Anal. Chem. 2007, 79, 7097-7103
Photophoretic Velocimetry for Colloid Characterization and Separation in a Cross-Flow Setup Clemens Helmbrecht, Reinhard Niessner, and Christoph Haisch*
Chair for Analytical Chemistry, Institute of Hydrochemistry, Technische Universita¨t Mu¨nchen, Marchioninistrasse 17, D-81377 Munich, Germany
We introduce photophoretic velocimetry as a new technique for characterization of particulate matter on the basis of optical particle properties. Complementary to well-established techniques, we could show that, by measuring the photophoretic velocity of the single particles, it is possible to distinguish particles of different sizes as well as particles of one size but different refractive indices. The difference in photophoretic migration of particles can be applied to the separation of particles. Polystyrene, melamine, and SiO2 microparticles (0.310 µm) suspended in purified water were used as test samples for validation of a cross-flow setup. The particles were pushed perpendicular to a uniform, pulsation-free fluid flow by a focused He-Ne laser (λ ) 633 nm, P ) 47 mW, Imax ) 14.0 kW cm-2) providing a well-defined Gaussian-shaped flux distribution. The migration behavior was observed by means of a video camera system, and the velocities and displacements were calculated by using an adapted particle imaging velocimetry code as an approach to automatic characterization. The photophoretic displacement depends on both flow conditions and particle properties and can be applied for separation means. Colloidal systems are suspensions of particles in a size range from some nanometers to several micrometers, suspended in water or other media. The term colloid refers only to the particulate property of a colloid and does not reveal any information about its chemical composition. As colloids are important in research and industry, e.g., environmental chemistry,1 biology, hydrogeology,2 finishing, and cosmetics, an exact analysis of numerous parameters such as particle size, number density, composition, and physical properties is of particular interest. A further step beyond the analysis of particle ensembles is the continuous separation of the particles according to their physical and chemical properties. State-of-the-art separation systems mainly address dielectrical,3 magnetic,4-6 hydrodynamic,7,8 or thermal properties9 of the particle/fluid system. * To whom correspondence should be addressed. E-mail: Christoph.Haisch@ ch.tum.de. (1) Buffle, J.; Leeuwen, H. P. v. Environmental Particles; Lewis Publishers, Inc.: Chelsea, MI, 1992. (2) Saiers, J. E.; Ryan, J. N. Water Resour. Res. 2006, 42, W12S01. (3) Gascoyne, P. R. C.; Vykoukal, J. Electrophoresis 2002, 23, 1973-1983. (4) Suwa, M.; Watarai, H. Anal. Chem. 2001, 73, 5214-5219. (5) Watarai, H.; Monjushiro, H.; Tsukahara, S.; Suwa, M.; Iiguni, Y. Anal. Sci. 2004, 20, 423-434. 10.1021/ac070875x CCC: $37.00 Published on Web 08/18/2007
© 2007 American Chemical Society
A new technique for the characterization of particles is the application of light-induced forces by an intense laser beam. Different refractive indices of transparent particles relative to the surrounding carrier fluid as well as light absorption by the particles result in a net force exerted on the particle due to momentum transfer of photons.5,10 Focusing a laser beam with high numerical aperture (NA) leads to immobilization of the particles in the focus. This effect is known as “optical trapping”. In a light beam only slightly focused with low numerical aperture or a collimated beam, the particles start to migrate along the beam axis while being trapped in radial direction. The migration induced by optical forces depends on the optical properties of the particle with respect to the fluid properties and is referred to as photophoresis (PP). Optical radiation forces have been widely studied and utilized for manipulation of microparticles and biological cells in liquid media. In 1970, Ashkin11 proved for the first time the viability of radiation pressure for migration and trapping on