Restricted Geometry Conditions Promoted by AlOOH Nanoparticles

9240

J. Phys. Chem. C 2008, 112, 9240–9246

Restricted Geometry Conditions Promoted by AlOOH Nanoparticles: Variable Strength and Character of AlOOH-Cluster/Charged Ligand Interactions As a Consequence of Changes in the Solvent R. Sanchez,† M. Villar,‡ A. Guiraum,‡ and R. Prado-Gotor*,† Department of Physical Chemistry and Department of Analytical Chemistry, Faculty of Chemistry, UniVersity of SeVilla, C/ Profesor Garcıá Gonza´lez s/n 41012 SeVilla, Spain ReceiVed: March 14, 2008; ReVised Manuscript ReceiVed: April 17, 2008

AlOOH nanoparticles have been used to study the strength and character of the binding of the persulphate ion (S2O82-), at pH ) 5.4, to them. The strength of the binding has been studied using a kinetic approach which consists of the study of the oxidation kinetics of a metal cation complex ([Ru(NH3)5pz]2+ (pz ) pyrazine)) by S2O82- at different NaCl concentrations. When the ionic strength increases, the strength of the binding decreases, as a consequence of the partial neutralization of the charge on the AlOOH surface which, at pH ) 5.4, is positively charged. The increase of the ionic strength also produces a change in the character of the binding, which changes from anticooperative to noncooperative when the ionic strength increases. The nonelectrostatic and electrostatic components of the free energy of binding are determined. The nonelectrostatic component of the free energy of binding is almost zero. On the other hand, the values of the differences of electrostatic potential at the AlOOH/solutions interface have been obtained from the electrostatic component. Introduction

∆Gs ) RT ln γs

(1a)

Problems in the use of different kinds of nanoparticles are usually related to their stability in the solvent under different conditions. This stability depends strongly on the valency of the counterions in the solution. For example, for negatively charged gold colloids, the flocculation value is about 20 mmol/L for monovalent cations, about 0.4 mmol/L for divalent cations, and in the range of 10-6 mol/L for trivalent cations.1

γs )

1 1 + K[R]

(1b)

Colloidal dispersions consisting of AlOOH nanoparticles (AlOOH NPs), compared with gold nanoparticles, are stable and transparent in a broad pH range and at relatively high ionic strength.2 As it will be described, this property has been used in order to measure the surface potential of the AlOOH nanoparticle, working at different NaCl concentrations. AlOOH NPs present a surface charge density which is a function of the pH of the medium. That is, it is possible to control the surface charge on the nanoparticle and, therefore, to modulate the interaction between the AlOOH NPs and charged ligands. Although direct applications of these AlOOH nanoparticles have been recently described, for example, as biosensors,3 and studies of adsorption of proteins have been done, such as lysozyme and bovine serum albumin on AlOOH NPs,4 there are very few systematic studies in relation to the strength and character of the binding of AlOOH nanoparticles to small charged ligands through noncovalent interactions, that is, through interactions between chemical species other than covalent bound. Generally speaking, these noncovalent interactions between two species produce a change in their properties. So the union of a substrate S to a receptor, R, promotes a change in the free energy of the substrate given by5 * Author to whom correspondence should be addressed. Phone: 34-954 557177. Fax: 34-954557174. E-mail: [email protected]. † Department of Physical Chemistry. ‡ Department of Analytical Chemistry.

Here the activity coefficient of the substrate, γs, is defined with respect to a reference state in which [R] ) 0. On the other hand, in eq 1b, K represents the equilibrium constant for the process:

S(free) + R h S/R (substrate linked to the receptor) (2) By measuring some properties at different receptor concentrations, for example, changes of the rate constants of a given reaction in which S participates, it is possible to obtain K and from this the standard free energy corresponding to the union substrate/receptor. Following this approach, we have done a systematic study of the interaction between a small anionic ligand, S2O82-, and AlOOH NPs positively charged at pH ) 5.4. Besides their stability at relatively high ionic strength, another advantage of this kind of nanocluster, compared, for example, with gold nanoparticles, is that they are transparent and so kinetic measurements can be performed by using spectrophotometric techniques. The equilibrium binding constant K and, therefore, the free energy of binding of the persulphate ion (negatively charged) to the AlOOH NPs were obtained following the changes in the kinetics of the electron transfer reaction between the [Ru(NH3)5pz]2+ and S2O82-. From these kinetic data, a two-state-model allows us to evaluate not only the strength of the binding, but also its character as function of the AlOOH NPs concentration and the ionic strength of the medium. On the other hand, in working at different ionic strengths, it is possible to separate the electrostatic and nonelectrostatic contributions to the binding free energy. In this way, a complete picture of the binding can be obtained, and the values of the differences of electrostatic potential at the AlOOH/solution interface can be determined from the electrostatic component.

