Influence of Salt Concentration and Surfactant Concentration on the

Langmuir 2001, 17, 4825-4835

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Influence of Salt Concentration and Surfactant Concentration on the Microstructure and Rheology of Lamellar Liquid Crystalline Phases P. Versluis* and J. C. van de Pas Unilever Research Vlaardingen, Olivier van Noortlaan 120, 3133 AT Vlaardingen, The Netherlands

J. Mellema Rheology Group, Twente Institute of Mechanics, J.M. Burgerscentrum, Faculty of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Received June 1, 2000. In Final Form: May 8, 2001 The microstructures and linear rheological properties of onion phases prepared from sodium dodecylbenzenesulfonate, a C13-15 ethoxylated alcohol with on average 7 EO groups at a fixed weight ratio of 7:3, sodium citrate and water were investigated over a broad concentration range of surfactant and salt. At low salt concentration a lamellar phase in equilibrium with a micellar phase is found. When more salt is added (9-15%), a colloidally stable, swollen onion phase is found. The repulsion between the surfactant bilayers is caused by thermal undulations. The effect of the undulations can be observed on electron microscope photographs. At salt concentrations between approximately 15 and 20% the appearance of the onion phase changes from translucent to milky white and the onions are (weakly) flocculated. The hydration of the surfactant molecules, the bilayer repeat distance, and, as a consequence of this, the obtained volume fraction of onions decrease rapidly. Thermal undulation of the bilayers is no longer observed because of stiffening of the layers. At even higher salt concentrations between 20 and 30% severe flocculation of the onions occurs. For the linear rheological behavior of the colloidally stable onion dispersions at 9.5 and 12.7% salt, a model taking into account the undulation potential as given by Helfrich and the length scale of the affine deformation is derived. The model satisfactorily explains the magnitude of the found elastic modulus G′ at low frequencies, suggesting affine motion at a length scale larger than the size of the onions. The curved parts of the onions are assumed to be relaxed. The volume fraction dependence of G′ of the onion dispersions at 16.9 and 28% salt is similar to that of a flocculated dispersion. At salt concentrations of 9.5 and 12.7% and onion volume fractions of 0.6 and above a broad relaxation transition in G′′ is observed. The strength of the relaxation (∆G) can be explained if we assume that the transition is caused by the inclusion of the curved part of the onions. At constant salt level, the characteristic time (τ) of the transition and ∆G vary proportionally, showing that the viscosity (∆η) associated with the transition is constant. Going from 9.5 to 12.7% salt ∆η increases by a factor of 2.5. Some possible explanations for this effect are offered.

1. Introduction When surface-active molecules, commonly known as surfactants, are dissolved in water, many types of aggregates can be formed. The geometry and nature of the aggregates will depend mostly on concentration and type of the surfactant or the surfactant mixture. Also, the presence of electrolyte can have a marked influence on the type and shape of the aggregate. Common aggregates are micelles, either spherical, disklike, or rodlike, vesicles, or lamellar phases. The latter phase can be either plane like lamellar or dispersed in the form of multilamellar droplets or onions (because of the resemblance of the concentric lamellar arrangement with the structure of an onion). The driving force for the formation of the surfactant aggregates is the hydrophobic attraction between the alkyl part of the surfactants.1 The alkyl tails of the surfactant molecules are not soluble in the continuous phase. A way of preventing contact with the water is for the alkyl chains to form small separate pools, which are shielded by the soluble headgroups of the surfactant molecules. According to theory, the shape of the surfactant aggregate is mainly * To whom correspondence should be addressed. (1) Komura, S. In Vesicles; Rosoff, M., Ed.; Marcel Dekker: New York, 1996; pp 197-236.

determined by the ratio between the volume divided by the length of the alkyl part (v/L) and the effective surface area of the headgroup, a0.2 Wedge-shaped molecules will form micelles while molecules with a truncated conical shape will tend to from curved or flat lamellae. The present study is dedicated to the surfactant aggregate microstructure and rheological properties for a given mixture of surfactants, commonly encountered in laundry detergent preparations.3-5 The effect of surfactant concentration and salt level was investigated. Since the work described here was carried out for industrial purposes, industrial materials were used. This makes interpretation of the results in terms of molecular properties more difficult but makes the translation of the results to real products much easier. 2. Experimental Section 2.1. Materials. The anionic surfactant used was Marlon AS3, from Huls, a commercial preparation of DoBS-acid, which is (2) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991; Chapter 17. (3) van de Pas, J. C. Tenside Surf. Det. 1991, 28, 158. (4) Schepers, F. J.; Toet, W. K.; van de Pas, J. C. Langmuir 1993, 9, 956. (5) van de Pas, J. C.; Buytenhek, C. J.; Brouwn, L. F. Recl. Trav. Chim. Pays-Bas 1994, 113, 231.

10.1021/la000779q CCC: $20.00 © 2001 American Chemical Society Published on Web 07/06/2001

