Diffuse-transmission spectroscopy: A structural probe of opaque colloidal mixtures

Transparent porous films with real refractive index close to unity for photonic applications

Herein, we demonstrate mechanically stable large-area thin films with a purely real refractive index (n) close to 1 in the optical range. At specific wavelengths, it can reach values as small as n = 1.02, the lowest reported for thin solid slabs. These are made of a random network of interwoven spherical silica shells, created by chemical vapour deposition of a thin layer of silica on the surface of randomly packed monodisperse polymer nanoparticles that form a film. Thermal processing of the composites results in highly porous silica-based transparent thin films. We demonstrate the potential of this approach by making novel photonic materials such as strong optical diffusers, built by integrating scattering centers within the ultralow n transparent films, or highly efficient light-emitting slabs, in which losses by total internal reflection are practically absent as a result of the almost null optical impedance at the film-air interface.

A Rule for Response Sensitivity of Structural-Color Photonic Colloids

To mimic natural photonic crystals having color regulation capacities dynamically responsive to the surrounding environment, periodic assembly structures have been widely constructed with response materials. Beyond monocomponent materials with stimulus responses, binary and multiphase systems generally offer extended color space and complex functionality. Constructing a rule for predicting response sensitivity can provide great benefits for the tailored design of intelligently responsive photonic materials. Here, we elucidate mathematical relationships between the response sensitivity of dynamically structural-color changes and the location distances of photonic co-phases in three-dimensional Hansen space that can empirically express the strength of their interaction forces, including dispersion force, polarity force, and hydrogen bonding. Such an empirical rule is proven to be applicable for some typical alcohols, acetone, and acetic acid regardless of their molecular structures, as verified by angle resolution spectroscopy, in situ infrared spectroscopy, and molecular simulation. The theoretical method we demonstrate provides rational access to custom-designed responsive structural coloration.

Mechanism of structural colors in binary mixtures of nanoparticle-based supraballs

Inspired by structural colors in avian species, various synthetic strategies have been developed to produce noniridescent, saturated colors using nanoparticle assemblies. Nanoparticle mixtures varying in particle chemistry and size have additional emergent properties that affect the color produced. For complex multicomponent systems, understanding the assembled structure and a robust optical modeling tool can empower scientists to identify structure-color relationships and fabricate designer materials with tailored color. Here, we demonstrate how we can reconstruct the assembled structure from small-angle scattering measurements using the computational reverse-engineering analysis for scattering experiments method and use the reconstructed structure in finite-difference time-domain calculations to predict color. We successfully, quantitatively predict experimentally observed color in mixtures containing strongly absorbing nanoparticles and demonstrate the influence of a single layer of segregated nanoparticles on color produced. The versatile computational approach that we present is useful for engineering synthetic materials with desired colors without laborious trial-and-error experiments.

Effect of scatterer interactions on photon transport in diffusing wave spectroscopy

We calculate the effect of particle size, concentration, and interactions on the photon transport mean-free path l^{*} that characterizes the multiple light scattering in diffusing wave spectroscopy (DWS). For scatterers of sufficient size, such that the first peak of the suspension structure factor S(q_{max}) remains in the range of accessible scattering vectors, neither repulsive nor attractive interactions between scatterers contribute strongly to l^{*}; its values are bounded by those for hard spheres and scatterers without interactions. However, for scatterers smaller than the wavelength of light, crowding induced by attraction or repulsion can lead to nonmonotonic behavior in l^{*} with increasing scatterer concentration. The effect is strongest for repulsive particles.

