Analysis of the mesh size in a supramolecular hydrogel by PFG-NMR spectroscopy

Abstract

Pulsed field gradient NMR (PFG-NMR) spectroscopy has been used to determine the network mesh size in stable hydrogels formed upon addition of Ca²⁺ to solutions of naphthalene diphenylalanine (2FF). At pH 12, the solutions at 0.55 wt% 2FF comprise worm-like micelles. Addition of Ca²⁺ results in cross-linking of these micelles. The self-diffusion of dextran guests of nominal 6, 40, 70, 100, 500, 670, 1400 and 2000 kDa, possessing hydrodynamic diameters (2R_h) similar to the expected pore sizes in these systems, was studied both in the precursor micellar solutions and in the hydrogels. The diffusivity of probes with 2R_h < 40 nm is restricted to a similar extent in both types of network with diffusion coefficients scaling as ∼M_r^−0.5, where M_r is the nominal mass of the probe, consistent with relatively unrestricted diffusion. Diffusion coefficients fit well the equation D_n/D_o = exp(−R_h/ξ), where D_n and D_o are the diffusion coefficients in the presence and absence of network respectively and ξ is the mesh size, giving a mesh size of approximately 40 nm. The heaviest ca. 10% of the nominal 2000 kDa dextran fraction having approximate mass and hydrodynamic diameter 3300 kDa and 84 nm respectively was almost immobilised by the gel, consistent with this estimate of the mesh size. The restriction was much weaker in the micellar solution, which is attributed to the transient nature of this micellar network in the absence of Ca²⁺. Finally, the mesh size for micellar solutions prepared at 1.1 wt% 2FF is smaller than that of micellar solutions prepared at lower concentrations of 2FF. However, the corresponding gels have a larger mesh size than those prepared at lower concentrations of 2FF. We attribute this to increased fibre aggregation at the higher 2FF concentration. This correlates with lower rheological moduli at higher 2FF concentrations.