10.1021/jp802223x CCC: $40.75  2008 American Chemical Society Published on Web 05/31/2008

AlOOH-Cluster/Charged Ligand Interactions

J. Phys. Chem. C, Vol. 112, No. 25, 2008 9241

Figure 1. Titration curve of AlOOH NPs with strong base. Titrations were performed by adding 0.1-0.5 mL aliquots of 2 mM KOH. The pH meter output was recorded initially and after each addition of base. Temperature was maintained at 298.2 ( 0.1 K. Full circles correspond to the left ordinate and the open circles to the right scale.

performed at 220 nm. Samples were injected by pressure of 0.5 psi for a period of 5 s. Daily, before being used, the capillary was successively rinsed with 0.1 M NaOH, water, and the running buffer for 5 min each. Between runs, it was also conditioned with 0.1 M NaOH (2 min), water (3 min), and the running buffer (5min). Kinetic Measurements. Kinetic runs were carried out in a stopped-flow spectrophotometer from Applied Photophysics. The reaction was monitored by following the changes in absorbance of the [Ru(NH3)5pz]2+ complex at 472 nm. All of the kinetic runs were carried out under first-order conditions using an excess of the oxidant: [Ru(NH3)5pz]2+ ) 2 × 10-5 mol dm-3 and [S2O82-] ) 2.5 × 10-4 mol dm-3 in the reaction mixture . Pseudofirst-order rate constants were obtained from the slopes of the linear plots of ln(At - A∞) versus time, where At and A∞ were the absorbances at times t and when the reaction was finished, respectively. All of the experiments were repeated at least five times. The estimated uncertainty in the rate constant was less than 5%.The temperature was maintained at 298.2 ( 0.1 K.

Materials and Methods

Results

Materials. All chemicals were of analytical reagent grade and were used without further purification. Sodium peroxodisulphate was purchased from Fluka and NaCl from Merck. [Ru(NH3)5pz](ClO4)2 was prepared and purified according to published procedures.6 The AlOOH dispersion, consisting of the AlOOH nanoparticles (boehmite structure), was kindly obtained from Kawaken Fine Chemicals Co. Ltd., Japan. The sol has a pH of 3.8, which means that the colloid particles are positively charged. Colloidal particles have a rather narrow size distribution centered at 10 nm. The Al content (wt %) is 5.2% and [AlOOH NPs] concentrations are referred to the aluminum content. Solutions were prepared with deionized water, its conductivity being less than 10-6 S m-1. Buffers were prepared according to standard laboratory procedure in order to obtain pH ) 5.4. These buffers were prepared with 5 × 10-3 mol dm-3 of cacodylic acid (dimethylarsinic acid) from Sigma and 3 × 10-3 mol dm-3 of HCl from Merck. Spectra. The spectra of the AlOOH NPs in the presence and in the absence of NaCl were recorded with a Cary 500 spectrophotometer at 298.2 K in the UV region. No aggregation between nanoparticles was observed in the presence of the electrolyte, and the ruthenium metal complex was stable in the presence of the AlOOH nanoparticles at pH ) 5.4. Neutralization of AlOOH NPs: Acid/Base Titration. The surface hydroxyl groups in the AlOOH colloid dispersion allow a direct approach to the study of their acidity, carried out by titrating them with a strong base. KOH was used in order to determine the point of zero charge, pHpzc. Figure 1 represents the titration curve of the AlOOH NPs with KOH as strong base. Titrations were performed by adding 0.1-0.5 mL aliquots of 1 mM KOH to 0.04 M solutions of the acid AlOOH NPs in water (initial pH at 25° C ) 3.8). The pH meter output was recorded initially and after each addition of base. Capillary Zone Electrophoresis. Capillary zone electrophoresis was carried out with a P/ACE MDQ system (BeckmanCoulter, Fullerton, CA) equipped with diode-array detector (DAD) and a Karat 33 ChemStation for system control, data collection, and data analysis. Uncoated fused-silica capillaries (Supelco, Bellefonte, PA) of 75 µm i.d. and an effective length of 50 cm (total length 57 cm) were used. The separation voltage was 20 Kv (detection at the cathode) and the temperature of the capillary was 298.2 K. Direct photometric detection was

