Effect of ethylene glycol on the special counterion binding and microstructures of sodium dioctylsulfosuccinate micelles

Journal of Colloid and Interface Science 414 (2014) 103–109

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Effect of ethylene glycol on the special counterion binding and microstructures of sodium dioctylsulfosuccinate micelles J. Dey a, S. Kumar c, A. Srivastava a, G. Verma b, P.A. Hassan b, V.K. Aswal c, J. Kohlbrecher d, K. Ismail a,⇑ a

Department of Chemistry, North-Eastern Hill University, Shillong 793022, India Chemistry Division, Bhabha Atomic Research Center, Trombay, Mumbai 400085, India c Solid State Physics Division, Bhabha Atomic Research Center, Trombay, Mumbai 400085, India d Laboratory for Neutron Scattering, Paul Scherrer Institut, CH-5232 PSI Villigen, Switzerland b

a r t i c l e

i n f o

Article history: Received 21 August 2013 Accepted 4 October 2013 Available online 18 October 2013 Keywords: Sodium dioctylsulfosuccinate Ethylene glycol Critical micelle concentration Counterion binding Small angle neutron scattering

a b s t r a c t Sodium dioctylsulfosuccinate (AOT) micelle has a special counterion binding behavior (SCB), which refers to the abrupt twofold increase in the counterion binding constant (b) at a critical concentration (c) of added NaCl (in water c  0.015 mol kg1). In this paper, the SCB of AOT has been studied in a mixture of water and ethylene glycol (EG) by applying surface tension, fluorescence, and small angle neutron scattering (SANS) methods. The SCB exists in water + 10% (w/w) EG as well, but disappears when the EG% is P20. It has been found out that the SCB of AOT occurs in media having cohesive energy density values in the range of 2.3–2.75 J m3. SANS data indicate co-existence of vesicles and cylindrical micelles of AOT in water + 10% EG when the added NaCl concentration is greater than c thereby revealing that change in the morphology of aggregated species is the probable cause for the SCB of AOT. From this study it has become clear that the Corrin–Harkins (CH) equation, commonly used for determining b, can be applied   only above a limiting concentration c# of added electrolyte. In aqueous organic or pure organic polar e # solvents below ce sharp deviation from the CH equation occurs with reversal of slope rendering this equation inapplicable for the determination of b. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction As aggregation of amphiphilic molecules is a solvent – induced phenomenon, investigating the aggregation process of surfactants in solvents of varying polarity is considered to throw light on fundamental aspects of aggregation behavior of amphiphiles. Moreover, tuning the aggregation process as well as the characteristics of the aggregated species is possible by adjusting the composition of a mixed solvent medium. These viewpoints have led to reprising the study on the aggregation of surfactants in different solvent media time and again, which is reflected in the papers published in recent past [1–18]. Besides solvents, counterions play important role in inducing structural or shape transitions of surfactant aggregates. Some of the applications of ionic micelles, e.g., as drug delivery system, are attributed to the occurrence of structural changes in micelles (such as transition from micelle to vesicle). It is therefore important to understand the counterion binding behavior of ionic micelles in mixed solvents. In the studies on the aggregation of surfactants in mixed solvents, the attention paid to the binding behavior of counterions to ionic micelles, particularly in ⇑ Corresponding author. Address: Department of Chemistry, North-Eastern Hill University, NEHU Campus, Shillong 793022, India. Fax: +91 364 2550486. E-mail addresses: [email protected], [email protected] (K. Ismail). 0021-9797/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2013.10.005

