Catherine Henry De Villeneuve
email: catherine.henry-de-villeneuve@polytechnique.edu

Keywords: Fulgimide, Photochromism, surface functionalization, monolayer, silicon

Influence of Light Polarization on Photoswitching of Fulgimide Monolayers on surfaces

The photo isomerization characteristic parameters (photo-stationary states (PSS), cross section quantum yield) of indolyl fulgimide compounds dispersed in solution are quantitatively compared to those of the same compounds covalently immobilized as a monolayer on a functionalized Si(111) surfaces (see Advanced Materials 25, 416 (2013)). The photo isomerization kinetics of fulgimide compounds in solution is monitored using UV-Vis spectroscopy and that of monolayers by in situ calibrated FTIR spectroscopy. While the isomeric composition at photo stationary states are very similar in solution and at surfaces, a strong influence of the incident light polarization is found on photo isomerization cross section  ( ). Accounting for the local excitation electromagnetic field indicates that the fulgimide groups adopt a preferential tilt angle with respect to the surface normal and that their transition dipole is almost parallel to the surface plane for either C or E/Z isomers. DFT indicates that this orientation corresponds to photochromic groups that are lying in contact with the underlying monolayer. This interaction plausibly explains why the quantum yield of photoisomerization is found nearly twice lower at the surface than in the solution.

Introduction:

Photochromic molecules are molecules capable of changing conformation upon absorption of electromagnetic radiation [START_REF] Bouas-Laurent | Organic photochromism[END_REF]. This unique property is exploited in many different fields. For instance photochromic molecules were incorporated into polymers [START_REF] Kumar | Photochemistry of azobenzene-containing polymers[END_REF] [START_REF] Natansohn | Photoinduced Motions in Azo-Containing Polymers[END_REF] or thin films [START_REF] Yagai | Recent advances in photoresponsive supramolecular selfassemblies[END_REF] [START_REF] Pardo | Photochromic organic-inorganic hybrid materials[END_REF] [6] [START_REF] Finkelmann | A New Opto-Mechanical Effect in Solids[END_REF] [8] [START_REF] Yu | Photomechanics: Directed bending of a polymer film by light[END_REF] [START_REF] Fabbri | Alternating photoinduced mass transport triggered by light polarization in azobenzene containing sol-gel films[END_REF] to realize multifunctional layers, in particular to store information [START_REF] Liu | Photoelectrochemical information storage using an azobenzene derivative[END_REF] [START_REF] Rath | Periodic Organic Nanodot Patterns for Optical Memory[END_REF] [13] or modulate charge transport [START_REF] Jan Van Der | Charge transport through molecular switches[END_REF] [START_REF] Zhang | Interface Engineering of Semiconductor/Dielectric Heterojunctions toward Functional Organic Thin-Film Transistors[END_REF]. Photochromic molecules can also be used in the context of biological systems [START_REF] Szymański | Reversible Photocontrol of Biological Systems by the Incorporation of Molecular Photoswitches[END_REF], to structure soft matter with light [START_REF] Fabbri | Alternating photoinduced mass transport triggered by light polarization in azobenzene containing sol-gel films[END_REF], to control the function of biomaterials [START_REF] Willner | Control of the Structure and Functions of Biomaterials by Light[END_REF], or to promote catalytic activity [START_REF] Arif | Bimetallic gold(i) complexes of photoswitchable phosphines: synthesis and uses in cooperative catalysis[END_REF]. Immobilization of photochromic molecules on surfaces [START_REF] Jung | Photoswitching Behavior of Azobenzene-Containing Alkanethiol Self-Assembled Monolayers on Au Surfaces[END_REF] [START_REF] Wen | Photochemical-Controlled Switching Based on Azobenzene Monolayer Modified Silicon (111) Surface[END_REF] [21] [START_REF] Henry De Villeneuve | Quantitative IR Readout of Fulgimide Monolayer Switching on Si(111)[END_REF] [23] [START_REF] Garah | Reversible Photoswitching of Azobenzene-Based Monolayers Physisorbed on a Mica Surface[END_REF] [25] [START_REF] Nickel | Reversible Switching of Spiropyran Molecules in Direct Contact With a Bi(111) Single Crystal Surface[END_REF] [START_REF] Snegir | STM Observation of Open-and Closed-Ring Forms of Functionalized Diarylethene Molecules Self-Assembled on a Au(111) Surface[END_REF], very often on gold, or self-assembled as Langmuir-Blodgett (LB) layers [START_REF] Wang | Investigation of the Surface Morphology and Photoisomerization of an Azobenzene-Containing Ultrathin Film[END_REF] is a further approach to control wettability of surfaces with external light [START_REF] Ichimura | Light-Driven Motion of Liquids on a Photoresponsive Surface[END_REF], which is crucial in microfluidics, or to tailor surface conductance [START_REF] Smaali | High On-Off Conductance Switching Ratio in Optically-Driven Self-Assembled Conjugated Molecular Systems[END_REF] [31] [START_REF] Crivillers | Optical Modulation of the Charge Injection in an Organic Field-Effect Transistor Based on Photochromic Self-Assembled-Monolayer-Functionalized Electrodes[END_REF] [33] [START_REF] Zhang | Molecularly Controlled Modulation of Conductance on Azobenzene Monolayer-Modified Silicon Surfaces[END_REF] and surface work function. [START_REF] Yoshihiro | Switching surface polarization of atomic force microscopy probe utilizing photoisomerization of photochromic molecules[END_REF] [36] [START_REF] Kumar | Reversible Photo-Switching of Single Azobenzene Molecules in Controlled Nanoscale Environments[END_REF] [START_REF] Bronsch | Fast optical workfunction tuning at an organic/metal interface[END_REF] Photochromic molecules can be also adsorbed on nanoparticles to control their properties [START_REF] Klajn | Nanoparticles functionalised with reversible molecular and supramolecular switches[END_REF].

