Brillouin study of the quantization of acoustic modes in nanospheres

Excitation and detection of acoustic phonons in nanoscale systems

Phonons play a key role in the physical properties of materials, and have long been a topic of study in physics. While the effects of phonons had historically been considered to be a hindrance, modern research has shown that phonons can be exploited due to their ability to couple to other excitations and consequently affect the thermal, dielectric, and electronic properties of solid state systems, greatly motivating the engineering of phononic structures. Advances in nanofabrication have allowed for structuring and phonon confinement even down to the nanoscale, drastically changing material properties. Despite developments in fabricating such nanoscale devices, the proper manipulation and characterization of phonons continues to be challenging. However, a fundamental understanding of these processes could enable the realization of key applications in diverse fields such as topological phononics, information technologies, sensing, and quantum electrodynamics, especially when integrated with existing electronic and photonic devices. Here, we highlight seven of the available methods for the excitation and detection of acoustic phonons and vibrations in solid materials, as well as advantages, disadvantages, and additional considerations related to their application. We then provide perspectives towards open challenges in nanophononics and how the additional understanding granted by these techniques could serve to enable the next generation of phononic technological applications.

Quantization of Acoustic Modes in Dumbbell Nanoparticles

The vibrational eigenmodes of dumbbell-shaped polystyrene nanoparticles are recorded by Brillouin light spectroscopy (BLS), and the full experimental spectra are calculated theoretically. Different from spheres with a degeneracy of (2l+1), with l being the angular momentum quantum number, the eigenmodes of dumbbells are either singly or doubly degenerate owing to their axial symmetry. The BLS spectrum reveals a new, low-frequency peak, which is attributed to the out-of-phase vibration of the two lobes of the dumbbell. The quantization of acoustic modes in these molecule-shaped dumbbell particles evolves from the primary colloidal spheres as the separation between the two lobes increases.

Influence of Surfactant-Mediated Interparticle Contacts on the Mechanical Stability of Supraparticles

Colloidal supraparticles are micron-scale spherical assemblies of uniform primary particles, which exhibit emergent properties of a colloidal crystal, yet exist as a dispersible powder. A prerequisite to utilize these emergent functionalities is that the supraparticles maintain their mechanical integrity upon the mechanical impacts that are likely to occur during processing. Understanding how the internal structure relates to the resultant mechanical properties of a supraparticle is therefore of general interest. Here, we take the example of supraparticles templated from water/fluorinated oil emulsions in droplet-based microfluidics and explore the effect of surfactants on their mechanical properties. Stable emulsions can be generated by nonionic block copolymers consisting of a hydrophilic and fluorophilic block and anionic fluorosurfactants widely available under the brand name Krytox. The supraparticles formed in the presence of both types of surfactants appear structurally similar, but differ greatly in their mechanical properties. While the nonionic surfactant induces superior mechanical stability and ductile fracture behavior, the anionic Krytox surfactant leads to weak supraparticles with brittle fracture. We complement this macroscopic picture with Brillouin light spectroscopy that is very sensitive to the interparticle contacts for subnanometer-thick adsorbed layers atop of the nanoparticle. While the anionic Krytox does not significantly affect the interparticle bonds, the amphiphilic nonionic surfactant drastically strengthens these bonds to the point that individual particle vibrations are not resolved in the experimental spectrum. Our results demonstrate that seemingly subtle changes in the physicochemical properties of supraparticles can drastically impact the resultant mechanical properties.

Phononic and photonic properties of shape-engineered silicon nanoscale pillar arrays

We report the results of Brillouin-Mandelstam spectroscopy and Mueller matrix spectroscopic ellipsometry of the nanoscale 'pillar with the hat' periodic silicon structures, revealing intriguing phononic and photonic-phoxonic-properties. It has been theoretically shown that periodic structures with properly tuned dimensions can act simultaneously as phononic and photonic crystals, strongly affecting the light-matter interactions. Acoustic phonon states can be tuned by external boundaries, either as a result of phonon confinement effects in individual nanostructures, or as a result of artificially induced external periodicity, as in the phononic crystals. The shape of the nanoscale pillar array was engineered to ensure the interplay of both effects. The Brillouin-Mandelstam spectroscopy data indicated strong flattening of the acoustic phonon dispersion in the frequency range from 2 GHz to 20 GHz and the phonon wave vector extending to the higher-order Brillouin zones. The specifics of the phonon dispersion dependence on the pillar arrays' orientation suggest the presence of both periodic modulation and spatial localization effects for the acoustic phonons. The ellipsometry data reveal a distinct scatter pattern of four-fold symmetry due to nanoscale periodicity of the pillar arrays. Our results confirm the dual functionality of the nanostructured shape-engineered structure and indicate a possible new direction for fine-tuning the light-matter interaction in the next generation of photonic, optoelectronic, and phononic devices.