The surface of a given inorganic oxide in an aqueous solution consists of amphoteric hydroxyl groups which can be either protonated or deprotonated, depending on the solution pH value and thus acquire electrical charge. The pH titrations (see Figure 1) show that AlOOH NPs are positively charged at pH lower than 6.1. That is, in more acid media, the hydroxyl surface groups are protonated (AlOOH2+) providing a dispersed positively charged surface in solution. Petkovic et al.7 give a value of pHpzc ) 6.8 and Nedeljkovic et al.2 obtain pHpzc ) 7.1. In both cases, by considering all of these values, it is clear that AlOOH nanoparticles must be positively charged at pH 5.4, the pH value of our working conditions. In order to confirm that, in the presence of the buffer used in this study, which corresponds to pH 5.4 (at which the ruthenium complex is not still protonated8), the AlOOH nanoparticles are positively charged, capillary zone electrophoresis technique was used. Migration time for the AlOOH NPs was measured at different pH, below and above the point of zero charge. Figure 2 shows the electropherograms obtained from the AlOOH sol at pH ) 5.4 and pH ) 6.8 (using buffers prepared with cacodylic acid and HCl) maintaining the same ionic strength with NaCl (I ) 0.01). At pH ) 5.4, as it can be seen in Figure 2, the migration time is shorter for the positively charged AlOOH nanoparticle, a consistent result considering that detection was done at the cathode. The results of the kinetic runs are shown in Tables 1 through 5 in Supporting Information and in Figures 3–7 as pseudofirstorder rate constants. These rate constants correspond to the first electron transfer from the ruthenium complex to the peroxodisulfate:9

[Ru(NH3)5pz]2+ + S2O82- f [Ru(NH3)5pz]3+ + S2O83-(SO42- + SO4-•) (3) This step is slower than the second electron transfer:

[Ru(NH3)5pz]2+ + SO4-• f [Ru(NH3)5pz]3+ + SO42- (4) because the redox potential of the S2O82-/3- couple is lower than that of the SO4-•/ SO42- couple10 and the reorganization energy of S2O82- is greater than that of SO4-•.

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Figure 4. Plot of the experimental rate constants of the reaction Ru(NH3)5pz2+ + S2O82- vs [AlOOH NPs] concentration at [NaCl] ) 0.001 mol dm-3. Symbols (µ) are experimental data and line is the best fit using eq 7.

Figure 2. Electropherograms for AlOOH NPs at pH ) 5.4 (on top) and pH ) 6.8 (below). Photometric detection was performed at 220 nm. Samples were injected by pressure of 0.5 psi for a period of 5s and temperature was maintained at 298.2 ( 0.1 K.


Figure 3. Plot of the experimental rate constants of the reaction Ru(NH3)5pz2+ + S2O82- vs [AlOOH NPs] concentration at [NaCl] ) 0 mol dm-3. Symbols (µ) are experimental data and line is the best fit using eq 7.

Discussion According to data in Figures 3–7, we see clearly the efficiency of the AlOOH nanoparticles (AlOOH NPs) for decreasing the rate of the electron transfer reaction. These results corresponding to an anion-cation reaction are consistent with that of Nedeljkovic et al.2 corresponding to a detailed study of an anion-anion reaction showing how the sensitivity of the rate constant to the pH provides a convenient method for precise detection of the point of zero charge of dispersed material. In the present paper, we describe how to separate the electrostatic and nonelectrostatic

contributions to the binding free energy and to how to obtain the values of the differences of electrostatic potential at the AlOOH/solution interface. The oxide particles are positively charged at pH ) 5.4. By taking into account the charges of the reactants in the present study, S would correspond to the persulphate ion and R would correspond to the AlOOH nanoparticle in eq 2. If the reactant is designed as S2O82-, an equilibrium constant K can be defined as:

K)

[S2O28 B] [S2O28 F][AlOOH NPs]

(5)

where S2O82-F represents the free state of the persulphate ion, AlOOH NPs is the dispersed material (or pseudophase) to which the solute binds, and S2O82-B represents the bound state of the solute (or the solute at the pseudophase).




