Kinetics Study of the Binding of Multivalent Ligands on Size-Selected

Mar 17, 2011 - Physikalische und Theoretische Chemie, Institut für Chemie und .... Synthesis and co-assembly of gold nanoparticles functionalized by ...
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Kinetics Study of the Binding of Multivalent Ligands on Size-Selected Gold Nanoparticles Suguna Perumal, Andreas Hofmann, Norman Scholz, Eckart R€uhl,* and Christina Graf* Physikalische und Theoretische Chemie, Institut f€ur Chemie und Biochemie, Freie Universit€at Berlin, Takustr. 3, D-14195 Berlin, Germany

bS Supporting Information ABSTRACT: The effect of ligand multivalency and nanoparticle size on the binding kinetics of thiol ligands on gold nanoparticles is investigated by exchanging monovalently bound pyrene on gold nanoparticles against flexible mono- and multivalent thiol ligands. Variable-sized gold nanoparticles of 2.2 ( 0.4, 3.2 ( 0.7, and 4.4 ( 0.9 nm diameter are used as substrates. The particles are coated by thiol functionalized pyrene ligands and the binding kinetics of the thiol ligands is studied by time-resolved fluorescence spectroscopy. The effect of multivalency on the binding kinetics is evaluated by comparing the rate constants of ligands of different valency. This comparison reveals that the multivalent ligands are exchanging substantially more rapidly than the monovalent ones. A particle size dependence of the rate constants is also observed, which is used to derive structural information on the binding of the mono- and multivalent ligands to the nanoparticle surface.

’ INTRODUCTION Multivalent interactions are known from biological systems, which have a high avidity and a high affinity. These interactions are characterized by simultaneous binding of multivalent ligands on one entity to multiple receptors located on another one.1 Multivalent interactions have several characteristics that the monovalent ones do not have. In particular, chemical bonding in multivalent systems is considerably stronger than in the corresponding monovalent ones.1 As a result, multivalent ligands can act as powerful inhibitors1 or potent effectors.2 Moreover, the concept of multivalency is useful for developing novel strategies for designing multivalent carbohydrates3 and pharmaceutical agents, such as anticancer vaccines.4 In the past, multivalent systems have been developed based on dendrimers,5 polymers,5 cyclic peptide scaffolds,6 and metal nanoparticles.7 Among the metal nanoparticles, gold nanoparticles are promising candidates for systematic studies of multivalent effects, since there are well-established strategies for their controlled synthesis and a rich variety of surface chemistry.8-10 Gold nanoparticles are usually synthesized by the citrate method, as pioneered by Turkevich et al.11 or by phase transfer methods, which were established by Brust et al..12 This class of nanoparticles is unique from other nanoparticles in terms of efficient surface coverage by thiol-based ligands which act as a robust periphery due to strong interactions between the thiol group and the gold surface. Thiol stabilized gold particles have numerous possible applications in the fields of biosensors, catalysis, and opto-electronics.13 Gold nanoparticles functionalized by multivalent saccharides that are bound via the thiol group on a gold surface are used as synthetic analogues of antigens.7 The structural and interfacial properties of self-assembled monolayers (SAMs) of bidentate and tridentate r 2011 American Chemical Society

chelating alkyl thiols on flat gold surfaces have been studied.14 Previous work reveals that the packing density, conformational order, and the thermal stability of self-assembled monolayers strongly changes with the degree of multivalency.14 The nanoparticles stabilized by di- or trivalent thiol ligands show a strongly enhanced stability against aggregation compared to those particles which are stabilized by the corresponding monovalent ligands.13,15 Trithiol ligand stabilized gold nanoparticles with three gold-thiol bonds per ligand molecule show no ligand exchange after addition of a concurrent monothiol.16 This is explained by a model in which the enhanced stabilization arises largely or solely from an entropy-driven multidentate chelate effect.13,16,17 Jin et al. reported that the melting curves of DNAlinked gold nanoparticle assemblies are sharper if the surface density of the oligonucleotides on the nanoparticles is higher. This is explained by a cooperative effect of gold-bound DNA as binding partners of the other nanoparticles in the assembly.18 The ligands on monolayer-protected gold nanoparticles can be tuned in order to design the nanoparticles for various technical13,19 and biological applications.20 Tuning the ligands on gold nanoparticles can be achieved by ligand exchange reactions and can be used to design novel functionalities on nanoparticles.16,17,21-28 These ligand exchange reactions allow one to manipulate the chemical properties of surface functionalized gold nanoparticles by changing the composition of the monolayer.26 The first mechanistic studies of ligand exchange reactions on monolayerprotected clusters were carried out by Murray and co-workers.22,23 Received: December 30, 2010 Revised: February 9, 2011 Published: March 17, 2011 4456

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Figure 1. Chemical structures of the ligands dodecanethiol (monovalent ligand), 2-octylpropane-1,3-dithiol (divalent ligand), 1,1,1-tris (mercaptomethyl) nonane (trivalent ligand), and 4-pyrenebutyl-11-mercaptoundecanoate (dye ligand).

