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Kinetics of alkaline fading of malachite green and crystal violet in critical solutions
Journal of Molecular Liquids 230 (2017) 423–428
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Kinetics of alkaline fading of malachite green and crystal violet in critical solutions Zhiyun Chen a, Zilin Yang a, Weiguo Shen a,b,⁎ a b
School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China Department of Chemistry, Lanzhou University, Lanzhou 730000, China
a r t i c l e
i n f o
Article history: Received 25 October 2016 Accepted 4 January 2017 Available online 06 January 2017 Keywords: Reaction in critical media Critical singularity in reaction Critical slowing down Alkaline fading Three-wavelength spectrophotometry
a b s t r a c t The reaction kinetics for alkaline fading of malachite green (MG) in the critical binary solution 2butoxyethanol + water and of crystal violet (CV) in the critical microemulsion water/bis(2-ethylhexyl) sodium sulfosuccinate (AOT)/n-decane with the molar ratio of water to AOT being 30 have been studied by the threewavelength UV-spectrophotometry at initial reaction stage and various temperatures. It was found that the reaction rates kobs for both above reactions were well described by the Arrhenius equation in the temperature ranges far away from the critical points. The critical slowing down effects were observed in the near-critical regions and the corresponding critical slowing down exponents were determined to be 0.146 ± 0.014 and 0.035 ± 0.006 for the two reactions, respectively. The former exhibited both the dynamic and thermodynamic critical slowing down effects; while the latter showed no thermodynamic singularity. It was attributed to the particular experimental design in this work that made the dimer/monomer droplet equilibrium in the critical microemulsion system no longer affect the reaction kinetics. © 2017 Elsevier B.V. All rights reserved.
1. Introduction It is well-known that binary solutions near the critical solution points exhibit the universal critical singularity resulting from the critical fluctuations. When the critical solutions are used as media for chemical reactions, their critical anomalies may possibly affect the reaction kinetics. This phenomenon has been studied both theoretically and experimentally for several decades [1–7], most of which revealed a critical slowing down effect in the near-critical region [3–7]. The critical slowing down effect of the reaction may be explained by two aspects: (1) from dynamic anomaly, relating to the divergence of the viscosity or the vanishing of the mutual diffusion coefficient; (2) from thermodynamic anomaly, being attributed to the vanishing of the derivative of the Gibbs free energy change of the reaction with respect to the extent of Þ ð∂ΔGÞ=∂cÞce , which obeys the the reaction at the equilibrium ð∂ΔG ∂c e Griffiths and Wheeler rule [8]. In our previous work, we studied the kinetics of a series of chemical reactions in a few critical binary solutions and observed both the dynamic and thermodynamic slowing down effects for almost all the first order reactions we investigated, where the thermodynamic slowing down effects were characterized by exponents with the values coinciding with the predictions of the Griffiths and Wheeler rule [9–12]. ⁎ Corresponding author at: School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China. E-mail address: [email protected] (W. Shen).
http://dx.doi.org/10.1016/j.molliq.2017.01.012 0167-7322/© 2017 Elsevier B.V. All rights reserved.
It is well known that mixing water, bis(2-ethylhexyl) sodium sulfosuccinate (AOT) and n-decane can form a thermodynamically stable, homogeneous and transparent water-in-oil microemulsion, where the water cores are stabilized by surfactant interfaces. The resulting water droplets are uniformly dispersed in the non-polar solvent n-decane [13,14]. The water-in-oil microemulsion droplets serve as microreactors for chemical reactions by dissolving water soluble reactants in their cores [15]. These microemulsion systems are considered as pseudo binary solutions exhibiting liquid-liquid equilibria under certain conditions, where the water droplets have different concentrations in the coexisting liquid phases. This kind of coexistence curve and the corresponding critical phenomena have already been the subject of study [16–18]. We have previously used the microemulsion water/AOT/n-decane reaction system as the solvent medium to study the critical slowing down effect in the case of the oxidation of iodide ion by persulfate ion [19]. In that study, iodide ion and persulfate ion were first dissolved in separate but identical microemulsion droplets. The concentration of iodide ion was sufficiently dilute that the number density of iodide ions was much less than the number density of the droplets. By comparison, the number density of persulfate ions was rather much larger. These two microemulsions then were mixed to start the reaction and the reaction kinetics was investigated by the isothermal titration microcalorimeter (ITC) method. With this experimental design, the reaction was analogous to a pseudo-first-order reaction in which the dilute microemulsion droplets containing iodide ion reacted with the
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water/AOT/n-decane with the molar ratios ω of water to AOT being 30 (reaction II): CVþ þ OH− →CVOH
ð2Þ
where the quantities of both reactants in the reaction system are significantly larger than that of the droplet. Above two reactions are pseudo-first-order reactions in the forward and backward directions as long as the concentration of OH− is sufficiently larger than that of the dye, and their reaction media have lower critical points. Each of these reactions is monitored by a UV spectrophotometer in a wide temperature range below the critical point. The reaction rates are deduced from the dependence of the absorbance of the dye on the reaction time at different temperatures. The measurements confirm both the dynamic and thermodynamic slowing down effects for the first reaction, while ruling out the thermodynamic singularity for the second reaction.
Fig. 1. Structures of (a) MG, (b) CV, (c) 2BE, and (d) AOT.
