Association Equilibrium of Methylene Blue by Spectral Titration and

Journal of the Chinese Chemical Society, 2009, 56, 459-468

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Communication

Association Equilibrium of Methylene Blue by Spectral Titration and Chemometrics Analysis: A Thermodynamic Study Jahan B. Ghasemia,* and M. Miladib a

Chemistry Department, Faculty of Sciences, K. N. Toosi University of Technology, Tehran, Iran b Chemistry Department, Razi University, Kermanshah, Iran

The monomer-dimer equilibrium of methylene blue (MB, Scheme I) has been investigated by means of UV-Visible spectroscopy in aqueous solutions. The self aggregation of MB in water has been investigated by recording absorption spectra in the wavelength range of 450-750 nm, and in different ionic strengths using concentrated KCl solutions in the temperature range of 20-90 °C. Chemometrics analysis of the spectral data gave a dimerization constant, individual spectra of the monomer and dimer forms of the dye molecule. The quantitative analysis of the data of the undefined mixture was carried out by simultaneous resolution of the overlapping spectral bands in the whole set of absorption spectra. The dimerization constants of MB determined by mathematical deconvolution of the thermometric spectral titration data show dependency on temperature variations. The concentration range of MB was 6.00 ´ 10-5-3.00 ´ 10-4 M. Utilizing the van’t Hoff relation, which describes the dependence of the equilibrium constant on temperature, the thermodynamics parameters DH° and DS° of the aggregation process were determined. The compensation effect was verified by the thermodynamics results of the dimerization process of the dye. Keywords: Thermodynamics; Dimerization; Chemometrics; Dye; Methylene blue; Titration; Ionic strength.

1. INTRODUCTION The aggregation of dyes, drugs, surfactants, etc. in aqueous solutions is of extreme importance in biological, colloid, surface, textile, photographic and analytical chemistry.1 In general, a wide variety of applications of phenothiazine dyes have been reported, for example, as sensitizers in solar energy conversion,2 redox mediators in catalytic oxidation reactions, 3 active species in electrochromism4 and dye lasers,5 ingredients in pharmaceutical preparations,6 candidates for cancer therapy by intercalating between DNA base layers7 as sensors or for probing chemical properties at interfaces, especially in biochemistry and molecular biology.8 However, all of these applications are often complicated due to the dimerization of dye molecules in aqueous media such as the great decrease in light sensitivity,9 which results from increased inner conversion of the dimer exciter state. In order to determine the mode of aggregation, the aggregation constant in equilibrium and the aggregation number, the aggregation of dyes has been in-

Scheme I N

N

S

N

Cl-

vestigated by a variety of methods, viz. polarography,10,11 conductometry12 UV-Vis spectrophotometry,13-19 NMR,20-22 light scattering23 and electrolytic effect24 measurements. The nature of the self-association of dyes in aqueous solutions, aside from its intrinsic interest, is important in the understanding and interpretation of a great variety of problems, such as dyeing of fibers, tissue staining in biology, spectral change and energy transfer studies, adsorption, and photography. Dye association is also one of the simplest examples of “stacking” interactions. Many dyes show appreciable association at concentrations as low as 10-6-10-4 M, and the qualitative evidence from many studies suggests that a series of multimers are formed.25

* Corresponding author. Tel: +0098-21-22853306; Fax: +0098-21-22850266; E-mail: [email protected]

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J. Chin. Chem. Soc., Vol. 56, No. 3, 2009

