1538 for polydispersed droplets with more confidence at higher volume fractions. The dependence of the polydispersity index on zyxwvut I? found in this analysis suggests that the droplet shape fluctuation maybe caused by thermal fluctuations. It also suggests that the surfactant layer, which stabilizes the micelles, is much more floppy than expected from previous liquid crystal measurements. J. zyxwvutsrqp Phys. Chem. zyxwvut 1988, 92, 1538-1541 Acknowledgment. We gratefully acknowledge the Brookhaven National Laboratory for granting beam time on the H-9 small angle spectrometer and the expert assistance of Dr. D. Schneider. We have also benefited greatly from discussions with S. A. Safran and W. D. Dozier and received experimental assistance from J. Sung. Steady-State Chemical Kinetics on Surface Clusters and Islands: Segregation of Reactants J. S. Newhouse and zyxwvut R. Kopelman* Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (Received: July 20, 1987) Supercomputer simulations of the elementary A zyxwvut + B - 0, diffusion-limited reaction were performed, under steady-state conditions, on twedimensional percolation clusters and monodisperse islands. While the reaction orders are roughly comparable to those of the A + A - 0 reactions, a dramatic segregation ("morphogenesis") appears (while no such segregation occurs on square lattices). This segregation is even more striking under direction bias (external field). These studies are relevant to heterogeneous catalysis, to the annealing of radiation and other surface damage, and to surface and bulk charge polarization and recombination. It may also be of interest to biomorphogenesis and to population biology. Introduction The elementary binary reaction A + A - products has been of much interest recently1-I0 in connection with the problems of heterogeneous chemical kinetics. For a nonclassical behavior has been demonstrated for the reaction order zyxwvut X, defined by R = Kpx (1) where R is the steady-state reaction rate, zyxwvuts p the steady-state reactant concentration, and K the rate constant. Specifically, instead of the classical result of X = 2, values of 2.45, 2.5, and 3 have been obtained for the Sierpinski gasket, the critical per- colation cluster, and the one-dimensional lattice, re~pectively."-'~ This problem is of direct interest to chemical reactions and to exciton fusion (annihi1ation)l-l3 and of indirect interest to radiation damage in semiconductors, electron-hole recombination, and matter-antimatter distribution in the universe.14 In view of the (1) deGennes, P. G. C. R. Seances Acad. Sci., Ser. A 1983, 296, 331. (2) Evesque, P.; Duran, J. J. Chem. zyxwvutsrqpon Phys. 1984, 80, 3016. (3) Klafter, J.; Blumen, A.; Zumofen, G. J. Stat. Phys. 1984, 36, 561. (4) Yang, C. L.; Evesque, P.; El-Sayed, M. A. J. Phys. Chem. 1985, 89, (5) Klymko, P. W.; Kopelman, R. J. Phys. Chem. 1982, 86, 3686. (6) Klymko, P. W.; Kopelman, R. J. Phys. Chem. 1983, 87, 4565. (7) Kopelman, R.; Hmhen, J.; Newhouse, J. S.; Argyrakis, P. J. Stat. Phys. (8) Kang, K.; Redner, S. Phys. Rev. A 1985, 32, 435. (9) Kopelman, R.; Parus, S.; Prasad, J. Phys. Rev. Lett. 1986, 56, 1742. (10) Kopelman, R. J. Stat. Phys. 1986, 42, 185. (11) Anacker, L. W.; Kopelman, R. J. Chem. Phys. 1984, 81, 6402. (12) Newhouse, J. S.; Kopelman, R. Phys. Rev. B Condens. Matter 1985, 3442. 1983, 30, 355. 31. 1677. (13) Anacker, L. W.; Parson, R . P.; Kopelman, R. J. Phys. Chem. 1985, 89, 4758. electron-hole problem, as well as that of charge polarization in gels, membranes, and clouds (the segregation of positive and negative ions),I4 it appears to be of interest to also investigate the effects of direction bias ("external" electric field effects). Recently, a theoretical relation has been given] ],I3 for the steady-state reaction order X = 1 + 2/ds for d, C 2, where d, is the spectral dimension. This gives X = 3 for a linear lattice (d, = l), and for d, < 1 obviously X > 3. In principle, for a finely divided reaction space, whether "fractal dust"15 or Euclidean dust, one expects d, - 0 and thus X - QJ. Experimental annihilation studie~,~ 5 years ago, and more recent Monte Carlo studied6 have indeed shown X values of the order of 5-50 for finite percolation cluster^^^^^ and for monodisperse islands.I6 In view of these surprising results, as well as the surprising (steady-state) results for A + B reactions on fractals,I4 we undertook an investigation of the A + B reaction (steady state) on percolating clusters and monodisperse islands. One surprise is the striking segregation of reactants (at steady state). The other surprise is that, in spite of this segregation, the reaction orders seem to be similar to those of the (nonsegregating) A + A reaction. In addition, it is grat- ifying to find that a steady state is easily achieved under direction bias (field); the resulting steady-state densities and segregation are strikingly increased. Simulations The simulation method is that of ref 12 (and references therein). Percolation clusters at criticality (0.593 site occupation probability) (14) Anacker, L. W.; Kopelman, R. Phys. Rev. Lett. 1987, 58, 289. (15) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: San (16) Newhouse, J. S.; Kopelman, R. J. Chem. Phys. 1986, 85, 6804. Francisco, 1983. 0022-3654/88/2092-1538$01.50/0 0 1988 American Chemical Society