Electric-Field-Induced Reversible Phase Transitions in Two

Sep 7, 2015 - Two-dimensional colloidal crystals confined within electric field traps on the surface of a dielectrophoretic cell undergo reversible ph...
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Electric-Field-Induced Reversible Phase Transitions in TwoDimensional Colloidal Crystals Kelsey A. Collins,‡ Xiao Zhong,‡ Pengcheng Song,‡ Neva R. Little,‡ Michael D. Ward,‡ and Stephanie S. Lee*,† †

Department of Chemical Engineering and Materials Science, Stevens Institute of Technology, Hoboken, New Jersey 07030, United States ‡ Molecular Design Institute and Department of Chemistry, New York University, New York, New York, 10003, United States ABSTRACT: Two-dimensional colloidal crystals confined within electric field traps on the surface of a dielectrophoretic cell undergo reversible phase transitions that depend on the strength of the applied AC electric field. At low field strengths, the particles adopt a two-dimensional hexagonal close-packed lattice with p6m plane group symmetry and the maximum achievable packing fraction of φ = 0.91. Higher electric field strengths induce dipoles in the particles that provoke a phase transition to structures that depend on the number of particles confined in the trap. Whereas traps containing N = 24 particles transform to a square-packed lattice with p4m symmetry and φ = 0.79 is observed, traps of the same size containing N = 23 particles can also pack in a lattice with p2 symmetry and φ = 0.66. Traps with N = 21, 22, and 25 particles exhibit a mixture of packing structures, revealing the influence of lateral compressive forces, in addition to induced dipole interactions, in stabilizing loosely packed arrangements. These observations permit construction of a phase diagram based on adjustable parameters of electric field strength (0−750 V/cm) and particle number (N = 21−25).

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INTRODUCTION Colloidal particles typically assemble in entropically favored close-packed structures as a consequence of hard sphere repulsion and decreased excluded volume.1,2 The formation of non-close-packed structures has been accomplished by a variety of methods, including manipulating particles with optical tweezers,3 endowing particles with specific and directional interactions,4−6 and confining particles in tailored geometries.7−10 Reversible fluid−solid transitions can be achieved by adjusting the temperature,11−13 electric field strength14,15 or other parameters,16,17 and phase transitions between different solid-state packing structures have been provoked in threedimensional colloidal crystals.18,19 Reversible phase transitions between different packing arrangements in two-dimensional colloidal crystals, however, have not been observed. Switching between different packing arrangements in response to external stimuli can be challenging because it requires the controlled modulation of interparticle interactions. Recent investigations have employed dielectrophoresis (DEP) to organize colloidal particles, wherein an external AC electric field induces dipolar interactions between particles that provoke assembly into solidlike structures in both two5,15,20−22 and three dimensions.19,23,24 For two-dimensional colloidal crystals assembled in DEP cells with opposing electrodes deposited on the same flat surface, the electric field polarizes colloidal particles along the field lines, typically resulting in the formation of linear chains that aggregate into colloidal crystals. © XXXX American Chemical Society

The formation of two-dimensional colloidal crystals in electric fields hinges on the balance of forces exerted on the particles. In the absence of an applied force, the formation of twodimensional colloidal crystals is often precluded by Brownian motion at low particle concentrations. DEP forces can overcome Brownian motion and guide particle assembly through in-plane and out-of-plane gradients in the electric field strength, E.25 The DEP force can either concentrate particles into a region of maximum field strength (positive DEP) or repel them from that region (negative DEP), depending on the relative dielectric constants of the particles and medium.26 The DEP force depends on the magnitude of the electric field (actually the square of E) and the gradient of the field. DEP is independent of field direction, allowing the use of AC fields. We herein report reversible phase transitions in 2D colloidal crystals in a negative DEP cell through a combination of electric field strength and geometric confinement in electric field “traps.” These traps, defined by dielectric posts fabricated by conventional lithography, serve as an array of local potential wells on the cell surface, thereby stabilizing particle assemblies by screening the lateral and vertical DEP forces. At E < 300 V/ cm, spherical colloidal particles of poly(methyl methacrylate) (PMMA) in the traps exhibit the customary hexagonal closeReceived: August 27, 2015

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Langmuir packed lattice with p6m plane group symmetry. At higher electric field strengths, the p6m lattice transforms to less densely packed lattices with p4m symmetry or p2 symmetry. Modeling of the electric field in the traps suggests that the transformation is provoked by increased dipolar interactions between adjacent particles as a consequence of increasing electric field strength and lateral compressive forces at the open sides of the traps. Surprisingly, the packing arrangements at high electric field strengths are sensitive to the number of particles in the traps. These observations permit construction of a phase diagram based on adjustable parameters of electric field strength (0−750 V/cm) and particle number (N = 21−25). Collectively, these observations reveal the effect of steric confinement and anisotropic forces on colloidal particle packing.

