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Langmuir 2001, 17, 4126-4128
Critical Size and Surfactant Coverage of Styrene Miniemulsion Droplets Stabilized by Ionic Surfactants
in the interaction energy potential (see Figure 1). This threshold of surface charge density, above which the droplets are stable against coalescence, is given by2,3
Vesselin N. Paunov,† Stanley I. Sandler, and Eric W. Kaler*
U(h*) ) 0
Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received August 10, 2000. In Final Form: March 14, 2001
Here, we present a simple model for the surface charge density of latex particles produced by miniemulsion polymerization that provides understanding of the recent experimental data of Landfester et al.1 The model describes the stability of the miniemulsion droplets to coalescence in the presence of a fixed amount of surfactant and allows for the calculation of the final size of the miniemulsion droplets and the degree of saturation of the surface with surfactant. The experimental results with ionic surfactants cannot be understood in terms of only electrostatic and van der Waals (DLVO)2,3 forces acting between the styrene droplets. An additional attractive force must be active to account quantitatively for the observed stability of both the miniemulsion droplets and the final colloidal dispersions. This hydrophobic force between the two oil (hydrophobic) surfaces in water is represented here by the phenomenological theory of Eriksson, Ljunggrenn, and Claesson.4 The preexponential factor and the decay length are determined by fitting the experimental data of Claesson and Christenson5 for the interaction between monolayers of dimethyldioctadecylammonium bromide (DDOA) on mica. The results of the model agree well with the experimental data of Landfester et al.1 for an ionic surfactant (SDS). The equilibrium surface charge density of styrene miniemulsion droplets stabilized by ionic surfactants is much lower than the maximum possible value given by close packing. The typical surface coverage in SDSstabilized miniemulsions is about 28%. The miniemulsion droplets are highly monodisperse, and the equilibrium diameters of both the droplets and the resulting latex particles vary from 80 to 300 nm, depending on the experimental conditions. The basic ideas of the model are as follows. Initially, oil is dispersed by shearing into very fine droplets with almost all of the ionic surfactant adsorbed at the oil/water interface. Because the interfacial area is large, the adsorption of surfactant is low, and the corresponding surface charge density is too low to prevent coalescence. Droplet coalescence stops when the surface charge of the droplets is high enough that an energy barrier appears * Corresponding author. Phone: 1 (302) 831 3553. Fax: 1 (302) 831 4466. E-mail:
[email protected]. † Present address: Surfactant & Colloid Group, Department of Chemistry, University of Hull, Cottingham Road, Hull HU6 7RX, United Kingdom. E-mail:
[email protected]. (1) Landfester, K.; Bechthold, N.; Tiarks, F.; Antonietti, M. Macromolecules 1999, 32, 2679. (2) Derjaguin, B. V. Theory of Stability of Colloids and Thin Films; Plenum Press: New York, 1989. (3) Verwey, E. J. W.; Overbeek, J. T. G. Theory of Stability of Lyophobic Colloids; Elsevier: New York, 1948. (4) Eriksson, J. C.; Ljunggren, S.; Claesson, P. J. Chem. Soc., Faraday Trans. 2 1989, 85, 163. (5) Claesson, P.; Cristenson, H. J. Phys. Chem. 1988, 92, 1650.
F(h*) ) -
|
∂U ∂h
h*
(1) )0
(2)
Equation 1 gives the position of the energy barrier, and eq 2 determines the minimal surface charge density required for stabilization. Here, U(h) and F(h) are the interaction energy and force, respectively, between two miniemulsion droplets of radius R, and h is the minimal surface-to-surface distance between the droplets. If the droplet size is much larger than the Debye length
κR . 1
(3)
then estimates for U(h) and F(h) can be obtained using the Derjaguin approximation6 and the disjoining pressure isotherm for a thin liquid film of water between two oil/ water surfaces in the presence of surfactant. Electrostatic and van der Waals forces alone cannot account for the stability of the droplets for any sensible value of the Hamaker constant. The accepted value for the Hamaker constant between two polystyrene surfaces in water is AH ) (0.95-1.4) × 10-20 J.7 Reasonable agreement between the experimental values of the droplet radius and degree of coverage of the droplet surface and the values calculated from DLVO theory can only be achieved with a value of the Hamaker constant of AH ) 5.3 × 10-19 J, that is, about 40-50 times larger than expected. On the other hand, the experimental results1 can be explained by using the real value of the Hamaker constant and assuming a counterion condensation on the adsorbed SDS ions. However, the degree of surface ionization of SDS obtained appears to be only 4.7% for 28% surface coverage with SDS. This value is in conflict with those obtained in other studies,8 where the degree of ionization of a densely packed SDS monolayer is estimated at about 20%, i.e., the surface charge density of the miniemulsion droplets1 appears to be 14 times lower than its value for a densely packed SDS monolayer. The latter is an indication that another, much stronger, attractive force is operative between the miniemulsion droplets, so we consider here the effect of a hydrophobic force contribution to the disjoining pressure. Thus
Π(h) ) Πel(h) + Πvw(h) + Πhydrophobic(h)
(4)
Πel(h) ≈ 64n0kTγ 2 exp(-κh), κh . 1
(5)
where
Πvw(h) ) -
AH 6πh3
(6)
are the electrostatic and the van der Waals contributions, (6) Derjaguin, B. V.; Churaev, N. V.; Muller, V. M. Surface Forces; Plenum Press: New York, 1987. (7) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1992. (8) Tajima, K. Bull. Chem. Soc. Jpn. 1971, 44, 1767.
