Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T19:58:58.691Z Has data issue: false hasContentIssue false

Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis

Published online by Cambridge University Press:  13 June 2011

JEFFREY L. MORAN
Affiliation:
Mechanical Engineering, Chemical Engineering, Arizona State University, Tempe, AZ 85287-6106, USA
JONATHAN D. POSNER*
Affiliation:
Mechanical Engineering, Chemical Engineering, Arizona State University, Tempe, AZ 85287-6106, USA
*
Email address for correspondence: [email protected]

Abstract

Mitchell originally proposed that an asymmetric ion flux across an organism's membrane could generate electric fields that drive locomotion. Although this locomotion mechanism was later rejected for some species of bacteria, engineered Janus particles have been realized that can swim due to ion fluxes generated by asymmetric electrochemical reactions. Here we present governing equations, scaling analyses and numerical simulations that describe the motion of bimetallic rod-shaped motors in hydrogen peroxide solutions due to reaction-induced charge auto-electrophoresis. The coupled Poisson–Nernst–Planck–Stokes equations are numerically solved using Frumkin-corrected Butler–Volmer equations to represent electrochemical reactions at the rod surface. Our simulations show strong agreement with the scaling analysis and experiments. The analysis shows that electrokinetic locomotion results from electro-osmotic fluid slip around the nanomotor surface. The electroviscous flow is driven by electrical body forces which are generated from a coupling of a reaction-induced dipolar charge density distribution and the electric field it creates. The magnitude of the electroviscous velocity increases quadratically with the surface reaction rate for an uncharged motor, and linearly when the motor supports a finite surface charge.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, J. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21, 61100.CrossRefGoogle Scholar
Anderson, J., Lowell, M. & Prieve, D. 1982 Motion of a particle generated by chemical gradients. Part 1. Non-electrolytes. J. Fluid Mech. 117, 107121.CrossRefGoogle Scholar
Babich, Y., Dukhin, S. & Tarovsky, A. 1989 The 2nd-kind electrophoresis in strong fields. Dopovidi Akademii Nauk Ukrainskoi RSR Seriya B-Geologichni Khimichni Ta Biologichni Nauki (7), 2932.Google Scholar
Balasubramanian, S., Kagan, D., Manesh, K. M., Calvo-Marzal, P., Flechsig, G. & Wang, J. 2009 Thermal modulation of nanomotor movement. Small 5 (13), 15691574.CrossRefGoogle ScholarPubMed
Baran, A., Babich, Y., Tarovsky, A. & Mishchuk, N. 1992 Superfast electrophoresis of ion-exchanger particles. Colloids Surf. 68 (3), 141151.CrossRefGoogle Scholar
Barany, S., Mishchuk, N. A. & Prieve, D. C. 1998 Superfast electrophoresis of conducting dispersed particles. J. Colloid Interface Sci. 207 (2), 240250.CrossRefGoogle Scholar
Bard, A. J. & Faulkner, L. R. 2000 Electrochemical Methods: Fundamentals and Applications, 2nd edn. Wiley.Google Scholar
Bazant, M. Z., Chu, K. T. & Bayly, B. J. 2005 Current-voltage relations for electrochemical thin films. SIAM J. Appl. Maths 65 (5), 14631484.CrossRefGoogle Scholar
Bazant, M. Z. & Squires, T. M. 2004 Induced-charge electrokinetic phenomena: Theory and microfluidic applications. Phys. Rev. Lett. 92 (6), 066101.CrossRefGoogle ScholarPubMed
Biesheuvel, P., van Soestbergen, M. & Bazant, M. 2009 Imposed currents in galvanic cells. Electrochim. Acta 54 (21), 48574871.CrossRefGoogle Scholar