A microstructural investigation of an industrial attractive gel at pressure and temperature

Oil-continuous drilling fluids used in the oil and gas industry are formulated to be pseudoplastic with a relatively weak yield stress. These fluids are required to maintain their properties over wide temperature and pressure ranges yet there are few methods that can sensitively study the inherent structure and mechanical properties in the fluids under such conditions. Here we study a model oil-continuous drilling fluid formulation as a function of both temperature (up to 153 °C) and pressure (up to 1330 bar) with Diffusive Wave Spectroscopy (DWS). The system comprises a colloidal gel network of clay particles and trapped emulsion droplets. As a function of temperature the system undergoes local structural changes reflected in the DWS dynamics which are also consistent with macroscopic rheological measurements. On cycling to high pressure the system exhibits similar structural and dynamic changes with a strong hysteresis. Although multiple scattering in multicomponent non-ergodic samples does not directly yield self diffusion probe dynamics, the use of microrheology analysis here appears to be in good agreement with direct rheological measurements of the sample linear viscoelasticity at ambient pressure. Thus DWS microrheology succesfully probes irreversible changes in the structure and the mechanical response of the drilling fluid formulation under a high pressure cycle.

Spectral Properties of Foams and Emulsions

The optical and spectral properties of foams and emulsions provide information about their micro-/nanostructures, chemical and time stability and molecular data of their components. Foams and emulsions are collections of different kinds of bubbles or drops with particular properties. A summary of various surfactant and emulsifier types is performed here, as well as an overview of methods for producing foams and emulsions. Absorption, reflectance, and vibrational spectroscopy (Fourier Transform Infrared spectroscopy-FTIR, Raman spectroscopy) studies are detailed in connection with the spectral characterization techniques of colloidal systems. Diffusing Wave Spectroscopy (DWS) data for foams and emulsions are likewise introduced. The utility of spectroscopic approaches has grown as processing power and analysis capabilities have improved. In addition, lasers offer advantages due to the specific properties of the emitted beams which allow focusing on very small volumes and enable accurate, fast, and high spatial resolution sample characterization. Emulsions and foams provide exceptional sensitive bases for measuring low concentrations of molecules down to the level of traces using spectroscopy techniques, thus opening new horizons in microfluidics.

Investigating the trade-off between color saturation and angle-independence in photonic glasses

Photonic glasses-isotropic structures with short-range correlations-can produce structural colors with little angle-dependence, making them an alternative to dyes in applications such as cosmetics, coatings, and displays. However, the low angle-dependence is often accompanied by low color saturation. To investigate how the short-range correlations affect the trade-off between saturation and angle-independence, we vary the structure factor and use a Monte Carlo model of multiple scattering to investigate the resulting optical properties. We use structure factors derived from analytical models and calculated from simulations of disordered sphere packings. We show that the trade-off is controlled by the first peak of the structure factor. It is possible to break the trade-off by tuning the width of this peak and controlling the sample thickness. Practically, this result shows that the protocol used to pack particles into a photonic glass is important to the optical properties.

Light scattering from colloidal aggregates on a hierarchy of length scales

Disordered dielectrics with structural correlations on length scales comparable to visible light wavelengths exhibit interesting optical properties. Such materials exist in nature, leading to beautiful structural non-iridescent color, and they are also increasingly used as building blocks for optical materials and coatings. In this article, we explore the angular resolved single-scattering properties of micron-sized, disordered colloidal assemblies. The aggregates act as structurally colored supraparticles or as building blocks for macroscopic photonic glasses. We obtain first experimental data for the differential scattering and transport cross-section. Based on existing macroscopic models, we develop a theoretical framework to describe the scattering from densely packed colloidal assemblies on a hierarchy of length scales.

Effects of multiple scattering on angle-independent structural color in disordered colloidal materials

Disordered packings of colloidal spheres show angle-independent structural color when the particles are on the scale of the wavelength of visible light. Previous work has shown that the positions of the peaks in the reflectance spectra can be predicted accurately from a single-scattering model that accounts for the effective refractive index of the material. This agreement shows that the main color peak arises from short-range correlations between particles. However, the single-scattering model does not quantitatively reproduce the observed color: the main peak in the reflectance spectrum is much broader and the reflectance at low wavelengths is much larger than predicted by the model. We use a combination of experiment and theory to understand these features. We find that one significant contribution to the breadth of the main peak is light that is scattered, totally internally reflected from the boundary of the sample, and then scattered again. The high reflectance at low wavelengths also results from multiple scattering but can be traced to the increase in the scattering cross section of individual particles with decreasing wavelength. Both of these effects tend to reduce the saturation of the structural color, which limits the use of these materials in applications. We show that while the single-scattering model cannot reproduce the observed saturations, it can be used as a design tool to reduce the amount of multiple scattering and increase the color saturation of materials, even in the absence of absorbing components.

