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Adsorption of Fluorescent Dyes on Oxide Nanoparticles Studied by Fluorescence Correlation Spectroscopy Xiaojing Leng,* Konstantin Starchev, and Jacques Buffle CABE (Analytical and Biophysical Environmental Chemistry), Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, Science II, 30 Quai Ernest Ansermet, 1211 Geneva 4, Switzerland Received May 29, 2001. In Final Form: November 19, 2001 In the present work, we have studied the adsorption of Rhodamine 6G on negative colloidal particles (Silica-Bindzil, Ludox-SM30 and Ludox-HS30) and Calcein on positive colloidal particles (Ludox-CL and Alumina) at very low concentrations by use of fluorescent correlation spectroscopy (FCS). In this relation we have introduced a set of equations which take into account the different quantum yield of the dye molecules and the particles as well as the adsorption of the dye molecules on the sample cell. The concentrations of fluorescent dye were varied between 2 × 10-9 and 2 × 10-7 M, and the concentrations of particles were in the range of 0.01-0.03 g/L. The adsorption data fit well with a Langmuir adsorption isotherm. The values of the adsorption constants at pH 5.5-5.7, ionic strength NaCl 1 mM, and room temperature (22 ( 0.5 °C) were in the range (0.2-2.5) × 108 L/mol, and the adsorption energy varied between -10 and 13 kJ/mol. The cooperative binding model (generalized Freundlich) was also checked but showed less satisfactory results. This work demonstrates the high performance of the FCS method for investigation of the adsorption equilibrium at solid-liquid interface. In particular the technique does not required any separation step of the adsorbed and nonadsorbed species and is not influenced by the adsorption on the sample cell walls which is often a source of artifacts when working with very low concentrations.
1. Introduction The adsorption of fluorescent dye on colloidal particles has been studied extensively.1-3 Such fluorescent labeled particles can be used in different biomedical applications in cells in vivo or in vitro. Inorganic colloidal particles such as silica or alumina are present in natural water reservoirs, where they are carriers of adsorbed pollutant as well as vital molecules.4-6 The knowledge of adsorption equilibrium between particles and small molecules is thus important for both fundamental (modeling of natural processes) and practical (labeling of particles) applications. A Langmuir isotherm7 has already been used to describe the adsorption of Rhodamine 6G (R6G) onto polymer membrane,8 biological cells,9 and anionic polystyrene latex particles.1-3 In particular electrostatic interactions were found to play an important role on the adsorption on anionic polystyrene latex particles at low R6G dye concentration (8 × 10-8 to 8 × 10-5 M).1 Usually such investigations are performed by centrifuging the particle suspension and measuring of the fluorescent intensity of the supernatant solution. However such experiments are limited to relatively high concentrations of dye because of two major artifacts: (1) Charreyre, M. T., Zhang P.; Winnik M. A.; Pichot C.; Grailla C. J. Colloid Interface Sci. 1995, 170, 374-382. (2) Gong Y. K.; Nakashima K.; Xu R. L. Langmuir 2000, 16, 85468548. (3) Gong Y. K.; Miyamoto T.; Nakashima K.; Hashimoto S. J. Phys. Chem. 2000, 104, 5772-5778. (4) Buffle J.; DeVitre R. R.; Perret D.; Leppard G. G. Geochim. Cosmochim. Acta 1989, 53, 399. (5) Perret D.; Leppard G. G.; Mu¨ller M.; Belzile N.; DeVitre R. R.; Buffle J. Water Res. 1991, 25, 1333. (6) Filella M.; Zhang J. W.; Newman M. E.; Buffles J. Colloids Surf., A 1997, 120, 27-46. (7) Langmuir I. Chem. Rev. 1933, 13 (No. 2), 147-191. (8) Kost, S. H.; Breuer, H. D. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 134. (9) Bunting, R. J.; Phan, T. V.; Kamali, E.; Dowben, R. M. Biophys. J. 1989, 56, 979.