A key feature of gold nanoparticles is the fact that their surface is imperfect, which results in two defect sites, corresponding to the vertices and the edges, and there is one nondefect (terrace) site for binding ligands.22-24,27,28 These sites have different electron densities and steric behavior and, hence, different chemical reactivity.23,24 Different sites have been studied in clusters, where distinct changes in electronic properties are probed by X-ray spectroscopies.29,30 Several authors have explained changes in the reactivity of gold nanoparticles with increasing particle size by the size dependence of the ratio of defect to nondefect sites.23 Several authors observed an increase of the ligand exchange rate of gold nanoparticles with decreasing particle size,23,31 whereas others reported contradictory results.32 Systematic studies of the size dependence of the kinetics of ligand exchange reactions on gold nanoparticles of 2-15 nm have not been reported to date. In the past, the exchange kinetics of aromatic thiolate ligands on gold nanoparticles has been studied by NMR,23,24 whereas the kinetics of short-chain thiolates, amines, and disulfides was investigated by EPR spectroscopy.25 Typical acquisition times of g15 s per spectrum were required, which usually resulted in time intervals of 1-5 min between measurements in kinetics experiments. This limits the dynamic range of ligand exchange reactions, which can be studied by these approaches. However, the very initial stage of the temporal development of a ligand exchange reaction is required to reliably derive the mechanisms of ligand exchange. Specifically, thiol ligands are highly reactive with gold surfaces. This requires kinetics approaches, which are considerably faster than NMR and EPR spectroscopy. Optical spectroscopy or fluorescence spectroscopies represent suitable ways to probe fast ligand exchange processes. For the first time, Montalti et al. investigated exchange reactions of dye-coated gold nanoparticles with different concentrations of monovalent alkyl thiols using time-resolved fluorescence spectroscopy.27 Key to this approach is the quenched fluorescence of particle-bound dye molecules, which completely recovers when they are exchanged against thiol ligands. This technique is versatile for the investigation of fast reactions involving changes in optical properties of reactants and products, providing a temporal resolution in the subsecond regime. In another study, it has been shown by fluorescence spectroscopy that the rates of pyrene disulfide exchange on gold nanoparticles are higher for desorption compared to chemisorption.28 In this work, we investigate the binding kinetics of mono-, di-, and trivalent alkyl thiol ligands on gold nanoparticles of 2.2 nm, 3.2 nm, and 4.4 nm diameter. Pyrene-capped gold nanoparticles are synthesized by wet colloidal chemistry. The kinetics of the exchange reactions between monovalently bound pyrene by mono- and multivalent thiol ligands are studied by using timeresolved fluorescence spectroscopy. We evaluate via the rate constants the influence of multivalency on the binding kinetics of alkyl thiols and whether the size of the gold nanoparticles affects this process.

’ EXPERIMENTAL SECTION Materials. Gold(III) chloride hydrate (HAuCl4) (99.999%), chloro(triphenylphosphine) gold(I) (99.9%), 1-pyrene butanol (99%), dodecane thiol (98%) (monovalent ligand), tetraoctylammonium bromide (TOAB) (98%), sodium borohydride (NaBH4) (99%), 11-mercapto undecanoic acid (95%), 1,3-dicyclohexylcarbodiimide (99%), 4(dimethylamino)pyridine (99%), and all dry solvents used for preparation were purchased from Sigma-Aldrich and were used as received. Benzene p.a. was purchased from Acros Organics and ethanol p.a. was purchased from VWR. Both solvents were also used as received. Syntheses. Multivalent and Dye Ligands. The monovalent ligand dodecanethiol (Figure 1) is obtained from Sigma-Aldrich (see above). The flexible di- and trivalent alkyl thiol ligands (shown in Figure 1) are prepared by reported procedures.14,33-35 The synthetic routes and procedures followed are described in detail in the Supporting Information. The thiol-functionalized pyrene dye ligand (4-pyrenebutyl-11mercaptoundecanoate) (Figure 1) was prepared according to the method of Montalti et al.27 Gold Nanoparticles. Detailed procedures for the synthesis of gold nanoparticles are given in the Supporting Information. All nanoparticle syntheses are carried out under argon. Dye coated 2.2 ( 0.4 nm gold nanoparticles (Au-Small) were prepared by a modification of the synthesis described in ref 36. AuPPh3Cl, 4-pyrenebutyl-11-mercaptoundecanoate, and tert-butylamine-borane are stirred together in dichloromethane and ethanol for 24 h, which results in the formation of gold nanoparticles. Dye-capped 3.2 ( 0.7 nm gold nanoparticles (AuMedium) are prepared as described in ref 27. Note that particle diameters are communicated throughout this work. Gold nanoparticles of 4.4 ( 0.9 nm (Au-Large) are prepared by a modification of a reported procedure:37 Typically, HAuCl4 in water and tetra-octyl ammonium bromide (TOAB) in chloroform are stirred for 24 h. The weak binding of TOAB to the Au surface permits the particle to grow to larger sizes. The aqueous layers are discarded, and subsequently, the gold salt is reduced by the addition of sodium borohydride (NaBH4). This is followed by adding 4-pyrenebutyl-11-mercaptoundecanoate, and the reaction mixture is stirred for 2 h, which results in formation of 4.4 ( 0.9 nm gold particles (Au-Large). Subsequently, all pyrene-functionalized gold nanoparticles are precipitated in ethanol in order to remove the dye that is not particle-bound. The particles are centrifuged at 1000 g for 10 min, and subsequently, the supernatant is removed. This procedure is repeated until the fluorescence signal from the dye in the supernatant becomes negligibly small. The kinetic experiments reported herein required stable, monodisperse gold nanoparticles with a variable, well adjustable particle size. This is accomplished by modifying the reported procedures by optimizing the dye to gold ratio and the reaction time (see Supporting Information). Characterization of the Samples. Transmission Electron Microscopy (TEM). Samples for TEM are prepared by dipping carboncoated copper 400-mesh grids (Quantifoil) in particles dispersed in CH2Cl2. Low resolution transmission electron microscopy images are recorded using a Zeiss EM 10 CR microscope at 60 kV. High resolution electron microscopy (HRTEM) images are recorded by using a Philips 4457

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Figure 2. Transmission electron microscopy images of 4-pyrenebutyl11-mercaptoundecanoate (dye ligand) coated gold nanoparticles with an average diameter of 2.2 ( 0.4 nm (Au-Small, a), 3.2 ( 0.7 nm (Au- M, b), and 4.4 ( 0.9 nm (Au-Large, c).