Figure 8. Plot of the experimental rate constants of the reaction Ru(NH3)5pz2+ + S2O82- vs calculated rate constants at [NaCl] ) 0.01 mol dm-3 using eq 7 and K given by eq 13.

TABLE 1: Values of the Best Fit Parameters for eq 7 and eq 8a Kmax [NaCl] [NaCl] [NaCl] [NaCl] [NaCl]

) ) ) ) )

0M 0.001 M 0.01 M 0.02 M 0.04 M

11 ×105 3050 160 28 10b

kF

kB

j

7.8 7.6 5.7 4.4 3.6

2.5 × 10-9 5 × 10-5 6 × 10-2 0.07 0.05

0.025 0.025 0.045 0.013

a kF, s-1; kB, s-1; Kmax, mol-1 dm3. b In this case, K is independent of [AlOOH NPs]


Generally speaking, as the properties of the local media, or phases, corresponding to the bound and free states are different, these states react at different rates:

S2O28 F

kF

98 products kB

S2O28 B 98 products

(6a)

(6b)

From eqs 5 and 6, it follows that the observed rate constant is given by11

kF + kBK[AlOOH NPs] kobs ) 1 + K[AlOOH NPs]

(7)

This equation (it is indeed the equation of the pseudophase model) opens the possibility of obtaining free energies of binding

by using specific reactions as probes.12 This equation, in fact the Olson-Simonson equation,13 corresponds to the behavior expected for a two-state reactive system. It is worth pointing out that, strictly speaking, eq 7 can be applied only in the case of unimolecular processes. However, as it has been shown in a previous paper,14 eq 7 is still valid for a second order process provided that only one of the reactants (the [S2O82-] in the present case, given the positive charge of the nanoparticles) is partitioned between the two states and the other (the ruthenium complex) remains essentially in the aqueous pseudophase. It is interesting to note that the activity coefficients for the reactant species are incorporated into the surface binding model (eq 7). According to the transition-state theory, the rate constant for a given reaction

A + B f products

(8)

is given by the equation

kobs ) k0

γAγB γ*

(9)

In this equation γA, γB, and γ* are the activity coefficients of the reactants and of the activated complex, respectively, and k0 is the rate constant of the process in the reference state (the solute in the aqueous pseudophase in contact with the nanoparticles). In this way, it is easily shown15,16 that

γi )

1 1 + Ki[T]

i ) A, B, *

(10)

with Ki being the equilibrium constant defined in eq 5 for solute i (A, B, *). Notice that, with the reference state used, k0 in eq 9 is identical to kw in eq 7. Before applying eqs 9 and 10 to the present case, some comments are in order. It is so because, in

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the study presented here, one of the reactants, the ruthenium complex (Ru(NH3)5pz2+), bears a positive charge. Thus, it can be assumed that, on the average, it will remain far from the positively charged AlOOH NPs, that is, in the aqueous pseudophase. In other words, it will stay at the reference state, and therefore, by definition, γi (i ) Ru(NH3)5pz2+) will be unity. According to this, in the present case, a combination of eqs 9 and 10 gives

kobs )

k0 + k0K*[T] 1 + K[T]

(11)

Given that17

k0K* ) kBK

(12)

