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Thermodynamics and Kinetics of Adsorption of Poly(amido amine) Dendrimers Surface Functionalized with Ruthenium(II) Complexes Kazutake Takada,† Gregory D. Storrier,† Moise´s Mora´n,‡ and He´ctor D. Abrun˜a*,† Department of Chemistry, Baker Laboratory, Cornell University, Ithaca, New York 14853-1301, and Departamento de Quı´mica Inorga´ nica, Universidad Auto´ noma de Madrid, Canto Blanco 28049, Madrid, Spain Received March 31, 1999. In Final Form: June 22, 1999 The thermodynamics and kinetics of adsorption of the redox-active tris(bipyridyl)ruthenium(II) pendant poly(amido amine) (PAMAM) dendrimers and bis(terpyridyl)ruthenium(II) pendant PAMAM dendrimers (generations 0, 1, 2, 3, and 4) have been studied using electrochemical methods. All of these metallodendrimers adsorb onto Pt electrodes at +0.8 V vs Ag/AgCl where the Ru sites of the dendrimers have 2+ charges and the adsorption thermodynamics are well characterized by the Langmuir adsorption isotherm. The kinetics of adsorption were found to be activation controlled with the rate constant decreasing with decreasing dendrimer generation. Electrochemically determined coverages were significantly larger than calculated values determined from the dimensions of the metallodenrimers obtained from molecular modeling. These comparisons suggest that upon adsorption, the dendrimers appear to compress to dimensions significantly smaller than those calculated.
Introduction Recently, the study of dendrimers has moved from the development of synthetic protocols to the application of specific functionalities.1-4 A number of novel dendrimers, capable of exhibiting electrochemical activity through redox-active units located either at the core, within the branches, or at the periphery of the dendritic structure have been prepared. In particular, the electrochemical behavior of redox-active metallodendrimers containing iron,5-12 osmium and ruthenium,13-15 and zinc16 metal centers has been reported. † ‡
Cornell University. Universidad Auto´noma de Madrid.
(1) Matthews, O. A.; Shipway, A. N.; Stoddart, J. F. Prog. Polym. Sci. 1998, 23, 1. (2) Smith, D. K.; Diederich, F. Chem. Eur. J. 1998, 4, 1353. (3) Zeng, F.; Zimmerman, S. C. Chem. Rev. 1997, 97, 1681. (4) Issberner, J.; Moors, R.; Vo¨gtle, F. Angew. Chem., Int. Ed. Engl. 1994, 33, 2413. (5) Cuadrado, I.; Mora´n, M.; Losada, J.; Casado, C. M.; Pascual, C.; Alonso, B.; Lobete, F. Advances in Dendritic Macromolecules. In Advances in Dendritic Macromolecules; Newkome, G. R., Ed.; JAI Press: Greenwich, CT, 1996; Vol. 3; p 151. (6) Cuadrado, I.; Moran, M.; Casado, C. M.; Alonso, B.; Lobete, F.; Garcia, B.; Ibisate, M.; Losada, J. Organometallics 1996, 15, 5278. (7) Alonso, B.; Mora´n, M.; Casado, C. M.; Lobete, F.; Jose´ Losada; Cuadrado, I. Chem. Mater. 1995, 7, 1440. (8) Fillaut, J.-L.; Linares, J.; Astruc, D. Angew. Chem., Int. Ed. Engl. 1994, 33, 2460. (9) Chow, H.-F.; Chan, Y. Y.-K.; Chan, D. T. W.; Kwok, R. W. M. Chem. Eur. J. 1996, 2, 1085. (10) Gorman, C. B.; Parkhurst, B. L.; Su, W. Y.; Chen, K.-Y. J. Am. Chem. Soc. 1997, 119, 1141. (11) Vale´rio, C.; Fillaut, J.-L.; Ruiz, J.; Guittard, J.; Blais, J.-C.; Astruc, D. J. Am. Chem. Soc. 1997, 119, 2588. (12) Shu, C.-F.; Shen, H.-M. J. Mater. Chem. 1997, 7, 47. (13) Newkome, G. R.; Gu¨ther, R.; Moorefield, C. N.; Cardullo, F.; Echegoyen, L.; Pe´rez-Cordero, E.; Luftmann, H. Angew. Chem., Int. Ed. Engl. 1995, 34, 2023. (14) Campagna, S.; Denti, G.; Serroni, S.; Juris, A.; Venturi, M.; Ricevuto, V.; Balzani, V. Chem. Eur. J 1995, 1, 211. (15) Storrier, G. D.; Takada, K.; Abrun˜a, H. D. Langmuir 1999, 15, 872. (16) Dandliker, P. J.; Diederich, F.; Gross, M.; Knobler, C. B.; Louati, A.; Sanford, M. Angew. Chem., Int. Ed. Engl. 1994, 33, 1739.
