Influence of Shear Stress Jumps in Self-Assembly and Growth of Nanopillars by Thermocapillary Forces

Recent theoretical and experimental studies have confirmed how thermocapillary forces can spontaneously generate periodic, 3D nanopillar arrays in viscous nanofilms exposed to a very large and uniform transverse thermal gradient [1,2]. These formations are quite sensitive to local growth conditions and exhibit variations in location, in-plane symmetry and growth rates. Here we explore the role of shear stress jumps in localizing and self-assembling pillar arrays for more rapid and regular formations. Finite element simulations and Fourier analysis of growing waveforms are used to quantify trends observed when a molten viscous nanofilm is held adjacent to a cold protrusion with sharp sidewalls. The sidewalls enforce a jump in the lateral thermal gradient along the free surface of the film which triggers formation of nanopillar trains. We investigate their number, height, spacing and growth rate as a function of the magnitude in shear stress jump and initial noise amplitude. We discuss why the characteristic wavenumber closely matches predictions from linear stability theory despite the large amplitude perturbation. \\[4pt] [1] M. Dietzel and S. M. Troian, Phys. Rev. Lett. 103, 074501 (2009); J. Appl. Phys. 108, 074308 (2010) \\[0pt] [2] E. McLeod, Y. Liu, and S. M. Troian, Phys. Rev. Lett. 106, 175501(2011)