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EXPERIMENTAL SECTION

Figure 1. Optical micrographs of the working region of DEP cells containing 1.3 μm spherical colloids dispersed in water in the absence (A, B) and presence (C,D) of dielectric posts at electric field strengths of E = 200 and 750 V/cm.

Fabrication of Dumbbell-Shaped Posts. Dumbbell-shaped posts were patterned onto borosilicate glass wafers (University Wafer) using a top-down approach. SU-8 2002 negative photoresist (Microchem Corporation) was spun cast at 5000 rpm for 30 s onto an O2 plasma-treated wafer and subsequently baked at 95 °C for 60 s. After cooling to room temperature, the wafer assembly was exposed to 360 nm UV light at an intensity of 80 mJ/cm2 for 55 s through a photomask (Image Technology). The wafer assembly was then baked for 95 °C for 60 s and allowed to cool to room temperature prior to submersion in SU-8 developer for 60 s to remove unexposed photoresist. After developing, the wafer assembly was rinsed with fresh SU-8 developer and isopropyl alcohol and then dried with air. Fabrication of DEP Cell. Ag (50 nm) was thermally evaporated onto the wafer assembly. A 40 μm-diameter rectangular capillary tube (Vitrocom) was used as a shadow mask to define the electrodes. Two glass coverslip spacers were attached on either side of the electrodes using a UV-curable adhesive (Norland Products). A third coverslip was attached on top of the spacers to define the crystallization chamber. Copper wires were attached to the electrodes using silver paint. Directed Assembly of Particles. Spherical PMMA-based particles (1 wt %, 1.3 μm; Bangs Laboratories) were dispersed in deionized water with 0.2 wt % BASF 108 pluronic block copolymer surfactant to prevent particle aggregation. After sonication at room temperature for 1 h, the dispersion was loaded into the crystallization chamber via capillary forces. Once filled with the colloidal suspension, the ends of the chamber were sealed with a UV-curable adhesive (Norland Products). After allowing approximately 15 min for the particles to settle on the cell surface, an AC electric field was applied across the electrodes using a function generator (BK Precision) at a frequency of 10 kHz and voltages ranging from 0 to 30 V. During application of the AC electric field, the working region of the DEP cell was observed via optical microscopy. For electric field switching experiments, the working region of the DEP cell was observed as the voltage was repeatedly switched between 8 and 300 V, corresponding to electric field strengths of 200 and 750 V/cm, respectively. At each voltage, a set of 25 images was collected at 0.5 s intervals. COMSOL Modeling. The predefined electrostatics package in COMSOL Multiphysics version 4.4 (www.comsol.com) was used to simulate the electric field strength in the working region of a DEP cell during application of an AC electric field. The dielectric constants of water and the SU-8 posts were assumed to be 78.4 and 2.8, respectively. The modeling was performed in the absence of colloidal particles.