On the molecular scale, photo isomerization implies the absorption of a photon by the molecule which promotes the molecule to a Frank-Condon state before the excited electron relaxes to a lower-energy state which brings the photochromic molecules either to its starting state or to another isomeric state [START_REF] Petra | Optically and thermally induced molecular switching processes at metal surfaces[END_REF]. The probability of the latter event corresponds to the quantum yield ( ) and it has been established that depends on chemical substituents and polarity of the solvent in the case of azobenzenes [START_REF] Bandara | Photoisomerization in different classes of azobenzene[END_REF] [42] [START_REF] Lednev | Femtosecond time-resolved UV-visible absorption spectroscopy of trans-azobenzene: dependence on excitation wavelength[END_REF] [START_REF] Levine | Isomerization Through Conical Intersections[END_REF], fulgides [START_REF] Yokoyama | Fulgides for Memories and Switches[END_REF] [START_REF] Draxler | Ultrafast reaction dynamics of the complete photo cycle of an indolylfulgimide studied by absorption, fluorescence and vibrational spectroscopy[END_REF] [ [START_REF] Malkmus | Ultrafast ring opening reaction of a photochromic indolyl-fulgimide[END_REF][START_REF] Koller | Ultrafast Ring-Closure Reaction of Photochromic Indolylfulgimides Studied with UV-pump-IR-Probe Spectroscopy[END_REF] and spiropyrans [START_REF] Berkovic | Spiropyrans and Spirooxazines for Memories and Switches[END_REF] [50] [START_REF] Kohl-Landgraf | Ultrafast Dynamics of a Spiropyran in Water[END_REF] or diarylethenes [START_REF] Irie | Diarylethenes for Memories and Switches[END_REF] [START_REF] Tian | Recent progresses on diarylethene based photochromic switches[END_REF] dispersed in a solvent. The behaviour at the surface depends strongly on the architecture of the assembly (for a review at metallic surfaces see Ref. [START_REF] Petra | Optically and thermally induced molecular switching processes at metal surfaces[END_REF]). When the photoswitching molecules are in direct contact with the substrate, the photoswitching occurs but seems very slow {Comstock, 2007 #758} {Safiei, 2012 #752}. This may partly due to steric hindrance, chemical and/or electronic coupling with the substrate. This motivated studies aiming at increasing the free volume around photochromic compounds [START_REF] Pei | Correlation between the Structure and Wettability of Photoswitchable Hydrophilic Azobenzene Monolayers on Silicon[END_REF] [19] [START_REF] Baisch | Mounting Freestanding Molecular Functions onto Surfaces: The Platform Approach[END_REF][START_REF] Jung | Azobenzene-Containing Triazatriangulenium Adlayers on Au(111): Structural and Spectroscopic Characterization[END_REF] and to reduce the electronic coupling with the substrate [START_REF] Dietrich | An anchoring strategy for photoswitchable biosensor technology: azobenzene-modified SAMs on Si(111)[END_REF] [33] [START_REF] Uchida | Reversible On/Off Conductance Switching of Single Diarylethene Immobilized on a Silicon Surface[END_REF] using chemical spacers or a semimetal as substrate {Nickel, 2017 #1352}. In such constructs the photo kinetics of photo isomerization of photochromic molecules, characterized by its effective cross section ( ), may be as fast as in solution. This has been demonstrated with azobenzene derivatives {Wagner, 2009 #1473} {Krekiehn, 2015 #1286} {Moldt, 2016 #1409}. However is yet found to be much smaller than in solution for fulgimides tethered on an organic monolayer on silicon{Schulze, 2015 #1314} or spirosyran {Nickel, 2017 #1352} evaporated on Bi(111), which minimizes electronic coupling. Lateral steric effects, mechanical and/or electronic coupling with the substrate are frequently invoked to explain the different behaviour at surfaces. and this motivated various strategies to increase the free volume around photochromic compounds [START_REF] Pei | Correlation between the Structure and Wettability of Photoswitchable Hydrophilic Azobenzene Monolayers on Silicon[END_REF] [19] [START_REF] Baisch | Mounting Freestanding Molecular Functions onto Surfaces: The Platform Approach[END_REF][START_REF] Jung | Azobenzene-Containing Triazatriangulenium Adlayers on Au(111): Structural and Spectroscopic Characterization[END_REF] or to reduce the electronic coupling with the substrate [START_REF] Dietrich | An anchoring strategy for photoswitchable biosensor technology: azobenzene-modified SAMs on Si(111)[END_REF] [33] [START_REF] Uchida | Reversible On/Off Conductance Switching of Single Diarylethene Immobilized on a Silicon Surface[END_REF] using chemical spacers or using semimetals with a small density of states at Fermi level [START_REF] Nickel | Reversible Switching of Spiropyran Molecules in Direct Contact With a Bi(111) Single Crystal Surface[END_REF]. In spite of significant improvements, when the photo isomerization cross section ( ) is determined [START_REF] Schulze | Nonlinear optical response of photochromic azobenzene-functionalized self-assembled monolayers[END_REF] [START_REF] Nickel | Reversible Switching of Spiropyran Molecules in Direct Contact With a Bi(111) Single Crystal Surface[END_REF] [61] [START_REF] Munford | The preparation of ideally ordered flat H-Si(111) surfaces[END_REF], is generally smaller than the value measured for the same photochromic molecule dispersed in a solvent and the behaviour at the surface depends on the architecture of the assembly (for a review at metallic surfaces see Ref. [START_REF] Petra | Optically and thermally induced molecular switching processes at metal surfaces[END_REF]). Therefore other effects need to be considered and substituent effects seem too small to account for above mentioned differences between the kinetics of the photoswitching at surfaces and in solution. One key physical effect that has been largely ignored in the past is the influence of the local excitation electromagnetic field although it is well known that photochemistry is strongly influenced by the presence of a substrate [START_REF] Zhou | Photochemistry at adsorbate/metal interfaces[END_REF].

Such a knowledge appears however indispensable to discuss the influence of local chemical environment on the photoisomerization cross sections.

In this work we have investigated the photoswitching properties of fulgimide compounds because they present the key advantage of a very good thermal stability and a large quantum yield [START_REF] Yokoyama | Fulgides for Memories and Switches[END_REF]. (Z-isomer). Amino-fulgimide may be immobilized as a monolayer on a surface (see scheme

2) [START_REF] Henry De Villeneuve | Quantitative IR Readout of Fulgimide Monolayer Switching on Si(111)[END_REF]. The photo isomerization kinetics are monitored in solution using UV-Vis spectroscopy and at surfaces using in situ calibrated FTIR spectroscopy. A new experimental protocol has been developed with respect to Ref. [START_REF] Henry De Villeneuve | Quantitative IR Readout of Fulgimide Monolayer Switching on Si(111)[END_REF] in order to determine the photo isomerization cross section () and the composition of the surface at the photo-stationary states (PSS) with high precision. In the case of fulgimide MLs, is investigated as a function of the incident light polarization and the fulgimide surface density. Results are discussed within the framework of a molecular model and the properties of the local electromagnetic field.

Experimental:

All chemicals used for surface modification (purchased from Aldrich) were of the highest available purity and used as received. Indolyl fulgimide compounds substituted with an ethylamino linker were synthesized as detailed in reference [START_REF] Rück-Braun | Formation of Carboxy-and Amide-Terminated Alkyl Monolayers on Silicon(111) Investigated by ATR-FTIR, XPS, and X-ray Scattering: Construction of Photoswitchable Surfaces[END_REF]. For silicon etching, electronicgrade chemicals (Carlo Erba, RSE) were used. ATR-FTIR silicon prisms were cut from double-side polished (FZ-purified, 800 .cm) n-type Si(111) wafers with 0.2° miscut angle along the direction (Sil'tronix, France). For AFM observations one-side polished (CZ purified, 1-10 .cm, with a similar miscut) were used. In situ monitoring of photoswitching:

In the case of monolayers, photo switching was monitored by in situ FTIR spectroscopy using a specifically home-designed optical experimental setup installed within the custom chamber of the IR spectrophotometer (see scheme in supplementary information, section S1). Both sides of the sample were irradiated with a quasi-parallel beam using LEDs (UV: 365 nm, 35.9 mW/cm 2 ; Vis: 525 nm, 51.5 mW/cm 2 ) and cylindrical lenses. Neutral filters were used to adjust the photon flux. For most of the experiments, a 45° incidence angle is used. Polarizers were added for experiments with p-polarized light. For experiments with s-polarized light, it has been found more reliable to work at normal incidence rather than using polarizers, in order to ensure the absence of any residual electromagnetic-field component normal to the surface. A computer controlled shutter allowed for irradiating the sample with short light pulses (few ms) at the very initial stages of the photo-switching and longer ones (1-100 s) at the subsequent stages to control the photon dose. Photon fluxes were calibrated in each configuration with a photodiode to determine the photon dose during light pulses. The nominal photon flux (in the absence of neutral filters and polarizers) was 6.6 10 16 photons cm - 2 s -1 and 1.4 10 17 photons cm -2 s -1 for UV and visible light, respectively. FTIR spectra (150 scans, resolution 4 cm -1 ) were recorded between light pulses, i.e., in the dark where the system is stable. This procedure allows for recording FTIR spectra corresponding to controlled photon dose for an accurate determination of the photokinetics.

Photo switching in solution was characterized with a similar approach using in situ UV-Vis spectroscopy. 20 µM of either E-or C-fulgimide were dissolved in acetonitrile. A simplified optical setup was installed in the spectrophotometer (Agilent Technologies, Cary 50) to monitor the process. The nominal photon flux (in the absence of neutral filters and polarizers) was 3.3 10 16 photons cm -2 s -1 and 2.2 10 17 photons cm -2 s -1 for UV and visible light, respectively. A similar protocol, recording UV-Vis spectra between light pulses, was used.