Ghasemi and Miladi

Methylene blue (MB), one of the most commonly used thiazine dyes, is known for its pronounced methachromatic behavior and aggregation in various solutions.26-27 The fact that the visible absorption spectra of aqueous MB solutions do not obey Beer’s law has been ascribed to MB molecular aggregation,26-27 which is influenced by the concentration of the dye, the dielectric constant of the solvent, the addition of salt, and so on. Most attempts to study this aggregation quantitatively have been focused on dimerization.26 Deciphering solution complexes is one of the most challenging problems in analytical chemistry, because the varying species exist in equilibria and cannot be isolated. The amounts of the various species are functions of the controlling equilibria. As such, their concentrations are sensitive to solvent composition, temperature, reagent concentrations, pH, etc. Although dyes are very individualistic in structure and of course behavior, certain broad rules are well established regarding aggregation in general. It may increase with an increase of dye concentration or ionic strengths; it will decrease with raising the temperature or adding organic solvents; addition to the dye structure of ionic soubilizing groups will decrease aggregation, whereas the inclusion of long alkyl chains increases aggregation because of a higher hydrophobic interaction in solution. Absorption UV-vis spectroscopy is one of the most suitable methods for quantitatively studying the aggregation phenomena of dyes as a function of concentration. In the commonly used concentration range (10-3 to 10-6 M) the main equilibrium is a monomer-dimer reaction. In this work we used some physical constraints to determine the dimeric concentration of MB in pure water and at different ionic strengths. Data analysis was carried out by the DATAN package that was developed by the Kubista groups.28-36 The theory and application of the physical constraints method were discussed by Kubista et al. in several papers.28-38 However, the general principal will be outlined here briefly. The results of the DATAN package were compared to the results of a single wavelength or classical regression method of the absorbance data which is written in MATLAB. The absorption spectra are digitized and arranged as rows in a data matrix A. Matrix A is then decomposed into an orthogonal basis set using, for example, the NIPLAS routine:21 r

A = TP¢ + E » TP¢ = å t i p¢i i=1

(1)

where ti are orthogonal target vectors and pi¢ the orthogonal projection vectors, E the error matrix, and r the number of spectroscopically distinguishable components, which is two in this case. Assuming linear response the recorded spectra are also linear components: r

A = CV + E » CV = å c i n i

(2)

i=1

where ci are vectors containing the component concentrations at different temperatures. Eqs. (3) and (4) are related by a rotation: C = TR-1 V = RP'

(3) (4)

where R is r ´ r rotation matrix, which for a two-component system has the element: ér R = ê 11 ër21

r12 ù 1 and R -1 = r22 úû r11 r22 - r12 r21

é r22 ê-r ë 21

-r12 ù (5) r11 úû

Two constraints are used to determine three of the elements in R. The first is the spectrum of the monomer, which is measured separately, and the second is the constant total concentration of the dye: cX(T) + 2cX2(T) = ctot

(6)

Matrix R can now be described by a single scalar r21, and other factors that are determined by the constraints. The value of r 21 determines the dimer spectrum and the monomer concentration profiles. Although a value of r21 produces a mathematically acceptable solution, reasonable results, in terms of spectral intensities and nonnegative concentrations and spectral responses, are obtained in a relatively narrow range of r21 values. Still, the range is, in general, too large for a quantitative analysis. The final constraint, which produces a unique solution, is the thermodynamic relation between temperature and the equilibrium constant. The component concentrations are related by the law of mass action39 K D (T ) =

c x 2 (T ) / c o ( c x (T ) / c o ) 2

(7)

where c° = 1 mol/dm3. Assuming that the dimerization constant KD(T) depends on temperature according to the van’t Hoff equation,39

Chemometric Study of Methylene Blue Association

d ln K D (T ) = -DH o / R d (1/ T )


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3. RESULTS AND DISCUSSION (8)