(i) At low dye concentration the adsorption equilibrium between the dye and the walls of the glassware starts to play an important role. (ii) For very small particles an important part of the particles cannot be separated by centrifugation. Since 1974, fluorescence correlation spectroscopy (FCS) method was introduced and has been substantially developed.10-21 Some important advantages of FCS particularly to discussed problems are as follows: (i) The method is very sensitive thus fluorescent nanoparticles and molecules in very diluted concentrations (down to 10-9 M) can be reliably detected. (ii) FCS allows in situ measurements of both fluorescent dye molecules and labeled particles, thus no separation step or other perturbing manipulation is needed. (iii) The calibration of FCS is independent from the adsorption of molecules on the cell walls; therefore the measured concentration is not influenced by this effect. (10) Magde, D.; Elson, E. L.; Webb, W. W. Phys. Rev. Lett. 1972, 29, 705-708. (11) Elson, E. L.; Magde, D. Fluorescence Correlation Spectroscopy. I. Conceptual Basis and Theory. Biopolymers 1974, 13, 1-27. (12) Magde, D.; Elson, E. L.; Webb, W. W. Biopolymers 1974, 13, 29-61. (13) Koppel, D. E.; Axelrod, D.; Schlessinger, J.; Elson, E. L.; Webb, W. W. Biophys. J. 1976, 16, 1315-1329. (14) Magde, D.; Webb, W. W.; Elson, E. L. Biopolymers 1978, 17, 361-376. (15) Qian, H.; Elson, E. L. Biophys. J. 1990, 57, 375-380. (16) Thompson, N. L. Fluorescence correlation spectroscopy. In Topics in Fluorescence spectroscopy; Lakowicz, J. R.; Eds.; Plenum Press: New York, 1991; Vol. 1, Techniques, pp 337-378. (17) Rigler, R.; Mets, U ¨ .; Widendren, J.; Kask, P. Eur. Biophys. J. 1993, 22, 169-175. (18) Widengren, J.; Mets, U ¨ .; Rigler, R. J. Phys. Chem. 1995, 99, 13368-13379. (19) Meseth, U.; Wohland, T.; Rigler, R.; Vogel, H. Biophys. J. 1999, 76, 1619-1631. (20) Starchev, K.; Zhang, J. W.; Buffle, J. J. Colloid Interface Sci. 1998, 203, 189-196. (21) Starchev, K.; Buffle, J.; Pe´rez, E. J. Colloid Interface Sci. 1999, 213, 479-487.
10.1021/la010787m CCC: $22.00 © 2002 American Chemical Society Published on Web 08/31/2002
Fluorescent Dye Adsorption on Oxide Nanoparticles
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The goal of this work is to demonstrate the capacity of FCS to investigate the adsorption behaviors of fluorescent dyes, R6G and Calcein, onto the colloidal particles at very low concentrations. Equilibrium constants and adsorption capacity will be measured. The adsorption process was compared with the classical Langmuir isotherm7 and the cooperative binding model (generalized Freundlich).1,22 The hydrodynamic radius rh of the particles will be also measured by FCS and compared with those obtained by photon correlation spectroscopy (PCS). Transmission electronic microscopy (TEM) was also used to measure the radius, r, of these particles.
2.1. FCS Theory. In FCS the fluctuations of light emitted by the fluorescent particles and/or molecules diffusing in an open sample volume (SV) defined by a laser beam are measured. The autocorrelation function (ACF) of these fluctuations is calculated in real time. These light fluctuations can be due either to chemical changes or to random diffusion of the molecules in the SV. In this study, we have assumed that no chemical change occurs during the measurement, and only translational diffusion is considered. The frequent component due to the adsorption-desorption process is not observed with FCS since this process is very fast (time scale of nanoseconds) compared to the diffusion process (milliseconds). The ACF of the fluorescence intensity is defined by
G(τ) ) 〈F(0)F(τ)〉/〈F(τ)〉2
(1)
where F(0) is the fluorescence intensity at time 0 and F(τ) the intensity at time τ. 〈F(τ)〉 represents the time average fluorescence intensity of the system. The intensity profile of the laser beam is assumed to be Gaussian23
[
] [ ]
2(x2 + y2) ωxy2
2z2 exp - 2 ωz
( )( τ
Qi2〈ni〉 1 + ∑ τ i)1 G(τ) ) DC +
N
[
-1
1+
i
τ p2τi
)
(5)
The value of Di obtained from eq 5 allows us to calculate the hydrodynamic radius rh of particles with the StokesEinstein relationship
(6)
where k is the Boltzmann constant, T the absolute temperature, and η0 the viscosity of solvent. By fitting the experimental autocorrelation function with eq 3 in the case of solutions containing both free dye molecules and labeled particles (N ) 2), the diffusion times (their hydrodynamic size) and the proportion of both components y1 and y2 weighted by the square of the fluorescence intensity are obtained
y1 )
y2 )
Q12〈n1〉 (Q1〈n1〉 + Q2〈n2〉)2 Q22〈n2〉 (Q1〈n1〉 + Q2〈n2〉)2
(7)
(8)
The autocorrelation function extrapolated to zero delay time
Q12〈n1〉 + Q22〈n2〉 (Q1〈n1〉 + Q2〈n2〉)2
(9)
and the mean fluorescent intensity
where ωxy is the radius of sample volume in the x, y plane perpendicular to the propagation of the light and ωz is the half-height in z direction. IO is the intensity at the center of the laser beam. This assumption holds approximately for the experimental setup of an epi-illuminated microscope with a pinhole in the image plane.17 For a system which contains N independent diffusing components with their corresponding fluorescent quantum yield, we have the normalized relationship16,19 N
τi ) ωxy2/4Di
G(0) ) DC + (2)
(4)
The characteristic diffusion time τi of ith component is related to the diffusion coefficient Di
rh ) kT/6πη0D
2. Theory
I(x,y,z) ) I0 exp -
p ) ωz/ωxy
-0.5
(3)
Qi〈ni〉]2 ∑ i)1
where DC is the limiting value of G(τ) for τ f ∞ (usually 1.0). τ is the delay time; 〈ni〉 is the average number of particles (molecules) of the ith component in SV, Qi is the fluorescent intensity of one labeled particle or fluorescent molecule of ith component, and p is the structure parameter defined as (22) Kinniburgh, D. G.; Barker, J. A.; Whitefield, M. J. Colloid Interface Sci. 1983, 95, 370-384. (23) Aragon, S. R.; Pecora, R. J. Chem. Phys. 1975, 64, 1791.
