Anal. Chem. 1999, 71, 4338-4343
Single-Microparticle Measurements: Laser Trapping-Absorption Microspectroscopy under Solution-Flow Conditions Haeng-Boo Kim,* Osamu Kogi, and Noboru Kitamura*
Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
A laser trapping-microspectroscopy system combined with a fluid manifold was developed to manipulate and analyze “single” microparticles. A sample solution containing microparticles was introduced to a flow cell set on a microscope stage, and a single particle was trapped by a 1064-nm laser beam. With the particle being trapped, the other particles were pumped out by flowing water to hold the unique microparticle in the flow cell. Under solutionflow conditions, a single microparticle was laser trapped in balance with the gradient (Fg) and Stokes forces (Fs) experienced by the particle, and thus, the trapped position was shifted to the downstream side of the 1064-nm laser beam focus. Flow rate and particle size dependencies of this particular positional displacement of the particle were discussed in terms of Fg and Fs. On the basis of these studies, optical requirements to conduct absorption microspectroscopy of a laser-trapped particle were optimized, and the technique was applied to study a time course of dye adsorption processes in single microparticles. The adsorption rate of Rhodamine B was determined for individual microparticles for the first time. In a series of publications, we demonstrated that a laser trapping-microanalytical technique had a high potential for study of single microparticles in solution.1-13 So far, studies on microparticles have been conducted on the basis of ensemble measure(1) Masuhara, H., DeSchryver, F. C., Kitamura, N., Tamai, N., Eds. Microchemistry-Spectroscopy and Chemistry in Small Domains; Elsevier: Amsterdam, 1994. (2) Kitamura, N.; Nakatani, K.; Kim, H.-B. Pure Appl. Chem. 1995, 67, 79-86. (3) Kim, H.-B.; Hayashi, M.; Nakatani, K.; Kitamura, N.; Sasaki, K.; Hotta, J.; Masuhara, H. Anal. Chem. 1996, 68, 409-414. (4) Kitamura, N.; Hayashi, M.; Kim, H.-B.; Nakatani, K. Anal. Sci. 1996, 12, 49-54. (5) Kim, H.-B.; Habuchi, S.; Hayashi, M.; Kitamura, N. Anal. Chem. 1998, 70, 105-110. (6) Nakatani, K.; Chikama, K.; Kim, H.-B.; Kitamura, N. Chem. Lett. 1994, 793796. (7) Nakatani, K.; Chikama, K.; Kim, H.-B.; Kitamura, N. Chem. Phys. Lett. 1995, 133-136. (8) Nakatani, K.; Suto, T.; Wakabayashi, M.; Kim, H.-B.; Kitamura, N. J. Phys. Chem. 1995, 99, 4745-4749. (9) Yao, H.; Inoue, Y.; Ikeda, H.; Nakatani, K.; Kim, H.-B.; Kitamura, N. J. Phys. Chem. 1996, 100, 1494-1497. (10) Kim, H.-B.; Yoshida, S.; Miura, A.; Kitamura, N. Chem. Lett. 1996, 923924. (11) Kim, H.-B.; Yoshida, S.; Kitamura, N. Anal. Chem. 1998, 70, 51-57. (12) Kim, H.-B.; Yoshida, S.; Miura, A.; Kitamura, N. Anal. Chem. 1998, 70, 111-116.