where DH° is the molar enthalpy change, R = 8.314 J mol-1 K-1 is the universal gas constant, and T the Kelvin temperature. A linear regression of equilibrium constant with respect to 1/T is then performed, which determines a trial enthalpy change of the reaction. Several studies based on the application of this method to evaluate spectrometric data have been reported.28-41 2. EXPERIMENTAL 2.1. Artificial Data Set The artificial data sets were generated based on BeerLambert’s law. Concentration profiles are constructed according to mass-balance equations and the spectrum of each species constructed by using a Gaussian formula with respect to the physico-chemical behavior of the system under study. To evaluate the robustness of the proposed method, different random noise levels were superimposed on each absorbance reading. The spectra were simulated in the wavelength range of 540-700 nm and the temperature range is 20-90 °C (5 °C intervals) with initial guesses of enthalpy and entropy values. The simulated data series have been refined by using the DATAN program. 2.2. Real Data Set 2.2.1. Instrumentation and Software Absorption spectra were measured on a CARY 100 UV-Visible Spectrophotometer (Varian) equipped with a 1 mm quartz cell with a temperature controller and a 1 nm bandwidth spectral bandpass, and were digitized with five data points per nanometer. The cuvettes were treated with repel-silane prior to measurements to avoid dye adsorption. All absorption spectra in the wavelength range of 540-700 nm were transferred (in ASCII format) to an Athlon 2000 XP computer for analysis by MATLAB (Mathworks, Version 6.5) and DATAN package ver 3.1.42 2.2.2. Chemical Reagents All the chemicals used were of analytical reagent grade. Subboiling, distilled water was used throughout. MB (for microscopy grade) was purchased from Fluka and used without additional purification. A stock solution of MB (1.00 ´ 10-3 M) was prepared. In all experiments the ionic strength was adjusted using KCl (Fluka).

3.1. Absorption spectra Two sets of simulated and experimental absorption spectra were prepared to examine the ability of the DATAN package in determination of dimerization constants. The first set obtained was based on Beer-Lambert’s law and using a Gaussian formula with specifications mentioned in the experimental section. The quantity of added noise to the generated absorption spectra is random. The sample three dimensional plot of the generated absorption spectra loaded with random noise is shown in Fig. 1. The wavelength and temperature range of the spectra were 600-700 nm and 20-90 °C temperature units, respectively. The second sets are experimental data of MB obtained at different total dye concentrations, and ionic strengths were recorded in the wavelength range of 540-700 nm. The typical absorption spectra of the MB in aqueous solution are shown in Fig. 2. 3.2. Determination the dimerization constant of simulated and experimental data set As expected, by increasing the temperature and decreasing the concentration, the monomer form would be predominant over the dimer form. So, it is wise to choose the spectrum of the dye at the highest temperature and at the

Fig. 1. The simulated absorption spectra of methylene blue loaded with 2% noise. (a: 6.00 ´ 10-5, b: 9.00 ´ 10-5, c: 3.00 ´ 10-4 M) with 5 °C intervals from 20-90 °C.

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lowest concentration as an initial estimate for the monomer in subsequent calculations. According to Equations (1)-(8), the DATAN program starts with a trial value of r21, at a predefined interval, and iterates all the calculation steps. The iteration stops when all r21 values in the preset interval are tested. The KD, dimer spectrum, DS° and DH°, corresponding to a minimum value of the c2 statistics, are selected as the final results. The c2 is the sum of squared residuals29 and generally used as a goodness of fit criterion and its value indicates the predictability of the model, i.e., how well the monomer spectrum and r21 are determined. The general formula of the c2 is: n

c 2 = å ( A exp - A calc ) 2 / A exp i=1

where Aexp is the expected value and Acalc the value calculated from the experimental data over n data points. By a rising the temperature, an absorption peak, for MB, around 664 nm grows and an absorption shoulder around 610 nm decreases (Fig. 2). We analyzed the temperature titrations assuming monomer-dimer, monomerdimer-trimer and even some models including higher order aggregates. It was found that a monomer-dimer model most adequately describes the data in these ranges of dye concentrations. The presence of exactly two species is also evidenced by the appearance of an isosbestic point at 620 nm

Fig. 2. Experimental absorption spectra of MB in water (a: 6.00 ´ 10-5, b: 9.00 ´ 10-5, c: 3.00 ´ 10-4 M) with 5 °C intervals from 20-90 °C.

Ghasemi and Miladi

(Fig. 2). The dimerization constants of the simulated absorption spectra loaded with noise are calculated by the DATAN program. The dimerization constant at 25 °C and different concentrations are shown in Table 1. The general outputs of the program involve a linear van’t Hoff plot, the spectral responses of the monomer and dimer species, their concentration as a function of temperature (Fig. 3) and changes in the DH° and DS° of the reaction (Table 2). The dimerization constants (KD) were calculated at different temperatures and dye concentrations in pure water. As expected, KD decreased with increasing temperature, while it is virtually independent of total dye concentration. The dimerization constant at 25 °C and at different concentrations and thermodynamic parameters of the dimerization reaction are listed in Table 3. It is clear from the

Fig. 3. Linear van’t Hoff plots, molar ratios as a function of temperature and spectral profiles of the monomer and dimer species for simulated data of MB, 9 ´ 10 -5 , with and without noise (subscribes 1 and 2 for letters a to c denote absence and the presence of noise, respectively).