Preparation of fulgimide monolayers with variable surface densities: Pure C-and Efulgimide were synthesized as reported in ref. [START_REF] Rück-Braun | Formation of Carboxy-and Amide-Terminated Alkyl Monolayers on Silicon(111) Investigated by ATR-FTIR, XPS, and X-ray Scattering: Construction of Photoswitchable Surfaces[END_REF] and immobilized on the silicon surface using the multistep protocol described in Scheme 2. The primer COOH-terminated monolayer (step 1) was grafted by photochemical reaction (wavelength 312 nm) between the Hterminated surface and neat undecylenic acid as detailed in Ref. [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF]. The "activation" of the carboxylic groups (step 2) was performed in MES buffer (pH=5, 15°C, under Ar bubbling)

containing N-Hydroxysuccinimide (HOSuc, 100 mM and 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC, 100 mM). The reaction time was 1h. The samples were then rinsed successively (10 min, 40°C, pH = 5) in 0.1M NaH 2 PO 4 , 0.01M NaH 2 PO 4 , in ultra-pure water and blown dry using an Ar stream. The coupling of the fulgimide (step 3) was conducted in an acetonitrile solution containing 5 mM of fulgimide (2h at room temperature, in the dark).

More details are given in Ref. [START_REF] Henry De Villeneuve | Quantitative IR Readout of Fulgimide Monolayer Switching on Si(111)[END_REF]. To vary the photochromic molecule density, step 3 (scheme 2) was also conducted in an acetonitrile solution containing amino-fulgimide and ethylamine. An excess of fulgimide was used to account for the slower coupling rate of fulgimides (4000 s -1 ) with respect to that of ethylamine (200 s -1 ) (measured from complementary in situ FTIR measurements, data not shown). Ethylamine /fulgimide ratios of 0.17, 0.26, 0.33 and 0.66 were used.

Full range FTIR spectra recorded at the different steps of the preparation of the fulgimide MLs are given in supplementary information (section S2). They are perfectly consistent with previous results [START_REF] Henry De Villeneuve | Quantitative IR Readout of Fulgimide Monolayer Switching on Si(111)[END_REF]. Also explained in supplementary information (section S2) all samples studied in this work present a contamination level that is below 0.1 equivalent monolayer. The chemical composition of all surfaces was quantitatively determined from careful calibration of the C=O band at 1715 cm -1 related to COOH groups [65] [66]. More details are given in supplementary information, section S2. e

Computational methods:

The geometries of the fulgimide compound in the C, E and Z forms were fully optimized using the Becke-3-Lee-Yang-Parr (B3LYP) exchange functional [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF] with the 6-311+G(d,p) basis set, in vacuum, as implemented in the Gaussian 09 software package [START_REF] Frisch | Gaussian 09, Revision A.02[END_REF]. The absence of negative frequencies was checked to ensure true minima for all geometries. Frank-Condon energy transitions and corresponding transition dipole moments were calculated using the time-dependent DFT formalism (TD-DFT) with the same functional and basis set. As explained in the text, the functionalized monolayer on Si(111) surface was sketched without minimization. The DFT cell consists of alkylamide molecules as spacer chains (optimized separately) along a 3.84  6.65 Å rectangular 2D-assembly and one fulgimide-terminated chain.

Results:

3.1 Photoswitching in solution vs. at surfaces: under UV is possible but requires longer exposure times [START_REF] Henry De Villeneuve | Quantitative IR Readout of Fulgimide Monolayer Switching on Si(111)[END_REF]. This also leads to some photodegradation of the monolayer. In the following we only present experiments corresponding to short illumination times, leading to incomplete photoconversion.

The data in Fig. 1 may be replotted as a function of the photon dose p, as justified in supplementary information (Fig. S5) to determine the photo isomerization cross section () and the isomeric compositions at the photo-stationary state (PSS) as it is explained in the Appendix. It is found that  is approximately constant in the initial stages of the photochromic reaction but then decays above a critical photon dose p* (see Fig. A1). In other words only a fraction of the monolayer reacts upon illumination according to a single exponential law with a well-defined value of the cross section . In the following we only discuss this value of . The decay of  above p* will be the subject of a separate article.

Notice that the same analysis gives a single exponential law for the complete photoisomerization of C-isomers dissolved in acetonitrile (under Vis light). Under UV,  decays (by 20%) for high-enough photon doses. surfaces we consider monolayers with less than D* ~ 0.9 isomers/nm 2 because steric hindrance may be neglected. Steric hindrance is expected for denser monolayers [START_REF] Henry De Villeneuve | Quantitative IR Readout of Fulgimide Monolayer Switching on Si(111)[END_REF]. With this precaution, Table 1 shows that the PSS Vis is equal in solution and at the surface and that the PSS UV is somewhat richer in E/Z isomers at the surface than in the solution.

Isomeric composition at PSS

Photokinetics at surfaces

The results of Figure 4 have been obtained on a sample with an initial isomer density of 1.6 E-isomers/nm 2 . After a few incomplete photoswitching cycles like in Fig. 2 2 gives also the -values measured for isomers dispersed in acetonitrile. In solution, the absorption cross section can conveniently be measured and the isomerization quantum yield  is simply determined as the ratio of  to  abs .

According to Table 2 the magnitude of  follows the trend s-pol (surface) < p-pol (surface) < solution for a given wavelength and  UV >  Vis in all conditions. Complementary experiments (see Table S1) indicate that is quasi-independent of the isomer surface density, suggesting that this parameter is well representative of the photo isomerization of the fraction of photochromic molecules that switch from one configuration to the other one without any specific (e.g., steric) limitation. The -values measured in solution are close to those reported previously ( UV = 5 10 -18 cm 2 and  Vis = 2 10 -18 cm 2 [START_REF] Deblauwe | Quantum yields of the photochromic reactions of heterocyclic fulgides and fulgimides[END_REF]). The differences may come from the substituent and/or the solvent which are different in our work. Concerning the cross sections measured at the surface, our values with non-polarized light are also in fair agreement, within a factor 2-4, with recently published data ( UV = 2.3 10 -18 /cm 2 and  Vis 1.2 10 -18 /cm 2 ) for fulgimides immobilized on a silicon surface [START_REF] Schulze | Reversible Photoswitching of the Interfacial Nonlinear Optical Response[END_REF].

Discussion

All in all, the data in Table 2 are consistent with past literature and confirm that the experimental values of  UV or  Vis are smaller at the surface than in solution. To the best of our knowledge, the light polarization dependence of the photoswitching efficiency is quantitatively investigated for the first time. The main purpose of this section is therefore to discuss the photo isomerization cross section  and particularly its dependence on light polarization at surfaces. The quantum yield is also discussed.

As recalled in the introduction, photo isomerization implies that absorption of a photon by the molecule brings it into an excited transition state before it relaxes either in its initial state or into another isomeric state with a probability (quantum yield). Therefore, the photo isomerization cross section of a molecule may be written:

The absorbance cross section  abs is proportional to:

This integral outlines that the absorption of a photon by a photochromic molecule does depend on the alignment between the local electric field and the transition dipole of the molecule.

In solution is randomly oriented,  min = 0,  max = 4 and N = 4 and 2 [START_REF] Polo | Infrared Intensities in Liquid and Gas Phases[END_REF], with the electric field in vacuum and n the refractive index of the solvent (n = 1.34 for acetonitrile). Therefore

In the case of a monolayer of photochromic molecules immobilized on a substrate, one must take into account two points: (i) is affected by the close proximity of the substrate and

(ii) may be constrained in certain directions of space. To the best of our knowledge, these considerations were not discussed at surfaces in literature although light polarization is known to induce reorientation of azobenzene in a polymer matrix [START_REF] Wang | Investigation of the Surface Morphology and Photoisomerization of an Azobenzene-Containing Ultrathin Film[END_REF][START_REF] Klaus | Laser-induced reorientation of the optical axis in liquid-crystalline side chain polymers[END_REF].