〈F(τ)〉 ) Q1〈n1〉 + Q2〈n2〉
(10)
are also measured during the accumulation of the autocorrelation curves. The intensity of the dye molecules alone, Q1, could be measured in separate experiments. Combining eqs 7-10 〈n1〉 and 〈n2〉 and the concentration of the free diffusing dyes, molecules C1 and the labeled particles C2 can be determined by Ci ) 〈ni〉/NAV, where NA is the Avogadro number, V is the volume of the SV defined as
V ) π3/2ωxy2ωz
(11)
Thus FCS allows correct concentration measurement of two components with different quantum yield. It is important to point out here for clarity that in FCS experiments only moving fluorescent species are measured. Therefore dye molecules adsorbed on the particle surface are not counted separately. This is the reason that quenching of the fluorescence on the particle surface did not perturb the correct determination of the particle numbers. Equation 3 allows as well determination of the polydispersity distribution of the particles in the sample volume by means of the histogram method.21,24,25
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Table 1. Physicochemical Properties of the Studied Oxide Particles Bindzila stock concn (wt %) size (nm) specific area (m2/g) density (g/cm3) pH (25 °C) a
15 16 500 1.10 10
Ludox-SM30
Ludox-HS30
Ludox-Cl
30
30
30
345 1.22 10
220 1.21 9.8
230 1.23 4-5
alumina powder 5-30b 100 3.4 4-5c
Marcelo Avena, personal communication. b Elementary particle size, measured by EM (by Degussa SA). c 4% in water at 25 °C.
2.2. Adsorption Isotherms. The Langmuir adsorption isotherm7 is described by
Γ)
ΓmKC 1 + KC
(12)
where Γ is the surface concentration of fluorescent dye molecules adsorbed on the surface, Γm is the maximum surface concentration of molecules, C is the concentration of free fluorescent dyes in solution at equilibrium, and K is the adsorption constant at the tested pH, ionic strength, and temperature. This nonlinear form of the Langmuir isotherm (eq 12) can be transformed in linear forms. One of the most used forms is given by26,27
1 1 1 ) + Γ Γm ΓmKC
(13)
The values of K and Γm can be determined by fitting eq 12 or 13 to the experimental data. The application of the linear method requires a proper weighting of the experimental data.28 In the work of Kinniburgh,28 the weight functions Γ4 and Γ2 are proposed for eq 13, which are used in the present work. On the other hand the nonlinear fitting can give correct results without weighting but can bring significant error when the fitted parameters are correlated.29 Advantage of the nonlinear fitting is that the results can be easily compared with other isotherms. In this work we have compared both models (eq 13 with three different weight modes and eq 12) in order to confirm the results of the nonlinear model by the linear fitting. If the experimental data cannot suit the Langmuir isotherm, then another isotherm should be used. The Cooperative adsorption model (generalized Freundlich) was used to fit experimental data for comparative purposes.22 Named the local adsorption isotherm by Kinniburgh et al.22), the Cooperative model is a composite isotherm which assumes that all sites on surface are not equivalent. This model is written as1,22
(1 +KCKC)
Γ ) Γm
γ
(14)
where γ (0 < γ < 1), related to the heterogeneity of the surface, describes the adsorption of one dye molecule onto the different sites on the surface. The smaller the value of γ, the greater the heterogeneity. When γ ) 1, the composite isotherm reverts to the classical Langmuir isotherm model (eq 12). Equation 14 can be written as (24) Gulari, E.; Tsunashima, Y.; Chu, B. J. Chem. Phys. 1979, 70, 3965. (25) Provencher, S. Compt. Phys. Commun. 1982, 27, 213. (26) Rubin, A. J.; Mercer, D. L.; Adsorption of inorganics at solidliquid interfaces; Anderson, M. A., Rubin, A. J. Eds.; Ann Arbor Science Publishers: Ann Arbor, MI, 1981; Chapter 8. (27) Atkins P. W. Physical chemistry, 3rd ed.; Oxford University Press: Oxford, 1986; part 1. (28) Kinniburgh, D. G. Environ. Sci. Technol. 1986, 20 (9), 895. (29) Farinha, J. P. S.; Martinho, J. M. G.; Pogliani, L. J. Math. Chem. 1997, 21, 131.