the equivalence of eq 7 (pseudophase or two-state model) and eq 8 (Bro¨nsted equation) is proved. In fact, considering the values of kobs in the present study, only the data in Figure 7 (corresponding to [NaCl] ) 0.04 mol dm-3) can be fitted to eq 7 with the set of parameters appearing in Table 1, for all of the [AlOOH NPs] concentrations used (see Figure 7 where the points are experimental data and the line is the best fit obtained by using eq 7). The values of these parameters merit some comments. First of all, the value of kF is almost the same as the value of kobs in the absence of oxide nanoparticles, a fact (see Table 5, Supporting Information, and Table 1) which confirms the quality of the fit. It is also important to realize that the reactivity of the bound state is much lower than the reactivity of the free state. That is, the reaction between the persulphate adsorbed on the nanoparticle and the ruthenium complex is practically nonexistent. This confirms our assumption that the [Ru(NH3)5pz]2+ is practically absent at the AlOOH NPs surface. As to the results corresponding to the absence of electrolyte, in the presence of [NaCl] ) 0.001 mol dm-3, [NaCl] ) 0.01 mol dm-3, and in the presence of [NaCl] ) 0.02 mol dm-3, Figures 3–6 show that only the data corresponding to small ranges of the [AlOOH NPs] concentrations can be fitted to eq 7. In Figures 3–6, the curves correspond to a fit of the experimental data if K is considered to be a true constant, that is, using eq 7 with a single value for K and, so, independent of the AlOOH NPs concentration. Only the first part of the curve goes through the experimental points. As it can be seen, experimental rate constants are smaller than the calculated values for the higher [AlOOH NPs] concentrations. This deviation is more pronounced in the absence of NaCl and decreases as the [NaCl] concentration increases (compare Figures 3–6). That is, K changes (and, therefore, it is not a true constant) as the [AlOOH NPs] concentration changes when NaCl is not present or at the three smaller NaCl concentrations used. So results corresponding to Figures 3–6 cannot be fitted to eq 7 in the whole range of [AlOOH NPs] concentrations, unless allowance is made for a variation of K with the ratio between the concentrations of the [S2O82-] anion and those of the oxide nanoparticles. However, since the concentration of the persulphate ion is constant in our experiments, K only depends on the concentration of the AlOOH NPs. At first, this dependence is unknown. However, in order to have a physical meaning, K must show a saturation behavior; that is, it must reach a constant value after a given concentration of the nanoparticles. A dependence of K accomplishing this requirement, frequently found in many systems, is given by eq 13 which corresponds to a sigmoidal dependence:18

K)

Kmaxet 1 + et

(13)

This sigmoidal dependence is also described by the famous Hill eq 19 or the von Hippel model20 for binding of small ligands to macromolecules. In eq 13, t ) ([AlOOH NPs] - h)/j, Kmax is the maximum (limiting) value of K, h is the value of the concentration of the nanoparticles, [AlOOH NPs], for which K ) (1/2)Kmax, and j is an adjustable parameter. By using this equation, the data corresponding to Figures 3-6 can be fitted in the whole range of [AlOOH NPs] concentrations used. The results of the fit are displayed in Figure 8 for [NaCl] ) 0.01 mol dm-3. Similar results are obtained in the absence of NaCl and for [NaCl] ) 0.001 mol dm-3 and [NaCl] ) 0.02 mol dm-3. The values of Kmax, kF, and kB are given in Table 1. The effect of the ionic strength on the activity coefficients of the reactants can be observed in the values of kF for different NaCl concentrations. In fact, the reaction rate at [AlOOH NPs] ) 0 (see Tables 1-5, Supporting Information) is very close to a linear function of [NaCl]1/2, a classic dependence of aqueous ion activity coefficients on the square root of ionic strength. The fact that the values of K increase when the [S2O82-]/ [AlOOH NPs] decreases means that the union of the persulphate ion and the nanoparticles is anticooperative. This fact implies that, in comparison with higher ionic strength, the oxide nanoparticles change not only the strength of binding, but also its character: it is noncooperative in the case of [NaCl] ) 0.04 mol dm-3 and anticooperative for lower [NaCl] concentrations.20 This anticooperative character has also been observed in the case of the binding of small ions to DNA,21 peptides,22 and dendrimers.23 Of course, part of this anticooperativity arises as a consequence of the fact that when one persulphate anion is bound, a second ion will feel repulsion from the first bound one. The screening effect induced by NaCl addition causes a reduction of the repulsive interaction and, consequently, of the anticooperative behavior. However, other causes of anticooperativity cannot be ruled out. Thus, the binding of a persulphate ion, with a charge sign opposite from the charge of the nanoparticle, would produce a screening between the charges on the oxide ligands in the AlOOH NPs, allowing in this way a more compact conformation of the receptor, with binding properties which can be different from those related to the less compact conformation in the absence of the persulphate anion. The values of the equilibrium binding constant obtained for each NaCl concentration also allow an estimation of the nonelectrostatic and electrostatic components of the binding. K (or Kmax) can be expressed in function of the free energy corresponding to the process in eq 2. This free energy, ∆G, can be written as the sum of two contributions: (i) an electrostatic potential independent contribution, ∆Gnel (nonelectrostatic or intrinsic), and (ii) an electrostatic potential dependent contribution, ∆Gel (electrostatic). This separation has been discussed extensively in refs 24–27

∆G ) ∆Gnel + ∆Gel

(14)

