# Optimization of Nonspherical Gold Nanoparticles for Photothermal Therapy
## 3 Results and Discussion  
To obtain the optimal size parameters, the values of the volume absorption coefficient \(\alpha_{abs}\) of the gold nanospheroid, nanocylinder, and nanorod were calculated at an excitation wavelength of 800 nm as a function of the aspect ratio and length (Figure 2). Clearly, all three particles exhibited a distinct peak corresponding to the maximum \(\alpha_{abs}\). Data obtained in this study indicate that the optimized nanospheroids with an aspect ratio of 3.7 and a length of 59 nm exhibited the best light absorption ability compared to that of the optimized nanocylinders and nanorods. The maximum \(\alpha_{abs}\) of a nanospheroid is 8.7% higher than that of a nanocylinder, and 9.7% higher than that of a nanorod. [PERSON] and [PERSON] [10] reported that the absorption efficiency of optimized nanorods was slightly higher than those of optimized nanospheroids and nanocylinders. Their results were inconsistent with the results of this study because of the different selections of objective function and processing of particle random orientation. To provide more comprehensive data for experimental workers, the optimized size parameters and the corresponding maximum volume absorption coefficients of gold nanospheroids, nanocylinders, and nanorods were computed at four typical excitation wavelengths (800, 808, 820, and 1064 nm) commonly used in PTT (Table 1). The results indicated that the light absorption ability of optimized nanoparticles could be enhanced by using lasers with longer wavelengths. The volume absorption coefficient of an optimized nanospheroid at a wavelength of 1064 nm was found to be 26.8% higher than that at 800 nm. The optimal size parameters of the gold nanoparticles became larger with the increase of the excitation wavelength. Gold nanoshells are the most commonly used nanoparticles in PTT. The light absorption ability of a hollow gold nanoshell, calculated by using the Mie theory of coated sphere [13; 14], was compared with that of a gold nanospheroid (Table 2). The maximum volume absorption coefficient of a gold nanospheroid was found to be three times that of a gold nanoshell at a wavelength of 800 nm. With an increase in the wavelength, the gap between the two nanoparticles became larger. In short, the optimized nanospheroids exhibited the best light absorption ability at all excitation wavelengths. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\lambda\) **(nm)** & **Shape** & \(R_{opt}\) & \(L_{opt}\) **(nm)** & \(\alpha_{abs,max}\) **(\(\mu\)m\({}^{-1}\))** \\ \hline \multirow{3}{*}{800} & nanospheroid & 3.7 & 59 & 348.7 \\  & nanocylinder & 3.1 & 47 & 320.7 \\  & nanorod & 3.5 & 52 & 317.8 \\ \hline \multirow{3}{*}{808} & nanospheroid & 3.7 & 66 & 352.1 \\  & nanocylinder & 3.1 & 52 & 324.9 \\  & nanorod & 3.5 & 58 & 322.9 \\ \hline \multirow{3}{*}{820} & nanospheroid & 3.8 & 68 & 359.0 \\  & nanocylinder & 3.2 & 53 & 332.2 \\  & nanorod & 3.6 & 59 & 330.0 \\ \hline \multirow{3}{*}{1064} & nanospheroid & 5.9 & 94 & 442.0 \\  & nanocylinder & 5.1 & 74 & 409.5 \\ \cline{1-1}  & nanorod & 5.4 & 84 & 407.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum volume absorption coefficients \(\alpha_{abs,max}\) and the corresponding optimal aspect ratio \(R_{opt}\) and optimal length \(L_{opt}\) of gold nanospheroid, nanocylinder, and nanorod at four typical excitation wavelengths (800, 808, 820, and 1064 nm). The refractive index of tissue is 1.44. Figure 2: Volume absorption coefficient \(\alpha_{abs}\) of gold (**a**) nanospheroid, (**b**) nanoclylinder, and (**c**) nanorod at an excitation wavelength of 800 nm as a function of the aspect ratio and length. The plus sign (+) is a point corresponding to the maximum \(\alpha_{abs}\), and the numbers in the brackets are the values of optimal aspect ratio, optimal length, and maximum \(\alpha_{abs}\), respectively. The refractive index of tissue is 1.44.