Characterizing randomness in photonic glasses using autocorrelation functions of two-dimensional images

We have developed a simple method to quantify randomness in photonic glasses in relation to the ideal random limit, using autocorrelation functions obtained from two-dimensional images. In our case, the photonic glasses consist of randomly packed silica microspheres which serve as a model system representing isotropic random media. Conventional methods of characterizing randomness in photonic materials often entail technical complexities, such as chemical functionalization, three-dimensional rendering, and particle tracking. Our method circumvents these difficulties based on a mathematical relation that we derive between the autocorrelation function and the radial distribution function. This relation enables us to find the autocorrelation function in the ideal random limit. The autocorrelation function of experimentally fabricated photonic glasses is then obtained from images of a single cross-sectional plane and directly compared to that of the ideal limit. The comparison shows that the autocorrelation function of real structures deviates only slightly from the ideal limit. We find that the deviation can be explained in part by the microsphere polydispersity. Our general method would be useful in characterizing a large class of photonic random media, encompassing biological materials, radiative cooling coatings, and random lasing photonic glasses.

White zein colloidal particles: synthesis and characterization of their optical properties on the single particle level and in concentrated suspensions

Growing interest in using natural, biodegradable ingredients for food products leads to an increase in research for alternative sources of functional ingredients. One alternative is zein, a water-insoluble protein from corn. Here, a method to investigate the optical properties of white zein colloidal particles is presented in both diluted and concentrated suspensions. The particles are synthesized, after purification of zein, by anti-solvent precipitation. Mean particle diameters ranged from 35 to 135 nm based on dynamic light scattering. The value of these particles as white colorant is examined by measuring their optical properties. Dilute suspensions are prepared to measure the extinction cross section of individual particles and this was combined with Mie theory to determine a refractive index (RI) of 1.49 ± 0.01 for zein particles dispersed in water. This value is used to further model the optical properties of concentrated suspensions. To obtain full opacity of the suspension, comparable to 0.1-0.2 wt% suspensions of TiO2, concentrations of 2 to 3.3 wt% of zein particles are sufficient. The optimal size for maximal scattering efficiency is explored by modeling dilute and concentrated samples with RI's matching those of zein and TiO2 particles in water. The transport mean free path of light was determined experimentally and theoretically and the agreement between the transport mean free path calculated from the model and the measured value is better than 30%. Such particles have the potential to be an all-natural edible alternative for TiO2 as white colorant in wet food products.

Core-shell colloidal particles with dynamically tunable scattering properties

We design polystyrene-poly(N'-isopropylacrylamide-co-acrylic acid) core-shell particles that exhibit dynamically tunable scattering. We show that under normal solvent conditions the shell is nearly index-matched to pure water, and the particle scattering is dominated by Rayleigh scattering from the core. As the temperature or salt concentration increases, both the scattering cross-section and the forward scattering increase, characteristic of Mie scatterers. The magnitude of the change in the scattering cross-section and scattering anisotropy can be controlled through the solvent conditions and the size of the core. Such particles may find use as optical switches or optical filters with tunable opacity.

Structural arrest and dynamic localization in biocolloidal gels

Casein micelles interacting via an entropic intermediate-ranged depletion attraction exhibit a fluid-to-gel transition due to arrested spinodal decomposition. The bicontinuous networked structure of the gel freezes shortly after formation. We determine the timescales of structural arrest from the build-up of network rigidity after pre-shear rejuvenation, and find that the arrest time as well as the plateau elastic modulus of the gel diverge as a function of the volume fraction and interaction potential. Moreover, we show using scaling from naïve mode coupling theory that their mechanical properties are dictated by their microscopic dynamics rather than their heterogeneous large scale structure.

