Volume Fraction

Figure 6.27. Equations of state (dashed curves) plotted as a function of fraction of 720-nm styrene spheres in a 3-mM salt solution. The constant N0 is Avogadro's number. [Adapted from A. P. Gast and W. B. Russel, Phys. Today (Dec. 1998.)]

repulsions the lattice structure is face-centered cubic. Increasing the range of the repulsion, or lowering the concentration, allows the formation of the slightly less compact body-centered structure. Figure 6.28 shows the phase diagram of a system of soft spherical particles. The excluded volume is the volume that is inaccessible to one particle because of the presence of die other particles. By adjusting the fraction of particles, a structural phase transition between the face-centered and body-centered structures can be induced. The particles can also be modified to have attractive potentials. For the case of charged particles in aqueous solutions, this can be accomplished by adding an electrolyte to the solution. When this is done, abrupt aggregation occurs.

6.2.6. Photonic Crystals

A photonic crystal consists of a lattice of dielectric particles with separations on the order of the wavelength of visible light. Such crystals have interesting optical properties. Before discussing these properties, we will say a few words about the reflection of waves of electrons in ordinary metallic crystal lattices.

The wavefunction of an electron in a metal can be written in the free-electron approximation as

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