Bonnefont, A., Argoul, F. & Bazant, M. 2001 Analysis of diffuse-layer effects on time-dependent interfacial kinetics. J. Electroanalyt. Chem. 500 (1–2, Sp. Iss. SI), 5261.CrossRefGoogle Scholar
Brennen, C. & Winet, H. 1977 Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9 (1), 339398.CrossRefGoogle Scholar
Burdick, J., Laocharoensuk, R., Wheat, P. M., Posner, J. D. & Wang, J. 2008 Synthetic nanomotors in microchannel networks: Directional microchip motion and controlled manipulation of cargo. J. Am. Chem. Soc. 130 (26), 81648165.CrossRefGoogle ScholarPubMed
Calvo-Marzal, P., Manesh, K. M., Kagan, D., Balasubramanian, S., Cardona, M., Flechsig, G., Posner, J. & Wang, J. 2009 Electrochemically-triggered motion of catalytic nanomotors. Chem. Commun. (30), 45094511.CrossRefGoogle Scholar
Catchmark, J. M., Subramanian, S. & Sen, A. 2005 Directed rotational motion of microscale objects using interfacial tension gradients continually generated via catalytic reactions. Small 1 (2), 202206.CrossRefGoogle ScholarPubMed
Chang, H. & Jaffé, G. 1952 Polarization in electrolytic solutions. Part I. Theory. J. Chem. Phys. 20 (7), 10711077.CrossRefGoogle Scholar
Córdova-Figueroa, U. M. & Brady, J. F. 2008 Osmotic propulsion: The osmotic motor. Phys. Rev. Lett. 100 (15), 158303.CrossRefGoogle ScholarPubMed
Delahay, P. 1965 Double Layer and Electrode Kinetics. Interscience.Google Scholar
Derjaguin, B., Dukhin, S. & Korotkova, A. 1961 Diffusiophoresis in electrolyte solutions and its role in mechanism of film formation from rubber latexes by method of ionic deposition. Kolloidn. Z. 23 (1), 53.Google Scholar
Derjaguin, B. V., Sidorenkov, G., Zubashchenkov, E. & Kiseleva, E. 1947 Kinetic phenomena in boundary films of liquids. Kolloidn. Z. 9 (5), 335348.Google Scholar
Dhopeshwarkar, R., Hlushkou, D., Nguyen, M., Tallarek, U. & Crooks, R. M. 2008 Electrokinetics in microfluidic channels containing a floating electrode. J. Am. Chem. Soc. 130 (32), 1048010481.CrossRefGoogle ScholarPubMed
Dougherty, G. M., Rose, K. A., Tok, J. B. H., Pannu, S. S., Chuang, F. Y. S., Sha, M. Y., Chakarova, G. & Penn, S. G. 2008 The zeta potential of surface-functionalized metallic nanorod particles in aqueous solution. Electrophoresis 29 (5), 11311139.CrossRefGoogle ScholarPubMed
Dukhin, S., Babich, Y. & Baran, A. 1988 Electrophoresis of the 2nd kind in a Hydrodynamic Flow. Colloid J. USSR 50 (5), 890891.Google Scholar
Dukhin, S. & Mishchuk, N. 1987 Unrestricted increase in the current through a granule of an ion-exchanger. Colloid J. USSR 49 (6), 10471049.Google Scholar
Dukhin, S. & Mishchuk, N. 1989 Disappearance of limiting current phenomenon in the case of a granule of an ion exchanger. Colloid J. USSR 51 (4), 570581.Google Scholar
Dukhin, S. & Mishchuk, N. 1990 Concentration polarization of conducting particle in strong fields. Colloid J. USSR 52 (3), 390393.Google Scholar
Dukhin, S., Mishchuk, N., Tarovsky, A. & Baran, A. 1987 The 2nd-kind Electrophoresis. Dopovidi Akademii Nauk Ukrainskoi RSR Seriya B-Geologichni Khimichni Ta Biologichni Nauki (12), 4244.Google Scholar
Duval, J. F. L. 2004 Electrokinetics of the amphifunctional metal/electrolyte solution interface in the presence of a redox couple. J. Colloid Interface Sci. 269 (1), 211223.CrossRefGoogle ScholarPubMed
Duval, J. F. L., Buffle, J. & van Leeuwen, H. P. 2006 Quasi-reversible faradaic depolarization processes in the electrokinetics of the metal/solution interface. J. Phys. Chem. B 110 (12), 60816094.CrossRefGoogle ScholarPubMed
