LETTER pubs.acs.org/Langmuir
Electrorotation of Metallic Microspheres Yu K. Ren,†,‡ Diego Morganti,† Hong Y. Jiang,‡ Antonio Ramos,§ and Hywel Morgan*,† †
School of Electronics and Computer Science, University of Southampton, Highfield, Southampton SO17 1BJ, U.K. School of Mechatronics Engineering, Harbin Institute of Technology, West da-zhi Street 92, Harbin, Heilongjiang, PR China, PC 150001 § Departamento de Electronica y Electromagnetismo, Universidad de Sevilla, Avda Reina Mercedes s/n, Sevilla 41012, Spain ‡
ABSTRACT: Electrorotation (ER) experiments of gold-coated micrometer-sized spheres suspended in an electrolyte are presented for three different ionic conductivities over the frequency range of 100 Hz to 40 MHz. The direction of rotation was observed to be counter-field (opposite to the rotating field vector) with a single rotation peak. The maximum in rotation occurs for a frequency on the order of the reciprocal RC time constant for charging the double layer at the gold surface. Dielectrophoresis (DEP) experiments showed that the goldcoated particles undergo negative DEP at low frequencies and positive DEP at high frequencies with the same relaxation frequency as electrorotation. No induced charge electrophoresis was noticeable in ER or DEP experiments.
T
he dielectric properties of single particles are generally characterized using ac electrokinetic techniques, including electrorotation (ER) and dielectrophoresis (DEP). When an induced dipole on a particle is in a nonuniform electric field, the particle experiences a DEP force; the direction and magnitude of this force depend on the particle polarizability (among other things). ER occurs when a rotating ac electric field is applied to an aqueous solution containing the particles of interest. The rotating field phasor induces a dipole moment in the particle, and if there is a phase difference between the dipole and the field vector, a torque on the particle is induced, which leads to a steady-state rotation.1-4 The rotation rate varies with the frequency of the applied electric field, and an ER spectrum is commonly used to characterize the dielectric properties of single particles, including cells. These measurements are typically made in the megahertz region where interfacial polarization dominates (e.g., the β dispersion of the cell membrane). Impedance or dielectric measurements of suspensions of particles can also be made, where each method is equivalent and measures the induced dipole moment of the particle(s) in question. The ER and DEP spectra are governed by the imaginary and real parts of the polarizability of the particles, respectively, which in turn are related through the Kramers-Kronig relations. This means that a relaxation in the real part of the dipole must be mirrored in the imaginary part. From electrical impedance measurements, it is known that charged dielectric particles exhibit an additional large dispersion at low frequencies, termed the R relaxation.5 This dispersion has its origins in the concentration polarization of the electrical double layer around the particle.6 In terms of ER, a second ER spectrum is observed at lower frequencies (kHz), which is cofield. Field-induced changes in the concentration of charge around the particles cause an asymmetry in the electrical double r 2011 American Chemical Society
layer. For the thin double layer approximation, the properties of the low-frequency dispersion have been calculated,6-8 and the typical time constant of the relaxation is on the order of the diffusion time around the particle radius. The general theory for the low-frequency ER behavior of charged dielectric particles has been developed by Grosse and Shilov.9 They showed that the total particle rotation is the sum of the rotation due to the electrical torque acting on the particle and the rotation due to the electroosmotic flow in the double layer around the particle. The ER of perfectly polarizable metallic particles has not been studied experimentally. The transition in the electrokinetic behavior of particles as they move from nonpolarizable to perfectly polarizable may also be of interest for the label-free sensing of particle behavior. In contrast to polymer particles (that have fixed surface charges), a metallic particle suspended in an electrolyte behaves as an insulator at low frequencies and low voltages because the current passes around the particle. Effectively, below the threshold voltage for Faradaic reactions and then to a good approximation, the electrolyte/metal surface can be considered to be perfectly polarizable. At dc or low frequencies (much smaller than the reciprocal RC time for charging the metal/electrolyte double layer), the double layer is fully charged and the electric field lines run around the particle (i.e., no current flows into the particle). This is under the assumption that the electric field E is weak so that Ea , kT/q and the double layer is thin λ , a (a is the particle radius, λ is the Debye length, and kT/ q ≈ 0.025 V at room temperature). From the perspective of an observer, the situation is equivalent to that of an insulating sphere Received: December 1, 2010 Revised: January 19, 2011 Published: February 08, 2011 2128
dx.doi.org/10.1021/la104784m | Langmuir 2011, 27, 2128–2131
Langmuir
Figure 1. Electric field lines in the two cases at (a) low (ω , ωRC) and (b) high (ω . ωRC) frequencies. The maximum rotation rate occurs at a characteristic angular frequency given by ωRC = 1/TRC.
