**Determination of the Viscosity**

We now have all parameters needed to extract the viscosity *η* from the measured correlation functions of the samples S1 to S5. This analysis can be done using the *DWS RheoLab* software, where the correlation functions are loaded and the parameters *n _{solv}*,

*l** and tracer particle size are edited. In the "Analysis" tab in the user interface the frequency dependent storage and loss moduli can be calculated and extracted. The viscosity

*η*is related to the loss modulus

*G’'*via:

\( \eta =G^{''}(\omega )/\omega , \)

(2)

where *ω* is the frequency. Figure 2 shows the obtained viscosity *η* using Equation 2 and *G" *given by the *DWS RheoLab* software. The results show basically no frequency dependency as expected for a Newtonian system. Moreover, the results demonstrate that the accessible frequency range depends on the viscosity. This range is shifted to higher frequencies for lower viscosities, and can be tuned to some extent by modifying *L *and/or* l**.

**Figure 2. **The measured viscosity η of the samples S1 to S5. The values are independent of the frequency as expected for a Newtonian system.

From these results we calculate the mean values for *η* over the frequency range (see Table 1). Figure 3 shows the obtained viscosities of S1 to S5 (circles) and compares with tabulated values (line) for the viscosity of glycerol-water mixtures. Error bars represent the standard deviation of 6 independent measurements and an estimated error in glycerol concentration of 1 wt%. The measured values are on the order of 10 % larger than the tabulated values (except S1 and S5, which are 20 % larger).

The constant shift towards higher values suggests a deviation of the glycerol concentration of the samples (e.g. due to erroneous glycerol concentration of the stock solution or evaporation). The experimental data is consistent with an error of about 3 wt% in the glycerol concentration.

**Figure 3. ***Viscosity versus the glycerol concentration. The experimental values (circles) *

*correspond to S1 to S5 and the line represents tabulated values [5].*

**Conclusion**

We applied DWS to initially transparent glycerol-water-mixtures. Tracer particles were added to ensure sufficient turbidity. This allowed us to access viscosities over a wide range (1:200) depending on the glycerol content of the sample. The measured values are highly reproducible and independent of the frequency as expected for a Newtonian system and agree well with the literature. This demonstrates that DWS microrheology is well suited for the quantitative characte-rization of non-turbid systems if tracer particles are added.

**References**

^{[1] D.A. Weitz, and D.J. Pine, Diffusing-Wave Spectroscopy. In Dynamic Light Scattering; Brown, W., Ed.; Oxford }

^{ University Press: New York, 652-720 (1993).}

^{[2] D. Lopez-Diaz, and R. Castillo, Microrheology of solutions embedded with thread-like supramolecular structures, }

^{ Soft Matter 7, 5926–5937 (2011).}

^{[3] W. M. Haynes, Handbook of Chemistry and Physics, 81st Edition, CRC press (2004).}

^{[4] Mie-theory based scattering calculator for suspension of spherical particles, }

^{ http://www.lsinstruments.ch/mie_calculator/}

^{[5] N.E. Dorsey, The Properties of Ordinary Water Substance, New York (1940).}