Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations

Abstract

We have developed a new technique to measure viscoelasticity in soft materials such as polymer solutions, by monitoring thermal fluctuations of embedded probe particles using laser interferometry in a microscope. Interferometry allows us to obtain power spectra of fluctuating beads from 0.1 Hz to 20 kHz, and with subnanometer spatial resolution. Using linear response theory, we determined the frequency-dependent loss and storage shear moduli up to frequencies on the order of a kHz. Our technique measures local values of the viscoelastic response, without actively straining the system, and is especially suited to soft biopolymer networks. We studied semiflexible F-actin solutions and, as a control, flexible polyacrylamide (PAAm) gels, the latter close to their gelation threshold. With small particles, we could probe the transition from macroscopic viscoelasticity to more complex microscopic dynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G ′ = 0.11±0.03 Pa and 0.17±0.07 Pa for 1 and 2 mg/ml actin solutions, close to the onset of the elastic plateau, and scaling behavior consistent with G * (ω) ∼ ω 3/4 at higher frequencies. For polyacrylamide we measured plateau moduli of 2.0, 24, 100 and 280 Pa for crosslinked gels of 2, 2.5, 3 and 5% concentration (weight/volume) respectively, in agreement to within a factor of two with values obtained from conventional rheology. We also found evidence for scaling of G * (ω) ∼ ω 1/2 , consistent with the predictions of the Rouse model for flexible polymers.

Broad Bandwidth Optical and Mechanical Rheometry of Wormlike Micelle Solutions

“…Qr, 82.70.ÿy, 83.60.Bc, 83.85.Ei Significant progress has been made over the past decade in developing optical microrheology as a noninvasive means to study the rheological properties of soft complex fluids. Following the seminal Letter of Mason and Weitz in 1995 [1], several hundred studies have reported on the application of optical microrheology to such diverse systems as polymers, emulsions, gels, biomaterials, hydrogel scaffolds, stomach mucus, magnetic fluids, ceramics, slurries, and many more [1][2][3][4][5]. The underlying idea is to study the response of small (colloidal) particles embedded in the system under study.…”

Faxén's theorem for nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow

“…[29]. In the Newtonian limit for which (20) applies, one recovers from Eq. (21) the result given by Mazur and Bedeaux in Ref.…”

“…In these experiments, the video tracking of the position of a diffusing Brownian particle is used in order to infer the viscoelastic properties of the media. Many new techniques have appeared for the study of such fluids involving embedded colloidal particles, such as one-particle [18][19][20][21], two-particle [22][23][24], and many-particle microrheology [25,26] as well as optical tweezers [27,28]. The extraction of the viscoelastic properties from the diffusion of the particles is done through a generalized Stokes-Einstein relation (GSER), which is a heuristic approximate expression relating the particle mean square displacement with the complex modulus of the suspending fluid.…”

A Dual Optical Tweezer for Microrheology of Bacterial Suspensions

“…For each set of data, PSD is calculated. 7,8 Figure 2 shows the PSD values of the trapped particles embedded in (a) Bacillus subtilis-active cells suspension and (b) Pseudomonas°uorescens-active cells suspension at di®erent cell counts. The data shown in this plot for both samples are a normalized average of 25 data sets collected at the same temperature and the same environment.…”