Direct Analysis of Intraparticle Mass Transfer in Silica Gel Using Single

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Langmuir 2000, 16, 9256-9260

Direct Analysis of Intraparticle Mass Transfer in Silica Gel Using Single-Microparticle Injection and Microabsorption Methods Kiyoharu Nakatani* and Tomomi Sekine Department of Chemistry, University of Tsukuba, Ibaraki 305-8571, Japan Received June 23, 2000. In Final Form: September 5, 2000 Sorption and desorption processes of cationic dyes occurring in single silica gel microparticles in an aqueous solution were kinetically studied by microcapillary manipulation/injection and microabsorption methods. The sorption and desorption rates of rhodamine 6G were limited by diffusion of the dye in the particle interior. For methylene blue, the desorption rate was slow compared with the sorption rate, and the rate-determining step was not the diffusion of the dye. The sorption and desorption processes of the dyes were discussed in terms of intraparticle diffusion as well as of that accompanied by slow desorption.

1. Introduction Sorption and desorption processes of a solute in a microparticle system are governed by adsorption/desorption at the solid/liquid interface, mass transfer from the surrounding solution phase to a microparticle, intraparticle diffusion of the solute, and so forth. So far, these processes have been frequently analyzed for a large number of microparticles. However, individual microparticle measurements are indispensable for quantitative and detailed analyses, because these processes are expected to highly depend on the particle size and the surface area of the particle. Individual microparticle measurements in solution containing a large number of microparticles have been reported for chemical processes in the particle interior and on the surface using microspectroscopy and microelectrochemistry.1-3 For sorption processes, extremely slow intraparticle diffusion proceeding in polymer microparticles was spectroscopically analyzed on the basis of the individual particle measurements under stationary conditions.4,5 Nevertheless, the sorption and desorption processes of a solute in a microparticle system under stationary conditions are influenced by the distance from the surrounding particles and the number of particles as a change in the solute concentration in the vicinity of the measured microparticle. Thus, analyses of these processes on the basis of the individual particle measurements are scarcely performed except for limited cases.4,5 Recently, the sorption rate of a solute into a single microparticle introduced in a thin-layer cell has been reported by laser trapping and microspectroscopy under solution-flow conditions.6 This technique is based on single-particle measurements in the absence of other particles, so that the technique will enable one to quantitatively analyze the sorption/desorption processes in a microparticle system. However, the dead volume of the flow cell was large and (1) Masuhara, H., DeSchryver, F. C., Kitamura, N., Tamai, N., Eds. Microchemistry: Spectroscopy and Chemistry in Small Domains; NorthHolland: Amsterdam, 1994. (2) Kitamura, N.; Nakatani, K.; Kim, H.-B. Pure Appl. Chem. 1995, 67, 79. (3) Nakatani, K.; Chikama, K.; Kitamura, N. In Advances in Photochemistry; Neckers, D. C., Volman, D. H., von Bunau, G., Eds.; John-Wiley & Sons: New York, 1999; Vol. 25. (4) Kim, H.-B.; Habuchi, S.; Hayashi, M.; Kitamura, N. Anal. Chem. 1998, 70, 105. (5) Kim, H.-B.; Hayashi, M.; Nakatani, K.; Kitamura, N. Anal. Chem. 1996, 68, 409. (6) Kim, H.-B.; Kogi, O.; Kitamura, N. Anal. Chem. 1999, 71, 4338.

