Formation of nanopillar arrays in ultrathin viscous films: the critical role of thermocapillary stresses

Phase-field numerical study on the dynamic process of thermocapillary patterning

It is well known that surface tension is dependent on temperature, and thus a nonuniform temperature may cause thermocapillary flow which is referred to as the Marangoni effect. For a thin liquid-air film confined between a flat hot plate and a topographical cold template, it undergoes deformation due to thermocapillary flow. This phenomenon is termed as thermocapillary patterning, and has been used to fabricate micro- and nanostructure in polymer films. In most cases, the obtained structure conforms to the template; i.e., it can be considered as a replication technique. In this paper, we developed a two-phase flow numerical model based on the phase field to study the dynamic process of thermocapillary patterning. As a remeshing-free method, the phase field enables the incorporation of thermal field and multiphase flow with free surface deformation. The numerical model was employed to study the dynamic process of thermocapillary patterning. Meanwhile, the effects of some parameters, e.g., temperature, geometry parameters, and contact angle, were also investigated.

Mechanism and performance relevance of nanomorphogenesis in polyamide films revealed by quantitative 3D imaging and machine learning

Biological morphogenesis has inspired many efficient strategies to diversify material structure and functionality using a fixed set of components. However, implementation of morphogenesis concepts to design soft nanomaterials is underexplored. Here, we study nanomorphogenesis in the form of the three-dimensional (3D) crumpling of polyamide membranes used for commercial molecular separation, through an unprecedented integration of electron tomography, reaction-diffusion theory, machine learning (ML), and liquid-phase atomic force microscopy. 3D tomograms show that the spatial arrangement of crumples scales with monomer concentrations in a form quantitatively consistent with a Turing instability. Membrane microenvironments quantified from the nanomorphologies of crumples are combined with the Spiegler-Kedem model to accurately predict methanol permeance. ML classifies vastly heterogeneous crumples into just four morphology groups, exhibiting distinct mechanical properties. Our work forges quantitative links between synthesis and performance in polymer thin films, which can be applicable to diverse soft nanomaterials.

Ordered high aspect ratio nanopillar formation based on electrical and thermal reflowing of prepatterned thin films

Creating well-ordered, submicron-sized pillars have been stated as main limitation for electrically induced patterning of nanofilms (thickness <100 nm) [1]. In our previous works, it was shown that the aspect ratio of formed nanopillars was increased to about 0.35 when thermocapillary induced instabilities (Thermally Induced Patterning, TIP) is combined with electrodynamics instabilities (Electrically Induced Patterning, EIP). However, further reduction of pillar size resulted in a coarse and randomly distributed pillars [2,3]. Here, the reflowing of initially prepatterned nanofilms are examined in the EIP and combined EIP-TIP process to create a well-ordered and high aspect ratio nanopillar arrays without sacrificing the fidelity of the final structure. The long-wave approximation is used to simplify the governing equations and boundary conditions leading to a fourth order nonlinear partial differential equation called thin film equation that describes the spatio-temporal evolution of the interface. The mechanism of pattern reflowing is discussed for both linear (initial) and nonlinear (long-term) deformations in EIP and EIP-TIP process. The optimum initial pattern width, height and the center-to-center distance is found based on the characteristic wavelength for growth of instabilities predicted by linear stability analysis and nonlinear simulation results.

Effect of an insoluble surfactant on the dynamics of a thin liquid film flowing over a non-uniformly heated substrate

The stability analysis of a gravity-driven thin liquid film with an insoluble surfactant flowing over a surface with embedded, regularly spaced heaters is investigated. At the leading edge of a heater, the presence of a temperature gradient induces an opposing Marangoni stress at the interface leading to the formation of a capillary ridge. This ridge has been shown to be susceptible to thermocapillary (oscillating in the flow direction) and rivulet (spanwise periodic pattern) instabilities. The presence of an insoluble surfactant is shown to have a stabilizing effect on this system. The governing equations for the evolution of the film thickness and surfactant concentration are obtained within the lubrication approximation. The coupled two-dimensional base solutions for the film thickness and surfactant concentration show that there is no significant change in the height of the capillary ridge at the subsequent heaters downstream. The height of the capillary ridge is reduced by the presence of the surfactant. For very small Peclet number, the presence of multiple heaters has almost no significant effect on the film stability as compared to a single heater and similar trends are observed between the two configurations in the presence of the surfactant as for the case of a clean interface. However, for large Peclet number, the effect was observed on both types of instabilities for certain heater configurations. The Biot number is shown to have a strong effect on the stability results wherein the dominant mode of instability is altered (from rivulet to thermocapillary instability) for a passive or no surfactant case with increase in the Biot number. For an active surfactant thermocapillary instability is found to remain the dominant mode of instability for all the values of the Biot number. It is shown that increasing the number of heaters beyond a couple does not further affect the stability results.