We are particularly interested in polypyridyl transition metal complexes, especially those of ruthenium(II), which have been extensively applied in areas such as light harvesting and information storage,17 since they exhibit a wide range of photophysical and electrochemical properties.18-20 In this context, we have recently reported on the spectroscopic and electrochemical properties of tris(bipyridyl)ruthenium(II) pendant poly(amido amine) (PAMAM) dendrimers (dend-n-[Ru(bpy)3]) and bis(terpyridyl)ruthenium(II) pendant PAMAM dendrimers (dendn-[Ru(tpy)2] where n ) 4, 8, 16, 32, and 64 for generations 0, 1, 2, 3, and 4, respectively).15 Figure 1 represents the molecular structures of the generation 4, polypyridylruthenium(II) terminated dendrimer complexes, dend-64[Ru(tpy)2] and dend-64-[Ru(bpy)3]. Parts A-C of Figure 2 present (a) space-filling and (b) ball-and-stick models of dend-4-[Ru(bpy)3], dend-8-[Ru(bpy)3], and dend-16-[Ru(bpy)3], respectively, obtained from molecular modeling using CaChe. It is clear from these that as the generation increases, the molecules become increasingly denser and globular. We have previously reported that these dendrimers adsorb onto Pt electrodes at potentials where the Ru sites of the dendrimers have 2+ charges.15 More recently we have also found that adsorbed species can significantly affect the electrochemical properties such as diffusion coefficient.21 We have also reported on the thermodynamics and kinetics of adsorption of diaminobutane-based ferrocenyl dendrimers using electrochemical and electrochemical quartz crystal microbalance (EQCM) techniques.22 Herein, we report on the adsorption (17) Meyer, T. J. Chem. Res. 1989, 22, 163. (18) Kalyanasundaram, K. Photochemistry of Polypyridine and Porphyrin Complexes; Academic Press: London, U.K., 1991. (19) Sauvage, J.-P.; Collin, J.-P.; Chambron, J. C.; Guillerez, S.; Coudret, C.; Balzani, V.; Barigeletti, F.; DeCola, L.; Flamingi, L. Chem. Rev. 1994, 94, 993. (20) Balzani, V.; Juris, A.; Venturi, M.; Campagna, S.; Serroni, S. Chem. Rev. 1996, 96, 759. (21) Takada, K.; Storrier, G. D.; Abrun˜a, H. D. Unpublished data. (22) Takada, K.; Dı´az, D. J.; Abrun˜a, H. D.; Cuadrado, I.; Casado, C.; Alonso, B.; Mora´n, M.; Jose´ Losada. J. Am. Chem. Soc. 1997, 119, 10763.
10.1021/la9903752 CCC: $18.00 © 1999 American Chemical Society Published on Web 08/10/1999
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Figure 1. Structures of (a) dend-64-[Ru(bpy)3] and (b) dend-64-[Ru(tpy)2].
