Lateral Diffusion of Thiol Ligands on the Surface of Au Nanoparticles

Nov 28, 2007 - The lateral mobility of the thiolate ligands on the surface of Au nanoparticles was probed by EPR spectroscopy. This was achieved by us...
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Anal. Chem. 2008, 80, 95-106

Lateral Diffusion of Thiol Ligands on the Surface of Au Nanoparticles: An Electron Paramagnetic Resonance Study Petre Ionita,† Aleksei Volkov,‡ Gunnar Jeschke,*,‡ and Victor Chechik*,†

Department of Chemistry, University of York, Heslington, York YO10 5DD, UK, and Max Planck Institute for Polymer Research, Postfach 3148, 55021 Mainz, Germany

The lateral mobility of the thiolate ligands on the surface of Au nanoparticles was probed by EPR spectroscopy. This was achieved by using bisnitroxide ligands, which contained a disulfide group (to ensure attachment to the Au surface) and a cleavable ester bridge connecting the two spin-labeled branches of the molecule. Upon adsorption of these ligands on the surface of Au nanoparticles, the two spin-labeled branches were held next to each other by the ester bridge as evidenced by the spin-spin interactions. Cleavage of the bridge removed the link that kept the branches together. CW and pulsed EPR (DEER) experiments showed that the average distance between the adjacent thiolate branches on the Au nanoparticle surface only marginally increased after cleaving the bridge and thermal treatment. This implies that the lateral diffusion of thiolate ligands on the nanoparticle surface is very slow at room temperature and takes hours even at elevated temperatures (90 °C). The changes in the distance distribution observed at high temperature are likely due to ligands hopping between the nanoparticles rather than diffusing on the particle surface. The dynamics of ligands on the metal surface has received much attention in the past decade. For instance, ligand-exchange reaction in self-assembled monolayers (SAMs) and particularly in nanoparticles is an extremely important method for preparation of functionalized surfaces/materials.1 Ligand desorption from the monolayers (which obviously leads to the loss of stability) has been one of the main reasons hindering applications of SAMs in biological applications.2 Understanding the factors that control phase separation in mixed monolayers3 is essential for rational design of functional surfaces. * To whom correspondence should be addressed. E-mail: [email protected]. † University of York. ‡ Max Planck Institute for Polymer Research. (1) Love, J. C.; Estroff, L. A.; Kriebel, J. K.; Nuzzo, R. G.; Whitesides, G. M. Chem. Rev. 2005, 105, 1103. (2) Flynn, N. T.; Tran, T. N. T.; Cima, M. J.; Langer, R. Langmuir 2003, 19, 10909. (3) Chambers, R. C.; Inman, C. E.; Hutchison, J. E. Langmuir 2005, 21, 4615. Jackson, A. M., Myerson, J. W., Stellacci, F. Nat. Mater. 2004, 3, 330. Jackson, A. M.; Hu, Y.; Silva, P. J.; Stellacci, F. J. Am. Chem. Soc. 2006, 128, 11135. DeVries, G. A.; Brunnbauer, M.; Hu, Y.; Jackson, A. M.; Long, B.; Neltner, B. T.; Uzun, O.; Wunsch, B. H.; Stellacci, F. Science 2007, 315, 358. 10.1021/ac071266s CCC: $40.75 Published on Web 11/28/2007

© 2008 American Chemical Society

Figure 1. Lateral diffusion of thiolate ligands on the Au nanoparticle surface.

