Mechanism for spontaneous growth of nanopillar arrays in ultrathin films subject to a thermal gradient

Abstract

Several experimental groups have reported spontaneous formation of periodic pillar arrays in molten polymer nanofilms confined within closely spaced substrates held at different temperatures. These formations have been attributed to a radiation pressure instability caused by interface reflection of acoustic phonons. We demonstrate here how variations in thermocapillary stress at the air/polymer interface can produce significant periodic protrusions in any viscous film no matter how small the transverse thermal gradient. The linear stability analysis of the interface evolution equation corresponds to an extreme limit of Bénard–Marangoni flow peculiar to films of nanoscale dimensions—deformation amplitudes are small in comparison to the pillar spacing and hydrostatic forces are negligible. Finite element simulations of the full nonlinear equation provide estimates of the array pitch and growth rates beyond the linear regime. Results of the Lyapunov free energy as a function of time also confirm that pillarlike elongations are energetically preferred in nanofilms, in contrast to cellular instabilities in macroscopically thick films. If not mass limited, fluid elongations continue to grow until contact with the cooler substrate is achieved. These predictions should facilitate the fabrication of extended arrays for nanoscale optical, photonic, and biological applications.