Langmuir 1998, 14, 4251-4260
4251
Behavior of Soap Films Stabilized by a Cationic Dimeric Surfactant A. Espert,† R. v. Klitzing,‡ P. Poulin,† A. Colin,*,† R. Zana,§ and D. Langevin† Centre de Recherche Paul Pascal, Av. A. Schweitzer, 33600 Pessac, France, Institut fuˆ r Physikalische und Theoretische Chemie, Strasse des 17 Juni 112, D-10632 Berlin, Germany, and Institut Charles Sadron, 6 rue Boussingault, 67083 Strasbourg Cedex, France Received January 23, 1998. In Final Form: May 15, 1998 We report a study on thin liquid films made of a cationic dimeric surfactant referred to as 12-2-12. This kind of surfactant enables one to form charged wormlike micelles whereas classical systems such as CTAB or CPClO3 require added salt to form only screened wormlike micelles. The disjoining pressure has been measured as a function of film thickness at various surfactant and salt concentrations. In a dilute surfactant regime, we observed a stable common black film which undergoes a transition to a Newton black film by addition of salt. This behavior, classical with anionic surfactant, is shown for the first time with a cationic surfactant. A comparison with the monomeric surfactant DTAB is presented showing the important role of the twin structure on film stability. In the concentrated regime or overlap regime, pressure oscillations have been measured. They correspond to a structuring effect in the film. The number of oscillations increases with c, the concentration, whereas the period decreases as c-1/2. By comparison with the theory developed for charged chains, we propose to relate the observed stratification to the correlation length of semidilute solutions. SANS experiments have been performed to determine the peak position dependence on concentration and temperature.
Introduction Foams or emulsions are important metastable systems that are obtained by dispersing two immiscible fluids in the presence of surfactants. Their stability is related to the lifetime of the individual thin films that separate the two phases. Addition of appropriate surfactants allows the film lifetime to be increased from few seconds to years. Thus, a great deal of effort has been spent studying the influence of the molecular surfactant structure on the film stability. Hence, the understanding of such relationships stimulates the synthesis and the design of new molecules. The aim of this work is to quantify the interactions in thin liquid films stabilized by a new class of cationic surfactant referred to as 12-2-12 (ethanediyl-1,2-bis dodecyldimethylammonium bromide) and to analyze the influence of the twin structure of the surfactant on the soap film behavior. This double headed surfactant is formed by two single DDAB (dodecyldimethylammonium bromide) chains linked by a hydrocarbon spacer at the level of the two headgroups. Such surfactant at low concentrations forms micellar solutions as monomeric surfactant. However, when the surfactant concentration is increased, the DTAB and the 12-2-12 compounds exhibit different phase diagrams. The self-assembly of surfactant molecules or the aggregate formation (such as spherical micelles, bilayers, and other varied structures) depends strongly on the interactions between the surfactant molecules. For charged chains the aggregate shape is determined by the balance between the electrostatic repulsion between the polar parts of the molecules and the steric repulsion between the hydrophobic chains. For a double chain surfactant like the 12-2-12, the steric repulsion between the side chains becomes larger than for the monomeric surfactant. As a result DTAB forms spherical micelles in salt free solutions whereas 12-2-12 †
Centre de Recherche Paul Pascal. Institut fu¨r Physikalische und Theoretische Chemie. § Institut Charles Sadron. ‡
forms threadlike and entangled (above a critical concentration c*) micelles.1 In opposition to other systems, such as CPClO3 or CTAB, the wormlike micelle formation do not require added salt to favor the steric repulsion in the delicate balance described above. A theoretical explanation of charged micelles growth has been recently proposed by MacKintosh and co-workers.2,3 The growth process involves two opposite contributions to the scission energy of a micelle. The electrostatic repulsive energy Ee of the surface charges supports the breaking of micelles whereas the end cap energy Ec favors the micelle growth (Ec is the energy required to create two end caps). The minimization of the total free energy with respect to surfactant concentration leads to distinguish three different regimes: a dilute regime (c < c*) where the size growth is weak, a semidilute regime (c > c*) where a fast increase of micelle size takes place, and a concentrated regime. Due to a charged wormlike structure, a polyelectrolyte-like behavior could be expected. Recently, oscillatory structuring forces have been measured in polyelectrolyte solutions in the semidilute regime.4-6 From the theory for polyelectrolyte solutions7 and experimental results, the authors have demonstrated that the experimental oscillatory periods are related to the mesh size or the correlation length of the semidilute polyelectrolyte solutions. The new 12-2-12 dimeric surfactant and others m-s-m (m and s being the carbon numbers of the alkyl chains and of the alkanediyl spacer, respectively) have been the subject of recent studies which report on rheological and (1) Zana, R.; Talmon, Y. Nature 1993, 362, 228-230. (2) Mackintosh, F. C.; Safran, S. A.; Pincus, P. A. Europhys. Lett. 1990, 12, 697-702. (3) Safran, S. A.; Pincus, P. A.; Cates, M. E.; Mackintosh, F. C. J. Phys. 1990, 51, 503-510. (4) Bergeron, V.; Langevin, D.; Asnacios, A. Langmuir 1996, 12, 1550. (5) Asnacios, A.; Espert, A.; Colin, A.; Langevin, D. Phys. Rev. Lett. 1997, 78, 4974-4977. (6) Milling, A. J. J. Phys. Chem. 1996, 100, 8986-8993. (7) Barrat, J. L..; Joanny, J. F. Adv. Chem. Phys. 1996, 94.