relatively concentrated droplet containing persulfate ion. The droplets merge and separate rapidly, therefore it can be assumed that the chemical equilibrium exists between the dimer and monomer droplets [19]. Indeed, we observed slowing down effects arising from both the dynamic and thermodynamic sources in the case of this reaction. The latter was thought to have its origin in the singularity in the dimer/monomer equilibrium of the droplets in the critical microemulsion. The effect was characterized by an exponent having a value which was in accordance with the prediction by the Griffiths-Wheeler rule. By inference, if an iodide ion aqueous solution, instead of the water/ AOT/n-decane microemulsion containing iodide ion, was added into the critical microemulsion containing persulfate ion used to start the reaction, and the quantities of the both reactants were significantly larger than that of the microemulsion droplet, one could expect that no thermodynamic slowing down effect would be detected. It is interesting to try an experiment based on this idea in order to test the above inference. However, it cannot be achieved by the ITC measurement method, because the heat of mixing of iodide ion aqueous solution with the microemulsion is significant. On the other hand, the studies on the kinetics of the reactions for the alkaline fading of triphenylmethane dyes such as crystal violet (CV) and malachite green (MG) in aqueous media are convenient because the reactions may be easily monitored by measurements of the absorbance of the dyes in the solutions [20–22]. The critical slowing down effects for alkaline fading of CV in the critical binary solution of 2-butoxyethanol (2BE) + water have been studied by ITC and UV spectrophotometry in our previous work and both the dynamic and thermodynamic effects were observed. The effects were characterized by critical slowing down exponents with values consistent with the theoretical predictions [10]. In this work, as a further test of the universal critical anomaly of alkaline fading of triphenylmethane dye in a critical binary solution, we first investigate the reaction of alkaline fading of MG in the critical binary solution of 2BE + water (reaction I): MGþ þ OH− →MGOH
ð1Þ
Then we focus on the kinetics of alkaline fading of CV started by adding OH− aqueous solution into the critical microemulsion CV/
2. Experimental section 2.1. Chemicals Both MG (analytical grade) and CV (analytical grade) were provided by Sinopharm Chemical Reagent Co., Ltd. Sodium hydroxide (NaOH, analytical grade), potassium hydrogen phthalate (≥99.8% mass fraction) were purchased from Shanghai Ling Feng Chemical Reagent Co., Ltd. The n-decane (≥ 98% mass fraction), 2BE (≥ 99% mass fraction) and AOT (≥ 96% mass fraction) were purchased from Aladdin Chemistry Co., Ltd., Alfa Aesar and Sigma, respectively. The structures of MG, CV, 2BE and AOT are shown in Fig. 1. All reagents were used as received except for AOT, which was dried over P2O5 in a desiccator for 2 week. Ultrapure water used in this study was taken from an Ultra-pure water machine (DZG-303A, Leading, China) with a resistivity 18.2 MΩ cm.
2.2. Determination of the critical compositions and critical temperatures of the reaction media We applied the equal-volume principle [10,16] to search for the critical compositions of the binary solution of 2BE + water and water/AOT/ n-decane microemulsion. With this method, the critical mass fraction wc of 2BE in its binary aqueous solution was determined to be 0.295 ± 0.001, which agreed well with the literature values of 0.294 [23] and 0.2953 [9–10]. The critical mass fraction wc of n-decane in the water/AOT/n-decane microemulsion with ω being 30.0 was determined to be 0.860 ± 0.002, which agreed with the reported value 0.863 [16]. The phase separation temperatures at the critical compositions were then determined, which were taken as the critical temperatures Tc. The value of Tc for 2BE + water solution was determined to be 321.86 K, in well agreement with the literature values 321.7 K [23] and 321.80 K [10]. The value of Tc for water/AOT/n-decane microemulsion reported in this work and the literature [16] was 316.77 K and 318.26 K, respectively; the difference may be attributed to using chemicals from different sources and different techniques for drying, and the difference in impurities introduced in the experimental process.
Table 1 Values of lower critical temperature for binary solution of 2BE + water and water/AOT/n-decane microemulsion with the molar ratio of water to AOT ω = 30 and their reaction systems. Tc/K 2BE 2BE 2BE 2BE
+ + + +
water MG + water NaOH + water NaOH + MG + water (after reaction)
21.86 21.86 21.92 21.93
Tc/K ± ± ± ±
0.05 0.05 0.05 0.05
Water/AOT/n-decane (CV + water)/AOT/n-decane (NaOH + water)/AOT/n-decane (NaOH + CV + water)/AOT/n-decane (after reaction)
316.77 316.79 317.44 317.49
± ± ± ±
0.05 0.05 0.05 0.05
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Fig. 2. Variations of the absorption spectrum with the reaction time and wavelength for: (a) the alkaline fading of MG in 2BE + water at T = 321.760 K; (b) the alkaline fading of CV in water/AOT/n-decane microemulsion with ω = 30 at T = 310.493 K.
2.3. Sample preparation The amounts of reagents for preparing samples with the required concentrations in this work were determined by weighing. A NaOH aqueous solution was prepared and titrated with potassium hydrogen phthalate to determine its accurate concentration, which was used as a stock solution to prepare various NaOH aqueous solutions with required concentrations. A properly diluted NaOH stock solution was mixed with 2BE to form a ternary aqueous solution denoted as (1) where the mass fraction of 2BE was 0.295 and the concentration of NaOH was 1.725 × 10− 4 mol L−1. A MG aqueous solution was prepared and mixed with 2BE to form a ternary aqueous solution denoted as (2) where the mass fraction of 2BE was also 0.295 and the concentration of MG was 3.70 × 10−3 mol L−1. We mixed 3.0 mL of solution (1) and 7.2 μL of solution (2) to form reaction system I and rechecked the critical concentration again by the equal-volume principle and no shift of wc was detected. A microemulsion containing appropriate amounts of AOT, CV aqueous solution and n-decane, was prepared where the mass fractions of ndecane and CV aqueous solution were 0.863 and 0.073, respectively; which was denoted as microemulsion (3). We mixed about 2.2 g microemulsion (3) and about 9 μL of NaOH aqueous solution with the concentration of NaOH being 0.100 mol L−1 to form the microemulsion reaction system II with ω being 30 and the mass fraction of n-decane
being 0.860, the concentration ratio of NaOH to CV being about 100. The critical concentration of reaction system II was examined and found that it had the same critical mass fraction of n-decane with the critical microemulsion water/AOT/n-decane. The critical temperatures for those systems after additions of the reactants were also re-measured and are listed in Table 1. It can be seen from Table 1 that no significant shifts of the critical temperature after addition of the reactants into the two critical reaction media were observed except for addition of NaOH into water/AOT/n-decane microemulsion, where as much as a 0.7 K upward shift was detected. Thus we used the values of the critical temperatures of the systems after reactions in quantitative examinations of the critical singularities of the reactions in Section 3. 2.4. UV spectrophotometry and kinetics measurement The kinetics of alkaline fading reactions were investigated by UV–vis spectrophotometer (UV-2450, Shimadzu, Japan) with a thermostatted cell holder in a temperature region far away from the critical point, where the temperature was stabilized by continuously circulating water to the holder from a water bath with temperature stability better than ±0.05 K. In the near-critical region, much less temperature fluctuations are required for examination of the critical phenomena in the reaction, thus a home-built metal bath with the temperature being controlled within ± 0.005 K was used for kinetic studies. The
Fig. 3. Plots of the absorbance resulted from the light scattering versus wavelength: (a) for the critical solution of 2BE + water at 321.71 K; (b) for the critical microemulsion water/AOT/ndecane with ω = 30 at 316.76 K.