the light of the thermodynamic approach developed by Corrin and Harkins [19], is however quite limited [20]. Sodium dioctylsulfosuccinate (AOT), a double-chained anionic surfactant, is known for its special features [21–23]. One of the recently reported [22,23] special features of AOT is its special counterion binding behavior (SCB), viz., the counterion binding constant (b) value of AOT suddenly doubles (from about 0.4 to 0.8) in the presence of about 0.015 mol kg1 NaCl in aqueous medium. The small angle neutron scattering (SANS) measurements [23] revealed that the shape change of AOT micelle is responsible for the SCB of AOT. In order to obtain further insight into the SCB of AOT, it is interesting to study the effect of solvent on the SCB. An earlier study [5] in water + propylene carbonate (PC) media has indicated the dependence of the SCB of AOT on solvent, but this study was limited to only 18 wt.% PC due to miscibility problem. In the present study, we chose water + ethylene glycol (EG) mixtures to study the effect of solvent on the SCB of AOT. EG is an important solvent due to its large applications in industry and cryobiology [24–26] and it has got complete miscibility with water. It has been reported [4] recently that in water + EG mixed solvent AOT undergoes hydrogen bonding with the solvent molecules and therefore it is important to explore whether this hydrogen bonding has any influence on the SCB. For these reasons, we considered water + EG to be an interesting mixed solvent

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medium. Surface tension, fluorescence and SANS methods were employed for the characterization of SCB in the present study. 2. Materials and methods AOT (Sigma, 99% assay) and sodium chloride (Merck, 99.5% assay) were used without further purification. Stock solutions of AOT and the salts were prepared in Milli-Q water and the required concentrations were obtained by dilution. For SANS measurements D2O (99.9 atom% D) was used. Surface tension measurements were made by using a K11 Krüss tensiometer and Wilhelmy plate. Before every use, the plate was first rinsed with acetone to remove any organic material sticking to the plate and thereafter washed with Millipore water. Finally, the plate was heated to red hot with a Bunsen burner and then cooled. Fluorescence emission intensities of probe molecule in the experimental medium were recorded using a Hitachi F4500 FL spectrophotometer. Pyrene (Fluka, >97%) was used as a probe. SANS measurements were performed at SANS-I facility, Swiss Spallation Neutron Source SINQ, Paul Scherrer Institut, Switzerland [27]. The wavelength (k) of neutron beam was 6 Å and the scattered neutrons from samples were detected using two-dimensional 96 cm  96 cm detector. Data were collected at two sample-to-detector distances (2 and 8 m) to cover a wave vector transfer (Q = 4psin (h/2)/k, where h is scattering angle) range of 0.008–0.3 Å1. In SANS measurements for a particular composition of D2O + EG, the concentration of AOT was kept fixed and the concentration of NaCl was varied. The samples were held in HELLMA quartz cells having thickness 1 mm and temperature were kept fixed at 25 °C. The measured SANS data were corrected for the background, the empty cell contributions, and normalized to absolute cross-sectional unit using standard protocols. 3. Results and discussion 3.1. Surface tension Surface tension (c) plots of AOT solution in water + EG media (EG amount = 10% and 80% by weight) with varying amounts NaCl are shown in Fig. 1. Similar surface tension plots of AOT in 20%, 30%, 40%, 50%, 60%, 70%, 90% and 100% EG are shown in Figs. S1– S4. The break in the surface tension plot corresponding to the cmc shifts to lower surfactant concentration when the amount of NaCl in the medium increases indicating the lowering of cmc with increase in NaCl concentration. On the other hand, the premicellar surface tension break occurring in solutions containing 60% or more EG (Figs. 1 and S1–S4) tends to vanish gradually or becomes

less and less pronounced with increasing amount of NaCl. As reported recently [4], this premicellar surface tension break is due to hydrogen bonding between water, EG and AOT and it tends to disappear eventually by adding NaCl because of the tendency of added electrolyte to weaken the hydrogen bonding [28]. The values of cmc obtained from the surface tension plots are listed in Tables S1–S3 and also shown in Fig. 2. The cmc values of AOT in water as a function of NaCl concentration were taken from our previous study [22]. 3.2. Fluorescence An attempt was made to determine the cmc as a function of NaCl in water + EG media by the fluorescence technique using pyrene as the probe. The representative plots of I1/I3 ratio of pyrene as a function of AOT concentration in water + 10% EG containing different amounts of NaCl are shown in Fig. 3 and similar plots in other compositions of water + EG are shown in Figs. S5–S6. I1 and I3 refer to the intensities of the fluorescence emission spectra of pyrene at 374 and 384 nm, respectively. Applying the method of Aguiar et al. [29] to estimate cmc, we fitted the I1/I3 data to the sigmoidal equation

