Growth Behavior, Geometrical Shape, and Second CMC of Micelles

Article pubs.acs.org/Langmuir

Growth Behavior, Geometrical Shape, and Second CMC of Micelles Formed by Cationic Gemini Esterquat Surfactants L. Magnus Bergström,*,† Alireza Tehrani-Bagha,‡ and Gergely Nagy§ †

Department of Chemistry, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden Department of Chemical and Petroleum Engineering, American University of Beirut, Beirut, Lebanon § Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, Villigen PSI, Switzerland ‡

S Supporting Information *

ABSTRACT: Micelles formed by novel gemini esterquat surfactants have been investigated with small-angle neutron scattering (SANS). The growth behavior of the micelles is found to differ conspicuously depending on the length of the gemini surfactant spacer group. The gemini surfactant with a long spacer form rather small triaxial ellipsoidal tablet-shaped micelles that grow weakly with surfactant concentration in the entire range of measured concentrations. Geminis with a short spacer, on the other hand, form weakly growing oblates or tablets at low concentrations that start to grow much more strongly into polydisperse rodlike or wormlike micelles at higher concentrations. The latter behavior is consistent with the presence of a second CMC that marks the transition from the weakly to the strongly growing regime. It is found that the growth behavior in terms of aggregation number as a function of surfactant concentration always appear concave in weakly growing regimes, while switching to convex behavior in strongly growing regimes. As a result, we are able to determine the second CMC of the geminis with short spacer by means of suggesting a rather precise definition of it, located at the point of inflection of the growth curve that corresponds to the transition from concave to convex growth behavior. Our SANS results are rationalized by comparison with the recently developed general micelle model. In particular, this theory is able to explain and reproduce the characteristic appearances of the experimental growth curves, including the presence of a second CMC and the convex strongly growing regime beyond. By means of optimizing the agreement between predictions from the general micelle model and results from SANS experiments, we are able to determine the three bending elasticity constants spontaneous curvature, bending rigidity, and saddle-splay constant for each surfactant.

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frequently studied using time-resolved fluorescence quenching (TRFQ)19 or small-angle scattering techniques.20,21 From such studies, it is usually found that the growth behavior depends strongly on the length of the spacer group. Typical growth behaviors for gemini surfactants, in terms of measurements of the aggregation number N as a function of surfactant concentration csurf, was investigated in detail by Danino et al.,19 using TRFQ for micelles formed by the dimeric surfactant series 12-s-12 with different lengths of the spacer group (s = 3, 4, 5, 6, 8, and 10). It was found that close to their critical micelle concentration (CMC), all these surfactants form rather small micelles irrespective of the length of the spacer. However, micelles formed by geminis with a short spacer (s = 3, 4) were found to grow strongly in size by increasing the surfactant concentration. The rate of growth, in terms of the derivative of aggregation number with respect to surfactant concentration (dN/dcsurf), was clearly seen to decrease with increasing spacer

INTRODUCTION Gemini (or dimeric) surfactants consist of two conventional unimeric surfactants that are covalently linked together with a spacer group.1,2 Gemini surfactants have attracted much attention since 1991 as they self-assemble in bulk and at interfaces at much lower concentration than their monomeric counterparts.2,3 Like unimeric surfactants, gemini surfactants may be anionic,4−6 cationic,7−14 or nonionic,15,16 depending on the charge of the headgroup. Out of these, cationic gemini surfactants are the most common type to be found in the literature as they have typically easier synthesis and purification procedures. In particular, bis-quaternary surfactant, alkanediylα,ω-bis(dodecyldimethylammonium bromide) (CmH2m+1N(CH3)2(CH2)sN(CH3)2CmH2m+1Br2) or in shorter form, m-sm gemini surfactants, have been frequently investigated, where m denotes the number of carbon atoms in the aliphatic hydrocarbon chain of a surfactant tail and s is the number of methylene units in the spacer group.3,17−19 A general phenomenon of surfactant micelles is that they grow in size while increasing the surfactant concentration. The growth behavior of m-s-m cationic gemini surfactants have been © 2015 American Chemical Society