Photo isomerization cross section at surfaces:

Figure 5 defines the relative orientation of and . is set within the (y,z) plane at an angle  with respect to the surface normal (direction z) and the orientation of is given by its angle  with respect to surface normal and the azimuth angle  of its projection on (x,y) plane.

Two extreme hypotheses are considered.

Within the first one, the immobilized fulgimides adopt a random orientation with respect to surface normal. In this case, 0 ≤  ≤ /2, 0 ≤  ≤ 2,  min = 0,  max = 2 and N = 2 in Eq. ( 2). The integral J therefore reduces to , independently of , i.e., the polarization of the illumination. In that case the ratio and it depends only on the illumination energy. Under UV light, would be ~0.12 and under Vis light would be ~0.04. These values are sufficiently different from the experimental ones (~ 0.23 ± 0.05 for either UV or Vis illumination, see Table 2) to rule out this hypothesis.

Within the second hypothesis, the fulgimide are constrained by their environment and adopt a specific orientation. In this second case an angle  in Fig. 5 may probably be defined but the angle  is likely to be random between 0 and 2. Therefore, J reduces to 2 , where  depends on light polarization and is given by Eqs. (S1-S2) in the supplementary information [START_REF]Surface infrared spectroscopy[END_REF]. In s-pol conditions, = /2 and with given by (Eq. S1). At the incidence  = 45° and with ppol light, , with p  and p  the components of parallel and perpendicular to the surface, which expressions are given in section S5 in the supplementary information. For the numerical evaluation, the dielectric constant of silicon was taken from Ref. [START_REF] Edwards | Handbook of Optical Constants of Solids[END_REF] at the relevant wavelength. At the silicon/air interface these equations yield 2 << 2 . Assuming that the isomerization quantum yield is independent on light polarization, the ratio can be computed as a function of  either to UV or Vis illumination By comparing to the experimental ratio, one obtains the value of corresponding to the UV and Vis transition dipoles. For the UV excitation,  is found to be ~74° and for the Vis excitation,  ~64°. In either case, appears close to the surface plane.

DFT and TD-DFT calculations were performed with the Gaussian 09 package with the B3LYP functional and the 6-311+G(d,p) basis set in vacuum, and provided the minimized geometries, relative energies and Franck-Condon electronic transition energies for the three isomers C, E and Z (Fig. 6a). Given the orientation of of the two relevant isomeric forms C and E as derived from TD-DFT computations, the experimental values of  mean that the Cand E-forms are similarly oriented and are almost lying parallel to the surface plane. This large tilt angle between the direction of the transition moment of the molecules and the surface normal may be accounted for by a rotation around the C-C and C-N bonds of the amide linkage to the monolayer. The configuration of the fulgimide is therefore different from that assumed in Ref. [START_REF] Henry De Villeneuve | Quantitative IR Readout of Fulgimide Monolayer Switching on Si(111)[END_REF] where a nearly upright orientation was postulated because this corresponds to the equilibrium configuration of the isolated molecule (the fulgimide molecule coupled to the carboxylic acid).

According to Fig. 6, the experimental angle implies that the fulgimide groups must be almost parallel to the surface plane. To check the feasibility of this configuration, the grafted monolayer was modelled with alkylamide molecules (optimized separately) assembled along a 3.84  6.65 Å rectangular mesh (see atomic model in Fig. 7a). This corresponds to a density of 3.9 chains grafted per nm 2 which is the maximum packing density on a Si(111)

surface [START_REF] Sieval | Molecular Modeling of Covalently Attached Alkyl Monolayers on the Hydrogen-Terminated Si(111) Surface[END_REF]. The DFT cell is limited to 3 x 3 chains and a photochromic molecule in its Cform is attached on one site located at the perimeter of the rectangular cell. It is tilted such as to bring its transition dipole moment at an angle  = 74° with respect to the surface normal.

The model shown in Figs. 7b-c corresponds to a situation where a vacancy is assumed to be present in the center of the DFT cell. In the side view (Fig. 7c), one clearly sees that the photochromic molecule is partially embedded inside the molecular carpet. Though these structures are not an optimized configuration of the supramolecular assembly, which is beyond the DFT computations performed here, such a tilted configuration is energetically affordable and a similar energy is found if the C-fulgimide is anchored on any other sites at the perimeter of the DFT cell. Similar energies are also found with a tilted E-fulgimide instead of a C-fulgimide. As to be expected, however, the energy barrier becomes too large for either a C-or a E-fulgimide without the vacancy at the center of the 3 x 3 cell. This shows that the vacancies in the grafted monolayer play a crucial role.

The model presented in Fig. 7 closely corresponds to real molecular surface concentration since the DFT cell is equivalent to ~3 chains / nm 2 and ~1 fulgimide / nm 2 whereas a dilute fulgimide monolayer is composed of 2.8 chains grafted per nm 2 and 0.9 Cfulgimide / nm 2 . Experimentally, there are enough vacancies (1.1 / nm 2 ) to accommodate all the immobilized photochromic molecules with a tilt compatible with experimental results.

Given the influence of the light polarization on the cross section, we therefore postulate that the majority of immobilized fulgimides must adopt such a tilted configuration, without excluding that a small fraction of the photochromic molecules may adopt a non-tilted configuration.

A tilted molecular configuration was not to be expected and appears counter intuitive.

Explain its origin would require dedicated supramolecular calculation. Nevertheless, based on above observations, one may suspect that this configuration comes from strong interactions between the fulgimide and the acid-terminated monolayer prior to the formation of the amide bond. In fact a large angle  is already measured after immobilization since the cross sections are constant from the very first photoswitching cycle for either pure C-or E-fulgimide monolayers. This tilted configuration may be maintained upon successive photoswitching because there is a small difference between the  values for the UV and Vis transition. This strongly suggests that the photochromic reaction mainly involves the CE and EC photoisomerization, with a negligible contribution of the Z form because the direction of for the Z form is significantly rotated, with regard to the N-C bond of the alkylamide chain, see Fig. 6c).

Isomerization quantum yield at surfaces:

The quantitative determination of the optical absorption of a monolayer on an absorbing substrate like silicon is difficult and an absolute value of the isomerization quantum yield  (Eq. 1) appears out of reach here. However, the determination of J in different environments and that of the angle  allows for estimating the ratio of the isomerization quantum yield in solution with that at the surface.

On the basis of Eq. ( 1) and the above expressions of , it comes (for experiments at 45° incidence angle in p polarization and normal incidence in s polarization):

Numerical evaluation of these expressions using the above  values allows a comparison with the experimental values given in Table 2. For the UV transition, the computed values are and , to be compared with the experimental values and . In either case, one finds .

Similarly, for the Vis transition, the computed values are and , to be compared with the experimental values and . Once again, in either case, one finds . Therefore, within the framework of this quantitative analysis, the isomerization quantum yield is found to be independent on light polarization, which appears reasonable since  is expected to depend mostly on the properties of the transition state and the coupling of the molecule to its environment, both independent on the photon field. For both the UV and Vis transitions, the ratio is found to exhibit nearly the same value of 0.55, which can be paralleled to the closely similar configuration of C and E isomers at the surface. It corresponds to an isomerization quantum yield about twice less efficient at the surface than in solution.

The origin of this difference cannot be sought for in terms of local electric field (already taken into account in the above analysis), steric effect between neighbour molecules (since the experimental cross sections do not significantly depend on the surface molecule concentration), or electronic interaction with the substrate (shielded by the molecular layer grafted at the surface). Therefore, we tentatively assign the loss of efficiency of the isomerization at surfaces to the interaction of fulgimide molecules with the surface molecular layer grafted on silicon, which makes them adopt the tilted configuration determined in Section 4.1.

