Wavelength and concentration-dependent optical constants of NaCl, KCl, MgCl2, CaCl2, and Na2SO4 multi-component mixed-salt solutions

C. C. Wang; J. Y. Tan; L. H. Liu

doi:10.1364/AO.56.007662

Applied Optics
Vol. 56,
Issue 27,
pp. 7662-7671
(2017)
•https://doi.org/10.1364/AO.56.007662

Wavelength and concentration-dependent optical constants of NaCl, KCl, MgCl₂, CaCl₂, and Na₂SO₄ multi-component mixed-salt solutions

C. C. Wang, J. Y. Tan, and L. H. Liu

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C. C. Wang, J. Y. Tan, and L. H. Liu, "Wavelength and concentration-dependent optical constants of NaCl, KCl, MgCl₂, CaCl₂, and Na₂SO₄ multi-component mixed-salt solutions," Appl. Opt. 56, 7662-7671 (2017)

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About this Article
History
- Original Manuscript: July 5, 2017
- Revised Manuscript: August 25, 2017
- Manuscript Accepted: August 25, 2017
- Published: September 19, 2017

Abstract

The optical constants of sodium chloride (NaCl), potassium chloride (KCl), magnesium chloride ( ${MgCl}_{2}$ ), calcium chloride ( ${CaCl}_{2}$ ) and sodium sulfate ( ${Na}_{2} {SO}_{4}$ ) solutions at weight fractions ranging from 0 to 16.6667% are measured by the combined ellipsometry-transmission method in the spectral range 0.3–1.0 μm. In the combined method, a modified ellipsometry method is used to measure the refractive indices of liquids, and then the transmission method is conducted to obtain the extinction coefficients using the refractive indices obtained by the ellipsometry method. The experimental refractive indices of these binary solutions are utilized to obtain a mole-fraction weighted mixing rule, which relates the refractive index of multi-component mixed-salt solutions to the wavelength and concentration of each component. The effects of wavelength and concentration are taken into account by empirical expressions of the Lorentz–Lorenz formulized molar refraction. A mole-fraction weighted linear combined mixing rule is proposed to study the wavelength and concentration-dependent extinction coefficients of mixed-salt solutions. The optical constants of NaCl-KCl and $NaCl - {Na}_{2} {SO}_{4}$ ternary solutions, $NaCl - KCl - {CaCl}_{2}$ quaternary solutions, and $NaCl - KCl - {MgCl}_{2} - {CaCl}_{2} - {Na}_{2} {SO}_{4}$ multi-component solutions are measured to verify the mixing rules. The results show that the optical constants calculated based on the mixing rules are in good agreement with experimental data, which demonstrate the feasibility of the proposed mixing rules. As the experimental analysis indicates, both the refractive indices and the extinction coefficients of the saline solutions increase with solute concentrations in the spectral range 0.3–1.0 μm.

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NaCl Solution ( $w %$ )	KCl Solution ( $w %$ )	${MgCl}_{2}$ Solution ( $w %$ )	${CaCl}_{2}$ Solution ( $w %$ )	${Na}_{2} {SO}_{4}$ Solution ( $w %$ )
2.4390	2.4390	2.4390	2.4390	2.4390
4.7619	4.7619	4.7619	4.7619	4.7619
9.0909	9.0909	9.0909	9.0909	9.0909
13.0435	13.0435	13.0435	13.0435	13.0435
16.6667	16.6667	16.6667	–	–

No.	NaCl	KCl	${MgCl}_{2}$	${CaCl}_{2}$	${Na}_{2} {SO}_{4}$
#1	2.3810%	2.3810%	0	0	0
	25 g/L	25 g/L
#2	4.5455%	4.5455%	0	0	0
	50 g/L	50 g/L
#3	8.3333%	8.3333%	0	0	0
	100 g/L	100 g/L
#4	2.3810%	0	0	0	2.3810%
	25 g/L				25 g/L
#5	4.5455%	0	0	0	4.5455%
	50 g/L				50 g/L
#6	8.3333%	0	0	0	8.3333%
	100 g/L				100 g/L
#7	2.3356%	2.3356%	0	2.3356%	0
	25 g/L	25 g/L		25 g/L
#8	4.3478%	4.3478%	0	4.3478%	0
	50 g/L	50 g/L		50 g/L
#9	7.6923%	7.6923%	0	7.6923%	0
	100 g/L	100 g/L		100 g/L
#10	2.2756%	0.0644%	0.2414%	0.1068%	0.3797%
	23.48 g/L	0.664 g/L	2.49 g/L	1.102 g/L	3.917 g/L

Method	Author (Year)	Path Length	Ref.
Differential path length transmission method	Sawyer (1931)	500 cm	[34]
Differential path length transmission method	Quickenden (1980)	5, 9 cm	[35]
Reflection method	Palmer (1974)	–	[36]
Split-pulse laser method	Ravisankar (1988)	–	[10]
Transmission method	Brewster (1992)	–	[37]
Transmission method	Litjens (1999)	150 cm	[38]
Transmission method	Otanicar(2009)	1 cm	[39]
ATR-transmission method	Bertie (1996)	–	[40]
Double optical path length transmission method	Li (2015)	10 cm	[33]

Solutions	$A_{1}$	$A_{2}$
NaCl	0.0069	$3.1 E - 05$
KCl	0.0066	$6.0 E - 05$
${MgCl}_{2}$	0.0071	$5.9 E - 05$
${CaCl}_{2}$	0.0078	$5.2 E - 05$
${Na}_{2} {SO}_{4}$	0.0083	$5.1 E - 05$

