12164
Langmuir 2008, 24, 12164-12171
Dielectrophoresis and AC-Induced Assembly in Binary Colloidal Suspensions Peter D. Hoffman, Prasad S. Sarangapani, and Yingxi Zhu* Department of Chemical and Biomolecular Engineering, UniVersity of Notre Dame, Indiana 46556 ReceiVed April 29, 2008. ReVised Manuscript ReceiVed August 22, 2008 Dielectrophoretic behaviors and assembly of a binary suspension in aqueous media are examined in the presence of nonuniform alternating current (AC) electric field. A peculiar low-frequency threshold and dielectrophoresis (DEP) crossover frequency determine the applicable frequency window for binary assembly under positive DEP, which can be effectively tuned by medium conductivity and particle size, suggesting that the dynamic double-layer effect is responsible for the interfacial polarization of micrometer to submicrometer-sized particles in aqueous suspensions. Strong effects of AC-field frequency, medium conductivity, and size ratio on binary assembly morphology have been observed. A frequency-medium conductivity phase diagram is obtained to illustrate the morphological transition of assembled colloidal aggregates from segregated, ordered assemblies to inverted segregation with the appearance of amorphous phases upon increasing frequency and/or medium conductivity, which is a direct consequence of the competition between DEP and hydrodynamic mobility. Significantly, our results demonstrate a rapid method to form hybrid nanostructured materials.
Introduction Dielectrophoresis (DEP) combined with the emerging technologies in microfluidics has been proven as a robust method to rapidly manipulate, sort, and assemble biological and synthetic materials for a wide range of applications from novel material synthesis to biomedical diagnostics.1-3 In comparison to many other assembly techniques that employ interparticle and surface forces, such as electrostatic and van der Waals interparticle interaction4,5 and surface tension6,7 for spontaneous assembly, DEP offers an effective and controllable means for directed assembly of colloidal particles into structured materials. The manipulation and assembly of colloidal particles result from the acting dielectrophoretic force in a nonuniform AC electric field, where colloidal particles are polarized and move toward the high or low field points, depending on the orientation of induced dipoles with respect to the applied fields. The DEP force, FDEP, exerted on a colloidal particle (p) of radius a and complex permittivity ε˜ p, suspended in a medium (m) of ε˜ M, is derived from the classical Maxwell-Wagner (M-W) theory;1,2 and the time-averaged FDEP is given by
brms|2 〈FDEP 〉 ) 2πεMa3Re[ fcm(ω) ∇ |E
(1)
where the dipolar Clausius-Mossotti factor
fCM ) (ε˜p - ˜εm) ⁄ (ε˜p + 2ε˜m)
(2)
determines the orientation of induced dipoles; fCM is frequency (ω) - and medium conductivity-dependent, owing to the complex permittivity, ε˜ ) ε - iσ/ω where ε is the static permittivity and *
[email protected]. (1) Morgan, H.; Green, N. G. AC Electrokinetics: Colloids and Nanoparticles; Research Studies Press: Hertfordshire, U.K., 2003. (2) Pohl, H. A. Dielectrophoresis; Cambridge University Press: Cambridge, U.K., 1978. (3) Chang, H.-C. AIChE J. 2007, 53, 2486–2492. (4) Velikov, K. P.; Christova, C. G.; Dullens, R. P. A.; van Blaaderen, A. Science 2002, 296, 106–109. (5) Imhof, A.; Pine, D. J. Nature 1997, 389, 948–951. (6) Shmuylovich, L.; Shen, A. Q.; Stone, H. A. Langmuir 2002, 18, 3441– 3445. (7) Zhang, L.; Maheshwari, S.; Chang, H.-C.; Zhu, Y. Langmuir 2008, 24, 3911–3917.
