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# Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials

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## Acknowledgements

This work was supported by NIH grants EY022359 (D.R.O.) and EY019696 (D.R.O.), a PhD studentship from the Ministry of Education, Republic of China (P.-J.W.) and the Imperial College Junior Research Fellowship (I.V.K.). We thank C. Song (Imperial College London) for help in acquiring the Brillouin measurements.

## Author information

Authors

### Contributions

P.-J.W., I.V.K., C.P., P.T., J.W.R., J.M.S., I.E.D. and D.R.O. planned the study. P.-J.W. and I.K. conducted experiments. All authors participated in and contributed to data analysis. D.R.O. and P.-J.W. wrote the manuscript. All authors contributed to editing and revision of the manuscript.

### Corresponding authors

Correspondence to Peter Török or Darryl R. Overby.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Integrated supplementary information

### Supplementary Figure 1 Polyacrylamide hydrogel swelling.

a, Hydrogel mass m increased during swelling, with larger swelling observed for lower cross-linker concentrations. b, The swelling ratio Q increased during swelling, as calculated by equation S6. Data are taken from the studies shown in Fig. 1c,d. Each data point represents an individual hydrogel made from the same stock solution. Data from four hydrogels are shown here. Curves show exponential fits.

### Supplementary Figure 2 Setup of the Brillouin microscope and associated frequency analysis.

a, Schematic of the Brillouin microscope. Laser light is directed into an inverted confocal microscope. Backscattered light is collected and filtered by an interferometer to reduce the intensity of the Rayleigh peak by up to 40 dB. The filtered signal is passes through a VIPA to separate spectral components that are detected by an sCMOS camera. b, Pixel locations in the spectrum are converted into frequency (Supplementary Methods) to identify the Brillouin frequency shift $$\omega _b$$ after the peaks are fitted by a Lorentzian function, where $$\omega _b = \left( {{\mathrm{FSR}} - \Delta f} \right)/2$$. FSR, full spectral range. $$f\left( {x_i} \right)$$ represents the frequency at pixel location $$x_i$$, as needed for equation S8. Similar results were obtained for each individual Brillouin measurement, 50 of which were acquired at each location, averaging over three locations per hydrogel.

### Supplementary Figure 3 Representative measurement of the Young’s modulus of a PEO hydrogel by rheometry.

a, The viscoelastic storage modulus (G′) as a function of oscillatory strain magnitude. b, The viscoelastic loss modulus (G″) as a function of frequency. Young’s modulus E was calculated as E=3 G′. For this sample, the molecular weight was 8 MDa with ε = 1.5%. Similar results were obtained for each of the 2–3 hydrogel samples per condition.

### Supplementary Figure 4 Representative measurement of the Young’s modulus of a PA hydrogel by uniaxial unconfined compression.

The stress-strain data were used to calculate Young’s modulus as the slope of the linear regression to a full cycle (blue line). The initial bis-acrylamide concentration of this sample was 0.06%, measured after 12 h of swelling. One similar compression measurement was done per hydrogel per time point.

## Supplementary information

### Supplementary Text and Figures

Supplementary Figures 1–4, Supplementary Methods and Supplementary Note

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Wu, PJ., Kabakova, I.V., Ruberti, J.W. et al. Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials. Nat Methods 15, 561–562 (2018). https://doi.org/10.1038/s41592-018-0076-1

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