Skip to main content
PMC home page
ACS Omega logoLink to ACS Omega
. 2020 Nov 11;5(46):29801–29815. doi: 10.1021/acsomega.0c03830

Visible Light Spectroscopic Analysis of Methylene Blue in Water; What Comes after Dimer?

Amparo Fernández-Pérez 1, Gregorio Marbán 1,*
PMCID: PMC7689667  PMID: 33251415

Abstract

graphic file with name ao0c03830_0016.jpg

As in our previous work, most attempts to study the self-aggregation of methylene blue (MB) in water have been limited to the dimer. In the present work, we have analyzed the self-aggregation of MB in water beyond the dimeric form. For this purpose, the visible light absorption spectra of a large number of aqueous solutions of MB (1.1 × 10–6 to 3.4 × 10–3 M) and NaCl (0.0–0.15 M) at different temperatures (282–333 K) have been fed to a mathematical routine in order to determine the potential existence of a unique higher-order aggregate without any preconception about the aggregation order or about the need of counterions, such as chloride, for compensating the positive charge of the aggregates. Contrary to the common belief that the trimer is the dominant aggregate at high MB concentration, to our surprise we found that the tetramer acting alone, and without any counterion, is the higher-order aggregate that yields the best fitting to all the experimental absorbance spectra, with a very low average relative error of 0.04 ± 0.34%. Also contrary to previous assumptions, it has emerged quite evidently that this aggregate is present in the solution at MB concentrations below 3.4 × 10–5 M (11 ppm), though to a rather low extent. This has brought the need for the recalculation of the visible light absorption spectrum and the thermodynamic parameters for the dimer, which along with those for the tetramer are the main contributions of the present work.

1. Introduction

Methylene blue (MB) is a widely used dye in the textile industry in wool, cotton, and silk dyeing.1 It is also used to dye specific tissues and fluids of the body before or during surgery and diagnostic examinations,2 as an antiseptic and inner cicatrizer3 and as a staining agent for microscope analysis.1 On the negative side, MB accounts for a significant part of the approximately 85,000 tons of dyes and pigments that are discharged in the rivers and lakes of the world each year, affecting the freshwater aspects of the water cycle.4 The negative impacts of MB on human beings and animals comprise irritation of mouth, throat, esophagus, and stomach with symptoms of nausea, abdominal discomfort, vomiting, and diarrhea.5 Thus, the removal of MB dye from wastewater is of great concern both from a human and an environmental point of view. For this reason, MB is commonly used as a model contaminant in adsorption or photocatalytic processes.6,7 These processes may be greatly affected by the ability of the aqueous MB dye molecules to organize themselves into aggregates of different orders, depending on the total MB concentration and the temperature. Just as an example, an adsorbent that may prove efficient for adsorbing the MB monomer might, on the other hand, have a pore system unable to accommodate the aggregates. Furthermore, the evaluation of the MB concentration itself by means of spectroscopic techniques is greatly affected by the aggregation degree because all species in solution, whether or not aggregated, show fairly different optical spectra.8 The self-aggregation of MB in water to form a dimeric species has been researched for many decades, resulting in several scientific works,9−18 in which the evaluation of the visible light absorption spectra for the monomer and the dimer, as well as the thermodynamic parameters for the equilibrium between both species (in most cases the equilibrium constant at room temperature and, less often, the enthalpy and entropy of dimerization), has been claimed to be performed with greater or lesser success. However, in our previous work,8 we proved that the molar attenuation coefficients and the thermodynamic parameters obtained in those works are subject to a considerable level of uncertainty. This is a consequence of considering that the spectroscopic behavior of the monomer is unaffected by the solution temperature. This universally employed assumption is, however, in contradiction with the long known fact that the maximum attenuation coefficient of the monomer spectrum obtained via extrapolation at a very low MB concentration, 6.3 × 10–7 M, shows a slight decrease at increasing temperatures.9 In our work,8 we have proven that the temperature-dependent absorption behavior of the monomer is provoked by the change in its electron charge distribution with the variation in the temperature-dependent dielectric constant of water.

The monomer charge distribution stands between those of the virtual resonance forms, being the absorption spectrum of the monomer, a composition of the theoretical spectra for the virtual mesomers, whose proportion is established by a temperature-dependent virtual equilibrium constant (resonance virtual equilibrium hypothesis). In practice, this means that the light absorption curve of MB in water in the absence of aggregate forms beyond the dimer is formed by the convolution of the dimer spectrum and the spectra for the two virtual monomeric mesomers, whose proportion is established by the thermodynamic parameters for the monomer/dimer equilibrium and for the resonance virtual equilibrium (Figure 1A).

Figure 1.

Figure 1

Open in a new tab

Summarized results of our previous work.8 (A) Monomer charge distribution stands between those of the virtual resonance forms, being the absorption spectrum of the monomer a composition of the theoretical spectra for the virtual mesomers I and II, whose proportion is established by a temperature-dependent virtual equilibrium constant, Km (resonance virtual equilibrium hypothesis). At low MB concentration (below ∼10 ppm) the only aggregate in solution is the dimer, whose concentration is determined by the equilibrium constant Kd. (B) Optical spectra for the mesomers and the dimer. (C) Experimental (symbols) vs calculated (lines) absorbance spectra at different MB concentrations and temperatures.

The application of this hypothesis at MB concentrations below 3.4 × 10–5 M (11 ppm) allowed the thermodynamic parameters for the equilibria displayed in Figure 1A and the spectra for the dimer and mesomers (Figure 1B) to be evaluated with remarkable accuracy (Figure 1C).8 These spectra were obtained under the hypothesis that below 3.4 × 10–5 M the aggregates in solution beyond the dimer have a negligible presence, as has been often claimed.19−22 As we will prove in the present work, this is not completely precise, and though the optical and thermodynamic parameters of the mesomers remain the same as in our previous work,8 those of the dimer will be changing a bit.

