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

TL;DR

This paper demonstrates how thermocapillary stresses can induce spontaneous, energetically favored pillar-like structures in ultrathin viscous films under thermal gradients, with implications for nanoscale fabrication.

Contribution

It introduces a new mechanism based on thermocapillary stress variations for spontaneous nanopillar formation in ultrathin films, contrasting previous acoustic phonon explanations.

Findings

Thermocapillary stress variations can produce periodic protrusions in nanofilms.

Pillar elongations are energetically preferred and grow until contact with the cooler substrate.

The mechanism enables potential fabrication of nanoscale optical, photonic, and biological structures.

Abstract

Several groups have reported spontaneous formation of periodic pillar-like arrays in molten polymer nanofilms confined within closely spaced substrates maintained at different temperatures. These formations have been attributed to a radiation pressure instability caused by acoustic phonons. In this work, we demonstrate how variations in the thermocapillary stress along the nanofilm interface can produce significant periodic protrusions in any viscous film no matter how small the initial transverse thermal gradient. The linear stability analysis of the interface evolution equation explores an extreme limit of B\'{e}nard-Marangoni flow peculiar to films of nanoscale dimensions in which hydrostatic forces are altogether absent and deformation amplitudes are small in comparison to the pillar spacing. Finite element simulations of the full nonlinear equation are also used to examine the array pitch and growth rates beyond the linear regime. Inspection of the Lyapunov free energy as a function of time confirms that in contrast to typical cellular instabilities in macroscopically thick films, pillar-like elongations are energetically preferred in nanofilms. Provided there occurs no dewetting during film deformation, it is shown that fluid elongations continue to grow until contact with the cooler substrate is achieved. Identification of the mechanism responsible for this phenomenon may facilitate fabrication of extended arrays for nanoscale optical, photonic and biological applications.