S0743-7463(98)00095-X CCC: $15.00 © 1998 American Chemical Society Published on Web 07/03/1998
4252 Langmuir, Vol. 14, No. 15, 1998
air-water interface behaviors.8-10 It was shown that dimeric surfactants can exhibit strongly different behaviors from the monomeric ones. To quantify the lifetime and the stability of liquid films stabilized by dimeric surfactant, we have investigated the interactions which take place when the dimeric surfactant solutions are confined between two air-water interfaces. The interactions in thin liquid films are directly related to the disjoining pressure (πd), first introduced by Derjaguin and Obuchov.11 πd is defined as the excess pressure acting normal to a flat film interface which results from the interactions between the two adsorbed layers. As defined, the disjoining pressure is a function of the film thickness and can be either positive or negative (conjoining pressure). The measurements of πd is critical if one is to understand the delicate balance of surface interactions that governs emulsions and foams stability. The first disjoining pressure measurements on a single soap film were performed in 1966 by Mysels and Jones12 on an experimental setup now referred to as a thin film balance.13 Over the years, this setup enabled researchers to investigate forces in soaps films made from monomeric anionic, non ionic, and cationic surfactants.14-17 In the first part of this paper, we report disjoining pressure measurements of dimeric surfactant in the dilute regime (as defined below) with and without added electrolyte. A comparison between the new dimeric surfactant and DTAB (dodecyltrimethylammonium bromide) is presented. Striking differences between DTAB and 12-2-12 foam film behaviors are observed. In contrast to pure DTAB, the 12-2-12 surfactant enables to form very stable films even in the presence of electrolyte. Ultrathin Newton Black films have been evidenced for the first time for cationic systems. This new behavior is linked to differences in physical properties of the surfactant layers. The second part is focused on the forces in the 12-2-12 concentrated or semidilute regime as defined by Kern and co-workers18 from viscosity measurements or by Narayanan and co-workers from self-diffusion measurements19 (c > c*). Pressure oscillations have been measured in this regime. The number of oscillations increases with c, the concentration, whereas the period decreases as c-1/2. Such oscillations arise from specific structuration of wormlike micelles. By comparison with theory developed for charged chains, we propose to relate the observed stratification to the correlation length of semidilute charged solutions. To support this explanation, small angle neutron scattering (SANS) studies have been performed at various temperatures. A pronounced peak in the structure factor has been found demonstrating the existence of a well-defined characteristic length in the system. This characteristic length is close to the jump (8) Zana, R.; Benrraou, M.; Rueff, R. Langmuir 1991, 7, 1072-1075. (9) Schmitt, V.; Schosseler, F.; Lequeux, F. Europhys. Lett. 1995, 30, 31-36. (10) Alami, E.; Beinert, G.; Marie, P.; Zana, R. Langmuir 1993, 9, 1465-1467. (11) Derjaguin, B. V.; Obuchov, E. Acta Physiochim. USSR 1936, 5, 1. (12) Mysels, K.; Jones, M. N. Discuss. Faraday Soc. 1966, 42, 42-50. (13) Claesson, P.; Ederth, T.; Bergeron, V.; Rutland, M. Surface Force Techniques; Marcel Dekker: New York, 1996. (14) Exerowa, D.; Kolarov, T.; Kristov, K. H. R. Colloids Surf. 1987, 22, 171-185. (15) Kolarov, T.; Cohen, R.; Exerowa; D. Colloids Surf. 1989, 42, 49. (16) Bergeron, V.; Radke, C. J. Langmuir 1992, 8, 3020-3026. (17) Bergeron, V. Langmuir 1997, 13, 3474-3482. (18) Kern, F.; Lequeux, F.; Zana, R.; Candau, S. J. Langmuir 1994, 10, 1714-1723. (19) Narayanan, J.; Urbach, W.; Langevin, D.; Manohar, C.; Zana, R.; Submitted for publication in Phys. Rev. Lett.
Espert et al.
