Spatially Resolved Analysis of Small Particles by Confocal Raman

Anal. Chem. 2004, 76, 576-584

Spatially Resolved Analysis of Small Particles by Confocal Raman Microscopy: Depth Profiling and Optical Trapping Travis E. Bridges, Michael P. Houlne, and Joel M. Harris*

Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850

Raman microscopy is a powerful method to provide spatially resolved information about the chemical composition of materials. With confocal collection optics, the method is well suited to the analysis of small particles, either resting on a surface or optically trapped at a laser focus, where the confocal collection volume optimizes the signal from the particle. In this work, the sensitivity and spatial selectivity of detecting Raman scattering from single particles was determined as a function of particle size. An inverted confocal Raman microscope was used to acquire spectra of individual surface-bound and optically trapped polystyrene particles with sizes ranging between 200 nm and 10 µm. The particles are in contact with aqueous solution containing perchlorate ion that served as a solution-phase Raman-active probe to detect interferences from the surrounding medium. The collection volume is scanned through single particles that are attached to the surface of the coverslip, and the sensitivity and selectivity of detection are measured versus particle size. The results compare favorably with a theoretical analysis of the excitation profile and confocal collection efficiency integrated over the volumes of the spherical particles and the surrounding solution. This analysis was also applied to the detection of particles that are optically trapped and levitated above the surface of the coverslip. The results are consistent with the optical trapping of particles at or near the excitation beam focus, which optimizes excitation and selective collection of Raman scattering from the particle. Raman microscopy has been shown to be a powerful method to provide spatially resolved information about chemical composition of materials in many fields, including study of composites, pigments, semiconductors, and biological structures.1 Most recently, the technique has been coupled with confocal light collection, which defines a small excitation/collection volume for probing local structure by imaging the collected scattering through a small aperture. The confocal volume also provides depth resolution along the optical propagation axis, allowing small threedimensional regions of a sample to be interrogated while minimizing signal from surrounding material. Confocal light collection can * To whom correspondence should be addressed: chemistry.chem.utah.edu. (1) Huong, P. V. Vib. Spectrosc. 1996, 11, 17-28.

(e-mail) harrisj@

576 Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

be achieved through the use of a small pinhole2 or small fiberoptic bundle3 in the image plane of the objective or by manipulation of the entrance slit to the monochromator combined with selection of a specific active area of a CCD detector.4 The depth resolution of confocal Raman microscopy is important for profiling chemical composition as a function of distance into a sample. The method has been used extensively for the analysis of layered thin films of polymeric materials,5-11 semiconductors,12 silicates,13 and porous solids.14 Confocal Raman microscopy is also a very useful technique for the analysis of small particles attached to the surface of a slide or coverslip. Kador et al.15 have shown that 3D images could be constructed for small TiO2 particles (∼5 µm) using scanning confocal Raman microscopy. It has also been shown that ligand16 or functional group17 distributions on adsorbent particles are measurable with this technique, although long integration times were necessary in these applications. This limitation could be overcome through the use of a higher numerical aperture (NA) oil-immersion objectives to increase signal collection and shorten the integration times. (2) Puppels, G. J.; Colier, W.; Olminkhof, J. H. F.; Otto, C.; de Mul, F. F. M.; Greve, J. J. Raman Spectrosc. 1991, 22, 217-25. (3) Schrum, K. F.; Ko, S. H.; Ben-Amotz, D. Appl. Spectrosc. 1996, 50, 11505. (4) Williams, K. P. J.; Pitt, G. D.; Batchelder, D. N.; Kip, B. J. Appl. Spectrosc. 1994, 48, 232-5. (5) Schrof, W.; Klingler, J.; Heckmann, W.; Horn, D. Colloid Polym. Sci. 1998, 276, 577-88. (6) Tabaksblat, R.; Meier, R. J.; Kip, B. J. Appl. Spectrosc. 1992, 46, 60-8. (7) Garton, A.; Batchelder, D. N.; Cheng, C. Appl. Spectrosc. 1993, 47, 922-7. (8) Hajatdoost, S.; Yarwood, J. Appl. Spectrosc. 1996, 50, 558-63. (9) Kasteleiner, T.; Evans, R.; Yarwood, J.; Hodge, D.; Swart, R. J. Raman Spectrosc. 1996, 27, 695-8. (10) Hajatdoost, S.; Olsthoorn, M.; Yarwood, J. Appl. Spectrosc. 1997, 51, 178490. (11) Sacristan, J.; Mijangos, C.; Reinecke, H.; Spells, S.; Yarwood, J. Macromolecules 2000, 33, 6134-9. (12) Matthews, M. J.; Hsu, J. W. P.; Gu, S.; Kuech, T. F. Appl. Phys. Lett. 2001, 79, 3086-8. (13) Matthews, M. J.; Harris, A. L.; Bruce, A. J.; Cardillo, M. J. Rev. Sci. Instrum. 2000, 71, 2117-20. (14) Brenan, C. J. H.; Hunter, I. W.; Brenan, J. M. Anal. Chem. 1997, 69, 4550. (15) Kador, L.; Schittkowski, T.; Bauer, M.; Fan, Y. Appl. Opt. 2001, 40, 496570. (16) Ljunglo ¨f, A.; Larsson, M.; Knuuttila, K.; Lindgren, J. J. Chromatogr., A 2000, 893, 235-44. (17) Larsson, M.; Lindgren, J.; Ljunglo ¨f, A.; Knuuttila, K. J. Chromatogr., A 2002, 954, 151-8. 10.1021/ac034969s CCC: $27.50

