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J. Phys. Chem. C 2008, 112, 20276–20283
Mass Spectrometrically Detected Statistical Aspects of Ligand Populations in Mixed Monolayer Au25L18 Nanoparticles Amala Dass,† Kennedy Holt, Joseph F. Parker, Stephen W. Feldberg,‡ and Royce W. Murray* Kenan Laboratories of Chemistry, UniVersity of North Carolina, Chapel Hill, North Carolina 27599-3290 ReceiVed: August 28, 2008; ReVised Manuscript ReceiVed: October 21, 2008
Ligand exchange reactions of Au25(SCH2CH2Ph)18 with hexanethiol (HSC6) and thiophenol (HSPh) as incoming ligands, and Brust reaction nanoparticle syntheses using mixtures of thiols (HSCH2CH2Ph and HSC6), produce nanoparticles having different, ideally statistically determined, relative populations of the two thiolate ligands (X and Y), i.e., Au25(X)m(Y)m′, where m and m′ vary but always sum to 18. By choice of reactant concentrations, the exchange reaction can reach an equilibrium state or a near-complete exchange of ligands or be at a kinetically determined (nonequilibrium) mixed population, at the time of reaction quenching and subsequent matrixassisted laser desorption ionization-time-of-flight (MALDI-TOF) mass spectrometric examination. With the assumption that the reactivities of the 18 ligand sites are identical and independent, the equilibrium distributions of ligand populations of the mixed monolayer exchange products should adhere to a binominal distribution. A simulated kinetic model for ligand exchange shows that mixed ligand distributions in nanoparticles not at exchange equilibrium also conform to the binominal distribution. The theory successfully describes MALDI mass spectrometrically determined experimental ligand populations produced in the ligand exchange reaction between Au25(SCH2CH2Ph)18 and hexanethiol, while that between Au25(SCH2CH2Ph)18 and thiophenol yields a more narrow distribution than predicted by random exchanges and no interactions between ligands. Previous nanoparticle ligand analyses by methods such as nuclear magnetic resonance, gas-liquid chromatography, and infrared spectroscopies yield average ligand populations in mixed monolayers and are incapable of detecting such nonrandom ligand distributions. Introduction Completely or partially thiolated gold nanoparticles1 are highly studied materials with promise in applications to nanoelectronics, biosensors, bioanalysis, and optical devices. Gold nanoparticles that are very small (99.9%), methylene chloride (Fisher, 99.9%), hexanethiol (Fluka, >95%), phenylethanethiol (Aldrich, 98%), thiophenol (Acros, 99%), methanol, and dodecanethiol were used as received. Mixed monolayer Au25(SCH2CH2Ph)x(SC6)y was prepared by a mixed ligand Brust reaction2 synthesis as reported previously.10e Ligand Exchange. In a typical ligand exchange reaction, a 1 mg sample of Au25(SCH2CH2Ph)18 dissolved in 200 µL of CH2Cl2 is mixed with the incoming thiol (hexanethiol or thiophenol) in a desired mole ratio and stirred in the dark for a specified period of time, after which the reaction was quenched by removing the solvent (by rotovap) and washing with methanol (typically ∼5 times) to remove excess thiol. The product yield was usually >80%. An example of a MALDI spectrum of the reaction product for a 1:1 mole ratio of incoming thiol and nanoparticle ligands and an 8 h reaction time is shown in Figure 1c. Ligand exchange products were obtained at various reaction times (0.5, 2.5, 8, 24, 48, and 72 h) using hexanethiol and thiophenol, nanoparticle concentrations (2 and 5 mg/mL) and mole ratios of incoming thiol to nanoparticle ligands (0.02:1, 0.05:1, 0.33:1, 1:1, 3:1, 20:1, and 50:1). The mole ratio, rY, is based on the number of moles of exchangeable nanoparticle ligands (18 per nanoparticle), not the moles of nanoparticles. Thus, rY ) [Y]t)0/(18cNP]), where cNP is the nanoparticle concentration. It is known that all 18 of the initial ligands can be exchanged,8d but in practice this involved large values of rY. Conditions producing complete exchange were not sought here. Mass Spectrometry. MALDI-time-of-flight (MALDI-TOF) mass spectrometry experiments were performed using an