period measured with the thin film balance, confirming the origin of the disjoining pressure oscillations. Experimental Section 1. Disjoining Pressure Isotherms. To quantify the thin film forces by measuring the disjoining pressure isotherms, a modified version of the porous plate technique first developed by Mysels and Jones12 has been realized. The modified version includes some improvements made by several authors20,21 and ourselves.22 A thick liquid lens is formed in the center of a small hole drilled in a porous glass disk fused to a capillary tube. The disk is enclosed in a 200 cm3 hermetically sealed Plexiglas box, with the capillary tube exposed to a constant reference pressure. Under the effect of a constant pressure difference ∆P between the box and the reference, the liquid drains and a flat horizontal liquid film is formed. The film can be stabilized at a thickness h if the surface force per area unit balances the pressure difference (∆P) applied. To prevent evaporation from the film (e.g. to keep 100% degree of humidity), an excess of solution is located under the porous glass disk during the experiments. The temperature control is activated to 22 or 37 °C (our experimental temperatures), and several hours are needed to reach the equilibrium. Our experimental setup enables one to measure simultaneously the equilibrium thickness of the film and its disjoining pressure under a constant pressure applied in the box. The film thicknesses are determined by an interferometric method developed by Sheludko.23 Heat-filtered white light from an Oriel 200 W Hg-Xe arc lamp is conducted via a fiber optic cable to a specially reflected light microscope fitted with two T50-R50 beam splitters (cf. Figure 1a). After reflection on the two interfaces at normal incidence, the light passes through the second beam splitter where it is transmitted both to a digital Thomson control video camera and to a fiber optic probe located at the top of the microscope. The reflected light is filtered at a 547 nm wavelength to analyze the intensity and to measure the film thickness by eq 1 derived by Sheludko and Platikanov,24,25
hf )
λ (2πn ) arcsin[∆/1 + (4R/(1 - R) (1 - ∆))] 2
1/2
(1)
where ∆ ) (I - Imin)/(Imax - Imin), hf is the film thickness calculated assuming a homogeneous refractive index n equal to the bulk value, R is defined by R ) [(n - 1)/(n + 1)]2, λ is the wavelength of the filter located before the photomultiplier, and I is the intensity of reflected light. The pressure in the cell is modified to form various films and to provide the interference maximum (Imax) and minimum (Imin) needed in the thickness determination. Notice that the Imin value corresponds to the reflective intensity when the film is broken (Imin is only due to the light noise of our setup). For very stable films, like 12-2-12, a jet of air is blown on the film by a specially mobile handle that allows us to break the film. A three-layers model is used for the Newton Black film thickness determination to take into account the refractive index of surfactant layer at each interface. This model enables one to provide a better film thickness determination including the surfactant tails contribution and its effect on the refractive index. For thicker film (more than 10 nm), eq 1 leads to less than a 5% mistake in thickness values by comparison with the three-layers model. We then use only eq 1 for the description of Common Black film. Once the interference extremes are defined, a constant capillary pressure is applied in the experiment box and kept constant thanks to a syringe pump and a computer during the measurement. The intensity reflected by the film is recorded on a strip chart recorder and a multimeter until it reaches the equilibrium value. Repeating this procedure several times by increasing or decreasing the applied pressure allows us to obtain the entire “static” disjoining pressure isotherm. The “static” (20) Exerowa, D.; Sheludko, A. Chim.-phys. 1971, 24, 47-50. (21) Bergeron, V. Thesis, University Of California, Berkeley, 1993. (22) Espert, A. Unpublished results. (23) Sheludko, A. Adv. Colloid Interface Sci. 1967, 1, 391-464. (24) Sheludko, A.; Platikanov, D. Kolloid Z. 1961, 175, 150-158. (25) Sheludko, A. Proc. K. Ned. Akad. Wet. Ser B 1962, 97.
Behavior of Soap Films
Langmuir, Vol. 14, No. 15, 1998 4253 the film radius (e.g. πdeq) is kept constant, and the reflected intensity is recorded vs the time, the disjoining pressure πd(h,t) can be measured from the Stefan-Reynolds drainage equation eq 4, assuming two immobile plane parallel interfaces,
2h3 dh )(πdeq - πd(h)) dt 3ηbRf2
Figure 1. (a) Schematic view of the experimental setup referred to as thin film balance (TFB) (b) Film support: a hole drilled in a porous medium fused to a capillary tube. The disjoining pressure is evaluated by the liquid height in the capillary tube and by the surface tension using eq 2. disjoining pressure is determined from eq 2 (cf. Figure 1b), where
πd ) ∆P - Fghc + (2γ/rcap)
(2)
hc is the liquid height in the capillary tube above the film position, rcap is the capillary tube radius, γ is the surface tension, F is the liquid density, and g is the gravity constant. For very low disjoining pressure around 30 Pa, the disjoining pressure uncertitude becomes too large due to the determination of hc. Instead of eq 2, πdeq can be calculated from the ratio of the film radius to the hole radius, assuming a complete wetting between the film and the porous medium, by using eq 3, where
πdeq ) 2γRw/(Rw2 - Rf2)
(3)
Rw and Rf are respectively the hole and film radius and γ is the surface tension. The available pressure range goes from 20 Pa to 50 kPa. The maximum imposed capillary pressure πdmax must not exceed the entry pressure for the porous disk. Therefore, disks with smaller pores are required for higher capillary pressure. The minimum value referred to as πdmin depends on the hole shape (e.g. its thickness and its radius) drilled in the porous medium. Some examples of πdmin values (approximately around 30 Pa) are available in the literature.21 For low pressure range, an alternative method is used15 for disjoining pressure isotherms measurements referred to as a “dynamic” method.26 This method is often used when stepwise thinning and/or oscillatory structuring effects are observed. If
