Donnan Electric Potential Dependence of Intraparticle Diffusion of Malachite Green in Single Cation Exchange Resin Particles: A Laser Trapping-Microspectroscopy Study ()
1. Introduction
Ion-exchange processes are known to undergo via three steps: 1) mass transfer of ions in the external solution phase to the resin surface (film diffusion); 2) diffusion of ions inside the resin phase (particle diffusion); and 3) exchange of ions in the vicinity of the exchange groups [1-3]. Since the ion-exchange reactions at the exchange groups in the resin phase are in general very fast, the rate determining step is predicted to be either film diffusion or particle diffusion, depending on various experimental conditions: solution pH, temperature, the molecular size of an ion, the pore-size of the three-dimensional network of a resin, and so forth. Besides these factors governing the ion-exchange processes, the role of the Donnan electric potential in the ion-exchange processes has been sometimes discussed [4-9]. In practice, since the Donnan electric potential generated at the resin/solution boundary influences the particle diffusion processes of ions, its effects on ion-exchange reactions have been hitherto studied theoretically and experimentally for both film membrane [4,7] and bead systems [8,9]. In micrometer-sized spherical ion-exchange resin particles, particular, the electric potential effects on the particle diffusion processes are expected to play a more decisive role compared with those in film membrane systems, since the electric potential is generated three-dimensionally at the spherical particle/solution boundary. To obtain an inside look at the electric potential effects on the diffusion processes of ions, in situ and single microparticle measurements on the diffusion coefficients of ions are of primary importance. However, a study on the ion-exchange processes of ions in single resin particles has been rarely conducted owing to limitation of an experimental technique. In 1998, we reported the direct observation method of particle diffusion of an organic cation dye in single ion-exchange resin microparticles on the basis of an excitation energy transfer method combined with a laser trappingmicrospectroscopy technique [10]. In our previous report, we employed divinylbenzene-styrene polymeric resin particles (diameter (d) ~ 20 μm) having 
as an ion-exchange group and Malachite Green (MG+) as an organic cation dye, and reported that the diffusion coefficient (D) of MG+ in the resin particle was as slow as 8 × 10–11 cm2∙s–1 in an aqueous pH = 4 solution. The experimental system studied is very unique since one can evaluate directly the D values of MG+ in single resin microparticles, although MG+ is a model ion and not necessarily important as an actual ion-exchange reaction. Nevertheless, the methodology determining the diffusion coefficients of ions in single resin particles is very important for elucidating the factors governing the ion-exchange processes. The D(MG+) value in a single 
resin particle in an aqueous pH = 4 solution has been determined successfully as mentioned above [10], while pH effects on D(MG+) have not been studied yet, which would provide information on Donnan electric potential effects on D(MG+) in single ion-exchange microparticles. In the present paper, we report pH effects on the diffusion coefficient of MG+ in single 
type cation-exchange microparticles in the solution pH range of 4 - 9 in special reference to the Donnan electric potential effects on D(MG+).
2. Experimental
2.1. Chemicals and Sample Preparation
Malachite Green (MG+, Kanto Chemicals, G grade) and Rhodamine B (RB+, Tokyo Kasei, GR grade) were used as supplied. Pure water (conductivity > 17 MW∙cm) was obtained from a GSR-200 system (Advantec Toyo) or Elix Advantage Water Purification System (M Millipore). A cation-exchange resin, made of a divinylbenzene-styrene copolymer (cross-linking density = 8%) having 
groups (CK08H), was used as an ion-exchange material and prepared by repeated soaking of the corresponding 
resin (1 g, MCI-GEL, CK08S, Mitsubishi Chemicals Co. Ltd.) in 100 mL of 2 mol/dm3 (= M) HCl solution for 1 h. The resin was washed thoroughly by deionized water and dried in air at room temperature. The pH of an aqueous MG+ solution was adjusted by adding a 0.1 M NaOH or HCl solution and was measured by using a Horiba pH meter D-51.