© 2004 American Chemical Society Published on Web 12/20/2003

For Raman microscopy analysis of particles in suspended liquids, tightly focused excitation from a high-NA objective produces strong spatial gradients in light intensity that can be used for optical trapping. The phenomenon of optical trapping was first described by Ashkin in 1970,18 where micrometer-sized particles were trapped in a stable, potential well defined by a tightly focused laser beam. Since its discovery, the method has become a powerful tool19-22 for the manipulation and analysis of biological cells,23-26 vesicles,26-28 and inorganic and organic colloids.29-32 The combination of optical trapping and Raman scattering has allowed the analysis of micrometer-33,34 and submicrometer-sized35 solid particles, liquid droplets,36 photopolymerizing aerosols,37 and organic microdroplets in aqueous emulsions.38-39 The method has recently been shown to be useful for probing chemical reactions on small particles, including polymerization of emulsion particles,40 photoconjugation of polystyrene,41 and chemical synthesis reactions on solid-phase support particles.42 In the present work, the small-volume sampling capabilities of confocal Raman microscopy are evaluated for spatially resolved analysis of single small particles. An inverted Raman microscope is used to acquire depth profiles of single, surface-attached polymer colloids over the size range of 0.2-10 µm. High numerical aperture (1.4 NA), oil-immersion optics and the confocal design provide high optical throughput and submicrometer spatial resolution. The spatial selectivity for analyzing the composition of the particle and excluding the surrounding medium is evaluated by incorporating a Raman-active reporter ion in solution. An analysis43,44 of the excitation profile and confocal collection efficiency (18) Ashkin, A. Phys. Rev. Lett. 1970, 24, 156-9. (19) Ashkin, A.; Dziedzic, J. M.; Bjorkholm, J. E.; Chu, S. Opt. Lett. 1986, 11, 288-90. (20) Wright, W. H.; Sonek, G. J.; Berns, M. W. Appl. Phys. Lett. 1993, 63, 7157. (21) Ashkin, A. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 4853-60. (22) Ashkin, A. IEEE J. Sel. Top. Quantum Electron. 2000, 6, 841-56. (23) Ashkin, A.; Dziedzic, J. M. Science 1987, 235, 1517-20. (24) Liu, Y.; Sonek, G. J.; Berns, M. W.; Tromberg, B. J. Biophys. J. 1996, 71, 2158-67. (25) Wei, X.; Tromberg, B. J.; Cahalan, M. D. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 8471-6. (26) Stro ¨mberg, A.; Karlsson, A.; Ryttse´n, F.; Davidson, M.; Chiu, D. T.; Owar, O. Anal. Chem. 2001, 73, 126-30. (27) Chiu, D. T.; Hsaio, A.; Gaggar, A.; Garza-Lo´pez, R. A.; Owar, O.; Zare, R. N. Anal. Chem. 1997, 69, 1801-7. (28) Chiu, D. T.; Lillard, S. J.; Scheller, R. H.; Zare, R. N.; Rodriguez-Cruz, S. E.; Williams, E. R.; Orwar, O.; Sandberg, M.; Lundqvist, J. A. Science 1998, 279, 1190-3. (29) Mio, C.; Marr, D. W. M. Adv. Mater. 2000, 12, 917-20. (30) Clapp, A. R.; Dickinson, R. B. Langmuir 2001, 17, 2182-91. (31) Clapp, A. R.; Ruta, A. G.; Dickinson, R. B. Rev. Sci. Instrum. 1999, 70, 262736. (32) Viravathana, P.; Marr, D. W. M. J. Colloid Interface Sci. 2000, 221, 301-7. (33) Thurn, R.; Kiefer, W. Appl. Spectrosc. 1984, 38, 78-83. (34) Lankers, M.; Popp, J.; Urlaub, E.; Stahl, H.; Ro¨ssling, G.; Kiefer, W. J. Mol. Struct. 1995, 348, 265-8. (35) Ajito, K.; Torimitsu, K. Appl. Spectrosc. 2002, 56, 541-4. (36) Thurn, R.; Kiefer, W. Appl. Opt. 1985, 24, 1515-9. (37) Esen, C.; Kaiser, T.; Schweiger, G. Appl. Spectrosc. 1996, 50, 823-8. (38) Lankers, M.; Popp, J.; Kiefer, W. Appl. Spectrosc. 1994, 48, 1166-8. (39) Ajito, K. Appl. Spectrosc. 1998, 52, 339-42. (40) Urlaub, E.; Lankers, M.; Hartmann, I.; Popp, J.; Trunk, M.; Kiefer, W. Chem. Phys. Lett. 1994, 231, 511-4. (41) Crawford, D.; Hughes, K. J. Phys. Chem. B 1998, 102, 2325-8. (42) Houlne, M. P.; Sjostrom, C. M.; Uibel, R. H.; Kleimeyer, J. A.; Harris, J. M. Anal. Chem. 2002, 74, 4311-9. (43) Koppel, D. E.; Axelrod, D.; Schlessinger, J.; Elson, E. L.; Webb, W. W. Biophys. J. 1976, 16, 1315-29. (44) Hill, E. K.; de Mello, A. J. Analyst. 2000, 125, 1033-6.

