Visible Spectroscopy and Static Light

The spectroscopic data were interpreted as a monomer/dimer equilibrium in the ... The equilibrium constants were determined as 20 000 ( 3 000 L mol-1 ...
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Langmuir 2001, 17, 2675-2682

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Combined Study of UV/Visible Spectroscopy and Static Light Scattering on the Aggregation Behavior of Acid Red 266 in Aqueous Solution Bernd Neumann* University of Paderborn, Department of Physical Chemistry, Warburger Strasse 100, 33098 Paderborn, Germany Received November 9, 2000. In Final Form: February 8, 2001 The aggregation behavior of the azo dye Acid Red 266 has been investigated in pure water and in the presence of additional electrolyte (0.05 M NaCl) at 20 °C by UV/vis spectroscopy and static light scattering (SLS). The spectroscopic data were interpreted as a monomer/dimer equilibrium in the absence and presence of electrolyte. The equilibrium constants were determined as 20 000 ( 3 000 L mol-1 (in pure water) and 43 000 ( 4 000 L mol-1 (in 0.05 M NaCl), respectively. Although application of SLS revealed much larger species than dimers, the spectroscopic data were evaluated in terms of a monomer/dimer equilibrium to correct the light scattering data, for the first time, by the amount of residual monomers. This is possible because aggregates of this dye, reflecting the same local arrangement between the interacting molecules as in dimers, revealed no differences between dimers and higher multimers in the absorption spectra measured.1 Thus, the concentration of all aggregated species is represented by the apparent dimer concentration. The comparison of the corrected mass-based data of the dyestuff aggregates with former uncorrected ones revealed a non-negligible impact of the residual monomer concentration on those quantities. The growth of the aggregates both in length and in cross section has been confirmed by this procedure. Comparison of a former, different spectroscopic analysis with that of the present study gave good agreement in the equilibrium constants for both the salt-free and salt-containing cases.

Introduction Although dyestuff aggregation is a well-known phenomenon,2-5 it has recently experienced a certain renaissance since the discovery of lyotropic liquid crystalline6-8 phases (chromonics), nonlinear optical properties,9,10 and the capability of energy conversion in photovoltaic cells.11,13 However, apart from those interesting effects, little work has been reported on the corresponding aggregate structures,1,14-17 being responsible for those phenomena. This is of essential importance for a better understanding and control of the aforementioned effects. * Present address: The University of Hull, Surfactant & Colloid Group, Hull HU6 7RX, U.K. E-mail: [email protected]. (1) Neumann, B.; Huber, K.; Pollmann, P. Phys. Chem. Chem. Phys. 2000, 2, 3687. (2) Coates, E. J. Soc. Dyers Colour. 1969, 85, 355. (3) Herz, A. H. Adv. Colloid Interface Sci. 1977, 8, 237. (4) Mason, S. F. J. Soc. Dyers Colour. 1968, 84, 604. (5) Edwards, D. J.; Ormerod, A. P.; Tiddy, G. J. T.; Jaber, A. A.; Mahendrasingham, A. Advances in Colour Chemistry Series; Peters, A. T., Freeman, H. S., Eds.; Blackie Academic & Professional, Chapman & Hall: London, 1990; Vol. 4, p 83. (6) Tiddy, G. J. T.; Mateer, D. L.; Ormerod, A. P.; Harrison, W. J.; Edwards, D. J. Langmuir 1995, 11, 390. (7) Harrison, W. J.; Mateer, D. L.; Tiddy, G. J. T. J. Phys. Chem. 1996, 100, 2310. (8) Harrison, W. J.; Mateer, D. L.; Tiddy, G. J. T. Faraday Discuss. 1996, 104, 139. (9) Kobayashi, S. Mol. Cryst. Liq. Cryst. 1992, 217, 77. (10) Wang, Y. J. Opt. Soc. Am. B 1991, 8, 981. (11) Tamiaki, H.; Miyatake, T.; Tanikaga, R.; Holzwarth, A. R.; Schaffner, K. Angew. Chem. 1996, 108, 810. (12) Morel, D. L.; Stogryn, E. L.; Ghosh, A. K.; Feng, T.; Purwin, P. E.; Shaw, R. F.; Fishman, C.; Bird, G. R.; Piechowski, A. P. J. Phys. Chem. 1984, 88, 923. (13) Piechowski, A. P.; Bird, G. R.; Morel, D. L.; Stogryn, E. L. J. Phys. Chem. 1984, 88, 934. (14) Shimode, M.; Urakawa, H.; Yamanaka, S.; Hoshino, H.; Harada, N.; Kajiwara, K. Sen’i Gakkaishi 1996, 52, 293. (15) Ingles, E. S.; Katzenstein, A.; Schlenker, W.; Huber, K. Langmuir 2000, 16, 3010. (16) von Berlepsch, H.; Bo¨ttcher, C.; Ouart, A.; Burger, C.; Da¨hne, S.; Kirstein, S. J. Phys. Chem. B 2000, 104, 5255.

