spectroscopic techniques
Optical Properties of Sodium Chloride Solution Within the Spectral Range from 300 to 2500 nm at Room Temperature Xingcan Li,a Linhua Liu,a,b,* Junming Zhao,a Jianyu Tanb,* a b
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China School of Automobile Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, China
The optical properties of sodium chloride (NaCl) solution were experimentally determined by double optical pathlength transmission method in the spectral range from 300 to 2500 nm at the NaCl concentration range from 0 to 360 g/L. The results show that the refractive index of NaCl solution increases with NaCl concentrations and correlates nonlinearly with the concentration of NaCl solution. The absorption index of NaCl solution increases with NaCl concentrations in the visible spectral range of 300–700 nm, but varies little in the near-infrared spectral range of 700–2500 nm at room temperature. For the sake of applications, the fitted formulae of the refractive index and absorption index of NaCl solution as a function of wavelength and NaCl concentration are presented. Index Headings: Optical properties; Sodium chloride solution; Transmission measurement; Solar irradiation.
INTRODUCTION Solar energy is the basic resource for solar thermal technologies.1 A salt gradient solar pond can directly collect and convert solar energy into thermal power and store thermal energy longer than other solar thermal storage systems.2 A solar pond is a solar collector with a certain quantity of salt in the water; the layers of salt solution increase in concentration with depth, varying from a rather low concentration on the surface to a concentration close to saturation at the deepest depths. The storage performance of the solar pond is based on the separation of the upper cool freshwater from the underside hot saline water by a natural diffusive interface that prevents the upward loss of the accumulated heat from the bottom layer.3 An evaluation of the dependence of optical constants of sodium chloride (NaCl) solution on NaCl concentration and wavelength will aid in calculating and analyzing the solar irradiation distribution in the solar pond or natural seawater. As a basic optical property, the optical constants of NaCl solution also have important applications in physics, chemistry, and atmospheric aerosol science.4,5 Received 16 October 2014; accepted 8 December 2014. * Author to whom correspondence should be sent. E-mail: lhliu@hit. edu.cn. DOI: 10.1366/14-07769R
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Several experiments have been performed to obtain the optical constants of NaCl solution. Yunus6 reported the variation in the refractive index with temperature and investigated the optical absorption of NaCl solution at a wavelength of 632.8 nm with a NaCl concentration of 14.6 g/L. The results indicated that the variation in the refractive index of NaCl solution with temperature is ,0.0001/8C. Pegau et al.7 measured the absorption coefficient of pure water and saltwater in the visible and near-infrared spectrum (412–975 nm) using absorption and attenuation meters. In their work, the water temperature varied from 15 and 30 8C, and the salinity varied from 0 and 3.8%. The results shown that the absorption index was relatively insensitive to temperature in the visible region, and the variation of the absorption index of NaCl solution with temperature was found to be ,6 3 1011/ 8C. Tang4 and Tang et al.5 reported the thermodynamic and light-scattering properties of aqueous solution containing NaCl and other sea salt particles over a wide concentration range up to supersaturation (46 wt% of total solute) at 632.8 nm. In addition, Yunus,8 Singh et al.,9 Ravisankar et al.,10 and Dair et al.11 also have reported the refractive index of NaCl solution within the concentration range 0240 g/L and wavelength range 193632.8 nm. However, there are few studies on the optical constants of NaCl solution with high concentration and wide bandwidth of light. The aim of this work is to obtain the optical constants of NaCl solution with NaCl concentration from zero to saturation. Based on the measured transmissions at two different optical pathlengths, an inverse identification model using a ray tracing approach is proposed, which is more suitable to obtain the optical constants of liquid. The optical constants of NaCl solution with NaCl concentration from zero to saturation over the spectral range from 300 to 2500 nm were measured and analyzed.
EXPERIMENTAL Double Optical Pathlength Transmission Method (DOPTM). Many experimental methods have been implemented to obtain the optical constants of liquid.12–15 These methods can be classified into the transmission method, the Kramers–Kronig transform method, and the ellipsom-
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FIG. 1.
Schematic diagram of DOPTM.
etry method. The Kramers–Kronig transform method requires experimental measurement over a wide spectral range to ensure scientific accuracy.16–18 Although the ellipsometry method is very convenient to obtain the refractive index n, some limitations will be introduced into acquiring the absorption index k of transparent materials that absorb less of the incident light. For example, there is considerable difficulty in the characterization of low absorption coefficients (a , 100 cm1) using the ellipsometry method.19 In this work, the absorption coefficient of NaCl solution is small (a , 25 cm1) in the spectral band of interest, and the transmission method is more suitable than the ellipsometry to obtain the k value of liquid with reasonable accuracy by changing the optical pathlength of the measured liquid. In this work, a DOPTM is implemented to obtain the optical constants of NaCl solution. Figure 1 shows the schematic of DOPTM, where light transmits through a three-layer (glass–liquid–glass) system with multiple reflections. Layer 2 is NaCl solution. Layers 1 and 3 are made of the same glass that comprises the cuvette (containing by weight 95% or more of silica) and n1 þ ik1 = n3 þ ik3. The optical constants of the glass of the cuvette were directly measured using ellipsometry with the V–VASE ellipsometer produced by J.A. Woollam Company. The measurement data with uncertainty are shown in Fig. 2. The transmittance (Tk and Tk0 ) of this three-layer system with two different liquid layer thicknesses (L2 and L20 ) can be formally expressed as follows: Tk ¼ f ðn1 ; n2 ; n3 ; k1 ; k2 ; k3 ; L1 ; L2 ; L3 Þ
ð1Þ
Tk0 ¼ f ðn1 ; n2 ; n3 ; k1 ; k2 ; k3 ; L1 ; L20 ; L3 Þ
ð2Þ
where n1 þ ik1 is the complex refractive index of the medium; the subscript 1, 2, and 3 denote the left glass, the measured liquid, and the right glass, respectively. L1 is the thickness of the left glass, and L3 is the thickness of the right glass. In principle, with the known complex refractive index (n1þ ik1 = n3þ ik3) and thickness (L1 = L3) of glass layers, the complex refractive index (n2 þ ik2) of the measured liquid can be determine by measuring the transmittances Tk and Tk0 of the systems with two different liquid thicknesses (L2 and L20 ). Double optical pathlength transmission method has been widely used to obtain the optical constants of liquid. Large et al.20 described formulations for evaluating the reflectance and transmittance of optical media that
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FIG. 2. Optical constants of the glass of cuvette used in this study measured using an ellipsometer.
