ARTICLE pubs.acs.org/Langmuir
Self-Assembly of Mixed Anionic and Nonionic Surfactants in Aqueous Solution I. Grillo*,† and J. Penfold‡,§ †
Institut Laue Langevin, DS/LSS, 6 rue Jules Horowitz, B.P. 156, 38042 Grenoble Cedex 9 ISIS Facility, STFC, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, United Kingdom § Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford, United Kingdom ‡
bS Supporting Information ABSTRACT: We present the phase diagram and the microstructure of the binary surfactant mixture of AOT and C12E4 in D2O as characterized by surface tension and small angle neutron scattering. The micellar region is considerably extended in composition and concentration compared to that observed for the pure surfactant systems, and two types of aggregates are formed. Spherical micelles are present for AOTrich composition, whereas cylindrical micelles with a mean length between 80 and 300 Å are present in the nonionic-rich region. The size of the micelles depends on both concentration and molar ratio of the surfactant mixtures. At higher concentration, a swollen lamellar phase is formed, where electrostatic repulsions dominate over the Helfrich interaction in the mixed bilayers. At intermediate concentrations, a mixed micellar/lamellar phase exists.
’ INTRODUCTION Self-assembly in surfactant system is driven mainly by hydrophobic forces in order to avoid unfavorable contact between water and nonpolar parts of the molecules. The size and shape of the aggregate depend on intrinsic parameters such as the geometrical constraints and charge of the monomers and also upon external criteria such as concentration, ionic strength, or temperature. The mixture of ionic and nonionic surfactants enables the nature of these interactions to be varied continuously from one dominated by electrostatic forces to one dominated by steric forces. Such mixed systems have been extensively studied in recent years, because of their fundamental interest and their industrial applications, where synergistic effects can be used to optimize performance, to minimize the amount of surfactant required, and to reduce costs and side effects on environment. The prediction of phase behavior from the knowledge of the basic interaction forces involved has made considerable progress in recent years.1 In the purely micellar region and in most of the binary systems, departures from ideal mixing in the critical micellar concentration (cmc) can be modeled by the regular solution theory (RST) introduced by Rubingh2 and where the magnitude of interaction between the different surfactant molecules is described by a single interaction parameter β, which accounts for the enthalpy of mixing. (β equals 0 for ideal mixing; a negative value indicates synergism and a positive value indicates antagonism in mixed micelle formation.) However, the validity and limits of the RST has been challenged, in particular, in mixed systems where β varies with the surfactant composition or where the excess of entropy is not zero. r 2011 American Chemical Society
More recently, the molecular-thermodynamic theory developed by Eriksson et al.3 and Naragajan et al.4 for single surfactants has been extended to binary surfactant systems.5,6 The introduction of parameters like the charge7,8 and packing constraints9,10 provides some ability to predict the shape and size of micellar aggregates.11 In particular, the molecular thermodynamic theory describes and predicts the growth in nonionic/ ionic system.5,12,13 The growth occurs due to the screening of the electrostatic repulsion between headgroups and modification of the apparent surface per headgroup. The fine balance between the different contributions to the free energy of micellization can result in a maximum in the aggregation number for particular compositions.6 The packing parameter p introduced by Tanford14 and Isrealachvili et al.15 is a simpler approach that can successfully predict the evolution in self-assembled structures in surfactant systems. Here, packing constraints are used to define the packing parameter p = ν/a0lc, with v the hydrocarbon volume, a0 the area per headgroup, and lc the critical length chain. p = 1/3 favors spherical micelles, p = 1/2 gives cylinder, and p close to 1 allows the formation of objects with a locally plane structure as vesicles or lamellar phases. These latter lamellar structures have been widely studied in the recent years. Considered as model for biological membranes, they are also used as templates for the formation of new nanostructured inorganic systems as mesoporous materials16,17 or nanoparticles.18 Received: March 8, 2011 Revised: April 23, 2011 Published: May 19, 2011 7453
dx.doi.org/10.1021/la200874g | Langmuir 2011, 27, 7453–7463
Langmuir
ARTICLE
Table 1. Mass, Density, Length, Volume, and Scattering Length Densities of the Polar and Apolar Parts of the Surfactants AOT molar mass (g/mol) density
C12E4
444.57
362.54
1.13
molecular volume (Å3)a lc(Å)b
0.946
650
640
11.0
16.9
vtail (Å3)b lhead (Å)
540 7.0d
350 14.2e
vhead (Å3)
110
270
68
44
surface per headgroup in D2O (Å2)c
scattering length densities for SANS: Faverage (dehydrated) (cm-2)
6.4 109
7.6 108
FH (dehydrated) (cm-2)
5.7 1010
6.5 109
FT (cm ) -2
2.5 10
9
3.9 109
a
Dehydrated molecular volume is deduced from density and molar mass according to: νm = M/dNa; Na is the Avogadro number. b Length and volume of the fully extended chain estimated from Tanford.12 c Surface per headgroup taken from the surface tension measurements presented in the MS. d see ref 35. e see ref 38.
Although lamellar phases of nonionic surfactants are stabilized by a long-range Helfrich repulsion due to fluctuations,19 the membrane elastic properties can be modified by different additives. The insertion of ionic surfactants, even in a very small quantity, tends in general to stabilize and stiffen the lamellar phases, due to the interplay between thermal undulations and electrostatic repulsions.20 Recently, the dilute part of the phase diagram of DDAB/ C12E4/D2O has been characterized using surface tension and small angle neutron scattering (SANS).21 An unusual region of very small vesicles, with radii smaller than 100 Å, was found. In order to investigate further the relative role of charge and molecular geometry on the shape and size of mixed aggregates, in this study the double chain cationic surfactant DDAB has been replaced by the double chain anionic surfactant AOT. AOT is a small surfactant molecule that forms small micelles in aqueous solution at low surfactant concentration, and its structure also favors a curved interface toward the polar core, and so promotes the formation of inverse micelles.22 Here, we present surface tension (ST) and SANS results on the AOT/C12E4 mixtures of surfactants for surfactant volume fractions in the range 130%. ST has been used to evaluate the departure from ideal mixing and SANS the solution microstructure.
’ EXPERIMENTAL DETAILS Tetraethylene glycol monododecyl ether, C12E4, has been used as the nonionic surfactant and sodium bis(2-ethyl hexyl)sulfosuccinate, AOT, as the anionic surfactant. The surfactants were obtained from Fluka, with purity higher than 98%, and used without additional purification. The molecular data for the surfactants and length scattering densities for neutron experiments are listed in Table 1. The phase diagram of C12E4 in water was established by Mitchell23 as a function of temperature. Between the cmc Φ = 0.002 vol % (5 105 mol/L) and 25%, a two-phase region is observed, and at room temperature, the swollen lamellar phase LR is formed between Φ = 25% and 80%. The phase diagram of AOT in water or in brine and as a function of temperature has been extensively studied.2427 Above the cmc
measured at Φ = 0.1 vol % (2.3 103 mol/L) up to Φ = 1.2 vol % in H2O (or 0.85% in D2O), a micellar phase is formed. Between Φ = 1.2 vol % and up to 8.8 vol %, the micelles are in equilibrium with a lamellar phase at its maximum swelling. Between 8.8 vol % and 15 vol %, the existence of a single-phase lamellar domain is still the subject of some conjecture, since the suspensions are birefringent but slightly turbid. The composition of the binary system is fully described with two parameters Φ, the total volume fraction of surfactant in the sample, and Rn, the mole ratio of AOT to total surfactant concentration. Φ¼
vAOT þ vC12E4 vAOT þ vC12E4 þ vD2O
and Rn ¼
nAOT nAOT þ nC12E4
ð1Þ
Rn varies between 0 and 1, Rn = 0 characterizes a sample containing C12E4 only, and Rn = 1 is neat AOT only.
