Elasticity of microscale volumes of viscoelastic soft matter by cavitation rheometry

Abstract

Measurement of the elastic modulus of soft, viscoelastic liquids with cavitation rheometry is demonstrated for specimens as small as 1 ll by application of elasticity theory and experiments on semi-dilute polymer solutions. Cavitation rheometry is the extraction of the elastic modulus of a material, E, by measuring the pressure necessary to create a cavity within it [J. A. Zimberlin, N. Sanabria-DeLong, G. N. Tew, and A. J. Crosby, Soft Matter 3, 763-767 (2007)]. This paper extends cavitation rheometry in three ways. First, we show that viscoelastic samples can be approximated with the neo-Hookean model provided that the time scale of the cavity formation is measured. Second, we extend the cavitation rheometry method to accommodate cases in which the sample size is no longer large relative to the cavity dimension. Finally, we implement cavitation rheometry to show that the theory accurately measures the elastic modulus of viscoelastic samples with volumes ranging from 4 ml to as low as 1 ll. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4896108]The linear elastic modulus of a soft material is a mechanical property measurable by techniques such as mechanical rheometry, microrheology, and atomic force microscopy (AFM). 1,2 Needs for both in vivo characterization of linear elasticity (such as in tissue viability) as well as rapid measurement (such as in quality control applications) have driven recent methods development. [3][4][5] Mechanical rheometry typically requires approximately milliliter sample volumes and, if sample loading and testing durations are considered, requires as much as 5 min to test one specimen at one deformation frequency. Passive microrheology is a widely used technique to study the mechanical properties of small volumes (between $3 and 50 ll) of soft matter. One method of microrheology-which uses the multiple scattering technique of diffusing wave spectroscopy-requires as much as an hour of measurement time. This method can probe elastic moduli up to $2000 Pa. 1,6,7 Microrheology measurements can also be impacted by the stability of the dispersed probes and the heterogeneity of the material studied. 8,9 AFM can also be used to characterize the elastic modulus of very small volumes (<1 ll) of material; however, this technique requires long durations for measurements and sample preparation time. 3,10 The duration of these techniques makes them challenging for high throughput applications, while their lack of portability complicates their use as in vivo diagnostics.The cavitation rheometry technique of Zimberlin et al. characterizes the linear elastic modulus of soft matter with Young's modulus in the range of 0.12 kPa < E < 40 kPa. 11,12 It is an inexpensive, fast, and portable method that estimates the elastic modulus by measurement of the critical pressure (P c ) required for internal cavitation. Cavitation is induced by air pumped through a needle inserted into the sample. The critical pressure predicts the elastic modulus, E, through the theory of cavitation in an incompressib...

Higher-dimensional DBI solitons

“…Second, can we smooth out the singular uncharged p-branes in arbitrary dimensions? Using the generalization of chiral Born-Infeld theory [20] we found that the answer for both questions is positive.…”

“…Here we will review the theory of chiral Born-Infeld [20]. As in the Skyrme model [15] the chiral Born-Infeld theory can be conveniently formulated in terms of a chiral field U (t, x), a unitary 2 × 2 scalar matrix transforming under SU (2).…”

“…This led people to find generalizations of the Skyrme term that can generate any possible higher order terms [16][17][18][19]. One attractive proposal is the so-called chiral Born-Infeld theory [20]. In this theory, the texture appears in the Born-Infeld-type Lagrangian [21] and the higher-order terms are generated automatically via Taylor expansion for small mass-scale parameter.…”

On DBI Textures with generalized Hopf fibration

“…One way to stabilize it is by having higher order kinetic terms, as shown by Skyrme [8]. More recently scalar field theories with noncanonical kinetic terms have been extensively studied in [9,10] where it is shown that stable defects exist. In [11] we prove numerically that SO(N ) textures with Dirac-Born-Infeld (DBI) kinetic term can be stabilized in any arbitrary spatial dimensions N ≥ 3.…”

“…Without loss of generality we can set β = 1 for simplicity 3. The case for N = 3 is discussed in[10].…”