Andrei G. Melnikov

Absorption and scattering of light by a dimer of metal nanospheres: comparison of dipole and multipole approaches

Recently, the polarizability tensor of metal bispheres located near a plane metal substrate was analytically derived in dipole approximation and was used to calculate the extinction spectra of silver dimers (Pinchuk and Schatz 2005 Nanotechnology 16 2209). To evaluate the accuracy of dipole approximation for this problem, we compare the optical properties of silver and gold dimers, embedded in a homogeneous dielectric medium, by using electrostatic and electrodynamic dipole approximations and an exact electrodynamic multipole solution. For longitudinal TM-excitation (the electric field is directed along the bisphere axis), the dipole and multipole absorption and scattering spectra differ dramatically, whereas for transversal TE-excitation the dipolar approximation gives acceptable results. The physical origin of the inaccuracies of the dipole electrostatic solution is related to the highly inhomogeneous electric-field distribution near the contact point of the spheres. Thus, we have to include several multipole orders even in the electrostatic solution for dimer particles that are, individually, well within dipole approximation. Although we do not consider the effects of a plane metal substrate, we believe that the multipole interaction of constituent dimer spheres can also be important in this case. The T-matrix plasmon resonance spectral shifts for randomly oriented 42 nm gold bispheres with various separations are in satisfactory agreement with the experimental measurements by Reinhard et al (2005 Nano Lett. 5 2246), whereas the electrostatic dipole approximation gives too underestimated shifts.

Preparation and optical scattering characterization of gold nanorods and their application to a dot-immunogold assay

We describe optical monitoring of the synthesis of gold nanorods (NRs) based on seed-mediated growth in the presence of the soft surfactant template cetyltrimethyilammonium bromide. To separate NRs from spheres and surfactants we fractionated samples in the density gradient of glycerol. The optical properties of NRs were characterized by extinction and differential light-scattering spectra (at 90 degrees, 450-800 nm) and by the depolarization light-scattering ratio, I(vh)/I(vv), measured at 90 degrees with a helium-neon laser. Theoretical spectra and the I(vh)/I(vv) ratios were calculated by the T-matrix method as applied to randomly oriented NRs, which were modeled by right-circular cylinders with semispherical ends. The simulated data were fitted to experimental observations by use of particle length and width as adjustable parameters, which were close to the data yielded by transmission electron microscopy. The sensitivity of the long-wavelength resonance of NRs to the dielectric surroundings was examined both experimentally and theoretically by comparison of the extinction spectra of NRs in water and in a 25% glycerol solution. Finally, we discuss the application of NR-protein A conjugates to a dot-immunogold assay with the example of biospecific staining of human IgG molecules adsorbed onto small membrane spots.

Optical Properties and Biomedical Applications of Nanostructures Based on Gold and Silver Bioconjugates

We discuss optical properties of single and aggregated colloidal gold and silver conjugates that can be fabricated by adsorption of a biopolymer onto nanoparticle surfaces. We start with a discussion of two-layer and multilayer optical models for colloidal gold and silver nanoparticle conjugates that consist of a metal core and a polymer shell formed by recognizing and target molecules. The point at issue is the core-size optimization of conjugate-based nanosensors as elementary transducers of molecular binding events into optical signals. We present a detailed discussion of optical properties of various aggregated conjugate-based structures such as bispheres, linear chains, plane arrays on a rectangular lattice, compact and porous clusters embedded on a cubic body-centerd lattice, and random fractal aggregates. Our attention is focused on the following topics: (1) statistical and orientation averaging of optical observables; (2) dependence of extinction and scattering spectra on the optical binary coupling of conjugates; (3) optical effects related to the chain-like structures; (4) effects of polymer coating, interparticle spacing, and cluster structure; (5) simulation of kinetic changes in the optical properties of aggregated sols formed during biospecific binding. Finally, we discuss experimental data and biomedical applications of metal nanoparticles and their biospecific conjugates in various biomedical studies.

The linear dichroism and birefringence of colloidal dispersions: Approximate and exact approaches

The Mueller matrix elements for transmission by a dilute suspension of axially symmetric anisotropic particles with axially symmetric orientation are obtained in the single-scattering approximation. The optical properties of the particles are described by the classical Rayleigh and Rayleigh-Debye-Gans approximations, the Integral Equation Method (IEM) for the scattering tensor, and the exact (for materially isotropic particles) approach based on the T-matrix method (EBCM). The orientational distribution of particles is described by Boltzmanns function in terms of the Langevin-Debye orientational model. The dependence of dichroism and birefringence on particle size, shape, refractive index, and anisotropy of polarizability as well as on the degree of orientation is considered. The effect of particle parameters on the time-dependent orientational processes is considered with the decay ofdiehroism taken as an example. The spectral dependence of dichroism due to scattering of the Escherichia coli cells dispersed in water is measured experimentally. The theoretical calculation (EBCM) performed for the isotropie spheroid model is found to agree well with measurements.