(4)
where ηb is the bulk viscosity. The experimental thinning curve provides the disjoining pressure πd(h,t) in the film until it reaches the last value πdeq equal to the same as the one determined by eq 3. The comparison between static and dynamic for multimicellar concentration data leads to a good agreement between the two methods as shown in ref 16, concluding that the film seems to remain plane parallel with no slip surfaces for the thickness range analyzed. One of the very important point is to note that the time scale for thinning can be long enough to establish equilibrium of the surfactant structures that lead to the thickness transitions. Some experimental details are available in the literature21 and also in the Ivanov and Dimitrov review.27 In this experimental work, two various pore sizes (d) are used, referred to as P2 (40 µm < d < 90 µm) for the dynamic method and P4 (10 µm < d < 20 µm) for the static method. 2. Surface Tension Experiments. Experiments were performed at 22 ( 1 °C (room temperature). Measurements were carried out in a Teflon trough housed in a special Plexiglas box with an opening for the tensiometer. The surface tension was measured with an open-frame version of the Wilhelmy plate allowing us to avoid the wetting problems of a classical full plate.28 The rectangular open frame, made from a 0.19 mm diameter platinum wire, was attached to a force transducer (HBM Q11) mounted on a motor allowing it to be drawn away from the surface at a controlled constant rate. The equilibrium surface tension is quickly reached for the more concentrated solutions (close to the cmc) whereas a slightly longer time (around 10 min) is required in the very dilute part. 3. SANS Experiments. SANS data have been obtained on the PAXY spectrometer at the Laboratoire Leon Brillouin (LLB) at Saclay (France). The XY detector of the PAXY spectrometer is used with an incident neutron wavelength of λ )10 Å and a sample-detector distance of D ) 2.84 m. This experimental setup corresponds to wavevector q in the range 0.01 < q (Å-1) < 0.08. Data treatment proceeds through the usual steps, involving electronic noise and incoherent background subtraction as well as normalization by the intensity scattered from 2 mm D2O corrected by the intensity scattered from the empty cell. Data acquisition was performed over 20 min for each sample. Various spectra were recorded as a function of the massic surfactant concentration (between 2% and 7%) and also of temperature (from 22 to 52 °C). 4. Materials. The surfactant used in this study was synthesized and purified as described in ref 15. The solubilized samples were prepared using only ultrapure water from a Millipore-Milli-Q system. The other surfactant (dodecyltrimethylammonium bromide from Aldrich) is recrystallized four times by classical method before use (2 g of DTAB, 10 mL of ethyl acetate, 1 mL of ethyl alcohol). NaCl (supplied by Fluka) was used as received with a minimum 99% degree of purity.
Results and Discussion 1. Dilute Regime. Several attempts have been made to measure disjoining pressure isotherms with four times recrystallized DTAB solutions. We have found like Bergeron recently17 that it was practically impossible to generate stable films from DTAB solutions at the critical micellar concentration (cmcDTAB ) 15 mM). (26) Sheludko, A.; Exerowa, D. Kolloid Z. 1960, 168, 24. (27) Ivanov, I. B.; Dimitrov, D. S. Thin Liquid Films; Marcel Dekker: New York, 1988; Vol 29, p 418. (28) Mann, E. K. Thesis, University Of Paris VI, Paris, 1992.
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Espert et al.
πelec(h) ) G(Ψ0) exp(-κh)
( [
G(Ψ0) ) 432c12-2-12kT tanh2
(7)
])
1 2eφ + 1 ln ; 4 3 φ)
∑i zi2ci ) 24πlBc12-2-12
κ2 ) 4πlB
σ02 ) 20kT( Figure 2. Disjoining pressure (Pa) profile measured for a dilute surfactant concentration. c12- 2-12 ) 0.814 mM. The continuous line is the best fit using classical Debye-Hu¨ckel model for the electrostatic part in DLVO theory.30 The theoretical Debye length is κth-1 ) 6.25 nm; the experimental Debye length is κexp-1 ) 6.71 nm.
Moreover, foam formation by shaking is clearly impossible from DTAB solutions whereas a very stable one is made with 12-2-12 solutions even in a very dilute regime (c < 0.1 mM). Figure 2 shows the disjoining pressure isotherm measured for a 12-2-12 solution with a 0.05% (0.814 mM) massic fraction concentration. This concentration corresponds to the cmc.8 Data added to foam observations show that the chemical modifications of the molecule greatly enhance the stability of a single soap film as compared to the DTAB surfactant. Figure 2 reveals a classical Common Black film (CBF) which can be also obtained with classical surfactant like TTAB29 or SDS (sodium dodecyl sulfate).16 Ultrathin Newton Black films are never observed even at the maximum applied pressure of 10 kPa, the highest experimental limit where a homogeneous thickness can be still measured. We have measured an exponential decay of πd as a function of the thickness over a large thickness range. Such behavior is commonly observed in Common Black soap films. DLVO theory can be used to account for the forces that governs the stability of CBF. This theory combines two kinds of interactions: electrostatic double layers repulsive forces which contribute to stabilize the film and attractive van der Waals dispersion forces.30
πd(h) ) πvdW(h) + πelec(h)
(5)
The attractive van der Waals force is given by the following relation:
πvdW(h) ) -AH/12πh3
(6)
Here AH is the nonretarded Hamaker constant for two infinite air media interacting across a water medium (AH ) 3.7 × 10-20 J). The repulsive double layer pressure is directly obtained from the Poisson-Boltzmann equation using the weak overlap approximation assuming constant potential boundary conditions30,31 for a 2:1 electrolyte (29) Espert, A.; Richetti, P.; Mondain-Monval, O.; Colin, A. Unpublished results. (30) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: Orlando, FL, 1985. (31) Derjaguin, B. V.; Churaev, N. V.; Muller, V. M. Surface Forces; Plenum Publishing Corporation: New York, 1987.