Many aspects of complex ligand behavior on the surface of metals are now well understood. For example, ligand adsorption or exchange has been very thoroughly studied in both planar monolayers and nanoparticles, and despite the complexity of the processes involved, much quantitative information was obtained.4 Monolayer stability and the rate of ligand desorption have also been explored by several research groups.5 Lateral diffusion of ligands on the metal surface (Figure 1), however, proved more controversial. In planar monolayers, this process can be best studied using surface probe microscopy (SPM), electrochemistry, or both. The most studied system is the monolayers of thiols on the gold surface. It was found that lateral diffusion in this system is certainly not fast. The estimated diffusion coefficients were generally reported around 10-17-10-18 cm2 s-1 at elevated temperatures (e.g., 90-100 °C).6 This corresponds to the rate of lateral diffusion ∼1 nm/h. There are, however, significant discrepancies in the literature data, with some (4) Hong, R.; Fernandez, J. M.; Nakade, H.; Arvizo, R.; Emrick, T.; Rotello, V. M. Chem. Commun. 2006, 2347. Kassam, A.; Bremner, G.; Clark, B.; Ulibarri, G.; Lennox, R. B. J. Am. Chem. Soc. 2006, 128, 3476. Baralia, G. G.; Duwez, A. S.; Nysten, B.; Jonas, A. M. Langmuir 2005, 21, 6825. Lin, P.-H.; Guyot-Sionnest, P. Langmuir 1999, 15, 6825. Kakiuchi, T.; Sato, K.; Iida, M.; Hobara, D.; Imabayashi, S.-i.; Niki, K. Langmuir 2000, 16, 7238. Guo, R.; Song, Y.; Wang, G. L.; Murray, R. W. J. Am. Chem. Soc. 2005, 127, 2752. (5) Schlenoff, J. B.; Li, M.; Ly, H. J. Am. Chem. Soc. 1995, 117, 12528. Pesika, N. S.; Stebe, K. J.; Searson, P. C. Langmuir 2006, 22, 3474. Shadnam, M. R.; Amirfazli, A. Chem. Commun. 2005, 4869. Garg, N.; Molina, E. C.; Lee, T. R. Langmuir, 2002, 18, 2717. Shon, Y. S.; Lee, T. R. J. Phys. Chem. B 2000, 104, 8192. (6) Imabayashi, S.-i.; Hobara, D.; Kakiuchi, T. Langmuir 2001, 17, 2560, and references cited therein.

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Figure 2. Schematic drawing of the EPR experiment directly probing the lateral diffusion of ligands on the surface of Au nanoparticles. The dipole-dipole interactions between nitroxide spin labels are shown with dotted arrows.

reports of much higher mobility (e.g., 10-14 cm2 s-1).7 Presumably, the rate of lateral diffusion is to a large extent dependent on the packing of the organic layer and the defects in the underlying gold surface. The absence of fast lateral diffusion is essential for the preparation and stability of microscopically patterned surfaces. For instance, lateral diffusion can cause the blurring of domain boundaries prepared by microcontact printing techniques.8 The situation with thiol-protected Au nanoparticles is more complicated. Due to the curvature, the packing of the organic layer is not as high as in SAMs. However, the packing of the thiol groups on the surface can be very tight. Besides, the arrangement of underlying gold layer is significantly different from planar SAMs, and hence, the kinetics of diffusion can also be expected to be different. Unlike planar SAMs, the lateral diffusion of ligands on the nanoparticle surface cannot be readily visualized with SPM techniques. Hence, most estimates of the rate of lateral diffusion rely on indirect evidence. For instance, the diffusion of adsorbed ligands on the surface of the Au nanoparticle was first proposed by the Murray group to explain the dynamics of the ligandexchange reaction.9 The proposed rate of diffusion was quite slow, taking weeks at room temperature; this estimate is supported by the observation that the ligands adsorbed on some binding sites are very resistant to exchange. Rotello and co-workers observed time evolution of the binding of a flavin by multifunctional Au nanoparticles. The increased binding was explained by the lateral diffusion of the complementary ligands along the Au surface. The changes of binding constant were observed over a period of ∼80 h at room temperature.10 Workentin and co-workers studied a photochemical reaction at the surface of Au nanoparticles. The extent of reaction was postulated to depend on the location of the reactive groups on the Au surface, and hence, the increased extent of reaction for aged samples (up to two weeks) was attributed to the slow lateral diffusion of the ligands on the Au surface.11 On the other hand, some literature reports suggest rather rapid lateral diffusion. Bjørnholm and co-workers explored the behavior of Au nanoparticles coated with a mixture of hydrophilic and hydrophobic ligands at the air-water interface.12 The geometrical parameters of the Langmuir monolyers obtained using grazing incidence X-ray diffraction led the authors to suggest that the ligands possess high mobility on the Au surface on the time scale of their experiments (minutes). Werts et al. used fluorescence titration to monitor adsorption of ligands on the Au surface. The authors proposed that equilibration of ligands on the nanoparticle surface takes 1-2 h.13 In order to solve the discrepancies in the literature reports, one needs to develop a method for directly observing lateral 96

