Clouding in charged micelles as studied by SANS

Chemical Physics Letters 424 (2006) 91–96 www.elsevier.com/locate/cplett

Clouding in charged micelles as studied by SANS V.K. Aswal a

a,*

, J. Kohlbrecher

b

Solid State Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai, Maharashtra 400085, India b Laboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 PSI Villigen, Switzerland Received 30 January 2006; in final form 5 April 2006 Available online 21 April 2006

Abstract Charged micellar solution of sodium dodecyl sulfate (NaDS) in presence of quaternary salt tetrabutylammonium bromide (TBABr) shows a clouding on increasing temperature. Small-angle neutron scattering (SANS) measurements have been performed on equimolar (25 mM) solution of NaDS and TBABr at different temperatures below and above the cloud point. Micelle size increases and average charge on the micelle decreases on approaching the cloud point. Micelles coexist with clouding phase at the cloud point and even after much higher temperature. Contrast variation SANS study has been used to understand the mechanism of clouding in this system.  2006 Elsevier B.V. All rights reserved.

1. Introduction It is understood that nonionic micelles on raising the temperature become cloudy and phase separate at a welldefined temperature Tcp [1]. On the other hand, for charged micelles, the phenomenon of clouding usually does not occur, presumably because electrostatic repulsion between micelles prevents the phase separation. Charged micelles bind counterions selectively and their solution properties are sensitive to the nature of the counterion. In contrast to alkali metal cations, quaternary ammonium ions (R4N+) are somewhat hydrophobic and show interesting micellar growth on their presence in an aqueous anionic surfactant solution. Recently, it has been seen that adding electrolyte with large hydrophobic counterions to a charged micellar solution lead to the clouding otherwise absent in pure micellar solution [2–6]. For example, the addition of tetraalkylammonium bromide N(CnH2n+1)4Br (TAABr) for n P 4 to the charged sodium dodecyl sulfate (NaDS) micelles show the clouding in these systems [7,8]. This Letter reports the contrast variation SANS studies to understand the mechanism of clouding on a charged *

Corresponding author. Fax: +91 22 25505151. E-mail address: [email protected] (V.K. Aswal).

0009-2614/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.04.025

micellar solution of NaDS in presence of tetrabutylammonium bromide (TBABr). 2. Experiment Small-angle neutron scattering experiments were carried out using SANS diffractometer at the Swiss Spallation Neutron Source SINQ, Paul Scherrer Institute, Switzerland ˚ and the [9]. The wavelength of the neutron beam was 8 A experiments were performed at two different samples to detector distances of 2 and 6 m to cover a Q range of ˚ 1. The scattered neutrons were detected using 0.01–0.35 A a two-dimensional 96 · 96 cm2 detector. Surfactant (NaDS) and salt (TBABr) used were obtained from Fluka. Deuterated surfactant (d-NaDS) as purchased from Cambridge Isotope was used to contrast match it with the solvent. Samples were prepared by dissolving known amount of surfactant and salt in D2O and were held in quartz sample holder of thickness 2 mm during the SANS experiment. The use of D2O as solvent instead of H2O provides better contrast in neutron experiments. Measurements were made on equimolar concentration (25 mm) of NaDS and TBABr. This sample has a cloud point of 51 C and the SANS measurements were performed below and above the cloud point at temperatures 31, 45, 49, 51, 55