’ EXPERIMENTAL METHODS Surface Tension. The surface tension measurements were performed with a Kr€uss K11 tensiometer using a Wilhemy plate. The samples were thermostatted at 25 C and kept one hour at rest before the first measurement. The surface tension of water, measured systematically before each new solution to check the vessel and plate cleanness, was (71.8 ( 0.2) mN/m. Each value of surface tension is the average value of 10 measurements taken automatically every 40 s. The series of measurements was repeated at least three times to control the film stability. DSC. Differential scanning calorimetry (DSC) measurements were carried out with a Micro DSCIII apparatus from SETARAM which allows high sensitivity with dilute solutions. Samples of about 0.6 mL were investigated at heating/cooling rates of 0.2, 0.4, and 0.6 C/min to ensure the reversibility of the transition at temperatures ranging from 10 to 80 C. The samples were placed in Hastelloy cells and D2O was used as reference. After normalization by the scanning rate and the total number of moles of surfactant, the curves in kJ/mol1.K1 are all superimposed. This demonstrates the reversibility of the transition. SANS. The SANS experiments were carried out on the spectrometer D22 (ILL, Grenoble).28 Three different instrument configurations (λ = 6 Å, detector offset 390 mm, sample-to-detector distances 1.4, 5, and 17.6 m, collimation 17.6 m) were used to cover a broad q-range from 2. 103 to 0.6 Å1. The samples were measured in 1 mm path length Hellma cell and thermostatted at 25 C using a circulating water bath. The raw scattering data were corrected for electronic background and empty cell and normalized on the absolute scale using the incoherent scattering cross section of water using standard ILL software.29 Data Analysis. For a solution of globular polydisperse interacting particles, the scattered intensity can be written, in the “decoupling approximation” as30 2 2 2 # dσ Φ4 2 ð2Þ ðqÞ ¼ SðqÞÆFðqÞæq þ jFðqÞj q ÆFðqÞæq dΩ V where the averages denoted by Æ æq are averages over particle size and orientation, N is the micelle number density, S(q) the structure factor, and F(q) the form factor. The three different form factors used for this study to describe globular and elongated micelles and vesicles are presented in annex 3 in the Supporting Information. For the multilamellar vesicles and lamellar phase, the scattering model proposed by Nallet et al.31 was used and is described in detail in annex 4 in the Supporting Information.
’ RESULTS Surface Tension Measurements. The surface tension has been measured for eight different molar ratios (Rn = 0, 0.16, 0.35, 0.55, 0.78, 0.91, 0.97 and 1). The γlog c curves for five of them 7454
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
Langmuir
ARTICLE
Figure 1. Surface tension as a function of surfactant concentration for Rn = 0, 0.5, 0.78, 0.91, and 1 at 25.5 C. The break points between the fitted lines give the values of the cmc.
Table 2. Values of the Mixed CMC as a Function of Rn Rn
cmc (mmol/L)
0
4.91 102
0.165
5.33 102
0.348
7.11 102
0.558 0.778
9.07 102 0.156
0.916
0.355
0.966
0.633
1
2.29
(Rn = 0, 0.5, 0.78, 0.91, and 1) are shown in Figure 1 and the values of the cmc are summarized in Table 2. The solutions were prepared in D2O. It is known that D2O can slightly modify the phase boundaries both in concentration and in temperature, but there are few measurements relating to the effects of D2O on the cmc. The cmc's of the pure surfactants in H2O were also measured for comparison. For AOT, the cmc increases from 2.29 mmol/L to 3.13 mmol/ L replacing D2O by H2O. For C12E4, the cmc was found at 4.91 102 mmol/L in D2O and at 5.65 102 mmol/L in H2O. For both surfactants, the same tendency is observed: the cmc is shifted toward lower values in D2O. Hydrogen bonding plays an important role in the solubility of the surfactant and hence micellar formation. This result indicates that D2O is a poorer solvent for these two surfactants. In the range of the concentrations investigated, the surface tension decreases up to the cmc, and for concentrations greater than the cmc, different behaviors are observed depending on Rn. For pure C12E4, the surface tension is constant at 28.5 mN/m. Between Rn values of 0 and 0.7, the surface tension increases slightly with concentration. Above Rn = 0.7, a non-monotonic behavior is observed with an initial small increase of the surface tension followed by a decrease. Finally, for pure AOT, the surface tension continues to decrease after the cmc but with a much lower slope. It is important to note that impurities are often manifested with a minimum in the surface tension at the cmc, and there are no such effects observed here.32 The behavior of many mixed surfactant systems both in selfassembly in solution and in their adsorption at the interface can be understood in the context of the departure from ideal mixing using the regular solution theory (RST) as developed by Rubingh
Figure 2. Evolution of the mixed cmc as a function of surfactant composition Rn. Symbols represent the experimental points. The solid line is an RST calculation for an interaction parameter β of 1.9.
and others.2,33 The magnitude of the nonideality between the two surfactants is expressed in terms of a single interaction parameter β. From this approach, the mixed cmc c* can be expressed as a function of the total surfactant concentration and cmc of the surfactants as 1 xAOT 1 xAOT ¼ þ c fAOT cmcAOT fC12 CC12E4
ð3Þ
where xAOT is the total molar fraction of AOT in the system. The activity coefficients fAOT and fC12E4 are given by fAOT = exp[β(1 2 2 m m xm AOT) ] and fC12E4 = exp[β(xDDAB) ] with xAOT the molar fraction of AOT in the micelles. The variation of the cmc with composition is shown in Figure 2. The solid line in the figure is for a β of 1.9. The negative value of β implies a synergism in the mixing behavior. The synergism arises from the screening of the electrostatic repulsion between the negatively charged head groups by insertion of nonionic head groups. A smaller number of counterions are bound and there is an entropy gain in forming mixed micelles. The surface coverage and average area per headgroup at the air/liquid interface can be determined from surface tension experiments using the Gibbs adsorption equation (see annex 1 in the Supporting Information). Calculating the area/molecule with m = 2 for AOT gives a physically unrealistic value of 136 Å2. Assuming m = 1, the area per headgroup is 66 Å2 in D2O and 64 Å2 in H2O. These values are smaller than those reported in ref 34 (75 Å2) and 35 (78 Å2) obtained from neutron reflectivity, but broadly consistent. For C12E4, we obtain an area per headgroup of 48 Å2 in H2O and 44 Å2 in D2O, a slightly higher value than the 42 Å2 previously obtained for this surfactant by surface tension measurement,36 inferred from measurements of the lamellar phase37 and measured directly by neutron reflectivity.38 It is now possible to calculate the values of packing parameter p15 for AOT and C12E4, and this provides an initial guide as to the expected morphologies. Values of 0.74 and 0.48, respectively, were obtained, and on this basis, the preferred aggregate morphologies are expected to be planar for AOT and highly elongated structures for C12E4. SANS Structural Characterization. Micellar Region. The data in Figures 3 and 4 are typical scattering curves measured at 25 C in the micellar region of the phase diagram. The solid lines are model calculations as described earlier and in more detail in annex 3 in the Supporting Information. 7455
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
Langmuir
Figure 3. Micellar phase: scattering intensities at constant molar ratio Rn = 0.2. T = 25 C. (green O) Φ = 0.01; (gray ]) Φ = 0.02; (blue 0) Φ = 0.05; (red 4) Φ = 0.1.
