18880
J. Phys. Chem. C 2010, 114, 18880–18885
Anomalous Dielectrophoresis of Nanoparticles: A Rapid and Sensitive Characterization by Single-Particle Laser Spectroscopy Victoria E. Froude, James I. Godfroy, Shengqin Wang, Hannah Dombek, and Yingxi Zhu* Department of Chemical and Biomolecular Engineering, UniVersity of Notre Dame, Notre Dame, Indiana 46556, United States ReceiVed: September 16, 2010; ReVised Manuscript ReceiVed: September 23, 2010
Although much experimentation has focused on the dielectrophoretic behavior of submicrometer colloids, few studies have provided advanced understanding of the ac electric polarization mechanism for nanoparticles, largely due to the paucity of sensitive and rapid experimental techniques. By using ultrafast fluorescence correlation spectroscopy (FCS) at a single-particle level, we have examined the dielectrophersis (DEP) behavior of nanoparticles of varied radii, a ) 10-50 nm, in aqueous media under varied ac electric fields in situ, where direct and real-time microscopic methods become inapplicable for nanoparticles of a < 50 nm. The characteristic dipole relaxation frequency (the DEP crossover frequency, ωc) is determined from the acfrequency-dependent nanocolloidal concentration profile by FCS. In stark contrast to a single ωc predicted from classical DEP theory, we have observed two distinct ωc’s with a strong dependence on particle size and medium conductivity. The anomalous lower ωc inversely scales with the screening length and particle size, suggesting the dynamic double-layer charging effect on the interfacial polarization of nanocolloids whose size is comparable to the double-layer thickness. Rapid manipulation, aggregation and sorting of particles by electric fields has been widely used in recent years. Dielectrophoresis (DEP), which exploits nonuniform ac electric fields, has emerged as one of the most prevalent methods for colloidal manipulation and directed assembly. For instance, DEP has been exploited for the precise control of the assembled structure of binary colloidal mixtures1,2 and photonic crystals,3 as well as biological particles such as live cells4-6 or viruses.7,8 However, DEP manipulation has been largely focused on micrometer sized particles, because the DEP force, FDEP, exerted by the electric field on particles, diminishes rapidly with decreasing particle radius, a, as FDEP scales with a3 according to classical Maxwell-Wagner (MW) theory. Due to the severely weakened FDEP with reduced a, it has been theorized that the deterministic DEP force cannot overcome colloidal Brownian motion, and thus, DEP becomes inapplicable for colloidal manipulation and directed assembly at nanoscales.11 However, recent studies have demonstrated the assembly of functional microwires12-15 and many other hierarchical nanostructures7,8,16 from nanoparticles in solutions by DEP. Because these studies have focused mainly on characterizing the final assembled nanostructures of colloidal aggregates12-15 after the completion of DEP under ac electric fields by using techniques such as scanning electron microscopy (SEM), the ac polarization and dynamic DEP behavior of nanometer sized particles remain little investigated experimentally due to the paucity of sensitive and rapid experimental techniques for in situ characterization. Recent theories have endeavored to elucidate the induced dipole and DEP behaviors of submicrometer colloids of a ) 47-500 nm with the focus largely on the double layer effects on the interfacial polarization mechanism.9,17,22 It has been suggested that submicrometer particles experience a DEP force stronger than that predicted by classic MW theory because acfield-induced tangential ionic currents in the Stern and diffuse * Corresponding author. E-mail:
[email protected].
