A schematic diagram of the two pole piece magnetic bead microrheometer. Coil currents were controlled using an analog to digital card in the PC. Digital images were captured with a frame grabber card. The position of the bead between the pole pieces could be adjusted using two micrometer screw gauges attached to an aluminum sample holder.
(a) The two components of the displacement of a single superparamagnetic particle immersed in a 90% glycerol/water mixture at . The output signal applied to the pole piece coils is a sinusoidal wave with amplitude of and frequency of . (b) Comparison between the velocity (black) and the force (red) calculated from the component of the bead motion parallel to the coil axis, with (red) and without (black) the smoothing function. The superparamagnetic Carbox bead is suspended in a 90% wt glycerol/water mixture. The applied output signal is a sinusoidal wave with amplitude of and frequency of . (c) and (d) Calibration curves of the force versus current. The data refer to the same sample as (b) with the same output amplitude of , but at different frequency values (c) 0.008 and (d) .
(a) The dependence of the phase shift on the frequency for Carbox beads in two glycerol/water mixtures (100% and 90%) at . forces were applied to the beads. (b) and (c) The amplitude of the displacement versus frequency for different combinations of beads and glycerol/water mixtures. (b) in 80% and 90% glycerol/water mixtures ( forces) and (c) in 90% and 100% glycerol/water mixtures ( forces).
Applied magnetic force on superparamagnetic beads versus the solenoidal coil current for both the (a) 2.8 and (b) diameter Carbox beads in glycerol/water mixtures for an applied voltage frequency of at .
(a) Viscosity measurements of glycerol/water mixtures performed with both the 2.8 and diameter Carbox beads at (2 and forces, respectively). The lines refer to previous bulk rheology measurements (Gustavo, 2003). 100%, 90%, and 80% glycerol/water mixtures were examined. Error bars on the viscosity measurements are below the 3% level and are not shown. Loss and storage moduli versus frequency for PAM solutions at (b) 0.024% w/w polymer concentration probed with magnetic beads ( applied forces). The open symbols indicate the passive PTM measurements, whereas the closed symbols indicate measurements performed with the magnetic microrheometer using the oscillatory method.
Schematic diagram of the creep compliance behavior versus time when a rectangular stress pulse is applied (green) for different materials: Newtonian fluid (red), rubber (dashed), and viscoelastic fluid (black).
Creep compliance data for a 0.2% w/w PAM solution probed with magnetic Carbox beads at ( applied forces). The red line is the best data fit of Eq. (11). The blue and the green lines are guides for the gradient. The inset shows the tracked bead displacements as a function of time used to calculated the compliance.
Loss and storage moduli versus frequency evaluated using Eqs. (8)–(11) for a PAM solution at a concentration of 0.2% w/w probed with magnetic Carbox beads at ( applied forces).
Comparison between the passive and active microrheology measurements of the loss and storage moduli versus frequency for a PAM solution at concentration of 0.07% w/w probed with magnetic Carbox beads at ( applied forces). The inset shows the good agreement of the compliance calculated using active and passive microrheology experiments.
The complex viscosity evaluated at a frequency of versus PAM concentration probed with magnetic Carbox beads at ( applied forces). The figure shows the agreement between bulk rheology and both passive and active microrheology results. The solid lines are a guide for the gradient. The entanglement concentration is indicated in addition to the predictions for semi-dilute , and entangled flexible polyelectrolytes.
(a) Elastic modulus of a peptide gel ( [Aggeli et al., 2001]) calculated from force extension measurements probed with magnetic Carbox beads at . The inset shows the elastic modulus as a function of the applied force. (b) Complex shear modulus of a fibrous actin solution prepared at probed with magnetic Carbox beads ( applied forces) at showing transverse flexural models (Gittes et al., 1997; Morse, 1998; Xu et al., 1998).
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