Figure 4. Micellar phase: scattering intensities at constant surfactant volume fraction Φ = 0.01. T = 25 C. (pink þ) Rn = 0.06; (red /) Rn = 0.12; (brown ) Rn = 0.2; (green 0) Rn = 0.46; (blue )) Rn = 0.69; (gray O) Rn = 1. Full lines are the fitted curves.
Figure 3 shows the effect of concentration at a constant molar ratio Rn = 0.2 in a region where elongated micelles are formed. A strong correlation peak is present even for the lowest concentration (Φ = 1%) and dominates the scattered intensity at low q. It shifts toward high q with increasing concentration. Figure 4 shows the effects of the surfactant mole ratio Rn on the scattering (and hence on the micelle shape and size) at Φ = 1%. A strong transition in the scattering is obtained between Rn = 0 and Rn = 0.06 (see Figure S1 in the Supporting Information). The nonionic CiEj-type surfactants in aqueous solution have a tendency to form very large aggregates as cylindrical or wormlike micelles at relatively low concentrations39,40 if the i/j ratio is sufficiently large; the solutions are strongly turbid. With the addition of a small amount of charged molecules (6% mol of AOT), the solution becomes optically transparent and much smaller
ARTICLE
Figure 5. Evolution of the average distance between micelles at constant volume fraction, Φ = 1% as a function of Rn. Two linear domains are clearly separated and correspond to the transition from cylindrical to spherical micelles.
aggregates are formed, inducing a strong decrease of the scattered intensity at low q. At high q, the form of the scattering data is dominated by the particle form factor. The minimum of the form factor related to the smaller size of the aggregates is not welldefined here due to both polydispersity and instrument resolution smearing. In Figure 5, the average distance between micelles (Dm ≈ 2π/qmax) is plotted as a function of Rn for the constant total volume fraction of 1%. The average distance between micelles decreases when Rn increases, an indication that the number of micelles per volume unit increases and thus that the mean size of the micelles decreases. Two linear regions can be distinguished, with a break point at Rn = 0.27. This behavior is also evident in Figure 4 where there is a jump in the intensity scattered with a factor of 5 between Rn = 0.2 and Rn = 0.46. The two regions correspond clearly to a transition from very elongated micelles (fitted with a coreshell cylinder) to smaller spherical micelles. We observed systematically a discrepancy at low q, where the fitting curve is below the experimental one. We are reaching here the limit of the model, especially in the case of a very elongated cylinder, where the decoupling approximation is not valid anymore. Nevertheless, we estimate that physically reasonable (if not precise) parameters can be derived. The validity of the analysis for cylinders is justified in the following discussion. We verified a posteriori that we are below the critical concentration c* and that the average distance between two neighboring aggregates, Dm = 2π/qmax, is larger than the cylinder length. Moreover, the variation of Dm as a function of the surfactant volume fraction scales as 1/Φ1/3, indicative of globular micelles in dilute solution.41 The size distribution in length has not been included in the model. However, theory predicts a broad distribution of the lengths of cylindrical micelles,42 but the strong correlation peak hinders the Guinier regime and the q-domain where polydispersity effects are quantified from the SANS data. The error in length from the data fitting is estimated at (5 Å. On the contrary, at large q, a much more accurate radius value is obtained with an error of (1 Å. The key model parameters are summarized in Table 3 for the elongated micelles and in Table 4 for the spherical micelles. The aggregation number is calculated from the volume of the core. 7456
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
Langmuir
ARTICLE
Table 3. Key Model Parameters and Deduced Aggregation Numbers from Model Fits for the AOT/C12E4 Cylindrical Mixed Micellesa Rn Fc (cm )
0.06
0.09
Table 4. Key Model Parameters and Deduced Aggregation Numbers from Model Fits for the AOT/C12E4 Spherical Mixed Micellesa Rn
0.12
3.6 10
0.27
0.46
0.7
0.84
1
Fc (cm ) 3.1 10 2.9 10 2.7 10 2.6 10 2.5 109
-2
3.7 10
Φ
0.01
0.01 0.02 0.05 0.01 0.02 0.05 0.08 0.1
Φ
0.01
0.01 0.02 0.01 0.02
0.01
0.01
Rc (Å) ((1 Å)
13.0
13.5 14.0 14.5 13.0 13.5 13..0 13.0 13.0
Rc (Å)
20.0
15.0 16.5 13.5 15.5
13.5
13.0
8.0
7.5
4.0
5.0
9
3.5 10
9
9
-2
9
9
9
9
esh (Å) ((1 Å)
9.0
8.5
8.5
((1 Å)
L (Å) ((5 Å) ε
240 10.7
203 181 163 154 164 135 127 122 9.3 8.1 7.4 7.5 7.5 6.3 5.8 5.7
esh (Å) ((1 Å) Z
22
19
18
20
23
14
15
Nagg
79
33
43
16
24
22
14
8.5
7.5
8.5
8.0
8.5
8.5
Z
40
36
Nagg
358
307 271 289 212 251 189 186 176
42
26
25
39
34
26
22
7.0
7.5
6.0
Fc, scattering length density of the core; Rc, radius of the core; esh, thickness of the polar shell; Z, surface charge; Nagg, aggregation number. a
Rn
0.2
Fc (cm-2)
3.3 109
Φ
0.01
0.02
0.05
0.08
0.1
0.12
0.16
Rc (Å) ((1 Å)
12.5
12.5
12.0
13.5
12.5
13.0
12.5
esh (Å) ((1 Å) L (Å) ((5 Å)
8.0 106
8.5 132
8.0 113
7.5 97
8.0 96
8.0 95
7.5 106
ε
5.2
6.3
5.6
4.6
4.6
4.6
5.3
Z
19
30
43
29
31
26
22
Nagg
130
162
134
139
119
126
134
Rn
0.27
Fc (cm )
0.46
3.1 10
-2
2.9 109
9
Φ
0.02
0.05
0.08
0.1
0.05
0.08
0.1
Rc (Å) ((1 Å) esh (Å) ((1 Å)
11.0 8.5
11.0 8.5
11.5 7.5
12.0 7.5
8.5 9.0
10.5 7.5
11.0 7.0
L (Å) ((5 Å)
73
103
88
87
67
78
77
ε
3.7
5.2
4.6
4.5
3.8
4.3
4.3
Z
16
28
30
29
16
26
28
Nagg
72
97
90
95
34
60
68
Fc, scattering length density of the core; Rc, radius of the core; esh, thickness of the polar shell; L, length of the cylinder; e, axial ratio; Z, surface charge; Nagg, aggregation number. a
The total aggregation number varies from 350 for the longest cylinders to 14 for the pure small AOT micelles. In the elongated micellar region, the rod length is strongly linked to Rn. The longest rods are formed for Rn = 0.06, where they reach 240 Å for Φ = 1%. The smallest rods are around 70 Å for Rn = 0.46, and at constant volume fraction, the aggregation number decreases continuously when Rn increases. The rod length is also sensitive to the total surfactant concentration. As a general tendency, below Rn = 0.2 a decrease in length is measured as the concentration increases. Above Rn = 0.2, the length remains constant with concentration, within the relative error in data fitting. This atypical behavior will be discussed later, since for threadlike micelles, the cost in end-cap energy controls the contour length and energy calculations show that the length increases as the concentration increases.42 The total radius (Rc þ esh) is relatively constant between 22.4 and 17.5 Å and decreases slightly as Rn increases. This can be rationalized by the relative sizes of the C12E4 and AOT molecules, since AOT is shorter than C12E4. The axial ratio that quantifies the anisotropy of the elongated aggregates varies from 11 to 4 when Rn increases from 0.06 to 0.46.