over the volumes of the particle and surrounding solution predicts the relative sensitivity and spatial selectivity of the method for particles of differing size. This analysis is then applied to the analysis of particles that are optically trapped and levitated above the surface of the coverslip. The results are consistent with the trapping of particles near the excitation beam waist, which optimizes excitation of the sample and selective collection of particle Raman scattering. EXPERIMENTAL SECTION Confocal Raman Microscope. A detailed description and block diagram of the microscope optics was previously published.42 Briefly, sample excitation was provide by a Kr+ laser (Innova 90, Coherent, Inc.) operating at 647.1 nm with an output power of 25 mW. The laser beam was directed optically through a 4× beam expander (model 50-25-4X-647, Special Optics, Inc.) mounted on a Nikon TE 300 inverted fluorescence microscope. The expanded beam passed through the rear of the microscope into a cube that held a band-pass filter (D647/10, Chroma Tech, Inc.), a dichroic beam splitter (655DCLP, Chroma Tech, Inc.) and a high-pass filter (E660LP, Chroma Tech, Inc.) The beam is reflected by the dichroic beam upward into a 100×, 1.4 NA oil immersion microscope objective (CFL PLAN APO, Nikon, Inc.) and was focused through a No. 1 1/2-thickness coverslip (BK-7 glass, Esco), which is the bottom window of a flow cell; the solution in the flow cell is confined with a silicone gasket between the coverslip and a round top disk with inlet and outlet tubes.42 Raman scattering from the sample was collected by the same objective and passed through the dichroic and high-pass filter into the microscope frame, where it could then be directed to a 10× eyepiece for visual observations, a monochromator (250IS, Chromex, Inc.) and CCD (DV420, Andor, Inc., cooled to -60 °C) for spectral analyses, or a digital camera (CoolPix 950, Nikon, Inc.) for imaging. Whitelight, bright-field illumination of the sample was provided by an overhead 30-W tungsten illuminator. The confocal aperture was established in a manner similar to Williams et al.4 by focusing the sample image onto the entrance slit of the monochromator to define a horizontal position and binning three rows of pixels of the CCD image to define a vertical position. The monochromator slit was set at 50 µm to define a 500-nm region in the horizontal plane within the sample (100× magnification) while three rows of the CCD (equivalent to 66 µm) were sampled and binned to define a 660-nm vertical region in the sample. Sample Preparation. Polybead carboxylated microspheres of the following sizes were acquired from Polysciences, Inc. with the following diameters (and Polysciences lot numbers): 0.21 ( 0.01 (503687), 0.45 ( 0.01 (499320), 0.79 ( 0.02 (451094), 2.02 ( 0.05 (490088), 4.34 ( 0.24 (505229), 6.1 ( 0.6 (496902), and 9.8 ( 0.9 µm (505946). These microspheres are monodisperse polystyrene latex particles that contain surface carboxyl groups and are packaged in aqueous suspension ranging from 2.5 to 2.7%. Dilute suspensions were created in 0.5 M NaClO4 aqueous solution. Perchlorate ion was chosen as a solution-phase marker due to its insolubility in the polystyrene particle, its negligible surface association with anionic carboxylate groups on the particle surface, and its Raman scattering at ∼933 cm-1 in the vicinity of a strong Raman band from polystyrene at ∼1000 cm-1. The average number of particles per field of view was kept around Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

