We report that triangular gold nanoprisms in the presence of attractive depletion forces and repulsive electrostatic forces assemble into equilibrium one-dimensional lamellar crystals in solution with interparticle spacings greater than four times the thickness of the nanoprisms. Experimental and theoretical studies reveal that the anomalously large d spacings of the lamellar superlattices are due to a balance between depletion and electrostatic interactions, both of which arise from the surfactant cetyltrimethylammonium bromide. The effects of surfactant concentration, temperature, ionic strength of the solution, and prism edge length on the lattice parameters have been investigated and provide a variety of tools for in situ modulation of these colloidal superstructures. Additionally, we demonstrate a purification procedure based on our observations that can be used to efficiently separate triangular nanoprisms from spherical nanoparticles formed concomitantly during their synthesis.

We obtain exact expressions for the Casimir forces between arbitrary materials using the concept of surface impedance. We verify their consistency with the well-known expressions for perfect conductors and with Lifshitz formula for semi-infinite local homogeneous media. As an application we present a full and rigorous calculation of the Casimir force between two metallic half spaces described by a hydrodynamic nonlocal dielectric response.

The surface impedance approach is discussed in connection with the precise calculation of the Casimir force between metallic plates. It allows us to take into account the nonlocal connection between the current density and electric field inside of metals. In general, a material has to be described by two impedances $Z_s(\omega ,q)$ and $Z_p(\omega ,q)$ corresponding to two different polarization states. In contrast with the approximate Leontovich impedance they depend not only on frequency $\omega$ but also on the wave vector along the plate $q$. In this paper only the nonlocal effects happening at frequencies $\omega <{\omega }_p$ (plasma frequency) are analyzed. We refer to all of them as the anomalous skin effect. The impedances are calculated for the propagating and evanescent fields in the Boltzmann approximation. It is found that $Z_p$ significantly deviates from the local impedance as a result of the Thomas-Fermi screening. The nonlocal correction to the Casimir force is calculated at zero temperature. This correction is small but observable at small separations between bodies. The same theory can be used to find more significant nonlocal contribution at $\omega \sim {\omega }_p$ due to the plasmon excitation.

A 2×2 transfer matrix approach is used to study the elastic response of multilayered systems. Superlattices with a period of n layers are considered to calculate the dispersion relations of the normal modes for both longitudinal and transverse waves, and the reflectivity of longitudinal modes for finite and semi-infinite structures. Numerical results of the dispersion relation for a two- and three-layer period superlattice are presented to show the band structure of wave propagation. For transverse waves, it is considered that the single layer may support surface modes and it is found that their interaction with those of the adjacent layers also yield a band structure. The calculated reflectivity of longitudinal elastic waves for the semi-inifinite superlattices resembles the allowed and forbidden regions of the dispersion relations. The theoretical reflectivity curves of sound waves are compared with the experimental results for the three-layer systems. A good agreement between theory and experiment is obtained.

The effect of the Casimir force in micro- and nanoelectromechanical systems is examined taking fully into account the dielectric properties of the materials, as well as the finite thickness of movable elements in micro- and nanosystems. The resulting equations are exact, and from the bifurcation diagrams the critical separation before jump-to-contact is determined. It is shown how the critical separation changes, for example, with the dielectric properties of the materials and how these systems can be rescaled based on the information from the bifurcation diagrams.

We present the basic principles of non-local optics in connection with the calculation of the Casimir force between half-spaces and thin films. At currently accessible distances $L$, non-local corrections amount to about half a percent, but they increase roughly as 1/L at smaller separations. Self consistent models lead to corrections with the opposite sign as models with abrupt surfaces.