2.2. Experimental Procedures
A RB+ pre-adsorbed resin (RB+-resin) was prepared by soaking the CK08H resin (20 mg, dry weight) in an aqueous RB+ solution (100 mL, [RB+] = 1.0 × 10–7 M) in 1 week for homogeneous distribution of RB+ in the resin particles [11]. Under the present experimental conditions, since the total mole number of RB+ (~10–8 mole/100 mL) is far below the ion-exchange capacity of the resin (9 × 10–5 equiv/20 mg), all of the RB+ ions are distributed homogeneously in the resin phase. After filtration of the particles, the RB+-resin was dried in air at room temperature and, then, 1.5 mg of the RB+-resin was soaked in 50 mL of an aqueous MG+ solution ([MG+] = 1.0 × 10–7 M) for a given period. At a given soaking time (t), an aliquot of the colloidal solution was sampled onto a slide glass and covered with a cover slip, which was set on the stage of an optical microscope. A single resin particle was manipulated by a laser trapping technique [12], and the absorption spectrum of RB+/MG+ and/or the fluorescence spectrum of RB+ in the single resin particle were measured by a laser trapping-microspectroscopy system.
2.3. Optical Setup for Laser Trapping-Microspectroscopy
A laser trapping-microspectroscopy system used in the present study is shown in Figure 1 [10]. For fluorescence measurements, a 150-W Xe light beam (L2273, Hamamatsu Photonics) was introduced to an optical microscope (Optiphoto 2, Nikon) coaxially with a 1064-nm laser beam for trapping (CW Nd3+: YAG laser, SL902T, Spectron) and irradiated to a single laser-trapped particle through an oil-immersed objective lens. The excitation wavelength for RB+ was selected at 532 nm by a band-pass filter (532FS03-25, Andover) to avoid absorption of incident light by MG+ and to minimize inner filter effects by RB+ absorption. In the actual experiments, a low magnified objective lens (×40) was used for both trapping and fluorescence excitation, and the spot size of the excitation beam was adjusted to be slightly larger than the particle diameter by using an iris. This gave rise to excitation of RB+ in the whole volume of the particle. The fluorescence from the laser-trapped particle was collected by the same objective lens and led to a multichannel photodetector (PMA-11, Hamamatsu Photonics) to record the fluorescence spectrum.
For absorption microspectroscopy of individual microparticles, the Xe light beam mentioned above was used as probe light (objective lens, ×100; probe beam size, ~1 mm). The Xe light beam being passed through a laser trapped particle was collected by the condenser lens of the microscope, reflected by the half-mirror set under the microscope stage and, then, led to the detector system to record the transmitted light intensity (I) as shown in Figure 1. The incident light intensity (Io) was determined under the same optical conditions without a resin particle.
2.4. Experimental Model
For determination of the diffusion coefficient of Malachite Green (MG+, a non-fluorescent organic dye) in the CK08H resin, we employed direct excitation energy transfer from RB+ to MG+ whose model was shown schematically in Scheme 1. First, the 
resin was
Figure 1. A block diagram of a laser trapping-absorption/fluorescence microspectroscopy system.
Scheme 1. Schematic illustration of diffusion of MG+ in a RB+-pre-adsorbed single cation-exchange microparticle.
homogeneously adsorbed by RB+. By an appropriate choice of the experimental conditions, the total amount of RB+ adsorbed on the single particle can be controlled below the ion-exchange capacity of the resin as mentioned before (Step 1).
