Adsorbed on a solid surface, a molecule can migrate and carry an electric dipole moment. A nonuniform electric field can direct the motion of the molecule. A collection of the same molecules may aggregate into a monolayer island on the solid surface. Place such molecules on a dielectric substrate surface, beneath which an array of electrodes is buried. By varying the voltages of the electrodes individually, it is possible to program molecular patterning, direct an island to move in a desired trajectory, or merge several islands into a larger one. The dexterity may lead to new technologies, such as reconfigurable molecular patterning and programmable molecular cars. This paper develops a phase field model to simulate the molecular motion and patterning under the combined actions of dipole moments, intermolecular forces, entropy, and electrodes.self-assembly ͉ diffusion ͉ adsorbate ͉ electric dipole W hen a molecule from vacuum adsorbs on a solid surface, the total energy of the molecule and the solid reduces by an amount. Provided this binding energy is much larger than the thermal energy, the molecule will stay adsorbed on the solid surface. Under no external field, the adsorbate performs a random walk on the surface, as observed by using the field-ion microscope (1) and the scanning tunneling microscope (2, 3). The motion is thermally activated, its rate depending on the ratio of the migration barrier energy to the thermal energy.The adsorbate carries an electric dipole moment. Even if the molecule is symmetric and nonpolar when isolated in vacuum, the act of binding to a substrate breaks the symmetry. The resulting asymmetric charge distribution gives rise to an electric dipole moment. (The clean solid surface itself has an asymmetric charge distribution. What concerns us is the excess dipole moment induced by the adsorbate.)