Received: February 26, 2015 Revised: April 1, 2015 Published: April 2, 2015 4644

DOI: 10.1021/acs.langmuir.5b00742 Langmuir 2015, 31, 4644−4653

Article

Langmuir length up to s = 8. Moreover, the appearances of the N versus csurf plots seem to capture some typical features. The surfactants with longer spacer group (s = 5, 6, 8, and 10) grow weakly in the entire range of measured concentrations, where the upper limit ranges between 150 and 250 mM depending on the surfactant. In addition, the N versus csurf curves for these surfactants display an always downward concave appearance with a negative second derivative d2N/dc2surf < 0. On the other hand, the surfactants with a shorter spacer group (s = 3, 4) have a (downward) concave appearance at low surfactant concentrations while switching to a convex (or upward concave) behavior with d2N/dc2surf > 0 at higher concentrations. The transition between the two regimes is characterized by a point of inflection in the N versus csurf curve where the second derivative equals zero (d2N/dc2surf = 0) [cf. Figure 3 in ref 19]. More recently, the geometrical shape of micelles formed by a series of 12-s-12 gemini surfactants (s = 3, 4, 6, 8, 10, and 12) was investigated with small-angle neutron scattering (SANS).21 Micelles formed by geminis with a short spacer group (s = 3 and 4) were observed to be shaped as elongated tablets, and the corresponding data were best fitted with a model for general triaxial ellipsoids with a distinct thickness, width, and length. Micelles formed by surfactants with a longer spacer group (s = 6, 8, 10, and 12) were found to be much smaller in size. Due to the limited range of measured scattering vectors, it was not possible from the SANS data to distinguish between prolate and oblate spheroidal and general triaxial ellipsoidal shapes for the smallest micelles formed by gemini surfactants with a longer spacer group. Nevertheless, due to the rather weak growth behavior, it was argued that these surfactants form oblate rather than prolate spheroidal micelles. The typical behavior where micelles grow weakly at lowsurfactant concentrations and start to grow more strongly at higher surfactant concentrations have also been observed for several unimeric surfactants.22−30 The point of transition from the weakly to the strongly growing regime has been referred to the second critical micelle concentration (second CMC).23 The behavior has usually been reported for pure surfactant systems, but recently it was also reported for the mixed surfactant system hexadecyltrimethylammonium bromide (CTAB)/sodium octlyl sulfate (SOS) studied with small-angle neutron scattering (SANS).31 It was found that pure CTAB micelles as well as mixed micelles with a low fraction of SOS always grow weakly with surfactant concentration while mixed micelles with a mole fraction of SOS equal to or exceeding 0.15 display a Second CMC above which the micelles grow more strongly with surfactant concentration. From a theoretical point of view, the growth behavior of micelles is usually rationalized as spherical micelles growing exclusively in the length direction to form spherocylindrical micelles.32 According to the spherocylindrical micelle model, the aggregation number as a function of surfactant concentration is expected to always be concave. As a result, this model is inconsistent with the strong convex growth behavior above the second CMC as frequently observed for many surfactants, including the gemini surfactants 12-3-12 and 12-4-12. On the other hand, it was recently demonstrated that the general micelle model,33 which assumes that micelles are able to grow with respect to both width and length, may reproduce experimentally observed growth behaviors for virtually any surfactant system.34 The general micelle model is based on thermodynamics of self-assembly combined with bending elasticity theory, and it was demonstrated that the detailed

growth behavior is determined by the three bending elasticity constants spontaneous curvature, bending rigidity, and saddlesplay constant. In the present paper, we investigate the growth behavior of micelles formed by a novel type of gemini surfactants that contain an ester group which is cleavable in alkaline conditions. Gemini esterquat surfactants may be denoted with abbreviations on the form mE2Q-s-Q2Em, and we have studied the three surfactants N,N′-bis(2-(decanoyloxy)ethyl)-N,N,N′,N′tetramethyl-1,3-propanediammonium dibromide (9E2Q-3Q2E9), N,N′-bis(2-(decanoyloxy)ethyl)-N,N,N′,N′-tetramethyl-1,6-hexanediammonium dibromide (9E2Q-6-Q2E9) and N,N′-bis(2-(dodecanoyloxy)ethyl)-N,N,N′,N′-tetramethyl-1, 3propanediammonium dibromide (11E2Q-3-Q2E11). We are able to demonstrate that a second CMC exists for gemini esterquat surfactants with a short spacer group, while the corresponding gemini with a longer spacer lacks a second CMC within the investigated dilute regime. The surfactant growth behaviors are rationalized with the general micelle model, and we are able to determine the various bending elasticity constants for the three surfactants.

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MATERIALS AND METHODS Materials. Decanoyl chloride, dodecanoyl chloride, 2-(N,Ndimethyl)aminoethanol, 1,3-dibromopropane, 1,6-dibromohexane, dichloromethane, acetone, ethanol, diethyl ether, sodium hydrogen carbonate, and magnesium sulfate were all purchased from Sigma-Aldrich. Deuterium oxide (99.8 atom % D) was purchased from Dr. Glaser AG (Basel, Switzerland). The syntheses of monomeric and gemini esterquats are shown in Figure 1. C10/C12 acyl chloride was first reacted with

Figure 1. Chemical structure and synthesis routes for the preparation of decyl and dodecyl esterquat gemini surfactants.

