Langmuir 1990,6, 1696-1700
1696
Letters Measurements of Interdroplet Attractions and the Onset of Percolation in Water-in-Oil Microemulsions Robert T. Hamilton Weyerhaeuser Paper Co., Weyerhaeuser Technology Center 2B22, Tacoma, Washington 98477
John F. Billman Department of Chemical Engineering, BF-IO, University of Washington, Seattle, Washington 98195
Eric W. Kaler* Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received June 1 1 , 1990. In Final Form: August 24, 1990 Both the percolation thresholds and the attractive interdroplet interactions for water-in-oil microemulsions made with sodium 1-(4’-heptylnonyl)benzenesulfonate(SHBS),isobutyl alcohol, water, and NaCl with octane, decane, dodecane, and tetradecane have been measured. We find for this particular microemulsion formulation that percolation occurs when the attractive interdroplet interaction is 2.0 f 0.3 kT. The existence of a critical value of the interdroplet interactions of the same magnitude for other microemulsion mixtures also rationalizes many observations in the literature. Thus we confirm experimentally that the strength - of the microscoDic interdrodet interactions is directly related to the macroscopic percolation threshold.
Introduction Water-in-oil microemulsions usually contain roughly l00-A water pools surrounded by surfactant sheets. Many of these microemulsions display two remarkable features, namely, the interdroplet interaction is much stronger than that expected to arise from van der Waals interactions and the aqueous cores of the droplets percolate as the volume fraction of droplets increases. The model surfactant sodium 1-(4’-heptylnonyl)benzenesulfonate(SHBS)forms microemulsions with alkanes in the presence of brine and a cosurfactant such as isobutyl alcohol, and they have been reported on elsewhere.’ Of particular interest is the occurrence of percolation thresholds, as measured with pulsed-field gradient spin-echo NMR, for both oil-inwater and water-in-oil microemulsions. The absence of long-range electrostatic forces in waterin-oil microemulsions makes it likely that van der Waals forces govern the droplet interactions, as is the case in other colloidal dispersions. However, the first quantitative study2 of the osmotic compressibility of such dispersions showed that the measured attractive interactions between droplets were roughly 100 times those calculated for van der Waals forces acting alone. Lemaire et al.3 and Roux e t ala4 proposed the origin of these strong attractive interactions to be the favorable energy of overlap of the tips of surfactant tails as neighboring droplets touched. The Lemaire potential consists of essentially a hard-core repulsion and a short-ranged attractive well, the details of which depend on the molecular features of the oil and surfac(1) Billman, J. F.; Kaler, E. W. Langmuir 1990,6, 611. (2) Calje, A. A.; Agterof, W. G. M.; Vrij, A. Micellization, Solubilization, and Microemulsions;Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2. (3) Lemaire, B.; Bothorel, P.; Roux, D. J.Phys. Chem. 1983,87, 1023. (4) Roux, D.; Bellocq, A. M.; Bothorel, P. Surfactants in Solution, Mittal, K. L., Lindman, B., Eds.,Plenum Press: New York, 1984.
tant. The magnitude of interactions calculated by using this theory match the measured values as determined by light scattering nearly exactly. There may, in fact, be a universal solvent-induced interaction between micelles or microemulsion globule^.^ A powerful probe of colloidal interactions is smallangle neutron scattering (SANS), and SANS spectra can be analyzed to give information about the size and shape of microemulsion droplets and about their interactions when the interdroplet potential is of one of several relatively simple forms.6 The complete Lemaire potential is too complicated for easy use in the interpretation of SANS measurements, but fortunately the potential can be well approximated by a square well. The structure factor, and thus the neutron-scattering intensity, can be calculated analytically for a square-wellfluid.’ The squarewell potential U(r)for particles of hard-sphere radius RHS is characterized by a depth 6 (in units of kT, where k is the Boltzmann constant and T the temperature) and width X such that U ( r )= m for r < 2R,,
u(r)= -6
for 2RRs < r < 2RHs
+
U(r) = 0 for r > 2R,, + X (1) Since the physical origin of the potential is the overlap of surfactant tails, the value of X is a few angstroms. In the case of water-in-oil microemulsions, the data from several different microemulsions can be fit as a dispersion of monodisperse droplets interacting through a square-well potential, although the depth of the square well must be ( 5 ) Pincus, P. A,; Safran, S. A. J. Chem. Phys. 1987,86,1644. (6) Chen, S.-H. Ann. Reu. Phys. Chem. 1986,37,351. (7) Sharma, R. V.; Sharma, K. C. Physica 1977, 89A, 213.
0743-7463/90/2406-1696$02.50/00 1990 American Chemical Society
Letters rescaled8 to an effective value t' = In (1+ e ) when h / R ~ s