Analysis of granular packing structure by scattering of THz radiation

Scattering methods are widely used to characterize the structure and constituents of matter on small length scales. This motivates this introductory text on identifying prospective approaches to scattering-based methods for granular media. A survey to light scattering by particles and particle ensembles is given. It is elaborated why the established scattering methods using X-rays and visible light cannot in general be transferred to granular media. Spectroscopic measurements using terahertz radiation are highlighted as they probe the scattering properties of granular media, which are sensitive to the packing structure. Experimental details to optimize a spectrometer for measurements on granular media are discussed. We perform transmission measurements on static and agitated granular media using Fourier transform spectroscopy at the THz beamline of the Bessy II storage ring. The measurements demonstrate the potential to evaluate degrees of order in the media and to track transient structural states in agitated bulk granular media.

Concentration-dependent correlated scattering properties of Intralipid 20% dilutions

Dilutions of Intralipid 20% are widely used as optical phantoms for mimicking scattering properties of turbid media such as tissues. One of the frequently used methodologies for quantifying the scattering coefficient and anisotropy of Intralipid 20% is the use of single-particle Mie scattering theory, which in fact is not valid for nontenuous media. Hence, two methodologies consisting of analytical wave theory and effective medium theory, incorporating particle size distribution and concentration-dependent correlated scattering phenomena, are used to estimate the effective scattering coefficient and anisotropy of Intralipid 20% dilutions (1%-100% v/v) from 380 to 1000 nm.

Absence of red structural color in photonic glasses, bird feathers, and certain beetles

Colloidal glasses, bird feathers, and beetle scales can all show structural colors arising from short-ranged spatial correlations between scattering centers. Unlike the structural colors arising from Bragg diffraction in ordered materials like opals, the colors of these photonic glasses are independent of orientation, owing to their disordered, isotropic microstructures. However, there are few examples of photonic glasses with angle-independent red colors in nature, and colloidal glasses with particle sizes chosen to yield structural colors in the red show weak color saturation. Using scattering theory, we show that the absence of angle-independent red color can be explained by the tendency of individual particles to backscatter light more strongly in the blue. We discuss how the backscattering resonances of individual particles arise from cavity-like modes and how they interact with the structural resonances to prevent red. Finally, we use the model to develop design rules for colloidal glasses with red, angle-independent structural colors.

Introducing diffusing wave spectroscopy as a process analytical tool for pharmaceutical emulsion manufacturing

Emulsions are widely used for pharmaceutical, food, and cosmetic applications. To guarantee that their critical quality attributes meet specifications, it is desirable to monitor the emulsion manufacturing process. However, finding of a suitable process analyzer has so far remained challenging. This article introduces diffusing wave spectroscopy (DWS) as an at-line technique to follow the manufacturing process of a model oil-in-water pharmaceutical emulsion containing xanthan gum. The DWS results were complemented with mechanical rheology, microscopy analysis, and stability tests. DWS is an advanced light scattering technique that assesses the microrheology and in general provides information on the dynamics and statics of dispersions. The obtained microrheology results showed good agreement with those obtained with bulk rheology. Although no notable changes in the rheological behavior of the model emulsions were observed during homogenization, the intensity correlation function provided qualitative information on the evolution of the emulsion dynamics. These data together with static measurements of the transport mean free path (l*) correlated very well with the changes in droplet size distribution occurring during the emulsion homogenization. This study shows that DWS is a promising process analytical technology tool for development and manufacturing of pharmaceutical emulsions.