Simultaneous Existence of Confined and Delocalized Vibrational Modes in Colloidal Quantum Dots

Coupling to phonon modes is a primary mechanism of excitonic dephasing and energy loss in semiconductors. However, low-energy phonons in colloidal quantum dots and their coupling to excitons are poorly understood because their experimental signatures are weak and usually obscured by the unavoidable inhomogeneous broadening of colloidal dot ensembles. We use multidimensional coherent spectroscopy at cryogenic temperatures to extract the homogeneous nonlinear optical response of excitons in a CdSe/CdZnS core/shell colloidal quantum dot ensemble. A comparison to the simulation provides evidence that the observed lineshapes arise from the coexistence of confined and delocalized vibrational modes, both of which couple strongly to excitons in CdSe/CdZnS colloidal quantum dots.

Brillouin Light Scattering: Development of a Near Century-Old Technique for Characterizing the Mechanical Properties of Materials

Brillouin light scattering (BLS), a technique theoretically described nearly a century back by the French physicist Léon Brillouin in 1922, is a light-scattering method for determining the mechanical properties of materials. This inelastic scattering method is described by the Bragg diffraction of light from a propagating fluctuation in the local dielectric. These fluctuations arise spontaneously from thermally populated sound waves intrinsic to all materials, and thus BLS may be broadly applied to transparent samples of any phase. This review begins with a brief historical overview of the development of BLS, from its theoretical prediction to the current state of the art, and notes specific technological advancements that enabled the development of BLS. Despite the broad utility of BLS, no commercial spectrometer is currently available for purchase, but rather individual components are assembled to suit a specific application. Central to any BLS spectrometer is the interferometer, and its performance characteristics-scanning or non-scanning, multi-passing, and stabilization-are critical considerations for spectrometer design. Consistent with any light-scattering method, the frequency shift is a key observable in BLS, and we summarize the connection of this measurement to evaluate the mechanical properties of materials. With emphasis toward pharmaceutical materials analysis, we introduce the traditional BLS approach for single-crystal elasticity, and this is followed by a discussion of more recent developments in powder BLS. We conclude our review with a perspective on future developments in BLS that may enable BLS as a novel addition to the current catalog of process analytical technologies.

Characterization of microresonator-geometry-deformation for cavity optomechanics

We have studied the effect of geometry deformation on the mechanical frequencies and quality factors for different modes in the Whispering Gallery Mode (WGM) microresonators, that is unavoidable in the practical fabrication. The subsidence of the sphere and a more general condition with fewer symmetries and complex deformation of eccentricity, subsidence, and offset are first modeled in this paper, which could tune the mechanical frequency in a much wider spectral range than the pillar-diameter-induced perturbation. we also show that the mechanical quality factors for the non-whispering-gallery mechanical mode could be increased in the order of 4 magnitudes at a specific subsidence, and form a mechanical bound state in the continuum (BIC) which is induced by the symmetry breaking and reveals new mechanisms to confine radiation. A much broader BIC window width with higher mechanical quality factor could be achieved, which is of great importance in both fundamental research and scientific applications.

Direct observation of polymer surface mobility via nanoparticle vibrations

Measuring polymer surface dynamics remains a formidable challenge of critical importance to applications ranging from pressure-sensitive adhesives to nanopatterning, where interfacial mobility is key to performance. Here, we introduce a methodology of Brillouin light spectroscopy to reveal polymer surface mobility via nanoparticle vibrations. By measuring the temperature-dependent vibrational modes of polystyrene nanoparticles, we identify the glass-transition temperature and calculate the elastic modulus of individual nanoparticles as a function of particle size and chemistry. Evidence of surface mobility is inferred from the first observation of a softening temperature, where the temperature dependence of the fundamental vibrational frequency of the nanoparticles reverses slope below the glass-transition temperature. Beyond the fundamental vibrational modes given by the shape and elasticity of the nanoparticles, another mode, termed the interaction-induced mode, was found to be related to the active particle-particle adhesion and dependent on the thermal behavior of nanoparticles.