In the present work, we have analyzed the self-aggregation of MB in water beyond the dimeric form for highly concentrated solutions. At high MB concentrations, the existence of MB trimers and higher-order aggregates in water has been assumed since long,10,20,23−25 especially when they are adsorbed on solid surfaces.12,26,27 According to different authors,19−22 the threshold of the trimer formation at room temperature lies in the range 10–5 to 5 × 10–5 mol L–1. Since 1968, there have been a limited number of works attempting to determine the equilibrium constants for the formation of the higher-order aggregates, which are typically assumed to be trimers alone or at most accompanied by tetramers.11,19,21−23,28,29 The results of these works are summarized in Table 1.

Table 1. Values of Cumulative Constants for MB Aggregate Formation in Water Reported in the Literaturea.

refs year T (K) Kd × 10–3 (L mol–1) K3&0 × 10–6 (L2 mol–2) K3&1 × 10–10 (L3 mol–3) K4&0 × 10–10 (L3 mol–3)
(23) 1968 303 2.00 6.00    
(28) 1970 298 2.09–2.50 6.25–9.40   1.53–2.73
(11) 1975 300 2.50 15.75    
(22),29 1979 298 2.54 3.43   0.07
(19) 1999 298 6.67 27.93    
(19) 1999 298 6.94   3.11  
(21) 2011 298 6.41b   3.14c  
    308 5.88   2.58  
    318 5.71   2.35  
    328 5.29   2.04  
    338 5.00   1.85  
    348 4.72   1.71  
this work 2020 282 20.77d     953.89e
    296 11.22     124.54
    313 5.72     13.43
    333 2.83     1.31
Open in a new tab
a

Kd: equilibrium constant of dimer formation [2MB+ ↔ (MB+)2]. K3&0: equilibrium constant of trimer formation without chloride [3MB+ ↔ (MB+)3]. K3&1: equilibrium constant of trimer formation with chloride [3MB+ + Cl– ↔ (MB+)3(Cl–)]. K4&0: equilibrium constant of tetramer formation without chloride [4MB+ ↔ (MB+)4].

b

ΔSd = 56 J mol–1 K–1, ΔHd = −5.2 kJ mol–1.

c

ΔS3&1 = 166 J mol–1 K–1, ΔH3&1 = −10.4 kJ mol–1.

d

ΔSd = −25.6 J mol–1 K–1, ΔHd = −30.5 kJ mol–1.

e

ΔS4&0 = 109.4 J mol–1 K–1, ΔH4&0 = −100.9 kJ mol–1.

The assumption that the higher-order aggregate at high MB concentrations is a trimer was first postulated by Braswell,23 who became a major referent for all the later authors. He assumed that the Debye–Hückel limiting law applies and only the cation aggregates in a MB concentration range in which the monomer and dimer are absent (0.017–0.055 M) and concluded that the limiting form of aggregation is a trimer, which is in good agreement with the conclusions arrived at from his spectral studies. However, the limiting case of the Debye–Hückel law can hardly be applied for such high MB concentration levels, unless a negligible ionic radius of the aggregate is considered, a fact that can in no way be justified. In addition, his spectral studies were biased by the use of the mean activity coefficients instead of the individual activity coefficients in the equilibrium constants.19

Few of the works included in Table 1 consider the need that chloride is bonded to the trimer to compensate the excess of the positive charge.19,21 The inclusion of counterions in the trimer composition has been an issue in scientific discussions for decades now. From the original works by McKay and Hilson, back in 1965,17,30 the metachromatic effect of adding salts to the MB solutions became evident. However, the way the counterion acts in solution, whether by changing the aggregate structure or by affecting the activity coefficients, has never been fully clarified. The association of chloride with the aggregates is implicitly questioned from the analysis of the results provided by Rabinowitch and Epstein.31 Ghosh and Mukerjee28,32,33 also considered that the spectral changes provoked by the addition of salt were those expected from changes in activity coefficients, with a negligible counterion participation in association equilibria at low ionic strengths. At the other extreme, Braswell reported that, in the absence of NaCl, the aggregates formed are charged.34 Zhao and Malinowski19 and Hemmateenejad et al.(21) also assumed the association of chloride with the trimer for their calculations. In all cases, the uncertainty is hovering over the results.

In the present work, we have measured the visible light absorption spectra of a large number of aqueous solutions of MB (1.1 × 10–6 to 3.4 × 10–3 M) and NaCl (0.0–0.15 M) at different temperatures (282–333 K). The spectra have been inputted into a mathematical routine executed in a Microsoft Excel sheet in order to determine the potential existence of a unique higher-order aggregate without any preconception about the aggregation order or about the need of counterions such as chloride for compensating the positive charge of the aggregates. The routine considers the nonideality of the activity coefficients as well as the ionic radii of the different charged species. The goodness of the results becomes patently clear through the direct comparison of experimental and calculated visible light absorption spectra, not only for all the solutions prepared in this work but also for a number of different curves taken from the most cited literature works. The molar attenuation coefficients in the 500–700 nm range for all the species in solution, as well as their thermodynamic parameters of aggregation (entropy and enthalpy) have been determined. The results are, at the very least, surprising.

2. Mathematical Routine

Following the resonance virtual equilibrium hypothesis8 and assuming a unique higher-order aggregate, formed by the association of n monomers with c chloride ions [nMB+ + cCl– ↔ (MB+)n(Cl–)c], coexisting in solution with the monomeric and dimeric forms of MB, the application of the Beer–Lambert equation at a given wavelength yields

2. 1

Aλ and Aλi are the absorbances at a given wavelength, λ, of the solution and the i species, respectively, where i represents each of the different MB species (mI and mII: mesomers I and II; d: dimer; n&c: higher-order aggregate). The optical path length, L, is expressed in cm. ελ and ελi are the molar attenuation coefficients of the solution and the i species, respectively (L mol–1 cm–1). CMB and Ci are the total molar concentration of MB (expressed as monomeric units) and the molar concentration of species i, respectively (mol L–1). As explained in the Experimental Section, IF is the instrumental factor.