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a mixture of 98.0-98.5% isomerically impure 4-(sec-dodecyl)benzenesulfonic acids, about 1.5% non-sulfonated organic matter, and 0.3% sulfuric acid. The nonionic surfactant was Synperonic A7 from ICI, which is a C13-15 ethoxylated alcohol, with an average of 7 mol of ethylene oxide per mole of surfactant material. The salt used was trisodium citrate dihydrate cryst. extra pure obtained from Merck. All materials were used without further purification. Model samples were prepared by dissolving the surfactants in demineralized water under stirring at 50 °C, until a clear isotropic surfactant solution was obtained. A sufficient amount of sodium hydroxide was added to neutralize the acid surfactant. After addition of the citrate, the liquid was allowed to cool to room temperature under stirring. Finally, the pH of the liquid was adjusted to around 8 by adding NaOH solution. Variation in surfactant concentration was obtained by preparing samples at high surfactant concentration and subsequent dilution with a salt solution at the same concentration as in the continuous phase of the concentrated samples. The samples were stored at least 1 week in closed bottles at room temperature before any measurement was made. The final sample characteristics like average onion size and onion volume fraction do not depend on the sample preparation method. A different order of addition or mixing of the ingredients by shaking in a closed container leads to samples with identical properties. The samples are stored for at least 1 year at room temperature and turned out to be stable. In the present study, the effect of surfactant concentration and salt concentration on the microstructure and the rheological properties of the onion phases were investigated. The surfactant concentration in the samples was varied between 1 and 55 wt %, at a fixed anionic:nonionic weight ratio of 7:3 (based on the sodium salt). The amount of sodium citrate was varied between 0 and 32 wt %. At the highest salt concentration sometimes crystallization of the salt occurred. These samples were discarded from the test series. 2.2. Measurements. The measurements were performed at 25 ( 0.1 °C except the light microscopic observations, which were done at room temperature (20-25 °C). Electron micrographs of selected samples were obtained by freeze fracture/etching/heavy metal replication. A 5 µL aliquot of the samples was slam-frozen in a Reichert MM80 slam freezer and transferred to a Cressington CFE50 freeze fracture and etching apparatus. After fracturing the samples were etched for 2 min at -100 °C and replicated with a 2 nm layer thickness of W/Ta and a 7 nm carbon backing. The replicas were washed and observed in a Philips CM12 transmission electron microscope (TEM) at 120 kV accelerating voltage. Digital image acquisition was done with a Gatan slow scan CCD camera type 694 and printing by a Fujix pictographic 3000 printer. Best results were obtained when previous to freezing, the sample holder with the sample in place was allowed to rest for several minutes in a saturated water vapor atmosphere to prevent drying of the sample. The micrographs were inspected visually to assess the microstructure of the samples. Samples were also inspected with a Zeiss Axioplan light microscope using polarized light. A small drop of material was placed on a microscope slide and quickly covered with a cover glass. The sample flows to fill the gap between the slide and the cover glass. Images of relevant structures were obtained using a JVC KY-F55B CCD video camera attached to a computer with a frame grabber card. To calculate the volume fraction onions, the electrical conductivity of the samples was measured in a cell with platinized electrodes using a Radiometer CDM 83 conductivity meter. The conductivity cell was calibrated with sodium citrate of known concentration and conductivity. Most samples were centrifuged for 16 h at 40 000g. The height of separated layers, if any, was measured with a ruler. This allows a rough calculation of the volume of the layers. The refractive index of the continuous phase was measured using a Bellingham & Stanley RFM 91 multiscale automatic refractometer. The refractive index was used to calculate the sodium citrate concentration. Dynamic rheological measurements were made with a Bohlin VOR constant shear rate rheometer equipped with a smooth

Versluis et al. couette geometry (C25, bob diameter 25 mm, gap 0.125 mm) in the linear viscoelastic region. The sample was carefully introduced into the cylindrical geometry, avoiding high rates of deformation as much as possible. Subsequently, several frequency sweeps from 10 to 0.001 Hz and reverse were done on the sample. Only data were used when no systematic changes in G′ and G′′ occurred anymore, indicating that the sample had fully relaxed. It was assured that the strain was well within the linear viscoelastic region.

3. Theory Several authors have discussed extensively the forces between surfactant bilayers.3,6,7 The total energy of interaction is usually given as the sum of several individual potentials. Some of these potentials lead to repulsion and others to attraction over the bilayer. The total potential energy is approximated by

Vtot ) Vvdw + Ves + Vvr + Vos

(1)

with Vvdw the van der Waals, Ves the electrostatic, Vvr the volume restriction, and Vos the osmotic potential energy of interaction. The origin of the van der Waals and electrostatic potential is obvious. The volume restriction potential is steric in nature and comes from the loss in confirmational energy when the EO chains start to overlap. The osmotic contribution is due to the preference of the EO chains to dissolve in the solvent. We have used the equations given by van de Pas6 to calculate these potentials for our particular case. For the van der Waals potential energy of interaction between two plates of finite thickness we have used:8

Vvdw )

[

]

-A11 1 2 1 + 12π d 2 (d + d )2 (d + 2d )2 w w a w a

(2)

with A11 the Hamaker constant, which we estimated to be 3 × 10-21 J, and dw and da the thickness of the water layers and alkyl layers, respectively. For da we have taken 1.62 nm, which is a reasonable value as will be shown later. Here and subsequently the energy is per unit area. The electrostatic potential for two charged plates can be described by9

Ves )

64nikTγ2 -kdw e κ

(3)

with

ni ) NAci × 103

( ) [ ( κ)

γ ) tanh

2nie2 0kT

1/2

)]

1 e2 sinh-1 2 8ni0kTA02

1/2

ni is the number ion concentration, ci is the molar salt concentration, e is the elementary charge, NA is Avogadro’s number, and 0 are the dielectric constant of water and (6) van de Pas, J. C. A Study of the Physical Properties of Lamellar Liquid-Crystalline Dispersions. Ph.D. Thesis, Rijksuniversiteit Groningen, 1993; Chapter 3. (7) de Haas, K. H.; Blom, C.; van de Ende, D.; Duits, M. G. H.; Haveman, B.; Mellema, J. Langmuir 1997, 13, 6658. (8) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of Stability of Lyophobic Colloids; Elsevier: Amsterdam; 1948. (9) Overbeek, J. Th. G. In Colloid Science; Kruyt, H. R., Ed.; Elsevier: Amsterdam, 1952; Vol. 1.

