The Impact of the Polymer Chain Length on the Catalytic Activity of Poly(N-vinyl-2-pyrrolidone)-supported Gold Nanoclusters

Poly(N-vinyl-2-pyrrolidone) (PVP) of varying molecular weight (M w = 40-360 kDa) were employed to stabilize gold nanoclusters of varying size. The resulting Au:PVP clusters were subsequently used as catalysts for a kinetic study on the sized-dependent aerobic oxidation of 1-indanol, which was monitored by time-resolved in situ infrared spectroscopy. The obtained results suggest that the catalytic behaviour is intimately correlated to the size of the clusters, which in turn depends on the molecular weight of the PVPs. The highest catalytic activity was observed for clusters with a core size of ~7 nm, and the size of the cluster should increase with the molecular weight of the polymer in order to maintain optimal catalytic activity. Studies on the electronic and colloid structure of these clusters revealed that the negative charge density on the cluster surface also strongly depends on the molecular weight of the stabilizing polymers.


Results
Size matters, but 'smaller' is not necessarily better than 'larger'. AuNCs of varying size, stabilized by PVPs of varying molecular weight, were prepared according to previously reported procedures (Fig. S1-S3 in Supplementary Information) 18,20,21 . The size-dependent AuNC-catalyzed oxidation of 1-indanol (Fig. 2a) was selected due to its very short reaction times, the absence of potential alternative pathways, and the possibility to  monitor the reaction in situ 22,23 . This allows avoiding the agglomeration of AuNCs during the reaction, and hence only the catalytic activity of AuNCs is determined. To quantify the matrix effect as well as the size-dependence on the catalytic activity, we examined the aerobic oxidation of 1-indanol (1a) catalyzed by AuNCs containing PVP of varying molecular weight, i.e., PVP (K-30) (M W = 40 kDa), PVP (K-60) (M W = 160 kDa), and PVP (K-90) (M W = 360 kDa). The progress of this reaction was monitored in situ using a fourier transform infrared (FTIR) spectrophotometer with an attenuated total reflection (ATR) accessory unit, which allowed recording the C = O stretching frequency of the reaction product 1-indanone (2a). The IR spectra were collected in intervals of 27 seconds, and the obtained time-resolved IR spectra are shown in Fig. 3. The AuNC size and the properties depending on the length of the PVP chain are summarized in Table S1 and Fig. S4 (in Supplementary Information), wherein the normalized rate constant k norm refers to the reaction rate per unit of surface area which can be obtained by assuming a spherical shape (Supplementary Information) 1,24 .
The size-dependent properties of Au:PVP (K-30) exhibited a trend similar to that observed in the reaction of p-hydroxy benzyl alcohol: 1 smaller catalysts promote the reaction faster than larger catalyst (Fig. S5 in Supplementary Information). After normalizing the rate constants, the catalytic activity of larger clusters was slightly elevated. In case of Au:PVP (K-60), a similar result was obtained, although the trend was found to shift in favor of larger clusters. However, the size-dependence of Au:PVP (K-90) was substantially different to those of Au:PVP (K-30) and Au:PVP (K-60). For smaller clusters (core size < 2 nm), Au:PVP (K-90) showed inferior activity compared to Au:PVP (K-30), while the activity increased drastically upon increasing the particle size in  the range of 0.8-7.0 nm (Fig. 4). The normalized rate constant of Au:PVP (K-90) (core size: 7 nm) was five times higher than that of Au:PVP (K-30) (core size: 1.3 nm), which was previously used as a benchmark catalyst.
Subsequently, we investigated the size and matrix effects of these reactions under previously reported conditions [25][26][27] . The aerobic homocoupling of potassium trifluorophenyl boronate (2a) affords biphenyl (2b), while the intramolecular hydroalkoxylation of 1,1-diphenyl-4-penten-1-ol (3a) furnishes cyclization product 3b. The approximate activity of each catalyst was determined based on the yield of the corresponding products. The reaction was stopped after 4 h, and the yield of 2b and 3b was determined by GC (Table S2 and S3, Fig. S6 in Supplementary Information). In these reactions, similar trends as in the aerobic oxidation of 1a were observed, i.e., the highest catalytic activity was observed for Au:PVP (K-90) (core size: 7 nm). It should also be noted that the reaction time for the aerobic homocoupling, as well as for the intramolecular hydroalkoxylation was substantially shortened from 16-24 h (conventional conditions) to 4 h when Au:PVP (K-90) (core size: 7 nm) was used.
