Electric field mediated assembly of three dimensional equilibrium colloidal crystalsElectronic supplementary information (ESI) available: Supplemental Videos: CSLM xyt.avi (3.87 MB) CSLM measured XY slices show individual layers from bottom to top. CSLM xzt.avi (3.39 MB) CSLM measured XZ slice shows cross-sectional view of hemisphere. MC xzt.avi (2.10 MB) MC simulated XZ rending shows cross-sectional view of hemisphere. CSLM rotate.avi (2.98 MB) CSLM measured XY stack rendered as 3D rotating vie

We report confocal laser scanning microscopy (CLSM) measurements, Monte Carlo (MC) simulations, and an analytical model of the assembly of three dimensional (3D) equilibrium colloidal crystals within quadrupole electrodes on microscope cover slip surfaces. Micron sized fluorescent silica colloids in an index matching dimethylformamide (DMF) medium enable three dimensional CSLM imaging to measure particle coordinates. By matching density profiles from CSLM measurements and MC simulations, we obtain electrostatic, dipole-field, dipole-dipole, and gravitational potentials that accurately capture the three dimensional microstructure and morphology. We also report analytical density profiles with fluid-solid coexistence by balancing gravitational and electric field mediated compression against local osmotic pressure, which agree with CSLM and MC results. These results provide fundamental information on the assembly of three dimensional equilibrium colloidal crystals in the presence of multiple external fields and with coexisting inhomogeneous fluid and solid phases. We report confocal microscopy measurements of equilibrium colloidal crystals assembled in quadrupole electrodes at MHz frequencies and include models that capture microstructure and morphology by including all kT -scale interactions.