Table 1. Ligand Types and Concentrations of the Ligands Used in the Kinetics Measurements ligand type concentration (mM)

monovalent 3.78 ( 0.02

divalent 1.89 ( 0.02

trivalent 1.26 ( 0.02

CM 200 FEG microscope at 200 kV. Around 800 nanoparticles are analyzed for each sample in order to determine the average diameter and the polydispersity of the nanoparticles by using the Simple PCI software (C-Images). TEM images of all three samples are shown in Figure 2. These images show that the particles obtained from various syntheses used in this work all have an almost spherical shape. All three samples have a polydispersity of about 20%. Aggregation of nanoparticles is not observed. Additionally, the preparation of different batches of gold nanoparticles by the same modified procedure shows that reproducible, almost identical particle sizes within (0.2 nm and size distributions are observed. UV/vis/NIR Spectroscopy. Absorption spectra of dichloromethane dispersions of nanoparticles are measured in 1.00 cm SUPRASIL quartz cells (Hellma) by using a Perkin-Elmer Lambda 9 spectrophotometer. Ligand Exchange Kinetics Measurements. Studies on the ligand exchange kinetics of nanoparticles are carried out by using dilute dichloromethane dispersions of gold nanoparticles in 1.00 cm Suprasil quartz stirring cells (Hellma). These studies are performed with a Horiba Jobin Yvon Fluoromax-4 spectrofluorometer. In a typical experiment, a dilute dichloromethane dispersion of the dye-capped gold nanoparticles of variable size (see above and Figure 2) is placed in a quartz stirring cell. Subsequently, the mono-, di-, or trivalent alkyl thiol ligands of variable concentrations, as indicated in Table 1, are quickly added to the dispersion at 20 °C. Table 1 indicates that the concentration of the thiol functional groups is kept constant in all reactions. An increase in fluorescence intensity indicates that the dye bound to gold nanoparticles exchanges against the mono- or multivalent ligand as a function of time. No spectral shifts in the fluorescence spectrum of the dye are observed during the ligand exchange reactions. The ligand exchange kinetics is studied by measuring the fluorescence intensity of the dye. The excitation wavelength is 328 nm. The fluorescence intensity at the emission maximum at 376 nm is collected at regular time intervals with an initial temporal resolution of about 0.25 s for the first 500 s. This is followed by temporal steps of 120 s for typically up to 16-30 h. No quenching effects are observed for the pure dye below a concentration of (3.00 ( 0.04)  10-5 M under an air or argon atmosphere. Repeated experiments indicate that the temporal evolution of the fluorescence signal is fully reproducible. All kinetics data and rate constants shown in this work are based on an average of at least three independent data sets. The rate constants of the ligand exchange reaction were obtained from eqs 1 or 2 (see below) in fitting algorithms of the program OriginPro 8G.

’ RESULTS AND DISCUSSION The kinetics of the exchange reaction between (4-pyrenebutyl-11-mercaptoundecanoate) dye ligands bound to variable size gold nanoparticles and competing multivalent alkyl thiol ligands has been systematically studied by time-resolved fluorescence spectroscopy. A schematic depiction of this ligand exchange reaction is represented in Figure 3. It is known that the fluorescence of pyrene dye ligands binding to gold nanoparticles is entirely quenched.27,28,38 This is due to an electron transfer from the excited state of the dye to the nanoparticles. Quenching of the fluorescence on gold surfaces depends on the distance between the chromophore and the gold surface.39 Pyrene derivatives with a long alkyl chain (C8-C14), as used in this work, are expected to be oriented in an angle of 45-48° relative to the surface normal of the gold surface, according to recent calculations by Zerbetto and co-workers.38,40 Hence, the probability of charge transfer to gold is high and the fluorescence of the dye is completely quenched. It is assumed that the quenched fluorescence of the dye completely recovers when they are released from the gold surface.27 Therefore, the increase in fluorescence intensity of the released dye is a quantitative probe for ligand exchange, permitting study of the kinetics of this process. The number of pyrene ligands bound to gold nanoparticles can be quantified from the amount of free dye removed after purification from the nanoparticles. This implies that all dye molecules used in the synthesis are either found in the supernatants removed during purification (see Experimental Section) or bound to gold particles. The total mass of the free dye ligands is calculated by comparing the UV-vis absorption intensity at 344 nm to a calibration curve for the pure dye of known concentration in order to accurately derive the concentration of pyrene ligands bound to gold nanoparticles. This quantity is used to adjust the initial dye concentration for kinetics experiments. The concentration of mono- or multivalent ligands is chosen to be about 3 orders of magnitude higher than the pyrene dye concentration in order to achieve complete ligand exchange (see Table 1). The number of dye molecules is also obtained from a comparison of the fluorescence intensity at λ = 376 nm after the ligand exchange, when the reaction reaches saturation. This yields an average pyrene ligand concentration of (2.79 ( 0.31)  10-6 M, where no nanoparticle precipitation occurs (see below). The same final pyrene concentration is reached in all ligand exchange kinetic experiments, which is independent of the size of the gold particles and the type of thiol ligands. This supports the assumption that the dye is always completely exchanged. Additional control experiments indicate that any conditions quenching the free pyrene dye can be fully excluded. Further, fluorescence quenching due to oxygen is also ruled out (see Experimental Section). Multivalency Effects. The concentration of competing thiol groups was kept constant in order to study multivalency effects of ligand exchange. During ligand exchange, the dye molecules bound on the particle were replaced by monovalent (3.78 mM), divalent (1.89 mM), or trivalent (1.26 mM) thiol ligands. Figure 4 shows the fluorescence intensity at 376 nm for the first 500 s of the ligand exchange reaction as a function of time. After a steep rise in fluorescence intensity at the beginning of the reaction, all curves flatten out considerably, as shown in the inset of Figure 4. Note that such a steep increase in fluorescence intensity indicates a rapid ligand exchange, which is too fast to be monitored by NMR but can easily be probed by fluorescence spectroscopy. The inset in Figure 4 shows that the free dye concentration 4458

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Figure 3. Ligand exchange reaction kinetics studied by fluorescence spectroscopy. Monovalently bound dye ligands (4-pyrenebutyl-11mercaptoundecanoate) are exchanged by mono-, di-, or trivalent thiol ligands. Particle-bound pyrene shows no fluorescence due to complete quenching. After ligand exchange, the fluorescence of free pyrene in solution recovers completely.