As these results clearly demonstrate that the polymer matrix effect is not limited to specific substrates or reactions, the polymer matrix should play an important role for the catalyst activity. Moreover, these results suggest that it should be possible to tune the catalytic activity of the PVP-stabilized AuNCs via the polymer matrix.
The electronic structure of Au:PVP. Among the series of Au:PVP derivatives tested, Au:PVP (K-90) (core size: 7 nm) exhibited extremely high catalytic activity in all three reactions. In order to better understand the origins of this outstanding catalytic performance, we wanted to determine the electronic structure of these AuNCs, and find out if an effect of the polymer matrix could be established. The analysis of the electronic structure was achieved by X-ray adsorption (EXAFS and XANES) and X-ray photoelectron spectroscopy (XPS) (Fig. S7-S8 in Supplementary Information). Table 1 and Table S4 (in Supplementary Information) show the EXAFS and XANES data, whereby the former are in good agreement with the TEM results. The Au-Au coordination number CN, as well as the interatomic bond lengths R increase with increasing core size. All Au:PVP clusters show a noticeable decrease of bond lengths compared to Au foil (2.88 Å). The contraction of the metallic bond distance in these AuNCs should also lead to changes of their electronic properties 28 . However, the relatively small alteration of the bond lengths in the larger AuNCs relative to Au foil suggests that these should be less effective in catalytic reactions. Moreover, in most of the cases and virtually for all core sizes, Au:PVP (K-90) exhibited significantly smaller coordination numbers than PVP (K-30) and PVP (K-60) (cf. entries 1-4, 7-9, 13-15). It can therefore be concluded that the increasing molecular weight of the stabilizing polymer resulted in a morphological change of the metal surface.
Although an analysis of the XANES-derived edge energy values for the Au:PVP clusters suggested that their Au cores exhibit a more anionic character than Au foil, it should be noted that the comparison of the observed small edge energy differences was difficult, mostly due to the low resolution and concentration of gold in these clusters system. Therefore, we decided to further examine the size-dependence of the electronic structures of the Au:PVP clusters by XPS. The electron density of the Au cores can be determined experimentally by XPS via the binding energy (BE) of Au4f 7/2 . The XPS data showed a primary Au4f 7/2 band for the Au atoms accompanied by the corresponding satellite peaks. The width of the observed peaks is thereby indicative of a contribution of Au atoms with different electron density. Particularly, the significantly smaller BE of Au4f 7/2 relative to bulk gold (84.0 eV) suggests that the negative charge on the gold surface in Au:PVP arises from the interaction between the gold surface and the polymer matrix ( Table 1, Fig. S8 in Supplementary Information) 2 . The BE of Au:PVP (K-90) (entries 13-17) decreases with increasing core size (≤ 9 nm) before increasing with further increasing core size. Au:PVP (K-90) (core size: 9 nm) (entry 18) exhibits a significantly increased BE relative to the smaller clusters, due to the decreased electron density on the gold surface. The Au 4f 7/2 BE for Au:PVP (K-90) (core size: 7 nm) (entry 17) is clearly smaller than that for the other clusters, indicating the highest negative charge on its surface, which is in good agreement with the results of the catalytic activity study.
Although the BE of Au4f 7/2 and its catalytic activity are not perfectly proportional (Fig. 5), it should nevertheless be useful to compare these correlations with similar catalyst systems, e.g., with Au:PVP (core size: 1.3 nm). The smallest BE value was observed for Au:PVP (K-30) (entry 1), followed by Au:PVP (K-60) (entry 7), and Au:PVP (K-90) (entry 14). These results are consistent with the experimental data that Au:PVP (K-30) with small cores exhibited the highest catalytic activity (Fig. 4a).
Another possible explanation is the geometrical effect by changing the crystallinity. For example, the TiO 2 -supported poly-crystalline Au showed twice the activity of that single crystalline Au/TiO 2 system 29 . Tsukuda and co-workers also reported that icosahedral Au 144 clusters supported on hierarchically porous carbon exhibited superior catalytic activity to the smaller fcc Au clusters 30 . To confirm the structural differences in each clusters, we carried out the high-resolution TEM (HR-TEM) and powder X-ray diffraction (PXRD) measurements. HR-TEM measurement revealed that, in case of relatively larger cluster (more than 5 nm), most of the cores were polycrystals regardless to the polymer length (Fig. S2, Supplementary Information). In addition, PXRD measurement suggested that the larger clusters mainly keep fcc structures (Fig. S3, Supplementary Information) 31 . Although this morphological effect on the catalytic activity should not be ignored, it is difficult to explain the significant difference of the catalytic activity of 7 nm-sized Au:PVP (K-30) and Au:PVP (K-90). Therefore, AuNCs should thus be intimately correlated with mainly the electronic properties on the surface of the gold cluster, and it can hence be concluded that the excellent catalytic activity of Au:PVP (K-90) (core size: 7 nm) may be attributed to the highly negative charge density on its surface.
