  Self-assembly of Janus (or `patchy') particles is dependent on the precise
interaction between neighbouring particles. Here, the orientations of two
amphiphilic Janus spheres within a dimer in an explicit fluid are studied with
high geometric resolution. Molecular dynamics simulations and first-principles
energy calculations are used with hard- and soft-sphere Lennard-Jones
potentials, and temperature and hydrophobicity are varied. The most probable
centre-centre-pole angles are in the range 40{\deg} to 55{\deg}, with
pole-to-pole alignment not observed due to orientational entropy. Angles near
90{\deg} are energetically unfavoured due to solvent exclusion, and we
unexpectedly found that the relative azimuthal angle between the spheres is
affected by solvent ordering.
