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Intraparticle Diffusion and Adsorption Isotherm for Sorption in Silica Gel Studied by Single-Microparticle Injection and Microabsorption Methods Tomomi Sekine and Kiyoharu Nakatani* Department of Chemistry, University of Tsukuba, Ibaraki 305-8571, Japan Received July 9, 2001. In Final Form: October 25, 2001 The sorption of rhodamine 6G from water into a single silica gel microparticle was analyzed using microcapillary manipulation/injection and microabsorption methods. The rate-determining step of the sorption process was diffusion of the cationic dye in the particle interior, and the intraparticle diffusion coefficient was highly dependent on the pH and the ionic strength of the water phase. The adsorption coefficient of the dye determined from the Langmuir adsorption isotherm was also influenced by the pH and the ionic strength. The relationship between these kinetic and isotherm parameters was quantitatively discussed based on a pore diffusion model.
1. Introduction The studies of the sorption and desorption processes in microparticle/solution systems are significant for colloid chemistry, separation chemistry, and so forth. Sorption processes in a microparticle system such as silica gel and active carbon are governed by mass transfer from the surrounding solution phase to a microparticle (external mass transfer), adsorption/desorption at the solid/liquid interface, and intraparticle diffusion of a solute in the pores of the particle. A distribution (or adsorption) coefficient (Kdis) of the solute in the microparticle system is measured as an isotherm parameter and is generally independent of the particle size. In the kinetic analysis, the intraparticle diffusion in the pores is frequently the rate-determining step of the sorption processes in the microparticle system.1,2 In this case, the sorption rate will depend on the particle size and the surface area. Furthermore, if the interparticle distance is short, the sorption rate will be influenced by the complicated external mass transfer rate. So far, kinetic analyses of the sorption processes were demonstrated for a large number of microparticles in solution and the intraparticle diffusion coefficient (Da) was determined as an average value. However, single microparticle measurements are indispensable for quantitative analyses of the sorption rates. The relationship between Kdis and Da in sorption processes has been theoretically predicted from an intraparticle diffusion model consisting of pore diffusion (in pore solution) and surface diffusion (at the pore walls).3,4 However, the relevant experimental results would not be quantitatively reported as systematic studies. The intraparticle mass transfer rate for analogous-sized particles depends on the pore size, pore volume, and so on. To experimentally discuss the relationship between Kdis and Da, these parameters are preferred to be changed with the analogous microparticle system. In a silica gel/water system, the surface charge can be controlled by pH (isoelectric point at pH ) 2).5 Besides pH, the surface (1) Weber, W. J., Jr.; McGinley, P. M.; Katz, L. E. Water Res. 1991, 25, 499-528. (2) Pignatello, J. J.; Xing, B. Environ. Sci. Technol. 1996, 30, 1-11. (3) Ball, W. P.; Roberts, P. V. Environ. Sci. Technol. 1991, 25, 12371249. (4) Wu, S.-c.; Gschwend, P. M. Environ. Sci. Technol. 1986, 20, 717725.
charge is varied by the ionic strength (I).5-9 Since the sorption processes in the silica system are influenced by the surface charge, changes in pH and I will be used for studying the relationship between Kdis and Da. Recently, we have developed a microabsorption technique combined with microcapillary injection of a single microparticle. Kinetic analyses of the sorption and desorption processes of a cationic dye occurring in a single silica gel microparticle could be quantitatively demonstrated in detail by this technique.10,11 The sorption and desorption rates of rhodamine 6G (R6G) were highly dependent on the particle size and limited by the intraparticle diffusion at pH ) 2.11 In the present article, the pH and I dependencies of Kdis and Da of R6G in a single silica gel microparticle/water system were analyzed by the single-particle injection and microabsorption methods to examine the relationship between Kdis and Da. We also discuss whether the intraparticle diffusion is pore or surface diffusion in this system. 2. Experimental Section 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), R6G (Wako Pure Chemical Industries, Ltd., Pr. grade), 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). As a sample solution, an aqueous R6G solution (concentration: Cw ) 2 × 10-7 to 1 × 10-5 M, 1 M ) 1 mol/dm3) containing HCl (pH ) 2 or 7) and KCl (10-4-10-1 M) was used for the extraction measurements. Absorption spectra of the dye in a single microparticle were measured using microcapillary manipulation/injection and microabsorption methods, which were described in detail elsewhere.11 Briefly, a single spherical silica gel microparticle in an (5) Kosmulski, M. J. Colloid Interface Sci. 1998, 208, 543-545. (6) Schlautman, M. A.; Morgan, J. J. Environ. Sci. Technol. 1994, 28, 2184-2190. (7) Colic, M.; Franks, G. V.; Fisher, M. L. Langmuir 1998, 14, 61076112. (8) Milonjic, S. K. Colloids Surf., A 1999, 149, 461-466. (9) Huang, X.; Kovaleski, J. M.; Wirth, M. J. Anal. Chem. 1996, 68, 4119-4123. (10) Nakatani, K.; Sekine, T. J. Colloid Interface Sci. 2000, 225, 251253. (11) Nakatani, K.; Sekine, T. Langmuir 2000, 16, 9256-9260.
