Mean and Gaussian curvatures of randomly decorated Voronoi and cubic tesselations
It is now generally accepted that some midrange microemulsions are bicontinuous, i.e., continuous in both oil and water simultaneously. The first model of the microstructure of microemulsion that could account for a progression from discrete to bicontinuous was the Talmon--Prager or ''randomly decorated Voronoi'' model. Space is tessellated into Voronoi polyhedra and the polyhedra are randomly decorated with oil and water. In variations of the model DeGennes and Taupin and Widom decorate a cubic tesselation of space. At first glance it might appear that the decorated Voronoi and cubic tessellations are zero-mean-curvature models, since they are constructed from polyhedra with planar faces. However, the edges of the polyhedra are concentrations of mean curvature, and the vertices are concentrations of Gaussian curvature. The area-averaged mean and Gaussian curvatures of the oil--water interface in the randomly decorated Voronoi and cubic models are calculated. The area-averaged mean curvatures of the two models are linear functions of oil volume fraction, change sign at a volume fraction of 0.5, and are within 0.2% of one another in magnitude. The area-averaged Gaussian curvature of the Voronoi model varies quadratically with volume fraction, and is negative for oil volume fractions from 0.18 to 0.82 (oil and water are bicontinuous for volume fractions ranging from 0.135 to 0.865). The area-averaged Gaussian curvature of the randomly decorated cubic model is a sixth-order polynomial function of oil volume fraction and is negative for volume fractions ranging from 0.23 to 0.77 (oil and water are bicontinuous over the volume fraction range 0.25 to 0.75). As an additional application, the model results are used to interpret curvature aspects of the bilayer theory of the /ital L//sub 3/ phase of surfactant solutions presented recently by Cates /ital et/ /ital al/. (Europhys. Lett. /bold 5/, 733 (1988)).
- Research Organization:
- Physical Chemistry 1, Chemical Center, S-221 00 Lund, Sweden (SE); Chemical Engineering Department, University of Minnesota, Minneapolis, Minnesota 55455
- OSTI ID:
- 6048721
- Journal Information:
- J. Chem. Phys.; (United States), Vol. 91:5
- Country of Publication:
- United States
- Language:
- English
Similar Records
Clipped random wave analysis of isometric lamellar microemulsions
[Structure and dynamics of microemulsions in bulk, at interfaces, and in confined geometries]. Progress report