AC electrokinetics of conducting microparticles: A review*
Summary (4 min read)
1. Introduction
- The use of AC electric fields for manipulating and characterising small particles in suspension is well-known [1, 2] and many applications have appeared over the last decades in fields such as colloidal science and biotechnology.
- The research community is also exploring the use of nanowires and nanotubes as biosensors [7], as building blocks for novel nanocircuits [8], and/or elements of dense arrays for light absorption in solar cells [9].
- Reversible assembly of patterns of metal nanowires has also been demonstrated using AC fields [14].
- Importantly, the authors show that the charging of the electrical double layer (EDL) is the interfacial polarization mechanism responsible for particle behaviour.
- 2 AC C EP TE D M AN U SC R IP T ACCEPTED MANUSCRIPT Furthermore, the inclusion of the EDL charging implies that the motion of the particles is not only generated by the electrical forces on the induced dipole (or multipoles), but electroosmotic slip velocities on the particle surface play an important role.
1.1. Polarization of a conducting particle
- When an uncharged conducting particle is suddenly exposed to an electric field, electrons in the conductor move almost instantaneously so as to make the electric field inside equal to zero; electric field lines intersect the particle surface perpendicularly (see fig. 1a).
- In the following analysis, the authors assume that the induced voltage across the double layer ∆φ ∼ Eℓ (where E is applied electric field and ℓ is typical particle size) is below the threshold voltage for these Faradaic reactions Vredox so that no direct current passes through the EDL, i.e. the electrolyte/conductor interface is perfectly polarizable.
- The typical time for charging the electrolyte/metal interface is tRC = εℓ/λDσ [22, 23], where ε and σ are, respectively, the electrical permittivity and conductivity of the electrolyte, and λD is the Debye length.
- When an AC field is applied, then for frequencies of applied signal much higher than the reciprocal of the charging time (f ≫ fRC ≡ 2π/tRC), the induced EDL charge is negligible, field lines intersect the particle surface perpendicularly, and the situation is equivalent to a conductor in a dielectric (see fig. 1a).
- In other words, the particle has a low Dukhin number [24], where the Dukhin number is given by σs/σℓ, with σs the particle surface conductivity.
1.2. Induced motion of a conducting particle
- The electrically induced motion of an uncharged conducting particle in an electrolyte arises from the interaction of the electric field with the induced dipole of the particle plus its double layer, together with the viscous stresses of the induced electrokinetic flow around the particle, a combination of effects called dipolophoresis by Shilov and co-workers [25, 26].
- Early observations of ICEO flow around a metal sphere were reported by Gamayunov et al [32].
- The experiments are quantitatively compared with the theoretical predictions of the previous section.
- Finally, the authors include a section on the assembly of particles on the surface of microelectrodes or between them, and self-assembly induced by electric fields.
2. Mathematical formulation for small voltage and thin double layer
- The authors assume that the typical induced particle velocity is small enough so that convection of charge is negligible.
- Here the authors have assumed that the signal frequency is much smaller than the charge relaxation frequency ω ≪ σ/ε in order that the diffuse layer can be considered to be in quasi-equilibrium [51].
- Experimental observations show that the slip velocity is usually smaller than the ideal case (Λ < 1) and sometimes very much smaller [53].
- The translational and rotational velocities are determined by imposing equilibrium of forces and torques.
- The authors mainly deal with particles with sufficient symmetry (orthotropic bodies) so that the coupling tensor is zero, C = 0.
3. Induced translational motion
- In electrophoresis charged particles move in a fluid due to the action of a spatially uniform electric field [63].
- In general, using AC electric fields, particles 8 AC C EP TE D M AN U SC R IP T ACCEPTED MANUSCRIPT undergo translational motion if the electric field is inhomogeneous.
- If the electric field is homogeneous, particles can move by ICEP if they are asymmetric, but only using low frequency AC fields.
- For high-frequency fields (ω ≫ ωRC) the translational motion is only due to the force on the dipole, (p · ∇)E, and this force is zero in homogeneous fields.
3.1. Uniform field
- At low frequencies, including DC, the induced flow around an asymmetric particle can produce particle motion [42].
- Breaking the geometric symmetry of the ICEO flow around a conducting object generally leads to net pumping of fluid past the object, which for a suspended microparticle leads to translation.
- This idea was experimentally demonstrated using Janus spherical particles [45].
- The particle then moves perpendicularly to the electric field lines, advancing in the direction of the non-conducting dielectric end.
