Critical Size and Surfactant Coverage of Styrene Miniemulsion Droplets Stabilized by Ionic Surfactants Vesselin N. Paunov, † Stanley I. Sandler, and Eric W. Kaler* 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 surfac- tants 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 Christenson 5 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 SDS- stabilized 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 in the interaction energy potential (see Figure 1). This threshold of surface charge density, above which the droplets are stable against coalescence, is given by 2,3 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 then estimates for U(h) and F(h) can be obtained using the Derjaguin approximation 6 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 A H ) (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 A H ) 5.3 × 10 -19 J, that is, about 40-50 times larger than expected. On the other hand, the experimental results 1 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 droplets 1 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 mini- emulsion droplets, so we consider here the effect of a hydrophobic force contribution to the disjoining pressure. Thus where are the electrostatic and the van der Waals contributions, * Corresponding author. Phone: 1 (302) 831 3553. Fax: 1 (302) 831 4466. E-mail: kaler@che.udel.edu. † Present address: Surfactant & Colloid Group, Department of Chemistry, University of Hull, Cottingham Road, Hull HU6 7RX, United Kingdom. E-mail: V.N.Paunov@chem.hull.ac.uk. (1) Landfester, K.; Bechthold, N.; Tiarks, F.; Antonietti, M. Macro- molecules 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. (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. U(h * ) ) 0 (1) F(h * ) )- ∂U ∂h | h * ) 0 (2) κR . 1 (3) Π(h) ) Π el (h) + Π vw (h) + Π hydrophobic (h) (4) Π el (h) ≈ 64n 0 kTγ 2 exp(-κh), κh . 1 (5) Π vw (h) )- A H 6πh 3 (6) 4126 Langmuir 2001, 17, 4126-4128 10.1021/la0011580 CCC: $20.00 © 2001 American Chemical Society Published on Web 05/30/2001