microparticles. This discovery opened the door to levitate and trap cells and other particles by various optical beam configurations and completed in single-beam optical traps.12-15 While stabilizing the position of single particles by a laser beam, different forces acting on single particles were measured undisturbed by Brownian motion.16 An industrial application is noncontact cleaning, where optical forces are applied to remove particles from surfaces.17 A slightly focused beam of an argon ion laser and an ytterbium fiber laser, respectively, moving cells over a distance of several millimeters, was tested as an approach to automated cell sorting systems by several groups.18-20 Optical tweezers for the sorting and manipula(6) Watarai, H.; Suwa, M.; Iiguni, Y. Anal. Bioanal. Chem. 2004, 378, 16931699. (7) Prestel, H.; Niessner, R.; Panne, U. Anal. Chem. 2006, 78, 6664-6669. (8) Giddings, J. C. Science 1993, 260, 1456-1465. (9) Geelhoed, P. F.; Lindken, R.; Westerweel, J. Chem. Eng. Res. Des. 2006, 84, 370-373. (10) van de Hulst, H. C. Light Scattering by Small Particles; Dover Publications: New York, 1981. (11) Ashkin, A. Phys. Rev. Lett. 1970, 24, 156-159. (12) Ashkin, A.; Dziedzic, J. M.; Bjorkholm, J. E.; Chu, S. Opt. Lett. 1986, 11, 288-290. (13) Ashkin, A. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 4853-4860. (14) Ashkin, A. IEEE J. Sel. Top. Quantum Electron. 2000, 6, 841-856. (15) Svoboda, K.; Block, S. M. Annu. Rev. Biophys. Biomol. Struct. 1994, 23, 247-285. (16) Walz, J. Y.; Prieve, D. C. Langmuir 1992, 8, 3073-3082. (17) Liebert, R. B.; Prieve, D. C. Ind. Eng. Chem. Res. 1995, 34, 3542-3550. (18) Buican, T. N.; Smyth, M. J.; Crissman, H. A.; Salzman, G. C.; Stewart, C. C.; Martin, J. C. Appl. Opt. 1987, 26, 5311-5316. (19) Mark, W.; Polatkan, A. E.; Esener, S. C. U.S. Patent 7,068,874 B2, 2006.
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tion of trapped particles in a microfluidic system have been described, e.g., by Applegate et al.21,22 The above-named techniques perform so-called “decision-based” separation grounded on distinct single-particle features like size, shape, color, or fluorescence. For discrimination between different types of particles, auxiliary information is needed. Hence, these techniques require sample pretreatment like fluorescence staining or additional measurements, e.g., analysis of the scattered light. In optical chromatography, a laser beam is guided into a flow tube in the direction opposite to the flow in a way that optic and fluid forces are balancing. The measuring parameter is the equilibrium position of particles in the flow tube. This parameter is directly linked to the particle’s intrinsic properties like size, refractive index, and shape. Imasaka23 et al. demonstrated for the first time separation of polystyrene particles with different sizes by means of optical chromatography. Eleven years later, two closely related spores Bacillus anthracis and Bacillus thuringiensis were separated in a microfluidic setup.24 Kononenko et al.25 used optical chromatography as a sample pretreatment in order to separate different colloid samples with identical hydrodynamic diameter before separation with asymmetric flow-field flow fractionation (FFF). Another promising approach to apply optical forces for the separation of colloids is based on a slightly different physical principle. Optical fields generating photophoretic gradient forces are applied, for example, by McDonald et al.26 and Lacasta et al.27 in the form of an optical lattice and by Cheong et al.28 in the form of a line-shaped focus with intensity gradient. These methods address the particle ensemble rather than single particles, which allows a high throughput but complicates the characterization of single particles. In this paper, we introduce a cross-flow approach as a further step toward a continuous separation system addressing optical properties. The setup’s advantage is its easy implementation, e.g., in microstructured devices as no complex beam shaping is required. The required laser power is