Optical properties of colloidal particles : Silver colloidal particles evaporated in high vacuum on Formvar supporting film (a)- absorption spectrums, (b)(b) - sizes distribution histogramms, (c)(c) - electron microscopic photos of three typical layers

Optical properties of colloidal particles : It is established that colloidal particles of silver with the size less than 3 nm in a diameter lose metallic properties, silver becomes dielectric. Dependence of maximum position in the distribution of silver particles sizes upon maximum in an attenuation spectrum. ( o ) - for coated particles, ( x ) - for ultra-thin sections of particles, immersed in gelatin. Dotted lines correspond to boundary values for metallic silver (derived from theoretical calculations): 420 nm on the wavelength axis, and 2.2 nm on the diameter axis.

Optical properties of colloidal particles : Investigation of absorption spectra of colloidal particles in different media Calculated dependencies of colloidal silver particles diameters upon the maximum of the absorption spectra in different media: 1 - H 2 O; 2 - gelatin; 3 - AgCl; 4 - AgBr

Optical properties of colloidal particles : Task is D=f( ) coefficients of в absorption k a, scattering k s, reflection k r : k a = k r - k s Theory G.Mie (1908) 2π k a = Im f(f+1). (-1) f. (a f – b f ), k a 2 f=1 2π f 2. (f + 1) 2 k r = (|a f | 2 – |b f | 2 ), k a 2 f=1 2f + 1 where 2f + 1 ψ f (ρ).ψ f (mρ) – m. ψ f (ρ). ψ f (mρ) a f = i 2f f(f+1) ζ f (ρ). ψ f (mρ) – m. ζ f (ρ). ψ f (mρ) 2f + 1 ψ f (ρ). ψ f (mρ) – m. ψ f (ρ). ψ f (mρ) b f = (-1) 2f f(f+1) ζ f (ρ). ψ f (mρ) – m. ζ f (ρ). ψ f (mρ) where ψ, ζ – Bessel functions. For arguments ρ and mρ, called as z: z f+1 (-1) k z 2 1 Ψ f (z) = (-----) k …. (2f+1) k=1 k! 2 (2f+3). …. (2f+2k+1) z f+1 (f+1) (-1) k z 2 1 f+2k+1 Ψ f (z) = (-----) k (2f+1) k=1 k! 2 (2f+3). …. (2f+2k+1) f+1 (2f)! ζ f (z) = i f+1. e iz. (-1) f k=1 (2f) f. f! f ζ f (z) = ζ f-1 (z) ζ f (z) z where k a = (2.. n a )/, m = (n – i )/n a, ρ = (2.. a. n a )/λ, i = (-1) 1/2 For Ag particles with diameter 30 nm k a = k r We should know the spectral dependence of reflection coefficient n and absorption of metal, reflection coefficient of medium n a and 2a –diameter of metals particles and wave length of light in vacuum.

Optical properties of colloidal particles : n 5 (469) = n 5 (422) = 0,063 5 (469) = 5 (422) = 2,156. n 15 (614) = n 15 (433) = 0, (614) = 15 (433) = 2,257 n 25 (729) = n 25 (443) = 0, (729) = 25 (443) = 2,318 n 25 (828) = n 35 (454) = 0, (828) = 35 (454) = 2,448 Correction of optical constants of silver Dependencies of colloidal silver particles diameters upon the maximum of the absorption spectra : 1 – theoretical calculated and 2 – experimental produced dependences Lines correspond to particles with diameters 5, 15, 25 and 35 nm., nm d, nm massive ,138/0,063 2,146/0,063 2,153/0,064 2,159/0,064 2,165/0,066 2,169/0,068 2,173/0,072 2,176/0,075 2,178/0,080 2,179/0,085 2,180/0, ,138/0,063 2,154/0,060 2,169/0,057 2,183/0,055 2,197/0,054 2,201/0,053 2,222/0,054 2,232/0,054 2,242/0,056 2,251/0,058 2,269/0,061 2,285/0, ,138/0,063 2,156/0,058 2,176/0,053 2,196/0,049 2,212/0,046 2,228/0,044 2,244/0,042 2,259/0,041 2,272/0,040 2,285/0,041 2,300/0,042 2,338/0,052 2,355/0,065 2,368/0, ,138/0,063 2,161/0,056 2,184/0,050 2,206/0,044 2,226/0,039 2,247/0,035 2,266/0,032 2,284/0,029 2,302/0,027 2,318/0,025 2,334/0,024 2,399/0,028 2,416/0,036 2,438/0,048 2,454/0,065 2,138/0,063 2,321/0,059 2,503/0,056 2,685/0,053 2,865/0, /0,050 3,224/0,049 3,401/0,049 3,579/0,050 3,756/0,052 3,931/0,054 4,624/0,069 5,051/0,085 5,472/0,104 5,887/0,128

Optical properties of colloidal particles : Correction of the optical constants of small silver particles, which are strongly differ from properties of massive silver Dependence of optical constants for silver – (absorption coefficient, full line) and n (refraction index, dotted line) upon the wavelength. The curves, corresponding to massive samples – in black; silver particles with diameter 5 nm – in yellow, 15 nm - in blue, 25 nm – in green, 35 nm - in red.