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diffusion on the Au surface. This requires an analytical technique that is sensitive to the distance between the functional groups adsorbed on the Au surface. EPR spectroscopy is a powerful example of such a technique. The through-space dipole-dipole interactions between spin labels in the range of 1-2.5 nm can be directly observed by conventional CW methods. Pulsed EPR (e.g., electron-electron double resonance, DEER) can extend this range to ∼7-8 nm.14-16 We have therefore aimed to exploit the sensitivity of EPR to interspin distances in order to observe directly the lateral diffusion of thiolate ligands on the surface of Au nanoparticles. Ligand Design. The idea behind the proposed experiments was quite simple. A ligand containing two spin labels connected by a cleavable bridge is adsorbed on the surface of Au nanoparticle (Figure 2). The bridge is then broken, and lateral diffusion of the two spin-labeled branches away from each other can be directly probed by EPR spectroscopy (as such diffusion increases interspin distance). The ligand for this experiment needs to have the following features: (1) Two spin-labeled branches connected by a disulfide bridge. (2) An additional linker connecting the two branches. The disulfide bridge is known to break during adsorption on Au, and the two branches of disulfides do not adsorb next to each other.17 In order to ensure the juxtaposition of the two spin labeled branches, they must be connected by a second bridge. (3) The bridge must be cleavable under mild conditions that the nanoparticle can survive. The cleavage reaction must be fast. (4) The spin labels in the two branches must be close to each other in order to ensure that their interactions are easily detected by EPR. (5) The spin labels must be attached to the disulfide group with short tethers. Otherwise, the conformational flexibility of the tethers will lead to a broad distribution of distances in the ligand, which can obscure the observation of lateral diffusion. (7) Ishida, T.; Yamamoto, S.; Mizutani, W.; Motomatsu, M.; Tokumoto, H.; Hokari, H.; Azehara, H.; Fujihira, M. Langmuir 1997, 13, 3261. (8) Dameron, A. A.; Hampton, J. R.; Smith, R. K.; Mullen, T. J.; Gillmor, S. D.; Weiss, P. S. Nano Lett. 2005, 5, 1834. (9) Hostetler, M. J.; Templeton, A. C.; Murray, R. W. Langmuir 1999, 15, 3782. (10) Boal, A. K.; Rotello, V. M. J. Am. Chem. Soc. 2000, 122, 734. Boal, A. K.; Rotello, V. M. J. Am. Chem. Soc. 2002, 124, 5019. (11) Kell, A. J.; Donkers, R. L.; Workentin, M. S. Langmuir 2005, 21, 735. (12) Nørgaard, K.; Weygand, M. J.; Kjaer, K.; Brust, M.; Bjørnholm, T. Faraday Discuss. 2004, 125, 221. (13) Werts, M. H. V.; Zaim, H.; Blanchard-Desce, M. Photochem. Photobiol. Sci. 2004, 3, 29. (14) Milov, A. D.; Salikhov, K. M.; Shirov, M. D. Fiz. Tverd. Tela 1981, 23, 975. (15) Jeschke, G. Macromol. Rapid Commun. 2002, 23, 227. (16) Jeschke, G. Chem. Phys. Chem. 2002, 3, 927. (17) Ionita, P.; Caragheorgheopol, A.; Gilbert, B. C.; Chechik, V. Langmuir 2004, 20, 11536.

Figure 3. Structures and synthesis of ligands 1-4.