layer result in high surface conductivity of dielectric colloidal particles. However, when further reduced particle size becomes comparable to the Debye length, λ (i.e., a ≈ λ), the normal conductive field due to counterion migration in the diffuse layer cannot be negligible. An advanced DEP theory has predicted the scaling of ωc with ion diffusivity, Dion, and the reciprocal of λ and a; i.e.,17
ωc ∼ Dion /(λa)
(1)
using a resistance-capacitance (RC) time analysis of the diffusive layer capacitor and resistor. Yet, few experiments have been conducted with nanoparticles suspended in aqueous media, where the condition of a ≈ λ is fully realized. In this work, we experimentally examine the DEP characteristics of nanoparticles of a e 50 nm in aqueous media of varied medium conductivity, σm. To enable in situ, ultrafast characterization of nanocolloidal DEP behaviors to elucidate the dynamics of induced particle dipoles at nanoscales, we employ fluorescence correlation spectroscopy (FCS) to determine the dynamic behavior of nanocolloids under ac fields of varied high frequency (ω ) 5 kHz-20 MHz) at a single-particle level, which offers distinct adVantages over traditional microscopic visualization methods inapplicable for direct and realtime characterizing of nanocolloids of a < 50 nm due to the optical diffraction limit. In addition, thanks to the single-particle/ molecule resolution, FCS experiments are often conducted at very dilute suspensions containing ∼1 particle or molecule per 0.1 µm3 focal volume; thereby, the problem of colloidal aggregation commonly encountered with nanoparticles in suspensions can be easily avoided while it ensures the investigation of the DEP characteristics of single nanoparticles, not the nanoparticle clusters. Compared with many other analysis methods for the current microfluidics-based diagnosis, the FCS characterization allows
10.1021/jp108862d 2010 American Chemical Society Published on Web 10/18/2010
Anomalous Dielectrophoresis of Nanoparticles
J. Phys. Chem. C, Vol. 114, No. 44, 2010 18881
Figure 1. (a) Schematic illustration of the FCS setup, in which a sample cell sits atop a coverslip fabricated with a quadrupole array of microelectrodes with a gap spacing of 20 µm between two neighboring microelectrodes, whose computed ac field strength profile is exhibited in part d. The laser is positioned in the center between two microelectrodes near the coverslip substrate. (b) A representative spectrum of fluorescence intensity fluctuation detected by FCS, producing an autocorrelation function, G(τ) normalized by G(τ ) 0) as shown in part c. (d) Schematic illustration of the connection of microelectrodes with a function generator and the computed ac field strength profile.
for sensitive detection of extremely dilute samples of 10-9-10-12 M in molar concentration, typically 2-3 orders of magnitude lower than the current concentration limit using microscopic visualization. Hence, in this study, we explore the FCS technique to examine the dynamic DEP characteristics of nanocolloids of varied a e 50 nm in aqueous media of varied σm under high-frequency ac electric fields on the basis of measured ac-frequency-dependent nanocolloidal concentration profiles. A one-photon FCS setup on an inverted microscope (Zeiss, Z1) with an oil immersion 100× objective lens (NA ) 1.6),18 as illustrated in Figure 1a, is used to examine the dynamic processes of fluorescence-tagged polystyrene (PS) nanoparticles (Invitrogen Inc.) in aqueous suspensions with varied amounts of NaCl salt (purity >99.5%, Sigma-Aldrich). The tiny fluctuations, I(t), in fluorescence intensity, due to the motion of nanoparticles in and out of the laser excitation volume, with an Ar laser (Melles Griot, λ ) 488 nm) are measured by singlephoton counting modules (Hamamatsu) at a time interval of typically 10-100 µs in a confocal detection geometry, as illustrated in Figure 1b. The autocorrelation function, G(τ), of measured I(t),18-20