K ) KnelKel

(15)

In this way: We used Lippard′s equation in order to separate these contributions. According to Howe-Grant and Lippard,28 log Kel is proportional to -log[Cl-]; that is,

log K ) log Knel - β 1og[C1-]

(16)

The values of log K (or Kmax) appearing in Table 1 are plotted in Figure 9. The perclorate ion from the ruthenium complex



Figure 9. Plot of log K vs log([Cl-] + [ClO4-]) (see eq 11) for the process Ru(NH3)5pz2+ + S2O82- in AlOOH NPs systems. The perchlorate from the ruthenium complex ([Ru(NH3)5pz](ClO4)2) has been also taken into account.

[Ru(NH3)5pz](ClO4)2 has also been taken into account, in order to calculate the total anion concentrations in Figure 9. From the intercept, a value of log Knel ) -1.3 is found which gives a value of 5 × 10-2 mol-1 dm3 for Knel. That is, by taking into account the values of K (or Kmax) appearing in Table 1 (Kmax ) K when the binding is noncooperative), it can be established that the nonelectrostatic component of the free energy of binding is practically nonexistent. This result agrees with previous studies of adsorption of lysozyme and bovine serum albumin on AlOOH-coated silica particles representing negatively and positively charged oxide surfaces. Electrostatic interactions also dominate the adsorption process, in this case, for macromolecules and not small ligands.4 Once the value of Knel (5 × 10-2 mol-1 dm3) has been determined, Kel for each [Cl-] concentration can be obtained as Kel ) K/Knel (see eq 15). From Kel, by taking into account that

ln Kel )

-nF∆Ψ RT

(17)

where ∆Ψ is the difference of the electrostatic potential between the nanoparticle surface and the solution, this parameter can be easily obtained. The values of ∆Ψ at different [Cl-] concentrations are given in Figure 10. An exponential decrease of the ∆Ψ values are observed as the NaCl concentration increases. It is interesting to note that the values of ∆Ψ are of the same order of magnitude as those existing at the interfaces of micelles.29 In conclusion, the binding of the persulphate anion to positively charged AlOOH nanoparticles has been studied following a kinetic approach. It has been shown that the character and strength of the binding of the anions to AlOOH NPs is dependent on the ionic strength of the aqueous phase in contact with the oxide nanoparticle. When the ionic strength increases, (i) there is a partial neutralization of the charge on the AlOOH NPs, in such a way that the free energy of binding increases, and thus Kmax decreases. (ii) The effect of the persulphate anion on AlOOH NPs, which causes the anticooperative character of the binding, becomes less important, a fact which permits the modulation of this noncovalent interaction.

Figure 10. Plot of the difference of electrostatic potential between the nanoparticles surface and the solution, ∆Ψ/volts vs [Cl-]/mol dm-3.

This is so because the same effect is produced by the anions of the supporting electrolyte which are present at a (constant) concentration much higher than that of the persulphate ion. This effect seems to be “saturated” at ionic strengths of about 0.04 mol dm-3. On the other hand, working at different NaCl concentrations, the nonelectrostatic and electrostatic contributions to the binding free energy have been separated. The first one is practically zero, which indicates that electrostatic interactions dominate the adsorption process. From the latter one, the values of the differences of electrostatic potential at the AlOOH NPs/solutions interface have been determined, obtaining in this way a complete picture of the binding by following a kinetic approach based on an electron transfer reaction as probe, which is one of the simplest of chemical processes (an electron is transferred from a donor to an acceptor without breaking or forming new bonds), and using a stable and transparent colloidal dispersion in a broad pH and ionic strength range. Acknowledgment. This work was financed by the D.I.GYT (CTQ-2005-01392/BQU) and the Consejerıá de Educacioń y Ciencia de la Junta de Andalucıá. The authors are indebted to Mr. Gouzou Matsuda (Kawaken Fine Chemicals Co., Ltd., Tokyo, Japan) for alumina sol sample. Supporting Information Available: Rate constants. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1998. (2) Vucina-Vujovic, A.; Jankovic, I. A.; Milonjic, S. K.; Nedeljkovic, J. M. Colloids and Surfaces A: Physicochem. Eng. Aspects 2003, 223, 295. (3) Aucejo, R.; Alarcoń, J.; Soriano, C.; Guillen, M. C.; Garcıá-Espanã, E.; Torres, F. J. Mater. Chem. 2005, 15, 2920. (4) Rezwan, K.; Meier, L. P.; Gauckler, L. J. Biomaterials 2005, 26, 4351. (5) (a) Muriel-Delgado, F.; Jimeńez, R.; Go´mez-Herrera, C.; Sańchez, F. Langmuir 1999, 15, 4334. (b) Davies, K; Hussam, A. Langmuir 1993, 9, 3270. (6) Creutz, C.; Taube, H. J. Am. Chem. Soc. 1973, 95, 1086. (7) Petkovic, M. J.; Milonjic, S. K.; Dondur, V. T. Sep. Sci. Technol. 1994, 29, 627.