Figure 4. Changes in fluorescence intensity at 376 nm as a function of time for the initial part of the ligand exchange reaction of mono- and multivalent ligands against the pyrene dye on Au-Medium (3.2 ( 0.7 nm) gold nanoparticles. The inset shows the kinetics of the same reaction in a wider time interval. F.i. is the fluorescence intensity.

reaches saturation during ligand exchange, corresponding to a dye concentration bound to gold nanoparticles of (2.79 ( 0.31)  10-6 M (see above). The fluorescence intensity was identical after 16 h within the limits of experimental error in all three cases. The equilibrium of the reaction lies completely on the side of the product, due to the large excess (about 385 times) of the competing ligand. Hence, a significant reverse reaction is not observed. This is further confirmed by control experiments, in which pyrene is exchanged by multivalent ligands of different concentration at identical gold nanoparticle concentration. These experiments also yielded the same fluorescence intensity. After significantly longer reaction times reaching up to 30 h, no changes in fluorescence intensity are observed. The reproducibility of these experiments is confirmed by additional kinetics studies using different freshly prepared batches of nanoparticles as well as nanoparticles which were stored as a dry precipitate at 25 °C under argon for at least one month. Previous kinetics studies have concluded that ligand exchange reactions occur either via dissociative39-43 or associative27,44,45 mechanisms. In some cases, a combination of associative and dissociative mechanisms is involved.46 A general overview of the mechanism of ligand exchange reactions on Au nanoparticles, especially with thiols, is given in ref 47. Montalti et al. have shown that exchange reactions of pyrene-coated gold nanoparticles of different concentrations of monovalent alkyl thiols most

likely follow an associative pathway.27 Therefore, we assume that the present exchange reaction also occurs via an associative mechanism. Previous studies indicate that a variety of different mechanisms can be used to fit the experimental results of ligand exchange reactions on gold nanoparticles17,24,27,28,42,48 and gold clusters.22,23 These include pseudo-first-order (monoexponential) and second-order mechanisms,17,22-24,32,42 various types of Langmuir models (first order, second order, diffusion-limited first order, and diffusion-limited second order),48 as well as biexponential fit functions.27,28,32 The use of biexponential functions is motivated by the assumption that inhomogeneities of the particle surface lead to a rapid ligand exchange at defect sites, whereas the remaining nondefect sites are subsequently exchanged.22-24,27,28 In the present study, it turns out that an excellent fit (see R2 values in Tables S1 and S2 in the Supporting Information) to the experimental data is obtained from biexponential fits (see eq 1). IðtÞ ¼ I f , 1 ð1 - e-k1 t Þ þ I f , 2 ð1 - e-k2 t Þ

ð1Þ

Here, If,1 and If,2 are the amplitudes of the fluorescence intensity function and k1 and k2 are the rate constants. An alternative monoexponential kinetics model bears no resemblance with the experimental results (see Figure S1(c) and Table S3 in the Supporting Information). The results from free fits according to eq 1 are summarized in Table S1 in the Supporting Information. The rate constant k1 represents the faster process at the beginning of the ligand exchange reaction, whereas the rate constant k2 describes the slower process at longer reaction times (cf. Figure 4). The ratio of the amplitudes If,1 and If,2 varies significantly for the different types of ligands; especially for the monovalent ligands, this ratio is significantly smaller (see Table S1). According to Murray and co-workers, the necessity for a description of the exchange kinetics by a biexponential function is due to fact that different sites of the gold nanoparticles, i.e., edges, vertices, and faces have a different reactivity.23,24 Therefore, we attempted to scale the two amplitudes to the number of gold atoms on the edges and vertices, corresponding to the first amplitude of the faster process If1, and the number of gold atoms on face sites, corresponding to the second amplitude of the slower process If2. For this model calculation, we assume that the gold nanoparticles are regular icosahedra and applied the results communicated by Benfield.49 However, this calculation yield a 3-7 lower ratio If1/If2. Further, no agreement between the ratio of the different sites of the gold 4459

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Table 2. Comparison of the Rate Constants of the Ligand Exchange Reaction of Mono- and Multivalent Ligands against Pyrene on Medium-Sized (Au-Medium) and Small-Sized (Au-Small) Gold Nanoparticles Using a Biexponential Fit Function (see eq 1) with a Fixed Amplitude Ratio and a Second-Order Langmuir Diffusion-Limited Fit Function (see eq 2)a ligand

type of the fit function

particle size (nm) Au-Medium (3.2 ( 0.7)

biexponential fit with fixed amplitude ratio

a

k1  10

-1

divalent

monovalent

(1.89 mM)

(3.78 mM) 2.55 ( 0.56

(s )

5.75 ( 0.85

5.52 ( 0.35

k2  10-5 (s-1)

11.20 ( 2.02

6.45 ( 3.14

5.30 ( 1.47

second-order Langmuir diffusion-limited

kL  10-3 (s-1)

61.5 ( 5.8

50.8 ( 7.7

34.7 ( 3.6

biexponential fit with fixed amplitude ratio (If,1/If,2 = 2.5)

k1  10-3 (s-1) k2  10-5 (s-1)

0.85 ( 0.07 5.58 ( 1.28

3.93 ( 0.63 15.80 ( 2.45

0.94 ( 0.03 9.0 ( 0.82

second-order Langmuir diffusion-limited

kL  10-3 (s-1)

22.7 ( 2.8

66.3 ( 8.4

29.4 ( 1.2

(If,1/If,2 = 2.5) Au-Small (2.2 ( 0.4)

-3

trivalent (1.26 mM)

The use of this model as well as possible alternatives are discussed further below in greater detail.