For relatively highly concentrated solutions, recent cryoTEM (transmission electron microscopy) and neutron scattering experiments have shown rodlike structures of the aggregated species16 in the presence and absence of surfactants.17 Conversely, in more dilute solutions, most studies were done by optical spectroscopy. Accordingly, application of such different techniques can lead to different results, which is reflected especially in differing aggregation numbers.1,18 Because both aforementioned methods focus on different organizational levels of the aggregates, some of those apparent contradictions can be explained.1 Light scattering methods, being restricted to more dilute solutions, can be better compared with those obtained from optical spectroscopy with respect to the similar range of concentration. In very recent investigations of small surfactants and penicillins in aqueous solution, combining such different methods as NMR, conductivity, and light scattering19-22 has revealed a very consistent picture. In those studies, only small aggregation numbers and no significant effect of added electrolyte have been found. Contrastingly, for some azo dyes it has been shown that their aggregation numbers can be very sensitive to changes of dyestuff or electrolyte concentration1 or even to the type of the electrolyte15 added. (17) von Berlepsch, H.; Bo¨ttcher, C.; Ouart, A.; Regenbrecht, M.; Akari, S.; Keiderling, U.; Schnablegger, H.; Da¨hne, S.; Kirstein, S. Langmuir 2000, 16, 5908. (18) Reeves, R. L.; Maggio, S. M.; Harkaway, S. A. J. Phys. Chem. 1979, 83, 2359. (19) Taboada, P.; Attwood, D.; Ruso, M. J.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 2022. (20) Ruso, M. J.; Attwood, D.; Rey, C.; Taboada, P.; Mosquera, V.; Sarmiento, F. J. Phys. Chem. B 1999, 103, 7092. (21) Ruso, M. J.; Attwood, D.; Taboada, P.; Mosquera, V.; Sarmiento, V. Langmuir 2000, 16, 1620. (22) Taboada, P.; Attwood, D.; Ruso, M. J.; Garcia, M.; Sarmiento, F.; Mosquera, V. Langmuir 2000, 16, 3175.

10.1021/la001564j CCC: $20.00 © 2001 American Chemical Society Published on Web 03/28/2001

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Figure 1. Structural formula of Acid Red 266.

Only a few studies have been reported using a combination of UV/vis spectroscopy and scattering techniques to elucidate the aggregation behavior of dyestuff solutions.1,16,17,23 However, in all those studies where scattering methods were applied to dyestuff solutions, always the initial concentration of dye was used for evaluation of the scattering data. If the exact concentration of scattering particles is not known, this approximation introduces additional inaccuracies by the amount of residual monomers when calculating the apparent molecular weights. Therefore, care has to be taken when interpreting the results obtained under this assumption. In this study, which is an extension of a previous work,1 a combination of UV/vis spectroscopy and static light scattering (SLS) results on aqueous solutions of the azo dye Acid Red 266 is reported in the absence and presence of added electrolyte (0.05 M NaCl). The additional aspects in this article are mainly based on the extraction of an apparent dimer spectrum at that electrolyte concentration where light scattering experiments were performed previously. It will be shown that UV/vis spectroscopy allows for a correction of the scattering data by the amount of residual monomers as calculated from the equilibrium constants obtained in the presence and absence of sodium chloride. Experimental Section Materials. The molecular structure of Acid Red 266 is given in Figure 1. The purity of the dye was found to be >97% by elemental analysis. Calculated: 43.64% C, 2.14% H, 8.98% N, corresponding to C17H10N3ClF3SO4Na. Observed: 44.77% C, 2.24% H, 8.95% N. NaCl was obtained from Merck Ltd. and used as received because the purity was given as >99.5%. UV/Vis Spectroscopy. Absorption spectroscopy was performed with an UV/vis/NIR double-beam double-monochromator spectrometer, Lambda 19 DM (Perkin-Elmer). The spectral bandwidth was chosen as 1 nm, and the recording speed was 60 nm min-1. The dyestuff was dissolved in distilled water under gentle heat. To obtain the desired concentrations, the respective stock solutions were adjusted by dilution. Prerinsing the cuvettes with the respective solutions prevented adsorption loss of dye. Rectangular cuvettes (Hellma) with a path length of 1 cm were used. The measuring temperature was held constant at 20 °C by a thermostat (Haake). Static Light Scattering. The data were collected by an ALV instrument ALV-1800 (ALV-GmbH, Langen, Germany). As the light source, a krypton ion laser (Stabilite 2016, Spectra-Physics) emitting at 647.1 nm was chosen to avoid any absorption of the dye molecules. The power of the incident beam was 250 mW. All scattering data were collected simultaneously at 18 different angles, covering a range of scattering angles, θ ) 32-143°. The Rayleigh ratio, ∆Rθ, of each solution was referred to the intensity of a toluene standard. Cylindrical cuvettes with 2 cm inner diameter (Hellma) were used and placed into a refractive-indexmatching toluene bath. The temperature of the bath was held constant at 20 °C by a thermostat (Lauda). The cuvettes were cleaned prior to use by injecting distilled acetone for several (23) Wojtyk, J.; McKerrow, A.; Kazmaier, P.; Buncel, E. Can. J. Chem. 1999, 77, 903.