1 1 1 ) + Γ1/γ (Γm)1/γ (Γm)1/γKC
(14b)
In practice, two adsorption processes of the fluorescent dye occur simultaneously in our system: the adsorption of dyes onto the surface of the sample cell wall characterized by the surface concentration on the wall (Γwall) and the adsorption onto the surface of tested particles (Γpart). They were studied with both the Langmuir and Cooperative binding models. If only the dye molecules are present in solution, then the surface concentration of fluorescent dye adsorbed onto the surface of sample cell wall, Γwall, can be calculated by
Γwall )
(Cin - C)VC Aw
(15)
where Cin is the concentration of fluorescent dye initially introduced in the cell, C is the concentration of free fluorescent dye at equilibrium, VC is the total volume of sample solution (500 µL), and Aw is the surface of sample cell wall (0.8 cm2). Combining eq 15 with eq 12 or 14 and the concentration C measured by FCS enables determination of the adsorption constant Kwall and the maximum surface concentration of fluorescent dye on the sample cell wall Γmwall. When particles and dye molecules are simultaneously present in the system, the surface concentration Γpart of adsorbed fluorescent dye, onto the surface of tested particles, is calculated as
(
Γpart )
)
ΓwallAw VC VC A
Cin - C -
(16)
where A is the total surface area of the particles in solution (A ) mass × specific surface of particlesssee Table 1). The value of Γwall can be calculated and substituted in eq 16 since Kwall and Γmwall are known from measurements of the dye alone. After determining Γpart, the adsorption constant Kpart and the maximum surface concentration, Γmpart, on the surface of particles can be computed using eq 12 or 14. 3. Materials and Methods 3.1. Reagents. We have studied four types of silica particles, Silica-Bindzil particles (AKZO NOBEL), LudoxSM30, Ludox-HS30, and Ludox-CL (DU PONT product), purchased from Fluka SA and one type of alumina powder (aluminum oxide, P110C1, γ-Al2O3, Degussa SA). The physicochemical properties of these particles given by the corresponding companies are shown in Table 1. Calcein (negatively charged dye at pH > 4)30,31 and R6G (positively (30) Hoelzl Wallach, D. F.; Surgenor D. M.; Soderberg J.; Delano E. Anal. Chem. 1959, 31 (No. 3), 456-460. (31) Hoelzl Wallach, D. F.; Steck, T. L. Anal. Chem. 1963, 35 (No. 8), 1035-1044.
Fluorescent Dye Adsorption on Oxide Nanoparticles
Figure 1. Structures of Rhodamine 6G and Calcein molecules. Printed with permission. Copyright 2001 Molecular Probes Inc., http://www.probes.com.
