Photoswitching of Azobenzene-Functionalized Molecular Platforms on

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Photoswitching of Azobenzene-Functionalized Molecular Platforms on Au Surfaces Ulrich Jung,† Christian Schütt,‡ Olena Filinova,† Jens Kubitschke,‡ Rainer Herges,*,‡ and Olaf Magnussen*,† †

Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, Leibnizstrasse 19, 24118 Kiel, Germany Otto-Diels-Institut für Organische Chemie, Christian-Albrechts-Universität zu Kiel, Otto-Hahn-Platz 3, 24098 Kiel, Germany



S Supporting Information *

ABSTRACT: The photo- and thermally induced switching of well-ordered molecular arrays of free-standing functional groups, formed by self-assembly on Au surfaces, were studied by photoelectrochemical methods (cyclic voltammetry, chronoamperometry) and surface plasmon resonance spectroscopy. These molecular adlayers exhibit azobenzene functions mounted vertically on the surface via molecular platforms on the basis of triazatriangulenium. Detailed quantitative studies of the switching kinetics revealed that the photoinduced trans−cis isomerization of the azobenzene groups in these adlayers proceeds very fast and highly reversible. Cis−trans backisomerization by thermal relaxation occurs surprisingly 4−5 orders of magnitude faster than in solution. A rapid thermal cis−trans relaxation that dominates over the photoinduced processes is also supported by the pronounced increase of the cis fraction in the adlayers with irradiation intensity and the weak dependence of the isomerization time constants on the intensity. In complementary density functional theory calculations of the cis isomer on a Au cluster, no significant electron density depletion of the azo moiety, but strong electronic coupling of the switchable group with the Au substrate, were found. We propose that the latter leads to a spin exchange between conduction electrons in the metal and the azo moiety, enabling a relaxation mechanism that is forbidden for the free molecule.



INTRODUCTION Attaching photoswitchable molecules to solid surfaces is of substantial interest for the preparation of advanced nanosystems, leading to a wide variety of applications, for example, information storage, (bio)sensors, and molecular machines.1,2 Such systems are commonly prepared by self-assembly of photofunctional molecules onto appropriate substrates.3−5 However, photoswitching in these adsorbate layers is often considerably affected or even completely quenched because of interactions between the substrate and the adsorbate molecules (e.g., electronic coupling)6 as well as intermolecular interactions (e.g., steric hindrances7,8 or excitonic coupling9). Typical approaches to reduce these interactions and thus to preserve the function employ molecules with additional spacer groups10 or mixed adlayers of the functional molecules with appropriate spacer molecules.7,8 Unfortunately, these systems often lack structural order and, in the case of mixed adlayers, exhibit a tendency for phase separation.7,8 To overcome these problems of conventional (photo)functional adlayers, recent studies employed more sophisticated approaches based on specially designed molecules (e.g., molecular tripods11,12). We have introduced the so-called platform concept13−16 and implemented it using derivatives of the triazatriangulenium (TATA) ion (Figure 1a). The TATA platforms can be functionalized vertically at the center as well as © XXXX American Chemical Society

laterally at the edges, providing a very modular template. Extensive structural studies by scanning tunneling microscopy,13−15 surface-enhanced Raman and X-ray photoelectron spectroscopy,15 and electrochemical methods15 revealed that the TATA molecules form well-defined hexagonally ordered adlayers on Au(111), with the platforms lying flat on the substrate, the central functional groups oriented perpendicular to the surface, and the intermolecular distances controlled by the steric demand of the side groups attached to the platforms. As the central functional groups, derivatives of azobenzene were used, which arguably are the most extensively studied class of photoswitchable compounds. Azobenzene can be converted from the thermodynamical stable trans to the metastable cis isomer by irradiation with UV light of 365 nm, and backisomerization can be induced by irradiation with blue light of 435 nm or occurs via thermal relaxation.17 In addition, both isomers can be reduced in a two-electron/two-proton transfer to hydrazobenzene, from which they are oxidized back to the trans isomer18 (Figure 1b). The isomerization reactions are accompanied by large changes in the geometrical, electronic, and optical properties and occur fast and highly reversible.19 Azobenzene-containing adlayers attached to solid Received: October 22, 2012