2-(N,N-dimethyl)aminoethanol to get the intermediate ester amine. The gemini esterquat surfactants (9E2Q-3-Q2E9, 9E2Q-6-Q2E9, and 11E2Q-3-Q2E11) were prepared by reacting the amine with the corresponding alkyl dibromide in ethanol (yield > 80%).35−37 More details are provided in the Supporting Information. Experiments. The small-angle neutron scattering (SANS) experiments were carried out at the SANS-II instrument at the Paul Scherrer Instiut (PSI), Switzerland. The measurements were carried out with the two settings combining sample-todetector distance d and neutron wavelength λ (i.e., [d = 1.1 m, λ = 4.5 Å] and [d = 5 m, λ = 4.7 Å], giving a range of scattering vectors 0.012−0.32 Å−1). The wavelength resolution was 10% (full width at half-maximum value). 4645


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Figure 2. Normalized scattering cross section as a function of the scattering vector q for micelles formed by the gemini surfactant 9E2Q-6-Q2E9 (A) and 9E2Q-3-Q2E9 (B) in deuterium oxide at surfactant concentrations 0.5, 1.0, and 3.0 wt %. Symbols represent SANS data and the solid lines represent the best available fits with a model for general ellipsoids. The results of the model fits are given in Table 1. The quality of the fits as measured by χ2 is 1.0 (○), 1.3 (□) and 1.7 (△) for 9E2Q-6-Q2E9 and 1.8 (○), 1.9 (□), and 0.8 (△) for 9E2Q-3-Q2E9.

function of surfactant concentration was measured at 25 °C. Measurements were performed with a CDM 210 conductometer (Radiometer, France), using a water bath with stirring to control the temperature. For each series of measurements, an exact initial volume (10 mL) of pure H2O or D2O was introduced into the vessel, and the specific conductivity was measured. The solution was then titrated with the surfactant solution, and the conductivity was measured 2−3 min after each addition. The concentration at which there was a break on the curve of conductivity versus surfactant concentration was taken as the CMC. Theory. It was recently demonstrated that the behavior of generally shaped triaxial micelles with distinct thickness, width, and length may be rationalized from a theoretical point of view by the general micelle model.33 The general micelle model combines thermodynamics of self-assembly with bending elasticity theory, and the following relation may be deducted that gives the volume fraction ϕmic of surfactants aggregated in triaxial, generally shaped, micelles as a function of the dimensionless half width r33

The samples were kept in quartz cells (Hellma) with path lengths 2 mm at ambient temperature 23 °C. The raw spectra were corrected for background from the solvent, sample cell, and other sources by conventional procedures.38 The SANS data were set to absolute scale units and normalized by means of dividing with the concentration in (g mL−1) giving the unit (mL g−1 cm−1) for the normalized scattering cross section. The latter may be written as dσm(q) 1 dσ(q) ≡ = dΩ cmic dΩ Δρm2 M w P(q)[1 + β(q)(S(q) − 1)]

(1)

for weakly interacting aggregates in a dispersion, where Δρm is the difference in scattering length per unit mass solute between aggregates with a homogeneous core and solvent and Mw is the mass of a single aggregate.39 The model fits of best quality were obtained by a form factor P(q) for either monodisperse triaxial ellipsoids (small micelles) or polydisperse rods with an elliptical cross section (large and considerably polydisperse micelles). Electrostatic interactions between micelles in a rather dilute solution were taken into account using a structure factor S(q) as derived with the rescaled mean spherical approximation (RMSA) by Hansen and Hayter40 in combination with a decoupling approximation.41,42 The structure factor introduces three fitting parameters related to the relative effective charge of the micelles (α = zeff/zid), electrolyte concentration (cel), and concentration of surfactant aggregated in micelles (cmic) (see Table 1 below). The detailed models with form factors are provided in the Supporting Information. The average excess scattering length density per unit mass of solute (i.e., scattering length density divided by density of solute39) for the three surfactants in D2O, Δρm = −5.59 × 1010 cm/g (9E2Q-6-Q2E9), Δρm = −5.47 × 1010 cm/g (9E2Q-3Q2E9), and Δρm = −5.59 × 1010 cm/g (9E2Q-6-Q2E9) were calculated from appropriate molecular volumes and molar weights. The molecular volumes were calculated by combining experimentally obtained partial molar volumes for different chemical species and functional groups.43 More details are provided in the Supporting Information. The critical micelle concentrations (CMC) of the surfactants were determined with conductivity. The conductance as a

ϕmic =

πξ 6e−α ν 2̂

∫0

∞

8r 2 + 6πr + π 2 −δψ (r) − πβr − 2πλr 2 e dr β + 4λr (2)

The general micelle model demonstrates that at least three parameters are necessary to fully describe the behavior of surfactant micelles. In accordance, the three bending elasticity constants44 spontaneous curvature (H0), bending rigidity (kc), and saddle splay constant (k̅c) are able to describe various properties of a micelle.