thermodynamics and kinetics of dendrimers surfacefunctionalized with polypyridyl transition metal complexes of Ru onto Pt electrodes by means of cyclic voltammetry. These studies could provide valuable insights not only toward the understanding of interfacial reactions but also toward the modification of electrodes for applications such as electron transfer mediators, catalysts, sensors, electrochromic and electronic devices. We also compare electrochemically determined coverages with those calcu-
lated from the dimensions of the dendrimers obtained by molecular modeling. Experimental Section Materials. Dend-n-[Ru(bpy)3] and dend-n-[Ru(tpy)2] (n ) 4, 8, 16, 32, 64) were synthesized according to the previously reported methods.15 Acetonitrile (AN) was purchased from Burdick and Jackson (distilled in glass) and dried over 4 Å molecular sieves. Tetra-n-butylammonium perchlorate (TBAP)
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Figure 2. (a) Space-filling and (b) ball-and-stick models of (A) dend-4-[Ru(bpy)3], (B) dend-8-[Ru(bpy)3], and (C) dend-16-[Ru(bpy)3] obtained from molecular modeling using CaChe. (G. F. S. Chemicals) was recrystallized three times from ethyl acetate and dried under vacuum for 72 h. All other reagents (analytical grade) were used without further purification. Apparatus and Procedures. Electrochemical experiments were carried out with a BAS CV-27 potentiostat. Data were recorded on a Soltec XY recorder. Three-compartment electrochemical cells (separated by medium-porosity sintered glass disks) were employed. A platinum disk (area ) 0.006 cm2)
electrode was used as the working electrode. Prior to use the electrode was polished with 1 µm diamond paste (Buehler) and rinsed thoroughly with water and acetone. The electrode was pretreated by continuous potential cycling between -0.4 and +0.9 V vs Ag wire in a 0.10 M H2SO4 solution until the voltammetry of a clean polycrystalline platinum electrode was obtained. A large area coiled platinum wire was used as a counter electrode. Potentials are referenced to a Ag/AgCl electrode without
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regard for the liquid junction potential. The dendrimer was injected as a concentrated AN solution, and the solution was homogenized by purging with nitrogen gas. The volume injected varied according to the desired final concentration of the dendrimer. The surface coverages of dendrimers were monitored as a function of time and were calculated, assuming that all Ru sites are electrochemically active, from the charge passed during the oxidation reaction of the ruthenium(II) center obtained at 100 mV s-1, where the peak current was directly proportional to the scan rate. The applied potential was held at +0.80 V vs Ag/AgCl, where the Ru centers have 2+ charges, except when measuring the surface coverage where the potential was swept across the RuII/III redox potential as mentioned above. Since the solution concentrations of the dendrimers were in the micromolar regime, their contribution to the measured current (charge) was negligible.23 Therefore, the measured current (charge) arises only from the surface-confined species, and thus, surface coverage measurements can be carried out in the deposition solution with minimal error. Molecular Modeling. Molecular modeling calculations were carried out using CaChe. The optimized geometry was calculated with MM2 using augmented MM3 parameters until the average gradient was less than 1. Molecules were built in two different ways. In the first, the dendrons were initially built and minimized and subsequently attached to the core. In the second, the molecules were generated by adding successive generations to the previously minimized one. No significant differences were observed between the two methods.
Results and Discussion 1. Thermodynamics. Since the theory of adsorption thermodynamics has been described previously, especially for the self-assembly of redox-active units,24 only a brief description will be given here. The equilibrium relationship between the bulk solution concentration C* and coverage Γ of adsorbate molecules is represented by an adsorption isotherm. Several types of isotherms have been proposed,25 and the differences among them depend on the type of adsorbate-adsorbate interactions allowed. The simplest adsorption isotherm is the Langmuir isotherm, which describes the adsorption process when the only adsorbate interaction is due to size, assuming that no other interactions are present. The Langmuir isotherm can be expressed as
βC* )
θ 1-θ
(1)
where β is the adsorption coefficient, C* is the concentration of the adsorbate in solution, and θ is the fractional coverage defined as Γ/Γs, where Γs is the saturation surface coverage. If interactions such as attraction or repulsion between adsorbates are taken into account, an exponential term is added to the Langmuir adsorption isotherm. One of the simpler isotherms for such a system is the Frumkin adsorption isotherm25
βC* )
θ exp(-2aθ) 1-θ
(2)
where a represents an interaction parameter. When no interactions exist between adsorbates, this equation reduces to the Langmuir isotherm (eq 1), while positive and negative values of a indicate repulsive and attractive interactions, respectively. (23) Acevedo, D.; Abrun˜a, H. D. J. Phys. Chem. 1991, 95, 9590. (24) Acevedo, D.; Bretz, R. L.; Tirado, J. D.; Abrun˜a, H. D. Langmuir 1994, 10, 1300. (25) Trasatti, S. J. Electroanal. Chem. 1974, 53, 335.