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temperature in the baths was measured by a thermistor connected to a Keithley 2700 digital multimeter with a precision of 0.001 K. The kinetic measurements started after adding 7.2 μL of solution (2) into 3.0 mL of solution (1) for reaction I and after adding 9 μL of NaOH aqueous into 3.0 mL microemulsion (3) for reaction II, respectively. The spectrophotometer automatically recorded the absorbance of each system at various reaction times and wavelengths. The measurements were repeated at least 2 times, which were used to deduce the average values of the reaction rates and to evaluate their uncertainties as we will describe in the next sections. Fig. 2a and b show variations of absorption spectrums of the reactants MG and CV with the reaction time, respectively. It can be seen from Fig. 2 that the absorbance of MG at λmax = 624 nm or CV at λmax = 595 nm decreases with the reaction time significantly. In the near-critical temperature region, large critical fluctuations result in large light scattering; hence they significantly disturb the kinetics measurements. Therefore, a three-wavelength correction must be applied to resolve this problem. As described in our previous work, the relative absorbance (ΔA) instead of absorbance A was measured to eliminate the critical scattering, which is expressed by [24]: mAλ1 þ nAλ3 ¼ ΔA ¼ Aλ2 − mþn
mελ1 þ nελ3 ε λ2 − lc ¼ Δεlc mþn
ð3Þ
where Aλi and ελi are the absorbance and the molar absorption coefficient at wavelength λi (i = 1, 2, 3); λ2 is the maximum absorption wavelength of the reactant, λ1 and λ3 are wavelengths being selected on flanks of λ2, m or n is the difference of λ2 and λ1 or λ3 and λ2, i.e. m = λ2 − λ1 and n = λ3 − λ2; Δε, l and c are the relative molar absorption coefficient, the light path length of the cuvette and the concentration of the dye, respectively. In order to achieve sufficiently large values of ΔA and linear wavelength dependences of the absorbance resulted from the critical light scattering in the region of λ1 ≤ λ ≤ λ3 for both critical media in the near-critical regions we carefully selected λ1 = 620 nm, λ3 = 650 nm for reaction I and λ1 = 520 nm, λ3 = 600 nm for reaction II, respectively. With this arrangement the critical light scattering was essentially irrelevant to ΔA [9–10]. Fig. 3a and b show the linear relations between the absorbance and the wavelength for the critical 2BE aqueous solution at 321.71 K and for the critical microemulsion water/AOT/n-decane with ω = 30 at 316.76 K, respectively.
Table 2 Values of observed rate constant kobs for alkaline fading of MG in 2BE + water at various temperatures. T(K)
1000kobs/s−1
T/K
1000kobs/s−1
307.94 308.90 309.86 310.80 311.76 312.72 313.69 314.60 315.53 316.55 317.53 318.28 319.07 319.77 319.98
0.63 0.72 0.78 0.86 0.92 1.03 1.10 1.19 1.29 1.41 1.52 1.60 1.75 1.86 1.88
320.27 320.34 320.41 320.86 321.02
1.98 1.94 1.99 2.14 2.05
± ± ± ± ±
0.05 0.05 0.06 0.06 0.06
321.708 321.757 321.760 321.781 321.808 321.852 321.884 321.901 321.908
1.93 1.90 1.85 1.91 1.73 1.66 1.64 1.51 1.35
± ± ± ± ± ± ± ± ±
0.16 0.16 0.16 0.15 0.14 0.14 0.14 0.13 0.13
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05
2.5. Data analysis All of the experimental data were collected in the one-phase region. The concentration of OH− was much higher than that of dye in our experimental design, thus both of the reactions may be taken as pseudofirst-order reactions. In the initial reaction stage, the reaction rate can be expressed by −
dc ¼ k2 cc0 ¼ kobs c dt
ð4Þ
where k2 is the second-order reaction rate constant, kobs is the observed rate constant, c and are the concentrations of dye and NaOH, respectively. Initially, the absorbance decreases exponentially due to the hydrolysis yielding the colorless carbinol. Using the Lambert-Beer law and integrating Eq. (4) yields ln A ¼ lnA0 −kobs t
ð5Þ
where A0 is the absorbance of the dye at the initial time of the reaction. Combination of Eqs. (3) and (4) yields dΔA ¼ −kobs ΔA dt
ð6Þ
Integration of Eq. (6) gives lnΔA ¼ ln ΔA0 −kobs t
ð7Þ
where ΔA0 is the relative absorbance at the initial time. We plotted lnA and lnΔA versus reaction time for non-critical region and near-critical Table 3 Values of observed rate constant kobs for alkaline fading of CV in water/AOT/n-decane microemulsion with the molar ratio of water to AOT ω = 30 at various temperatures.
Fig. 4. Plots of lnA and lnΔA versus reaction time t for alkaline fading of MG in 2BE + water at 313.69 K (■) and 321.760 K ( ). The lines represent the results of the fittings with Eqs. (5) and (7), respectively.
