Diffusion within nanometric and micrometric spherical-type domains limited by nanometric ring or pore active interfaces. Part 1: conformal mapping approach

Prediction of Local pH Variations during Amperometric Monitoring of Vesicular Exocytotic Events at Chromaffin Cells

“…Furthermore, this intrinsic effect should depend on the electrode size because this parameter conditions the geometry of the discoid electrode-cell cleft, and hence, the dynamics of diffusion. [26] Note that a similar issue potentially exists also in TIRF experiments since the intravesicular pH is approximately 5.5. [25] The corresponding pH gradient relative to the buffered extracellular medium necessarily sets thermodynamic conditions which imply a release of protons in the thin discoid electrode-prism cleft.…”

Diffusion with Moving Boundary on Spherical Surfaces

“…p) but finite value to q 0 is crucial for the successful solution of the diffusion-agglomeration problem at hand, as will be discussed below. [17] Though any specific rate law of aggregation may easily be implemented by an adequate boundary condition, for simplifying the following presentation and to be consistent with the above Brownian approach we assume in the following that the particle aggregation to the growing cluster edge is thermodynamically irreversible and not controlled kinetically within the time ranges investigated. Hence, we may assume that the concentration of free particles in the 2D-solution at its boundary is zero, as shown in Equation (8):…”

Electrochemical Determination of Diffusion Anisotropy in Molecularly-Structured Materials

“…This important result suggests that any analytical result obtained in isotropic media can be explicitly employed for the special form of two-dimensional anisotropy considered here, using the geometric mean of the direction-dependent diffusion coefficients as the “average” value ; this view will be ratified for the case of potential-step chronoamperometry in subsequent subsections. Furthermore, in returning to the concept presented earlier for electrode surfaces modified with objects and immersed into isotropic media, by measuring diffusion coefficients under steady-state conditions versus planar conditions, it is possible to use differential flux calculations, based on distortions in the diffusion regime, to deduce the size and shape of species (such as nano-objects, microparticles, or microdroplets) that may be located on the electrode surface, viz. D obs = D iso (γ z γ r ) 1/2 , in which D obs is the measured diffusion coefficient at the partially blocked electrode, D iso is the true diffusion coefficient in the isotropic medium, and γ i represents the fraction of the flux in the i -director ( viz.…”

“…In other words, the quantitative deconvolution of the diffusion rates in planar and radial directions in isotropic media enables the voltammetric sizing of immobilized species. Such concepts have been exploited recently to describe quantitatively, using voltammetry, the structure of “designer interfaces” …”