I1 =I3 ¼ A2 þ fðA1  A2 Þ=½1 þ expððcs  x0 Þ=b0 Þg

where cs represents AOT concentration, x0 is the value of cs corresponding to the center of the sigmoid, A1 and A2 are the upper and lower limits of the sigmoid, respectively, and b0 is a term that reflects the range of cs where sudden change in I1/I3 occurs. The values of the parameters of Eq. (1) obtained from the fitting are listed in Table S4 and the value of x0 is taken as cmc. As the amount of EG increases the agreement between x0 and the cmc obtained from the surface tension becomes poor. Earlier studies have also revealed that the value of x0 does not always match with the cmc [29,30]. Thus, cmc values estimated from the fluorescence technique become less reliable when the EG amount in the mixture is about 50% or more, because population of pyrene in the bulk increases with increasing EG amount in the mixture. 3.3. Counterion binding constant Counterion binding constant (b) of an ionic surfactant is determined from the well known Corrin–Harkins (CH) equation [19]

ln c0 ¼ A  b lnðc0 þ ce Þ

ð2Þ

where c0 and ce represent cmc and electrolyte concentration, respectively. The sum c0 + ce is equal to the total concentration of

70

Surface Tension / mN m-1

10 % EG 60

0 2.0 5.3 7.6 11.0 21.0 31.0 41.0 63.0

A

50

40

80 % EG

50

0 0.5 1.0 14.0 29.0 42.5 62.5 100.0 200.0

45

40

35

30

30

-6

-5

-4

-3

log ([AOT] / mol kg-1 )

-2

ð1Þ

-5

-4

-3

-2

-1

0

log ([AOT] / mol kg-1)

Fig. 1. Surface tension isotherms of AOT in 10% and 80% EG containing different amounts of NaCl. Concentrations of NaCl in mmol kg1 are shown in the inset.

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10

cmc / mmol kg -1

8

150 0 10 20 30 40 50

6

4

60 70 80 90 100

100

50 2 0 0.00

0.05

0.10

0.00

[NaCl]/ mol

0.10

0.20

0.30

kg -1

Fig. 2. Cmc values of AOT in water + EG mixtures as a function of NaCl concentration. The w/w% values of EG in the mixed solvent are shown in the inset.

1.8 1.6

I1 / I3

Table 1 Values of the counterion binding constant of AOT in water + EG media at 25 °C.

2.0 5.3 7.6 11.0 22.0 41.0

1.4

0 10 20 30 40 60 70 80 90 100

1.2 1.0 0.0

5.0

10.0

c/mol kg1

Wt.% EG

15.0

[AOT]/ mmol kg-1

b

0.015 0.010 – – – – – – – –

[NaCl] < c

[NaCl] > c

0.39 0.29 0.39 0.44 0.48 0.57 0.69 0.52 0.56 0.41

0.82 0.74 – – – – – – – –

Fig. 3. Variation of I1/I3 of pyrene with AOT concentration at 25 °C in water + 10% EG. The concentrations of NaCl in mmol kg1 are indicated in the inset.

free counterion in the solution. The CH plots for AOT in varying compositions of water + EG are shown in Fig. 4. From Fig. 4, it is evident that the SCB of AOT exists in 10% EG similar to that in water, but not when the EG amount is P20%. In 10% EG, the two values of b and the concentration c at which the value of b suddenly changes are found to be different from those in water (Table 1). Thus, the medium affects the SCB of AOT. A phase diagram has been drawn in Fig. 5 to depict the SCB region of AOT in water + EG + NaCl medium. The physical appearance of the solution above c in 10% EG was found to be turbid and no phase separation was observed (images shown in Fig. 6). This indicated the formation of a different kind of an aggregate as compared to that below c where the samples