significantly lower than for any similar approach described in the literature. Another difference to systems reported elsewhere is that our system addresses the properties of single particles rather than particle ensemble properties. A nearly Gaussian-shaped radiation field created by a focused laser beam is directed perpendicularly to the bulk flow in order to manipulate selected particles. This approach could be applied, for example, to push particles in regions of different flow conditions or even different flow channels and promises to have (20) Wang, M. M.; Tu, E.; Raymond, D. E.; Yang, J. M.; Zhang, H.; Hagen, N.; Dees, B.; Mercer, E. M.; Forster, A. H.; Kariv, I.; Marchand, P. J.; Butler, W. F. Nat. Biotechnol. 2005, 23, 83-87. (21) Applegate, R. W., Jr.; Squier, J.; Vestad, T.; Oakey, J.; Marr, D. W. M. Opt. Express 2004, 12, 4390-4398. (22) Applegate, R. W., Jr.; Squier, J.; Vestad, T.; Oakey, J.; Marr, D. W. M.; Bado, P.; Dugan, M. A.; Said, A. A. Lab Chip 2006, 6, 422-426. (23) Imasaka, T.; Kawabata, Y.; Kaneta, T.; Ishidzu, Y. Anal. Chem. 1995, 67, 1763-1765. (24) Hart, S. J.; Terray, A.; Leski, T. A.; Arnold, J.; Stroud, R. Anal. Chem. 2006, 78, 3221-3225. (25) Kononenko, V. L.; Giddings, J. C.; Myers, M. N. J. Microcolumn Sep. 1997, 9, 321-327. (26) MacDonald, P. M.; Spalding, C. G.; Dholakia, K. Nat. Biotechnol. 2003, 426, 421-424. (27) Lacasta, M. A.; Khoury, M.; Sancho, M. J.; Lindenberg, K. Mod. Phys. Lett. B 2006, 20, 1427-1442. (28) Cheong, C. F.; Sow, H. C.; Wee, S. A. T.; Shao, P.; Bettiol, A. A.; Kan, v. A. J.; Watt, F. Appl. Phys. B: Lasers Opt. 2006, 83, 121-125.
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Figure 1. Illustration of the Ray optics model to describe the forces acting on a microsphere for an off-axis and an aligned particle with respect to a Gaussian flux distribution. Magnitude of both flux and force is represented by the length of the arrows; reflected light is not shown.
the perspective of a continuous, noncontact, and gentle separation of microparticles. Both flow conditions and optical setup are substantially different from the techniques listed above. First, with the cross-flow setup, the beam is slightly focused whereas in the case of optical tweezers a high numerical aperture (typically NA > 1.0) is used. Second, a liquid flow is present perpendicular to the direction of photophoretic migration. This is different from optical chromatography where laser beam propagation and fluid flow act in opposing directions. Third, a HeNe laser system with a completely characterized flux distribution is applied allowing a precise correlation of experimental results with theoretical predictions. THEORY Detailed deduction of the theoretical background of PP can be found elsewhere;10,15,16,29-31 therefore, we focus on the fundamentals relevant for this work. Optical forces acting on macroscopic media by exchange of momentum are generally minute regarding the involved masses. Hence, no effect is observed. However, when geometrical dimensions shrink, as for microparticles, inertia, gravitational, and friction forces diminish, and optical forces are capable of moving, levitating, or trapping particles. A further requirement is that optical forces are dominant toward Brownian forces and other thermal induced forces. Figure 1 sketches the PP behavior of a small spherical particle with radius a depending on its position relative to a low divergent, coherent beam of wavelength λ and nominally Gaussian-shaped flux distribution (TEM00 mode) from, for example, a laser. The effective power Peff acting on a circular area with radius a is calculated from the flux distribution I(r)
Peff ) 2π
∫
a
0
rI(r) dr
(1)
whereas r denotes the distance from the center of a circular beam. In PP, Peff means the laser power acting on a centered, spherical particle with radius a. The total laser power P of the beam (29) Kerker, M. The Scattering of Light; Academic Press: New York, 1969. (30) Ashkin, A. Biophys. J. 1992, 61, 569-582. (31) Monjushiro, H.; Hirai, A.; Watarai, H. Langmuir 2000, 16, 8539.