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ments. However, chemical and physical properties of microparticles are expected to depend on their sizes, shapes, and/or microstructures, so that a clear picture of the properties of microparticles cannot be obtained by such studies. Indeed, we have shown experimentally that the rates of electron transfer and mass transfer across single microdroplet/water interfaces depend on the size of the droplet on the basis of a laser trappingmicrospectroscopy-electrochemistry technique.6-8 Dimer formation efficiency of a dye in single water droplets9 and dye distribution characteristics in microcapsules10-12 have also been shown to be dependent on the particle size. These studies demonstrate clearly the importance of single-particle measurements to understand chemical and physical properties of various microparticles. The laser trapping and microanalytical methods are thus the indispensable basis for studying size-dependent chemical/physical processes in or across microparticles. By a strict definition, nonetheless, such an experimental mode is not a “single-particle measurement” but is a “particle-resolved mode”, since a sample cell involves a large number of particles with different sizes and properties. Namely, although our technique can select and manipulate one particle among others and analyze the particle simultaneously by a spectroscopic or electrochemical technique, the method cannot apply to study temporal profile measurements of a single microparticle upon an external stimulus, owing to interference by other untrapped particles. To study dynamics of chemical/physical processes in microparticles, therefore, a new laser trapping method, capable of “single-microparticle measurements”, is worth developing. As a possible approach to single-particle measurements, we explored development of a laser trapping-microspectroscopy technique combined with a fluid manifold. Our idea is as follows. By using a flow cell set on a microscope stage, an aqueous solution containing microparticles is introduced to the cell. With a single particle being trapped by a focused laser beam, other nontrapped particles are pumped out completely by flow of a sufficient amount of water to the cell. These procedures can hold exclusively the single particle in the cell. By using an appropriate fluid manifold, furthermore, an arbitrary reagent can be introduced to the cell, so that a temporal profile of chemical/physical responses of the particle would be monitored by a microspectroscopic method without interference by other particles. For further advances in (13) Kitamura, N.; Sekiguchi, N.; Kim, H.-B. J. Am. Chem. Soc. 1998, 120, 19421943. 10.1021/ac990450d CCC: $18.00
© 1999 American Chemical Society Published on Web 08/24/1999
Figure 1. Block diagram of a laser trapping-microspectroscopy system combined with a flow system.
microparticle chemistry, such an experimental approach is worth exploring. In the case of laser trapping-absorption microspectroscopy of individual microparticles so far reported, both trapping and probe beams are introduced coaxially to a microscope, so that the probe beam is always irradiated to the center of a trapped particle.4,11 This is the necessary condition for precise absorption microspectroscopy. For laser trapping under flow conditions, however, a particle is not necessarily trapped at the focal spot of an incident laser beam, since the particle experiences both trapping (gradient) and Stokes forces (viscous flow). Depending on the forces exerted on a particle, therefore, coaxial introduction of trapping and probe beams does not warrant precise absorption microspectroscopy, and optics for absorption measurements must be optimized. In the initial part of the paper, therefore, we discuss factors governing the trapped position of a particle in a flow cell in special reference to the Stokes (Fs) and trapping forces (Fg) exerted on the particle. On the basis of detailed analyses of Fs and Fg, we succeeded in precise absorption microspectroscopy of “single” microparticles even under solution-flow conditions. As an example of an application of the system, temporal profiles of the absorption spectrum of Rhodamine B (RhB) adsorbed on single ion-exchange resin particles are also discussed. EXPERIMENTAL SECTION Materials. Distilled and deionized water (Toray, Toraypure LV-08) was used throughout this work. Rhodamine B (Tokyo Kasei, Ace grade) was used as supplied. A cation-exchange resin (MCI-GEL; CK08Y, diameter d ) 25-30 µm; CK08C, d )16-22 µm; or CK08S, d ) 11-14 µm; Mitsubishi Chemicals), made of a divinylbenzene-styrene copolymer having SO3Na groups, was washed thoroughly with water prior to experiments. Apparatus. Figure 1 shows an experimental setup for laser trapping-microspectroscopy of “single” microparticles under solu-
tion-flow conditions. A glass microtube (100 µm depth, 1 mm width, and 5 cm length) was used as a flow cell. Two syringes equipped with the relevant syringe pump (pump 1 or pump 2, Harvard, model 44) were connected with the cell by Teflon tubing (860 µm i.d.) via a three-way valve. The length of the tube from the three-way valve to the cell was 5 cm. Details of a laser trapping-absorption spectroscopy system have already been reported.2,4 Briefly, a 1064-nm laser beam from a CW Nd:YAG laser (Spectron, SL902T) and a Xe lamp (Hamamatsu Photonics, L2274) were used as light sources for trapping and a probe beam for absorption measurements, respectively. Both light beams were introduced to an optical microscope (Nikon, Optiphoto 2) and focused on a sample solution (∼1 µm spot) through an oil immersion objective lens (×100, NA ) 1.30). The focal point of the Xe beam was set at the center of the cell along the beam axis (z axis). The Xe beam being passed through a laser-trapped particle was reflected by a half-mirror set under the microscope stage and led to a multichannel photodetector (Oriel, ICCD InstaSpec V with Multispec 275 polychromator) via an optical fiber. Under solution-flow conditions, a microparticle experiences viscous flow, so that laser power necessary for trapping of the particle should be adjusted to be much higher than that for conventional trapping (∼1 W). In the present experiments, therefore, laser power (P1064) was set at 5 W throughout the study. Under the present conditions, actual laser power irradiated to a microparticle was estimated to be 300 mW (6% of incident laser power). The large decrease in laser power is due to the low transparency of the microscope optics and the objective lens at 1064 nm and the aperture of the objective lens.14 Procedures. The following procedures were employed to trap “single” microparticles in a flow cell. First, an aqueous solution (14) Misawa, H.; Koshioka, M.; Sasaki, K.; Kitamura, N.; Masuhara, H. J. Appl. Phys. 1991, 70, 3829-3836.
