR backscatter geometry, which deviate by some 7 percent from purely Gaussian profiles at realistic sub-atmospheric pressures occurring at 3-5 km altitude in the Earth's atmosphere

Rayleigh-Brillouin light scattering spectroscopy of nitrous oxide (N2_2O)

High signal-to-noise and high-resolution light scattering spectra are measured for nitrous oxide (N$_2$O) gas at an incident wavelength of 403.00 nm, at 90$^\circ$ scattering, at room temperature and at gas pressures in the range $0.5-4$ bar. The resulting Rayleigh-Brillouin light scattering spectra are compared to a number of models describing in an approximate manner the collisional dynamics and energy transfer in this gaseous medium of this polyatomic molecular species. The Tenti-S6 model, based on macroscopic gas transport coefficients, reproduces the scattering profiles in the entire pressure range at less than 2\% deviation at a similar level as does the alternative kinetic Grad's 6-moment model, which is based on the internal collisional relaxation as a decisive parameter. A hydrodynamic model fails to reproduce experimental spectra for the low pressures of 0.5-1 bar, but yields very good agreement ($< 1$\%) in the pressure range $2-4$ bar. While these three models have a different physical basis the internal molecular relaxation derived can for all three be described in terms of a bulk viscosity of $\eta_b \sim (6 \pm 2) \times 10^{-5}$ Pa$\cdot$s. A 'rough-sphere' model, previously shown to be effective to describe light scattering in SF$_6$ gas, is not found to be suitable, likely in view of the non-sphericity and asymmetry of the N-N-O structured linear polyatomic molecule

Extraction of the translational Eucken factor from light scattering by molecular gas

Although the thermal conductivity of molecular gases can be measured straightforwardly and accurately, it is difficult to experimentally determine its separate contributions from the translational and internal motions of gas molecules. Yet, this information is critical in rarefied gas dynamics as the rarefaction effects corresponding to these motions are different. In this paper, we propose a novel methodology to extract the translational thermal conductivity (or equivalently, the translational Eucken factor) of molecular gases from the Rayleigh–Brillouin scattering (RBS) experimental data. From the numerical simulation of the Wu et al. (J. Fluid Mech., vol. 763, 2015, pp. 24–50) model we find that, in the kinetic regime, in addition to bulk viscosity, the RBS spectrum is sensitive to the translational Eucken factor, even when the total thermal conductivity is fixed. Thus it is not only possible to extract the bulk viscosity, but also the translational Eucken factor of molecular gases from RBS light scattering spectra measurements. Such experiments bear the additional advantage that gas–surface interactions do not affect the measurements. By using the Wu et al. model, bulk viscosities (due to the rotational relaxation of gas molecules only) and translational Eucken factors of N2 , CO2 and SF6 are simultaneously extracted from RBS experiments

H-Theorem and Boundary Conditions for Two-Temperature Model: Application to Wave Propagation and Heat Transfer in Polyatomic Gases

Polyatomic gases find numerous applications across various scientific and technological fields, necessitating a quantitative understanding of their behavior in non-equilibrium conditions. In this study, we investigate the behavior of rarefied polyatomic gases, particularly focusing on heat transfer and sound propagation phenomena. By utilizing a two-temperature model, we establish constitutive equations for internal and translational heat fluxes based on the second law of thermodynamics. A novel reduced two-temperature model is proposed, which accurately describes the system's behavior while reducing computational complexity. Additionally, we develop phenomenological boundary conditions adhering to the second law, enabling the simulation of gas-surface interactions. The phenomenological coefficients in the constitutive equations and boundary conditions are determined by comparison with relevant literature. Our computational analysis includes conductive heat transfer between parallel plates, examination of sound wave behavior, and exploration of spontaneous Rayleigh-Brillouin scattering. The results provide valuable insights into the dynamics of polyatomic gases, contributing to various technological applications involving heat transfer and sound propagation