consists of discrete layers. The model is based on discrete elements consisting of multiple reflections, all forward- and backward-traveling fluxes combined into a single flux. This model operates under the one-dimensional approximation, and there is one vacuum interspace between two discrete elements. For this reason, the model of Large et al.20 is widely applied to medium consisting of solid slide stack. Otanicar et al.21 proposed a method to iteratively calculate the optical constants of fluids by using transmittance measurements of two different pathlengths cuvettes. A significant difference between their work and present work is the inversion model of optical constants. The model of Otanicar et al.21 model is cited from Large et al.20 in which the overall medium was divided into discrete elements. However, as shown in Fig. 1, because there is no vacuum interspace among the three-layer system, an error will be introduced in Otanicar et al. model. Here, we proposed an inversion model of optical constants based on continuous absorbing layers consisting of multiple reflections that is more suitable for liquid measurement. As shown in Fig. 1, a collimated light beam irradiates normally on the left side of the glass layer 1. The light beam travels within the threelayer system (glass–oil–glass). Here, I0 is the traveling light flux in the incident medium (air), I1 is the forwardtraveling light flux to the interface between layer 2 and layer 3, I2 is the traveling light flux in the exit medium, J0 is the backward-traveling light flux in the incident medium, and J1 is the backward-traveling light flux to the interface between layer 2 and layer 1. By considering the multiple reflections22 within the three-layer system, we have the following relations as t23 t32 r30 e 2a3 L3 ð3Þ J1 ¼ I1 r23 þ e a2 L2 1 r32 r30 e 2a3 L3
t01 t12 e a1 L1 e a2 L2 1 r10 r12 e 2a1 L1 t21 t12 r10 e 2a1 L1 þ J1 r21 þ e a2 L2 1 r12 r10 e 2a1 L1
I1 ¼ I0
ð4Þ
I2 ¼ I1
t23 t30 e a3 L3 1 r32 r30 e 2a3 L3
ð5Þ
where rij and tij are the reflectance and the transmittance coefficients of the interface between two neighboring medium i and j, respectively, and can be expressed as23 rij ¼
ðnj ni Þ2 þ ðkj ki Þ2 ðnj þ ni Þ2 þ ðkj þ ki Þ2
ti j ¼ 1 ri j
ð6Þ ð7Þ
The absorption coefficient of the medium i is given by ai ¼
4pki k
ð8Þ
Based on Eqs. 3, 4, and 5, the transmittance of the system can be written as I2 t01 t12 e a1 L1 t23 t30 e a3 L3 Tk ¼ ¼ I0 1 r10 r12 e 2a1 L1 1 r32 r30 e 2a3 L3 t23 t32 r30 e 2a3 L3 a2 L2 3e 1 r23 þ 1 r32 r30 e 2a3 L3 1 t21 t12 r10 e 2a1 L1 2a2 L2 ð9Þ 3 r21 þ e 1 r12 r10 e 2a1 L1 The optical constants (n2 and k2) of the NaCl solution could not be directly solved from Eqs. 1 and 2. Here, the genetic algorithm iterative process is applied to minimize the difference between the calculated and measured values. For each wavelength, the objective function fk was defined as 0 j fk ¼ jTk Tk;EXP j þ jTk0 Tk;EXP
ð10Þ
0 where Tk;EXP and Tk;EXP are two different liquid thicknesses of experimental transmittance at wavelength k, and Tk and Tk0 are two different liquid thicknesses of calculated transmittance at wavelength k. The convergence criteria was set as fk , 103. Experimental Procedure. For NaCl solutions with different concentrations of NaCl, standard NaCl solutions with a NaCl concentration of 0, 60, 120, 180, 240, 300, and 360 g/L were prepared. For a 60 g/L NaCl solution, 60 g of NaCl dissolves in 1 L of deionized water, and 360 g of NaCl dissolves in 1 L of deionized water and can reach the saturation point at 20 8C. In addition, the variation of temperature from 10 to 30 8C has less effect on the solubility of NaCl. Cuvettes are optical cells that hold the liquids under this study, and the thicknesses of glass layer (L1 and L3) are 1.2 mm. Two cuvettes (L2 = 5 cm and L20 = 10 cm) were used for transmittance measurement over the spectral range from 300 to 1000 nm. Another two, different thicknesses of cuvettes (L2 = 3 mm and L20 = 5 mm) were used for transmittance measurement over the spectral range from 1000 to 2500 nm. The main reason for this selection of the liquid thickness is little absorption of NaCl solution in the visible light spectrum and strong absorption in the near-infrared light
spectrum. This selection can improve the measurement accuracy and obtain better results. The solar energy in this wavelength range (300– 2500 nm) is .90% of the total energy of solar radiation. Here, the normal–normal spectral transmittance was measured over the spectral range from 300 to 2500 nm at a wavelength resolution of 10 nm using the V–VASE ellipsometer. The ellipsometer consists of an HS-190 monochromator combined with a xenon lamp to produce monochromatic light from the ultraviolet to the nearinfrared. The V–VASE uses silicon and indium gallium arsenide photodiode detectors. All the measurements were carried out under the normal atmospheric pressure. Experimental Uncertainty. To assess the experimental uncertainty of the DOPTM, each sample was measured six times. The normal spectral transmittance measurement has good repeatability, with a standard deviation rTk ¯ ,0.5 %. The accuracy of the transmission measurement Dk was directly given by the instrument at each wavelength. The combined standard uncertainty of the measured transmittance (Uk) at a confidence level of 68% was calculated by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð11Þ Uk ¼ ð1:11rT k Þ2 þ D2k Due to the complex relation between the measured transmittance and the inversely identified optical constants, the uncertainty of the optical constants cannot be directly obtained. By using the uncertainty of liquid thickness measurement DL1, DL2, and DL3 (0.1 mm) and the uncertainty of optical constants of glass (with known uncertainty Dn1, Dn3; Dk1, Dk3), the uncertainty of optical constants of NaCl solution can be obtained from Eqs. 1, 2, 9, and 10 by iteration.