Mechanisms of resonant low frequency Raman scattering from metallic nanoparticle Lamb modes

The low frequency Raman scattering from gold nanoparticle bimodal assemblies with controlled size distributions has been studied. Special care has been paid to determining the size dependence of the Raman intensity corresponding to the quadrupolar Lamb mode. Existing models based on a microscopic description of the scattering mechanism in small particles (bond polarizability, dipole induced dipole models) predict, for any Raman-active Lamb modes, an inelastic intensity scaling as the volume of the nanoparticle. Surprisingly experimental intensity ratios are found to be anomalously much greater than theoretical ones, calling into question this scaling law. To explain these discrepancies, a simple mechanism of Raman scattering, based on the density fluctuations in the nanoparticles induced by the Lamb modes, is introduced. This modeling, in which the nanoparticle is described as an elastic isotropic continuous medium-as in Lamb theory, successfully explains the major features exhibited by low frequency Raman modes. Moreover this model provides a unified picture for any material, suitable for handling both small and large size ranges, as well as non-resonant and resonant excitation conditions in the case of metallic species.

Thermomechanical Properties and Glass Dynamics of Polymer-Tethered Colloidal Particles and Films

Polymer-tethered colloidal particles (aka "particle brush materials") have attracted interest as a platform for innovative material technologies and as a model system to elucidate glass formation in complex structured media. In this contribution, Brillouin light scattering is used to sequentially evaluate the role of brush architecture on the dynamical properties of brush particles in both the individual and assembled (film) state. In the former state, the analysis reveals that brush-brush interactions as well as global chain relaxation sensitively depend on grafting density; i.e., more polymer-like behavior is observed in sparse brush systems. This is interpreted to be a consequence of more extensive chain entanglement. In contrast, the local relaxation of films does not depend on grafting density. The results highlight that relaxation processes in particle brush-based materials span a wider range of time and length scales as compared to linear chain polymers. Differentiation between relaxation on local and global scale is necessary to reveal the influence of molecular structure and connectivity on the aging behavior of these complex systems.

Core and surface microgel mechanics are differentially sensitive to alternative crosslinking concentrations

Microgel mechanics are central to the swelling of stimuli-responsive materials and furthermore have recently emerged as a novel design space for tuning the uptake of nanotherapeutics. Despite this importance, the techniques available to assess mechanics, at the sub-micron scale, remain limited. In this report, all mechanical moduli for a series of air-dried, polystyrene-co-poly(N-isopropylacrylamide) (pS-co-NIPAM) microgels of varying composition in monomer and crosslinker (N,N'-methylene-bisacrylamide (BIS)) mol% have been determined using Brillouin light scattering (BLS) and AFM nanoindentation. These techniques sample the material through distinct means and provide complementary nanomechanical data. An initial demonstration of this combined approach is used to evaluate size-dependent nanomechanics in pS particles of varying diameter. For the pS-co-NIPAM series, our BLS results demonstrate an increase in Young's (E) and shear moduli with increasing NIPAM and/or BIS mol%, while the Poisson's ratio decreased. The same rank order in E was observed from AFM and the two techniques correlate well. However, at low BIS crosslinking, an inverted particle structure persists and small increases in BIS yield a higher increase in E from AFM relative to BLS, consistent with a higher density at the particle surface. At higher BIS incorporation, the microgel reverts to a typical, dense-core structure and further increasing BIS yields changes to core-particle mechanics reflected in BLS. Lastly, at 75 mol% NIPAM, the microgels displayed a broad volume phase transition and increased crosslinking resulted in a minor, yet unexpected, increase in swelling ratio. This complementary approach offers new insight into nanomechanics critical for microgel design and application.

