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Dielectrophoretic Crossover Frequency of Single Particles: Quantifying the Effect of Surface Functional Groups and Electrohydrodynamic Flow Drag Force

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Dielectrophoretic Crossover Frequency of Single Particles: Quantifying the Effect of Surface Functional Groups and Electrohydrodynamic Flow Drag Force nanomaterials Article Dielectrophoretic Crossover Frequency of Single Particles: Quantifying the Effect of Surface Functional Groups and Electrohydrodynamic Flow Drag Force Yun-Wei Lu y, Chieh Sun y, Ying-Chuan Kao y, Chia-Ling Hung and Jia-Yang Juang * Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan; [email protected] (Y.-W.L.); [email protected] (C.S.); [email protected] (Y.-C.K.); [email protected] (C.-L.H.) * Correspondence: [email protected] These authors contributed equally to this work. y Received: 5 June 2020; Accepted: 11 July 2020; Published: 13 July 2020 Abstract: We present a comprehensive comparison of dielectrophoretic (DEP) crossover frequency of single particles determined by various experimental methods and theoretical models under the same conditions, and ensure that discrepancy due to uncertain or inconsistent material properties and electrode design can be minimized. Our experiment shows that sulfate- and carboxyl-functionalized particles have higher crossover frequencies than non-functionalized ones, which is attributed to the electric double layer (EDL). To better understand the formation of the EDL, we performed simulations to study the relationship between initial surface charge density, surface ion adsorption, effective surface conductance, and functional groups of both functionalized and nonfunctionalized particles in media with various conductivities. We also conducted detailed simulations to quantify how much error may be introduced if concurrent electrohydrodynamic forces, such as electrothermal and electro-osmotic forces, are not properly avoided during the crossover frequency measurement. Keywords: dielectrophoresis (DEP); electrohydrodynamics (EHD); electrothermal effect (ETE); AC electro-osmosis (ACEO); electric double layer (EDL); co-ion adsorption; surface conductance; optical tweezers (OTs); surface charge density 1. Introduction Dielectrophoresis (DEP) is a phenomenon in which suspended dielectric particles are polarized and moved relative to the medium by a non-uniform alternating current (AC) or direct current (DC) electric field [1–3]. AC DEP has been widely used in lab-on-a-chip systems [4,5] for particle/cell trapping [6–11], manipulation [12–15], and tissue engineering [16–19]. The magnitude and direction of the AC DEP force depend on the electric field gradient, the applied frequency, and the polarizability of the particle, which depends on the dielectric properties of the particle and the medium. The crossover frequency, at which the DEP force reverses its direction, is of particular importance since it is a key characteristic that enables particle/cell separations [20,21] and contains critical information on the mechanisms of the electric double layer (EDL) [22]. Despite intensive investigation over the years, accurate determination of the DEP crossover frequency, both theoretically and experimentally, of a single particle remains challenging. Several experimental methods were proposed to measure the crossover frequency of colloidal particles by using observation and estimation [23–26], the direct optical tweezers (OTs) force method [27,28], and a combination of optical tweezers and phase-sensitive lock-in detection (phase shift method) [28,29]. However, experimental results reported by different groups using different methods still show a certain discrepancy, especially for larger particles and/or a Nanomaterials 2020, 10, 1364; doi:10.3390/nano10071364 www.mdpi.com/journal/nanomaterials Nanomaterials 2020, 10, 1364 2 of 22 more conductive medium [23,29,30]. A significant discrepancy is also observed between experimental results and the theory based on Clausius–Mossotti (CM) factor, especially for larger particles, e.g., 5 µm, in the low-frequency regime [27]. On the theoretical side, the prevailing dipole model treats particles as point dipoles and does not consider the volume effect nor the distortion of the electric field caused by the particles [3]. The more comprehensive Maxwell stress tensor (MST) considers the effects mentioned above, but cannot predict the surface ion adsorption and the forming of an electric double layerNanomaterials (EDL), although 2020, 10, x FOR PEER an eREVIEWffective surface conductance can be assigned to2 of account 24 for the EDL effect [30However,,31]. More experimental recently, results Zhao reported et al.by differe proposent groups a new using volumetric-integrationdifferent methods still show a (VI) method, which addressescertain those discrepancy, limitations especially and for applies larger particle to particless and/or ofa more various