nanoparticles and the amplitude ratio is found for the smaller and larger particles also investigated in this study (see below). Hence, the different reaction rates cannot be simply ascribed to different geometric positions of the ligands in perfectly shaped icosahedra. Notably, neither additional defects in the nanocrystals nor cooperative effects between the pyrene ligands during the ligand exchange process (see refs 27 and 40 and discussion below) are considered in this simple model. For a better comparison of the experimental results of the rate constants k1 and k2, the ratio If,1/If,2 was set to the constant value of 2.5, which corresponds to the average ratio of these parameters regarding all exchange kinetics studied in this work. However, no systematic dependency of this ratio from the multivalency of the ligands or the size of the nanoparticles was observed. The averaged rate constants obtained from this fit procedure are given in Table 2 (complete sets of fit parameters as well as exemplarily fitted experimental curves are given in the Supporting Information in Table S2 and Figure S1(b)). The rate constant k1 denotes the value resulting from the biexponential fit function with fixed amplitudes (If,1/If,2 = 2.5). The values of the rate constant k2 are considerably smaller than those of k1, corresponding to a slower process of the second reaction. The values for k1 depend significantly on the ligand multivalency and the particle size. In contrast, no such behavior is found for the values of k2. Thus, only the rate constant k1 is taken into account for the subsequent discussion. We also applied various types of Langmuir models (secondorder, first-order diffusion-limited, and second-order diffusionlimited) as possible fit functions for the kinetics data.48 A detailed explanation for the motivation of the use of this fit model is given in the Supporting Information. A Langmuir first-order model is identical with a monoexponential fit function (see above). A fit with a Langmuir first-order diffusion-limited or a Langmuir second-order model yields poor agreement with the experimental data for all data sets on medium-sized particles (see Table S4 and S5 in the Supporting Information). Note that for smaller particles (sample Au-Small) a better agreement between fit and experiment is found (see Figure S1 (d) and (e) in the Supporting Information). In contrast, an excellent fit of the experimental results is obtained from a second-order Langmuir diffusion-limited model for medium-sized gold nanoparticles Au-Medium (see also R2 values in Table S6 in the Supporting Information and eq 2). pffiffi I 0 kL t IðtÞ ¼ 3 pffiffi ð2Þ 1 þ kL t Here, I0 is the fluorescence intensity, if the entire dye is released from the gold surface, and kL is the rate constant. This

model turns out to be most appropriate for describing the kinetics of the alkylthiol exchange reactions on 2.2 nm gold nanoparticles, as shown in a comparative study by Kassam et al.48 The averaged rate constants obtained from this fit procedure and a biexponential fit function using a fixed amplitude ratio are compiled in Table 2. The rate constant k1 of the trivalent ligand is 2.25 ( 0.83 times and that of the divalent ligand 2.16 ( 0.61 times higher than that of the monovalent one on Au-Medium (3.2 ( 0.7 nm) particles (see Table 3). The fact that the rate constants k1 of the di- and trivalent ligands are identical within the experimental error might be explained by the extended bulkiness of the trivalent ligand which effectively hinders its penetration through the ligand shell and hence strongly reduces the reaction rate of this ligand. Note that this result does not imply that only two thiol groups of the trivalent ligand are binding on the gold nanoparticles, since the concentration of the thiol groups is kept constant and not the ligand concentration (see Table 1). Thus, if all trivalent ligands would bind only with two thiol groups, each trivalent ligand is replacing only two dye ligands from the gold surface. Consequently, if the concentration of functional groups is constant and assumimg that the number of gold thiol bonds per nanoparticle remains constant, the trivalent ligands would replace only 2/3 of the dye ligands which would be replaced by the divalent ligands under identical conditions. As a result, the rate constant of the trivalent ligands should be considerably lower than that of the divalent ligands. For comparison, the multivalent enhancement factors, i.e., the ratio between the multivalent and the monovalent rate constants for the ligand exchange reaction, are summarized in Table 3. Particle Size Effects. Particle size effects on the ligand exchange kinetics are investigated using mono- and multivalent ligands binding to gold nanoparticles of three different sizes: 2.2 ( 0.4 nm (Au-Small), 3.2 ( 0.7 nm (Au-Medium), and 4.4 ( 0.9 nm (Au-Large). The surface curvature of the smaller particles is increased, and therefore, it is expected that the binding of multivalent ligands which bind on two or three different geometric positions on the nanoparticle surface should be strongly influenced by the particle size. Figure 5 shows the fluorescence intensity at 376 nm as a function of time for the initial first 500 s of the ligand exchange reaction for the mono- and the divalent ligands against dye on Au-Small particles. The results from the Au-Medium (3.2 nm) particles are also shown in Figure 5. This comparison clearly shows that the initial ligand exchange reaction on the Au-Small particles is significantly 4460

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Table 3. Comparison of the Multivalency Enhancement Factors, i.e., the Ratio between the Multivalent and the Monovalent Rate Constants Calculated from either the k1 or the kL Values on Medium-Sized (Au-Medium) and Small-Sized (Au-Small) Gold Nanoparticles by Using a Biexponential Fit Function (see eq 1) with a Fixed Amplitude Ratio and a Second-Order Langmuir Diffusion-Limited Fit Function (see eq 2)

particle size (nm)

ratio of rate constants (biexponential fit function with fixed amplitude ratio

ratio of rate constants (second-order diffusion-limited

If,1/If,2 = 2.5)

Langmuir model)

trivalent/monovalent

divalent/monovalent

trivalent/monovalent

divalent/monovalent

Au-Medium (3.2 ( 0.7)

2.25 ( 0.83

2.16 ( 0.61

1.77 ( 0.35

1.47 ( 0.37

Au-Small (2.2 ( 0.4)

0.90 ( 0.10

4.16 ( 0.78

0.77 ( 0.13

2.26 ( 0.38

Figure 5. Changes in the fluorescence intensity at 376 nm as a function of time for the initial part of ligand exchange reaction of mono- and divalent ligands against dye on Au-Small (2.2 ( 0.4 nm) nanoparticles. Curves for Au-Medium (3.2 ( 0.7 nm) nanoparticles are also displayed for a comparison. The inset shows the kinetics for the same reactions in a wider time scale. F.i. is the fluorescence intensity.

