Photon Transport Mean Free Path Research Articles

TiO2–SiO2 Self-Standing Materials bearing Hierarchical Porosity: MUB-200(x) Series toward 3D-Efficient VOC Photoabatement Properties

Three-dimensional photoactive self-standing porous materials have been synthesized through the integration of soft chemistry and colloids (emulsions, lyotrope mesophases, and P25 titania nanoparticles). Final multiscale porous ceramics bear 700-1000 m2 g-1 of micromesoporosity depending on the P25 nanoparticle contents. The applied thermal treatment does not affect the P25 anatase/rutile allotropic phase ratio. Photonic investigations correlated with the foams' morphologies suggest that the larger amount of TiO2 that is introduced, the larger the walls' density and the smaller the mean size of the void macroscopic diameters, with both effects inducing a reduction of the photon transport mean free path (lt) with the P25 content increase. A light penetration depth in the range of 6 mm is reached, thus depicting real 3D photonic scavenger behavior. The 3D photocatalytic properties of the MUB-200(x) series, studied in a dynamic "flow-through" configuration, show that the highest photoactivity (concentration of acetone ablated and concentration of CO2 formed) is obtained with the highest monolith height (volume) while providing an average of 75% mineralization. These experimental results validate the fact that these materials, bearing 3D photoactivity, are paving the path for air purification operating with self-standing porous monolith-type materials, which are much easier to handle than powders. As such, the photocatalytic systems can now be advantageously miniaturized, thereby offering indoor air treatment within vehicles/homes while drastically limiting the associated encumbrance. This volumetric counterintuitive acting mode for light-induced reactions may find other relevant advanced applications for photoinduced water splitting, solar fuel, and dye-sensitized solar cells while both optimizing photon scavenging and opening the path for the miniaturization of the processes where encumbrance or a foot-print penalty would be advantageously circumvented.

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.

Particle sizing in non-dilute dispersions using diffusing wave spectroscopy with multiple optical path lengths

Non-dilute dispersed phase systems, such as foams, emulsions, and suspensions, are an important class of final formulations and chemical process intermediates in a variety of industries. The utility of these systems hinges on their stability over the lifetime of use, and therefore an accurate assessment of chemical and physical dynamics, asformulated, is required. We describe a unified treatment of diffusing wave spectroscopy (DWS) data using a range of optical path length with a goniometric instrument. DWS correlation data from multiple angles and robust Monte Carlo simulations are used to determine accurate values of the photon transport mean free path length. The variance on each correlation function is used to determine the physical time range that the mean squared displacement can be analyzed. Using standard solid particle suspensions of polystyrene and SiO2, we determine the average particle size with accuracy comparable to dynamic light scattering.

Effective Radiative Cooling by Paint-Format Microsphere-Based Photonic Random Media

We demonstrate that photonic media, when properly randomized to minimize the photon transport mean free path, can be used to coat a black substrate and reduce its temperature by radiative cooling. Even under strong solar radiation, the substrate temperature could reach substantially below that of the ambient air. Our random media that consist of silica microspheres considerably outperform commercially available solar-reflective white paint for daytime cooling. We have achieved the outstanding cooling performance through a systematic study on light scattering, which reveals that the structural parameters of the random media for maximum scattering are significantly different from those of the commercial paint. We have created the random media to maximize optical scattering in the solar spectrum and to enhance thermal emission in the atmospheric transparency window. In contrast to previous studies, our random media do not require expensive processing steps or materials, such as silver, and can be applied to ...

Scanning-fiber-based imaging method for tissue engineering

A scanning-fiber-based method developed for imaging bioengineered tissue constructs such as synthetic carotid arteries is reported. Our approach is based on directly embedding one or more hollow-core silica fibers within the tissue scaffold to function as micro-imaging channels (MIC). The imaging process is carried out by translating and rotating an angle-polished fiber micro-mirror within the MIC to scan excitation light across the tissue scaffold. The locally emitted fluorescent signals are captured using an electron multiplying CCD camera and then mapped into fluorophore distributions according to fiber micro-mirror positions. Using an optical phantom composed of fluorescent microspheres, tissue scaffolds, and porcine skin, we demonstrated single-cell-level imaging resolution (20 to 30 μm) at an imaging depth that exceeds the photon transport mean free path by one order of magnitude. This result suggests that the imaging depth is no longer constrained by photon scattering, but rather by the requirement that the fluorophore signal overcomes the background "noise" generated by processes such as scaffold autofluorescence. Finally, we demonstrated the compatibility of our imaging method with tissue engineering by visualizing endothelial cells labeled with green fluorescent protein through a ≈ 500 μm thick and highly scattering electrospun scaffold.