conductive sizes medium and shapes [23,29,30]. [31 ,A32 ]. One major challenge of comparingsignificant discrepancy different is also experimental observed between methods experimental and results theoretical and the modelstheory based is on that the results Clausius–Mossotti (CM) factor, especially for larger particles, e.g., 5 μm, in the low-frequency regime were obtained[27]. by On di thefferent theoretical research side, the groups.prevailing dipole Hence, model the treats experimental particles as point/simulation dipoles and does conditions were often not thenot same. consider However, the volume theeffect particle nor the distortion surface of the property electric field and caused the by fluid the particles drag force[3]. The are known to greatly affect themore DEP comprehensive crossover Maxwell frequency, stress tensor and (MST) hence considers must the be effects carefully mentioned considered above, but cannot when interpreting predict the surface ion adsorption and the forming of an electric double layer (EDL), although an results obtainedeffective using surface diff conductanceerent methods can be assigned or diff toerent account microfluidic for the EDL effect systems. [30,31]. More For recently, instance, although polystyrene (PS)Zhao particles et al. propose have a new a volumetric-integration low material electrical (VI) method, conductivity, which addresses they those have limitations shown anda high overall applies to particles of various sizes and shapes [31,32]. One major challenge of comparing different conductivity, whenexperimental suspended methods inand medium, theoretical models according is that to the dielectric results were measurements obtained by different [25 research], which is evidence that the surfacegroups. charge Hence, exists the experimental/simulation and is dominant. cond Anotheritions were possible often not source the same. of However, discrepancy the in the DEP crossover frequencyparticle surface is the property fluid motion and the causedfluid drag by forc thee are electrohydrodynamic known to greatly affect the eff DEPect (EHD),crossover including AC frequency, and hence must be carefully considered when interpreting results obtained using different electro-osmosismethods (ACEO) or different [33] and microfluidic the electrothermal systems. For instance, effect although (ETE) [polystyrene26]. Unlike (PS) DEP, particles electrohydrodynamic have a forces (FEHD)low cause material fluid electrical motion, conductivity, which they in turn have resultsshown a high in a overall viscous conductivity, drag on when the suspended particles [26]. Such a flow-driven particlein medium, motion according couples to dielectric with measurements the pure [25], DEP-induced which is evidence particle that the surface motion, charge and affects the exists and is dominant. Another possible source of discrepancy in the DEP crossover frequency is the measurementfluid accuracy motion caused of the by DEP the electrohydrodynamic crossover frequency. effect (EHD), The including competing AC electro-osmosis behaviors (ACEO) of ACEO and DEP have also been[33] shown and the forelectrothermal microfluidic effect (ETE) devices [26]. [Unlike34–37 DEP,]. electrohydrodynamic forces (FEHD) cause fluid motion, which in turn results in a viscous drag on the particles [26]. Such a flow-driven particle In this paper,motion we couples aim with to provide the pure aDEP-induced comprehensive particle motion, direct and comparison affects the measurement between theaccuracy above-mentioned experimentalof methods the DEP crossover and theoretical frequency. The models competing under behaviors the same of ACEO conditions and DEP have to also minimize been shown the discrepancy due to uncertainfor microfluidic/inconsistent devices material [34–37]. properties and electrode design. We consider a functionalized In this paper, we aim to provide a comprehensive direct comparison between the above- particle, locatedmentioned at di ffexperimentalerent distances methods and from theoretical the electrode models under (Figure the same1 ).conditions We quantify to minimize how the the particle functional groupdiscrepancy and initial due to surfaceuncertain/inconsistent charge aff ectmaterial the crossoverproperties and frequency. electrode design. The We contribution consider a of DEP and electrohydrodynamicfunctionalized forces particle, (F located) cannot at different be distan easilyces dissectedfrom the electrode experimentally. (Figure 1). We quantify To quantify how the precise the particle functionalEHD group and initial surface charge affect the crossover frequency. The effect of electrohydrodynamiccontribution of DEP andforces electrohydrodynamic on the DEP forces crossover (FEHD) cannot frequency, be easily dissected we established experimentally. finite element models usingTo a commercialquantify the precise finite-element effect of electrohydrodynamic package COMSOL forces
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