First, the total MB and NaCl concentrations (mol L–1) are evaluated from the MB and NaCl molalities (mMB and mNaCl, mol kg–1) and the solution density (ρs, g cm–3), neglecting the influence of MB in the solution density

2. 2

where ρs is calculated for the different temperatures and salt concentrations, as indicated in the Supporting Information (Figure S1). The activity coefficients of the different ionic species in solution are evaluated by means of the equation proposed by Samson et al.,35 which is a modification of the Davies equation36 to cover a wide range of ionic strength values (I ≤ 1 mol L–1)

2. 3

In this equation, Zi and ri are the electronic charge and the ionic radius (m) of species i, T is the solution temperature (K), I is the ionic strength (mol L–1), and ϵr is the relative permittivity (dielectric constant) of water. From values reported in the literature,37 the following ϵr versus T relationship was found

2. 4

The ionic radii for chloride and sodium ions take values of 2 × 10–10 and 3 × 10–10 m, respectively.35 For the MB ions, approximate radii can be calculated considering the dimensions of the MB molecule (17.0 × 7.6 × 3.3 Å).22,38 For the sake of simplicity, we assume that an aggregate is a simple stack of MB molecules and its ionic radius is that of the sphere with the same volume as the stack. This simplified picture yields the ionic radius of a MB aggregate formed by n monomers as

2. 5

With this equation, the ionic radii for the monomer, dimer, trimer, and tetramer are estimated to be 4.7 × 10–10, 5.9 × 10–10, 6.7 × 10–10, and 7.4 × 10–10 m, respectively.

Considering the mass and charge balances and neglecting the influence of hydrogen and hydroxyl ions, the ionic strength can be evaluated as follows

2. 6

where Km is the dimensionless equilibrium constant for the virtual equilibrium between mesomeric forms8

2. 7

The values for ΔSm and ΔHm are indicated in Figure 1. Similar equations can be introduced for the cumulative formation constants of the dimer and the higher-order aggregate

2. 8
2. 9

where CCl is the chloride concentration (mol L–1) and Kd (L mol–1) and Kn&c (Ln+c–1 mol1–n–c) are the equilibrium constants for the formation of the dimer and the higher-order aggregate.

From the mass and charge balances and the equilibrium constants, the concentration of the mesomers and the dimer can be expressed as

2. 10
2. 11
2. 12

and the following identity can be arrived at

2. 13

For given integer values of n and c, the Solver tool of Microsoft Excel was used to find the values of the molar attenuation coefficients at seven specific wavelengths for the mesomers, the dimer and the higher-order aggregate, as well as their thermodynamic parameters of formation [entropy and enthalpy parameters in eqs 7–9] that minimize the following average error (total error)

2. 14

where s is the counter for the 224 spectra taken at the different temperatures, MB concentrations, and NaCl concentrations and w is the counter for selected wavelengths (530, 560, 590, 610, 630, 660, and 680 nm) at which the fitting has been performed. The reason for using a limited number of wavelengths is only a matter of the Solver capabilities, though the results will show the validity of this approach. Aλs,w,exp and Aλs,w are the experimental and calculated [eq 1] absorbances, respectively, for the s spectrum at the w wavelength. As,expmax is the highest value of absorbance for the experimental s spectrum in the 500–700 nm wavelength range. By using this parameter in eq 14, all the spectra are equally weighted during the fitting procedure, regardless of the MB concentration or the used cuvette. An Excel function was designed to evaluate CmII and Cn&c at each iteration step of the Solver tool. The values of these concentrations are used in eqs 10 and 12 to calculate CmI and Cd, respectively, and ultimately Aλs,w [eq 1]. The function solves eq 13 by the Newton–Raphson method and comprises the following steps: [#1] the initial values of Cn&c and γi are set to 0.5 × CMB/n and 1, respectively; [#2] CmII is evaluated viaeq 11; [#3] the ionic strength is evaluated viaeq 6; [#4] the activity coefficients are calculated viaeq 3; [#5] a new value of Cn&c is calculated as

2. 15

where Cn&c* and CmII come from steps #1 and #2, respectively, and E′(CmII*,Cn&c) is the derivative of E(CmII,Cn&c) with respect to Cn&c evaluated at CmII* and Cn&c. This derivative is calculated as

2. 16

where

2. 17
2. 18
2. 19

To derive eq 16, it was assumed that ∂γi/∂Cn&c ≈ 0, which is essentially true at high ionic strength values. The evaluation of h must be performed as indicated above to avoid overflow errors. Finally, [#6] γi and the new Cn&c value are fed to step #2 and a new iteration is performed within the function. The convergence was considered sufficient when the relative difference of values fed into and obtained from eq 15 was below 10–4%. The mass and charge balances were used to prove the viability of the function.

With the thermodynamic values obtained by means of the Solver tool in combination with the Excel function described above, the rest of attenuation coefficients needed to fill the spectrum in the whole wavelength range (500–700 nm) were obtained by repeating the routine at each wavelength value, in a process that was automated by a number of Excel macros.

For a more complete understanding of the goodness of fit, the average relative error (%) was evaluated as

2. 20

Finally, the molar fractions of the different species in solution were evaluated as

2. 21

3. Results and Discussion

Three different scenarios have been analyzed: (A) the optical and thermodynamic parameters for the mesomers and the dimer are set to those evaluated in our former work8 (Figure 1) and only the parameters of the higher-order aggregate are varied to minimize the total error (hereafter called the “n&c scenario”); (B) the optical and thermodynamic parameters for all MB species in solution are varied (hereafter called the “m/d/n&c scenario”) and (C) the optical and thermodynamic parameters for the mesomers are set to those evaluated in our former work (Figure 1) and the parameters of both the dimer and the higher-order aggregate are varied (hereafter called the “d/n&c scenario”). Figure 2 shows the errors obtained in the three scenarios, for different values of n and c.