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Langmuir, Vol. 17, No. 16, 2001 4827

the permittivity of vacuum, and A0 is the interfacial area per unit charge. For A0 a value of 53 nm2 was calculated from the dimensions of an average anionic molecule and the alkyl layer thickness. The volume restriction and osmotic potentials are written as10

Vvr ) 2νkTV(ıj,dw) Vos ) 2

(2π9 )

(4)

3/2

(R2 - 1)kTν2〈r2〉M(ıj,dw)

(5)

with

〈r2〉1/2 ) R〈r2〉θ1/2 V(ıj,dw) ) 2e-3dw /2〈r 〉 2

()(

6π M(ıj,dw) ) 5

1/2

12dw2 5〈r 〉 2

2

)

- 1 e-6dw /5〈r 〉 2

2

where ν is the number of EO tails per unit area, jı is the mean number of segments in an EO chain, R is the socalled expansion factor which is a measure of the quality of the solvent for the ethylene oxide chains, and 〈r2〉 is the mean-square end-to-end distance of an ethylene oxide chain. The subscript θ refers to “theta conditions” for R ) 1. Under these conditions the EO chains are just soluble. Vvdw is always attractive, and Ves and Vvr are always repulsive, while Vos can be either attractive or repulsive depending on the solvent quality of the electrolyte solution for the ethylene oxide chains of the nonionic surfactant. For a good solvent (R > 1) the potential is repulsive; for a bad solvent (R < 1) the osmotic potential is attractive. In Figure 1 the potentials as a function of bilayer repeat distance are plotted for R ) 1.1 and R ) 0.9 with appropriate estimates of the other parameters. It can be seen that in both cases the electrostatic potential does not significantly contribute to the total interaction potential. For R ) 1.1, the dominating contribution comes from the osmotic and van der Waals potentials, while at R ) 0.9 the dominant contributions are from the van der Waals and the volume restriction potential. The calculations predict a bilayer repeat distance of about 8 nm for a good solvent and around 4 nm for a bad solvent. The calculations show that these potential energies lead to a water layer thickness between the lamellae of a few nanometers at most. In many cases, however, much thicker water layers are found, up to 20 nm or more. This is caused by thermal undulation of the layers as described by Helfrich:11

Vun )

3π2(kT)2 128Kdw2

(6)

with K the bending modulus of the bilayers. For our type of surfactant molecules, the value of K is estimated to be on the order of 1kT, both from theoretical calculations12 and from experiment. Experimental values for K ) 0.7kT13 and K ) 2.5kT14 are found for an LR phase consisting of (10) Hesselink, F. Th.; Vrij, A.; Overbeek, J. Th. G. J. Phys. Chem. 1971, 75, 2094. (11) Helfrich, W. Z. Naturforsch. 1978, 33A, 305. (12) Barneveld, P. A. The Bending Elasticity of Surfactant Monolayers and Bilayers. Ph.D. Thesis, Landbouwuniversiteit Wageningen, 1991; Chapter 5. (13) Freyssingeas, E.; Roux, D.; Nallet, F. J. Phys. II 1997, 7, 913. (14) Bagger-Jo¨rgensen, H.; Olsson, U. Langmuir 1996, 12, 4057.

Figure 1. Potential energy as a function of bilayer repeat distance. The top graph (A) gives the results of the calculations for a good solvent (R ) 1.1) and relatively low salt concentration. The graph on the bottom was obtained for high salt concentration and R ) 0.9. The numbers in the graphs refer to the specific potential. 1 is the electrostatic potential, 2 is the volume restriction potential, 3 is the osmotic potential, and 4 represents the van der Waals potential. The dotted line is the sum of the individual contributions.

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Figure 2. Surfactant hydration as a function of the salt concentration in the continuous phase for samples with 10% surfactants.

n-dodecyl pentaethylene glycol monoether, 1-hexanol, and water; using different techniques, K ) 1.3kT was found for the same nonionic surfactant in water only,15 and K ) 2.1kT16 and K ) 2.617 for an LR phase prepared from SDS-water-pentanol-dodecane. Values of K ranging from 10kT to 50kT are reported for systems with more bulky hydrophobic tails like lipids.18 Undulation always leads to repulsion and should, when it is the dominating potential, in practice lead to infinite swelling of the bilayer separation. For systems where the bilayers are arranged in parallel planes sometimes repeat distances order 100 nm are reported.15 In the case of onions, however, the swelling is restricted by the fact that the bilayers are ordered in closed concentric shells, and therefore at some point, at low onion volume fraction, the tension in the membrane will prevent further swelling. The swelling can also be restricted by the sample boundaries, occurring at high volume fraction of onions. 4. Results and Discussion 4.1. Microstructure. Only samples will be discussed where the surfactants are salted out in multilamellar vesicles (onions) as determined by polarized light microscopy. Furthermore, we restrict ourselves to samples where the continuous phase is virtually surfactant-free. This was judged from the viscosity of the continuous phase, from the absence of foam after vigorous shaking, and by examining the transparency and color. When these criteria are passed, we assume that at most a very low monomeric concentration of surfactant is present. 4.1.1. Surfactant Hydration. The salt concentration in the continuous phase is always found to be higher than anticipated from the applied weights. We assume that the salt concentration is increased over the nominal concentration by hydration of the surfactants. When a simple model for the lamellar phase is adapted, where the salt concentration in the continuous phase outside the onions is equal to the salt concentration in the water layers between the surfactant lamellae, the hydration of the surfactant can be calculated as grams of water per gram surfactant. In Figure 2 the surfactant hydration as a function of salt concentration is given for samples with (15) Strey, R.; Schoma¨cker, R.; Roux, D.; Nallet, F.; Olsson, U. J. Chem. Soc., Faraday Trans. 1990, 86, 2253. (16) Lei, N.; Lei, X. Langmuir 1998, 14, 2155. (17) Lei, N.; Safinya, C. R.; Bruinsma, R. F. J. Phys. II 1995, 5, 1155. (18) Cevc, G.; Marsh, D. In Phospholipid bilayers; John Wiley & Sons: New York, 1987; Chapter 12. Marsh, D. CRC Handbook of Lipid Bilayers; CRC Press: Boca Raton, FL, 1990.

