The ultraviolet–visible absorption spectra are given for 10 nm diameter colloidal particles of 52 of the metallic elements, calculated from the optical constants of the metals by means of Mie theory. For most of the elements the spectra cover the range 200–900 nm. Well resolved absorption bands are observed for colloidal Sc, Ti, V, Y, Cd, Eu, Yb, Hg and Th as well as for colloids of Cu, Ag, Au and the s-block metals. However, for the majority of the colloidal metallic elements in this size range there is only a continuous absorption in the visible range, rising to broad and poorly resolved absorption bands in the ultraviolet near 200 nm. The difference in the way that the spectra of colloidal particles of different metals change when the particle shape is varied from spherical to spheroidal is investigated systematically in the dipole approximation. This is achieved by means of contour plots of the absorbance cross-section for the particles vs. the real and imaginary parts of the dielectric function for the metals, and this method of investigation is extended also to hollow spherical particles. The results suggest that Ca, Sr, Ba, Eu, Yb, Th and possibly Sc, Ti, V and Y may merit experimental investigation as new metals for exhibiting surface-enhanced Raman scattering.

Ultraviolet–visible absorption spectra of the colloidal metallic elements

The extinction coefficient, albedo of single scattering, and differential scattering and polarization properties of water clouds and hazes in the visible and infrared have been computed using the complete Mie series. The results with three types of size distributions are presented and compared with observations. These show a strong dependence of angular intensity and polarization patterns on the size distribution, the size range, and the dielectric and absorbing properties of water droplets at each wavelength. A peculiarity of scattering at angles near 45°, observed experimentally and independently by two authors, is corroborated by the numerical results. Prominent observational features characteristic of natural fog, such as an extremely bright and narrow aureole, cloudbows, and glories, are reproduced in a model cloud of spherical water droplets, with a wide distribution in droplet radius and a maximum concentration at a 4-μ radius.

Scattering and Polarization Properties of Water Clouds and Hazes in the Visible and Infrared

In this work, we examine the formation mechanisms of nanoscale silver particles produced by the reduction of silver perchlorate with sodium borohydride. Evidence is presented that the reaction pathway does not follow classical nucleation and growth theory, but is dominated by colloidal interactions. Upon injection of silver into a sodium borohydride solution, a molecular species absorbing at 220 nm is produced in less than 1 s. We suggest that this species contains borohydride and small particles of reduced silver. The reaction mixture is initially dark as the result of the aggregation of the small silver particles into larger particles which have broad absorption spectra. During an “intermediate” stage, transmission electron microscopy and absorbance data show that even larger (∼6−10 nm) particles grow at the expense of the “monomeric” silver particles. Later in the reaction, electrochemical potential measurements show that the borohydride concentration suddenly decreases. Direct measurement of interpart...

Formation mechanisms and aggregation behavior of borohydride reduced silver particles

The treatment, initiated in Paper I [J. Math. Phys. 10, 82 (1969)], of the high‐frequency scattering of a scalar plane wave by a transparent sphere is continued. The main results here are an improved theory of the rainbow and a theory of the glory. The modified Watson transformation is applied to the third term of the Debye expansion of the scattering amplitude in terms of multiple reflections. Only the range 1<N<√2, where N is the refractive index, is considered. In the geometrical‐optic approximation, this term is associated with rays transmitted after one internal reflection, and there are three angular regions, corresponding to one ray, two rays, or no ray (shadow) passing through each direction. Together with transition regions, this leads to six different angular domains. In the 1‐ray and 2‐ray regions, geometrical‐optic terms are dominant. Correction terms corresponding to the 2nd‐order WKB approximation are also evaluated. In the 0‐ray region, the amplitude is dominated by complex rays and surface waves. The 1‐ray/2‐ray transition is a Fock‐type region. The rainbow appears in the 2‐ray/0‐ray transition region. The extension of the method of steepest descents due to Chester, Friedman and Ursell is applied. The result is a uniform asymptotic expansion for the scattering amplitude. It reduces to Airy's theory in the lowest‐order approximation, but its domain of validity is considerably greater, both with regard to size parameter and to angles. The glory is an example of strong ``Regge‐pole dominance'' of the near‐backward scattering amplitude. Van de Hulst's conjecture that surface waves are responsible for the glory is confirmed. However, besides surface waves taking two shortcuts through the sphere, higher‐order terms in the Debye expansion must also be taken into account. By considering also the effect of higher‐order surface‐wave contributions, all the features observed in the glory (apart from the polarization) are explained. Resonance effects associated with nearly‐closed paths of diffracted rays lead to large, rapid, quasiperiodic intensity fluctuations. The same effects are responsible for the ripple in the total cross‐section. Similar fluctuations appear in any direction, but their amplitude increases with the scattering angle, becoming a maximum near the backward direction, where they are dominant. They can also be interpreted as a collective effect due to many nearly‐resonant partial waves in the edge domain. The dominant surface‐wave contributions can also be summed to all orders for N < 1, leading to a renormalization of the propagation constants of surface waves.

High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory

In optical particle characterisation and aerosol science today light scattering simulations are regarded as an indispensable tool to develop new particle characterisation techniques or in solving inverse light scattering problems. Mie scattering and related computational methods have evolved rapidly during the past decade such that scattering computations for spherical scatterers a few order of magnitudes larger, than the incident wavelength can be easily performed. This significant progress has resulted from rapid advances in computational algorithms developed in this field and from improved computer hardware. In this chapter the history and a review of the recent progress of Mie scattering and Mie-related light scattering theories and available computational programs is presented. We will focus on Mie scattering theories but as there is much overlap to related scattering theories they will also be mentioned where appropriate. Short outlines of the various methods are given. This review is of course biased by my interest in optical particle characterisation and my daily reading.

Mie Theory: A Review

A new set of computations of the exact Mie functions, related to the scattering of electromagnetic waves on dielectric and partially absorbing spheres, is described. Numerical results with sufficient accuracy and detail in size and angular variation were obtained by means of the IBM-704 computer system for a set of complex indexes of refraction and size ranges mainly corresponding to atmospheric particles illuminated by visible and infrared radiation. The effects of increased absorption index on the extinction and absorption cross section, on the complex amplitude, and on the intensity and polarization of the scattered flux are illustrated by means of diagrams.

W. Viezee

Papers

Mie Scattering with Complex Index of Refraction