Micellar and Thermodynamic Properties of Sodium Dodecyl Sulfate in Binary Aqueous Solutions of Di-, Tri-, and Tetraethylene Glycols

Micellar and Thermodynamic Properties of Sodium Dodecyl Sulfate in Binary Aqueous Solutions of Di-, Tri-, and Tetraethylene Glycols

JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO. 202, 359–368 (1998) CS985484 Micellar and Thermodynamic Properties of Sodium Dodecyl Sulfate i...

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202, 359–368 (1998)


Micellar and Thermodynamic Properties of Sodium Dodecyl Sulfate in Binary Aqueous Solutions of Di-, Tri-, and Tetraethylene Glycols Dale Turner, 1 Kim Gracie, 2 Trudy Taylor, and R. Palepu 3 Department of Chemistry, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5 Received August 20, 1997; accepted February 19, 1998

Thermodynamic and micellar properties of sodium dodecyl sulfate in aqueous solutions of di-, tri-, and tetraethylene glycols were determined employing conductivity, potentiometric, and fluorescence spectroscopic techniques. Intermicellar properties such as effective degree of dissociation, monomer and counter ion concentrations, and activity coefficients were obtained from the mass action model. From the evaluated intermicellar parameters, the hydrophobic and electrostatic contributions to Gibbs free energy of micellization were evaluated. The difference in Gibbs energies of micellization of SDS between water and mixed solvent systems and the results were also interpreted in terms of hydrophobic and electrostatic contributions to the micellization process. Surfactant aggregation numbers (Nagg ) obtained from the fluorescence quenching method decrease with increasing glycol content in the solvent composition. The micropolarity of the micellar interior was determined from the pyrene I1 /I3 ratios. q 1998 Academic Press Key Words: thermodynamics; micellization; aggregation numbers; intermicellar properties; mass action model.


As part of a comprehensive study of the micellar process in mixed solvent systems containing water plus polar organic compounds with hydrogen bonding ability, we report in this paper the micellar and thermodynamic properties of sodium dodecyl sulfate (SDS) in binary aqueous mixtures containing di-, tri-, and tetraethylene glycols (DG, TEG, and TTEG). The aggregation phenomena of ionic surfactant molecules is a balance between the repulsive forces primarily from electrostatic repulsion between polar head groups (1) and the attractive forces mainly due to hydrophobic interactions (2). Recently, considerable emphasis has been placed on 1 Present address: Department of Chemistry, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4. 2 Present address: Department of Chemistry, McMaster University, ABB203, 1280 Main St. W., Hamilton, Ontario, Canada L8S 4MI. 3 To whom correspondence should be addressed. E-mail: [email protected] stfx.ca.

London-dispersion interactions as the driving force for the micellization process (3, 4). The satisfactory way to investigate the effect of hydrophobic interaction on ionic micelle formation would be to study the micellar properties of ionic surfactants in altered water structure by adding alcohols of varying chain length. All substances containing hydrophobic moities decrease the hydrophobic effect, that is, it would decrease the standard chemical potential of the monomer for the micelle-forming amphiphile without any effect on the standard chemical potential of the micelle and would therefore increase the cmc. If alcohols are dissolved in water, the solvent hydrophobicity will increase. This results in an increase of the critical micellar concentration because the micellization energy gained by the system decreases. This is the case when adding short chain alcohols. Following the alcohol addition, the micellar aggregation number decreases and when the alcohol concentration exceeds a certain threshold value, the micelles are known to breakdown ultimately (5). Many studies have been dedicated to the study of alcohol/micelle system in recent years (6–13). Lengthening of the alkyl chains in alcohols leads to a decrease of the lower critical solution temperature (LCST). This causes a miscibility gap in aqueous solutions, thereby limiting the alcohol concentration in the mixed solvent system. It has been shown that the inclusion of one or more oxyethylene groups into a glycol molecule increases the LCST and consequently the aqueous miscibility (14, 15). We have reported recently the micellization process of alkyl trimethyl and pyridinium bromides in pure ethylene glycol employing the membrane selective electrodes (16) and extended the study in aqueous binary mixtures of ethylene glycol with water in the entire composition range (17, 18). In this investigation we present micellar properties such as cmc, effective degree of dissociation ( a ), equivalent conductance at infinite dilution, and aggregation numbers of sodium dodecyl sulfate in binary mixtures of water containing different amounts of di-, tri-, and tetraethylene glycols. Techniques employed are conductance, potentiometry, and fluorescence spectroscopy. Also by employing a mass action model, a complete analysis of thermodynamic proper-



