Exact polarization energy for contacting dielectrics

The induced polarization charge appears to diverge as curved dielectrics approach and form close contacts. Resolving the diverging charge density slows down the convergence rate in numerical calculations of electrostatic energy. We show that this divergence depends on both the gap distance and the dielectric permittivity logarithmically. We propose a parameterized form of the electrostatic energy, which generalizes the known logarithmic singularity for conductors to dielectrics. Isolating this singular contribution allows for the calculation of exact cohesive energy for ensembles of dielectric particles in close contact. Explicit calculations are presented to illustrate how the contact singularity affects the cohesive energy of aggregates for a range of permittivity values.