Figure 6. Scattering intensities at constant surfactant mole ratio Rn = 0.03 as a function of the volume fraction. T = 25 C. (gray ) Φ = 0.001; (blue O) Φ = 0.02; (green 0) Φ = 0.05; (red ]) Φ = 0.1. The solid lines are fitted curves using models described in the Supporting Information for parameters given in Table 5.
In the spherical micellar region, we observe a decrease of the radius and of the thickness of the polar head, with the increase of Rn, which is consistent with the increasing AOT composition and hence the incorporation of a smaller molecular volume. The total size of the micelle varies from 28 Å for Rn = 0.27 to 18 Å for Rn = 1. Highly Swollen Lamellar Region. The scattering data for measurements along the dilution line Rn = 0.03 are presented in Figure 6. This molar ratio corresponds to a re-entrant domain, where the lamellar phase reaches a maximum swelling. At a very low surfactant volume fraction, Φ = 0.1%, the characteristic scattering from very small vesicles is measured. The data are modeled using a coreshell model with a core radius of 85 Å and a shell thickness of 28 Å. However, the sample is slightly turbid. By increasing the concentration by a factor of 10, the microstructure changes as a multilamellar vesicle region is entered. The solid lines in the figure are model calculations using the Nallet formalism.31 The number of bilayers increases from 2 to 5 as the concentration increases from 1% to 5%. The large lamellar periodicity and swelling are driven by the electrostatic repulsions between the now partially charged bilayers. In this concentration 7457
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
Langmuir
ARTICLE
Table 5. Key Model Parameters from Model Fits for the AOT/C12E4 Multilamellar Vesicles and Lamellar Phases for Rn = 0.03a Φ
Table 6. Key Model Parameters for the AOT/C12E4 Lamellar Phase at Φ ≈ 0.3 as a Function of Rna Rn
0 0.01 0.03 0.10 0.23 0.36 0.52 0.72 0.85 0.91 1
0.01
0.02 0.03 0.05 0.1 0.12 0.15 0.18 0.3
d* (Å)
805
648
e (Å)
28.2
29.2 29.0 30.0 29.8 28.8 29.0 28.6 25.8
esh (Å) ((0.2 Å)
8.4
8.7
7.1
7.2
7.1
6.8
6.1
5.0
4.5
ec (Å) ((0.2 Å) 7.9 8.5 8.4 7.2 7.2 6.2 5.6 4.2 4.2 3.4 3.9
ec (Å) ((0.2 Å)
5.7
5.9
7.4
7.8
7.8
7.6
8.4
9.3
8.4
Φ*
0.28 0.27 0.23 0.25 0.26 0.27 0.28 0.28 0.26 0.27 0.29
η
1.05 0.4 0.23 0.17 0.17 0.19 0.19 0.19 0.21 0.19 0.21
Φ* η Nstack
0.035 0.045 0.05 0.06 0.10 0.12 0.15 0.16 0.23 0.33 0.2 0.16 0.15 0.09 0.16 0.18 0.18 0.23 2
2
d* (Å)
570 510 310 252 200 177 120
3
5
>50 >50 >50 >50 >50
a
d*, lamellar spacing; e, total bilayer thickness; esh, shell thickness; ec, core thickness; Φ*, apparent volume fraction; η, caille parameter; Nstack, number of stacked bilayers.
100 102 120 100 89
a
range, the swelling behavior does not follow the classical 1-D swelling law, d* = e/Φ. From the bilayer thickness obtained from the data fitting and lamellar spacing d*, it is possible to calculate an apparent volume fraction Φ*. Up to Φ = 5%, Φ* is higher than Φ with the factor varying from 2.8 to 2.1. It is still a biphasic region, where the multilamellar vesicles at their maximum swelling are in equilibrium with smaller aggregates (very likely the small vesicles) formed at the lower concentration. Above 5%, a true swollen monophasic lamellar phase is formed and the swelling follows the classical 1-D swelling law. Φ* values are consistent with the experimental Φ. The bilayer thickness remains constant, around 29 Å. The Caille parameter η reaches a minimum at 0.09 for Φ = 0.1 and increases again with the concentration up to 0.23; these relatively low values are typical of rigid lamellar phases. Lamellar Phase Region. Figure 7 shows the SANS data in the lamellar region for Φ = 0.3 and for Rn varying from 0 (C12E4 only) to 1 (AOT only). The lowest curve, Rn = 1, is plotted in absolute units (cm1) and the intensities of the following spectra are incrementally multiplied by a factor 10 for clarity. The scattering curves were modeled using the lamellar phase model developed by Nallet31 described in detail in annex 4 in the
74
67
68
63
58
Same parameters as in Table 5.
Supporting Information. The key model parameters are Fc, F, and d* and the main refinable parameters are η, eh, ec, Fh, and σ. The eh and ec values are obtained from the analysis of the data at high angles, where the bilayer form factor is not perturbed by the Bragg peaks. No pronounced minimum is observed, due to smearing in the instrument resolution and because of bilayer thickness fluctuations since the AOT and C12E4 molecules have different lengths. From the total bilayer thickness e = 2(esh þ ec), the apparent volume fraction Φ* is calculated. Φ* values correctly match the experimental volume fractions except for Rn = 0.03 (see below). The key model parameters are summarized in Table 6. The important parameter coming from data fitting is the Caille parameter η.43 It is proportional to the inverse square root of the product of the bending modulus K (J/cm) and the compression modulus B (J/cm3) and is characteristic of the interactions between the membranes. For the pure surfactant system, we can calculate the specific area Σ and the area per headgroup σ, according to σ ¼
Figure 7. SANS scattering from mixed lamellar phases, Φ = 0.3. The bottom curve is in absolute scale; the following are multiplied by 10. The solid lines are the fitted curves and the parameters are listed in Table 6.