are clear. On the other hand, the samples above 10% EG were all found to be clear in the range of NaCl studied (images for 20% shown in Fig. 6). As the amount of EG increases in the medium, dielectric constant and solvophobic effect of the mixed solvent decrease. Although dielectric constant of the medium is expected to influence the binding of counterions to ionic micelles, earlier studies indicated that b is controlled mainly by the solvophobicity of the medium [13–16,30,31]. Solvophobicity of a medium is sometimes expressed in terms of cohesive energy density (CED) defined as c/V1/3, where V is the molar volume of the solvent. The CED (which is also called Gordon parameter) values of water + EG mixed solvent at 25 °C vary [1,32,33] from 2.74 (CED of water) to 1.25

50 60 70 80 90 100

-5

ln (c0 / mol kg-1 )

-2

-3

-6

-4 0 10 20 30 40

-7

-8

-5

-6 -6

-5

-4

-3

-5

-4

-3

-2

-1

ln [(c0 + c e ) / mol kg -1 ] Fig. 4. CH plots of AOT in water + EG media. The values of wt.% of EG are shown in the insets.

J. Dey et al. / Journal of Colloid and Interface Science 414 (2014) 103–109

bin d io n

Region of higher β values

c* boundary

H 2O

Region of lower β values

Sp

10

ec

ia l

co

un te r

[N a

Cl]

40

30

20

in g

/m

mo

reg ion

l k g -1

106

10

20

30

40

EG (%, w/w)

Fig. 5. Phase diagram showing the SCB region of AOT (25 mM) in water + EG + NaCl medium.

this anomalous deviation from the CH equation could arise from the changes in the activity of counterion due to ion–ion interaction. Using the Debye–Hückel equation logf± = Al1/2 for activity coefficient (f± is the mean activity coefficient, l is the ionic strength and A is the parameter dependent on the dielectric constant of medium; at 25 °C A = 0.5115 for water and 0.6554 for 40% EG), we calculated the activity, ac, of the counterion in the solution. For calculating the values of A we used the reported [34–36] values of dielectric constant of water + EG mixture. The shape of the plot of ln c0 versus ln ac has been found to be similar to that of ln c0 versus ln(c0 + ce), thus ruling out the possibility of ion–ion interaction as responsible for the anomalous deviation from the CH equation. At very low electrolyte concentration, the CH plots show a positive slope contrary to the usual negative slope observed at high electrolyte level. Such reversal in the slope of the plot cannot be accounted by the SCB of AOT. To confirm this, we measured the surface tension of AOT in 10%, 20% and 50% EG in the presence of sodium salicylate (NaSa) instead of NaCl. NaSa was chosen because in presence of this salt AOT does not exhibit SCB [23]. The surface tension plots of AOT + water + EG + NaSa systems are shown in Fig. S7 and the CH plots for these systems are shown in Fig. 7. Herein also, we observed the anomalous deviation from the CH equation in 50% EG medium, which shows that the SCB of AOT is not responsible for such a deviation from the CH equation. The observed anomalous deviation from the CH equation in the mixed solvent is attributable to the changes in the association behavior in mixed solvents, as reflected from the trend in the variation of c0 + ce with ce. In mixed solvents or polar organic solvents, the solvophobic interaction between the amphiphile and solvent molecules is greatly diminished as compared to that in water. This results in high values of cmc for the surfactant in mixed solvents or polar organic solvents. Addition of electrolytes to these mixed solvents favors the association process of the surfactants by decreasing the unfavorable electrostatic repulsion of surfactant head groups leading to a drastic decrease in the cmc of the surfactant. Initially the extent of decrease in cmc with the addition of electrolyte is so much that c0 controls the value of c0 + ce (total concentration of free counterion) and beyond a particular electrolyte   concentration c# the value of c0 + ce is controlled by ce. In other e words, the concentration of free counterion in solution is controlled by (i) the surfactant below c# e and (ii) by the electrolyte above c# e . As a result, the plot of c0 + ce versus ce passes through a minimum at c# e (Fig. 8). Such a variation of c0 + ce with ce has not been observed for any surfactant in water. Therefore, if c0 + ce does not monotonically increase with increasing ce in a medium, then in such a medium the CH equation can be applied only above a