T/K
10000kobs/s−1
T/K
10000kobs/s−1
309.161 310.493 311.145 312.450 312.556 313.439 313.814 314.643 314.823 315.478 316.054 316.392
0.62 0.72 0.80 0.88 0.88 1.00 1.08 1.20 1.17 1.24 1.32 1.44
316.492 316.587 316.688 316.688 316.789 316.891 316.976 317.063 317.063 317.156 317.266 317.364 317.457
1.42 1.43 1.39 1.37 1.39 1.35 1.38 1.39 1.38 1.36 1.34 1.40 1.34
± ± ± ± ± ± ± ± ± ± ± ±
0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03
± ± ± ± ± ± ± ± ± ± ± ± ±
0.03 0.03 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
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Fig. 5. Plots of ln{kobs} versus 1000/T: (a) for alkaline fading of MG in 2BE + water; (b) for alkaline fading of CV in water/AOT/n-decane microemulsion with ω = 30. The lines represent the results of linear fittings according to the Arrhenius formula.
region, respectively. The critical region was defined as (Tc − T) b 0.91 K for reaction I, and (Tc − T) b 0.82 K for reaction II. As examples, these plots for reaction I at (Tc − T) = 8.24 K and (Tc − T) = 0.17 K respectively are shown in Fig. 4. 3. Results and discussions Linear least-squares fittings of the kinetic data of the two reactions gave the values of kobs at various temperatures. As we described in Section 2.4, the measurements were repeated at least 2 times, and the average values of kobs were taken as the results; which, together with their estimated uncertainties, are listed in Tables 2 and 3. The uncertainties were evaluated by the differences of the repeated measurements. The Arrhenius formula is written as ln fkb g ¼ −Ea =RT þ B;
ð8Þ
where Ea is the activation energy, R is the gas constant, T is the temperature and B is a constant. Fig. 5a and b show good linear relations between ln{kobs} and 1/T in the non-critical regions, indicating the validity of the Arrhenius formula in the temperature ranges far away from the critical points, where the observed rate constants kobs are
called the background rate constants kb. Linear least-squares fittings of the values kobs in the non-critical regions (i.e. the values of kb) listed in Tables 2 and 3 with Eq. (8) gave the values of activation energy Ea, which were 73.0 ± 0.8 kJ mol− 1 for reaction I and 92.2 ± 1.9 kJ mol−1 for reaction II, respectively. For a first-order or a pseudo-first-order reaction in both directions, the reaction rate in the critical region may be expressed as [10] ln
kobs ¼ flnτ k1
ð9Þ
where k1 is the first-order rate constant in the forward direction without thermodynamic slowing down effect, τ = |Tc − T| / Tc, Tc is the critical temperature of the reaction system, f is the critical exponent characterizing the thermodynamic slowing down effect of a reaction. According to the Griffiths-Wheeler rule [8], f is dependent on the number of inert components in a reaction system. As only one density variable is held fixed (the mass fraction of 2BE is constant in the process of Þ should go to zero weakly as the temperature apreaction), ð∂ΔG ∂c e proaches to the critical point, and the critical exponent f in Eq. (9) is expected to be about 0.11. In addition, a dynamic slowing down effect with an exponent y = 0.041 contributed by weak divergence of viscosity of the reaction system should be also considered when the
Fig. 6. Plots of ln{kobs/kb} versus lnτ: (a) for alkaline fading of MG in 2BE + water, (b) for alkaline fading of CV in water/AOT/n-decane microemulsion with ω = 30 near the critical points. The lines represent the results of the fittings with Eq. (11).
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temperature approaches the critical point [9–10,25] ln
k1 ∝ylnτ kb
ð10Þ
where kb may be calculated by Eq. (8) for each of temperatures in the critical region. Combination of Eqs. (9) and (10) gives ln
kobs ∝ð f þ yÞlnτ ¼ plnτ kb
ð11Þ
where f + y = 0.151 is the theoretical prediction. As shown in the Fig. 6a, a plot of ln{kobs/kb} ln kkobs versus lnτ for alkab
line fading of MG in the critical solution of 2BE + water yields a straight line. The value of the slope p was found to be 0.146 ± 0.014 by the leastsquares fit, which agreed with the experimental results p = 0.133 ± 0.012 for alkaline fading of CV in the same critical binary solution [10] and the theoretical prediction p = 0.151. Fig. 6b shows linear dependences of ln{kobs/kb} on lnτ for alkaline fading of CV in the critical microemulsion water/AOT/n-decane near the critical point. The critical slowing down exponent p was given to be 0.035 ± 0.006 by fitting the experimental results with Eq. (11), which was close to the value of 0.041 of the dynamic slowing down exponent y, indicating that no thermodynamic slowing down effect (f = 0) was detected. It failed to agree with the result reported for the oxidation of iodide ion I− by persulfate ion S2O28 − in the same critical microemulsion with ω = 35, where the thermodynamic slowing down exponent f was found to be 0.187 which was associated with the singularity in the dimer/monomer droplet equilibrium in this critical microemulsion [19]. This inconsistency may be attributed to the fact that in this work OH− aqueous solution, instead of the water/ AOT/n-decane microemulsion containing OH−, was added into the water/AOT/n-decane microemulsion containing CV to start the reaction, and the quantities of both reactants OH− and CV are significantly larger than that of the microemulsion droplet; hence the reaction occurred essentially in the water core of the droplet, independently of the dimer/ monomer droplet equilibrium in the microemulsion. As a result, no thermodynamic singularity was observed. However, the reaction is expected to involve the transport of CV and OH−, which occurs in the form of the diffusion of the droplets as their carriers in the critical microemulsion. Therefore, the reaction exhibits only a weak dynamic slowing down effect in the critical microemulsion system. 4. Conclusions The kinetics of alkaline fading of MG and CV near and far away from the critical temperatures in the critical solution of 2BE + water and the critical microemulsion water/AOT/n-decane with ω being 30 were studied by UV-spectrophotometry with the three-wavelength corrections.
Both of the reactions obeyed the Arrhenius equation when the reaction temperatures were far away from the critical points. Slowing down effects from both the thermodynamic and the dynamic sources were observed for the alkaline fading of MG in 2BE aqueous solution in the nearcritical region characterized by the critical slowing down exponent with the value of 0.146 which agreed well with the previous experimental observations [10] and the theoretical prediction of 0.151. However, the value of the critical exponent determined for the alkaline fading of CV in the critical microemulsion water/AOT/n-decane was only 0.035, which indicates that only a dynamic critical slowing down could be detected. It was attributed to the fact that the reaction is independent of the dimer/monomer droplet equilibrium in the microemulsion. The cause appears to be the fact that insufficiently diluted OH− aqueous solution instead of the water/AOT/n-decane microemulsion containing sufficiently diluted OH−, was added into the microemulsion containing CV to start the reaction.
Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 21403067, 21373080, and 21373085), the Fundamental Research Funds for the Central Universities (No. WJ1516001). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
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Kinetics of alkaline fading of malachite green and crystal violet in critical solutions Zhiyun Chen a, Zilin Yang a, Weiguo Shen a,b,⁎ a b
School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China Department of Chemistry, Lanzhou University, Lanzhou 730000, China
a r t i c l e
i n f o
Article history: Received 25 October 2016 Accepted 4 January 2017 Available online 06 January 2017 Keywords: Reaction in critical media Critical singularity in reaction Critical slowing down Alkaline fading Three-wavelength spectrophotometry
a b s t r a c t The reaction kinetics for alkaline fading of malachite green (MG) in the critical binary solution 2butoxyethanol + water and of crystal violet (CV) in the critical microemulsion water/bis(2-ethylhexyl) sodium sulfosuccinate (AOT)/n-decane with the molar ratio of water to AOT being 30 have been studied by the threewavelength UV-spectrophotometry at initial reaction stage and various temperatures. It was found that the reaction rates kobs for both above reactions were well described by the Arrhenius equation in the temperature ranges far away from the critical points. The critical slowing down effects were observed in the near-critical regions and the corresponding critical slowing down exponents were determined to be 0.146 ± 0.014 and 0.035 ± 0.006 for the two reactions, respectively. The former exhibited both the dynamic and thermodynamic critical slowing down effects; while the latter showed no thermodynamic singularity. It was attributed to the particular experimental design in this work that made the dimer/monomer droplet equilibrium in the critical microemulsion system no longer affect the reaction kinetics. © 2017 Elsevier B.V. All rights reserved.
1. Introduction It is well-known that binary solutions near the critical solution points exhibit the universal critical singularity resulting from the critical fluctuations. When the critical solutions are used as media for chemical reactions, their critical anomalies may possibly affect the reaction kinetics. This phenomenon has been studied both theoretically and experimentally for several decades [1–7], most of which revealed a critical slowing down effect in the near-critical region [3–7]. The critical slowing down effect of the reaction may be explained by two aspects: (1) from dynamic anomaly, relating to the divergence of the viscosity or the vanishing of the mutual diffusion coefficient; (2) from thermodynamic anomaly, being attributed to the vanishing of the derivative of the Gibbs free energy change of the reaction with respect to the extent of Þ ð∂ΔGÞ=∂cÞce , which obeys the the reaction at the equilibrium ð∂ΔG ∂c e Griffiths and Wheeler rule [8]. In our previous work, we studied the kinetics of a series of chemical reactions in a few critical binary solutions and observed both the dynamic and thermodynamic slowing down effects for almost all the first order reactions we investigated, where the thermodynamic slowing down effects were characterized by exponents with the values coinciding with the predictions of the Griffiths and Wheeler rule [9–12]. ⁎ Corresponding author at: School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China. E-mail address: [email protected] (W. Shen).
http://dx.doi.org/10.1016/j.molliq.2017.01.012 0167-7322/© 2017 Elsevier B.V. All rights reserved.
It is well known that mixing water, bis(2-ethylhexyl) sodium sulfosuccinate (AOT) and n-decane can form a thermodynamically stable, homogeneous and transparent water-in-oil microemulsion, where the water cores are stabilized by surfactant interfaces. The resulting water droplets are uniformly dispersed in the non-polar solvent n-decane [13,14]. The water-in-oil microemulsion droplets serve as microreactors for chemical reactions by dissolving water soluble reactants in their cores [15]. These microemulsion systems are considered as pseudo binary solutions exhibiting liquid-liquid equilibria under certain conditions, where the water droplets have different concentrations in the coexisting liquid phases. This kind of coexistence curve and the corresponding critical phenomena have already been the subject of study [16–18]. We have previously used the microemulsion water/AOT/n-decane reaction system as the solvent medium to study the critical slowing down effect in the case of the oxidation of iodide ion by persulfate ion [19]. In that study, iodide ion and persulfate ion were first dissolved in separate but identical microemulsion droplets. The concentration of iodide ion was sufficiently dilute that the number density of iodide ions was much less than the number density of the droplets. By comparison, the number density of persulfate ions was rather much larger. These two microemulsions then were mixed to start the reaction and the reaction kinetics was investigated by the isothermal titration microcalorimeter (ITC) method. With this experimental design, the reaction was analogous to a pseudo-first-order reaction in which the dilute microemulsion droplets containing iodide ion reacted with the
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water/AOT/n-decane with the molar ratios ω of water to AOT being 30 (reaction II): CVþ þ OH− →CVOH
ð2Þ
where the quantities of both reactants in the reaction system are significantly larger than that of the droplet. Above two reactions are pseudo-first-order reactions in the forward and backward directions as long as the concentration of OH− is sufficiently larger than that of the dye, and their reaction media have lower critical points. Each of these reactions is monitored by a UV spectrophotometer in a wide temperature range below the critical point. The reaction rates are deduced from the dependence of the absorbance of the dye on the reaction time at different temperatures. The measurements confirm both the dynamic and thermodynamic slowing down effects for the first reaction, while ruling out the thermodynamic singularity for the second reaction.
Fig. 1. Structures of (a) MG, (b) CV, (c) 2BE, and (d) AOT.