Multimodality characterization of microstructure by the combination of diffusion NMR and time-domain diffuse optical data

Combining datasets with a model of the underlying physics prior to mapping of tissue provides a novel approach improving the estimation of parameters. We demonstrate this approach by merging near infrared diffuse optical signal data with diffusion NMR data to inform a model describing the microstructure of a sample. The study is conducted on a homogeneous emulsion of oil in a dispersion medium of water and proteins. The use of a protein based background, rich in collagen, introduces a similarity to real tissues compared to other models such as intralipids. The sample is investigated with the two modalities separately. Then, the two datasets are used to inform a combined model, and to estimate the size of the microstructural elements and the volume fraction. The combined model fits the microstructural properties by minimizing the difference between experimental and modelled data. The experimental results are validated with confocal laser scanning microscopy. The final results demonstrate that the combined model provides improved estimates of microstructural parameters compared to either individual model alone.

Temperature-dependent gelation process in colloidal dispersions by diffusing wave spectroscopy

Temperature-dependent microrheology of a concentrated charge-stabilized poly(methyl methacrylate) colloidal dispersion with different salt concentrations was investigated by diffusing wave spectroscopy in backscattering mode. The critical temperature where the system undergoes aggregation and gelation depends upon the particle volume fraction or salt concentration. The viscoelastic properties of the systems have been discussed using Maxwell and Kelvin-Voigt models. Temperature-dependent crossover (G' = G″) frequency has been used to calculate activation energies representing a critical energy of interaction of gel formation.

Rapid high resolution imaging of diffusive properties in turbid media

We propose a laser speckle based scheme that allows the analysis of local scattering properties of light diffusely reflected from turbid media. This turbid medium can be a soft material such as a colloidal or polymeric material but can also be biological tissue. The method provides a 2D map of the scattering properties of a complex, multiple scattering medium by recording a single image. We demonstrate that the measured speckle contrast can be directly related to the local transport mean free path l* or the reduced scattering coefficient μt = 1/l* of the medium. In comparison to some other approaches, the method does not require scanning (of a laser beam, detector or the sample itself) in order to generate a spatial map. It can conveniently be applied in a reflection geometry and provides a single characteristic value at any given position with an intrinsic resolution typically on the order of 5-50 μm. The actual resolution is however limited by the transport mean free path itself and can thus range from microns to millimeters.

Optical analog of Matthiessen's rule in a one-dimensional model for diffusive light transport in foams

We study photon diffusion in a one-dimensional model foam composed of thin films and Plateau borders. Each thin film or Plateau border is characterized by its own intensity transmittance. We relate l(Foam)*, the transport-mean-free path of photons diffusing in the foam, to the foam microstructure. Denoting by l(Film)* (l(PB)*) the transport-mean-free path of photons in a medium composed only of thin films (Plateau borders), we find 1/l(Foam)*=φ(F)/l(Film)*+φ(P)/l(PB)*. Here φ(F) and φ(P)=1-φ(F) are the fraction of films and Plateau borders, respectively.

Doubly responsive polymer-microgel composites: rheology and structure

Mixtures of alkali swellable microgels and linear PNIPAm chains exhibit doubly responsive properties both with pH and temperature. Below the lower critical solution temperature (LCST), the linear chains of PNIPAm are soluble and increase the osmotic pressure outside the microgels, which causes them to deswell. Above the LCST, the PNIPAm chains become insoluble and form spherical colloidal particles confined between the microgels that subsequently reswell. The swelling and deswelling of the microgels change the rheological properties of the composites, providing a unique way to tune the elasticity of the composites with temperature. The structure of the composites above the LCST is studied using multiple light scattering and fluorescence confocal microscopy. The phase separation of PNIPAm above the LCST is strongly affected by the confinement of the PNIPAm chains between the microgels.

Diffusive transport of light in a two-dimensional disordered packing of disks: analytical approach to transport mean free path

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular media and wet foams. We assume that the intensity reflectance of disks is a constant r . We present an analytic expression for the transport mean free path l;{*} in terms of the velocity of light in the disks and host medium, radius R and packing fraction of the disks, and the intensity reflectance. For glass beads immersed in air or water, we estimate transport mean free paths about half the experimental ones. For air bubbles immersed in water, l;{*}R is a linear function of 1epsilon , where epsilon is the liquid volume fraction of the model wet foam. This throws light on the empirical law of Vera [Appl. Opt. 40, 4210 (2001)] and promotes more realistic models.