Figure 3. Langmuir isotherms (a) dend-n-[Ru(tpy)2] and (b) dend-n-[Ru(bpy)3] fitted to experimental points for (A) n ) 4, (B) n ) 8, (C) n ) 16, (D) n ) 32, and (E) n ) 64 adsorbed to a Pt electrode at +0.80 V vs Ag/AgCl in a 0.10 M TBAP/AN solution.
Curves a and b in parts A-E of Figure 3 show the adsorption isotherms of the dend-n-[Ru(tpy)2] and dendn-[Ru(bpy)3] (n ) 4, 8, 16, 32, 64), respectively. From these isotherms, parameters characterizing the adsorption thermodynamics including Γs, β and adsorption free energy, ∆G°′ads, were determined. The values for each dendrimer were obtained using a least-squares best fit of the experimental data to the parameters of the Langmuir equation (eq 1). The calculated values of Γs and β for the studied dendrimers are summarized in Table 1. The Γs values of the dendrimers decreased with increasing dendrimer size after generation 1, as anticipated from the relative sizes of the dendrimers. In the case of the generation 0 dendrimers (dend-4-[Ru(bpy)3] and -[Ru(tpy)2]), Γs values were lower than expected (based on size) and we believe that this is due, at least in part to the limited flexibility that the short links allow so that these dendrimers cannot form compact structures on the electrode surface. The Γs value for the [Ru(tpy)2]-pendant dendrimers appears to be about 1.5 times larger than those of the [Ru(bpy)3]-pendant dendrimers. This is somewhat sur-
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Table 1. Values of Γs, β, and ∆G°′ads for dend-n-[Ru(bpy)3] and dend-n-[Ru(tpy)2] (n ) 4, 8, 16, 32, 64) Adsorbed at +0.80 V vs Ag/AgCl in 0.1 M TBAP /AN Γs (mol cm-2) dend-4dend-8dend-16dend-32dend-64-
β (L mol-1)
∆G°′ads (kJ mol-1)
[Ru(bpy)3]
[Ru(tpy)2]
[Ru(bpy)3]
[Ru(tpy)2]
[Ru(bpy)3]
[Ru(tpy)2]
(1.2 ( 0.1) × 10-11 (2.0 ( 0.2) × 10-11 (9.4 ( 0.2) × 10-12 (6.5 ( 0.7) × 10-12 (3.3 ( 0.4) × 10-12
(1.8 ( 0.1) × 10-11 (3.0 ( 0.4) × 10-11 (1.7 ( 0.1) × 10-11 (9.6 ( 0.8) × 10-12 (4.7 ( 0.7) × 10-12
(1.3 ( 0.4) × 106 (1.9 ( 0.5) × 106 (5.3 ( 2.1) × 106 (9.8 ( 3.1) × 106 (1.3 ( 0.4) × 107
(1.8 ( 0.2) × 106 (2.7 ( 1.2) × 106 (3.8 ( 0.9) × 106 (1.1 ( 0.3) × 107 (2.4 ( 1.0) × 107
-42 ( 1 -43 ( 1 -46 ( 1 -47 ( 1 -48 ( 1
-43 ( 0 -44 ( 2 -45 ( 1 -47 ( 1 -49 ( 1
prising since the sizes of [Ru(tpy)2] and [Ru(bpy)3] would be anticipated to be very similar. One possibility for such behavior may be solubility differences between the two dendrimer groups. For example, it was found that as the dendrimer concentration was increased, dend-64-[Ru(tpy)2] precipitated before dend-64-[Ru(bpy)3] did (cf. ca. 4 µM for dend-64-[Ru(tpy)2] and ca. 20 µM for dend-64-[Ru(bpy)3]) in a 0.10 M TBAP/AN solution. Therefore, higher coverages of the [Ru(tpy)2]-pendant dendrimers could be due to the deposition (precipitation) of the perchlorate salt of the dendrimer onto the electrode surface, even though the concentrations used were much lower than those at which precipitation took place. In addition, van der Waals interactions could also be responsible, at least in part, for the observed behavior. To be able to compare the electrochemically determined coverage values with theoretically predicted ones, we carried out molecular modeling using CaChe so as to estimate the size of the various dendrimers. Parts A-C of Figure 2 show the space-filling models of the