Van der Waals Forces Between Plasmonic Nanoparticles

Abstract

We propose a new approach to calculate van der Waals forces between nanoparticles where the van der Waals energy can be reduced to the energy of localized plasmons in nanoparticles. The general theory is applied to describe the interaction between two metallic nanoparticles and between a nanoparticle and a perfectly conducting plane. Our results could be used to prove experimentally the existence of new, recently predicted type of plasmon oscillation (Klimov and Guzatov, Phys Rev B 75:024303, 2007a; Klimov and Guzatov, Quantum Electron 37:209, 2007b) and to elaborate new control mechanisms for the adherence of nanoparticles between each other or onto surfaces.Keywords Two-sphere cluster · Plasmon resonance · Van der Waals force In recent years, metallic nanoparticles have regained new and vivid interest. Especially noble-metal nanoparticles are used in biological sensing applications [3], in imaging, and as optical materials [4]. The optical response of nanoparticles is governed by the excitation of their plasmon resonances. Localized plasmons play an important role in many fields of physics, for example, in the enhancement of the transmission of light through metallic structures [5,6] or for dispersion forces in 2-dimensional Wigner-like crystals [7]. The properties of localized plasmons and, thus, the optical response of the nanoparticle depends critically on their material, shape, and size [8]. For example, optical forces between silver nanoparticle aggregates are known to be enhanced by exciting plasmon resonances conveniently [9]. Here, we investigate a similar phenomenon, that is the tailoring of van der Waals interaction between nanoparticles via localized plasmons. This interaction is mediated not by a photon field but by the electromagnetic vacuum fluctuations [10] and is particularly interesting for the design of control mechanisms of the adherence of nanoparticles among each other or onto a surface.To describe the van der Waals interactions between a nanoparticle and a surface, usually a dipole approximation is used [11,12], which is valid only for large enough distances between the particle and the surface. Recently, van der Waals forces between a spherical particle and planar substrate have been considered with the help of expansion of electromagnetic fields over usual spherical harmonics [13][14][15][16]. In [17][18][19], the van der Waals energy between realistic metallic surfaces was shown to be dominated by surface plasmon oscillations for small distances.In the present paper, we study the van der Waals energy between two nanospheres and between a nanosphere and a perfectly conducting plane as the energy of localized plasmons in such a system. Plasmonic oscillations in this system have a very complicated spatial and spectral structure [1, 2]. We will show that both recently predicted [1, 2] and previously known [20][21][22] plasmon oscillations give contributions to the van der Waals energy that are approximately equal in amplitude but opposite in sign. As a result, the van der Waals

Asymptotic approximations for the plasmon resonances of nearly touching spheres

“…Approximations have been suggested in the limit of high azimuthal number m based on the bi-spherical scheme [15]; it has been shown that these modes are important when calculating the van der Waals attraction between spheres [37,52]. It would be interesting to consider limits where either or both n and m are large using singular perturbation techniques.…”

Current-dependent anisotropic conductivity of locally assembled silver nanoparticles in hybrid polymer films

“…±2 V. The observed change in the microstructure is assumed to be the reason for the significant decrease in the sample resistance after applying a high enough voltage. An increased mobility of the particles after exceeding T g can induce secondary agglomeration of the particles driven by the dispersion forces [18] and the applied electric field, which enhances the attraction of the particles towards each other and aligns them into chains [19]. Dipole moments induced in the particles by an external electric field significantly enhance attractive interparticle forces along the chains.…”

Loss compensation symmetry in dimers made of gain and lossy nanoparticles

“…It is also very important that one can strictly prove that any eigensolution of (1) satisfies the condition of full loss compensation, that is: (7) where G L V , V are the volumes of gain and lossy nanoparticles. Thereby if one attributes effective permittivity [27] to the whole system, its imaginary part will be equal to zero, so our system is similar to pseudo-Hermitian systems [28].…”

“…In dimers, i.e. systems consisting of two particles, in the case of small losses and small distances between the particles, an essentially new type of localized oscillations ("plasmonic molecules") can be seen [5][6][7].…”