An Optimal Expression for Henry Function for the Calculation of Zeta Potential

Fuyuan Qin; Wei Liu; Wenjing Wang; C. Thomas John; Yajing Wang; Jin Shen

doi:10.3788/AOS201737.1029003

Journals >Acta Optica Sinica >Volume 37 >Issue 10 >Page 1029003 > Article

Acta Optica Sinica
Vol. 37, Issue 10, 1029003 (2017)

An Optimal Expression for Henry Function for the Calculation of Zeta Potential

Fuyuan Qin¹, Wei Liu^1、*, Wenjing Wang¹, C. Thomas John^1、2, Yajing Wang¹, and Jin Shen¹

Author Affiliations

¹ College of Electrical and Electronic Engineering, Shandong University of Technology, Zibo, Shandong 255049, China

² Group Scientific Pty Ltd., Grange, South Australia 5022, Australia

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DOI: 10.3788/AOS201737.1029003 Cite this Article Set citation alerts

Fuyuan Qin, Wei Liu, Wenjing Wang, C. Thomas John, Yajing Wang, Jin Shen. An Optimal Expression for Henry Function for the Calculation of Zeta Potential[J]. Acta Optica Sinica, 2017, 37(10): 1029003 Copy Citation Text

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Fig. 1. Curves obtained by different Henry functions

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Fig. 2. ka curves for spherical particles of different concentrations and different types of electrolyte

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Fig. 3. Schematic of the electrophoretic light scattering experiment setup

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ka	Wiersema	Ohshima		Optimization
ka	f(ka)	f(ka)	Error /%	f(ka)	Error /%
0.01	1.000	1.000	0	1.000	0
0.1	1.000	1.001	0.1	1.000	0
0.2	1.000	1.003	0.3	1.001	0.1
0.5	1.000	1.014	1.4	1.005	0.5
1	1.009	1.034	2.5	1.015	0.6
2	1.040	1.064	2.3	1.038	0.2
5	1.134	1.150	1.4	1.118	1.4
10	1.220	1.256	3.0	1.222	0.2
20	1.325	1.351	2.0	1.324	0.08
50	1.418	1.432	1.0	1.417	0.07
100	1.450	1.464	1.0	1.456	0.5
200	1.470	1.482	0.8	1.477	0.5
500	1.490	1.493	0.2	1.491	0.07
1000	1.500	1.496	0.3	1.495	0.3

Table 1. Comparison of the errors of different Henry functions

Type of electrolyte	Ionic strength
1∶1	I= $\begin{matrix} \frac{1}{2} \end{matrix}$ (c×1²+c×1²)=c
1∶2 or 2∶1	I= $\begin{matrix} \frac{1}{2} \end{matrix}$ (2×c×1²+c×2²)=3c
2∶2	I= $\begin{matrix} \frac{1}{2} \end{matrix}$ (c×2²+c×2²)=4c
1∶3 or 3∶1	I= $\begin{matrix} \frac{1}{2} \end{matrix}$ (3×c×1²+c×3²)=6c
3∶3	I= $\begin{matrix} \frac{1}{2} \end{matrix}$ (c×3²+c×3²)=9c
2∶3 or 3∶2	I= $\begin{matrix} \frac{1}{2} \end{matrix}$ (3×c×2²+2×c×3²)=15c

Table 2. Expressions of ionic strength for different types of electrolyte

Type of electrolyte	Double layer thickness /nm
Type of electrolyte	10^-7 mol·L^-1	10^-6 mol·L^-1	10^-5 mol·L^-1	10^-4 mol·L^-1	10^-3 mol·L^-1	10^-2 mol·L^-1	10^-1 mol·L^-1
1∶1	962	304	96.2	30.4	9.62	3.04	0.962
1∶2 or 2∶1	555	176	55.5	17.6	5.55	1.76	0.555
2∶2	481	152	48.1	15.2	4.81	1.52	0.481
1∶3 or 3∶1	393	124	39.3	12.4	3.93	1.24	0.393
3∶3	321	101	32.1	10.1	3.21	1.01	0.321
2∶3 or 3∶2	248	78.5	24.8	7.85	2.48	0.785	0.248

Table 3. Double layer thickness of different concentrations and different types of electrolyte

Parameter	Sample 1	Sample 2	Sample 3	Sample 4
a /nm	101.5	101.5	101.5	101.5
1/k /nm	0.962	3.04	9.62	962
ka	105.51	33.388	10.551	0.1055
f(ka)₀	1.4528	1.3961	1.2267	1.0000
f(ka)₁	1.4661	1.4026	1.2642	1.0006
f(ka)₂	1.4583	1.3827	1.2303	1.0001

Table 4. Henry function for the samples to be measured

No.	Sample 1				Sample 2				Sample 3				Sample 4
No.	μ	ζ₀	ζ₁	ζ₂	μ	ζ₀	ζ₁	ζ₂	μ	ζ₀	ζ₁	ζ₂	μ	ζ₀	ζ₁	ζ₂
1	-2.992	-39.4	-39.0	-39.2	-4.284	-58.8	-58.3	-59.2	-5.590	-87.3	-84.5	-86.8	-3.316	-64.1	-63.7	-64.1
2	-3.085	-40.6	-40.2	-40.4	-4.165	-57.1	-56.7	-57.5	-5.533	-86.4	-83.6	-85.9	-3.345	-64.7	-64.3	-64.6
3	-2.895	-38.2	-37.7	-37.9	-4.140	-56.8	-56.4	-57.2	-5.567	-86.9	-84.1	-86.4	-3.368	-65.1	-64.7	-65.1
4	-2.930	-38.6	-38.2	-38.4	-4.222	-58.0	-57.5	-58.3	-5.392	-84.2	-81.5	-83.7	-3.409	-65.9	-65.5	-65.9
5	-3.063	-40.4	-39.9	-40.1	-4.133	-56.7	-56.3	-57.1	-5.388	-84.1	-81.4	-83.6	-3.399	-65.7	-65.3	-65.7
6	-2.984	-39.3	-38.9	-39.1	-4.312	-59.1	-58.7	-59.6	-5.546	-86.6	-83.8	-86.1	-3.434	-66.4	-66.0	-66.3
Average	-2.992	-39.4	-39.0	-39.2	-4.209	-57.8	-57.3	-58.2	-5.503	-85.9	-83.2	-85.4	-3.379	-65.3	-64.9	-65.3
Relative error /%	-	-	1.0	0.5	-	-	0.9	0.7	-	-	3.1	0.6	-	-	0.5	0
Repeatability /%	-	-	2.5	2.4	-	-	1.8	1.8	-	-	1.6	1.6	-	-	1.3	1.3

Table 5. Comparison of Zeta potentials calculated by different Henry functions

Fuyuan Qin, Wei Liu, Wenjing Wang, C. Thomas John, Yajing Wang, Jin Shen. An Optimal Expression for Henry Function for the Calculation of Zeta Potential[J]. Acta Optica Sinica, 2017, 37(10): 1029003

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