Optical properties of gold spheroidal particles and nanoshells: Effect of the external dielectric medium

Dependence of optical properties of gold solid nanospheroids and spheroidal nanoshells on the dielectric environment has been studied in comparison with standard spherical models, i.e. with solid spheres and spherical nanoshells, respectively. The extinction and light scattering spectra were calculated using Mie theory, T-matrix, and the separation of variables methods. The sensitivity of plasmon resonance (PR) tuning to variations of the refractive index (n=1.3-l.7) was studied for particles with different equivolume size. In the case of nanoshells, the metal layer thickness was also varied. For nanoparticles with 15-nm equivolume diameter, the maximal PR shifts are observed in the case of spheroidal nanoshells and the calculated PR shifts decrease in the order: spheroidal nanoshells, solid spheroids, and spherical nanoshells. For particles with the 60-nm equivolume diameter, almost equal PR shifts are observed both for solid spheroids and spherical nanoshells, whereas the spheroidal nanoshells exhibit the maximal PR shifts. Other things being equal, the PR of silver nanoparticles is more sensitive to the dielectric environment as compared to the gold counterparts.

Plasmon resonances of silver and gold nanorods

We studied the extinction and integral scattering spectra of gold and silver nanorods with random or ordered orientations. The calculations were carried out for spheroids, right circular cylinders, circular cylinders with hemispherical ends (T-matrix method), and the rectangular prisms (Discrete Dipole Approximation, DDA). For particles with equivolume diameters greater than 20 nm, we have found a new resonance that is located between the usual plasmon resonances corresponding to the excitation of nanorods by the longitudinal or transversal electric fields. The new resonance can be excited only by TM incident wave, and its magnitude is maximal for orientation of the particle symmetry axis at 54° with respect to the light propagation direction. By contrast to the dominant scattering nature of the longitudinal resonance, the new resonance corresponds to the strong absorption comparable with scattering contribution to the total extinction. It is shown that the new resonance can be attributed to the quadrupole excitation of metal nanorods.

Relaxation optic phenomena in polydisperse suspensions and determination of particle sizes using transmitted light parameters

Abstract We discuss the physical mechanisms of orientational optic effects measured for polarized or unpolarized light transmitted through a densely packed or dilute particulate medium. The main attention is paid to particle size effects for transient linear dichroism, linear birefringence, and change in transmittance of dilute suspensions after an orienting field is switched off. A general integral equation is derived for relaxation of the transmitted light parameters for a polydisperse dilute suspension with axially symmetrical particles of arbitrary size and axial orientation distribution. Theoretically predicted non-exponential decay of the turbidimetric electrooptic effect is illustrated by an experimental example. We have also derived equations that define the average rotational diffusion coefficients and the average particle sizes calculated from the initial slope and the area of the relaxation curve, respectively. The dependence of relaxation curve on particle parameters (size, shape, refractive index, polydispersity) has been studied by using the T-matrix method and an isotropic spheroid model. For dichroism and birefringence, we have found that the dependence of the optical contribution to the integral equation kernel on the equivolume fraction size r can be described by power functions with exponents that are close to the Rayleigh exponents if r λ / π and decrease abruptly at r > λ / π . These exponents define the moments of particle size distribution to which the average diffusion constant and the average particle size correspond.

Anisotropic and spectral properties of biological scattering objects with the ordered particle orientation

Particle orientation in a disperse medium results both in anisotropic properties and in the changes in spectral transmittancy. To determine theoretically the effects of such kind a general approach based on the joint use of both the equation of Brownian rotation diffusion and the Mueller matrix for a thin slab of anisotropic medium has been developed. The optical properties of scatterers are described in terms of the first and second Born approximation and the exact T-matrix method. The goal of the investigations is to develop adequate optical models for interpretation of the experimental data obtained for the ordered disperse systems. In this paper, anisotropic properties of oriented disperse systems are discussed in a review manner, while the orientational turbidimetric effect is considered in detail.

Integral equation for light scattering problems: Application to the orientationally induced birefringence of colloidal dispersions

Abstract The exact integral equations for the amplitude matrix and the light scattering tensor for anisotropic particles of arbitrary shape are obtained. The birefringence theory based on the approximate solution of the exact equations for dispersions of axially oriented optically soft particles is developed. The numerical results for a spheroidal particle model are presented. The Peterline-Stuart (Rayleigh) type of model is shown to be in complete error when the particles approach the size of a wavelength. The connection of the developed theory to the modern theory of birefringence in polymer solutions is discussed.

ELECTROOPTIC EFFECTS IN DILUTE SUSPENSIONS OF BACTERIAL CELLS AND FRACTAL AGGREGATES

Abstract The relative change in optical density (orientational turbidimetric effect) of dilute suspensions of bacterial cells is studied theoretically and experimentally. Optical properties of bacterial cells are modeled by homogeneous spheroids using the T-matrix method. Calculated differential spectra of the steady-state turbidimetric effect, as well as its electric field dependence at fixed wavelengths, are shown to be in good agreement with experimental measurements for dilute suspensions of Escherichia coli and Bacillus polymyxa cells. The theoretically predicted unusual non-exponential decay of optical density (after removal of the orienting field) has been illustrated by an experimental electrooptical example. By using the Rayleigh–Debye–Gans approximation, we have also computed orientational effects for dilute suspensions of 3D-lattice ballistic and diffusion-limited fractal aggregates built from optically soft small spheres. We have found that the turbidimetric effect is determined solely by the gyration radius diffraction parameter and is essentially independent of the cluster mass. In terms of orientational effects, the effective structural anisotropy of the random fractal aggregates is close to the anisotropy of the homogeneous spheroidal model with the axial ratio 2 for small clusters and reduces to 1.5 for larger clusters.