We study the swelling behavior of finlike
polymer line gratings supported on a rigid substrate and
show that the edge-supported polymer laminae undergo a
rippling instability with a well-defined ripple wavelength λ
transverse to the plane of the solid supporting substrate and a
ripple amplitude that monotonically decreases from its
maximum at the free-edge. These ripple patterns develop
due to inhomogeneous compressive strains that arise from the
geometric constraints that progressively suppress swelling near
the supporting substrate where the laminae are clamped. By experimentally examining the influence of swelling strain and pattern
geometry on the observed rippling instability, we find that the ripple wavelength λ scales with line width w for sufficiently long
gratings, which is consistent with a simple theory. These trends were validated for polymer nanoline test patterns having w
between (50 to 250) nm and a height-to-width aspect-ratio in the range 0.5 to 5. Our results suggest that line geometry, rather
than material properties, governs the onset of rippling and suggest simple rules for their control.