energyminimized structures for dend-4-[Ru(bpy)3], dend-8-[Ru(bpy)3] and dend-16-[Ru(bpy)3], respectively. As can be ascertained from the figures, for the lower generation dendrimer, e.g., dend-4-[Ru(bpy)3], the resulting structure is quite open. As the generation increases, e.g., for dend8-[Ru(bpy)3] and dend-16-[Ru(bpy)3], the resulting structures become increasingly compact, denser, and globular. Average diameters estimated from an analysis of the structures were 58, 65, and 70 Å for dend-4-[Ru(bpy)3], dend-8-[Ru(bpy)3], and dend-16-[Ru(bpy)3], respectively. (It should be mentioned that calculations of the larger dendrimers were not feasible with our current computational capabilities.) From these values and assuming a hexagonal packing, Γmax values were calculated to be 5.7 × 10-12, 4.5 × 10-12, and 3.9 × 10-12 mol/cm2 for dend4-[Ru(bpy)3], dend-8-[Ru(bpy)3], and dend-16-[Ru(bpy)3], respectively. These values are all significantly smaller than those obtained experimentally (see Table 1). These differences would suggest that upon adsorption the dendrimers are significantly compressed or that Γs values exceed a monolayer. However, since isotherms for both dend-[Ru(tpy)] and dend-[Ru(bpy)] are well fitted to the Langmuir isotherm, this would suggest that the dendrimers formed a monolayer and are thus significantly packed. We thus conclude that upon adsorption, these materials are significantly compressed. Crooks et al.26,27 have previously proposed that coadsorption of PAMAM dendrimers with alkanethiols results in a compression of the dendrimers similar to that proposed here. However, in our case there is no coadsorbate present. The coverages of these dendrimers appeared to be slightly smaller than those of diaminobutane-based fer(26) Zhao, M.; Tokuhisa, H.; Crooks, R. M. Angew. Chem., Int. Ed. Engl. 1997, 36, 596. (27) Tokuhisa, H.; Zhao, M.; Baker, L. A.; Phan, V. T.; Dermody, D. L.; Garcia, M. E.; Peez, R. F.; Crooks, R. M.; Mayer, T. M. J. Am. Chem. Soc. 1998, 120, 4492.
Figure 4. Adsorption kinetics at various concentrations of (A) dend-64-[Ru(bpy)3] and (B) dend-64-[Ru(tpy)2] adsorbed to a Pt electrode at +0.80 V vs Ag/AgCl in a 0.10 M TBAP/AN solution.
rocenyl dendrimers,22 although direct comparison is difficult since those experiments were performed in a different solvent. This would appear reasonable since the sizes of the [Ru(tpy)2]- and [Ru(bpy)3]-pendant dendrimers are larger than those of the diaminobutane-based ferrocenyl dendrimers resulting in lower coverages. From the adsorption coefficient β, the adsorption free energy, ∆G°′ads, was also determined, using
∆G°′ads ) -RT ln(18.9β)
(3)
The calculated ∆G°′ads values are also summarized in Table 1. Although these dendrimers do not have groups with pendant adsorption sites, such as pyridyl, isocyanyl, or thiol groups, they nonetheless have relatively large adsorption free energies, similar to those of [Os(bpy)2ClL]+ (ca. -49 kJ mol-1)24 (where bpy ) 2,2′-bipyridine, and L are various dipyridyl groups including 4,4′-bipyridine, trans-1,2-bis(4-pyridyl)ethylene, 1,3-bis(4-pyridyl)propane, or 1,2-bis(4-pyridyl)ethane). Anson et al.28 have recently shown that similar complexes with phenyl (rather than pyridine) pendant groups also adsorb, albeit not as (28) Campbell, J. L. E.; Anson, F. C. Langmuir 1996, 12, 4008.