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Table 1. Dimeric constant (KD) value for the simulated data loaded with noise at different concentrations of MB Concentration of MB Data set 0% Noise 2% Noise

6.00 ´ 10 M

9.00 ´ 10-5 M

3.00 ´ 10-4 M

21.9 ´ 10 19.9 ´ 103

19.4 ´ 10 19.6 ´ 103

13.2 ´ 103 13.1 ´ 103

-5

3

LogKD (25° C) LogKD (25° C)

Table 2. Thermodynamic parameter values of MB for simulated data loaded with noise at different concentrations Data set

Concentration

0% Noise

6.00 ´ 10-5 M 9.00 ´ 10-5 M 3.00 ´ 10-4 M 6.00 ´ 10-5 M 9.00 ´ 10-5 M 3.00 ´ 10-4 M

2% Noise

DH° (KJ mol-1) DS° (J mol-1 K-1) -49.2 -49.4 -41.8 -48.4 -49.8 -41.2

-82 -84 -61 -79 -85 -59

result that the obtained dimerization constants obtained are the same within the margin of the experimental errors. From the dependence of log KD on 1/T (Fig. 4), DS° and DH° values were determined; the DH° values range from -41.8 KJ mol-1 to -49.3 KJ mol-1 with mean -46.84 KJ mol-1 while DS° ranges from -62 to -85 J mol -1 K -1 with mean -76 J mol-1 K-1. As described, the above dimerization

Fig. 4. The van’t Hoff plot at different concentrations of MB for experimental data in water (a: 6.00 ´ 10-5, b: 9.00 ´ 10-5, c: 3.00 ´ 10-4 M).

3

Table 3. Dimeric constant (KD) and thermodynamic parameter values for the experimental data of MB at different concentrations in pure water Concentration 6.00 ´ 10 M 9.00 ´ 10-5 M 3.00 ´ 10-4 M -5

LogKD (25 °C) DH° (KJ mol-1) DS° (J mol-1 K-1)

4.31 -49.2 -82

4.26 -49.4 -84

4.13 -41.7 -61

is presumed to be the dominant form of aggregation in applied concentration ranges in aqueous MB. This is corroborated by the constancy of the apparent enthalpy of association. In general, the extent of aggregation depends reciprocally on the temperature of the solution and is fully re-

Fig. 5. Molar ratio of MB dye monomer (o) and dimer (D), compared to molar ratios predicted by the temperature dependence of the equilibrium constant (shown as solid line) at different concentrations of MB dye in water (a: 6.00 ´ 10-5, b: 9.00 ´ 10-5, c: 3.00 ´ 10-4 M).

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Ghasemi and Miladi

Table 4. Dimeric constant (KD) and thermodynamic parameters values of methylene blue dye (5 ´ 10-5 M) at different ionic strengths by potassium chloride Concentration of KCl (M) LogKD (25 °C) DH° (KJ mol-1) DS° (J mol-1 K-1)

0.5

1

1.4

1.5

1.6

1.8

2.2

5.09 -63.4 -117

5.15 -63.6 -116

5.22 -55.5 -87

5.33 -62 -107

4.38 -43.2 -52

5.25 -76.8 -157

5.46 -157.3 -142

versible. The observed relationship between entropy and enthalpy reflects an electronic nature of the dimerization phenomenon of MB. The relative dependence of the concentrations of the monomer and dimer of MB on the temperature in different concentrations are shown diagrammatically in Fig. 5. The calculated absorption spectra of MB in monomer and dimer forms are shown in Fig. 6. For studying the effect of ionic strength on dimerization of MB using potassium chloride, the dimerization was investigated at different ionic strengths. Spectra of MB (5 ´ 10-5 M) at different ionic strengths in the temperature range of 20-90 °C with 5 °C intervals are shown in Fig. 7. Hydrophobic bonding, hydrophobic forces, and electrostatic interactions may be all considered important for dimeriza-