Optical Microresonator-Based Flow-Speed Sensor

Optical sensors have become more prominent in atmospheric measurement systems, with LiDAR instruments deployed on a variety of earth-bound, air-borne, and space-based platforms. In recent years, the interest in the human exploration of Mars has created a substantial push towards reliable and compact sensing elements for Mars exploration missions, particularly during a spacecraft’s entry, descent, and landing stages. Real-time sensors able to reliably measure the craft’s speed relative to the surrounding atmosphere during these stages are thus of great interest. In this dissertation, a proof-of-concept for an optical microfabricated sensor, which leverages the whispering-gallery-mode (WGM) and Doppler shift principles, is developed to measure wind speed from atmospheric particles through light scattering. WGM micro-resonators could replace Fabry–Perot interferometers and other optical frequency discriminators often employed in remote sensing applications, thereby significantly reducing the size and weight of the measurement system. The capabilities of the presented sensor concept are first studied under the aerosol scattering regime, and the measurement resolution of the WGM resonators is assessed. An optical system is developed, and velocity measurements near the exit of a seeded air jet nozzle are carried out to validate the velocity measurement capabilities from aerosol streams. The feasibility of employing WGM resonators for molecular scattering-based measurements of atmospheric properties is also investigated. A modified mathematical model for coherent and spontaneous scattering is implemented in the performance analyses of the resonators for different altitudes of Earth and Mars atmospheres. Spectral profiles generated from the model are compared to those in the literature under similar conditions. An analysis for photon count under various atmospheric conditions and altitudes is also carried out. The analyses indicate that WGM resonator-based spectral instruments may be viable as part of future compact and lightweight atmospheric sensors

Effects of temperature and dissolved lithium perchlorate on the viscoelastic and dynamic properties of poly(ethylene oxide), (Peo) melts

Poly(ethylene oxide)/lithium perchlorate (PEO/LiClO4) complexes are widely studied as a prototype solid polymer electrolyte in rechargeable lithium-polymer batteries. Characterizing the structure and dynamics of the system in its molten state is important for understanding the role of the polymer environment in lithium ion transport and conductivity. A fiber-optic coupled Fabry-Perot interferometer is employed in the investigation of the electrolyte viscoelastic and dynamic properties, which are both related to the intrachain local mobility and therefore to ion diffusion. The properties of the system are studied as a function of composition, temperature, and frequency. Structural relaxation processes are observed both in the neat polymer melt and in the salt containing electrolytes. For the neat PEO-1K melt the relaxation is identified as Maxwell-Debye single-exponential relaxation (beta = 1). The relaxation time follows Arrhenius temperature dependence with activation energy of the order of 10-11 kJ/mol. Upon addition of salt, the character of the relaxation persists with beta = 1, while the characteristic relaxation time slows down and the activation energy increases slightly. The slowdown of the dynamics is more pronounced at lower temperatures. In addition, with increasing salt concentration the elastic modulus increases significantly making the system stiffer at all temperatures, while the maximum of the storage modulus is shifted to higher temperatures. These effects result in a decrease in polymer segmental mobility and consequently in reduction of lithium ion diffusivity, with increased salt concentration. A unique q-dependent measurement is performed, allowing the investigation of the Brillouin frequency and linewidth as a function of frequency. It revealed a double-step relaxation in the electrolyte. The two relaxations are identified as secondary relaxations with Maxwell-Debye character (beta=1). The lower-frequency relaxation is stronger and has Arrhenius temperature behavior of the relaxation time. It is attributed to conformal fluctuations of the chain segments between transient crosslinks formed by the EO-Li+ complexation in the melt. The higher-frequency relaxation is weaker, especially at higher temperatures and more difficult to resolve. It is possible it results from librational motions or conformal rearrangements of the uncomplexed polymer dihedrals and seems to be strongly affected by the specifics of the local chain conformation and the EO-Li+ complexation in the melt

The Multiscale Biomechanics and Mechanochemistry of the Extracellular Matrix Protein Fibres: Collagen & Elastin

