Flocculation of Weakly Charged Oil−Water Emulsions - Langmuir

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Langmuir 1999, 15, 970-980

Flocculation of Weakly Charged Oil-Water Emulsions R. Aveyard, B. P. Binks, J. Esquena, and P. D. I. Fletcher* Surfactant Science Group, Department of Chemistry, University of Hull, Hull HU6 7RX, U.K.

R. Buscall and S. Davies ICI Wilton Research Centre, PO Box 90, Wilton, Cleveland TS6 8JE, U.K. Received August 25, 1998. In Final Form: November 12, 1998 This study concerns dodecane-water emulsions stabilized primarily by the nonionic surfactant decylβ-D-glucoside (C10βGlu). The emulsions are stable with respect to coalescence and Ostwald ripening but unstable with respect to flocculation and creaming. Emulsions stabilized by monolayers of pure C10βGlu flocculate and show rapid creaming. A sharp transition from a flocculated state to a nonflocculated state can be induced by the addition of small mole fractions of either the anionic sodium octadecylsulfate or the cationic octadecyltrimethylammonium bromide surfactants. The nonflocculated emulsions show slower creaming and the discontinuous change in creaming rate can be used to detect the flocculation transition. We have measured the concentration of ionic surfactant required to induce the flocculation transition as a function of sodium chloride concentration in the continuous aqueous phase. Using a model in which the colloidal interactions between the deformable emulsion drops are taken to consist of electrostatic repulsion, van der Waals attraction, and a short-range repulsion modeled as a “hard wall”, we show how the flocculation transition can be quantitatively predicted using no adjustable parameters.

Introduction Oil-water (o-w) emulsions consist of thermodynamically unstable dispersions of micrometer-sized oil drops in water, coated by a monolayer of surfactant. In general, the instability of emulsions arises from the processes of creaming (or sedimentation), Ostwald ripening, flocculation, and coalescence, which may occur concurrently at different rates leading eventually to complete phase separation if equilibrium is achieved. Kinetically stable emulsions are formed when the rates of the instability processes are slow. The main focus of this study is on the quantitative modeling of the flocculation stability for an emulsion system where Ostwald ripening and coalescence rates are negligible. We have investigated dodecane-water emulsions stabilized primarily by the nonionic surfactant n-decyl-β-Dglucoside (C10βGlu). These emulsion drops mutually adhere (flocculate) but do not exhibit either droplet coalescence or Ostwald ripening. The droplets can be deflocculated by the addition of a low mole fraction (with respect to the total surfactant) of a strongly adsorbing ionic surfactant where the electrostatic charging of the drops produces a repulsion strong enough to overcome the van der Waals attraction responsible for the flocculation. The amount of ionic surfactant required to induce the sharply defined flocculation/deflocculation transition depends on the electrolyte concentration in the continuous aqueous phase. To probe the nature of the colloidal forces between emulsion drops, we have compared quantitative theoretical models of the locus of the flocculation transition (i.e., ionic surfactant concentration at the transition vs salt concentration) against the experimental data. This approach, using bulk emulsions, extends previous investigations of the colloidal forces between emulsion-drop surfaces made with single drops and bulk oil-water interfaces.1-3 It forms an alternative approach to the * To whom correspondence should be addressed: Department of Chemistry, University of Hull, Hull HU6 7RX, U.K. E-mail: [email protected].

elegant method developed by Calderon et al.4-6 who used the effect of magnetic fields on magnetic emulsion drops to determine the force as a function of distance between drops in bulk emulsions. Their method is, of course, restricted to magnetic emulsion drops. This paper is organized as follows. Following a section giving experimental details, we first describe the basic properties of the emulsion system studied here. We then detail a theoretical approach showing how the flocculation transition for such weakly charged emulsion drops may be calculated quantitatively. The distribution of ionic surfactant between the emulsion-drop surfaces and micelles present in the continuous phase is then discussed. In the next section, theoretical and experimental results are compared and discussed. Finally, the conclusions from this study are summarized. Experimental Section Water was purified by reverse osmosis and subsequent passage through a Milli-Q water reagent system. n-Dodecane (Avocado, 99%) was columned over alumina twice to remove polar impurities. NaCl (BDH, 99.9%) and the surfactants C10βGlu (Sigma, 98%), n-octadecyltrimethylammonium bromide (OTAB, Fluka, 97%), and sodium n-octadecyl sulfate (SODS, Lancaster, 99%) were used as received. For C10βGlu, the air-water surface tension showed no minimum with respect to concentration and gave tensions and a critical micelle concentration (cmc; 2.0 mM) in good agreement with literature.7,8 (1) Aveyard, R.; Binks, B. P.; Cho, W.-G.; Fisher, L. R.; Fletcher, P. D. I. Klinkhammer, F. Langmuir 1996, 12, 6561. (2) Cho, W.-G.; Fletcher, P. D. I. J. Chem. Soc., Faraday Trans. 1997, 93, 1389. (3) Binks, B. P.; Cho, W.-G.; Fletcher, P. D. I. Langmuir 1997, 13, 7180. (4) Leal Calderon, F.; Stora, T.; Mondain Monval, O.; Poulin, P.; Bibette, J. Phys. Rev. Lett. 1994, 72, 2959. (5) Mondain Monval, O.; Leal Calderon, F.; Phillip, J.; Bibette, J. Phys. Rev. Lett. 1995, 75, 3364. (6) Mondain Monval, O.; Leal Calderon, F.; Bibette, J. J. Phys. II 1996, 6, 1313. (7) Shinoda, K.; Yamaguchi, T.; Hori, R. Bull. Chem. Soc. Jpn. 1961, 34, 237.