Versluis et al.

Figure 3. Number-average diameter of the onions as a function of salt concentration in the continuous phase as estimated from electron micrographs. The error bars indicate the standard deviation of the distribution. Samples contain 10% surfactant.

10% surfactant. It can be seen that the surfactant hydration decreases as the salt concentration in the continuous phase increases. This indicates that as the salt concentration increases, the hydrophilic surfactant headgroups become less well soluble in the continuous phase. The sodium citrate concentrations reported in this paper are the actual concentrations found in the continuous phase. 4.1.2. Appearance of the Lamellar Phase. For a series of samples with a surfactant concentration of 10 wt %, the influence of the sodium citrate concentration on the microstructure was examined. The salt level was increased in steps of 2%. Without salt, a clear, most likely micellar solution is obtained. At 2% some phase separation occurs. From light microscopic observations it appears that the separated phase is lamellar in nature, in equilibrium with a micellar solution. When more salt is added, more surfactant is salted out into an onion phase. At about 9% salt all surfactant material present is salted out, and a space-filling arrangement of onions is established with a translucent appearance. The average onion diameter is of order 1 µm as confirmed by light microscopy and electron microscopy. With the light microscope, using crossed polars, birefringence is observed when the sample flows, due to the presence of onions with a size in the order of the wavelength of the light. This effect has been described before.6 With increasing salt concentration a few of larger onions appear. This is a consequence of the broadening of the size distribution as can be seen in Figure 3, where the average onion diameter, as measured in electron microscope photographs, is given as a function of salt concentration. The error bars in the figure represent the width of the distribution rather than the uncertainty in the measurement. Note that increase in size also means increase in the width of the distribution. The appearance of the sample changes from translucent to milky white at 15% salt. The onions can easily be seen under the light microscope. A few large onions are seen which are approximately 5 µm in diameter; the bulk of the onions, however, is between 1 and 2 µm in diameter. At 16% salt, the lamellar phase no longer fills the space, and a layer of milky white lamellar material separates on standing and floats on top of the sample. Light microscopy shows that the onions present have a tendency to form flocs. The flocculation is rather weak as the lamellar phase is easily redispersed, and it takes several hours to separate again. For samples with salt concentrations of 20% and


Langmuir, Vol. 17, No. 16, 2001 4829

Figure 4. Volume fraction lamellar phase and the volume fraction of the lamellar layer as a function of salt concentration at 10% surfactants: (9) calculated from the layer separation after centrifugation for 1 h at 400g; ([) calculated from conductivity data.

above rigid flocs of onions are formed. With 16 and 18% salt the appearance of the lamellar phase is still milky white. At salt concentrations between 20 and 30% the flocculated state of the lamellar phase can be observed macroscopically. When the onions are redispersed, rapidly pieces of lamellar material are formed which float to the surface in a matter of minutes. This lamellar phase was identified using light and electron microscopy as highly flocculated onions. The onions show deformations due to the flocculation. As the average size of the onions in the flocs hardly increases, apparently only very limited fusion of onions occurs. From the electrical conductivity, the volume fraction lamellar phase was calculated using the Bruggeman equation19 adapted for lamellar dispersions:

1 - φlam )

(

)( )

κ - κlam κel κel - κlam κ

1/3

(7)

in which κ denotes the electrical conductivity of the total system, φlam is the volume fraction lamellar phase, and the subscripts“lam” and “el” refer to the dispersed onions and the continuous electrolyte solution, respectively. For the conductivity of the dispersed onions a value of 0.8 mS/cm was used,3 whereas for the continuous salt solution, the conductivity of the electrolyte solution obtained after centrifugation was used. In a single case we were unable to collect sufficient electrolyte phase. In that case the refractive index was measured and the conductivity, based on the citrate concentration calculated from this, was used. In Figure 4 the relation between the volume faction onions and the sodium citrate concentration in the continuous phase is given for samples prepared with a total surfactant level of 10%. Also plotted is the fraction of the separated lamellar layer calculated from the separation after mild centrifugation for 1 h at 400g. The microstructural description based on microscopic observations agrees with the observation presented in Figure 4. Samples containing between 9 and 14% salt are space-filling colloidally stable onion dispersions in a continuous salt solution. Centrifugation for 1 h at 400g does not lead to separation into layers. For the sample with 9% salt the absence of layer separation despite a volume fraction below the maximum random closed packing fraction of 0.63 is probably due to (19) Bruggeman, D. A. G. Ann. Phys. 1935, 24, 636.

Figure 5. Bilayer spacing as a function of salt concentration in the continuous phase: (9) calculated from X-ray; (]) calculated from the volume fraction lamellar phase, assuming da ) 1.62 nm. The dotted line was calculated assuming that the bilayer contains the surfactant molecules and the water, hydrated to the surfactant molecules only.

