Understanding the diffusion of small molecules in hydrogel system is of major importance in a variety of applications including drug delivery systems, tissue engineering and contact lens. Cross-linking density of hydrogels has been commonly used to tune key parameters like mesh size and molecular weight between cross-linkers, in order to change macroscopic properties of hydrogels. In this thesis, molecular dynamics investigations of chemically-cross-linked poly(ethylene glycol) (PEG) hydrogels are reported with the aim of exploring the diffusion properties of water, ions, and rhodamine within the polymer at the molecular level.The water structure and diffusion properties were studied at various cross-linking densities with molecular weights of the chains ranging from 572 to 3400. As the cross-linking density is increased, the water diffusion decreases and the slowdown in diffusion is more severe at the polymer-water interface. The water diffusion at various cross-linking densities is correlated with the water hydrogen bonding dynamics. The diffusion of ions and rhodamine also decreased as the cross-linking density is increased. The variation of diffusion coefficient with cross-linking density is related to the variation of water content at different cross-linking densities.Comparison of simulation results and obstruction scaling theory for hydrogels showed similar trends.ii To Father and Mother.iii