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Applied Biosystems Voyager-DE Pro (reflectron mode) timeof-flight mass spectrometer equipped with a nitrogen laser (337 nm). The accelerating voltage was held at 25 kV and as discussed previously,10e the laser pulse intensity was greatly reduced so as to avoid nanoparticle fragmentation. The effect of reducing laser pulse intensity is emphasized by reproducing previous data10e on the same nanoparticle, in Supporting Information Figure S-2. MALDI Sample Preparation. At matrix:analyte mole ratios varying from 1:1 to 1000:1, 1-100 mM DCTB matrix and nanoparticle solutions in CH2Cl2 were mixed in microcentrifuge tubes, applying 1-2 µL of this solution to the sample plate and air-drying. The rationale for choice of the DCTB matrix was discussed previously.10e Results and Discussion Ligand exchange reactions of Au25(SCH2CH2Ph)18 nanoparticles with two different ligands, hexanethiol and thiophenol, were conducted for various periods of time, nanoparticle concentrations, and mole ratios of incoming thiol to ligands present on the nanoparticles. A mole ratio (rY ) [Y]t)0/(18cNP)) ) 1 means that the initial concentration of incoming ligand, [Y]t)0, equals 18cNP, where cNP is the bulk concentration of the nanoparticles. This series of experiments led to a variety of nanoparticle ligand distributions suitable for statistical analysis. The generalized exchange reaction is kXoff
MXmYN-m + Y {\} MXm-1YN-m+1 + X
(1)
kXon
where m varies from N ()18) to zero and is measured by the mass position of peaks for different mixed monolayer populations on the nanoparticlessrelative to mass of the initially present nanoparticle MX18 (7394 Da in the case of Au25(SCH2CH2Ph)18). The displaced ligand product, X, appears in the solution as a thiol. Note that the rate constants are assumed to be independent of the value of m. The forward reaction can be assumed pseudo-first-order as long as rY g 10, but since [X]t)0 ) 0 for all experiments, the backward reaction will never be pseudo-first-order. Mixed monolayer nanoparticles were also prepared using mixtures of phenylethanethiol and hexanethiol in the Brust reaction synthesis of the Au25 nanoparticles. The ligand distributions were measured in the same manner as above. Ligand Exchange Reaction of Au25(SCH2CH2Ph)18 with Hexanethiol. The mole ratios of incoming to nanoparticle ligands were chosen to produce only a modest extent of exchange (rY g 1) or a more extensive one (rY . 1). We have reported on ligand exchange kinetics (measured by NMR) in the past,8 so the present experiments were not designed to extract kinetic information for the exchange kinetics, but rather the distributions of exchange products as seen by MALDI mass spectrometry. Thus, the rY values chosen did not uniformly produce pseudo-first-order conditions for the forward exchange process. We note below that, for the purposes of examining the distribution, pseudo-first-order conditions are, in fact, not required. Figure 1 shows the mass spectra of exchange products obtained using hexanethiol as the incoming ligand. The spectra at top right and lower left of each panel (peaks labeled 0 and 18) are unexchanged Au25(SCH2CH2Ph)18 nanoparticles and separately synthesized Au25(SC6)18 nanoparticles, respectively. The latter serves as a reference point corresponding to a 100% exchanged (Au25(S(CH2)7CH3)18) nanoparticle product. As seen, 100% exchange was not attained under any of the reaction