Control of random lasing in ZnO/Al2O3 nanopowders

We demonstrate that the random lasing wavelength of ZnO/Al2O3 nanopowders can be controlled by varying the weight fraction of Al2O3. This controllability is due to the fact that the extent of self-absorption by ZnO nanopowder can be modified by changing the photon-transport mean free path. The lasing threshold excitation power is also dependent on the weight fraction of Al2O3. The random lasing characteristic can be explained well by a theoretical model based on the photon-transport mean free path.

Resonant optical scattering in nanoparticle-doped polymer photonic crystals

A broadband hyperspectral technique is used to measure the coherent optical backscatter across a wide spectral bandwidth, showing the resonant suppression of the photon transport mean free path around the photonic bandgap of a shear-assembled polymer photonic crystal. By doping with carbon nanoscale scatterers that reside at specific points within the photonic crystal lattice, the ratio between photon mean free path and optical penetration is tuned from 10 to 1, enhancing forward scatter at the expense of back-scatter. The back-scattering strength of different polarisations is not explained by any current theory.

Diffusing Wave Spectroscopy Used to Study the Influence of Shear on Aggregation

In this study, diffusing wave spectroscopy (DWS) is used to investigate the effect of shear on a food-related aggregating emulsion. The principle of the method is validated using a nonaggregating, nearly monodisperse latex suspension. In general, with increasing shear rate the diffusive motion of the scatterers becomes negligible compared to the convective motion. This causes a decrease in the decay time of the autocorrelation curves and a change in the form of the autocorrelation curves from nearly exponential to Gaussian. This is reflected in the exponent of the mean square displacement that changes from 1 to 2. The effect of shear on the acidification of a sodium caseinate-stabilized emulsion was studied by DWS and by rheometry. The emulsion droplets in the food-related emulsion were uniformly dispersed at neutral pH. Upon acidification down to a pH of 5.2 +/- 0.05, the emulsion showed Newtonian behavior with constant viscosity over the whole pH range. At pH 5.17 +/- 0.05, independent of the applied shear rate during acidification, the viscosity suddenly increased. From this point on, the emulsion showed shear-thinning behavior. The photon-transport mean free path ( l*) was not influenced by the applied shear rate and did not change down to pH 5.2 +/- 0.05. Close to this pH, l* increased, and the decay of the autocorrelation curves shifted to longer correlation times when shear rates smaller than 1 s (-1) were applied. At lower pH (5.05 +/- 0.05), l* started to fluctuate, and the autocorrelation curves no longer decayed to zero, indicating that at these shear rates the system behaved nonergodicly. Assuming that the convective motion and the Brownian motion are independent of each other, the mean square displacement as a result of Brownian motion was determined. From this, the sol-gel point and the radius of the aggregates at this point as a function of the shear rate was determined. The results indicated that the radius of the aggregates at the sol-gel transition decreased with increasing shear rate and suggested that shear will result in a more open structure of the network formed by the aggregates.

Prediction of ceramic stereolithography resin sensitivity from theory and measurement of diffusive photon transport

A general, quantitative relationship between the photon-transport mean free path (l*) and resin sensitivity (DP) in multiple-scattering alumina/monomer suspensions formulated for ceramic stereolithography is presented and experimentally demonstrated. A Mie-theory-based computational method with structure factor contributions to determine l* was developed. Planar-source diffuse transmittance experiments were performed on monodisperse and bimodal polystyrene/water and alumina/monomer systems to validate this computational tool. The experimental data support the application of this l* calculation method to concentrated suspensions composed of nonaggregating particles of moderately aspherical shape and log-normal size distribution. The values of DP are shown to be approximately five times that of l* in the tested ceramic stereolithography suspensions.