Conclusion

In conclusion, the present results demonstrate that when photochromic molecules are immobilized at a surface in a well-controlled configuration, a quantitative analysis of the photoswitching kinetics allows for obtaining a detailed picture of the system at the molecular level. In the particular case of indolyl fulgimide compounds covalently anchored on functionalized Si(111) surfaces the data above show that the photoisomerization remains efficient and reversible and that the photo stationary compositions are close to those found in solution provided steric hindrance is avoided by limiting the surface density of immobilized photochromic molecules, here below 0.9 isomers / nm 2 .

However, from a dynamic view point, surface photokinetics strongly depart from that in solution. The photoisomerization cross sections measured at the surface are much smaller than in solution. In addition, the photokinetics is no longer following a pure first order law.

Appendix

It is worth recalling that typical photochromic reactions AB follow the general photokinetic differential equations [START_REF] Nakatani | Introduction: organic photochromic molecules, in Photochromic materials: preparation, properties and applications[END_REF] involving concentrations of all isomers, their related absorption coefficients, thermal reaction rates and photochromic quantum yields corresponding to AB and BA reactions. In the general case and in absence of any approximation, these differential equations show nonlinear terms (known as photokinetic factors) preventing any analytical solution. Nevertheless, in the case of the present fulgimide molecule, thermal reaction rates can be neglected and concentrations are extremely low: absorbance values of our samples at the irradiation wavelengths are smaller than 0.1 in solution and 0.001 at the surface, especially for surfaces functionalized with a (diluted) monolayer of photo-active molecules. Consequently, photochromic differential equations linearization gives simple first order photokinetics.

However, when photoswitching strongly deviates from a pure exponential law, it appears difficult to make a quantitative comparison between different configurations. To this end, a procedure described below was used to determine the isomeric composition at PSS and the isomerization cross section  from partial photoconversion experiments. but also extends it at photon doses for which photochromism was not measured (black dashed line). Such an extrapolation yields the isomeric composition at PSS. This analysis immediately captures that photoconversion was (voluntary made) incomplete, because p was too small to reach the PSSs. This also evidences that a fraction of the C-isomers remains blocked (the monolayer density is 1.6 /nm 2 which is above the maximum packing density of isomers in 2D). Panel (b) of Fig. A1, is a plot of the cross section which is obtained as , with the surface density of switched isomers after illumination with a photon dose p. This plot outlines that is constant up to a critical photon dose p* (regime featured by grey shaded regions) above which a progressive decrease of is observed. The initial (i.e., for p < p*) is accurately obtained by replotting the data as in Fig. 4 where ln(1 -E/E PSS ) is plotted against p (PSS is the above determined value). Linear regression restricted to p < p* yields with no ambiguity.

The back photo isomerization (panels c and d) was analysed by the same method.

However, it is important to note that the situation under UV irradiation is intrinsically more complicated because several photoreactions are expected to occur: EC, but also CE, EZ and ZE. As a consequence, the  UV values do not correspond strictly to the single EC isomerization. In initial stages of UV irradiation, starting from a E-terminated monolayer, and the EC and EZ reactions represent the major pathways. Under prolonged irradiation, the CE and ZE may play an important role in the system evolution. This time-dependent behaviour may be partly responsible for the decrease of as a function of UV photon dose, and the lower value of p* compared to the one determined under visible illumination. However, at low photon doses, the  UV value can be approximated to be mostly representative of the EC reaction because (i) the EZ photoisomerizations play a negligible role (there are only few percent of Z forms in the PSS composition) and (ii) the C form concentration is very low at initial stage.

It should be noted that the procedure above was tested over a large number of experiments and appears robust. The very same behaviour was indeed observed for all photoconversion experiments for all samples, regardless the surface density of the monolayer.

In particular, we emphasize that for the stabilization of the fitting procedure, the fitting with the pseudo Voigt function was performed keeping fixed the Lorentzian and Gaussian width and a fixed Gaussian/Lorentzian ratio for all experiments. In (a) the starting surface is composed of 1.1 E-isomers/nm 2 and 0.5 C-isomers/nm 2 . In (b) the starting surface contains 0.6 E-isomers/nm 2 and 1.0 C-isomers/nm 2 for the UV (resp. visible) illumination. Symbols correspond to experimental data, and dashed lines to linear fits. Vertical bars mark for each plot the maximum photon dose p* up to which the cross section remains constant. The top view is tilted with respect to the surface normal which explains that the red mesh is not rectangular. The side view shows that the fulgimide group is partly embedded in the molecular layer. This configuration is made possible by the presence of a vacancy in the centre of the red mesh. A similar configuration is found for the E form. See text for details.

  Klaes a , Catherine Henry de Villeneuve a *, François Ozanam a , Christoph Barta b , Karola Rück-Braun b Rémi Métivier c and Philippe Allongue a * a) Laboratoire de Physique de la Matière Condensée, Ecole Polytechnique, CNRS, IP Paris, 91128 Palaiseau, F (France) b) Institut für Chemie, Technische Universität Berlin, Strasse des 17 Juni 135, D-10623 Berlin (Germany) c) PPSM, ENS Cachan, CNRS, Université Paris-Saclay, 94235 Cachan (France) Abstract :

Scheme 1

 1 displays the structure of the fulgimide isomers and solid arrows indicate optical transitions under visible ( ~ 525 nm) and UV light ( ~ 365 nm). Both wavelengths refer to the main absorption band of the respective isomers. Visible irradiation promotes ring opening which transforms the closed form (C) into the open form (E). UV irradiation leads to the back formation of the C-isomer but also of another open form

Figure 1a shows series

  Figure1ashows series of UV-Vis spectra of a 20µM C-solution (in acetonitrile) irradiated

Figure

  Figure 1c displays narrow range FTIR spectra recorded during the photo switching of

Panel (a) of figure 2

 2 presents the evolution of the isomeric composition upon consecutive UV/Vis illumination cycles, starting from a dense E-surface (1.8 E-isomers/nm 2 ). About 50% of the monolayer is switched under each light exposure. Panel (b) of Fig.2gives the surface composition at PSS UV (left bar) and PSS Vis (right bar) for each cycle, determined as explained in the Appendix. The composition is given as (C) and (E/Z) surface densities because E-and Z-forms cannot be discriminated by FTIR. The data analysis according to the procedure in the Appendix also yields the cross-section values ( UV and  Vis ). Fig.S6supports this analysis since the resulting  UV and  Vis keep the same values over the successive illumination cycles.Overall the isomeric compositions at PSS appear rather stable upon successive UV/Vis irradiation cycles. A slight enrichment of the surface in C-isomers is noticeable at PSS UV after 6 irradiation cycles. The same trend is observed for PSS Vis . The isomeric compositions at PSS Vis and PSS UV in solution and at surfaces with various densities of immobilized fulgimides are compared in Figure3. In each case the left bar provides PSS Vis and the right one PSS UV after the first visible and the subsequent UV irradiation, starting from a pure C-solution or a pure C-monolayer. The isomeric compositions at PSSs are also summarized in Table1. One may notice that the PSS UV composition in solution departs from 100% C. Indeed, the presence of a significant proportion of open forms at PSS UV confirms that an additional reaction C  E must be taken into account under UV in Scheme 1 since the C-isomer presents an absorption band around 350 nm in Fig.1a. For a relevant comparison of the PSSs in solution and at

  , the starting surface consists of C and (E+Z) isomers. Therefore, and have been plotted as a function of the photon dose p. Here [C] and [E] designate the surface concentration of closed C and open (E+Z) isomers and the suffix refers to the starting surface and surface at PSS. Data analysis indicates that the total number of isomers is constant over successive illumination cycles. As justified in the Appendix, data (symbols in Fig. 4) may be fitted to a single exponential kinetics (straight dashed lines) up to a critical photon dose p* (indicated by the vertical bars in the figures). The photo isomerization cross section  is the inverse value of the straight-line slope. Above p*, whose value depends on photon energy and light polarization, the process no longer follows a simple exponential law (slow decay of  as in Fig. A1b,d). For a given monolayer, the cross section  was measured for s-and p-polarization of the excitation light (red and blue open squares respectively) and compared to that obtained with non-polarized light (black open squares). The different  values are reported in the left three blocks of Table 2. The right block of Table

  Only a fraction of the photochromic molecules switches with a constant photoisomerization cross section . Above a critical threshold,  continuously decreases with increasing photon dose. The initial  is representative of the isomers which can freely react upon light absorption and measurements under s-and p-polarized light indicate that the transition dipole of the switching isomers is almost lying in the surface plane, a configuration which corresponds to fulgimides partially embedded in the underlying monolayer. Noteworthy, the open (E) and closed (C) forms exhibit similar configuration. This configuration is likely at the origin of the reduced value of the isomerization quantum yield which can be derived when comparing experimental photo-isomerization cross sections recorded for "freely" switchable molecules at the surface with those measured in solution.