corresponds to an infinite radius. In practice, the value of the total laser power of the laser beam is directly accessible by power measurement. In the case of a sphere with radius much larger than the wavelength, i.e., a . λ, the conditions for Mie scattering are satisfied and optical forces can be computed from ray optics. For particles with a refraction index n1 larger than the refraction index n2 of the surrounding medium, the particle acts like a spherical lens. When the light is focused in a way that the beam waist ω is much larger than the particle radius (a , ω), the refraction of the incident light leads to transfer of momentum to the particle. According to refs 31 and 32, the resulting net photophoretic force F acts on the particle, which can be given as follows
F)2
n2 P a 2 Q c ω
()
(2)
The fraction n2P/c denotes the incident momentum of a beam with total power P of a laser beam and velocity of light in vacuum c. In general, the photophoretic efficiency Q is a measure of the conversion of incident momentum into movement, ranging from zero (no conversion) up to two (total reflection). The friction force of a particle moving in a surrounding medium
FStokes ) 6πηav
(3)
counteracts the PP force, as the sphere is migrating with a PP velocity vph in a medium of viscosity η. By equating eq 1 and eq 2, the equilibrium velocity results:
vph )
1 n2 P aQ 3πc η ω2
(4)
The parameters n2 and η are defined by the carrier fluid. P and ω2 are dependent on the laser system and the optical configuration, respectively. The last term with particle radius and PP efficiency reveals information about the intrinsic properties of the particles. Since vph, further on addressed as photophoretic velocity, is experimentally accessible, Q can be calculated in a well-defined medium as a function of only the particle parameters. As illustrated in Figure 1, the net force acting on the particle can be decomposed in an axial component
Fa ) 2
n2 P a 2 Qa c ω
()
(5)
n2 P a 2 Qr. c ω
(6)
and a radial component
Fr ) 2
()
In all cases considered in this communication, the radial component acts in the direction to beam axis, thus centering the particles on the beam. To each force component a separate PP efficiency, Qr and Qa, can be assigned, representing the fraction (32) Kaneta, T.; Ishidzu, Y.; Mishima, N.; Imasaka, T. Anal. Chem. 1997, 69, 2701-2710.
Figure 2. Optical system for measuring photophoretic migration of particles.
of incident momentum converted in radial and axial momentum, respectively. For the discrimination of particles, the PP efficiencies are the key factors since they depend on the particle’s optical properties. It has been shown by several authors that Q is a complex function of several parameters, including particle size and index of refraction. There is an ongoing discussion about the theoretical computation of Q in the range a ≈ λ, as neither electromagnetic wave models nor ray optics give acceptable results. This size range is relevant for a multitude of particles, e.g., biological cells.15 EXPERIMENTAL SECTION Apparatus. The experimental setup, as it is presented in Figure 2, consists of the laser system generating the PP force (excitation laser), a flow cell, where the PP takes place, an illumination laser in combination with a digital camera system for visualization of the particles, and a microfluidic system, providing the sample flow. A cw HeNe laser (λLaser ) 633 nm, P ) 47 mW, Coherent Inc., Santa Clara, CA) at TEM00 mode was used to generate the PP force. The beam was focused by a planar-concave f ′ 40-mm lens (all optical components: Linos Photonics GmbH & Co. KG, Go¨ttingen, Germany) into the in-house-made flow cell. A laser power meter and a beam profiler (FieldMaxII Top LaserCam-HR, Coherent Inc.) monitored the beam parameters. The flow cell was assembled completely from Suprasil glass windows (Hellma GmbH & Co. KG, Mu¨llheim, Germany). It has a length of 26 mm (flow direction) and a cross section of 2.5 mm × 12.5 mm. The excitation laser beam entered horizontally through the small side, and observation was carried out from above through the wider side. Each end of the rectangular flow cell is closed by an aluminum block. The complete cell is mounted on a homemade xyz stage, which allows precision alignment of the flow cell relative to laser beam and camera. The experiments were carried out in the center of the flow cell, where all the walls are at least 1 mm apart to prevent undesired particle/wall interactions. In addition to the HeNe laser, a cw Nd:YAG laser (λ ) 532 nm, P ) 15 mW, OEM) was employed to illuminate the particles for camera observation. The beam profile was shaped by a cylinder lens (f ′ ) 63 mm) into a line profile to illuminate a thin horizontal plane (∼20 µm). The strong scattering light generated by the HeNe laser was filtered out with a band-pass filter (FD1G, λcenter ) 540 nm, Thorlabs GmbH, Munich, Germany). The migration was then observed by using the 90° scattered light from the green illumination laser by a CCD camera (Guppy F 080B, Allied Vision Technologies GmbH, Stadtroda, Germany) controlled by a computer via an IEEE 1394 interface. The digital images were recorded on hard disk with a frame rate of 7.5 frames/s. The image was Analytical Chemistry, Vol. 79, No. 18, September 15, 2007
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Figure 3. Schematic of microfluidic flow system including pump, splitter, and flow cell.
