symmetries in the finite-difference grid. For example, the fault-parallel components of the velocity as well as the normal and an shear stresses are antisymmetric, whereas the fault-perpendicular component of the velocity and the uyx and a , stresses are symmetric across a vertical fault in the xz plane. By careful examination of the numerical implementation, it can be shown that, if the numerical values of the velocity and stress have the aforementioned symmetries about the fault plane at the Nth time step, then they do at upgraded (N + 1)th time step as well. Details of the numerical application of the boundary conditions are described in (76). 10. J. Virieux and R. Madariaga, Bull. Seismol. Soc. Am. 72, 345 (1 98'2). 11. Slip-weakening friction laws similar to Eq. 2 have been extensively studied by rock mechanicists in Japan; see, foiexample, M. Ohnaka, Y. Kuwahara, and K. Yamamoto [Tectonophysics 144, 109 (1987)], M. Ohnaka [Proc. Natl. Acad. Sci. U.S.A. 93, 3795 (1996)], and M. Matsu'ura, H. Kataoka, and B. Shibazaki [Tectonophysics. 21 1, 135 (1 992)J. 12. Actually, the only physical requirement is that friction dissipates energy, such that T integrated over the fault will be less than zero. To our knowledge, the consequences of this less strict requirement have not been reported in the literature. 13. The study of slip weakening and the conditions for spontaneous rupture were introduced in seismology by Y. Ida [J. Geophys. Res. 77, 3796 (1972)], although the conditions had been used in dynamic fracture mechanics [B. Kostrov, L. V. Nikitin, L. M. Flintman, Mech. Solids 4, 112 (1969)l. The friction law used in our simulation is described by A. Palmer and J. Rice [Proc. R. Soc. London Ser. A Recent studies have shown that certain tute for Chemical Biology, The Scripps ~esearch Instielectrochemical etches of single-crystal ptute,

Mesoporous (H(I)-ePt) platinum microelectrodes electrodeposited from the hexagonal (H(I)) lyotropic liquid crystalline phase are shown to be excellent amperometric sensors for the detection of hydrogen peroxide over a wide range of concentrations. Good reproducibility, high precision, and accuracy of measurements are demonstrated. Mesoporous microelectrodes retain the high rates of mass transport typical of conventional microelectrodes, and their high real surface area greatly enhances their catalytic activity. This unique combination of properties overcomes the limitations of previous amperometric hydrogen peroxide sensors and yields outstanding qualitative and quantitative results.

Metallic nickel was electrodeposited from aqueous nickel(II) acetate dissolved in the lyotropic liquid crystalline phases of Brij 56 and Brij 78 surfactant templates to form metal films with hexagonal arrays of nanometer-sized channels. The applicability of these materials as inexpensive, large area and low-resistance current collectors was demonstrated by cyclic voltammetry. The redox charge capacity of the surface oxide in aqueous KOH was enhanced by 2 orders of magnitude over that of a nontemplated sample with no detectable impedance of the reaction rate.

We report a new method for the production of ordered 3D metal-nanowire network fi lms. The method utilizes a coating of lipid inverse cubic phase as the template for electrodeposition. We have produced platinum fi lms which show a previously unreported "single diamond" nanoarchitecture with Fd3m symmetry and a lattice parameter of approximately 132 Å. Their electrochemically accessible surface area is estimated to be > 40 m 2 g − 1 . The new methodology represents a facile route to 3D cubic nanostructures and thus provides a synthetically attractive route to the preparation of 3D nanostructured devices with diverse potential applications.Nanostructured metals and semiconductors have many important technological uses. They are commonly produced by templating soft materials such as diblock copolymers [ 1 ] or lyotropic liquid-crystal phases that form by amphiphile selfassembly. [ 2 ] These soft templates exhibit a range of different nanostructures that include hexagonal phases, based on simple 2D arrays of cylinders, and the more complex 3D bicontinuous cubic structures, based on mathematical surfaces known as the triply periodic minimal surfaces. Three different symmetries of bicontinuous cubic structure have been reported, based on the gyroid (G), double diamond (D), and primitive (P) minimal surfaces, which correspond to the space groups Ia3d (Q 230 ), Pn3m (Q 224 ), and Im3m (Q 229 ), respectively. In the inverse (Type II) cubic phases whose use as an electrochemical template is described here, the minimal surface lies at the centre of a continuous amphiphile bilayer which separates two continuous, but non-intersecting, water channel networks.Direct electrodeposition of nanostructured materials from normal topology (Type I) lyotropic liquid-crystal phases was fi rst reported by Attard and co-workers in 1997. [ 3 ] The method represents a reliable route to a range of nanostructured materials [ 4 ] under conditions that are suffi ciently mild to preserve the lyotropic mesophase structure during the electrodeposition process. Reported uses of direct electrochemical lyotropic templating using the normal (Type I) hexagonal phase are numerous, but in contrast there is only one reported case involving electrochemical templating from normal topology cubic phases. [ 5 ] There are two main reasons for this: fi rst, the cubic phase typically occupies only a small region of the composition-temperature phase diagram, and second, perhaps more importantly, the bicontinuous cubic phases are much more viscous than their hexagonal counterparts; [ 6 ] the combined result being that electrochemical templating from a cubic phase via the true liquid-crystal templating route is very difficult to achieve in practice.Nonetheless, the production of nanostructured materials with a bicontinuous cubic morphology is highly desirable, and even though the lyotropic liquid-crystal templating route has not been used extensively in this way, some alternative (albeit multi-step) approaches have been reported in the literature. The resulting bicon...

A systematic investigation into the effects of deposition conditions on the electrochemical properties and nanostructure of high surface area (up to ∼460 m 2 cm -3 ) mesoporous platinum films (H I -ePt) obtained by electroreduction of hexachloroplatinic acid (HCPA) from an hexagonal lyotropic liquid crystalline phase is reported. The surface area, repeat distance, and regularity of the nanostructure and the surface morphology of the films were shown to depend on the deposition conditions. In particular, the deposition potential was found to have a notable effect on the film surface area and on the uniformity of nanostructure. The results obtained are explained by variations in the efficiency of the deposition process and the relative contributions of competing reactions. Increasing the temperature of electrodeposition was found to increase significantly the surface areas of the films and to increase the repeat distance of the nanostructure. In addition, a roughening of the films on both a microand a nanometer scale was observed with an increase in temperature. We also found that the thickness of the electrodeposited films scaled linearly and that the volumetric surface area was constant, with the charge passed during the electrodeposition process, indicating uniform accessibility of the pore system.

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Nanostructured platinum films were electrodeposited onto microelectrodes from an hexagonal lyotropic liquid crystalline plating mixture. Cyclic voltammetry in dilute sulfuric acid and copper underpotential deposition confirmed that the resulting platinum films had high surface areas (with roughness factors of ca. 210) as a direct consequence of their electrochemically accessible nanostructure. The microelectrodes were shown to combine a high real surface area with efficient mass transport characteristics. This combination of properties is unique and may be of significance to the fields of electrochemistry and electroanalysis.

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