charged dye at pH < 13)32 were purchased from Molecular Probes Inc. (Figure 1). 3.2. Solution Preparation. A one milliliter silica sample solution (0.03 g/L) was prepared by diluting the mixture of the tested particle stock solution and dye with Milli-Q water. The ionic strength was kept at 1 mM with NaCl. The pH was 5.5-5.7. The R6G concentrations in sample solutions varied from 2 × 10-9 to 8 × 10-8 M for Bindzil, Ludox-SM30, and Ludox-HS30. The Calcein concentrations varied from 2 × 10-8 to 10-7 M for the sample of Ludox-CL. Five hundred microliter solutions were used for measurements. For alumina samples, the suspension of small size of alumina particles was prepared by centrifugation of 18 mL of 1.005 g/L alumina solution (prepared with Milli-Q water) with a Beckman L7-type ultracentrifuge at 20 000 rpm (8.5 × 104g) for 6 h at 20 °C. After ultracentrifugation, 200 µL of supernatant33 was mixed with Calcein and then diluted with Milli-Q water. The ionic strength was kept at 1 mM with NaCl. The pH was 5.5-5.7 in open air. The concentration of alumina was constant in all experiments (0.012 g/L). The concentration of Calcein in the sample solutions varied from 6.3 × 10-9 to 1.5 × 10-7 M. Five hundred microliter solutions were used for measurement. 3.3. FCS Measurements. The FCS measurements were carried out with a ConfoCor produced by Carl ZEISS, based on confocal microscopy technology. The equipment consists of (i) a light source Ar+-laser emitting at 488 or 514 nm, (ii) a laser-adapted AXIOVERT 135TV microscope equipped with a 40× water immersion objective, (iii) a detector Avalanche photodiode SPCM-200PQ, (iv) a hardware correlator with sampling time from 200 ns to 3438.8 s in 288 channels, and (v) a PC microcomputer Intel Pentium 100 MHz, PCI/ISA bus system. The LABTEK glass sample cells (Nalge Nunc International) were used as sample cells. FCS calibration was performed by determining the structure parameters p, ωxy, and ωz with 2 × 10-8 M R6G. An argon ion laser at 488 nm was used as the excitation (32) JURO AG, personal communication. (33) The mass concentration of alumina in the supernatant was measured with an atomic absorption spectrophotometer (PYE-Unicam SP9). A 200 µL sample was treated with 1 M NaOH during one night and then the concentration of Al was measured. The concentration of Al2O3 was deduced from the concentration of Al, and we obtained 0.06 g/L.
Langmuir, Vol. 18, No. 20, 2002 7605
light source for the Calcein system (λex ) 490 nm, λem ) 520 nm) and the same laser at 514 nm was used for the R6G system (λex ) 500 nm, λem ) 551 nm). The attenuator filters OD1.0 and OD2.0 were used to control the intensity of the exciting laser. The measurements were performed 6 min after the samples were added into sample cell, which is enough to reach equilibrium. Each sample was measured 10 times, and the duration of each measurement was 100 s. The mean values and the standard deviations were calculated for these replica measurements. 3.4. PCS Measurements. PCS measurements were carried out with a Malvern 4700 PCS spectrometer equipped with a 1 W argon ion laser of λ ) 488 nm (Coherent, Innova 70). The concentrations of Bindzil, Ludox SM30, HS30, and Ludox CL for PCS were 3 g/L. HCl and NaOH were used to regulate the pH at 5.5-5.8 in all cases. For all these solutions, we added 1 mM NaCl. All the measurements were performed at room temperature (25 ( 0.5 °C). 3.5. TEM. Measurements were performed with a transmission electronic microscope, PHILLIPS EM410. The concentrations of silica suspension (Bindzil, LudoxSM30, Ludox-HS30, and Ludox-CL) were 0.03 g/L. The concentration of alumina was 0.06 g/L. pH ) 5.5-5.7. NaCl ) 1 mM. T ) 22 ( 0.5 °C. These sample suspensions were treated with a resin Nanoplast FB101 and then measured by TEM. More details about the sample preparation process were described in the work of Feretti.34 The size computation was based on 200 randomly chosen particles. 4. Results and Discussions Figure 2 compares the adsorption of R6G and Calcein on the surface of a sample cell wall. Figure 2a shows the time-dependence fluorescence curves which correspond to the adsorption of the dye on the sample cell wall. We observed that the adsorption of R6G reached equilibrium after 6 min, while Calcein reached equilibrium rapidly after being added into the sample cell. The equilibrium data with the nonlinear Langmuir isotherm fitting curves and the linear model (insert in Figure 2b) are shown in Figure 2b. The parameters obtained from different type of fitting are compared in Table 2. We can observe that the data nonweighted and weighted with the function Γ4 are associated to large errors. The presence of the weighting factor Γ2 can lead to values close to those of nonlinear fitting as well as low relative errors; therefore the Langmuir isotherm describes well the experimentally obtained data. The values from the non linear cooperative binding model are shown in Table 3. Compared with the results from Langmuir nonlinear model, we found that the standard deviations on Kwall for Calcein and R6G are too high and the value of γ > 1 for Calcein cannot be accepted by the cooperative binding model.22 Moreover, we have also calculated the variation of the sum of the relative error in the function of γ by using the linear cooperative binding model (eq 14b), where the values of γ are set as 0.3, 0.5, 0.7, 0.9, and 1. The sum of the relative error is given by S ) ∑∆2/(1/Γ1/γ)2, where ∆ is the difference between the observed value and the value from the linear fit. We can observe that the values of S decrease when γ tends to 1 (Table 3b). We concluded that, in the studied concentration ranges, the Langmuir model is more adequate to describe the adsorption of these two fluorescent dye on the surface of sample cell. (34) Ferretti, R. Thesis. CABE, Department of analytical chemistry, SCII, Geneva University, 1999.
