True microrheological measurements

This section considers true microrheological measurements in which external forces or displacements are imposed, and consequent displacements or forces are measured. True microrheological measurements, not to be confused with microrheology studies of Brownian motion, differ from classical macroscopic measurements only in that the apparatus functions on a mesoscopic length scale. It becomes interesting to compare viscoelastic parameters from classical instruments, parameters measured with true microrheological instruments built on the size scale of diffusing probes, and parameters inferred from the diffusion of those particles. 

Amblard, et al., used videomicroscopy and magnetic tweezers to study probe motion in viscoelastic F-actin systems(95). Videomicroscopy determines particle positions the tweezers apply known forces to a particle. The F-actin filaments had an estimated length of 20 p.m, persistence length c. 14 p.m, and at 0.1 g/1 a mesh size 1 p.m. With small beads (diameter d ), diffusion followed x t)) t.  

Bishop, et al. studied the driven rotational motion of 1-10 p,m birefringent vaterite (CaCOs) crystals(96). The driving force is provided by circularly polarized light. The rotation rate is obtained from the transntission of one linear polarization of the light. Within a drop of hexane and in bulk water, the measured microviscosity agreed with macroscopic values. 

Hough and Ou-Yang used optical tweezers to drive a 1.58 p,m silica microsphere through solutions of 85 kDa end-capped polyethylene oxide in water(97). Drive frequencies were as large as 40000 rad/s. Measurements of the ampUtude and phase (relative to the driving force) for sphere oscillations were inverted, treating the sphere as a forced damped harmonic oscillator, to obtain G (co) and G ( )). The dynamic moduli were. .. quite different from those obtained by a macroscopic rheometer, and are sensitive to surface treatment of the bead. 

Schmidt, et al. studied the rheological properties of solutions of fd-virus, using classical mechanical and magnetic tweezers rheometry to determine G and G (101). Macroscopic and microscopic measurements were in reasonable agreement. The observed frequency dependence of G at low frequency was much weaker than predicted by some modem theoretical calculations(102). Comparison was made with actin solutions to separate fundamental properties from single-system peculiarities. Actin aggregation is extremely sensitive to a wide variety of factors. 

---

The literature examined here includes three major experimental approaches, namely (i) optical probe diffusion studies, largely made with quasi elastic light scattering spectroscopy (QELSS), to observe diffusion of dilute probe particles, (ii) particle tracking studies in which the detailed motions of individual particles are recorded, and (iii) true microrheology measurements of the driven motion of mesoscopic probes. 

Here we examine the literature on diffusion of probes through polymer solutions. Nearly 200 probe size polymer molecular weight combinations have been examined at a range of polymer concentrations. There is a solid but not extremely extensive body of work on the temperature dependence of probe diffusion in polymer solutions. A half-dozen studies of probe rotational motion and more than a dozen reports based on particle tracking are noted, along with a half-dozen sets of true microrheological measurements, in which mesoscopic objects perform driven motion in polymer solutions. 

True microrheological studies examining the motion of mesoscopic particles under the influence of a known external force are examined. The viscosity determined with a true microrheological measurement using an instrument with micron-scale moving parts is sometimes substantially smaller than the viscosity measured with a macroscopic instrument. As a result, the observation that rjp, from some diffusion method does or does not agree with tj from a classical macroscopic rheometer does not reveal the merit of the diffusion method. 

---