A Microscale Statistics-Based Model to Characterize the Macroscopic Mechanical Properties of Polyacrylamide Hydrogel

Hydrogels are excellent soft materials that demonstrated great potential in applications ranging from biocompatible sensors to soft robots due to many excellent properties. And such macroscopic properties are commonly emerged from the statistical configurations of hydrogels at microscopic scale. Traditional hydrogel constitutive models rely on the ideal uniform polymer network assumption, ignoring the randomness of real microstructures and causing obvious deviations between theoretical predictions and experimental results. This work develops a novel statistical constitutive model for polyacrylamide hydrogels by combining thermodynamic derivation and molecular dynamics simulations. Molecular scale investigations reveal a log-normal probability density distribution function of polymer chain length, which is introduced to the hydrogel free energy density by a global integral. This model realizes quantitative characterization of microstructure effects on macroscopic mechanical behaviors. Model predictions of Young’s modulus, stretchability and swelling behavior are well verified by experimental tests. The results reveal that chain length statistics dominantly determine hydrogel mechanical performances, i.e., the randomness in chain length increases the modulus while decreases the stretchability when compared with ideal uniform networks. This work may provide a reliable theoretical support for hydrogel performance prediction and formula optimization.