From the de Broglie to Visible Wavelengths: Manipulating Electrons and Photons With Colloids
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be "integrated out" in a description of the particles. If such a description holds, the solvent can be approximated well by a continuum. The upper size limit is determined by the size at which external fields, like gravity, start to overshadow the effects of Brownian motion. In the absence of such disturbing fields, the Brownian displacements may simply become too small on a human time scale. Brownian motion is not only important in defining a colloid, it also allows these particles to travel through "phase space" of statistical mechanics. Consequently colloids have a well-defined thermodynamic temperature and strive to reach equilibrium structures with the lowest free energy. It is quite important to realize that this sets a dispersion of colloidal spheres apart from the "macroscopic" world of, for example, granular materials. For instance if granular material consisting of two sizes of spheres is shaken in a gravitational field, the larger spheres end up on top. This experiment, which can be performed at breakfast with muesli enriched by nuts, clearly demonstrates that granular materials do not behave in a "thermodynamic" sense seeking the lowest free-energy state. On the contrary, binary dispersions of colloids do form
equilibrium structures. This is the reason that colloidal dispersions are used as a model system in the study of condensedmatter problems like glass transition, crystallization, and melting (see, e.g., References 1-4 and references cited). The size of colloids not only leads to experimentally accessible time scales for processes like crystallization but also makes it possible to study such processes quantitatively in 3D real space.34 The knowledge obtained through these model studies is increasingly being used to design new materials based on colloidal building blocks. There are several reasons for this trend. One has to do with the development of better synthetic routes to make monodisperse particles, especially of the smallest size colloids. Such particles of several-nm size are called nanoparticles or quantum dots. Quantum dots are semiconductor or metal particles with highly size-dependent properties determined by quantum mechanics.56 The size of these particles is of the same order as the free-electron wavelength, which results in an increase of the electronic bandgap and tunability of—for instance—absorption and luminescence. In addition nonlinear effects may become important.6 Another impetus for new materials made from colloids was the realization some 10 years ago that, for sufficiently strong interactions with photons, a regular dielectric material would modulate the propagation of light in a similar way as a semiconductor modulates the propagation of electrons. Inside such a photonic crystal with a complete photonic bandgap, the propagation of photons with any polarization is forbidden in any direction. 7 These periodic dielectric structures can be doped dielectrically to open up transmission paths for specific wavelengths inside the bandgap.7 With such regular dielectric materials, both
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