Duval, J. F. L., Huijs, G. K., Threels, W. F., Lyklema, J. & van Leeuwen, H. P. 2003 a Faradaic depolarization in the electrokinetics of the metal-electrolyte solution interface. J. Colloid Interface Sci. 260 (1), 95106.CrossRefGoogle ScholarPubMed
Duval, J. F. L., van Leeuwen, H. P., Cecilia, J. & Galceran, J. 2003 b Rigorous analysis of reversible faradaic depolarization processes in the electrokinetics of the metal/electrolyte solution interface. J. Phys. Chem. B 107 (28), 67826800.CrossRefGoogle Scholar
Gibbs, J. G. & Zhao, Y. P. 2009 Autonomously motile catalytic nanomotors by bubble propulsion. Appl. Phys. Lett. 94 (16), 163104.CrossRefGoogle Scholar
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2005 Propulsion of a molecular machine by asymmetric distribution of reaction products. Phys. Rev. Lett. 94 (22), 220801.CrossRefGoogle ScholarPubMed
Gray, J. 1968 Animal Locomotion. Norton.Google Scholar
Green, N. G. & Jones, T. B. 2007 Numerical determination of the effective moments of non-spherical particles. J. Phys. D - Appl. Phys. 40 (1), 7885.CrossRefGoogle Scholar
Harold, F. M., Bronner, F. & Kleinzeller, C. L. S. A. 1982 Pumps and currents: A biological perspective. In Electrogenic Ion Pumps, Current Topics in Membranes and Transport, vol. 16, pp. 485516. Academic.Google Scholar
Henry, D. C. 1931 The cataphoresis of suspended particles. Part I. The equation of cataphoresis. Proc. R. Soc. Lond. Ser. A, Containing Papers of a Math. Phys. Character 133 (821), 106129.Google Scholar
Hlushkou, D., Perdue, R. K., Dhopeshwarkar, R., Crooks, R. M. & Tallarek, U. 2009 Electric field gradient focusing in microchannels with embedded bipolar electrode. Lab on a Chip 9 (13), 19031913.CrossRefGoogle ScholarPubMed
Hoburg, J. F. & Melcher, J. R. 1976 Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients. J. Fluid Mech. 73 (2), 333351.CrossRefGoogle Scholar
Hunter, R. J. 1987 Foundations of Colloid Science, 1st edn., vol. 1. Oxford University Press.Google Scholar
Hunter, R. J. 2001 Foundations of Colloid Science, 2nd edn. Oxford University Press.Google Scholar
Ismagilov, R. F., Schwartz, A., Bowden, N. & Whitesides, G. M. 2002 Autonomous movement and self-assembly. Angew. Chem. Intl Ed. 41 (4), 652654.3.0.CO;2-U>CrossRefGoogle Scholar
Jaffe, L. & Nuccitelli, R. 1974 Ultrasensitive vibrating probe for measuring steady extracellular currents. J. Cell Biol. 63 (2), 614628.CrossRefGoogle ScholarPubMed
Jones, T. B. 1995 Electromechanics of Particles. Cambridge University Press.CrossRefGoogle Scholar
Kagan, D., Calvo-Marzal, P., Balasubramanian, S., Sattayasamitsathit, S., Manesh, K. M., Flechsig, G. & Wang, J. 2009 Chemical sensing based on catalytic nanomotors: Motion-Based detection of trace silver. J. Am. Chem. Soc. 131 (34), 1208212083.CrossRefGoogle ScholarPubMed
Keller, A. A., Wang, H., Zhou, D., Lenihan, H. S., Cherr, G., Cardinale, B. J., Miller, R. & Ji, Z. 2010 Stability and aggregation of metal oxide nanoparticles in natural aqueous matrices. Environ. Sci. Technol. 44 (6), 19621967.CrossRefGoogle ScholarPubMed
Kline, T. R., Iwata, J., Lammert, P. E., Mallouk, T. E., Sen, A. & Velegol, D. 2006 Catalytically driven colloidal patterning and transport. J. Phys. Chem. B 110 (48), 2451324521.CrossRefGoogle ScholarPubMed
Kline, T. R., Paxton, W. F., Mallouk, T. E. & Sen, A. 2005 a Catalytic nanomotors: Remote-controlled autonomous movement of striped metallic nanorods. Angew. Chem. Intl Edn 44 (5), 744746.CrossRefGoogle ScholarPubMed