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RESULTS AND DISCUSSION

Results from SANS Data Analysis. Examples of normalized scattering data, with model fits, for the three gemini esterquat surfactants 9E2Q-6-Q2E9 (long spacer group) and 9E2Q-3-Q2E9 (short spacer group) are shown in Figure 2. Scattering data with model fits for the gemini surfactant 11E2Q-3-Q2E11 are shown in the Supporting Information. Results from the model fitting analysis for all three surfactants are given in Table 1. The aggregation number N was determined by simply dividing the total volume of a micelle, 4646


a

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polydisperse rods a = 17.3 b = 27.3

polydisperse rods

a = 17.2 b = 26.6

1.75% (25.8 mM)

2%

(29.6 mM) a = 17.4 b = 27.8

polydisperse rods

(22.0 mM)

a = 15.6 b = 22.0 c = 26.7 N = 35 α = 0.30 cmic = 52 mM cel = 21 mM 1.50%

a = 15.6 b = 22.1 c = 26.4 N = 35 α = 0.32 cmic = 64 mM cel = 27 mM

4% (60.5 mM)

5% (75.4 mM) ellipsoids

a = 14.8 b = 23.2

a = 14.8 b = 23.5

ellipsoids

polydisperse rods

polydisperse rods

4% (64.0 mM)

(18.4 mM)


ellipsoids

a = 17.8 b = 22.4 c = 103.4 N = 171 α = 0.10 cmic = 45 mM cel = 12 mM 3% (45.3 mM)

ellipsoids

3% (47.9 mM)

a = 17.3 b = 28.6 ⟨Λ⟩ = 130 σL/⟨L⟩ = 0.57 N = 181 α = 0.22 cmic = 9 mM cel = 9 mM

polydisperse rods

The surfactant concentration is given in weight percent (mM in parentheses).

11E2Q-3-Q2E11

9E2Q-6-Q2E11

9E2Q-3-Q2E11

5% (80.0 mM)


ellipsoids

(14.7 mM) a = 20.0 b = 30.2 c = 52.1 N = 117 α = 0.24 cmic = 8 mM cel = 5 mM

ellipsoids

(11.7 mM)

a = 15.6 b = 21.0 c = 26.9 N = 34 α = 0.33 cmic = 26 mM cel = 14 mM 1% 0.80%

ellipsoids


ellipsoids

2% (31.7 mM)


ellipsoids

(8.8 mM)


ellipsoids


ellipsoids

1% (15.9 mM)


ellipsoids

(5.8 mM)

0.20% (2.9 mM) a = 20.2 b = c = 34.5 N = 90 α = 0.09 cmic = 2 mM cel = 0.5 mM

a = 16.3 b = c = 27.6 N = 52 α = 0.11 cmic = 4 mM cel = 5 mM

oblate spheroids

0.25% (4.0 mM)

a = 19.7 b = c = 34.9 N = 90 α = 0.01 cmic = 4 mM cel = 0.3 mM

oblate spheroids

(1.4 mM)


ellipsoids

0.25% (3.8 mM)

oblate spheroids


ellipsoids

0.5% (7.5 mM)

a = 16.8 b = c = 27.8 N = 53 α = 0.15 cmic = 7 mM cel = 4.5 mM

oblate spheroids

0.5% (8.0 mM)

Table 1. Results from Least-Square Model Fitting Analysis of SANS Data. Dimensional Properties (a, b, c and ⟨L⟩) are Given in Units of Ångström (Å)a

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Langmuir Table 2. Properties of the Three Investigated Gemini Surfactantsa surfactant

molar mass (g mol−1)

molecular volume (Å3)

CMC (mM)

second CMC (mM)

kc/kT

k̅c/kT

ξH0

ξ (Å)

9E2Q-6-Q2E9 9E2Q-3-Q2E9 11E2Q-3-Q2E11

730.8 688.7 744.7

1091 1012 1120

2.2 (2.6) 1.7 (2.1) 0.2 (0.3)

− 18 11

2.0 1.0 1.5

0.59 0.65 0.48

15 17 20

a The (first) CMC were determined with conductivity in deuterium oxide D2O (values in parentheses refers to H2O as solvent). The Second CMC was determined from the growth curves as described in the text. The bending elasticity constants were obtained by optimizing the agreement between the general micelle model and experimental results.