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and 60 C. All the data were corrected and normalized to absolute scale using standard procedures [10]. 3. SANS analysis In small-angle neutron scattering experiment, one measures differential scattering cross-section per unit volume (dR/dX) as a function of scattering vector Q(=4p sin h/k, where 2h is the scattering angle and k is the wavelength of incident radiation), and for a micellar solution it can be expressed as [11] h i dR 2 2 ðQÞ ¼ n hF ðQÞ i þ hF ðQÞi ðSðQÞ  1Þ þ B ð1Þ dX where n is the number density of the particles. F(Q) is the single particle form factor and depends on the shape and size of the particles. S(Q) is the interparticle structure factor and is decided by the spatial distribution of the particles. B is a constant term that represents the incoherent scattering background, which occurs mainly due to hydrogen in the sample. Micelles formed at the critical micelle concentration are spherical. If the solution conditions (e.g. concentration, ionic strength, etc.) of the micellar solutions are changed that favors the growth of the micelles, they grow along one of the axial directions of the micelles. The growth of the micelles along other two axial directions is restricted by the maximum length of the surfactant molecule to avoid the energetically unfavorable any empty space or water penetration inside the micelle [12]. The prolate ellipsoidal shape (a 6¼ b = c) of the micelles is widely used in the analysis of small-angle scattering data because it also represents the other different possible shapes of the micelles such as spherical (a = b) and rod-like (a  b). For such an ellipsoidal core-shell structure of micelle [13] Z 1 2 2 hF ðQÞi ¼ ½F ðQ; lÞ dl ð2Þ 0

2 F ðQ; lÞdl 0   3j ðxc Þ F ðQ; lÞ ¼ ðqc  qshell ÞV c 1 xc   3j1 ðxt Þ þ ðqshell  qs ÞV t xt ðsin x  x cos xÞ j1 ðxÞ ¼ x2 2 2 xc ¼ Q½a l þ b2 ð1  l2 Þ1=2

hF ðQÞi2 ¼

Z

1

xt ¼ Q½ða þ tÞ2 l2 þ ðb þ tÞ2 ð1  l2 Þ1=2

ð3Þ

ð4Þ ð5Þ

cosine of the angle between the directions of a and the wave vector transfer Q. The expression for S(Q) depends on the relative positions of the particles. In case of isotropic system, S(Q) can be written as [14]: Z sin Qr 2 r dr ð8Þ SðQÞ ¼ 1 þ 4pn ðgðrÞ  1Þ Qr where g(r) is the radial distribution function. g(r) is the probability of finding another particle at a distance r from a reference particle centered at the origin. The details of g(r) depend on the interaction potential U(r) between the particles. In the present analysis, U(r) has been taken to be screened Coulomb potential and S(Q) calculated under mean spherical approximation [15]. The semimajor axis (b = c) of the micelles has a value that is decided by the length of the surfactant molecule. The polydispersity of the micelles is expected with the semimajor axis along which the growth of the micelles occurs. In that case Eq. (1) for polydisperse micelles can be written as [16] Z dR dR ðQÞ ¼ ðQ; RÞf ðRÞdR þ B: ð9Þ dX dX The polydispersity in the micellar size (R = a) has been accounted by a Schultz distribution as given by:  Zþ1     Zþ1 Zþ1 1 ; ð10Þ f ðaÞ ¼ aZ exp  a a a CðZ þ 1Þ where a is the mean value of the distribution and Z is the width parameter. The polydispersity of this distribution is 1=2 given by Da=a ¼ 1=ðZ þ 1Þ . The dimensions, aggregation number, polydispersity and the average charge of the micelles have been determined from the analysis. The semimajor axis ðaÞ, semiminor axis (b = c), thickness of shell (t), polydispersity (Z) and average charge (n) are the parameters in analyzing the SANS data. The aggregation number is calculated by the relation N = 4pab2/3v, where v is the volume of the surfactant tail. The parameters in the analysis were optimized by means of nonlinear least-square fitting program [17]. In addition, the scattering measured on absolute scale [18] has been used to determine the amount of adsorption of TBA+ counterions on the micellar surface and the penetration volume of counterion inside the core of the micelles. 4. Results and discussion

ð6Þ ð7Þ

where qc, qshell and qs are, respectively, the scattering length densities of the micellar core, shell and solvent. The dimensions a and b are, respectively, the semimajor and semiminor axes of the ellipsoidal micelle and t is the thickness of the shell of the micelle. Vc(=4pab2/3) and Vt (=4p(a + t) (b + t)2/3) are the volumes of the core and total volume of core along with shell, respectively. The variable l is the

Fig. 1 shows the SANS data on 25 mM NaDS + 25 mM TBABr at temperature 31 C with and without the deuterated NaDS. The scattering intensity is significantly reduced with d-NaDS as a result of surfactant gets contrast matched with the solvent D2O. The scaling of the data (see inset) shows different functionality of the two scattering curves at larger Q values. In particular, the SANS data ˚ 1, which is not of d-NaDS show a hump at Q  0.24 A seen with h-NaDS. This hump is an indication of a core-

