Phonons in colloidal systems

Architecture Controls Phonon Propagation in All-Solid Brush Colloid Metamaterials

Brillouin light scattering and elastodynamic theory are concurrently used to determine and interpret the hypersonic phonon dispersion relations in brush particle solids as a function of the grafting density with perspectives in optomechanics, heat management, and materials metrology. In the limit of sparse grafting density, the phonon dispersion relations bear similarity to polymer-embedded colloidal assembly structures in which phonon dispersion can be rationalized on the basis of perfect boundary conditions, i.e., isotropic stiffness transitions across the particle interface. In contrast, for dense brush assemblies, more complex dispersion characteristics are observed that imply anisotropic stiffness transition across the particle/polymer interface. This provides direct experimental validation of phonon propagation changes associated with chain conformational transitions in dense particle brush materials. A scaling relation between interface tangential stiffness and crowding of polymer tethers is derived that provides a guideline for chemists to design brush particle materials with tailored phononic dispersion characteristics. The results emphasize the role of interfaces in composite materials systems. Given the fundamental relevance of phonon dispersion to material properties such as thermal transport or mechanical properties, it is also envisioned that the results will spur the development of novel functional hybrid materials.

Origin of the Acoustic Bandgaps in Hypersonic Colloidal Phononics: The Role of the Elastic Impedance

How phonons propagate in nanostructures determines the flow of elastic and thermal energy in dielectric materials. However, a reliable theoretical prediction of the phonon dispersion relation requires experimental verification both near to and far from the Brillouin zone of the nanostructure. We report on the experimental hypersonic phonon dispersion of hard (SiO2) and soft (polymer) fcc colloidal crystals infiltrated in liquid polydimethylsiloxane with different elastic impedance contrast using Brillouin light spectroscopy. We discuss the distinct differences with first-principles full elastodynamic calculations involving a multiple-scattering theory. Interparticle contacts strongly impact the long-wavelength speed of sound and the nature of the particle vibration resonance-induced hybridization hypersonic bandgap. The absence of the order-induced Bragg bandgap in SiO2 and its presence in soft opals cannot be fully accounted for by the theory, limiting its predictive power. Bridging the elasticity of the two colloidal crystals with suitable SiO2 core-shell (polymer) particles reveals an unprecedented crossover behavior in the dispersion relation. In view of many conversational parameters, the control tuning of phonon propagation in soft matter-based hypersonic phononics remains challenging.

The Stability of a Hydrodynamic Bravais Lattice

We present the results of a theoretical investigation of the stability and collective vibrations of a two-dimensional hydrodynamic lattice comprised of millimetric droplets bouncing on the surface of a vibrating liquid bath. We derive the linearized equations of motion describing the dynamics of a generic Bravais lattice, as encompasses all possible tilings of parallelograms in an infinite plane-filling array. Focusing on square and triangular lattice geometries, we demonstrate that for relatively low driving accelerations of the bath, only a subset of inter-drop spacings exist for which stable lattices may be achieved. The range of stable spacings is prescribed by the structure of the underlying wavefield. As the driving acceleration is increased progressively, the initially stationary lattices destabilize into coherent oscillatory motion. Our analysis yields both the instability threshold and the wavevector and polarization of the most unstable vibrational mode. The non-Markovian nature of the droplet dynamics renders the stability analysis of the hydrodynamic lattice more rich and subtle than that of its solid state counterpart.

The damping of terahertz acoustic modes in aqueous nanoparticle suspensions

In this work, we investigate the possibility of controlling the acoustic damping in a liquid when nanoparticles are suspended in it. To shed light on this topic, we performed Inelastic X-Ray Scattering (IXS) measurements of the terahertz collective dynamics of aqueous suspensions of nanospheres of various materials, size, and relative concentration, either charged or neutral. A Bayesian analysis of measured spectra indicates that the damping of the two acoustic modes of water increases upon nanoparticle immersion. This effect seems particularly pronounced for the longitudinal acoustic mode, which, whenever visible at all, rapidly damps off when increasing the exchanged wavevector. Results also indicate that the observed effect strongly depends on the material the immersed nanoparticles are made of.