Brownian motion of the small onions. At high g-force, 40 000 for 24 h, some continuous phase could be isolated. For the samples with 18% salt and above the ratio between the volume fraction, calculated from conductivity, and the volume fraction of the separated lamellar layer rapidly approaches 1, showing that the continuous salt solution is expelled from in between the onions due to flocculation. 4.1.3. Bilayer Spacing. At high salt concentration the bilayer repeat distance can be directly derived from X-ray spacings. At lower salt concentrations we were unable to measure the spacings using X-ray. In these cases bilayer spacings were calculated from the respective volumes of the water layers and the alkyl layers, using da/dw ) Va/Vw. Va and Vw are the volumes of the alkyl layer and the water layer, respectively, and can be calculated from the sample composition, the onion volume fraction, the appropriate densities, and the molar composition of the surfactant molecules. The sum of da and dw (the alkyl layer thickness and water layer thickness, respectively) equals the bilayer repeat distance. The thickness of the alkyl layer has to be estimated. A value of 1.62 nm gave the best correlation with the X-ray spacings. This value is reasonably close to values quoted in the literature for comparable systems. References taken from literature quote thickness of 1.9 nm (comparable surfactant mixture),6 1.65 nm for C12EO4, 1.91 nm for C12EO3, and 1.36 nm for C12EO6, all in the LR state.20 For clarity, the alkyl layer contains only the surfactant alkyl chains. The water layer contains salt solution and the hydrated hydrophilic surfactant headgroups. In Figure 5 the measured and calculated bilayer spacings are given as a function of salt level. The dotted line in Figure 5 was calculated, assuming the bilayer consists of surfactant molecules and hydrated water only. At high salt concentrations the calculated line and the measured values overlap, indicating that (nearly) all of the continuous phase has been expelled from within the onions. In a previous paragraph we have concluded that the collapse of the bilayer spacings at salt concentrations of about 18% and higher is due to the fact that the salt solution is no longer a good solvent for the EO chains. This is indicated by the decrease in the hydration of the (20) Carvell, M.; Hall, D. G.; Lyle, I. G.; Tiddy, G. J. T. Faraday Discuss. Chem. Soc. 1986, 81, 223.

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Figure 6. Volume fraction lamellar phase, calculated from conductivity data as a function of surfactant concentration with Na-citrate‚0H2O concentrations in the continuous phase of 9.5% ([), 12.7% (9), 16.9% (2), and 28.0% (b).

surfactant headgroups. Now we will discuss the apparent swelling of the bilayer separation at lower salt concentrations. It is generally accepted that when electrostatic repulsion is absent, bilayer swelling is caused by the thermal undulation of the bilayers. In that case the compression modulus, B, is given by21,22

B ) 9π2(kT)2d/64Kdw4

(8)

According to eq 6, the undulation potential is inversely proportional to the bilayer bending modulus K. When K decreases, the bilayer becomes less stiff, and subsequently the thermal undulations of the bilayer will cause the water layer thickness to increase. This leads to the following interpretation of the results in Figure 5: At salt concentrations between 9% and about 15%, the surfactant headgroups are well dissolved in the continuous phase, leading to repulsion between the surfactant headgroups in the plane of the bilayer. This leads to a low bilayer rigidity (low K) and therefore to swelling of the bilayers due to the thermal undulation. As the bilayers inside the onions are, except for curvature, identical to the bilayers on the outside, the thermal undulations also lead to repulsion between the surfaces of the onions and therefore to colloidal stability of the onion dispersion. As the salt concentration increases, the surfactant headgroups become gradually less soluble in the continuous phase, leading to attraction between the headgroups in the plane. This causes the bilayers to become more rigid, and the undulations are suppressed. Dehydration of the surfactant headgroups also induces attraction between the headgroups in opposing bilayers, which causes collapse of the water layers and flocculation of the onions. In Figure 6 the volume fraction lamellar phase as a function of surfactant concentration at four different salt concentrations in the continuous phase is given. At the two highest salt concentrations the relation between φlam and surfactant concentration is (nearly) a straight line with a small intercept on the φlam-axis. This means that the bilayer spacing hardly varies with surfactant concentration. For the sample with 12.7% salt, the volume fraction onions decreases less than proportional upon dilution to a volume fraction of about 0.6. Apparently above φlam ) (21) Nallet, F.; Roux, D.; Prost, J. Phys. Rev. Lett. 1989, 62, 276. (22) van der Linden, E.; Hogervorst, W. T.; Lekkerkerker, H. N. W. Langmuir 1996, 12, 3127.