Neumann minutes. All solutions were filtered through Millex-GV filters (Millipore) with a pore size of 0.22 µm directly into the cuvettes. To prepare salt-containing samples, the respective solutions were passed separately through the filters to prevent adsorption loss of dyestuff because of the enhanced aggregation in the presence of added salt. Those solutions were carefully shaken to mix. Repeated measurements revealed no time-dependent effects within 2 days. The refractive index increment, dn/dc, of the dye solutions was determined at 20 °C, using a laser differential refractometer, Chromatix KMX-16. The operating wavelength was 633 nm, generated by a He-Ne laser. The instrument was calibrated with different concentrated NaCl solutions, and dn/dc for Acid Red 266 in distilled water was found to be 0.348 ( 0.004 g-1 cm3.

Results and Discussion I. UV/Vis Spectroscopy. Evaluation of Equilibrium Constants. To obtain the respective equilibrium constants in the absence and presence of electrolyte, the law of mass action was applied. According to an equilibrium between monomers and N-mers, an aggregation constant, KN, can be defined as24-26

KN ) NKeq ) cN/cMN

(1)

with cM and cN being the concentrations of monomer and N-mer, respectively. Note that Keq always represents the equilibrium constant of the first step, which is dimerization. By relation of these concentrations to the initial concentration, c0, it follows that

cM ) [(∆N - ∆)/∆N]c0

(2)

cN ) (∆/∆N)c0

(3)

and

By insertion of eqs 2 and 3 into eq 1, the following expression can be derived:24-26

(∆/c0N-1)1/N ) -(NKeq/∆N)1/N ∆ + (NKeq ∆N)1/N (4) where ∆ )  - M, ∆N ) N - M, and  is the molar extinction coefficient at a specific wavelength. M and N denote the extinction coefficients of monomer and N-mer, respectively. Thus, a plot of (∆/c0N-1)1/N versus ∆ should yield a straight line, provided an appropriate N is chosen. From this, in principle, the extinction coefficient of the respective N-mer and the equilibrium constants, KN and Keq, are accessible, which will be shown in detail in the next section. In the present case, the spectroscopic data were treated as a monomer/dimer equilibrium (N ) 2) for the following reasons: (i) A comparison of 19F NMR data in a former study evaluated in terms of a monomer/dimer or monomer/ N-mer equilibrium could not distinguish between the two equilibria.1 (ii) As will be shown in the present work, in salt-free solution and in the presence of 0.05 M NaCl the spectroscopic data could be modeled only as a monomer/ dimer equilibrium because fitting to higher N-mer equilibria did not give the linear dependence predicted by eq 4. To show the hypochromic and hypsochromic effects accompanying the aggregation of Acid Red 266, in Figure (24) Hamada, K.; Take, S.; Iijima, T.; Amiya, S. J. Chem. Soc., Faraday Trans. 1 1986, 82, 3141. (25) Hamada, K.; Fujita, M.; Mitsuishi, M. J. Chem. Soc., Faraday Trans. 1990, 86, 4031. (26) Hamada, K.; Kubota, H.; Ichimura, A.; Iijima, T.; Amiya, S. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 859.

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Figure 3. Variation of the molar extinction coefficient, , with initial concentration, c0, of Acid Red 266 at 20 °C. 0 M NaCl: (0) 500, (O) 510, and (4) 520 nm; 0.05 M NaCl: (9) 500, (b) 510, and (2) 520 nm.

Figure 2. (a) Normalized absorption spectra of Acid Red 266 in 0.05 M NaCl at 20 °C. The arrow indicates the hypsochromic shift upon increasing concentration. The numbers 1-5 denote 11.3 × 10-6, 30.2 × 10-6, 53.3 × 10-6, 104.8 × 10-6, and 250.9 × 10-6 mol L-1. (b) Derivative spectra of fourth order for Acid Red 266 in 0.05 M NaCl at 20 °C. The numbers 1-5 represent 11.3 × 10-6, 20.1 × 10-6, 53.3 × 10-6, 104.8 × 10-6, and 250.9 × 10-6 mol L-1.

