The calculated absorption, scattering, and extinction spectra of the surface plasmon band of gold nanorods have been shown in Figure (1). Figure (1) shows calculations for nanorods with a fixed aspectResults ratio R of 3.9 and effective radius reff =11.5, 18and 22nm. Thus the figure(1) shows that the plasmon maximumof the nanorods (corresponding to the mode with the electric field parallel to the long axis of the nanorod) lie in the desirable NIR region, thus making gold nanorods potentially useful forin vivo applications. figure(1D) comparsion between there extinctions (Qext) The magnitude of their NIR absorption and scattering C abs = 1.97 1014 m 2 and C sca = 1.07 1014 at max 762 nm for nanorods with reff =22 nm, R = 3.9 is comparable to that of the nanospheres at a much smaller size or volume A: spectra R eff=11.5nm
B: spectra R eff=18 nm
Q(ext) Q(abs) Q(sca)
Q(ext) Q(abs) Q(sca)
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where E loc ,i is the electric field at position ri due to the incident plane wave
Objectives E Loc (r j ) E 0 exp (i k . r j it )
A jl P l l j
and A ij Pj is the contribution to the electric field at position ri that is due to the dipole Pj at location ri , including retardation effects. Each element A ij is a 3 3 matrix defined by
A jl Pl
where N
A j 1
ij
exp (i k r jl ) r jl3 rij ri r j
{k 2 r
and
jl
(r jl P l )
k k
(1 i k r ij ) rjl2
. Defining Aii i 1 , reduces
Once Eq. (3.4) has been solved for the unknown polarizations Pi the extinction C ext ,absorption C abs , and scattering C sca cross sections may be evaluated from the optical theorem, thus giving 9 C ext
Qext
* Im{ E j,inc .P j }
j1
C ext R eff2
We used DDSCAt7.2 code 5to investigate optical properties of gold nanoparticles with different shapes
10-14 September 2012
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Figure 1: Calculated spectra of the efficiency of absorption Qabs (red triangles), scattering Qsca (black circles), and extinction Qext (green squares)for gold nanorods (a) with fixed aspect ratio R = 3.9 and reff =11.5, 18, and 22 nm B : Nanorod aspect (weight/diameter) 780
wavelenght max
wavelenght max
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Figure(2):(A) nanosphere diameter D. (B)nanorod aspect ratio R at fixed r ) 11.5 nm (and straight line fit).
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H/D
Dependence of the Plasmon Resonance Maximum on Nanoparticle Dimensions. Figure 1 summarizes the dependence of the nanoparticle plasmon resonance wavelength maximum ìmax on the nanoparticle dimensions. Figure (2A) shows the plot of max versus the nanosphere diameter D. With increase in the nanosphere diameter from 20nm to 100nm, there is a small redshift in the max Conclusions from 505nm to 530nm. Similar red-shift has been observed in the measured optical spectra of gold nanoparticles and is attributed to the effect of electromagnetic retardation in larger nanoparticles. Nevertheless, changing the diameter D of the nanospheres does not offersufficient change in the surface plasmon resonance maximum to be useful in the present applications. In the case of nanorods, the plasmon resonance maximum (corresponding to the mode with the electric field parallel to the nanorod axis) can be shifted by either a change in size or aspect ratio. Figure. 2D shows the change in nanorod ìmax by changing the effective radius (hence volume) of the nanorod at a fixed aspect ratio. From the point of view of imaging applications, size tunability of the resonance wavelength in gold nanoparticles would allow multicolor labeling of different cell structures, similar to that allowed by quantum dots with sizedependent fluorescence.
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the scattering problem to finding the polarizations Pj that satisfy a system of N inhomogeneous linear complex vector equations
N
R eff=11.5 R eff =18 R eff=22
[r jl Pl 3 r jl (r jl .P l )
Pj E loc ,i
4 k 2 E0
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A : Nanosphere diameter D(nm)
P j j E Loc (r j )
D:
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The DDA starts by replacing the solid particle (target) of interest by an array of N point dipoles of polarizability a i located at positions ri . Each dipole has an oscillating polarization in response to both an incident wave E loc ,i and the electric field due to all of the other N-1 dipoles in the array. The self– consistent solution for the dipole polarizations can be obtained as the solution to a set of N coupled complex vector equations of the form
C: spectra R eff=22 nm
Q (ext)
Gold nanoparticles have also been employed for many other applications such as immunoassay, protein assay6,time of fl ight secondary ion mass spectrometry, capillary electrophoresis (Tseng et al 2005), and detection of cancer cells7 (Kah et al 2007; Medley et Abstract al 2008). In one report, dynamic light scattering (DLS) enabled quantitative estimation of the concentration of intravenously injected gold nanoshells in mouse blood (Xie et al 2007). This technique may also be applicable towards estimating the circulation life time of other solid nanoparticles. The selection of nanoparticles for achieving efficient contrast for biological and cell imaging applications,as well as for photothermal therapeutic applications, is based on the optical properties of the nanoparticles. We use discrete dipole approximation (DDA) method to calculate absorption and scattering efficiencies and optical resonance wavelengths for three commonly used classes of nanoparticles: gold nanospheres, and gold nanorods. The calculated spectra clearly reflect the well-known dependence of nanoparticle optical properties viz. the resonance wavelength, the extinction cross-section, and the ratio of scattering to absorption, on the nanoparticle dimensions. A systematic quantitative study of the various trends is presented. By increasing the size of gold nanospheres from 20nm, 40nm and 100nm, the magnitude of extinction as well as the relative contribution of scattering to the extinction rapidly increases . Gold nanospheres in the size range commonly employed (40nm) show an absorption cross-section 5 orders higher than conventional absorbing dyes, while the magnitude of light scattering by 100nm gold nanospheres is 5 orders higher than the light emission from strongly fluorescing dyes. The variation in the plasmon wavelength maximum of nanospheres, i.e., from _520nm to 550 nm, is however too limited to be useful for in vivo applications. Additionally, their optical resonances lie favorably in the near-infrared region
To obtain a quantitative guide for selection of nanoparticles for light-scattering and absorption-based applications in biomedicine, a systematic study of the trends in the optical resonance wavelength, the extinction cross-section, and the relative contribution of scattering to the extinction with changes in the nanoparticle dimensions, was undertaken for two different classes of nanoparticles viz. gold nanospheres, and gold nanorods. It was clearly evident from the calculated spectra that the optical properties of nanoparticles were highly dependent on the nanoparticle size, shape, composition. All two nanoparticle types had optical cross-sections a few orders of magnitude higher than those of conventional dyes. For all two nanoparticle types, the increase in the size resulted in an increase in the extinction crosssection as well as the relative contribution of scattering. However, nanorods were found more favorable for in vivo applications due to their tunable optical resonance in the NIR region. Moreover, their relative scattering to absorption contribution could be easily tuned by a change in their dimensions. For the comparison of the optical properties of anoparticles across a range of sizes, size-normalized crosssections were calculated. From the numerical comparison, the gold nanorods are seen to offer the most superior NIR absorption and scattering at much smaller particle sizes. Smaller sized nanorods may also offer better cell uptake31 as compared to the nanospheres. This, in addition to the potential noncytotoxicity92 of the gold material, easy optical tunability, and facile synthesis, makes gold nanorods the most promising nanoparticle agents for use in biomedical imagingand photothermal therapy applications.
2nd Virtual Nanotechnology poster conference
Mh.Norouzi@aol.com
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