field traps and at an applied field of 200 V/cm ≤ E ≤ 750 V/ cm, Brownian motion of the particles precluded the formation of stable linear chains of particles, which otherwise can be observed for particles with larger diameters14,15,20,25 (Figure 1A, B). At the higher field, the upward DEP force on the particles exceeded the downward force of gravity, lifting the particles from the lower glass surface (Figure 1B). Dumbbell-shaped SU-8 photoresist posts, average height h = 2.5 μm, were fabricated on the surface of the DEP cell by lithography. In the absence of an electric field, the colloidal particles moved randomly due to Brownian motion, colliding with the posts. At E = 200 V/cm, in the direction perpendicular to the long axes of the posts, the colloidal particles densified within the regions between the posts. Excess particles remained in the intercolumn spaces (Figure 1C). At E = 750 V/cm, the particles residing between adjacent posts remained on the DEP cell surface. Excess particles outside the traps lifted from the cell surface and were disordered (Figure 1D; excess particles are not in the focal plane). Modeling of the electric field strength in the working region of the DEP cell using the electrostatics module in COMSOL software revealed the existence of local electric field minima in the regions between the dumbbell-shaped posts, creating isolated electric field traps (Figure 2A, B). Simulations of the electric field at 0 V/cm ≤ E ≤ 750 V/cm suggested linear dependence of the electric field strength in the traps on the applied electric field strength, with Etrap = 0.3Eapplied (Figure 2C). The dielectric constant of the PMMA-based particles (ε = 2.6) is significantly smaller than that of the dispersion medium, water (ε = 78.4). As such, the particles are attracted to regions of low electric field strengths (negative DEP), with the particles densifying in the traps between adjacent posts under an applied electric field. Moreover, the posts screen the electric field in the direction perpendicular to the substrate surface, such that the particles in the traps remain on the cell surface even at high field strengths of E = 750 V/cm, the highest field strength examined. These findings are consistent with similar modeling experiments of DEP microfluidic devices that employ insulating cylindrical posts to create electric field minima, where cells and microorganisms can be trapped.27−29 Closer inspection revealed that the particle packing arrangements depend on the electric field strengths and number of

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RESULTS AND DISCUSSION In a typical experiment, aqueous suspensions of PMMA-based colloidal particles, average diameter d = 1.3 μm, were added to a coplanar DEP cell, which was located in the optical path of a video microscope operated in transmission mode (see Experimental Section for details). In the absence of electric B

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Figure 4. Optical micrographs and corresponding Fourier transforms of the same trap at E = 750 V/cm and N = 23 particles at different time points in a switching experiment. The particles can either adopt (A) a square lattice with p4m symmetry (φ = 0.79) with a single vacancy or (B) a lattice with p2 symmetry (φ = 0.66).

particles, N, in the electric field trap. Hexagonal packing exhibiting p6m symmetry with a maximum packing fraction of φ = 0.91 was observed at E = 200 V/cm and N = 24 (Figure 3A). Increasing the electric field strength to E = 750 V/cm, however, provoked a transition to a square-packing arrangement exhibiting p4m symmetry and φ = 0.79, among the particles in the center rows of the trap, while particles in the top and bottom rows remained confined along the edge of the neck of the dumbell post (Figure 3B). Finite Fourier transforms (FFTs) of the images confirmed the phase transition from hexagonal to square packing at the higher field. The colloidal particles in the traps were easily distinguishable by optical microscopy, and their movement during the phase transition could be tracked directly. Superposition of the particle positions at E = 200 and 750 V/cm revealed that the phase transition from hexagonal to square packing occurred simply by a lateral shift of the center row (Figure 3C). At the lower field strength, induced dipole interactions between colloidal particles in traps appear to be insufficient to overcome random Brownian motion in the trap, which would favor the

Figure 2. (A,B) Top and side profiles of the simulated electric field strength in an array of dumbbell-shaped posts at E = 200 V/cm using the electrostatics package in COMSOL. Arrows indicate electric field direction. (C) Graph of the simulated electric field strength between adjacent dumbbell posts at different applied electric field strengths.

Figure 3. (A, B) Optical micrographs and corresponding finite Fourier transforms of colloidal crystals confined within a trap at E = 200 and 750 V/ cm, respectively. (C) Overlay of particle positions in cavities at E = 200 V/cm (red) and 750 V/cm (blue). (D) Intensities of the (11) reflection of hexagonally packed crystals (red) and the (10) reflection of square-packed crystals (blue) in the FFT images of a colloidal crystal confined in a trap (left y-axis) as the applied electric field strength is switched between 200 and 750 V/cm in 12.5 s intervals (right y-axis). C

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Figure 5. (A) Optical micrograph of a trap at E = 750 V/cm and N = 22. (B) Two possible configurations of particles when only square packing is present (top) and when both square and hexagonal packing are present (bottom). (C) Optical micrograph of a trap at E = 750 V/cm and N = 21. (B) Two possible configurations of particles when only square packing is present (top) and when both square and hexagonal packing are present (bottom). In (B) and (D), the experimentally observed particle configurations are highlighted by a box.