10.1021/la981099e CCC: $18.00 © 1999 American Chemical Society Published on Web 01/14/1999

Weakly Charged Oil-Water Emulsions Air-water surface tensions were measured using a Kru¨ss K10 instrument with a du Nou¨y ring. Dodecane-water interfacial tensions were determined using the Kru¨ss K10 (for values above 3 mN m-1) and a Kru¨ss Site 04 spinning-drop tensiometer for lower values. Densities and refractive indices of the solutions required for calculation of the tensions were determined using a Paar DMA 55 densitometer and an Abbe´ refractometer (Hilger & Watts), respectively. Emulsion samples were prepared by homogenization of 9.6 mL of aqueous phase containing surfactant and salt plus 2.4 mL of dodecane using an UltraTurrax T25 homogenizer with either an 18G or 8G head. Both the homogenization speed and time were controlled. Emulsion-drop sizes were obtained using a Malvern 2600C laser-diffraction instrument, which allows resolution of drop diameters between 1 and 500 µm. For the sizing measurements, the emulsion samples were diluted approximately 400-fold into water containing C10βGlu at a concentration equal to the cmc (2.0 mM). For the microscopic observation of the emulsions, undiluted emulsion samples were mounted directly onto slides and covered with a cover slip. For the determination of the contact angle in adhering emulsion drops (see Figure 7) using microscopy, a drop of the creamed emulsion was diluted approximately 100 fold with the continuous phase of the same emulsion sample. The diluted emulsion samples were held within hemocytometer cells (Weber Scientific, Ltd.), giving a sample thickness of 0.2 mm. In the cells, the emulsion drops cream to the underside of the coverslip, and the microscope field of view was set to include a doublet of adhering drops of approximately equal radii. The focal plane was set to lie in the plane of the centers of the drops by initially focusing on the underside of the coverslip and moving the focus down by a distance equal to the drop radius. Digital images from the microscope (Nikon Labophot) were obtained using a DIC-U high-resolution camera (World Precision Instruments) connected to a PC. Contact angles were determined by analysis of the perimeter profile of the doublet of adhering drops extracted from the images using Aldus PhotoStyler software. Emulsion-drop ζ potentials were measured using a Matec ESA8000 instrument. All measurements were made at 25 °C.

Basic Properties of Dodecane-Water Emulsions Stabilized by C10βGlu C10βGlu is a relatively hydrophilic surfactant. From the results previously described for C10βGlu in systems with various apolar oils,8 the phase-inversion temperature (PIT) of the water-C10βGlu-dodecane system is predicted to be high (greater than 65 °C). Thus, at 25 °C, a mixture containing comparable volumes of dodecane and water plus a low concentration of C10βGlu is expected to form a so-called Winsor I system at equilibrium. This consists of an aqueous phase containing both monomeric and micellar aggregates of C10βGlu with a coexisting phase of virtually pure dodecane. By use of methods outlined previously for different oil phases,8 the extent of partitioning of the monomeric C10βGlu into the dodecane phase was found to be negligibly small. Also, the solubility of C10βGlu in dodecane was found to be less than 0.05 mM at 25 °C. Because the PIT of the water-C10βGlu-dodecane is high, the extent of solubilization of the dodecane into the aggregates of C10βGlu should be small, and thus, the aggregates are probably better described as micellar rather than o-w microemulsions. Emulsification of the Winsor I two-phase system yields a dodecane-water emulsion in which the continuous phase contains monomeric and micellar C10βGlu. We note that the basic phase behavior of this system is not significantly affected by the addition of NaCl up to the highest concentration used in this study (0.25 M). We first determined the adsorption of C10βGlu at the dodecane-water interface using tensiometry. Figure 1 (8) Aveyard, R.; Binks, B. P.; Chen, J.; Esquena, J.; Fletcher, P. D. I.; Buscall, R.; Davies, S. Langmuir 1998, 14, 4699.

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Figure 1. Variation of the dodecane-water interfacial tension with aqueous-phase concentration of C10βGlu. The solid line shows a polynomial fit to the four data points below the cmc used to obtain As. The dashed line is a guide for the eye. Filled circles, at concentrations above the cmc, were used to obtain the (virtually) constant values of γ above the cmc.

Figure 2. Emulsion size distribution for dodecane-water emulsions stabilized by 10 mM C10βGlu. The emulsion, prepared by homogenization using an UltraTurrax 8G head homogenizer operating at 8000 rpm for 60 s, was unflocculated and contained 20 vol % dodecane, 0.007 mole fraction (with respect to surfactant) SODS, and 10 mM NaCl. Filled and open circles refer to the volume-weighted distribution (left-hand axis) and cumulative volume fraction (right-hand axis), respectively.

shows the variation of oil-water interfacial tension γ with C10βGlu concentration in the aqueous phase. The cmc in the aqueous phase for equilibrated systems with dodecane is 1.5 ( 0.1 mM, slightly lower than the value (2.0 mM) for oil-free aqueous solutions.7,8 The minimum area per adsorbed C10βGlu molecule As (corresponding to maximum adsorption at the cmc) was obtained by fitting the four data points at the highest concentration below the cmc to a third-order polynomial. Differentiation of the fitted curve together with use of the Gibbs adsorption equation yielded a value of As equal to 0.37 ( 0.04 nm2. For emulsions with aqueous-phase C10βGlu concentrations in excess of the cmc, the interfacial tension of the drop surfaces is equal to 1.0 mN m-1. A typical emulsion-drop size distribution is shown in Figure 2. For the preparation method used here, the emulsions were rather polydisperse with a bimodal distribution. The mean drop radius quoted in this work is the volume-weighted value of the radius corresponding to the cumulative volume fraction equal to 0.5. For constant emulsification conditions, the mean drop radius is independent of the NaCl concentration and the presence of small quantities of added ionic surfactant (Figure 3). We note also that the mean drop size is unaffected by whether the initial, undiluted emulsion is flocculated or unflocculated. Initially, flocculated samples appear to be unflocculated when diluted approximately 400-fold and agitated prior to the drop-size measurements. All emulsion

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Figure 3. Variation of mean initial drop radius with NaCl concentration for samples containing added SODS (filled circles) and OTAB (open circles). The emulsion samples contained 20 vol % dodecane and 10 mM surfactant and were emulsified using the 18G homogenizer at 8000 rpm for 60 s. The dashed line indicates the average radius of 3.6 µm.

Aveyard et al.

Figure 5. Cream height versus time for emulsion samples containing different concentrations of the anionic surfactant SODS. The emulsions contained 20 vol % dodecane, 10 mM NaCl, and 20 mM total surfactant and were emulsified using an 18G head at 8000 rpm for 60 s.