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Figure 1. Raman spectrum of a single 0.45-µm polystyrene particle adhering to the surface of a coverslip and in contact with 0.5 M sodium perchlorate in aqueous solution. The laser focus is centered within the particle, ∼0.2 µm above the coverslip surface. Prominent band assignments are listed in the text.

five for the larger particles and slightly higher for smaller particles to ensure single, well-separated particles could be located for scanning and trapping analyses. Particle Detection, Scanning, and Optical Trapping. For a typical experiment, the surface of the coverslip was first located by detecting the focused spot of the excitation laser beam reflected from the smooth surface of the glass coverslip.45 In particle scanning experiments, suspensions of a single size of carboxylated polystyrene colloids were introduced into the flow cell, and the particles were allowed to settle to the surface and attach. Particles were located visually in the eyepiece, and the stage was moved to center a particle in the airy pattern of the excitation laser in the x-y plane. Differential interference contrast was necessary for locating particles having diameters below 500 nm. Raman spectra were acquired in 0.5-µm steps in the z direction starting at the coverslip surface and scanning through the particle into solution. Spectra were acquired with 30-s integrations for particles greater than 1 µm in diameter and longer 2-min integration times for smaller particles to provide an adequate signal-to-noise ratio. The intensity counts for the longer integration times were divided by four to normalize the response to be equivalent to a 30-s integration. For optical trapping experiments, suspensions of carboxylated polystyrene colloids were again introduced into the flow cell. Before the particles settled onto the coverslip surface, a single colloid particle was located visually and trapped by manipulating the particle under the laser focus. Raman spectra of optically trapped particles were acquired with the particle held 10 µm above the coverslip surface; for comparisons with surface-attached particles, the particles were lowered to the coverslip surface in 1.0-µm steps. RESULTS AND DISCUSSION Raman Scattering Detection and Depth Profiling of SurfaceAttached Particles. An example Raman spectrum of a single 0.45µm polystyrene latex particle is shown in Figure 1. The particle is adhering to the surface of a coverslip and in contact with (45) Inoue´, S.; Spring, K. R. Video Microscopy; Plenum Press: New York, 1997.

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Figure 2. Normalized polystyrene Raman scattering at 1000 cm-1 versus position of the focus above the coverslip surface (or scan depth). The diameters of the polystyrene particles are listed as line legends.

aqueous solution containing 0.5 M sodium perchlorate, and the laser focus is centered within the particle, ∼0.2 µm above the coverslip surface. The prominent peaks in the Raman spectrum of the polystyrene polymer correspond to the ring deformation mode (614 cm-1), ring breathing mode (1000 cm-1), C-C stretches (1150-1200 cm-1), CH2 scissoring (1446 cm-1), and ringskeletal stretch (1597 cm-1). Raman scattering from the symmetric stretch of perchlorate ion in the surrounding solution is also detectable at 933 cm-1 because the particle does not fill the confocal probe volume. Multiple depth profile scans of the Raman scattering from polystyrene particles showed no changes in the spatial distribution of perchlorate over time, indicating that these ions do not diffuse into the polystyrene matrix; furthermore, perchlorate anions would have no binding affinity to negatively charged carboxylate groups on the polymer surface. Raman scattering from perchlorate at 933 cm-1, therefore, should report only contributions from surrounding solution to the confocal probe volume, while the ring breathing mode of the polystyrene (1000 cm-1) is a strong marker for contributions from the polymer colloid particle. The first study of the depth resolution of confocal Raman analysis of particles was to profile the sensitivity for a series of polystyrene particles of different sizes. Raman spectra were acquired at 0.5-µm intervals; the baseline-corrected scattering at 1000 cm-1 was normalized to the highest number of counts observed along any scan, and the results are plotted in Figure 2. The intensity of Raman scattering maximizes near the particle center for particles less than 2 µm in diameter. For particles larger than 2 µm, the sensitivity reaches a maximum at a depth of ∼2 µm and falls off slowly with distance from the coverslip. This falloff in intensity for larger particles is due to a decrease in collection efficiency of the objective as the focal plane moves into the sample. This loss of collection efficiency is apparent in a depth profile of a homogeneous sample, as shown in Figure 3. In this study, the Raman scattering from a 0.5 M sodium perchlorate solution at 933 cm-1 is plotted versus the depth of sampling. The scan shows that the collection efficiency of the objective drops at a rate of ∼20% for every 10-µm depth into the sample, indistinguishable from the falloff in intensity from the scans of larger particles. As

Figure 3. Normalized Raman scattering from 0.5 M perchlorate from particle-free solution (933 cm-1) superimposed on the scattering from a 9.8-µm polystyrene particle (1000 cm-1) versus scan depth.