Second, the RB+-pre-adsorbed resin particles (RB+- resin) were soaked in an aqueous MG+ solution for a given period (Step 2). It is very important to note that the total mole number of MG+ in the solution is set to adsorb all of the MG+ molecules onto the surface layers of the particles in the initial stage of soaking and, afterward, no MG+ molecule is provided from the water phase to the resin phase. Thus, the MG+ molecules adsorbed in the surface layer of the particle diffuse into the interior with time, t (Step 3). When the average distance between RB+ and MG+ in the MG+-diffused layer in the resin particle becomes shorter than the Förster energy transfer distance (discussed later again) [13], the RB+ fluorescence is quenched by MG+, while the RB+ molecules in the inner part without MG+ still show fluorescence. When MG+ is distributed to the whole volume of the particle, the RB+ fluorescence is quenched completely by excitation energy transfer from RB+ to MG+. The fluorescence intensity from the whole single RB+-resin particle should decrease in accord with the diffusion length of MG in the particle (q, see also Scheme 1). Since q is determined by the diffusion rate of MG+, the diffusion coefficient of MG+ in the particle can be determined on the basis of the time dependence of the quenching efficiency of the RB+ fluorescence by MG+.
3. Results and Discussion
3.1. Time Courses of the Absorption and Fluorescence Spectra of Single RB+-Resin Particle during Soaking in an MG+ Solution
Figure 2 shows the time course of the absorption spectrum of a single RB+-resin particle (diameter (d) ~ 16 μm) during soaking in an aqueous MG+ solution ([MG+] = 1.0 × 10–7 M, pH = 6.56). At t = 0, RB+ in the resin particle shows the absorption maximum at around 570 nm. Under present experimental conditions, since the total mole number of MG+ in the aqueous phase (5 × 10–9 mole/50 mL) is set far below the ion-exchange capacity of the resin (6.75 × 10–6 equiv/1.5 mg) as mentioned before, all of the MG+ molecules distribute completely from the water phase to the resin phase within the first 5 min as confirmed by the disappearance of the green color of the MG+ solution: Step 2 in Scheme 1. Upon diffusion of MG+ from the surface layer to the resin interior, the absorbance of MG+ at around 634 nm increased gradually with t without any appreciable changes in the spectral band shapes of both RB+ and MG+ as seen in Figure 2: Step 3 in Scheme 1. It is worth noting that the total mole number of MG+ in the particle is constant during soaking. Therefore, the increase in the absorbance of MG+ at around 634 nm with t is ascribed to that in the optical path length (l) in the single microparticle due to diffusion of MG+. Upon MG+ diffusion from the surface layer to the particle interior, the thickness of the diffusion layer of MG+ (θ in Scheme 1) increases and this gives rise to that in the optical path length for the absorption measurements: l. The increase in the MG+-diffused layer (i.e., l), however, also brings about dilution of the MG+ concentration in the MG+-diffused volume. For a spherical sample, it has been reported that the absorbance change of a solute is more sensitive to the change in l compared with that by the dilution effect [14], the absorbance increases with t as seen in Figure 2. After 150 min soaking, the absorbance of MG+ became constant, indicating homogeneous diffusion of MG+ in the RB+-resin particle.
Figure 3 shows a typical example of the time course of the fluorescence spectrum of a single RB+-resin particle during soaking in an aqueous MG+ solution ([MG+] = 1.0 × 10–7 M, pH = 6.96). The results clearly demonstrate that the RB+ fluorescence is quenched with t without any change in the spectral band shape, indicating diffusion of MG+ into the RB+-resin particle interior and subsequent excitation energy transfer from RB+ to MG+ in the MG+- diffused layer in the particle. Under the present conditions, the observed absorbance of RB+ (1.1 at 565 nm, t = 0 - 150 min in Figure 2) and MG+ (~0.6 at 634 nm, t = 150 min in Figure 2) correspond to the amount of RB+ and MG+ in the resin particle to be 1.3 × 10–14 and 1.0 × 10–14 mole/particle, respectively. These values indicate that the average distance between RB+ and MG+ in the resin particle at t = 150 min is ~50 Å, which is shorter than the critical energy transfer distance (R0 ~ 60 Å [15]) in the present RB+-MG+ system. Therefore, quenching of the RB+ fluorescence in the resin during soaking in the MG+ solution is the reasonable consequence and the data in Figure 3 are worth analyzing in more detail.