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Table 2. Comparison of Langmuir Model Fitting Results for the Adsorption of R6G and Calcein onto the Wall of Sample Cell dyes R6G
Calcein
weight
Kwall (10-7 L/mol)
Γmwall (107 mol/m2)
nonlinear linear no weight linear weight in Γ4 linear weight in Γ2 nonlinear linear no weight linear weight in Γ4 linear weight in Γ2
3.2 ( 0.3 5.8 ( 0.3 (1.4 × 10-2) ( 0.2 4.1 ( 0.2 5.6 ( 0.1 3.3 ( 0.04 (5.6 × 10-3) ( 0.7 4.5 ( 0.3
8.2 ( 0.6 6.4 ( 0.7 (2.7 × 102) ( 3.9 7.7 ( 0.5 4.2 ( 0.3 5.8 ( 0.5 (4.8 × 102) ( 6.9 4.1 ( 1.0
R2
χ2 (1016) 2.5
0.988 0 0.995 3.4 0.971 0.012 0.975
a Measurements were performed at pH 5.5-5.7, ionic strength 1 mM NaCl, and room temperature (22 ( 0.5 °C). The fits and the standard deviations from the fit were calculated by the Sigma Plot 2000.
Table 3 a. Comparison of Cooperative Model Fitting Results for the Adsorption of R6G and Calcein onto the Wall of Sample Cella dyes
Kwall (10-7 L/mol)
Γmwall (107 mol/m2)
γ
χ2 (1016)
R6G Calcein
0.9 ( 0.8 11.8 ( 11.0
11.7 ( 0.7 4.0 ( 0.4
0.7 ( 0.1 1.6 ( 1.0
12.1 3.5
b. Comparison of the Variation of the Sum of the Relative Error by Using the Linear Cooperative Binding Model as Function of γ for the Adsorption of Dye onto the Wall of Sample Cell S (R6G) S (Calcein) a
Figure 2. (a) Comparison of the adsorption of dyes R6G and Calcein onto the sample cell wall (concentrations of dyes ) 2 × 10-8 M) vs time. All measurements were performed at pH 5.5-5.7, ionic strength 1 mM NaCl, and room temperature (22 ( 0.5 °C). (b) Comparison of the nonlinear Langmuir isotherm fitting for dye adsorption on the surface of the sample cell wall. The symbols are the experimental data. Fitting curves are in solid lines. The inset compares the linear fitting with Γ2 weighting. All measurements were performed at pH 5.5-5.7, ionic strength 1 mM NaCl, and room temperature (22 ( 0.5 °C).
Figures 3 and 4 shows respectively the nonlinear and linear (the insets in figures) Langmuir adsorption isotherm fitting for R6G onto silica particles (Bindzil, Ludox-SM30 and Ludox-HS30) and Calcein onto Ludox-CL and alumina particles. The results are compared in Table 4 for the Langmuir model and in Table 5 for the cooperative binding model. We can observe that the nonweighted data are associated to large errors; however the presence of the weighting factor Γ2 leads to the values in good agreement with those of nonlinear fitting.
γ ) 0.3
γ ) 0.5
γ ) 0.7
γ ) 0.9
γ)1
5.94 × 106 5.29 × 105
876 295
4.3 6.5
0.4 0.3
0.1 0.1
Standard deviations were obtained by the software Origin 5.0.
Figure 3. Comparison of the nonlinear Langmuir isotherm fitting for R6G adsorption on the surface of the particles. The symbols are the experimental data. Fitting curves are in solid lines. The inset compares the linear fitting with Γ2 weighting.
The cooperative binding model (Table 5) gives standard deviations of Kpart for Bindzil, Ludox-SM30, and LudoxCL that are too high to be accepted. According to ref 29, this could be due to correlation between fitting parameters. Unfortunately we have no additional data which could fix some of the parameters. Nevertheless the values of γ are not far from 1, which imply no significant cooperative effect. The variation of the sum of the relative error in the function of γ has been calculated by using the linear cooperative binding model (eq 14b), where the values of γ are set as 0.3, 0.5, 0.7, 0.9, and 1 (Table 5b). We can observe that the values of S decrease when γ tends to 1. This result suggests that the Langmuir isotherm better fits the experimental data than the cooperative binding model.