the flow rate was very slow; therefore, a detailed kinetic analysis was not reported in the investigation. Therefore, other techniques based on single-particle measurements in the absence of other particles are necessary for the kinetic analyses of the sorption and desorption processes. Studies on the sorption and desorption processes in silica gel systems are important because silica gel is a typical adsorbent and is used in various fields. Particularly, these processes are the underlying processes of analytical and preparative separations for chemical and biological compounds. Furthermore, the sorption and desorption processes in silica gel are significant as models of the transport and degradation of chemical compounds in natural particles in the environment. The adsorption rates of small molecules at a solid/liquid interface are very fast in silica gel systems;7,8 so the sorption rates of solutes into silica gel particles can be successfully analyzed by an intraparticle diffusion model.9 On the other hand, desorption processes are not clarified and generally very complicated compared with the sorption processes in microparticle systems. Fast and slow desorption processes have been reported in silica gel systems, and high-energy adsorption at the silica surface and diffusion in the micropores of the particle are proposed as explanations for the slow desorption processes.10-13 However, detailed kinetic analyses are required for the desorption processes in particle systems. Recently, we have developed a microabsorption technique combined with microcapillary injection of a single microparticle.14 By using the technique, only a single microparticle was injected into a dye solution, and the time dependence of the absorption spectrum of the dye extracted into the single microparticle was measured. The technique was shown to have sufficient potential to kinetically analyze the sorption process, as a preliminary report.14 In this article, after the sorption equilibrium of (7) Waite, S. W.; Marshall, D. B.; Harris, J. M. Anal. Chem. 1994, 66, 2052. (8) Waite, S. W.; Holzwarth, J. F.; Harris, J. M. Anal. Chem. 1995, 67, 1390. (9) Ghosh, A. C.; Satyanarayana, K.; Srivastava, R. C.; Dutta, N. N. Colloids Surf., A 1995, 96, 219. (10) Wirth, M. J.; Swinton, D. J. Anal. Chem. 1998, 70, 5264. (11) Werth, C. J.; Reinhard, M. Environ. Sci. Technol. 1997, 31, 697. (12) Farrell, J.; Grassian, D.; Jones, M. Environ. Sci. Technol. 1999, 33, 1237. (13) Pignatello, J. J.; Xing, B. Environ. Sci. Technol. 1995, 30, 1. (14) Nakatani, K.; Sekine, T. J. Colloid Interface Sci. 2000, 225, 251.

10.1021/la000885s CCC: $19.00 © 2000 American Chemical Society Published on Web 11/01/2000

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Figure 2. Absorption spectra of R6G in a single silica gel microparticle (d ) 90 µm) for (a) sorption (Cw ) 4 × 10-6 mol/ dm3) and (b) desorption (Cw ) 0) processes.

Figure 1. Block diagram of a microcapillary manipulation/ injection-microabsorption system.

a cationic dye in the single silica gel system, the microparticle was injected into an aqueous solution without the dye, and then the desorption process from the microparticle was analyzed using the technique. Desorption and intraparticle diffusion processes of cationic dyes in single silica gel microparticles are discussed in detail. 2. Experimental Section Chemicals and Sample Preparations. Spherical silica gel (Kanto Chemical Co., Inc., Silica Gel 60: particle size, 40-100 µm; surface area, 700 m2/g; bulk density, 0.40 g/cm3; pore size, 6.5 nm; pore volume, 1.15 cm3/g), rhodamine 6G (R6G; Wako Pure Chemical Industries, Ltd., Pr. grade), methylene blue (MB; Chroma Gesellschaft Schmidt & Co., alkaline (Loeffler)), HCl (Wako Pure Chemical Industries, Ltd., for volumetric analysis), and KCl (Wako Pure Chemical Industries, Ltd., S grade) were used without further purification. Water was used after distillation and deionization (Yamato Scientific Co., Ltd., Autostill WG221). For the sorption measurements, a single silica gel microparticle in an aqueous KCl (0.1 mol/dm3) and HCl (0.01 mol/dm3) solution was injected into an aqueous dye, KCl (0.1 mol/dm3), and HCl (0.01 mol/dm3) solution. HCl and KCl were used to minimize adsorption of the dye on the glassware during the sample preparation.15 For the desorption measurements, the same microparticle in the aqueous dye solution at the sorption equilibrium of the dye was injected into an aqueous solution (KCl (0.1 mol/dm3), HCl (0.01 mol/dm3)). Apparatus. Absorption spectra of the dye in a single microparticle were measured using microcapillary manipulation/ injection and microabsorption methods (Figure 1). A microcapillary (outer tip radius, 100-150 µm) prepared by a puller (Narishige Co., Ltd., PC-10) was connected to a manipulation/ injection system (Narishige Co., Ltd., MN-151, MMW-200/IM16) and was placed on an optical microscope (Olympus Co., IX70). A single spherical silica gel microparticle in solution was sucked into the microcapillary and then injected (< ∼5 × 10-9 dm3 as a solution volume containing the single microparticle in the microcapillary) into a sample solution (2 cm3) onto a glass dish placed on the scanning stage of the microscope using the manipulation/injection system. The silica gel microparticle sank in water, and no Brownian motion of the particle was observed under stationary conditions. As a monitor beam for the microabsorption method, a light beam from a halogen lamp (Mejiro Precision Co., PHL-150) was introduced into the optical microscope through a pinhole (100 µm). The single particle was positioned by the scanning stage, and the monitor beam was focused onto the single particle (spot size of the monitor beam, (15) Lee, C.; Sung, Y. W.; Park, J. W. J. Phys. Chem. B 1999, 103, 893.

