Nicholas J. Glassmaker

Biologically inspired crack trapping for enhanced adhesion

We present a synthetic adaptation of the fibrillar adhesion surfaces found in nature. The structure consists of protruding fibrils topped by a thin plate and shows an experimentally measured enhancement in adhesion energy of up to a factor of 9 over a flat control. Additionally, this structure solves the robustness problems of previous mimic structures and has preferred contact properties (i.e., a large surface area and a highly compliant structure). We show that this geometry enhances adhesion because of its ability to trap interfacial cracks in highly compliant contact regimes between successive fibril detachments. This results in the requirement that the externally supplied energy release rate for interfacial separation be greater than the intrinsic work of adhesion, in a manner analogous to lattice trapping of cracks in crystalline solids.

Can a fibrillar interface be stronger and tougher than a non-fibrillar one?

Elasticity analysis and finite element simulations are carried out to study the strength of an elastic fibrillar interface. The fibrils are assumed to be in perfect contact with a rigid substrate. The adhesive interaction between the fibrils and the substrate is modelled by the Dugdale–Barenblatt model (DB). The condition for a fibrillar interface to be stronger than a non-fibrillar one is obtained for two regimes: (i) small fibril or flaw insensitive regime; (ii) large fibril or flaw sensitive regime. The transition between the two regimes is characterized by a dimensionless parameter that incorporates the material constants of the elastic fibrils and interfacial properties. The condition for a fibrillar interface to be tougher is also given. Lateral collapse is found to be detrimental to the strength and toughness of a fibrillar interface.

Enhanced adhesion and compliance of film-terminated fibrillar surfaces

We present studies of a bio-inspired film-terminated fibrillar surface that has significantly enhanced adhesion and contact compliance compared with a flat control. We show that adhesion hysteresis arises from the architecture of the interfacial region. Measured in cyclic indentation experiments, it can be nearly five times the absolute work of adhesion for a flat control. Using a two-dimensional model, we propose that hysteresis develops as a result of crack trapping by fibril edges. The crack propagation mode is consistent with this model, as is the observation that with increasing hysteresis crack opening adhesion energy increases whereas crack closing adhesion energy decreases compared with a flat control. Contact compliance of the fibrillar structure is up to seven times more than that of a flat control. We present a model for the contact compliance of such structures which is in good agreement with measurements.

Collapse of single-walled carbon nanotubes

Single-walled carbon nanotubes with a circular cross section can collapse into ribbons under the influence of self-van der Waals interactions. We present closed-form results for the energetics of this self-collapse using continuum analysis verified by molecular simulations. Two critical tube radii are predicted by the continuum analysis: Rmin, below which there is no collapse; and Rmax, above which the collapsed configuration is energetically favored. We present simple and accurate analytical results for Rmin and Rmax as functions of two length scales, d0 and D∕Wflat, where d0 is the equilibrium distance between two flat parallel graphite sheets, Wflat is the work per unit area needed to separate the two sheets, and D is the effective bending stiffness of the tube.

How Compliance Compensates for Surface Roughness in Fibrillar Adhesion

ABSTRACT Fibrillar interfaces play an important role in the ability of many small animals to adhere to surfaces. Surface roughness is generally deleterious to adhesion because it hinders the ability of mating surfaces to make contact, but fibrillar surfaces compensate for surface roughness by virtue of their enhanced compliance. We examine the relationship between roughness and compliance by analyzing the mechanics of detaching an array of fibrils from a substrate. The theory of Johnson, Kendall, and Roberts is used to describe the interfacial adhesion of each fibril, and roughness is modeled by making the fibril length a random variable subject to a probability distribution. We solve for the mean force response of a fibrillar array as a function of the displacement of the entire array. From these results we extract the mean fibrillar pull-off force and work to separate the fibrillar array and substrate. We show how the mean fibrillar pull-off force decreases with increasing roughness-height standard deviation: the relationship is linear for small height standard deviation, and the pull-off force trails off to zero for very rough surfaces. Conversely, the work of separation is shown to be unaffected by small roughness-height standard deviation, although it decreases toward zero for rougher surfaces. The effects of roughness may be offset by increasing fibrillar compliance; for small roughness-height standard deviation, we show that the reduction in pull-off force is inversely proportional to the normalized compliance. We also show that the work of separation increases linearly with the compliance when the compliance is large compared with the roughness-height standard deviation. One of a collection of papers honoring Manoj K. Chaudhury, the February 2005 recipient of The Adhesion Society Award for Excellence in Adhesion Science, sponsored by 3M.

Strongly enhanced static friction using a film-terminated fibrillar interface

We examine the behavior under shear of a bio-inspired fibrillar interface that consists of poly(dimethlysiloxane) micro-posts terminated by a thin film. These structures demonstrate significantly enhanced adhesion due to a crack trapping mechanism. We study the response of this structure to shear displacement relative to a spherical indenter placed on its surface under a fixed normal force. The shear force required to initiate sliding between the indenter and the sample, its static friction, is strongly enhanced compared to a flat control, and increases with inter-fibril spacing. Examination of the contact region reveals that its area changes with applied shear and that static friction is controlled by a mechanical instability. The shear force resisting steady sliding, surprisingly, is independent of fibril spacing and is nearly the same as for the flat unstructured control samples. We interpret dynamic friction to result from the action of Schallamach-like waves. Our results show that the film-terminated architecture can be used to design an interface with significantly enhanced static friction without altering its sliding frictional resistance.

Design of bio-inspired fibrillar interfaces for contact and adhesion — theory and experiments

Geckos can adhere upside down on a horizontal surface and yet can climb rapidly on most vertical walls. This feat is accomplished using a hierarchical fibrillar interface. This paper reviews design principles of synthetic fibrillar interfaces that mimic surface structures in lizards and insects designed for enhanced contact and adhesion. In addition, we will address the role that statistics plays in quantifying fibrillar adhesion.

On the Inextensible Elastica Model for the Collapse of Nanotubes

In this work, we study the collapse of nanotubes using an inextensible elastica model. Through phase plane analysis, we show that there exist collapsed configurations of different orders, each involving a different number of collapsed layers. Solutions corresponding to each order only exist if the equilibrium separation in the contact zone (a material property) is smaller than a certain value. Below the critical separation, there are two solutions for each order corresponding to each separation, a high energy solution and a low energy one. Some of the collapsed configurations are not physically accessible due to material interpenetration. This work puts a limitation on the applicability of the inextensible elastica model for the collapse of nanotubes.