Principles of Imaging Porous Membranes

Transport within a pore can result from diffusion, migration, convection, or some combination of these mechanisms. For a relatively large ( 1 /xm ra- 

In the following discussion, we consider an ideal situation where the flux of a molecular species is localized to a single pore the membrane is otherwise impermeable to the molecule. Although this model is only an approximation of real samples, the resulting theory remains quite useful in the quantitative analysis of porous membranes, provided that the pores are not too closely spaced. The membrane separates donor and receptor solutions the donor solution contains an electroactive molecule that is transported across the membrane and detected by the SECM tip on the receptor side of the membrane (Fig. 1). 

3 Steady-state isoconcentration contours projected in the x-z plane corresponding to semi-infinite diffusion from hemispherical (solid lines) and disk-shaped (dashed lines) pore openings. Contours are plotted for Cs/2, Cs/4, and Cs/8, where CB is the concentration at the surface of the pore. The disk-shape pore drawn in the figure has a radius a the radius of the corresponding hemispherical pore opening (not shown), r0, is equal to lalrr. 

Here r and z are the radial and axial coordinates, respectively, in the two-dimensional cylindrical coordinate system. Comparison of Eqs. (1) and (3) indicates that the rate of mass transport from a disk is equivalent to that of a hemisphere with an effective radius, reff, given by 

Relationship Between Tip Current and Pore Transport Rate 

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