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0021-9797/98 $25.00 Copyright q 1998 by Academic Press All rights of reproduction in any form reserved.




ties of micellization was carried out. In the present study, glycols were regarded as a cosolvent rather than a cosurfactant forming mixed micelles. EXPERIMENTAL

Materials Sodium dodecyl sulfate (BDH) was crystallized several times from hot methanol, further purified through Soxhlet extraction with diethyl ether for 72–100 h, and dried under vacuum. All glycols are of the stated purity ú99% (Aldrich) and were used as received without any further purification. All solutions were prepared with Milli-Q water (Millipore), and the specific conductance of water was less than 2 mS cm01 . Pyrene (Aldrich ú99.1%) was purified by sublimation and crystallized from ethanol. Hexadecylpyridinium bromide (CPBr) was purified by crystallization from acetone. Measurements Conductivity measurements were made in a thermostated jacketed beaker with a dip cell having a cell constant of 0.978 cm01 and an automatic conductivity CDM 83 bridge operating at 1000 Hz. Conductivity titrations containing at least 25 different concentrations of surfactant at a fixed solvent composition were carried out at four different temperatures. A Fisher sodium ion selective electrode coupled with a double-junction reference electrode (Fisher 13-620-47) was used to measure the sodium ion activities. To prevent the precipitation of potassium dodecyl sulfate at the junction of the reference electrode, ammonium nitrate solution was used instead of potassium nitrate in the outer chamber. Fluorescence quenching measurements were carried out on a Shimadzu RF-1501 spectrophotometer. Pyrene is used as a fluorescence probe, and the concentration was held around 2 1 10 06 M. The concentration of the quencher, hexadecylpyridinium bromide was held low enough to not interfere with the assembly of the micelles. The emission and excitation slits were 5 nm, and a wavelength of 335 nm was selected for excitation. The emission intensity was measured from 350 to 600 nm. The intensities ( I) at 373 nm was used in the plots of ln(Io /I) versus quencher concentration. Ratios of the intensities of the first and third vibronic peaks were measured using a Perkin-Elmer MPF 66 fluorescence spectrophotometer to determine the micropolarity of the micellar interior and the corresponding solvent systems. The I1 /I3 ratios were measured directly from the spectra. Employing a computer program based on the mass action model as outlined by Moroi et al. (19), we obtained the monomer, counter ion, and micelle concentration in the post-


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FIG. 1. Specific conductance (K) vs concentration of SDS in aqueous mixtures of DEG at 298 K.

micellar region up to a concentration of ten times the cmc value. The input parameters required for these calculations are aggregation number, cmc value, and the degree of counter ion binding of the micelle. These parameters were obtained from static fluorescence quenching, conductometric, and potentiometric methods. RESULTS AND DISCUSSIONS

The cmc is defined as a break point on a plot of specific conductivity vs surfactant concentration plots (Fig. 1). The effective degree of dissociation of micelle ( a ) was obtained from the ratio of the slopes of the lines above and below the cmc in the plots of specific conductivity versus concen-




observed. The increase in cmc values with glycol concentration is attributed to the decrease in hydrophobic effect due to the structure-breaking ability of glycols in water. Also, the decrease in the dielectric constant of the aqueous phase would cause an increase in repulsion between the ionic head groups, thus opposing the micellization process. The increase in cmc values can also be attributed to the formation of small aggregates, like dimers, trimers, etc. Evidence for the formation of these aggregates was obtained from the differential equivalent conductivity plots. Molar conductivities ( L ) for SDS were calculated and fitted to the Onsager equation (22), q

