Cavitation rheology

Cavitation rheology is a method developed by Zimberlin et al. which can be used to look at localised points within a soft sample.¹ The gentle technique has been used to measure the modulus of materials such as hydrogels,^1-3 and soft biological tissues such as bovine eye lenses.⁴

The basic principle of cavitation rheology consists of forming a bubble, using a needle to push air into the sample. The growing of the bubble gives a rise in pressure and at a certain pressure, the critical pressure (P_C), this bubble will burst (Figure 1). This P_C value can then be used to establish the elastic modulus of the material being examined (Equation 1). The elastic modulus value is then related to G’ obtained from bulk rheology.^{1, 5, 6}

**Figure 1:** Example of cavitation rheology output data for 5 mg/mL 2NapFF and 16 mg/mL GdL with needle set to 3 mm from the surface of the gel. The blue circle represents the pressure at which the bubble bursts, P_C.

**Equation 1:** Equation to relate cavitation rheology critical pressure, P_C, to modulus, E_C. γ is the surface tension of the sample solvent and r is the radius of the needle.¹

Our custom-built cavitation rheometer system (Bart Dietrich, University of Glasgow) uses a needle and syringe filled with air attached to a syringe pump to control the rate of bubble growth within samples. We also use a 3D printer and probe circuit to set the (x,y,z) needle position within a sample. The 3D printer and probe are used to stop the needle on the surface of the sample and can then be lowered manually to the desired point within the sample using the 3D printer.⁵ The setting of the needle position, especially needle depth from the sample’s surface, is important as our systems show that increasing the needle depth from the surface of a homogeneous sample increases the P_Cof the bubbles.^{5, 7}

We have validated our cavitation rheology setup using gels of two different low molecular weight gelators both of which were triggered by two different methods, using a solvent or pH switch.⁵ Based on the work of Bentz et al.,⁶ we quoted a quantitative relationship between the results from bulk and cavitation rheology. This can be used to convert between the modulus found by bulk or by cavitation rheology. Using our systems, we found our constant used to convert between the two moduli were very different to other systems quoted values. However, our systems break at lower strains than others which accounts for this difference.⁵

Unlike bulk shear rheology, which looks at a sample as a whole, cavitation rheology can look at multiple, localised points within one sample, which can be utilised when examining scaffold structures or for monitoring changes within a sample.¹ We have previously used this concept to show controlled heterogeneity and changes over time within our photoacid generator triggered hydrogels.⁷ By irradiating 2NapFF samples containing a photoacid generator from above with UV light, we form a gel initially at the surface of the sample before the bottom of the sample. Therefore, we develop a stiffness gradient within the sample with the stiffness greatest at the top of the sample. After irradiation exposure, the cavitation rheometer needle probes the sample at different depths from the surface to prove the existence of the stiffness gradient (exemplar data are shown in Figure 2).⁷ We have shown that our homogeneous samples have a linear dependency with depth.^{5, 7} However, this is not the case here. For samples exposed to six hours of UV radiation, there is no P_c dependence as the depth of the needle from the surface is increased. When samples are left undisturbed overnight, however, we see changes in stiffness with time and observe a linear trend as needle depth from the surface is increased. This shows the stiffness gradient is not permanent and over time, the gels become homogeneous.

**Figure 2:** Exemplar data showing the direction of our stiffness gradient and the position of the cavitation rheometer needle to prove the existence of this gradient.⁷ For homogeneous gels, the P_c value increases with increasing depth.^{5, 7} For this system and after six hours of UV exposure, we only see this trend when samples are left undisturbed overnight and allowed to homogenise. We do not see this trend when samples are examined straight after UV exposure, showing the existence of a stiffness gradient and controlled heterogeneity.

Compared to bulk shear rheology, this technique is relatively cost effective.¹ Another advantage is that the cavity can be created by air, a readily available resource. Using water instead of air to create a cavity may also be considered advantageous as it has negligible interfacial tension.^{2, 4} Unlike bulk rheology, which requires a significant volume of sample (millilitres), cavitation rheology can use smaller volumes.⁸ Cavitation rheology looks at the micrometre length scale which is different from bulk shear rheology. This allows us to access a different length scale than can be measured using traditional bulk rheology.⁵

Currently, there is little work present which compares the values obtained from both bulk and cavitation rheology which is a significant drawback to using the cavitation rheology technique at this time.⁶ Another disadvantage of cavitation rheology is that the setup is not readily available commercially and hence must be custom-built which involves a great deal of expertise in many areas including electronics.

To see full details of our custom-built cavitation rheology setup, see https://pubs.rsc.org/en/content/articlelanding/2019/SM/C9SM01023H.⁵ We are also able to collaborate with others who wish to use this technique on their samples – please get in touch if you wish to discuss this further.

References

1. J. A. Zimberlin, N. Sanabria-DeLong, G. N. Tew and A. J. Crosby, Soft Matter, 2007, 3, 763-767.

2. J. A. Zimberlin and A. J. Crosby, Journal of Polymer Science Part B: Polymer Physics, 2010, 48, 1423-1427.

3. S. Kundu and A. J. Crosby, Soft Matter, 2009, 5, 3963-3968.

4. J. Cui, C. H. Lee, A. Delbos, J. J. McManus and A. J. Crosby, Soft Matter, 2011, 7, 7827-7831.

5. A. M. Fuentes-Caparrós, B. Dietrich, L. Thomson, C. Chauveau and D. J. Adams, Soft Matter, 2019, 15, 6340-6347.

6. K. C. Bentz, N. Sultan and D. A. Savin, Soft Matter, 2018, 14, 8395-8400.

7. L. Thomson, R. Schweins, E. R. Draper and D. J. Adams, Macromol. Rapid Commun., 2020, 41, 2000093. 8. F. Del Giudice, M. Tassieri, C. Oelschlaeger and A. Q. Shen, Macromolecules, 2017, 50, 2951-2963.