Figure 2.

Figure 2

Open in a new tab

Relative errors (upper plots) and total errors (lower plots) obtained for different values of n and c. (A) n&c scenario; (B) m/d/n&c scenario; and (C) d/n&c scenario.

In all cases, it was found that integer values of c over 1 (more than one chloride anion linked to the higher-order aggregate) produced significantly higher errors than those obtained for c = 0 or c = 1, so that the corresponding solutions were automatically dismissed. The n&c scenario yielded the errors displayed in Figure 2A. The best ⟨ET⟩ value was obtained by considering that the higher-order aggregate is a tetramer without chloride, n = 4 and c = 0 (or 4&0), although the parameters obtained with this solution were dismissed for the following reasons: (i) the total error was significantly higher than those obtained in the other scenarios, (ii) the standard deviation of the relative error was too high to comply with a stringent standard of goodness of fit and reflected a trend to underestimate the values of absorbance ⟨Er⟩ = 1.81 ± 2.75%), and (iii) the calculated fraction of tetramer (X4&0) for the solution with 11 ppm of MB and no NaCl at 282 K was as high as 0.08, conflicting with our previous assumptions,8 which included the absence of a higher-order aggregate at CMB below or equal to 11 ppm. Therefore, it must be assumed that some changes in the previously reported visible light absorption spectra8 must be introduced. In that work, the values of the activity coefficients were considered to be always one. In the absence of a higher order aggregate, this approximation is almost exact for CNaCl = 0 M because the lowest value for the dimer activity coefficient evaluated with eq 3 is 0.97. Thus, the m/d/n&c scenario, in which the attenuation coefficients and the thermodynamic parameters for all the species in solution are simultaneously evaluated, should provide either a different set of parameters for the mesomers and the dimer if the higher-order aggregate is present at a low concentration (CMB ≤ 11 ppm and CNaCl = 0 M) or very similar spectra to those previously reported8 if the higher-order aggregate is absent at such a concentration range. Any other combination should be considered the result of either a chaotic fit or the noncompliance with the model premises (a unique higher-order aggregate). The fitting process under the m/d/n&c scenario yielded the errors, as displayed in Figure 2B. Interestingly, the lowest ⟨ET⟩ error was obtained by considering that the higher-order aggregate is a hexamer with one chloride anion (6&1). This error was also the lowest of all the scenarios. However, the relative error (upper plot in Figure 2B) still involved a significant standard deviation, though now with a certain overestimation of the absorbance values (⟨Er⟩ = −0.55 ± 0.83%). Nevertheless, the reason that leads us, without a doubt, to dismiss this solution is the fact that even though the calculated fraction of the hexamer (X6&1) for the solution with 11 ppm of MB and no NaCl at 282 K was almost 0 (X6&1 = 0.001), the new absorption spectra for the mesomers were very different from those previously reported (Figure 3).8 In fact, the error in the low concentration zone (CMB ≤ 11 ppm and CNaCl = 0 M) for the m/d/n&c scenario was considerably higher than the error for the n&c scenario (2.4 × 10–4vs 1.8 × 10–4).

Figure 3.

Figure 3

Open in a new tab

Absorption spectra for the mesomers I and II evaluated in both the m/d/n&c scenario (c,a) and the n&c scenario (b,d).

Thus, either the unique higher-order aggregate premise is incorrect or the m/d/n&c scenario produces a chaotic fit. To check this second option, we have used a rational approach by which the optical spectra and the thermodynamic parameters for the mesomers, reported in our previous work,8 were considered to be correct and the parameters of both the dimer and the higher-order aggregate were varied (d/n&c scenario). This scenario is well in tune with the long-accepted principle that the extrapolation methods give good results with the monomer but are less reliable with respect to the dimer.10,12,31 In fact, by applying the extrapolation principle, if a certain amount of the higher-order aggregate is present in the most concentrated MB solutions used in our previous work,8 this would have only affected the evaluation of the dimer parameters. The errors produced by assuming the d/n&c scenario are displayed in Figure 2C. The lowest ⟨ET⟩ value was obtained when the higher-aggregate was set to be a tetramer without chloride (4&0). This error is somewhat higher than the lowest error obtained in the m/d/n&c scenario (4.2 × 10–4vs 3.3 × 10–4), though the error in the low concentration zone (CMB ≤ 11 ppm and CNaCl = 0 M) reaches its lowest value (1.4 × 10–4). Furthermore, the relative error is by far the lowest of all scenarios (⟨Er⟩ = 0.04 ± 0.34%). In addition, naturally, the tetramer is present at a low amount in the solutions at the highest concentration extreme of the low concentration range (X4&0 = 0.11 at CMB = 11 ppm and CNaCl = 0 M at 282 K), thus explaining the higher errors obtained in the n&c scenario. If the higher-order aggregate is considered to be a trimer (3&0) rather than a tetramer, as has always been believed, then the error values rise to ⟨ET⟩ = 4.7 × 10–4 and ⟨Er⟩ = 0.09 ± 0.45% and the fraction of trimer at CMB = 11 ppm and CNaCl = 0 M at 282 K appears to be excessively high (X3&0 = 0.24). The second most popular option, a trimer with a chloride anion, causes the errors to soar to ⟨ET⟩ = 9.3 × 10–4 and ⟨Er⟩ = 2.01 ± 1.43%. In conclusion, answering the question in the title, tetramer is what comes after the dimer.