as calculated from the geometrical dimensions in Table 1, with the appropriate molecular volume given in Table 2. It is obvious from the magnitudes in scattering intensity just below about q = 0.1 Å−1 that the micelles increase in size with increasing surfactant concentration. The micelle growth upon increasing the surfactant concentration is confirmed by the model fitting results. The SANS data for all measured samples of 9E2Q-6-Q2E9, as well as dilute samples of 9E2Q-3-Q2E9 and 11E2Q-3-Q2E11 (below about the second CMC, see further below) were best fitted with a model for monodisperse triaxial ellipsoids with half axes a < b < c. In accordance, the size of the micelles, in terms of aggregation number, is observed to increase slightly with increasing surfactant concentration for samples that are best fitted with the monodisperse ellipsoid model. For the most diluted samples of 9E2Q-3-Q2E9 and 11E2Q-3-Q2E11, the two larger half axes related to width and length, respectively, become close to one another (b ≈ c), and the corresponding SANS data could be fitted with an oblate spheroidal model. Above a certain surfactant concentration, roughly corresponding to the second CMC (see further below), the micelles formed by gemini surfactants with a short spacer (9E2Q-3Q2E9 and 11E2Q-3-Q2E11) start to grow more strongly as well as becoming considerably polydisperse. As a result, the corresponding SANS data could not be fitted with the model for monodisperse ellipsoids in a satisfactory way, but a model for polydisperse rods with an elliptical cross section must be invoked in order to yield good agreement between model and data. The rather strong repulsive interactions among considerably charged micelles are apparent from the reduction in scattering intensity in the lowest q regime and the shift of the peak in scattering intensity to higher q values in regimes where the micelles grow weakly. The RMSA structure factor invoked with a decoupling approximation results in excellent quality of all model fits, and reasonable order of magnitudes are obtained for the related fitting parameters (α, cmic, and cel). cmic is the molar concentration of surfactants aggregated in micelles, and cel corresponds to the free surfactant concentration in absence of added salt, which means that the sum cmic + cel is expected to be approximately equal to the total surfactant concentration csurf. The decoupling approximation, however, is expected to only be strictly valid for micelles with a low polydispersity. As a consequence, the results for the fitting parameters related to the scattering behavior in the low q regime (α, cmic, cel, N, σL/⟨L⟩ and persistence length) are expected to become less reliable as the micelles formed by 9E2Q-3-Q2E9 and 11E2Q-3-Q2E11 become increasingly more polydisperse at higher surfactant concentrations. For this reason, we have omitted these parameters for the most concentrated samples of 9E2Q-3Q2E9 and 11E2Q-3-Q2E11 in Table 1. Growth Behavior of Micelles. In Figure 3, we have plotted the aggregation number against surfactant concen-

Figure 3. Micelle aggregation number (N) plotted against surfactant molar concentration. Symbols represent experimental data obtained from SANS data analysis for the three gemini surfactants 9E2Q-6Q2E9 (○), 9E2Q-3-Q2E9 (□), and 11E2Q-3-Q2E11 (△). The lines represent theoretical predictions from the general micelle model. Arrows indicate the locations of the critical micelle concentrations (First CMC) as well as the second CMC. The latter quantity is characterized by the appearance of a point of inflection in the growth curves.

tration on a linear scale. The corresponding plot on a logarithmic scale is shown in the Supporting Information. It is seen that micelles formed by the gemini surfactant with longer spacer group (9E2Q-6-Q2E9) are rather small and grow only weakly in the entire range of measured concentrations (up to about 75 mM). The growth behaviors of the two gemini surfactants with a short spacer, however, appear conspicuously different. At low surfactant concentrations, the micelles grow weakly, in similarity to 9E2Q-6-Q2E9, but above a certain concentration the micelles start to grow much more strongly in size. Due to strong intermicellar interactions, we are not able to determine the aggregation numbers for the most concentrated samples of 9E2Q-3-Q2E9 and 11E2Q-3-Q2E11 (see above), but it is clear from the bare appearance of these samples that they become very viscous (in the case of 11E2Q-3-Q2E11 extremely viscous), indicating that the micelles grow strongly in length to form very long wormlike aggregates. The aggregation numbers determined for the always weakly growing surfactant 9E2Q-6-Q2E9 agree very well with recent TRFQ measurements using H2O as solvent.45 However, the growth behavior of 9E2Q-3-Q2E9, with a short spacer group, differ considerably between SANS and TRFQ.45 In particular, the strongly growing regime at higher concentrations evident in our SANS measurements (in D2O) is not observed with TRFQ (in H2O), indicating that the growth behaviors of gemini esterquat surfactants may be different depending on whether H2O or D2O is used as solvent. However, the expected concave behavior in the N versus csurf curves, as determined by TRFQ, is clearly seen at low surfactant concentrations for both 9E2Q-64648


