Researching | Particle Size Concentration of Monodisperse AuAg Alloy Nanospheres Retrieved by Light Extinction Method

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 7 >Page 0729001 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 7, 0729001 (2022)

Particle Size and Concentration of Monodisperse Au-Ag Alloy Nanospheres Retrieved by Light Extinction Method

Yuxia Zheng^1、2, Tuersun Paerhatijiang^1、2、*, Abulaiti Remilai^1、2, Dengpan Ma^1、2, and Long Cheng^1、2

Author Affiliations

¹School of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi , Xinjiang 830054, China

²Key Laboratory of Mineral Luminescent Material and Microstructure of Xinjiang, Urumqi , Xinjiang 830054, China

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DOI: 10.3788/LOP202259.0729001 Cite this Article Set citation alerts

Yuxia Zheng, Tuersun Paerhatijiang, Abulaiti Remilai, Dengpan Ma, Long Cheng. Particle Size and Concentration of Monodisperse Au-Ag Alloy Nanospheres Retrieved by Light Extinction Method[J]. Laser & Optoelectronics Progress, 2022, 59(7): 0729001 Copy Citation Text

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Abstract

Variation of light extinction properties of monodisperse Au-Ag alloy nanospheres with particle size and wavelength are analyzed based on Mie theory. In the theoretical calculations, the dielectric function of Au-Ag alloy nanoparticles is corrected for the effect of the reduced mean free path of the free electrons in metal nanoparticles. Three fitting equations for determining particle size and concentration methods based on the extinction properties are proposed in this paper, including resonance wavelength method, dual-wavelength extinction method, and improved dual-wavelength extinction method. The results show that as long as the extinction spectrum of the particles is measured, the particle size and concentration can be retrieved by using the fitting equations. In addition, comparing the sensitivity and the particle size range of three methods are found that the resonance wavelength method is easier and faster than other methods.

Keywords

Au-Ag alloy nanospheres light extinction method localized surface plasmon resonance Mie theory retrieval scattering

T = I_{t} / I_{i} = e x p (- τ L)

，（1）

τ = N C_{e x t} (λ, D, n_{p}, n_{m})

，（2）

\begin{array}{l} A = l o g_{10} (I_{i} / I_{t}) = l o g_{10} (1 / T) = \\ \frac{L N}{l n (10)} C_{e x t} (λ, D, n_{p}, n_{m}) \end{array}

。（3）

C_{e x t} = \frac{2 π}{k^{2}} \sum_{n = 1}^{\infty} (2 n + 1) R e (a_{n} + b_{n})

，（4）

ε (ω, x) = ε_{\infty} - \frac{[ω_{p} {(x)]}^{2}}{ω^{2} + i ω Γ_{p} (x)} + ε_{C P 1} [ω, ω_{01} (x), ω_{g 1} (x), Γ_{1} (x), A_{1} (x)] + ε_{C P 2} [ω, ω_{02} (x), Γ_{2} (x), A_{2} (x)]

，（5）

\begin{array}{l} ω_{p} (x) = x^{2} (2 ω_{p A u} - 4 ω_{p A u A g} + 2 ω_{p A g}) + \\ x (- ω_{p A u} + 4 ω_{p A u A g} - 3 ω_{p A g}) + ω_{p A g} \end{array}

，（6）

Γ_{p} = Γ_{p - B u l k} + α \frac{h v_{f}}{L_{e f f}}

，（7）

n_{m}^{2} = 1 + \frac{0.5684027565 λ^{2}}{λ^{2} - 0.005101829712} + \frac{0.1726177391 λ^{2}}{λ^{2} - 0.01821153936} + \frac{0.02086189578 λ^{2}}{λ^{2} - 0.02620722293} + \frac{0.1130748688 λ^{2}}{λ^{2} - 10.69792721}

，（8）

S = |Δ y / Δ D|

。（9）

λ_{r e s} (D) = λ_{0} + f_{1} D + f_{2} D^{2}

，（10）

D (λ_{r e s}) = \frac{- f_{1} + \sqrt[]{f_{1}^{2} - 4 f_{2} (λ_{0} - λ_{r e s})}}{2 f_{2}}

。（11）

N = \frac{l n (10) A (λ_{r e s})}{L C_{e x t} (λ_{r e s}, D, n_{p}, n_{m})}

。（12）

R_{λ_{1}, λ_{2}} = A_{λ_{1}} / A_{λ_{2}}

。（13）

\begin{array}{l} R_{450 n m, 600 n m} (D) = m_{0} + \frac{m_{3}}{m_{2} \sqrt[]{π / 2}} \times \\ e x p [- 2 {(\frac{D - m_{1}}{m_{2}})}^{2}], \end{array}

（14）

D (R_{450 n m, 600 n m}) = m_{1} + m_{2} \sqrt[]{- \frac{1}{2} l n [\frac{(R_{450 n m, 600 n m} - m_{0}) m_{2} \sqrt[]{π / 2}}{m_{3}}]} 。

（15）

N = \frac{l n (10) A (λ_{1})}{L C_{e x t} (λ_{1}, D, n_{p}, n_{m})} = \frac{l n (10) A (λ_{2})}{L C_{e x t} (λ_{2}, D, n_{p}, n_{m})}

。（16）

R_{λ_{r e s}, λ_{2}} = A_{λ_{r e s}} / A_{λ_{2}}

，（17）

\begin{array}{l} R_{λ_{r e s}^{}, 650 n m} (D) = R_{0} + \frac{R_{3}}{R_{2} \sqrt[]{\frac{π}{2}}} e x p [- 2 {(\frac{D - R_{1}}{R_{2}})}^{2}], \end{array}

（18）

D (R_{λ_{r e s}, 650 n m}) = R_{1} + R_{2} \sqrt[]{- \frac{1}{2} l n [\frac{(R_{λ_{r e s}, 650 n m} - R_{0}) R_{2} \sqrt[]{\frac{π}{2}}}{R_{3}}]}

。（19）

N = \frac{l n (10) A (λ_{r e s})}{L C_{e x t} (λ_{r e s}, D, n_{p}, n_{m})} = \frac{l n (10) A (λ_{2})}{L C_{e x t} (λ_{2}, D, n_{p}, n_{m})}

。（20）

λ_{r e s} (D) = λ_{1} + f_{3} D + f_{4} D^{2}

，（21）

D (λ_{r e s}) = \frac{- f_{3} + \sqrt[]{f_{3}^{2} - 4 f_{4} (λ_{1} - λ_{r e s})}}{2 f_{4}}

，（22）

N = \frac{l n (10) A (λ_{r e s})}{L C_{e x t} (λ_{r e s}, D, n_{p}, n_{m})}

。（23）

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Yuxia Zheng, Tuersun Paerhatijiang, Abulaiti Remilai, Dengpan Ma, Long Cheng. Particle Size and Concentration of Monodisperse Au-Ag Alloy Nanospheres Retrieved by Light Extinction Method[J]. Laser & Optoelectronics Progress, 2022, 59(7): 0729001

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