Onset of interfacial waves in the terahertz spectrum of a nanoparticle suspension

We used inelastic x-ray scattering to gain insight into the complex terahertz dynamics of a diluted Au-nanoparticle suspension in glycerol. We observe that, albeit sparse, Au nanoparticles leave clear signatures on the dynamic response of the system, the main one being an additional mode propagating at the nanoparticle-glycerol interface. A Bayesian inferential analysis of the line shape reveals that such a mode, at variance with conventional acoustic modes, keeps a hydrodynamiclike behavior well beyond the continuous limit and down to subnanometer distances.

Direct Three-Dimensional Measurement of Refractive Index via Dual Photon-Phonon Scattering

We developed a microscopy technique that can measure the local refractive index without sampling the optical phase delay of the electromagnetic radiation. To do this, we designed and experimentally demonstrated a setup with two colocalized Brillouin scattering interactions that couple to a common acoustic phonon axis; in this scenario, the ratio of Brillouin frequency shifts depends on the refractive index, but not on any other mechanical and/or optical properties of the sample. Integrating the spectral measurement within a confocal microscope, the refractive index is mapped at micron-scale three-dimensional resolution. As the refractive index is probed in epidetection and without assumptions on the geometrical dimensions of the sample, this method may prove useful to characterize biological cells and tissues.

Ultrathin Shell Layers Dramatically Influence Polymer Nanoparticle Surface Mobility

Advances in nanoparticle synthesis, self-assembly, and surface coating or patterning have enabled a diverse array of applications ranging from photonic and phononic crystal fabrication to drug delivery vehicles. One of the key obstacles restricting its potential is structural and thermal stability. The presence of a glass transition can facilitate deformation within nanoparticles, thus resulting in a significant alteration in structure and performance. Recently, we detected a glassy-state transition within individual polystyrene nanoparticles and related its origin to the presence of a surface layer with enhanced dynamics compared to the bulk. The presence of this mobile layer could have a dramatic impact on the thermal stability of polymer nanoparticles. Here, we demonstrate how the addition of a shell layer, as thin as a single polymer chain, atop the nanoparticles could completely eliminate any evidence of enhanced mobility at the surface of polystyrene nanoparticles. The ultrathin polymer shell layers were placed atop the nanoparticles via two approaches: (i) covalent bonding or (ii) electrostatic interactions. The temperature dependence of the particle vibrational spectrum, as recorded by Brillouin light scattering, was used to probe the surface mobility of nanoparticles with and without a shell layer. Beyond suppression of the surface mobility, the presence of the ultrathin polymer shell layers impacted the nanoparticle glass transition temperature and shear modulus, albeit to a lesser extent. The implication of this work is that the core-shell architecture allows for tailoring of the nanoparticle elasticity, surface softening, and glass transition temperature.

Single-crystal Brillouin spectroscopy with CO2 laser heating and variable q

We describe a Brillouin spectroscopy system integrated with CO2 laser-heating and Raman spectroscopic capabilities. Temperature is determined by measurements of the grey-body thermal radiation emitted by the hot sample, with the system response calibrated relative to a standard tungsten ribbon lamp. High-pressure laser-heating Brillouin scattering measurements of acoustic velocities on liquid water and ice compressed in a diamond-anvil cell were performed at temperatures up to 2500 ± 150 K at high pressure. Single-crystal laser-heating Brillouin measurements were made on the (111) plane of San Carlos olivine at ∼13 GPa, 1300 ± 200 K. The pressure as measured by ruby fluorescence is shown to be within ±0.5 GPa of the pressure on the olivine sample during laser heating when KCl and KBr are used as pressure-transmitting media. In addition, the system is designed for continuously variable scattering angles from forward scattering (near 0° scattering angle) up to near back scattering (∼141°). This novel setup allows us to probe a wide range of wave vectors q for investigation of phonon dispersion on, for example, crystals with large unit cells (on the scale of hundreds of nm).

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.

Tunable dynamic response of magnetic gels: impact of structural properties and magnetic fields

Ferrogels and magnetic elastomers feature mechanical properties that can be reversibly tuned from outside through magnetic fields. Here we concentrate on the question of how their dynamic response can be adjusted. The influence of three factors on the dynamic behavior is demonstrated using appropriate minimal models: first, the orientational memory imprinted into one class of the materials during their synthesis; second, the structural arrangement of the magnetic particles in the materials; and third, the strength of an external magnetic field. To illustrate the latter point, structural data are extracted from a real experimental sample and analyzed. Understanding how internal structural properties and external influences impact the dominant dynamical properties helps to design materials that optimize the requested behavior.