magnified with a macrooptic (ROD Makro CCD 6, Rodenstock GmbH, Munich, Germany) resulting in a field of 770 µm × 580 µm. Figure 3 shows the integration of the flow cell in the microfluidic system. The sample is pumped out of an open vessel by a microannular gear pump (mzr-2905, HNP Mikrosysteme GmbH, Parchim, Germany) into a homemade splitter. The pump allows high reproducible flow rates in the range of 100-5000 µL min-1 without pulsation. Yet, the flow rates are too high for a continuous PP separation. The flow was adjusted by a flow splitter according to the ratio of pressure drop along two PEEK capillaries 1 and 2, depending on the length and the inner diameter of the capillaries. In our case, the split ratio was set to ∼1:300, resulting in flow velocities in the flow cell up to ∼40 µm s-1 corresponding to a bulk flow of ∼1 µL s-1. In the experimental margin of error, a uniform flow profile with constant flow velocity free of pulsation over the area of view was ensured. The flow cell was filled with particle suspension via the microfluidic flow system. Careful filling was required in order to avoid the inclusion of air bubbles. Determination of Particle Velocity. The flow and PP velocities of particles were calculated using a particle imaging velocimetry (PIV) code. To our knowledge, it is the first approach of an automatic evaluation of PP migration. The code was developed under Matlab 7.1 (Mathworks, Natick, MA) and is based on the code MatPIV 1.6.1 published by Sveen.33 Generally, PIV is applied to calculate flow velocities of ensemble flows and neither for single particles nor for the tracking of pathways of single particles. It computes instantaneous velocities for two sequential images by pattern matching of several subwindows. Only by choosing a sufficiently small size of the subwindows in combination with low particle densities, velocity calculation of single particles becomes feasible. The algorithm output consists of the two-dimensional velocities found in each subwindow. A high particle density, where several particles are found in one subwindow, leads to an output velocity averaged over all particles in the window. For the present study, it was important to achieve single-particle properties; therefore, manual verification of the data was necessary to avoid mismatch of data. The PIV algorithm will be further improved; details and evaluation of relevant parameters will be published elsewhere. Following the procedures discussed there, we found an optimum subwindow size of 64 by 64 pixels, corresponding to an actual size of approximately 50 µm by 50 µm. Samples. PP migration was measured on the following selection of particles and sizes: The spherical polystyrene particles with diameters of 0.312, 0.68, 0.99, 1.90, 2.88, 4.13, and 5.09 µm (33) Sveen, J. K.: MatPIV 1.6.1, http://www.math.uio.no/∼jks/matpiv/, 2004.
