Multiscale homogenisation of diffusion in enzymatically-calcified hydrogels

Area of Science:

• Materials Science
• Chemical Engineering
• Biomedical Engineering

Background:

• Hydrogels are versatile materials with tunable mechanical and diffusion properties for various applications.
• Creating tough, stiff hydrogels has been challenging, with recent advances using mineralization to create heterogeneous microstructures.
• Understanding diffusion in these complex structures is crucial for optimizing their performance.

Purpose of the Study:

• To develop and apply a homogenization method for predicting macroscopic diffusion in heterogeneous hydrogels.
• To investigate the diffusion behavior of mineralized poly-dimethyl-acrylamide (PDMA) and polyacrylamide (PAAm) hydrogels.
• To analyze the impact of porosity and microstructure on solute diffusion.

Main Methods:

• Finite element framework implementing a homogenization method.
• Application to calcified PDMA hydrogels with porous inclusions and PAAm hydrogels with spherical pores.
• Multiscale analysis to determine the relationship between diffusivity, porosity, and solute size.

Main Results:

• The unobstructed volume was identified as a primary parameter for tuning hydrogel diffusivity.
• PDMA hydrogels showed a strong, non-linear dependence of diffusivity on solute radius due to obstruction porosity.
• The developed framework accurately predicted diffusion behavior and was validated against literature data.

Conclusions:

• The homogenization method provides an effective approach to model diffusion in complex heterogeneous hydrogels.
• Microstructural features, particularly porosity, significantly influence solute transport properties.
• This framework can be extended to diverse materials for predicting diffusion in engineered soft materials.