9246 J. Phys. Chem. C, Vol. 112, No. 25, 2008 (8) Ford, P. C; Rudd, D. F. P.; Saunder, R.; Taube, H. J. Am. Chem. Soc. 1968, 90, 1187. (9) Fu¨rholz, U.; Haim, A. Inorg. Chem. 1987, 26, 3243. (10) Eberson, L. In Electron Transfer Reactions in Organic Chemistry; Springer-Verlag: New York, 1987; p 88. (11) In order to obtain eq 7 from eqs 5 and 6, an additional hypothesis is necessary on the equilibrium distribution described by eq 5: the concentration of the partitioned substrate must be low enough in order to avoid saturation of the dispersed pseudophase. Indeed, even in this case, it is implicit that the presence of a substrate molecule in the dispersed pseudophase neither encourages nor discourages the union of a second molecule of substrate: in other words, the binding of the substrate to the dispersed pseudophase is noncooperative in character. (12) Villa, I.; Prado-Gotor, R. Chem. Phys. Lett. 2007, 434, 210. (13) Olson, A. R.; Simonson, J. R. J. Phys. Chem. 1949, 17, 1167. (14) Lopez-Cornejo, P.; Sańchez, F. J. Phys. Chem. B 2001, 105, 10523. (15) Ise, N.; Okubo, T.; Shigern, K. Acc. Chem. Res. 1982, 15, 171. (16) Muriel-Delgado, F.; Jimeńez, R.; Go´mez-Herrera, C.; Sańchez, F. Langmuir 1999, 15, 4344. (17) Go´mez-Herrera, C.; Jimeńez, R.; Pe´rez-Tejeda, P.; Lo´pez-Cornejo, P.; Prado-Gotor, R.; Sańchez, F. Prog. React. Kinet. Mech. 2004, 29, 289.

Sanchez et al. (18) Hammes, G. G. In Thermodynamics and Kinetics for the Biological Sciences; Wiley-Interscience: New York, 2000; p 124 and ff. (19) Haynie D. T. In Biological Thermodynamics; University Press: Cambridge, 2001; p 233. (20) Mc Ghee, J. D.; Von Hippel, P. H. J. Mol. Biol. 1974, 86, 469. (21) Secco, F.; Venturini, M.; Lo´pez, M.; Pe´rez, P.; Prado, R.; Sańchez, F. Phys. Chem. Chem. Phys. 2001, 3, 4412. (22) Chavanieu, A.; Guichou, J. F.; Prado-Gotor, R.; Pe´rez-Tejeda, P.; Jimeńez, R.; Lo´pez-Cornejo, P.; Sańchez, F. J. Phys. Chem. B 2005, 109, 19676. (23) de la Vega, R.; Pe´rez-Tejeda, P.; Prado-Gotor, R.; Lo´pez-Cornejo, P.; Jimeńez, R.; Pe´rez, F.; Sańchez, F. Chem. Phys. Lett. 2004, 398, 82. (24) Dolcet, C.; Rodenas, E. Can. J. Chem. 1990, 68, 932. (25) Ortega, F.; Rodenas, E. J. Phys. Chem. 1987, 91, 837. (26) Bunton, C. A.; Moffat, J. R. J. Phys. Chem. 1986, 90, 538. (27) Al-Lohedan, H. A. J. Chem. Soc., Perkin Trans 2 1995, 1707. (28) Howe-Grant, M.; Lippard, S. J. Biochemistry 1979, 18, 5762. (29) Bernas, A.; Grand, D.; Hautecloque, S.; Giannotti, C. J. Phys. Chem. 1986, 90, 6189.

JP802223X

Restricted Geometry Conditions Promoted by AlOOH Nanoparticles

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