prevented by the presence of the dumbbell posts, thus enforcing lateral alignment of particle chains. The reversibility of the electric field-induced phase transition was examined by switching the electric field between E = 200 and 750 V/cm at 12.5 s intervals. The relative amounts of hexagonal and square particle packings were determined from the intensities of the hexagonal (11) reflection and the square (10) reflection in the Fourier transform, as denoted in Figure 3A and B. The phase transition was reversible and rapid on the measurement time scale, such that both phases were never observed simultaneously (Figure 3D). The transition from hexagonal packing to square packing requires expansion of the 2D lattice. The area available for 2D expansion during the phase transition is determined by the size and shape of the electric field trap and the number of particles in the trap. The colloidal particles are initially distributed randomly when first introduced to the DEP cell, exhibiting nonuniform concentrations locally as they settle on the DEP cell surface due to random density fluctuations. Consequently, the number of particles confined in the traps varies somewhat. The traps are uniform in area; therefore the area available for expansion during a phase transition is expected to depend on the number of particles in a trap. For example, traps with N = 23 particles exhibited a square packing phase with a single vacancy at E = 750 V/cm (Figure 4A). Interestingly, a lattice exhibiting p2 symmetry (α = 103°) also was observed when switching from E = 200 to 750 V/cm (Figure 4B), with near equal occurrence (ca. 40%). The packing fraction of the p2 phase is φ = 0.66, less than either the square or hexagonal phase. Traps containing N = 23 particles have more room for expansion than for N = 24, enabling the formation of phases with lower packing fractions. Traps with N = 22 particles exhibited the close-packed hexagonal phase at E = 200 V/cm, but at E = 750 V/cm the FFTs revealed a mixture of square and hexagonal packing within a single trap (Figure 5A). In the setting of Figure 5A, the upper and lower two rows exhibited square and hexagonal packing, respectively, and the middle row was incorporated into both crystal structures. This mixed phase can be explained by the unique dumbbell shape of the trap posts. The number of particles in the top and bottom rows is fixed at N = 3, whereas the number of particles in the middle three rows can vary somewhat. Traps with N = 22 requires five particles in two of the center rows and six in the third. In the square packing at high electric field strengths, one particle in the N = 6 row does not contact any particles along the electric field direction, which would be expected to be unstable because dipole−dipole

Figure 6. Optical micrographs and corrresponding Fourier transforms of a trap with N = 25 particles at (A) E = 200 V/cm and (B) E = 750 V/cm. (C) An overlay of the particle positions at E = 200 V/cm (red) and E = 750 V/cm (blue). Blue arrows indicate the direction of the lateral DEP force under negative DEP conditions. Outermost particles in the center row are labeled “1” and “2”.

close-packed hexagonal phase due to entropic considerations. At higher field strengths, the induced dipole interactions between adjacent particles are larger, encouraging alignment as linear chains along the field direction. The solid-state phase transition from hexagonal to square packing can be viewed as a competition between entropy maximization from excluded volume effects, favoring the closepacked hexagonal phase at low field strengths, and the maximization of interparticle dipole−dipole interactions at high field strengths. Interestingly, this phase transition is not observed for larger spherical particles crystallized in unconfined spaces, where particle chains can slide past one another along the electric field direction to achieve the lowest-energy hexagonal packing arrangement.15,21 Within the traps, however, particle chain shifting along the electric field direction is D

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Figure 7. (A) Phase diagram of the structures observed for different numbers of particles in traps. (B) Optical micrographs and corresponding FFT images of the various phases observed within the dumbbell traps. Packing structures were observed at 0 V/cm ≤ E ≤ 500 V/cm in 100 V/cm increments, at E = 625 V/cm, and at E = 750 V/cm for traps with 21 ≤ N ≤ 25 particles. The observed structures are labeled as fluid (F), hexagonal (H), square (S), oblique (O), or a combination of the different phases. The size of each frame is 13 × 13 μm. (C) Fraction of traps with 21 ≤ N ≤ 25 particles. Sample size = 71 traps. (D) Fraction of traps with 21 ≤ N ≤ 25 particles at various electric field strengths, E. Colors correspond to the phases labeled in A.

