Swelling-Induced Deformation of Nanopatterned Polymer Lines

The deformation behavior of isolated poly ($N$-isopropylacrylamide) nanolines due to swelling is studied to quantitatively establish the parameters governing their mechanical stability. The features are patterned using electron-beam lithography and are supported on a rigid substrate. In the range of 50-250 nm linewidth, we show that the swollen lines undergo Euler buckling with stable higher order modes due to the constraint for polymer chain expansion at the substrate interface. The critical wavelength for buckling surprisingly increases with decreasing line length. The linear swelling strain thus becomes a function of the initial length and decreases dramatically as the line length approaches twice the buckling wavelength for infinitely long lines. A critical length, \textit{larger} than the buckling wavelength for infinitely long features, exists below which the lines remain mechanically stable regardless of their crosslink density. For sufficiently long lines with height-to-width aspect-ratio in the range 0.5-1.7, the scaling relationship for buckling wavelength vs. linewidth suggests that swelling is anisotropic and is more dominant through height than width. The results established in this study are more generally applicable to nanopatterned polymer lines since buckling instabilities involve simultaneous bending and compression, which deform the material with equal force but in opposite directions.