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 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 derive 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. Numerical calculations of these quantities, evaluated using a spectrally accurate Ewald summation method, are validated using thermodynamic integration. We also compare the stress obtained using the mutual dipole model, which accounts for the mutual polarization of particles, to the stress expected from calculations using a fixed dipole model, which neglects mutual polarization. We find that as the conductivity of the particles increases relative to the surrounding medium, the fixed dipole model does not accurately describe the dipolar contribution to the stress. The thermodynamic pressure, calculated from the trace of the stress tensor, is compared to the virial expression for the pressure, which is simpler to calculate but inexact. We find that the virial pressure and the thermodynamic pressure differ, especially in suspensions with a high volume fraction of particles.