relatively concentrated droplet containing persulfate ion. The droplets merge and separate rapidly, therefore it can be assumed that the chemical equilibrium exists between the dimer and monomer droplets [19]. Indeed, we observed slowing down effects arising from both the dynamic and thermodynamic sources in the case of this reaction. The latter was thought to have its origin in the singularity in the dimer/monomer equilibrium of the droplets in the critical microemulsion. The effect was characterized by an exponent having a value which was in accordance with the prediction by the Griffiths-Wheeler rule. By inference, if an iodide ion aqueous solution, instead of the water/ AOT/n-decane microemulsion containing iodide ion, was added into the critical microemulsion containing persulfate ion used to start the reaction, and the quantities of the both reactants were significantly larger than that of the microemulsion droplet, one could expect that no thermodynamic slowing down effect would be detected. It is interesting to try an experiment based on this idea in order to test the above inference. However, it cannot be achieved by the ITC measurement method, because the heat of mixing of iodide ion aqueous solution with the microemulsion is significant. On the other hand, the studies on the kinetics of the reactions for the alkaline fading of triphenylmethane dyes such as crystal violet (CV) and malachite green (MG) in aqueous media are convenient because the reactions may be easily monitored by measurements of the absorbance of the dyes in the solutions [20–22]. The critical slowing down effects for alkaline fading of CV in the critical binary solution of 2-butoxyethanol (2BE) + water have been studied by ITC and UV spectrophotometry in our previous work and both the dynamic and thermodynamic effects were observed. The effects were characterized by critical slowing down exponents with values consistent with the theoretical predictions [10]. In this work, as a further test of the universal critical anomaly of alkaline fading of triphenylmethane dye in a critical binary solution, we first investigate the reaction of alkaline fading of MG in the critical binary solution of 2BE + water (reaction I): MGþ þ OH− →MGOH
ð1Þ
Then we focus on the kinetics of alkaline fading of CV started by adding OH− aqueous solution into the critical microemulsion CV/
2. Experimental section 2.1. Chemicals Both MG (analytical grade) and CV (analytical grade) were provided by Sinopharm Chemical Reagent Co., Ltd. Sodium hydroxide (NaOH, analytical grade), potassium hydrogen phthalate (≥99.8% mass fraction) were purchased from Shanghai Ling Feng Chemical Reagent Co., Ltd. The n-decane (≥ 98% mass fraction), 2BE (≥ 99% mass fraction) and AOT (≥ 96% mass fraction) were purchased from Aladdin Chemistry Co., Ltd., Alfa Aesar and Sigma, respectively. The structures of MG, CV, 2BE and AOT are shown in Fig. 1. All reagents were used as received except for AOT, which was dried over P2O5 in a desiccator for 2 week. Ultrapure water used in this study was taken from an Ultra-pure water machine (DZG-303A, Leading, China) with a resistivity 18.2 MΩ cm.
2.2. Determination of the critical compositions and critical temperatures of the reaction media We applied the equal-volume principle [10,16] to search for the critical compositions of the binary solution of 2BE + water and water/AOT/ n-decane microemulsion. With this method, the critical mass fraction wc of 2BE in its binary aqueous solution was determined to be 0.295 ± 0.001, which agreed well with the literature values of 0.294 [23] and 0.2953 [9–10]. The critical mass fraction wc of n-decane in the water/AOT/n-decane microemulsion with ω being 30.0 was determined to be 0.860 ± 0.002, which agreed with the reported value 0.863 [16]. The phase separation temperatures at the critical compositions were then determined, which were taken as the critical temperatures Tc. The value of Tc for 2BE + water solution was determined to be 321.86 K, in well agreement with the literature values 321.7 K [23] and 321.80 K [10]. The value of Tc for water/AOT/n-decane microemulsion reported in this work and the literature [16] was 316.77 K and 318.26 K, respectively; the difference may be attributed to using chemicals from different sources and different techniques for drying, and the difference in impurities introduced in the experimental process.
Table 1 Values of lower critical temperature for binary solution of 2BE + water and water/AOT/n-decane microemulsion with the molar ratio of water to AOT ω = 30 and their reaction systems. Tc/K 2BE 2BE 2BE 2BE
+ + + +
water MG + water NaOH + water NaOH + MG + water (after reaction)
21.86 21.86 21.92 21.93
Tc/K ± ± ± ±
0.05 0.05 0.05 0.05
Water/AOT/n-decane (CV + water)/AOT/n-decane (NaOH + water)/AOT/n-decane (NaOH + CV + water)/AOT/n-decane (after reaction)
316.77 316.79 317.44 317.49
± ± ± ±
0.05 0.05 0.05 0.05
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Fig. 2. Variations of the absorption spectrum with the reaction time and wavelength for: (a) the alkaline fading of MG in 2BE + water at T = 321.760 K; (b) the alkaline fading of CV in water/AOT/n-decane microemulsion with ω = 30 at T = 310.493 K.
2.3. Sample preparation The amounts of reagents for preparing samples with the required concentrations in this work were determined by weighing. A NaOH aqueous solution was prepared and titrated with potassium hydrogen phthalate to determine its accurate concentration, which was used as a stock solution to prepare various NaOH aqueous solutions with required concentrations. A properly diluted NaOH stock solution was mixed with 2BE to form a ternary aqueous solution denoted as (1) where the mass fraction of 2BE was 0.295 and the concentration of NaOH was 1.725 × 10− 4 mol L−1. A MG aqueous solution was prepared and mixed with 2BE to form a ternary aqueous solution denoted as (2) where the mass fraction of 2BE was also 0.295 and the concentration of MG was 3.70 × 10−3 mol L−1. We mixed 3.0 mL of solution (1) and 7.2 μL of solution (2) to form reaction system I and rechecked the critical concentration again by the equal-volume principle and no shift of wc was detected. A microemulsion containing appropriate amounts of AOT, CV aqueous solution and n-decane, was prepared where the mass fractions of ndecane and CV aqueous solution were 0.863 and 0.073, respectively; which was denoted as microemulsion (3). We mixed about 2.2 g microemulsion (3) and about 9 μL of NaOH aqueous solution with the concentration of NaOH being 0.100 mol L−1 to form the microemulsion reaction system II with ω being 30 and the mass fraction of n-decane
being 0.860, the concentration ratio of NaOH to CV being about 100. The critical concentration of reaction system II was examined and found that it had the same critical mass fraction of n-decane with the critical microemulsion water/AOT/n-decane. The critical temperatures for those systems after additions of the reactants were also re-measured and are listed in Table 1. It can be seen from Table 1 that no significant shifts of the critical temperature after addition of the reactants into the two critical reaction media were observed except for addition of NaOH into water/AOT/n-decane microemulsion, where as much as a 0.7 K upward shift was detected. Thus we used the values of the critical temperatures of the systems after reactions in quantitative examinations of the critical singularities of the reactions in Section 3. 2.4. UV spectrophotometry and kinetics measurement The kinetics of alkaline fading reactions were investigated by UV–vis spectrophotometer (UV-2450, Shimadzu, Japan) with a thermostatted cell holder in a temperature region far away from the critical point, where the temperature was stabilized by continuously circulating water to the holder from a water bath with temperature stability better than ±0.05 K. In the near-critical region, much less temperature fluctuations are required for examination of the critical phenomena in the reaction, thus a home-built metal bath with the temperature being controlled within ± 0.005 K was used for kinetic studies. The
Fig. 3. Plots of the absorbance resulted from the light scattering versus wavelength: (a) for the critical solution of 2BE + water at 321.71 K; (b) for the critical microemulsion water/AOT/ndecane with ω = 30 at 316.76 K.