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Table 2. Kinetic Parameters for dend-n-[Ru(bpy)3] (n ) 4, 8, 16, 32, 64) Adsorbed at +0.80 V vs Ag/AgCl in 0.1 M TBAP/AN dend-4-[Ru(bpy)3]
dend-8-[Ru(bpy)3]
dend-16-[Ru(bpy)3]
dend-32-[Ru(bpy)3]
dend-64-[Ru(bpy)3]
concn (µM)
k′ (M-1 s-1)
concn (µM)
k′ (M-1 s-1)
concn (µM)
k′ (M-1 s-1)
concn (µM)
k′ (M-1 s-1)
concn (µM)
k′ (M-1 s-1)
3.5 2.5 2.0 1.5 1.0 0.50 0.25 0.10
(2.9 ( 0.6) × 103 (1.3 ( 0.2) × 103 (2.7 ( 0.1) × 103 (2.0 ( 0.2) × 103 (1.8 ( 0.1) × 103 (2.5 ( 0.3) × 103 (6.8a ( 0.6) × 103 (1.2a ( 0.1) × 104
1.8 1.3 1.0 0.75 0.50 0.25 0.13 0.050
(2.9 ( 0.5) × 103 (1.3 ( 0.1) × 103 (1.6 ( 0.1) × 103 (2.6 ( 0.2) × 103 (3.2 ( 0.2) × 103 (5.0 ( 0.4) × 103 (7.0a ( 0.3) × 103 (3.0a ( 0.1) × 104
0.88 0.63 0.50 0.38 0.25 0.13 0.063 0.025
(1.1 ( 0.5) × 104 (6.9 ( 0.8) × 103 (4.1 ( 0.2) × 103 (4.2 ( 0.3) × 103 (7.8 ( 0.3) × 103 (4.5 ( 0.3) × 103 (1.9a ( 0.1) × 104 (3.0a ( 0.4) × 104
0.44 0.31 0.25 0.19 0.13 0.063 0.031 0.013
(4.8 ( 0.6) × 103 (7.1 ( 0.8) × 103 (7.5 ( 0.5) × 103 (7.6 ( 0.2) × 103 (5.5 ( 0.3) × 103 (1.1a ( 0.1) × 104 (8.2a ( 0.4) × 104 (8.7a ( 0.4) × 104
0.22 0.16 0.13 0.094 0.063 0.031 0.016 0.006
(3.2 ( 0.4) × 104 (2.2 ( 0.1) × 104 (1.4 ( 0.1) × 104 (1.9 ( 0.1) × 103 (1.1 ( 0.1) × 103 (2.2 ( 0.1) × 103 (8.4a ( 0.4) × 103 (1.9a ( 0.2) × 105
a
Not reliable. Table 3. Kinetic Parameters for dend-n-[Ru(tpy)2] (n ) 4, 8, 16, 32, 64) Adsorbed at +0.80 V vs Ag/AgCl in 0.1 M TBAP/AN dend-4-[Ru(tpy)2]
dend-8-[Ru(tpy)2]
dend-16-[Ru(tpy)2]
dend-32-[Ru(tpy)2]
dend-64-[Ru(tpy)2]
concn (µM)
k′ (M-1 s-1)
concn (µM)
k′ (M-1 s-1)
concn (µM)
k′ (M-1 s-1)
concn (µM)
k′ (M-1 s-1)
concn (µM)
k′ (M-1 s-1)
3.5 2.5 2.0 1.5 1.0 0.50 0.25 0.10
(1.5 ( 0.3) × 103 (1.7 ( 0.3) × 103 (3.4 ( 0.5) × 103 (1.0 ( 0.1) × 103 (1.9 ( 0.1) × 103 (4.3 ( 0.2) × 103 (4.6 ( 0.2) × 103 (1.3a ( 0.1) × 104
2.0 1.3 1.0 0.75 0.50 0.25 0.13 0.050
(1.0 ( 0.2) × 103 (1.9 ( 0.2) × 103 (2.3 ( 0.3) × 103 (1.6 ( 0.3) × 103 (3.7 ( 0.7) × 103 (5.0 ( 0.4) × 103 (7.2a ( 0.4) × 103 (2.9a ( 0.2) × 104
0.88 0.63 0.50 0.38 0.25 0.13 0.063 0.025
(3.2 ( 0.6) × 103 (3.0 ( 0.5) × 103 (1.1 ( 0.1) × 104 (1.2 ( 0.1) × 104 (1.0 ( 0.1) × 104 (8.4 ( 0.4) × 103 (1.5a ( 0.7) × 104 (2.3a ( 0.2) × 104
0.44 0.31 0.25 0.19 0.13 0.063 0.031 0.013
(2.1 ( 0.5) × 104 (8.2 ( 1.1) × 103 (1.5 ( 0.2) × 104 (1.2 ( 0.1) × 104 (2.0 ( 0.1) × 104 (2.7 ( 0.2) × 104 (9.8a ( 0.6) × 103 (6.2a ( 0.3) × 104
0.25 0.16 0.13 0.094 0.063 0.031 0.016 0.006
(2.1 ( 0.4) × 104 (3.8 ( 0.1) × 104 (2.2 ( 0.2) × 104 (3.0 ( 0.2) × 104 (2.3 ( 0.3) × 104 (2.4 ( 0.2) × 104 (8.6a ( 0.2) × 104 (1.4a ( 0.1) × 105
a
Not reliable.
strongly, suggesting the presence of significant van der Waals interactions. We have also reported similar large adsorption free energies for diaminobutane-based ferrocenyl dendrimers.22 In the present case we believe that the adsorption is governed, at least in part, by surface/ dendrimer interactions, as well as by van der Waals interactions, likely due to the relatively large molecular size of the dendrimers. The increase in ∆G°′ads with dendrimer size is also consistent with this. It should also be mentioned that even the discrete molecules