Optical Properties of Colloidal Crystals

Alberto Fernandez de las Nieves, Darren Link, Daniel Rudhardt and David A. Weitz

We make monodisperse droplets and study self-assembled periodic arrays of them. By using particles with a non-uniform or externally controllable refractive index these colloidal crystals are expected to show interesting optical properties with a large variety of possible technical applications. In particular, we aim to realize Bragg-switches by using liquid crystal droplets. In this system an external electric field can be used to vary the refractive index of the single particles in the lattice, which allows to "switch Bragg-scattering on and off". At present, we have been able to create bi-dimensional hexagonal close packed structures and employed them as switchable diffraction gratings.

By using a technique based on the drop break off in a co-flowing stream [1] we are able to make monodisperse droplets. We can use different types of liquids and both monodisperse oil and liquid crystal emulsions in water have been produced so far. The small polydispersity of the emulsion droplets allows the ordering into crystalline periodic structures. Figure 1 shows examples of both silicone oil (a, b) and liquid crystals droplets (c, d) suspended in water and ordered into two-dimensional periodic arrays.

Figure 1: Example of monodisperse oil (a,b) and liquid crystal (c,d) droplets suspended in water. The diameters of the oil droplets are 9 and 17 microns respectively. The pictures of the liquid crystal droplets are taken between crossed polarizers and the size of the droplets is 9 microns.

The mechanically stabilization of the liquid crystal droplets is crucial for the realization of a Bragg-switch. The droplets discussed so far are only stable in suspension. Upon drying, the drops coalesce and the periodic arrays are destroyed. So far, we have achieved this stabilization by dispersing the droplets in a polymer solution and slowly evaporating the solvent. This yields to an increase of the polymer concentration until eventually only the pure polymer remains, embedding the droplets in a solid matrix. If particle and polymer concentration are correctly chosen also the self-assembly of the droplets into crystalline structures during the drying process is possible. Figures 2 and 3 show examples of monodisperse liquid crystal droplets that are deposited on a glass substrate as stable two-dimensional periodic structures.

Figure 2: Example of a periodic array of liquid crystal droplets that are deposited on a glass substrate. The crystal was formed in a ~ 4% polyvinyl alcohol (PVA) solution and thus each liquid crystal droplet is completely enclosed by solid PVA walls. Due to strong hydrodynamic forces that occur during the drying process the liquid crystal droplets are deformed from a perfect hexagonal to the stretched honeycomb structure observed. The length, width and thickness of the liquid crystal droplets are a=(18 ± 1) mm, b=(13 ± 1) mm and d=(7 ± 1) mm, respectively. The labels correspond to increasing electric fields (applied perpendicularly to the pictures). In (f), optical birefringence is reduced to zero. This occurs when the liquid crystal molecules are perfectly aligned with the field and therefore color disappears. As a result at high fields the picture appears dark. The inset shows an image taken at a very high voltage, U = 80 V, with the illumination increased by more than an order of magnitude.

Figure 3: Periodic array of liquid crystal bipolar droplets formed by drying from a ~ 1% PVA solution. The evaporation seems to be less severe at lower polymer concentration. The size of the droplets are ~ 30 mm. In (b) additional crystalline layers are being formed. The colors observed during the experiment are absent since the pictures were taken with a black and white camera.

The liquid crystal droplets can be embedded in a polymer matrix of suited refractive index to form a Polymer Dispersed Liquid Crystal (PDLC) [2]. Since in our system the droplets are ordered into periodic arrays, an interesting system combining the scattering properties of a colloidal crystal and the switching ability of a conventional PDLC can be realized. This system can be used as a switchable phase grating by varying the scattering behavior applying an external electric field. In Figure 4 the scattering patterns obtained by illuminating the two-dimensional crystal of Figure 2 are shown. The unscattered beam in the center is blocked in each of the pictures and the images are taken at four different electrical field strengths.

Figure 4: Diffraction pattern of the two-dimensional hexagonal ordered array of liquid crystal droplets for four electrical fields: U=0V (a), U=5.4V (b), U=8V (c) and U=80V (d). The unscattered beam in the center of each picture is blocked. In (e) the intensities of a first order diffraction peak (dashed line) and the unscattered zero order beam (full line) are plotted as a function of applied field. Also shown is the unscattered intensity of a polydisperse PDLC film (dotted line).

With no field applied (Figure 4a) the pattern consists of an overlay of diffuse and coherently scattered light. The diffuse scattering is due to the highly birefringent liquid crystal droplets having effective refractive indices that slightly change between different droplets. By increasing the electric field the liquid crystal molecules start to align with the field yielding to an effective refractive index that becomes the same for all drops. Thus the diffuse scattering decreases while the intensity of the diffraction peaks increases. The diffraction peaks express the long-range hexagonal order of our sample. By further improving the alignment applying higher voltages however, the intensity of the peaks decreases again since the optical contrast between the droplets and the polymer matrix decreases. At the same time the intensity of the unscattered beam increases. In Figure 4d almost all the light travels through the cell without being scattered. This is the realization of a device that can be used to switch on and of the diffraction of a light beam by means of an applied voltage [3].

We are presently trying to build three dimensional crystals made from liquid crystal droplets in order to obtain a true Bragg-diffraction switch. We are interested in the response times of the switch that will eventually inform of the relaxation mechanism of the liquid crystal. In addition, we are exploring the possibility of using a polymer liquid crystal, that will allow the particles to be solidified (by a photopolymerization reaction, for example) once formed, while retaining the optical anisotropies of the liquid crystal state. We aim to grow crystalline structures out of these novel particles. This last part of the project is tackled in collaboration with Prof. G.P. Crawford (Brown University, USA).

References

[1] Umbanhowar, P. B., V. Prasad, et al. (2000). "Monodisperse Emulsion Generation Via Drop Break Off in a Coflowing Stream." Langmuir 16: 347-351.

[2] Doane, J. W., A. Golemme, et al. (1988). "Polymer Dispersed Liquid Crystals for Display Application." Mol. Cryst. Liq. Cryst. 165: 511-532.

[3] D. Rudhardt, A. Fernandez-Nieves, D. A. Weitz, paper in preparation

Any suggestions?

Contact: Alberto Fernandez de las Nieves

Physics Department and DEAS

Harvard University
Cambridge, MA 02138 (USA)

afnieves@deas.harvard.edu