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紫外-可见吸收光谱结合高斯多峰拟合技术测定甲基红酸离解常数


1030 [Article]

物理化学学报(Wuli Huaxue Xuebao) Acta Phys. -Chim. Sin. 2012, 28 (5), 1030-1036 doi: 10.3866/PKU.WHXB201203025

May www.whxb.pku.edu.cn

紫外-可见吸收光谱结合高斯多峰拟合技术测定甲基红酸离解常数
张建华 刘 琼 陈玉苗 刘兆清 徐常威*
(广州大学化学化工学院, 广州 510006)
摘要:

在一定 pH 值范围内, 甲基红(MR)水溶液紫外-可见吸收光谱特征是酸式甲基红(HMR)最大吸收峰

((530±15) nm)与碱式甲基红(MR-)最大吸收峰((435±20) nm)叠合在一起. 本文用高斯多峰拟合技术实现了 HMR 和 MR- 叠合峰的分峰拟合计算. 拟合计算输出两个吸收峰的积分面积即峰强度 A1 和 A2, A1 和 A2 之比与 MR- 和 HMR 浓度之比. 进而计算甲基红水溶液酸离解平衡常数 pKa. 用本方法测量 298.15 K 时的 pKa 值为 4.76. 拟合优度高, 拟合度 R2、 拟合优度χ2 分别达到 0.998 和 10-5 以下. 深入探讨了表面活性剂十二烷基硫酸钠 (SDS)、 十六烷基三甲基溴化铵(CTAB)聚集行为对甲基红 pKa 的影响. 与传统分光光度测量方法相比, 紫外-可 见吸收光谱结合高斯多峰拟合技术结果更可靠, 测量步骤和数据处理过程更简单, 更具有普适性.
关键词:

甲基红; 紫外-可见吸收光谱; 叠合峰; 酸离解常数; 高斯多峰拟合 O648

中图分类号:

Determination of Acid Dissociation Constant of Methyl Red by Multi-Peaks Gaussian Fitting Method Based on UV-Visible Absorption Spectrum
ZHANG Jian-Hua LIU Qiong CHEN Yu-Miao LIU Zhao-Qing XU Chang-Wei*
(School of Chemistry and Chemical Engineering, Guangzhou University, Guangzhou 510006, P. R. China)
Abstract: UV-visible electronic absorption spectra of methyl red (MR) aqueous solutions are characterized by the overlap of a principal peak at λmax ((520±15) nm) with a shoulder peak at λmax ((435±20) nm), which are assigned to acidic species (HMR) and basic species of methyl red, respectively. In this study, the spectra and the integrated absorbance of the MR- and HMR peaks (denoted A1 and A2, respectively) were interpreted using a new multi-peaks Gaussian fitting method. From the absorbance ratio A1/A2 and the concentration ratio cMR-/cHMR, the average acid dissociation constant (pKa) was determined as 4.76 at 298.15 K. The goodness is high and the values of R2 (degree of fitting) and χ2 (chi-square test for goodness of fit) were 0.998 and below 10-5, respectively. The effects of aggregation behavior of sodium dodecyl sulfate (SDS) and cetylammonium bromide (CTAB) on pKa were also investigated via this method. The multi-peaks Gaussian fitting method was shown to determine pKa more reliably and simply than traditional spectrophotometric techniques. Key Words:

Methyl red; UV-visible absorption spectrum; Multi-peaks Gaussian fitting

Overlap peak; Acid dissociation constant;

Received: December 22, 2011; Revised: March 1, 2012; Published on Web: March 2, 2012. ? Corresponding author. Email: cwxuneuzsu@126.com; Tel: +86-20-39366908. The project was supported by the National Natural Science Foundation of China (20903028), Scientific Research Foundation for Returned Scholars from Ministry of Education of China, and Scientific Research Foundation for Yangcheng Scholar, China (10A041G). 国家自然科学基金(20903028), 留学回国人员科研启动基金及羊城学者青年科研骨干培养对象项目(10A041G)资助

? Editorial office of Acta Physico-Chimica Sinica

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ZHANG Jian-Hua et al.: Determination of pKa of Methyl Red by Multi-Peaks Gaussian Fitting Method