show a propensity to adsorb onto Pt surfaces. For example, Van Duyne and co-workers29 have observed, via SERS, that [Os(bpy)3]2+ adsorbs onto Pt. They suggested that in this case (and presumably related cases) the 5 and 6 carbons in the pyridine ring act, at least to some extent, as an isolated olefin and that their interaction with the Pt surface is responsible, at least in part, for their adsorption. In the present case it was difficult to estimate values of the interaction parameter, a, in the Frumkin equation (eq 2). As can be seen in Figure 3, fits to the Langmuir model were very close to the experimental data suggesting that, at best, a would have a small magnitude. Since experimental errors of the equilibrium coverages were not negligible, we could not, based on our data, unambiguously distinguish between the Langmuir and Frumkin models. However, the obtained thermodynamic parameters such as Γs and ∆G°′ads are still reliable because the Frumkin isotherm uses the same Γs and ∆G°′ads values in the Langmuir isotherm (i.e., the interactions between adsorbate molecules are much smaller than those between the adsorbate and the substrate) and the Frumkin isotherm reduces to the Langmuir isotherm as the interaction parameter approaches zero. 2. Kinetics. There are two general models that can be used to explain the kinetics of adsorption of the dendrimers (or any adsorbate, in general) assuming an adsorption equilibrium. The first model involves kinetic (activation) control of the system,30 whereas the second model involves
fast adsorption with mass transport or diffusion control.31 The detailed theory of these models, especially for redoxactive self-assembling monolayers, has been previously reported.32 Briefly, the kinetic control model under Langmuirian adsorption conditions can be expressed as
Γt ) Γe (1 - exp(-k′ C* t ))
(4)
where Γt is the surface coverage of the adsorbate at time t, Γe is the equilibrium surface concentration at a given bulk concentration, and k′ is the rate constant which contains the activity coefficient of the adsorbate in solution. In this equation, the equilibrium surface coverage, Γe, will increase until the saturation value, Γs, is reached, as the bulk concentration C* increases. Therefore Γe, will be controlled by the bulk concentration until this concentration is reached. The second model, i.e., the fast adsorption with mass transport or diffusion control model, assumes semi-infinite linear diffusion of a species in solution to a stationary plane with Langmuirian adsorption at the boundary and can be expressed as
( )
Γt C* )K (Dt)1/2 Γs Γs
(5)
where D is the diffusion coefficient of the adsorbate in solution and K is a constant equal to 2π-1/2. Parts A and B of Figure 4 show the time dependence of the surface coverage at different concentrations for the dend-64-[Ru(bpy)3] and dend-64-[Ru(tpy)2], respectively. Similar curves were obtained for the all dendrimers examined. All the curves in the figures were obtained by (29) Van Duyne; R. P. Private communication. (30) Parsons, R. In Advances in Electrochemistry; Delahay, Ed.; Interscience: New York, 1961; Vol. 1. (31) Reinmuth, W. H. J. Phys. Chem. 1961, 65, 473. (32) Tirado, J. D.; Acevedo, D.; Bretz, R. L.; Abrun˜a, H. D. Langmuir 1994, 10, 1971.