Thermodiffusion as a means to manipulate liquid film dynamics on chemically patterned surfaces

The model problem examined here is the stability of a thin liquid film consisting of two miscible components, resting on a chemically patterned solid substrate and heated from below. In addition to surface tension gradients, the temperature variations also induce gradients in the concentration of the film by virtue of thermodiffusion/Soret effects. We study the stability and dewetting behaviour due to the coupled interplay between thermal gradients, Soret effects, long-range van der Waals forces, and wettability gradient-driven flows. Linear stability analysis is first employed to predict growth rates and the critical Marangoni number for chemically homogeneous surfaces. Then, nonlinear simulations are performed to unravel the interfacial dynamics and possible locations of the film rupture on chemically patterned substrates. Results suggest that appropriate tuning of the Soret parameter and its direction, in conjunction with either heating or cooling, can help manipulate the location and time scales of the film rupture. The Soret effect can either potentially aid or oppose film instability depending on whether the thermal and solutal contributions to flow are cooperative or opposed to each other.

Spreading of Thin Droplets of Perfect and Leaky Dielectric Liquids on Inclined Surfaces

The spreading of droplets may be influenced by electric fields, a situation that is relevant to applications such as coating, printing, and microfluidics. In this work we study the effects of an electric field on the gravity-driven spreading of two-dimensional droplets down an inclined plane. We consider both perfect and leaky dielectric liquids, as well as perfectly and partially wetting systems. In addition to the effects of electric fields, we examine the use of thermocapillary forces to suppress the growth of the capillary ridge near the droplet front. Lubrication theory is applied to generate a set of coupled partial differential equations for interfacial height and charge, which are then solved numerically with a finite-difference method. Electric fields increase the height of the capillary ridge in both perfect and leaky dielectric droplets due to electrostatic pressure gradients that drive liquid into the ridge. In leaky dielectrics, large interfacial charge gradients in the contact-line region create shear stresses that also enhance ridge growth and the formation of trailing minor ridges. The coalescence of these ridges can significantly affect the long-time thinning rate of leaky dielectric droplets. In partially wetting liquids, electric fields promote the splitting of smaller droplets from the primary droplet near the receding contact line due to the interplay between electrostatic forces and disjoining pressure. Cooling from below and heating from above generates thermocapillary forces that counteract the effects of electric fields and suppress the growth of the capillary ridge. The results of this work have important implications for manipulating the spreading of droplets down inclined surfaces.

Thermo-Electrohydrodynamic Patterning in Nanofilms

To improve the electrically assisted patterning process and create smaller sized features with the higher active surface area, the combined thermocapillary-electrohydrodynamic (TC-EHD) instability of liquid nanofilms is considered. First, the 3-D thin film equation is rederived for nonisothermal films and then the influential factors on the dynamics and stability of thin liquid film are found using linear stability (LS) analysis. Nonlinear studies are also conducted to investigate the long-time evolution of the interface using an in-house developed Fortran code employing high order finite difference and adaptive time step solver for the spatial and time derivatives. The number density of pillars (columnar raised structure) formed in 1 μm(2) area is significantly increased compared to the EHD base-case and nanosized pillars are created due to the thermocapillary effects. Relative interface area increases of up to 18% due to this pattern miniaturization are realized. It is also found that increase in the thermal conductivity ratio of layers changes the mechanism of pattern formation resulting in nonuniform and randomly distributed micro pillars being generated.

Instability, self-organization and pattern formation in thin soft films

The free surface of a thin soft polymer film is often found to become unstable and self-organizes into various meso-scale structures. In this article we classify the instability of a thin polymer film into three broad categories, which are: category 1: instability of an ultra-thin (<100 nm) viscous film engendered by amplification of thermally excited surface capillary waves due to interfacial dispersive van der Waals forces; category 2: instability arising from the attractive inter-surface interactions between the free surface of a soft film exhibiting room temperature elasticity and another rigid surface in its contact proximity; and category 3: instability caused by an externally applied field such as an electric field or a thermal gradient, observed in both viscous and elastic films. We review the salient features of each instability class and highlight how characteristic length scales, feature morphologies, evolution pathways, etc. depend on initial properties such as film thickness, visco-elasticity (rheology), residual stress, and film preparation conditions. We emphasize various possible strategies for aligning and ordering of the otherwise isotropic structures by combining the essential concepts of bottom-up and top-down approaches. A perspective, including a possible future direction of research, novelty and limitations of the methods, particularly in comparison to the existing patterning techniques, is also presented for each setting.