a comparison, a depth profile of a 9.8-µm polystyrene particle is included in Figure 3 showing the comparable rates of collection efficiency decay. The confocal probe is filled with polystyrene close to the surface for these particles, and thus, this point corresponds to a theoretical collection maximum for our instrument. At the coverslip surface (scan depth, 0 µm), the confocal probe should be approximately half-occupied with polystyrene for larger particles and the signal should be at half-maximum. This fraction is indeed observed in the scans of larger particles and of the homogeneous solution sample in Figures 2 and 3, respectively. The volume of polystyrene sampled at the coverslip surface decreases with decreasing particle size, as the particle becomes smaller than the confocal probe. Scanning beyond the outer edge of the particles produces a rapid falloff in the polymer signal as the confocal probe volume samples the solution above the particle surface. The intensity counts from polystyrene should exhibit this rapid decrease as the focus is scanned through the outer diameter of the particle. The scan distances at which this transition is observed for larger particles are ∼30% greater than the particle diameter. The shift is due to the particle acting as a refractive element, which changes the propagation of the excitation beam through the sample, moving the focus closer to the coverslip and requiring a greater scan depth to reach the outer surface of the particle. Modeling of the effect of the spherical particle interface using a Gaussian beam propagation model based on simple ray-transfer matrixes46 correctly predicts the direction of this shift and the observed trend with particle size; development of this model to interpret the size of particles is currently in progress. The spatial sampling by confocal optics for selectively detecting the Raman scattering of small particles and excluding the surrounding solution can be tested by monitoring the signal from perchlorate ion in solution at 933 cm-1. Figure 4 shows depth profile scans for the polystyrene Raman scattering from the 2.02and 4.34-µm particles together with the accompanying perchlorate ion signal from the surrounding solution. At the coverslip surface, these results show that the confocal probe volume samples the solvent that lies between the particle and the coverslip, as indicated (46) Siegman, A. E. An Introduction to Lasers and Masers; McGraw-Hill: New York, 1971.

Figure 4. Comparison of normalized polystyrene Raman intensity (1000 cm-1) to normalized perchlorate intensity (933 cm-1) for a 2.02and a 4.34-µm particle versus scan depth.

by slightly higher perchlorate ion counts. The fraction of solvent in the confocal volume at this surface should be greater for smaller particle sizes due to the tighter radius of curvature that allows more solvent to penetrate into this volume, which is confirmed by these results. As the confocal volume is scanned upward into the particle, the solution within the confocal probe is replaced by polystyrene, and the signal from solution is almost completely excluded. Once the confocal probe moves above the particle, solution fills the confocal space formerly occupied by polystyrene and results in return of the perchlorate signal. The smallest ratio of the perchlorate to polystyrene counts occurs at the approximate center of the particle, which is the expected region for greatest exclusion of the solution signal. Since the Raman microscope utilizes high-throughput optics (high NA oil-immersion objective, low F-number monochromator), strong scattering can be detected on a relatively short time scale for all particle sizes studied. Thousands of counts can be detected from particles of g0.79 µm in a 30-s integration, allowing experiments on small particles to be completed in a few minutes. The maximum number of Raman counts for each particle sampled at the particle center is plotted in Figure 5. The increase in Raman scattering detected as a function of particle size begins to maximize for particles greater than 2 µm in diameter; at this size, it can be concluded that the confocal probe volume has been nearly filled and larger particles will not significantly increase the amount of Raman scattering detected. The Raman scattering from perchlorate ion in the confocal probe volume centered within each particle is plotted in Figure 6. For particles greater than 2 µm in diameter, the perchlorate signal is nearly completely excluded from the confocal probe volume, which is behavior consistent with the polystyrene signal maximizing for larger particles. The ratios of perchlorate ion counts to polystyrene counts were calculated for each of the steps for all scanned particles and tabulated. The minimum ratios were then plotted against particle size on a log scale to produce Figure 7. The ratio remains relatively unchanged for particles larger than 2 µm in diameter where the particle has filled the confocal probe volume; the fraction of light collected from the solution levels off to a very small value of less than 0.003. Modeling the Collection of Raman Scattering from Small Particles. To better understand the spatial selectivity of confocal Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

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Figure 5. Raman scattering intensity from polystyrene (1000 cm-1) detected at the particle center versus particle size. The data are compared with the collection model of eq 13 that is scaled by a linear least-squares fit to the data.

Figure 6. Solution-phase perchlorate Raman intensity (933 cm-1) detected at the particle center versus particle size. The data are compared with the collection model of eq 16 that is scaled by a linear least-squares fit to the data.

