Optimal Selection of Correlation Function Fitting Window in Bimodal Particle Size Inversion by Dynamic Light Scattering

Yuexin LIU; Wei LIU; Hongyan JIA; Jizhou CHEN; Yajin WANG; Jin SHEN

doi:10.3788/gzxb20235206.0629001

Journals >Acta Photonica Sinica >Volume 52 >Issue 6 >Page 0629001 > Article

Acta Photonica Sinica
Vol. 52, Issue 6, 0629001 (2023)

Optimal Selection of Correlation Function Fitting Window in Bimodal Particle Size Inversion by Dynamic Light Scattering

Yuexin LIU, Wei LIU^*, Hongyan JIA, Jizhou CHEN..., Yajin WANG and Jin SHEN|Show fewer author(s)

Author Affiliations

School of Electrical Engineering, Shandong University of Technology, Zibo 255049, China

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DOI: 10.3788/gzxb20235206.0629001 Cite this Article

Yuexin LIU, Wei LIU, Hongyan JIA, Jizhou CHEN, Yajin WANG, Jin SHEN. Optimal Selection of Correlation Function Fitting Window in Bimodal Particle Size Inversion by Dynamic Light Scattering[J]. Acta Photonica Sinica, 2023, 52(6): 0629001 Copy Citation Text

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Fig. 1. Example of sequential extraction of late exponentials method corresponding to bimodal particle systems

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Attenuation characteristics of the correlation function derived from the electric field correlation function Η(τ)

Fig. 2. Attenuation characteristics of the correlation function derived from the electric field correlation function

Η (τ)

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Fig. 3. Electric field correlation function and attenuation rate of correlation function for 140.9 nm equivalent mean particle size

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Fig. 4. Electric field correlation function and attenuation rate of correlation function for 70.6 nm equivalent mean particle size

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Fig. 5. Bimodal particle correlation function relative attenuation characteristics plots

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Fig. 6. Extraction results of 95 nm/285 nm bimodal correlation function by SELE method under the first fitting window

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Fig. 7. Extraction results of 95 nm/285 nm bimodal particle correlation function by SELE method under the second fitting window

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Fig. 8. H-RAC plots and reference points of bimodal particles for different equivalent mean particle sizes

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Fig. 9. Extraction results of 95 nm/285 nm bimodal correlation function by ACSELE method

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Fig. 10. Extraction results of 100 nm/400 nm bimodal correlation function by ACSELE method

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Fig. 11. ACSELE method for 60 nm/220 nm measured bimodal particle correlation function extraction results

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Fig. 12. ACSELE method for 65 nm/450 nm measured bimodal particle correlation function extraction results

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$D_{m e a n} /$ nm	$D_{m a x}$ / nm	$D_{m i n} /$ nm	$D_{1} /$ nm	$D_{2} /$ nm	$E_{d d 1} /$ %	$E_{d d 2} /$ %	$D_{p e a k 1} /$ nm	$D_{p e a k 2} /$ nm	$E_{p p 1} /$ %	$E_{p p 2} /$ %	$V_{r m s}$	Window1	Window2
140.9	285.0	95.0	134.8	4.5	52.6	95.2	187.3	3.5	34.2	96.3	0.104	3.63×10^-4：1.10×10^-3	4.25×10^-5：1.245×10^-4
			159.1	78.5	44.1	17.3	231.0	1000.0	18.9	95.2	0.122	6.20×10^-4：1.80×10^-3	1.45×10^-5：4.25×10^-5
			250.8	85.4	11.9	10.0	265.6	70.5	6.8	25.7	0.277	1.10×10^-3：5.30×10^-3	4.25×10^-5：3.63×10^-4
	400.0	100.0	365.0	94.1	8.7	5.8	376.4	75.6	5.8	24.3	0.306	1.10×10^-3：9.00×10^-3	1.45×10^-5：3.63×10^-4
			465.8	100.6	16.4	0.6	464.1	81.1	16.0	18.8	0.361	1.10×10^-3：1.54×10^-2	4.25×10^-5：3.63×10^-4
			404.9	99.1	1.2	0.8	432.8	93.2	8.2	6.7	0.524	1.80×10^-3：9.00×10^-3	1.245×10^-4：6.20×10^-6
	630.0	105.0	517.1	101.7	17.9	3.0	600.5	86.9	4.6	17.1	0.349	1.80×10^-3：9.00×10^-3	1.45×10^-5：3.63×10^-4
			570.6	108.5	9.4	3.3	705.4	86.9	11.9	17.1	0.380	3.10×10^-3：9.00×10^-3	4.25×10^-5：3.63×10^-4
			702.0	111.4	11.4	6.1	811.1	100.0	28.7	4.7	0.519	3.10×10^-3：1.71×10^-2	7.30×10^-5：5.57×10^-4
70.6	144.0	48.0	156.5	52.0	8.7	8.4	162.9	49.7	13.1	3.6	0.222	1.10×10^-3：3.10×10^-3	1.45×10^-5：3.63×10^-4
			95.6	42.8	33.6	10.7	114.9	32.7	20.1	31.7	0.213	3.63×10^-4：1.60×10^-3	4.25×10^-5：1.245×10^-4
			137.9	46.6	4.2	2.9	141.7	40.3	1.5	15.9	0.354	6.20×10^-4：3.10×10^-3	4.25×10^-5：2.125×10^-4
	200.0	50.0	180.3	50.5	9.8	1.0	215.4	46.4	7.7	7.1	0.459	1.10×10^-3：3.10×10^-3	1.45×10^-5：3.63×10^-4
			239.2	58.4	19.6	16.9	247.7	53.3	23.8	6.7	0.612	1.80×10^-3：4.70×10^-3	4.25×10^-5：4.04×10^-4
			221.2	54.0	10.6	8.0	231.0	46.4	15.5	7.1	0.458	1.10×10^-3：5.30×10^-3	7.30×10^-5：2.125×10^-4
	300.0	50.0	235.4	45.9	21.5	8.0	284.8	40.3	5.0	19.2	0.130	1.10×10^-3：3.10×10^-3	1.45×10^-5：2.125×10^-4
			289.5	48.6	3.4	2.6	327.4	46.4	9.1	7.1	0.066	1.80×10^-3：4.70×10^-3	4.25×10^-5：4.04×10^-4
			272.1	46.9	9.2	6.1	305.3	46.4	1.8	7.1	0.059	1.10×10^-3：5.30×10^-3	4.25×10^-5：3.63×10^-4