Figure 4 shows the optical spectra of all (virtual and real) species in the MB solution. The main difference of the dimer spectrum, with respect to that evaluated in our previous work (Figure 1),8 is the conspicuous increase of the shoulder at λ = 660 nm to become a peak by its own merit. The tetramer has a single maximum at 600 nm and is responsible for the blue shift at high values of the ionic strength. All the optical and thermodynamic parameters for the monomer and the aggregates are summarized in Table 2. The new thermodynamic parameters of the dimer do not differ substantially from those evaluated in our previous work.8

Figure 4.

Figure 4

Open in a new tab

Optical spectra for all the MB species either virtually (mesomers) or truly contained in aqueous solutions.

Table 2. Optical and Thermodynamic Parameters of MB in Water.

optical parameters
species λmax nm ελmax × 10–4 L mol–1 cm–1
Tetramer 600 13.85
Dimer 607 10.14
monomer (mesomer II) 664 10.78
monomer (mesomer I) 650 4.40
thermodynamic parameters
Monomer ↔ Tetramer
ΔS4&0 (J mol–1 K–1) –109.4
ΔH4&0 (kJ mol–1) –100.9
Monomer ↔ Dimer
ΔSd (J mol–1 K–1) –25.6
ΔHd (kJ mol–1) –30.5
Mesomer II ↔ Mesomer I
ΔSm (J mol–1 K–1) 24.0
ΔHm (kJ mol–1) 8.1
Open in a new tab

With respect to the tetramer, the negative increment of enthalpy indicates, as in the case of the dimer, that aggregation is an exothermic process, whereas the negative entropy change is because of the association of similarly charged species,39 which might be more reasonable than the positive values found by Klika et al.(22)Figures 5–7 show the experimental and calculated values of absorbance for all the solutions analyzed in this work. Beyond the low value of the relative error, these figures provide visual proof of the goodness of fit, which can be considered more than satisfactory.

Figure 5.

Figure 5

Open in a new tab

Experimental (crosses) and calculated (lines) absorbance curves for the solutions prepared at different MB concentrations and temperatures in the absence of NaCl.

Figure 7.

Figure 7

Open in a new tab

Experimental (crosses) and calculated (lines) absorbance curves for the solutions prepared at high MB concentrations and different temperatures in the presence of NaCl.

Figure 6.

Figure 6

Open in a new tab

Experimental (crosses) and calculated (lines) absorbance curves for the solutions prepared at low MB concentrations and different temperatures in the presence of NaCl.

The molar fractions of the different species in solution were evaluated with eq 21 for different temperatures and NaCl concentrations in the 1 × 10–6 to 3.5 × 10–3 mol L–1 range of the MB concentration. The results are shown in Figure 8. The increase in the aggregation level with the decrease of the temperature or with the increment of the NaCl concentration is conspicuous. As observed in the figure, for CMB = 3.5 × 10–3 M and CNaCl = 0.15 M most of the MB molecules in solution are associated as tetramers (X4&0 = 0.93).

Figure 8.

Figure 8

Open in a new tab

Variation of the molar fractions of the monomer, mesomer I, mesomer II, dimer, and tetramer with the MB concentration at different temperatures. (A) CNaCl = 0 M and (B) CNaCl = 0.15 M.

As commented in the Introduction section, Braswell23 proceeded from the assumption that the Debye–Hückel limiting law is applicable to prove that the limiting form of aggregation is a trimer. As observed in Figure 9, the activity coefficients evaluated by eq 3 are comparable to those calculated with the Debye–Hückel limiting law only in the case of the monomer and, in such cases, only at low ionic strength values. It should be emphasized that these coefficients are raised to the positive integer exponents in the expressions for the equilibrium constants [eqs 8 and 9], so that the differences observed in Figure 9 are in fact being magnified in such expressions. The effect of adding salt on the activity coefficients is evident from the results shown in the figure. This ends the argument about the real effect of chloride on the MB aggregation, proving correct the theory that favors the variation in the activity coefficients over the structural changes in the agglomerates as the consequence of adding salt, at least in the concentration ranges studied in this work.

Figure 9.

Figure 9

Open in a new tab

Variation of the activity coefficients with the ionic strength for the different species (the subscript DH refers to the values evaluated with the Debye–Hückel limiting law).

Finally, we have applied the optical (Figure 4) and thermodynamic (Table 2) parameters obtained in this work to a number of absorbance spectra reported in some of the oldest and most cited works dealing with the phenomenon of MB aggregation.11,12,23,30 Their authors used optical cells made of different materials and with different path lengths, and in one case achieved with the help of spacers.11 The variability of cells results in unavoidable differences among spectra measured at the same concentration with different cuvettes. Added to this, there is a known wavelength sensitivity in the equipment used before 1975 that is assumed to be around ±3 nm.40 These two issues were accounted for in the application of eq 1 to the experimental data by means of two parameters. The first is the instrumental factor, IF, that eliminates differences between cells. The second parameter is the difference in sensitivity between the equipment used in this work and those employed in the works referred above, expressed as a shift in the wavelength (Δλ). Both parameters have been optimized to minimize the error between the experimental attenuation coefficients and those calculated by eq 1. The instrumental factor was evaluated for each paper assuming that similar IF values obtained in a first fitting for a given group of MB solutions implied that the corresponding spectra had been obtained with the same cell, and thus, in a second fitting, an unique IF value was optimized for the whole group of MB solutions. Naturally, a unique value of Δλ was optimized for each paper. The results are shown in Figures 10–13. The values of IF and Δλ are indicated in the captions of the figures. As can be observed, the goodness of fit is rather satisfactory in all cases.

Figure 10.

Figure 10

Open in a new tab

Application of eq 1 with the optical and thermodynamic parameters obtained in this work to the experimental data obtained by Braswell23 [Δλ = −2.0 nm, IF = 1.157 (A, B) 1.359 (C)].

Figure 13.