V.K. Aswal, J. Kohlbrecher / Chemical Physics Letters 424 (2006) 91–96

10 -1

dΣ /dΩ (cm )

10

d-SDS

0.1 h-SDS

0.01 0.01

h-SDS

-1

dΣ/dΩ (cm )

1

1

0.1

0.3

-1

Q (Å )

d-SDS

0.1

0.01 0.01

0.3

0.1 -1

Q (Å ) Fig. 1. SANS data on 25 mM NaDS + 25 mM TBABr micellar solution with hydrogenous (h-NaDS) and deuterated (d-NaDS) surfactants at temperature 31 C. Inset shows the scaling of the two data sets in the low Q region.

shell structure of the micelles [19], which is made visible by contrast matching the surfactant. The scattering contrast for any component of the micelle depends on the square of the difference of scattering length densities of that component with the solvent. Fig. 2 shows the calculated variation of scattering length densities of the components of the micelle with that in presence of TBA+ counterions. The scattering lengths are determined from the chemical compositions of the components. The molec˚3 ular volumes have been used are 350.2, 135, 58 and 30 A + for the tail length of NaDS, per chain of TBA (as

8

8

(a)

solvent shell

10

-2

ρ (10 cm )

6

2 h-NaDS Core

0

-2

ρ (10 cm )

6

solvent

shell

4

0

4

10

20

30

10

distance from the centre of micelle (Å) 8

(b) solvent

-2

ρ (10 cm )

d-NaDS core

10

2

6 shell

h-NaDS Core

0

4

0

10

20

30

distance from the centre of micelle (Å)

0

10

20

30

distance from the centre of micelle (Å) Fig. 2. The variation in scattering length densities of the different components in core-shell model of hydrogenous (h-NaDS) micelles. Insets show the changes in the scattering length densities on the adsorption of the TBA+ counterions with (a) hydrogenous (h-NaDS) and (b) deuterated (dNaDS) surfactants.

93

obtained from the Tanford’s Formula [20]), –SO4 head group and water molecule (as known in the literature [21]), respectively. It is clear from Fig. 2 that in the case micelles of h-NaDS, the contrast for the shell of micelles consisting of mostly –SO 4 headgroups with hydrated water is very weak as compared to that from the core of the micelle. The neutrons in this case only see the core of the micelle [22]. If it is assumed that TBA+ counterions are adsorbed at the micelle surface, it can enhance the contrast of the shell to some extent [see inset (a) of Fig. 2]. The best way to make the shell clearly visible is to contrast match the surfactant [see inset (b) of Fig. 2] and the corresponding SANS data are shown in Fig. 1. The characteristics of coreshell structure as observed with d-NaDS confirm the adsorption of the TBA+ counterions at the micellar surface. These data thus have been used to get the information on the role of TBA+ counterions that leads the clouding in NaDS micelles. Fig. 3 shows the SANS data before the cloud point of 25 mM NaDS + 25 mM TBABr micellar system at different temperatures approaching the cloud point. The data with both d-NaDS and h-NaDS show the increase in the scattering intensity in the lower Q region. The micellar parameters in these systems as obtained using Eq. (10) are shown in Table 1. As discussed in the previous paragraph, the data with d-NaDS shows the adsorption of the TBA+ counterions at the micellar surface. The analysis in addition to the dimensions of the micelles gives the thickness over which the counterions are adsorbed along with the percentage of these counterions. It is found that only about 40% of TBA+ counterions in the solution are adsorbed at the micellar surface. This amount of adsorption may be limited due to the fact the TBA+ counterions are bulky and the micellar surface do not provide enough space to accommodate all of them [23]. The value of adsorbed counterions does not change with the increase in the temperature. Table 1 shows that micelle size increases and the average charge (or surface charge density) on the micelle decreases with the increase in the temperature. The average charge on the micelle using the Dressed Model of micelles [24] is compared along with that obtained with SANS data. It is seen unlike the results of SANS, the average charge on the micelle increases with the increase in temperature. This difference could be due to the hydrophobic nature of the counterion, whereas the Dressed Model is for the counterions those are totally condensed by the electrostatic attractions. Usually, the charge on the charged micelles is known to increase with the increase in the temperature [25]. However, in the present sample the adsorbed TBA+ counterions play important role for opposite dependence of the charge on the charged micelle with temperature. The hydration water on the TBA+ counterions decreases with increase in temperature and this will reduce the effective size of the counterion to fit at the micellar surface. It means more number of surfactants can pack and hence the aggregation number increases with the increase in temperature. The

