(477i) The Stress in a Dispersion of Mutually Polarizable Spheres

Dispersions of dielectric and paramagnetic nanoparticles polarize in response to an external electric or magnetic field and can form chains or other ordered structures depending on the strength and implementation of the applied field. The mechanical properties of these materials are of interest for a variety of applications, however computational studies in this area have so far been limited. In this work, we present expressions for two important properties for dispersions of polarizable spherical particles with dipoles induced by a uniform external field-- the isothermal stress tensor and the pressure. These expressions account for induced dipole interactions between particles based on the mutual dipole model which accounts for many-body interactions. We calculate these quantities numerically using a spectrally accurate Ewald summation method and show that the numerical error in our calculations is well controlled. We show that the expression for the pressure is thermodynamically consistent by comparing thermodynamic integration of our derived expression for the pressure to independent calculations of the internal energy in a dispersion of particles. We compare the pressure we compute to the commonly used virial pressure to confirm that these expressions are different, as expected for long-ranged forces. Finally, we compare the stress calculations derived based on the mutual dipole model to a much simpler model, the fixed dipole model, and identify the regimes in which the simpler model fails to accurately predict the stress.