G(τ) ) 〈δI(t) δI(t + τ)〉/〈I(t)〉2
(2)
as obtained in Figure 1c is used to extract the relevant diffusion coefficient, D, and concentration, C, of fluorescent nanoparticles under varied experimental conditions. The excitation focal volume, Veff, is calibrated by dilute rhodamine 6G aqueous
solution of a nanomolar concentration to be ∼ 260 nm in the lateral dimension and z ∼ 2 µm in the vertical dimension.19,20 To study the DEP characteristics of polarized nanoparticles of a ) 10-50 nm, a dilute carboxylate-stabilized PS nanocolloidal suspension in deionized water (Barnstead Nanopure II) at a dilute concentration of 0.005 vol % (∼0.95 particles per 0.1 µm3 solution) is, after sonication to minimize nanocolloidal aggregates, placed in a liquid cell glued onto a glass coverslip that is patterned with gold microelectrode arrays in a quadruple configuration as detailed elsewhere.10 In this work, ac electric potential at a peak-to-peak voltage, Vpp ) 10 V, and varied frequency, ω ) 5 kHz-20 MHz, is applied by a function generator (Agilent 33220A) across quadruple microelectrodes separated by 20 µm, which produce the field maxima between adjacent electrodes and minima at the center of the microelectrode array, as illustrated in Figure 1d. We have examined the impedance spectra of the microelectrodes immersed in aqueous media in the range of ω ) 0.1 kHz-100 kHz by impedance spectroscopy (Gamry Instruments), as depicted in Supporting Information Figure 1. Over this low ac frequency range, the measured real part of impedance decreases from 106 Ω to 2 × 104 Ω with increasing ω and approaches the value for bulk aqueous solutions without microelectrodes, suggesting the negligible contribution of the artifacts arising from the microelectrodes or the function generator for the intriguing low-frequency DEP behaviors reported below. The field-driven motion and concentration of PS nanoparticles near the microelectrode are simultaneously characterized by FCS, where the laser is focused at the center between two adjacent microelectrodes near the substrate. FCS
18882
J. Phys. Chem. C, Vol. 114, No. 44, 2010
Froude et al.
(
)( ) [( ) ( ) ]
4Dτ G(τ) ) (Cπ1.5ω ¯ 2z)-1 1 + 2 ω ¯
-1
exp -
Figure 2. (a) Normalized autocorrelation functions, G(τ)/G(τ ) 0), for PS nanoparticles of a ) 50 nm suspended in deionized water in the absence of ac electric field (O) and under an applied ac field of VPP ) 10 V and ω ) 50 kHz (0), 250 kHz (4), and 5 MHz (3). The solid line is a theoretical fitting with eq 3, giving the diffusion coefficient, D, as shown in panel b. Inset: The blowout of G(τ) at short lag time exhibits a considerable difference in G(0) under varied ac fields, which is inversely proportional to the concentration, C, of fluorescent nanoparticles in the laser focal volume according to eq 3. (b) The acfrequency-independent diffusion coefficient, D ≈ 3.5 µm2/s, of PS nanoparticles of a ) 50 nm, indicating the equivalent hydrodynamic radius of 55 nm using the Stokes-Einstein relation, in good agreement with the known particle size of a ) 50 nm. (c) The ac-frequencydependent concentration profile, C, of fluorescent PS nanoparticles of a ) 50 nm in the focal volume normalized by the concentration in the absence of ac fields, C0, according to measured G(0) ) ([C]π1.5z2)-1, which depicts a distinct concentration effect due to the ac-frequencydependent DEP response of nanoparticles under applied nonuniform ac fields. The solid red line is the theoretically estimated real part of the CM factor, fCM(ω), plotted on the right coordinate axis. The dashed line is a guideline only and provides a comparison to the theoretical Re[fCM(ω)] to determine the DEP crossover frequency, ωc. Two distinct crossover frequencies, ωc,L and ωc,H, are determined by finding the intersection between a straight line through the highest values in the C/C0 plateau to the low C/C0 values and the baseline of C/C0 ) 1 as illustrated in detail in Supporting Information Figure 3.