conditions (although under more forcing conditions 100% exchange has been shown8d to be possible). The vertical scales of the spectral peaks in Figure 1 differ, being adjusted for display purposes. As judged by the midpoints of the mixed monolayer distributions, the obtained extent of exchange increases (the midpoint moves to the left) with increasing reaction time, higher nanoparticle concentration, and higher mole ratio of incoming thiol to nanoparticle ligands. In Figure 1a, at a very low mole ratio (0.05:1), at the longest (72 h) exchange time the spectra show three partially exchanged products (x ) 1-3, where x ) N – m) and unexchanged material. The spectra at the two longest exchange times (24, 72 h) are similar; the reaction is very close to equilibrium. Increasing the mole ratio to 1:1 produces (Figure 1b) at the larger (72 h) exchange reaction times, a larger number of different mixed monolayer nanoparticles; the reaction mixture is clearly still continuing to evolve with time. In Figure 1c,d, at higher nanoparticle and incoming thiol concentrations, the exchange reaction (being bimolecular8c) proceeds at a faster pace and a wider range of different mixed monolayers can be seen, with a total of ca. 10 peaks seen at 8 h in Figure 1d. In each case in Figure 1b-d, the continuing changes in the midpoints of the distributions (moving toward the left, or larger x) show that the reactions had not reached an equilibrium state before being quenched. A comment is in order here regarding the aVerage number of exchanged ligands versus the actual relative ligand population distributions seen in the mass spectra of Figures 1-4. The average number of exchanged ligands has been obtained from NMR spectra as the fractional change in resonance peaks8c,d for either the incoming ligand or for the displaced thiol. In the mass spectra, on the other hand, the average number of remaining X-ligands, NX,av (eq 1). is easily computed from the amplitudes, Am, of all the peaks in the distribution:NX,av ) ∑Nm)0 N mAm/∑m)0 Am (see the Supporting Information). Only when the distribution is symmetrical (or nearly so) will the interpolated maximum of the distribution correspond to NX,av. We did not compare NMR and MALDI data, with the exception of one example from a mixed thiol Brust synthesis, discussed later. On another point regarding average numbers of ligands, the average in Figure 1c at 2.5 h reaction time indicates that approximately one X-ligand has been replaced by one Y-ligand. The presence of additional peaks clearly shows that there is a distribution corresponding to zero, two, and three replacements. Peaks corresponding to additional replacements are too small to see, as would be expected if the distribution is statistically driven. This stepwise replacement clearly illustrates that it is impossible to carry out a ligand exchange and obtain a sample with one and only one new ligand on all of the nanoparticles. Some further feature of the experiment, such as a subsequent separation, or a nanoparticle that somehow has a single unique reaction site, is required to obtain such a product. Ligand Exchange Reaction of Au25(SCH2CH2Ph)18 with Thiophenol. Results from a second example of ligand exchange for Au25(SCH2CH2Ph)18 nanoparticles, using thiophenol, are shown in Figure 2. Again, as judged by the midpoints of the mixed monolayer distributions, the extent of exchange increases with increasing reaction time (top-to-bottom in each set of spectra), higher nanoparticle concentration (Figure 2c,d as compared to Figure 2a,b), and higher mole ratio of incoming thiol to nanoparticle ligands (Figure 2d as compared to Figure 2a). In Figure 2a, the very slow reaction exchanges only a portion of the starting material with one thiophenolate ligand even after 72 h, whereas in Figure 2d at the longest reaction
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Figure 2. Monolayer ligand distributions of the ligand exchange product Au25(SCH2CH2Ph)18-x(SPh)x as observed by MALDI-MS spectra, for exchanges conducted for indicated times, at different concentrations and at different mole ratios (rY) of incoming thiols to exchangeable ligands on the nanoparticles: (a) concentration is 2 mg/mL and rY ) 0.02:1; (b) concentration is 2 mg/mL and rY ) 3:1; (c) concentration is 5 mg/mL and rY ) 0.33:1; (d) concentration is 5 mg/mL and rY ) 50:1. The vertical gray lines correspond to x ) 5, 10, and 15 and are intended to aid visualization of peak assignments.
