Mathias Dietzel

Formation of Nanopillar Arrays in Ultrathin Viscous Films: The Critical Role of Thermocapillary Stresses

Experiments by several groups during the past decade have shown that a molten polymer nanofilm subject to a large transverse thermal gradient undergoes spontaneous formation of periodic nanopillar arrays. The prevailing explanation is that coherent reflections of acoustic phonons within the film cause a periodic modulation of the radiation pressure which enhances pillar growth. By exploring a deformational instability of particular relevance to nanofilms, we demonstrate that thermocapillary forces play a crucial role in the formation process. Analytic and numerical predictions show good agreement with the pillar spacings obtained in experiment. Simulations of the interface equation further determine the rate of pillar growth of importance to technological applications.

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

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 Benard–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.

Thermocapillary Patterning of Nanoscale Polymer Films

We investigate a method for non-contact patterning of molten polymer nanofilms based on thermocapillary modulation. Imposed thermal distributions along the surface of the film generate spatial gradients in surface tension. The resulting interfacial stresses are used to shape and mold nanofilms into 3D structures, which rapidly solidify when cooled to room temperature. Finite element simulations of the evolution of molten shapes illustrate how this technique can be used to fabricate features of different heights and separation distances in a single process step. These results provide useful guidelines for controlling proximity effects during evolution of adjacent structures.