Figure 13

Open in a new tab

Application of eq 1 with the optical and thermodynamic parameters obtained in this work to the experimental data obtained by McKay and Hillson30 [Δλ = −1.3 nm, IF = 1.149 (A,B) 1.255 (C–F)].

Figure 11.

Figure 11

Open in a new tab

Application of eq 1 with the optical and thermodynamic parameters obtained in this work to the experimental data obtained by Ghosh11 [Δλ = −0.7 nm, IF = 1.164 (A–C) 1.435 (D,E)].

Figure 12.

Figure 12

Open in a new tab

Application of eq 1 with the optical and thermodynamic parameters obtained in this work to the experimental data obtained by Bergmann and O’Konski12 [Δλ = −0.7 nm, IF = 1.220 (A–F) 1.281 (G,H)].

As commented in the Experimental Section, at a high NaCl concentration (0.9 M) the extensive precipitation of MB aggregates took place (Figure S2). This is consistent with the significant blueshift in the absorption spectrum that McKay and Hillson30 found for solutions at CNaCl = 0.9 M, although these authors did not report the precipitation of MB at such conditions. This blueshift could not be reproduced with the attenuation coefficients and thermodynamic parameters obtained in this work (Figure 14) with the same level of precision reached for lower NaCl concentrations (Figure 13).

Figure 14.

Figure 14

Open in a new tab

Application of eq 1 with the optical and thermodynamic parameters obtained in this work to the experimental data obtained by McKay and Hillson30 at CNaCl = 0.9 M [Δλ = −1.3 nm, IF = 1.149 (A) 1.255 (B,C); equal to the values in Figure 13].

As the activity coefficients are independent of the ionic strength for values of I higher than around 0.1 M (Figure 9), it seems evident that at very high chloride concentrations, the Cl– anions must participate in the formation of over-aggregates of MB, possibly by linking together tetramers, which ultimately precipitate. However, this phenomenon does not occur in the MB/NaCl concentration and temperature ranges analyzed in this work.

4. Conclusions

The visible light absorption spectra of a large number of aqueous solutions of MB (1.1 × 10–6 to 3.4 × 10–3 M) and NaCl (0.0–0.15 M) at different temperatures (282–333 K) have been fed to a mathematical routine in order to determine the potential existence of a unique higher-order MB aggregate without any preconception about the aggregation order or about the need of counterions such as chloride for compensating the positive charge of the aggregates. The routine considers the nonideality of the solutions in the calculation of the activity coefficients. From the analysis of different scenarios, it was found that the tetramer acting alone and without any counterion is the higher-order aggregate that yields the best fitting to all the experimental absorbance spectra, with a very low average relative error of 0.04 ± 0.34%. In the absence of NaCl, this aggregate is present in solution at MB concentrations below 3.4 × 10–5 M (11 ppm), though to a rather low extent. Due to this fact, the visible light absorption spectrum and the thermodynamic parameters for the dimer had to be recalculated with respect to those evaluated in our previous work.8 The goodness of fit has been shown to be rather satisfactory by comparing experimental and calculated light absorption spectra obtained both in this work and from the literature.

5. Experimental Section

The absorption spectra (400–800 nm at 1 nm step) of different MB (C.I. 52015; analytical grade) and NaCl (supplied by Sigma-Aldrich; analytic grade) solutions in deionized water were measured at temperatures in the 282–333 K range using an UV–vis spectrometer (Shimadzu UV-2401PC). The temperature of the optical cuvettes was kept constant using a LAUDA Alpha RA8 thermo-circulating bath. Every measure was repeated thrice, with exhaustive cleaning of the cuvettes (water, ethanol and air drying) between measures. Four salt concentrations were employed, 0.00, 0.05, 0.10, and 0.15 mol L–1. The solutions with MB concentrations in the 1.1 × 10–6 to 3.4 × 10–5 mol L–1 (0.35–11 ppm) range were poured into UV quartz cuvettes of 700 μL volume and 1 cm path length. At higher MB concentrations [9.4 × 10–5 to 3.4 × 10–3 mol L–1 (30–1100 ppm)], the visible light absorption spectra were obtained using a flow-through UV quartz cuvette of 6 μL volume and 0.01 cm path length. The MB and NaCl concentration ranges were selected to avoid deficiencies in the absorbance measurements due to the presence of the dispersed particles and/or precipitates formed through the over-aggregation of MB molecules. As shown in Figure S2, specific solutions prepared at a high NaCl concentration (0.9 M) suffered from extensive precipitation. Before analysis, all solutions were allowed to stabilize under magnetic stirring in complete darkness overnight. A total of three optical cuvettes were used for all the analyses (two cuvettes of 1 cm and one cuvette of 0.01 cm). To take account of small variations in the quartz transmittance and path lengths with respect to the nominal values, an instrumental factor, IF, was evaluated for each cuvette so that the molar attenuation factors evaluated with a given solution were independent of the cuvette used for the evaluation. For this to happen, the nominal path length, L, is multiplied by IF in the Beer–Lambert equation. The instrumental factor takes the value of one for the first cuvette, and then is evaluated for successive cuvettes [IF = 1, 1.004 (1 cm) and 1.145 (0.01 cm)]. Ad hoc Microsoft Excel macros and functions were designed to perform the error minimization tasks, incorporating the Solver complement of Microsoft Excel. The molar attenuation coefficients, as shown in Figures 10–14, are evaluated from absorbance data extracted from literature graphs by means of a Visual Basic program fed with bmp-formatted scanned images of the graphs.41

Acknowledgments

The financial support for this research work provided by the Spanish MINECO (CTM2014-56770-R project) and FEDER Funds (GRUPIN2018 (IDI/2018/000148), Principado de Asturias) is gratefully acknowledged. AFP is grateful to the Spanish MINECO for the award of a contract (BES-2015-072274).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c03830.