Application of transmission diffusing wave spectroscopy to the study of gelation of milk by acidification and rennet

Transmission diffusing wave spectroscopy has been used to study and compare three milk gelling systems (acid gelation of heated and unheated milks and rennet coagulation of unheated milk). In all cases, DWS was able to demonstrate the point of gelation as indicated by a rapid increase in particle size, as well as the small decreases in casein micelle radius attributed to the collapse or removal of the hairy κ-casein layer. More importantly, the photon transport mean free path ( l *) was measured. This parameter is unique to transmission DWS and can potentially give information about developing microstructures and the mechanical properties between different types of gels. The values of l * changed during the gelation processes, and these changes were manifested earlier than any change in particle aggregation or rheology of the systems. All three different gelling systems showed different changes in l * with time, showing the development of different interactions as the acidification or renneting reactions proceeded. Although a full analysis of the l * parameter and its changes cannot be made, it is concluded that they can provide important information on the pre-gelation states of aggregating systems.

Theory of photon statistics and optical coherence in a multiple-scattering random-laser medium.

We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.

Structure, Dynamics, and Optical Properties of Concentrated Milk Suspensions: An Analogy to Hard-Sphere Liquids

A systematic study of the effects of volume fraction increment on the optical properties, the structure, and the dynamics of the casein micelles and fat droplets in milk was performed using diffusing wave spectroscopy. Four types of milk were investigated, NIDO full fat milk, fat-free milk, whey and fat-free milk, and finally lactose and fat-free milk. Independent measurements to calculate the dependence of the viscosity and the index of refraction of the milk serum and casein micelles as a function of the volume fraction were also performed. We compare the experimentally determined quantities photon transport mean free path ( l*) and self-diffusion coefficient D s with the predictions from theoretical calculations using classical colloidal models such as a hard-sphere fluid. We demonstrate that all types of milk with and without fat content behave, structurally, like colloidal hard-sphere systems up to volume fractions well over 45%. In the case of dynamic measurements, both lactose- and fat-free and whey- and fat-free milk behave also like hard-sphere systems whereas fat-free milk and fat-containing NIDO milk deviate slightly at volume fractions over 35%. Finally, a comparative measurement and theoretical calculation of the casein micelle's size was performed.

Direct measurement of the spatial distribution of light intensity in a scattering medium

A direct nonperturbative measurement of the spatial distribution of the light intensity in a strongly scattering medium is performed using an optoacoustic method. It is shown that near a surface the intensity can be five times greater than the incident intensity, and the absolute maximum of the intensity is observed at a depth l(1–R)(1–4.0R) determined by the photon transport mean free path l and the effective light reflection coefficient R of the boundary separating the scattering and external media.

Static imaging of dynamic fluctuations in multiple light scattering media

Multiple light scattering experiments in backscattering geometry are performed on highly viscous and solid turbid media which contain macroscopic inclusions of a low viscosity colloidal suspension. We demonstrate that the intensity probability distribution P( I) of the multiple scattering speckle patterns can be used to image an inclusion even if its photon transport mean free path matches the value of the surrounding medium. The main difference between solid and liquid samples is discussed.

Penetration depth for diffusing-wave spectroscopy

The depth at which diffusing photons are assumed to be deposited in a random scattering medium has traditionally been treated as a phenomenological parameter comparable to the photon transport mean free path. We show how to average properly over an exponential distribution of depositions weighted additionally by the transmission probability, and compare our prediction for the autocorrelation of intensity fluctuations in the transmitted light with experimental data on an ideal system. The improved correlation function, where distinguishable from the prior form, provides slightly better agreement with data as long as the sample is thicker than approximately 10 transport mean free paths. However, in contrast with static transmission, proper averaging over a range of penetration depths does not extend the validity of diffusing-wave spectroscopy to significantly smaller slab thicknesses. The most significant errors in the theory must therefore arise from approximations other than the treatment of the source of diffusing photons.