Fig. 6. Calculated absorption spectra of MB dye monomer (—) and dimer (---) at different concentrations in water (a: 6.00 ´ 10 -5 , b: 9.00 ´ 10-5, c: 3.00 ´ 10-4 M).

tion. What effect we expected from the increasing of the ionic strength on the dimerization constants according to the extended Debye-Huckel equation,43-44 totally depends on the relative charge of the dimer species with respect to the two monomer moieties. As can be seen from the data obtained at different ionic strengths (Table 4), the increasing of the ionic strength results in an increase of the dimerization constants. The dimeric constant at 25 °C and thermodynamic parameters values of MB at different concentrations of ionic strengths are listed in Table 4. One of the most interesting points of the change of the ionic strength on the dimerization reactions of the MB is the spectral changing of the dimer form. The dimer spectra of MB show enhancement of the spectral band with lmax’s around 664 nm as compared with those in water. Patil et al.45 reported a similar spectral change from the effect of the addition of some solutes to the aqueous solution of MB. They showed that these spectral variations depend on the angle between the two dye molecule planes which in turn depend on the concentration of the inert solutes. The decrease in dimer formation constant values with an increase in the concentration of each on inert salts also indicates the decreased tendency of MB molecules to undergo aggregation. The random variations in the formation constants by changing ionic strength may be returned to the presence of the un-accounted interactions such as anion–cation attractive type interactions, etc., in addition to monomer-dimer equilibrium. Despite the abovementioned variations which have a deterministic effect on the thermodynamics parameters of dimerization at MB, the TDS versus DH° plot, Fig. 8 shows a fairly good linear correlation indicating the existence of enthalpy-entropy compensation in dimeric reactions. The linear correlation observed between TDS and DH° values can be expressed as TDS = TDS° + a DH° with TDS° = 17.54 KJ mol-1, a = 0.82 (R2 = 0.9711) for thermodynamics data of the dimerization process of MB. The same trends



are reported from the thermodynamics study of the reactions largely accompanying changes in electrostatic interactions during the association reactions or host-guest phenomena.46-49 The result suggests that the entropic effect consists of two components. The first component TDS° is independent of enthalpy change and the second is proportional to it. The proportionality constant a might be considered as a quantitative measure of the enthalpy-entropy compensation. For MB, a = 0.82, only about 18% of the increase in DH contributed to dimeric stability. The close-to-zero intercept of TDS° KJ mol-1 reveals that the dimerization process here in

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nature can be classified as enthalpy driven. These results can be supported by the fact that the dimerization constant is increased by the increase of the ionic strengths of the medium which in turn show the increasing of the charge of the dimer that are more solvated by the solvents molecules, and entropic change would have less positive values. Another point that appears to be true about Fig. 8 which indicates the compensation effect is that the linear plot shows that a single mechanism is most likely to dominate the range of ionic strengths investigated. The ionic strength will affect the solubility such as salt-in and salt-out effects. Recently there have been some reports on the kinetic and thermody-

(Continued)

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Ghasemi and Miladi

Fig. 7. Experimental traces (left) absorption spectra of MB (5.00 ´ 10-5 M) with 5° interval between 20-90 °C at different ionic strengths (a: 0.5, b: 1, c: 1.4, d: 1.5, e: 1.6, f: 1.8 M of KCL). The right side indicates monomer (—) and dimer (---) of MB at corresponding concentrations and ionic strengths.

namic study on adsorption and desorption of MB on different activated charcoals.50-53 These papers report that the association of the MB have a pronounced effect on the adsorption desorption phenomena.

Fig. 8. Plot of TDS vs. DH° for dimerization of MB of different concentrations in various ionic strengths media.

4. CONCLUSION In this study we reported, for the first time to our knowledge, dimerization constants, concentration profiles, and spectral responses of monomer and dimers obtained by computer refinement of temperature photometric titrations. We also report a thermodynamic study of the dimerization


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