Kline, T. R., Paxton, W. F., Wang, Y., Velegol, D., Mallouk, T. E. & Sen, A. 2005 b Catalytic micropumps: Microscopic convective fluid flow and pattern formation. J. Am. Chem. Soc. 127 (49), 1715017151.CrossRefGoogle ScholarPubMed
Lammert, P. E., Prost, J. & Bruinsma, R. 1996 Ion drive for vesicles and cells. J. Theor. Biol. 178 (4), 387391.CrossRefGoogle Scholar
Laocharoensuk, R., Burdick, J. & Wang, J. 2008 Carbon-nanotube-induced acceleration of catalytic nanomotors. ACS Nano 2 (5), 10691075.CrossRefGoogle ScholarPubMed
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.CrossRefGoogle Scholar
Laws, D. R., Hlushkou, D., Perdue, R. K., Tallarek, U. & Crooks, R. M. 2009 Bipolar electrode focusing: Simultaneous concentration enrichment and separation in a microfluidic channel containing a bipolar electrode. Anal. Chem. 81 (21), 89238929.CrossRefGoogle Scholar
Lin, H., Storey, B. D., Oddy, M. H., Chen, C. H. & Santiago, J. G. 2004 Instability of electrokinetic microchannel flows with conductivity gradients. Phys. Fluids 16 (6), 19221935.CrossRefGoogle Scholar
Lund, E. 1947 Bioelectric Fields and Growth. University of Texas Press.CrossRefGoogle Scholar
Mano, N. & Heller, A. 2005 Bioelectrochemical propulsion. J. Am. Chem. Soc. 127 (33), 1157411575.CrossRefGoogle ScholarPubMed
Melcher, J. & Taylor, G. 1969 Electrohydrodynamics - a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1, 111146.CrossRefGoogle Scholar
Mishchuk, N. & Dukhin, S. 1990 Space-charge of a conducting particle in the over-limit current regime. Colloid J. USSR 52 (3), 427431.Google Scholar
Mishchuk, N. & Takhistov, P. 1995 Electroosmosis of the 2nd kind. Colloids Surf. A-Physicochem. Engng Aspects 95 (2–3), 119131.CrossRefGoogle Scholar
Mitchell, P. 1956 Hypothetical thermokinetic and electrokinetic mechanisms of locomotion in micro-organisms. Proc. R. Phys. Soc. Edin. 25, 3234.Google Scholar
Mitchell, P. 1972 Self-Electrophoretic locomotion in microorganisms – bacterial flagella as giant ionophores. FEBS Lett. 28 (1), 14.CrossRefGoogle ScholarPubMed
Moran, J. L., Wheat, P. M. & Posner, J. D. 2010 Locomotion of electrocatalytic nanomotors due to reaction induced charge autoelectrophoresis. Physical Rev. E 81 (6), 065302.CrossRefGoogle ScholarPubMed
Moya, A. A., Castilla, J. & Horno, J. 1995 Ionic transport in electrochemical cells including electrical Double-Layer effects. A network thermodynamics approach. J. Phys. Chem. 99 (4), 12921298.CrossRefGoogle Scholar
Murphy, W. D., Manzanares, J. A., Mafe, S. & Reiss, H. 1992 A numerical study of the equilibrium and nonequilibrium diffuse double layer in electrochemical cells. J. Phys. Chem. 96 (24), 99839991.CrossRefGoogle Scholar
Navaneetham, G. & Posner, J. D. 2009 Electrokinetic instabilities of non-dilute colloidal suspensions. J. Fluid Mech. 619, 331365.CrossRefGoogle Scholar
Nuccitelli, R. & Jaffe, L. 1976 Ionic components of current pulses generated by developing fucoid eggs. Develop. Biol. 49 (2), 518531.CrossRefGoogle ScholarPubMed
Paxton, W. F., Baker, P. T., Kline, T. R., Wang, Y., Mallouk, T. E. & Sen, A. 2006 Catalytically induced electrokinetics for motors and micropumps. J. Am. Chem. Soc. 128 (46), 1488114888.CrossRefGoogle ScholarPubMed
Paxton, W. F., Kistler, K. C., Olmeda, C. C., Sen, A., Angelo, S. K. S., Cao, Y. Y., Mallouk, T. E., Lammert, P. E. & Crespi, V. H. 2004 Catalytic nanomotors: Autonomous movement of striped nanorods. J. Am. Chem. Soc. 126 (41), 1342413431.CrossRefGoogle ScholarPubMed
Paxton, W. F., Sen, A. & Mallouk, T. E. 2005 Motility of catalytic nanoparticles through self-generated forces. Chem. - A Eur. J. 11 (22), 64626470.CrossRefGoogle ScholarPubMed