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Figure 2. Relationships between flow rate and ∆y for the MCI resin particles with d ) 14 (closed circles), 19 (open circles), and 28 µm (closed triangles).
containing sample microparticles was sucked into the cell by using pump 2 (Figure 1) and only one particle among them was trapped by a 1064-nm laser beam. Second, other untrapped particles were pumped out by flowing a sufficient amount of water through pump 2. These procedures made it possible to trap and hold only one particle in the cell. In the present system, the cell volume was 5 µL so that it took a few minutes to pump out completely the untrapped particles at a solution flow rate of 2 µL/min. With the single microparticle being trapped, third, an aqueous RhB solution was introduced to the cell through pump 1 by switching the flow direction of the three-way valve. The time response of the absorption spectrum of a particle (transmitted light intensity, I) during dye solution flow was measured every 1 min. The incident light intensity of the Xe beam being passed through a dye-free particle (I0) was determined before introducing the dye solution. RESULTS AND DISCUSSION Under ordinary laser trapping conditions without solution flow, a microparticle whose refractive index is larger than that of the surrounding medium is trapped and fixed at the focal point of a laser beam owing to the gradient force (Fg) exerted on the particle.15-18 Therefore, one can conduct precise and reproducible absorption spectroscopy of individual microparticles by introducing both probe and laser beams coaxially to a microscope. Under flow conditions, on the other hand, a trapped particle experiences viscous flow (Stokes force, Fs) in addition to the gradient force, so that the position of the trapped particle shifts toward the downstream side of the laser beam focus (along the y axis in Figure 1) and the particle is trapped in balance with Fs and Fg; the displacement of the particle between the focal point of the laser beam and the actual trapped position is defined as ∆y as schematically illustrated in Figure 1. To conduct precise absorption microspectroscopy, therefore, quantitative discussion about ∆y as a function of a solution flow rate, particle size, and laser power (P1064) is needed. Laser Trapping of a Single Microparticle under Flow Conditions. In Figure 2, relationships between a flow rate (V) (15) Ashkin, A. Phys. Rev. Lett. 1970, 24, 156-159. (16) Ashkin, A. Biophys. J. 1992, 61, 569-582. (17) Ashkin, A. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 4853-4860. (18) Sheets, M. P., Ed. Laser Tweezers in Cell Biology; Academic Press: San Diego, 1998.
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and ∆y for the particles with different diameters (d ) 14-28 µm) are shown. The results demonstrate clearly that ∆y increases with an increase in V. For the particle with d ) 14 µm, as an example, ∆y was 2.5 µm at V ) 2.5 µL/min and a further increase in V resulted in detrapping of the particle from the laser beam focus. The ∆y value also depended on the particle diameter. For a given flow rate, the displacement was larger for a larger particle as seen in Figure 2. Although the data are not shown here, ∆y at a given V increased as laser power decreased. In the present experiments, laser power was set constant at 300 mW, so that ∆y is determined by V and d. The magnitude of ∆y is determined by the Stokes (Fs) and gradient forces (Fg) experienced by a particle as mentioned before, and both forces can be analyzed experimentally and theoretically. Therefore, before describing the results of absorption measurements, we discuss Fs and Fg exerted on a particle in reference to the flow characteristics in a microflow cell. Flow Characteristics in a Rectangular Cell and Stokes Force. For a spherical particle, the magnitude of Fs is given by the Stokes equation,19
Fs ) 6πηu(d/2)
(1)
