Morphological Instability of a Confined Polymer Film in a Thermal Gradient

Abstract

We report the experimental observation of a morphological instability of a confined polymerair double layer sandwiched between two plates set to different temperatures. The homogeneous temperature gradient across the double layer causes the breakup of the polymer film into columns or stripes spanning the two plates. Experimentally, the characteristic wavelength of these patterns varies with the inverse of the initial heat flux through the bilayer. To gain insight into the nature of the instability, we have developed a phenomenological model that describes the heat flow in terms of diffusion through the bilayer. In an idealized microscopic model for the heat flow through the bilayer system, thermal modes in the polymer film with wavelengths ranging from the film thickness to the Debye limit contribute to the heat flux. The low end of this frequency spectrum causes a thermal radiation pressure at the polymer-air surface that destabilizes the film, while the high-frequency modes ascertain the heat conduction through the bilayer.

Experimental Verification of the Formation Mechanism for Pillar Arrays in Nanofilms Subject to Large Thermal Gradients

“…The wavelength of the fastest growing mode in the limit ðh 0 = max Þ 2 ( 1 for the three models discussed above [2,3,8] is given by…”

“…Here, denotes the polymer surface charge density, " 0 is the vacuum permittivity, Q is the nanofilm acoustic quality factor [3], and ¼ k air =k p , which represents the thermal conductivity ratio of air to polymer film. Remaining variables are defined in Fig.…”

“…There is significant interest in this phenomenon since external field gradients can be used to generate three dimensional nanostructures directly from the melt, which after solidification exhibit ultra smooth surfaces befitting the most demanding optical applications. Controlled growth of desired shapes, however, requires identification of the dominant growth mechanism, the material and geometric properties affecting structure formation, and the principles that establish the minimum feature size.Three different mechanisms have been proposed as the source of instability: electrostatic attraction from surface induced charge between the film and overlying substrate (SC model [2,5]), internal film pressure caused by interfacial reflections of low frequency acoustic phonons (AP model [3,6]), and thermocapillary flow from temperature variations along the interface which draw fluid toward cooler regions (TC model [7,8]). The first two mechanisms rely on properties specific to polymeric films.…”

“…We find excellent agreement with theoretical predictions provided the nanofilm out-of-plane thermal conductivity is several times larger than bulk, an enhancement suggestive of polymer chain alignment. DOI: 10.1103/PhysRevLett.106.175501 PACS numbers: 81.16.Dn, 47.55.nb, 66.70.Hk, 68.35.bm For the past decade, researchers have been exploring the effects of large thermal gradients on molten nanofilms in the hope of harnessing pillar instabilities for generating microarrays [1][2][3][4]. When the free surface of a molten nanofilm is exposed to large thermal gradients, periodic protrusions form and grow toward the cooler target until contact is achieved.…”

“…Three different mechanisms have been proposed as the source of instability: electrostatic attraction from surface induced charge between the film and overlying substrate (SC model [2,5]), internal film pressure caused by interfacial reflections of low frequency acoustic phonons (AP model [3,6]), and thermocapillary flow from temperature variations along the interface which draw fluid toward cooler regions (TC model [7,8]). The first two mechanisms rely on properties specific to polymeric films.…”