Passive microrheology of soft materials with atomic force microscopy: A wavelet-based spectral analysis

International audienceCompared to active microrheology where a known force or modulation is periodically imposed to a soft material, passive microrheology relies on the spectral analysis of the spontaneous motion of tracers inherent or external to the material. Passive microrheology studies of soft or living materials with atomic force microscopy (AFM) cantilever tips are rather rare because, in the spectral densities, the rheological response of the materials is hardly distinguishable from other sources of random or periodic perturbations. To circumvent this difficulty, we propose here a wavelet-based decomposition of AFM cantilever tip fluctuations and we show that when applying this multi-scale method to soft polymer layers and to living myoblasts, the structural damping exponents of these soft materials can be retrieved. Local stiffness and internal friction of soft materials (passive or active such as living cells) have lately been addressed at the nanoscale thanks to the development of pico-to nano-Newton force sensing systems and of nanome-ter resolution position detection devices. 1 Atomic force mi-croscopy (AFM) is one of these methods, where a sharply tipped flexible cantilever is indented inside a material to extract its local viscoelasticity from the shift and spreading of the cantilever spectral resonance modes. 2–4 However, these estimations are limited to rather narrow frequency bands surrounding the cantilever resonance modes or their higher harmonics. Spectral decomposition of cantilever fluctuations in contact with soft living tissues in the low frequency range has more rarely been explored. The few attempts which can be found in the literature were performed with small amplitude harmonic excitations (50 nm) of the sample position driven by a piezo-translator, in the 0.1 to 100 Hz frequency range, for a small and finite number of frequencies. 5,6 Whereas passive (driven by thermal fluctuations) microrheology has been performed for the past two decades by a variety of techniques capturing micro-probe spatial fluctuations , 7 it has not been applied yet to AFM cantilever fluctuations. The limitation of AFM-based passive rheology in the low frequency range comes from the mixing of the background vibrations of the liquid chamber with the cantilever fluctuations given by the rheological response of the material which are difficult to disentangle by standard FFT-based spectral averaging methods. In this work, we show that in quasi-stationary situations, these limitations can be circumvented using a wavelet-based spectral analysis of micro-cantilever fluctuations under passive excitation. Two experimental applications to passive polymer layers and living adherent myoblast cells are reported. Based on the generalized Stokes-Einstein relation (GSER) and associated generalizing assumptions, 8 passive microrheology of soft materials enables the extraction of the frequency-dependent complex modulus GðxÞ which is common to a large class of soft materials (foams, emulsions, slur-ries, and cells). 9–11 The observed scaling laws are explained by a characteristic structural disorder and the metastability of these materials which are embodied under the name of " soft glassy materials " or structural damping model. 12 Their complex shear modulus behaves a

Extensomètres à fibre optique Longue Base pour l'évaluation dynamique des structures

Divers traitements et études réalisés sur les réponses dynamiques, numériques et expérimentales, d'Extensomètres à fibre optique de Longue Base de mesure ont permis de dégager quelques caractéristiques de ces nouveaux capteurs. Certaines sont spécifiques à la base de mesure du capteur (filtrage modal, détection de défauts). D'autres, comme la sensibilité aux non-linéarités géométriques ou l'obtention de formes modales différentes, sont liées au type de mesure réalisée et peuvent s'appliquer à tous les extensomètres

Fluid-structure interaction and homogenization: from spatial averaging to continuous wavelet transform

Fluid-structure interaction (FSI) is classicaly modeled according a separated and local approach. It enables to take full advantage of the numerical methods specifically designed for each medium. However, it requires to take great care of the interface, and to exchange, between the algorithms, the information related to boundary conditions [1]. This treatment of the interface can quickly become too cumbersome in complex flow geometries, as in the industrial case study driving this work: an inviscid compressible flow interacting with French PWR fuel assemblies (Fig. 1a). In such specific applications, where the solid medium exhibits a discontinuous but periodic design, an homogenized and global approach is preferred [2]. Inspired by porous media [3, 4], multiphase flows, or Large Eddy Simulation (LES), it relies on a spatial averaging of the balance equations, thus allowing to remove all interfaces. However, such filtering techniques exhibit two major limitations: first, they do not deal properly with boundary conditions, due to the non-commutativity between the filtering operator and spatial derivatives, as detailed in [5, 6, 7] for LES; second, filtering implies loss of microscopic information, and thus requires a closure model to describe interactions between resolved and unresolved scales