where η and u are the viscosity and linear velocity of a fluid, respectively. To calculate Fs, the linear velocity should be known. In the present experiments, flow characteristics in the flow cell can be described as laminar flow owing to low Reynolds number flow (Re < 0.1). In such a case, the velocity of a fluid is purely axial along the flow direction in the cell (y axis; see Figure 1) but is dependent on the x and z coordinates: u(x, z). For a cylindrical cell with the radius of r0, the flow profile is described by parabolic or Hagen-Poiseuille flow; u becomes maximum (umax) at the center of the cell and is equal to 2 times the average velocity, uav ) (volume flow rate)/(cross-sectional area of the cell), while that at a position r from the center of the cell is given by umax [1 - (r/r0)2]. For a rectangular cell, however, the description of the relevant flow profile is not simple. Recently, rectangular or trapezoidal microchannels fabricated on silicon wafers or glass plates by micromachining technologies have been used as microfluidic devices,20,21 so that the flow characteristics in a rectangular cell and its implication to ∆y are worth discussing. For laminar flow, the mechanics of an incompressible liquid is given by the Navier-Stokes equation,22
∂u 1 + (u‚∇)u ) - ∇p + ν∇2u ∂t F
(2)
where F and ν are the density and viscosity of a liquid, respectively. Under the laminar flow condition, the components of the velocity (u) must satisfy u ) uy(x, z) and ux ) uz ) 0 (for the definitions (19) Faber, T. E. Fluid Dynamics for Physicists; Cambridge University Press: Cambridge, 1995. (20) Harrison, D. J., Van Den Berg, A., Eds. Micro Total Analysis Systems ’98; Kluwer: Dordrecht, 1998. (21) Kitamura, N.; Kim, H.-B.; Habuchi, S.; Chiba, M. Trends Anal. Chem., in press. (22) Ferziger, J. H.; Peric, M.; Computational Methods for Fluid Dynamics; Springer-Verlag: New York, 1996.
Figure 3. Contour map of u (a) along the cell width (x) and height (z), and relevant sectional views: (b) u(x, z ) 0) and (c) u(x ) 0, z). The numbers inserted in (a) are the u values, which are normalized to that at u(0, 0). Closed circles are the trapped-position dependence of ∆y (see main text), which are normalized to that at ∆y(0, 0).
of the coordinates, see Figure 1). Furthermore, div u ) 0 and the hydraulic pressure of a liquid (p) is a function of y alone. Also, the pressure gradient defined as dp/dy should be constant. Thus, eq 2 can be simplified to eq 3. Applying a nonslip condition
∂2u ∂2u 1 dp + )0 ∂x2 ∂z2 ν dy
(3)
(u ) 0 at the cell wall), the equation can be solved by using a finite element method. The results are shown in Figure 3 as a contour map of the velocity (a) along the cell width (x) and height (z), together with the relevant sectional view at z ) 0 (b) or x ) 0 (c). In this figure, the maximum u values are set at umax ) 1. The results show clearly that the velocity becomes maximum (u(0, 0) ) umax) at the center of a rectangular cell (x ) 0 and z ) 0) and is almost constant (∼umax) at |x| < 380 µm along the cell width (x axis), while that exhibits a parabolic profile along the z axis (cell height). It is very important to note that the flow profiles along the x and z axes depend on the aspect ratio (short axis/ long axis) of a rectangular cell (data are not shown). Along the long axis, u shows a relatively plateaulike profile, particularly that in the middle part of the cell in the present case, while the velocity profile along the short axis is always parabolic. The difference in the velocity profile between the two axes and its aspect ratio dependence influence the ratio of umax to uav: R ) umax/uav. The uav value is calculated by dividing a volume flow rate (summation of u in the x-z plane) by the cross-sectional area of the cell. An increase in the aspect ratio from 0 to 1 (square) brings about that in R from 1.5 to 2.1. These are the characteristic features of a rectangular cell as compared with the flow profile in a cylindrical tube: point-symmetric flow profile with respect to the center of a tube, and R ) 2 irrespective of the tube radius. The aspect ratio of the cell used in this study is 0.1 so that umax is calculated to be 1.6 uav. The volume flow rate of 2.5 µL/ min implies uav ) 0.42 mm/s. The linear velocity of water in the center of the cell, u(0, 0), is then calculated to be 0.67 mm/s. Knowing the flow velocity, therefore, the Stokes force exerted on the particle with d ) 14 µm can be determined to be 87 pN based on eq 1.
Figure 4. Relationship between Stokes force and ∆y: d ) 14 (closed circles), 19 (open circles), and 28 µm (closed triangles). The solid line is the theoretical curve of the gradient force calculated from the Ashkin’s theory (see text and ref 16). Following values were used for the calculation: actual laser power (P1064) ) 300 mW, n(H2O) ) 1.33, and n(particle) ) 1.5.