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immersion was carried out at room temperature, but in some cases the solutions were heated to 30−80 °C to increase the surface mobility of the adsorbate molecules. Afterward, excess TATA molecules were removed by immersing the samples for 1−30 min in the pure solvent, were dried in air, and were immediately used for the experiments. Instrumentation. For irradiation of the samples, LEDs at 365 ± 9 nm (Nichia) and 450 ± 10 nm (Seoul Semiconductors) were used. The photoelectrochemical experiments were performed in hanging-meniscus geometry using a homemade electrochemical cell, in which the sample could be irradiated from below through a quartz glass window,26 and a Compactstat (Ivium) or an Autolab (Eco Chemie) electrochemical workstation. As reference electrode a saturated calomel electrode (SCE) was used. The electrolyte was 0.1 M NaClO4 with Britton−Robinson buffer at pH 5 (suprapure grade, Merck and Sigma Aldrich) and deaerated with Ar (5.0 purity, Air Liquide). The roughness factor of the electrode obtained from the charge of the gold oxide reduction was approximately 1.2 for freshly polished crystals. The SPR measurements were performed using a SR7000DC dual channel SPR instrument (Reichert). The sample was mounted in a flow cell with two reaction channels filled with ethanol (spectroscopy grade, Merck). In one of the channels, the sample could be irradiated through a quartz glass window; the other channel with the sample in the dark served as reference. The SPR signal was measured as the difference of the nearsurface refractive index Δn between the channels at a rate of 0.5 Hz. Residual long-term linear drift of the signal, caused by small pressure or temperature changes, which are common problems of this technique,36 was subtracted from the data. DFT Calculations. DFT calculations of a molecule of type 1a/2a, but with methyl side chains, in trans and cis configurations on a Au cluster (see Figure 1b) were performed at the PBE37/SV(P) level of theory including Grimme D338 parameters for dispersion treatment using TURBOMOLE 6.2.39 The cluster includes 170 Au atoms in 4 layers and exhibits D3d symmetry. On both extended Au(111) facets a molecule was adsorbed. Advantages of this model are in particular its inherent Ci symmetry and cancelation of induced dipole errors. First, the Au cluster was fully geometryoptimized. Afterward, the coordinates of the Au atoms were fixed and the TATA molecules optimized. It is obvious that Au clusters of limited size cannot adequately describe the properties of bulk Au. However, for a TATA molecule with an ethynyl azobenzene unit that extends to more than 14 Å above the gold surface, and with a distance to its next neighbor of more than 10 Å, calculations including plane wave methods and periodic boundary conditions are difficult. Moreover, the PBE functional in conjunction with the atom-centered SV(P) basis predicts the molecular properties of the free azobenzene exceedingly well. Focusing on the properties of azobenzene and their perturbation by the interaction with the Au surface rather than on the perturbation of the gold surface by the molecule, the atom centered MO approach is preferred here.

Figure 1. Azobenzene-functionalized TATA molecules. (a) Derivatives used in this study. (b) Simplified TATA molecules of type 1a/2a with methyl side groups in trans (left) and cis configuration (right) on a Au cluster illustrating the trans and cis isomerization in the investigated adlayers. The molecular structure is based on the results of the DFT calculations.

surfaces, predominantly thiols on Au, have been widely studied.5 While electrochemical reduction and oxidation of the azobenzene moieties in these adlayers is commonly observed,20−28 resulting in characteristic redox peaks in cyclic voltammetry studies, photoswitching is only reported in comparably few cases.23,26,28 A comprehensive overview about the properties of photoswitchable azobenzene-containing thiol adlayers can be found in our previous publication.26 Here, we describe quantitative studies of the photoswitching of azobenzene-containing TATA adlayers on Au surfaces. Our results demonstrate that the novel platform concept indeed enables fast and highly reversible photoisomerization, but also reveal an unexpected acceleration of the thermal cis−trans backisomerization of the adsorbed molecules by several orders of magnitude as compared to solution. On the basis of density functional theory (DFT) calculations, we attribute the latter tentatively to the interaction with the metal substrate, specifically a qualitative change in the backisomerization mechanism.