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Langmuir Q2E9 and 9E2Q-3-Q2E9.45 As already mentioned in the introduction, a point of inflection as N obtained by TRFQ is plotted against csurf, indicating the presence of a second CMC, has been observed for the gemini surfactants 12-3-12 and 12-412.19 The behavior where micelles grow weakly at low concentrations, while rather abruptly start to grow more strongly at higher concentrations, has been reported for several surfactant systems, and the concentration that marks the transition from the weakly to the strongly growing regime is usually denoted the second critical micelle concentration (second CMC).22−30 In some recent works of ours, we have demonstrated that this characteristic behavior of weakly growing micelles at low surfactant concentrations, followed by a strongly growing regime above the second CMC, agrees very well with predictions deduced from the general micelle model.31,34 It was demonstrated that the general micelle model could explain the experimental growth curves by means of fitting aggregation number versus surfactant concentration data with respect to the three bending elasticity constants spontaneous curvature (H0), bending rigidity (kc), and saddlesplay constant (k̅c). The growth behaviors as predicted from the general micelle model are shown in Figure 3 for the three gemini esterquat surfactants. The bending elasticity constants as obtained by means of optimizing the theoretical curves with respect to experimentally determined aggregation numbers are provided in Table 2. It is evident that the general micelle model is able to capture the weak growth behavior at low surfactant concentrations as well as the abrupt transition to a strongly growing regime above the second CMC. The micelles are seen to increase in size in the entire range of concentrations and the first derivative of N with respect to csurf is always found to be positive. The rate of changing the aggregation number is, on the other hand, found to differ in a characteristic manner depending on surfactant and surfactant concentration. The always weakly growing micelles formed by the gemini surfactant with a longer spacer group display an N versus csurf function that is always (downward) concave, with a negative second derivative d2N/dc2surf < 0 in the entire range of investigated concentrations. The two geminis with short spacer group, on the other hand, form micelles with the N versus csurf function appearing (downward) concave at low surfactant concentrations, with a negative second derivative, while becoming convex at higher concentrations with a positive second derivative. This particular behavior suggests a rather precise definition of the second CMC, namely, at the point of inflection at the transition from the concave to the convex region where d2N/dc2surf = 0. This definition gives a second CMC for the two gemini esterquat surfactants with short spacer group equal to 11 mM (11E2Q-3-Q2E11) and 18 mM (9E2Q3-Q2E9), respectively. The gemini surfactant with a longer spacer group (9E2Q-6-Q2E9) lacks a second CMC in the investigated region of surfactant concentrations. In Figure 3, we have also indicated the conventional (first) CMC for the three surfactants as measured with conductivity. It is interesting to note that the conventional spherocylindrical micelle model, that assumes micelles being able to grow only in the length direction, predicts an always concave growth behavior (negative second derivative) and is neither able to predict the convex growth behavior at higher concentrations nor the existence of a second CMC.34 The growth behaviors of gemini esterquat surfactants, and its dependence on spacer

group, very much resembles the behaviors previously reported for the common 12-s-12 surfactant series.19 The influence of the bending elasticity constants on the growth behavior of micelles has been extensively discussed in a recent paper by ours.34 It was demonstrated that decreasing spontaneous curvature H0 mainly has the effect of shifting the curve vertically upward along the ordinate, whereas the curve is shifted horizontally along the abscissa as the saddle-splay constant is changed. As a result, the second CMC is found to decrease with increasing k̅c. The bending rigidity kc has a certain effect on the position of the second CMC but mainly determines the shape of the growth curve. In accordance, we have been able to determine kc for all three gemini esterquat surfactants, including 9E2Q-6-Q2E9 that lacks a second CMC. The bending rigidity determines the slope of the approximately linear growth curve in a log−log plot and the magnitude of the slope increases with decreasing kc. On the other hand, we are able to determine all bending elasticity constants for micelles formed by geminis with a short spacer that display a Second CMC, whereas only a maximum value of k̅c and a minimum value of H0 may be determined for the gemini with longer spacer group. From the results shown in Table 2 for 9E2Q-6-Q2E9 and 9E2Q-3-Q2E9, we may conclude that the effect of increasing the length of the spacer group from s = 3 to s = 6 is to increase kc and to decrease k̅c. Likewise, by comparing the growth behaviors of micelles formed by 9E2Q-3-Q2E9 and 11E2Q-3-Q2E11, we may conclude that kc increases, whereas H0 and k̅c decreases as the length of the surfactant tails is increased. The thickness of a single surfactant layer in the micelles was set to ξ = 15, 17, and 20 Å for 9E2Q-6-Q2E9, 9E2Q-3-Q2E9, and 11E2Q-3-Q2E11, respectively, when optimizing the growth curves with respect to the three bending elasticity constants. These values were chosen as they approximately correspond to the half axis related to thickness (a) as determined from our SANS measurements [cf. Table 1]. In a recent study,21 we demonstrated that surface charges become significantly nonuniformly distributed over the interface of a micelle formed by 12-s-12 gemini surfactants with a short spacer group (s ≤ 5). As the length of the spacer reaches s = 6, however, the surface charge may become more or less evenly distributed over the micelle interface. This may explain the considerable difference in growth behaviors between gemini surfactants with short and long spacer groups, respectively, and the large impact on the two bending constants, kc and k̅c. A nonuniform charge distribution may favor a more geometrically heterogeneous structure, where the curvature may differ significantly over the micelle interface. As a result, the surface charge density may become much higher in the more curved parts of a micelle such as the end-caps of elongated micelles. This is expected to lower the bending rigidity kc in agreement with our present observations.46,47 Moreover, a nonuniform charge distribution may implicate an effect due to anisotropy in surfactant interactions where different curvatures are favored in different directions. Such a behavior is expected to be favored by large and possibly positive values of the saddle-splay constant k̅c. It has been demonstrated that mean-field effects that lack an orientational dependence may contribute with a negative value to k̅c. On the other hand, a saddle-shaped interface, which is favored by positive values of k̅c, is characterized by a positive curvature in one direction and a negative curvature in the perpendicular direction. 4649