Figure 1 .

 1 Figure A1is an example of such a full data analysis. In top panels the solid black lines

Fig. A1 :

 A1 Fig. A1: Example of data analysis starting for a pure C-monolayer with 1.6 isomers/nm 2 exposed to visible illumination (left column) and then to UV illumination (right column). This analysis corresponds to the data presented in Fig. 1: (a) and (c) the black solid and dashed lines correspond to experimental and calculated variations of the number of switched isomers, respectively, as a function of log(p), with p the photon dose. Blue symbols are the derivative of the black line and the red line is the best fit using a Voigt function; (b) and (d) variations of the numerical cross section as a function of log(p). Notice the plateau below a critical value p* (grey shaded regions).

Figures: Figure 1 :

 1 Figures:

Figure 2 :

 2 Figure 2:

Figure 3 :

 3 Figure 3:

Figure 4 :

 4 Figure 4:

Figure 5 :

 5 Figure 5:

Figure 6 :

 6 Figure 6:

Figure 7 :

 7 Figure 7:

Acknowledgements

This work has been supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" program (Labex charmmmat, ANR-11-LABX-0039-grant). We also thank Technische Universität and the Deutsche Forschungsgemeinschaft (SFB 658) for financial support. PSS UV (b) (d) (a) (c)

Tables:

Table 1:

PSS composition given as C / E+Z relative proportions, in solution (acetonitrile) and at surfaces. D is the initial fulgimide concentration at the surface and D* ~ 0.9 isomers/nm 2 is the density below which no steric hindrance occurs (see text).

Solution


Catherine Henry-De-Villeneuve
email: catherine.henry-de-villeneuve@polytechnique.edu

Thang Long

François Ozanam

Philippe Allongue
email: philippe.allongue@polytechnique.edu

Catherine Henry De Villeneuve

Structure of mixed acid/decyl monolayers grafted on oxide free Si(111) surfaces

Keywords: surface functionalization, mixed monolayer, carboxylic acid monolayer, silicon, IR spectroscopy, AFM

The structure of mixed acid / decyl monolayers (MLs) grafted on oxide free Si(111) surfaces by photochemical hydrosilylation in a mixture of neat undecylenic acid and 1-decene is studied in detail. After appropriate surface cleaning of as grafted surfaces, AFM (topography and phase imaging) and calibrated FTIR analysis demonstrate that a mixed monolayer is formed, free of residue. When the acid-molecule fraction (Γ SOL ) is > 0.1 mixed monolayers are homogeneous on the scale of observations and they are only slightly enriched in acid chains with respect to the solution. Conversely, when Γ SOL < 0.1 the acid chain fraction within the ML becomes quasiindependent of the solution composition and may become much larger than Γ SOL . In addition, dark domains are observed in AFM phase images. Correlations between the characteristic parameters of CO IR band and AFM phase images suggest a strong phase separation of acid and alkyl chains at various length scales. A model involving a structuration of the grafting solution is proposed to explain observations.

Introduction

Self-assembled monolayers (SAMs) consisting of more than one molecular component (mixed monolayers) are important for chemical separation, [START_REF] Wirth | Mixed Self-Assembled Monolayers in Chemical Separations[END_REF] Langmuir-Blodgett 2 and in surface science [START_REF] Love | Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology[END_REF][START_REF] Ulman | Formation and structure of self-assembled monolayers[END_REF][START_REF] Buriak | Organometallic Chemistry on Silicon and Germanium Surfaces[END_REF][START_REF] Sagiv | Organized monolayers by adsorption. 1. Formation and structure of oleophobic mixed monolayers on solid surfaces[END_REF][START_REF] Silberzan | Silanation of silica surfaces. A new method of constructing pure or mixed monolayers[END_REF][START_REF] Thissen | Wet chemical surface functionalization of oxidefree silicon[END_REF] because mixed monolayers are frequently used to tailor surface properties such as wetting [START_REF] Laibinis | Structure of monolayers formed by coadsorption of two n-alkanethiols of different chain lengths on gold and its relation to wetting[END_REF][START_REF] Laibinis | Comparison of the structures and wetting properties of self-assembled monolayers of nalkanethiols on the coinage metal surfaces, copper, silver, and gold[END_REF][START_REF] Chen | Concomitant tuning of metal work function and wetting property with mixed self-assembled monolayers[END_REF] and work function. [START_REF] Crivillers | Large Work Function Shift of Gold Induced by a Novel Perfluorinated Azobenzene-Based Self-Assembled Monolayer[END_REF][START_REF] Chen | Concomitant tuning of metal work function and wetting property with mixed self-assembled monolayers[END_REF] Bio-sensing systems [START_REF] Wink | Self-assembled Monolayers for Biosensors[END_REF][START_REF] Ciampi | Wet chemical routes to the assembly of organic monolayers on silicon surfaces via the formation of Si-C bonds: surface preparation, passivation and functionalization[END_REF] make also use of mixed-monolayers that contain specific sites for anchoring the biomolecules in a controlled amount and complementary sites to prevent non-specific adsorption of the target molecule. However, the spatial arrangement of the components within the monolayer is very often overlooked in the literature although this is a very important issue to obtain the targeted functionality. In other words, it is important to study the monolayer structure to know whether the different components are phase separating or form a solid solution.

There are different approaches to prepare a mixed monolayer. The most popular and simplest one consists in co-adsorbing (or co-reacting) the different components on a surface. The formation of such monolayer is a dynamic process where the adsorption energy, the interactions between adsorbed molecules and the interactions between molecules in the monolayer and in solution, play a key role. In the case of a multifunctional monolayer, pair interaction energies must be considered and these will depend, for instance, on relative length and/or structure of the chain and also on their terminal groups. Two categories of systems may therefore be considered.

(i) Systems for which the adsorption energy is low enough to allow a reorganization of the molecules to take place via desorption from the surface and/or a surface mobility. In this case, the monolayer formation process is close to thermodynamic equilibrium and phase segregation may be expected when the contribution of the interaction between molecules overcomes that of entropic origin. (ii) Systems for which the surface linkage is such strong that it becomes irreversible in the conditions of the functionalization. In this case a simple statistical repartition of the grafted chains is rather anticipated and therefore perfect mixing should occur.