L Å Lo 0 (ALo / B) C,

FIG. 2. Differential equivalent conductance vs mean concentration.

tration. To differentiate between a cooperative micellization and a more gradual association prior to cmc, the differential equivalent conductance ( DLeq ), which is given by the following equation (20, 21), DLeq Å 10 03

i 1 i 1

K1 0 K , C1 0 C


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to determine the limiting molar conductivities at infinite dilution ( Lo ) in the premicellar region as described in the literature (23, 24). The values of Lo obtained from Eq. [2] are plotted in Fig. 3 as a function of wt % of glycols. The values of Lo decrease with increase in glycol concentration, indicating the association of the surfactant monomer and counter ions with the glycols. In view of the large size and hydrophobic nature of the DS 0 ion, the major contribution of the molar conductivity can be attributed to solvated Na / ions in solution. The potentiometric determination of degree of dissociation using a sodium specific ion electrode and a reference electrode was detailed in our previous publications (17, 18), and the values obtained by this method are presented in Table 1. TABLE 1 Micellar Properties of SDS in Various Glycol / Water Mixtures aa



Method 1

Method 11

Method 111







(where K1 0 K i1 is the increment in conductivity and C1 0 C i1 is the corresponding increment in concentration) is plotted vs mean concentration C Å (C1 / C i1 )/2. A cooperative micelle formation is accompanied by a vertical decrease over a narrow concentration range compared to a decrease over a wider range of concentration for a noncooperative micelle formation (Fig. 2). The cmc values and a values obtained from conductivity measurements are presented in Table 1 along with the values obtained by other techniques. In all cases, it is observed that the cmc values increase with increasing glycol concentration and beyond a certain concentration of glycol, no aggregate formation was

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10 20 30 40


1.01 1.09 1.49 2.29

0.51 0.59 0.61 0.69

0.47 0.55 0.61 0.64

0.40 0.50 0.55 0.59

10 20 30 40


0.93 1.24 1.74 2.27

0.56 0.57 0.61 0.67

0.47 0.53 0.64 0.69

0.40 0.49 0.57 0.60

10 20 30 40


0.95 1.27 1.66 2.15

0.55 0.60 0.63 0.70

0.51 0.62 0.67 0.68

0.46 0.53 0.58 0.60

a Method 1, conductometric; Method 11, potentiometric; Method 111, model. Estimated error in a is {0.05.




FIG. 3. Plot of Ú7 vs of wt % of glycols.

Micellar Aggregation Numbers and Sizes

Micellar aggregation numbers were determined by the static quenching method developed by Turro and Yetka (25). This method has been successfully applied to the determination of aggregation numbers of SDS micelles in water and in the presence of additives (25–27). Pyrene–hexadecylpyridinium ion pair is found to be suitable for the determination of the aggregation numbers of ionic surfactants in micellar solutions (28, 29). When the steady-state fluorescence quenching method is applicable, the ratio of luminescence ratio (Io /I) without and with quencher Q is related to the micelle concentration [M] by the equation




[Q] . [M]


The micelle concentration [M] is given by

[M] Å

S 0 cmc , Nagg


where S is the total surfactant concentration and Nagg is the micelle aggregation number. Substitution of [M] in Eq. [3] resulted in the following equation:




Nagg [Q]. S 0 cmc


Plots of ln(Io /I) vs [Q] for all the systems depicted good


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linearity (Fig. 4), and the aggregation numbers were determined from the values of the slopes of these plots, and are listed in Table 2. The aggregation numbers and I1 /I3 ratios obtained in the present study for SDS in 2 and 6% TTEG solutions are in agreement with the results of Marangoni et al. (30). The ratios of the intensities of the first and third vibronic peaks of the pyrene for the solvent system and in the presence of micelles are presented in Table 2. The intensity ratios of I1 /I3 are sensitive to the microenvironment around the probe (28–32). Therefore, this parameter can be used to detect the changes in the microenvironment sensed by the probe in the micelle on addition of glycols. From the examination of Table 2, it is obvious that the probe in the micelles sensed an increase in the polarity of its microenvironment on addition of glycols. It is known that pyrene is solubilized in the Palisade layer of micelles, near the polar head groups, where it senses relatively high polar environment (33). When glycol is added to the solution, the surface area per head group increases, thereby inducing the incorporation of water molecules or glycol molecules intercalated between the head groups. It is also possible that the increase of surface area per head group and the small micellar size force the probe to be located slightly outward in the micelle, thereby sensing higher polarity. The volume of the individual chain in the micelle ( £ ), and the critical chain length lc were obtained using Tanford’s equation (34): £ Å 27.4 / 26.9n (AL 3 ),