EXPERIMENTAL SECTION Synthesis and Adlayer Preparation. TATA platform synthesis30 and adlayer preparation13,14 were described in detail in our previous publications. All compounds were characterized by NMR and mass spectroscopy and exhibit a purity of >99%. For the photoelectrochemical experiments, flame-annealed Au(111) single crystals (MaTecK) and for the SPR measurements thin Au films (40 nm) on glass (XanTec) were employed. These substrates were immersed for 30−60 min into 5 × 10−7 to 1 × 10−3 M solutions of the TATA molecules in ethanol or toluene (spectroscopy grade, Merck). Typically,



RESULTS AND DISCUSSION The isomerization reactions in azobenzene-functionalized TATA adlayers on Au(111) were predominantly studied by systematic photoelectrochemical experiments, in which sequences of cyclic voltammograms (CVs) were recorded to explore the effect of UV irradiation (365 nm). As an example, data for a 2a adlayer are shown in Figure 2a, starting with the sample B

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different redox reactivity was obtained than in the subsequent cycles, demonstrating that cis azobenzene was stable in these adlayers against thermal relaxation. The highly reversible behavior of the azobenzene-functionalized TATA adlayers already gives a first indication for an unusually rapid thermal cis−trans backisomerization, an issue that will be addressed in detail in the following. The UV-induced change of the charge density of hydrazobenzene oxidation provides a convenient method for studying the isomerization reactions in these adlayers (Figure 2b). Although the photoisomerization yield cannot be determined directly, because only a fraction of the azobenzene moieties is accessed in the redox reactions, comparison of the light-induced oxidation charge density (1.1 μC cm−2) with that of the peak obtained in full redox cycles (9.6 μC cm−2) indicates that a considerable fraction (∼10%) of the azobenzene moieties is interconverted from the trans to cis state. For the adlayers of all studied azobenzene-functionalized TATAs, a very similar isomerization behavior was identified (Figure 2b). In particular, no effect of the head groups attached to the azobenzene moiety was found, as it is expected, because steric hindrances should not have a strong effect on the redox reactivity in these very open adlayers. According to the data shown in Figure 2a, the trans−cis photoisomerization as well as the (thermal) backisomerization are completed in the time between two subsequent potential cycles (∼150 s). To assess the kinetics of the isomerization reactions more quantitatively, additional CV experiments were performed, in which the irradiation conditions were systematically varied. The trans−cis photoisomerization was studied as follows: UV irradiation of the sample in the trans state was started at variable times before sweeping the potential through the oxidation peak. To obtain only the additional current associated with the reduction of cis azobenzene, the anodic current of the adlayer in the trans-saturated state, measured in a subsequent CV, was subtracted. The resulting data show a clear increase in the differential peak current with increasing irradiation time up to saturation, reached after ∼20 s (Figure 2c). The corresponding differential charge density of the hydrazobenzene oxidation peak (Figure 2c, inset) was obtained by peak fitting after subtracting the nonlinear background resulting from azobenzene reduction (see the Supporting Information). It indicates a first-order trans−cis isomerization kinetics with a time constant of 4.3 ± 0.1 s for this adlayer (the data for irradiation times less than 5 s were omitted from this analysis due to the overlap of the oxidation peak with the current jump due to the start of UV irradiation). Analog experiments were carried out to study the cis−trans isomerization by thermal relaxation. Here, the sample was initially irradiated with UV light until a photostationary mixed cis−trans state was obtained (cis-saturated state). Next, the relaxation from this state was studied by switching off the UV light at variable times before sweeping the potential through the oxidation peak. Figure 2d shows a series of differential anodic half-cycles for different relaxation times after UV irradiation. The corresponding differential oxidation charge density (Figure 2d, inset) again reveals a first-order kinetics with a time constant of 4.3 ± 0.8 s. For all studied adlayers of different azobenzene-functionalized TATA adlayers on Au(111), highly reversible first-order kinetics with time constants of 3−16 s were identified (Figure 3a). These time constants were reproducibly obtained with average errors of ∼30% for identically prepared samples and

Figure 2. (a) Cyclic voltammograms (CVs) of a 2a adlayer on Au(111) in the dark (cycles 1, 2), during UV irradiation (365 nm, 25.6 ± 1.4 mW cm−2, cycles 3, 4), and again in the dark (cycles 5, 6). The measurements were performed in 0.1 M NaClO4 and Britton− Robinson buffer (pH 5) at a sweep rate of 0.02 V s−1. (b) Lightinduced changes of the oxidation charge density for adlayers of different azobenzene-functionalized TATAs. For better comparison, the data are displayed with an offset. Zero currents or charge densities, respectively, are marked by dotted lines. (c) Kinetics of the trans−cis photoisomerization and (d) cis−trans isomerization by thermal relaxation for a 2a adlayer, assessed from the anodic half-cycles of the CVs, recorded for (c) different UV irradiation times and (d) different relaxation times in the dark, respectively. Shown are the changes in current density relative to the trans state, obtained after full relaxation in the dark. Corresponding differential oxidation charge densities as a function of time are shown in the insets.

