For a three-dimensional microelectrode or a planar microelectrode inlaid on an insulating plane, in order to model surface roughness or adsorption effects, we calculate the leading-order change in the steady, diffusion-limited current when "monticles" (i.e., small lumps or "pimples"), either active or insulating, are added to the microelectrode surface. As a model for an assembly of ultramicroelectrodes, or for adsorption affecting a large fraction of the surface area of a microelectrode, we also consider the steady diffusion-limited current for a random distribution of active monticles on an insulating surface of microscopic size and show that the average current is equal to that due to a reaction over the whole surface with a certain finite rate constant. In contrast to the time-dependent case, the extent of the interactions between monticles is shown to depend on the overall size of the surface as well as on the size and separation of the monticles. Similar results apply in all these cases for non diffusion-limited transport in the limit where a suitable dimensionless reaction rate constant becomes infinite.Over the last decade microelectrodes have been increasingly used in a variety of fields including physiology. Their small size and the associated short diffusion time scale and low double-layer capacitance result in high resolution of both spatial and temporal variation. Practical and theoretical aspects of microelectrode measurements have recently been reviewed by Wightman and Wipf (1). Most previous theory has treated microelectrodes with smooth, homogeneous surfaces; treatments of surface heterogeneity effects, following the experimental studies, have concentrated on time-dependent situations, generally using numerical-solution techniques. In this paper we consider the effects of surface heterogeneity, using asymptotic techniques to derive comparatively simple approximate solutions. To model surface roughness and adsorption effects, and the behavior of ultramicroelectrode assemblies, we calculate the steady current in three situations in which a surface is modified by the addition of small lumps or "pimples," which we call monticles. Either the surface is insulating and the monticles are active (ultramicroelectrode assembly or adsorption over a large area fraction), or the surface is active and the monticles are either active (roughness) or insulating (adsorption over a small area fraction).Consider the steady current for a microelectrode with a reaction O(soln) + he-~ R(soln)[1] at its surface. Denote the bulk concentrations of the two species by c~ and c~, their diffusion coefficients by Do and DR, and the forward and backward reaction rate constants by kf and kb, respectively. If I denotes a representative lengthscale of the microelectrode, we can define a dimensionless reaction rate constantsimilar to those used by other authors (2, 3). In a previous paper we have calculated the steady current for a microelectrode when K is large (4). Here we consider the case where K is infinite for all the active s...