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temperature in the baths was measured by a thermistor connected to a Keithley 2700 digital multimeter with a precision of 0.001 K. The kinetic measurements started after adding 7.2 μL of solution (2) into 3.0 mL of solution (1) for reaction I and after adding 9 μL of NaOH aqueous into 3.0 mL microemulsion (3) for reaction II, respectively. The spectrophotometer automatically recorded the absorbance of each system at various reaction times and wavelengths. The measurements were repeated at least 2 times, which were used to deduce the average values of the reaction rates and to evaluate their uncertainties as we will describe in the next sections. Fig. 2a and b show variations of absorption spectrums of the reactants MG and CV with the reaction time, respectively. It can be seen from Fig. 2 that the absorbance of MG at λmax = 624 nm or CV at λmax = 595 nm decreases with the reaction time significantly. In the near-critical temperature region, large critical fluctuations result in large light scattering; hence they significantly disturb the kinetics measurements. Therefore, a three-wavelength correction must be applied to resolve this problem. As described in our previous work, the relative absorbance (ΔA) instead of absorbance A was measured to eliminate the critical scattering, which is expressed by [24]: mAλ1 þ nAλ3 ¼ ΔA ¼ Aλ2 − mþn
mελ1 þ nελ3 ε λ2 − lc ¼ Δεlc mþn
ð3Þ
where Aλi and ελi are the absorbance and the molar absorption coefficient at wavelength λi (i = 1, 2, 3); λ2 is the maximum absorption wavelength of the reactant, λ1 and λ3 are wavelengths being selected on flanks of λ2, m or n is the difference of λ2 and λ1 or λ3 and λ2, i.e. m = λ2 − λ1 and n = λ3 − λ2; Δε, l and c are the relative molar absorption coefficient, the light path length of the cuvette and the concentration of the dye, respectively. In order to achieve sufficiently large values of ΔA and linear wavelength dependences of the absorbance resulted from the critical light scattering in the region of λ1 ≤ λ ≤ λ3 for both critical media in the near-critical regions we carefully selected λ1 = 620 nm, λ3 = 650 nm for reaction I and λ1 = 520 nm, λ3 = 600 nm for reaction II, respectively. With this arrangement the critical light scattering was essentially irrelevant to ΔA [9–10]. Fig. 3a and b show the linear relations between the absorbance and the wavelength for the critical 2BE aqueous solution at 321.71 K and for the critical microemulsion water/AOT/n-decane with ω = 30 at 316.76 K, respectively.
Table 2 Values of observed rate constant kobs for alkaline fading of MG in 2BE + water at various temperatures. T(K)
1000kobs/s−1
T/K
1000kobs/s−1
307.94 308.90 309.86 310.80 311.76 312.72 313.69 314.60 315.53 316.55 317.53 318.28 319.07 319.77 319.98
0.63 0.72 0.78 0.86 0.92 1.03 1.10 1.19 1.29 1.41 1.52 1.60 1.75 1.86 1.88
320.27 320.34 320.41 320.86 321.02
1.98 1.94 1.99 2.14 2.05
± ± ± ± ±
0.05 0.05 0.06 0.06 0.06
321.708 321.757 321.760 321.781 321.808 321.852 321.884 321.901 321.908
1.93 1.90 1.85 1.91 1.73 1.66 1.64 1.51 1.35
± ± ± ± ± ± ± ± ±
0.16 0.16 0.16 0.15 0.14 0.14 0.14 0.13 0.13
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05
2.5. Data analysis All of the experimental data were collected in the one-phase region. The concentration of OH− was much higher than that of dye in our experimental design, thus both of the reactions may be taken as pseudofirst-order reactions. In the initial reaction stage, the reaction rate can be expressed by −
dc ¼ k2 cc0 ¼ kobs c dt
ð4Þ
where k2 is the second-order reaction rate constant, kobs is the observed rate constant, c and are the concentrations of dye and NaOH, respectively. Initially, the absorbance decreases exponentially due to the hydrolysis yielding the colorless carbinol. Using the Lambert-Beer law and integrating Eq. (4) yields ln A ¼ lnA0 −kobs t
ð5Þ
where A0 is the absorbance of the dye at the initial time of the reaction. Combination of Eqs. (3) and (4) yields dΔA ¼ −kobs ΔA dt
ð6Þ
Integration of Eq. (6) gives lnΔA ¼ ln ΔA0 −kobs t
ð7Þ
where ΔA0 is the relative absorbance at the initial time. We plotted lnA and lnΔA versus reaction time for non-critical region and near-critical Table 3 Values of observed rate constant kobs for alkaline fading of CV in water/AOT/n-decane microemulsion with the molar ratio of water to AOT ω = 30 at various temperatures.
Fig. 4. Plots of lnA and lnΔA versus reaction time t for alkaline fading of MG in 2BE + water at 313.69 K (■) and 321.760 K ( ). The lines represent the results of the fittings with Eqs. (5) and (7), respectively.