experiments are also conducted by using a pair of coplanar microelectrodes1,2 with the laser focused at the center between the two electrodes, and results similar to those reported below are obtained. We start with PS nanoparticles of a ) 50 nm suspended in deionized water of σm ) 2.0 × 10-6 S/m under varied ac frequency. As depicted in Figure 2a, as well as Supporting Information Figure 2a, G(τ) is obtained by FCS in response to applied ac fields at varied ω. Using eq 3, developed for particles in 3D free diffusion with an induced velocity, V,19
1+
τ·ν ω ¯
2
4Dτ z2
1+
-0.5
4Dτ ω ¯2
×
-1
(3)
we can obtain D and C in response to varied ac fields. As evidently shown in Figure 2a, normalized G(τ) by G(τ ) 0) under an applied ac field of ω ) 50, 250, and 5000 kHz exhibits little difference from the one obtained in the absence of ac fields. As shown in Figure 2a as well as in Supporting Information Figure 2b-e for individual autocorrelations obtained at varied ω, the fitting is excellent, producing reliable D and C. Thus, as shown in Figure 2b, the measured D ) 3.5 µm2/s remains the same for nanoparticles at varied ω as for the one without ac fields applied, which corresponds to a particle radius of a ≈ 55 nm, according to the Stokes-Einstein relation, in good agreement with reported nanoparticle size. The constant D also suggests that colloidal aggregation under applied ac fields is negligible. It should also be noted that the obtained DEP-induced particle velocity, V ≈ 2 µm/s, is negligibly small, which is well expected from the theoretical DEP mobility9 for nanoparticles of such small size. However, G(τ ) 0) shows a strong dependence on ω, as exemplified in the inset of Figure 2a. Because G(τ ) 0) is known to inversely scale with Cπ1.5z2, as shown in eq 3, we normalize the measured C by the bulk nanoparticle concentration without ac fields, C0, and thereby obtain the concentration profile against ω, as shown in Figure 2c. We expect that the time-averaged concentration of nanoparticles under applied ac fields is proportional to FDEP, which scales with the ω-dependent dipolar Clausius-Mossotti (CM) factor, fCM, for a polarized particle (p) of radius a and complex permittivity ε˜ p suspended in a medium (m) of ε˜ m as
fCM ) (ε˜ p - ε˜ m) / (ε˜ p + 2ε˜ m)
(4)
Due to higher surface conductance on carboxylated PS nanoparticles, resulting from the surfactant stabilizers, than that of aqueous medium, PS nanoparticles are expected to experience positive DEP (pDEP) at low ac frequency, by which particles are driven toward high-field regions between any two of the microelectrode posts, and negative DEP (nDEP) at high frequency, by which they are driven toward low-field regions at the center of four quadruple microelectrodes. Thus, ωc exists at Re[fCM(ω)] ) 0 upon the transition between pDEP and nDEP, whereby the particles experience zero or weak nDEP as the ac frequency approaches the crossover, as described by classical DEP theory. Compared with the theoretically estimated real part of the CM factor, fCM(ω), as plotted on the right coordinate axis of Figure 2c, the measured concentration profile in the left coordinate axis in Figure 2c shows a shape similar to the plot of Re[fCM(ω)], particularly at high ω. We have tentatively determined ωc by finding the intersection between a straight line through the highest values in the C/C0 plateau to the low C/C0 values and the baseline of C/C0 ) 1, as illustrated in Supporting Information Figure 3a-c; therefore, the crossover frequency reported in this work describes the point where minimal pDEP effects are experienced by the nanoparticles. Thus, slightly different from the traditionally defined crossover frequency, the crossover frequency reported below corresponds to the frequency where nanoparticles no longer experience a strong pDEP force, but instead, experience zero DEP or significantly weak nDEP forces. However, due to greatly
Anomalous Dielectrophoresis of Nanoparticles
J. Phys. Chem. C, Vol. 114, No. 44, 2010 18883
Figure 3. Representative fluorescence micrographs exhibit PS nanoparticles of a ) 50 nm particles (a) in the absence of applied ac fields and its DEP behavior under a field strength of 10 VPP and varied ac frequency of ω ) (b) 1, (c) 5, (d) 7, and (e) 10 MHz, indicating a pDEP-to-nDEP transition at ω ≈ 5 MHz. All micrographs are acquired after ∼10 min of ac field application. A crossover frequency, ωc ≈ 5 MHz, is determined from the fluorescence micrographs below, consistent with the value obtained by FCS and in previously reported work.22