2a the normalized spectra of the dye in 0.05 M NaCl are presented together with their respective fourth derivatives (Figure 2b). Normalization was performed to emphasize the changes of the absorption curves upon increasing dyestuff concentration. The fourth derivative was taken to yield an idea about the individual band positions contributing to the spectra measured. Because the absorption spectra are lacking in a detailed fine structure, the fourth derivative revealed a better resolution than the second one. Interestingly, two major sub-bands were isolated, the maxima of which are centered at 472 and 560 nm. This finding is in accordance with a previous result where the NaCl concentration was 0.1 M.1 Both peaks show a convergence of their wavelength positions upon increasing dyestuff concentration (Figure 2b); above 11.3 × 10-6 mol L-1, they are peaked at fixed wavelength. This point will be referred to again later. In Figure 3, for clarity the extinction coefficients at only three selected wavelengths (500, 510, and 520 nm) in aqueous solution (open symbols) and in the presence of 0.05 M NaCl (full symbols) are shown. The decrease of  is more pronounced when electrolyte is added, indicating enhanced aggregation. The presentation given above is analogous to that of NMR data when the chemical shift, δ, is plotted versus c0.1,26 Although in Figure 4 the represented data sets (according to eq 4 with N ) 2) are restricted to 4 different wavelengths, evaluation was based on 10 different wavelengths, the changes of which are largest in .

Figure 4. Plot of (∆/c0)1/2 versus ∆ for Acid Red 266 at 20 °C: (0) 500, (O) 503, (4) 505, and (3) 510 nm at 0 M NaCl; (9) 500, (b) 503, (2) 505, and (1) 510 nm at 0.05 M NaCl.

The only case yielding the predicted straight line dependence is that for N ) 2. This finding reflects the principal difficulties in absorption spectroscopy in revealing further differences between dimers and higher aggregates when the basic aggregate structure is realized by vertical stacking of the molecules. (The vertical stacking mode of the aggregates of Acid Red 266 was confirmed by the concentration-dependent shifts obtained from 19F NMR spectroscopy in addition to the hypo- and hypsochromic shifts of the respective absorption spectra.1) It obviously demonstrates that optical spectroscopy detects only an equilibrium between two different absorbing species, which are monomers and aggregates of various sizes. Note that in a recently reported theoretical study on the H-aggregates of a simple merocyanine dye, only small differences of the corresponding energy levels of the molecules at terminal positions within the aggregates were calculated in comparison to those at central positions.27 From the data obtained by application of eq 4, the respective apparent equilibrium constants, Keq ) KD, were obtained (Table 1). The KD values were averaged to reduce the scatter, which is still quite high for the individual data points (not shown here). In the presence of 0.05 M NaCl, a KD of 39 000 ( 4 000 L mol-1 is found, which is twice the value obtained in the absence of salt (KD ) 21 000 ( 3 000 L mol-1). In a former study, a different method (27) Millie, P.; Momicchioli, F.; Vanossi, D. J. Phys. Chem. B 2000, 104, 9621.

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Table 1. Comparison of Equilibrium Constants, KD, Obtained from Different Methods for Acid Red 266 in Aqueous Solution at 20 °C

a

cNaCl/mol L-1

KD/L mol-1

method

0 0 0 0.05 0.05

7800 ( 600 20000 ( 3000 21000 ( 3000 43000 ( 4000 39000 ( 4000

NMR UV/visa UV/visb UV/visa UV/visb

According to eq 7. b According to eq 4.

was applied (vide infra), also based on the law of mass action, to obtain the equilibrium constant in aqueous solution.1 In that case, KD was determined as 20 000 ( 3 000 L mol-1, which compares fairly well with the value in the present work. The values determined here are slightly below 20 000 L mol-1 because the same wavelength range as in the other cases is chosen for a better comparison, whereas averaging was performed for a larger number of values (not shown here). The respective equilibrium constants are summarized in Table 1. Extraction of the Individual Spectra. Also in that previous study, a method was established to resolve the monomer and dimer spectra from the spectra of various concentrations measured. According to this method, here the respective spectra of monomers and apparent dimers will be isolated in the presence of 0.05 M NaCl. The basic equations needed for this will be described briefly. The starting point is again the assumption of a monomer/dimer equilibrium for which eq 1 should hold. Thus, the measured extinction coefficient, , represents a linear combination of the individual monomer and dimer spectra, denoted as M(λ) and D(λ), respectively.28