VALIDATION The experimental transmittance spectra measured for deionized water using two different thicknesses of cuvettes of 5 and 10 cm over the spectral range from 300 to 1000 nm is presented in Fig. 3, and transmittance measurements for deionized water with two different sample thicknesses of 3 mm and 5 mm over the spectral range from 1000 to 2500 nm is presented in Fig. 4. There is significant difference between the spectral transmittances of different sample thicknesses over a majority of the spectral range. This obvious difference can improve the DOPTM result accuracy. Figure 5 shows the uncertainty of transmittance measurements over the spectral range from 300 to 2500 nm. The uncertainty of our transmittance measurement is ,1.4%. The refractive index n of deionized water in the wavelength range from 300 to 2500 nm is determined by DOPTM. The results were compared with the data provided by Segelstein24 and shown in Fig. 6. Segelstein24 completed an extensive compilation of absorption spectrum for water previously published by Hale and Querry, 25 and acquired the n by Kramers–Kronig relation. From Fig. 6, the relative difference between the two curves is ,1% in the 300–2500 nm range. Figure 7 shows the k of water measured by DOPTM and the data obtained by Segelstein. The DOPTM provides accurate
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FIG. 3. Transmittance measurements for deionized water from 300 to 1000 nm by using two different sample thicknesses of 5 and 10 cm.
FIG. 4. Transmittance measurements for deionized water from 1000 to 2500 nm by using two different sample thicknesses of 3 and 5 mm.
FIG. 6. Refractive index n of deionized water obtained by DOPTM and Segelstein.
FIG. 7. Absorption index k of deionized water obtained by DOPTM and Segelstein.24
results over the spectral range, and the data points agree well with the results provided by Segelstein.24 Figure 7 shows that strong absorption bands exist for water with absorption peaks locating at 740, 960, 1200, 1450, and 1950 nm. The water absorption spectrum is the direct result of light absorbed at the frequencies (or wavelength) of the molecular vibrations of chemical bonds (O–H) and interactions within and between water molecules. The absorption peaks of water are especially complex because each fundamental vibration also has harmonic or overtone modes at higher frequencies (lower wavelengths) that absorb light at different intensities.26 in addition to absorption at the fundamental frequencies.
RESULTS AND DICUSSION
FIG. 5. Uncertainty of transmittance measurements for different sample thicknesses of deionized water.
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Refractive Index n. Because of the measurement of transmittances with two different pathlengths, the n particularly sensitive to transmittance error.21 Figure 8 compares the n of NaCl solution determined by DOPTM
FIG. 8. Refractive index n obtained by DOPTM and data provided by Topac Inc. for the NaCl solution at 589 nm.
FIG. 10. Difference of the refractive index n between the fitted function and DOPTM value.
with data provided by Topac Inc.27 at 589 nm using refractometer. Good agreement is found for NaCl concentration up to 200 g/L. The results of n measured by DOPTM at different NaCl concentrations in the spectral range between 300 and 2500 nm are plotted in Fig. 9. The n of NaCl solution decreases with wavelength within the spectral range from 300 to 2500 nm but increases with NaCl concentrations. The NaCl has a higher refractive index than water, and it is noted that the higher the NaCl concentration, the higher the n of NaCl solution. For the sake of applications, the function of n was fitted based on Sellmeier equation28 in the spectral range 300– 2500 nm and the NaCl concentration in the range 0– 360 g/L: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a1 k2 a2 k2 a 3 k2 þ a4 c þ 2 þ 2 nðc; kÞ ¼ a0 þ 2 2 2 k k1 k k2 k k23 ð12Þ a5 c 2
where k is wavelength (nanometers), c is concentration (grams per liter), a0 = 0.385, a1 = 1.32, a2 = 1, a3 = 0.0244, a4 = 2.07 3 105, a5 = 1.75 3 107, k12 = 8.79 3 103, k22 = 1.1 3 108, and k32 = 6.09 3 104. Figure 10 shows the difference of the n between the fitted function and measured value. The difference between the fitting function and DOPTM value is less than 60.005 over a majority of the spectrum. Absorption Index k. Figure 11 shows the k measured by DOPTM at different concentrations in the spectral range from 300 to 2500 nm. The k of NaCl solution increases with NaCl concentrations in visible light spectral range from 300 to 700 nm, but there is no obvious variation with concentration in the near-infrared spectrum. Actually, NaCl absorbs much less than water in the spectral range between 700 and 2500 nm.28 As shown in Fig. 11, the absorption peaks of NaCl solution at 960, 1200, 1450, and 1950 nm are dominated by water in the spectral range from 700 to 2500 nm, and the
FIG. 9. Refractive index n measured by DOPTM at various concentrations of NaCl solution from 300 to 2500 nm.