Fig. 6. Top: images of samples of AOT (25 mM) in 10% EG + water. NaCl concentrations in mM are 0 (A1), 2.0 (A2), 5.0 (A3), 15.0 (A4) and 25.0 (A5). Bottom: images of samples of AOT (35 mM) in 20% EG + water. NaCl concentrations in mM are 0 (B1), 10.0 (B2), 15.0 (B3), 25.0 (B4) and 25.0 (S; this sample contains NaSa instead of NaCl).

10 % 20 %

(CED of EG) J m3. In water + EG medium, the SCB of AOT exists when CED of the medium is 2.74 (water) and 2.40 (10% EG) J m3, but not when the CED is 2.18 (20% EG) J m3 or less. It has been reported earlier [5] that in water + propylene carbonate (PC) medium the SCB of AOT exists in 5% PC (CED is 2.33 J m3), but not when the PC amount is P10% (CED is 62.04 J m3). It may therefore be concluded that the SCB of AOT exists if the medium has CED value in the range of 2.3–2.75 J m3. When the EG amount is P40%, we observed an anomalous deviation from the CH equation (Fig. 4) at low amounts of added electrolyte as reflected by a change in the sign of the slope of CH plot. This is different from the deviation due to the SCB of AOT observed in water and 10 wt.% EG and such deviation has not been reported till now in any of the solvent medium. One possibility for

ln (c0 / mol kg-1)

-5

50 %

-6

-7 -6

-5

-4

-3 -1

ln [(c 0 + ce )/ mol kg ] Fig. 7. CH plots of AOT in water + EG media containing NaSa. The values of wt.% of EG are shown in the inset.

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J. Dey et al. / Journal of Colloid and Interface Science 414 (2014) 103–109

Table 2 Neutron scattering length densities of different components of the experimental system.

(c0 + ce ) / mol kg- 1

0.070

0.060

0.050

0.035

Component

Scattering length density  1010/cm2

AOT EG D2O 90% D2O + 10% EG 80% D2O + 20% EG 70% D2O + 30% EG

0.62 0.27 6.38 5.77 5.16 4.55

70 80

0.030 0.00

0.01

ce /m ol kg

0.02

0.03

-1

Fig. 8. Representative plots of variation of total counterion concentration (c0 + ce) with added electrolyte concentration in water + EG (70% and 80%) media.

critical electrolyte concentration, c# In water + EG media, e . 1 c# in 40% EG and the value of c# e  0.001 mol kg e increases as the EG% increases. The values of b obtained from the CH plots are listed in Table 1. In media with EG P40%, b values were determined by considering the data above c# e . Generally, the value of b decreases with increase in the amount of polar organic solvent. Surprisingly, such a general trend is not observed in the case of AOT in water + EG media. The present study therefore clearly shows that for applying the CH equation there is a lower limit on  the concentration of added salt c# e . In the case of mixed solvent, as observed in this study, the value of c# e depends on the relative amounts of the two solvents. The value of c# e may also depend on the nature of solvent and surfactant. In water, c# e tends to zero. It is further estimated that the CH equation is applicable in a medium if only 0 > oc0/oce > 1. For determining b, another common method used is the sloperatio method from the conductivity data. However, conductance method is not a suitable method for AOT in water as no break in the plot of specific conductivity (j) versus concentration occurs near the cmc [4,37–39]. In water + EG media also conductivity method does not give reliable cmc values [4,40]. Therefore no attempt has been made to estimate b value from the slope-ratio method. 3.4. Small-angle neutron scattering Having noticed anomalous variation in CH plots, it is worth investigating the microstructure of aggregates in mixed solvents. In order to get an insight into the structure of AOT aggregates in water + EG + NaCl media, SANS measurements were carried out in D2O + EG mixtures. In SANS measurements one usually measures differential scattering cross section as a function of wave vector transfer (Q), which can be given by