slower than on the Au-Medium particles. The inset in Figure 5 depicts the kinetics of the ligand exchange reaction in a wider time frame. After about 16 h, the fluorescence intensity of all samples is identical within experimental error independent of the ligand type and particle size. This supports the assumption that a reversible reaction can be excluded and a complete exchange reaction on the Au-Small nanoparticles takes place. These particles also reach the same final fluorescence intensity value as that of Au-Medium, which corresponds to the total amount of dye molecules bound on the nanoparticles. The same fluorescence intensity is recorded for the reaction of Au-Small with the trivalent ligand, which is not included in the data shown in Figure 5. The rate constants k1 and k2 or kL obtained from experiments on Au-Small particles using a fit with eq 1 or eq 2 are summarized in Table 2. As a consequence of the slower reaction rate, the corresponding rate constants k1 are significantly lower for the Au-Small particles than for the Au-Medium particles. Remarkably, the rate constant k1 of the trivalent ligand is smaller than that of the monovalent ligands on the Au-Small particles. Obviously, steric effects which decelerate the exchange process of the trivalent ligand against the pyrene dye become more important when the surface curvature of the particles increases. In contrast, the multivalency effect of the divalent ligand is almost two times stronger on the Au-Small particles compared to the Au-Medium particles (see Table 3). This effect is explained below in detail (see also Figure 7). Finally, we investigate the ligand exchange kinetics for particles with an average diameter of 4.4 ( 0.9 nm (Au-Large). These particles show partial precipitation during the exchange reaction studies, probably due to insufficient surface stabilization of the gold nanoparticles after ligand exchange. The alkyl chain ligands

Figure 6. Changes in the fluorescence intensity at 376 nm as a function of time for the initial part of the ligand exchange reaction of divalent and monovalent ligands on Au-Small (2.2 ( 0.4 nm), Au-Medium (3.2 ( 0.7 nm), and Au-Large (4.4 ( 0.9 nm) gold nanoparticles.

which replace pyrene on the nanoparticles surface are less bulky than the dye molecules, and hence, they do not provide sufficient steric stabilization. This effect becomes more important if the particle size is increasing. As a consequence, only incomplete exchange reactions are observed. For a comparison, the initial part (first 80 s) of the exchange kinetics of the mono- and divalent ligands against pyrene on Au-Small, Au-Medium, and Au-Large particles are displayed in Figure 6. A quantitative analysis of the initial 80 s of the exchange kinetics data of the samples Au-Small, Au-Medium, and Au-Large is not possible. The application of a biexponential fit function with free or fixed amplitudes (see eq 1) as well as a second-order Langmuir diffusion-limited fit function (see eq 2) results in different I0 values for differently sized nanoparticles. This is in contradiction to those results which are obtained from the same data analysis and fit functions over longer time periods (see above), i.e., the kinetics data of the initial time period are not sufficient to describe the ligand exchange process properly. The use of a monoexponential fit function is also not possible, since it does not match sufficiently the experimental data (see discussion above). However, in agreement with the results discussed above, the kinetics data in Figure 6 clearly show that the rate of the ligand exchange process systematically increases with the particle size. This is also true for the case of Au-Large particles, where the ligand exchange by divalent ligands is significantly faster than with the monovalent ones. We observe in all cases that the reaction rate is increasing with particle size (see Figure 6). In contrast, Guo et al. observed for the exchange of phenylethanethiolate by p-nitrothiophenol on small Au38 and Au140 clusters that the initial ligand exchange is 4461

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Langmuir independent of the cluster size.23 This is explained by the fact that the initial ligand exchange mainly takes place at the nanocrystal vertices. In addition, the rates of later stages of ligand exchange are significantly lower for larger clusters, which is ascribed to their increased terrace-like surface atom content.23,29,30 Also, Kell et al. reported that the reactivity of gold nanoparticles with average gold core sizes of 1.7 nm, 2.2 nm, and 4.5 nm functionalized by aryl ketons decreases with increasing particle size.31 However, Wan et al. observed for gold nanoparticles of 5-20 nm a higher efficiency of the polymerase chain reaction on larger particles compared to smaller-sized nanoparticles.32 The observations in the present work which appears to be contradictory to the increased reactivity of small particles observed by Kell et al. and Guo et al.23,31 might be explained by applying a theoretical model developed by Zerbetto and co-workers.27,40 According to this model, the ligand exchange process of pyrene by functionalized thiols bound to a gold surface occurs through the interaction among several ligands. It is assumed that pyrene ligands form stacked layers on gold surfaces, where all molecules in the same plane have almost the same tilt angle, which maximizes the intermolecular pyrene-pyrene interactions.38,40 As a result, insertion of thiols weakens the thio-gold bond of several adsorbed pyrene ligands. This model is supported by the experimental finding that the order of the exchange reaction of pyrene bound on gold nanoparticles against dodecanethiol is considerably smaller than one, where values between 0.33 and 0.38 are reported.27 This result clearly implies that in the rate-determining step the competing thiol group weakens the thiol-gold bond of more than one pyrene molecule on the gold nanoparticles. The present results can be explained as follows by using a simplified model of ideal icosahedral nanoparticle structures, as depicted in Figure 7. We assume that the cooperative effect is less distinct if the nanoparticles are smaller, since for small nanocrystals, the areas of the face sites are smaller and the edges are shorter than in larger particles (see Figure 7 a). Consequently, the regions where the pyrene functionalized thiols form an ordered stacking with the same orientation are particle size dependent. An incoming ligand weakens on the average a decreasing number of pyrene molecules if the particle size is decreased (see Figure 7a,b). If a second thiol ligand is exchanged on the gold nanoparticle surface, the probability that it will be bound in a region, where the pyrene ligand shell is already weakened, is increased as a function of particle size (see Figure 7c,e). Thus, in this case binding of another thiol ligand is more probable and the rate constant of this process is increased. If the thiol is divalent (see Figure 7d, f), the second thiol group will bind on a gold atom directly neighboring the gold atom, where the first thiol group is bound. This expectation comes from geometrical arguments, since the distance between two gold atoms in a gold nanoparticle is on the order of 220-260 pm. This is similar to the distance between the two thiol groups in divalent thiols, which is known to be 254 pm.50 Consequently, in this case the cooperative weakening effect is high and the binding of the second thiol group of the divalent thiol is more enhanced than the binding of a second monovalent thiol group, which is in agreement with the present results on ligand exchange kinetics (see Tables 2 and 3 and Figure 6). The preference to divalent binding of the second thiol group of a divalent ligand compared to monovalent binding increases with decreasing particle size, since the probability that an incoming second monovalent thiol displaces those pyrene molecule where the