T/K
10000kobs/s−1
T/K
10000kobs/s−1
309.161 310.493 311.145 312.450 312.556 313.439 313.814 314.643 314.823 315.478 316.054 316.392
0.62 0.72 0.80 0.88 0.88 1.00 1.08 1.20 1.17 1.24 1.32 1.44
316.492 316.587 316.688 316.688 316.789 316.891 316.976 317.063 317.063 317.156 317.266 317.364 317.457
1.42 1.43 1.39 1.37 1.39 1.35 1.38 1.39 1.38 1.36 1.34 1.40 1.34
± ± ± ± ± ± ± ± ± ± ± ±
0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03
± ± ± ± ± ± ± ± ± ± ± ± ±
0.03 0.03 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
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Fig. 5. Plots of ln{kobs} versus 1000/T: (a) for alkaline fading of MG in 2BE + water; (b) for alkaline fading of CV in water/AOT/n-decane microemulsion with ω = 30. The lines represent the results of linear fittings according to the Arrhenius formula.
region, respectively. The critical region was defined as (Tc − T) b 0.91 K for reaction I, and (Tc − T) b 0.82 K for reaction II. As examples, these plots for reaction I at (Tc − T) = 8.24 K and (Tc − T) = 0.17 K respectively are shown in Fig. 4. 3. Results and discussions Linear least-squares fittings of the kinetic data of the two reactions gave the values of kobs at various temperatures. As we described in Section 2.4, the measurements were repeated at least 2 times, and the average values of kobs were taken as the results; which, together with their estimated uncertainties, are listed in Tables 2 and 3. The uncertainties were evaluated by the differences of the repeated measurements. The Arrhenius formula is written as ln fkb g ¼ −Ea =RT þ B;
ð8Þ
where Ea is the activation energy, R is the gas constant, T is the temperature and B is a constant. Fig. 5a and b show good linear relations between ln{kobs} and 1/T in the non-critical regions, indicating the validity of the Arrhenius formula in the temperature ranges far away from the critical points, where the observed rate constants kobs are
called the background rate constants kb. Linear least-squares fittings of the values kobs in the non-critical regions (i.e. the values of kb) listed in Tables 2 and 3 with Eq. (8) gave the values of activation energy Ea, which were 73.0 ± 0.8 kJ mol− 1 for reaction I and 92.2 ± 1.9 kJ mol−1 for reaction II, respectively. For a first-order or a pseudo-first-order reaction in both directions, the reaction rate in the critical region may be expressed as [10] ln
kobs ¼ flnτ k1
ð9Þ
where k1 is the first-order rate constant in the forward direction without thermodynamic slowing down effect, τ = |Tc − T| / Tc, Tc is the critical temperature of the reaction system, f is the critical exponent characterizing the thermodynamic slowing down effect of a reaction. According to the Griffiths-Wheeler rule [8], f is dependent on the number of inert components in a reaction system. As only one density variable is held fixed (the mass fraction of 2BE is constant in the process of Þ should go to zero weakly as the temperature apreaction), ð∂ΔG ∂c e proaches to the critical point, and the critical exponent f in Eq. (9) is expected to be about 0.11. In addition, a dynamic slowing down effect with an exponent y = 0.041 contributed by weak divergence of viscosity of the reaction system should be also considered when the
Fig. 6. Plots of ln{kobs/kb} versus lnτ: (a) for alkaline fading of MG in 2BE + water, (b) for alkaline fading of CV in water/AOT/n-decane microemulsion with ω = 30 near the critical points. The lines represent the results of the fittings with Eq. (11).
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temperature approaches the critical point [9–10,25] ln
k1 ∝ylnτ kb
ð10Þ
where kb may be calculated by Eq. (8) for each of temperatures in the critical region. Combination of Eqs. (9) and (10) gives ln
kobs ∝ð f þ yÞlnτ ¼ plnτ kb
ð11Þ
where f + y = 0.151 is the theoretical prediction. As shown in the Fig. 6a, a plot of ln{kobs/kb} ln kkobs versus lnτ for alkab
line fading of MG in the critical solution of 2BE + water yields a straight line. The value of the slope p was found to be 0.146 ± 0.014 by the leastsquares fit, which agreed with the experimental results p = 0.133 ± 0.012 for alkaline fading of CV in the same critical binary solution [10] and the theoretical prediction p = 0.151. Fig. 6b shows linear dependences of ln{kobs/kb} on lnτ for alkaline fading of CV in the critical microemulsion water/AOT/n-decane near the critical point. The critical slowing down exponent p was given to be 0.035 ± 0.006 by fitting the experimental results with Eq. (11), which was close to the value of 0.041 of the dynamic slowing down exponent y, indicating that no thermodynamic slowing down effect (f = 0) was detected. It failed to agree with the result reported for the oxidation of iodide ion I− by persulfate ion S2O28 − in the same critical microemulsion with ω = 35, where the thermodynamic slowing down exponent f was found to be 0.187 which was associated with the singularity in the dimer/monomer droplet equilibrium in this critical microemulsion [19]. This inconsistency may be attributed to the fact that in this work OH− aqueous solution, instead of the water/ AOT/n-decane microemulsion containing OH−, was added into the water/AOT/n-decane microemulsion containing CV to start the reaction, and the quantities of both reactants OH− and CV are significantly larger than that of the microemulsion droplet; hence the reaction occurred essentially in the water core of the droplet, independently of the dimer/ monomer droplet equilibrium in the microemulsion. As a result, no thermodynamic singularity was observed. However, the reaction is expected to involve the transport of CV and OH−, which occurs in the form of the diffusion of the droplets as their carriers in the critical microemulsion. Therefore, the reaction exhibits only a weak dynamic slowing down effect in the critical microemulsion system. 4. Conclusions The kinetics of alkaline fading of MG and CV near and far away from the critical temperatures in the critical solution of 2BE + water and the critical microemulsion water/AOT/n-decane with ω being 30 were studied by UV-spectrophotometry with the three-wavelength corrections.
Both of the reactions obeyed the Arrhenius equation when the reaction temperatures were far away from the critical points. Slowing down effects from both the thermodynamic and the dynamic sources were observed for the alkaline fading of MG in 2BE aqueous solution in the nearcritical region characterized by the critical slowing down exponent with the value of 0.146 which agreed well with the previous experimental observations [10] and the theoretical prediction of 0.151. However, the value of the critical exponent determined for the alkaline fading of CV in the critical microemulsion water/AOT/n-decane was only 0.035, which indicates that only a dynamic critical slowing down could be detected. It was attributed to the fact that the reaction is independent of the dimer/monomer droplet equilibrium in the microemulsion. The cause appears to be the fact that insufficiently diluted OH− aqueous solution instead of the water/AOT/n-decane microemulsion containing sufficiently diluted OH−, was added into the microemulsion containing CV to start the reaction.
Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 21403067, 21373080, and 21373085), the Fundamental Research Funds for the Central Universities (No. WJ1516001). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
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