- For saline (NaCl) concentrations greater than approximately 10 mM, no particle motion was observed.
3.2. Non-uniform field
- The authors begin by analysing the case of a conducting sphere subjected to a nonuniform electric field.
- The Au-coated microparticles were slightly heavier than water and sedimented so that the observed motion was for particles confined to the bottom wall of the sample cell.
- For a polarizable rod, the induced dipole at low frequencies is very small since the electric field lines surround the rod almost without deviation (see fig.
4. Induced rotational motion
- In this section the authors describe results where rotation of a conducting particle occurs upon application of an AC field.
- Alignment of a non-spherical particle in an AC field with fixed direction, called electroorientation; and the continuous rotation of a particle subjected to a rotating electric field, called electro-rotation, also known as Two cases are distinguished.
- In both cases, the particle angular velocity is usually much smaller than the frequency of the AC field.
- Electro-orientation (electro-rotation) results from the interaction of the applied field with the inphase (out-of-phase) induced charge, which means that the frequency dependence of EOr (ROT) mirrors the real part of the particle polarizability.
- In both cases, the authors analyse rotation due to the electrical torque on the induced dipole and rotation due to the ICEO flow at the metal-electrolyte interface.
4.1. Unidirectional field
- When exposed to an applied field, slender metal particles (e.g. rods) tend to align with the applied electric field for all frequencies.
- The expression for the ICEP rotational velocity for slender particles at low frequencies is ΩICEP = (ε/2η)ΛE 2 0 cos θ sin θ.
- The ICEP orientation of a nanowire can be qualitatively understood according to the schematic diagrams in Figure 4a which shows a metal nanowire subjected to an electric field of arbitrary direction [20].
- This is particularly useful when the goal is to compare experiments with electrokinetic theories, which are mainly developed for small voltage drops across the EDL (∆φ < kBT/e ≈ 25 mV).
- It was shown that an assembly of three Janus particles will rotate as a consequence of the individual ICEP motion of each Janus particle.
4.2. Rotating field
- It was observed that for spheres with rough surface the capacitance was greater than that predicted by the Debye-Huckel theory ε/λD [65], but for Ti spheres with smooth surfaces the capacitance was approximately close (CDL ∼ ε/λD) [79].
- According to theory [20, 71], when subjected to a rotating field, slender conducting particles rotate due to ICEO flow around the particle and to the torque on the induced dipole.
5. Electric-field induced assembly of metal particles
- In previous sections the authors focused on the electrical manipulation of a single metal particle immersed in a electrolyte.
- Several publications also describe the behaviour of a collection of metal particles subjected to AC fields.
- Both electrical and hydrodynamic particle-particle interactions occur upon application of an electric field.
- These interactions usually lead to reconfigurable particle patterns with potential applications in microelectronics and sensing.
- In the following section the authors review experiments on the assembly of metal particles.
5.1. Metal particle assembly on microelectrode structures
- Electric fields in microdevices are usually generated using planar microelectrode structures fabricated on glass or other insulating substrates.
- Several publications describe experiments where metal nanocolloids dispersed in an electrolyte move towards electrodes and thereby accumulate.
- This motion of metal particles could be due to positive DEP at high frequencies, as described in section 3.2, and/or by fluid flow induced on the electrodes at low frequencies, such as AC electroosmosis [22].
- Since then, several works have extensively reported the use of metal nanoparticles for bridging electrodes [81–88].
- AC electric fields are used to bring and place a nanowire between microelectrodes [10, 89], see figure 5c.
5.2. Chaining and self assembly of metal particles
- As previously mentioned, particle-particle interactions occur upon application of an electric field to an aqueous dispersion of metal particles.
- As schematically depicted in figure 6a, if the particles are oriented with their line of centers parallel to the applied field, the interaction between induced dipoles is attractive irrespective of the signal frequency.
- For low frequencies, assembly into a different pattern was ob- 19 AC C EP TE D M AN U SC R IP T ACCEPTED MANUSCRIPT served (see fig. 6c).
- As observed in ref. [74], when two nanowires are close they first align end-to-end, then slide next to one another, and finally move apart from their centers.
- The formation of bands takes longer for increasing conductivity of the electrolyte [14].
6. Conclusions and outlook
- Electrical forces on conducting particles can lead to linear motion, rotation and orientation, which can be used for particle alignment, separation and assembly.
- Particle dynamics can be explained from the action of the applied field on the charges induced within the EDL.
