Experimental Studies of Diffusion on Fractal Surfaces

Abstract

Composites are formed by sorption of Nafion, an ion exchange polymer, onto inert substrates of two different microstructures: microcylinders (neutron track etched membranes) and microspheres. Flux of a neutral redox probe (hydroquinone) through the composites is measured voltammetrically. Data for the microsphere composites are presented for variation in volume fraction and bead radii. Flux is shown to increase as the ratio of surface area of the substrate to volume of Nafion increases. The enhancement is ascribed to a facile surface diffusion domain at the interface between the Nafion and the inert substrates. Enhancements are larger in the microcylinder composites. Images of the microsphere composites appear fractal. For the microsphere composites, the power law relating flux to a characteristic dimension (microsphere radius) has an exponent of 0.78. A similar analysis for the cylinders has an exponent of 1. The analysis also shows that the fundamental transport rates of surface and bulk diffusion are little different in the two composites. Thus, the difference in the flux characteristics of the two classes of composites is ascribed to the microstructure of the interface as opposed to a change in the basic flux properties. (A linear fit of the microsphere composite data is statistically comparable that of the fractal fit; however, the conductivity exponent of one for the linear fit does not capture the dimensionality of the microsphere/Nafion interface.) The smallest microspheres of radius 0.055 μm form agglomerates of radius 1.25 to 1.5 μm, while their flux characteristics are consistent with an effective radius of 0.24 μm.

Excited‐State Reversible Geminate A*+B↔C*+D Reaction in Two Dimensions

“…When geminate pairs are initially produced in the system, the reversibility makes it possible that some geminate pairs are produced as an A* + B state and others are C* + D. For this mixed initial state, which is often encountered experimentally, the generalization helps us to obtain the corresponding results straightforwardly. For instance, when the initial pair is separated by r 0 1 with the probability of S 1 ð0Þ and by r 0 2 with S 2 ð0Þ, in which S 1 ð0Þ þ S 2 ð0Þ ¼ 1, the probability density function for the mixed initial state can be given by Equations (11)-(13) by inserting Equation (A10) (see Appendix A) into Equation (8).…”

“…Substantial effort in the chemical and biological sciences has been devoted to investigating the diffusion on a two-dimensional system such as nanostructured metal surfaces and lipid membrane surfaces. [1][2][3][4][5][6][7][8][9] Numerous experimental results necessitate quantitative theoretical explanations; however, rigorous theoretical approaches for diffusion-reaction systems are rare since two dimensions (2D) are more difficult to tackle mathematically than one dimension (1D) and three dimensions (3D).…”

Film Permeation by Rotating Disk Voltammetry at Electrodes Modified with Electrochemically Inert Layers and Heterogeneous Composites

“…If permeabilities are determined as a function of the composition and dimensions of the microstructural components, additional information about mass transport associated with the microstructures can be extracted. 43,44 When δ 0 is comparable to the scale of the microstructural characteristic lengths, these analyses will likely fail. Under these conditions, scanning electrochemical microscopy (SECM), first introduced by Bard and coworkers, 45 may be appropriate as SECM exploits interrogation of the boundary layers established about micro-to nanostructures.…”

Characterizing Flux through Micro- and Nanostructured Composites

“…Example 1. Nano- and microscopic composites have been formed by sorbing ion exchange polymers into impermeable substrates with regular geometries. − Hollow cylindrical pores in films of alumina and polycarbonate provide a readily parametrizable geometry.…”

“…Example 1. Composite films were formed by cocasting Nafion and polymerized polystyrene microspheres ,, with diameters of 0.11−1.1 μm. Scanning electron micrographs taken at a magnification which was a fixed multiple of the microsphere radius were visually self-similar.…”