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

C. Martinez-Torres (1) , A. Arneodo (2, 1) , L. Streppa (1) , P. Argoul (3) , Françoise Argoul (1, 2)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 LOMA - Laboratoire Ondes et Matière d'Aquitaine
3 IFSTTAR/MAST/SDOA - Sécurité et Durabilité des Ouvrages d'Art

Compared 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 as

Domaines: Matière Molle [cond-mat.soft]

C. Martinez-Torres, A. Arneodo, L. Streppa, P. Argoul, Françoise Argoul. Passive microrheology of soft materials with atomic force microscopy: A wavelet-based spectral analysis. Applied Physics Letters, 2016, 108 (3), pp.034102 (1-4). ⟨10.1063/1.4940220⟩. ⟨hal-01275848⟩