F IG . 11. Absorption index k measured by DOPTM at various concentrations of NaCl solution from 300 to 2500 nm.
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absorption bands of NaCl solutions are almost the same as those observed for water. The k was fitted in the form of Gaussian function29 in the spectral range between 300 and 700 nm: jðc; kÞ ¼ expðb0 b1 k þ b2 k2 Þ þ b3 ðc b4 Þ
ð13Þ
where k is wavelength in nanometers, c is concentration in grams per liter, and b0 = 13.15, b1 = 0.02, b2 = 2.13 3 105, b3 = 5 3 109, and b4 = 240. The variation of k is linearly correlated with NaCl concentration in the spectral range from 300 to 700 nm. The deviation between the fitted and measured data is estimated by R jy yf jd k ð14Þ e¼ R yf d k where yf is the value of fitting function, and y is the DOPTM value. The deviation of k is ,10% between the fitting function and DOPTM value.
CONCLUSIONS The optical constants of NaCl solution with different concentrations were experimentally determined by the double optical pathlength transmission method. An analysis of optical properties with various concentrations has been conducted over the spectral range from 300 to 2500 nm. The results show that the refractive index n of NaCl solution increases with NaCl concentrations. Interestingly, there is a nonlinear relationship between n and NaCl concentration. More attention should be given in the 300–700 nm range where the regular variation of absorption index k occurs. The absorption of NaCl solution varies little with NaCl concentration in the near-infrared light spectrum. Fitted formulae of the n and k of NaCl solution as a function of wavelength and NaCl concentration are presented for engineering applications, such as, to calculate and analyze solar irradiation distribution in solar pond or natural seawater. ACKNOWLEDGMENTS This work is supported by grants from the National Basic Research Program of China (2013CB733004) and the National Natural Science Foundation of China (51336002, 51076038, and 51121004). A portion of this work was supported by the Key Laboratory of Micro-Optics and Photonic Technology of Heilongjiang Province. 1. D.R. Myers. ‘‘Solar Radiation Modeling and Measurements for Renewable Energy Applications: Data and Model Quality’’. Energy. 2005. 30(9): 1517-1531. 2. W.C. Dickinson, A.F. Clark, J.A. Day, L.F. Wouters. ‘‘The Shallow Solar Pond Energy Conversion System’’. Sol. Energy. 1976. 18(1): 3-10. 3. K. Hanjalic, R. Musemic. ‘‘Modeling the Dynamics of Double Diffusive Scalar Fields at Various Stability Conditions’’. Int. J. Heat. Fluid. Flow. 1997. 18(4): 360-367. 4. I.N. Tang. ‘‘Thermodynamic and Optical Properties of Mixed-Salt Aerosols of Atmospheric Importance’’. J. Geophys. Res. 1997. 102(D2): 1883-1893. 5. I.N. Tang, A.C. Tridico, K.H. Fung. ‘‘Thermodynamic and Optical Properties of Sea Salt Aerosols’’. J. Geophys. Res. 1997. 102(D19): 23269-23275.
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6. W.M. Yunus. ‘‘Temperature Dependence of Refractive Index and Absorption of Naci, Mgci2, and Na2SO4 Solutions as Major Components in Natural Seawater’’. Appl. Opt. 1992. 31(16): 29632964. 7. W.S. Pegau, D. Gray, J.R.V. Zaneveld. ‘‘Absorption and Attenuation of Visible and Near-Infrared Light in Water: Dependence on Temperature and Salinity’’. Appl. Opt. 1997. 36(24): 6035-6046. 8. W.M. Yunus, A.B. Rahman. ‘‘Refractive Index of Solutions at High Concentrations’’. Appl. Opt. 1988. 27(16): 3341-3343. 9. V.K. Singh, B.B.S. Jaswal, V. Kumar, R. Prakash, P. Rai. ‘‘Application of He–Ne Laser to Study the Variation of Refractive Index of Liquid Solutions with the Concentration’’. J. Integr. Sci. Technol. 2013. 1(1): 13-18. 10. M. Ravisankar, A.T. Reghunath, K. Sathianandan, V.P.N. Nampoori. ‘‘Effect of Dissolved NaCI, MgCI2, and Na2SO4 in Seawater on the Optical Attenuation in the Region from 430 to 630 nm’’. Appl. Opt. 1988. 27(18): 3887-3894. 11. G.T. Dair, R.A. Ashman, R.H. Eikelboom, F. Reinholz, P.P. van Saarloos. ‘‘Absorption of 193 and 213 nm Laser Wavelengths in Sodium Chloride Solution and Balanced Salt Solution’’. Arch. Ophthalmol. 2001. 119(4): 533-537. 12. A. Tuntomo, C.L. Tien, S.H. Park. ‘‘Optical Constants of Liquid Hydrocarbon Fuels’’. Combust. Sci. Technol. 1992. 84(1-6): 133-140. 13. Y. Fujita, T. Ohba, S. Ikawa. ‘‘Measurements 0f Far-Infrared Optical Constants of Liquids with a Synchrotron Radiation Source’’. Can. J. Chem. 1991. 69(11): 1745-1751. 14. K.Y. Bang, S. Lee, H. Oh, I. An, H. Lee. ‘‘Determination of the Optical Functions of Various Liquids by Rotating Compensator Multichannel Spectroscopic Ellipsometry’’. Bull. Korean Chem. Soc. 2005. 26(6): 947-951. 15. C.F. Bohren, D.R. Huffman. ‘‘Absorption and Scattering of Light by Small Particles’’. New York: John Wiley and Sons, 1998. 16. Z.Y. Zhang, M.F. Modest, S.P. Bharadwaj. ‘‘Measurement of Infrared Absorption Coefficient of Molten Glasses’’. Exp. Heat. Transfer. 2001. 14(3): 145-156. 17. J.E. Bertie, H.H. Eysel. ‘‘Infrared Intensities of Liquids I: Determination of Infrared Optical and Dielectric Constants by FT-IR Using the CIRLE ATR Cell’’. Appl. Spectrosc. 1985. 39(3): 392-401. 18. C.D. Keefe, J.K. Pearson. ‘‘New Technique for Determining the Optical Constants of Liquids’’. Appl. Spectrosc. 2002. 56(7): 928-934. 19. H. Fujiwara. ‘‘Introduction to Spectroscopic Ellipsometry’’. In: H. Fujiwara, editor. Spectroscopic Ellipsometry: Principles and Applications. Chichester, UK: John Wiley and Sons, 2007. 20. M.C.J. Large, D.R. McKenzie, M.I. Large. ‘‘Incoherent Reflection Process: A Discrete Approach’’. Opt. Commun. 1996. 128(4-6): 307314. 21. T.P. Otanicar, P.E. Phelan, J.S. Golden. ‘‘Optical Properties of Liquids for Direct Absorption Solar Thermal Energy Systems’’. Sol. Energy. 