In contrast to van der Waals (vdW) forces, Coulombic dipolar forces may play a significant role in the coagulation of nanoparticles (NPs) but has received little or no attention. In this work, the effect of dipole - dipole interaction on the enhancement of the coagulation of two spherically shaped charge-neutral TiO2 NPs, in the free molecular regime, is studied using classical molecular dynamics (MD) simulation. The enhancement factor is evaluated by determining the critical capture radius of two approaching NPs for different cases of initial dipole direction with respect to path (parallel/perpendicular) and orientation with respect to each other (co-orientated/counterorientated). As particle diameter decreases, the enhancement of coagulation is augmented as the ratio of dipole - dipole force to vdW force becomes larger. For 2nm TiO2 NPs at 273 K, the MD simulation predicts an average enhancement factor of about 8.59, which is much greater than the value of 3.78 when only the vdW force is considered. Nevertheless, as temperature increases, the enhancement factor due to dipole - dipole interaction drops quickly because the time-averaged dipole moment becomes small due to increased thermal fluctuations (in both magnitude and direction) of the instantaneous dipole moment.