lc Å 1.5 / 1.265n (AL ),


where n is the number of carbon atoms in the chain. Assuming spherical shape for the micelles, the surface area per head group (ao ), micellar size, and the critical packing parameter ( £ /aolc ), which is a parameter controlling the micellar shape, were calculated (35). The micellar parameters are also presented in Table 2. The surface area per head group increases linearly with glycol content (Fig. 5), and this may be attributed to the replacement of water molecules in the solvation layer of the micelle head group by glycol molecules. The decrease in the critical packing parameter indicates that the addition of glycols favors the formation of smaller spherical micelles (36). Thermodynamic Properties

Free energy of micellization can be treated as a sum of DsG o and DHPG o (37). The value of DHPG o represents the hydrophobic free energy of transfer of the surfactant hydrocarbon chain from the medium to the interior of the micelle. The energy associated with the surface contributions consisting of electrostatic interactions between the head groups and counter ions along with all other contributions due to




FIG. 4. Plot of ln(Io /I) vs quencher concentration in binary mixtures of glycols containing 50 mM SDS.

specific interactions is represented in the value of DsG o . By employing the equilibrium model proposed by Ueno et al. (37), we determined the value of DHPG o as described below: The equilibrium between monomers, counter ions, and monodispersed micelles can be written as follows (38): ns 0 / (n 0 p)c / T M p0 ,

stant can be written in terms of the standard free energy of micelle formation per monomer ( DMG o ) as follows:


DMG o Å RT 0


1 ln XM p0 n / ln Xs 0 /

S D G 10

p ln Xc / n



where s 0 , c / and M p0 stand for monomer, counterion, and micelle concentrations, respectively. The equilibrium con-

A generally accepted procedure in the literature (10– 18 )



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TABLE 2 Aggregation Numbers, Micellar Parameters, and I1/I3 Ratios I1/I3

% Glycol

Nagg ({3)

˚) Ra (A

˚ 2) aob (A



0.05 M SDS in glycol


0 2 6 10 20 30 40

62 58 51 43 35 27 20

17.3 16.9 16.2 15.3 14.3 13.1 11.9

60.7 62.1 64.8 68.6 73.5 80.1 88.5

0.34 0.34 0.32 0.31 0.29 0.26 0.24

1.83 1.79 1.80 1.77 1.75 1.71 1.71

1.26 1.24 1.24 1.23 1.25 1.28 1.34


2 6 10 20 30 40

53 50 44 36 29 18

16.4 16.1 15.4 14.4 13.4 11.5

64.0 65.2 68.0 72.8 78.2 91.7

0.33 0.32 0.31 0.29 0.27 0.23

1.80 1.78 1.76 1.73 1.71 1.69

1.25 1.26 1.27 1.28 1.30 1.36


2 6 10 20 30 40

52 43 41 30 22 16

16.3 15.3 15.1 13.6 12.3 11.0

64.4 68.6 69.7 77.3 85.7 95.4

0.33 0.31 0.30 0.27 0.24 0.22

1.80 1.78 1.80 1.79 1.77 1.76

1.25 1.27 1.29 1.29 1.33 1.43



Micellar radius calculated assuming spherical micelles. Surface area per head group. c Critical packing parameter. b

is to neglect the term 0 (1 /n )ln XM p0 and to substitute ln Xcmc for the concentrations of the surfactant monomers and counter ions. This modification results in the following equation: DMG o Å (2 0 a )RT ln Xcmc .