Raman microscopy for small particles, the excitation and collection characteristics of the experiment are modeled for the specific case of microscopic analysis of spherical particles. This analysis begins with a measurement of the spot size, w(z), which is the radius at which the intensity of a Gaussian beam drops to a fraction 1/e2 from its center intensity according to

I(r,z) ) (2P/πw2(z)) exp(-2r2/w2(z))

(1)

where P is the total optical power in the beam. For a laser of wavelength, λ, the numerical aperture of the objective defines the minimum spot size of the diffraction-limited beam at its waist, w0:47

w0 ) 0.61λ/NA

(2)

which for our 1.4 NA objective at 647.1 nm is predicted to be 0.28 µm. The image of the focused laser spot at the coverslip surface (47) Everall, N. J. Appl. Spectrosc. 2000, 54, 773-82.

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Figure 7. Ratios of detection efficiencies for solution-phase perchlorate to polystyrene particle versus particle size. The Raman scattering intensity ratios for perchlorate over polystyrene (triangles, left axis) are compared with the theoretical prediction, Xsolution/Xparticle (circles, right axis), from eqs 16 and 13, respectively. The two logscale axes are offset by the ratio of the intensity scaling factors for detecting solution-phase perchlorate and polystyrene.

Figure 8. Profile of the excitation laser beam spot at its waist (reflected from the coverslip).

was acquired and calibrated, and the resulting profile of the beam is plotted in Figure 8. The measured profile fits the Gaussian distribution of eq 1, with a spot size at the beam waist of 0.30 ((0.01) µm, which is ∼10% larger than predicted from the numerical aperture of the objective. This is likely due to incomplete filling of the aperture of the objective with the incident beam; the effective NA indicated by eq 2 is 1.32 for the conditions of our experiment. The excitation profile of the laser beam within the sample is determined by the evolution of the beam spot size, w, with propagation distance, z:43,44,46

w(z) ) [w02 + z2(tan R)2]1/2

(3)

where R is the far-field divergence angle within the sample and is related to the effective numerical aperture of the objective according to45

R ) sin-1(NA/n)

(4)

where n is the index of refraction of the medium between the

Figure 9. Diagram of the confocal probe volume showing the boundaries of the laser beam spot size (left) along with the predicted planar detection efficiency, E(z) (right). The outer perimeters of particles having diameters of 0.21, 0.45, 0.79, and 2.02 µm are included in the diagram of the probe volume.

objective and the sample (n ) 1.515) corresponding to a halfangle, R ) 60.6°, in this experiment. The resulting variation of the spot size, w, with propagation of the beam through its focus is shown on the left side of Figure 9. Koppel et al.43 developed a model for confocal excitation and collection efficiency based on the intensity distribution produced by a laser focus and a collection volume defined by a circular aperture at the image plane of the objective. In our experiment, the binning of three pixel rows on the CCD detector (66 µm) combined with a slit width of 50 µm defines an aperture with an area corresponding to a circle of radius, s, of 32.4 µm. This radius corresponds to an aperture in the object or sample plane (so) that is smaller by the magnification of the objective, M:

so ) s/M

(5)

In our case, M is 100× and so is 0.324 µm. The aperture in the object plane also defines the depth of focus, l, based on collection half-angle:43

l ) so cot(R)

(6)

which is 0.18 µm in this work. The radial point-source collection efficiency, (r,z), for light emitted in a plane at a distance, z, away from the focal plane has been shown43 to be

[

(r,z) = 1 + (1/2)

(zl) ]

2 -1

{ ( )[

exp -

r so

2

1 + (1/2)

2 -1

(zl) ]

}

and dividing by the integrated excitation intensity profile:

∫I(r,z)(r,z)d r E(z) ) ∫I(r,z)d r 2

2

(8)

If the aperture in the object plane, so, is greater than the resolution limit, wo, then the radial dependence of the detection efficiency is governed by the diffraction-limited excitation intensity profile, I(r,z), so that E(z) reduces to a simple Lorentzian profile in z:43

E(z) ≈ [1 + (z/l)2]-1

(9)

Figure 9 shows a plot of the planar detection efficiency, E(z) from eq 9, along with the z dependence of the excitation laser beam spot size from eq 3. This plot shows how quickly the detection efficiency falls off with distance from the focus. To use these expressions to model the detection of signal from particles centered in the confocal volume, it is necessary to calculate the fraction of particle or solvent found within the confocal probe in a series of planes versus distance, z, away from the focus. To visualize this problem, the outer boundaries of particles ranging in diameter from 0.21 to 2.02 µm are included in Figure 9. To develop this model, we first define a distance, z′, at which the outer edge of a larger particle intersects the boundary of the laser beam. When the focal plane is at the center of the particle, z′ satisfies the following condition:

R2 ) (w2(z′) + z′2)