10.1021/la0011580 CCC: $20.00 © 2001 American Chemical Society Published on Web 05/30/2001
Notes
Langmuir, Vol. 17, No. 13, 2001 4127
Figure 1. Schematic representation of the miniemulsion system: (a) unstable, immediately after ultrasonification, and (b) after reaching the “critical” droplet size. The graphs represent the corresponding interaction potential U(h) between two charged emulsion droplets (of radius R) in water. h is the shortest surface-to-surface distance between the droplets.
respectively; n0 is the electrolyte concentration
8πe2n0 κ ) kT 2
(7)
is the Debye parameter; and γ ) tanh(φs/4), with φs ) eψs/kT being the dimensionless surface potential of the droplets. (All quantities are in CGSE.) The hydrophobic surface force6,7 is described by Eriksson et al.,4 where the result for the geometry of two crossed cylindrical surfaces is
[ (bh2 ) - 1]
-Fhydrophobic(h)/R ) 2πf(h) ) B coth
Here, Fhydrophobic(h) is the free interaction energy per unit area of a plane parallel film, R is the radius of curvature of the cylinders, and B and b are phenomenological parameters. The corresponding expression for the disjoining pressure due to hydrophobic interactions is
-Πhydrophobic(h) )
∂fhydrophobic Bb 1 ) (8) ∂h 4π sinh2(bh/2) 4
According to the theory of Erikson et al., the decay length, b-1, should be the same for all hydrophobic surfaces under identical solution conditions, and the coefficient B determines the strength of the hydrophobic attraction. The values of the phenomenological parameters B and b have been estimated4 by fitting the experimental data of Claesson and Christenson5 for the interaction between deposited monolayers of dimethyldioctadecylammonium bromide (DDOA) on mica. The fitted values4 are
1 ) 15.8 nm, B ) 0.6 mJ/m2 b
∫h∞Π(h) dh )
F(h) ≈ πR
(9)
The Derjaguin approximation,6 applied to eqs 4-8 gives
πR
[
64n0kTγ2 -κh AH B bh e -1 coth κ 2 12πh2 2π
U(h) ≈
(
∫h∞F(h) dh )
πR
[
)] (10)
]
AH 64n0kTγ2 -κh B + ln(1 - exp(-bh)) e 2 12πh 2π κ (11)
The combination of eqs 10 and 11 and eqs 1 and 2 determines the threshold of droplet stability, because γ is related to the surface charge density (surface potential) of the droplets, which is a function of the surfactant adsorption Γ
|σs| ) eΓ
(12)
The surface charge density, σs, is related to the surface potential through the first integral of the PoissonBoltzmann equation
φ′′(z) ) κ2 sinh φ(z), φ(z) ) eψ(z)/kT
(13)
For a single interface, the boundary conditions for eq 14 are
dψ dz
|
)-
z)0
4πσs , ψ(z f ∞) ) 0
(14)
The first integral of eq 13 is
λ)
2πe2Γ∞θ φs ) sinh κkT 2
On the other hand, using the relation
(15)
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Langmuir, Vol. 17, No. 13, 2001
Notes Table 1. Characteristics of the Latexes (Miniemulsion Droplets) Stabilized by SDSsComparison of Theory and Experimental Dataa
φs 2 tanh φs 4 2γ ) λ ) sinh ) , 2 φ 1 γ2 s 2 1 - tanh 4 γ ) (x1 + λ2 - 1)/λ (16) the degree of surface coverage with surfactant, θ ≡ Γ/Γ∞, is related to the radius of the droplets
V0 R ) 3Γ∞θ Ns
droplet diameter (nm) surfactant std dev surface saturation Γ/Γ∞ weight fraction of exptl S (%) expt theory expt theory data 1.2 2.4 a
0.28 0.28
0.258 0.258
138 93
141 71
0.086 0.150
Landfester et al.1
(17)
