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

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 Bénard-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.

arXiv comment20 pages, 9 figures

References in corpus (2)

• Long-Wavelength Instability in Surface-Tension-Driven Benard Convection
• Formation of Nanopillar Arrays in Ultrathin Viscous Films: The Critical Role of Thermocapillary Stresses

Cited by in corpus (5)

• Conjugated liquid layers driven by the short-wavelength Bénard-Marangoni instability: experiment and numerical simulation
• Directionally asymmetric self-assembly of cadmium sulfide nanotubes using porous alumina nanoreactors: Need for chemohydrodynamic instability at the nanoscale
• Differential Colorimetry Measurements of Fluctuation Growth in Nanofilms Exposed to Large Surface Thermal Gradients
• Coupled self-organization: Thermal interaction between two liquid films undergoing long-wavelength instabilities
• Self-Similar Cusp Formation in Thin Liquid Films By Runaway Thermocapillary Forces