Undulational instabilities of smectic thin films on heterogeneous patterned surfaces under positive and negative strain: The case of diblock copolymers

We consider the problem of a thin smectic film placed on a periodically str iped solid surface, with stripe width lambda, and with the upper surface fr ee. The striped surface-smectic fluid interfacial energy induces the lamell ae to align perpendicularly to the surface. We show that in many cases both the bulk liquid and the free upper surface will undulate to relieve the fr ustration caused by the stripes. In marked contrast to the traditional Helf rich-Hurault instability we show that this new instability occurs under bot h extension and compression. As a concrete example we consider a symmetric diblock copolymer thin film melt, with bulk equilibrium AB-BA bilayer spaci ng L-2. When L-2 <2 lambda these undulations will be enhanced while for L-2 >2 lambda they will be diminished. (C) 1999 American Institute of Physics. [S0021-9606(99)70318-1].