diminishing DEP force with nanometer-sized particles, nDEP is rarely observed in our experimentation. Surprisingly, we observe two apparent crossover frequencies, one designated as a low crossover threshold, ωc,L ≈ 25 kHz and the other as a high crossover frequency, ωc,H ≈ 5 MHz, the latter of which appears consistent with the previously reported ωc ) 5 MHz for a PS particle of a ) 47 nm in deionzied water.21 The nearly overlapping of the measured concentration profile with the theoretically estimated Re[fCM(ω)] at high ω also gives the credibility of the determined ωc,H. In addition, ωc,H ≈ 5 MHz is also confirmed by confocal microscopic observation using concentrated fluorescent PS nanoparticles in a procedure detailed elsewhere,10 below which nanoparticles are observed to aggregate between adjacent microelectrode posts by pDEP and above which nanoparticles aggregate in the center of the quadruple microelectrodes by nDEP, as illustrated in Figure 3, where the detected fluorescence intensity is remarkably increased by the application of ω less than 5 MHz. The agreement of measured ωc,H by two distinct techniques with their different data analyses has two important implications: First, it imparts credibility to our rather empirical analysis with inherent uncertainty to determine the crossover frequency from the concentration profile obtained by FCS. Second, it confirms the applicability of FCS for rapid and sensitive detection of the DEP characteristics of nanoparticles under high frequency ac fields. However, the determination by direct microscopic observation becomes inapplicable with smaller nanoparticles of a < 50 nm due to the optical diffraction limit, while the FCS spectroscopic characterization becomes advantageous. It should be also noted that the amplitude of the applied voltage remained constant in this work; from current DEP theory, the DEP force, but not the crossover frequency, is proportional to the applied voltage. We thus expect that although the shape and crossover frequencies of the concentration profiles remain similar, the amplitude of the concentration profile would decrease with decreasing applied voltage. To verify the existence of two distinct ωc’s for nanoparticles, we further examine the particle size and medium conductivity
Figure 4. The normalized concentration profiles, C/C0, plotted on the left coordinate axis, against ac frequency, ω for PS nanoparticles of a ) (a) 10, (b) 20, and (c) 50 nm, suspended in deionized water under applied nonuniform ac fields. The theoretically estimated real part of the CM factor, fCM(ω), is plotted in the red solid lines on the right coordinate axis. The dashed line is a guideline only and provides a comparison to the theoretical Re[fCM(ω)].
dependence of ωc,L and ωc,H. Concentration profiles obtained by FCS for PS nanoparticles of a ) 10, 20, and 50 nm suspended in deionized water are summarized in Figure 4a-c, respectively. The concentration profiles for a ) 10 and 20 nm appear highly similar to the one obtained for a ) 50 nm, confirming the presence of both ωc,L and ωc,H: ωc,L ) 100 kHz
18884
J. Phys. Chem. C, Vol. 114, No. 44, 2010
Froude et al.
Figure 6. The collapse of experimental measured ωc,L with varied a and σm, suggesting the scaling of ωc,L with Dion/(λa), shown in the left panel (i) in solid symbols, and ωc,H with varied a, suggesting the scaling of ωc,H with Dion/(λsa), shown in the right panel (ii) in semifilled symbols, for a ) 10 nm (black squares), 20 nm (semifilled red circles), and 50 nm (semifilled blue triangles).
Figure 5. The normalized concentration profiles, C/C0, plotted on the left coordinate axis, against ω for PS nanoparticles of a ) 20 nm suspended in aqueous media of varied medium conductivity, σm) (a) 2 × 10-6, (b) 8.1 × 10-5, and (c) 4.4 × 10-4 S/m. The theoretically estimated real part of the CM factor, fCM(ω) is plotted in the red solid lines on the right coordinate axis. The dashed line is a guideline only and provides comparison with the theoretical Re[fCM(ω)].
