Self-consistent fractal geometry in polyampholyte hydrogels undergoing exchange and correlation charge-density

Polyampholyte (PA) hydrogels are incorporated of many internally charged polymer chains, which play an important role to influence the fractal networks and dynamic elasticity of the PA hydrogels owing to their different exchange and correlation charge-densities. Many properties of the PA hydrogels, such as mechanical strength and deformation, are significantly dependent on their fractal networks. However, working principles of chemo-mechanical coupling between the fractal networks and the elasticity of PA hydrogels have not been fully understood. In this study, a self-consistent fractal geometry model integrated with a complex function is proposed to understand the constitutive relationship between dynamic networks and tailorable mechanics in the PA hydrogels. The newly developed model is uniquely incorporated with the mechanochemistry, and describes the chemical polarization reactions of charged networks and their mechanical behaviors using complex fractal functions. Based on the rubber elasticity theory, constitutive stress-strain relationships of fractal networks have been described using their elastic, conformational, repulsive and polarization free-energy functions. Finally, effectiveness of the proposed model has been verified using both finite element analysis and experimental results of the PA hydrogels reported in literature.