Figure 3. Absorption spectra of MB in a single silica gel microparticle (d ) 55 µm) for (a) sorption (Cw ) 4 × 10-6 mol/ dm3) and (b) desorption (Cw ) 0) processes. 2-3 µm) using an objective lens (Olympus Co., LCPlanFl 60xPh). The transmitted light intensity that passed through the particle center was collected by a condenser lens (Olympus Co., IX-LWUCD) and detected by a multichannel photodetector (Hamamatsu Photonics Co., PMA11, C7473-36). To cancel out the dye absorption in water, the incident light intensity in the vicinity of the particle was used as a reference to record the absorption spectrum. Manipulation/injection of a single particle was monitored by a CCD camera (Olympus Co., CS220). All singleparticle measurements were performed at 25 ( 0.5 °C by a temperature controller (Kitazato Supply Co., Ltd., MD-10RFO).

3. Results A single silica gel microparticle was injected into an aqueous R6G or MB solution (dye concentration in water, Cw), and the absorption spectra of the dye in the single microparticle (particle diameter, d) for the sorption process were measured versus time (t). When the particle was injected into the solution, the time was assumed to be 0. The absorbance (A) of the dye increased with t and became saturated, as shown in Figures 2a and 3a. After the saturation of A of the dye, the same microparticle was sucked from the solution and then injected into an aqueous solution in the absence of the dye (Cw ) 0). The absorption spectra of the single microparticle for the desorption process were measured versus t (Figures 2b and 3b). With sufficient time, the dye was completely desorbed from the microparticle. Light scattering of the monitor beam from the spherical surface of the particle will increase with decreasing d. However, the shape of the spectrum of the dye in the silica gel (d ) 40-100 µm) was analogous to that of the monomer band in water (determined by separate experiments using a conventional absorption method).15 Moreover, the correct absorption spectra were reported to be measured at d > ∼10 µm for microdroplets

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Figure 4. Time dependencies on peak absorbance (520 nm) of R6G in a single silica gel microparticle (d ) (a) 90 or (b) 56 µm) for sorption (Cw ) 4 × 10-6 mol/dm3) and desorption (Cw ) 0) processes. The solid curves represent the simulations of A(t) by eqs 1-5.