parallel to the electric field and compressive forces perpendicular to the electric field are necessary for its formation. The presence of a lateral compressive force exerted on particles was observed readily in traps with N = 25 particles, for which the center row contains N = 7 particles and the rows above and below contain N = 6. The trapped particles form the hexagonal phase at E = 200 V/cm (Figure 6A), but at E = 750 V/cm the Fourier transform revealed the simultaneous existence of the p6m and p2 phases (Figure 6B). Figure 6C depicts an overlay of the particle positions in the trap at E = 200 V/cm (red) and 750 V/cm (blue), with the direction of the lateral DEP force exerted on the particles denoted by blue arrows. In the center row, the particles labeled “1” and “2” shifted toward the center of the trap due to the lateral DEP force. The particles near Particle 2 adopted a packing structure with p2 symmetry as a consequence of the lateral force and interparticle dipole−dipole interactions combined. Because the available area for particle rearrangement within the trap was small compared with traps having fewer particles, the hexagonal-packed phase could not expand sufficiently to form a square-packed phase. The lateral compressive force thus frustrated formation of the less dense lattice arrangements, resulting in the formation of a defect near Particle 1 instead. The ability to examine packings over a range of electric field strengths and numbers of particles in the traps permitted construction of a phase diagram based on these adjustable parameters (Figure 7A). Six distinct phases are observed, the corresponding optical micrographs and FFTs of which are displayed in Figure 7B. The phase diagram was constructed by identifying the packing arrangements in 71 traps with 21 ≤ N ≤ 25 particles at 100 V/cm ≤ E ≤ 750 V/cm. The distribution of

interactions with adjacent particles along the field direction would be absent (Figure 5B, top). A lateral shift of this row results in hexagonal packing wherein all particles have nearest neighbors along the field direction (Figure 5B, bottom). The observation of a mixture of square and hexagonal packing in traps with N = 22 is consistent with the relative instability of the square packing phase compared to the hexagonal packing phase due to fewer nearest-neighbor contacts. Traps with N = 21 particles at E = 750 V/cm also exhibited mixed square and hexagonal packing (Figure 5C), with all center rows containing five particles. A square-packing arrangement would maximize interparticle dipole−dipole interactions at high field strengths (Figure 5D, top). Nevertheless, the particles adopted a mixed hexagonal and square packing configuration with a vacancy (Figure 5D, bottom), contrasting with the exclusive formation of square packing for N = 24 at E = 750 V/cm, in which every center row contains six particles. The formation of mixed packings at high electric field strengths when N = 21, accompanied by a vacancy, suggests the contribution of factors other than interparticle dipole−dipole interactions to packing in the traps. The calculated electric field strength map in Figure 2A reveals a sharp gradient at the open sides of the traps. This gradient results in a lateral negative DEP force exerted on the particles at the open sides of the traps, perpendicular to the electric field direction. This force compresses particles laterally within the traps to stabilize high-energy packing arrangements. The gradient in the electric field strength is limited to a narrow region at the edges of the posts; therefore the ends of center rows with N = 5 are sufficiently far from this edge that the lateral DEP force is weak. Because the square packing phase is less stable than the hexagonal packing phase, strong induced dipole interactions E

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intermolecular interactions, leading to the formation of structures with higher packing fractions.30,31 The phase diagram displayed in Figure 7A reveals the rich diversity in packing arrangements attainable over a range of electric field strengths and numbers of particles confined in the traps. It is reasonable to expect that the post geometry, orientation and spacing would affect orientation, structure and size of these packing arrangements. This can be illustrated by traps with N = 23, wherein rotating the dumbbell posts relative to the field direction altered the packing of the trapped particles. When the long axes of the posts were rotated 15° from an alignment perpendicular to the field direction, hexagonal packing persisted at E = 750 V/cm (Figure 8A), but the corresponding FFT revealed that the crystal orientation rotated 15° as well. Further rotation by 30° produced an oblique packing arrangement at E = 750 V/cm, however (Figure 8B). The dependence of packing arrangement on the applied electric field strength was also observed for larger traps, albeit to a weaker degree. Particles confined in dumbbell traps with twice the area of those above displayed mixtures of square, oblique and hexagonal packing structures within a single trap (Figure 8C). The presence of multiple packing arrangements in a single trap suggests that the spatial distribution and strength of the electric field within the traps can influence packing. The influence of post geometry, post spacing, and electric field distribution on specific packing structures warrants further examination through experiment and simulations.

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CONCLUSIONS The introduction of dielectric posts to the channels of coplanar DEP cells enables reversible and adjustable solid-state phase transitions in two-dimensional colloidal crystals. The posts create traps with tunable electric field strength that densify the particles and screen lateral and vertical DEP forces. Moreover, the geometrical confinement provided by the posts and tunable electric field strength within the traps can provoke particle alignment into non-close-packed structures. Examining the dependence of the packing behavior on the number of particles in the traps reveals the importance of both strong induced dipole interactions between particles parallel to the electric field lines and lateral compressive forces at the sides of the traps in stabilizing non-close-packed structures. These observations suggest that, through design of the sizes and shapes of the particles and traps, reversible solid-state phase transitions between close-packed structures and less accessible non-closepacked arrangements can be reliably achieved.

