Magnetic ellipsoidal particles adsorbed
at a liquid interface provide
exciting opportunities for creating switchable functional materials,
where self-assembly can be switched on and off using an external field
[Davies et al.,
Adv. Mater
.,
2014
,
26
, 6715]. In order to gain a deeper understanding of this
novel system in the presence of an external field, we study the capillary
interaction and self-assembly of tilted ellipsoids using analytical
theory and finite element simulations. We derive an analytical expression
for the dipolar capillary interaction between tilted ellipsoids in
elliptical polar coordinates, which exhibits a 1/
r
2
power law dependence in the far field (i.e., large particle
separations
r
) and correctly captures the orientational
dependence of the capillary interactions in the near field. Using
this dipole potential and finite element simulations, we further analyze
the energy landscape of particle clusters consisting of up to eight
tilted ellipsoids in contact. For clusters of two particles, we find
that the side-to-side configuration is stable, whereas the tip-to-tip
configuration is unstable. However, for clusters of more than three
particles, we find that circular loops of side-to-side particles become
globally stable, whereas linear chains of side-to-side particles become
metastable. Furthermore, the energy barrier for the linear-to-loop
transition decreases with increasing particle number. Our results
explain both thermodynamically and kinetically why tilted ellipsoids
assemble side-to-side locally but have a strong tendency to form loops
on larger length scales.