- This influence could not be observed in experiments, which showed that ROT of nanowires could be explained by the torque on the induced dipole.
- ICEP velocities in experiments are often one order of magnitude smaller than predicted by the simplest theory.
- Exploiting electric and hydrodynamic particle-particle interactions could be used for programmable assembly or synthesis of large nano-scale structures.
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Frequently Asked Questions (18)
Q2. What are the future works in "Ac electrokinetics of conducting microparticles: a review" ?
Future work could focus on an improved analysis of the effect of the wall on both the electrical and hydrodynamic problems. Future work could lead to bottom-up methods for assembling a diverse range of nano-systems from simple building blocks. From a fundamental perspective, the AC electrokinetics of conducting particles is a problem where the particle velocity is measured for a known EDL potential. This implies that the zeta potential can be measured for a controlled voltage drop across the double layer.
Q3. What is the MW frequency for a spheroid?
The MW frequency for a leaky dielectric slender spheroid in a leaky dielectric liquid is approximately ωMW ≈ (σf +σpL)/(εf + εpL), where subscripts f and p refer to the fluid and particle, respectively, and L is the depolarization factor along the particle axis [1].
Q4. What is the typical time for charging the electrolyte/metal interface?
The typical time for charging the electrolyte/metal interface is tRC = εℓ/λDσ [22, 23], where ε and σ are, respectively, the electrical permittivity and conductivity of the electrolyte, and λD is the Debye length.
Q5. What are the main applications of AC electric fields?
The use of AC electric fields for manipulating and characterising small particles in suspension is well-known [1, 2] and many applications have appeared over the last decades in fields such as colloidal science and biotechnology.
Q6. What is the recent research on electrokinetic fabrication of carbonnanotube/poly?
Electrokinetic fabrication of vertically aligned carbonnanotube/polymer composites has been reported using electro-orientation at low frequencies so that the ICEO flow favored individually aligned CNTs rather than tip-to-tip chaining [72].
Q7. What is the common method of generating electric fields in microdevices?
Electric fields in microdevices are usually generated using planar microelectrode structures fabricated on glass or other insulating substrates.
Q8. What is the effect of the native double layer on the surface conductance of a particle?
In this case, the native double layer may contribute to surface conductance implying a high Dukhin number, which can lead to concentration polarization phenomena [24].
Q9. What is the theory for uncharged particles and gold nanoparticles?
the theory is for uncharged particles and gold nanoparticles are highly charged in order that they form stable suspensions.
Q10. What is the theory of the ROT of nanowires?
According to theory, the ROT of spheres is only affected by the electrical torque on the dipole, and experiments are in close agreement with theory.
Q11. What is the effect of the electric field on the particle?
When an uncharged conducting particle is suddenly exposed to an electric field, electrons in the conductor move almost instantaneously so as to make the electric field inside equal to zero; electric field lines intersect the particle surface perpendicularly (see fig. 1a).
Q12. What is the effect of the polarizable rod on the dipole?
For a polarizable rod, the induced dipole at low frequencies is very small since the electric field lines surround the rod almost without deviation (see fig.
Q13. What is the angular velocity of a metal nanowire?
The observation that metal nanowires align with its main axis parallel to the applied electric field direction has been extensively reported [12, 17, 68], idem for carbon nanotubes [72].
Q14. What is the threshold voltage for Faradaic reactions?
In the following analysis, the authors assume that the induced voltage across the double layer ∆φ ∼ Eℓ (where E is applied electric field and ℓ is typical particle size) is below the threshold voltage for these Faradaic reactions Vredox so that no direct current passes through the EDL, i.e. the electrolyte/conductor interface is perfectly polarizable.
Q15. What was the effect of the unidirectional field on the composite particles?
In these experiments, the composite particles rotated and translated on a substrate and the unidirectional field was applied perpendicularly to the substrate.
Q16. What is the effect of the dielectrophoretic assembly of metal nanoparticles?
Bridging of18AC CEP TED MAN USC RIP TACCEPTED MANUSCRIPTlarger gaps between electrodes has also been reported by the dielectrophoretic assembly of several metallic nanowires [69] or carbon nanotubes [90], see figure 5d.
Q17. What is the main observation concerning the translational motion of metal rods?
The main experimental observation concerning the translational motion of metal rods is that they move to high field regions [16, 68, 69].
Q18. What is the effect of ICEP on the translational motion of Janus spheres?
The translational motion of Janus spheres in uniform fields is only possible due to ICEP, and observed particle velocities are smaller than for the ideal case.