(10)

(7) where r is the radial distance from the center of the aperture, so, in the object plane and z is the axial distance from the focal plane, also in the object space. The overall detection efficiency, E(z), from the plane at distance z from the focus is determined by integrating the product of the excitation function, I(r,z), (eq 1) and collection function, (r,z), (eq 7) over the radial dimension

which for large particles (R . wo) is satisfied when z′ ) R cos R (see eq 3). For small particles that never intersect the beam profile boundary, z′ is zero. Between the focus and the distance z′, the excitation laser profile is entirely within the sampled particle so that the sample resembles a thick film. To estimate the signal contribution from this region, one can simply integrate E(z) from z ) 0 to z ) z′. For values of z greater than z′, we must calculate Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

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an area fraction that indicates how much of the confocal probe area is occupied by the particle. The area of the circular slice of the particle sphere at a distance z is given by

Aparticle(z) ) π(R2 - z2)

(11)

Dividing by the total area of the beam at this distance, πw2(z), gives the fraction of the laser beam area that is filled by the particle:

Fparticle(z) )

R 2 - z2 w2(z)

(12)

The integrated detection efficiency from the particle, Xparticle(z), can, therefore, be described by a sum of two integrals:

Xparticle(R) ) 2[

∫

z′

0

E(z) dz +

∫

R

z′

E(z)Fparticle(z) dz] (13)

The values of Xparticle(R) are calculated numerically and produce fractions that are proportional to the Raman signal. The comparison of the modeled detection efficiency and the experimental data is completed by scaling the model to the data by linear least squares. The resulting model intensities are plotted together with the data in Figure 5. The model accounts for the rate of growth in Raman signal with particle size that maximizes for particles that overfill the confocal depth. The actual signal continues to grow slightly for the largest particles beyond what is predicted by the model. This could be due to reflection of the excitation beam back into the confocal volume at the particle/solution interface or changes in the shape of the confocal volume due to refraction by the particle; a more sophisticated model is being developed in an attempt to account for these effects. By the same approach, one can analyze the expected Raman signal collection from the surrounding solution. For z > z′ or for regions where the spot size of the beam is beyond the boundary of the particle, there is solution within the excitation/collection volume of the experiment. At a distance z, the area of the beam that is in solution is

Asolution(z) ) π[ω2(z) - (R2 - z2)]

(14)

and the area fraction in solution is

Fsolution(z) ) 1 -

[ ] R 2 - z2 ω2(z)

(15)

Note that Fsolution(z) is simply [1 - Fparticle(z)]. The integrated detection efficiency for species in solution is evaluated for regions where z g z′:

Xsolution(R) ) 2[

∫

R

z′

Figure 10. Raman scattering intensity at 1000 cm-1 from an optically trapped 2.02-µm polystyrene particle versus the distance of the focus from the coverslip surface.

E(z)[1 - Fparticle(z)] dz] +

∫ E(z) dz ∞

R

(16) The term for the detection of solution surrounding the particle is inside the brackets, which is doubled due to the symmetry of the 582 Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

solution fraction and the collection functions about z ) 0; detection of signal from solution above the particle is represented by the indefinite integral of the last term. Since this model applies to particles resting on the coverslip, the final term is not doubled since there is no solution below the coverslip (z < -R). Linear least squares is used to scale the solution detection function to fit the Raman intensity from perchlorate in solution, and the comparison is shown in Figure 6. Again the general trend of the model in showing the exclusion of solution-phase signal from the confocal volume matches the observed results. Finally, the ratio of the detection efficiencies predicted by the model for solution and particle Raman scattering is determined, Xsolution/Xparticle, and compared with the observed ratio, Isolution/Iparticle, from the experiment. The results are compared in Figure 7, where the log plots are offset by the ratio of the intensity scaling factors for detecting solution-phase perchlorate and polystyrene. The model predicts a >25-fold rejection of solution-phase scattering from particles larger than 5 µm, which is within 30% of what is observed from the data. The trends with particle size in the model and the observed results are very similar throughout the range of particle sizes investigated. Analysis of Optically Trapped Particles. Optical trapping of particles for confocal Raman microscopy analysis allows longterm observation of single particles and avoids the requirement that the particles adhere to a surface to be immobilized. In this section, the sensitivity and spatial selectivity for detecting Raman scattering from optically trapped particles is compared with detection from surface-immobilized particles. For example, a 2.02µm polystyrene particle is trapped in solution and then lowered in 1.0-µm steps to the surface, recording the Raman signal from polystyrene at each step. The resulting polystyrene scattering intensity at 1000 cm-1 is plotted versus the distance of the focus from the coverslip surface in Figure 10. From these results, it is clear that the distance dependence for observing an optically trapped particle is much less critical compared observing surfaceattached particles (see Figure 2). The detection efficiency for the particle at z ) 0, when the focus is at the coverslip surface, is smaller by a factor of ∼1/2 as with surface-attached particles because half of the excitation and collection volume are within the coverslip. The detection efficiency rises steeply as z equals R,