2009. 83(7): 969-977. 22. Z.M. Zhang. ‘‘Nano/Microscale Heat Transfer’’. New York: McGrawHill, 2007. 23. O. Stenzel. ‘‘The Physics of Thin Film Optical Spectra: An Introduction’’. New York: Springer, 2005. 24. D.J. Segelstein. ‘‘The Complex Refractive Index of Water’’. Kansas City: University of Missouri—Kansas City, 1981. 25. G.M. Hale, M.R. Querry. ‘‘Optical Constants of Water in the 200-nm to 200-mm Wavelength Region’’. Appl. Opt. 1973. 12(3): 555-563. 26. J.M. Sullivan, M.S. Twardowski, J.R.V. Zaneveld, C.M. Moore, A.H. Barnard, P.L. Donaghay, B. Rhoades. ‘‘Hyperspectral Temperature and Salt Dependencies of Absorption by Water and Heavy Water in the 400–750 nm Spectral Range’’. Appl. Opt. 2006. 45(21): 5294-5309. 27. Topac Inc. ‘‘Relationship Between Salt Solution and Sugar Concentration (Brix) and Refractive Index at 20 8C’’. 2002. http:// www.topac.com/salinity_brix.html [accessed 10 Dec 2013]. 28. E.D. Palik. ‘‘Handbook of Optical Constants of Solids’’. Orlando: Academic Press, 1985. 29. M. Jonasz, G.R. Fournier. ‘‘Light Scattering by Particles in Water: Theoretical and Experimental Foundations’’. Orlando: Academic Press, 2007.
Optical Properties of Sodium Chloride Solution Within the Spectral Range from 300 to 2500 nm at Room Temperature Xingcan Li,a Linhua Liu,a,b,* Junming Zhao,a Jianyu Tanb,* a b
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China School of Automobile Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, China
The optical properties of sodium chloride (NaCl) solution were experimentally determined by double optical pathlength transmission method in the spectral range from 300 to 2500 nm at the NaCl concentration range from 0 to 360 g/L. The results show that the refractive index of NaCl solution increases with NaCl concentrations and correlates nonlinearly with the concentration of NaCl solution. The absorption index of NaCl solution increases with NaCl concentrations in the visible spectral range of 300–700 nm, but varies little in the near-infrared spectral range of 700–2500 nm at room temperature. For the sake of applications, the fitted formulae of the refractive index and absorption index of NaCl solution as a function of wavelength and NaCl concentration are presented. Index Headings: Optical properties; Sodium chloride solution; Transmission measurement; Solar irradiation.
INTRODUCTION Solar energy is the basic resource for solar thermal technologies.1 A salt gradient solar pond can directly collect and convert solar energy into thermal power and store thermal energy longer than other solar thermal storage systems.2 A solar pond is a solar collector with a certain quantity of salt in the water; the layers of salt solution increase in concentration with depth, varying from a rather low concentration on the surface to a concentration close to saturation at the deepest depths. The storage performance of the solar pond is based on the separation of the upper cool freshwater from the underside hot saline water by a natural diffusive interface that prevents the upward loss of the accumulated heat from the bottom layer.3 An evaluation of the dependence of optical constants of sodium chloride (NaCl) solution on NaCl concentration and wavelength will aid in calculating and analyzing the solar irradiation distribution in the solar pond or natural seawater. As a basic optical property, the optical constants of NaCl solution also have important applications in physics, chemistry, and atmospheric aerosol science.4,5 Received 16 October 2014; accepted 8 December 2014. * Author to whom correspondence should be sent. E-mail: lhliu@hit. edu.cn. DOI: 10.1366/14-07769R
Volume 69, Number 5, 2015
Several experiments have been performed to obtain the optical constants of NaCl solution. Yunus6 reported the variation in the refractive index with temperature and investigated the optical absorption of NaCl solution at a wavelength of 632.8 nm with a NaCl concentration of 14.6 g/L. The results indicated that the variation in the refractive index of NaCl solution with temperature is ,0.0001/8C. Pegau et al.7 measured the absorption coefficient of pure water and saltwater in the visible and near-infrared spectrum (412–975 nm) using absorption and attenuation meters. In their work, the water temperature varied from 15 and 30 8C, and the salinity varied from 0 and 3.8%. The results shown that the absorption index was relatively insensitive to temperature in the visible region, and the variation of the absorption index of NaCl solution with temperature was found to be ,6 3 1011/ 8C. Tang4 and Tang et al.5 reported the thermodynamic and light-scattering properties of aqueous solution containing NaCl and other sea salt particles over a wide concentration range up to supersaturation (46 wt% of total solute) at 632.8 nm. In addition, Yunus,8 Singh et al.,9 Ravisankar et al.,10 and Dair et al.11 also have reported the refractive index of NaCl solution within the concentration range 0240 g/L and wavelength range 193632.8 nm. However, there are few studies on the optical constants of NaCl solution with high concentration and wide bandwidth of light. The aim of this work is to obtain the optical constants of NaCl solution with NaCl concentration from zero to saturation. Based on the measured transmissions at two different optical pathlengths, an inverse identification model using a ray tracing approach is proposed, which is more suitable to obtain the optical constants of liquid. The optical constants of NaCl solution with NaCl concentration from zero to saturation over the spectral range from 300 to 2500 nm were measured and analyzed.