10.1021/la0110500 CCC: $22.00 © 2002 American Chemical Society Published on Web 01/05/2002
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Figure 1. Absorption spectra of R6G in a single silica gel microparticle (d ) 94 µm) after injection of the particle into an aqueous R6G solution (Cw ) 2 × 10-6 M, pH ) 7, I ) 0.02). aqueous solution containing the same KCl and HCl concentrations of the sample solution without R6G was sucked into a microcapillary (outer diameter, 100-120 µm) using a manipulation/injection system (Narishige Co., Ltd., MN-151, MMW-200/ IM-16). The single particle was then injected into the sample solution (2 cm3) onto a glass dish placed on the stage of an optical microscope (Olympus Co., IX-70). The silica gel microparticle sank in the water, and no Brownian motion of the particle was observed under stationary conditions. A light beam from a halogen lamp (Mejiro Precision Co., PHL-150) was introduced into the optical microscope through an objective lens (×60) and focused onto the single particle (spot size, ∼3 µm). The transmitted light intensity that passed through the particle center was collected by a condenser lens and detected by a multichannel photodetector (Hamamatsu Photonics Co., PMA11, C7473-36). As a reference, the incident light intensity in the vicinity of the particle was used to record the absorption spectrum. All single-particle measurements were performed at 298 ( 0.5 K using a temperature controller (Kitazato Supply Co., Ltd., MD-10RF-O).
Figure 2. Adsorption isotherms at pH ) 7 (I ) 0.001, 0.005, and 0.01) for single silica gel microparticles (d ) 40-100 µm).
3. Results and Discussion Adsorption Isotherm. An absorption spectrum of R6G extracted into a single silica gel microparticle (particle diameter d) was measured with time (t) after injection of the single microparticle into the aqueous dye solution (t ) 0) (Figure 1). The spectrum shape of R6G in the particle was analogous to that of the R6G monomer in water and was not changed under the present experimental conditions. The absorbance (A) of the dye increased with t and became saturated. If the dye molecules were adsorbed on the spherical surface of the particle alone, A at the adsorption equilibrium should be independent of d.12 However, the saturated A, corresponding to A at the sorption equilibrium, was directly proportional to d (40100 µm) for the same Cw, I, and pH. This result indicates that R6G is extracted into the particle interior and the dye concentration in the single particle at the sorption equilibrium (Cp,eq) is independent of d, as previously reported.11 Using the molar extinction coefficient of R6G in water (κ at 520 nm ) 9.14 × 104 cm-1 M-1), Cp,eq was determined from Lambert-Beer’s law as an optical path length equal to d. Figure 2 shows the Cw dependence of Cp,eq for various I at pH ) 7. According to the Langmuir adsorption isotherm, Cp,eq is given by eq 1:
Cp,eq ) KadsCp,∞Cw/(1 + KadsCw)
(1)
where Kads is the Langmuir isotherm constant and Cp,∞ is the Langmuir constant. As seen in Figure 2, 1/Cp,eq was proportional to 1/Cw as predicted from the Langmuir adsorption isotherm. Kads and Cp,∞ for various pH and I values were determined from eq 1 and are summarized (12) Kim, H.-B.; Hayashi, M.; Nakatani, K.; Kitamura, N. Anal. Chem. 1996, 68, 409-414.