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1

Introduction

The acid-base ionization equilibrium exists in aqueous solution of many organic dyes. Acid dissociation constant is a very important parameter to indicate degree of ionization at the different pH values in acidic organic dye solutions.1-3 The acidbase ionization equilibrium of organic dyes and the determination of acid dissociation constant in aqueous solution are of great significance for many practical applications and scientific research areas such as acid-base titration, complex formation, solvent extractions, capillary electrophoresis,4 chromatographic retention characteristics,5,6 potentiometric titration, fabric dyeing and finishing,7 environmental monitoring and protection,8-12 drug research and development. In particular, drug synthesis, production, purification, formulation, dissolution, absorption, distribution and metabolism processes are closely related with the pKa.13,14 Many determination methods for acid dissociation constants of organic dyes have been developed.3,15-17 The most commonly used methods are potentiometric titration,5,18-21 conductivity,22,23 capillary electrophoresis,15 capillary electrophoresis mass spectrometry,24 nuclear magnetic resonance spectroscopy,25-28 liquid chromatography,6,16,29 infrared spectroscopy,30,31 Raman scattering,32 fluorescence spectroscopy,33,34 UV-visible spectrophotometry,35-37 theoretical calculation38 and so on. Among them, spectrophotometric method has high precision and accuracy. The linear relationship between absorbance and concentration of color solution with a certain thickness is determined by Lambert-Beer?s law, which gives a theoretical foundation of the spectrophotometric determination of the pKa of an acidbase indicator. In 1958, Tobey39 determined the pKa of methyl red using singlewavelength spectrophotometry and the pKa is 5.02 at 300.35 K. Since then, a lot of work to determine the pKa of organic dyes using single-wavelength spectrophotometry has been reported.3,35-37 Single-wavelength spectrophotometry is very suitable to determine the position of absorption peaks of acid and base species which are separated. However, in most cases, the maximum absorption peaks of acid and base species are association with each other in organic dye aqueous solutions. This situation leads to difficulties in data processing and determination of the pKa.3 The multi-wavelengths spectrophotometric method has been adopted to determine the value of pKa.4,40,41 Target factor analysis,4 rank annihilation factor analysis42,43 and other methods6,44 have been developed to deduce the pKa values from the multi-wavelengths spectrophotometric data obtained at different pH values. UV-visible absorption spectra of methyl red were measured at different pH values regulated by a series of acetic acid (HAc)-sodium acetate (NaAc) buffer solutions with different concentrations and characterized by an overlap of a principal peak of acidic specie of methyl red (HMR) at 520-550 nm and a shoulder peak of basic specie of methyl red (MR-) at 425-460 nm. A multi-peaks Gaussian fitting method based on Origin from Microcal Company was used to interpret the spec-

tra in this study. The multi-peaks Gaussian fitting calculation45-47 on the overlap peaks gave the integrated absorbance ratio A1/A2, then the pKa of methyl red was obtained. The studies on organic dye-surfactant interactions in aqueous buffered systems are of great importance in analytical chemistry, pesticide efficiency, pharmaceutical development, fabric dyeing and so on. Therefore, a new procedure based on multi-peaks Gaussian fitting method was firstly performed in dye-surfactant interactions of methyl red with sodium dodecyl sulfate (SDS), cetylammonium bromide (CTAB), which will enrich research methods in this research area.