σ is the conductivity. Thus, a crossover frequency, ωc, may be defined as
ωc )
1 2π
(σp - σm)(σp + 2σm) (εm - εp)(εp + 2εm)
(3)
at Re[fCM(ω)] ) 0 where fCM changes its sign.1,2 The DEP force can effectively vary particle mobility and interparticle interaction, resulting from AC-field induced dipoles on colloidal particles.1,2 For low-permittivity particles in aqueous media, particles move toward the high-field region at AC-field frequency, ω < ωc, referred to as positive DEP (p-DEP) and toward the low-field region at ω > ωc, referred to as negative DEP (n-DEP). DEP can be controlled by tuning multiple parameters such as AC-field strength and frequency as well as electrode geometry and wave function. For example, DEP has been recently applied to direct the assembly of colloidal particles into three-dimensional photonic crystals8 much more easily than lithographic and other microfabrication technologies5-7,9,10 DEP-induced colloidal assembly has also been used to fabricate micro/nanodevices and biosensors.3,11-13 However, most studies of DEP-induced colloidal assembly have focused on monodisperse systems. The coassembly of polydisperse particles or different particles in nature, such as live cells and synthetic particles to form functional hybrid structures, biomaterials, and nano/biodevices, have been few. Furthermore, the capability of precisely controlling the functionality, selectivity, and final structure of assembled synthetic or biological micro/nanoparticles under DEP remains very limited, due to inadequate understanding of the subtleties of DEP mechanisms. Puzzling DEP behaviors arise in a broad range of complex fluids. For example, recent experiments with latex particles,14,15 nanocolloids,16,17 and nanowires18 have shown strong size and frequency dependence of the DEP behaviors of colloidal particles (8) Docoslis, A.; Alexandridis, P. Electrophoresis 2002, 23, 2174–2183. (9) Yang, P. D.; Deng, T.; Zhao, D. Y.; Feng, P. Y.; Pine, D.; Chmelka, B. F.; Whitesides, G. M.; Stucky, G. D. Science 1998, 282, 2244–2246. (10) Braun, P. V.; Wiltzius, P. Nature 1999, 402, 603–604. (11) Velev, O. D.; Kaler, E. W. Langmuir 1999, 15, 3693–3698. (12) Gagnon, Z.; Chang, H.-C. Electrophoresis 2005, 26, 3725–3735. (13) Gordon, J. E.; Gagnon, Z.; Chang, H.-C. Biomicrofluidics 2007, 1, 044102.
10.1021/la8013392 CCC: $40.75 2008 American Chemical Society Published on Web 10/09/2008
Binary Colloidal Suspensions
Langmuir, Vol. 24, No. 21, 2008 12165
and their resulting assemblies, deviating from the predictions of the classical Maxwell-Wagner theory1,2 in which ωc is independent of particle size. Recent DEP theory has significantly advanced by taking the double-layer conduction effects into account:14,19,20 The surface ionic current arises from distinct contributions from Stern-layer and diffuse-layer conductance of the low-permittivity latex particles and produces the effective particle conductivity, σp. Thus, σp is defined as the combination between the bulk conductivity, σo, and the surface conductance over particle radius, a, in the following expression:
σp ) σo + 2(Kd + Ks) ⁄ a
(4)
where Kd and Ks are the surface conductance of the diffuse layer and Stern layer, respectively. Furthermore, the crossover frequency is predicted to be inversely proportional to the product of particle size and characteristic length of the double layer, which could be the Stern-layer thickness or Debye length depending on medium conductivity.20 However, direct experiments to examine the dynamic double-layer effect on DEPinduced colloidal assembly in aqueous media where medium conductivity is varied have been few. Furthermore, complexity could arise from charged and/or highly polydisperse colloidal particles20,21 in that particle polarization and the screening effect might become more complicated, owing to the presence of neighboring charged nanocolloids to vary the mutual polarization interactions between particles.21 In this work, we examine the structural evolution of binary colloidal suspensions under DEP. We simultaneously manipulate and visualize latex particles of two different sizes under positive DEP to examine the effects of particle size ratio, frequency, and medium conductivity on the segregation and structure of binary colloidal suspensions. Surprisingly, we find a curious lowfrequency threshold for the onset of colloidal accumulation, which is unique for polydisperse colloidal suspensions. Medium conductivity and particle size ratio are found to shift both threshold frequency and crossover frequency of colloidal particles; we can thereby effectively tune the frequency window to direct colloidal assembly under positive DEP. Below, we report the enriched phase diagram for DEP-induced assembly of binary colloidal suspensions on the dependence of frequency, medium conductivity, and size ratio in details.
