We have studied the equilibrium structure of a grafted polymer layer c
omposed of two distinct species of homopolymers, the ''binary brush'',
in various solvent conditions. By using a coarse-grained simulation m
ethod that involves direct calculation of the Edwards hamiltonian, we
are able to simulate much larger systems than would otherwise be possi
ble with a more standard lattice simulation. If the two species are ma
de sufficiently immiscible, we find lateral binary microphase separati
on over a wide range of solvent conditions. Due to the presence of sol
vent, we find a stage where the brush expands in a laterally homogeneo
us manner as immiscibility increases. In this stage, laterally average
d quantities are well-described by a single solvent-related parameter:
a modified excluded volume parameter. This is followed by lateral mic
rophase separation in which the brush volume remains relatively consta
nt. In Theta solvent, this phase separation sets in at a degree of imm
iscibility consistent with a mean field prediction for melt layers. Th
e onset of phase separation is delayed as solvent quality increases. F
urthermore, a reduction in solvent quality results in a stronger cross
over between mixed and phase-separated configurations. Under poor solv
ent conditions, we find interesting structural variations as a result
of the combination of phase separation from solvent and phase separati
on of the two species.