# Stress-relaxation behavior in gels with ionic and covalent crosslinks

Entry by Jianyu Li, AP225, Fall, 2010

## Summary

This paper reports that the stress-relaxation behavior of gels strongly depends on the type of crosslinks, whether ionic or covalent crosslinks. For gels with ionic crosslinks, the relaxation mainly involves breaking and reforming of ionic crosslinks, so the process is independent of the size of the sample. However, gels with covalent crosslinks tend to hold the covalent bonding, and migrate water through the network under stress. Obviously, migration of water is time-dependent process. Experiments were conducted to prove this statement.

## Summary of experiment

### Materials

Sodium alginate(62% guluronic acid), phosphate buffered saline(PBS), calcium sulfate, adipic acid dihydrazide(AAD), 1-ethyl-3-(dimethylaminopropyl) carbodiimide(EDC), 2-(N-morpholino)ethanesulfonic acid hydrate(MES), 1-hydroxybenzotriazole(HOBt), ethylenediamidetetraacetic acid.

### Mechanical Testing

An Instron 3342 was used to perform compression tests on the disks of hydrogels.Figure 2 is the schematic of the compression test.
Fig.2.Schematic of compression tests from:Xuanhe Zhao, Nathaniel D. Huebsch, David J. Mooney, Zhigang Suo, Stress-relaxation behavior in gels with ionic and covalent crosslinks. Journal of Applied Physics 107, 063509 (2010).

## Summary of result

• Two types of hydrogels, one crosslinked by calcium ions, the other one by AAD, exhibit distinct stress-relaxation behaviors, as illustrated by Fig. 3. The stress in gels with covalent crosslinks decreases much slowly, and finally reaches a plateau instead of zero.
Fig.3.The stress-relaxation curves of gels from:Xuanhe Zhao, Nathaniel D. Huebsch, David J. Mooney, Zhigang Suo, Stress-relaxation behavior in gels with ionic and covalent crosslinks. Journal of Applied Physics 107, 063509 (2010).
• After compression tests, the gels were stored in PBS for 24 h. Figure 4 shows the covalent gel recovered fully while the ionic gel remained plastic deformation.
Fig.4.Photographs of gels before and after deformation from:Xuanhe Zhao, Nathaniel D. Huebsch, David J. Mooney, Zhigang Suo, Stress-relaxation behavior in gels with ionic and covalent crosslinks. Journal of Applied Physics 107, 063509 (2010).
• The weight of the ionic gel didn`t change under compression, but the weight of the covalent gel decreases by 6%. Through soaking in PBS, covalent gel can recover(Fig. 5).
Fig.5.The weights of gel disks during tests from:Xuanhe Zhao, Nathaniel D. Huebsch, David J. Mooney, Zhigang Suo, Stress-relaxation behavior in gels with ionic and covalent crosslinks. Journal of Applied Physics 107, 063509 (2010).

## Summary of Disucssion

• In the covalent gel, the time scale of relaxation is dependent of the size of the sample. In Figure 6, the stress relaxes slower as the sample size increases.
Fig.6.The relaxation curves of two types of gels with different radius from:Xuanhe Zhao, Nathaniel D. Huebsch, David J. Mooney, Zhigang Suo, Stress-relaxation behavior in gels with ionic and covalent crosslinks. Journal of Applied Physics 107, 063509 (2010).
By contrast, the ionic gels of different size exhibit an identical stress-relaxation curve.
• The covalent gel relaxes by migration of water, following the function:$\sigma=f(\frac{\sqrt{t}}{R})$, where $\sigma$ is the stress, $t$ is the time, $R$ is the radius of the disk. Using this function, Figure 7 plot $\sigma$ as a function of $\frac{\sqrt{t}}{R}$
Fig.7.The effect of the radius R of the disk from:Xuanhe Zhao, Nathaniel D. Huebsch, David J. Mooney, Zhigang Suo, Stress-relaxation behavior in gels with ionic and covalent crosslinks. Journal of Applied Physics 107, 063509 (2010).
, showing the curves collapse into a single curve. The coefficient of diffusion, $D$ is estimated from the curves.
• The ionic gel reforms the ionic crosslinks through migration of calcium ions over a distance about the size of molecular chains. This process takes time $\tau$, the characteristic time. A characteristic length is defined as: $\lambda=\sqrt{D*\tau}$, its scale is much smaller than $R$.It comes to the conclusion the dominant deformation here is the reformation of ionic crosslinks.