Fluorescent Dye Adsorption on Oxide Nanoparticles
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Table 4. Comparison of Langmuir Model Fitting Results for the Adsorption of Fluorescent Dyes R6G and Calcein onto the Surface of Particlesa dyes R6G
particles Bindzil Ludox-SM30 Ludox-HS30
Calcein
Ludox-Cl γ-alumina
a
weight
Kpart (10-8 L/mol)
Γmpart (108 mol/m2)
nonlinear linear no weight linear weight in Γ2 nonlinear linear no weight linear weight in Γ2 nonlinear linear no weight linear weight in Γ2 nonlinear linear no weight linear weight in Γ2 nonlinear linear no weight linear weight in Γ2
1.9 ( 0.4 3.6 ( 0.2 1.9 ( 0.2 0.6 ( 0.04 2.5 ( 0.08 0.5 ( 0.03 2.5 ( 0.6 5.5 ( 0.2 3.1 ( 0.2 1.8 ( 0.4 2.6 ( 0.1 2.0 ( 0.2 1.4 ( 0.1 1.3 ( 0.03 1.3 ( 0.03
0.3 ( 0.02 0.2 ( 0.03 0.3 ( 0.05 0.3 ( 0.02 0.1 ( 0.01 0.2 ( 0.05 0.4 ( 0.04 0.3 ( 0.03 0.4 ( 0.05 1.5 ( 0.1 1.3 ( 0.1 1.4 ( 0.1 6.3 ( 0.2 6.6 ( 0.2 6.7 ( 0.2
R2
χ2 (1016)
∆G (kJ/mol)
2.6
-12.7 ( 0.3
0.988 0.914 28 0.971 0.875 2.4 0.995 0.967
-10.0 ( 0.1 -13.4 ( 0.4
26
-11.4 ( 0.4
65
-10.8 ( 0.1
0.994 0.971 0.999 0.998
pH 5.5-5.7, ionic strength 1 mM NaCl, 22 ( 0.5 °C. Table 5 a. Comparison of Cooperative Binding Model Fitting Results for the Adsorption of Fluorescent Dyes dye
Rhodamine 6G Calcein
particles Bindzil Ludox-SM30 Ludox-HS30 Ludox-Cl γ-alumina
Kpart (10-8 L/mol)
Γmpart (108 mol/m2)
γ
χ2 (1021)
0.2 ( 0.2 0.2 ( 4.7 0.4 ( 0.3 7.8 ( 9.5 2.4 ( 0.7
2.9 ( 1.4 0.5 ( 0.8 0.6 ( 0.2 1.8 ( 0.5 5.9 ( 0.2
0.9 ( 0.1 0.8 ( 0.2 0.7 ( 0.1 0.7 ( 0.3 1.3 ( 0.2
0.3 2.2 4.8 2.7 4.0
b. Comparison of the Variation of the Sum of the Relative Error by Using the Linear Cooperative Binding Model in Function of γ for the Adsorption of Dye onto the Particles Rhodamine 6G Calcein
Bindzil Ludox-SM30 Ludox-HS30 Ludox-Cl γ-alumina
γ ) 0.3
γ ) 0.5
γ ) 0.7
γ ) 0.9
γ)1
5.4 × 2.6 × 104 6.1 × 103 2.1 × 102 3.5 × 106
27 75.5 6.0 1.2 629
1.9 4.5 0.3 0.03 7.2
1.8 1.8 0.1 0.02 0.1
1.5 1.4 0.1 0.02 0.004
105
Table 6. Comparison of the Maximum Numbers of Dye on the Surfaces of Particles and the Ratio of Particle Surface/Dye Surface dye
particles
Ap (nm2)
RA
Nma
Rhodamine 6G
Bindzil Ludox-SM30 Ludox-HS30 Ludox-Cl γ-alumina
1328.0 1957.2 3593.3 6822.2 10641.3
713 1051 1929 2172 3385
2 4 9 62 378
Calcein
Figure 4. Comparison of the nonlinear Langmuir isotherm fitting for Calcein adsorption on the surface of the particles. The symbols are the experimental data. Fitting curves are in solid lines. The inset compares the linear fitting with Γ2 weighting.
The standard free energies of adsorption ∆G have been calculated according to1,35
∆G ) -RT ln(K/Adh0)
(17)
and the results are noted in Table 4. In eq 17, Ad is the limiting area of the adsorbed molecules (Ad ) πrh2: 186 (35) Crisp, D. J. J. Colloid Sci. 1956, 11, 356-376.