0.6 the onions are compressed (the average bilayer repeat distance is reduced) due to packing constraints. Below this volume fraction we find a linear relation between the surfactant level and the onion volume fraction, suggesting that at φlam < 0.6 the onions are swollen freely. This means that above the volume fraction where the onions just touch the observed φlam is a result of a balance between the constraints imposed by the packing of the onions and the undulation of the bilayers. For the samples with 9.5% salt at high surfactant level even lower onion volume fractions are found, suggesting that in these cases the bilayer undulations are suppressed even more. This suggests that the bilayer rigidity modulus K is lower for the sample with 9.5% salt than for the samples containing 12.7% salt. In Figure 7 electron micrographs are presented of the surface of a single onion. We ascribe the surface roughness, which can easily be detected, to the bilayer undulations. This has been observed before in a brine-SDS-pentanol lamellar system with the aid of cryo-TEM on thin vitrified films.23 Apparently the high freezing rate is sufficient to prevent damping out of the undulations. Note that the typical size of the undulations decreases as the salt concentration increases. This points at increasing bilayer rigidity. We therefore conclude that increasing salt concentrations lead to more rigid bilayers. For clarity also two images are reproduced taken at the lowest and highest salt concentration but at much reduced magnification. The electron micrographs A until E were obtained after freezing from room temperature. Photograph F was obtained after freezing the same sample as shown in C, but now starting at 4 °C. The decrease in the observed surface roughness is striking, showing the thermal nature of the undulations. 4.2. Rheology. 4.2.1. Linear Experiments. The linear rheology was studied by measuring G′ and G′′ as a function of frequency for the samples with varying surfactant concentration at three different salt concentrations (9.6, 12.7, and 16.9%). Samples prepared with 28.0% salt in the continuous phase separated rapidly into two layers. Therefore, no frequency sweeps were recorded as the rheology changed with time. Only G′ and G′′ at 1 Hz were recorded. The measured values were stable for a few minutes before changing. The measurement as a function of frequency was performed well within the linear viscoelastic area. For the samples with 9.5 or 12.7% salt the critical deformation is about 0.045; for the sample with 16.9% salt the linear region terminates at a strain of 0.020. In Figure 8, G′ and G′′ for samples with 12.7% salt are given at six volume fractions. The rheological behavior depicted in Figure 8 is in many ways characteristic of the behavior of the samples at salt concentrations of 9.5 and 16.9%. At volume fractions lamellar phase of 0.6 and above G′ is nearly independent of frequency because the onions are close packed. G′ is about 10 times higher than G′′, indicating a solidlike behavior. Even at a volume fraction of 0.42, G′ is larger than G′′ by a factor 3, but G′ decreases with decreasing frequency. This indicates relatively longrange interactions between the onions with respect to their size. 4.2.1.1. The Elastic Modulus. In Figure 9, G′ at 1 Hz as a function of surfactant concentration is given. It appears that G′ depends on the level of the surfactants rather than on the volume fraction of the onions. Note (23) Ponsinet, V.; Talmon, Y. Langmuir 1997, 13, 7287.


Langmuir, Vol. 17, No. 16, 2001 4831

Figure 7. Detail electron microscopic image of samples with 7.8 (A), 10.0 (B), 12.2 (C and F), 14.4 (D) and 16.6% Na-citrate (E) in the continuous phase. Images A-E were obtained after freezing from room temperature; for image F the sample was frozen, starting at 4 °C. Image size 0.65 × 0.65 µm. The samples in images G and H are the same as in A and E, but at much reduced magnification. Image width is 6 µm.

that the colloidal stability of the sample does not affect this relation. Apparently the characteristic time of flocculation is much larger than the time of the experiment, and therefore the properties of the onions are measured rather than the properties of the flocs. Panizza et al.24 found the same power law dependency for G0 (highfrequency plateau modulus) as a function of the membrane mass fraction. For a proper explanation of the dependence of the elastic modulus on the frequency and consequently for the magnitude of G′, one has to consider whether the imposed frequency and deformation will cause an affine deformation of the sample. It is anticipated that this can only be (24) Panizza, P.; Roux, D.; Vuillaume, V.; Lu, C. Y. D.; Cates, M. E. Langmuir 1996, 12, 248.

the case at very high frequencies, with associated small length scales. At low and moderate frequencies, as applied in this study we assume affine motion at a length scale larger than the size of the onions. The second question to answer is how the different geometrical configurations of the bilayers for packed onions will contribute to G. We have adopted the schematic microstructural picture given by Panizza et al.24 A schematic drawing of a cross section of the contact between two onions is given in Figure 10. Panizza proposes two contributions to the high-frequency elastic modulus based on experimental results. One contribution is attributed to the pre-deformation present in the strongly curved parts of the deformed onions. On the basis of theoretical arguments, they find G ∼ 1/a. Their second contribution is calculated as G ) γ02B, where γ0

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Versluis et al.

Figure 10. Schematic representation of the contact between two onions at high volume fraction. For clarity, the number of bilayers in the onions has been reduced. Thick lines represent the sheets of surfactant molecules.

Figure 8. G′ (solid symbols) and G′′ (open symbols) as a function of radial frequency for samples with 12.7% salt and a volume fraction lamellar phase of 0.83 (b), 0.81 (9), 0.77 (2), 0.70 ([), 0.60 (1), and 0.42 (`).

same line of reasoning has been followed by Safran et al.25 to explain the spontaneous, equal but opposed curvature of the outer and inner layer of a vesicle membrane. For a lamellar system, stabilized by Helfrich undulation, B is given by eq 8. Since it has been shown that a deformation of an onion penetrates nearly to the center the onion,26 one can calculate the force as

6 F ) Bd tan2 θ∆l π

(9)

with 2θ the top angle of the cone over which two adjacent onions interact and ∆l the motion of the outer surface of the onion with respect to its core. In the literature the relation between the pair interaction potential V and the elastic modulus for a system with affine deformation on a length scale of the radius of a sphere is given as27,28

G0 )

φmaxn

[

δ2V δV 4 + 5π(2a + H) δH2 δH 2a + H

(

)]

(10)

with φmax the maximum volume fraction, n the number of neighbors, H the surface-to-surface separation, and a the radius of the spheres. Omitting the right-hand side of eq 10, and substitution of the second derivative of the potential by the first derivative of the force as given in eq 9, a first-order estimate of G can be made. Figure 9. G′ at 1 Hz as a function of surfactant concentration for samples with 9.5% salt ([), 12.7% salt (9), 16.9% salt (2), and 28.0% salt (b). Least-squares fit gives G′ ) 0.0039cs3.24, with cs the percent surfactant in the sample.

