Photonic Properties of Strongly Correlated Colloidal Liquids

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Rojas-Ochoa, L.F., Mendez-Alcaraz, J.M., Saenz, J.J., Schurtenberger, P., and Scheffold, F., Physical Review Letters, 2004, 93, 7, 073903

Author: Sofia Magkiriadou, Fall 2011

Keywords: Bragg, resonance, disorder, photonic liquid, scattering, asymmetry parameter, Coulomb interaction, structure factor, Debye length, screening, small-angle neutron scattering,spectrometer

Introduction

The authors study the optical properties of colloidal suspensions of highly charged particles. By manipulating the strength of electrostatic interactions between the particles, they show how light propagation through the suspensions can be controlled.

The interaction of light with a material is strongly dependent on the material structure at the scale of the relevant wavelength. The interplay between structural order and disorder is key for light transport, with ordered structures generally giving rise to Bragg-type interference and disordered structures having somewhat less straightforward but equally interesting wavelength-dependent optical properties.

Relevant Optical Quantities

The quantities used to characterise the suspensions are: a. the scattering mean free path, l, which is a measure of the average distance a photon traverses between two scattering events; and b. the transport mean free path, l*, which is a measure of the average distance a photon traverses within a material before its direction is randomised. The scattering and transport lengths are related to each other via the asymmetry parameter, g, which is a measure of the angular distribution of the scattered radiation and which is defined as g = <cos(theta)>, theta being the scattering angle. Physically, g > 0 describes a sample which scatters preferentially in the forward direction, g = 0 descrives a sample that scatters symmetrically (Rayleigh scattering) and g < 0, a rare case, describes a sample that preferentially backscatters. Using g, l and l* are related via l/l* = 1-g. By controlling the inter-particle interactions, the authors show how using the same building blocks they can create suspensions where g ranges from negative values, corresponding to backscattering, to positive values, corresponding to forward scattering.

The System

The colloidal suspensions used in this study contained highly charged particles, to the effect that strong Coulomb repulsion caused them to seek the maximum possible distance from each other. However, in order to avoid full crystallization of the system (thus loosing control over the degree of disorder in it), the solvent used was a mixture of ethanol and water. To further control the strength of the Coulomb interaction salt was added at various concentrations. The particles were negatively charged polystyrene beads with a diameter of about 114nm, mixed with the solvent at various concentrations. Since control of the electrostatic forces was important for this study, the authors ensured there were no free ions in the stock solutions by deionizing them via contact with ion exchanger resin.

Measurements

The authors first studied the dependence of the total transmission through a suspension, T, on its thickness L. For a sample containing uncorrelated particles, the analogue of Ohm's law allows the estimation of l* via simple transmission measurements: T ~ l*/L (L>>l*), just like in a system of electrons in metals. While in dilute samples T (and thus 1/l*) depends linearly on the particle volume fraction, if their concentration increases to a level where inter-particle correlations are introduced l* is enhanced, and if their concentration is increased even more the refractive index contrast diminishes to zero and there is no scattering, thus T->0.

Contrary to these theoretical expectations, the authors observed a reduction in l* over a wide range of concentrations, implying that their suspensions scattered more strongly than expected (i.e. photons lost memory of their direction sooner than expected). This discrepancy was attributed to the nature of the positional correlations between the scattering particles. Small-angle neutron scattering (SANS) revealed, in agreement with calculations for reasonable particle charges, a peak of the structure factor at q ~ 2*pi/d, where d ~ rho^(-1/3) is the inter-particle distance. However, when Coulomb interactions were short-ranged, this distance d was only maintained within a certain area around each particle since particles far enough away did not interact; in other words, the suspensions had short-range order but long-range disorder. Nonetheless, this particle arrangement is thought to give rise to Bragg-type interference in the backscattering direction between waves that scattered from neighboring particles, which is the suggested reason for the enhancement of l*, most pronounced at a wavelength satisfying the Bragg condition for d (see Figure 1(a)).

Photonic-liquids-figure1.jpg

Photonic-liquids-figure2.jpg

The authors also calculated the asymmetry parameter, g, by measuring the scattering mean free path l in their samples - a quantity that is related to the light-of-sight transmission of relatively thin samples. By then taking the ratio l*/l (see Figure 1(b)) they observed that, for a given charge per sphere, g depends strongly on the volume fraction: in dilute samples g was slightly greater than or about zero, as expected from an ensemble of spheres smaller than the wavelength of light by Rayleigh scattering; at intermediate volume fractions φ ~ 0.07, g approached -1, a rather unusual case arising, as speculated, from Bragg-type interference; and at higher volume fractions, where the inter-particle distance became smaller than that required for a resonance, g rose again towards 0. This observation is very interesting, as it means that it is possible to tune the angular distribution of scattering of a suspension by simply changing the charge of its constituent particles and their concentration.

To complete the picture, the authors compared the transmission through two suspensions containing charged and neutral spheres at the same volume fraction as a function of wavelength and observed a dip at the wavelength corresponding to the Bragg condition in the case of charged spheres (Figure 3).

Photonic-liquids-figure3.jpg

Besides scientific interest, these suspensions, whose optical properties can be tuned to depend strongly on the wavelength, have promising applications. Achieving a high degree of control over the dispersion of a material is a general goal of current research and this study provides a way to do exactly that. Taking the thought one step further, if the inter-particle interactions can be tuned dynamically, for instance with electric fields, one can imagine applications relating to optical switches or dynamic filters.