Ridge energy for thin nematic polymer networks.

Area of Science:

• Materials Science
• Solid Mechanics
• Polymer Physics

Background:

• Mainstream theory minimizes elastic free energy in thin nematic polymer networks via smooth isometric immersions.
• This approach overlooks deformations leading to sharp ridges on immersed surfaces.

Purpose of the Study:

• To broaden the scope of admissible spontaneous deformations in nematic polymer networks.
• To introduce and model the energy associated with ridged isometric immersions.
• To investigate the spontaneous deformation of a disk with a radial hedgehog pattern.

Main Methods:

• Developing a model to calculate the energy contribution from ridges, considering bending effects.
• Analyzing how this ridge energy scales with the sheet's thickness (quadratically).
• Testing the model by examining the spontaneous deformation of a crosslinked polymer disk with a radial defect.

Main Results:

• A new class of deformations, ridged isometric immersions, is considered.
• The energy associated with ridges scales quadratically with thickness, falling between stretching and bending energies.
• The number of folds in a deformed disk is predicted based on the degree of material order.

Conclusions:

• The proposed model accounts for ridge energy in nematic polymer networks.
• This framework enhances the understanding of spontaneous deformations beyond smooth surfaces.
• The study provides a predictive tool for fold formation influenced by external factors like heat and light.