Pitta, T. & Berg, H. 1995 Self-electrophoresis is not the mechanism for motility in swimming cyanobacteria. J. Bacteriol. 177 (19), 57015703.CrossRefGoogle Scholar
Posner, J. D. & Santiago, J. G. 2006 Convective instability of electrokinetic flows in a cross-shaped microchannel. J. Fluid Mech. 555, 142.CrossRefGoogle Scholar
Prieve, D., Anderson, J., Ebel, J. & Lowell, M. 1984 Motion of a particle generated by chemical gradients. Part 2. electrolytes. J. Fluid Mech. 148, 247269.CrossRefGoogle Scholar
Prieve, D., Gerhart, H. & Smith, R. 1978 Chemiphoresis – method for deposition of polymer coatings without applied electric current. Ind. Engng Chem. Product Res. Develop. 17 (1), 3236.CrossRefGoogle Scholar
Purcell, E. M. 1977 Life at low Reynolds number. Am. J. Phys. 45 (1), 311.CrossRefGoogle Scholar
Rica, R. A. & Bazant, M. Z. 2010 Electrodiffusiophoresis: Particle motion in electrolytes under direct current. Phys. Fluids 22 (11), 112109.CrossRefGoogle Scholar
Rose, K. A., Meier, J. A., Dougherty, G. M. & Santiago, J. G. 2007 Rotational electrophoresis of striped metallic microrods. Phys. Rev. E 75 (1), 011503.CrossRefGoogle ScholarPubMed
Saintillan, D., Darve, E. & Shaqfeh, E. S. G. 2006 a Hydrodynamic interactions in the Induced-Charge electrophoresis of colloidal rod dispersions. J. Fluid Mech. 563 (1), 223259.CrossRefGoogle Scholar
Saintillan, D., Shaqfeh, E. S. G. & Darve, E. 2006 b Stabilization of a suspension of sedimenting rods by induced-charge electrophoresis. Phys. Fluids 18 (12), 121701.CrossRefGoogle Scholar
Schenk, O. & Gärtner, K. 2004 Solving unsymmetric sparse systems of linear equations with PARDISO. Future Generation Comput. Syst. 20 (3), 475487.CrossRefGoogle Scholar
Schenk, O. & Gärtner, K. 2006 On fast factorization pivoting methods for sparse symmetric indefinite systems. Electron. Trans. Numer. Anal. 23, 158179.Google Scholar
Shaw, D. 1970 Introduction to Colloid and Surface Chemistry, 2nd edn. Butterworth-Heinemann.Google Scholar
van Soestbergen, M., Biesheuvel, P. M. & Bazant, M. Z. 2010 Diffuse-charge effects on the transient response of electrochemical cells. Phys. Rev. E 81 (2, Part 1), 021503.CrossRefGoogle ScholarPubMed
Spek, J. 1930 Zustandsnderungen der plasmakolloide bei befruchtung und entwicklung des Nereis-Eies. Protoplasma 9 (1), 370427.CrossRefGoogle Scholar
Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217252.CrossRefGoogle Scholar
Squires, T. M. & Bazant, M. Z. 2006 Breaking symmetries in induced-charge electro-osmosis and electrophoresis. J. Fluid Mech. 560, 65101.CrossRefGoogle Scholar
Sundararajan, S., Lammert, P. E., Zudans, A. W., Crespi, V. H. & Sen, A. 2008 Catalytic motors for transport of colloidal cargo. Nano Lett. 8 (5), 12711276.CrossRefGoogle ScholarPubMed
Wang, Y., Hernandez, R. M., Bartlett, J., Bingham, J. M., Kline, T. R., Sen, A. & Mallouk, T. E. 2006 Bipolar electrochemical mechanism for the propulsion of catalytic nanomotors in hydrogen peroxide solutions. Langmuir 22 (25), 1045110456.CrossRefGoogle ScholarPubMed
Waterbury, J., Willey, J., Franks, D., Valois, F. & Watson, S. 1985 A cyanobacterium capable of swimming motility. Science 230 (4721), 7476.CrossRefGoogle ScholarPubMed
Went, F. W. 1932 Jahrb. Wiss. Botanik 76 (4), 528557.Google Scholar
Yates, G. 1986 How microorganisms move through water. Am. Sci. 74 (4), 358365.Google Scholar
Zhang, Y., Chen, Y., Westerhoff, P., Hristovski, K. & Crittenden, J. C. 2008 Stability of commercial metal oxide nanoparticles in water. Water Res. 42 (8–9), 22042212.CrossRefGoogle ScholarPubMed