  The optical and infrared colors of L and T dwarfs are sensitive to cloud
sedimentation and chemical equilibrium processes in their atmospheres. The
i'-z' vs. J-K color-color diagram provides a window into diverse atmospheric
processes mainly because different chemical processes govern each color, and
cloud opacity largely affects J-K but not i'-z'. Using theoretical atmosphere
models that include for the first time a self-consistent treatment of cloud
formation, we present an interpretation of the i'-z' vs. J-K color trends of
known L and T dwarfs. We find that the i'-z' color is extremely sensitive to
chemical equilibrium assumptions: chemical equilibrium models accounting for
cloud sedimentation predict redder i'-z' colors--by up to 2 magnitudes--than
models that neglect sedimentation. We explore the previously known J-K color
trends where objects first become redder, then bluer with decreasing effective
temperature. Only models that include sedimentation of condensates are able to
reproduce these trends. We find that the exact track of a cooling brown in J-K
(and i'-z') is very sensitive to the details of clouds, in particular to the
efficiency of sedimentation of condensates in its atmosphere. We also find that
clouds still affect the strength of the J, H, and K band fluxes of even the
coolest T dwarfs. In addition, we predict the locus in the i'-z' vs. J-K
color-color diagram of brown dwarfs cooler than yet discovered.