Figure 4. Variation of mean drop size with time for emulsions containing the different concentrations of C10βGlu indicated on the figure. The emulsions all contained 20 vol % dodecane and no NaCl and were homogenized using the 8G head at 8000 rpm for 120 s.

samples showed no change in mean drop radius over periods of up to a week, and a representative set of time measurements is shown in Figure 4. In addition to the constant mean drop sizes measured over approximately 1 week, it was noted that the emulsion samples showed no visible separation of dodecane layer over periods of up to 9 months. It appears that drop coalescence and Ostwald ripening rates are negligible for these systems. As explained in the Introduction, the emulsion drops stabilized by pure C10βGlu flocculate. The flocculation can be prevented by addition of a small mole fraction of ionic surfactant (either the anionic SODS or the cationic OTAB). For the oil volume fraction used in this study, the flocculation is found to accelerate the rate of creaming. Figure 5 shows the variation of the height of the interface between the lower, drop-lean emulsion and the upper, drop-rich cream layer for emulsion samples containing different concentrations of SODS. There is a sharp transition in creaming rate between 0.0022 mole fraction (flocculated, rapid creaming) and 0.0031 mole fraction (unflocculated, slow creaming). The creaming observations were used to provide a simple measure of the location of the flocculation transition point. The criterion used was whether the cream layer height reached 10 mm within 3 min. Micrographs of the emulsion samples containing 0.0022 and 0.0031 mole fraction SODS (with all other conditions as in Figure 5) are shown in Figure 6. It can be seen that the composition at which the creaming acceleration is observed does indeed correspond to the flocculation

Figure 6. Optical micrographs of emulsions containing 0.0022 mole fraction (upper plot) and 0.0031 mole fraction (lower plot) of SODS. All other conditions were as those in Figure 5.

transition. It was checked that the creaming acceleration and flocculation transition points were coincident over the entire range of NaCl concentrations used in this study. In the flocculated state, the drops adhere with the formation of a flat, aqueous emulsion film separating them and a finite contact angle θ between the film and adjoining spherical drop surface. Figure 7 shows a higher magnification optical micrograph of a doublet of adhering drops. Image analysis of the micrograph was used to determine θ which, as discussed by Aronson and Princen,9 provides a measure of the droplet (attractive) interaction energy in the flocculated state. The variation of θ with [NaCl] for flocculated emulsion-drop doublets containing no added ionic surfactant is shown in Figure 8. The contact angle is virtually constant at approximately 30° for all salt concentrations. Theory Related to the Flocculation Transition For the development of the theory, we consider the interactions between noncoalescing, monodispersed o-w emulsion drops stabilized by a monolayer of nonionic surfactant containing a mole fraction mem of an ionic surfactant. For deformable emulsion drops, it is necessary (9) Aronson, M. P.; Princen, H. M. Colloids Surf. 1982, 4, 173.

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Figure 7. Optical micrograph of a doublet of adhering emulsion drops showing the formation of a flat thin film and finite contact angle θ.

Figure 9. Diagram showing the geometrical parameters relevant to the planar film separating adhering emulsion drops (upper diagram), separated spherical drops (middle diagram), and adhering drops (lower diagram). Figure 8. Variation of contact angle with [NaCl] for flocculated emulsions containing 10 mM C10βGlu and no added ionic surfactant.

to consider the interactions between undeformed, spherical drops at large separations and the interactions between adhering, deformed drops at small separations. For the different separation regimes, it is convenient to discuss the interactions in terms of either the total energy of interaction or the disjoining pressure (equal to the force per unit area normal to the planar film surfaces). The relevant geometrical parameters for thin emulsion films, separated, spherical drops, and a doublet of adhering, deformed drops with an intervening thin film are shown in Figure 9. The total interactions are assumed to be equal to the sum of (i) a short-range, “hard-wall” repulsion, (ii) attractive van der Waals force, and (iii) electrostatic repulsion. The short-range repulsion is included for the system considered here to account for the fact that the emulsions are indefinitely stable with respect to coalescence. It is envisaged that this short-range repulsion may include contributions from hydration, undulation, and protrusional forces10 and is therefore likely to be a steeply decaying force with a range comparable to the thickness of the surfactant headgroup region of the adsorbed surfactant monolayer. It is modeled here as a “hardwall” with disjoining pressure Πhw and energy of interaction Whw given by

hard-wall interaction. As shown in Figure 9, h ) 0 is taken to correspond to the contact between the surfaces separating the tail and headgroups of the adsorbed surfactant monolayers. Within the model assumed here, the lowest accessible value of film thickness h is equal to hhw (i.e., h cannot equal zero), corresponding to film rupture and drop coalescence. Calculation of Disjoining Pressure versus Film Thickness. We first consider the disjoining pressure operating across the thin, planar emulsion film formed between two equal-sized, adhering emulsion drops. The disjoining pressure is a function of the film thickness h and is taken to be the sum of contributions due to the van der Waals, electrostatic, and hard-wall pressures; i.e., Π ) Πvdw + Πel + Πhw. The van der Waals component of the disjoining pressure Πvdw can be expressed

Πvdw ) -A/6πh3

(2)

where h is the film thickness and hhw is the range of the

where A is the Hamaker constant for the oil-water-oil film (where the oil drops are taken to include the surfactant monolayer tail region). For dodecane-water-dodecane films, the value of A is 5.0 × 10-21 J.11 Equation 2 neglects the effects of the headgroups of the adsorbed surfactant monolayers. As discussed in ref 10, this is valid only for film thicknesses greater than twice the thickness of the headgroup region (estimated from molecular models to be about 0.6 nm). Equation 2 also neglects effects due to retardation which cause the dispersion component of the van der Waals force to decrease to a magnitude less than that predicted by eq 2 for h greater than approximately 10 nm. This approximation is less serious for emulsion films than for foam films in air because the zero-frequency component of A (not subject to retardation) has a greater

(10) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd Edition; Academic Press: London, 1992.

3.