dR=dX ¼ nðqm  qs Þ2 V 2 ½hF 2 ðQÞi þ hFðQ Þi2 ðSðQ Þ  1Þ þ B

ð3Þ

where n is number density and V is particle volume. qm and qs are scattering length densities of micelles and solvent respectively. F(Q) is single particle form factor and S(Q) is structure factor. B is a constant term representing incoherent background. F(Q) gives information about shape and size of the scatterers and S(Q) is decided by the interaction present in the system. The scattering length densities of the different components are given in Table 2. Although we did not use deuterated EG, it is clear from Table 2 that AOT micelles still have reasonable good contrast even with highest EG concentration (30%) used. The details of SANS data analysis are given in the supporting information. For analyzing the SANS data,

the semi-minor axis (b = c) and volume (v) of AOT monomer were taken from the literature as 12.6 Å and 611 Å3, respectively [22,41]. The values of the aggregation number (N = 4pab2/(3v)), fractional charge, and the semi major axis (a) were determined from the fitting (Table 3). The SANS data dR/dX versus Q for D2O + 10% EG are shown in Fig. 9. The similar features observed in the SANS profiles of AOT + NaCl in D2O have also been observed in D2O + 10% EG. The system shows correlation peaks in the SANS data (even up to 5 mM NaCl; M = mol dm3), indicating the presence of interacting charged micelles. Usually, this peak occurs at Q  2p/ d, where d is the distance between the particles [42]. These micelles are found to be forming prolate ellipsoidal (a – b = c) shape where the interaction is accounted by structure factor as calculated by Hayter and Penfold analysis under Mean Spherical Approximation for charged macroions [43]. There is slight micellar growth up to 5 mM and the correlation peaks occur at almost the same Q value 0.062 Å1, whereas for AOT in D2O the peak occurs at Q  0.059 Å1. This difference in Q value may be the solvent effect, as it is well known that the aggregate size in mixed solvents containing H2O and polar organic liquids is smaller as compared to that in H2O alone. In Fig. 10, we have shown the plot of SANS data for AOT in 15 mM NaCl in 10% EG + D2O. In this case, the data exhibit interesting behavior which is different from that shown in Fig. 9 and is also consistent with the observation made from the corresponding CH plots. The correlation peak disappears at 15 mM NaCl and the scattering pattern shows Q2 behavior at low Q values followed by Q1 behavior at intermediate Q values in log–log scale. The SANS intensity variation with Q1 is an indication of rod-like structures whereas Q2 behavior is a typical characteristic feature of bilayer formation [44]. This suggests coexistence of vesicles with rod-like micelles at 15 mM NaCl [45]. The data have been analyzed by summing the individual scattering contributions from both these components (rod-like micelles and vesicles) in the overall intensity. The scattering data do not show any lower Q cut off in the present Q range, hence larger dimensions of both the structures was kept fixed to a value more than 2p/Qmin (1200 Å) in the fitting of the data. The radius of the rod-like micelles is found to be 11.5 Å and vesicle thickness 18 Å. The radius of the micelles is governed by the tail length of the surfactant and less than double the tail length thickness could be due to interdigitation of hydrophobic tails. Further characterization of the AOT aggregates in the SCB region requires SANS measurements in an extended Q range which could not be done at the moment. Nevertheless, shape change of AOT aggregate undoubtedly takes place above c in 10% EG + D2O medium similar to the shape transition at 15 mM NaCl in D2O observed in our previous study [23]. Shape change from spherical to vesicle 0 0 (external radius = 396 Å A and bilayer thickness = 19.7 Å A) reported by Grillo et al. [44] on adding 21 mM NaCl (which is above c) to 0.75 wt.% (16 mM) AOT in 75% D2O + 25% H2O (v/v) medium also confirms that in the SCB region above c shape transition of AOT aggregate does take place. In Figs. 11 and 12, we have shown the SANS data for AOT in 20% and 30% EG + D2O containing varying amounts of NaCl. In 20%

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J. Dey et al. / Journal of Colloid and Interface Science 414 (2014) 103–109

Table 3 Parameters of AOT aggregates in presence of NaCl at 25 °C obtained from the fitting of SANS data and Q values at the correlation peak.