Spiral Waves in Chaotic Systems

Spiral waves are investigated in chemical systems whose underlying spatially-homogeneous dynamics is governed by a deterministic chaotic attractor. We show how the local periodic behavior in the vicinity of a spiral defect is transformed to chaotic dynamics far from the defect. The transformation occurs by a type of period doubling as the distance from the defect increases. The change in character of the dynamics is described in terms of the phase space flow on closed curves surrounding the defect.Comment: latex file with three postscript figures to appear in Physical review Letter

A propensity criterion for networking in an array of coupled chaotic systems

We examine the mutual synchronization of a one dimensional chain of chaotic identical objects in the presence of a stimulus applied to the first site. We first describe the characteristics of the local elements, and then the process whereby a global nontrivial behaviour emerges. A propensity criterion for networking is introduced, consisting in the coexistence within the attractor of a localized chaotic region, which displays high sensitivity to external stimuli,and an island of stability, which provides a reliable coupling signal to the neighbors in the chain. Based on this criterion we compare homoclinic chaos, recently explored in lasers and conjectured to be typical of a single neuron, with Lorenz chaos.Comment: 4 pages, 3 figure

Does ohmic heating influence the flow field in thin-layer electrodeposition?

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. We measured the resulting temperature field by means of an infrared camera. The properties of the temperature field correspond closely with the development of the concentration field. In particular we find, that the thermal gradients at the electrodes act like a weak additional driving force to the convection rolls driven by concentration gradients.Comment: minor changes: correct estimation of concentration at the anode, added Journal-re

Diffusion-limited aggregation as branched growth

I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys. Rev. A {\bf 46}, 7793 (1992)]. This leads to a result for the cluster dimensionality, D \approx 1.66, which is close to numerically obtained values. In addition, the multifractal exponent \tau(3) = D in this theory, in agreement with a proposed `electrostatic' scaling law.Comment: 13 pages, one figure not included (available by request, by ordinary mail), Plain Te

Experimental investigation of the initial regime in fingering electrodeposition: dispersion relation and velocity measurements

Recently a fingering morphology, resembling the hydrodynamic Saffman-Taylor instability, was identified in the quasi-two-dimensional electrodeposition of copper. We present here measurements of the dispersion relation of the growing front. The instability is accompanied by gravity-driven convection rolls at the electrodes, which are examined using particle image velocimetry. While at the anode the theory presented by Chazalviel et al. describes the convection roll, the flow field at the cathode is more complicated because of the growing deposit. In particular, the analysis of the orientation of the velocity vectors reveals some lag of the development of the convection roll compared to the finger envelope.Comment: 11 pages, 15 figures, REVTEX 4; reference adde

Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Ultra-low density polymers, metals, and ceramic nanofoams are valued for their high strength-to-weight ratio, high surface area and insulating properties ascribed to their structural geometry. We obtain the labrynthine internal structure of a tantalum oxide nanofoam by X-ray diffractive imaging. Finite element analysis from the structure reveals mechanical properties consistent with bulk samples and with a diffusion limited cluster aggregation model, while excess mass on the nodes discounts the dangling fragments hypothesis of percolation theory.Comment: 8 pages, 5 figures, 30 reference

Multiparticle Biased DLA with surface diffusion: a comprehensive model of electrodeposition

We present a complete study of the Multiparticle Biased Diffusion-Limited Aggregation (MBDLA) model supplemented with surface difussion (SD), focusing on the relevance and effects of the latter transport mechanism. By comparing different algorithms, we show that MBDLA+SD is a very good qualitative model for electrodeposition in practically all the range of current intensities {\em provided} one introduces SD in the model in the proper fashion: We have found that the correct procedure involves simultaneous bulk diffusion and SD, introducing a time scale arising from the ratio of the rates of both processes. We discuss in detail the different morphologies obtained and compare them to the available experimental data with very satisfactory results. We also characterize the aggregates thus obtained by means of the dynamic scaling exponents of the interface height, allowing us to distinguish several regimes in the mentioned interface growth. Our asymptotic scaling exponents are again in good agreement with recent experiments. We conclude by discussing a global picture of the influence and consequences of SD in electrodeposition.Comment: 15 pages, 20 figures, accepted for publication in Physical Review