Piercing an interface with a brush: Collaborative stiffening

Abstract

Abstract. -The hairs of a painting brush withdrawn from a wetting liquid self-assemble into clumps whose sizes rely on a balance between liquid surface tension and hairs bending rigidity. Here we study the situation of an immersed carpet in an evaporating liquid bath : the free extremities of the hairs are forced to pierce the liquid interface. The compressive capillary force on the tip of flexible hairs leads to buckling and collapse. However we find that the spontaneous association of hairs into stronger bundles may allow them to resist capillary buckling. We explore in detail the different structures obtained and compare them with similar patterns observed in micro-structured surfaces such as carbon nanotubes "forests".Introduction. -Everyday's life experience teaches us that wet hairs assemble into bundles. This phenomenon is however amplified at the scale of Micro-Electro-MechanicalSystems (MEMS) since surface forces tend to dominate over bulk forces when the scale is reduced. Indeed, if L is the typical size of a structure, surface forces are proportional to L, while elastic or gravity forces scale as L 2 and L 3 , respectively. Controlling 'stiction' is then a challenging issue in micro-engineering technologies since it often leads to the fatal collapse of microstructures [6][7][8]. Nevertheless, the self-assembly of micro-structures through capillary forces can also be viewed as a useful tool to build complex shapes [1][2][3][4][5]. Beyond engineering applications, surface forces may also have a strong effect on living structures. For instance, filamentous fungi living in aqueous environment have difficulty in growing their hypha through the water interface into the air. Indeed some species have to produce surfactant molecules that reduce capillary forces in order to develop the aerial structures necessary for dissemination [24].In the case of slender structures, the interaction between elasticity and interfacial forces can be defined by a typical elastocapillary length scale, L EC = B/γ ∼ Eh 3 /γ, where E is the Young modulus of the material, h and B are the thickness and the bending stiffness per unit width of the structure, respectively, and γ the liquid surface tension or the solid adhesion energy [25][26][27][28][29]. The validity of this macroscopic length scale has recently been confirmed at the scale of graphene sheets through atomistic simulations [30].In this paper we study the case of a carpet-like structure immersed in a drying liq-

Control of Shape and Size of Nanopillar Assembly by Adhesion-Mediated Elastocapillary Interaction

“…The zippered shape of the four-pillar assembly observed at high adhesion (Figure 5c) may effectively behave as a single pillar with a larger diameter and a shorter height, with less flexibility than if the posts were connected only at their tips, possibly analogous to "collaborative stiffening" described for wet hair bundles. 40 The specific differences between zipped and twisted structures that might make the former less likely to form larger assemblies are unknown, but include differences in effective height or diameter, total contact or exposed area, symmetry, or a more complex liquidϪsolid contact line, any of which would www.acsnano.org change the propensity for capillary-induced bending and stability. For a more quantitative understanding, we have compared our experimental results for the changes in diameter, modulus, adhesion, and wetting of the pillars with theoretical predictions based on the literature 25,27 using eq 1 for various conditions (Figure 7).…”

Elasto-capillary coalescence of multiple parallel sheets

“…The study of the interaction between elastic and capillary forces is relevant to phenomena such as self-folding of solid sheets (commonly referred to as capillary origami, Py et al 2007b;Pineirua, Bico & Roman 2010;Antkowiak et al 2011), densification of patterned arrays of carbon nanotubes (Journet et al 2005;Huang et al 2007;Zhao et al 2010;De Volder et al 2010, and self-assembly and modification of the mechanical and geometrical properties of arrays of solid structures (Chandra et al 2009;Pokroy et al 2009;Chiodi, Roman & Bico 2010;Duan & Berggren 2010;Elwenspoek et al 2010;Kang et al 2011).…”

Deformation of a free interface pierced by a tilted cylinder: Variation of the contact angle

“…They appear in applications throughout biology and engineering, and include animal locomotion [1][2][3][4]; surface processing for nano-micro-applications, for example fiber coating and cleaning [5][6][7], the assembly of hairs, carbon nanotubes and biological filaments [8][9][10][11][12][13][14][15][16]; uses of AFM probes [6,17,18]; and impact of liquid jets [19].…”