and ωc,H ) 9 MHz are determined from Figure 4b for a ) 20 nm; ωc,L ) 125 kHz is determined from Figure 4a for a ) 10 nm, yet ωc,H appears to shift to a much higher frequency, exceeding our experimental upper ω window of 20 MHz. Despite undetectable ωc.H for a ) 10 nm, the trend of increased ωc,H with decreased particle size is well expected according to the theoretical scaling prediction in eq 1, by which ωc,H is estimated to range in 20-25 MHz. Thus, both ωc,L and ωc,H are observed to shift consistently to higher crossover frequency with reduced nanoparticle size. Moreover, a dependence of medium conductivity on ωc,L and ωc,H is examined with PS nanoparticles of a ) 20 nm. Concentration profiles similar to the one in deionzied water in Figure 4a are obtained in aqueous media of slightly higher medium conductivity, σm ) 8 × 10-5 and 4.4 × 10-4 S/m in Figure 5b-c, respectively. Accordingly, the respective ωc,L and ωc,H are 500 kHz and 9 MHz at σm ) 8 × 10-5 S/m, and 1.05 and 9 MHz at σm ) 4.4 × 10-5 S/m. It is intriguing to observe that ωc,L increases with increasing medium conductivity, yet ωc,H remains nearly the same. The confirmed presence of two distinct ωc’s for PS nanoparticles is rather surprising, in stark contrast to previously reported single ωc for PS particles of varied a ) 47 nm-5 µm in the literature,1,2,7-9 whereas the existence of two ωc’s is often observed with multilayered dielectric particles with complex structures or coatings.10 We have excluded the possible contribution of other ac electrokinetic phenomena that are prevalent in the low frequency regime, such as ac electroosmosis (ACEO) and ac electrothermal flow due to Joule heating, to the presence of two distinct ωc’s. ACEO flow often arises from the dynamic
charging of the double layer, with a dependence on applied ac frequency, ω, and the electrode separation distance, L. According to the capacitance charging theory,22 the optimum frequency for ACEO flow scales with D/λL, where D is ion diffusivity (∼1.31 × 10-9 m2/s for Na+) and λ is the Debye length. For the microelectrodes used in this work of L ) 20 µm, the optimum frequency is estimated in the range of 98 Hz to 4.6 kHz, corresponding to σm) 2 × 10-6 to 4.4 × 10-5 S/m, respectively, which is apparently well below the onset of lower frequency crossover, ωc,L ≈ 30 kHz to 1 MHz. Because the temperature gradient arising from ac electrothermal flow scales with σmVrms2/κ,1,9 where Vrms is the root-mean-square ac voltage and κ is the thermal conductivity, we have estimated that the temperature difference between the electrodes and the bulk solution is ωc,L, the particles are polarized with net charges accumulated at two poles due to the space charging in a nonuniform ac field. Conversely, despite a similar particle size dependence, all the measured ωc,H in the range of 5 to over 20 MHz show an independence of σm, suggesting a contribution from the time scales of counterion associate and dissociation in the Stern layer, whose thickness, λs, is ∼1-2 nm and independent of σm. Tentatively, we plot all the measured ωc,H, including a theoretical
Anomalous Dielectrophoresis of Nanoparticles ωc,H ≈ 20-25 MHz for a ) 10 nm in deionized water, against Dion/(λsa). Surprisingly, the data collapse well, as shown in the right panel (ii) of Figure 6, strongly suggesting the shorter time scales (∼1/ωc,H) of the induced dipole on PS nanoparticles is determined by the RC time of the capacitive Stern layer. Yet, advanced DEP theory and modeling to distinguish the contribution of the Stern and diffuse layers to the dipolar relaxation times of nanoscaled colloids are highly desired to further examine the obtained scaling behaviors for both ωc,L and ωc,H. In summary, we have demonstrated that FCS can be used as a highly sensitive, accurate method to rapidly characterize the DEP behavior of nanoparticles of a < 50 nm, for which in situ microscopic characterization becomes inapplicable. For nanoparticles whose particle sizes are comparable to the double layer length scales (i.e. a ≈ λ), we have surprisingly observed two DEP crossover frequencies, ωc,L and ωc,H, indicating two distinct dipole relaxation time scales of a polarized nanoparticle under nonuniform ac fields. The obtained scaling of ωc,L ∼ Dion/(λa) and ωc,H ∼ Dion/(λsa) indicates the respective contributions from the normal space charging in the diffuse layer and counterion adsorption in the Stern layer, whereas the normal conductivity and current in the diffuse layer are negligible for particles of a . λ, and thus, only the tangential conductive current in the double layer is accountable, leading to one single ωc observed with large particles of a . λ. However, a more rigorous theory to better predict the experimental DEP behaviors of nanoparticles whose characteristic dimension becomes comparable to the double-layer thickness is highly demanded. In perspective, we anticipate that the ac polarization mechanism and induced dipole characterization of complex nanocolloids can be further explored by the application of FCS. Acknowledgment. This work is supported in part by NSF (CBET-0730813) (colloid assembly) and in part by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Science and Engineering (DE-FG02-07ER46390) (ultrafast spectroscopy of interfacial dynamics).