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were purchased from Bangs Labs (Fishers, IN) and referred to as 300 nm, 700 nm, and 1, 2, 3, 4, and 5 µm hereafter. SiO2 particles with diameters of 1.0 µm were purchased from Merck (Darmstadt, Germany) and melamine particles from Bangs Labs (Fishers, IN), both spherical, with diameters of 1.1, 2.88, and 4.68 µm, respectively. The stock suspensions with colloidal contents between 7 and 12% were diluted with water purified by a Milli-Q system (Milli-Q 185 Plus, Millipore, Bedford, U.K.). In that way, the particle number density was adjusted to 1.2 × 10-6 cm-3 for all particle sizes, which corresponds to a visible number of ∼30 particles in each image. To avoid sedimentation of the bigger particles and agglomeration, all samples were prepared freshly for each experiment and were treated in an ultrasonic bath for 10 min immediately before application and never used for more than 30 min in an experiment. Ultrasonic treatment of the colloidal dispersions was necessary especially in the case of the 5.09-µm particles, as both sedimentation and agglomeration were observed. As predicted by theory and confirmed by our and other authors findings,11,13,30,31 particles in the laser beam instantaneously reach equilibrium velocity and stop immediately when the beam is blocked. PP migration of the particles in this work always points away from the light source; so-called negative PP migration was not observed. In all our experiments, the radial force centered the particles in the beam. RESULTS AND DISCUSSION Determination of Effective Power. Relevant for all PP motions is the effective power Peff, acting on the particle. As stated above, the PP force can be described according to eq 2 only on the assumption of a nearly Gaussian flux distribution of the incident beam and for particle dimensions significantly smaller than the beam waist, i.e., a , ω. Generally, these prerequisites are not fulfilled precisely and deviations lead to a significant error of the effective power calculation. Possible that the spot size is not known precisely, (2) the flux distribution of the laser beam differs considerably from a Gaussian distribution, and (3) the size of the particle is not small compared to the laser beam dimension. A more precise, but substantially more complex determination of the PP force requires the calculation of Peff by integrating the actual measured flux distribution in the limits of the illuminated particle surface as described by eq 1. For that purpose, the spot of the focused laser beam was magnified via a 20:1 projection on the beam profiler. Figure 4a documents the nearly perfect Gaussian distribution, which was recorded in the beam waist of the HeNe laser, for comparison correlated to the size of particles that are 2 and 5 µm in diameter. The characteristic 1/e2 diameter of the beam waist in air (2ω) is 22.1 ( 0.2 µm; the maximum flux in the beam center is 14.0 ( 0.2 kW cm-2 (n ) 10, 1 s). Due to the different refractive index the actual size of the focus in water slightly differs, which has to be accounted for when calculating the effective power. Under the above-described assumption concerning the laser beam and the particle size, eq 2 describes the correlation between Peff and the total power P
Peff ) 2P(a/ω)2
(7)
This idealized correlation is plotted in Figure 4b by a dotted line (1) for ω ) 11.05 µm. The numerical calculation of Peff from
Figure 5. Photophoretic velocity as a function of particle radius and laser flux (n ) 20, 1 s).
Figure 4. (a) Measured photon flux distribution of the HeNe laser beam (2ω ) 22.1 µm) and Gaussian fit. The total laser power of the beam at the focal plane is 27 mW, and the flux in the center of the beam 14.0 kW cm-2. (b) For a , ω, the effective power can be theoretically approximated (1). By measuring the beam profile, the exact effective power acting on the particle can be computed as a function of the particle radius (2). The data are highlighted for particle diameters of 2, 3, 4, and 5 µm (3).
the measured flux distribution according to eq 1 is depicted as a solid line (2). The data points are highlighted for particles diameters 2, 3, 4, and 5 µm (3). As expected, the idealization (1) is in good agreement with the experimental data for a , ω, while the deviations become considerably larger when the particle radius increases and Peff approaches the total laser power. After the full characterization of the beam parameter, a first set of experiments was carried out to quantify the correlation between the maximum flux in the center of the beam and PP velocity in the axial direction pointing in the propagation of the light. The laser beam was attenuated by a set of neutral density filters, thus delivering maximum fluxes of 14.0, 11.0, 7.6, and 4.0 kW cm-2. Neutral density filters for attenuation were chosen because of their negligible influence on the beam profile. The field of view of the camera was set on the focal zone of the laser beam. During a few measurements, especially with large particles, agglomerates of two or more particles were observed. They could be identified not only by direct, visual inspection but also by their significantly higher PP velocities. These increased velocities even gave clear indication of how many particles formed the agglomerate. In the interest of well-defined experimental conditions, we abstained from the use of chemical agents to avoid agglomeration and excluded agglomerates manually from the data sets. For calculation of PP velocities, data of single particles moving in the area illuminated by the focused laser beam were evaluated. During image capturing of particle migration, the sample flow remained stopped. The velocities of single particles were determined by averaging all velocities calculated by the PIV code for a particle migrating in the center of the beam over the full screen width of
Figure 6. Photophoretic velocity as a function of normalized effective power Peff/a (n ) 20, m ) 16, 1 s). By normalizing the effective power on the corresponding particle radius, a linear correlation to the PP velocity can be found for a particular index of refraction.