(λ) c0 ) M(λ) cM + 2 D(λ) cD

(5)

From eq 5 and the common expression for a dimerization equilibrium,

KD ) cD/cM2

(6)

it follows that

(λ, c0) ) [(M - D)/(4KDc0)][(1 + 8KDc0)1/2 - 1] + D (7) By use of eq 7, M, D, and KD were determined in a threeparameter fit in the wavelength range of largest changes in , based on a least-squares method. (For small changes in , fitting was impossible.) From these KD values, a mean value was taken, and the fitting parameters, M and D, were optimized again (now as a two-parameter fit). The resulting individual spectra are depicted in Figure 5 and the relevant spectroscopic data are listed in Table 2. A similar dimer spectrum is obtained in 0.05 M NaCl (Figure 5b) when compared with the salt-free case (Figure 5a). Although both monomer spectra agree in their extinction coefficient at the absorbance maximum (M ≈ 20 000 L mol-1 cm-1) and possess a similar overall shape, larger differences turned out in the short wavelength part (Figure 5c). Thus, these differences deserve attention. According to the fitting procedure based on eq 7, the data could be matched only by leaving M and D variable for KD ) 43 000 L mol-1 (solid line), instead of using the M values obtained from the spectra of salt-free solutions, (28) Monahan, A. R.; Germano, N. J.; Blossey, D. F. J. Phys. Chem. 1971, 75, 1227.

Figure 5. (a) Monomer (M) and dimer (D) spectra of Acid Red 266 in 0 M NaCl at 20 °C, according to ref 1. (b) Monomer (M) and dimer (D) spectra of Acid Red 266 in 0.05 M NaCl at 20 °C, according to eq 7. (c) Comparison of the monomer spectra obtained in 0 (O) and 0.05 (b) M NaCl for Acid Red 266 at 20 °C. The differences (+) between both spectra are shown as well. (The errors bars were obtained from the fitting procedure according to eq 7 at constant KD.)

which is demonstrated by the dashed line in Figure 6 for a selected wavelength of λ ) 450 nm. Hence, the differences in the short-wavelength region could be attributed tentatively to an effect caused by the presence of electrolyte. Resolution of the Apparent Dimer Spectra: Structural Aspects. To gain more information on the specific arrangement of the molecules within the aggregates in the presence of added salt, the apparent dimer spectrum, D, must be resolved into its vibrational sub-bands. Following

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Table 2. Spectroscopic Parameters of Acid Red 266 in the Absence and Presence of Electrolyte at 20 °C parametera

in 0 M NaCl

νJ/cm-1 νH/cm-1 fJ fH M,max/L mol-1 cm-1 D,max/L mol-1 cm-1 J/L mol-1 cm-1 H/L mol-1 cm-1 β/deg R/nm ∆νH,J/cm-1

18100 20200 0.034 0.159 19800 15600 5200 14800 50 0.69 2100

in 0.05 M NaCl 17700 21200 0.011 0.108 20300 14300 1800 12500 35 0.63 3500

a The symbols denote the following: ν and ν , wavenumbers of J H the J- and H-bands; fJ and fH, oscillator strengths of the corresponding J- and H-bands; M,max and D,max, extinction coefficients of the monomer and dimer at the respective absorption maximum; J and H, extinction coefficients of the J- and H-bands; β, twist angle between adjacent molecules (see Figure 7); R, interplanar distance between neighboring molecules (see Figure 7); ∆νH,J, “splitting energy” between J- and H-band positions.

Figure 8. Qualitative energy diagram to illustrate the spectroscopic consequences for monomeric and dimeric species according to refs 28 and 29. EG and EE denote the energy levels of the ground and excited states of the monomer, respectively. The low-energy transition corresponds to the J-band, and the high-energy transition corresponds to the H-band.

The energy difference between the two band positions, expressed in cm-1, is denoted as “dimer-splitting”, ∆νH,J. The apparent dimer spectrum was represented by a sum of several symmetrical Gaussian bands, according to eq 8.

D(ν) ) J exp[-4(ln 2)(ν - νJ)2/∆ν1/2,J2] + 3

i exp[-4(ln 2)(ν - νi)2/∆ν1/2,i2] ∑ i)0

Figure 6. Comparison of curves corresponding to eq 7, fitted to the data of Acid Red 266 in 0.05 M NaCl at 20 °C for a selected wavelength of 450 nm (9). In both cases, KD ) 43 000 L mol-1 was used: (s) M and D were variable and (- - -) only D was variable for M (0 M NaCl) ) 8560 L mol-1 cm-1.