With these considerations in mind, we have designed a series of ligands shown in Figure 3. The polyfunctionality of amino acids was exploited to construct the breakable bridge and attach the spin labels. The breakable bridge was an ester group. Esters are rapidly hydrolyzed under mild basic conditions and the use of an ester group in the ligands for Au nanoparticles is well documented; this justified our choice of this functionality. Disulfide 1 is symmetrical; however, the ethylene oxide bridge makes the distance between the spin labels rather long. Molecule 2 required longer synthesis but had a shorter distance between the spin labels. Unfortunately, attempts to hydrolyze the ester bridge in compounds 1 and 2 unexpectedly led to the elimination of a disulfide group. This was confirmed by the detection of dehydroalanine derivatives among the products of this reaction (by 1H NMR and mass spectrometry). Therefore, 1 and 2 cannot be used to probe lateral diffusion. This problem was solved by using

homocysteine derivatives rather than cysteine (3, 4). Compounds 1-4 were synthesized using standard organic synthetic methodology (Figure 3). The CW EPR spectra of frozen toluene solutions of radicals 1-4 are shown in Figure 4. The distance between the nitroxide groups can be crudely assessed using an empirical ratio of peak heights d1/d (e.g., the higher the ratio, the shorter the distance between the radical centers).18 The EPR spectrum of a dilute TEMPO solution recorded under the same conditions (see Figure 10) shows the d1/d ratio of 0.53. This value is significantly smaller than the d1/d ratio for diradical 4 (0.69). This suggests that the (18) Kokorin, A. I.; Zamaraev, K. I.; Grigoryan, G. L.; Ivanov, V. P.; Rozantsev, E. G. Biofizika 1972, 17, 34 (in Russian). Likhtenshtein, G. I. Spin Labeling Methods in Molecular Biology; Wiley & Sons: New York, 1976. Likhtenshtein, G. I. Biophysical Labeling Methods in Molecular Biology; Cambridge University Press: New York, 1993.

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Figure 4. CW EPR spectra of frozen solutions of diradicals 1 (a), 3 (b), 2 (c). and 4 (d) in toluene. The spectra were normalized by the spin count. DEER decay (e) and the fitted distance distribution (Tikhonov regularization, f) for diradical 3 in toluene.

distance between the radical centers in molecule 4 is quite short, which makes it possible to study lateral diffusion of this spin probe by CW EPR. However, for radical 3, the d1/d ratio is only ∼0.59. This is fairly close to the monoradical values; hence, in this molecule, the distance between the two nitroxides is too long for reliable observation by CW EPR. The lateral diffusion of ligand 3 on the surface of Au nanoparticles can therefore only be studied by pulsed EPR methods (e.g., DEER). Figure 4e,f shows the DEER decays and the corresponding distance distribution obtained for diradical 3. The distance distribution is quite narrow, with the average interspin distance ∼1.4 nm. This absolute value of average distance should be treated with caution as DEER data for short distances are partially suppressed. In order to enable the spin labels to diffuse away from each other on the surface of Au nanoparticles, one has to develop a procedure for quickly breaking the ester bridge in molecules 3 and 4. We used based-catalyzed solvolysis to achieve this goal. We found that solvolysis by a 0.155 M. NaOH solution in 9/1 (v/v) MeOH/water is complete within a few seconds. For radical 3, solvolysis can be directly monitored by EPR, as this molecule shows no exchange interaction at room temperature (presumably the conformation makes it impossible for the nitroxides to approach each other). After solvolysis, however, the molecule was more flexible, and the exchange interaction became visible, particularly in nonpolar solvents. EPR spectra of ligand 3 before and after solvolysis are shown in Figure 5. Solvolysis was independently monitored by TLC. Interestingly, a similar effect (e.g., appearance of a 5-line pattern in CW spectra due to exchange interaction) can be achieved by breaking the other bridge in molecule 3, e.g., the disulfide bridge (ligand 3 with the broken disulfide bridge was an intermediate in synthesis, see Experimental Section). This 98 Analytical Chemistry, Vol. 80, No. 1, January 1, 2008