Πhw ) ∞ for h < hhw and Πhw ) 0 for h > hhw Whw ) ∞ for h < hhw and Whw ) 0 for h > hhw (1)

(11) Hough, D. B.; White, L. R. Adv. Colloid Interface Sci. 1980, 40,

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contribution to the total value of A in the case of emulsion films.10 Overall, eq 2 is likely to lead to fairly accurate values of Πvdw for thicknesses greater than about 2 nm and less than some tens of nm. The electrostatic component, Πel, of the disjoining pressure in an emulsion film is given by

( )

Πel ) 64ckT tanh2

zeeψ exp(-κh) 4kT

(3)

where c is the concentration of inert electrolyte of valence ze/ze, k is Boltzmann’s constant, T is the absolute temperature, e is the electronic charge, ψ is the surface potential, and κ (the inverse Debye length) is

κ)

( ) 0kT

-1/2

(4)

2 2

2z e c

where  is the dielectric constant of the aqueous phase and o is the permittivity of free space. Equation 3 (as shown previously10) is valid for κh < 1, the “weak-overlap” approximation. For large film thicknesses, both the surface potential ψ and surface charge density σ remain constant with changing film thickness. At lower film thickness however, charge regulation processes may cause ψ or σ or both to change with film thickness. In the general case, Πel at low film thicknesses has a value intermediate between that obtained by either of the limiting cases of constant surface potential or constant surface charge density. For the emulsion-drop surfaces considered in this study, the surface potential is generally small ( 2R + hfilm), the drops are undeformed and spherical. At lower separations, the drops are assumed to deform to the shape of truncated spheres with a flat film of thickness hfilm separating them (Figure 9). The interaction of (14) de Vries, A. J. Recueil 1958, 77, 441.

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deformable drops has been considered in detail by Danov et al.,15-18 and their treatment is followed here except that hydrodynamic interactions are neglected and the film thickness in the deformed droplet state is equated with hfilm. Because the surface separation is always equal to or larger than hhw, the total energy of interaction W does not include a contribution from the short-range interactions modeled here as a hard wall. We first consider separated, spherical drops; i.e., z/(2R + hfilm) > 1. For drop surface separations H (equal to z 2R) much less than the drop radius R, the Derjaguin approximation19 is valid, and Wvdw is10

Wvdw ) -AR/12H

(9)

The electrostatic interaction Wel is given by eqs 10-12 for the weak-overlap approximation, constant surface potential, and constant surface charge density cases, respectively.

( )

zeeψ exp(-κH) Wel ) 64πRckTκ-2 tanh2 4kT

(10)

Wel ) 2πR0ψ2 ln[1 + exp(-κH)]

(11)

Wel ) -2πR0ψ2 ln[1 - exp(-κH)]

(12)

Equations 11 and 12 are valid for low surface potentials (less than approximately 25 mV) and are taken from refs 12 and 20. For doublets of deformed drops [i.e., for z/(2R + hfilm) < 1], the total energy of interaction includes an additional contribution Ws arising from the droplet surface deformation energy.15 For r/R , 1 (small deformations), Ws is given by

(

Ws ) πR2

)

EGr8 γr4 + 2R4 64R8

(13)

where r is the radius of the thin film, R is the radius of the spherical part of the truncated sphere, γ is the oilwater interfacial tension, and EG is the effective Gibbs elasticity of the surface. Deformation of the drops changes the value of the radius of the spherical regions of the drops R. Conservation of drop volume gives the value of R in terms of z as the solution of the cubic equation

(

) (

)

3(z - hfilm) 2 (z - hfilm)3 + 2R3sphere R 0)R + 4 16 (14) 3

where Rsphere is the radius of the spherical drop before deformation. The radius r of the circular thin film is given by

r)

x ( R2 -

)

z - hfilm 2

2

(15)

(15) Danov, K. D.; Petsev, D. N.; Denkov, N. D.; Borwankar, R. J. Chem. Phys. 1993, 99, 7179. (16) Danov, K. D.; Petsev, D. N.; Denkov, N. D.; Borwankar, R. J. Chem. Phys. 1993, 99, 7179. (17) Denkov, N. D.; Petsev, D. N.; Danov, K. D. J. Colloid Interface Sci. 1995, 176, 189. (18) Denkov, N. D.; Petsev, D. N.; Danov, K. D. J. Colloid Interface Sci. 1995, 176, 201. (19) Derjaguin, B. V.; Kolloid-Z. 1934, 69, 155. (20) Hunter, R. J. Foundations of Colloid Science, Vol. 1; Clarendon Press: Oxford, 1986.

For hfilm/R < 0.3 and r/R < 0.7, Wvdw is given accurately by15-18

Wvdw ) -

[

]

( )

hfilm R A 3 r2 2r2 + + 2ln + 2 12 4 hfilm R hfilm Rhfilm (16)

For κR . 1, Derjaguin’s approximation is valid and Wel is

Wel )

64ckT eψ R tanh2 exp(-κhfilm) r2 + κ 4kT κ

{[

( )

Wel ) π0ψ2 1 - tanh

Wel ) -

{[

( )]

(

)

(17)

}

(18)

}

(19)

κhfilm 2 2R r + ln[1 + 2 κ

( )]

exp(-κhfilm)]

κhfilm 2 2R π 2 σ 1 - coth ln[1 r + 0κ 2 κ

exp(-κhfilm)]

for the cases of weak overlap, constant potential, and constant surface charge density, respectively.15 We note that for deformed drops the Laplace pressure inside the drops and hence hfilm is a function of the deformation because R changes with z. This correction has been incorporated into the calculations presented here. Through use of the series of equations presented above, the droplet pair interaction energy can be calculated for both the undeformed and deformed regimes. If the minimum energy occurs within the deformed droplet regime, the droplets adhere (flocculate) with the formation of a finite contact angle between the thin film and the adjoining spherical drop surface. At such an energy minimum, the equilibrium contact angle θ is related to the film and drop radii according to

θ ) sin-1(r/R)

(20)