(8)

To account for the dimer splitting, the sum for D was split into two terms. The long-wavelength part is referred to as J, and the short-wavelength part is referred to as i. The respective peak positions of the J-band and the remaining bands are designated as νJ and νi, and the half widths are designated as ∆ν1/2,J and ∆ν1/2,i. To further resolve the short-wavelength part of the apparent dimer spectrum, the same fundamental vibronic progression, ∆νvib, was used as found by derivative spectroscopy in methanolic solution.1 The remaining band positions, νi, were related to the most intensive band at νH:

νi ) νH + i(∆νvib) ) 20200 cm-1 + i(1350 cm-1) i ) 0, 1, 2, 3 (9) The twist angle, β (Figure 7), can be calculated from eq 10,18

β ) 2 arctanxfJ/fH

(10)

provided the respective oscillator strength, f, is known, which can be obtained from eq 11: Figure 7. Sketch of a dimer sandwich showing R, the interplanar distance, M1 and M2, the transition dipole moments, and the inclined twist angle, β, between them.

exciton theory,29,30 the excited state of the interacting monomers is split into two as a consequence of the electronic perturbation in a dimeric aggregate. If the respective transition dipole moments of the interacting molecules incline at a twist angle, β (Figure 7), then both transitions can be observed. (In the case of β ) 0, only one transition is allowed. The low-energy transition corresponds to the J-band and the high-energy transition corresponds to the H-band in the spectrum (Figure 8). (29) Kasha, M.; Rawls, H. R.; Ashraf El-Bayoumi, M. Pure Appl. Chem. 1965, 11, 371. (30) McRae, E. G. Aust. J. Chem. 1961, 14, 229, 344, 354.

f ) 4.32 × 10-9

∫band (ν) dν

(11)

Applying those equations, one finds that the dimer splitting is significantly enlarged; with 3500 cm-1, it is much larger when compared with the spectrum in the absence of salt (2100 cm-1) and even larger than estimated by derivative spectroscopy (from Figure 2b, ∆νH,J ) 3300 cm-1 was inferred). Also, the twist angle, β ) 35°, is smaller than that in the absence of electrolyte and even smaller as calculated previously, based on a more simplified analysis of the spectra.1 Besides, such a diminished angle is consistent with a greater overlap of the aromatic planes, which enables enhanced π,π interaction as a consequence of a better screening of the charges on the dye molecules. The reduced interplanar spacing, R, between the dye molecules, when compared to the salt-free case, further

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is ∼9% smaller than the value obtained in the absence of salt (Table 2). Comparison of the Equilibrium Constants. In Figure 9, a comparison between the relative monomer concentrations, cM/c0, obtained from 19F NMR1 and from different methods based on UV/vis spectroscopy is displayed. From eq 6 and the mass balance, c0 ) cM + 2cD, it follows that

cM/c0 ) {-(4KD)-1 + [(4KD)-2 + (2KD)-1c0]1/2}/c0 (13)

Figure 9. Comparison of the relative residual monomer concentration, cM/c0, as a function of the initial concentration, c0, for Acid Red 266 at 20 °C according to eq 13: NMR (s), UV/vis at (- - -) 0 and (‚‚‚‚‚) 0.05 M NaCl, and (b) approximated relative residual monomer concentration after ref 1.

In that figure, it becomes apparent that NMR gives the lowest values and therefore bad coincidence with UV/vis. Furthermore, cM/c0 obtained from a previous semiempirical fitting procedure1 of the spectra in 0.05 M NaCl (solid spheres) is not in accord with the present results. This is due to the crude approximation of a residual monomer spectrum by a single Gaussian band only, which is obviously too simple. Although UV/vis spectroscopy revealed a simple monomer/dimer equilibrium, the light scattering data described in the next section clearly prove the existence of much larger species ranging from hundreds up to thousands of molecules per aggregate. The physical reason for this is the method itself: optical spectroscopy discriminates only between different absorbing species. Unfortunately, differences between true dimers and higher aggregates in the corresponding individual spectra cannot be registered because the actual spectrum recorded is measured as an integral spectrum. It is the net outcome of averaging over all local inhomogeneities within the aggregates of various lengths, simply repeating (nearly) the same local arrangement as in true dimers.1 Therefore, it is obvious that such a “two-state model”, confirmed by eq 4 (Figure 4), holds in the present case. Nevertheless, apart from the fact that no clear assignment of the real size of such apparent dimers can be given by UV/vis spectroscopy, an estimation of the residual monomer concentration becomes possible because all aggregated species are summed up by an apparent dimer concentration. II. Static Light Scattering. Correction of Scattering Data. To evaluate the scattering data according to Zimm,31 the concentration of scattering particles must be known. This concentration was calculated by subtracting the amount of residual monomers (obtained from optical spectroscopy) from the initial dyestuff concentration, c ) c0. Similar to the case of micellar solutions (however, dyestuff aggregation is commonly unidirectional, and therefore the aggregation number is, in principle, unlimited), where the total concentration is reduced by the critical micelle concentration, cmc,32 one can write