∑i c0,i - ∑i cm,i)
eΨ0 kT (8) (9)
where ψ0 is the surface potential, c12-2-12 is the surfactant concentration, co,i are the ionic species concentrations at the surface, cm,i are the ionic species concentrations in the film midplane, lb is the Bjerrum length, and κ-1 is the Debye length, which quantifies the range of electrostatic forces. The solid line in the figure corresponds to a fit using DLVO theory imposing constant potential boundary conditions. In this respect, the surface potential is directly evaluated from the G function given by the fit prefactor. The experimental Ψ0 can be also determined by numerical results presented in Figure 12.11 of ref 30. This evaluated value is close to the one calculated from eq 7 and justifies the weak overlap approximation use. The surface charge or apparent charge density σ0 (C‚m-2) is directly obtained from the Grahame equation, 9. The surface concentration (Γ12-2-12) is deduced from results of surface tension measurements (cf. Figure 3) with the Gibbs equation, eq 10, and enables one to measure the ionization coefficient of the monolayer β.
dγ ) -3RTΓ12-2-12 d(ln c12-2-12)
(10)
All values are reported in Table 1. The experimental Debye length evaluated with the fit is in a good agreement with the theoretical one obtained from eq 8 and shows that DLVO theory accounts correctly for the behavior of 12-2-12 films in the dilute regime. Table 1 also reports the DLVO parameters expected for DTAB films. Theses values are presented in ref 17. The surface charge and the surface potential measured with 12-2-12 films are smaller than the ones expected for DTAB. We claim that the counterions of the 12-2-12 monolayers are more condensed than those of DTAB monolayers. The larger condensation effect may be probably due to a weaker hydration of 12-2-12 surfactant molecules. This assumption will be discussed below in the case where salt is added. A classical DLVO treatment which simply balances repulsive and attractive forces cannot fully explain the difference between 12-2-12 and DTAB film stability. Hence, in both cases, the attractive force is the same and the repulsive force is greater for DTAB than for 12-2-12. DLVO theory predicts exactly the opposite of the experimental observations. To explain the different behavior between monomeric and dimeric surfactants, we refer to an interesting study made by Bergeron.17 The author claims that DLVO theory concepts applied to thin liquid films neglect all the fluctuations which can take place at the interface. DLVO theory considers film surfaces as solid uniformly charged walls, whereas spatial fluctuations and surfactant fluctuations (cf. Figure 4) occur in thin-liquid films. So, fluctuations may induce domain formation in a thin liquid film where the attractive force becomes greater than the repulsive one. The probabilities that spatial and density
Behavior of Soap Films
Langmuir, Vol. 14, No. 15, 1998 4255 Table 1.
ψ0 (mV) DTAB 12-2-12
A (Å2‚molecule-1)
95 43
45 69
σ0 (C‚m-2)
βmicelle
βfilm
βmicelle, (e nm-1)
Gibbs (mN‚m-1)
0.046 0.0047
0.2332
0.13 0.01
0.26 (22 °C) 0.1719 (35 °C)
50 62
Figure 3. 12-2-12 (b) and DTAB (O) surface tensions as a function of surfactant concentration measured at T ) 22 °C. The Gibbs elasticities are directly evaluated with it.
Figure 4. Schematic view of undulation and concentration fluctuations.
fluctuations arise are controlled by energy barriers which depend directly on the monolayer rheological parameters. Both spatial and density fluctuations are related to the Gibbs elasticity (0) defined as
0 ) -
dγ d(ln Γ)
where γ is the surface tension and Γ the surface concentration. The probabilities that fluctuations occur decrease exponentially with the Gibbs elasticity. A cohesive surfactant monolayer with a high surface Gibbs elasticity will promote film stability. For instance, a small amount of long chain alcohol to purified DTAB solutions produces highly stable films only due to a large increase of the Gibbs elasticity.17 Table 1 reports the measurements of 0 for the two surfactants as deduced from the surface tension measurements (cf. Figure 3). The 12-2-12 Gibbs elasticity is clearly greater than the DTAB one and can explain the higher 12-2-12 films stability. As expected, the chemical bond between the two DDAB headgroups enhances the cohesion of the 12-2-12 monolayer and dampens the fluctuations in the thin liquid film.
0.22
Figure 5. Disjoining pressure (Pa) isotherm vs thickness in a 10 mM DTAB - 7 mM NaCl mixture. The continuous line is the best fit using the classical Debye-Hu¨ckel equation like that for Figure 2. The theoretical Debye length is kth-1 ) 2.50 nm; the experimental Debye length is kexp-1 ) 3.60 nm.