completely relaxed in the dark, that is, with all azobenzene moieties in the trans state. The negative potential limit of the CVs was set to the onset of trans reduction (manifesting as an increasing cathodic current negative of ∼ −0.1 V), resulting in a small hydrazobenzene oxidation peak in the subsequent anodic potential sweep (Figure 2a, cycles 1, 2). Upon UV irradiation (cycles 3, 4), the cathodic current in the positive shoulder of the redox peak increases, starting from potentials as positive as ∼0.1 V, and the oxidation peak increases accordingly. These changes of the redox reactivity are fully reversible, as illustrated by the subsequent cycles (cycles 5, 6) recorded after switching off the UV irradiation. They can be attributed to the photoinduced generation of cis azobenzene, which is reduced at more positive potentials.26 Different redox potentials of the trans and cis isomer, although not observed for the physisorbed pure compound,18 have already been reported previously for azobenzene-containing Langmuir−Blodgett films29 and thiolbound species.23,26 In contrast, irradiation with blue light (450 nm) was found to affect the redox reactivity only insignificantly, as expected from the low trans−cis photoisomerization cross section at this energy (see the Supporting Information). The UV-induced changes of the redox reactivity occur highly reversible. This is in clear contrast to the results of our previous study of SAMs of azobenzene-containing thiols on Au(111),15 where in the first cycles after UV irradiation a distinctively C

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changes of the refractive index of a 2a adlayer is shown in Figure 5a. Upon UV irradiation, the signal decreases gradually, whereas after switching off the irradiation it recovers again. Multiple repetition of this irradiation cycle demonstrates that these changes are highly reversible as in the photoelectrochemical experiments and can be analogously attributed to the photoinduced trans−cis and thermal cis−trans backisomerization, respectively. Both reactions follow first-order kinetics (Figure 5b and c) with very similar time constants of τtc = 48.1 ± 8.6 and τct = 54.0 ± 9.9 s. Figure 3. (a) Time constants of the trans−cis and cis−trans isomerization for different TATA adlayers. (b) Dependence of the saturated cis fraction in a 2a adlayer on the UV irradiation intensity demonstrated by the differential oxidation charge density (top) and of the time constants of the trans−cis and cis−trans isomerization (bottom).

were virtually independent of the irradiation intensity (Figure 3b). In contrast, the charge density difference between the cisand trans-saturated state clearly depends on the irradiation intensity, as it is expected for the case of fast thermal relaxation (see below). Further evidence for fast isomerization reactions in azobenzene-functionalized TATA adlayers comes from chronoamperometry measurements. As illustrated in Figure 4, the

Figure 5. (a) SPR measurement showing the photoinduced variations of the refractive index for a 2a adlayer on a Au thin film sample in ethanol upon irradiation with UV light (365 nm, 7.3 ± 2.2 mW cm−2). (b) Trans−cis and (c) cis−trans isomerization kinetics.

The photoelectrochemical and SPR measurements reveal a very similar behavior for the adlayers of all studied azobenzenefunctionalized TATA derivatives. Specifically, fast and highly reversible first-order isomerization reactions were identified in all cases, demonstrating facile switching in these adlayers. Moreover, the time constants of these processes determined by cyclic voltammetry are for all species in the range of a few seconds (Figure 3a). The time constants obtained in the SPR experiments are approximately 1 order of magnitude larger than those found in the photoelectrochemical experiments. The difference might be caused by the different sample environment (ethanol instead of aqueous electrolyte), the different kind of substrate (thin, rough Au films rather than well-defined Au(111) single crystals), and the 3 times lower irradiation intensity. Similar differences between the time constants obtained in SPR and CV measurements were also observed in our previous study of azobenzene-containing thiols on Au.26 The isomerization behavior can be explained by a simple model in which the isomerization reactions are described by the rate constants of the photoinduced trans−cis and cis−trans isomerization ktc and kct, respectively, and the rate constant of the thermal relaxation kT (see the Supporting Information). In this case, the time constant for trans−cis transition in the adlayer is given by τtc = (ktc + kct + kT)−1, whereas the time constant for cis−trans transition is τct = k−1 T , that is, solely determined by the thermal relaxation. In our experiments, the time constants of the trans−cis isomerization are similar to those of the cis−trans isomerization. Within the model, this is only possible if the rate constant for cis−trans isomerization is