Light propagation in strongly scattering, random colloidal films: the role of the packing geometry

We study the propagation of light through randomly packed films of micron-sized spheres. Dried films consist of strongly scattering core-shell particles mixed with polymer spheres, which are then dissolved to tune the number of contacts, Z, among the remaining scatterers. The transport mean free path l* is measured from the width of the coherent backscattering cone; l*=2.1 microm when Z ~ 4-5, but increases twofold (scattering weakens) in a film with Z ~ 9-10. The results contradict the standard diffusive transport model, but are explained by accounting for optical coupling of contacting spheres.

Influence of correlations between scatterers on the attenuation of the coherent wave in a random medium

Experimental measurements of the coherent wave transmission for ultrasonic waves propagating in water through a random set of scatterers (metallic rods) are presented. Though the densities are moderate (6% and 14%) the experimental results show that the mean-free path deviates from the classical first-order approximation due to the existence of correlations between scatterers. Theoretical results for the mean free path obtained from different approaches are compared to the experimental measurements. The best agreement is obtained with the second-order diagrammatic expansion of the self-energy.

Photon channelling in foams

Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction epsilon. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of epsilon.

Diffusive transport of light in a Kelvin foam

Although diffusing-wave spectroscopy has already been successfully applied to study dynamic properties of foams, we still lack a clear understanding of the diffusive transport of photons in foams. In this paper, we present a thorough study of photon diffusion in the Kelvin structure as an example for a three-dimensional model foam. We consider the photons' random walk as they are reflected or transmitted by the liquid films according to the rules of ray optics. For constant reflectance and special one- and two-dimensional photon paths, we are able to calculate diffusion constants analytically. Extensive numerical simulations reveal a remarkable similarity with our previous two-dimensional investigations. To implement a more realistic model, we use thin-film reflectances. The simulated diffusion constants exhibit oscillations for varying film thickness d which vanish when disorder is introduced in d. Absolute values and the behavior at small d agree with measurements in very dry foams providing a strong argument for the importance of liquid films in the diffusive photon transport. An analytical theory with a minimum of input parameters reproduces the numerical results.

Persistent random walk in a honeycomb structure: light transport in foams

We study light transport in a honeycomb structure as the simplest two-dimensional model foam. We apply geometrical optics to set up a persistent random walk for the photons. For three special injection angles of 30 degrees, 60 degrees, and 90 degrees relative to a hexagon's edge, we are able to demonstrate by analytical means the diffusive behavior of the photons and to derive their diffusion constants in terms of intensity reflectance, edge length, and velocity of light. Numerical simulations reveal an interesting dependence of the diffusion constant on the injection angle in contrast to the usual assumption that in the diffusive limit the photon has no memory for its initial conditions. Furthermore, for injection angles close to 30 degrees, the diffusion constant does not converge to the value at 30 degrees. We explain this observation in terms of a two-state model.

Assessment of Small-Angle and Angle-Averaged Structure Factor for Monitoring Electrostatic Colloidal Interactions Using Multiply Scattered Light

The isotropic scattering coefficients of 143-nm diameter polystyrene latex suspensions were measured using frequency-domain photon migration (FDPM) at 687 and 828 nm as a function of volume fraction (0.05-0.3) and ionic strength (1.0 to 120 mM NaCl equivalents) in order to derive the angle-integrated structure factor, S(q), and structure factor at zero wave vector, S(0). The effective surface charges of the dispersions were estimated by fitting the measured isotropic scattering coefficients at each wavelength as a function of volume fraction to the solution of the Orstein-Zernike integral equation using the hard sphere Yukawa potential model and mean spherical approximation as a closure relation. The estimates of surface charges were comparable at both wavelengths, but decreased with ionic strength. At 120 mM NaCl equivalents, the values of S(0) obtained from FDPM matched those predicted by the Percus-Yevick model, and decreased with volume fraction, consistent with prediction by the Carnahan-Starling equation.

Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions

We have studied the properties of dense colloidal suspensions with a combination of small-angle neutron scattering (SANS) and diffusing wave spectroscopy (DWS). Contrary to single light scattering, DWS provides dynamic information on length scales, from 1 to 100 nm, comparable to SANS. This offers a unique range of accessible length and time scales perfectly suited for the (noninvasive) investigation of highly concentrated systems. By this we obtain valuable information about the structural properties and the short-time diffusion of electrostatically stabilized, but strongly screened, hard-sphere-like colloidal suspensions with volume fractions up to 30%. We furthermore discuss the consequences of local structural ordering on the optical properties, such as optical density and polarization. Quantitative agreement is found when comparing transmission measurements (optical density) with parameter-free numerical calculations based on the structural characterization from SANS.

Investigation of Particle Interactions in Concentrated Colloidal Suspensions Using Frequency Domain Photon Migration: Monodisperse Systems

Frequency domain photon migration (FDPM) measurements were conducted to assess particle interactions of concentrated, monodisperse, polystyrene samples obtained directly from industry by using multiple scattering light. The angle-integrated static structure factor, S(q), and static structure factor at small wave vector q, S(0), were obtained from FDPM measurements at high volume fractions ranging from 0.05 to 0.3, and were compared with those obtained from the monodisperse hard sphere Percus-Yevick (HSPY) model. Effects of different colloid sizes on structure factor evaluated at two different wavelengths were also investigated. Results show that the monodisperse HSPY model is suitable for accounting for particle interactions and local microstructures in these colloidal suspensions. Upon using the HSPY model, particle sizes of polystyrene suspensions were recovered from FDPM measurements at high volume fractions (up to 0.3), which agree well with the DLS measurement of diluted sample ( approximately 0.001). The study of polydispersity effect shows that the FDPM method can be successfully used for recovering the mean particle size of polydisperse colloidal suspension with low polydispersity (<16%) under the assumption of monodisperse hard sphere systems.

Scattering optics of foam

The multiple scattering of light by aqueous foams is systematically studied as a function of wavelength, bubble size, and liquid fraction. Results are analyzed in terms of the transport mean free path of the photons and an extrapolation length ratio for the diffuse photon concentration field. The wavelength dependence is minimal and may be attributed entirely to the wavelength dependence of the refractive index of water rather than thin-film interference effects. The transport mean free path is found to be proportional to the bubble diameter and the reciprocal of the square root of liquid fraction. The extrapolation length ratio varies almost linearly with liquid fraction between the values for water-glass-air and air-glass-air interfaces.

Spatial sampling by diffuse photons

The contribution of some region in an opaque multiple-scattering sample to the detected signal is considered. Because diffusion theory gives only the total photon concentration and not the fraction of that which ultimately reaches the detector, it must be supplemented. We show how to do so by making further use of the assumption that photon migration is Markovian. This procedure is illustrated for illumination-detection geometries and scattering parameters of interest for diffusing-light spectroscopies. Specifically, we explore slab geometries with plane-wave illumination and detection as well as a semi-infinite sample with point illumination and detection. For the former the photon behavior as a function of slab thickness, scattering anisotropy, absorption, and boundary reflectivity is predicted and shown to compare well with Monte Carlo random-walk simulations.

Diffusing-wave spectroscopy of nonergodic media

We introduce an elegant method that allows the application of diffusing-wave spectroscopy (DWS) to nonergodic, solidlike samples. The method is based on the idea that light transmitted through a sandwich of two turbid cells can be considered ergodic even though only the second cell is ergodic. If absorption and/or leakage of light take place at the interface between the cells, we establish a so-called "multiplication rule," which relates the intensity autocorrelation function of light transmitted through the double-cell sandwich to the autocorrelation functions of individual cells by a simple multiplication. To test the proposed method, we perform a series of DWS experiments using colloidal gels as model nonergodic media. Our experimental data are consistent with the theoretical predictions, allowing quantitative characterization of nonergodic media and demonstrating the validity of the proposed technique.