Nanoscale directional motion towards regions of stiffness

How to induce nanoscale directional motion via some intrinsic mechanisms pertaining to a nanosystem remains a challenge in nanotechnology. Here we show via molecular dynamics simulations that there exists a fundamental driving force for a nanoscale object to move from a region of lower stiffness toward one of higher stiffness on a substrate. Such nanoscale directional motion is induced by the difference in effective van der Waals potential energy due to the variation in stiffness of the substrate; i.e., all other conditions being equal, a nanoscale object on a stiffer substrate has lower van der Waals potential energy. This fundamental law of nanoscale directional motion could lead to promising routes for nanoscale actuation and energy conversion.

Nano-imaging enabled via self-assembly

Imaging object details with length scales below approximately 200 nm has been historically difficult for conventional microscope objective lenses because of their inability to resolve features smaller than one-half the optical wavelength. Here we review some of the recent approaches to surpass this limit by harnessing self-assembly as a fabrication mechanism. Self-assembly can be used to form individual nano- and micro-lenses, as well as to form extended arrays of such lenses. These lenses have been shown to enable imaging with resolutions as small as 50 nm half-pitch using visible light, which is well below the Abbe diffraction limit. Furthermore, self-assembled nano-lenses can be used to boost contrast and signal levels from small nano-particles, enabling them to be detected relative to background noise. Finally, alternative nano-imaging applications of self-assembly are discussed, including three-dimensional imaging, enhanced coupling from light-emitting diodes, and the fabrication of contrast agents such as quantum dots and nanoparticles.

Tunable vapor-condensed nanolenses

Nanostructured optical components, such as nanolenses, direct light at subwavelength scales to enable, among others, high-resolution lithography, miniaturization of photonic circuits, and nanoscopic imaging of biostructures. A major challenge in fabricating nanolenses is the appropriate positioning of the lens with respect to the sample while simultaneously ensuring it adopts the optimal size and shape for the intended use. One application of particular interest is the enhancement of contrast and signal-to-noise ratio in the imaging of nanoscale objects, especially over wide fields-of-view (FOVs), which typically come with limited resolution and sensitivity for imaging nano-objects. Here we present a self-assembly method for fabricating time- and temperature-tunable nanolenses based on the condensation of a polymeric liquid around a nanoparticle, which we apply to the high-throughput on-chip detection of spheroids smaller than 40 nm, rod-shaped particles with diameter smaller than 20 nm, and biofunctionalized nanoparticles, all across an ultralarge FOV of >20 mm(2). Previous nanoparticle imaging efforts across similar FOVs have detected spheroids no smaller than 100 nm, and therefore our results demonstrate the detection of particles >15-fold smaller in volume, which in free space have >240 times weaker Rayleigh scattering compared to the particle sizes detected in earlier wide-field imaging work. This entire platform, with its tunable nanolens condensation and wide-field imaging functions, is also miniaturized into a cost-effective and portable device, which might be especially important for field use, mobile sensing, and diagnostics applications, including, for example, the measurement of viral load in bodily fluids.

Creating self-organized submicrometer contact instability patterns in soft elastic bilayers with a topographically patterned stamp

The surface of a thin elastic bilayer becomes spontaneously unstable when it is brought in proximity to another rigid contactor. The instability patterns, which are random and isotropic, exhibit a dominant lateral length scale of instability λ, which linearly scales with the bilayer thickness (h) as: λ = R(F)h. It is known that for an elastic bilayer, R(F) exhibits a nonlinear dependence on the ratios of individual film thicknesses (H) and shear moduli (M) of the two constituent layers, and can have values as low as 0.5 under specific conditions. This is in contrast to a near constant value of R(F) ≈ 3 for a single layer elastic film. (1) These isotropic contact instability patterns in a bilayer can be ordered, aligned and modulated using a topographically patterned stamp. The precise morphology of the aligned structures depends on commensuration between λ and the stamp periodicity (λ(P)), and on the intersurface separation distance. A variety of patterns, like an array of circular holes, double periodic channels, etc., in addition to a positive and a negative replica of the stamp pattern, can be engineered with a simple stamp having 1D grating structure. A lower value of R(F) in a bilayer allows generating patterns with sub 500 nm lateral resolution, which is impossible to create by elastic contact lithography (ECL) of a single layer film due to strong surface tension effects in ultrathin films. Thus, control of elastic instability in a bilayer with a patterned stamp represents a flexible soft lithography tool allowing modulation of length scales, morphology, and order.

Experimental verification of the formation mechanism for pillar arrays in nanofilms subject to large thermal gradients

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.