EXPERIMENTAL Double Optical Pathlength Transmission Method (DOPTM). Many experimental methods have been implemented to obtain the optical constants of liquid.12–15 These methods can be classified into the transmission method, the Kramers–Kronig transform method, and the ellipsom-
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FIG. 1.
Schematic diagram of DOPTM.
etry method. The Kramers–Kronig transform method requires experimental measurement over a wide spectral range to ensure scientific accuracy.16–18 Although the ellipsometry method is very convenient to obtain the refractive index n, some limitations will be introduced into acquiring the absorption index k of transparent materials that absorb less of the incident light. For example, there is considerable difficulty in the characterization of low absorption coefficients (a , 100 cm1) using the ellipsometry method.19 In this work, the absorption coefficient of NaCl solution is small (a , 25 cm1) in the spectral band of interest, and the transmission method is more suitable than the ellipsometry to obtain the k value of liquid with reasonable accuracy by changing the optical pathlength of the measured liquid. In this work, a DOPTM is implemented to obtain the optical constants of NaCl solution. Figure 1 shows the schematic of DOPTM, where light transmits through a three-layer (glass–liquid–glass) system with multiple reflections. Layer 2 is NaCl solution. Layers 1 and 3 are made of the same glass that comprises the cuvette (containing by weight 95% or more of silica) and n1 þ ik1 = n3 þ ik3. The optical constants of the glass of the cuvette were directly measured using ellipsometry with the V–VASE ellipsometer produced by J.A. Woollam Company. The measurement data with uncertainty are shown in Fig. 2. The transmittance (Tk and Tk0 ) of this three-layer system with two different liquid layer thicknesses (L2 and L20 ) can be formally expressed as follows: Tk ¼ f ðn1 ; n2 ; n3 ; k1 ; k2 ; k3 ; L1 ; L2 ; L3 Þ
ð1Þ
Tk0 ¼ f ðn1 ; n2 ; n3 ; k1 ; k2 ; k3 ; L1 ; L20 ; L3 Þ
ð2Þ
where n1 þ ik1 is the complex refractive index of the medium; the subscript 1, 2, and 3 denote the left glass, the measured liquid, and the right glass, respectively. L1 is the thickness of the left glass, and L3 is the thickness of the right glass. In principle, with the known complex refractive index (n1þ ik1 = n3þ ik3) and thickness (L1 = L3) of glass layers, the complex refractive index (n2 þ ik2) of the measured liquid can be determine by measuring the transmittances Tk and Tk0 of the systems with two different liquid thicknesses (L2 and L20 ). Double optical pathlength transmission method has been widely used to obtain the optical constants of liquid. Large et al.20 described formulations for evaluating the reflectance and transmittance of optical media that
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FIG. 2. Optical constants of the glass of cuvette used in this study measured using an ellipsometer.
consists of discrete layers. The model is based on discrete elements consisting of multiple reflections, all forward- and backward-traveling fluxes combined into a single flux. This model operates under the one-dimensional approximation, and there is one vacuum interspace between two discrete elements. For this reason, the model of Large et al.20 is widely applied to medium consisting of solid slide stack. Otanicar et al.21 proposed a method to iteratively calculate the optical constants of fluids by using transmittance measurements of two different pathlengths cuvettes. A significant difference between their work and present work is the inversion model of optical constants. The model of Otanicar et al.21 model is cited from Large et al.20 in which the overall medium was divided into discrete elements. However, as shown in Fig. 1, because there is no vacuum interspace among the three-layer system, an error will be introduced in Otanicar et al. model. Here, we proposed an inversion model of optical constants based on continuous absorbing layers consisting of multiple reflections that is more suitable for liquid measurement. As shown in Fig. 1, a collimated light beam irradiates normally on the left side of the glass layer 1. The light beam travels within the threelayer system (glass–oil–glass). Here, I0 is the traveling light flux in the incident medium (air), I1 is the forwardtraveling light flux to the interface between layer 2 and layer 3, I2 is the traveling light flux in the exit medium, J0 is the backward-traveling light flux in the incident medium, and J1 is the backward-traveling light flux to the interface between layer 2 and layer 1. By considering the multiple reflections22 within the three-layer system, we have the following relations as t23 t32 r30 e 2a3 L3 ð3Þ J1 ¼ I1 r23 þ e a2 L2 1 r32 r30 e 2a3 L3
t01 t12 e a1 L1 e a2 L2 1 r10 r12 e 2a1 L1 t21 t12 r10 e 2a1 L1 þ J1 r21 þ e a2 L2 1 r12 r10 e 2a1 L1
I1 ¼ I0
ð4Þ
I2 ¼ I1
t23 t30 e a3 L3 1 r32 r30 e 2a3 L3
ð5Þ
where rij and tij are the reflectance and the transmittance coefficients of the interface between two neighboring medium i and j, respectively, and can be expressed as23 rij ¼
ðnj ni Þ2 þ ðkj ki Þ2 ðnj þ ni Þ2 þ ðkj þ ki Þ2
ti j ¼ 1 ri j
ð6Þ ð7Þ
The absorption coefficient of the medium i is given by ai ¼
4pki k
ð8Þ
Based on Eqs. 3, 4, and 5, the transmittance of the system can be written as I2 t01 t12 e a1 L1 t23 t30 e a3 L3 Tk ¼ ¼ I0 1 r10 r12 e 2a1 L1 1 r32 r30 e 2a3 L3 t23 t32 r30 e 2a3 L3 a2 L2 3e 1 r23 þ 1 r32 r30 e 2a3 L3 1 t21 t12 r10 e 2a1 L1 2a2 L2 ð9Þ 3 r21 þ e 1 r12 r10 e 2a1 L1 The optical constants (n2 and k2) of the NaCl solution could not be directly solved from Eqs. 1 and 2. Here, the genetic algorithm iterative process is applied to minimize the difference between the calculated and measured values. For each wavelength, the objective function fk was defined as 0 j fk ¼ jTk Tk;EXP j þ jTk0 Tk;EXP