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V.K. Aswal, J. Kohlbrecher / Chemical Physics Letters 424 (2006) 91–96

2.0

1.5

1.1

(a)

1.1

(a)

1.0 S(Q)

1.0 S(Q)

0.9

1.5

0.8 -1

dΣ/dΩ (cm )

0.6 0.5 0.0

-1

dΣ/dΩ (cm )

0.8 0.7

0.7

0.1

1.0

0.2

0.3

-1

Q (Å )

1.0

0.6 0.5 0.0

0.1

0.2

0.3

-1

Q (Å )

0.5

o

T = 49 C o

o

T = 51 C o

T = 45 C

0.5

0.9

T = 55 C

o

o

T = 31 C

T = 60 C

0.0 0.01

0.0 0.01

0.1

0.3

0.1

0.3

-1

0.1

Q (Å )

0.3

-1

Q (Å ) 0.30

(b)

0.4 (b)

0.25 0.20

-1

dΣ/dΩ (cm )

-1

dΣ/dΩ (cm )

0.3

0.2

0.15 0.10 o

T = 51 C o

T = 49 C

0.1

0.05

o

T = 55 C

o

T = 45 C

o

T = 60 C

0.00 0.01

o

T = 31 C

-1

Q (Å )

0.0 0.01

0.1

0.3

-1

Q (Å ) Fig. 3. SANS data on 25 mM NaDS + 25 mM TBABr micellar solution with (a) hydrogenous and (b) deuterated surfactants at different temperatures (31, 45 and 51 C) before the cloud point. This system has the cloud point at 51 C. Inset in Fig (a) shows the variation of S(Q), where S(Q = 0) increases with increase in the temperature.

increase in micelle size will attract more counterions and the average charge on the micelles decreases [26]. Since the percentage of TBA+ counterions does not change, we believe that Na+ ions being small are responsible to reduce the average charge on the micelle. As the average charge on

Fig. 4. SANS data on 25 mM NaDS + 25 mM TBABr micellar solution with (a) hydrogenous and (b) deuterated surfactants at the cloud point (51 C) and higher temperatures after the cloud point (55 and 60 C). Inset in Fig (a) shows the variation of S(Q), where S(Q = 0) increases with increase in the temperature.

the micelle decreases, it is possible for TBA+ counterions present in the solution to bind these micelles and the clouding occurs [27]. The thickness of the shell as measured with d-NaDS and h-NaDS data are significantly different (Table 1). It can be understood in terms of the intercalation of the butyl chains of TBA+ in the core of the micelle. The modeling of the

Table 1 Micellar parameters as obtained by SANS on 25 mM NaDS + 25 mM TBABr micellar solution at different temperatures before the cloud point Temperature (C)

Aggregation number (N)

Semiminor ˚) axis b = c (A

Semimajor ˚) axis a (A

Polydispersity Da=a (%)

(a) With hydrogenous (h-NaDS) surfactant 31 82 ± 6 16.7 ± 0.4 45 97 ± 7 16.7 ± 0.4 49 106 ± 8 16.7 ± 0.4

30.2 ± 0.8 35.8 ± 1.0 39.2 ± 1.2

20 ± 5 25 ± 5 25 ± 5

5.0 ± 1.0 5.0 ± 1.0 5.0 ± 1.0

16.4 ± 2.4(19.5) 13.6 ± 2.2(21.8) 11.7 ± 2.1(22.9)

(b) With deuterated (d-NaDS) surfactant 31 82 ± 6 45 97 ± 7 49 106 ± 8

24.0 ± 1.0 29.6 ± 1.2 33.0 ± 1.2

22 ± 5 25 ± 5 25 ± 5

11.5 ± 1.2 12.3 ± 1.4 13.0 ± 1.4

16.4 ± 2.4(19.5) 13.6 ± 2.2(21.8) 11.7 ± 2.0(22.9)

10.5 ± 0.8 10.5 ± 0.8 10.5 ± 0.8

Shell ˚) thickness t (A

The values in parentheses for average charge are calculated using Dressed Model of micelle as described in Ref. [28].