In the following, we analyze the role of monovalent electrolyte NaCl added directly to DTAB and 12-2-12 solutions (NaCl is hereafter also referred to as salt). In contrast to the unstable DTAB films made with purified surfactant, addition of enough salt to a DTAB solution (10 mM DTAB + 7 mM NaCl) promotes stable foam films at low applied pressure ( c*). The zero shear bulk viscosity depends strongly on the temperature and decreases, for instance, from approximately 1 (20 °C) to 10-2 Pa‚s (40 °C) at 3% surfactant massic fraction concentration. Due to experimental difficulties (flow of the 12-2-12 solution through the porous medium), we have chosen to perform our measurements at 37 °C. To control the influence of possible evaporation of water during experiments, the solution concentrations are checked before and after each isotherm by conductivity measurements. Figure 7 shows the disjoining pressure isotherm (disjoining pressure vs the film thickness) obtained for a 4.8% surfactant massic fraction solution. All the points are measured using the dynamic method and are calculated from eqs 3 and 4. The first interesting remark is that a stepwise thinning is observed vs the time at a given capillary pressure. As
Behavior of Soap Films
Langmuir, Vol. 14, No. 15, 1998 4257
Figure 9. Disjoining pressure vs film thickness for semidilute surfactant solution. The concentration is x % or y mM. The solid arrows are a guide for the eyes and enable us to reveal the oscillatory force behavior. Key: a (+), x ) 3.00, y ) 48.8; b (9), x ) 2.60, y ) 42.0; c (2), x ) 2.05, y ) 33.4; d ([), x ) 1.60, y ) 26.0 at 37 °C or (×) at 22 °C.
observed with spherical anionic micelles,16 the step pressures for 12-2-12 surfactant are very low (roughly 60 Pa) and justify the use of the dynamic method. When a thickness jump occurs during thinning, some darker circular spots appear on the film (characteristic of smaller thickness) which unify into a new homogeneous film. When the number of spots is small enough, attempts to measure the spot radius growth leads to a law proportional to the square root of the time as shown in Figure 8. The same time dependence was observed for micellar solutions.35 A theoretical model is developed in this reference considering two different behaviors in growth process which directly depends on the formation of “liquid bubbles” instabilities around the spots. Further work is currently underway to extract from this time evolution information about the viscosity in the surfactant films. Finally, the upper and lower parts of the last branch (e.g., the parts of the curve after the last thickness jump) of the disjoining pressure isotherms are straightened out by increasing and decreasing slightly the pressure in the cell. The system requires only about a few minutes to reach its equilibrium thickness after changing the pressure. When the pressure is decreased, no hysteresis is observed but the jumps are not reversible. We point out here an oscillatory behavior at a weight fraction of 4.8%. The influence of surfactant concentration was investigated at the same temperature. Figure 9 shows behaviors analogous to Figure 7 by varying the bulk surfactant concentration. First, for the same thickness range analyzed, the number of jumps increases with the surfactant concen(35) Sonin, A.; Langevin, D. Europhys. Lett. 1993, 22, 271-277.
tration. There is an evolution of oscillatory period as a function of c. The experimental oscillatory period, measured at the lower disjoining pressure, depends clearly on the concentration and decreases as a -0.54 power law (cf. Figure 10a). The power law corresponds to the best fit to our experimental data. Second, the greater the surfactant concentration, the thinner the thickness of the last branch. Assuming wormlike micelles are completely pushed away from the film bulk when the last jump occurs, this effect may be explained by a micelle number increase with concentration leading to a rise in depletion attractive forces.36,37 For more dilute solution in this regime (c ) 1.6%), the disjoining pressure isotherm is also determined at 22 °C using the static method. The curve measured is directly compared to the one obtained at 37 °C in Figure 9d. Although an oscillatory force always occurs, the experimental oscillatory period increases slightly when the temperature decreases. An experimental explanation for the temperature dependence is presented below by SANS results. Finally, when salt is added to the solution (cNaCl ) 0.54 M for c12-2-12 ) 0.025 M), the oscillatory behavior disappears and only a classical CBF-NBF transition occurs as described in the first part of this paper. This added salt regime emphasizes the great influence of electrostatic interactions in oscillatory forces. Therefore, the addition of electrolyte screens the electrostatic interactions between the micelles of cylindrical shape and also between surfactant molecules along a cylinder causing a strong micelle growth. All these results are very close to the recent ones obtained for polyelectrolyte solutions4,5 even in the added (36) Dalhgreen, M. A.; Leermakers, A. M. Langmuir 1995, 11, 2996. (37) Kekicheff, P.; Nallet, F.; Richetti, P.; J. Phys. 2, Fr. 1994, 4, 735.