Figure 11. Bright-field images and Raman spectra from two 6.1-µm polystyrene particles. The top particle is optically trapped, and the lower particle is surface attached. When the images were made, Raman spectra were acquired from the optically trapped particle (top) with the overhead illuminator off; the trapped particle was then dislodged from the beam, and the focus was centered on the surface-attached particle (bottom) to acquire spectra at the same elevations.

but then it levels off for long distances into solution as the particle is trapped in the confocal volume of the microscope. At scan distances z > ∼5 µm, the collection efficiency begins to fall off slowly with distance, as was observed for scans of large surfaceattached particles or homogeneous solution samples (see Figure 3). Another comparison of optically trapped and surface-attached particles is available from bright-field images with the corresponding Raman signal, shown in Figure 11. This figure compares the images and Raman spectra from two 6.1-µm particles in the same sample, one of which is optically trapped and the second of which is surface attached, at two values of z. With the elevation of the focus at z ) R or ∼3 µm, the bright-field profiles of the two particles are equivalent and in good focus, with the laser spot in the center of the optically trapped particle. The Raman scattering intensities are also equivalent. At an elevation of z ) 10 µm, the surface-attached particle is out of focus, and the corresponding Raman scattering intensity has dropped by more than 1 order of magnitude. For the optically trapped particle with the focal plane at z ) 10 µm, the Raman scattering intensity has decreased by 15% as expected from the homogeneous solution results (Figure 3). The edges of the particle remain in sharp focus in the image, equivalent in sharpness for the images of the trapped and attached particles where z ∼ R in the right-side panels. This equivalence is evidence that the optically trapped particle is centered or very nearly centered within the laser focus. This conclusion can be further tested by comparing the spatial selectivity for confocal detection of optically trapped particles to that established by scanning of surface-attached particles and the theory that fit those data (see above). In Table 1, the ratios of the measured intensities of solution-phase perchlorate scattering (933 cm-1) and polystyrene scattering (1000 cm-1) are compared for surface-attached and optically trapped particles. These results show that the spatially selective analysis of optically trapped particles is very similar to the results for immobilized particles where the focus

Table 1. Ratios of Solution-to-Particle Raman Scattering for Surface-Attached and Optically Trapped Polystyrene Particlesa Isolution/Iparticle particle diameter (µm)

for surfaceattached particles

for optically trapped particles

0.21 0.45 0.79 2.02 4.34 6.10 9.76

0.42 0.18 0.036 0.0113 0.0039 0.0025 0.0022

n/ab n/ab 0.030 0.0107 0.0053 0.0024 0.0022

a Measured intensities of solution-phase perchlorate scattering (933 cm-1) are divided by the polystyrene scattering (1000 cm-1) for surfaceattached and optically trapped particles. b Particles smaller than 0.5 µm in diameter are difficult to observe in suspension and to reliably trap as single particles.

was located at the centers of the particles. Since the exclusion of solvent scattering for these two methods of particle sampling is comparable, we conclude that the optically trapped particles are also centered or nearly centered at the focus of the excitation, which indicates that the theory of spatial selectivity developed above should also apply to optical trapping, confocal detection Raman scattering experiments. CONCLUSIONS Confocal Raman microscopy is a powerful tool for investigating the chemical structure and reactivity of discrete particles, in the size range of hundreds of nanometers to tens of micrometers. With high-numerical oil-immersion optics, the confocal volume defined by the excitation beam profile and by the collection aperture in the image plane can be quite small, ∼1.3 fL, in the present work. This small sampling volume allows spatially selecAnalytical Chemistry, Vol. 76, No. 3, February 1, 2004

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tive analysis of individual particles. The selectivity for detecting the spectrum of the particle and excluding the surrounding medium was evaluated experimentally by incorporating a Ramanactive reporter ion in solution. A theoretical analysis of the excitation profile and confocal collection efficiency over the volumes of the particle and surrounding solution predicted the sensitivity and selectivity of the method versus particle size. This analysis was then applied to the analysis of particles that are optically trapped and levitated above the surface of the coverslip. The results are consistent with the trapping of particles near the

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excitation beam focus which optimizes excitation and selective collection of Raman scattering from the particle. ACKNOWLEDGMENT This research was supported in part by the National Science Foundation under Grant CHE-0137569 and by the University of Utah Research Foundation. Received for review August 19, 2003. Accepted November 10, 2003. AC034969S