Multiscale Microrheology Using Fluctuating Filaments as Stealth Probes

The mechanical properties of soft materials can be probed on small length scales by microrheology. A common approach tracks fluctuations of micrometer-sized beads embedded in the medium to be characterized. This approach yields results that depend on probe size when the medium has structure on comparable length scales. Here, we introduce filament-based microrheology using high-aspect-ratio semiflexible filaments as probes. Such quasi-1D probes are much less invasive than beads due to their small cross sections. Moreover, by imaging transverse bending modes, we simultaneously determine the micromechanical response of the medium on multiple length scales corresponding to the mode wavelengths. We use semiflexible single-walled carbon nanotubes as probes that can be accurately and rapidly imaged based on their stable near-IR fluorescence. We find that the viscoelastic properties of sucrose, polyethylene oxide, and hyaluronic acid solutions measured in this way are in good agreement with those measured by conventional micro- and macrorheology.

Figure 1

(a) A near-infrared fluorescence image of a SWNT in a $4.5\mathrm{mg}/\mathrm{ml}$ hyaluronic acid solution. (b) The first three spatial dynamic eigenmodes of an elastic beam with free ends.

Figure 2

(a) Amplitudes of modes 1 to 3 of a $5\mu \mathrm{m}$ SWNT in a $3\mathrm{mg}/\mathrm{ml}$ HA solution. (b) MSADs for the same modes (5 recordings). Inset: variance of mode amplitudes plotted vs wave number (18 recordings from five SWNTs in the same solution, lengths $4.5\sim 8.5\mu \mathrm{m}$) black (blue lines). Averages smoothed by binning (red circles). Expected dependence $⟨a_q(0{)}^2⟩=k_{B}T/\kappa q^4$ with $\kappa =1.26\times {10}^{-25}\mathrm{J}·\mathrm{m}$ [20] (black dashed line).

Figure 3

(a) Viscoelasticity of HA solutions measured from the bending dynamics of SWNTs. HA concentrations given in graphs. Upper row: 18 recordings from 5 SWNTs, lengths $4.5\sim 8.5\mu \mathrm{m}$. Middle row: 14 recordings from 8 SWNTs, lengths $4.5\sim 7.5\mu \mathrm{m}$. Bottom row: 1 SWNT, length $19\mu \mathrm{m}$. Shear elastic moduli of each HA solution were also measured by conventional bead MR (black crosses). Power-law fits of $G_{\mathrm{bead}}^{\prime \prime }$ MR are shown as solid light blue lines. (b) Viscoelasticity of a $5\mathrm{mg}/\mathrm{ml}$ 8 MDa PEO solution measured from the bending dynamics of SWNTs (20 recordings from three SWNTs averaged). (c) Global 2D fit of PSDs as a function of wave number $q$ and frequency $f(=\omega /2\pi )$ (10 recordings from three SWNTs with lengths of 9.15, 6.13, and $5.03\mu \mathrm{m}$). Three modes (1 to 3) of each SWNT are plotted. The fit with Eq. (4) is shown as light-blue mesh plane. Black solid lines represent slices of the fitted plane at $q=0.515$, 0.769, 0.858, 0.937, 1.20, 1.28, 1.56, 1.79, and $2.19\mu {\mathrm{m}}^{-1}$, which correspond to the wave numbers of three modes (1 to 3) of SWNTs with lengths of 9.15, 6.13, and $5.03\mu \mathrm{m}$, respectively.