Depolarized Dynamic Light Scattering Method for Rod-Shaped Particle Measurement Based on Tikhonov Inversion

Fig. 3. Intensity autocorrelation function at different concentrations. (a) DKAU-3.2,VV; (b) DKAU-3.2,VH; (c) DKAU-6.0,VV; (d) DKAU-6.0,VH; (e) DKAU-15,VV; (f) DKAU-15,VH

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Fig. 4. Scattered light intensities of three samples. (a) DKAU-3.2; (b) DKAU-6.0; (c) DKAU-15

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Fig. 5. Intensity autocorrelation function of three samples. (a) DKAU-3.2; (b) DKAU-6.0; (c) DKAU-15

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Fig. 6. Electric field autocorrelation functions of three samples. (a) DKAU-3.2; (b) DKAU-6.0; (c) DKAU-15

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Fig. 7. Attenuation linewidth distribution inverted by Tikhonov. (a) To invert $g_{V H}^{(1)}$ ; (b) to invert $g_{V V}^{(1)}$

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Fig. 8. Electric field autocorrelation function fitted by Tikhonov method. (a) To fit $g_{V H}^{(1)}$ ; (b) to fit $g_{V V}^{(1)}$

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Fig. 9. Three-dimensional models of three gold nanorods. (a) DKAU-3.2; (b) DKAU-6.0; (c) DKAU-15

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Table 1. TEM measurement results
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Table 1. TEM measurement results
Number Sample model Nominal value /（nm×nm） TEM measurement value /（nm×nm）
1 DKAU-3.2 80×25 88×31
2 DKAU-6.0 78×13 82×12
3 DKAU-15 300×20 247×21

Table 2. Single measurement results of three samples

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Table 2. Single measurement results of three samples

Sample model	$α_{V H}$	$α_{V V}$	$Γ_{t}$ /kHz	$Γ_{r}$ /kHz	$D_{t}$ /10^-12（m²/s）	$D_{r}$ /s^-1	$p$	$L$ /nm	$D$ /nm
DKAU-3.2	0.55	0.11	3.52	16.85	7.14	2808.9	2.49	98.6	39.6
DKAU-6.0	0.44	0.24	5.17	35.29	10.47	5881.6	4.88	94.1	19.3
DKAU-15	0.29	0.17	2.31	2.18	4.67	363.6	9.20	271.9	29.6

Table 3. Measurement and correction results of gold nanorods

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Table 3. Measurement and correction results of gold nanorods

Sample model	TEM measurement value		Regularized fitting result		Correction result		Relative error		PI
Sample model	L /nm	D /nm	L /nm	D /nm	L /nm	D /nm	$δ_{L}$ /%	$δ_{D}$ /%	PI
DKAU-3.2	88.1±7.7	31.3±3.4	99.5±3.9	39.0±2.6	93.5±3.9	33.0±2.6	6.1	5.4	0.18
DKAU-6.0	81.8±10.4	12.5±1.5	93.9±1.9	19.2±1.6	87.9±1.9	13.2±1.6	7.4	5.6	0.20
DKAU-15	247.4±64.5	21.4±3.7	272.6±6.0	29.0±3.5	266.6±6.0	23.0±3.5	7.8	7.5	0.36

Table 4. Exponential fitting results with different initial values

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Table 4. Exponential fitting results with different initial values

Sample model	Initial value				L /nm	D /nm
Sample model	A	$Γ_{t}$	B	$Γ_{m i x}$	L /nm	D /nm
DKAU-3.2	0.9	1000	0.1	1000	74.3	158.2
	0.9	1000	0.1	10000	68.3	64.4
	0.9	3500	0.1	20000	101.2	38.0
DKAU-6.0	0.9	1000	0.1	1000	62.5	142.0
	0.9	1000	0.1	3000	70.6	220.7
	0.9	2000	0.1	20000	98.4	17.9
DKAU-15	0.9	1000	0.1	1000	116.4	187.8
	0.9	1000	0.1	10000	123.6	121.2
	0.9	2000	0.1	5000	273.1	31.2

Table 5. Exponential fitting results and correction results

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Table 5. Exponential fitting results and correction results

Sample model	Exponential fitting result		Correction result		Relative error
Sample model	L /nm	D /nm	L /nm	D /nm	$δ_{L}$ /%	$δ_{D}$ /%
DKAU-3.2	101.5±3.8	37.7±2.8	95.5±3.8	31.7±2.8	8.4	1.3
DKAU-6.0	95.3±1.8	19.6±1.0	89.3±1.8	13.6±1.0	9.1	8.8
DKAU-15	271.1±6.2	28.7±2.8	265.1±6.2	22.7±2.8	7.2	6.1

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Xiuwen Yin, Wei Liu, Huayu Qi, Yajing Wang, Fuyuan Qin. Depolarized Dynamic Light Scattering Method for Rod-Shaped Particle Measurement Based on Tikhonov Inversion[J]. Acta Optica Sinica, 2024, 44(4): 0412002

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