* **

[NaCl]/mM

Semi-major axis (a)/Å

Semi-minor axis (b = c)/Å

Poly-dispersity (r)

Fractional charge (a)

Aggregation number (N)

Qp/Å1

D2O + 10% EG 0.0 2.0 5.0

21.9 ± 0.8 24.9 ± 0.9 25.7 ± 1.0

12.6 ± 0.4 12.6 ± 0.4 12.6 ± 0.4

0.15 ± 0.02 0.15 ± 0.02 0.15 ± 0.02

0.63 ± 0.05 0.55 ± 0.04 0.53 ± 0.04* (0.7)

24 ± 2 (23**) 27 ± 3 (27) 28 ± 3 (28)

0.06317 0.06024 0.05932

D2O + 20% EG 0.0 2.0 5.0 15.0

22.7 ± 0.8 23.5 ± 0.9 24.9 ± 0.9 33.4 ± 1.3

12.6 ± 0.4 12.6 ± 0.4 12.6 ± 0.4 12.6 ± 0.4

0.15 ± 0.02 0.15 ± 0.02 0.15 ± 0.02 0.15 ± 0.02

0.58 ± 0.05 0.59 ± 0.05 0.53 ± 0.04 0.42 ± 0.03* (0.6)

25 ± 2 26 ± 3 27 ± 3 36 ± 4

(23) (23) (27) (38)

0.06901 0.06901 0.06609 0.06024

D2O + 30% EG 0.0 5.0 15.0

23.6 ± 0.9 26.9 ± 1.1 33.0 ± 1.3

12.6 ± 0.4 12.6 ± 0.4 12.6 ± 0.4

0.15 ± 0.02 0.15 ± 0.02 0.15 ± 0.02

0.56 ± 0.04 0.51 ± 0.04 0.50 ± 0.03* (0.55)

26 ± 3 (24) 29 ± 3 (28) 40 ± 4 (43)

0.07776 0.07485 0.06609

From CH plot. Aggregation number in the parentheses are from Eq. (5).

0.24 0.22

0.28

0.20

0.24

0.18

dΣ /dΩ (cm-1)

dΣ/dΩ (cm-1)

0.16 0.14 0.12

0.20

0.16

0.10 0.12 0.08

25 mM AOT 25 mM AOT + 2mM NaCl 25 mM AOT + 5mM NaCl

35 mM AOT 35 mM AOT+ 2 mM NaCl 35 mM AOT + 5 mM NaCl 35 mM AOT +15 mM NaCl

Q (Å -1 )

0.06

0.10

0.10 Fig. 11. Plots of SANS data for AOT (35 mM) with varying amounts of NaCl at 25 °C in D2O + 20% EG. The lines are the theoretical fits.

-1

Q (Å ) Fig. 9. SANS data for AOT (25 mM) with varying amounts of NaCl at 25 °C in D2O + 10% EG. The lines are the theoretical fits.

0.40 55 mM AOT 55 mM AOT + 5mM NaCl 55 mM AOT +15mM NaCl

0.35

25 mM AOT + 15 mM NaCl -1

dΣ/dΩ (cm )

dΣ/dΩ (cm-1)

10.00

1.00

Slope ~ -2

0.10

0.30

0.25

Slope ~ -1 0.20 0.01

-1

0.10

Q (Å ) Fig. 10. SANS data for AOT (25 mM) in D2O + 10% EG + 15 mM NaCl at 25 °C.

