Photonic Properties of Strongly Correlated Colloidal Liquids

The optical and structural properties of dense colloidal suspensions in the presence of long-range electrostatic repulsion are determined from both light and small-angle neutron scattering experiments. Short-range structural order induces an enhancement of the scattering strength while at the same time the total transmission shows strong wavelength dependence, reminiscent of a photonic crystal. Interestingly, the interplay between diffusive scattering and local order leads to negative values of the scattering anisotropy parameter. The tunable optical properties of these liquids furthermore suggest potential applications such as transparency switches or filters.

Figure 1

(a) Optical density $1/l^{*}$ of polystyrene particle suspensions (mean radius 57 nm) at different concentrations (volume fraction $\Phi$) for $\lambda ={\lambda }_L/n_s=\mathrm{390}\mathrm{n}\mathrm{m}$ (full symbols: charged spheres; open symbols: hard spheres). Solid line: Calculation for charged spheres with an effective charge per particle $Z_{\mathrm{e}\mathrm{f}\mathrm{f}}=300e^{-}$. Dotted line: theoretical calculations for hard-sphere interactions. Dashed line: no interactions [$S(q)\equiv 1$]. (b) Ratio of the transport mean free path and the scattering mean free path (solid circles). Solid line: theoretical calculation based on Eq. (3).

Figure 2

Liquid structure for charged spheres: $q$-dependent neutron scattering intensity $I(q)$ for different particle concentrations $\Phi$. The position of the scattering peak (solid circles) scales with the typical interparticle distance, $q_{\max }=2\pi /d\sim {\Phi }^{1/3}$. Solid lines: Numerical fits to the data with an effective charge ranging from $Z_{\mathrm{e}\mathrm{f}\mathrm{f}}=275e^{-}$ to $325e^{-}$. A maximum in the optical density, Fig. 1, is observed when $q_{\max }$ crosses the orange line at $2k_0=0.0322{\mathrm{n}\mathrm{m}}^{-1}$.

Figure 3

Transmission wavelength dependence. Experimental values for charged spheres (solid symbols) and hard spheres (open symbols), $\Phi =0.097$. Cell thickness: $L=2\mathrm{m}\mathrm{m}$. Solid lines: Theoretical calculations taking into account low order scattering and surface reflectivity. Inset: The transmission ratio shows a minimum at $\lambda \approx 341\mathrm{n}\mathrm{m}$ [Bragg condition $\lambda =2d=4\pi /q_{\mathrm{m}\mathrm{a}\mathrm{x}}=356\mathrm{n}\mathrm{m}$].