Average charge (n)

V.K. Aswal, J. Kohlbrecher / Chemical Physics Letters 424 (2006) 91–96

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Table 2 Micellar parameters as obtained by SANS on 25 mM NaDS + 25 mM TBABr micellar solution at different temperatures after the cloud point Temperature (C)

Aggregation number N

Semiminor ˚) axis b = c (A

Semimajor ˚) axis a (A

Polydispersity Da=a (%)

(a) With hydrogenous (h-NaDS) surfactant 51 99 ± 8 16.7 ± 0.4 55 88 ± 9 16.7 ± 0.6 60 79 ± 8 16.7 ± 0.6

36.6 ± 1.0 32.4 ± 0.8 29.2 ± 0.8

20 ± 5 20 ± 5 20 ± 5

5.0 ± 1.0 5.0 ± 1.0 5.0 ± 1.0

(b) With deuterated (d-NaDS) surfactant 51 99 ± 8 55 88 ± 9 60 79 ± 8

30.4 ± 1.2 26.2 ± 1.2 23.0 ± 1.2

20 ± 5 20 ± 5 20 ± 5

13.0 ± 1.4 13.0 ± 1.8 13.0 ± 1.8

10.5 ± 0.8 10.5 ± 1.2 10.5 ± 1.2

Shell ˚) thickness t (A

Average charge (n) 10.0 ± 2.0(22.4) 8.8 ± 1.8(21.5) 7.0 ± 2.0(20.8) 10.0 ± 2.0 8.8 ± 1.8 7.0 ± 2.0

The values in parentheses for average charge are calculated using Dressed Model of micelle as described in Ref. [28].

amount of intercalation in the micellar core will decide the scaling of the calculated scattering intensity and its comparison with the measured scattering on absolute scale thus gives the information on the conformation of adsorbed counterions. In the case of h-NaDS any intercalation of butyl chains inside the micellar core will not be visible separately as both of them are hydrogenous having similar scattering length densities and will enhance the scattering from the core. We find from these data that two butyl chains intercalate into micellar core and about 75% volume of these two tails reside in the core. This value does not show any change with increasing temperature. On the other hand, intercalation of butyl chains with deuterated core will make it visible even inside the core similar to that at the level of head group and results in larger thickness measured for the counterions adsorbed with d-NaDS micelles. The scattering from cloud phase is expected to be in the quite low Q range that is measured in SANS experiments [28]. If all the micelles convert to cloud phase, we would only measure the background from the sample. It is interesting to note that scattering from micelles still exists at clouding point and even after much higher temperature (Fig. 4). The magnitude of scattering intensity curve decreases with increase in the temperature after the cloud point. These data look as if the number density of micelles in the samples is decreasing with increasing temperature. The micellar parameters after the cloud points are shown in Table 2. Polydispersity for this purpose is important that the micelles with large sizes have low surface charge density and they are responsible for clouding. Smaller micelles with higher charge density coexist in clouding. As temperature is further increased, the average charge on the micelles decreases, it allows smaller micelles to network to give rise clouding. Thus volume fraction of micelles in clouding decreases with increasing temperature. The volume fractions of micelles that coexist with clouding at temperatures 51, 55 and 60 C have been found to be 83, 60 and 40%, respectively. The variation of S(Q) for different temperatures in the insets of Figs. 3a and 4a shows the changes in the isothermal compressibility [S(Q = 0)] at the clouding [15]. The value of osmotic compressibility increases significantly on approaching the cloud point and it continues to increase