Micro-/nanostructured mechanical metamaterials

Mechanical properties of materials have long been one of the most fundamental and studied areas of materials science for a myriad of applications. Recently, mechanical metamaterials have been shown to possess extraordinary effective properties, such as negative dynamic modulus and/or density, phononic bandgaps, superior thermoelectric properties, and high specific energy absorption. To obtain such materials on appropriate length scales to enable novel mechanical devices, it is often necessary to effectively design and fabricate micro-/nano- structured materials. In this Review, various aspects of the micro-/nano-structured materials as mechanical metamaterials, potential tools for their multidimensional fabrication, and selected methods for their structural and performance characterization are described, as well as some prospects for the future developments in this exciting and emerging field.

Tuning and switching the hypersonic phononic properties of elastic impedance contrast nanocomposites

Anodic aluminum oxide (AAO) containing arrays of aligned cylindrical nanopores infiltrated with polymers is a well-defined model system for the study of hypersound propagation in polymer nanocomposites. Hypersonic phononic properties of AAO/polymer nanocomposites such as phonon localization and anisotropic sound propagation can be tailored by adjusting elastic contrast and density contrast between the components. Changes in density and elastic properties of the component located in the nanopores induced by phase transitions allow reversible modification of the phononic band structure and mode switching. As example in case, the crystallization and melting of poly(vinylidene difluoride) inside AAO was investigated.

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.

Damping by Bulk and Shear Viscosity of Confined Acoustic Phonons for Nanostructures in Aqueous Solution

A nanoparticle in aqueous solution is modeled as a homogeneous elastic isotropic continuum sphere in contact with an infinite viscous compressible Newtonian fluid. The frequencies and damping of the confined vibrational modes of the sphere are calculated for the material parameters of a CdSe nanoparticle in water and a poly(methyl methacrylate) nanosphere in water. Although the effects of viscosity are found to be negligible for macroscopic objects, for nanoscale objects, both the frequency and damping of the vibrational modes are significantly affected by the viscosity of the liquid. Furthermore, both shear viscosity and bulk viscosity play an important role. A model of the spherical satellite tobacco mosaic virus consisting of outer solid layers with a water core is also investigated, and the viscosity of the water core is found to significantly damp the free vibrational modes. The same approach can be applied for nonspherical geometries and also to viscoelastic nanoparticles.

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.

Observation and tuning of hypersonic bandgaps in colloidal crystals

Composite materials with periodic variations of density and/or sound velocities, so-called phononic crystals, can exhibit bandgaps where propagation of acoustic waves is forbidden. Phononic crystals are the elastic analogue of the well-established photonic crystals and show potential for manipulating the flow of elastic energy. So far, the experimental realization of phononic crystals has been restricted to macroscopic systems with sonic or ultrasonic bandgaps in the sub-MHz frequency range. In this work, using high-resolution Brillouin spectroscopy we report the first observation of a hypersonic bandgap in face-centred-cubic colloidal crystals formed by self-assembly of polystyrene nanoparticles with subsequent fluid infiltration. Depending on the particle size and the sound velocity in the infiltrated fluid, the frequency and the width of the gap can be tuned. Promising technological applications of hypersonic crystals, ranging from tunable filters and heat management to acousto-optical devices, are anticipated.

Orientation dynamics in isotropic phases of model oligofluorenes: Glass or liquid crystal

Orientation molecular dynamics were investigated in a series of "defect-free" oligofluorenes by depolarized dynamic light scattering and dynamic NMR spectroscopy. Typical liquid crystalline pretransitional dynamics were observed upon cooling the isotropic phase to the liquid crystalline phase with strong increase of the scattered intensity and slowing down of the characteristic time of the probed collective relaxation. This is well accounted for by the Landau-de Gennes theory, however, with a strong temperature dependence of the viscosity coefficient, reflecting the proximity of the glass transition. For the trimer the two transitions almost overlap and the molecular orientation coincide with the alpha-relaxation associated with the glass transition. The NMR measurements confirm that the time scale of the dynamics is completely governed by the glass process, yet the geometry of the motion is anisotropic, yielding order parameters ranging from 0.15 to 0.25 for the long axis in the liquid crystalline phase. The glass transition is therefore geometrically restricted with poorly ordered mesophase which is consistent with the weak transverse phonons in the light scattering experiment down to Tg+20 K.