In the present study, a computer program was developed to calculate the concentrations of monomers, counter ions and micelles in the post micellar region for SDS in the concentration ranging from 0.02 to 0.10 M, as outlined by Moroi (19). It can also be shown that DsG o Å 0 bRT ln Xc / ,


and experimental values at higher concentrations can be attributed to micelle–micelle interactions. Various thermodynamic and equilibrium properties of micellization of SDS such as mean activity coefficient ( g{ ), effective degree of dissociation ( a ), and free energy of micellization in mixed solvent systems were evaluated. The mean activity coefficient ( g{ ) values were obtained using the modified Debye–Hu¨ckel equation (22): q

log g{ Å

0 I


1/ I



where the ionic strength I is given by

1 where b is the counterion binding. Therefore, by evaluating I Å [Cs 0 / Cc / / CM p0 ]. [13] o o o 2 DMG and DsG values, one can obtain DHPG values. The monomer concentrations obtained by the model in the postmicellar region were compared to the experimentally The values of mean activity coefficients obtained were obtained values from specific ion membrane electrode mea- compared with the experimentally determined ( 39 ) values surements (39) for the tetradecylpyridinium bromide plus and presented in Fig. 7 for tetradecylpyridinium bromide water system. The calculated and experimental values are in water. The agreement between the calculated and experirepresented in the Fig. 6. There was excellent agreement mental values illustrates that the concentrations obtained between these values. Any deviation between the calculated from theory are reliable and can be used to calculate other


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FIG. 5. Surface area per head group (a0 ) of SDS micelles vs glycol composition.

parameters with confidence. The slight differences between measurements. In the latter procedures, it is assumed that the values obtained by these two methods can be attributed the concentration of the monomer in the postmicellar region to the fact that micelle concentrations were not included remain constant and equal to the cmc value. To calculate the DHPG 7 values, initially the values of in the calculations of ionic strength in the experimental DMG 7 and DsG 7 were evaluated. The procedure employed procedure. The monomer concentrations for 2% and 10% of DEG was as follows: system are presented in Fig. 8. The monomer concentration By equating DMG 7( 1 ) Å RT[ 01/n ln XM p / ln Xs 0 ] and decreases and depends on the glycol concentration. For a DMG 7( 11 ) Å RT(1 0 (p/n))ln Xc , the values of DMG 7( 1 ) and given glycol it can be seen from Fig. 9 that the relative DMG 7( 11 ) were evaluated in the range 0.02–0.10 M SDS. decrease in monomer concentration depends on the number The values were then extrapolated to cmc value by numerical of EO groups present in the glycol. methods. The sum of these quantities yielded DMG 7. The The effective degree of dissociation was calculated from value of DsG 7 is obtained by changing the sign of the slopes of a plot of log m1g{ vs log m2g{ where m1 and DMG 7( 11 ) . These values along with DMG 7 obtained by Eq. m2 represent the monomer and counter ion concentrations. [10] are listed in Table 3. The differences in DMG 7 values The values of a calculated are presented in Table 1. A typical between the two methods reflects in the assumption made plot for 10% DEG is presented in Fig. 10. The values of a in Eq. [10]. are slightly lower than the values obtained from the slope Now the effect of an additive on the free energy of micelliratios of conductivity plots or from the counter ion electrode zation (40, 41) can be calculated as follows: 0


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FIG. 6. Monomer concentration of tetradecylpyridinium bromide vs total concentration.

FIG. 8. Monomer concentration of SDS in the postmicellar region as a function of DEG composition.

DHPG 7( 11 ) Å DHPG 7glycol/H2O 0 DHPG 7H2O ,


DsG 7( 11 ) Å DsG 7glycol/H2O 0 DsG 7H2O .


The free energy of micellization is negative and becomes less favorable with increasing glycol concentration in the solvent system. The overall free energy change when micelles were transferred from water to mixed solvent system becomes less negative. The decrease in hydrophobic effect is reflected

The values of DHPG 7( 11) and DsG 7( 11) are listed in Table 3.

FIG. 7. Activity coefficients vs total concentration of tetradecylpyridinium bromide micelles in water of SDS.


