Electric field mediated particle alignment and rotation

T. B. Jones

Professor Emeritus
Department of Electrical and Computer Engineering
University of Rochester

Introduction

Because they can be controlled in time by voltage and localized in space by proper electrode design, electrical forces and torques are well-suited for manipulating particles from the millimeter scale all the way down to nanoparticles. Furthermore, their inherent dependence upon both dielectric constant and electrical conductivity facilitates certain critical sorting operations based on adjusting the frequency. According to Pohl‘s original coinage, the word dielectrophoresis (DEP) refers to translational force effects [1]. On the other hand, there is no commonly accepted term for electric torque-induced motions. Here, the relevant phenomenology are categorized as either electrical particle alignment (EPA) or electrorotation (EROT).

The electrical torque responsible for both EPA and EROT is easily explained in terms of effective moments [2]. To first order, the net torque exerted on a finite dipole at position r consisting of two charges +q and –q separated by vector distance d is

(1)
where p = qd is the effective moment and E0 is the imposed electric field, which can be uniform or non-uniform. See Fig. 1. For non-zero torque, the moment and electric field must be non-parallel. Torque corrections due to field non-uniformity are second-order and often ignored.

Fig. 1. A Coulombic mechanism leads to the electrical torque exerted on a dipole.

Electric particle alignment

Electric field alignment of non-spherical particles was certainly observed over a century ago, possibly before the DEP effect itself was first noted. Shape anisotropy dictates that p and E0 will be parallel only when an axis of the particle - usually the longest - is aligned with the field. If not so aligned, then the nonzero torque nudges the particle into alignment, ordinarily with its longest axis parallel to the field.

The range of proposed applications for electric field particle orientation is broad. As early as 1948, a torque measurement method was devised to study dielectric properties of individual Rochelle salt crystals [3] and later extended to certain photosensitive materials [4] and wood fibers [5]. Another proposed application was for orienting ceramic fibers in reinforced composite materials [6]. For conductive, non-spherical particles, including biological cells such as mammalian erythrocytes, alignment becomes frequency-dependent; the particles change their stable axis of orientation at a set of discrete, predictable frequencies called the orientational spectra [7] [8] [9].

The early work cited above almost exclusively involved particles in the range from ~10 to ~1000 microns. In the last decade, however, nanoparticulate technology has reinvigorated interest in E field particle orientation. While the physical basis of nanoparticle orientation is the same, the reduced scale introduces new challenges, such as strong aggregation effects. Combining DEP and EPA to manipulate particle ensembles from ~1000 nm down to ~10 nm enables formation of layers, webs, and other useful configurations not previously dreamt of. Much of this new effort exploits electrical forces and torques in combination to manipulate nanowires [10] [11], nanobelts [12], and carbon nanotubes [13] [14] [15].

Electrorotation

Electrorotation (EROT), possibly first reported in 1892 by Arno [16], is the steady-state rotational response of a particle to an externally imposed, rotating electric field [2]. Usually, the field is established in a pseudo-two-dimensional chamber with a set of four co-planar electrodes excited by a two-phase, harmonic or square-wave voltage source. To establish steady-state rotation requires that the imposed rotating E field and the particle‘s dipole moment p remain non-parallel, a situation achievable if there is a phase lag between the two vectors. Such a phase lag occurs if ohmic conductivity or some form of dielectric dispersion is present. At steady state, p lags behind (or leads) the rotating field E at a fixed angle Θ. Fig. 2 depicts the two vectors rotating at radian frequency ω with lag angle Θ. The steady-state electrical torque is:

(2)

The particle responds by rotating, ordinarily at a much smaller angular velocity |Ω | << ω. The sign of Θ, and thus the direction of rotation, depend on the relative values of the charge relaxation times of the particle εpp and the surrounding fluid medium εmm, where ε and σ are permittivities and conductivities, respectively. For εpp < εmm, co-rotation is observed while for εpp > εmm anti-rotation occurs.

Fig. 2. Electric field rotating at angular velocity ω inducing a dipole that rotates at the same angular velocity but at constant lagging angle Θ. The particle responds by itself rotating at velocity |Ω | << ω. This rotation can be with or opposite the field rotation.

Arnold pioneered electrorotation to interrogate critical properties of biological cells, employing a precision nulling technique based on superposition of two oppositely rotating E fields at close-spaced frequencies [17]. EROT has been used for many years to investigate cell biology. Recent examples include measurements on fish embryos [18] and budding yeast cells [19]. Furthermore, EROT can be combined with DEP levitation to simplify cell handling [20]. Electrorotation, so widely employed to study the physical properties of biological particles, has now been extended to non-biological particles such as metallized polymer spheres [21].

In a linearly polarized electric field, particle rotation can interfere with the formation of pearl chains if a particle perturbs the electric field sufficiently to create a rotating component, to which an adjacent particle responds by starting to rotate [22]. It might be possible to exploit this effect to reduce aggregation in nanoparticles.

Conclusion

The electrical torque exerted on a particle can be used to align individual particles or ensembles. There is considerable interest in exploitation of this well-known effect to create useful nanoparticle structures and composites with nanowires and carbon nanotubes. Electrorotation, the continuous steady-state rotation of small particles, still serves broad purposes to measure precisely certain critical properties of biological cells and functionalized polystyrene spheres. Opportunities to exploit EROT in the manipulation of nanoparticles certainly exist and merit examination.

References
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