0.10 -1

Q (Å ) EG + D2O, the correlation peaks occur at Q  0.069 Å1 for 2 and 5 mM NaCl indicating almost no change in the aggregate size. However, for 15 mM NaCl, the correlation peak shifts to a slightly low Q value 0.06 Å1 indicating an increase in the size of the micelle (Table 3). In 30% EG + D2O (Fig. 12), the correlation peaks for pure AOT (55 mM) and 5 mM NaCl occur at 0.074 Å1. For 15 mM NaCl, the correlation peak shifts to 0.066 Å1, once again indicating growth of the micelles similar to that in 20% EG solvent. Thus, SANS measurements indicate dramatic change in microstructure of AOT in 10% EG which are missing in micellar structure in 20% and 30% EG. These results confirm that change in the morphology of AOT

Fig. 12. Plots of SANS data for AOT (55 mM) with varying amounts of NaCl at 25 °C in D2O + 30% EG. The lines are the theoretical fits.

micelles is the probable cause for the SCB in water + EG media as was also in water [23]. Aggregation number can also be estimated from the Q value of the correlation peak (Qp) using an empirical approach without going through the details of model fitting. The empirical formula to correlate peak position with the distance between the micelles (d) is given by [46]

J. Dey et al. / Journal of Colloid and Interface Science 414 (2014) 103–109

Q p d ¼ 6:8559 þ 0:0094d

ð4Þ

Eq. (4) is combined with the face centered cubic (fcc) packing of the micelles to calculate aggregation number N as

pffiffiffi 3 3 1024 d ð 2Þ NA cs N¼ 4000

ð5Þ

where NA is the Avogadro number and cs is the molar concentration of AOT [46]. The aggregation numbers estimated thus are listed in Table 3 and it varies as a function of Q 3 p . The values of aggregation number obtained from the model fitting and correlation peak position are found to be in good agreement (Table 3). The values of the fractional charge (1  b) obtained from the CH equation and the SANS measurements (Table 3) are also found to be comparable. As described earlier [23], on adding NaCl more counterions bind to the micelle and the aggregation number increases due to reduction in the repulsion between the head groups. Thus, added electrolyte causes increase in the size of the micelle, but the value of b being the ratio of the bound counterions to the aggregation number remains almost constant. However, at some critical concentration of added electrolyte, the shape of the micelle must also change due to geometric factors such that the increased number of hydrocarbon tails can be packed in the micelle. Moreover, reduction in the repulsion between the head groups and increased aggregation number decreases the surface area of the head group causing the value of the packing parameter [47] to increase, which also lead to shape change. When such a shape change of the ionic micelle takes place due to geometric constraints, a sudden change in the value of b also appears to take place making it a micellar shape dependent parameter. 4. Conclusions This study confirmed that the SCB of AOT, which manifests as a sudden change in the slope of the CH plot, has a dependence on the quality of solvent. Based on the reported [5,22,23] and present studies it has been concluded that the SCB of AOT exists in a medium having the CED value in the range of 2.3–2.75 J m3. SANS study shows that when NaCl concentration is above c in 10% EG (SCB exists) both cylindrical micelles and vesicles co-exist, whereas in 20% and 30% EG (no SCB) such microstructures are not found. These results confirm that change in the morphology of micelles is the probable cause for the SCB of AOT. An important observation made in this study is about the dependence of b on micellar shape, which reaffirms the finding of earlier study [23]. Effect of micellar shape on b has been reported by others also [48,49]. Fujio et al. [48] reported that the values of b follow the order sphere < oblate ellipsoidal < rod-like. In didodecyldimethylammonium bromide + water system, Ono et al. [49] reported that due to micelle-to-vesicle transition the value of b changed from 0.35 to 0.93. Thus, b may emerge as a shape indicator of ionic surfactant aggregates. The present study has revealed for the first time that for applying the CH equation there is a limitation on the  concentration of added salt. Below a limiting salt concentration c# sharp deviation e from the CH equation occurs with reversal of slope and the value of c# e is dependent on the nature of solvent and surfactant. This anomalous deviation from the CH equation below c# e arises due to the dependence of the total concentration of free counterion in a micellar solution on the nature of the solvent. It is estimated that the CH equation is applicable in a solvent if only 0 > oc0/oce > 1. Further study is needed to establish the role of solvent and surfactant in causing this particular deviation from the CH equation below c# e .

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