Surface-functionalized nanoparticles with liquid-like behavior: the role of the constituent components

Ionically modified silica nanoparticles with large counter anions (sulfonate, isostearate) at two silica volume fractions (13 and 27%) form a viscous fluid and a glass but not crystalline solids. Dielectric spectroscopy, Brillouin scattering and shear rheometry were employed to investigate these new nanoparticle-based fluids. The glass transition temperature and hence the local dynamics are governed by the large counter anions, whereas the flow properties can be controlled by the spatial correlation between the nanoparticles, e.g. by tuning the volume fraction of hard cores and local interactions between segments in the soft corona. Liquid-like ordering of the cores was revealed by X-ray scattering and found to influence significantly the macroscopic flow properties of these salts.

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.

Hypersonic phononic crystals

In this Letter we propose the use of hypersonic phononic crystals to control the emission and propagation of high frequency phonons. We report the fabrication of high quality, single crystalline hypersonic crystals using interference lithography and show that direct measurement of their phononic band structure is possible with Brillouin light scattering. Numerical calculations are employed to explain the nature of the observed propagation modes. This work lays the foundation for experimental studies of hypersonic crystals and, more generally, phonon-dependent processes in nanostructures.

Structure and dynamics of polymer-grafted clay suspensions

The structure and dynamics of polymer-grafted two-dimensional silicate layers in solution were investigated. The geometry of the individual silicate layers was examined by looking at both polarized and depolarized light scattering from dilute solutions, while higher-concentration systems were used to study the interaction and dynamics of polymer-grafted silicate layers in suspension. The form factor for an oblate ellipsoid was used to fit the polarized intensity profile, and values of a approximately 80 nm and b approximately 380 nm for the semi-axes were obtained. The 80 nm value compares reasonably with the dimensions of the polymer brushes grafted on the surface of the silicate layers. The modulus of the grafted silicate in solution, as determined by Brillouin scattering, is of the order of 10 GPa. The cooperative diffusion mechanism, typical of interacting polymer chains, is suppressed due to the high polymer osmotic pressure. The osmotic pressure is also responsible for the weak interpenetration of the densely grafted polymer chains on the surface of the silicate layers. The scattering data indicates that the polymer-grafted nanoparticles move via collective diffusion and experience significant decrease in mobility above their overlap concentration.

High frequency acoustic excitations in ordered diblock copolymer studied by inelastic x-ray scattering

The phonon propagation in lamellar nanostructures formed via self-assembling of short styrene-b-isoprene (SI) as well as of its more incompatible styrene-b-(ethylene-alt-propylene) (SEP) counterpart was studied by inelastic x-ray scattering. Irrespective of the physical state of the block copolymers, a single acoustic phonon was observed in SI (ordered and disordered) and SEP (ordered). At GHz frequencies, inelastic light scattering from the same samples revealed very small dispersion in the sound phase velocity but a short phonon lifetime.

Harmonic lattice behavior of two-dimensional colloidal crystals

Using positional data from videomicroscopy and applying the equipartition theorem for harmonic Hamiltonians, we determine the wave-vector-dependent normal mode spring constants of a two-dimensional colloidal model crystal and compare the measured band structure to predictions of the harmonic lattice theory. We find good agreement for both the transversal and the longitudinal modes. For q-->0, the measured spring constants are consistent with the elastic moduli of the crystal.

Phonons in suspensions of hard sphere colloids: Volume fraction dependence

The propagation of sound waves in suspensions of hard sphere colloids is studied as a function of their volume fraction up to random close packing using Brillouin light scattering. The rich experimental phonon spectra of up to five phonon modes are successfully described by theoretical calculations based on the multiple scattering method. Two main types of phonon modes are revealed: Type A modes are acoustic excitations which set up deformations in both the solid (particles) and the liquid (solvent) phases; for type B modes the stress and strain are predominantly localized near the interface between the solid particles and the surrounding liquid (interface waves). While the former become harder (increase their effective sound velocity) as the particle volume fraction increases the latter become softer (the corresponding sound velocity decreases).