The electronic structure studies also revealed that Au:PVP (K-90) (core size: 7 nm), which exhibited high reactivity, possessed more anionic nature. This behavior may be rationalized in terms of electron affinity on the gold surface, as the partial electron transfer from PVP to the core gold leads to bond activation of the substrate prior to participation in the catalytic cycle 25 .
Structural analysis of the colloidal Au:PVP. Considering the aforementioned results in their entirety, it can be concluded that the excellent catalytic activity of Au:PVP (K-90) (core size: 7 nm) should be ascribed to the high negative charge on the cluster surface. This however poses the question: why does Au:PVP (K-90) (core size: 7 nm) possess such a highly electronegative surface? In order to answer this question, we examined the physical structure of the AuNCs and the effect of the stabilizing PVP on the AuNCs surface. We measured the size of the Au:PVP colloids by the induced grating method (IG method), which includes an activation procedure induced by dielectrophoresis to form a particle grating and measures the decay of the diffracted light. It thus provides a highly sensitive and reproducible means to measure single colloids down to the nanometer scale. The advantage of the IG method over dynamic light scattering (DLS) is that the former is immune to the inaccuracies arising from contamination with large particles, with which the results of the latter are inevitably associated 32,33 . Fig. 6 and   Supplementary Information) show the relationship between Au:PVP colloid size and core size. The colloid size of most Au:PVP (K-30) was 40 ± 10 nm, irrespective of the core size and the polymer chain length, while the colloid size of free PVP was ~100-200 nm. The colloid size of both Au:PVP (K-60) and Au:PVP (K-90) decrease with increasing core size (Fig. S9-S10 in Supplementary Information).
Judging from the volume in the presence of short-chained polymers, Au:PVP colloids consist predominantly of water (>90%), indicating that the gold cluster should be drifting in diluted aqueous PVP solutions, reminiscent to an egg of frog model (Fig. 7a), which reminds us a frog egg surrounded by jelly-like blob in frogspawn. Recent results obtained from MD-DFT calculations indicated that PVP moieties bind much closer to metal surfaces than H 2 O. Consequently, the PVP concentration should be increased in close spatial proximity of the cluster, which might explain the stabilizing effect of PVP 31 . However, the physical structure of the interface between the gold surface and the PVP matrix must be loose and soft. In contrast, when the bigger clusters are wrapped with high-molecular-weight polymers, the polymer should wrap around the Au core and thus afford higher surface coverage 34 and more entangled structures (Fig. 7b). In such entangled structures, the hydrogen-bonding network should be eliminated, which would result in contracted colloids. Indeed, the aforementioned calculations suggested that virtually no water should be included in Au:PVP (K-90) (core size: 7 nm) colloids. Therefore, it can be  concluded that a strong interfacial interaction is induced when the chain length of the stabilizing polymer and the core size of the metal cluster are matched, emerging the highly electronegative surface on the metal core.

Conclusion
In summary, we were able to demonstrate that Au:PVP catalysts promote a variety of reactions. In all cases, the properties of Au:PVP depend on the cluster size. However, morphological effects can surpass the size effect and control the catalytic activity. From an applications-driven perspective, it is highly promising that the catalytic activity of AuNCs can be modulated by the cluster size and by the polymer matrix. Our experimental results revealed that Au:PVP (K-90) (core size: 7 nm) exhibited a catalytic activity that was up to five times higher than that of Au:PVP (K-30) (core size: 1.3 nm). The extremely high activity of the former should be ascribed to the high surface coverage of the gold core with PVP (K-90), which should lead to a high density of negative charges on the core surface. The analysis of the physical structure suggested a difference in surface morphology. Even though the interface between the Au surface and the PVP matrix is usually loose, this is not the case for long PVP chains. AuNCs stabilized by long-chain polymers result in highly entangled structures via entanglement of the Au surface with PVP, which increases the electronegativity on the surface of the cluster. However, it is still extremely difficult to experimentally determine the structure of this interface precisely, and new experimental methods as well as the computational studies are required to advance research in this area.