Optical detection of nanometric thermal fluctuations to measure the stiffness of rigid superparamagnetic microrods

The rigidity of numerous biological filaments and crafted microrods has been conveniently deduced from the analysis of their thermal fluctuations. However, the difficulty of measuring nanometric displacements with an optical microscope has so far limited such studies to sufficiently flexible rods, of which the persistence length ([Formula: see text]) rarely exceeds 1 m at room temperature. Here, we demonstrate the possibility to probe 10-fold stiffer rods by a combination of superresolutive optical methods and a statistical analysis of the data based on a recent theoretical model that predicts the amplitude of the fluctuations at any location of the rod [Benetatos P, Frey E (2003) Phys Rev E Stat Nonlin Soft Matter Phys 67(5):051108]. Using this approach, we report measures of [Formula: see text] up to 0.5 km. We obtained these measurements on recently designed superparamagnetic [Formula: see text]40-[Formula: see text]m-long microrods containing iron-oxide nanoparticles connected by a polymer mesh. Using their magnetic properties, we provide an alternative proof of validity of these thermal measurements: For each individual studied rod, we performed a second measure of its rigidity by deflecting it with a uniform magnetic field. The agreement between the thermal and the magnetoelastic measures was realized with more than a decade of values of [Formula: see text] from 5.1 m to 129 m, corresponding to a bending modulus ranging from 2.2 to 54 (×[Formula: see text] Jm). Despite the apparent homogeneity of the analyzed microrods, their Young modulus follows a broad distribution from 1.9 MPa to 59 MPa and up to 200 MPa, depending on the size of the nanoparticles.