in water using similar microabsorption methods.16-18 Therefore, the contribution of light scattering to the absorption spectrum is negligibly small in the present system. To analyze the sorption and desorption processes without any solute-solute interaction such as aggregation of the dye in the particle and the solution, the sorption of R6G or MB was performed at Cw e 1 × 10-5 or 4 × 10-6 mol/dm3, respectively. The time dependence of A of R6G (520 nm) or MB (664 nm) in a single microparticle for the sorption (Cw ) 4 × 10-6 mol/dm3) and desorption processes is shown in Figure 4 or 5, respectively. The saturated A during the sorption process for each dye was directly proportional to d (40100 µm) at the same Cw, indicating that the dye is extracted into the particle interior. Therefore, the dye concentration in a particle at the sorption equilibrium (Cp,eq) can be determined from Lambert-Beer’s law as an optical path length equal to d. The molar extinction coefficients of R6G (520 nm) and MB (664 nm) () were assumed to be equal to 9.14 × 104 and 6.82 × 104 cm-1 mol-1 dm3 in water, respectively (determined by separate experiments). The Cp,eq value of R6G in a single silica gel particle with d ) 90 µm is calculated to be 4.0 × 10-4 mol/dm3 (Figure 4a). The error in determining Cp,eq is mainly caused by an uncertainty in d due to the slight distortion from spherical of the silica gel ((5% as d) and is estimated to be (5%. The amount of R6G molecules in the particle (d ) 90 µm) is 1.5 × 10-13 mol while that in water (in 2 cm3) is 8 × 10-9 mol (Cw ) 4 × 10-6 mol/dm3) at the sorption equilibrium. On the other hand, the R6G concentration in water is estimated to be 7.5 × 10-11 mol/dm3 (1.5 × 10-13 mol in 2 cm3) after complete desorption of the dye from the particle (d ) 90 µm) during the desorption process. Therefore, changes in Cw in the sorption and desorption processes can be neglected due to the small single-microparticle/ water volume ratio in the present single-particle measurements. The time required to saturated A in the sorption process (ts) decreased with decreasing d (Figures 4 and 5). On the other hand, the ts value was independent of Cw for similar sized particles in the present Cw range, as previously reported.14 Because 1/Cp,eq was proportional to 1/Cw for each dye, the Langmuir isotherm constant (K, 1.3 × 105 (R6G), 1.1 × 105 mol-1 dm3 (MB)) and the Langmuir (16) Funakura, S.; Nakatani, K.; Misawa, H.; Kitamura, N.; Masuhara, H. J. Phys. Chem. 1994, 98, 3073. (17) Nakatani, K.; Suto, T.; Wakabayashi, M.; Kim, H.-B.; Kitamura, N. J. Phys. Chem. 1995, 99, 4745. (18) Nakatani, K.; Suzuki, T.; Shitara, S.; Kitamura, N. Langmuir, 1998, 14, 2286.

Nakatani and Sekine

Figure 5. Time dependencies on peak absorbance (664 nm) of MB in a single silica gel microparticle (d ) (a) 103 or (b) 55 µm) for sorption (Cw ) 4 × 10-6 mol/dm3) and desorption (Cw ) 0) processes. The solid curves represent the simulations of A(t) by eqs 1-5.

constant (Cp,∞, 1.2 × 10-3 (R6G), 3.9 × 10-3 mol/dm3 (MB)) were determined on the basis of the Langmuir isotherm: Cp,eq ) KCp,∞Cw/(1 + KCw). Using the known values (bulk density, 0.40 g/cm3; surface area, 700 m2/g), the saturated R6G and MB concentrations on the silica gel surface were determined to be 4.3 × 10-13 and 1.4 × 10-12 mol/cm2, respectively. Besides ts, the time to A ) 0 in the desorption process (td) decreased with decreasing d (Figures 4 and 5) and was independent of Cw of the sorption process for similar sized particles as well. 4. Discussion Intraparticle Diffusion. The sorption and desorption processes depend on the diffusion in water, adsorption/ desorption at the solid/water interface, and intraparticle diffusion of the dye. Since the diffusion of the dye from the bulk water phase to the micrometer-sized particle is spherical, the mass transfer rate is very efficient.19 Indeed, the mass transfer rate constant (kdif) between the bulk water phase and the microparticle surface with d ) 55 µm is estimated to be 2 × 10-3 cm/s on the basis of the equation kdif ) 2D/d,19 where D is the diffusion coefficient of the solute in water (5 × 10-6 cm2/s as a typical value). On the other hand, the time scale of the sorption and desorption processes is several minutes (Figures 4 and 5). Therefore, the time dependencies of A (A(t)) for the sorption/ desorption processes can be analyzed as the dye concentration in water near the particle surface, which is equal to Cw. Frequently, sorption processes of a solute in silica gel are analyzed by an intraparticle diffusion model due to the fast adsorption/desorption rates.9,20,21 In the present system, Cw is relatively low, and ts and td are independent of Cw of the sorption process so that surface diffusion is expected to proceed in the particle interior.21 According to a surface diffusion model in the spherical particle, the time dependence of the radial concentration profile of the dye in the particle (Cp(r,t)) is given by eq 19, 20,21

