# Inhomogeneous and anisotropic equilibrium state of a swollen hydrogel containing a hard core

## Information

Wiki entry by : Dongwoo Lee, AP225 Fall 2010.

Paper in this Wiki : Xuanhe Zhao, Wei Hong, Zhigang Suo, Inhomogeneous and anisotropic equilibrium state of a swollen hydrogel containing a hard core. Applied Physics Letters 92, 051904 (2008).

## Summary

The papers describes inhomogeneous and anisotropic equilibrium state of a swollen hydrogel which has a hard core by formulating a nonlinear differential equation. Fig. 1 shows the schematic diagram of the system that is considered in the paper. Since the core is assumed to be rigid and bonded to the gel, the network near the interface is expected to have low concentration of water and high stress. Fig. 2 shows the equation of state of the system and Fig. 3 shows the solutions to those equations. As expected, the water concentration goes up and stresses decreaes as R(radius of the structure) increases. One noticeable thing is that stress in circumferential direction is compressive and that in radial direction is tensile near the interface. Those values are converges to zero as R increases. Those results show that diffusion in gels should not be analyzed using Fick's law, which assumes that the diffusion flux is proportional to the concentration gradient.

## Discussion

The authors derived an equation to describe the equilibrium state of a hydrogel containing a hard core. They expected the low concentration of water and high stress near the interface and proved this phenomenon by using the equation. This general equation can be useful for various applications. For example, nowadays soft-hard combined structures are employed by bio-inspired robots and deep understanding of material properties are necessary to design them appropriately. Since the system concerned here has bone-skin like structure, the analysis can be applied to such field of study. Analysis about more complicated structure that consists of hydrogel-core system will be helpful in the future as well.