Probing Static Structure of Colloid-Polymer Suspensions with Multiply Scattered Light

Time-dependent measurements of light propagation were conducted in aqueous dispersions of 523 nm diameter polystyrene at concentrations between 0.1 and 0.4 solids volume fraction in order to assess how particle correlation is influenced by depletion interactions arising from the addition of soluble polyethyleneoxide (PEO). In the absence of polymer, the transport scattering length can be predicted from Mie scattering theory and the Percus-Yevick (P-Y) model for static structure of a dense hard-sphere colloidal solution. Depletion forces arising from the addition of PEO of varying molecular weights influenced the spatial ordering of the dispersion and caused a further increase in the transport scattering length beyond that predicted by hard-sphere static structure factor but similar to that predicted by the mean sphere approximation (MSA) to the P-Y model described by Ye et al. (1996). Onset of flocculation occurred with increased PEO addition and correlated with PEO molecular weight. Phase separation was noted by no further change in the transport scattering length, except when flocculation was induced by the highest molecular weight PEO. The use of time-dependent measurements of light propagation in dense systems provides an alternative to small-angle light, neutron, and X-ray scattering characterization of interaction potentials in dense, multiply scattering samples and promises further fruitful investigation of colloidal particle interactions in suspensions. Copyright 1999 Academic Press.

Characteristic scales of optical field depolarization and decorrelation for multiple scattering media and tissues

Decorrelation and depolarization properties of multiply scattering media and tissues in the case of propagation of coherent probe beams are analyzed in terms of photon path distribution. A specific correlation time determining the relationship between correlation and polarization states of scattered optical fields is introduced. Results of correlation and polarization experiments with phantom scatterers (such as water suspensions of polystyrene spheres) and tissues with controlled optical properties (such as the human sclera) are presented. © 1999 Society of Photo-Optical Instrumentation Engineers.

Investigation of static structure factor in dense suspensions by use of multiply scattered light

Near-infrared, frequency-domain photon migration measurements of phase shift are used to derive accurate values of isotropic scattering coefficients in concentrated, interacting suspensions of aqueous polystyrene microspheres with volume concentrations ranging from 1% to 45% by solids and mean diameters ranging from 135 to 500 nm. Under conditions of high ionic strength, the isotropic scattering coefficient can be quantitatively predicted by the Percus-Yevick model for hard-sphere interactions and Mie theory. In addition, the attractive interactions between scatterers arising from the addition of soluble poly(ethylene glycol) with molecular weights of 100 and 600 K cause hindered scattering. The increases in static structure and decreases in isotropic scattering coefficient agree with that predicted by Mie theory and the depletion interaction model developed by Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)]. These results demonstrate the success of monitoring interaction between particles by use of multiple-scattered light and the necessity of incorporating models for these interactions when predicting scattering of dense, concentrated suspensions.

Applicability Limits of Beer's Law for Dispersion Media with a High Concentration of Particles

This study analyzes the values of volume concentrations of scatterers at which radiation extinction in dispersion media obeys Beer's law. The dependence of the maximum particle concentration at which Beer's law holds on the properties of the dispersion medium is investigated. It is shown that the maximum concentration is strongly dependent on the scatterers' parameters and varies over a wide range, from tenths to tens of percent.

Light transmission by a monolayer of particles: comparison of experimental data with calculation as a single-scattering approximation

The laws of light transmission by particle monolayers are investigated. The results of measurement of coherent transmission for monolayers formed by large nonabsorbing particles are presented. The obtained results are compared to the calculation in the single-scattering approximation. Good agreement between experimental and calculated data is shown.