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Langmuir There exists an important expression, derived almost 50 years ago by Hall and Pethica48 that relates the detailed growth behavior with polydispersity of the micelles, ⎛ σN ⎞ ⎜ ⎟= ⎝ ⟨N ⟩ ⎠

d ln⟨N ⟩ d ln csurf

(3)

In accordance with eq 3, micelles are expected to be comparatively monodisperse as long as they grow weakly (d ln N/d ln csurf is small), whereas micelles displaying a second CMC are predicted to become considerably polydisperse at higher concentrations in the strongly growing regime (d ln N/d ln csurf is large). This is exactly what we observe in our present SANS study of gemini esterquat surfactants, where data are consistent with a model for monodisperse ellipsoids in weakly growing regimes, whereas polydispersity must be invoked into the model in order to generate good agreement between data and model at concentrations above the second CMC. Correlation between Growth Behavior and Geometrical Shape. The general micelle model does not only predict the detailed growth behavior in micellar systems. The general micelle model was primarily developed to account for the triaxial tablet-shape of micelles as observed from SANS experiments.31,49−53 This means that we are able to compare theoretical predictions of micellar dimensions related to thickness, width and length, and how they are influenced by surfactant concentration, with experiments. In Figure 4, we have plotted the half axes related to thickness (a), width (b), and length (c) for 9E2Q-6-Q2E9 (gemini with

Figure 5. Thickness (solid line), average width (dashed line), and average length (dotted line) of micelles formed by the gemini surfactant 9E2Q-6-Q2E9 plotted against volume fraction of surfactants aggregated in micelles. The lines represent theoretical predictions using the general micelle model with the bending elasticity constants H0, kc, and k̅c set to their optimized values given in Table 2.

weakly growing micelles formed by 9E2Q-6-Q2E9 is expected to slightly increase with increasing surfactant concentration. A slight increase of half axes b and c are also indicated from the experimental results shown in Figure 4 and Table 1. However, due to the larger statistical errors of our fitting results for b and c, as compared to a, these particular trends cannot be unambiguously concluded from our experimental results. The corresponding behavior for the gemini surfactants with short spacer appears rather differently [cf. Figure 6]. At low

Figure 4. Half axes related to thickness (□), width (○) and length (△) of micelles formed by the gemini surfactant 9E2Q-6-Q2E9, as determined by the SANS data analysis, plotted against the surfactant concentration.

Figure 6. Half axes related to thickness (□), width (○), and length (△) of micelles formed by the gemini surfactant 9E2Q-3-Q2E9, as determined by the SANS data analysis, plotted against the surfactant concentration.

long spacer) as obtained from the SANS data analysis versus surfactant concentration in terms of weight fraction. In Figure 5, the corresponding average micelle dimensions plotted against volume fraction of surfactant aggregated in micelles, as predicted by the general micelle model for the optimized growth behavior displayed in Figure 3, are shown. The concentrations in terms of weight and volume fraction are virtually identical; the relative difference is always less than 2% for the investigated samples. The thickness is found to be rather constant with respect to concentration and equal to a = 15 Å, and in the model, we have set the monolayer thickness ξ = 15 Å, giving a constant thickness of the micelles equal to 2ξ = 30 Å. According to the theory both width and length of the always

surfactant concentrations, the micelles are small and grow weakly. According to the SANS measurements, the half axes related to width and length appear to be close to one another and the corresponding data could be fitted with a model for oblate spheroids. At higher concentrations, above about the second CMC, the length of the micelles is found to increase strongly, in a similar way as the aggregation number does. The width, however, is seen to decrease with increasing surfactant concentration. A comparison with predictions from the general micelle model shows similar trends as observed from the SANS experiments (i.e., both width and length increases slightly at 4650