K(c - cM)/∆Rθ ) 1/MW,app[1 + (RG2/3)q2 + 2A2(c - cM) + ...] (14) Figure 10. (a) Zimm plots of scattering data for Acid Red 266 in 0 M NaCl at 20 °C. Uncorrected data: (0) 100 × 10-6, (O) 500 × 10-6, and (4) 1000 × 10-6 mol L-1; corrected data: (9) 100 × 10-6, (b) 500 × 10-6, and (2) 1000 × 10-6 mol L-1. (b) Zimm plots of scattering data for Acid Red 266 in 0.05 M NaCl at 20 °C. Uncorrected data: (0) 20 × 10-6, (O) 100 × 10-6, and (4) 250 × 10-6 mol L-1; corrected data: (b) 20 × 10-6, (2) 100 × 10-6, and (2) 250 × 10-6 mol L-1.

supports this finding. R is given by eq 12:18 3

R ) x2.14 × 107 cos(β)/(νM ∆νH,J)

(12)

With νM ) 19 880 cm-1, one obtains R ) 0.63 nm, which

Here, K is an optical constant, representing the contrast of the scattering particles to the solvent. ∆Rθ is the Rayleigh ratio, which represents the solvent-corrected excess scattering intensity. The corrected concentration of scattering particles in g L-1 is denoted as c - cM. MW,app is the apparent molecular mass; extrapolation of the scattering data to zero concentration was not performed because the molecular weight itself may depend on c. RG is the radius of gyration, and q is the scattering vector, the magnitude of which is |q| ) (4πn/λ) sin(θ/2), where n (31) Zimm, B. H. J. Chem. Phys. 1948, 16, 1093, 1099. (32) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain, Where Physics, Chemistry, Biology, and Technology Meet; VCH Publishers: Cambridge, U.K., 1994; Chapter 4, p 149.

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Table 3. Comparison of Uncorrected and Corrected Mass Data Obtained from Light Scattering for Acid Red 266 in Aqueous Solution at 20 °C c0/10-6 mol L-1

cM/10-6 mol L-1

MW,app/106 g mol-1

100 500 1000

39 100 159

0.26 0.32 0.36

20 100 250

13 38 65

1.0 2.1 2.2

MW/106 g mol-1 0 M NaCl 0.40 0.43 0.43 0.05 M NaCl 2.1 2.9 2.7

∆MW,app in %

ML,app/g nm-1

ML/g nm-1

2200 3000 3100

4300 4300 3900

35 26 7 52 28 19

is the refractive index of the solution, λ is the wavelength of the incident light beam, and θ is the scattering angle. A2 is the second virial coefficient, and K is given as

K ) 4πn2(dn/dc)2/(λ4NA)

(15)

with NA being Avogadro’s number. The data according to eq 14 are plotted in Figure 10a. Comparison with the former uncorrected data reveals that the intercepts of the corrected data are closer together than in the latter case. This points to a less pronounced concentration dependence of the molecular weight when corrected by the amount of the residual monomers. Because in the presence of electrolyte a curvature of K(c - cM)/∆Rθ is observed when plotted versus q2 (Figure 10b), the following expression was used for data evaluation:1,15 2

2

4

K(c - cM)/∆Rθ ) 1/MW,app[1 + (RG /3)q + Bq ] (16) The additional term, Bq4, accounts for the curvature of the scattering data. Furthermore, the second virial coefficient was neglected, which is commonly small at low concentrations and in the presence of additional electrolyte, and therefore may be justified without introducing a large error. In both cases, the absence and presence of electrolyte, for the corrected data a concentration-dependent trend is much less pronounced than for the uncorrected data (Table 3). From Table 3, it is obvious that the differences between the corrected and uncorrected apparent molecular weights, expressed as ∆MW,app, are largest at the lowest dyestuff concentration and become smaller with increasing c0 because the relative amount of monomers decreases correspondingly. (Note that the corrected MW and ML values listed in Table 3 are still apparent values because no extrapolation to c ) 0 was performed.) In the case of rigid rods, the particle form factor scales as q-1 for large q values; thus, a presentation of the [K(c - cM)/∆Rθ]-1 values multiplied by q reveals constant plateau values, which gives a measure of the particle mass per unit length, ML:33,34

q[K(c - cM)/∆Rθ]-1 f πML

(17)

The largest effect of cM on the scattering data is found for the linear mass densities. To demonstrate this, in Figure 11 the corrected and uncorrected data are compared. As can be seen, the ranking of the respective plateau values has inverted. Now, the highest ML value is found for the lowest concentration. This becomes possible because at lower dyestuff concentrations the relative amount of residual monomers is essentially high (Figure (33) Holtzer, A. J. Polym. Sci. 1955, 17, 432. (34) Porod, G. J. Polym. Sci. 1952, 10, 157.