The functionalization of gold with thiol derivatives [START_REF] Love | Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology[END_REF][START_REF] Ulman | Formation and structure of self-assembled monolayers[END_REF] and oxides with silane, [START_REF] Ulman | Formation and structure of self-assembled monolayers[END_REF][START_REF] Sagiv | Organized monolayers by adsorption. 1. Formation and structure of oleophobic mixed monolayers on solid surfaces[END_REF][START_REF] Silberzan | Silanation of silica surfaces. A new method of constructing pure or mixed monolayers[END_REF] which is widely used in various contexts, obviously belongs to the first category of systems. A maximum packing is achieved after several hours or days of incubation and phase segregation is generally observed in mixed monolayer on Au [START_REF] Laibinis | Structure of monolayers formed by coadsorption of two n-alkanethiols of different chain lengths on gold and its relation to wetting[END_REF][START_REF] Folkers | Phase behavior of twocomponent self-assembled monolayers of alkanethiolates on gold[END_REF][START_REF] Stranick | Phase Separation of Mixed-Composition Self-Assembled Monolayers into Nanometer Scale Molecular Domains[END_REF][START_REF] Brewer | Chemical Force Microscopy of Mixed Self-Assembled Monolayers of Alkanethiols on Gold: Evidence for Phase Separation[END_REF][START_REF] Li | Molecular-Scale Mixed Alkanethiol Monolayers of Different Terminal Groups on Au(111) by Low-Current Scanning Tunneling Microscopy[END_REF][START_REF] Collman | Mixed Azide-Terminated Monolayers: A Platform for Modifying Electrode Surfaces[END_REF][START_REF] Alévêque | Electroactive mixed self-assembled monolayers: A numerical overview of phase segregations[END_REF] or on oxides [START_REF] Ulman | Formation and structure of self-assembled monolayers[END_REF][START_REF] Sagiv | Organized monolayers by adsorption. 1. Formation and structure of oleophobic mixed monolayers on solid surfaces[END_REF][START_REF] Silberzan | Silanation of silica surfaces. A new method of constructing pure or mixed monolayers[END_REF] depending on the relative length of the different chains and their respective terminal groups. Conversely, the functionalization of oxide-free Si surfaces [START_REF] Ulman | Formation and structure of self-assembled monolayers[END_REF][START_REF] Ciampi | Wet chemical routes to the assembly of organic monolayers on silicon surfaces via the formation of Si-C bonds: surface preparation, passivation and functionalization[END_REF] belongs to the second category of systems because the formed Si-C bond is such strong (binding energy ~4.5 eV) and chemically stable that it cannot be cleaved at temperatures below 150°C. [START_REF] Faucheux | Thermal decomposition of alkyl monolayers covalently grafted on (111) silicon[END_REF][START_REF] Faucheux | Mechanisms of Thermal Decomposition of Organic Monolayers Grafted on (111) Silicon[END_REF] Mixed monolayers have been prepared on silicon [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF][START_REF] Lattimer | Redox Properties of Mixed Methyl/Vinylferrocenyl Monolayers on Si(111) Surfaces[END_REF][START_REF] Fabre | Single-Component and Mixed Ferrocene-Terminated Alkyl Monolayers Covalently Bound to Si(111) Surfaces[END_REF] but their composition is generally assessed qualitatively only and is more rarely quantified. [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF] To date, there are no studies describing the structure of mixed monolayers on oxidefree silicon. Titration experiments indirectly suggest that carboxy-alkyl and alkyl chains phase separate on the surface. [START_REF] Aureau | The Titration of Carboxyl-Terminated Monolayers Revisited: In Situ Calibrated Fourier Transform Infrared Study of Well-Defined Monolayers on Silicon[END_REF] In this work, we investigate the composition and structure of mixed monolayer prepared by photochemical reaction of atomically flat H-terminated Si(111) surfaces with a solution composed of 1-decene and undecylenic acid in variable proprotions. We present AFM observations and calibrated IR spectroscopy characterizations over a wide range of acid chain concentrations, exploring in particular extreme dilution of acid chains in decene. At low dilution (acid molecule fraction  SOL > 0.1 in the grafting solution), results confirm those of Faucheux et al., [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF] but new features are observed as soon as  SOL becomes smaller than 0.1. Quantitative correlations between AFM phase images and IR spectroscopic data are used to rationalize the observations and discuss the structure of the mixed monolayers as function of the composition of the grafting solution. A schematic mechanism is proposed.

Experimental

Preparation of the H-Si(111) surfaces: Silicon samples were cut in n-type Si(111) wafers with 0.2° miscut angle along the [11-2] direction (Siltronix, France). One-side polished (CZ purified, 1-10 .cm) and double-side polished wafers (FZ-purified, 10-60 .cm) were used for AFM characterizations and FTIR analysis, respectively. Samples were carefully cleaned in H 2 O 2 /H 2 SO 4 piranha solution ([1:2] in vol.) to remove organic contaminants and then etched in oxygen-free 40% NH 4 F solutions to obtain H-terminated surface with a staircase structure at the atomic scale. [START_REF] Munford | The preparation of ideally ordered flat H-Si(111) surfaces[END_REF] After etching the samples were rinsed with ultrapure water (UPW 18.2 , Millipore) and carefully dried and stored under argon until their introduction into the grafting solution.

Surface functionalization: Organic monolayers (MLs) were prepared by photochemical hydrosilylation (UV light 312 nm, 6 mW/cm 2 ) in a mixture of neat undecylenic acid (99% Acros Organics) and neat decene (97% Sigma-Aldrich). As previously reported, [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF] a freshly prepared H-Si(111) surface was introduced into the grafting solution outgassed by argon bubbling. The reaction time was 3h to 4h.

Post-cleaning procedure:

In order to obtain atomically smooth functionalized surface free of residual reaction products and/or solvent, different rinsing procedures were used. In the case of mixed monolayers prepared in solutions with acid chain fraction greater than 0.1 or decyl monolayers, glacial hot acetic acid (RSE Carlo Erba) or THF and dichloromethane (DCM) HPLC grade were used, respectively, as previously described. [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF][START_REF] Faucheux | Thermal decomposition of alkyl monolayers covalently grafted on (111) silicon[END_REF] In the case of mixed monolayers prepared in solutions with acid chain fraction smaller than 0.1, a mechanical cleaning was applied as shown in Supplementary Information (Fig. S1-S2). After a final rinse in hot acetic acid (70°C for 20 min) and boiling dichloromethane (10 min), atomically smooth surfaces, exempt of residues, were routinely obtained.

AFM observations: AFM characterizations were performed under N 2 atmosphere using a PicoSPM (Molecular Imaging) AFM operating in AC Mode. Sharp silicon tips (nominal tip radius ≤ 7 nm) were used for high-resolution imaging (PointProbesPlus, Nanosensors, spring constant ~ 40 N m -1 , resonance frequency ~160 kHz). Imaging was carried out in the attractive force regime, where the tip is in very weak interaction with the surface so as to achieve high resolution and non-destructive imaging of soft materials. [START_REF] Pérez | Dynamic atomic force microscopy methods[END_REF][START_REF] Garcia | Amplitude curves and operating regimes in dynamic atomic force microscopy[END_REF] Topography and phase images were recorded simultaneously to investigate the topography and the chemical homogeneity of the surfaces, respectively. [START_REF] Pérez | Dynamic atomic force microscopy methods[END_REF] FTIR measurements: FTIR measurements were performed in ATR geometry with an Equinox 55 spectrometer (Bruker, Germany) equipped with a liquid-nitrogen cooled Mercury-Cadmium Telluride photovoltaic detector. The ATR samples (FZ-purified Si(111) wafer, thickness 500-550 µm) were shaped as prisms with two opposite sides bevelled at ~ 45°. Their length (~15 mm, for ca ~30 internal reflections) was chosen to obtain wide-range FTIR spectra (1000-4000 cm -1 ).