The evolution of the curves of W versus z with ionic surfactant mole fraction in the monolayers stabilizing the droplets (mem) is shown in Figure 11 for 0.1 mM NaCl (the same salt concentration represented in Figure 10). We emphasize here that W is the equilibrium interaction energy for a given z; i.e., nonequilibrium effects such as hydrodynamic interactions are neglected. The drop separation is represented as the dimensionless ratio z/(2R + hfilm) for which the value unity corresponds to the separation at which the drops first deform. For each value of mem in Figure 11, the right-hand plot shows the nondeformed regime [z/(2R + hfilm) > 1] and the left-hand plot [z/(2R + hfilm) < 1] the deformed regime. The upper plots with mem ) 0.00149 show that the interaction is repulsive for all separations. Decreasing mem slightly to 0.00145 (middle plots) causes the maximum in Π to fall below Pc and hfilm to decrease to hhw. In this case, the energy minimum occurs around z/(2R + hfilm) ) 0.85, corresponding to adhesive, deformed drops with contact angle of 29°. Importantly, for this value of mem, W shows a maximum of approximately 2000 kT, which must be overcome before the lowest energy state can be reached. As shown in the lower plots, the value of mem must be further decreased to 0.000155 before the maximum in W is reduced to zero. For this salt concentration, the analysis shows that two types of transitional values of mem are present. The first (between mem of 0.00149 and 0.00145) corresponds to a decrease in hfilm to hhw and leads to the formation of the

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The approximate eq 21 shows that ccfc for weakly charged -2/3, and A -4/3 drops is expected to scale with z-2, m4/3 s em, A and to be independent of the drop radius. Distribution of Ionic Surfactant between Emulsion Drops and Micelles. The theory for the flocculation transition allows the prediction of mem, the mole fraction of ionic surfactant in the monolayers coating the emulsion droplets, at the flocculation transition. Experimentally, the mole fraction of ionic surfactant (with respect to the total moles of surfactant) in the total system mtot at the transition is determined. Thus, to compare theory and experiment, we require a relationship between mem and mtot. For an oil-water emulsion containing surfactant in excess of the cmc, the total surfactant is present as monomers, micellar aggregates within the continuous aqueous phase, and as a monolayer adsorbed at the emulsion-drop surfaces. As noted earlier, neither the hydrophilic C10βGlu nor the ionic surfactants partition to the dodecane oil drops to a significant extent. For the case of a low concentration of a long-chain ionic surfactant added to a nonionic system, the low water solubility of the long-chain ionic surfactant ensures that its monomeric concentration is negligibly small. Thus, the added ionic surfactant may distribute between the micelles and the emulsion-drop surface monolayers. The total mole fraction of ionic surfactant, mtot, is given by Figure 11. Calculated curves of total drop interaction energy W versus the reduced separation z/(2R + hfilm) for different values of mem obtained using the weak-overlap approximation. Both the deformed [z/(2R + hfilm) < 1; left-hand plots] and nondeformed [z/(2R + hfilm) > 1; right-hand plots] regimes are shown. The upper plots (mem ) 0.00419) correspond to a nonadhesive state, the middle plots (mem ) 0.00145) correspond to an adhesive state with energy barrier, and the lower plots (mem ) 0.000155) correspond to an adhesive state with a zeroenergy barrier. The value of EG is taken to be zero, and other parameters are the same as those in Figure 10.

energy minimum at z/(2R + hfilm) < 1. This is denoted here the “film transition”. The second transition (denoted the “drop transition”) occurs at mem ) 0.000155 and corresponds to the point at which the energy maximum during the approach of the undeformed drops equals zero. Further calculations (not shown here) reveal that, at high salt concentrations, the film transition occurs at a value of mem at which there is no positive maximum in W versus separation; i.e., the adhesive (flocculated) state is reached without the need to overcome an interaction energy barrier. For the case of the drop transition it is possible to derive an analytical relationship between the salt concentration and mem at the transition. As discussed in Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory for nondeformable spheres,21 the transition is taken to occur when W ) 0 and dW/dH ) 0. Through use of the weak-overlap approximation for Wel, the transition is predicted to occur at a separation corresponding to κH ) 1. If it is assumed that the low potential approximation for the Grahame equation (σ ) oψ/κ) is valid, the following expression for the critical flocculation concentration of a ze/ze electrolyte (ccfc in molar units) in terms of mem is obtained (where the ionic surfactant charge zs ) 1).

ccfc )

4.5816kT(0)1/3m4/3 em NAA

A4/3 s

2/3

z2e e2/3

(21)

(21) Shaw, D. J. Introduction to Colloid and Surface Chemistry, 4th ed.; Butterworth-Heinemann: Oxford, 1992.

mtot ) cI/(cI + cN) ≈ cI/cN for small mtot

(22)

where cI and cN are the total concentrations of ionic and nonionic surfactant, respectively, expressed as moles per total volume of the emulsion system. The partition coefficient P for the ionic surfactant between the emulsiondrop surfaces and the micellar aggregates is defined as

P)

cIem/(cIem + cNem) cIem/(cNem) mem ) ≈ (23) mmic cImic/(cImic + cNmic) cImic/(cNmic)

where the subscripts “em” and “mic” indicate the concentrations of the species located in the emulsion surfaces and micelles (again expressed as mol per total volume of the emulsion system). Noting that

cIem ) memcNem and cImic ) mmiccNmic

(24)

we obtain

mem(cNem + cNmic/P) cIem + cImic cI ) ) mtot ) cN cNem + cNmic + cmc cNem + cNmic + cmc (25) where cImic ) mmiccNmic ) memcNmic/P. Rearranging eq 25 gives the final equation for mtot in terms of mem valid for cI , cN.

mtot )

mem(cNem + cNmic/P) cN

(26)

For an emulsion containing an oil volume fraction φ, the value of cNem (in molar units) is given by

cNem ) 3φ/1000RsphereAsNAv

(27)

where Rsphere is the radius of the emulsion drops in meters and NAv is Avogadro’s number. The value of cNmic ) cN cNem - cmc. For o-w emulsion surfaces with micelles present in the continuous phase, P as defined here is expected to be less than unity because the ionic headgroups are more spaced on the highly curved micellar surface