time, some product is obtained (lower left) in which all 18 of the original ligands have been replaced. The mass spectral range of the exchange is of course different from that in Figure 1 due to the mass difference between hexanethiol and thiophenol. Inspection of the distributions of peaks in the spectra of Figures 1 and 2 indicates that there is a qualitative difference between the exchange reactions of hexanethiol and thiophenol. In Figure 1c, at 8 h, the largest peak in the distribution is ca. x ) 4, and there are nine different peaks in the distribution. In Figure 2c at 2.5 h reaction time, the largest peak is also at ca. x ) 4, but now one can see only seven peaks in the distribution. Careful study of background noise showed that this was not a signal-to-noise artifact, but a real difference in the breadth of the two distributions. The difference between exchanges using hexanethiol and thiophenol is probed further using the exchange kinetics model described below. Mixed Monolayer Synthesis Using Two Different Thiols in the Brust Reaction. In syntheses using mixtures of two thiols in the nonaqueous phase transfer (Brust) method, it is often assumed that the resultant average ratio of the thiols bound to the nanoparticles is approximately the same as the reaction-feed ratio of thiols. There are some known exceptions,5b and numerous caveats in the relationship between reactant feed ratio and the nanoparticle products. These include the following: (a) the relative rates of thiol reaction with the growing Au nanoparticle, (b) product workup issues where solubility fractionation may occur among nanoparticles having ligands with substantially differing polarity or charge, (c) concurrent production of mixtures of nanoparticles with quite different ligand content, (d) formation of AuI(SR) complexes during the synthesis that favor one ligand over another.11a Averages measured by NMR (or vibrational spectroscopy or voltammetry) would generally be blind to these caveats. The first two caveats (a and b) also apply to the experiment presented here, but the third (c) can be explicitly ruled out by
Figure 3. Monolayer ligand distribution of the mixed Brust reaction product Au25(SCH2CH2Ph)18-x(SC6)x as observed by MALDI-MS spectrum using different starting ligand ratios 25:75, 50:50,10e) and 75: 25.
the MALDI mass spectrometry results presented in Figure 3, in which Au25 nanoparticles have been prepared in a Brust reaction using a mixture of phenylethanethiol and hexanethiol at mole ratios of 25:75, 50:50, and 75:25. A portion of the data in Figure 3 was presented earlier,10e where it was noted that the reaction has some selectivity toward incorporating phenylethanethiolate ligands into the mixed monolayer (by either of caveat a or b above), since the center of the distribution of peaks produced in the 50:50 reactant mixture lies to the right of the average masses of the Au25(SCH2CH2Ph)18 and Au25(S(CH2)5CH3)18 nanoparticles. The statistically expected average number of hexanethiolate ligands obtained in the 50: 50 synthesis would be 9, if kXon ) kXoff eq 1. The actual average obtained from the center point of total mass spectral peak areas
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is about 6. By comparison, that obtained from an NMR inspection (Figure S-1) of this reaction product was 7.4. By either result, the hexanethiolate is somewhat disfavored. Figure 3 also reveals the absence of any bimodal ligand distribution such as might occur through caveat c above. This observation is possible using the mass spectral analysis, but not the others mentioned above. An attempt was made to induce a bimodal ligand distribution by using mixtures of very dissimilar thiols, such as mixtures of fluorinated alkyl thiols and phenylethanethiol but was not fruitful since Au25 nanoparticles could not be isolated in the products. Kinetic Model for Ligand Exchange Reactions. The preceding experiments in Figures 1 and 2 have qualitatively described the monolayer mixtures that result from ligand exchange reactions of the Au25(SCH2CH2Ph)18 nanoparticle. We turn next to a more quantitative description of the shapes of the ligand distributions presented in these figures. Given that the nanoparticle starts as MXN, using the notation of eq 1 and assuming that the ligand sites on each nanoparticle are identical and independently reactive, it can be shown that at equilibrium (see the Supporting Information) the fraction of any given species, θm ) [MXmYN-m]eq/cNP, is given by the binomial distribution:
θm )
[MXmYN-m]eq N! ) pYN-mpXm ) cNP m ! (N - m)! (1 - pX)N-mpXm
N! (2) m ! (N - m)!