ð10Þ
0 where Tk;EXP and Tk;EXP are two different liquid thicknesses of experimental transmittance at wavelength k, and Tk and Tk0 are two different liquid thicknesses of calculated transmittance at wavelength k. The convergence criteria was set as fk , 103. Experimental Procedure. For NaCl solutions with different concentrations of NaCl, standard NaCl solutions with a NaCl concentration of 0, 60, 120, 180, 240, 300, and 360 g/L were prepared. For a 60 g/L NaCl solution, 60 g of NaCl dissolves in 1 L of deionized water, and 360 g of NaCl dissolves in 1 L of deionized water and can reach the saturation point at 20 8C. In addition, the variation of temperature from 10 to 30 8C has less effect on the solubility of NaCl. Cuvettes are optical cells that hold the liquids under this study, and the thicknesses of glass layer (L1 and L3) are 1.2 mm. Two cuvettes (L2 = 5 cm and L20 = 10 cm) were used for transmittance measurement over the spectral range from 300 to 1000 nm. Another two, different thicknesses of cuvettes (L2 = 3 mm and L20 = 5 mm) were used for transmittance measurement over the spectral range from 1000 to 2500 nm. The main reason for this selection of the liquid thickness is little absorption of NaCl solution in the visible light spectrum and strong absorption in the near-infrared light
spectrum. This selection can improve the measurement accuracy and obtain better results. The solar energy in this wavelength range (300– 2500 nm) is .90% of the total energy of solar radiation. Here, the normal–normal spectral transmittance was measured over the spectral range from 300 to 2500 nm at a wavelength resolution of 10 nm using the V–VASE ellipsometer. The ellipsometer consists of an HS-190 monochromator combined with a xenon lamp to produce monochromatic light from the ultraviolet to the nearinfrared. The V–VASE uses silicon and indium gallium arsenide photodiode detectors. All the measurements were carried out under the normal atmospheric pressure. Experimental Uncertainty. To assess the experimental uncertainty of the DOPTM, each sample was measured six times. The normal spectral transmittance measurement has good repeatability, with a standard deviation rTk ¯ ,0.5 %. The accuracy of the transmission measurement Dk was directly given by the instrument at each wavelength. The combined standard uncertainty of the measured transmittance (Uk) at a confidence level of 68% was calculated by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð11Þ Uk ¼ ð1:11rT k Þ2 þ D2k Due to the complex relation between the measured transmittance and the inversely identified optical constants, the uncertainty of the optical constants cannot be directly obtained. By using the uncertainty of liquid thickness measurement DL1, DL2, and DL3 (0.1 mm) and the uncertainty of optical constants of glass (with known uncertainty Dn1, Dn3; Dk1, Dk3), the uncertainty of optical constants of NaCl solution can be obtained from Eqs. 1, 2, 9, and 10 by iteration.
VALIDATION The experimental transmittance spectra measured for deionized water using two different thicknesses of cuvettes of 5 and 10 cm over the spectral range from 300 to 1000 nm is presented in Fig. 3, and transmittance measurements for deionized water with two different sample thicknesses of 3 mm and 5 mm over the spectral range from 1000 to 2500 nm is presented in Fig. 4. There is significant difference between the spectral transmittances of different sample thicknesses over a majority of the spectral range. This obvious difference can improve the DOPTM result accuracy. Figure 5 shows the uncertainty of transmittance measurements over the spectral range from 300 to 2500 nm. The uncertainty of our transmittance measurement is ,1.4%. The refractive index n of deionized water in the wavelength range from 300 to 2500 nm is determined by DOPTM. The results were compared with the data provided by Segelstein24 and shown in Fig. 6. Segelstein24 completed an extensive compilation of absorption spectrum for water previously published by Hale and Querry, 25 and acquired the n by Kramers–Kronig relation. From Fig. 6, the relative difference between the two curves is ,1% in the 300–2500 nm range. Figure 7 shows the k of water measured by DOPTM and the data obtained by Segelstein. The DOPTM provides accurate
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FIG. 3. Transmittance measurements for deionized water from 300 to 1000 nm by using two different sample thicknesses of 5 and 10 cm.
FIG. 4. Transmittance measurements for deionized water from 1000 to 2500 nm by using two different sample thicknesses of 3 and 5 mm.
FIG. 6. Refractive index n of deionized water obtained by DOPTM and Segelstein.
FIG. 7. Absorption index k of deionized water obtained by DOPTM and Segelstein.24
results over the spectral range, and the data points agree well with the results provided by Segelstein.24 Figure 7 shows that strong absorption bands exist for water with absorption peaks locating at 740, 960, 1200, 1450, and 1950 nm. The water absorption spectrum is the direct result of light absorbed at the frequencies (or wavelength) of the molecular vibrations of chemical bonds (O–H) and interactions within and between water molecules. The absorption peaks of water are especially complex because each fundamental vibration also has harmonic or overtone modes at higher frequencies (lower wavelengths) that absorb light at different intensities.26 in addition to absorption at the fundamental frequencies.