∂Cp(r,t)/∂t ) Dp[∂2Cp(r,t)/∂r2 + (2/r)∂Cp(r,t)/∂r] (1) where Dp and r are the diffusion coefficient of the dye in the particle interior and the spatial coordinate radially directed, respectively. The initial and boundary conditions (19) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; John Wiley & Sons: New York, 1980; Chapter 5. (20) Mathews, A. P.; Weber, W. J., Jr. AIChE Symp. Ser. 1976, 73, 91. (21) Yoshida, H.; Yoshikawa, M.; Kataoka, T. AIChE J. 1994, 40, 2034.

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are given by

Cp(r,0) ) 0 or Cp,eq (sorption or desorption)

(2)

Cp(d/2,t) ) Cp,eq or 0 (sorption or desorption) (3) ∂Cp(0,t)/∂r ) 0

(4)

A(t) can be calculated using eq 5.

A(t) ) 2

∫0d/2Cp(r,t) dr

(5)

Cp(r,t) and A(t) were simulated by a finite form for various Dp values under the conditions of ∆t ) 0.5 s, ∆r ) 1 µm, and Dp∆t/(∆r)2 < 0.5. In the R6G system, the time dependencies of the sorption and desorption processes are fitted by Dp ) (4-5) × 10-9 cm2/s with an error of about (15% (solid lines in Figure 4). It is noteworthy that the Dp value is independent of the particle size. The average diffusion coefficients of quaternary salts in silica gel (pore size, 7.5 nm; pore volume, 0.4-0.5 cm3/g) have been reported to be 1 × 10-8 cm2/s for various sized particles using a batch uptake method.9 The Dp value of R6G nearly agrees with those of the quaternary salts, so that the rate-determining step of the sorption/desorption processes in the R6G system is the surface diffusion in the particle interior. In the MB system, data for the sorption or desorption process are apparently reproduced by a simulation. However, the best-fitted Dp value in the sorption process (2 × 10-9 cm2/s at d ) 55 µm) is twice that in the desorption process (1 × 10-9 cm2/s at d ) 55 µm), as seen in Figure 5. Analogous results were obtained for Cw ) 1 × 10-6 and 2 × 10-6 mol/dm3 in the MB system, and the Dp values in the sorption process were 1.5-2 times as large as those in the desorption process. The variations of Dp in these processes exceed the error limit ((15%). If the ratedetermining step of the mass transfer process in the MB system is the intraparticle diffusion, Dp in the sorption process should be in good agreement with that in the desorption process. Therefore, the sorption and desorption processes in the MB system cannot be analyzed on the basis of the intraparticle diffusion model. Slow Desorption. Fast and slow desorption processes have been reported in silica systems.10-13 The fast and slow desorption rates are explained as diffusion in the mesopores (2-50 nm) and micropores (< ∼2 nm) of the particle interior or low- and high-energy adsorption on the silica surface, respectively. In the present system, the time dependence of the desorption process of MB is apparently fitted by the diffusion equation with a single diffusion coefficient, different from that in the sorption process. Therefore, simultaneous-reaction-type kinetics with fast and slow diffusion coefficients would not explain the present results, and the time dependencies of the sorption/desorption processes should be analyzed on the basis of consecutive-reaction type kinetics. As a consecutive-reaction type model, the time dependencies of these processes were simulated by an intraparticle diffusion model accompanied by slow desorption. In this model, the adsorption/desorption equilibrium is not assumed to be established due to slow desorption. In the particle interior, Cp(r,t) is approximated to eq 1 using the effective diffusion coefficient of the dye (Dpe) including the contribution of the slow desorption. Although Cp(d/2,t) is Cp,eq due to fast adsorption in the sorption process, it is not approximated to be 0 in the desorption process. Therefore, Cp(r,t) in the surface layer of a microparticle in the desorption process

Figure 6. Time dependencies on peak absorbance (664 nm) of MB in a single silica gel microparticle (d ) (a) 103 or (b) 55 µm) for sorption (Cw ) 4 × 10-6 mol/dm3) and desorption (Cw ) 0) processes. The solid curves represent the simulations of A(t) by eqs 1-7.

is simulated by eq 6.