Experimental Section Materials. Fluorescent latex particles of radius a in the range of 150 to 460 nm and polydispersity 99%) is added to binary latex suspensions to vary (14) Green, N. G.; Morgan, H. J. Phys. Chem. B 1999, 103, 41–50. (15) Castellanos, A.; Ramos, A.; Gonzalez, A.; Green, N. G.; Morgan, H. J. Phys. D 2003, 36, 2584–2597. (16) Gierhard, B. C.; Howitt, D. G.; Chen, S. J.; Smith, R. L.; Collins, S. D. Langmuir 2007, 23, 12450–12456. (17) Yuan, Y. J.; Andrews, M. K.; Marlow, B. K. Appl. Phys. Lett. 2004, 85, 130–132. (18) Dimaki, M.; Boggild, P. Nanotechnology 2005, 16, 759–763. (19) Ermolina, I.; Morgan, H. J. Colloid Interface Sci. 2005, 285, 419–428. (20) (a) Basuray, S.; Chang, H.-C. Phys. ReV. E 2007, 76, 060501. (b) Chang, H.-C. Basuray, S.; Wei, H.-H. Phys. ReV. E. preprint. (21) Huang, J. P.; Karttunen, M.; Yu, K. W.; Dong, L. Phys. ReV. E 2003, 67, 021403.
Table 1. Binary Latex Particles of Radii aL and aS Mixed in 1:1 Volume Ratio in Aqueous Media small particle, aS (nm)
large particle, aL (nm)
size ratio, aL/aS
150 250 360 200 200
460 460 460 360 250
3.07 1.84 1.28 1.8 1.25
σm from 5.6 × 10-4 S/m to 2.71 S/m (corresponding to salt molar concentration from 5 × 10-6 to 9.1 × 10-4 mol/L), which is measured by a conductivity meter (Cole-Parmer, model #1481-90). Microelectrode Device. A pair of coplanar microelectrodes are fabricated onto a glass coverslip (Fisher Scientific) using the photolithographic technique as shown in Figure 1b. The glass substrate is first spin-coated with a thin layer of hexamethyldisilazane (HMDS) followed by a thin layer of photoresist (PR5413) coating before the microelectrode pattern is imposed by ultraviolet light. Subsequently, we symmetrically deposit a pair of square gold thin layers of 40 × 40 µm2 in area and 30 nm in thickness with a separation distance of 50 µm by the method of chemical vapor deposition onto a glass coverslip that was predeposited with a thin layer of titanium of ∼10 nm thick to enhance gold-glass bonding. The fabrication is completed by photoresist dissolution and metal liftoff in acetone. The center of electrodes is connected to a function generator (Agilent 33220A) via copper tape and wire. In the experiments to examine the effect of applied AC-electric field strength, we also use the microelectrodes in a quadrupole design using the same photolithographic technique, in which, as shown in Figure 1c, an array of microelectrodes are designed as four triangular posts with an inner square of 40 µm × 125 µm and separated by 20 µm from each other.13 The quadrupole electrode array produced an electric field of absolute minimum at the center of the array and absolute maximum along the edge of the electrodes with AC-field strength more than 40 times stronger than that of the coplanar design at the same peak-to-peak amplitude, Vpp. A clean plastic sample cell, injected with 300 µL of binary latex suspension, is sealed onto the microelectrode-embedded glass surface with UV optical glue, as illustrated in Figure 1. AC-electrical potential of constant Vpp ) 5 V at varied frequency ω from 20 kHz to 4 MHz is applied across two microelectrodes by the function generator. The detailed AC-field gradient for this electrode design has been reported in the literature.1,15 The simplified electrical field lines are idealized, indicating that the electrical field becomes the strongest near the edges of electrodes and weakens into the suspension. Characterization. We visualize the motions and structural evolution of the binary suspension using confocal laser scanning microscopy (Zeiss LSM 5 Pascal) with a 63× objective lens (NA ) 1.4, oil immersion) at real-time and single-particle resolution. Fluorescent latex particles labeled with the same dye are illuminated by a tunable argon laser at excitation wavelength λex ) 488 nm, and image acquisition is taken at emission wavelength λem ) 508 nm. Z-stack and time-series fluorescent micrographs are taken in the resolution of 512 × 512 pixels over an area of 50 × 50 µm2. Particle centroids are identified using ImageJ between the two electrodes above the glass substrate to distinguish particles of different sizes and analyze their packing configuration at varied AC-field frequencies. Centroids are then reconstructed using the persistence of vision raytracer (POV-Ray)22,23 with false colors to distinguish particles of different sizes (see Figures 3 and 5).
