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A review of anomalous diffusion phenomena at fractal interface for diffusion-controlled and non-diffusion-controlled transfer processes

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Abstract

This article reviewed anomalous diffusion phenomena coupled with facile and sluggish charge-transfer reactions at fractal interface. Firstly, the generalised diffusion equation (GDE) involving a fractional derivative which describes diffusion towards and from fractal interface was briefly introduced. And then, anomalous diffusion coupled with facile charge-transfer reaction at fractal interface, i.e., diffusion-controlled transfer process across fractal interface, was mathematically examined by the generalised Cottrell, Sand, Randles-Sevcik and Warburg equations theoretically derived from the analytical solutions to the GDE under the semi-infinite boundary condition. Finally, in order to provide a guideline in analysing anomalous diffusion coupled with sluggish charge-transfer reaction at fractal interface, i.e., non-diffusion-controlled transfer process across fractal interface, this review covered the recent researches into the effect of surface roughness on non-diffusion-controlled transfer process within the intercalation electrodes.

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Abbreviations

BC:

Boundary condition

CPE:

Constant phase element

CTRW:

Continuous time random walk

EIS:

Electrochemical impedance spectroscopy

FDE:

Fractional diffusion equation

GDE:

Generalised diffusion equation

IC:

Initial condition

LSV:

Linear sweep voltammogram

MC:

Monte Carlo

MCS:

Monte Carlo step

MH x :

Metal hydride

MSD:

Mean squared displacement

Ox:

Oxidised species

PCT:

Potentiostatic current transient

Red:

Reduced species

TEISI:

Transfert d’Energie sur Interface à Similitude Interne

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Acknowledgements

This research was supported by a grant from the Center for Advanced Materials Processing (CAMP) of the 21st Century Frontier R&D Program funded by the Ministry of Commerce, Industry and Energy (MOCIE), Republic of Korea. Furthermore, this work was partly supported by the Brain Korea 21 project.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dongYuseong-gu, Daejeon, 305-701, Republic of Korea

    Joo-Young Go & Su-Il Pyun

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  1. Joo-Young Go
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  2. Su-Il Pyun
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Correspondence to Su-Il Pyun.

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Go, JY., Pyun, SI. A review of anomalous diffusion phenomena at fractal interface for diffusion-controlled and non-diffusion-controlled transfer processes. J Solid State Electrochem 11, 323–334 (2007). https://doi.org/10.1007/s10008-005-0084-9

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