Two-Point Microrheology of Inhomogeneous Soft Materials

Abstract

We demonstrate a novel method for measuring the microrheology of soft viscoelastic media, based on cross correlating the thermal motion of pairs of embedded tracer particles. The method does not depend on the exact nature of the coupling between the tracers and the medium, and yields accurate rheological data for highly inhomogeneous materials. We demonstrate the accuracy of this method with a guar solution, for which other microscopic methods fail due to the polymer's mesoscopic inhomogeneity. Measurements in an F-actin solution suggest conventional microrheology measurements may not reflect the true bulk behavior. PACS numbers: 87.19.Tt, 83.70.Hq, 83.80.Lz Many interesting and important materials such as polymers, gels, and biomaterials are viscoelastic; when responding to an external stress, they both store and dissipate energy. This behavior is quantified by the complex shear modulus, G ‫ء‬ ͑v͒, which provides insight into the material's microscopic dynamics. Typically, G ‫ء‬ ͑v͒ is measured by applying oscillatory strain to a sample and measuring the resulting stress. Recently a new method, called microrheology, has been developed which determines G ‫ء‬ ͑v͒ from the thermal motion of microscopic tracer particles embedded in the material [1,2]. Microrheology offers significant potential advantages: it provides a local probe of G ‫ء‬ ͑v͒ in miniscule sample volumes and can do so at very high frequencies. While microrheology provides an accurate measure of G ‫ء‬ ͑v͒ for simple systems, its validity in common complex systems is far from certain. If the tracers locally modify the structure of the medium, or sample only pores in an inhomogeneous matrix, then bulk rheological properties will not be determined. Such subtle effects currently limit many interesting applications of microrheology.In this Letter, we introduce a new formalism, which we term "two-point microrheology," based on measuring the cross-correlated thermal motion of pairs of tracer particles to determine G ‫ء‬ ͑v͒. This new technique overcomes the limitations of single-particle microrheology. It does not depend on the size or shape of the tracer particle; moreover it is independent of the coupling between the tracer and the medium. We demonstrate the validity of this approach with measurements on a highly inhomogeneous material, a solution of the polysaccharide guar. Two-point microrheology correctly reproduces results obtained with a mechanical rheometer, whereas single-particle microrheology gives erroneous results. We also compare ordinary and two-point microrheology of F-actin [2-4], a semiflexible biopolymer constituent of the cytoskeleton. Different results are obtained with the two techniques, suggesting that earlier interpretations of F-actin microrheology should be reexamined. Conventional microrheology [1,2] uses the equation:wherer 2 ͑s͒ is the Laplace transform of the tracers' mean squared displacement, ͗Dr 2 ͑t͒͘, as a function of Laplace frequency s, and a is their radius. Equation (1) (1) is subject to the same conditions as the...

Colloidal dynamics in polymer solutions: Optical two-point microrheology measurements

“…Photodetection of scattered light was used to record the trajectories of the trapped particles with high spatial and temporal resolution. This new technique differs from previous two-point microrheological studies [7] in its spatial resolution and access to high frequencies; frequencies up to 10 4 rad s −1 are readily detectable. In comparison, the frequency range of previous two-point measurements [7] have been limited by the speed of video microscopy to ω ∼ 10 2 rad s −1 .…”

“…This new technique differs from previous two-point microrheological studies [7] in its spatial resolution and access to high frequencies; frequencies up to 10 4 rad s −1 are readily detectable. In comparison, the frequency range of previous two-point measurements [7] have been limited by the speed of video microscopy to ω ∼ 10 2 rad s −1 . Faster A/D data acquisition should enable the optical tweezer technique to be extended to still higher frequencies approaching 10 7 rad s −1 .…”

“…Our approach allows access to a much faster range of timescales than previous measurements [7], as we show later. In consequence we are able to measure the rheological properties in a frequency range from typically ∼ 10 1 to 10 4 rad s −1 .…”

Active mechanical stabilization of the viscoplastic intracellular space of Dictyostelia cells by microtubule–actin crosstalk

“…Moreover, studies of the local viscoelastic moduli of the cell envelope or the cytoplasm can yield valuable insights into the structure of the membrane associated actin cortex and structural changes induced by cell stimulating or damaging agents [7,10], deceases [21] or by application of external forces [22]. A variety of colloidal probe microrheometry techniques have been developed over the last few years based on the analysis of Brownian motion [10,23,24] or of the viscoelastic responses evoked by local forces applied through optical traps [10,23] and magnetic tweezers. With magnetic tweezers, viscoelastic responses can be evoked by linear [25] or by torsional [26,27] excitations.…”

Spatially resolved microrheology of heterogeneous biopolymer hydrogels using covalently bound microspheres

“…As the length scale of heterogeneity is often comparable to the cell dimension (Raub et al 2008;Wolf et al 2009) and as cellular processes are known to be affected by their microenvironment (Collins et al 2010;Hanahan and Weinberg 2011;Tse and Engler 2011), it remains a significant challenge to examine the effects of the mechanical properties of local microenvironment on cell behavior. Particle-tracking microrheology has been used extensively to characterize the mechanical properties of individual fibers (Pampaloni et al 2006;Jahnel et al 2008), biomaterial networks (Crocker et al 2000;Valentine et al 2001;Gardel et al 2003;Dasgupta and Weitz 2005), and cells (Li et al 2009;Selvaggi et al 2010;Wu et al 2012). In "passive" particle-tracking microrheology (PTM), the thermal motion of embedded micron-or submicron-sized probe particles is analyzed to extract the viscoelastic properties of the surrounding local environment using the generalized Stokes-Einstein relation (GSER) (Levine and Lubensky 2000;Squires and Mason 2010).…”