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Espert et al. Table 2. Massic Fraction of 12-2-12, the Corresponding Concentration c, Mesh Size ξ Calculated Using Eq 11, Mesh Size Calculated Using Eq 12, and Experimental Jump Size h
Figure 10. (a) Key: (() evolution of the oscillatory periods vs the concentration at 37 °C; (0) evolution of d evaluated by the peak positions at 37 °C. (b) Key: (+) evolution of d evaluated by the peak positions at 22 °C; (0) evolution of d evaluated by the peak positions at 37 °C; (b) evolution of d evaluated by the peak positions at 52 °C. The continuous lines are the best fit to our data using power laws as predicted by scaling laws for charged chains solutions.38,39
c (%)
10-25c (molecules/m3)
ξOSF (nm)
ξKK (nm)
h (nm)
4.80 3.00 2.60 2.05 1.60
4.7062 2.9414 2.4707 2.0099 1.5393
1.94 2.45 2.67 2.96 3.40
12.20 15.47 16.82 18.65 21.31
13.50 17.50 19.50 22.00 24.50
studied by several authors38,39,40,41 from a theoretical point of view using classical methods such as mean field and scaling theories. Their considerations allowed the phase diagram of highly and weakly charged chains to be predicted as a function of concentration, temperature (solvent effect, ...), and added salt fractions. Like the neutral polymer,42 the polyelectrolyte exhibits an overlap concentration (c*) which is a function of molecular weight. Above c*, the system is directly controlled by the correlation length ξ or the “blob” size which describes the solution behavior in the semidilute regime. Odijk39 for highly charged compounds and Khokhlov and Khachaturian40 for weakly charged systems have directly related the characteristic length ξ to the polymer concentration. These authors showed that the “blob” size depends strongly on the strength of the electrostatic interactions in the bulk solution. We propose to calculate the blob size in the special case of a 12-2-12 wormlike micelle assuming a polyelectrolyte structure. We assume a linear chain of charged surfactant despite the relevant radius value for each cylinder as found in ref 18 (r ) 20 Åscf. Figure 11b). Furthermore, a close packing of surfactant molecules is accounted for; e.g., the size of each headgroup is found using the area per molecule evaluated from the same assumptions (equations in ref 43) as the ones used by Zana32 for spherical cationic micelles. For highly charged polyelectrolytes, ξ is directly related to the distance between charges A and concentration c by39
ξ ) 1/xAc
(11)
In the more complicated case of weakly charged chains, the blob size is given by40
ξ) Figure 11. (a) Polyion solution in the semidilute regime. On scales r < ξ, the chains are nearly stiff whereas they are ideal on the scale r > ξ. (b) Going from a 3D wormlike micelle to a lineic charged chain of surfactants.
salt regime. Assuming a finite fraction charge on each cylinder, we propose that, as for highly charged and weakly charged polyelectrolytes, the wormlike micelles form a mesh of size ξ corresponding to the average distance between micelles crosspoints38 (cf. Figure 11a). The transient network formed by objects such as polyelectrolytes or wormlike micelles is directly related to the strong electrostatic interactions between the monomers along and between the chains. The existence of charge along the chain has been measured in ref 8 and more recently in ref 19. The authors evaluated a 0.18 e‚nm-1 micelle ionization degree for 12-2-12 surfactant at the semidilute concentration c* leading to weakly charged polyelectrolytelike behavior (e ) 1.6 × 10-19 C). The structure of polyelectrolyte solutions has been (38) De Gennes, P. G.; Pincus, P.; Velasco, R. M.; Brochard, F. J. Phys. 1976, 37, 1461-1473.
(
σ4/7 (lB/a)2/7a
)
1/2
c-1/2
(12)
where one monomer or one headgroup carries a charge among σ headgroups, a is the monomer or headgroup size along the cylinder, and lB is the Bjerrum length at T ) 37 °C (6.76 Å). Results are presented in Table 2 with A ) 5.6 nm, σ ) 11, a ) 5 Å, and the 12-2-12 concentration c. Using the Odijk model, a large difference is found between theory and experiments; the degree of charge is too low to use eq 11. The results issue from Khokhlov and Khachaturian show a good agreement with experimental values deduced from surface force experiments, concluding only that charged wormlike micelles present a polyelectrolyte-like behavior. Nevertheless, the assumptions made involve a careful reading of the results reported in Table 2. (39) Odijk, T. Macromolecules 1979, 12, 688-693. (40) Khoklov, A. R.; Khachaturian, K. A. Polymer 1982, 23, 17421750. (41) Pfeuty, P. J. Phys. 1978, 39, C2149-C2160. (42) De Gennes, P. G. Scaling Concepts In Polymer Physics; Cornell University Press: London, 1979.
Behavior of Soap Films
Furthermore, some guess improvements remain possible, leading to a better description of charged wormlike micelles. b. SANS. One of the great difference between neutral polymer and charged chains is their scattering behavior (c > c*). In semidilute solution, charged chains exhibit a peak in their structure factor whereas neutral polymer does not. The existence of the peak at a finite wavevector q* is directly related to the small compressibility of the small ion gas.7 In the contrast to this, the structure factor of neutral polymers is characterized by a large value at q ) 0 and decays monotically at larger q. The peak position can define the correlation length of the solution and one expects that it is of the order of the inverse mesh size value. A previous SANS work has been realized with the same surfactant with and without shear9,44 only at T ) 22 °C. The results have evidenced the presence of a peak at a wavevector q* corresponding to a characteristic distance which varies with surfactant concentration as c-1/2. The peak detected confirms the idea of semirigid “rods” with strong electrostatic interactions. In ref 29, the peak disappears when salt is added at a concentration similar to the surfactant one (e.g., the electrostatic interactions are screened) showing the major role of electrostatic interactions. From Fourier transform, a peak in the structure factor S(q) leads to an oscillation in the pair correlation function g(r).45 Clearly, our force data confirm the existence of such oscillatory structural forces in semidilute wormlike micelles solutions. So, when the wormlike micelles are confined between the two film surfaces and when the film thickness h is comparable to a period of the oscillations of g(r), the oscillatory forces arise.46 Nevertheless, it is important to note that the oscillatory forces are not related to the structuration of the molecules into semiordered layers at surfaces but instead occur because of the ordering change during the approach of the second surface, e.g., the confinement. To obtain information about the influence of temperature on the structure of semidilute 12-2-12 solutions, SANS experiments are carried out in the semidilute regime for various temperature from 22 to 52 °C. Figure 10b shows the peak positions (d ) 2π/q*) vs the surfactant concentration and temperature. The peak position q* is determined from the structure factor S(q) deduced from the scattered intensity I(q) assuming a q-1 dependence on the form factor (cf. Figure 12). This assumption was clearly checked for the two more dilute samples (2% and 4%) whereas the analyzed q range does not allow us to verify it for the more concentrated solutions (5%, 6%, and 7%). However, one expects the same behavior for these samples because we remain in the semidilute regime. Identically, experiments carried out by Schmitt et al.9 lead to q-1 dependence in the high q range at 22 °C. It is important to note that from 22 to 52 °C, the same c-1/2 scaling behavior is observed. The effect of temperature increase leads only to decrease slightly the distance d calculated by the Bragg relation at a given concentration above the overlap one. Furthermore, heating the more dilute sample up to 52 °C enables one to observe a relevant deviation to the c-1/2 power law determined from other samples at the same temperature. As mentioned by Kern et al.,18 one expects to decrease the size of a micelle when (43) Tanford, C. J. Phys. Chem. 1974, 78, 2649. Israelachvili, J. N.; Mitchell, D. J.; Nimham, B. W. J. Chem. Soc., Faraday Trans. 1976, 72, 1525-1568. (44) Schmitt, V.; Lequeux, F. See ref 9. (45) Cabane, B. Summershool, Les Editions De Physique; Aussois, France, 1983. (46) Pollard, M. L.; Radke, C. J. J. Chem. Phys. 1994, 101, 6979.