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than in the (virtually) flat emulsion-drop surfaces. This intuitive expectation is confirmed by the thermodynamic analysis and experiments for Winsor I microemulsion systems by Aveyard et al.22 Interfacial properties of emulsion drops stabilized by mixtures of nonionic and ionic surfactants have been considered by Stalidis et al.23,24 Two approaches have been taken to estimate the value of P. In the first, we calculate P using the result quoted by Evans and Wennerstro¨m.12 The difference in electrostatic free energy per monovalent surface charge in a spherically curved micellar surface and that of the (virtually) flat surface of an emulsion drop ∆Gel is

∆Gel ≈ -

[

]

1 + (1 + s2)1/2 2 ln sκRmic 2

(28)

where Rmic is the micellar radius and the dimensionless charge density s ) σ(8kTcsalto)-1/2 for a 1:1 electrolyte at concentration csalt. The approximate eq 28 is valid only for high salt concentrations such that κRmic > 1. Assuming that the distribution coefficient P is governed entirely by the difference in electrostatic free energy between the curved and flat surfaces, we obtain P ) exp(∆Gel/kT). Inspection of eq 28 shows that P is predicted to be less than unity and that it should be a function of Rmic, salt concentration, and mem (which determines s). The second approach uses the fact that the difference between mem and mtot is dependent on the total surfactant concentration as described in eqs 26 and 27. Although the value of mem required to induce the flocculation transition at a particular salt concentration is constant, the value of mtot required to achieve the transition should depend on the total surfactant concentration and the value of P. Thus, measurement of the variation of mtot at the transition with surfactant concentration allows P to be determined. The results of both approaches are described in the following section. Comparison of Theory and Experiment. The theory outlined above provides a prediction of mtot at the flocculation transition as a function of salt concentration, which can be compared with experimental data. The necessary input parameters were obtained as follows. Values of the mean emulsion-drop radius and the oilwater interfacial tension were measured as described earlier. As shown in Figure 2, the emulsion-drop size distribution for the systems studied is bimodal. However, calculations show that the input value of the mean drop size has only a small effect on the predicted value of mtot at the flocculation transition (either drop or film) under most conditions, and thus polydispersity of the emulsions is expected to have a relatively minor effect on the locus of the flocculation transition. Indeed, the analytical eq 21 shows that ccfc is independent of drop radius. As, equal to 0.37 nm2, was determined tensiometrically as described earlier. The Hamaker constant for the dodecane-waterdodecane films was taken to be 0.50 × 10-20 J.11 The range of the hard-wall repulsive interactions (hhw) was obtained by adjusting the value until the predicted value of the contact angle for adhesive drop doublets was in agreement with the measured value of 29° (for mem ) 0 and independent of [NaCl]). The value of hhw determined in this way must be regarded as an apparent or “effective” value because the calculation of the van der Waals (22) Aveyard, R.; Binks, B. P.; Mead, J. J. Chem. Soc., Faraday Trans. 1 1987, 83, 2347. (23) Stalidis, G.; Avranas, A.; Jannakoudakis, D. J. Colloid Interface Sci. 1990, 135, 313. (24) Avranas, A.; Stalidis, G. J. Colloid Interface Sci. 1991, 143, 180.

Figure 12. Variation of mean emulsion-drop radius with total surfactant concentration for 0.1 mM and 10 mM NaCl. The emulsions contained 20 vol % dodecane and low concentrations of SODS and were emulsified using an UltraTurrax homogenizer with an 18G head operating at 8000 rpm for 60 s.

attraction using eq 2 considers the dispersion properties of the surfactant headgroup region to be identical to those of water. The value was found to be 0.7 nm, reasonably similar in magnitude to twice the thickness of the headgroup region of the C10βGlu monolayer, and thus appears reasonable. The Gibbs elasticity of the surfaces EG (affecting the energy of interaction in the deformed drop regime) was taken to be zero. This corresponds to the assumption that the tension of the drop surfaces remains unaltered during the deformation. It is likely to be valid if the rate of drop deformation (and consequent increase of surface area) is slow relative to the rate at which surfactant can be supplied to the newly formed surface. Values of the dielectric constant of water and additional physical constants were taken from the literature.25 To compare the experimental and calculated flocculation transitions as a function of [NaCl], we require values of P for the different NaCl concentrations. We have used measurements of the variation of mtot at the flocculation transition as a function of the total surfactant concentration to obtain values of P at 0.1, 1, 10, and 100 mM NaCl. Figure 12 shows representative plots of the variation of the mean emulsion-drop size with surfactant concentration. The mean drop size increases as the concentration is reduced to values approaching the cmc, presumably due to a decrease in the rate at which surfactant can be supplied to the newly formed emulsion-drop surfaces during emulsification. The origin of the systematic variation with NaCl concentration is unclear at present. Figure 13 shows the variation of mtot of SODS at the flocculation transition with total surfactant. The fitted curves (solid lines) were obtained by floating P for each salt concentration. For these calculations, the transition was assumed to correspond to the film transition and the weak-overlap approximation was used because this combination was found to provide the best fit to the entire data set of flocculation transitions (see later). The additional salt concentrations showed similar qualities of fit, but for clarity, the results are not included in the figure. The values of P obtained by this procedure are shown in Figure 14 which includes two additional values at high [NaCl] calculated using eq 28 and taking Rmic ) 1 nm. We note that the agreement between calculated and experimental values of P at 0.1 M NaCl is not particularly good. As will be explained later, the calculated value of mem at (25) Handbook of Chemistry and Physics, 62nd Edition; CRC Press: Boca Raton, Florida, 1981.

978 Langmuir, Vol. 15, No. 4, 1999

Figure 13. Variation of mtot at the flocculation transition with total surfactant concentration for 0.1 and 10 mM NaCl. The solid curves are calculated using a single adjustable value of P for each salt concentration.

