This study aimed to explore a test method for evaluating the effective cross-linking density of hydrogels. A guar gum–epichlorohydrin hydrogel (GEH) was prepared using guar gum (GG) as the raw material and epichlorohydrin (ECH) as the cross-linking agent. The thermal and mechanical properties, equilibrium swelling rate (ESR), water uptake (WU), and mass cross-linking degree of the hydrogels were assessed. Furthermore, the diffusion behavior of water molecules in the freeze-dried GEH was investigated. The experimental results showed the significance of the initial decomposition temperature (T_i) and final decomposition temperature (T_f) of the freeze-dried GEHs in determining the effective cross-linking density. The water uptake kinetics of the freeze-dried GEH was consistent with the linear fitting of the pseudo-second-order kinetic model and nonlinear fitting of the Fickian diffusion model, suggesting that chemisorption dominated the water absorption process in the GEH. Therefore, the effective cross-linking density of the hydrogels could be determined from the thermodynamic analysis and the diffusive behavior of water molecules in the gels. The thermal stability and water diffusion kinetics of the hydrogels were closely linked to the effective cross-linking density and pendant modification.

Pinecone-based biomass carbon (PC) is a potential anode material for potassium-ion batteries because it is abundant, cheap, renewable, and easy to obtain. However, because of inferior kinetics and the effects of volume expansion due to the large radius of the K⁺ ion, it does not meet commercial performance requirements. In this study, nitrogen-doped PC (NPC) was prepared by carbonization in molten ZnCl₂ with urea as a nitrogen source. A strategy based on synergistic effects between N doping and ZnCl₂ molten salt was used to produce a hierarchically porous pie-like NPC with abundant defects and active sites and an enlarged interlayer distance—properties that enhance K⁺ adsorption, promote K⁺ intercalation/diffusion, and reduce the effects of volume expansion. This NPC exhibited a high reversible capacity (283 mA h g⁻¹ at 50 mA g⁻¹) and superior rate performance and cyclic stability (110 mA h g⁻¹ after 1000 cycles at 5 A g⁻¹), demonstrating its potential for use in potassium-ion batteries.