Figure 5. Room-temperature CW EPR spectra of DCM solution of ligand 3 before (a) and after (b) ester solvolysis.

confirms that the absence of exchange interaction in EPR spectra of diradical 3 is due to the conformational inflexibility of the 14member ring. We decided to limit the reaction time for ester solvolysis to 2 min. We found that significantly longer reaction times led to the appearance of paramagnetic byproducts, presumably due to solvolysis of the amide bond. Therefore, the reaction mixture was quenched after solvolysis by bubbling gaseous CO2 to neutralize the base. Spin-Labeled Nanoparticles. In order to break the ester bridge in ligands 3 and 4 adsorbed on the surface of Au nanoparticles, the nanoparticles must be soluble in polar solvents (e.g., alcohols). The most commonly used alkanethiol-protected Au nanoparticles do not dissolve in polar solvents and hence cannot be used in our study. Charge-protected, water-soluble nanoparticles are well-known; however, they do not possess high enough stability to enable extensive manipulation required for monitoring lateral diffusion.19 Besides, water-soluble nanoparticles will be difficult to label with water-insoluble ligands 3 and 4. We (19) Andreescu, D.; Sau, T. K.; Goia, D. V. J. Colloid Interface Sci. 2006, 298, 742.

Figure 6. Structure of nanoparticles used to monitor lateral diffusion and their TEM image.

decided therefore to prepare Au nanoparticle stabilized by a polar nonionic ligand derived from diethylene glycol20 (Figure 6). The nanoparticles protected by this ligand were prepared by the standard Brust et al. method.21 We found that this method gives more stable nanoparticles than those prepared by a one-phase procedure. The nanoparticles were characterized by transmission electron microscopy. The average particle diameter was 2.1 ( 0.5 nm. The nanoparticles were found to be very soluble in a variety of solvents from nonpolar (e.g., toluene) to polar (aqueous methanol). This high solubility significantly simplified nanoparticle handling, purification, and labeling. Ancona et al. reported that Au nanoparticles protected by the same ligand were prepared using a ligand-exchange reaction; they were not soluble in nonpolar solvents.20 The difference in solubility is likely due to the different organization of the organic layer in nanoparticles prepared by different methods. To confirm the efficiency of purification, we recorded the 1H NMR spectrum of nanoparticles. The spectrum showed only a very broad peak centered at ∼3.4 ppm (Figure 7 a) which is typical for nanoparticle-attached ligands. This spectrum is similar to the spectra reported in the literature for the diethylene glycolterminated nanoparticles prepared by ligand-exchange reaction.20 The absence of sharp peaks in the 1H NMR spectrum confirmed the absence of small-molecule contamination. In order to further check the composition and purity of the nanoparticles, they were destroyed with excess iodine in aqueous methanol. This procedure is known to release the ligands as disulfides.22 The 1H NMR spectrum of the residue (Figure 7b) shows expected peaks of the disulfide ligand. No peaks corresponding to tetraoctylammonium bromide (transfer agent used in nanoparticle synthesis, which often contaminates nanoparticles) were observed. The diradicals 3 and 4 were introduced into the nanoparticle shell via ligand exchange. It was important to keep the spin label coverage low, as otherwise, the spin-spin interactions between (20) Foos, E. E.; Snow, A. W.; Twigg, M. E.; Ancona, M. G. Chem. Mater. 2002, 14, 2401. (21) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. J. Chem. Soc., Chem. Commun. 1994, 801. (22) Templeton, A. C.; Hostetler, M. J.; Kraft, C. T.; Murray, R. W. J. Am. Chem. Soc. 1998, 120, 1906. Kim, J. B.; Breuning, M. L.; Baker, G. L. J. Am. Chem. Soc. 2000, 122, 7616.

