Gold Nanoparticles - Properties - Gold Nanorods' SPR vs. Aspect Ratio as a function of Diameter

We have used an experimental approach to determine the effect of gold nanorod diameter and length on the peak longitudinal Surface Plasmon Resonance.

After manufacturing over one thousand lots of gold nanorods from diameters as small as 6nm to lengths as long as 250nm, we have grouped our resultant data to some interesting results.

Background [1]

Gold nanorods (AuNRs) with diameters <25 nm typically show longitudinal dipole Surface Plasmon Resonance Wavelengths (SPR λ) that scale linearly with the aspect ratio almost independently of the actual diameter, thereby emphasizing the effect of the AuNR length. [2] This fact is routinely used in characterizing AuNRs based on their optical extinction spectra and agrees well with calculations using the quasi-static, i.e., dipole, approximation. [3, 4] On the other hand, the similarity to radio antennas has sparked considerable interest in using plasmonic AuNRs to concentrate and localize optical radiation thereby beating the diffraction limit of conventional optics. For such device applications, the AuNR length has to approach about half the wavelength of the light in order to act as a resonant antenna. [5, 6] For AuNRs with diameters of ∼80 nm but high aspect ratios (>10), the length remains the more important parameter. [7, 8] As the overall size increases in diameter > 25nm, however, the longitudinal dipole SPR λ starts to depend sensitively on the width as well. [9, 10] Phase retardation and dynamic depolarization effects [11, 12] become important, and a simple relationship between SPR λ and the aspect ratio therefore no longer applies. Numerical simulations accounting for the absolute dimensions of the AuNRs have predicted this departure from the quasi-static scaling of the longitudinal dipole SPR λ with aspect ratio. [13, 14]

Here we show this experimentally and in fact, according to our results, at diameters >50nm, the SPR max is dependent more on the diameter than on the width. Figures and Tables 1-4 show the resultant plots of Aspect Ratio vs. SPR for diameters 10nm, 25nm, 40nm, and 50nm respectively. Figure and Table 5 shows a plot of both slope and y-intercept for these curves as a function of diameter. This graph shows the dependence where at 50nm, the slope has decreased to a point where it is equal to the y-intercept showing the heightened dependence on diameter over aspect ratio.

 

Diameter (nm) Length (nm) Aspect Ratio (Length/Diameter) Longitudinal SPR (nm) Calculated SPR from AR Calculated AR from SPR
        (SPR-418)/96 (AR*96)+418
10 19 1.9 600 1.9 600
10 24 2.5 650 2.4 658
10 29 3 700 2.9 706
10 35 3.5 750 3.5 754
10 38 3.8 780 3.8 783
10 41 4.1 808 4.1 812
10 45 4.5 850 4.5 850
10 50 5 900 5 898
10 55 5.5 950 5.5 946
10 59 5.9 980 5.9 984
10 67 6.7 1064 6.7 1061
10 81 8.1 1200 8.1 1196
10 102 10.2 1400 10.2 1397
10 175 17.5 2100 17.5 2098

Figure and Table 1 showing Aspect Ratio vs. SPR for 10nm diameter gold nanorods of increasing length.

 

 

 

Diameter (nm) Length (nm) Aspect Ratio (Length/Diameter) Longitudinal SPR (nm) Calculated SPR from AR Calculated AR from SPR
        (SPR-418.4)/107.3 (AR*107.3)+418.4
25 34 1.36 550 1.23 564
25 57 2.28 600 1.69 663
25 71 2.84 650 2.16 723
25 75 3 700 2.62 740
25 85 3.4 750 3.09 783
25 87 3.48 780 3.37 792
25 90 3.6 808 3.63 805
25 93 3.72 850 4.02 818
25 96 3.84 900 4.49 830
25 102 4.08 950 4.95 856
25 119 4.76 980 5.23 929
25 137 5.48 1064 6.02 1006
25 245 9.8 1400 9.15 1470

Figure and Table 2 showing Aspect Ratio vs. SPR for 25nm diameter gold nanorods of increasing length

 

 

Diameter (nm) Length (nm) Aspect Ratio (Length/Diameter) Longitudinal SPR (nm) Calculated SPR from AR Calculated AR from SPR
        (SPR-380)/129.5 (AR*129.5)+380
40 60 1.5 550 1.31 574
40 68 1.7 600 1.7 600
40 80 2 650 2.08 639
40 92 2.3 700 2.47 678
40 112 2.8 750 2.86 743
40 124 3.1 780 3.09 781
40 134 3.35 808 3.31 814
40 148 3.7 850 3.63 859

Figure and Table 3 showing Aspect Ratio vs. SPR for 40nm diameter gold nanorods of increasing length

 

 

Diameter (nm) Length (nm) Aspect Ratio (Length/Diameter) Longitudinal SPR (nm) Calculated SPR from AR Calculated AR from SPR
        (SPR-223)/201.5 (AR*201.5)+223
50 100 2 600 1.87 626
50 110 2.2 700 2.37 666
50 145 2.9 800 2.86 807

Figure and Table 4 showing Aspect Ratio vs. SPR for 50nm diameter gold nanorods of increasing length

 

 

Diameter (nm) m b
10 96 418
25 107.3 418
40 129.5 380
50 201.5 223

Figure and Table 5 plotting slope and y-intercept values for each diameter shown in the previous plots.

 

References

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