Figure 11. Casassa-Holtzer plots for Acid Red 266 in 0.05 M NaCl at 20 °C. Uncorrected data: (0) 20 × 10-6, (O) 100 × 10-6, and (4) 250 × 10-6 mol L-1; corrected data: (9) 20 × 10-6, (b) 100 × 10-6, and (2) 250 × 10-6 mol L-1. The solid lines refer to the last 12 plateau values.

9) and subtraction of this amount leads to relatively low concentrations of scattering particles. The reciprocal of this, [K(c - cM)/∆Rθ]-1, is therefore quite large. On the other hand, it has to be taken into account that the experimental error may be estimated to be 10-15%, and thus the ML values found should be placed around an average value of 4000 g nm-1 for all concentrations in the presence of salt. Such a concentration insensitivity is in contrast to the previous results, where the initial dyestuff concentration was used. Apart from this, it has been confirmed that addition of electrolyte causes a significant increase of both the length and cross section of the aggregates, when compared with the data of salt-free solutions. The relatively high number of molecules per unit length (∼9 nm-1) verifies a multimolecular cross section of the aggregates even at low dyestuff concentrations, as concluded previously,1 and is consistent with a ropelike structure as suggested by Lydon.35 Consequently, the knowledge of cM is of crucial importance to ensure a more accurate interpretation of the light scattering data of dyestuff solutions. Conclusions It has been demonstrated that the absorption spectra of Acid Red 266, in both the absence and presence of 0.05 M NaCl, can be described in terms of a monomer/dimer equilibrium. In aqueous solution, the equilibrium constant KD was determined as 21 000 ( 2 000 L mol-1, confirming the result of a former study.1 In that work, a different method was applied and KD was found to be 20 000 ( 3 000 L mol-1, in excellent agreement with the afore(35) Lydon, J. Chromonics. In Handbook of Liquid Crystals;Demus, D., Goodby, J., Gray, G. W., Spiess, H.-W., Vill, V., Eds.; Wiley-VCH: Weinheim, 1998; Vol. 2B, Chapter XVIII, p 981.

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mentioned value. Roughly twice this value was obtained in the presence of electrolyte, namely, 43 000 ( 4 000 L mol-1, reflecting a higher aggregation tendency. This is presumably due to the better screened charges on the dye molecules and in accordance with the findings reported in ref 24. By means of a method established in a previous study,1 the apparent dimer spectrum of Acid Red 266 in 0.05 M NaCl was obtained and compared with an approximated former one. The corresponding dimer splitting, ∆νH,J, was determined as 3500 cm-1, and the twist angle, β, was determined as 35°. It turned out that the former procedure, where the spectrum of residual monomers was approximated by a single Gaussian band only, was too simple but gave nevertheless the correct trends. In both cases, salt-free and salt-containing, the respective equilibrium constants were used to calculate the amount of residual monomers and, for the first time, to correct the light scattering data. The comparison of the uncorrected with the corrected data revealed an impact of this residual amount on all mass-based data. After correction, significant concentration-dependent trends were no longer found in contrast to the previous results. On the other hand, it has been confirmed that the dyestuff aggregates increase significantly in length and cross section when electrolyte is added. This leads to molecular weights of 3 × 106 g mol-1 and linear mass densities of 4000 g nm-1, corresponding to ∼9 molecules nm-1. Acknowledgment. The author thanks Professor P. Pollmann (University of Paderborn) for permission to perform the UV/vis measurements, the Ciba-AG in

Neumann

Grenzach-Wyhlen for access to their light scattering instrument, Professor G. J. T. Tiddy (University of Salford) for the gift of a sample of Acid Red 266, and Professor P. D. I. Fletcher (University of Hull) for helpful comments. Appendix Equation 4 can be derived as follows. Insertion of eqs 2 and 3 into eq 1 gives

KN ) (∆/∆N)[∆N/(∆N - ∆)]Nc01-N

(A1)

The term in square brackets of eq A1 can also be written as

[∆N/(∆N - ∆)]N ) [1 - (∆/∆N)]-N

(A2)

Using expression A2 in eq A1 and taking the Nth root on both sides, one obtains after several rearrangements

(∆/c0N-1)1/N ) -(KN/∆NN-1)1/N ∆ + (KN ∆N)1/N (A3)

Finally, KN can be replaced by NKeq, leading to eq 4. LA001564J