Collagen is the most abundant protein in the animal kingdom and, together with elastin, forms extensive fibrous networks that constitute the primary structure of the mammalian extracellular matrix, respectively endowing it with the tensile and elastic properties that fulfil its principal role as the passive framework of the body. The fibrous proteins are distinctly hierarchically organised from the molecular scale upwards; for example, the nanoscale tropocollagen monomer assembles in arrays that form the micrometer scale microfibrils and fibrils, and thence into collections of millimetre scale collagen fibres, that in-turn, constitute functional tissues such as skin, tendon and bone. Much is known about the structure at each of these individual scales – collagen being the most extensively researched – and the macromechanics of the fibres are well established. However, far less is known about the micromechanics of these proteins, in particular how the monomers influence the functional mechanics of the macroscopic fibres. In this thesis, I explore the multiscale mechanics of collagen and elastin fibres over a range of hydrations – with fibres in direct contact with aqueous solution, and progressively dehydrated in humidity-controlled environments. I use quasi-static tensile testing to probe the macroscopic mechanical response (Young’s modulus and stress relaxation) of the fibres, and employ Brillouin and Raman microscopy to assess the longitudinal modulus in the GHz range and corresponding molecular properties of the proteins. Brillouin microscopy is an emerging technique in the biomedical field. It enables the all-optical, contact-free and non-destructive testing of tissue micromechanics through detection of frequency shifted light scattered off thermally excited acoustic waves or “phonons” in the GHz range. As one of the first studies of Brillouin light scattering in these fibres, it sets the basis for further investigation of tissue biomechanics. In particular, I provide the full description of the protein fibre micromechanics by performing angular measurements using a so-called platelet-like configuration with sample mounted onto a reflective substrate at 45° angle to the excitation beam. I derive the high-frequency longitudinal modulus, and discuss the results in comparison to the Young’s modulus, in terms of the different frequency and spatial scale of the measurements. I obtained a full description of elasticity using Brillouin spectroscopy applied to dried fibres; however, obtaining the same description in hydrated fibres is a challenge, as the Brillouin spectrum is dominated by water. An assessment of the mechanical differences between type-I and type-II collagens is also given here. Water is known to be a primary determinant of tissue biomechanics, and I identified for the first time, the critical hydration ranges between 100 and 85% relative humidity (RH) for collagen, and around 85% RH for elastin, at which point each macroscopic fibre switched from viscoelastic to plastic-like behaviour. Dehydration below these critical points was shown to severely diminish collagen fibrillar sliding, and completely rob elastin of its ability to reversibly deform under strain. The Young’s modulus increased markedly below these hydrations, and I observed a parallel increase in the longitudinal modulus at high frequencies in each protein, indicating a concomitant increase in stiffness at the two scales. The major difference observed between the two fibrous proteins is that, in the case of elastin, I observe a two-fold increase in the longitudinal modulus as the hydration is decreased from 100 to 21% RH, whilst the Young’s modulus increases by two orders of magnitude. This discrepancy was not observed in collagen, which confirmed that the protein maintained its long-range order in the form of the triple helix at all hydrations employed in this work, whilst the elastin ultrastructure experiences a liquid-to-solid state change at a critical hydration. I demonstrate through the analysis of the low-wavenumber region (<500 cm-1) of the Raman spectrum, that the increase in molecular stiffness of both proteins, is reflected in an increase in torsional rigidity of the peptide backbone upon dehydration. Moreover in collagen, I observe a reduction in the number of inter-protein water bridges, which I propose causes a collapse of the lateral spacing between monomers and an increase in direct backbone-backbone hydrogen bonding, that further stiffens the fibre. Small strain induced reorientations of the amide III and C–C stretching modes in dehydrated collagen fibres suggest that macroscopic stresses may be transferred to the triple helix, otherwise left unperturbed in the hydrated state. I postulate that this is a result of the degraded intra- and interfibrillar sliding mechanism below the critical hydration. Hence in its dehydrated state, the collagen whole-fibre mechanics are similar to those at the molecular scale. The role of proteoglycans and glycosaminoglycans and their potential connection to hydration, is also discussed. In agreement with previous work, I found no Raman spectral changes as a result of stretching hydrated elastin fibres, indicating that even large strains e.g. 80%, have no significant effect on the structural scale probed by Raman microscopy, nor in the air-dried state where the brittle fibres break at low strains. I suggest this may imply a limited sensitivity of Raman bands to these changes, possibly an indication of elastin’s dynamic ultrastructure, or that stress is dissipated at a higher level of the fibre structure. On the macroscopic scale, it is the poroelastic nature of elastin which controls the stress relaxation under strain, and the elastic recovery is mediated by an interplay of hydrophobic interactions and hydration forces