Adsorption of PAMAM Dendrimers
fitting the data to eq 4 with Γe and k′ as the adjustable parameters. For all the dendrimers at virtually all concentrations examined, calculated curves were in good accordance with experimental data. On the other hand, attempts to fit the data to eq 5 (diffusion control model) with Γt and K as adjustable parameters gave rise to much larger deviations from the experimental data than those for fits to eq 4. Thus, these results indicate that the kinetics of adsorption of the dendrimers are well described by the kinetic control model. We also investigated the effect of the concentration of the adsorbates on the kinetics of adsorption. Tables 2 and 3 list the rate constants, k′, for the dend-n-[Ru(bpy)3] and dend-n-[Ru(tpy)2], respectively, calculated using best fitting of the data to the activation control equation (eq 4). As can be seen in Tables 2 and 3, if the values at the lowest concentrations, in which there exists a large experimental error due to the small volume injected, are neglected, the values of the kinetic parameters of both [Ru(bpy)3]- and [Ru(tpy)2]-modified dendrimers generally increase with increasing dendrimer generation, with some exceptions, for dendrimer concentrations in the same range. For each dendrimer, the rate constant appears to be largely independent (with some exceptions) of concentration over the ranges of concentration examined. Therefore, it appears that the adsorption kinetics are dependent upon the identity of the dendrimer but largely independent of concentration. Similar tendencies were observed for the diaminobutane-based ferrocenyl dendrimers.22
Langmuir, Vol. 15, No. 21, 1999 7339
Conclusions We have studied the adsorption thermodynamics and kinetics of PAMAM dendrimers surface-functionalized with polypyridyl ruthenium(II) complexes onto a Pt electrode. In AN solution, the adsorption thermodynamics of the metallodendrimers which have a 2+ charge are well described by the Langmuir adsorption isotherm. The surface coverage of these dendrimers decreased as the generation increased except generation 0, suggesting that this is likely controlled by their molecular sizes. Comparison of the experimentally determined coverages with calculated ones (based on dimensions estimated from molecular modeling) suggest that upon adsorption, the dendrimers are significantly compressed. The adsorption free energies, ∆G°′ads, for dendrimers were found to increase with increasing dendrimer generation. We attribute these differences in ∆G°′ads values to an increase in van der Waals interactions with the increase in the dendrimer generation. The kinetics of adsorption appear to be activation controlled rather than diffusion controlled and to be dependent upon the identity of the dendrimer but independent of concentration. Acknowledgment. This work was supported by the Office of Naval Research, the Ministry of Education and Culture of Spain (Project No. PB97-0001) (M.M.), and the Programa Iberdrola de Profesores Visitantes (H.D.A.). LA9903752