Table 1. Results of the simulated bimodal correlation function calculation using SELE method

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nm $D_{m e a n} /$	$D_{m a x} /$ nm	$D_{m i n} /$ nm	$T_{s}$ /s	$T_{e}$ /s	$Y_{s} /$ $(\times 10^{- 3})$	$Y_{e} /$ $(\times 10^{- 3})$	$Y_{m} /$ $(\times 10^{- 3})$	$R_{s}$ = $Y_{s}$ /Y_m	$R_{e}$ = $Y_{e}$ /Y_m
140.9	285.0	95.0	3.45×10^-5	1.00×10^-2	0.026 4	0.172	8.800	0.003 0	0.019
	400.0	100.0	2.80×10^-5	1.24×10^-2	0.040 6	0.296	11.900	0.003 4	0.024
	630.0	105.0	2.25×10^-5	1.91×10^-2	0.039 6	0.260	12.300	0.003 2	0.021
70.6	144.0	48.0	1.80×10^-5	6.50×10^-3	0.025 0	0.142	7.600	0.003 2	0.018
	200.0	50.0	2.25×10^-5	6.50×10^-3	0.033 6	0.253	11.200	0.003 0	0.022
	300.0	50.0	1.45×10^-5	9.00×10^-3	0.039 6	0.300	12.400	0.003 1	0.024

Table 2. Calculation of start and end point of fitting window of simulated bimodal correlation function

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nm $D_{m e a n} /$	$D_{m a x} /$ nm	$D_{m i n} /$ nm	$T_{s}$ /s	$T_{i}$ /s	$T_{e}$ /s	$D_{1} /$ nm	$D_{2} /$ nm	$E_{d d 1} /$ %	$E_{d d 2}$ /%	$D_{p e a k 1} /$ nm	$D_{p e a k 2} /$ nm	$E_{p p 2} /$ %	$E_{p p 1} /$ %	$V_{r m s}$
140.9	285.0	95.0	3.45×10^-5	1.20×10^-3	9.00×10^-3	285.6	95.0	0.2	2.5×10^-2	327.4	93.2	14.9	1.8	0.066
	400.0	100.0	2.80×10^-4	1.30×10^-3	1.12×10^-2	403.7	98.6	0.9	1.3	432.8	100.0	8.2	0.0	0.531
	630.0	105.0	2.25×10^-5	1.50×10^-3	1.91×10^-2	631.6	104.1	0.2	0.8	657.9	107.2	4.4	0.2	0.056
70.6	144.0	48.0	1.80×10^-5	6.20×10^-4	5.30×10^-3	146.7	51.4	1.9	7.2	162.9	49.7	13.1	3.6	0.043
	200.0	50.0	2.25×10^-5	6.20×10^-4	5.30×10^-3	198.9	49.1	0.5	1.6	200.9	49.7	0.4	0.4	0.548
	300.0	50.0	1.45×10^-5	7.68×10^-4	8.10×10^-3	300.7	47.4	0.2	5.0	305.3	49.7	1.8	0.4	0.043

Table 3. Results of the simulated bimodal correlation function calculation using the ACSELE method

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nm $D_{m a x} /$	$D_{m i n} /$ nm	Method	$T_{s}$ /s	$T_{i}$ /s	$T_{i 1}$ /s	$T_{e}$ /s	$D_{1} /$ nm	$D_{2} /$ nm	$E_{d d 1} /$ %	$E_{d d 2} /$ %	$D_{p e a k 1} /$ nm	$D_{p e a k 2} /$ nm	$E_{p p 1} /$ %	$E_{p p 2} /$ %	$V_{r m s}$
220	60	ACSELE	7.65×10^-5	8.29×10^-4	/	3.60×10^-3	217.4	62.8	1.1	4.6	215.4	56.4	2.0	5.9	0.110
220	60	SELE	4.45×10^-5	2.85×10^-4	1.00×10^-3	3.60×10^-3	227.1	63.7	3.2	6.3	213.3	50.3	3.0	16.1	1.023
450	65	ACSELE	5.65×10^-5	1.00×10^-3	/	3.10×10^-3	452	64.7	0.4	0.4	442.6	62.4	1.6	4.2	0.011
450	65	SELE	2.85×10^-5	3.81×10^-4	7.01×10^-4	3.30×10^-3	457.2	66.1	1.6	1.7	422.9	59.9	6.0	7.7	0.735

Table 4. Results of correlation function calculation for two groups of real bimodal particles using different methods

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