In the case of laser trapping under flow conditions, a particle is trapped at a certain laser-irradiated position, at which the particle experiences Fs ) Fg. For the particle with d ) 14 µm, when the focal point of the trapping laser beam is shifted along the x or z axis from the center of the cell, Fs experienced by the particle decreases owing to the decrease in u as shown in Figure 3. Therefore, the trapped position also varies, ∆y. Since our experimental setup enables three-dimensional manipulation of the particle, a position dependence of ∆y in the flow cell at a given volume flow rate (2.5 µL/min) can be studied. The results are included in parts b and c of Figures (closed circles), which demonstrate clearly that the position dependence of ∆y agrees with that of u.23 The flow profile in the cell can be determined experimentally by using the laser trapping technique. Also, the results indicate that the flow characteristics in a rectangular cell are described satisfactorily by the Navier-Stokes equation. Determination of the Gradient Force. It is known that optical trapping of a particle can be understood in terms of the basic principle of conservation of momentum.1,15-18 Photons carry momentum, and the interaction of light with matter results in a change of photon momentum through the processes of reflection, refraction, and scattering. The corresponding forces, termed scattering and gradient forces, are the two specific force components that govern the trapping process. Under flow conditions, a trapped particle shifts its position along the flow direction (y axis) as discussed above, which implies that the main force restoring the particle toward the focal point of an incident light beam is the gradient force. Therefore, we consider here the gradient force in the following discussion. In the Mie scattering regime (2π(d/2)/λ . 1, where λ is the wavelength of incident light), Ashkin has reported that the gradient force can be analyzed by examining the change in momentum of propagating light rays.16,18 For the light beam with a given incident angle (θ), the gradient force (Fg(θ)) exerted on a particle is given by, (23) Strictly speaking, a microparticle should act as an obstacle of the HagenPoiseilli flow, which means that the parabolic flow vector distribution is influenced by presence of the particle. However, the Re number is small (,0.1) due to the small size of the particle (d ) 14 µm), so that flow around the particle is considered to be laminar and irrotational flow. Thus, we consider that such effects on ∆y can be neglected.
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Fg(θ) )
{
}
T2[sin(2θ - 2φ) + R sin 2θ] nP R sin 2θ c 1 + R2 + 2R cos 2φ
(4)
where φ is the angle of refraction and R and T are Fresnel reflection and refraction coefficients. n is the refractive index of the surrounding medium (n(water) ) 1.33), c is the speed of light, and P is power of incidence (300 mW at 1064 nm). The total force is obtained by summing the forces from all individual rays passed over the particle, where the gradient force is defined as the vector sum of the gradient component from each individual ray. As discussed in detail by Ashkin, Fg experienced by a particle at a given P is a function of the radius of the particle (d/2) and the mutual position between the particle and focal spot of a laser beam (i.e., ∆y).16 Referring to Ashkin, we introduce a normalized displacement defined as S ) ∆y/(d/2), and Fg(S) is Fg experienced by the particle with d at ∆y. When a spherical particle is trapped at the focal point of incident light, the gradient force is canceled in total and thus Fg(0) is zero. If the position of a trapped particle deviates from the laser focus, the force exerted on the particle directs toward the focal point: toward a higher light intensity region. Under flow conditions, a particle always experiences viscous flow so that the particle is trapped at the position satisfying Fg ) Fs. By measuring S, therefore, Fg can be determined experimentally. As an example, Fs exerted on the particle with d ) 14 µm is calculated to be 87 pN at V ) 2.5 µL/min as described in the preceding section. For this particle, ∆y was observed to be 2.5 µm, so that Fg(S ) 0.36) should be 87 pN. Analogous calculations were conducted for all the data in Figure 2, in which each Fs value was calculated from eq 1 with u(0, 0) ) umax ) 1.6 uav. The results are shown in Figure 4. Although the data are somewhat