Abstract
This work explores the nonlinear coupling between wall deformation and one-dimensional electrokinetic transport in a nanochannel with negatively charged walls. Within the framework of nonequilibrium thermodynamics, compact formulae are derived for the electrokinetic transport parameters in terms of Onsager phenomenological coefficients and, subsequently, for the energy conversion efficiency. Results confirm that Onsager’s reciprocity principle holds for rigid channels. However, the methodology used to reduce to 1D does not maintain the symmetry of Onsager’s matrix when the channel is deformed due to the introduction of a “fictitious” diffusion term of counter-ions. Furthermore, the model predicts a reduced efficiency of electrokinetic energy harvesting for channels with soft deformable walls.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Change history
12 September 2019
The original published article contains some errors which are corrected below.
12 September 2019
The original published article contains some errors which are corrected below.
References
H.L.F. Helmholtz, Wied. Ann. 7, 337 (1879)
M. Smoluchowski, Phys. Z. 6, 529 (1905)
P. Berg, K. Ladipo, Proc. R. Soc. A 465, 2663 (2009)
P. Berg, J. Findlay, Proc. R. Soc. A 467, 3157 (2011)
K.O. Ladipo, P. Berg, S. Kimmerle, A. Novruzi, Int. J. Chem. Phys. 134, 074103 (2011)
A.J. Bard, L.R. Faulkner, Electrochemical methods: fundamentals and applications, 2nd edn. (Wiley, New York, 1980)
M.Z. Bazant, K. Thornton, A. Ajdari, Phys. Rev. E 70, 021506 (2004)
S. Prakash, A.T. Conlisk, Lab Chip 16, 3855 (2016)
S. Chung, O.S. Anderson, S. Olaf, V.V. Krishnamurthy, Biological membrane ion channels: dynamics, structure, and applications (Springer Science & Business Media, 2007)
S.J. Kim, S.H. Ko, K.H. Kang, H. Kwan, J. Han, Nat. Nanotechnol. 5, 297 (2010)
M. Eikerling, A. Kulikovsky, Polymer Electrolyte Fuel Cells: Physical Principles of Materials and Operation (CRC Press, 2014)
H. Daiguji, P. Yang, A.J. Szeri, A. Majumdar, Nano Lett. 4, 2315 (2004)
L. Onsager, Phys. Rev. 37, 405 (1931)
L. Onsager, Phys. Rev. 38, 2265 (1931)
B.J. Kirby, Micro- and nanoscale fluid mechanics: transport in microfluidic devices (Cambridge University Press, 2010)
F.F. Reuss, Mem. Soc. Imp. Natur. Moscou. 2, 327 (1809)
G. Quincke, Pogg. Ann. Phys. 107, 1 (1859)
K. Kreuer, S.J. Paddison, E. Spohr, M. Schuster, Chem. Rev. 104, 4637 (2004)
M. Eikerling, A.A. Kornyshev, E. Spohr, Adv. Polym. Sci. 215, 15 (2008)
S.G. Rinaldo, C.W. Monroe, T. Romero, W. Mérida, M. Eikerling, Electrochem. Commun. 33, 5 (2011)
M. Eikerling, P. Berg, Soft Matter 7, 5976 (2011)
M. Safiollah, P.A. Melchy, P. Berg, M. Eikerling, J. Phys. Chem. B 119, 8165 (2015)
A.Z. Weber, J. Newman, Chem. Rev. 104, 4679 (2004)
M. Eikerling, A. Kulikovsky, Polymer Electrolyte Fuel Cells: Physical Principles of Materials and Operation (CRC Press, 2014)
A. Kusoglu, M.H. Santare, M.A. Karlsson, J. Polym. Sci. Part B: Polym. Phys. 49, 1506 (2011)
P.-E.A. Melchy, M.H. Eikerling, J. Phys.: Condens. Matter 27, 325103 (2015)
K. Oguro, N. Fujiwara, K. Asaka, K. Onishi, S. Sewa, Electr. Polym. Actuat. Dev. 3669, 64 (1999)
N. Fujiwara, K. Asaka, Y. Nishimura, K. Oguro, E. Torikai, Chem. Mater. 12, 1750 (1999)
A.J. Duncan, D.J. Leo, T.E. Long, Macromolecules 41, 7765 (2008)
Z. Peng, A. Morin, P. Huguet, P. Schott, J. Pauchet, J. Phys. Chem. B 115, 12835 (2011)
J.B. Benziger, M.J. Cheah, V. Klika, M. Pavelka, J. Polym. Sci. Part B: Polym. Phys. 53, 1580 (2015)
M. Matse, P. Berg, M. Eikerling, Phys. Rev. E 98, 053101 (2018)
P.B. Peters, R. van Roij, M.Z. Bazant, P.M. Biesheuvel, Phys. Rev. E 93, 053108 (2016)
F.A. Morrison Jr., J.F. Osterle, J. Chem. Phys. 43, 2111 (1965)
Y. Zhang, Y. He, M. Tsutsui, X.S. Miao, M. Taniguchi, Sci. Rep. 7, 46661 (2017)
J. Yang, F. Lu, L.W. Kostiuk, D.Y. Kwok, J. Micromech. Microeng. 13, 963 (2003)
Y. Xie, X. Wang, J. Jin, K. Chen, Y. Wang, Appl. Phys. Lett. 93, 163116 (2008)
C.C. Chang, R.J. Yang, Microfluid. Nanofluid. 9, 225 (2010)
Y. Yan, Q. Sheng, C. Wang, J. Xue, H.C. Chang, J. Phys. Chem. C 117, 8050 (2013)
C. Bakli, S. Chakraborty, Electrophoresis 36, 675 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Matse, M., Eikerling, M. & Berg, P. Electrokinetic Onsager coefficients and energy conversion in deformable nanofluidic channels. Eur. Phys. J. Spec. Top. 227, 2559–2573 (2019). https://doi.org/10.1140/epjst/e2019-800137-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2019-800137-2