Figure 7. 1H NMR spectra of Au nanoparticles (a) and the ligand released from the nanoparticle surface following treatment with iodine in aqueous methanol (b).

the two nitroxides of the diradicals would be obscured by the interactions between different diradical molecules adsorbed on the same nanoparticle. This is particularly important for the CW EPR measurements, which are sensitive to dipole-dipole interactions between all nitroxides within the ∼2.5-nm range. The ligand exchange was carried out using a 3:1 ratio of diradical/nanoparticle. We found that more than 70% of diradicals 3 and 4 did not adsorb on the nanoparticle surface during ligand exchange (the reaction mixture was left overnight in toluene at room temperature). We thus believe the average coverage of the spin label under these conditions was below 1 diradical/particle. The low coverage was confirmed by DEER measurements (vide infra). We have also found that the CW EPR spectra of frozen solutions were almost indistinguishable for nanoparticles prepared using 3:1 and 9:1 diradical/nanoparticle ratio, which further confirmed low coverage and insignificance of the interactions between several ligands adsorbed on the same nanoparticle. At this low coverage, the physical properties (e.g., solubility) of the nanoparticles are determined by the diethylene glycol ligand; the spin-labeled nanoparticles hence were soluble in aqueous alcohols, which was essential for breaking the ester bridge by hydrolysis. Analytical Chemistry, Vol. 80, No. 1, January 1, 2008

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Figure 8. Room-temperature CW EPR spectra of Au nanoparticles modified with ligands 3 (a) and 4 (b), respectively; EPR spectra of spinlabeled nanoparticles at 200 K after complete (c) and incomplete (d) separation from the excess spin label 4.

Figure 9. (a) Model used to analyze the distribution of interspin distances in spin-labeled Au nanoparticles. Intramolecular distances and the corresponding Gaussian distribution are shown with a dotted line; distances between different molecules adsorbed on the same nanoparticle and the triangular distance distribution are shown with a dashed line. The Gaussian distribution of nanoparticle diameters is shown with a dash-dotted line, and the overall distribution is shown as a solid line. (b) Comparison of DEER results for the Au nanoparticles modified with ligand 3 fitted with the model expression and model-free Tikhonov regularization.

The spin-labeled nanoparticles were characterized by CW and DEER EPR measurements. Room-temperature CW EPR spectra of Au nanoparticles exchanged with ligands 3 and 4 are shown in Figure 8. The spectra are markedly different from the free diradical spectra (cf. Figure 5a). The rotational dynamics of the spin labels is significantly reduced; the tumbling rates are at the boundary between fast and slow motion on the EPR time scale. This confirms attachment of the ligands 3 and 4 to the nanoparticles. Separation of spin-labeled nanoparticles from excess of free spin-labeled ligands was achieved by gel permeation chromatography. The efficiency of this separation is best probed by CW EPR spectroscopy at 200 K. At this temperature, free ligands give fastmotion-type EPR spectra, while nanoparticle-attached ligands show slow-motion spectra. As the slow- and fast-motion spectra are easily deconvoluted, this method enables one to quantify the amount of free and nanoparticle-attached ligands. Figure 8c,d shows Au nanoparticles spin labeled with ligand 4 in a purified form and in a mixture with excess diradical 4. One can see that the excess free ligand was completely removed in the purified sample. Rigid limit CW EPR spectra of spin-labeled nanoparticles were very similar to the spectra of free ligands. The dipolar broadening of the rigid limit spectra (particularly visible for diradical 4) confirms that the spin labels adsorbed on the Au surface are biradicals. 100

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The DEER measurements of spin-labeled nanoparticles have been analyzed as follows. We assumed that there are two types of interspin distances for diradicals adsorbed on the surface of the Au nanoparticles. One is the distance between the two nitroxides that belong to the same molecule. The distribution of these distances can be approximated by a Gaussian function. The second type is related to the distance between two different ligands adsorbed on the same nanoparticle. Approximating the nanoparticle shape as spherical, and assuming random distribution of ligands on this spherical surface, one can describe the distribution of ligands on the nanoparticle as a triangular function (distribution of distances between two points randomly positioned on the surface of a sphere).23 As the nanoparticles are not monodisperse, this function is smeared by the Gaussian distribution of particle sizes. The model distribution of distances thus calculated is schematically shown in Figure 9. This model was used to fit the DEER decay signal for spin-labeled Au nanoparticles. Model-free fits obtained, using the Tikhonov regularization algorithm, gave very similar shape of distance distribution, which confirmed the validity of our model (see example in Figure 9). Importantly, DEER measurements provide a clear distinction between diradicals (e.g., when two spin-labeled ligands are adsorbed next to each other on the nanoparticle surface) and radicals randomly distributed on the Au surface. Regardless of (23) Christopher, J. A.; Baldwin, T. O. J. Mol. Biol. 1996, 257, 175.