Optical-Based Analysis of Soft Tissue Structures

Fibrous structures are an integral and dynamic feature of soft biological tissues that are directly related to the tissues' condition and function. A greater understanding of mechanical tissue behavior can be gained through quantitative analyses of structure alone, as well as its integration into computational models of soft tissue function. Histology and other nonoptical techniques have traditionally dominated the field of tissue imaging, but they are limited by their invasiveness, inability to provide resolution on the micrometer scale, and dynamic information. Recent advances in optical modalities can provide higher resolution, less invasive imaging capabilities, and more quantitative measurements. Here we describe contemporary optical imaging techniques with respect to their suitability in the imaging of tissue structure, with a focus on characterization and implementation into subsequent modeling efforts. We outline the applications and limitations of each modality and discuss the overall shortcomings and future directions for optical imaging of soft tissue structure.

Mechanical Coupling in Gold Nanoparticles Supermolecules Revealed by Plasmon-Enhanced Ultralow Frequency Raman Spectroscopy

Acoustic vibrations of assemblies of gold nanoparticles were investigated using ultralow frequency micro-Raman scattering and finite element simulations. When exciting the assemblies resonantly with the surface plasmon resonance of electromagnetically coupled nanoparticles, Raman spectra present an ultralow frequency band whose frequency lies below the lowest Raman active Lamb mode of single nanoparticles that was observed. This feature was ascribed to a Raman vibration mode of gold nanoparticle "supermolecules", that is, nanoparticles mechanically coupled by surrounding polymer molecules. Its measured frequency is inversely proportional to the nanoparticle diameter and sensitive to the elastic properties of the interstitial polymer. The latter dependence as well as finite element simulations suggest that this mode corresponds to the out-of-phase semirigid translation (l = 1 Lamb mode) of each nanoparticle of a dimer inside the matrix, activated by the mechanical coupling between the nanoparticles. These observations were permitted only thanks to the resonant excitation with the coupling plasmon excitation, leading to an enhancement up to 10(4) of the scattering by these vibrations. This enhanced ultralow frequency Raman scattering thus opens a new route to probe the local elastic properties of the surrounding medium.

Time-domain investigation of the acoustic vibrations of metal nanoparticles: size and encapsulation effects

The acoustic vibrations of single-metal and multi-material nanoparticles are studied by ultrafast pump-probe optical spectroscopy and described in the context of the continuous elastic model. The applicability of this model to the small size range, down to one nanometer, is discussed in the light of recent experimental data and ab initio calculations. Investigations of multi-material nano-objects stress the impact of the intra-particle interface on the characteristics of their vibrational modes, also yielding information on the composition and spatial distribution of the constituting materials.

Anisotropic hypersonic phonon propagation in films of aligned ellipsoids

A material with anisotropic elastic mechanical properties and a direction-dependent hypersonic band gap is fabricated using ac electric field-directed convective self-assembly of colloidal ellipsoids. The frequency of the gap, which is detected in the direction perpendicular to particle alignment and entirely absent parallel to alignment, and the effective sound velocities can be tuned by the particle aspect ratio. We hypothesize that the band gap originates from the primary eigenmode peak, the m-splitted (s,1,2) mode, of the particle resonating with the effective medium. These results reveal the potential for powerful control of the hypersonic phononic band diagram by combining anisotropic particles and self-assembly.

Role of Polymer Graft Architecture on the Acoustic Eigenmode Formation in Densely Polymer-Tethered Colloidal Particles

The concurrent evaluation of the vibration eigenfrequencies in densely polymer-tethered particle systems ("particle brushes") by Brillouin light scattering and elastodynamic theory reveals a distinctive change of acoustic eigenmode formation associated with polymer graft modification of colloidal particles. The eigenfrequencies of particle brushes reveal a characteristic red-shift compared to uniform core-shell particles that can only be rationalized by assuming imperfect boundary conditions and anisotropic elastic properties of the graft layer. The distinct characteristics of vibration modes in particle brush materials provide direct evidence for the implications of chain confinement on the nanomechanical properties of tethered chains. The results highlight a rich and hitherto unexplored parameter-space for controlling properties and interactions in particle-brush based systems that could spur the development of hybrid materials with novel functionalities.

