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Several groups have reported spontaneous formation of periodic pillar-likearrays in molten polymer nanofilms confined within closely spaced substratesmaintained at different temperatures. These formations have been attributed toa radiation pressure instability caused by acoustic phonons. In this work, wedemonstrate how variations in the thermocapillary stress along the nanofilminterface can produce significant periodic protrusions in any viscous film nomatter how small the initial transverse thermal gradient. The linear stabilityanalysis of the interface evolution equation explores an extreme limit ofB\'{e}nard-Marangoni flow peculiar to films of nanoscale dimensions in whichhydrostatic forces are altogether absent and deformation amplitudes are smallin comparison to the pillar spacing. Finite element simulations of the fullnonlinear equation are also used to examine the array pitch and growth ratesbeyond the linear regime. Inspection of the Lyapunov free energy as a functionof time confirms that in contrast to typical cellular instabilities inmacroscopically thick films, pillar-like elongations are energeticallypreferred in nanofilms. Provided there occurs no dewetting during filmdeformation, it is shown that fluid elongations continue to grow until contactwith the cooler substrate is achieved. Identification of the mechanismresponsible for this phenomenon may facilitate fabrication of extended arraysfor nanoscale optical, photonic and biological applications.

Mechanism for Spontaneous Growth of Nanopillar Arrays in Ultrathin Films Subject to a Thermal Gradient