770 µm. Between the experiments, a low flow was applied to move particles into the laser beam. As theoretically predicted by eq 4, a linear correlation between the maximum flux and PP velocity was found (result not shown). The correlation of PP velocity and particle radius is shown in Figure 5. According to theoretical predictions, a linear relation was found for a , ω. For larger particle radii, however, the slope decreases. This finding can be explained by the Gaussian flux distribution. As the power of a Gaussian beam is concentrated mainly in the center of the beam, the effective power acting on particles in the size range of ω is lower than a simple surfaceproportional estimation would suggest. To demonstrate the efficiency of our calculation of Peff, we introduce the normalized effective power Peff/a. As Peff is a function proportional to the square of a, normalizing the effective power by a gives a direct proportionality as the PP velocity is proportional to the product of Peff and a. In Figure 6, linear dependency of the PP velocity on the normalized effective power is demonstrated for latex particles with diameters of 2, 3, 4, and 5 µm. Independently of the particle diameter, all these latex particles are found on one line, while particles with different optical properties are expected to have different slopes. It has to be mentioned that slight deviations from the linear correlation have to be expected as the photophoretic efficiency is a nonlinear function of the particle radius, too. Theoretical calculation of Q has been extensively Analytical Chemistry, Vol. 79, No. 18, September 15, 2007
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Figure 7. Photophoretic velocity of particles of different material polystyrene (closed diamonds), melamine (open circles), and SiO2 (open squares) over a diameter range from 300 nm up to 10 µm (n ) 10, 1 s).
performed by different approaches,31,34,35 but the expected effects are in the range of the experimental error and hence neglected in this work. Velocimetry of Samples with Different Refractive Index. Besides the particles’ dimensions, the PP velocities of particles depend on their optical properties. This effect was exemplarily shown with polystyrene microparticles, melamine, and SiO2 particles. The photon flux was 14.0 kW cm-2, and the flow remained stopped throughout each single-particle observation. Figure 7 shows the resulting PP velocities for particles with the three different materials and diameters ranging from 300 nm up to 10 µm. An important fact for a separation system based on PP velocimetry can be seen for the particles with a diameter of 1 µm. For particles with the same size, the PP velocity depends on the material of the particle. Melamine particles exhibit the highest PP velocity with 12 µm s-1, while the velocity of “transparent” SiO2 particles was ∼6 times lower. For small particles, PP migration is limited by Brownian motion as can be seen for the 300-nm particles. From these results it can be concluded that PP has the potential for characterization and separation of particles in the micrometer range according to their diameter, optical properties like refractive index, and absorption coefficient with respect to the wavelength of the laser beam. The dependency of the migration on the refractive index can reveal information about the chemical composition of the particles. This behavior is essential for discrimination and can be utilized for a separation driven by light-induced forces. Separation of particles of the same size but different optical properties seems to be feasible, especially hyphenating PP separation with size-selective techniques like FFF. Photophoresis in Flow. The experiments above stress the influence of laser power, particle radii, and different materials on the PP velocity and were carried out with a stopped flow of colloid suspension. As an approach to a continuous separation system based on PP forces, a continuous flow was induced and the migration of the colloids under the influence of PP force as well as fluid drag force was observed. Under the influence of the laser beam, the colloids in flow undergo a lateral shift caused by the (34) Arnold, S.; Lewittes, M. J. Appl. Phys. 1982, 53, 5314-5319. (35) Wright, W. H.; Sonkey, G. J.; Tadir, Y.; Berns, M. W. IEEE J. Quantum Electron. 1990, 26, 2148-2157.