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Figure 7. Schematic diagram of the cooperative model which can explain multivalency and size-dependent effects in the exchange of 4-pyrenebutyl-11-mercaptoundecanoate against mono- and multivalent thiol ligands: The yellow circles depict an incoming thiol ligand which displaces a pyrene ligand from the surface of the gold nanocrystal (step (a)). As a consequence, the thiol-gold bond of the pyrene ligands in the vicinity of the displaced pyrene ligand are also weakened (step (b)). The intensity of the red color of the gold atoms indicates qualitatively the magnitude of this cooperative weakening. Subsequently, either another monovalent ligand (yellow circle, step (c) or (e)) or the second thiol group of the divalent thiol ligand binds to the gold surface in a sequential binding process (step (d) or (f)).

gold-thiol bond is already weakened is lower on a smaller nanocrystal than on a larger nanocrystal (see Figure 7c,e). This is in agreement with the observation that the multivalency effect of the divalent ligand is higher for Au-Small particles than for AuMedium particles (see Table 3). It has to be considered that in reality the incoming thiol ligands from solution will be likely bound at vertices, surface defects, or at the borders of face sites, but rather not in the middle of face sites, as depicted in Figure 7, but in a less crowded region such as a vertex or a generic defect.40 However, for Au-Medium particles the fraction of the vertex atoms, where no cooperative effect is possible, accounts only for about 3% of the surface atoms, if an icosahedral particle shape is assumed. The corresponding values for the Au-Small and Au-Large particles are 7% and 1.5%, respectively. In addition, steric hindrance has to be considered to explain the reaction rates on highly curved particles, i.e., nanocrystals of small diameter, where a high proportion of the surface atoms are either edge or vertex sites. The binding of a trivalent thiol ligand to an edge or vertex site with all three functional groups is not possible due to geometric reasons. Similarly, in the case of a divalent thiol the possibilities for stable binding of both thiol groups are limited, if one thiol group is bound to an edge site, a vertex site, or a defect site, such as an adatom. Consequently, for 4462

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Langmuir the Au-Small particles the reaction rate of the trivalent ligands is even lower than that of the monovalent ones. The result that divalent and trivalent ligands show the same rate constant on the Au-Medium particles and that the rate constant of divalent ligands is lower on Au-Small compared to Au-Medium particles is fully explained by simple geometric arguments. It should be noted that the present model is not contradictory to previous results by Guo et al.23 In this case, the exchange kinetics of thiol-bound phenyl ligands with short ethyl chains was investigated. A strong cooperative effect between these ligands is not expected which might explain a different particle size dependence of both processes. The presented model is in good agreement with the biexponential model, according to eq 1, since this describes a ligand exchange process for a nanoparticle with different reactivities for different particle sites (see discussion above), such as vertices, edges, defect sites, as well as sites with an enhanced weakening of the pyrene-gold bond due to strong cooperative effects. The consideration of cooperative interactions between the pyrene ligands does also explain why the amplitude ratio If1/If2 is not simply proportional to the ratio of the edge and vertex sites to the face sites of the gold nanocrystals (see above). The fit of the experimental results by a second-order diffusionlimited Langmuir model (see eq 2) yields agreement also, as noted above. The use of this model might be rationalized as follows (see Figure S2 in the Supporting Information): The incoming species determine the adsorption rate.51 The first step of the ligand exchange process is the diffusion of the incoming thiol ligands through the pyrene ligand shell to the gold surface. Accordingly, we assume that this step is rate determining, if this fit model is correct. The adsorption rate is in the second-order Langmuir process proportional to the number of bound pyrene ligands and according to a model of Yan et al. to the number of physisorbed thiol ligands on the gold surface.51 Both quantities scale with (1 - θ(t)), where θ(t) is the time-dependent fractional coverage of the surface, where it is assumed that all active sites are equivalent and independent of each other.51-54 Hence, it might be assumed that, subsequent to the initial diffusion process, the thiol ligands physisorb on the gold surface and displace the 4-pyrenebutyl-11-mercaptoundecanoate molecules on the gold surface. Finally, the thiols chemisorb on the gold surface. However, a second-order diffusion-limited Langmuir model does not allow us to explain the size and multivalency dependences of the exchange kinetics for the following reasons: (i) The application of a diffusion-limited Langmuir model implies that diffusion of the ligands determines the reaction rate. A bi- or trivalent ligand is significantly bulkier than a monovalent one. Thus, the bulky ligands are expected to diffuse more slowly through the solvent and the pyrene ligand shell as the diffusion constant is inversely proportional to the hydrodynamic diameter55 and bulkier ligands can more easily entangle in the surface ligands. However, the experimental results indicate an opposite behavior in the ligand size dependence of the exchange kinetics. In addition, penetration of a thiol ligand through a shell of surface-bound pyrene should be enhanced, if the nanoparticle surface is significantly curved, as discussed above. If the surface coverage of the nanoparticle is identical, the end groups sticking into the solvent have a larger distance. This is evidently not in agreement with the observed particle size dependence of the ligand exchange process. If a rate-determining diffusive term is not taken

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into account, i.e., a first- or second-order Langmuir model is applied, the model function does not fit the experimental data. (ii) In a Langmuir model, the binding on all active sites is assumed to be independent from others. This does not explain why divalent ligands bind more rapidly than monovalent ones. Moreover, if all binding sites are equivalent there should be no differences in the reactivity of edge, vertex, face, and defect sites. Further cooperative effects among several binding sites cannot be explained. Consequently, the ligand exchange process should be within the framework of a Langmuir model independent of the nanocrystal size. This is in conflict with the experimental results, indicating that the reaction rates decrease with decreasing particle size. These considerations indicate, although a second-order diffusion-limited Langmuir model fits the experimental data well and it has been used before, that the processes occurring within this model are not compatible with the present results. Therefore, this model is discounted and we rather favor that a bi- or multiexponential ligand exchange model sufficiently explains the experimental size and multivalency dependency of the ligand exchange kinetics.

