Christian Fretigny

Measurement of elastic modulus of nanotubes by resonant contact atomic force microscopy

A resonant contact atomic force microscopy technique is used to quantitatively measure the elastic modulus of polymer nanotubes. An oscillating electric field is applied between the sample holder and the microscope head to excite the oscillation of the cantilever in contact with nanotubes. The nanotubes are suspended over the pores of a membrane. The measured resonance frequency of this system, a cantilever with the tip in contact with a nanotube, is shifted to higher values with respect to the resonance frequency of the free cantilever. It is experimentally demonstrated that the system can simply be modeled by a cantilever with the tip in contact with two springs. The measurement of the frequency shift thus enables the direct determination of the spring stiffness, i.e., the nanotube stiffness. The method also enables the determination of the boundary conditions of the nanotube on the membrane. The tensile elastic modulus is then simply determined using the classical theory of beam deflection. The obtained results fairly agree to previously measured values using nanoscopic three points bending tests. It is demonstrated that resonant contact atomic force microscopy allows us to quantitatively measure the mechanical properties of nanomaterials

Local friction at a sliding interface between an elastomer and a rigid spherical probe

Abstract.This paper reports on spatially resolved measurements of the shear stress distribution at a frictional interface between a flat rubber substrate and a glass lens. Silicone rubber specimens marked close to their surface by a colored pattern have been prepared in order to measure the surface displacement field induced by the steady-state friction of the spherical probe. The deconvolution of this displacement field then provides the actual shear stress distribution at the contact interface. When a smooth glass lens is used, a nearly constant shear stress is achieved within the contact. On the other hand, a bell-shaped shear stress distribution is obtained with rough lenses. These first results suggest that simple notions of real contact area and constant interface shear stress cannot account for the observed changes in local friction when roughness is varied.

Deformation of elastic coatings in adhesive contacts with spherical probes

This study addresses the problem of adhesive contacts between layered substrates and axisymmetric probes. A semi-analytical approach to adhesive contacts has been developed as an extension of a model recently published by Perriot and Barthel (2004 J. Mat. Res. 19 600–8) for the axisymmetric elastic indentation of non-adhesive, coated substrates. In addition to the load and penetration at equilibrium, the model allowed the derivation of the shape of the free surface in the contact zone. The validity of the approach was verified from experiments using contacts between acrylate films above their glass transition temperature (Tg) and spherical glass lenses. When the adhesive contacts were quenched below Tg, stable imprints were obtained which allowed determination of the surface deformations of the films. The latter were found consistent with the hypothesis of short range surface forces which were embedded in the contact model. Deviations from theory in the form of fingering instabilities at the periphery of the contact were observed when the confinement of the film was increased. A calculation of the stresses within the adhesive contacts indicated that these instabilities are probably driven by the release of lateral constraints within the confined films.

Depth sensing and dissipation in tapping mode atomic force microscopy

Tapping mode atomic force microscopy is frequently used to image the surface of soft materials; it is also a powerful technique for nanomechanical analysis of surfaces. We report here an investigation of the depth sensing of the method on soft polymers. The chosen approach is based on the analysis of phase images of a model filled elastomer material. It leads to the determination of the depths of the hard particles lying under the surface. We found that tapping mode can probe interfaces buried under up to 80 nm of polymer. Under given tapping conditions, the penetration depth of the tip into the polymer is observed to depend on the layer thickness. However we show that, for a given penetration depth, the dissipated energy is independent of the thickness of the polymer layer under the tip. This suggests that the phase signal does not originate in the bulk viscoelasticity of the elastomer. Our observations support the hypothesis that, in tapping mode experiments on elastomers, the phase signal has an adhesi...

Surface Pressure and Shear Stress Fields within a Frictional Contact on Rubber

This paper addresses the issue of the determination of the frictional stress distribution from the inversion of the measured surface displacement field for sliding interfaces between a glass lens and a rubber (poly(dimethylsiloxane)) substrate. Experimental results show that high lateral strains are achieved at the periphery of the sliding contacts. As a consequence, an accurate inversion of the displacement field requires that finite strains and non-linear response of the rubber substrate are taken into account. For that purpose, a Finite Element (FE) inversion procedure is implemented where the measured displacement field is applied as a boundary condition at the upper surface of a meshed body representing the rubber substrate. Normal pressure is also determined in the same way, if non-diverging values are assumed at the contact edge. This procedure is applied to linearly sliding contacts as well as on twisting contacts.