after the cloud point. Unlike in the case of nonionic micelles where S(Q) is known to diverge at low Q values [28], the same is not observed for clouding in charged micelles. This may be due to the fact that at the clouding the system is still dominated by the individual charged micelles those coexist with the clouding phase. 5. Conclusion Contrast variation SANS study has been carried to understand the role of TBA+ counterions in the clouding of NaDS charged micelles. It is found only about 40% of the total TBA+ counterions irrespective of the temperature are adsorbed on the micelle. Due to water dehydration from TBA+ counterions, the micelle size increases and the average charge on the micelle decreases with increase in the temperature. As the average charge on the micelle decreases, the TBA+ counterions present in the solution bind these micelles and the clouding occurs. Micelles coexist with clouding phase and volume fraction of micelles in clouding decreases with increasing temperature. References [1] V. Degiorgio, M. Corti, Physics of Amphiphiles: Micelles, Vesicles and Microemulsion, North-Holland, Amsterdam, 1985. [2] Z.-J. Yu, G. Xu, J. Phys. Chem. 93 (1989) 7441. [3] J. Eastoe, B.H. Robinson, R.K. Heenan, Langmuir 9 (1993) 2820. [4] E. Szajdzinska-Pietek, J.L. Gebicki, J. Phys. Chem. 99 (1995) 13500. [5] S. Kumar, V.K. Aswal, P.S. Goyal, Kabir-ud-Din, J. Chem. Soc., Faraday Trans. 94 (1998) 761. [6] B.L. Bales, K. Tiguida, R. Zana, J. Phys. Chem. B 108 (2004) 14948. [7] S. Kumar, V.K. Aswal, A.Z. Naqvi, P.S. Goyal, Kabur-ud-Din, Langmuir 17 (2001) 2549. [8] B.L. Bales, R. Zana, Langmuir 20 (2004) 1579. [9] J. Kohlbrecher, W. Wagner, J. Appl. Cryst. 33 (2000) 804. [10] V.K. Aswal, P.S. Goyal, Curr. Sci. 79 (2000) 947. [11] S.H. Chen, T.L. Lin, in: D.L. Price, K. Skold (Eds.), Methods of Experimental Physics, vol. 23B, Academic Press, New York, 1987, p. 489. [12] Y. Chevalier, T. Zemb, Rep. Prog. Phys. 53 (1990) 279. [13] J.S. Pedersen, Adv. Colloid Interface Sci. 70 (1997) 171. [14] P.A. Egelstaff, An Introduction to Liquid State Physics, Academic Press, London, 1967. [15] J.B. Hayter, J. Penfold, Colloid Polym. Sci. 261 (1983) 1022. [16] V.K. Aswal, P.S. Goyal, P. Thiyagarajan, J. Phys. Chem. B 102 (1998) 2469.

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[17] P.R. Bevington, Data Reduction and Error Analysis for Physical Sciences, McGraw-Hill, New York, 1969. [18] G.D. Wignall, F.S. Bates, J. Appl. Cryst. 20 (1987) 28. [19] B. Cabane, R. Duplessix, T. Zemb, J. Physique 46 (1985) 2161. [20] C. Tanford, J. Phys. Chem. 76 (1972) 3020. [21] K. Sumaru, H. Matsuoka, H. Yamaoka, G.D. Wignall, Phys. Rev. E 53 (1996) 1744. [22] V.K. Aswal, P.S. Goyal, Phys. Rev. E 61 (2000) 2947.

[23] R. Zana, M. Benrraou, B.L. Bales, J. Phys. Chem. B 108 (2004) 18195. [24] J.B. Hayter, Langmuir 8 (1992) 873. [25] V.K. Aswal, P.S. Goyal, Chem. Phys. Lett. 357 (2002) 491. [26] V.K. Aswal, P.S. Goyal, Chem. Phys. Lett. 364 (2002) 44. [27] Z.-J. Yu, X. Zhang, G. Xu, G.-x. Zhao, J. Phys. Chem. 94 (1990) 3675. [28] P.S. Goyal, S.V.G. Menon, B.A. Dasanacharya, P. Thiyagarajan, Phys. Rev. E 51 (1995) 2308.