scattered, Fs or Fg increased with an increase in S (either by an increase in ∆y or decrease in d) with a range of 10-90 pN. On the other hand, the theoretical Fg value was calculated on the basis of eq 4 by summing the forces from all individual rays passed over the particle, and the result is shown by the solid curve in Figure 4. It is clear from Figure 4 that the experimental observations almost fall on the theoretical curve. This demonstrates that ∆y and Fg can be determined precisely by the present experiments. Furthermore, the results indicate that the flow rate and particle diameter dependencies of ∆y in Figure 2 are explained within the framework of the theory by Ashkin. On the basis of fundamental understandings of the factors governing laser trapping under flow conditions, precise absorption measurements of single microparticles were made possible. In Situ Observation of Dye Adsorption Processes in Single Microparticles under Flow Conditions. As mentioned above, depending on V and d, the displacement of a particle must be compensated experimentally by shifting the position of either the probe beam or trapping beam to record a correct absorption spectrum. For absorption microspectroscopy, probe light should be a parallel beam and its beam size is adjusted as small as possible.11 In the actual experiments, a probe beam diameter is set at ∼1 µm as a paraxial ray of the objective lens. Thus, a shift of the probe beam position with a variation of V or d is very difficult. Depending on V and d, therefore, we varied the position of the trapping laser beam focus by controlling a movable mirror outside of the microscope (Figure 1). Under such conditions, we 4342 Analytical Chemistry, Vol. 71, No. 19, October 1, 1999
Figure 5. Time response of the absorption spectrum of a single microparticle (CK08C, d ) 20 µm) during flow of an aqueous RhB solution: V ) 2 µL/min, [RhB] ) 1 × 10-5 M. The spectrum taken every 2 min is shown here.
succeeded in observing correct absorption spectra of single microparticles at various V and/or d. As a typical example, a time response of the absorption spectrum of a single microparticle (CK08C, d ) 20 µm) during flow of an aqueous RhB solution ([RhB] ) 1 × 10-5 M, V ) 2 µL/min) is shown in Figure 5. An absorption band having a peak at around 565 nm increased with a time t after introducing the dye solution from pump 1 to the flow cell. However, absorption was not observed at t < 15 min, the induction period. This characteristic time agreed very well with the time predicted from the flow rate and the dead volume of the fluid channel, from the outlet of the three-way valve to the particle. The observed spectra in Figure 5 were in good agreement with that reported for RhB adsorbed on MCI resin beads.5,24 Furthermore, absorbance of the solution phase is predicted to be 0.01 as calculated from the molar absorptivity of RhB ((RhB) ) 1.1 × 105 M-1 cm-1) and the optical path length (100 µm). The value is much smaller than the observed values. Therefore, the observed spectrum is concluded to be ascribed to RhB adsorbed on the single MCI particle. Determination of the Mass-Transfer Coefficient for Ion Exchange. The time response of the absorption spectrum in Figure 5 provides information about the adsorption processes of RhB on the microparticle. Therefore, we conducted analogous experiments under different experimental conditions. In Figure 6, time courses of RhB absorbance at 566 nm observed for three single-microparticles are summarized. Although an induction period was observed in every case as discussed in the previous section, the absorbance increased almost linearly with time irrespective of the conditions, while the slope of the plot (dA/dt) was dependent on both flow rate and RhB concentration, as summarized in Table 1. As reported in the previous paper, diffusion of RhB in MCI resin particles is very slow and RhB is adsorbed exclusively on the surface layer (∼1 µm) of the particle during the first 1 h.3 In such a case, the observed absorbance becomes one-third of that at a homogeneous dye distribution in the whole particle for the same total number of dye molecules.11 Therefore, the adsorption rate (N) is calculated by eq 5. At V ) 2 µL/min and [RhB] ) 1 × 10-5 M, as an example, N for the resin particle with d ) 20 µm is calculated to be 5.2 × 10-15 mol min-1 particle-1 (Table 1). To (24) Kim, H.-B.; Habuchi, S.; Kitamura, N. Anal. Chem. 1999, 71, 842-848.