J. Phys. Chem. C, Vol. 114, No. 44, 2010 18885 Supporting Information Available: Data showing the real part of the impedance of the microelectrode setup against ac frequency and details regarding the determination of the crossover frequency from the measured FCS autocorrelation function. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Hoffman, P. D.; Sarangapani, P. S.; Zhu, Y. Langmuir 2008, 24, 12164–12171. (2) Hoffman, P. D.; Zhu, Y. Appl. Phys. Lett. 2008, 92, 224103. (3) Lumsdon, S. O.; Kaler, E. W.; Williams, J. P.; Velev, O. D. Appl. Phys. Lett. 2003, 82, 949. (4) Gordon, J. E.; Gagnon, Z.; Chang, H. C. Biomicrofluidics 2007, 1, 044102. (5) Talary, M.; Mills, K. I.; Hoy, T.; Burnett, A. K.; Pethig, R. Med. Biol. Eng. Comp. 1995, 33, 235–237. (6) Sebastian, A.; Venkatesh, A. G.; Markx, G. H. Electrophoresis 2007, 28, 3821–3828. (7) Hughes, M. P.; Morgan, H. J Phys D: Appl. Phys. 1998, 31, 2205– 2210. (8) Ermolina, I.; Milner, J.; Morgan, H. Electrophoresis 2006, 27, 3939– 3948. (9) Morgan, H.; Green, N. G. AC Electrokinetics: Colloids and Nanoparticles; Research Studies Press Ltd.: Baldock, Hertfordshire, England, 2003. (10) Froude, V. E.; Zhu, Y. J. Phys. Chem. B 2009, 113, 1552–1558. (11) Pohl, H. A. Dielectrophoresis; Cambridge University Press: Bristol, England, 1978. (12) Hermanson, K. D.; Lumsdon, S. O.; Williams, J. P.; Kaler, E. W.; Velev, O. D. Science 2001, 294, 1082–1086. (13) Ranjan, N.; Mertig, M.; Cuniberti, G.; Pompe, W. Langmuir 2010, 26, 552–559. (14) Lumsdon, S. O.; Scott, D. M. Langmuir 2005, 21, 4874–4880. (15) Liu, Y.; Chung, J. H.; Liu, W. K.; Ruoff, R. S. J. Phys. Chem. B 2006, 110, 14098–14106. (16) Morgan, H.; Hughues, M. P.; Green, N. G. Biophys. J. 1999, 77, 516–525. (17) Basuray, S.; Chang, H. C. Phys. ReV. E 2007, 75, 060501. (18) Elson, E. L.; Madge, D. Biopolymers 1974, 13, 1–27. (19) Rigler, R.; Elson, E. Fluorescence Correlation Spectroscopy: Theory and Applications; Springer: Berlin, Germany, 2001. (20) Wang, S.; Zhao, J. J. Chem. Phys. 2007, 126, 091101. (21) Green, N. G.; Morgan, H. J. Phys. D: Appl. Phys. 1997, 30, L41– L44. (22) Gagnon, Z.; Chang, H. C. Electrophoresis 2005, 26, 3725–3735.
JP108862D