Figure 3. Ionic strength dependencies of (a) the Langmuir constant (Cp,∞) and (b) the Langmuir isotherm constant (Kads).
in Figure 3. At pH ) 2, Kads and Cp,∞ were independent of I within the experimental error. Silica has been reported to show an isoelectric point at pH ) 2,5 so these parameters would not be changed in I. On the other hand, Kads and Cp,∞ increased with decreasing I at pH ) 7. The adsorption of the cationic dye is expected to be governed by the negative charge due to the dissociation of silanol on the silica surface at pH > 2.9,13 It has been reported that an alkali metal ion adsorbs on a silica surface.8 Therefore, Kads and Cp,∞ will be changed in I at pH ) 7. Intraparticle Mass Transfer Rate. The time dependence of A at 520 nm (A(t)) extracted into a single microparticle (d ) 97 ( 2 µm) is shown in Figure 4. The A(t) curve at pH ) 7 significantly depended on I (Figure 4a). On the other hand, A(t) at I ) 0.02 was similar to that at I ) 0.11 at pH ) 2 (Figure 4b). These results are consistent with those of the Langmuir adsorption isotherm (discussed above). Despite the pH values, the time required to saturate A (ts) decreased with decreasing d, while the ts value was independent of Cw for similar-sized particles, as previously reported.11 Since the mass transfer of the dye from the bulk water phase to the microparticle surface is efficient due to spherical diffusion,10 the external mass transfer is not the rate-determining step of the sorption rate in the single silica gel system. Furthermore, Cw at the sorption equilibrium is almost the same as that before injection of the (13) Kosmulski, M. J. Colloid Interface Sci. 1997, 195, 395-403.
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Figure 5. Ionic strength dependence of the intraparticle diffusion coefficient (Da) at pH ) 2 and 7 for single silica gel microparticles (d ) 40-100 µm).
Figure 4. Time dependence on peak absorbance (520 nm) of R6G in a single silica gel microparticle (d ) 97 ( 2 µm) injected into an aqueous R6G solution (Cw ) 4 × 10-6 M, I ) 0.11 and 0.02) at (a) pH ) 7 and (b) pH ) 2. The solid curves represent the simulations of A(t) by eq 2.
single particle due to the small single microparticle (4.5 × 10-7 cm3 at d ) 95 µm)/water (2 cm3) volume ratio. Therefore, the dye concentration in water near the particle surface is assumed to be equal to Cw during the sorption process. Frequently, sorption processes of a solute are analyzed by an intraparticle diffusion model.1,2,14-17 Applying Fick’s second law of diffusion, the time dependence of a radial concentration profile of the dye in the particle (Cp(r, t)) is expressed as eq 2: 2
2
∂Cp(r, t)/∂t ) Da[∂ Cp(r, t)/∂r + (2/r)∂Cp(r, t)/∂r]
(2)
where r is the spatial coordinate radially directed. The initial and boundary conditions are given by Cp(r, 0) ) 0, Cp(d/2, t) ) Cp,eq, and ∂Cp(0, t)/∂r ) 0. Since adsorption/ desorption rates of a solute from water to a silica surface have been reported to be fast,18,19 the R6G concentration adsorbed on the surface layer of the particle was assumed to be Cp,eq (Cp(d/2, t) ) Cp,eq). Thus, Cp(r, t) and A(t) were simulated by a finite form for various Da values under the conditions of ∆t ) 0.5 s, ∆r ) 1 µm, and Da∆t/(∆r)2 < 0.5 10,11 The observed data were as A(t) ) 2κ∫d/2 0 Cp(r, t) dr. satisfactorily fitted by eq 2 (solid lines in Figure 4), indicating that the rate-determining step of the sorption process in the R6G system is the diffusion in the particle interior. Figure 5 shows Da for various I values. At pH ) 7, Da at I ) 0.1 is 15 times that at I ) 1 × 10-4. Relationship between Da and Kads. Intraparticle diffusion in microparticles has been reported to consist of pore diffusion and surface diffusion.3,15 According to this (14) Mathews, A. P.; Weber, W. J., Jr. AIChE Symp. Ser. 1976, 73, 91-98. (15) Yoshida, H.; Yoshikawa, M.; Kataoka, T. AIChE J. 1994, 40, 2034-2044. (16) Pignatello, J. J.; Ferrandino, F. J.; Huang, L. Q. Environ. Sci. Technol. 1993, 27, 1563-1571. (17) Ghosh, A. C.; Satyanarayana, K.; Srivastava, R C.; Dutta, N. N. Colloids Surf., A 1995, 96, 219-228. (18) Waite, S. W.; Marshall, D. B.; Harris, J. M. Anal. Chem. 1994, 66, 2052-2061. (19) Waite, S. W.; Holzwarth, J. F.; Harris, J. M. Anal. Chem. 1995, 67, 1390-1399.