Figure 14. Variation of P (at the flocculation transition) with NaCl concentration. Filled circles were obtained by experiments, and open circles were calculated as described in the text. The solid curve shows a polynomial fit used to obtain P by interpolation for subsequent calculations.

the film transition is underestimated at high salt concentration when the range of the electrostatic repulsion is less than the range of the van der Waals attraction. This is likely to introduce an additional error into the value of P estimated experimentally at high [NaCl]. For this reason, we have chosen to use the values of P obtained by calculation for [NaCl] > 0.01 M in our further calculations. As expected, P is less than unity, showing that the ionic surfactant has a greater preference for the highly curved micellar surface than for the virtually flat emulsion-drop surfaces. The values of P shown in Figure 14 refer to different [NaCl] and to different values of mem, corresponding to the flocculation transition for each salt concentration. Because P is expected to depend on both mem and the salt concentration, the minimum in P seen in Figure 14 presumably results from the fact that both variables are changing in the plot. The variation of mtot at the flocculation transition with total concentration of 1:1 electrolyte in the aqueous phase is shown in Figure 15 for both the anionic SODS and the cationic OTAB surfactants. The solid lines correspond to the film transition curves taken to be the point at which the maximum in disjoining pressure is equal to the capillary pressure. The curves marked a, b, and c assume constant surface potential, weak overlap, and constant surface charge density, respectively. The values of P used were obtained by interpolation of the solid curve of Figure 14. The dashed curves a, b, and c correspond to the drop transition (i.e., when the maximum in W vs H for the approach of undeformed drops is equal to zero) and were calculated for the assumptions of constant surface po-

Aveyard et al.

Figure 15. Variation of mtot at the flocculation transition with electrolyte concentration in the continuous aqueous phase for emulsions containing 20 vol % dodecane and a total surfactant concentration of 10 mM. Open circles refer to cationic OTAB, and filled circles refer to anionic SODS. The solid lines show the calculated film transitions with assumption of constant potential, weak overlap, and constant surface charge density for curves a, b, and c, respectively. The dashed lines show the calculated drop transitions with assumption of constant potential, weak overlap, and constant surface charge density for curves a, b, and c, respectively.

tential, weak overlap, and constant surface charge density, respectively. The best fit to the experimental data is seen for the case of the film transition calculated using the assumption of weak overlap. It is important to note here that each of the calculated curves in Figure 15 has been generated using no adjustable parameters. One important point to emerge from Figure 15 is that, at salt concentrations of less than about 5 mM and in the region bounded by the solid and dashed curves, flocculation occurs despite the presence of a repulsive interaction energy barrier which may be several thousands of kT (see Figure 11). We first examine the possibility that buoyancy forces on the drops may overcome the repulsive force barrier. This is in principle feasible, because buoyancy forces must be greater than that of the dispersing effect of thermal, Brownian motion for the observed creaming to occur. For the calculated plots of Figure 11 with mem equal to 0.00145, the maximum force mutually repelling the undeformed drops is 2.4 × 10-10 N (calculated using force ) dW/dH). In comparison, the buoyancy force acting on a dodecane drop of radius 3.6 µm in water is approximately 5 × 10-13 N. Clearly, buoyancy forces are insufficient to overcome repulsive energy barriers of the magnitude calculated in Figure 11. A second possible explanation is that the repulsive interaction energy is overestimated by the calculations presented here. It has been assumed here that the electrostatic charge is uniformly distributed over the drop surfaces for all separations. However, because the surfactant monolayers coating the drops are mobile, it is speculated here that the surface charges may adopt a nonuniform distribution on close approach of the drops, thereby resulting in a lower repulsive energy of interaction. Additionally, as discussed in the literature, the effects of a distribution in surface properties26 and of random thermal fluctuations27,28 may also serve to reduce the energy barrier below the magnitude calculated here. Further theoretical calculations are required to resolve this issue. The experimental values of mtot for the anionic SODS fall slightly below those of the cationic OTAB. The origin (26) Prieve, D. C.; Lin, M. M. J. J. Colloid Interface Sci. 1982, 86, 17. (27) Warszynski, P.; Czarnecki, J. J. Colloid Interface Sci. 1989, 128, 127. (28) Bergeron, V. Langmuir 1997, 13, 3474.

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Figure 16. Comparison of measured ζ potentials (open circles) and surface potentials estimated from flocculation stability transitions for emulsion drops stabilized by C10βGlu in the absence of ionic surfactant.

of this effect probably lies in the fact that monolayers of the pure nonionic C10βGlu in the absence of added ionic surfactant generally bear a small negative charge. This charge, observed for both foam and emulsion films,3 is thought to result from the differential desorption of cations and anions present in the aqueous phase. Because of the small negative charge, a slightly greater concentration of cationic surfactant is required to achieve the overall, net surface charge density required to induce the flocculation transition than is expected for a completely uncharged surface. The theoretical line calculated assuming zero charge on the pure C10βGlu monolayer should lie halfway between the curves for SODS and OTAB as seen for low salt concentrations. From the differences in the values of mtot for SODS and OTAB, we have estimated the variation of the surface potential of the pure C10βGlu monolayer NaCl concentration and the curve is compared with measured ζ potentials in Figure 16. Although the potentials estimated from the flocculation stability transitions have a high uncertainty (because they are determined from the small differences between the SODS and OTAB curves), the agreement is reasonable. At high salt concentrations (above 0.02 M), the measured values of mtot lie significantly above the calculated curve b (solid line) which corresponds to the point at which the maximum in disjoining pressure becomes equal to the capillary pressure. For salt concentrations of less than approximately 0.01 M, this point corresponds to a transition from purely repulsive to net attractive as seen in the calculated curves of Figure 10. At higher salt concentrations, the range of the electrostatic repulsion becomes shorter than the range of the attractive van der Waals interaction. In this situation, shown in Figure 17, a residual net attractive interaction energy remains for mtot values such that the disjoining pressure maximum just exceeds the capillary pressure. Thus, as observed experimentally, a higher value of mtot than that predicted by curve b of Figure 15 is required to completely suppress flocculation at high salt concentrations. We now consider the validity of the approximate expressions used for the electrostatic interactions. As shown in Figure 15, the experimental data follow solid curve b corresponding to the weak-overlap approximation. This curve lies between the limiting curves a and c corresponding to constant surface potential and constant surface density, respectively. The two latter calculated curves are valid for low surface potentials of less than approximately 25 mV. Because the range of mem values at the flocculation transition correspond to surface po-