Langmuir, Vol. 14, No. 15, 1998 4259
Figure 12. Structure factor S(q) deduced from scattered intensity as a function of q. S(q) ) q*I(q) for a sample concentration c ) 2%. Key (0) evolution of scattered intensity vs q at 22 °C; (b) evolution of scattered intensity vs q at 37 °C; (×) evolution of scattered intensity vs q at 52 °C.
the temperature is increasing. We propose that c ) 2% at T ) 52 °C corresponds to a concentration where a network of entangled micelles is no longer formed in the bulk, concluding that this concentration is below the overlap one at 52 °C. These experiments show that the temperature increase enables one modify the overlap concentration by changing the size of micelles from a wormlike shape to a spherical one. The disjoining pressure isotherm determined at c ) 1.6% at 37 °C exhibits an oscillatory period which fits well as a c-1/2 power law with other concentrated solutions as can be seen in Figure 10. This experiment reveals that this concentration is always above the overlap one at 37 °C. Moreover, the force profile measured at c ) 1.2% at 37 °C shows an oscillatory behavior but the period does not fit well with ones determined above c ) 1.6% at the same temperature. These experimental results obtained by the two techniques enable one to emphasize the temperature effect and at the same time the concentration effect on the structure of the solution. So, an increase of temperature corresponds directly to the same effect as a concentration decrease. The more relevant consequence in these two cases is to decrease continuously the aggregate size until the wormlike shape vanishes. Our results show that an entangled network takes place for concentrations higher than 1.5% at 37 °C. As shown in Figure 10, a very good agreement is found at the same temperature (37 °C) between the two techniques (SANS and TFB) for, respectively, peak positions and oscillatory periods and also the same dependence on concentration. The same evolution with roughly the same values is observed at 37 and 22 °C by performing disjoining pressure experiments and SANS experiments, revealing a nice complementarity between the techniques. To end, our disjoining pressure data are also consistent with the disappearance of the scattering peak44 resulting from the addition of salt. Conclusion We have studied thin liquid films made from cationic dimeric surfactants both in the dilute regime and in the semidilute regime, where wormlike micelles form. The 12-2-12 efficiently stabilizes soap films even at very low concentrations. This behavior is in sharp contrast with that of the corresponding monomeric surfactant. Such new cationic surfactants thus indicate a great ability for the stabilization of foam and emulsion systems. The formation of stable Newton Black film is observed in the presence of an added electrolyte. As far as we know, this
4260 Langmuir, Vol. 14, No. 15, 1998
is the first time that such a property has been observed with a cationic surfactant. It might be useful for applications where adhesion and aggregation of particles is required.47 In the semidilute regime, we have measured oscillatory forces that we interpret as being structural forces associated with the wormlike structure. The same behavior was recently found with polyelectrolytes whereas neutral polymer does not lead to this kind of interaction. Moreover, due to the screening of electrostatic interactions, the structural forces vanish in the presence of added salt. These forces are directly related to strong electrostatic interactions and are specific for charged long cylinderlike systems (e.g. charged wormlike micelles and poly(47) Poulin, P.; Bibette, J. Phys. Rev. Lett. 1997, 79, 3290.
Espert et al.
electrolytes). Hence, a SFA study on screened wormlike micelles37 enabled one to measure only depletion forces whereas a recent work on the same kind of charged system (12-2-12-2-12) has led to results48 similar to the ones we report in the semidilute regime. Acknowledgment. We are grateful to Laurence Noirez (LLB) and Frederic Nallet for their great assistance during the SANS experiments. We have also benefited greatly from discussions with Franc¸ ois Lequeux, Didier Roux, Fernando Leal-Calderon, David Monin, Olivier Mondain-Monval, and Philippe Richetti. LA9800957 (48) Anthony, O.; In, M.; Marques, C. M.; Zana, R.; Richetti, P. To be submitted for publication in Langmuir.
