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Optical properties of colloidal particles : Silver colloidal particles evaporated in high vacuum on Formvar supporting film (a) (b) (c) - absorption spectrums, (b) - sizes distribution histogramms, (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. d , nm Dependence of maximum position in the distribution of 50 silver particles sizes upon maximum in an attenuation spectrum. (o) - for coated 40 particles, (x) - for ultra-thin sections of particles, immersed 30 in gelatin. Dotted lines correspond to boundary values for metallic 20 silver (derived from theoretical calculations): 420 nm on the 10 wavelength axis, and 2.2 nm on the diameter axis. 0 400 500 600 700 800 900 , nm Optical properties of colloidal particles : Investigation of absorption spectra of colloidal particles in different media d , nm 160 140 2 120 1 100 80 60 40 4 3 20 0 400 450 500 550 600 650 700 750 , nm Calculated dependencies of colloidal silver particles diameters upon the maximum of the absorption spectra in different media: 1 - H2O; 2 - gelatin; 3 - AgCl; 4 - AgBr Optical properties of colloidal particles : For arguments ρ and mρ , called as z: Task is D=f() coefficients of в absorption ka , z f+1 z2 Ψf(z) = ---------------- . -------- . (-----) k scattering ks , reflection kr: ka = kr - ks 1.3.….(2f+1) k=1 z f+1 (f+1) Theory G.Mie (1908) 2π ∞ ∞ k! 2 (-1)k z2 Ψf’(z) = ---------------- . -------- . (-----) k ka = -------- Im f(f+1).(-1)f.(af – bf) , ka2 (-1)k ∞ 1.3.....(2f+1) f=1 k=1 ∞ k! 1 . ----------------------(2f+3).….(2f+2k+1) 1 . f+2k+1 ------------------------- . ----------- 2 (2f+3).….(2f+2k+1) f+1 ρ = (2..a.na)/λ , i = (-1)1/2 (2f)! ζf(z) = if+1 . eiz . (-1)f . -------∞ f2.(f + 1)2 kr = -------- -------------. 2π k=1 (|af|2 – |bf|2) , ka2 f=1 2f + 1 where 2f + 1 ψf(ρ).ψf’(mρ) – m.ψf’(ρ).ψf(mρ) af = i2f+1 . --------- . ------------------------------------------f(f+1) ζf(ρ).ψf’(mρ) – m.ζf’(ρ).ψf(mρ) 2f + 1 ψf’(ρ).ψf(mρ) – m.ψf(ρ).ψf’(mρ) bf = (-1)2f+1 . --------- . ------------------------------------------f(f+1) ζf’(ρ).ψf(mρ) – m.ζf(ρ).ψf’(mρ) where ψ, ζ – Bessel functions. (2f)f.f! f ζf’(z) = ζf-1(z) - --- . ζf(z) z where ka = (2..na)/, m = (n – i)/na, For Ag particles with diameter 30 nm ka = kr We should know the spectral dependence of reflection coefficient n and absorption of metal, reflection coefficient of medium na and 2a –diameter of metal’s particles and wave length of light in vacuum . Optical properties of colloidal particles : n5(469) = n5(422) = 0,063 n15(614) = n15(433) = 0,060 n25(729) = n25(443) = 0,059 n25(828) = n35(454) = 0,057 5(469) = 5(422) = 2,156. 15(614) = 15(433) = 2,257 25(729) = 25(443) = 2,318 35(828) = 35(454) = 2,448 d, nm 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 5 15 25 35 massive 420 440 460 480 500 520 540 560 580 600 620 700 750 800 850 2,138/0,063 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 2,180/0,091 - 2,138/0,063 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 2,285/0,080 - 2,138/0,063 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 2,368/0,081 - 2,138/0,063 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 2,865/0,051 3.045/0,050 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 6 5 n, 4 Dependence of optical constants for silver – (absorption coefficient, full line) and n (refraction index, dotted line) upon the wavelength . 3 2 The curves, corresponding to massive samples – 1 in black; silver particles with diameter 5 nm – in yellow, 15 nm - in blue, 0 25 nm – in green, 35 nm - in red. n 300 400 500 600 700 800 , nm