Figure 6. Relationship between the kinetic (Da-1) and isotherm (Cp,∞Kads) parameters.
model, Da is given by eq 3:3
Da ) Dp/( + FKdis) + FKdisDs/( + FKdis)
(3)
where Dp and Ds are the pore and surface diffusion coefficients, respectively. and F are the internal porosity and the apparent density of the silica gel, respectively. The distribution coefficient has the dimension of cm3/g, namely, FKdis ) Cp,eq/Cw. At KadsCw , 1 in eq 1, FKdis is assumed to be equal to Cp,∞Kads. When the intraparticle diffusion is governed by the pore or surface diffusion, eq 3 is approximated by eq 4 or 5, respectively.
Da ) Dp/( + Cp,∞Kads)
(4)
Da ) Cp,∞KadsDs/( + Cp,∞Kads)
(5)
Equation 4 or 5 predicts that 1/Da is proportional to Cp,∞Kads or 1/Cp,∞Kads, respectively. As seen in Figures 3 and 5, Da decreases with increasing Cp,∞ and Kads at pH ) 7. Therefore, we could not explain the present experimental data by the surface diffusion model alone (eq 5). On the other hand, 1/Da was proportional to Cp,∞Kads for various I values at pH ) 2 and 7 (Figure 6). Furthermore, the 1/Da versus Cp,∞Kads plot at pH ) 4 fell on the same straight line (e.g., 1/Da ) 6.7 × 108, Cp,∞Kads ) 8.0 × 102 at I )1 × 10-4). On the basis of eq 4, Dp was determined to be 3.0 × 10-8 cm2/s from the intercept of the plot. From the slope of the plot, was determined to be 0.43, which was in good agreement with the value (0.46) calculated from the pore volume (1.15 cm3/g) and the bulk density (0.40 g/cm3) of the silica gel. These results indicate that the intraparticle diffusion is governed by the pore diffusion in the present system. In a previous report, we speculated
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that the intraparticle diffusion of cationic dyes is surface diffusion because of no Cw dependence of Da.11 Although Da has been reported to increase with increasing Cw,15 the previous and present measurements were limited in the narrow Cw range (e.g., Cw ) 2 × 10-6 to 1 × 10-5 M at pH ) 7 and I ) 0.11). Therefore, the contribution of Cw to Da would be negligibly small. The values of Da, Cp,∞, and Kads were highly dependent on pH and I. Nevertheless, it is noteworthy that Dp determined from the 1/Da versus Cp,∞Kads plot is a physical constant of R6G in the pore water, independent of pH and I.20
4. Conclusions
(20) We have performed analogous experiments using LiCl or NaCl as an electrolyte, instead of KCl. Although Da, Cp,∞, and Kads were slightly changed in the cation, the 1/Da versus Cp,∞Kads plot fell on the same straight line.
We could demonstrate the quantitative measurements of the intraparticle mass transfer of a single silica gel microparticle for various pH and I values using the single microparticle injection and microabsorption methods. The relationship between Da and Cp,∞Kads was independent of pH and I, and Dp and could be directly determined in the present experiments. The Dp and values are the characteristic constants for the curved and narrow pores of the silica gel. Therefore, determination of these values is expected to be significant for studies on separation and catalyst materials. We consider that the present approach is sufficient for analyzing sorption processes in microparticle systems. LA0110500