∂Cp(r,t)/∂t ) Dpe[∂2Cp(r,t)/∂r2 + (2/r)∂Cp(r,t)/∂r] AkdCp(r,t)/V (6) where A and V are the surface area facing the water phase and the volume of the surface layer of the particle, respectively, and kd is the slow desorption rate constant in the surface layer. The boundary condition in the surface layer of a particle is given by eq 7.

∂Cp(d/2,t)/∂r ) 0

(7)

For a simulation of the desorption curve, the Dpe value was fixed as the best-fitted value calculated from the sorption curve of the same particle (Dpe ) (2-3) × 10-9 cm2/s) and the curve fit of A(t) was performed by eqs 1-7 with kd as a variable parameter under the conditions of ∆t ) 0.5 s, ∆r ) 1 µm, A ) 4π(d/2)2, V ) 4π{(d/2)3 - (d/2 - ∆r)3}/3, and Dpe∆t/(∆r)2 < 0.5. The best fit of the data was attained with kd ) 2 × 10-6 cm/s, which was independent of d (40-100 µm) and Cw ((1-4) × 10-6 mol/ dm3), suggesting that the results can be analyzed by the slow desorption-diffusion model (Figure 6). The desorption of R6G is fast (discussed above) and the pore (mesopore) size of the silica gel (6.5 nm) is much larger than the molecular size of MB or R6G (∼1 nm), so that the slow desorption of MB is not caused by the mesopore size and the curved pore of the silica gel. The molecular size of R6G is slightly larger than that of MB. If a micropore (< ∼2 nm) exists on the mesopore (6.5 nm) wall in the present silica and MB could enter into the micropore alone, the desorption rate of MB may be slow compared with that of R6G. To confirm this, sorption and desorption measurements of acridine orange (AO) having a molecular size analogous to that of MB were performed in single silica gel particles, although the measurements could be performed only at Cw ) 4 × 10-6 mol/dm3 without any dimer formation of AO in the particle (peak wavelength ) 492 nm,  ) 4.40 × 104 cm-1 mol-1 dm3). In this case, the sorption and desorption curves were similar to those in the MB system, and Dpe and kd could be determined to be 6 × 10-9 cm2/s and 8 × 10-6 cm/s on the basis of the slow desorption-diffusion model, respectively. The kd value of AO is four times that of MB, suggesting that the slow desorption in the silica gel system is not ascribed to the trap in only the micropores. The component ratio of the adsorption site in such a micropore or a high-energy adsorption site has been reported to be relatively small (, ∼1),10-12 while the slow desorption observed in the MB

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or AO system is the main component with a component ratio of > ∼0.9. Therefore, the desorption at the silica/ water interface will be essentially slow in the MB or AO system. 5. Conclusions We succeeded for the first time in the quantitative measurements of the intraparticle mass transfer of a single silica gel microparticle and observed the slow desorption of MB or AO in the silica gel particle based on the singleparticle injection and microabsorption methods. In situ measurements of both the sorption and desorption processes for the same single particle and the particle size

Nakatani and Sekine

dependencies of the sorption and desorption rates are indispensable for discussing the microscopic mechanisms of the intraparticle mass transfer processes. We consider that the present approach is very significant for kinetically understanding the sorption and desorption processes occurring in microparticle systems. Acknowledgment. K.N. acknowledges the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 11640604, 1999-2000, and Shimadzu Science Foundation for partial support of the research. LA000885S