where the ratio V0/Ns of the volume of oil to the amount of surfactant is fixed by the experimental conditions and Γ∞ is the maximum possible adsorption of surfactant. The ratio V0/Ns can be calculated from the surfactant weight fraction S (%), V0/Ns ) SFoNA/(100Ms), where Fo ) 0.906 g/cm3 is the mass density of the oil (styrene), NA is Avogadro’s number, and Ms ) 288.38 g/mol is the molecular mass of the surfactant SDS. The calculation procedure is the following: (i) solve eqs 1 and 2 together with eqs 10 and 11 to determine the values of θ and h* corresponding to zero energy barrier and (ii) calculate the radius of the “stable” droplets from eq 17. The surface saturation and the droplet diameter of the stable droplets, stabilized by sodium dodecyl sulfate (SDS), are calculated for the experimental conditions in ref 1 for styrene miniemulsions and are shown Table 1, along with the experimental data. The calculated droplet saturations for two different ratios of SDS and styrene and the calculated diameters of the stable droplets generally match the experimental values. Figure 2 gives the interaction energy vs distance curve for two critical miniemulsion droplets of styrene stabilized by SDS (S ) 1.2%). The interaction potential energy U includes electrostatic, van der Waals, and hydrophobic contributions according to eq 11. For the sake of simplicity, we have assumed 100% SDS dissociation at the surface, as the monolayer is quite diluted (the experiment gives 28% surface coverage with SDS1). The calculated critical diameter of the droplets is 141 nm, which compares well with the average value of 138 nm that was measured experimentally. The critical surface coverage with SDS (100% ionized) that satisfies eqs 1 and 2 is θ ) 0.256 (25.6%), again very close to the experimental value of 28%. Surface coverage with SDS above that value produces an energy barrier and stops the coalescence of the miniemulsion droplets. The model used here could be improved further by accounting for the equilibrium between absorbed and dissolved surfactant molecules, i.e., by using an appropriate adsorption isotherm. Counterion condensation could also affect the results. Accounting for the changes in the hydrophobicity of the oil/water interface due to surfactant adsorption (i.e., how the coefficient B depends on the surfactant adsorption) could also prove useful for the quantitative description of the experimental data.
Figure 2. Interaction energy vs distance between two miniemulsion styrene droplets in the presence of sodium dodecyl sulfate (S ) 1.2%). The parameters of the system are A∞ ) 1/Γ∞ ) 0.48 nm2, Fo ) 0.909 g/cm3, Ms ) 288.38, AH ) 1.4 × 10-20 J, and Cel ) 8.2 mM. The critical degree of interface saturation with surfactant is Γ/Γ∞ ) 0.256 for the case of barrierless coalescence. The calculated droplet diameter is 141 nm.
Interpreting the experimental results without including the hydrophobic surface force gives droplet diameters that are 1-2 orders of magnitude lower than those measured if the correct value, AH ) 1.4 × 10-20 J, of the Hamaker constant is used. Thus, DLVO theory cannot explain the experimental results, even if one assumes that the droplets are deformed from a spherical shape and doublets are formed.9 The latter is energetically unlikely as adsorption of surfactant at the styrene/water interface is low and the interfacial tension is high. In conclusion, an attractive hydrophobic interaction between the bare oil/water interface seems to be an important factor in determining the energy balance and the stability of the miniemulsions. Acknowledgment. The authors appreciate the financial support of this study from the U.S. Department of Energy (Grant DE-FG02-85ER13436). LA0011580 (9) Petsev, D. N. Physica A 1998, 250, 115. Denkov, N. D.; Kralchevsky, P. A.; Ivanov, I. B.; Vassilieff, C. S. J. Colloid Interface Sci. 1991, 143, 157. Denkov, N. D.; Petsev, D. N.; Danov, K. D. Phys. Rev. Lett. 1993, 71, 3226.