84
e (Å) 27.8 27.6 25.8 24.2 23.0 22.2 20.2 18.6 17.8 17.4 17.0 esh(Å) ((0.2 Å) 6.0 5.3 4.5 4.9 4.3 4.9 4.5 5.1 5.1 5.3 4.6
2Σ Na
with
Σ¼
1 de
where d is the surfactant molecular density and Na the Avogadro number. This gives 46 Å2 for pure C12E4 lamellar phase, in very good agreement with the value determined by surface tension. For AOT, the value of 76 Å2 is higher than that from surface tension but in full agreement with what was measured by Nave et al. and Li et al.34,35 For Rn = 0, only one broad peak is observed, and the Caille parameter of 1.05 obtained is characteristic from very soft lamellar phase and larger than 0.7, the value predicted from Helfrich19 4 e 2 1 η¼ ð4Þ 3 d The addition of AOT molecules strongly enhances the intensity of the first Bragg peak, a second order become visible, and simultaneously, the low-q scattering decreases. These observations indicate an increased orientational order of the membranes and a decrease in the amplitude of undulation. Even for 1% added charges, η decreases to 0.4, a value smaller than what is calculated with eq 4, but still larger than values obtained for purely electrostatic stabilized lamellar phases.44 For Rn = 0.03 and larger, the first and second Bragg peak orders are clearly visible and typical η values range between 0.17 and 0.23, consistent with rigid lamellar phases stabilized by electrostatic repulsions. The lamellar periodicity d* reaches a maximum at 120 Å for Rn = 0.03. The apparent volume fraction (Φ* = 23%) is much lower than the known experimental value. In the case of fluctuating membranes, the interlamellar distance d* is related to the bilayer 7458
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
Langmuir
ARTICLE
Figure 8. Φ = 0.3. Evolution of the average bilayer thickness as a function of Rn. The error bars Δe = σee represent the “roughness” introduced in the model as described in annex 4 in the Supporting Information.
volume fraction Φ and bilayer thickness via Φd ΔA ¼ 1þ e A
ð5Þ
where (ΔA/A) is the fraction of bilayer associated with the thermally induced undulations.45 For given Φ and e, the swelling is larger than expected from an ideal swelling law, and consequently, the apparent volume fraction is smaller. Above Rn = 0.1, d* decreases continuously down 58 Å and the evolution of the average bilayer thickness as a function of Rn is plotted in Figure 8. A linear dependence from 17 Å (Rn = 1) to 24 Å (Rn = 0.1) is obtained as indicated by the dotted line. Between Rn = 0 and 0.03, the bilayer thickness appears slightly larger and this is again an indication of the contribution from membrane fluctuations. Phase Diagram. The phase diagram presented in Figure 9 for total surfactant volume fraction up to 0.3 is obtained by combining the results from visual inspection, surface tension, and SANS. The horizontal axis corresponds to the total volume fraction of surfactant and the vertical axis is the molar ratio of the two surfactants. The white areas represent the regions where the samples are optically fully transparent. In the lamellar region, birefringence is observed. The gray area is the region where the samples are turbid and where an increase of the scattering intensity at low q, indicating a phase separation at large length scale, is observed by SANS. A macroscopic phase separation also occurs after a few days at rest. In this region, micelles are in osmotic equilibrium with the lamellar phase at its maximum swelling. Micellar/lamellar, ULV/MLV, or micellar/vesicle coexistence are commonplace in surfactant systems. Quantitative calculation of osmotic pressure, the derivative of free energy against molar volume, allows one to determine the phase boundaries.46 The mixture of the two surfactants strongly enhances the micellar region compared to the pure surfactant systems, and it extends up to 15 vol % for Rn = 0.2. In the micellar region, two types of aggregates have been observed: spherical micelles in the AOT-rich part and more elongated micelles in the non-ionic-rich part. An interesting evolution in the microstructure is observed along the dilution line for Rn = 0.03. Small vesicles are observed at very low surfactant concentration (Φ = 0.1%), MLV between 1 and 3 vol %, and lamellar phase above 5%. This line also
Figure 9. Phase diagram for the binary surfactant mixture AOT/C12E4 in D2O up to 0.3 in volume fraction of surfactant. The gray area delimits the optically turbid samples where phase separation occurs after few days at rest; the two phases were also confirmed by SANS measurements. The small region where large multilamellar vesicles (MLV) are formed is surrounded with a dotted line. The arrow indicates the narrow region of small unilamellar vesicles (ULV). The white areas are regions where the samples are optically transparent. The symbols indicate points where SANS measurements have been made. L1 indicates the micellar part, separated into two regions. In the AOT-rich part, spherical micelles are formed, and in the C12E4-rich part, cylindrical micelles are present. The dotted line symbolizes the limit between cylindrical and spherical aggregates.
corresponds to a re-entrant domain in the lamellar phase. Indeed, the single LR phase of pure C12E4 in H2O appears at 20 vol % corresponding to a maximum swelling of ca. 180 Å. The addition of 5 mol % of AOT induces a relatively large swelling up to 510 Å. In weakly charged lamellar system, the equilibrium period between bilayers arises from the interplay between thermal undulations and electrostatic repulsions. Remark on the Temperature Effect. Nonionic CiEj molecules and C12E4 in particular are very sensitive to temperature,23 whereas AOT is not.25 The mixed system is also temperature sensitive, all the more with Rn being low. An example of effect of temperature for the sample Rn = 0.03 and Φ = 5% on the scattering pattern is presented in Figure 10. The DSC scan is shown in the inset. It exhibits a sharp endothermic peak, with Tonset = 18.2 C. It is important to note that, at 15 C, the sample is perfectly transparent, whereas at 25 C, it becomes slightly turbid. Below the transition, the scattering curve has been fitted with a cylinder model with the following parameters: Rc = 12.5 Å; esh = 9.8 Å; Rtot = 22.1 Å; L = 350 Å; Fsh = 106 cm2, and Z = 22. Above the transition, large multilamellar vesicles are formed. The curve fitting reveals a stacking of 5 membranes, a lamellar spacing of 510 Å, and the Caille parameter found at 0.15, a small value characteristic of relatively rigid bilayer as already seen previously (Table 5). It has been shown that nonionic micelles of surfactants with short polar heads grow with increasing temperature. The driving force is the dehydration of the polar headgroups at the aggregate surface that induces a smaller area per headgroup and favors the growth of aggregates.47 The phase transition observed in the mixed system is thus driven by the nonionic molecules and their hydration state. 7459
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
Langmuir
Figure 10. Temperature effect for the sample Rn = 0.03, Φ = 0.05 (]), Φ =15 C (0); T = 25 C. The full lines are fitted curves. In the inset, the DSC measurement exhibit a sharp endothermic peak, starting at Tonset = 18.2 C. A transition from cylindrical micelles to a swollen lamellar phase is observed as the temperature increases.