Figure 8. (A, B) Optical micrographs and corrresponding Fourier transforms of traps at E = 750 V/cm in which the dumbbell posts have been rotated 15° and 30° relative to previous experiments in which the long axes were perpendicular to the field direction. (C) Optical micrograph of a DEP cell in which the post size and spacing were doubled at E = 750 V/cm.

particle numbers in the traps, displayed in Figure 7C, is expected to depend on the concentration of the colloidal particles. Figure 7D displays the distributions of phases observed for different electric field strengths and particle numbers. When E ≤ 200 V/cm, a fluid-like phase was observed for all traps, regardless of the value of N. At these low electric field strengths, the lateral DEP force at the side openings of the traps was weak and particles could traverse the open sides in either direction via Brownian motion. When 200 V/cm ≤ E ≤ 300 V/cm, the lateral DEP force was sufficient to confine the particles within the traps and hexagonal packing dominated. When E > 300 V/cm, the dominant packing arrangement depended on the number of particles in the trap. The formation of non-close-packed structures at high electric field strengths is driven by induced interparticle dipole−dipole interactions along the electric field direction. The observation that increased directional interparticle interactions provoked the formation of non-close-packed polymorphs is reminiscent of pressuredependent polymorphism observed in molecular crystals. At low pressures, molecules often form non-close-packed structures that maximize directional intermolecular interactions, such as hydrogen bonding. At high pressures, however, the pressure−volume work exerted on the crystal overcomes

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation under Award Nos. DMR-0820341 and DMR-1420073. S.S.L. was supported by the New York F

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(22) Zhang, K.-Q.; Liu, X. Y. In Situ Observation of Colloidal Monolayer Nucleation Driven by an Alternating Electric Field. Nature 2004, 429, 739−743. (23) Leunissen, M. E.; Sullivan, M. T.; Chaikin, P. M.; van Blaaderen, A. Concentrating Colloids with Electric Field Gradients. I. Particle Transport and Growth Mechanism of Hard-Sphere-like Crystals in an Electric Bottle. J. Chem. Phys. 2008, 128, 164508. (24) Sullivan, M. T.; Zhao, K.; Hollingsworth, A. D.; Austin, R. H.; Russel, W. B.; Chaikin, P. M. An Electric Bottle for Colloids. Phys. Rev. Lett. 2006, 96, 015703. (25) Juárez, J. J.; Bevan, M. a. Interactions and Microstructures in Electric Field Mediated Colloidal Assembly. J. Chem. Phys. 2009, 131, 134704. (26) Mittal, M.; Lele, P. P.; Kaler, E. W.; Furst, E. M. Polarization and Interactions of Colloidal Particles in AC Electric Fields. J. Chem. Phys. 2008, 129, 064513. (27) Martínez-López, J. I.; Moncada-Hernández, H.; Baylon-Cardiel, J. L.; Martínez-Chapa, S. O.; Rito-Palomares, M.; Lapizco-Encinas, B. H. Characterization of Electrokinetic Mobility of Microparticles in Order to Improve Dielectrophoretic Concentration. Anal. Bioanal. Chem. 2009, 394, 293−302. (28) Cummings, E. B.; Singh, A. K. Dielectrophoresis in Microchips Containing Arrays of Insulating Posts: Theoretical and Experimental Results. Anal. Chem. 2003, 75, 4724−4731. (29) Saucedo-Espinosa, M. A.; Lapizco-Encinas, B. H. Experimental and Theoretical Study of Dielectrophoretic Particle Trapping in Arrays of Insulating Structures: Effect of Particle Size and Shape. Electrophoresis 2015, 36, 1086−1097. (30) Hemley, R. J. Effects of High Pressure on Molecules. Annu. Rev. Phys. Chem. 2000, 51, 763−800. (31) Moggach, S. A.; Parsons, S.; Wood, P. A. High-Pressure Polymorphism in Amino Acids. Crystallogr. Rev. 2008, 14, 143−184.

University Postdoctoral and Transition Program for Academic Diversity.

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