Calculated profiles of the PNP total concentration (free PNP plus PNP in the assemblies) versus time and radial distance from the center of the reaction well. Panels (b) and (c) refer to the HPNPP initial concentration 100 uM ('Case 1' below) while panels (d) and (e) refer to 500 uM ('Case 2' below). Panels (b) and (d) show the full profile while panels (c) and (e) report the time evolution at the five sampling distances of the experiments. The profiles were obtained from a minimal reaction-diffusion model (details are provided in the Supporting Information). In all cases, the binding/unbinding rate constants were set equal to 5x10−3s−1. The dissolution rate constant were set equal to 5x10−4s−1in Case 1 and to 10−4s−1in Case 2. The diffusion coefficient of each species was set equal to 5x10−10m2s−1. The fraction of assembled surfactants (φ) was set equal to 0.3 in Case 1 and 0.5 in Case 2. The threshold concentration (CL*) was set to 34 uM in Case 1 and 24 uM in Case 2. The dimensions of the reaction well are the experimental ones (radius 1.745 cm, depth 3.1 mm) and the injected surfactants correspond to 1 uL of the 60 mM stock solution. The assemblies are assumed to initially have a bell-shaped distribution that drops to zero at the distanceR* of about 1.45 mm in both Case 1 and Case 2; the concentration of free surfactants is depleted accordingly. The rate constant of the HPNPP reaction was taken equal to 7.1x10−6s−1. The numerical solution was obtained by means of a finite-difference scheme. The irregular features of the profiles are due to the dynamical discontinuities that are present in the model (see the Supporting Information).