		$k = 0$	$k = 1$	$k = 2$	$k = 3$	$k = 4$	$k = 5$
NaCl	$C_{k 1}$	$1.61177 E + 02$	$- 1.11869 E + 03$	$3.12482 E + 03$	$- 4.16368 E + 03$	$2.70485 E + 03$	$- 6.91206 E + 02$
	$C_{k 2}$	$- 5.73797 E + 01$	$3.99505 E + 02$	$- 1.10760 E + 03$	$1.45873 E + 03$	$- 9.34691 E + 02$	$2.35173 E + 02$
	$C_{k 3}$	$7.96883 E + 00$	$- 5.55120 E + 01$	$1.53563 E + 02$	$- 2.01351 E + 02$	$1.28299 E + 02$	$- 3.20648 E + 01$
	$C_{k 4}$	$- 4.83640 E - 01$	$3.37069 E + 00$	$- 9.32058 E + 00$	$1.22016 E + 01$	$- 7.75772 E + 00$	$1.93336 E + 00$
	$C_{k 5}$	$1.06750 E - 02$	$- 7.44300 E - 02$	$2.05870 E - 01$	$- 2.69400 E - 01$	$1.71169 E - 01$	$- 4.26100 E - 02$
KCl	$C_{k 1}$	$2.97126 E + 01$	$- 1.73503 E + 02$	$6.11173 E + 02$	$- 9.88706 E + 02$	$7.61524 E + 02$	$- 2.26721 E + 02$
	$C_{k 2}$	$- 9.24078 E + 00$	$5.62517 E + 01$	$- 2.01763 E + 02$	$3.28319 E + 02$	$- 2.52846 E + 02$	$7.49670 E + 01$
	$C_{k 3}$	$1.27079 E + 00$	$- 7.90692 E + 00$	$2.83431 E + 01$	$- 4.59514 E + 01$	$3.51842 E + 01$	$- 1.03533 E + 01$
	$C_{k 4}$	$- 7.79600 E - 02$	$4.91571 E - 01$	$- 1.75583 E + 00$	$2.83440 E + 00$	$- 2.15895 E + 00$	$6.31362 E - 01$
	$C_{k 5}$	$1.74200 E - 03$	$- 1.10800 E - 02$	$3.94440 E - 02$	$- 6.34500 E - 02$	$4.81440 E - 02$	$- 1.40200 E - 02$
${MgCl}_{2}$	$C_{k 1}$	$7.02925 E + 01$	$- 3.99940 E + 02$	$1.25727 E + 03$	$- 1.89298 E + 03$	$1.38942 E + 03$	$- 3.99425 E + 02$
	$C_{k 2}$	$- 2.11503 E + 01$	$1.17958 E + 02$	$- 3.70477 E + 02$	$5.58219 E + 02$	$- 4.10699 E + 02$	$1.18352 E + 02$
	$C_{k 3}$	$2.74727 E + 00$	$- 1.50963 E + 01$	$4.73915 E + 01$	$- 7.14469 E + 01$	$5.26357 E + 01$	$- 1.51859 E + 01$
	$C_{k 4}$	$- 1.60140 E - 01$	$8.67814 E - 01$	$- 2.72068 E + 00$	$4.09897 E + 00$	$- 3.01970 E + 00$	$8.71224 E - 01$
	$C_{k 5}$	$3.42700 E - 03$	$- 1.83200 E - 02$	$5.73020 E - 02$	$- 8.62000 E - 02$	$6.34500 E - 02$	$- 1.82900 E - 02$
${CaCl}_{2}$	$C_{k 1}$	$6.73753 E + 01$	$- 3.97704 E + 02$	$1.21945 E + 03$	$- 1.80963 E + 03$	$1.32535 E + 03$	$- 3.84753 E + 02$
	$C_{k 2}$	$- 2.00483 E + 01$	$1.20529 E + 02$	$- 3.58489 E + 02$	$5.18897 E + 02$	$- 3.73226 E + 02$	$1.07088 E + 02$
	$C_{k 3}$	$2.20096 E + 00$	$- 1.34210 E + 01$	$3.93051 E + 01$	$- 5.60699 E + 01$	$3.98188 E + 01$	$- 1.13070 E + 01$
	$C_{k 4}$	$- 7.89100 E - 02$	$4.85663 E - 01$	$- 1.40952 E + 00$	$1.99168 E + 00$	$- 1.40139 E + 00$	$3.94656 E - 01$
${Na}_{2} {SO}_{4}$	$C_{k 1}$	$6.55165 E + 01$	$- 4.00799 E + 02$	$1.35551 E + 03$	$- 2.19206 E + 03$	$1.69063 E + 03$	$- 5.00408 E + 02$
	$C_{k 2}$	$- 2.49502 E + 01$	$1.62844 E + 02$	$- 5.32240 E + 02$	$8.43438 E + 02$	$- 6.44121 E + 02$	$1.89841 E + 02$
	$C_{k 3}$	$2.98412 E + 00$	$- 2.00105 E + 01$	$6.48699 E + 01$	$- 1.02288 E + 02$	$7.79459 E + 01$	$- 2.29610 E + 01$
	$C_{k 4}$	$- 1.10950 E - 01$	$7.54279 E - 01$	$- 2.43758 E + 00$	$3.83624 E + 00$	$- 2.92110 E + 00$	$8.60450 E - 01$

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Applied Optics