RESULTS AND DICUSSION
FIG. 5. Uncertainty of transmittance measurements for different sample thicknesses of deionized water.
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Refractive Index n. Because of the measurement of transmittances with two different pathlengths, the n particularly sensitive to transmittance error.21 Figure 8 compares the n of NaCl solution determined by DOPTM
FIG. 8. Refractive index n obtained by DOPTM and data provided by Topac Inc. for the NaCl solution at 589 nm.
FIG. 10. Difference of the refractive index n between the fitted function and DOPTM value.
with data provided by Topac Inc.27 at 589 nm using refractometer. Good agreement is found for NaCl concentration up to 200 g/L. The results of n measured by DOPTM at different NaCl concentrations in the spectral range between 300 and 2500 nm are plotted in Fig. 9. The n of NaCl solution decreases with wavelength within the spectral range from 300 to 2500 nm but increases with NaCl concentrations. The NaCl has a higher refractive index than water, and it is noted that the higher the NaCl concentration, the higher the n of NaCl solution. For the sake of applications, the function of n was fitted based on Sellmeier equation28 in the spectral range 300– 2500 nm and the NaCl concentration in the range 0– 360 g/L: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a1 k2 a2 k2 a 3 k2 þ a4 c þ 2 þ 2 nðc; kÞ ¼ a0 þ 2 2 2 k k1 k k2 k k23 ð12Þ a5 c 2
where k is wavelength (nanometers), c is concentration (grams per liter), a0 = 0.385, a1 = 1.32, a2 = 1, a3 = 0.0244, a4 = 2.07 3 105, a5 = 1.75 3 107, k12 = 8.79 3 103, k22 = 1.1 3 108, and k32 = 6.09 3 104. Figure 10 shows the difference of the n between the fitted function and measured value. The difference between the fitting function and DOPTM value is less than 60.005 over a majority of the spectrum. Absorption Index k. Figure 11 shows the k measured by DOPTM at different concentrations in the spectral range from 300 to 2500 nm. The k of NaCl solution increases with NaCl concentrations in visible light spectral range from 300 to 700 nm, but there is no obvious variation with concentration in the near-infrared spectrum. Actually, NaCl absorbs much less than water in the spectral range between 700 and 2500 nm.28 As shown in Fig. 11, the absorption peaks of NaCl solution at 960, 1200, 1450, and 1950 nm are dominated by water in the spectral range from 700 to 2500 nm, and the
FIG. 9. Refractive index n measured by DOPTM at various concentrations of NaCl solution from 300 to 2500 nm.
F IG . 11. Absorption index k measured by DOPTM at various concentrations of NaCl solution from 300 to 2500 nm.
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absorption bands of NaCl solutions are almost the same as those observed for water. The k was fitted in the form of Gaussian function29 in the spectral range between 300 and 700 nm: jðc; kÞ ¼ expðb0 b1 k þ b2 k2 Þ þ b3 ðc b4 Þ
ð13Þ
where k is wavelength in nanometers, c is concentration in grams per liter, and b0 = 13.15, b1 = 0.02, b2 = 2.13 3 105, b3 = 5 3 109, and b4 = 240. The variation of k is linearly correlated with NaCl concentration in the spectral range from 300 to 700 nm. The deviation between the fitted and measured data is estimated by R jy yf jd k ð14Þ e¼ R yf d k where yf is the value of fitting function, and y is the DOPTM value. The deviation of k is ,10% between the fitting function and DOPTM value.
CONCLUSIONS The optical constants of NaCl solution with different concentrations were experimentally determined by the double optical pathlength transmission method. An analysis of optical properties with various concentrations has been conducted over the spectral range from 300 to 2500 nm. The results show that the refractive index n of NaCl solution increases with NaCl concentrations. Interestingly, there is a nonlinear relationship between n and NaCl concentration. More attention should be given in the 300–700 nm range where the regular variation of absorption index k occurs. The absorption of NaCl solution varies little with NaCl concentration in the near-infrared light spectrum. Fitted formulae of the n and k of NaCl solution as a function of wavelength and NaCl concentration are presented for engineering applications, such as, to calculate and analyze solar irradiation distribution in solar pond or natural seawater. ACKNOWLEDGMENTS This work is supported by grants from the National Basic Research Program of China (2013CB733004) and the National Natural Science Foundation of China (51336002, 51076038, and 51121004). A portion of this work was supported by the Key Laboratory of Micro-Optics and Photonic Technology of Heilongjiang Province. 1. D.R. Myers. ‘‘Solar Radiation Modeling and Measurements for Renewable Energy Applications: Data and Model Quality’’. Energy. 2005. 30(9): 1517-1531. 2. W.C. Dickinson, A.F. Clark, J.A. Day, L.F. Wouters. ‘‘The Shallow Solar Pond Energy Conversion System’’. Sol. Energy. 1976. 18(1): 3-10. 3. K. Hanjalic, R. Musemic. ‘‘Modeling the Dynamics of Double Diffusive Scalar Fields at Various Stability Conditions’’. Int. J. Heat. Fluid. Flow. 1997. 18(4): 360-367. 4. I.N. Tang. ‘‘Thermodynamic and Optical Properties of Mixed-Salt Aerosols of Atmospheric Importance’’. J. Geophys. Res. 1997. 102(D2): 1883-1893. 5. I.N. Tang, A.C. Tridico, K.H. Fung. ‘‘Thermodynamic and Optical Properties of Sea Salt Aerosols’’. J. Geophys. Res. 1997. 102(D19): 23269-23275.
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