suspended in a conducting medium in an electric field. Classically, the electric field outside the particle is the sum of the applied field plus the field of the induced dipole, with a direction against the applied field (Figure 1a). The RC time, TRC, of the double layer is the time required to charge the double-layer capacitance through the resistance of the bulk electrolyte. An estimate of this time is TRC = aε/σλ (where σ is the liquid conductivity and ε is the permittivity).10 For frequencies much greater than ωRC =1/TRC, there is negligible induced charge in the double layer and the electric field lines intersect the particle surface perpendicularly: the particle behaves as a perfect conductor. The electric field outside the particle is the sum of the applied field plus the field of an induced dipole that now lies parallel to the applied field (Figure 1b). The theory of dielectrophoresis (DEP) predicts that at frequencies of ω , ωRC the particle would be expelled from regions of high electrical energy density, εE2/2, (negative DEP) and at frequencies of ω . ωRC it would be attracted to regions of high electric energy density (positive DEP). In addition, it is expected that because the polarizability goes from negative to positive with increasing frequency the ER spectrum would peak at the relaxation frequency ωRC, with the direction of the torque against the field.
LETTER
This picture is not complete because at low frequencies (on the order of ωRC and below) induced charge electroosmotic flow also occurs around the particle, so-called induced charge electrophoresis (ICEP).11-15 The complete theory predicts that for translational motion and at low frequencies, DEP and ICEP act in opposite directions and cancel each other out for a perfectly polarizable spherical particle with a thin double layer.11,13 However, the ER analysis of metallic spheres demonstrates that the frequency of rotation is not affected by induced electroosmotic flows, in contrast to dielectric particles with a surface charge density.9 In essence, the induced EO slip velocity for a perfectly polarizable metal surface is proportional to the surface gradient of the square of the induced potential.16 Therefore, any closed line integral of the slip velocity around the particle is zero, which means that no rotating flow is induced by ICEO. However, for nonspherical (rods) or asymmetric (Janus) particles, ICEO may have a significant effect on both the ER and electro-orientational behavior. The behavior of spherical particles with thick double layers may also be influenced by ICEO. The ER spectrum of gold-coated micrometer-sized spheres suspended in different molarity KCl electrolytes was recorded by placing the particles in the center of an array made from four hyperbolic polynomially shaped planar electrodes (made from 300-nm-thick gold by photolithography) with a diagonal gap of 0.5 mm.17,25 The four electrodes were energized with a fourphase ac signal in the frequency range of 100 Hz to 40 MHz, generating a rotating field in the center of the array, and the rotation of individual particles was recorded with video. For ER, the applied voltage was 4 V peak to peak. The rotation rate of single particles was analyzed by eye, and the data shown is the average rotation rate for 10-15 separate particles from a single batch. The DEP properties of the particles were measured by placing single particles in the center of a 200-μm-gap polynomial array and applying a single-phase ac voltage (5 V peak to peak) to opposite electrodes. The center of these electrodes has a region where the DEP force is approximately linearly proportional to the radius, over the central 50% of the electrode array.2,17 The DEP velocity was measured by observing the trajectories of single particles along an arbitrary radius from the center. At low frequencies and low suspending medium conductivities (