2

Experimental

2.1 Reagents Methyl red, anhydrous NaAc, CTAB, SDS were of analytical grade and purchased from Sigma-Aldrich. Ethanol, HAc, HCl were of analytical grade and purchased from Guangzhou chemical reagent factory. All solutions were prepared with distilled water. (1) All the solutions of methyl red were prepared according to the literature37 and the pH values were achieved using a certain concentration of NaAc-HAc buffer solution. (2) A series of methyl red solutions with SDS were prepared by a concentration range of SDS from 0.001 to 0.018 mol·L-1 and the concentration of methyl red was fixed. (3) Instead of SDS, a series of methyl red solutions with CTAB were prepared by the concentration of CTAB at 0.0001 mol·L-1 (below the critical micelle concentration (CMC) of CTAB) and 0.001 mol·L-1 (above the CMC of CTAB) and the concentration of methyl red was fixed. 2.2 Apparatus UV-visible absorption spectra were recorded on Shimadzu UV2550-UV-visible spectrophotometer (Japan) equipped with 10 mm path length quartz cell. Distilled water was used as reference solution. All the spectra were obtained between 320 and 750 nm and the sampling interval was 0.5 nm. The pH values of the solutions were measured by PHSJ-4A-type PH meter furnished with a combined glass electrode (Shanghai Precision Division-Shanghai Lei magnetic) which was pre-calibrated with at least two buffer solutions at pH 4.00 and 10.00. Each pH value was obtained from the average of three measurements. All pH values and spectra were measured at a constant temperature which was controlled by a super-heated water circulating thermostat bath. The measurement data were imported into PC with Microcal Origin 7.0 for data processing. 2.3 Multi-peaks Gaussian fitting method The UV-visible spectrum data were imported and plotted with Origin 7.5 software. When menu command of Analysis/ Fit Multi-Peaks/Gaussian was selected, a dialog box with the number and the initial half-width estimated default values of the peaks appeared in the current graphics window. After doubleclicking the mouse at 425 and 520 nm of the spectra respectively, Origin 7.5 automatically completed a multi-peaks Gaussian

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Table 1

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fitting procedure on certain spectra and gave the line-shape parameters of the UV-visible spectra in the result window.

Results of the multi-peaks Gaussian fitting method on the spectra of methyl red solution at different pH values and 298.15 K
A2 λmax1/nm λmax2/nm w1/nm w2/nm Height1 Height2 456.5 448.9 445.5 436.5 532.0 535.1 541.8 546.9 122.0 120.5 124.7 114.0 66.3 63.1 46.2 46.2 0.30 0.38 0.46 0.49 0.85 0.59 0.27 0.15 R2 0.997 0.998 0.996 0.997

3

Results and discussion

pH

A1

3.1 Principle of multi-peaks Gaussian fitting method Ionization equilibrium of methyl red in aqueous solution is given as the following equation HMR?MR-+H+ (1) red yellow The pH value range of color change of methyl red in aqueous solution is well known as 4.4-6.2. When pH values are 4.63, 4.93, 5.39, 5.68, the UV-visible absorption spectra and their multi- peaks Gaussian fitting results are shown in Fig.1. It is shown that integrated absorbance A1 of base MR- peaks increases and integrated absorbance A2 of acid HMR peaks decreases with the increase of pH value. The increase and decrease of the integrated absorbance of the MR- and HMR are objectively due to the change of the relative concentrations of MR- and HMR. Existence simultaneously of HMR and MR- in methyl red solution results in spectra with two peaks at a certain pH value. Multi-peaks Gaussian fitting on the spectra with two peaks satisfies following equation A1 y = y0 + exp(-2((x - λ max1)/w1)2) + w1 π 2 A2 exp( - 2((x - λ max2)/w 2)2) (2) w2 π 2 where, y0 is baseline, λmax1 and λmax2 are the maximum absorption wavelengths, w1 and w2 are half peak widths, A1 and A2 are the integrated absorbances of the two peaks for MR- and HMR. Multi-peaks Gaussian fitting method based on the spectra

4.63 28.80 76.43 4.93 46.01 43.12 5.39 52.40 21.81 5.68 55.83 11.81

Height1 and Height2 are the heights of absorbance peaks for MR- and HMR.

gives the λmax1, λmax2, w1, w2, A1, A2 and these data are listed in Table 1. 3.2 Relationship between pKa and the relative integrated absorbance Acid dissociation constant of methyl red is given as following equation [H+][MR -] Ka = (3) [HMR] thus pKa = pH - lg where
[MR -] [HMR]

(4) (5)

A1 ε1[MR -] = A 2 ε 2[HMR]

[MR -] ε 2 A1 = (6) [HMR] ε1 A 2 where, ε1 and ε2 are the molar absorption coefficients of MRand HMR, respectively. Then, the methyl red absorption spectra (Fig.2) were measured in base (pH=9) and acid (pH=2) conditions respectively. When the value of pH is 9, there is only MR- in methyl red solution and the [MR-]=C, then A1=ε1[MR-]=ε1C (7) When the value of pH is 2, there is only HMR in methyl red so-

