Adenosine triphosphate diffusion through poly(ethylene glycol) diacrylate hydrogels can be tuned by cross-link density as measured by PFG-NMR

The diffusion of small molecules through hydrogels is of great importance for many applications. Especially in biological contexts, the diffusion of nutrients through hydrogel networks defines whether cells can survive inside the hydrogel or not. In this contribution, hydrogels based on poly(ethylene glycol) diacrylate with mesh sizes ranging from xi = 1.1 to 12.9 nm are prepared using polymers with number-average molecular weights between M-n = 700 and 8000 g/mol. Precise measurements of diffusion coefficients D of adenosine triphosphate (ATP), an important energy carrier in biological systems, in these hydrogels are performed by pulsed field gradient nuclear magnetic resonance. Depending on the mesh size, xi, and on the polymer volume fraction of the hydrogel after swelling, phi, it is possible to tune the relative ATP diffusion coefficient D/D-0 in the hydrogels to values between 0.14 and 0.77 compared to the ATP diffusion coefficient D-0 in water. The diffusion coefficients of ATP in these hydrogels are compared with predictions of various mathematical expressions developed under different model assumptions. The experimental data are found to be in good agreement with the predictions of a modified obstruction model or the free volume theory in combination with the sieving behavior of the polymer chains. No reasonable agreement was found with the pure hydrodynamic model.