Brillouin cavity optomechanics with microfluidic devices

Cavity optomechanics allows the parametric coupling of phonon- and photon-modes in microresonators and is presently investigated in a broad variety of solid-state systems. Optomechanics with superfluids has been proposed as a path towards ultra-low optical- and mechanical-dissipation. However, there have been no optomechanics experiments reported with non-solid phases of matter. Direct liquid immersion of optomechanics experiments is challenging, as the acoustic energy simply leaks out to the higher-impedance liquid surrounding the device. Here we confine liquids within hollow resonators to circumvent this issue and to enable optical excitation of mechanical whispering-gallery modes at frequencies ranging from 2 to 11,000 MHz. Our device enables optomechanical investigation with liquids, while light is conventionally coupled from the outer dry side of the capillary, and liquids are provided by means of a standard microfluidic inlet.

A high resolution ultraviolet Brillouin scattering set-up

We report on a high resolution inelastic UV scattering table-top setup conceived for Brillouin measurements. The system is based on a tandem 1+1 pass scanning Fabry-Perot interferometer of Sandercock type. Special optics were used in order to adapt such an interferometric device, nowadays only used at visible or IR wavelength, to the UV range. The advantages with respect to other UV Brillouin scattering instruments are the larger resolving power and the improved contrast in the low frequency spectral region. To corroborate these features we provide a comparison between data obtained using the described system and those from existing UV Brillouin scattering instruments.

Collective hypersonic excitations in strongly multiple scattering colloids

Unprecedented low-dispersion high-frequency acoustic excitations are observed in dense suspensions of elastically hard colloids. The experimental phononic band structure for SiO(2) particles with different sizes and volume fractions is well represented by rigorous full-elastodynamic multiple-scattering calculations. The slow phonons, which do not relate to particle resonances, are localized in the surrounding liquid medium and stem from coherent multiple scattering that becomes strong in the close-packing regime. Such rich phonon-matter interactions in nanostructures, being still unexplored, can open new opportunities in phononics.

Hypersonic vibrations of Ag@SiO2 (cubic core)-shell nanospheres

The intriguing optical and catalytic properties of metal-silica core-shell nanoparticles, inherited from their plasmonic metallic cores together with the rich surface chemistry and increased stability offered by their silica shells, have enabled a wide variety of applications. In this work, we investigate the confined vibrational modes of a series of monodisperse Ag@SiO(2) (cubic core)-shell nanospheres synthesized using a modified Stöber sol-gel method. The particle-size dependence of their mode frequencies has been mapped by Brillouin light scattering, a powerful tool for probing hypersonic vibrations. Unlike the larger particles, the observed spheroidal-like mode frequencies of the smaller ones do not scale with inverse diameter. Interestingly, the onset of the deviation from this linearity occurs at a smaller particle size for higher-energy modes than for lower-energy ones. Finite element simulations show that the mode displacement profiles of the Ag@SiO(2) core-shells closely resemble those of a homogeneous SiO(2) sphere. Simulations have also been performed to ascertain the effects that the core shape and the relative hardness of the core and shell materials have on the vibrations of the core-shell as a whole. As the vibrational modes of a particle have a bearing on its thermal and mechanical properties, the findings would be of value in designing core-shell nanostructures with customized thermal and mechanical characteristics.

The "music" of core-shell spheres and hollow capsules: influence of the architecture on the mechanical properties at the nanoscale

We report on the first measurement of elastic vibrational modes in core-shell spheres (silica-poly(methyl methacrylate), SiO2-PMMA) and corresponding spherical hollow capsules (PMMA) with different particle size and shell thickness using Brillouin light scattering, supported by numerical calculations. These localized modes allow access to the mechanical moduli down to a few tens of nanometers. We observe reduced mechanical strength of the porous silica core, and for the core-shell spheres a striking increase of the moduli in both the SiO2 core and the PMMA shell. The peculiar behavior of the vibrational modes in the hollow capsules is attributed to antagonistic dependence on overall size and layer thickness in agreement with theoretical predictions.

Simultaneous occurrence of structure-directed and particle-resonance-induced phononic gaps in colloidal films

We report on the observation of two hypersonic phononic gaps of different nature in three-dimensional colloidal films of nanospheres using Brillouin light scattering. One is a Bragg gap occurring at the edge of the first Brillouin zone along a high-symmetry crystal direction. The other is a hybridization gap in crystalline and amorphous films, originating from the interaction of the band of quadrupole particle eigenmodes with the acoustic effective-medium band, and its frequency position compares well with the computed lowest eigenfrequency. Structural disorder eliminates the Bragg gap, while the hybridization gap is robust.

