A Case for Fractal Electrodes in Electrochemical Applications

Abstract

Fractal electrode designs are proposed for electrochemical devices. A zeroth-order approximation fractal model is analyzed and basic insights into the scaling laws of the electrical properties and the surface-to-area ratio are derived. Fractal electrodes can minimize internal resistance while maximizing surface-to-volume ratios. Recent carbon microelectromechanical systems ͑C- where V is the variable in question, a is a constant, and b is the scaling exponent. The fascinating empirical observation that has perplexed many scientists and has been a source of much debate has been the fact that the exponents ͑b in Eq. 1͒ of many variables, including cellular metabolism ͑b = −1/4͒, heartbeat ͑b = −1/4͒, maximal population growth ͑b = −1/4͒, life-span ͑b = 1/4͒, blood circulation ͑b = 1/4͒, embryonic growth/development ͑b = 1/4͒, metabolic rates of entire organisms ͑b = 3/4͒, cross-sectional areas of mammalian aortas ͑b = 3/4͒, and cross-sectional areas of tree trunks ͑b = 3/4͒ are multiples of 1/4

MOF-derived multifractal porous carbon with ultrahigh lithium-ion storage performance

“…According to the theory of electrochemical reaction on fractal surface, surface or interface with higher surface fractal dimension can provide larger electrochemical active surface area and smaller internal resistance3940. The VFPC with a higher surface fractal dimension exhibits a better electrochemical performance due to the enhanced surface storage mode that has been proved by the transition zone analysis using SAXS method.…”

Fractal Electrochemical Microsupercapacitors

“…Due to this edging mechanism, IDE electrode designs show better capacitance performance compared to parallel plate capacitors due to increased lateral electrical flux. [30] A comparison of the electroactive surface area, volume, and perimeter to area ratio for different designs is shown in Figure S7 (Supporting Information). However, in the case of fractal designs, the lateral electrical flux due to the edging effects can be enhanced as compared to IDE www.advelectronicmat.de designs.…”

Synthesis of carbon xerogel particles and fractal-like structures

“…The present study reports for the first time the synthesis of highly folded, fractal-like, high external surface area carbon structures through sol-gel polycondensation. In many electrochemical energy conversion devices, such as batteries, fuel cells as well as sensors, where large surface area is advantageous, Park et al (2007) have shown that the fractal networks can prove to be a more favorable architecture. We are currently exploring the possible ways to integrate these RF gel-based fractal-like structures with three-dimensional high aspect ratio, carbon micro electrode arrays.…”

“…The patterned as well as non-patterned carbon electrodes in different forms (graphitic/non-graphitic) are used extensively in rechargeable batteries and fuel cells (Hasegawa et al, 2004;Park et al, 2007;Pekala et al, 1994Pekala et al, , 1998Wang et al, 2006). There are many other potential applications of engineered carbon structures yet to be fully explored.…”