Figure 4. Chronoamperometry measurements of a 2a adlayer on Au(111) in 0.1 M NaClO4 and Britton−Robinson buffer (pH 5) showing (a) the photoinduced trans−cis isomerization and (b) the thermal cis−trans relaxation at −0.025 V (365 nm, 24.9 ± 3.7 mW cm−2). For comparison, the absence of these currents at a potential clearly positive of the redox regime (0.1 V) is shown.

start and termination of the UV irradiation result in a pronounced transient photocurrent response, if the potential is kept in the range where the cis isomer can be reduced. In contrast, only small current steps can be found at potentials positive of the azobenzene redox regime. These current transients can be rationalized by changes in the coverage of the redox active cis isomer, caused by its photoinduced generation or thermal decay, and demonstrate that these isomerization reactions also occur at constant electrode potentials. Although the complex interplay between photoand electrochemically induced reactions hinders a facile quantitative determination of the various involved time constants from these data, it is obvious that they must proceed on a time scale similar to that in the CV experiments. In addition to the electrochemical experiments, the isomerization reactions of selected TATA adlayers on thin, rough Au substrates in ethanol were studied by surface plasmon resonance (SPR) spectroscopy, an established method to study the photoswitching in azobenzene-containing adlayers.7,8,26 A typical experiment revealing the photoinduced D

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dominant, that is, if the relaxation occurs faster than the photoinduced processes. Because of the relatively large experimental errors, a clear separation of the relaxation and the photoinduced processes is not possible. However, the rate constants ktc and kct must be at least 1 order of magnitude smaller than kT. Moreover, a dominant thermal relaxation can also explain the low fraction of cis isomer in the cis-saturated state in the adlayer as compared to solution (e.g., for 2a ∼10% in an adlayer versus ∼80% dissolved in dichloromethane), the weak dependence of the time constants on the irradiation intensity, and the increase in the cis saturation charge density with intensity. The pronounced thermal cis−trans relaxation of the platform-mounted azobenzene derivatives within adlayers on Au is unexpected and highly interesting. Whereas the cis state of the free molecules in solution is relatively stable and thermally relaxes back to the trans state with time constants of 38 000−125 000 s,30 this process occurs for the same species adsorbed on Au within a few seconds, that is, 4−5 orders of magnitude faster. Obviously, the interaction with the metal substrate very substantially lowers the kinetic barrier for relaxation into the stable trans state. To clarify this behavior, DFT calculations of a simplified azobenzene-functionalized TATA molecule on a Au cluster (see Figure 1b) were performed. According to these calculations, the main structural change is a flattening of the TATA platform as compared to the free molecule, whereas the azo moiety is virtually unaffected. A natural bond orbital analysis leads to the conclusion that the Au cluster is slightly negatively charged (by −0.33 e). However, the electron density of the azo group is not severely influenced by the Au cluster. Hence, lowering the stability of the cis isomer by a reduction of the electron density of the azo group, a well-known effect for azobenzenes substituted with electron pushing and pulling groups in solution,31 cannot explain the substantially accelerated thermal backisomerization in these systems. Additional model calculations of the isomerization mechanism of the azobenzenefunctionalized TATA reveal an energy barrier for cis−trans isomerization via inversion of 0.86 eV (Figure 6a), which is in good agreement with the results of temperature-dependent UV−vis spectroscopy experiments.32 For the singlet state rotation (Figure 6b), the S0 transition state could not be exactly determined because of a conical intersection, similar to that already reported previously,33 but the extrapolated value is 0.26 eV higher than the S0 inversion transition state. Interestingly, the calculated T1 transition state is 0.22 eV lower. For the bare molecules, the singlet−triplet conversion is spin-forbidden. However, the latter is not necessarily true for molecules adsorbed on a metal surface, for which spin exchange with the electrons of the conduction band is possible. Indeed, the calculations show that highly delocalized molecular orbitals are situated close to the Fermi energy, indicating strong electronic coupling to the Au substrate (Figure 6c and d). This opens a new pathway for cis−trans backisomerization on the Au substrate with a distinctively lower energy barrier than in solution. In contrast, the azo groups in SAMs based on thiol molecules are largely electronically decoupled from the metal. Relaxation via the T1 state is therefore forbidden, which would explain why these molecules exhibit a significant higher stability, similar to solution.26 Because of the enhanced cis−trans relaxation in the TATA adlayers, a direct comparison of the photoisomerization kinetics with literature data is not easily possible. However, in previous

