Abstract
We study theoretically the problem of a thin symmetric diblock
copolymer melt or other smectic film placed on a chemically
heterogeneous striped substrate. Recent experimental and
numerical studies of this system have
shown that the lamellae often align perpendicular to the
substrate but that they also tend to crinkle or
undulate. Here we show how this rippling can be understood
as an instability caused by the intrinsic
strain in the system. This instability is closely related
to the classical Helfrich-Hurault instability
which occurs when a smectic fluid is strained between two plates. However,
unlike this instability, the critical strain 
c
scales as H−2 for thin films
of thickness H. We also show that for a given thickness there is
both an upper and a lower
critical strain.
For very thin films there is no crinkling, irrespective of the strain.