Peeling off an elastica from a smooth attractive substrate

Effect of thin-film length on the peeling behavior of film-substrate interfaces

Compared with the classical Kendall's model to analyze the steady-state peeling behavior of an infinite length film attaching to a rigid substrate, this paper establishes a model of a finite length thin film adhering on a rigid substrate and analyzes the influence of film's initial adhesion length, film stiffness, and initial cantilever length of films on the whole interface peeling behavior. Both theoretical prediction and finite element calculation are carried out. The typical relationship between the peeling force and the separation distance at the loading point is obtained as well as the morphology of deformed films. It is found that the initial adhesion length has a significant effect on the peeling behavior. Differently from the case of infinite thin films, whether the steady-state peeling process can be achieved or not depends on the film's adhesion length. If the film is long enough, the whole peeling process can be divided into an initial peeling stage, a transition stage, a steady-state stage, and an unstable peeling stage. The maximum peeling force of the interface does not necessarily occur in the steady-state stage, which is influenced by the film's initial adhesion length, film stiffness, and initial cantilever length. The results achieved in this paper can not only provide a systematic understanding of peeling behavior of a thin film on a rigid substrate, but also be helpful for the design of high-quality interface and peeling tests in practical applications.

Chemical mediated elasto-capillarity of elastic sheets

Capillary forces can cause outstanding deformation of slender structures, and this behavior holds great potential in a plethora of areas. In this study, we propose a facile strategy to mediate the deformation of elastic structures via chemicals, which is named chemo-elasto-capillarity. The experiment shows that the added surfactant can significantly change the interfacial energy of the system, and then modulate the configuration of the adhered structures. The wetted length and deflection of each sheet can be predicted using the large and infinitesimal deformation theory of beams, and these theoretical values are in excellent agreement with the experimental results. Moreover, the proposed method can be successfully extended to unfold two adhered sheets, and one racket like sheet. The present scheme is accessible to accurately regulate elasto-capillarity, and provide some inspirations for engineering some chemical-sensitive devices and humidity-stimulated actuators.

Effect of relative humidity on the peeling behavior of a thin film on a rigid substrate

Inspired by gecko adhesion in humid environments, a modified Kendall's model is established in order to investigate the effect of relative humidity on the interfacial peeling behavior of a thin film adhering on a rigid substrate. When the humidity is less than 90%, a monolayer of water molecules adsorbed on the substrate surface induces a strong disjoining pressure at the interface. As a result, the steady-state peel-off force between the thin film and substrate is significantly enhanced. When the humidity is greater than 90%, water molecules condense into water droplets. Four different peeling models are established on this occasion, depending on the surface wettability of the film and substrate. It is found that the steady-state peel-off force is influenced by the water meniscus in a complicated manner, which is either enhanced or reduced by the water capillarity comparing to that predicted by the classical Kendall's model, i.e., a dry peeling model. It should be noted that, at the vicinity of the wetting transition, the peel-off force of the four models can be reduced to an identical one, which means the four peeling models can transit from one to another continuously. The present model, as an extension of the classical Kendall's one, should be useful not only for understanding gecko adhesion in humid environments, but also for analyzing interface behaviors of a film-substrate system in real applications.

Elastic membranes in confinement

An elastic membrane stretched between two walls takes a shape defined by its length and the volume of fluid it encloses. Many biological structures, such as cells, mitochondria and coiled DNA, have fine internal structure in which a membrane (or elastic member) is geometrically 'confined' by another object. Here, the two-dimensional shape of an elastic membrane in a 'confining' box is studied by introducing a repulsive confinement pressure that prevents the membrane from intersecting the wall. The stage is set by contrasting confined and unconfined solutions. Continuation methods are then used to compute response diagrams, from which we identify the particular membrane mechanics that generate mitochondria-like shapes. Large confinement pressures yield complex response diagrams with secondary bifurcations and multiple turning points where modal identities may change. Regions in parameter space where such behaviour occurs are then mapped.

Forced desorption of semiflexible polymers, adsorbed and driven by molecular motors

We formulate and characterize a model to describe the dynamics of semiflexible polymers in the presence of activity due to motor proteins attached irreversibly to a substrate, and a transverse pulling force acting on one end of the filament. The stochastic binding-unbinding of the motor proteins and their ability to move along the polymer generate active forces. As the pulling force reaches a threshold value, the polymer eventually desorbs from the substrate. Performing underdamped Langevin dynamics simulation of the polymer, and with stochastic motor activity, we obtain desorption phase diagrams. The correlation time for fluctuations in the desorbed fraction increases as one approaches complete desorption, captured quantitatively by a power law spectral density. We present theoretical analysis of the phase diagram using mean field approximations in the weakly bending limit of the polymer and performing linear stability analysis. This predicts an increase in the desorption force with the polymer bending rigidity, active velocity and processivity of the motor proteins to capture the main features of the simulation results.

Effect of bending stiffness on the peeling behavior of an elastic thin film on a rigid substrate

Inspired by the experimental observation that the maximum peeling force of elastic films on rigid substrates does not always emerge at the steady-state peeling stage, but sometimes at the initial one, a theoretical model is established in this paper, in which not only the effect of the film's bending stiffness on the peeling force is considered, but also the whole peeling process, from the initiation of debonding to the steady-state stage, is characterized. Typical peeling force-displacement curves and deformed profiles of the film reappear for the whole peeling process. For the case of a film with relatively large bending stiffness, the maximum peeling force is found arising at the initial peeling stage and the larger the stiffness of the film, the larger the maximum peeling force is. With the peeling distance increasing, the peeling force is reduced from the maximum to a constant at the steady-state stage. For the case of a film with relatively small stiffness, the peeling force increases monotonically at the initial stage and then achieves a constant as the maximum at the steady-state stage. Furthermore, the peeling forces in the steady-state stage are compared with those of the classical Kendall model. All the theoretical predictions agree well with the existing experimental and numerical observations, from which the maximum peeling force can be predicted precisely no matter what the stiffness of the film is. The results in this paper should be very helpful in the design and assessment of the film-substrate interface.