Fig.1

UV-visible absorption spectra of methyl red at different pH values and their multi-peaks Gaussian fitting results
experiment, fitting, MR-, HMR

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ZHANG Jian-Hua et al.: Determination of pKa of Methyl Red by Multi-Peaks Gaussian Fitting Method

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Fig.2 UV-visible absorption spectra of methyl red solution measured in basic (pH=9) and acid (pH=2) solutions

lution and [HMR]=C, then A2=ε2[HMR]=ε2C (8) Setting ε=ε1/ε2 and A1 or A2 are obtained with the same concentration of methyl red, then ε=A1/A2 (9) The value of ε is obtained as 0.56. From Eqs.(4)-(8), pKa can be calculated from Eq.(10) [MR -] ε A A pKa = pH - lg = pH - lg 2 1 = pH + lgε -lg 1 (10) ε1 A 2 A2 [HMR] A pH = lg 1 + pKa - lgε (11) A2 The value of pKa is obtained from Eq.(10) at different pH values. The Multi-peaks Gaussian Fitting results are shown in Table 2. 3.3 Error analysis for determination of pKa It is very clear that the values of pKa listed in Table 2 are slightly lower than the values (4.90 ± 0.20) in literature.39,42,48 However, the results are within the error range for the values of pKa and prove the reliability of multi-peaks Gaussian fitting
Table 2
T/K 298.15 No. 1 2 3 4 303.15 1 2 3 4 308.15 1 2 3 4 313.15 1 2 3 4 318.15 1 2 3 4

Relationship between Ka and temperature
A1/A2 0.38 0.89 2.40 4.73 0.52 1.01 2.50 4.78 0.50 0.99 2.47 4.75 0.48 0.95 2.44 4.69 0.46 0.93 2.40 4.72 lg(A1/A2) -0.42 -0.05 0.38 0.67 -0.28 0.00 0.40 0.68 -0.30 -0.01 0.39 0.68 -0.32 0.02 0.39 0.67 -0.34 -0.03 0.38 0.67 pH 4.63 4.95 5.39 5.68 4.65 4.97 5.36 5.63 4.58 4.90 5.30 5.62 4.56 4.88 5.28 5.58 4.54 4.86 5.25 5.54 pKa 4.79 4.74 4.75 4.75 4.68 4.71 4.71 4.69 4.62 4.65 4.65 4.68 4.62 4.64 4.63 4.65 4.62 4.63 4.61 4.60 4.61 4.63 4.65 4.70 Average of pKa 4.76

method for determination of pKa. The concentrations of MRand HMR in solutions are determined by the curves for absorbance of maximum absorption wavelength at 425 nm for MRand that at 520 nm for HMR. However the concentrations of MR- and HMR are determined by the methyl red color range which are unreliable because of blue shift of MR- and red shift of HMR absorption peak.18 The absorption peak of MR- bluely shifts from 456 to 436 nm and the absorption peak of HMR redly shifts from 531 to 546 nm when the pH value increases from 4.63 to 5.68 in Table 1. The shifts of absorption peaks make the relationship of the concentration and absorbance diverge obviously from the standard curve and cause about ±(3%-5%) systematic error for pKa measurement which is higher than true value. A multi-peaks Gaussian fitting based on the absorption spectra of methyl red within the color change interval has been made and gives the relative integrated absorbance of MR- and HMR absorption peaks which is used to determine the relative concentration of MR- and HMR instead of using the unreliable standard curves obtained from the acid and base conditions in this study. So the pKa measurement results are more reliable and repeatable. 3.4 Thermodynamics on ionization equilibrium of methyl red The pKa values of methyl red were determined by UV-visible absorption spectroscopy with multi-peaks Gaussian fitting method at different temperatures and shown in Table 2. The values of pKa decrease considerably with increase of temperature, which is consistent with the literature.49 Generally it is believed that the increase of temperature promotes ionization of organic dyes and leads to decrease of pKa. A few of thermodynamic models have been developed for acid dissociation equilibrium of oganic dyes.49 Here, the ‘density’model has been selected.49 The standard Gibbs free energy of reaction (ΔrG ) for the ionization equilibrium of methyl red satisfies the following Eq.(12) lgKa=-pKa ln10= -Δ r G /(RT) = (12) a + b/T + c/T 2 + d/T 3 + (e + f/T + g/T 2)ln ρ w where pKa=-lgKa, ρw is water density (kg m-3), T is the thermo· dynamic temperature (K), and a-g are model parameters. The relationship between the lgKa and 1/T is shown in Fig.3. The ΔrG obtained from Eq.(12) with parameters which were obtained from non-linear curve fitting on data of Fig.3 with change of temperature is shown in Fig.4. The ΔrG increases with increase of temperature and is consistent with the literature.49 3.5 Effect of surfactants on pKa 3.5.1 SDS-methyl red system The variety of CMC of surfactants can be measured accurately by UV-visible absorption spectrum combined with multipeaks Gaussian fitting method in order to study their aggregation behavior.45 To study the effects of aggregation behavior of surfactant on pKa, SDS-methyl red and CTAB-methyl red aque?