where cNP the total concentration of all nanoparticles is N
cNP )
∑ [MXmYN-m]
(3)
m)0
Note that a Poisson distribution approximates the binomial distribution when N is very large and p′X , 1 or (1 - p′X) , 1. To inspect distributions in reactions that had not reached equilibrium when sampled by the mass spectrometry, a computational model was established (see the Supporting Information) which assumes pseudo-first-order reaction conditions, with rate constants k′Xoff and k′Xon defined by
k′Xoff ) kXoff[Y]bulk k′Xon ) kXon[X]bulk
k′Xoff ) 1 - pX k′Xoff + k′Xon
pX ) QX )
m[MXmYN-m]
m)0
NcNP
(8)
The nonequilibrium distribution for any given value of QX can be exactly duplicated (within the limits of computational accuracy) by the binomial equation so that the preceding equation is applicable to mixed monolayer distributions under nonequilibrium as well as equilibrium conditions. At equilibrium,
QX,eq pX k′Xon ) ) QY,eq pY k′Xoff
(9)
This analysis has shown that the shape of the exchanged ligand distribution is given by the eq 3 binomial distribution. It does not matter whether the system is at equilibrium and pX is defined by eq 5 or 6 or if the system is not at equilibrium and pX is defined by eq 8 (a definition that is also valid for the equilibrium condition). While the finite difference equations were solved for pseudo-first-order reaction conditions, the analysis of the distributions requires only that the values of the rate constants, k′Xon and k′Xoff remain identical for all sites at any instant. Temporal changes in the values of k′Xon and k′Xoff would complicate the time course of the exchange reactions; however, the analysis of the distributions is unaffected. To fit the experimental data, the experimental distribution is represented by amplitudes (heights of the MALDI-TOF peaks) Am,exptl which are assumed to be proportional to the fraction of nanoparticles with m remaining ligands. These data can be renormalized (see eqs 8 and 9) to define θm,exptl
(4)
Am,exptl N
∑
(10)
Am,exptl
m)0
from which (see eq 8) N
(5)
and the corresponding probability of site occupancy by ligand Y is
pY )
N
∑
θm,exptl )
At equilibrium, the probability pX that any given site is occupied by ligand X is
k′Xon pX ) k′Xoff + k′Xon
equilibrium distribution. During computational examination of the finite difference model, we observed (see Table S-1 of the Supporting Information) that the distributions obtained for reactions not at exchange equilibrium are also exactly described by the binomial distribution if at any time t, pX is defined in terms of QX, the fraction of the total X-ligands which have been replaced by Y-ligands; i.e.,
(6)
Combining the above probability relations with the finite difference expression used in the computation gives a relation
(m + 1)k′Xoff[MXm+1YN-m-1]eq + (N - m + 1)k′Xon[MXm-1YN-m+1]eq [MXmYN-m]eq ) (7) mk′Xoff + (N - m)k′Xon that we demonstrate (see the Supporting Information) can be deduced directly from the binomial expression eq 2 for the
pX,exptl ) QX )
∑
1 mθ N m)0 m,exptl
(11)
where QX is the fraction of X-ligands at any given time (the system need not be at equilibrium (see the Supporting Information) and pY,exptl ) 1 - pX,exptl. In principle, since the value of N is known (N ) 18), a theoretical distribution, θm,theor, is straightforwardly computed from the binomial expression
N! ) (1 m ! (N - m)! N! (12) pX,exptl)N-m(pX,exptl)m m ! (N - m)!
θm,theor ) (pY,exptl)N-m(pX,exptl)m
No adjustable parameters are required to generate the values of θm,theor. The distribution θm,exptl (for a given value of N) depends only on the value of pX,exptl and, usefully, does not depend upon
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Figure 4. Simulated ligand exchange distributions (f ) relative peak amplitudes) obtained as a function of time using the kinetic ligand exchange model.