Figure 17. Calculated disjoining pressure isotherms for 100 mM NaCl with mem equal to 0.0212 (upper plot) and 0.0209 (lower plot) made using the weak-overlap approximation. All other conditions were the same as those in Figure 10.

tentials lower than 25 mV, this approximation is valid. Whether constant potential or constant charge density conditions apply depends on the extent to which surface charge regulation occurs during the close approach of the surfaces. The fact that the intermediate case of weak overlap is found to provide the best fit to the experimental data suggests that a degree of charge regulation does occur in these systems. For the weak-overlap approximation to be valid, the surface separation must exceed the Debye length. Because the calculations show that this is generally true at the film thicknesses corresponding to the maxima in the disjoining pressure isotherms, the error in the prediction of the flocculation transition is expected to be small. Finally, we note that the transition from the flocculated to the nonflocculated state has been predicted on the basis of drop-pair interaction energies; i.e., we have neglected entropic effects, which are expected to reduce the tendency to flocculate. This point has been discussed by Poulin and Bibette29 who show that entropic effects on the flocculation transition increase as the droplet size is decreased. From comparison with their results, entropic effects for the relatively large drop sizes used in this study are expected to be small. For the system studied by Poulin and Bibette, the flocculation transition was induced by decreasing temperature and occurred “sharply”, i.e., over a very narrow temperature range. This sharpness is also seen for the systems described here, for which the transition occurs over a narrow range of mem. Conclusions Dodecane-water emulsions stabilized (primarily) by C10βGlu are stable with respect to coalescence and Ostwald ripening but unstable with respect to flocculation and creaming. Flocculation increases the rate of creaming. A sharp transition from a flocculated state to a nonfloccu(29) Poulin, P.; Bibette, J. Phys. Rev. Lett. 1997, 79, 3290.

980 Langmuir, Vol. 15, No. 4, 1999

lated state can be induced by the addition of an ionic surfactant, and this transition is easily detected using the change in creaming rate of the emulsions. Assuming that the colloidal forces operating between the emulsion drops consist of electrostatic repulsion, van der Waals attraction, and a short-range, hard-wall repulsion, we have shown how the ionic surfactant concentration required for the flocculation transition can be calculated for different salt concentrations. The electrical charge properties of the drops can be systematically varied in a quantitative manner by adjustment of the concentration of added ionic surfactant. The range of the hard-wall interactions is estimated using measured values of the contact angle formed between doublets of adhering (flocculated) emulsion drops. Using no adjustable parameters, agreement with the experimental data is obtained for calculations based on the film transition stability criterion using the weak-overlap approximation for the electrostatic repulsion. An important conclusion is that the calculated energy barrier for the approach of the undeformed drops is overestimated. This may be due to the breakdown of the assumption that the charge density on the emulsion-drop surfaces remains uniform as the drops approach, or it may be due to the effects of a distribution or thermal fluctuations in surface properties of the droplets. The approach outlined in this paper appears to offer promise for the quantitative testing of models for the interactions between emulsion drops and the effects of interactions on aspects of emulsion stability. However, many questions remain unanswered including the points about the possible nonuniform charge distribution and distribution/fluctuation effects mentioned above. Under what conditions do hydrodynamic interactions and the elasticity of the surfactant monolayers (neglected here) play significant roles? Does the crude modeling of the shortrange interactions as a hard wall remain valid for surfactants other than C10βGlu? A hard-wall type interaction cannot be present for emulsion systems which exhibit coalescence. We hope to address some of these questions through both the further development of the approach and the broadening of the range of emulsion systems investigated. Acknowledgment. The authors gratefully acknowledge the award of an ICI Strategic Research Fund grant for the execution of the work reported in this paper. We thank Mr. Luben N. Arnaudov for the development of the computer program used for the determination of the contact angle of adhering emulsion drops. We thank Dr. J. Chen for the ζ potential measurements. Glossary A As c ccfc cI cIem cImic cmc

oil-water-oil Hamaker constant area per nonionic surfactant in the monolayer bulk concentration of salt critical flocculation concentration of salt concentration of ionic surfactant concentration of ionic surfactant in the emulsiondrop surfaces concentration of ionic surfactant in the micellar surfaces critical micelle concentration

Aveyard et al. cN cNem cNmic e EG H hfilm hfilm hhw k mem mmic mtot NAv P Pc r R Rmic Rsphere T W Wel Whw Ws Wvdw z ze zs ∆Gel Π Πel Πhw Πvdw  0 φ γ κ θ σ ψ

concentration of nonionic surfactant concentration of nonionic surfactant in the emulsion-drop surfaces concentration of nonionic surfactant in the micellar surfaces electronic charge Gibbs elasticity distance between undeformed droplet-droplet surfaces thickness thickness of the (meta)stable film range of the hard-wall interaction Boltzmann constant mole fraction of ionic surfactant in the emulsiondrop surfaces mole fraction of ionic surfactant in the micellar surfaces overall mole fraction of ionic surfactant in the total system Avogadro’s number partition coefficient for the distribution of ionic surfactant between emulsion and micellar surfaces emulsion-drop capillary pressure radius of circular emulsion film formed by the contact of two adhesive drops radius of the spherical portion of the deformed emulsion drop radius of the micelles radius of the initial, undeformed emulsion drop absolute temperature total energy of interaction electrostatic energy of interaction energy of interaction for the hard-wall interaction energy of interaction resulting from deformation of the droplet surfaces van der Waals energy of interaction separation between the centers of the spherical regions of two drops valence of symmetrical (ze/ze) electrolyte valence of ionic surfactant ion difference in electrostatic free-energy difference per monovalent charge for the curved, micellar and flat, emulsion-drop surfaces total disjoining pressure electrostatic disjoining pressure hard-wall disjoining pressure (taken to represent all short-range interactions) van der Waals disjoining pressure relative dielectric constant of continuous phase permittivity of free space volume fraction of emulsion drops oil-water interfacial tension inverse Debye length film contact angle surface charge density at infinite separation surface potential at infinite separation LA981099E