rate is related to the mass-transfer coefficient of an ion (kf) across a water/particle boundary and is given as in eq 6, where πd2 is
N ) kfπd2(Cs - Cp)
Figure 6. Time course of the RhB absorbance at 565 nm. The numbers in the figure correspond to the run number in Table 1. t ) 0 represents the time at which the dye absorbance is observed. Table 1. Adsorption Rates of RhB on Single MCI Resin Particles (d ) 20 µm) run
V/ µL min-1
[RhB]/ 10-6 M
dA/dt/ min-1
N/10-15 mol min-1
kf/10-4 cm s-1
1 2 3
1 2 2
10 10 5
0.046 0.091 0.053
2.6 5.2 3.0
3.6 6.9 7.9
N)3
dA 1 4 d π dt d 3 2
3
()
(5)
the best of our knowledge, this is the first determination of a single-microparticle-based adsorption rate. Thus, the results are worth comparing with those obtained by particle-unresolved measurements. In the previous experiments,3,5 we soaked 2 mg of MCI resin particles in 100 mL of an aqueous RhB solution ([RhB] ∼ 10-7 M). Knowing the specific gravity of the particle to be 0.7, the number of particles included in the sample is calculated to be ∼106. The adsorption rate of RhB can be thus estimated to be 5 × 10-9 mol min-1 per 2 mg of particles or 5 × 10-15 mol min-1 particle-1. The value agrees satisfactorily with that determined for the single microparticle; this proves the accuracy of the present experiments. These discussions also indicate that almost of all RhB molecules in the solution phase are adsorbed on the particle within a few minutes. Actually, this was confirmed by both present and previous experiments. All the results can be explained by the single context of very fast adsorption of RhB on the particle surface and subsequent slow diffusion/ion exchange of the ion toward the particle interior. It is worth further discussion of both the ratio of the adsorbed mole number of RhB to the ion-exchange capacity of the particle and the flow rate and concentration dependencies of N. First, the results in Figure 6 demonstrate that 5.2 × 10-14 mol of RhB is adsorbed on the particle during the first 10 min. Since the ionexchange capacity of a MCI particle is 10-11 equiv/particle, that in the surface layer with the thickness of 1 µm is calculated to be 1.4 × 10-12 equiv. The RhB molecules exchanged in the particle (3.7%) are far below the ion-exchange capacity of the particle. Second, as shown in Table 1, N is almost proportional to both flow rate and RhB concentration in the solution phase. These results suggest that ion exchange proceeds in a film-diffusion control.25,26 In such a case, it has been reported that the adsorption
(6)
the surface area of a particle and Cs and Cp are the concentrations of an ion in the solution phase and the particle surface, respectively. Assuming Cp ∼ 0 in the initial stage of ion exchange, we calculated the kf value as the data were included in Table 1. In the film-diffusion theory, kf can be related to the film thickness (δ) and the diffusion coefficient of an ion in a solution phase (Ds): kf ) Ds/δ. Assuming Ds ) 4 × 10-6 cm2 s-1, which is a typical value for Ds in water, the δ value can be estimated to be 50-100 µm, depending on V. The values are comparable to those reported for many mass-transfer processes across interfaces.25 We have already reported that the diffusion coefficient of an ion in the particle (Dp) can be determined directly by several microspectroscopy techniques. As a future study, therefore, discussion on both Dp and kf will be very fruitful for understanding the kinetics of the ion-exchange processes in detail. CONCLUSION In this paper, we demonstrated that a combination of a laser trapping-microspectroscopy technique with a microflow system had a high potential for conducting single-particle measurements, and the new methodology was applied successfully to studying adsorption processes of RhB on single ion-exchange resin particles. Different from conventional laser trapping-microspectroscopy for particle-resolved measurements, the present method can monitor directly time responses of single microparticles upon an external stimulus without interference from other particles. The absence of interference from nontrapped particles is of primary importance for obtaining quantitative information about time responses of single microparticles. As an example, the method would be applied to studying dynamic aspects of chemical responses of single biocells. Although various applications of the system are expected, further miniaturization of the system, in particular, that of the fluid manifold, is required since the dead volume of the system is very large compared to the volume of a microparticle: large volumes of the flow cell and tubing. By using a microfluidic device fabricated by micromachining technologies, the dead volume could be reduced. Such an approach is now under investigation in our research group. ACKNOWLEDGMENT The authors acknowledge a Grant-in-Aid from the Ministry of Education, Science, Sports and Culture, Japan (10440218 to H.B.K. and 08404051 and 10354012 to N.K.) for partial support of the research. The work is also supported partly by a Grant for the Priority Research Area B on “Laser Chemistry of Single Nanometer Organic Particles” to N.K. (10207201). Received for review April 28, 1999. Accepted July 7, 1999. AC990450D (25) Helfferich, F. Ion Exchange; McGraw-Hill: New York, 1962. (26) Cussler, E. L. Diffusion-Mass Transfer in Fluid Systems, 2nd ed.; Cambridge University Press: Cambridge, 1997.
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