maintaining pseudo-first-order reaction conditions (see the discussion in the Supporting Information). To illustrate results from the preceding theory, Figure 4 shows a series of predicted relative peak amplitudes (f), for N ) 18 and for selected values of normalized time kXoff t. The figure depicts the progress of replacing X (the -SCH2CH2Ph thiolate) with Y (another thiolate) that starts with a short-time distribution (at back) that is nonsymmetrical because it abuts the m ) 18 limit, progressing to a long time distribution (at front) that is also nonsymmetrical, abutting the limit of m ) 0. In between, the exchange causing the distribution to move from right to left, the amplitude distributions appear reasonably symmetrical on the scale shown, but close examination shows that, like Figure 3, there is some asymmetry as expected for small or large values of m. Strictly speaking the binomial distribution will be symmetrical only12 when pX ) 0.5. The asymmetry shown in Figure 4 is mirrored in the experimental data of Figure 5, which presents expanded views of selected spectra from Figures 1 and 2. The theoretical distributions shown in Figure 4 are qualitatively similar to the experimentally observed distributions for the exchange reactions shown in Figures 1 and 2. Experimental and theoretical distributions were quantitatively compared by computing θm,exptl and pX,exptl from the experimental data (see eqs 10 and 11 and associated discussion) and then computing θm,theor using eq 12. Figure 6 shows results of such comparisons for several of the experimental exchange results. These comparisons probe whethersor notsthe distributions of ligands on the exchanged nanoparticles are solely due to randomness in the exchange process; i.e., all ligand sites are identical to one another and react independently. Panels a and c in Figure 6 show exchange data (black points) for exchanges with hexanethiol and thiophenols, and the corresponding best fit of the binomial distribution shape (red points), centered on the experimental maximum. Figure 6b similarly compares the mixed ligand Brust synthesis results to the binominal distribution expectations. We see that the experimental distribution in Figure 6a is welldescribed by the theory, assuming that N ) 18, indicating that the exchange is reasonably random. The difference in the reactivities of the two kinds of ligand sites8d,11 (discussed in the Introduction) seems to be insufficient to disturb the apparent randomness. On the other hand, the distribution of ligand data in Figure 6c is clearly more narrow than anticipated by random
Figure 5. Ligand exchange product distributions demonstrating nearequilibrium state (a) thiophenol (1 to 0.33 mole ratio of incoming thiols to nanoparticle ligands) and illustrating the apparent asymmetry distributions as they change with time in (b) hexanethiol (1:1 mole ratio of incoming thiols to nanoparticle ligands) and (c) thiophenol (1: 50).
exchange statistics with the assumption that N ) 18. Evidently some specific chemical factors are at work. The near ideality of the Figure 6a fit suggests that the origin is not intrinsically different nanoparticle site reactivities but instead is associated with how the thiophenolate ligands interact with the phenylethanethiolate and other thiophenolate ligands during the ligand exchange reaction. While an explanation in more depth is not available at this time,13 the nonideality of the ligand exchange was uniquely detected by the MALDI experiment which offers a way to detect, for example, ligand effects on nanoparticles akin to microphase segregation in two-dimensional self-assembled monolayers.
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Dass et al. Research. We thank George R. Dubay, Duke University Department of Chemistry, for access to the MALDI instrumentation. S.W.F. thanks John Miller and the Chemistry Department, Brookhaven National Laboratory, for support of a Guest Appointment. Supporting Information Available: Details of kinetic model simulation, of NMR peak intensity integration, and of laser pulse intensity sensitivity (from ref 10e). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes
Figure 6. Comparison of experimental ligand exchange data (black circles) with the simulated binomial fit (red circles): (a) hexanethiol ligand exchange, (b) hexanethiol/phenylethane thiol mixed Brust synthesis, and (c) thiophenol ligand exchange. N ) 18 was used to compute θm,theor (see eqs 10-12); and the resultant values of pX and the residual, r, are indicated in each panel.
Finally, it is worth noting that numerous parallels can be drawn between the above analysis and other chemistries, such as protonation of polyprotic acids and ligand exchange on metal complexes. These cases both, however, carry extra complexities of electrostatic effects and alterations of metal electronic structure, so that the proton and ligation sites become not truly independent of one another. Perhaps exchange aquation of a metal ion by H2O and D2O would be a useful example, but we are not aware of a statistical analysis such as that above. In that sense, the multisite gold nanoparticles offer a unique view of randomness (at least for Figure 1) in chemical events that can take numerous different courses. Acknowledgment. This research was supported by grants from the National Science Foundation and the Office of Naval
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