Surface crinkling of strained diblock copolymer smectic thin films on striped substrates

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.