Å2 per R6G molecule and 310 Å2 per Calcein molecule) and h0 is the free space available for adsorption in the direction perpendicular to the solid surface. It will be noted that if the surface is regarded as a homogeneous region, h0 represents that part of the layer thickness across which the adsorbed molecules are free to undergo thermal movement (h0 ) 5.4 Å).35 Table 6 shows a comparison between two parameters, RA and Nma related to the adsorption surface area. RA is defined as the ratio of the surface area of one particle Ap (Ap ) 4πrh2) to the surface occupied by one dye Ad. This parameter reflects the number of accessible sites on the surface of one particle. Nma is defined as the maximum number of adsorbed dye molecules on the surface of one particle: Nma ) ΓmpartNAAp, where NA is the Avogadro number. We can observe that RA . Nma for all the systems which implies that the surface is very far to be covered. So a dye molecule can adsorb onto the surface without being influenced by other neighboring dye molecules. This is coherent with the fact that the interactions between the adsorbed dyes can be neglected and the Langmuir model is applicable.
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Leng et al.
Table 7. Comparison of Size of Particles Measured by Means of FCS, PCS, and TEM FCS particle type
107D
(cm2/s)
Bindzil Ludox-HS30 Ludox-SM30 Ludox-Cl alumina
2.34 ( 0.24 1.94 ( 0.21 1.44 ( 0.09 1.09 ( 0.17 0.88 ( 0.10
PCS
TEM
rh (nm)
polydisp
rh (nm)
polydisp
r (nm)
10.3 ( 1.1 12.5 ( 1.1 16.9 ( 0.6 23.3 ( 2.4 29.1 ( 3.1
0.36 0.23 0.24 0.25 0.29
9.6 ( 0.2 11.4 ( 0.2 17.2 ( 0.1 27.1 ( 1.7
0.50 0.26 0.19 0.23
7.5 ( 1.7 10.9 ( 3.9 14.4 ( 3.9 20.9 ( 6.2 25.1 ( 6.9
are shown in Table 7. In this table also shows the diffusion coefficients calculated by eq 5, rh values (calculated by eq 6) are compared with those measured by PCS and TEM. The polydispersity of particles was determined from FCS data with the histogram method.21,24,25 We found that the results of FCS are in good agreement with those of PCS for silica suspension despite the differences in the investigated concentration range. The suspension of alumina particles could be measured by FCS, but not by PCS. This is due to the fact that the concentration of alumina solution after ultracentrifugation is too low and the sensitivity of PCS is not sufficient to perform these measurements. The rh difference between FCS and TEM can be explained by the hydration state of charged particles.34 Figure 5. Fitting on the autocorrelation function of labeled Bindzil particles. The particle concentration is 0.03 g/L. The free R6G concentrations is 10-8 M. The pH of medium is 5.5, 1 mM NaCl, and room temperature (22 ( 0.2 °C). The solid line is for fitting curve. The symbol 0 curve is the experimental autocorrelation function.
A similar case of adsorption of dye onto nanoparticles has been studied by Charreyre et al.,1 which concerned the adsorption of R6G onto latex particles (r ) 49 nm). They found that the adsorption contains two different steps: when the R6G concentrations varied from 8 × 10-5 to 10-3 M, hydrophobic interactions are important; while if the R6G concentrations are lower and varied from 8 × 10-8 to 8 × 10-5 M, electrostatic adsorption plays an important role. They also found that in the low concentration regime the adsorption constant K ) 3.3 × 107 L/mol (T ) 293 K, pH 2.7, 1 mM NaCl), and the corresponding adsorption energy is -9.7 kJ/mol, which are of the same order of magnitude as the values reported here. Figure 5 illustrates the FCS fitting process on the experimental ACF of labeled Bindzil particles. In this figure, the data of ACF were obtained from one single measurement. The measurements and their fitting curves were repeated 10 times to determine its average characteristic diffusion time. The results of size measurements
5. Conclusions The high sensitivity and the capability of in situ measurements make FCS very useful for studying the adsorption equilibrium of small molecules on colloidal particles at low concentrations without a separation procedure and taking into account the adsorption of the molecules on the sample cell. In this condition, we found that the adsorption of dye on silica and alumina mineral particles can be well described with the Langmuir isotherm adsorption model. The cooperative model shows less satisfactory results. The size and the polydispersity of the particles can be correctly determined simultaneously by FCS at low particles concentrations (0.01-0.03 g/L in good agreement with PCS and TEM. Acknowledgment. We are grateful to Dr. Emile Pefferkorn (Institute Charles Sadron CNRS, Strasbourg), Dr. Serge Stoll (CABE Geneva University), Dr. K. J. Wilkinson (CABE Geneva University), and Dr. Nalini Parthasarathy (CABE Geneva University), for theirs advice, interest, and comments, to Dr. Marcelo Avena (Ciudad University, Argentina) for offering the sample of silica suspension (Bindzil AKZO NOBEL). The support of the Swiss National foundation is acknowledged (Project 2000-050629.97/1). LA010787M