Results and Discussion Frequency Limits for Binary Colloidal Assembly under p-DEP. We start our discussion by examining the frequency limits for coassembly of the binary suspension under p-DEP. The upper frequency limit for p-DEP in our system is determined (22) Crocker, J. C.; Grier, D. G. J. Colloid Interface Sci. 1996, 179, 298–310. (23) The POV-Ray routine is modified from the freeware POV-Ray downloaded from http://www.physics.emory.edu/∼weeks/idl/mkpov.html.
12166 Langmuir, Vol. 24, No. 21, 2008
Hoffman et al.
Figure 1. Schematic diagram of the DEP experimental setup. Simplified nonuniform AC-field lines (dash lines) are idealized, indicating that the electric field becomes the strongest at the edge of electrodes and weakened into the suspension.
Figure 2. Measured crossover frequency, ωc, for latex particles of a ) 460 nm (circles) and 250 nm (triangles) and threshold frequency, ωth, (squares) against medium conductivity, σm. The slope of 1/2 indicates that ωth scales with σm0.5 at the high σm regime. Inset: Fluorescent micrographs illustrate that colloidal particles are (i) driven toward the high field regions near the edge of microelectrodes and form aggregates under positive DEP (p-DEP) at applied frequency ω < ωc and (ii) repelled away from microelectrodes and diffuse into colloidal suspension under negative DEP (n-DEP) at ω > ωc.
by ωc of large particles at a given σm. The crossover frequency for latex particles is experimentally determined as the frequency, where collected fluorescent particles become repelled away from the electrode edges into the AC-field minima. As shown in Figure 2, the crossover frequency for latex particles of a ) 460 and 250 nm measured in the binary suspension shows a clear size dependence, consistent with recent reports on monodisperse latex particles of similar sizes;14 moreover, we observe that, for both particle sizes, ωc is σm-independent at low σm but decreases monotonically at increased σm in the limit of high salt concentrations. The strong dependence of measured ωc on particle size and medium conductivity agrees well with the improved Maxwell-Wagner theories. Combined surface conductance, K ()Ks + Kd) is obtained from measured ωc by fitting with eqs 3 and 4: For low σm ( 0.03 S/m, the binary latex system shows no sign of transient segregation or stable structures and instead shows a strong preference for accumulating large particles near the microelectrode edges. Instead, for the cases of σm increasing from 0.03 to 2.1 S/m, it is striking to observe the inverted segregation with disordered aggregates of small particles near the microelectrode edges at all the frequencies, ωth < ω < ωc,L as shown in Figure 5c, possibly due to the pronounced screening effect at high salt concentrations. In addition, the critical frequency for the onset of inverted segregation shifts to lower frequency at increased σm, suggesting the presence of a screening effect on the DEP behaviors of colloids as well as the resulting assembly under p-DEP. On the basis of the recent theoretical and experimental observation that ωc of nanocolloids of a ) 50-250 nm increase with increasing σm or decreasing a, we speculate that Re[fCM] of 250 nm latex particles increases much more than that of 460 nm particles at high σm,30,31 resulting in a shift in the intersection frequency of the frequency-dependent DEP mobility for 250 and 460 nm particles to lower frequency. Yet, the accurate scaling prediction of inversion frequency versus σm is unavailable due to the currently inadequate understanding of interfacial polarization mechanism for high ionic strengths.14,20,32 The ω-σm phase diagram of binary assembly structures is summarized in Figure 6 for the mixture of latex particles of a ) 250 and 460 nm in aqueous media. It clearly shows that the addition of salt could influence both the interfacial polarization of colloids and packing configuration of DEP-induced coassembly of particles: Higher σm results in higher threshold assembly frequency and conversely lowers the critical frequency for the transition of segregation to the disordered phases, both of which can be attributed to the dynamic double layer effects on colloid polarization in AC-fields.20 Effect of Size Ratio. To examine the generality of the effects of frequency and medium conductivity on DEP behaviors and resulting assembly in binary colloidal suspensions, we also study the size effect with binary latex particle mixtures of varied size ratios as listed in Table 1. Recently improved DEP theory predicts that ωc scales with D/λa, where D is ion diffusivity and ∼1.31 × 10-9 m2/s for Na+ ions,33 and λ is the characteristic length of particle