  • Density of NaCl solutions and images of precipitated MB aggregates (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao0c03830_si_001.pdf (179.9KB, pdf)

References

  1. Berneth H.Azyne Dyes. Ullmann’s Encyclopedia of Industrial Chemistry; Wiley-VCH, 2008. [Google Scholar]
  2. Mondal S. B.; Gao S.; Zhu N.; Liang R.; Gruev V.; Achilefu S.. Chapter Five - Real-Time Fluorescence Image-Guided Oncologic Surgery. In Advances in Cancer Research; Pomper M. G., Fisher P. B., Eds.; Academic Press, 2014; Vol. 124, pp 171–211. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Wainwright M.; Crossley K. B. Methylene Blue - a Therapeutic Dye for All Seasons?. J. Chemother. 2002, 14, 431–443. 10.1179/joc.2002.14.5.431. [DOI] [PubMed] [Google Scholar]
  4. Samchetshabam G.; Hussan A.; Gon Choudhury T.; Soholars P.; Hussan A. Impact of Textile Dyes Waste on Aquatic Environments and its Treatment. Environ. Ecol. 2017, 35, 2349–2353. [Google Scholar]
  5. Shakoor S.; Nasar A. Removal of methylene blue dye from artificially contaminated water using citrus limetta peel waste as a very low cost adsorbent. J. Taiwan Inst. Chem. Eng. 2016, 66, 154–163. 10.1016/j.jtice.2016.06.009. [DOI] [Google Scholar]
  6. Di Mauro A.; Fragalà M. E.; Privitera V.; Impellizzeri G. ZnO for application in photocatalysis: From thin films to nanostructures. Mater. Sci. Semicond. Process. 2017, 69, 44–51. 10.1016/j.mssp.2017.03.029. [DOI] [Google Scholar]
  7. Mills A. An overview of the methylene blue ISO test for assessing the activities of photocatalytic films. Appl. Catal., B 2012, 128, 144–149. 10.1016/j.apcatb.2012.01.019. [DOI] [Google Scholar]
  8. Fernández-Pérez A.; Valdés-Solís T.; Marbán G. Visible light spectroscopic analysis of Methylene Blue in water; the resonance virtual equilibrium hypothesis. Dyes Pigm. 2019, 161, 448–456. 10.1016/j.dyepig.2018.09.083. [DOI] [Google Scholar]
  9. Lewis G. N.; Goldschmid O.; Magel T. T.; Bigeleisen J. Dimeric and Other Forms of Methylene Blue: Absorption and Fluorescence of the Pure Monomer. J. Am. Chem. Soc. 1943, 65, 1150–1154. 10.1021/ja01246a037. [DOI] [Google Scholar]
  10. Lemin D. R.; Vickerstaff T. The aggregation of direct dyes and of Methylene Blue 2B in aqueous solution. Trans. Faraday Soc. 1947, 43, 491–502. 10.1039/tf9474300491. [DOI] [Google Scholar]
  11. Ghosh A. K. A New Variation of Rabinowitch and Epstein’s Method of Studying Self-Association of the Dyes: Dimerisation and Trimerisation Constants of Methylene Blue. Z. Phys. Chem. 1975, 94, 161. 10.1524/zpch.1975.94.4-6.161. [DOI] [Google Scholar]
  12. Bergmann K.; O’Konski C. T. A spectroscopic study of methylene blue monomer, dimer, and complexes with montmorillonite. J. Phys. Chem. 1963, 67, 2169–2177. 10.1021/j100804a048. [DOI] [Google Scholar]
  13. Dunken H.; Schmidt D.; Palm K. Zur Dimerisation von Methylenblau und Toluidinblau. Z. Chem. 1962, 2, 349. 10.1002/zfch.19620021121. [DOI] [Google Scholar]
  14. Spencer W.; Sutter J. R. Kinetic study of the monomer-dimer equilibrium of methylene blue in aqueous solution. J. Phys. Chem. 1979, 83, 1573–1576. 10.1021/j100475a004. [DOI] [Google Scholar]
  15. Yazdani O.; Irandoust M.; Ghasemi J. B.; Hooshmand S. Thermodynamic study of the dimerization equilibrium of methylene blue, methylene green and thiazole orange at various surfactant concentrations and different ionic strengths and in mixed solvents by spectral titration and chemometric analysis. Dyes Pigm. 2012, 92, 1031–1041. 10.1016/j.dyepig.2011.07.006. [DOI] [Google Scholar]
  16. Ghasemi J. B.; Miladi M. Association Equilibrium of Methylene Blue by Spectral Titration and Chemometrics Analysis: A Thermodynamic Study. J. Chin. Chem. Soc. 2009, 56, 459–468. 10.1002/jccs.200900069. [DOI] [Google Scholar]
  17. Hillson P. J.; McKay R. B. Aggregation of dye molecules in aqueous solution a polarographic study. Trans. Faraday Soc. 1965, 61, 374–382. 10.1039/tf9656100374. [DOI] [Google Scholar]
  18. Patil K.; Pawar R.; Talap P. Self-aggregation of Methylene Blue in aqueous medium and aqueous solutions of Bu 4 NBr and urea. Phys. Chem. Chem. Phys. 2000, 2, 4313–4317. 10.1039/b005370h. [DOI] [Google Scholar]
  19. Zhao Z.; Malinowski E. R. Window factor analysis of methylene blue in water. J. Chemom. 1999, 13, 83–94. . [DOI] [Google Scholar]
  20. Heger D.; Jirkovský J.; Klán P. Aggregation of Methylene Blue in Frozen Aqueous Solutions Studied by Absorption Spectroscopy. J. Phys. Chem. A 2005, 109, 6702–6709. 10.1021/jp050439j. [DOI] [PubMed] [Google Scholar]