(γ0 < 1) is related to the quenched strain present in highly deformed onions that form grain boundaries between monodomains of undeformed onions. We have taken a different approach for the calculation of G. We propose that for our onions the main contribution to G comes from the interaction between the relatively flat area where the onions are in contact. We expect the contribution of the curved area to be relaxed at low frequencies. One argument for our approach is that in a mixed surfactant situation specific surfactant molecules can move to specific places in the bilayer, thus relaxing any accumulated tension due to deformation because of the packing of the onions. The (25) Safran, S. A.; MacKintosh, F. C.; Pincus, P. A.; Andelman, D. A. Prog. Colloid Polym. Sci. 1991, 84, 3.

G ≈ φmaxn tan2 θ

1 d B 2π2 a

(11)

For K ) 1kT, d ) 8 nm, and dw ) 6.4 nm, which appear to be valid estimates for the situation with 12.7% salt, we find B ) 4400 Pa. After inserting φmax)1, n ) 10, tan2 θ ) 0.2, and a ) 0.5 µm, relevant for a φlam of approximately 0.7, we find an estimate of G ∼ 7 Pa, which is the correct order of magnitude for G at low frequency. Note that while K is independent of the bilayer spacing, B will depend on the spacing and hence on the volume fraction of onions for packed onions, in the situation with thermal undulations. Despite the difference in approach, we find the same dependence of G on the onion radius (a) as Panizza.24 (26) van der Linden, E.; Dro¨ge, J. H. M. Physica A 1993, 193, 439. (27) Wagner, J. N. J. Colloid Interface Sci. 1993, 161, 169. (28) van der Vorst, B.; van den Ende, D.; Mellema, J. J. Rheol. 1995, 39, 1183.


Langmuir, Vol. 17, No. 16, 2001 4833

Figure 11. G′ at 1 Hz as a function of d2/dw4 for samples with 9.5% salt ([) and 12.7% salt (9). Straight lines are drawn to guide the eye.

For affine motion at a length scale of the spacing between the layers we estimate

G≈

n tan2 θB 4

(12)

Figure 12. G′ at 1 Hz as a function of surfactant concentration for samples with 9.5% salt ([), 12.7% salt (9), 16.9% salt (2), and 28.0% salt (b). Least-squares fitting gives 601φ 4.7 for the sample with 16.9% salt and 2918φ 3.1 for the sample with 28% salt. The dashed lines are drawn to guide the eye.

For n ) 10 and tan2 θ ) 0.2 this gives G ∼ 2200 Pa, which is a rather high estimate. At a certain frequency also the contribution of the curved “corners” will have to be included as they will no longer be relaxed. This will also lead to an increase in G. The calculations indicate that at the frequencies we applied there is affine motion on the length scale of the onion size rather than on the scale of the bilayer spacing. Note that in both cases the contribution to G drops rapidly as φlam decreases. This is also found experimentally. Since G depends on B when the undulation potential is the determining potential, one would expect a straight line relation with intercept zero when G′ at low frequency is plotted as a function of d2/dw4, provided the prefactor in eq 11 is constant. As can be seen in Figure 11, we find a nearly linear relation for all samples with 9.5 and 12.7% salt. The small intercept, which is found with the d2/dw4 axis, is probably due to the fact that the prefactor in eq 11 is not constant. Tan θ will rapidly become 0 when the volume fraction of the onions approaches the volume fraction where the onions no longer touch. The uncertainty in the prefactor prevents calculation of K from a fit to the data but does show that the change in K is limited. This is in line with the range of K values reported in the literature (0.7kT-2.6kT). Although there is some indication that the undulation potential contributes to small extent to the elasticity of the sample with 16.9% salt, we were unable to measure at sufficient low frequencies to estimate a low-frequency plateau in G′. In Figure 12, G′ at 1 Hz is plotted as a function of the onion volume fraction. For the samples with 16.9 and 28% salt a simple power law dependency of G′ on φlam is found. The exponent found (3.1 for 28% salt and 4.7 for 16.9% salt) is in the range of what is normally found for respectively strongly flocculated dispersions and weakly flocculated dispersions with fractal aggregates.29 For reference, also the data for 9.5 and 12.7% are plotted in this figure to indicate that for these samples a simple power law approach is less satisfactory. The dashed lines are drawn to guide the eye.

4.2.1.2. The Loss Modulus. For the samples containing 9.5 or 12.7% salt, a broad relaxation transition in G′′ at low frequencies is observed. This behavior has been seen before and was explained as a relaxation due to fluctuations in the shape of the onions as observed with confocal laser microscopy.30 The transition is only found at φlam > 0.6. The frequency at which the relaxation transition occurs depends strongly on the salt concentration but hardly changes when the volume fraction lamellar phase changes. It appears that at a given salt concentration G′ and G′′ can be superimposed by shifting the curves along the frequency axis and the modulus axis. The superposition is shown in Figure 13 for samples containing 12.7% salt. This shows that the strength associated with the relaxation is an almost fixed percentage of the elastic modulus a low frequency. This is a strong indication that the mechanism responsible for the transition is the same as the mechanism that causes the main part of the elasticity of the sample. For both the samples with 9.5 and 12.7% salt approximately the same percentage is found. It averages at 17( 3% of the elastic modulus at the lowest frequency. We propose the following explanation for this observation. As was shown before, our data at low salt concentration is well explained by the model given in the previous paragraph, based on the interaction over the bilayers between the flat parts where the onions touch. It was assumed that curved area is relaxed at low frequencies and does not contribute to G. We estimate, on the basis of geometric calculations on a regular dodecahedron, that the volume of the curved parts of the onions is about 15-20% of the total volume of the onions. We propose that the transition is caused by the inclusion in the deformation of the curved parts of the onions. The approximately 15-20% extra volume that is subjected to affine deformation correlates well with the increase of the strength of the relaxation, which is about 17% of the elastic modulus at frequencies below the transition. The actual strength of the transition (∆G) can be estimated in two ways: (a) by subtracting G′ at the low-

(29) de Rooij, R.; van den Ende, D.; Duits, M. G. H.; Mellema, J. Phys. Rev. E 1995, 49, 3038.