double layer in aqueous media and approximates to the Stern-layer thickness or Debye length for low or high salt concentrations, respectively.20 As shown in Figure 7, the control experiment with monodisperse latex particles in deionized water of σm ) 5.6 × 10-4 S/m clearly exhibits the linearity of ωc versus 1/a, in good agreement with theoretical prediction.20 However, it is rather striking to see in Figure 7 that the presence of particles of different sizes in the binary suspension leads to a considerable change in ωc. Considering the size dependence of induced dipolar interactions, we speculate that the neighboring particles of different sizes might impose a considerable secondary dielectrophoretic force on a single particle in addition to the dominant electrokinetic effect directly from applied AC-fields as suggested by recent DEP theory.21 However, the quantification of the effect of additional components on AC-induced dipoles demands more rigorous DEP theory and future experimental investigation. In addition, we observe the interesting effect of size ratio on the critical frequency to induce inverted segregation, as shown in Figure 8. We focus on the particles of aL ) 460 nm mixed (31) Kumar, A.; Qiu, Z.; Acrivos, A.; Khusid, B.; Jacqmin, D. Phys. ReV. E 2004, 69, 021402. (32) Scott, M.; Paul, R.; S Kaler, K. V. I. J. Colloid Interface Sci. 2000, 230, 377–387. (33) Gonzalez, A.; Ramos, A.; Green, N. G.; Castellanos, A.; Morgan, H. Phys. ReV. E 2004, 61, 4019.
Binary Colloidal Suspensions
with aS ) 150 nm, 250, and 360 nm separately in deionized water. It shows that the critical frequency for the onset of inverted segregation shifts to much lower frequency upon increasing size ratio, R ()aL/as), which indicates the narrowed frequency window that produces ordered domains under p-DEP. We also explore the effect of size ratio on the formation of binary crystalline structures;4,34 yet, we do not observe any particular binary crystal structure possibly due to limited size ratios and fixed volume fraction in this work. In the future, binary colloidal crystal by DEP could be further explored by varying particle volume ratio and several parameters in applied ACfields such as electrode geometry and waveforms.
Conclusion Assembly of binary latex particles from aqueous suspensions under positive DEP by the application of nonuniform AC-electric field is systematically examined in this work. Strong dependence of AC-field frequency, colloidal particle size, and medium conductivity on dielectrophoretic behavior has been observed. The applicable assembly frequency window determined by the low-frequency threshold and DEP crossover frequency can be effectively tuned by varying medium conductivity and particle size, suggesting that the dynamic double-layer effect plays a critical role in the interfacial polarization of micrometer- to submicrometer-sized particles. The segregation and structure p-DEP induced colloidal aggregation in binary suspensions are (34) Schofield, A. B.; Pusey, P. N.; Radcliffe, P. Phys. ReV. E 2005, 72, 031407.
Langmuir, Vol. 24, No. 21, 2008 12171
a result of combined DEP mobility and hydrodynamic diffusivity of binary particles in aqueous suspension. On the basis of the above dielectrophoretic behaviors of binary latex particles, we obtain a frequency-medium conductivity phase diagram to map different assembly patterns observed in binary colloidal particles of selected size suspended in aqueous media of varied salt concentration under applied AC-fields of varied frequency. The transition from segregation of ordered assemblies by particle size to inverted segregation of amorphous aggregates can be determined by the relative strength of DEP mobility difference between particles of two different sizes to the diffusivity of small particles. Our results also demonstrate that peculiar binary crystalline assemblies could possibly be formed by strategically selecting the appropriate particle size ratio as well as applied AC-field frequency, which could be useful for the rapid synthesis of novel, functional nanostructured materials. Acknowledgment. We thank Hsueh-Chia Chang, Sagnik Basuray, and Zachary Gagnon for valuable discussions. We are grateful to Dan Ho for his experimental assistance. This work was supported by the National Science Foundation (CBET0730813) and the Department of Energy, Division of Materials Science (DE-FG02-07ER46390). Supporting Information Available: Micrographs of DEPinduced colloidal assembly in monodisperse suspensions, indicating no frequency dependence of assembly structures under p-DEP. This material is available free of charge via the Internet at http://pubs.acs.org. LA8013392