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11E2Q-3-Q2E11 and 9E2Q-3-Q2E9, respectively. The gemini surfactant with long spacer (9E2Q-6-Q2E9) grows weakly in the entire range of concentrations with an always concave N vs csurf curve and, as a consequence, it lacks a second CMC within the range of measured concentrations. From SANS data analysis, we are able to determine the detailed geometrical shape of the micelles and the correlation between geometry and growth behavior. Triaxial tablet-shaped micelles formed by the gemini with longer spacer (9E2Q-6Q2E9) grow weakly with respect to both width and length as the size of the micelles slightly increases. In conspicuous contrast to this behavior, the length of micelles formed by geminis with a short spacer group increases strongly, while the width decreases, as the micelles grow strongly above the second CMC. Our results as to growth behavior and geometrical shape of micelles are rationalized from the recently developed general micelle model. As a result, we are able to optimize the agreement between theory and our experimentally obtained N versus csurf curves and to determine the three bending elasticity constants spontaneous curvature (H0), bending rigidity (kc), and saddle splay constant (k̅c). It is found that and kc of the gemini esterquat surfactants increases, while k̅c decreases, as the length of the spacer group increases from 3 to 6 methylene units. Likewise, H0 and k̅c decreases while kc increases as the lengths of the tails are increased for gemini surfactants with a short spacer group (3 methylene units). The correlation between geometrical shape and growth behavior as predicted from the general micelle model agrees very well with our experimental observations that both width and length increases slightly in weakly growing regimes, whereas the length increases and the width decreases in strongly growing regimes above the second CMC.

low concentrations below the second CMC, whereas the length increases while the width decreases at high concentrations above the second CMC) [cf. Figures 6 and 7].

Figure 7. Thickness (solid line), average width (dashed line), and average length (dotted line) of micelles formed by the gemini surfactant 9E2Q-3-Q2E9 plotted against volume fraction of surfactants aggregated in micelles. The lines represent theoretical predictions using the general micelle model with the bending elasticity constants H0, kc, and k̅c set to their optimized values given in Table 2.

This particular correlation between growth behavior and geometrical shape of surfactant micelles, where both width and length are found to slightly increase in the weakly growing regime below the second CMC while the length increases and the width decreases in the strongly growing regime above the second CMC seems to be a general phenomenon. In accordance, this particular correlation between growth behavior and geometrical shape of surfactant micelles was recently observed for micelles formed in (CTAB-rich) mixtures of the cationic surfactant CTAB and the anionic surfactant SOS.31

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ASSOCIATED CONTENT

S Supporting Information *

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Synthesis of gemini esterquat surfactants, models employed in the least-square fitting data analysis. Small-angle neutron scattering (SANS) data with model fits, general micelle model, and growth behavior of micelles. This material is available free of charge via the Internet at http://pubs.acs.org.

CONCLUSIONS The growth behavior and geometrical shape of micelles formed by three novel cationic gemini esterquat surfactants have been investigated with SANS. Gemini surfactant with longer spacer group (9E2Q-6-Q2E9) is found to form rather small micelles that grow weakly in terms of aggregation number from N = 26 to 35 as the surfactant concentration is raised from 0.25 to 5.0 wt % (4−75 mM). Micelles formed by gemini surfactants with shorter spacer group (9E2Q-3-Q2E9 and 11E2Q-3-Q2E11) show a conspicuously different growth behavior, in accordance to which the micelles grow weakly at low surfactant concentrations while beginning to grow more strongly above a certain concentration corresponding to the second CMC. Eventually, the latter two surfactants form rather polydisperse long rodlike or wormlike micelles. We demonstrate that the growth curves in terms of aggregation number (N) plotted against surfactant concentration (csurf) always appear concave in the weakly growing regimes whereas turning convex in strongly growing regimes. From this characteristic appearance, we suggest a strict definition of the second CMC as the point of inflection (d2N/dc2surf = 0) that marks the transition from weakly to strongly growing micelles. As a result, we are able to determine the second CMC in deuterium oxide for the gemini esterquat surfactants with short spacer group to 11 and 18 mM for

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +46 8 790 99 21. Fax: +46 8 20 82 84. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Paul Scherrer Institut (PSI) is acknowledged for allocated SANS beam time (Proposal 20120660).

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REFERENCES

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Growth Behavior, Geometrical Shape, and Second CMC of Micelles

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