Oscillations, Waves, and Interactions - GWDG

454 S. Lakämper and C. F. Schmidt
Figure 16. Loss modulus (right axes) and elastic modulus (left axes) for four surfactant
concentrations 0.5 (A), 1 (B), 2 (C), and (D) 4 wt % are plotted as a function of frequency.
Curves are in (A) and (C): macrorheology (circles), 1PMR (black lines), and 2PMR (gray
lines) in 0.5 and 2 wt %; in (B) and (D): 1PMR with 20 kHz sampling rate (gray line) and
1PMR with 195 kHz sampling rate (black lines). All microrheology data were logarithmically
binned with the factor of 1.2 relating the widths of successive bins. (from Ref. [21]).
To characterize the new microrheology methods we have been developing in their
performance on polymer samples we performed a rigorous comparison between established
conventional rheology and microrheology on a stable, well known system
namely entangled solutions of wormlike micelles which behave like a simple
Maxwell fluid at low frequencies. To generate enough of an overlap in bandwidth
between macro- and microrheology we used a specialized design based on piezoelectric
actuators for the macrorheology. Wormlike micelles are cylindrical assemblies
of amphiphilic molecules that form spontaneously in aqueous solutions at particular
concentrations and temperature conditions. We have used cetylpyridinium chloride
(CPyCl) as the surfactant and sodium salicylate (NaSal) as a strongly binding counterion.
The wormlike micelles formed in this system have a diameter of 2 to 3 nm,
contour lengths of 100 nm to 1 µm, and a persistence length of order 10 nm. At the
concentrations we used, the mesh size varied from about 0 to 10 nm [20,21].
We have compared one-particle and two-particle microrheology with macrorheology.
With all three techniques we have obtained frequency dependent complex shear
moduli over large and overlapping frequency ranges (Fig. 16). Excellent agreement