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Table 3 Spectrum line-shape parameters of methyl red with different concentrations of SDS at 298.15 K and pH=5.40
CSDS/(mol L-1) · 0.001 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 A1 31.28 31.62 31.88 31.93 32.22 31.99 30.83 30.45 29.79 28.12 A2 6.95 7.11 7.13 6.95 6.88 7.60 8.00 9.17 9.59 10.01 λmax1/nm 443.8 444.5 444.5 444.2 444.3 445.2 446.0 447.9 446.9 449.5 λmax2/nm 542.8 542.7 542.7 543.0 543.1 542.1 540.9 539.1 538.7 537.9 w1/nm 123.5 124.3 124.7 124.6 125.2 125.2 123.6 123.8 121.7 120.0 w2/nm 52.0 51.2 51.2 50.9 50.9 52.2 53.8 55.6 57.3 58.1

Fig.3 Relationship between lgKa and 1/T

0.018

Fig.4 Relationship between ΔrG and temperature

ous solution systems were selected. Fig.5 shows the relationships between pKa of methyl red and the SDS concentration at different temperatures. The values of pKa decrease considerably with the increase of temperature, indicating that the ionization equilibrium of methyl red moves to the right in the existence of anionic surfactant SDS. When the SDS concentration is lower than the CMC, no significant change of pKa values is observed. When the SDS concentration is higher than the CMC, pKa values increase with the increase of SDS concentration. It is undoubted that the pKa is sensitive to the CMC and used for determination of the CMC of SDS, for example the CMC of SDS are 8.54×10-3, 8.68×10-3, 8.82×10-3, 9.66×10-3 mol·L-1 at 303.15, 308.15, 313.15, 318.15 K, respectively, which are consistent with the literature.50

In order to investigate further effect of SDS on ionization equilibrium of methyl red in solution, a multi-peaks Gaussian fitting method on UV-visible spectra of the series of solutions (pH=5.40) containing different concentrations of SDS from 0.001 to 0.018 mol·L-1 gives spectral line-shape parameters such as A1 and A2, λmax1 and λmax2, w1 and w2 of MR- and HMR at 298.15 K in Table 3. The spectral line-shape parameters listed in Table 3 are sensitive to the SDS concentration and changes suddenly at CMC of SDS which are shown in Fig.6 and Fig.7. The red shift of λmax1 and blue shift of λmax2 with the increase of the SDS concentration are observed and more obvious after formation of the SDS micelle. There is a sudden change at 0.0083 mol·L-1 in Fig.6 and Fig.7. At first, the λmax1 of MR- absorption peak increases slowly and then increases quickly with the increase of SDS concentration. Sudden change occurs at the CMC of SDS. The change of λmax2 is exactly the opposite with λmax1. The w1 of MRabsorption peak increases then decreases quickly with the increase of SDS concentration. Sudden change occurs at the CMC of SDS. The change of w2 is exactly the opposite with w1. Generally, relationship between spectral line-shape parameters such as A1, A2, λmax1, λmax2, w1, w2 and concentration of surfac-