Switch on, switch off: stiction in nanoelectromechanical switches

We present a theoretical investigation of stiction in nanoscale electromechanical contact switches. We develop a mathematical model to describe the deflection of a cantilever beam in response to both electrostatic and van der Waals forces. Particular focus is given to the question of whether adhesive van der Waals forces cause the cantilever to remain in the 'ON' state even when the electrostatic forces are removed. In contrast to previous studies, our theory accounts for deflections with large slopes (i.e. geometrically nonlinear). We solve the resulting equations numerically to study how a cantilever beam adheres to a rigid electrode: transitions between 'free', 'pinned' and 'clamped' states are shown to be discontinuous and to exhibit significant hysteresis. Our findings are compared to previous results from linearized models and the implications for nanoelectromechanical cantilever switch design are discussed.

High-energy deformation of filaments with internal structure and localized torque-induced melting of DNA

We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a double-stranded DNA oligomer (shorter than its thermal persistence length) whose free ends are linked by a single-stranded DNA chain. This construct, studied by H. Qu and G. Zocchi [Europhys. Lett. 94, 18003 (2011)], displays nonlinear strain softening associated with the local melting of the double-stranded DNA under applied torque and serves as a model system with which to study the nonlinear elasticity of DNA under large energy deformations. We show that one can account quantitatively for the observed bending mechanics using an augmented wormlike chain model, the helix-coil wormlike chain. We also predict that the highly bent and partially molten dsDNA should exhibit particularly large end-to-end fluctuations associated with the fluctuation of the length of the molten region, and propose appropriate experimental tests. We suggest that the augmented wormlike chain model discussed here is a useful analytic approach to the nonlinear mechanics of DNA or other biopolymer systems.

Strain energy and lateral friction force distributions of carbon nanotubes manipulated into shapes by atomic force microscopy

The interplay between local mechanical strain energy and lateral frictional forces determines the shape of carbon nanotubes on substrates. In turn, because of its nanometer-size diameter, the shape of a carbon nanotube strongly influences its local electronic, chemical, and mechanical properties. Few, if any, methods exist for resolving the strain energy and static frictional forces along the length of a deformed nanotube supported on a substrate. We present a method using nonlinear elastic rod theory in which we compute the flexural strain energy and static frictional forces along the length of single walled carbon nanotubes (SWCNTs) manipulated into various shapes on a clean SiO(2) substrate. Using only high resolution atomic force microscopy images of curved single walled nanotubes, we estimate flexural strain energy distributions on the order of attojoules per nanometer and the static frictional forces between a SWCNT and SiO(2) surface to be a minimum of 230 pN nm(-1).

Adhesion transition of flexible sheets

Intermolecular forces are known to precipitate adhesion events between solid bodies. Inspired by a macroscale experiment showing the hysteretic adhesion of a piece of flexible tape over a plastic substrate, we develop here a model of far-field dry adhesion between two flexible sheets interacting via a power-law potential. We show that phase transitions from unadhered to adhered states occur as dictated by a dimensionless bending parameter representing the ratio of interaction strength to bending stiffness. The order of the adhesion transitions, as well as their hysteretic nature, is shown to depend on the form of the interaction potential between the flexible sheets. When three or more sheets interact, additional geometrical considerations determine the hierarchical or sequential nature of the adhesion transitions.

Mechanical properties of an adsorbed elastic polymer in contact with a rigid membrane

A static and a dynamical model are introduced to study the physical properties of an elastic polymer adsorbed on a rigid membrane. We analyze the detailed microscopic model for the adhesion problem and show that in the force ensemble a critical force is expected. Forces smaller than the critical value are not able to peel off the filament, while larger forces will cause the filament to completely desorb from the membrane. To demonstrate the nonequilibrium properties of the moving states for forces larger than the critical value, we present the linear response of the system in the form of a force-velocity relation. In addition, we use a very simple short-range static model and obtain the equilibrium phases of the system in different cases where either a fixed force or a fixed height can be applied at the end. For the fixed force the equilibrium phases arising from the static model are in agreement with dynamical model. Forces smaller than the critical value are not able to peel off the filament while the larger forces will cause the filament to completely desorb as in the dynamical model.

Peeling force spectroscopy: exposing the adhesive nanomechanics of one-dimensional nanostructures

The physics of adhesion and stiction of one-dimensional nanostructures such as nanotubes, nanowires, and biopolymers on different material substrates is of great interest for the study of biological adhesion and the development of nanoelectronics and nanocomposites. Here, we combine theoretical models and a new mode in the atomic force microscope to investigate quantitatively the physics of nanomechanical peeling of carbon nanotubes and nanocoils on different substrates. We demonstrate that when an initially straight nanotube is peeled from a surface, small perturbations can trigger sudden transitions between different geometric configurations of the nanotube with vastly different interfacial energies. This opens up the possibility of quantitative comparison and control of adhesion between nanotubes or nanowires on different substrates.