  21. Hemmateenejad B.; Absalan G.; Hasanpour M. Application of multivariate curve resolution analysis for studying the thermodynamics of methylene blue aggregations in aqueous solutions. J. Iran. Chem. Soc. 2011, 8, 166–175. 10.1007/bf03246213. [DOI] [Google Scholar]
  22. Klika Z.; Čapková P.; Horáková P.; Valášková M.; Malý P.; Macháň R.; Pospíšil M. Composition, structure, and luminescence of montmorillonites saturated with different aggregates of methylene blue. J. Colloid Interface Sci. 2007, 311, 14–23. 10.1016/j.jcis.2007.02.034. [DOI] [PubMed] [Google Scholar]
  23. Braswell E. Evidence for trimerization in aqueous solutions of methylene blue. J. Phys. Chem. 1968, 72, 2477–2483. 10.1021/j100853a035. [DOI] [Google Scholar]
  24. Zhao Z.; Malinowski E. R. Determination of the Hydration of Methylene Blue Aggregates and Their Dissociation Constants Using Visible Spectroscopy. Appl. Spectrosc. 1999, 53, 1567–1574. 10.1366/0003702991946028. [DOI] [Google Scholar]
  25. Scheibe G. Reversible Polymerisation als Ursache neuartiger Absorptionsbanden von Farbstoffen. Kolloid Z. 1938, 82, 1–14. 10.1007/bf01509409. [DOI] [Google Scholar]
  26. Jockusch S.; Turro N. J.; Tomalia D. A. Aggregation of Methylene Blue Adsorbed on Starburst Dendrimers. Macromolecules 1995, 28, 7416–7418. 10.1021/ma00126a020. [DOI] [Google Scholar]
  27. Kobayashi M.; Maeda Y.; Hoshi T.; Okubo J.; Tanizaki Y. Analysis of the electronic absorption spectrum of adsorbed layers of methylene blue. J. Soc. Dyers Colour. 1989, 105, 362–368. 10.1111/j.1478-4408.1989.tb01187.x. [DOI] [Google Scholar]
  28. Mukerjee P.; Ghosh A. K. Multiple Association Equilibria in the Self-Association of Methylene Blue and Other Dyes. J. Am. Chem. Soc. 1970, 92, 6408–6412. 10.1021/ja00725a005. [DOI] [Google Scholar]
  29. Klika Z.Study of the polymerization of methylene species in water-based solvents. Sborník vědeckých prací VŠB-TUOstrava, 1979; Vol. 2, p 53.
  30. McKay R. B.; Hillson P. J. Metachromatic behaviour of dyes in solution. Interpretation on the basis of interaction between dye ions and counter-ions. Trans. Faraday Soc. 1965, 61, 1800–1810. 10.1039/tf9656101800. [DOI] [Google Scholar]
  31. Rabinowitch E.; Epstein L. F. Polymerization of Dyestuffs in Solution. Thionine and Methylene Blue1. J. Am. Chem. Soc. 1941, 63, 69–78. 10.1021/ja01846a011. [DOI] [Google Scholar]
  32. Mukerjee P.; Ghosh A. K. Isoextraction method and the study of the self-association of methylene blue in aqueous solutions. J. Am. Chem. Soc. 1970, 92, 6403–6407. 10.1021/ja00725a002. [DOI] [Google Scholar]
  33. Ghosh A. K.; Mukerjee P. Ionic strength effects on the activity coefficient of methylene blue and its self-association. J. Am. Chem. Soc. 1970, 92, 6413–6415. 10.1021/ja00725a004. [DOI] [Google Scholar]
  34. Braswell E. H. Equilibrium sedimentation studies of the aggregation of methylene blue. J. Phys. Chem. 1972, 76, 4026–4030. 10.1021/j100670a025. [DOI] [Google Scholar]
  35. Samson E.; Lemaire G.; Marchand J.; Beaudoin J. J. Modeling chemical activity effects in strong ionic solutions. Comput. Mater. Sci. 1999, 15, 285–294. 10.1016/s0927-0256(99)00017-8. [DOI] [Google Scholar]
  36. Davies C. W.Ion Association; Butterworths: Washington, 1962. [Google Scholar]
  37. Archer D. G.; Wang P. The Dielectric Constant of Water and Debye-Hückel Limiting Law Slopes. J. Phys. Chem. Ref. Data 1990, 19, 371–411. 10.1063/1.555853. [DOI] [Google Scholar]
  38. Arias M.; López E.; Nuñez A.; Rubinos D.; Soto B.; Barral M. T.; Díaz-Fierros F.. Adsorption of Methylene Blue by Red Mud, An Oxide- Rich Byproduct of Bauxite Refining. In Effect of Mineral-Organic-Microorganism Interactions on Soil and Freshwater Environments; Berthelin J., Huang P. M., Bollag J. M., Andreux F., Eds.; Springer US: Boston, MA, 1999; pp 361–365. [Google Scholar]
  39. Mukerjee P.; Ghosh A. K. The effect of urea on methylene blue, its self-association, and interaction with polyelectrolytes in aqueous solution. J. Phys. Chem. 1963, 67, 193–197. 10.1021/j100795a047. [DOI] [Google Scholar]
  40. Caffrey M.; Kinsella J. E. Sensitivity of the molar absorptivity value to sample and instrument characteristics, with reference to the ellman reagent (DTNB). Int. J. Biochem. 1975, 6, 877–883. 10.1016/0020-711x(75)90007-5. [DOI] [Google Scholar]
  41. Marbán G.; Fuertes A. B. Highly active and selective CuOx/CeO2 catalyst prepared by a single-step citrate method for preferential oxidation of carbon monoxide. Appl. Catal., B 2005, 57, 43–53. 10.1016/j.apcatb.2004.10.011. [DOI] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

ao0c03830_si_001.pdf (179.9KB, pdf)

Articles from ACS Omega are provided here courtesy of American Chemical Society

RESOURCES