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

Abstract

The free surface of molten nanofilms is known to undergo spontaneous formation of periodic protrusions when exposed to a large transverse thermal gradient. Early time measurements of the array pitch and growth rate in polymer melts confirm a formation process based on a long wavelength thermocapillary instability and not electrostatic attraction or acoustic phonon driven growth as previously believed. 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. 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. The thermocapillary mechanism is applicable to any liquid nanofilmit represents an extreme limit of (Bénard) Marangoni instability for long wavelength fluctuations in which gravitational effects are absent and thermocapillary forces overcome stabilization by capillary forces. Previous experimental investigations have confronted limitations imposed by the typical setup shown in Fig. 1(a), namely, no direct measure of the thermal gradient within the narrow gap, lack of parallelism between opposing substrates, and lack of visualization during structure formation and growth. In fact, all measurements to date have relied on solidified formations resulting from prolonged contact with the cooler target.We find that physical contact with the overlying substrate results in smaller wavelengths from fluid reorganization. While this ultimately reduces the array pitch, it compromises direct comparison to models based on linear stability analysis, which also require amplitude fluctuations small i...

Early time instability in nanofilms exposed to a large transverse thermal gradient: Improved image and thermal analysis

“…Experimental measurements have also confirmed that the characteristic wavelength k o varies strongly with the magnitude of the temperature drop across the bilayer film, DT, essentially ruling out the surface charge mechanism as the dominant source of instability. 16,17 In a previous work, we obtained good functional fits between the experiment and the thermocapillary (TC) model prediction for k o , but close quantitative agreement seemed to require input values of the liquid thermal conductivity many times larger than reported in the literature. We have since revisited our analysis to ascertain whether this problem can be resolved by making improvements to the image analysis in order to extract k o at much earlier times and improvements to the thermal simulations used to assess DT.…”

“…In this current work, we therefore also show how improved simulations result in revised values of DT which on average are half as large than previously reported. 16 In what follows, we describe the improved image analysis for isolating the fastest growing mode and a more accurate thermal model for assessing the temperature drop across the confined air/nanofilm bilayer. Feature extraction at much earlier times, coupled with more realistic thermal simulations, leads to a better overall functional and quantitative agreement with the thermocapillary model.…”

“…with experimental measurements. 11,16 In what follows, we therefore exclude this model from consideration and only explore differences between the AP and TC models. Experiments to date have used either polystyrene (PS) or poly(methylmethacrylate) (PMMA) films spun coat onto a silicon wafer to produce a flat and uniform film then melted in situ.…”

“…16 and reanalyzed in this work allowed access to a larger range D Շ 25. This feature, coupled with the ability to view the film instability in-situ, has allowed more accurate measurements of k o for several reasons, including rejection of runs suffering from nonparallel substrates or defective films containing pinholes, embedded or surface contaminant particles.…”

“…III, we briefly review some details of the experimental apparatus used in Ref. 16, from which the raw images analyzed in this current work were obtained. In Sec.…”