Figure 6. Results of the DFT calculations for a simplified azobenzenefunctionalized TATA molecule. (a) Inversion and (b) rotation mechanism for the thermal backisomerization of the free molecule. The dashed lines indicate the energy barriers determined from temperature-dependent UV/vis experiments in different solvents.32 (c) PBE/SV(P) energy levels for the Au cluster, the adsorbed, and the free azobenzene-functionalized TATA molecule (dashed lines indicate the HOMO). (d) HOMO−4 orbital of the cis isomer, demonstrating the electronic coupling of the azo moiety with the Au substrate.

studies of adlayers of azobenzene-containing thiols26,34 and asymmetric disulfides on Au(111),7,8 where the azobenzene groups likewise are oriented approximately perpendicular to the surface, photoisomerization cross sections σeff = (τtcnphoton)−1 = E·(τtcI)−1, estimated from the apparent time constants τtc, photon energies E, and light intensities I of ∼5 × 10−18 cm2, were obtained. In contrast, for azobenzene derivatives (i.e., tetra-tert-butyl azobenzene) oriented parallel to the surface, much lower cross sections of ≤5 × 10−21 cm2 due to pronounced electronic coupling with the substrate were reported.35 The effective cross sections for the different TATA adlayers, obtained from the apparent time constant of the trans−cis transition, range between 2 and 9 × 10−18 cm2 (see the Supporting Information). As discussed above, the trans−cis isomerization probably proceeds 1 order of magnitude slower. Nevertheless, the values are in the range expected for azobenzene moieties oriented perpendicularly to the surface, indicating that the photoisomerization is not strongly quenched by the pronounced electronic coupling to the substrate.



CONCLUSIONS According to the results presented in this work, azobenzenefunctionalized adlayers based on triazatriangulenium platforms exhibit fast, reversible, and highly reproducible photoizomerization on Au substrates, demonstrating that the molecular function is preserved after integration in solid-state systems. Together with the other advantages of this class of molecules, well-defined long-range lateral order, free-standing functional groups with rigid vertical orientation, and the possibility to customize functional groups and attached ligands, this makes them promising candidates for applications as molecular E

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machines. Key for the rigid, well-defined architecture of these species, which is a prerequisite for many advanced nanoscale functions, is the aromatic, fully conjugated framework. The latter leads to strong electronic coupling between metal substrate and functional unit in these species, which is of interest for their use as switches in molecular electronics, but also could adversely affect their functionality. Our data show that the latter effect apparently can be neglected for photoinduced isomerization reactions. However, the thermal stability of the cis state is strongly reduced as compared to solution, resulting in 4−5 orders of magnitude faster thermal backisomerization. While this does not fundamentally hinder the use of such adsorbates as molecular motors and actuators, it may limit other applications, for example, molecular storage devices. Understanding and controlling these effects will therefore be essential for the integration of such advanced molecular functions into nanoscale systems. As stated above, the pronounced electronic interaction with the metal may open new switching mechanisms not possible for free molecules in solution. Current work within our group therefore aims at employing rigid isolating spacer groups between the photoswitchable group and the platform, which may allow one to control the degree of electronic coupling and by this the thermal stability of the cis isomer.



ASSOCIATED CONTENT

S Supporting Information *

UV/vis spectra demonstrating the photoisomerization of the azobenzene-functionalized platforms in solution, additional adlayer switching experiments, a kinetical model of the isomerization reactions, and an overview about the isomerization kinetics parameters for the studied adlayers. This material is available free of charge via the Internet at http:// pubs.acs.org.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (R.H.); magnussen@physik. uni-kiel.de (O.M.). Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft via Sonderforschungsbereich 677.



REFERENCES

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