Mutual and self-diffusion of charged porphyrines in aqueous solutions

We have investigated the diffusion properties for an ionic porphyrin in water. Specifically, for the {tetrasodium tetraphenylporphyrintetrasulfonate (Na4TPPS) + water} binary system, the self-diffusion coefficients of TPPS4− and Na+, and the mutual diffusion coefficients were experimentally determined as a function of Na4TPPS concentration from (0 to 4) · 10−3 mol · dm−3 at T = 298.15 K. Absorption spectra for this system were obtained over the same concentration range. Molecular mechanics were used to compute size and shape of the TPPS4− porphyrin. We have found that, at low solute concentrations (<0.5 · 10−3 mol · dm−3), the mutual diffusion coefficient sharply decreases as the concentration increases. This can be related to both the ionic nature of the porphyrin and complex associative processes in solution. Our experimental results are discussed on the basis of the Nernst equation, Onsager–Fuoss theory and porphyrin metal ion association. In addition, self-diffusion of TPPS4− was used, together with the Stokes–Einstein equation, to determine the equivalent hydrodynamic radius of TPPS4−. By approximating this porphyrin to a disk, we have estimated structural parameters of TPPS4−. These were found to be in good agreement with those obtained using molecular mechanics. Our work shows how the self-diffusion coefficient of an ionic porphyrin in water is substantially different from the corresponding mutual-diffusion coefficient in both magnitude and concentration dependence. This aspect should be taken into account when diffusion-based transport is modelled for in vitro and in vivo applications of pharmaceutical relevance.