’ GENERAL DISCUSSION The phase behavior and the microstructure of ionic and nonionic surfactant mixtures are widely reported in the literature. Most of the studies report on the growth of micelles upon addition of nonionic molecules to the charged aggregates. Mixtures of SDS with C12Ej, j = 3 to 8, have been extensively studied.12,4852 These studies have provided an important advance in the understanding of the relative role of steric and electrostatic interactions to the micellization process. The screening of electrostatic repulsions between charged head groups by insertion of nonionic molecules promote the growth from sphere to ellipsoid with a corresponding increase of the aggregation number. The structure of the nonionic-rich aggregates depends critically upon the relative preferred curvature of the associated nonionic surfactants which is, for example, lower for C12E6 than for C12E8, which would also form globular micelles. This will also to some extent control the growth that is observed. Mixture of SDBS with C12E8 and C12E23 is reported in ref 53. SDBS forms small oblate micelles in water, and the nonionic surfactant has a packing parameter of 0.32, at the limit between spherical/elongated objects. Mixed aggregates are oblate, with an elliptical ratio around 1.6 and the aggregation number increases linearly with the amount of C12E8 molecules. By replacing C12E8 by C12E3, where the smallest headgroups promote the formation of planar aggregates (p = 0.57), a fully different phase behavior is observed.54 Nearly spherical micelles are formed for molar ratio of C12E3 lower than 0.8, and the aggregation number increases with increasing nonionic composition. This region is followed by a narrow range of composition over which mixtures of micelles and small monodisperse unilamellar vesicles coexist. For the richest C12E3 compositions, planar aggregates are observed. The formation of rodlike structures is, however, more unusual, but has been observed in some related systems. C12E5 in aqueous solution forms prolate sphero-cylinder micelles, and addition of DMPC molecules induces growth in the length of the micelles.55 A homogeneous mixture of the two molecules along the aggregates is assumed. After replacing DMPC by the cationic molecule
ARTICLE
DTAB, a very different behavior was observed where addition of small amount of DTAB induces a stiffening and shortening of the rodlike micelles.13 The decrease of the length as a function of the doping level was described well by molecular thermodynamic theory and was explained by the molecular structure of the surfactants. Moreover, at constant mole ratio between the two surfactants, an unexpected length shortening with the total surfactant concentration was observed.56 This behavior is similar to that reported herein, with AOT and C12E4 mixtures for mole ratio below Rn = 0.2. This observation was explained by the larger spontaneous curvature of DTAB in comparison to C12E5, leading to a phase separation of the molecules inside the aggregates— with the C12E5 molecules incorporating the cylindrical core and the DTAB molecules forming the end-caps—but there was no direct evidence to support this hypothesis. An interesting behavior has been demonstrated in the mixture of C12E6 with the nonionic surfactant n-dodecyl-β-D-maltoside (C12G2).57 Whereas C12E6 forms preferentially cylinders, C12G2 forms small micelles and a coexistence of spherical and spherocylindrical micelles is observed where the fraction of the latter objects increases with the amount of C12E6. The length increases with the total concentration as foreseen by the theory but decreases with the increase in the amount of the C12G2. In mixed systems, the length of the cylindrical micelles increases (i.e., endcaps are reduced) with the amount of molecules having the lowest energy curvature or by reducing the spontaneous curvature (change in temperature, ionic strength) of the amphiphile. There are some interesting and relevant difference between the DDAB/C12E4 and AOT/C12E4 behaviors. The phase diagram of DDAB/C12E4 in D2O has been established up to Φ = 2 vol %21 and Φ = 30 vol % with AOT. With AOT, only a cmc was measured by surface tension, whereas a cmc followed by a cvc (critical vesicular concentration) was evidenced for Rn > 0.4 with DDAB. The single phase micellar region is strongly enhanced with AOT, and reaches a concentration of 15 vol % for Rn = 0.2. This molar ratio also corresponds to the maximum of the micellar region with DDAB, but the upper concentration of the single phase region is only 2 vol %. In both systems, elongated micelles are formed in the rich nonionic part and the length decreases as Rn increases, i.e, with addition of double chain molecules, with higher packing parameters. With DDAB and for a given Rn, a systematic increase of the length with increasing concentration is measured. The packing parameter from DDAB is 0.65. Consequently, incorporation of DDAB molecules are more favorable in the cylindrical core that in the curve end-caps, and an increase of the concentration induces the growth of the micelles as has already been seen with DMPC.55 The axial ratio that quantifies the anisotropy of the elongated aggregated is higher for the AOT/C12E4 mixed micelles (up to 11) than for DDAB/C12E4 (up to 7). With increasing Rn, the main difference is the formation of very small vesicles, followed by large multilamellar vesicles with DDAB, whereas only small spherical micelles are present with AOT. With AOT, MLVs were found in a narrow region for Rn = 0.03, in the very rich nonionic part, an opposite behavior compared to that of DDAB. These differences cannot be explained in terms of charges and electrostatic interaction, since AOT and DDAB both bear one charge and their counterions are dissociated in water. Consequently, the intrinsic geometry of molecules and the associated preferred curvature play a crucial role for the shape of the aggregates at the equilibrium. 7460
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
Langmuir
ARTICLE
Table 7. Compression Modulus and Bending Energy of Mixed Bilayer for a Total Surfactant Volume Fraction Φ = 30% as a Function of Rna Rn
0.1
0.23 0.36 0.52 0.72 0.85 0.91
1
σ (A )
481
234
76
η
0.17 0.17 0.19 0.19 0.19 0.23 0.19 0.21
2
156
117
94
84
81
kcB (erg2.cm-3) 10-7 1.44 2.05 1.95 2.85 3.84 2.51 4.51 4.73 B (erg.cm-3) 106
1.6
kc (kBT)
2.18 2.25 1.78 1.91 2.03 1.38 2.13 1.78
membrane properties can be obtained from the Caille parameter, related to the compression modulus B in J/cm3 and the bending modulus K in J/cm following η¼
kc K ¼ d
a
The formation and shape of mixed micelles is a result of a delicate balance of the different contributions to the free energy of micellization, changes in conformation and hydration on mixing, and the contribution of interaggregate interactions, as well as the intra-aggregate interactions. From the different studies presented above and also pointed out in refs 58,59, the role of the packing parameter is clearly demonstrated. This results in tunable systems where the morphology of the aggregate can be predicted and controlled. In the system described here, at low Rn values, the shape of the aggregates is dominated by the geometric constraints imposed by the C12E4 molecules, and elongated aggregates are formed. At high molar ratio, the small spherical aggregates are close to the structure of the pure AOT micelles. We cannot in this system fully rationalize and predict the shape of the mixed micelles in terms of a mixed packing parameter value, as was possible in other mixed cationic/C12Ei systems,53,54,58 due to the large value of p for AOT. From the value derived from surface tension measurements and the known molecular dimensions, a preferred lamellar structure is predicted, but it is well-established that at low concentration AOT forms small micelles. With the branched chains, which can adopt different conformations, the value of p obtained from interface properties does not reflect well the packing constraints associated with the aggregates. This implies that, due to constraints associated with the chain packing, the effective area per molecule in the aggregates must be much larger. This could be a direct manifestation of the conformational changes reported in ref 60 resulting in a larger area per molecule in the micelle. Understanding the interactions between membranes has attracted much attention during the last 30 years, because of its relevance in biology, for example, membrane fusion or cellcell contact. The general behavior can be quantitatively explained in terms of osmotic pressure and phase equilibrium. The equation of state is the result of four contributions; the attractive van der Waals force is counter-balanced by the three repulsive forces: electrostatic, Helfrich, and hydration. The hydration force has a very short range of interaction for interlamellar distances lower than 15 Å61 and does not play an important role for the concentrations investigated here. In charged stacked membranes stabilized by electrostatic repulsion, the bending energy (or rigidity constant) kc of the membrane is much higher than kBT yielding to very flat membranes, and thermal fluctuations are not important. On the other side, nonionic lamellar phases are stabilized by thermal undulations, and can reach very large swelling distances, and the bending energy is on the order of kBT. Further insight into the
ð6Þ
The bending modulus K is derived from the bending energy (in J or kBT) according to
2.21 2.66 3.62 5.59 4.41 5.15 6.44
σ, average area per charged head group calculated assuming an ideal mixture of surfactants; η, Caille parameter; B, compression modulus; kc, membrane bending energy.