the flexibility of the chain, the randomly distributed ligands will give a triangular distribution curve (Figure 9a) that is dominated by long distances (3-4 nm). The diradical distance distributions will always be dominated by shorter distances (regardless of the chain flexibility, as 3-4-nm distances cannot be achieved without moving the two branches of the diradical onto the opposite poles of the Au surface). Hence, this method can provide a clear-cut answer to the main question of this MS (e.g., if the ligands can diffuse laterally on the nanoparitcle surface). The analysis of the DEER spectra of nanoparticles coated with ligand 3 showed the spin label coverage of ∼2.04 spin labels/ nanoparticle. As unlabeled nanoparticles are silent in the DEER experiment, this number is average over all nanoparticles that have at least one spin label but it does not include unlabeled nanoparticles (which are certainly present in the mixture). The coverage data thus suggest that most labeled nanoparticles have just one ligand (i.e., two spin labels). The population of nanoparticles with more than one ligand is small (otherwise the average coverage would be higher). The average interspin distance was 1.83 ( 0.26 nm. The vast majority of spin-spin interactions (83%) correspond to this short distance, and only a small number of longer distances describe interactions between two ligands adsorbed on the same nanoparticle. The long distance (4.5 nm) corresponds to the average diameter of the nanoparticle core (2.1 nm) plus twice the length of the ligand (∼1.2 nm). This is very consistent with what we aimed to achieve, e.g., low coverage, diradical-functionalized Au nanoparticles. The number of spins per nanoparticle is probably slightly underestimated, as very short distances (e.g., under 1.5 nm) are partially suppressed in the DEER experiment.24-26 Nonetheless, this number is also consistent with low coverage of the spin label. Unfortunately, due to extremely small coverage (e.g., 0. The resonator was overcoupled to Q ∼ 100, and the pump frequency νpump was set to the center of the resonator dip and coincided with the maximum of the nitroxide EPR spectrum, while the observer frequency νobs was 65 MHz higher and coincided with the low-field local maximum of the spectrum. All experiments were performed with a pump pulse length of 12 ns and with observer pulse lengths of 32 ns at a temperature of 50 K. Proton modulation was averaged by adding traces at eight different τ1 values, starting at τ1(0) ) 200 ns and having increments of ∆τ1 ) 8 ns. Data analysis by Tikhonov regularization was performed with the program DeerAnalysis2006,26 whose source code is available at http://www.mpip-mainz.mpg.de/∼jeschke/distance.html. The background decay (caused by intermolecular interactions between spin-labeled nanoparticles) was modeled as homogeneous 3D distribution of spin labels. The validity of this approach was confirmed by recording of DEER traces of spin-labeled nanoparticles at different concentrations. All DEER traces shown in this work are background-corrected. (30) Pannier, M.; Veit, S.; Godt, A.; Jeschke, G.; Spiess, H. W. J. Magn. Reson. 2000, 142, 331.

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The same program was used for model-based fitting with a user-defined model function. This function implements a superposition of a Gaussian peak in the distance distribution, corresponding to the distance in a biradical or between close neighbors on the label surface, with a homogeneous distribution of labels on the surface of spherical particles whose diameters exhibit a Gaussian distribution. The source code of this function can be obtained from the authors on request.

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ACKNOWLEDGMENT V.C. and P.I. gratefully acknowledge financial support from the EPSRC (ref GR/S45300/01) and the University of York (Anniversary Lectureship for V.C.). Received for review June 15, 2007. Accepted October 16, 2007. AC071266S