Spectroscopic Studies of Anomalous Hydrodynamic Behaviour in Complex Fluids

Brillouin spectroscopy probes the thermally generated pressure fluctuations (sound waves) which propagate in a material. The resulting information on sound velocity and absorption provides a fast and efficient method of monitoring high frequency (GHz) dynamics in the system being studied. In certain cases, structural information may also be inferred from changes in the Brillouin spectrum as a function of temperature, pressure or composition (in the case of multi-component systems). The aim of the work presented in this thesis was to integrate Brillouin spectroscopy into current soft condensed matter research projects at Edinburgh, namely (i) hydration in methanol-water mixtures and (ii) the behaviour of hard-sphere colloidal dispersions. A Brillouin spectrometer based on a Fabry-Perot interferometer was developed and tested, resulting in a high-resolution instrument operating at variable scattering vector (exchanged momentum), temperature and pressure. The technical aspects of this work were carried out in collaboration with a colleague. Data analysis routines were designed and implemented, enabling calibrated Brillouin spectra to be produced automatically from raw experimental data. Excellent agreement with results on several materials studied in the literature confirmed the accuracy and sensitivity of the spectrometer. The molecular details of hydration in methanol-water mixtures are of great interest due to the prototypical amphiphilic nature of the methanol molecule. The effect of deep cooling on the Brillouin spectrum across a wide range of methanol concentrations was studied in detail, resulting in the first observation of an anomalous increase in sound velocity and maximum in sound absorption at intermediate compositions. A similar effect was then found at higher temperature in aqueous tertiary butanol, and was identified in a brief survey of several other aqueous solutions. High pressure Brillouin spectra indicate that this anomalous behaviour may also be present in pure water. It is suggested that these novel effects may be due to the presence of a relatively unperturbed water structure in the aqueous solutions studied, even at quite high solute concentration. Preliminary results from a neutron diffraction experiment performed on a 40% by mass methanol-water mixture were consistent with this hypothesis. Brillouin spectroscopy was also used to study the propagation of high frequency sound in monodisperse colloidal suspensions of sub-micron hard spheres. A second longitudinal sound mode was observed for scattering vectors of magnitude greater than pi/d where d is the diameter of the spheres. These results are the first reproduction and extension of the pioneering work in the field, which identified the additional mode with a surface acoustic excitation, propagating between adjacent spheres via an evanescent wave in the solvent. The new results show that the second mode is extinguished at a particular scattering vector - an effect not reported previously. It is suggested that this extinction is due to the minimum in the form factor for elastic scattering from a single sphere

Two-point bend studies of glass fibers

The principal objective of this research is to advance our understanding of how glass breaks. Glass, a material well known for its brittleness, has been used widely but within a frustrating limit of its strength. Generally, strength is not considered as an intrinsic property of glass, due to the difficulty of avoiding the presence of flaws on the sample surface. The fiber drawing system and two-point bending (TPB) equipment developed at Missouri S&T allow the fabrication of pristine glass fibers and failure strain measurements while minimizing the effects of strength limiting critical flaws. Several conditions affect the failure behavior of glasses, including glass composition, thermal history of melts and environmental conditions during the failure tests. Understanding how these conditions affect failure helps us understand how glass fails. In this dissertation, failure strains for many different silicate and borate glasses were measured under a variety of experimental conditions. Failure stresses for various silicate glasses were calculated using values of the nonlinear elastic moduli reported in the literature. Inert intrinsic strengths for alkali silicate glasses were related to the structure and corresponding bond strengths, and the dependence of the inert strengths on faceplate velocity is discussed. Inert failure strains were also obtained for sodium borate glasses. Up to ~40% failure strain was measured for vitreous B₂O₃. The addition of soda to boron oxide increases the dimensionality and connectivity of the glass structure and hence increases its resistance to deformation, as was observed in elasticity and brittleness measurements reported in the literature. The increase in deformation resistance produces lower failure strains, a behavior also seen for alkali silicate and aluminosilicate glasses where the reduction of non-bridging oxygen increases the structure stiffness and leads to lower inert failure strain. Fatigue effects on silicate glasses were studied by measuring the failure strains in water at different temperatures and at different loading rates, and in air with a range of relative humidities. The dominant fatigue reaction for cross-linked network glasses is bond hydrolysis, whereas for alkali modified depolymerized glasses is ion-exchange reaction between alkali ions and water species. The fatigue mechanism difference results in the difference in the humidity sensitivity of the reaction rate. The dominant fatigue reaction also changes at around 50% relative humidity --Abstract, page iv