πkB T pffiffiffiffiffiffi 2d2 KB
ð7Þ
In the case of electrostatically stabilized systems, B may be estimate by62,63 " # π2 dkb T σ σ2 þ6 B¼ 13 þ ::: RLðd eÞ R2 L2 ðd eÞ2 2Lðd eÞ3 ð8Þ σ is the surface area per charged headgroup, R is a dissociation constant assumed to be one herein, and L is a characteristic length given by L¼
πe2e 4πε0 εr kb T
ð9Þ
ε0 is the permittivity of free space, εr the permittivity of water, and ee the electronic charge. L is on the order of 20 Å at room temperature. The addition of a very small (0.1 mol %) amount of charged molecules can drastically modify the phase behavior.62,6467 A nontrivial coupling between in-plan electrostatic repulsion between the headgroup and intermembrane electrostatic and steric repulsion exists that can lead to enhanced fluctuations68 or damped due to long-range electrostatic repulsion. In the latter case, a strong decrease of the lamellar periodicity is observed due to the decrease in membrane undulation. In our system, the decrease of the lamellar spacing has two origins. The suppression of undulations in the bilayers and the decrease of the average bilayer thickness (see Figure 9) is due to the difference of length between the two surfactant molecules. For molar ratio Rn equal to or above 0.1, the Caille parameter is consistent with that predicted for a relatively rigid membrane in which the electrostatic interaction dominates. In Table 7, the calculated values of kcB (obtained using the experimental η in eq 6), B (eq 8), and kc (eq 7) are given for Φ = 30% and Rn ranging from 0.1 to 1. The product kcB increases slightly from 1.4 to 4.7 107 erg2.cm3 with Rn. The calculated compression modulus also increases with Rn due to the reduction of the charge area. This finally yields to a nearly constant value of the membrane bending energy, close to 2kBT. We can conclude that AOT bilayers are relatively soft for charged membranes. It would be expected that the addition of a nonionic cosurfactant (such as the C12E4 added here) would result in a more flexible membrane in which thermal fluctuations would eventually dominate, as reported in ref 64 upon addition of pentanol in SDS of DMPC lamellar phases. This is not observed here, and the Caille parameter is relatively insensitive to the addition of C12E4. A similar trend was also reported for DHDAB/C12E369 and DDAB/C12E4.21 This was attributed to reduced electrostatic screening as a result of the reduced counterion concentration, as the cationic is replaced by the nonionic cosurfactant. Comparable behavior was also described in amphiphilic monolayers films 7461
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
Langmuir in microemulsion70 and explained by the fact that the mean bending constant increases with addition of charges; meanwhile, the Gaussian modulus decreases, in similar but opposite way.
’ SUMMARY The phase diagram and the microstructure in the binary system AOT/C12E4 in D2O have been characterized by SANS. In the dilute part of the phase diagram, and this is one important feature of the phase diagram, the combination of the two surfactants considerably enhances the micellar region, stable up to a concentration of 15% at 25˚ C for Rn = 0.2. With increasing AOT concentration and composition for AOT/ C12E4, aggregates are formed in the following sequence of multilamellar large vesicles (for very low Rn), cylindrical micelles, and spherical small aggregates. The decrease in the length as the concentration increases, observed for Rn below 0.2, remains an open question. Due to the close scattering length densities of both hydrogenated surfactants, there is no direct experimental evidence of phase separation inside the aggregates, as proposed in the literature to explain such behavior. SANS contrast variation measurements using deuterated surfactants, on a high flux spectrometer, are planned in order to obtain a more detailed description of the internal structure of the aggregates. At higher surfactant concentration, above 20% a swollen lamellar phase is formed. The average bilayer thickness is a linear combination of the bilayer thickness of the pure surfactants weighted by their respective molar ratios. Above 1% of charges, the electrostatic repulsion dominates over the Helfrich force, resulting in rigid bilayers. Mixture of surfactants, with very different packing parameters, sensitive to the ionic strength and temperature, gives rise to a very tunable system with a high capability for reorganization. ’ ASSOCIATED CONTENT
bS
Supporting Information. including SANS scattering data of pure C12E4 micelles, regular solution theory, calculation of the instrument resolution, SANS data modeling for micelle and lamellar phases. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The subcommittee 9 and the ILL are thanked for the beam time allocation. The modelling of the spherical and rodlike micelles was performed using the DANSE software provided by the University of Tennessee and the NCNR_SANS_package provided by NIST. ’ REFERENCES (1) The colloidal domain where physics, chemistry, biology and technology meet, Evans, D., Wennerstr€om, H., Eds.; Advances in interfacial engineering series; VCH Publishers, 1994; The aqueous phase behavior of surfactant, Laughlin, R., Ed.; Surfactant science series; M. Dekker, Inc., New York and Basel; 1994 (2) Rubingh, D. N. Solution Chemistry of Surfactants, Mittal, K. L., Ed.; New York, 1979; Vol 1.
ARTICLE
