Supporting Information

Transcription

1 This journal is The Owner Soieties 014 Supporting Information Extintion and Extra-High Depolarized Light Sattering Spetra of Gold Nanorods with Improved Purity: Diret and Inverse Problems Boris N. Khlebtsov, a,b Vitaly A. Khanadeev, a,b and Nikolai G. Khlebtsov a,b,* 1 Institute of Biohemistry and Physiology of Plants and Miroorganisms, Russian Aademy of Sienes, 13 Prospekt Entuziastov, Saratov , Russia Saratov State University, 83 Ulitsa Astrakhanskaya, Saratov 41006, Russia * Corresponding author: khlebtsov@ibppm.sgu.ru S1. Depolarization setup alibration Figure S1. Depolarization spetra of 137-, 140-, and 10-nm polystyrene latexes and of 114- and 160-nm silia nanospheres. 1 Beause of the small depolarization sattering from partiles, the erage ourse of the measured spetra gives an estimate of the instrumental error as a funtion of the welength

2 This journal is The Owner Soieties 014 Figure S. Osillating onvergene of the extended-preision T-matrix odes with an inrease in the T-matrix order. Calulations for randomly oriented GNRs with an erage length of 8.4 nm, an erage aspet ratio of 5.7 (log-normal distributions, σ r = 1.16 ), and hemispherial end-aps ( χ = 1). The perentage and radius of the impurity partiles are % and 16 nm, respetively. Extintions at 550 and 900 nm are normalized to the gold massvolume onentration g = 57 µg/ml, orresponding to the redution of 0.01% HAuCl 4. Figure S3. Extintion spetra of as-prepared GNR--0 rods (blue) and GNR- rods one week after preparation (green, TEM sample), as well as TEM-based T-matrix alulations (red). The FWHMs of GNR--0, GNR-, and the alulated spetra are 10, 140, and 156 nm, respetively. - -

3 This journal is The Owner Soieties 014 Figure S4. Overview images of GNR-1 nanorods with perentages of impurity partiles of 6.5 (a), 4.8 (b), (),.6 (d), 1.7 (e), and 1% (f). Eah image represents about partiles

4 This journal is The Owner Soieties 014 Figure S5. (a) Experimental (irles) and alulated (red and green) extintion spetra of Gem1-NRs. The T-matrix alulations are based on the erage geometrial TEM parameters of the rods: r = 3.6 ± 0.4, L = 43 ± 8 nm, and d = 1 ± nm. The hemispherial end-ap shape of Gem1-NRs with χ = 1 gives a slightly blue-shifted spetrum (the dashed green line, λ = 770 nm), whereas the end-ap parameter χ = 0.5 gives muh better agreement max between the alulated (red line) and the measured peak position ( λ max = 795 nm). The FWHMs for the measured and alulated spetra are 100 and 13 nm, respetively. (b) T- matrix alulations for Gem1-NRs-I and Gem1-NRs-II with the following TEM parameters: (I) r = 3.1± 0.4, L = 34 ± 7 nm, d = 10 ± nm (red) and (II) r = 4.1± 0.6, L = 4 ± 7 nm, d = 10 ± nm (blue). The hemispherial end-ap shape of Gem1-NRs with χ = 1 was used for the type II rods ( λ max = 840 nm), whereas the best-fitting χ = 0.5 was used for the type I rods to give λ max = 748 nm. Note that the alulated FWHMs (13 and 17 nm) for Gem1-NRs-I and Gem1-NRs-II are greater than the experimental ones (100 and 16 nm, respetively). For alulations, log-normal distributions for the aspet ratio and length of the rods were used with the orresponding standard deviations. The impurity partile fration was assumed to be as small as in the ase of GNR-1 rods. S6. Light sattering by small anisotropi partiles with random orientations In the general ase, the intensity of sattered light with a polarization vetor e s an be represented as the sum of three independent omponents orresponding to salar, symmetri, and antisymmetri ontributions, 3-4 -

5 This journal is The Owner Soieties 014 (0) ( s) ( a) * 1 * 1 ( a) I = I + I + I = G0 ee s 0 + Gs 1 s 0 s 0 I 0 1 s ee ee + 3 ee, (S1) 6 where e 0 defines the inident light polarization and G 0, G s, and G a are given by the expressions in Eq. (4). In the ase of a linearly polarized we, the polarization vetor e 0 is real and the sattered light is partially depolarized and an be deomposed into two inoherent omponents, one ( I ) polarized in the plane ( e, k ) and the other ( I ) polarized perpendiularly to the plane ( e, k ). In terms of the a and b onstants [see Eq. (4)], we he 3 o s = ee + I I0 a( 0 s ) b, I o o s = Ib. (S) For our sattering geometry, ( ee 0 s ) = 1 and = I / I = b/( a+ b), whih oinides with Eq. (3) at θ=90. In our previous paper 1, we derived the following expression for axially symmetri partiles: χ, α1 α = χ = 5 χ α + α 1. (S3) At first glane, Eq. (S3) looks somewhat different from the first expression in Eq. (10) of the main text: 3 = α + α 4+ 5 α α 1 1. (S4) To show the equivaleny of both expressions, we note that * * ( α α + α α ) = α + α α α (S5) and α + α = 3( α + α ) α α (S6) After substitution of these expressions into (S4), we he α1 α = = ( ) ( ) 4 5 α1 α + 3 α1 + α α1 α = = 5 α1 + α α1 α α α χ. 5 χ (S7) - 5 -

6 This journal is The Owner Soieties 014 This proves the equivalene of both expressions in Eq. (10). Referenes 1 B. N. Khlebtsov, V. A. Khanadeev, and N. G. Khlebtsov. Observation of extra-high depolarized light sattering spetra from gold nanorods. J. Phys. Chem. C, 008, 11, A. Guerrero-Martínez, J. Pérez-Juste, E. Carbó-Argibay, G. Tardajos, and L. M. Liz- Marzán. Gemini-surfatant-direted self-assembly of monodisperse gold nanorods into standing superlatties. Angew. Chem. Int. Ed., 009, 48, L. D. Landau, E. M. Lifshitz. Eletrodynamis of Continuous Media, Seond ed., Amsterdam: Elsevier Butterworth-Heinemann,