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Figure 8. Photophoretic displacement of polystyrene particles as a function of flow and particle diameter in purified water.
optical forces as soon as the colloids are irradiated by the laser beam. The lateral shift, which we term photophoretic displacement, depends on flow conditions and particle properties. The flow velocities, directed perpendicularly to the laser beam as described above, were varied from 0 to 15 µm s-1. For three sizes of polystyrene particles, 2, 3, and 4 µm, the influence of the flow velocity on the PP displacement of the particles in the crossflow field was observed. Results are summarized in Figure 8. A single data point represents the average PP displacement of n ) 20 particles, and the error bars are the standard deviation under the given conditions. The dotted lines are empirically found, second-order exponential decay fits, inserted for better visualization of the data sets. The qualitative dependency of the PP displacement on the flow conditions is similar for all particle diameters (see inset in Figure 8). In the case of a slow flow, all particles moving with the flow into the laser beam are picked up by the radial PP force and trapped in the beam. Driven by the axial PP force, the particles then move over the full field of view centered in the laser beam, orthogonally to the flow direction. This behavior can be observed as long as the radial PP force acting on a particle in the laser beam exceeds the fluid drag force acting on the downstream direction of the particle. Increasing the flow velocity to the point where the drag force becomes larger than the radial PP forces, the particles are pushed out of the laser beam and follow the flow field. Hence, with increasing flow velocity, the PP displacement diminishes. As expected, for constant flow settings, the PP displacement is larger for larger particle diameter. Generally spoken, particles with larger diameters or PP efficiencies Q show larger displacements; a fact that can be applied for continuous separation according to these particle properties. The best separation conditions can be selected according to Figure 9. By choosing, for example, a flow rate of ∼3 µm s-1, a clear separation between 4-µm particles and 3-µm particles is possible, while a flow rate of ∼1.4 µm s-1 has to be applied to separate 2-µm particles from 3-µm particles. The selectivity is higher for larger particles; this is a very important feature, as there is a general lack of suitable techniques for particle fractionation in the larger size range.14 It has to be stated that the comparably large standard deviations for particles with a diameter of 3 µm indicated a technical problem with this specific sample and should not be generalized. The selectivity of a separation system based on these effects is characterized by the difference in the PP displacement of two
Figure 9. Photophoretic displacement for polystyrene particles with diameters of 2, 3, and 4 µm at several flow velocities. The flow velocities represent data from constant flow conditions from Figure 7. Error bars are omitted for the sake of clarity.
particle species with well-defined PP properties. An example for such evaluation is given in Figure 9, where the PP displacement is plotted versus the particle size for fixed flow velocities. The plot is actually a vertical cross section of Figure 8 at different flows. CONCLUSIONS Photophoretic velocimetry as a new tool for colloid characterization has proven to be a feasible approach. The compensation of a complex microscopic body by a CCD and macroobjective shows versatile implementation to facilitate photophoretic velocimetry. The PP velocity depends on different parameters. Once knowing the physical parameters of the laser system and the
carrier fluid, respectively, the intrinsic properties as size or refractive index of the single particle can be revealed. The difference in photophoretic migration behavior can be utilized by separation means. Based on the results presented here, the development of a continuous separation system by PP forces seems feasible. One approach can be the described crossflow setup of a fluid flow perpendicular to a focused laser beam, where particles can be moved over displacements of several hundreds of micrometers by PP forces. The PP migration displacement is distinctly connected to particle diameter and thus may allow continuous separation by diameter or even PP efficiency Q. By separating the flow downstream of the laser beam and cycling the sample through the system several times, a mixture of particles could possibly be fractionated. A most relevant application can be the separation of cells and other biological materials as PP separation is a very gentle, noncontact method, showing promising resolution in this size range. The hyphenation with other continuous separation techniques, particularly with FFF, is very promising in order to fractionate according to both size and optical properties. ACKNOWLEDGMENT This work was financially supported by the Deutsche Forschungsgemeinschaft (DFG). The authors appreciate the help of Sebastian Wiesemann and Andrea Okroy for the fabrication of the flow cells and assistance in experimental work. Received for review April 28, 2007. Accepted July 5, 2007. AC070875X
Analytical Chemistry, Vol. 79, No. 18, September 15, 2007
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