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FIG. 9. Comparison of monomer concentration at a fixed composition of glycol.




in the degree of dissociation of the micelles. Removal of counter ions from the surface enhances the surface potential by increasing the electrostatic repulsion between the head groups which consequently destabilizes the micelles. The free energy of micellization as a function of temperature was calculated from the dependency of cmc and a on temperature, using Eq. [11]. The enthalpy and entropy of micellization were obtained as follows, and the values are listed in Table 3. DM S 7 Å 0

d [ DMG 7 ]p , dT


DM H 7 Å DMG 7 / TDM S 7.

FIG. 10. Plot of log(m1g{ ) vs log(m2g{ ) in aqueous 10% DEG solution.

in the increase in the values of DHPG 7( 11) with glycol. All these results lead to the conclusion that glycols act as structure breakers, thereby lowering the hydrophobic effect. The increasing negative values of DsG 7( 11 ) reflects in the increase


The values of DM H 7 and DM S 7 should be viewed only as approximate, since the equation used in the evaluation of DMG 7 strictly applies when the aggregation number is large (42). However, some general conclusions can be drawn from the analysis of the present data. The enthalpy of micellization value becomes increasingly negative and dominates in the micellization process at higher glycol content. SUMMARY

The increase in cmc values and a decrease in aggregation numbers with the addition of glycols can be attributed to

TABLE 3 Thermodynamic Properties of Micellizationa DMG(71)













2 DEG 6 DEG 10 DEG 20 DEG 30 DEG 40 DEG

012.8 011.6 011.1 08.8 08.1 06.1

021.1 020.9 020.7 020.3 019.0 017.0

033.9 032.5 031.9 029.1 027.1 023.1

034.8 033.4 032.3 030.0 028.1 024.9

12.8 11.6 11.1 8.8 8.1 6.1

2 TEG 6 TEG 10 TEG 20 TEG 30 TEG 40 TEG

012.7 011.4 010.6 010.1 09.2 06.5

021.9 021.4 021.0 020.0 018.9 017.9

034.6 032.9 031.7 030.1 028.1 024.4

034.9 033.5 031.3 030.1 027.6 025.1


012.1 010.3 09.9 07.9 07.6 05.3

020.8 020.5 020.2 019.4 018.3 016.7

032.9 030.8 030.2 027.3 025.9 022.1

033.8 031.3 030.8 028.4 025.9 023.7


a b






2.4 2.6 2.8 3.2 4.5 6.5

01.6 02.8 03.3 05.6 06.3 08.3

010.5 015.1 020.3 020.4

73 59 26 15

12.7 11.4 10.6 10.1 9.2 6.5

1.7 2.1 2.5 3.5 4.6 5.6

01.7 03.0 03.8 04.3 05.1 07.9

014.6 017.7 019.8 020.4

56 42 26 16

12.1 10.3 9.9 7.9 7.6 5.3

2.8 3.0 3.3 4.2 5.2 6.8

02.3 04.1 04.5 06.5 06.8 09.1

011.8 012.9 013.8 014.6

64 52 41 30

Units for DG and DH are kJ/mol with an error of {0.5 kJ. Units for DS are J/K mol with an error of {5 J. Calculated using Eq. [10].


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the decrease in the solvophobic effect due to the structure breaking abilities of the glycols. The increase in the effective degree of dissociation with glycol content is due to the decrease in the charge density at the micellar surface caused by the increase in the surface area per head group and a decrease in aggregation number. Employing the mass action model, the intermicellar properties such as effective degree of dissociation, monomer, counter ion concentrations, and activity coefficients were evaluated. The hydrophobic and electrostatic contributions toward Gibbs free energy of micellization were calculated from the intermicellar properties given by the model. Intermicellar properties are required in the interpretation of kinetic data on monomer/micelle equilibria and solubilization processes. ACKNOWLEDGMENTS This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC). D.T. acknowledges the grant of NSERC Undergraduate Summer Research Award (1994). We acknowledge Dr. G. Marangoni of St. Francis Xavier University for his interest in the work.

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