Solution for the elastic field in a layered medium under axisymmetric contact loading

This study addresses the problem of the calculation of the elastic stress and displacement field within isotropic layered media in frictionless contact with rigid axisymmetric indenters. For a prescribed surface stress distribution, the integral transform approach is recalled using a matrix formulation which lends itself to generalizations to multilayered systems. It leads to an analytical solution for the Hankel transform of the elastic field which can readily be numerically inverted in the real space using available discrete Hankel transform algorithms. As an example, the shear stresses induced by the sphere indentation of a coated substrate are calculated as a function of the geometrical confinement of the contact and of the compressibility of the layer. The calculation was carried out using the surface pressure distribution provided by an exact solution to the coated contact problem. In addition, the elastic fields were also determined using an elliptic approximation of the contact pressure distribution. It is shown that the interface shear stress is strongly dependent on the details of the applied pressure profile close to the edge of the contact. In confined layers close to incompressibility, the elliptic approximation is found to result in a systematic overestimate of the interface shear stresses.

DETERMINATION OF COMPLEX MODULUS BY ATOMIC FORCE MICROSCOPY

The static friction regime of an atomic force microscope tip on a soft material is analyzed. A mechanical model shows that the experimental response is characteristic of the complex modulus of the sample. Moduli deduced from experiments on styrene-butadiene films compare favorably with macroscopically determined ones. Small discrepancies can be attributed to the imprecise knowledge of the mechanical properties of the cantilever. Relative measurements should, however, be accurately made. Spatial resolution depends on mechanical and adhesive properties of the material. For the experiments shown, the resolution is a few microns. Contrary to others, this method is little dependent on the geometrical properties of the tip end since in this regime the tip is deeply intruded in the material. It applies on thin films and heterogeneous materials and provides a new method for determining the mechanical properties at a local scale.

Adhesive contact of elastomers: effective adhesion energy and creep function

For the adhesive contact of elastomers, we propose expressions to quantify the impact of viscoelastic response on effective adhesion energy as a function of contact edge velocity. The expressions we propose are simple analytical functionals of the creep response and should be suitable for experimental data analysis in terms of measured rheologies. We also emphasize the role of the coupling between local stress field at the contact edge and the macroscopic remote loading (far field). We show that the contrast between growing and receding contacts originates from the impact of viscoelastic response on coupling, while the separation process at the contact edge is similarly affected by viscoelasticity in both cases.

Multiscale Surface-Attached Hydrogel Thin Films with Tailored Architecture

A facile route for the fabrication of surface-attached hydrogel thin films with well-controlled chemistry and tailored architecture on wide range of thickness from nanometers to micrometers is reported. The synthesis, which consists in cross-linking and grafting the preformed and ene-reactive polymer chains through thiol-ene click chemistry, has the main advantage of being well-controlled without the addition of initiators. As thiol-ene click reaction can be selectively activated by UV-irradiation (in addition to thermal heating), micropatterned hydrogel films are easily synthesized. The versatility of our approach is illustrated by the possibility to fabricate various chemical polymer networks, like stimuli-responsive hydrogels, on various solid substrates, such as silicon wafers, glass, and gold surfaces. Another attractive feature is the development of new complex hydrogel films with targeted architecture. The fabrication of various architectures for polymer films is demonstrated: multilayer hydrogel films in which single-networks are stacked one onto the other, interpenetrating networks films with mixture of two networks in the same layer, and nanocomposite hydrogel films where nanoparticles are stably trapped inside the mesh of the network. Thanks to its simplicity and its versatility this novel approach to surface-attached hydrogel films should have a strong impact in the area of polymer coatings.

Contact compliance effects in the frictional response of bioinspired fibrillar adhesives

The shear failure and friction mechanisms of bioinspired adhesives consisting of elastomer arrays of microfibres terminated by mushroom-shaped tips are investigated in contact with a rigid lens. In order to reveal the interplay between the vertical and lateral loading directions, experiments are carried out using a custom friction set-up in which normal stiffness can be made either high or low when compared with the stiffness of the contact between the fibrillar adhesive and the lens. Using in situ contact imaging, the shear failure of the adhesive is found to involve two successive mechanisms: (i) cavitation and peeling at the contact interface between the mushroom-shaped fibre tip endings and the lens; and (ii) side re-adhesion of the fibres stem to the lens. The extent of these mechanisms and their implications regarding static friction forces is found to depend on the crosstalk between the normal and lateral loading directions that can result in contact instabilities associated with fibre buckling. In addition, the effects of the viscoelastic behaviour of the polyurethane material on the rate dependence of the shear response of the adhesive are accounted for.