(30) Versluis, P.; van de Pas, J. C.; Mellema, J. Langmuir 1997, 13, 5732.

4834


Figure 13. Result of superimposing the data from Figure 8 by shifting G′ and G′′ by a factor q along the y-axis and a factor p along the x-axis. Legends are the same as in Figure 8; the results at volume fraction 0.42 have been omitted.

Versluis et al.

is about a factor 4, while the shift in τ is about a factor 10. This means that ∆η increases by a factor of about 2.5 on going from 9.5 to 12.7% salt. When onion deformation occurs, the salt solution in between the bilayers has to flow. This offers two possible reasons for ∆η to increase with salt concentration. The observed increase might be explained at least partially by the increase of the fraction of free salt solution with a slightly higher viscosity inside the onions at equal volume fraction on going from 9.5 to 12.7% salt. From Figure 6 it can be seen that at 9.5% salt and volume fractions above 0.6, the onions contain more surfactant and hence less salt solution when compared to 12.7% salt. When we assume that the viscous contribution is proportional to the amount of free salt solution inside the onions, this account for about a factor 1.5-2 of the observed increase. A second explanation might be found in considering the flux of salt solution across the bilayers through defects arising from thermal fluctuations.31,32 One might envisage that defects will occur more readily when the bilayer rigidity is low, leading to potentially less resistance to flow and hence to a lower viscous contribution. In our case the lowest bilayer rigidity is found at 9.5% salt. The possible explanations put forward here point in the right direction. 5. Conclusions

Figure 14. G′ (solid symbols) and G′′ (open symbols) as a function of radial frequency for samples with a volume fraction of onions of 0.70 and 9.5% salt ([) or 12.7% salt (9).

frequency plateau from G′ at the high-frequency plateau and (b) by taking 2 times G′′ at the maximum of the transition. The characteristic time of the transition (τ) was taken as the inverse of the radial frequency where the maximum in G′′ is found. By definition, τ ) ∆η/∆G. It was found that at a given salt concentration ∆η varies only marginally with the volume fraction of onions. This is also shown by the fact that the shift factors p and q, used to superimpose the data in Figure 13, are approximately equal at a given volume fraction of onions. Hence, the observed change in τ is mainly a consequence of the change in ∆G, which in turn is due to the change in the volume fraction of the onions. This is most clear for the samples containing 12.7% salt. Both ∆G and τ can be easily determined from the curves presented in Figure 8. For the samples containing 9.5% salt the estimate of ∆G and τ is more difficult as the transition occurs at higher frequencies, but it was found that the trends are the same. In Figure 14, G′ and G′′ as a function of frequency are plotted for samples with different salt concentration and a volume fraction of onions of 0.70. The shift in ∆G (which is proportional to the shift in G at the lowest frequency)

The results presented in this paper seem to strongly suggest that the onion phase under investigation is colloidally stable between salt concentrations of 9-15%. Also, swollen onion phases are found. Both swelling and colloidal stability are caused by thermal undulation of the surfactant bilayers. The swelling is restricted by (a) the boundary of the sample holder at high surfactant concentrations and high volume fractions of onions and (b) tension in the membrane at low surfactant concentrations and low volume fractions of onions. The surfactant molecules are well hydrated, indicating that the surfactant hydrophilic headgroups are well dissolved. At salt concentrations between approximately 15 and 20% the appearance of the onion phase changes from translucent to milky white, and the onions are (weakly) flocculated. The hydration of the surfactant molecules, the bilayer repeat distance, and, as a consequence of this, the obtained volume fraction of onions decrease rapidly. Thermal undulation of the bilayers is no longer observed because of stiffening of the layers. At even higher salt concentrations between 20 and 30% severe flocculation of the onions occurs. All continuous phase is expelled from the onions. After redispersion, the flocculated onions phase rapidly floats on top of the continuous phase. Flocculation can be observed with the naked eye. For the linear rheological behavior of the colloidally stable onion dispersions at 9.5 and 12.7% salt, a model taking into account the undulation potential as given by Helfrich and the length scale of the affine deformation is derived. It is assumed that the elasticity is due to the interaction between the flat parts where the onions touch. The model satisfactorily explains the magnitude of the found elastic modulus G′ at low frequencies, suggesting affine motion of the cores of the onions at the frequencies applied. The curved parts of the onions are assumed to be relaxed. At onion volume fractions of 0.6 and above a broad relaxation transition in G′′ is observed. The strength of (31) Deamer, D. W.; Bramhall, J. Chem. Phys. Lipids 1986, 40, 167. (32) Jansen, M.; Blume, A. Biophys. J. 1995, 68, 997.


the relaxation can be explained if we assume that the transition is caused by the inclusion of the curved part of the onions. At a given salt concentration but with varying surfactant level the change in ∆G and τ is proportional, showing that the transition occurs at a constant ∆η and is a consequence of the change in onion volume fraction. On going from 9.5 to 12.7% salt, ∆η associated with the transition increases by a factor of about 2.5. Some possible explanations for this effect are offered. The onion disper-

Langmuir, Vol. 17, No. 16, 2001 4835

sions at 16.9 and 28% salt behave rheologically as flocculated dispersions. Acknowledgment. We thank Mr. A. J. van der Salm for experimental assistance and Mr. R. den Adel and Mr. E. C. Roijers for the electron microscopy work and the X-ray experiments, respectively. LA000779Q

Influence of Salt Concentration and Surfactant Concentration on the

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