’ CONCLUSIONS We have explored a novel approach to quantify the ligand exchange kinetics occurring on variable-sized gold nanoparticles, where pyrene ligands are exchanged against thiols of different valency. Multivalency and particle size play a crucial role in these processes, as deduced from time-resolved fluorescence spectroscopy. Various models are tried to explain the experimental results. All results from kinetics studies are fitted by a biexponential function, as well as a second-order Langmuir diffusion model. The use of the former is motivated by the assumption that different sites of the nanoparticles have different reactivities, which takes small gold nanoparticle edge, vertex, face, and defect sites into account. The latter model describes a diffusion-limited ligand exchange. Systematic investigations of the binding kinetics of the ligand exchange reactions of mono- and multivalent ligands on different-sized gold nanoparticles reveal a significant enhancement of the reaction rate of tri- and divalent ligands compared to monovalent ones. This is attributed to a distinct multivalency effect. In contrast, the exchange rates of the trivalent ligands are similar to or even lower than those of the divalent ones. This is explained by steric hindrance of bulky ligands. Furthermore, a clear particle size dependence of the ligand exchange rate constants is derived, which increases with particle size. The present results can be explained by a mechanism where the exchange of one pyrene ligand causes a weakening of the gold-thiol bond of the pyrene ligands in its vicinity. This cooperative mechanism is more effective on larger particles and promotes multivalent binding. The proposed model is in agreement with a biexponential fit model of the kinetics, since this model includes different reactivity of different particle sites. In contrast, a diffusion-limited process explains neither the observed multivalency effect nor the size dependence of the ligand exchange process, and is therefore discounted. ’ ASSOCIATED CONTENT

bS

Supporting Information. Preparation procedures for divalent and trivalent ligands, synthesis of 2.2 and 4.4 nm gold

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Langmuir nanoparticles, and models to fit the kinetics data. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*To whom correspondence should be addressed. E-mail: ruehl@ chemie.fu-berlin.de, [email protected].

’ ACKNOWLEDGMENT We thank Erwin Biller (Freie Universit€at Berlin) for the construction of the stirring cell with temperature control for the fluorescence spectrometer, Dr. Andreas Sch€afer (Freie Universit€at Berlin) for recording NMR spectra. This research is supported by the Deutsche Forschungsgemeinschaft (DFG) within Sonderforschungsbereich (SFB) 765, subproject C5, Freie Universit€at Berlin, and the Fonds der Chemischen Industrie. ’ REFERENCES (1) Mammen, M.; Choi, S. K.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998, 37, 2754. (2) Kiessling, L. L.; Gestwicki, J. E.; Strong, L. E. Curr. Opin. Chem. Biol. 2000, 4, 696. (3) Pieters, R. J. Org. Biomol. Chem. 2009, 7, 2013. (4) Danishefsky, S. J.; Allen, J. R. Angew. Chem., Int. Ed. 2000, 39, 836. (5) Gestwicki, J. E.; Cairo, C. W.; Strong, L. E.; Oetjen, K. A.; Kiessling, L. L. J. Am. Chem. Soc. 2002, 124, 14923. (6) Krauss, I. J.; Joyce, J. G.; Finnefrock, A. C.; Song, H. C.; Dudkin, V. Y.; Geng, X.; Warren, J. D.; Chastain, M.; Shiver, J. W.; Danishefsky, S. J. J. Am. Chem. Soc. 2007, 129, 11042. (7) Manea, F.; Bindoli, C.; Fallarini, S.; Lombardi, G.; Polito, L.; Lay, L.; Bonomi, R.; Mancin, F.; Scrimin, P. Adv. Mater. 2008, 20, 4348. (8) Ojeda, R.; Paz, J. L.; Barrientos, A. G.; Lomas, M. M.; Penades, S. Carbohydr. Res. 2007, 342, 448. (9) Svarovsky, S. A.; Szekely, Z.; Barchi, J. J. Tetrahedron: Asymmetr 2005, 16, 587. (10) Tsai, C. S.; Yu, T. B.; Chen, C. T. Chem. Commun. 2005, 4273. (11) Turkevich, J.; Stevenson, P. C.; Hillier, J. Discuss. Faraday Soc. 1951, 11, 55. (12) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. J. Chem. Soc., Chem. Commun. 1994, 801. (13) Weisbecker, C. S.; Merritt, M. V.; Whitesides, G. M. Langmuir 1996, 12, 3763. (14) Park, J. S.; Vo, A. N.; Barriet, D.; Shon, Y. S.; Lee, T. R. Langmuir 2005, 21, 2902. (15) Zhang, S.; Leem, G.; Srisombat, L. O.; Lee., T. R. J. Am. Chem. Soc. 2008, 130, 113. (16) Wojczykowski, K.; Meissner, D.; Jutzi, P.; Ennen, I.; H€utten, A.; Fricke, M.; Volkmer, D. Chem. Commun. 2006, 3693. (17) Agasti, S. S.; You, C. C.; Arumugam, P.; Rotello., V. M. J. Mater. Chem. 2008, 18, 70. (18) Jin, R.; Wu, G.; Li, Z.; Mirkin, C. A.; Schatz, G. C. J. Am. Chem. Soc. 2003, 125, 1643. (19) Glogowski, E.; He, J.; Russell, T. P.; Emrick, T. Chem. Commun. 2005, 4050. (20) Mclntosch, C. M.; Esposito, E. A., III; Boal, A. K.; Simard, J. M.; Martin, C. T.; Rotello, V. M. J. Am. Chem. Soc. 2001, 123, 7626. (21) Hong, R.; Fernandez, J. M.; Nakade, H.; Arvizo, R.; Emrick, T.; Rotello, V. M. Chem. Commun. 2006, 2347. (22) Hostetler, M. J.; Templeton, A. C.; Murray, R. W. Langmuir 1999, 15, 3782. (23) Guo, R.; Song, Y.; Wang, G.; Murray, R. W. J. Am. Chem. Soc. 2005, 127, 2752.

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