Fig.5

Relationships between pKa of methyl red and the SDS concentration at different temperatures

Fig.6 Dependence of the maximum absorption wavelengths of MR- and HMR on the concentration of SDS at 298.15 K

No.5
Table 4

ZHANG Jian-Hua et al.: Determination of pKa of Methyl Red by Multi-Peaks Gaussian Fitting Method

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Spectrum line-shape parameters and effect of aggregation behavior of CTAB on pKa of methyl red with different concentra
CCTAB/(mol L-1) · 0.0001 No. 1 2 3 4 0.001 1 2 3 4 A1/A2 0.45 0.94 2.81 5.30 8.83 25.10 absorption peak of MRabsorption peak of MRlg(A1/A2) -0.35 -0.03 0.45 0.74 0.94 1.40 5.37 5.66 pH 4.62 4.88 5.38 5.67 4.61 4.89 pKa 4.71 4.65 4.67 4.67 3.41 3.23 3.32 Average of pKa 4.67

tant has been used by us for CMC determination.45 3.5.2 CTAB-methyl red system CTAB with methyl red system is much more complicated than SDS with methyl red system. The UV-visible absorption spectrum of CTAB with methyl red solution is shown in Fig.8 when CTAB concentration is bellow and above the CMC. Table 4 gives the spectrum line-shape parameters and the effect of aggregation behavior of CTAB on the pKa of methyl red solutions at 303.15 K. When the CTAB concentration is 0.0001 mol·L-1 which is bellow the CMC of CTAB, the UV-visible absorption spectrum of CTAB with methyl red solution is similar with that of methyl red solution. However, the pKa value of methyl red with 0.0001 mol·L-1 CTAB obtained by multi-peaks Gaussian fitting method is 4.67 which is 0.09 lower than that of the methyl red (4.76) at the same temperature. Furthermore, pKa value decreases slowly with the increase of CTAB concentration. When the CTAB concentration is 0.001 mol·L-1, the pKa value decreases rapidly to below 3.32 and the color of solution system changes completely from red to yellow at the same time, which indicates that there is mainly MR- species in the solution. These results illustrate that formation of the CTAB micelle can changes the range of changed color of methyl red from

Fig.8

UV-visible absorption spectra of methyl red solution with different concentrations of CTAB at 303.15 K

4.4-6.2 to 3.0-5.0 and makes the pKa value of methyl red decrease remarkably. Generally the significant decrease of pKa value is attributed to electrical double layer of CTAB micelle which absorbs selectively MR- and makes the ionization equilibrium of methyl red move obviously to the right.

4

Conclusions

Fig.7

Dependence of the half-widths of MR- and HMR on the concentration of SDS at 298.15 K

In this study, a multi-peaks Gaussian fitting method based on the UV-visible absorption spectra is firstly used to determine the pKa value of organic dyes such as methyl red. The reliability of the method is adequately proved by an excellent agreement of the measurement results with literature. There are several advantages, such as the easy operational procedure, explicit physical meaning, and the accurate measurement results for the method. The relative concentration of the MR- and HMR in solution has been determined by the relative integrated absorbance calculated from multi-peaks Gaussian fitting method based on the UV-visible spectra. This method avoids successfully the systematic error of 3%-5% of pKa measurement from the standard curves which is established from the absorbance of MRmaximum absorption wavelength at 425 nm and HMR maximum absorption wavelength at 520 nm versus concentration of MR- and HMR at the methyl red color range, respectively.

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Moreover, the effect of SDS and CTAB on ionization equilibrium of methyl red also has been studied and some reliable results with the method have been obtained. The spectral lineshape parameters such as A1, A2, λmax1, λmax2, w1 and w2 of MRand HMR that obtained from multi-peaks Gaussian fitting method on the UV-visible spectra of SDS-methyl red and CTAB-methyl red solutions have been firstly discovered to be sensitive to aggregation behavior of surfactants SDS and CTAB. The CMC values can be determined by the dependence of the three sets of parameters on the surfactant concentration which should support each other. References
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