(3) Eriksson, J. C.; Ljunggren, S.; Henricksson, U. J. J. Chem. Soc., Faraday Trans. 2 1985, 81, 833–868. (4) Nagarajan, R.; Ruckenstein., E. Langmuir 1991, 7, 2934–2963. (5) Shiloach, A; Blankstein, D. Langmuir 1998, 14, 1618–1636. (6) Shiloach, A.; Blankstein, D. Langmuir 1998, 14, 7166–7182. (7) Shiloach, A.; Blankschtein, D. Langmuir 1997, 13, 3968–3981. (8) Bergstr€om, M.; Jonsson, P.; Persson, M.; Eriksson, J. C. Langmuir 2003, 19, 10719–1725. (9) Huang, L.; Somasundaran, P. Langmuir 1997, 13, 6683–6688. (10) Eads, C. D.; Robosky, L. C. Langmuir 1999, 15, 2661–2668. (11) Hines, J. D. Curr. Opin. Colloid Interface Sci. 2001, 6, 350–356. (12) Garamus, V. M. Langmuir 2003, 19, 7214–7218. (13) Kwon, S. Y. Langmuir 2008, 24, 10674–10679. (14) Tanford, C. J. Phys. Chem. 1972, 76, 3020–3024. (15) Israelachvili, J. N.; Mitchell, C. J.; White, B. W. J. Chem. Soc. Faraday Trans. I 1976, 72, 1525–1568. (16) Dubois, M.; Gulik-Krzywicki, T.; Cabane, B. Langmuir 1993, 9, 673–680. Dubois, M.; Cabane, B. Langmuir 1994, 10, 1615–1617. (17) Yamauchi, Y.; Kuroda, K. Chem. Asian J. 2008, 3, 664–676. (18) Adair, J. H.; Li, T.; Kido, T.; Havey, K.; Moon, J.; Mecholsky, J.; Morrone, A.; Talham, D. R.; Ludwig, M. H.; Wang, L. Mater. Sci. Eng. 1998, R23, 139–242. (19) Helfrich, W. Z. Naturforsch. 1978, 33a, 305–315. (20) Jonstr€omer, M.; Strey, R. J. Phys. Chem. 1992, 96, 5993–6000. (21) Grillo, I.; Penfold, J.; Tucker, I.; Cousin, F. Langmuir 2009, 25, 3932–3943. (22) De, T. K.; Maitra., A. Adv. Colloid Interface Sci. 1995, 59, 95–193. (23) Mitchell, J. J. Chem. Soc., Faraday Trans. I 1983, 79, 975–1000. (24) Fontell, K. J. Colloid Interface Sci. 1973, 44, 156–164. (25) Fontell, K. J. Colloid Interface Sci. 1973, 44, 318–329. (26) Skouri, M.; Marignan, J.; May, R. Colloid Polym. Sci. 1991, 269, 929–937. (27) Balinov, B.; Olsson, U.; Soderman, O. J. Phys. Chem. 1991, 94, 5931–5936. (28) http://www.ill.eu/instruments-support/instruments-groups/ instruments/d22/ (29) Ghosh, R.E.; Egelhaaf, S.U.; Rennie, A.R. Institut Laue Langevin Internal Report ILL98GH14T, 1998. (30) Hayter, J. B.; Penfold., J. J. Colloid Polym. Sci. 1983, 261, 1022–1030. (31) Nallet, F.; Laversanne, R.; Roux, D. J. Phys. II (France) 1993, 3, 487–502. (32) Eastoe, J.; Nave, S.; Downer, E.; Paul, A.; Rankin, A.; Tribe, K. Langmuir 2000, 16, 4511–4518. (33) Holland, P. M.; Rubingh, D. N. in Cationic Surfactants, Holland, P. H., Rubingh, D. N., Eds.; Surfactant Science Series; Marcel Dekker: New York, 1990; Vol 37. (34) Nave, S.; Eastoe, J.; Penfold, J. Langmuir 2000, 16, 8733–8740. (35) Li, Z. X; Lu, J. R.; Thomas, R. K.; Penfold, J. J. Phys. Chem. B 1997, 101, 1615–1620. (36) Kjellin, U. R. M.; Claesson, P. M.; Linse, P. Langmuir 2002, 18, 6745–6753. (37) Acharya, D. P.; Kunieda, H. J. Phys. Chem. B 2003, 107, 10168– 10175. (38) Lu, J. R.; Li, Z. X.; Su, T. J.; Thomas, R. K.; Penfold, J. Langmuir 1993, 9, 2408–2416. (39) Glatter, O.; Fritz, G.; Lindner, H.; Brunner-Popela, J.; Mittelbach, R.; Strey, R.; Egelhaaf, S. U. Langmuir 2000, 16, 8692–8701. (40) Grell, E.; Lewitski, E.; Schneider, R.; Ilgenfritz, G.; Grillo, I.; von Raumer, M. J. Therm. Anal. Calorim. 2002, 68, 469–478. (41) Meier, E. E.; Krause, R.; Deggelmann, M.; Hagenb€uchle, M.; Weber, R. Macromolecules 1992, 25, 1125–1133. (42) Cates, M. E.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869–6892. (43) Caille., A. C. R. Acad. Sci. Paris, B 1972, 891–893. (44) Brotons, G.; Dubois, M.; Belloni, L.; Grillo, I.; Narayanan, T.; Zemb, Th. J. Chem. Phys. 2005, 123, 0247041:18. 7462
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
Langmuir
ARTICLE
(45) Helfrich, W. Z. Naturforsch. 1975, 30c, 841–842. (46) Ricoul, F.; Dubois, M.; Zemb, T.; Plusquellec, D. Eur. Phys. J. B 1998, 4, 333–340. (47) Strey, R. Colloid Polym. Sci. 1994, 272, 1005–1019. (48) Penfold, J.; Staples, E.; Thompson, L.; Tucker, I.; Hines, J.; Thomas, R. K.; Lu, J. R. Langmuir 1995, 11, 2496–2503. (49) Penfold, J.; Staples, E.; Thompson, L.; Tucker, I.; Hines, J.; Thomas, R. K.; Lu, J. R.; Warren, N. J. Phys. Chem. B 1999, 103, 5204–5211. (50) Penfold, J.; Staples, E.; Thompson, L.; Tucker, I. J. Phys. Chem. B 2002, 106, 8891–8897. (51) Penfold, J.; Tucker, I.; Thomas, R. K.; Staples, E.; Schuermann, R. J. Phys. Chem. B 2005, 109, 10760–10770. (52) Patel, T; Ghosh, G.; Aswal, V.; Bahadur, P. Colloid Polym. Sci. 2009, 287, 1175–1181. (53) Penfold, J.; Thomas, R. K.; Dong, C. C.; Tucker, I.; Metcalfe, K.; Golding, S.; Grillo, I. Langmuir 2007, 23, 10140–10149. (54) Tucker, I.; Penfold, J.; Thomas, R. K.; Dong, C. C.; Golding, S.; Gibson, C.; Grillo, I. Langmuir 2010, 26, 10614–10626. (55) Kwon, S. Y.; Kim, M. W. Langmuir 2001, 17, 8016–8023. (56) Kim, S.; Kwon, S. Y.; Moon, J. H.; Kim, M. W. Chem. Phys. Lett. 2008, 464, 82–86. (57) B€averback, P.; Oliveira, C. L.P.; Garamus, V. M.; Varga, I.; Claesson, Per M.; Pedersen, J. S. Langmuir 2009, 25, 7296–7303. (58) Tucker, I.; Penfold, J.; Thomas, R. K.; Grillo, I.; Barker, J. G.; Mildner, D. F. R. Langmuir 2008, 24, 7674–7687. (59) Penfold, J.; Tucker, I.; Green, A.; Grainger, D.; Jones, C.; Ford, G.; Roberts, C.; Hubbard, J.; Petkov, J.; Thomas, R. K.; Grillo, I. Langmuir 2008, 24, 12209–12220. (60) Goon, P.; Das, S.; Clemett, C. J.; Tiddy, G. J. T.; Kumar, V. V. Langmuir 1997, 13, 5577–5582. (61) Parsejian, V. A.; Rand, R. P.; Fuller, N. L. J. Phys. Chem. 1991, 95, 4777–4782. (62) Roux, D.; Safinya, C. R. J. Phys. (Paris) 1989, 49, 307–318. (63) Richetti, P.; Kekicheff, P.; Parker, J. L.; Ninham, D. W. Nature 1990, 346, 252–254. (64) Safinya, C. R.; Sirota, E. B.; Roux, D.; Smith, G. S. Phys. Rev. Lett. 1989, 62, 1134–1137. (65) Salamat, G.; de Vries, R.; Kaler, E. W.; Satija, S.; Sung, L. Langmuir 2000, 16, 102–107. (66) Zou, A.; Hoffmann, H.; Freiberger, N.; Glatter, O. Langmuir 2007, 23, 2977–2984. (67) Schom€acker, R.; Strey, R. J. Phys. Chem. 1994, 98, 3908–3912. (68) Podgornick, R.; Parsegian, V. A. Langmuir 1992, 8, 557–562. (69) Tucker, I.; Penfold, J.; Thomas, R. K.; Grillo, I.; Barker, J. G.; Mildner, D. F. R. Langmuir 2008, 24, 10089–10098. (70) Farago, B.; Gradzielski, M. J. Chem. Phys. 2001, 114, 10105–10122.
7463
dx.doi.org/10.1021/la200874g |Langmuir 2011, 27, 7453–7463