Elastic properties of viruses

Viruses are compact biological nanoparticles whose elastic and dynamical properties are hardly known. Inelastic (Brillouin) light scattering was used to characterize these properties, from microcrystals of the Satellite Tobacco Mosaic Virus, a nearly spherical plant virus of 17-nm diameter. Longitudinal sound velocities in wet and dry Satellite Tobacco Mosaic Virus crystals were determined and compared to that of the well-known protein crystal, lysozyme. Localized vibrational modes of the viral particles (i.e., particle modes) were sought in the relevant frequency ranges, as derived assuming the viruses as full free nanospheres. Despite very favorable conditions, regarding virus concentration and expected low damping in dry microcrystals, no firm evidence of virus particle modes could be detected.

Hypersonic acoustic excitations in binary colloidal crystals: big versus small hard sphere control

The phononic band structure of two binary colloidal crystals, at hypersonic frequencies, is studied by means of Brillouin light scattering and analyzed in conjunction with corresponding dispersion diagrams of the single colloidal crystals of the constituent particles. Besides the acoustic band of the average medium, the authors' results show the existence of narrow bands originating from resonant multipole modes of the individual particles as well as Bragg-type modes due to the (short-range) periodicity. Strong interaction, leading to the occurrence of hybridization gaps, is observed between the acoustic band and the band of quadrupole modes of the particles that occupy the largest fractional volume of the mixed crystal; the effective radius is either that of the large (in the symmetric NaCl-type crystalline phase) or the small (in the asymmetric NaZn(13)-type crystalline phase) particles. The possibility to reveal a universal behavior of the phononic band structure for different single and binary colloidal crystalline suspensions, by representing in the dispersion diagrams reduced quantities using an appropriate length scale, is discussed.

Collective Dynamics of Lysozyme in Water: Terahertz Absorption Spectroscopy and Comparison with Theory

To directly measure the low-frequency vibrational modes of proteins in biologically relevant water environment rather than previously explored dry or slightly hydrated phase, we have developed a broadband terahertz spectrometer suitable for strongly attenuating protein solutions. Radiation is provided by harmonic multipliers (up to 0.21 THz), a Gunn oscillator (at 0.139 THz), and the UCSB free-electron lasers (up to 4.8 THz). Our spectrometer combines these intense sources with a sensitive cryogenic detector and a variable path length sample cell to detect radiation after it is attenuated by more than 7 orders of magnitudes by the aqueous sample. Using this spectrometer, we have measured the molar extinction of solvated lysozyme between 0.075 and 3.72 THz (2.5-124 cm(-1)), and we made direct comparison to several published theoretical models based on molecular dynamics simulations and normal-mode analysis. We confirm the existence of dense, overlapping normal modes in the terahertz frequency range. Our observed spectrum, while in rough qualitative agreement with these models, differs in detail. Further, we observe a low-frequency cutoff in terahertz dynamics between 0.2 and 0.3 THz, and we see no evidence of a predicted normal mode at approximately 0.09 THz for the protein.

The spectrum of vibration modes in soft opals

Numerous vibrational modes of spherical submicrometer particles in fabricated soft opals are experimentally detected by Brillouin light scattering and theoretically identified by their spherical harmonics by means of single-phonon scattering-cross-section calculations. The particle size polydispersity is reflected in the line shape of the low-frequency modes, whereas lattice vibrations are probably responsible for the observed overdamped transverse mode.

Mechanical strength of amorphous CaCO3 colloidal spheres

Amorphous glassy CaCO3 colloidal spheres of monomodal size distribution were studied by high-resolution Brillouin light scattering. The Young modulus of 37 GPa and shear modulus of 14 GPa of glassy CaCO3 at a density of 1.9 g/cm3 were extracted from the particle vibration frequencies by employing acoustic wave scattering cross-section calculations. The line shape of the low-frequency modes is a sensitive index of the particle polydispersity.

Comment on "Estimate of the vibrational frequencies of spherical virus particles"

This Comment corrects some errors which appeared in the calculation of an elastic sphere eigenenergies. As a result, the symmetry of the mode having the lowest frequency is changed. Also a direction for calculating the damping of these modes for embedded elastic spheres is given.