Measurements were carried out in a N 2 -purged chamber to minimize H 2 O vapour and CO 2 absorption. True quantitative determination of the composition of the monolayers was performed using a specially developed FTIR analysis method based on absorbance measurements in ATR geometry using polarized IR beam and a calibration of the absorbance cross sections of specific IR vibrations, using the same geometry. [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF]

Results:

Figures 1-2 display AFM topography and phase images of samples grafted in solutions with variable acid chain fractions (Γ SOL ) whose value is noted above each image. All images (except that of Fig. 1b) have been acquired on samples subjected to an appropriate cleaning procedure after grafting. Globally all surfaces are smooth with a staircase structure similar to that of the etched H-Si(111) surface with flat terraces separated by 3.1 Å high steps corresponding to two Si(111) atomic planes. For Γ SOL > 0.1 (Fig. 1a) a standard chemical rinsing in THF followed by hot acetic acid [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF][START_REF] Faucheux | Thermal decomposition of alkyl monolayers covalently grafted on (111) silicon[END_REF] is sufficient to obtain such residue free surface. At extreme dilution (Γ SOL =10 -4 , Fig. 1b), the same rinsing procedure leaves a quasi-perfect surface with however a homogeneous repartition of protrusions exhibiting narrow size distribution (height ~1 nm, see cross section in Fig. 1b1). Applying a mechanical cleaning leaves an atomically smooth surface (see Fig. 1c). At intermediate Γ SOL values (10 -3 < Γ SOL < 0.1) AFM and optical images reveal that a large amount of matter is left on as grafted surfaces, in spite of repeated rinsing in solvents (see supplementary information, Figs. S1-S2). A mechanical cleaning is indispensable to obtain residue-free surfaces as in Fig. 2. Therefore, phase domains are likely related to the protrusions observed prior to full surface cleaning. At intermediate dilution, wide circular dark domains of diameter 0.2 -2 µm are visible (images 2a1,2b1), which will be called µ-domains in the following. Outside µ-domains (inset of Fig. 2b1), a real phase contrast on the nm scale is found again, which we assign to nanoscale domains of a few tens of nm. These domains are called n-domains in the following. The coverage of n-domains falls in the range 0.2-0.5 and giving a more precise value turned out to be uncertain because of the difficulty to set properly an image background plane. Wide-range FTIR characterization confirms that the surfaces are covered by an organic monolayer. The silicon substrate is only weakly oxidized, with an average thickness of silicon oxide smaller than 0.15 nm (essentially formed during the cleaning procedure, see supplementary information Fig. S5). Fig. 4a and 4b display narrow-range FTIR spectra of grafted monolayers after cleaning. The band centered at ~1715 cm -1 (Fig. 4a) is assigned to the C=O vibration mode of carboxylic groups and the different bands in Fig. 4b are assigned to the CH 3 (~2960 and ~2880 cm -1 ) and CH 2 (~2921 and 2851 cm -1 ) vibration modes of alkyl chains (decyl and carboxydecyl). The presence of these IR bands is consistent with the grafting of an organic film composed of acid-and methyl-terminated alkyl chains. Figure 4c shows a plot of the total surface density of grafted chains (open circle) and of the number of acid chains (bold squares) as derived from the calibration of the CH and CO bands. [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF] Quite satisfying is that the total surface density N = N decyl + N acid stays around ~2.5 chains / nm 2 for all the Γ SOL values. This density corresponds to 1 chain per ~3 Si surface atoms (there are 7.8 Si atoms / nm 2 on a perfect H-terminated Si(111) surface). There is a slight decrease of the total chain density with increasing Γ SOL which we attribute to the fact that -COOH terminal groups are bulkier than -CH 3 groups. A straight way of comparing the monolayer composition with that of the solution is plotting the acid chain fraction in the monolayer (Γ SURF ) as a function of  SOL (Fig . 4c, open squares, right y-axis). From this graph, one immediately captures that Γ SURF stays quasi-constant in the range 0.3 -0.4 over a wide range of grafting solution composition, corresponding to a surface density of 0.7 -1 acid chains/nm 2 . An extreme dilution (Γ SOL ≤ 10 -4 ) must be used to decrease significantly Γ SURF . For Γ SOL ≥ 0.2, Γ SURF ~ Γ SOL in quantitative agreement with published data. [START_REF] Faucheux | Well-defined carboxyl-terminated alkyl monolayers grafted onto H-Si(111): Packing density from a combined AFM and quantitative IR study[END_REF] The strange behavior observed for Γ SOL ≤ 0.1 motivated specific experiments where a Hterminated surface is exposed to mixed solutions in the dark, i.e., in conditions such that no grafting occurs. Fig. 5 plots the surface density of acid chains physisorbed on the H-Si(111) surface as a function of Γ SOL . The data are derived from in-situ FTIR spectra given in supplementary information (Fig. S6). The log-log scale helps for visualizing that the adsorption of acid chains starts from an acid fraction as low as Γ SOL = 10 -4 (this dilution corresponds to an acid chain concentration of ~ 0.5 mM). Saturation of the surface is reached for Γ SOL ~ 10 -2 (50 mM) and there are about 10 acid chains / nm 2 in this case. Corresponding AFM images of Hterminated surfaces exposed to grafting solutions in the dark are presented in Fig. 6. The surface exposed to pure decene (Fig. 6a) presents nm-white spots of height 0.4 nm assigned to nm oxide clusters. [START_REF] Gorostiza | Water Exclusion at the Nanometer Scale Provides Long-Term Passivation of Silicon (111) Grafted with Alkyl Monolayers[END_REF] For increasing values of Γ SOL (Figs. 6b-d), the surface is progressively covered with spots and saturation occurs for Γ SOL = 0.01 in agreement with Fig. 5. The spots height is typically 1.5 nm in images 5b-5d. Performing an accurate particle analysis proved to be very difficult due to strong tip to sample interactions.

Figures 1a1, c1

Discussion:

The above observations demonstrate that clean and dense mixed monolayers with variable acid chain fraction ( SURF ) may be obtained on Si(111) surfaces after application of an appropriate cleaning procedure.

When Γ SOL > 0.1, the monolayer is homogenous on the scale of observations since phase images are featureless. Γ SURF is only somewhat larger than Γ SOL (Fig. 4c). Besides, FTIR results indicate that the absorption frequency of COOH groups f CO (~1714.8 cm -1 ) is quasi-independent of the monolayer composition in this range of dilution while the width (fwhm) of CO band progressively increases from 20 to 40 cm -1 when Γ SOL approaches 0.1 (Fig. 7a). Therefore, the acid groups remain in rather strong mutual interaction while disorder increases upon monolayer dilution by addition of non-functionalized chains. The existence of a close proximity between neighboring acid chains for all the corresponding  SURF values is consistent with the observation that the titration behavior of such mixed monolayers is almost independent of the monolayer composition. [START_REF] Aureau | The Titration of Carboxyl-Terminated Monolayers Revisited: In Situ Calibrated Fourier Transform Infrared Study of Well-Defined Monolayers on Silicon[END_REF] The rest of the discussion aims at explaining the mechanism responsible for the phaseseparation suggested by AFM phase images when Γ SOL < 0.1. In fact, a dark contrast in AFM phase images indicates an enhanced AFM tip-to-surface interaction which is plausibly assigned to a region locally enriched in hydrophilic COOH groups. Complementary information about the molecular environment of COOH groups is provided by CO IR band frequency (f CO ), which is a sensitive probe of the interactions between COOH groups (essentially H-bonding), [START_REF] Arnold | Preparation, Modification, and Crystallinity of Aliphatic and Aromatic Carboxylic Acid Terminated Self-Assembled Monolayers[END_REF] and its width (fwhm), which accounts for the homogeneity of the local vibrator configurations. To fix ideas, we recall that it is commonly accepted that f CO ~1740 cm -1 corresponds to isolated COOH groups while f CO ~1700-1710 cm -1 corresponds to cyclic ("face to face") acid dimers. [START_REF] Arnold | Preparation, Modification, and Crystallinity of Aliphatic and Aromatic Carboxylic Acid Terminated Self-Assembled Monolayers[END_REF] In the following, the number of acid chains located in dark domains and averaged per unit surface area over the whole surface will be designated N µ,n , with the subscripts referring to µand n-domains, respectively. Straightforwardly: N µ,n =  µ,n D µ,n , where  µ,n is the domain coverage and D µ,n is the local acid chain density in the dark µ-and n-domains, respectively.

Structure and formation mechanism of monolayers at extreme dilution ( SOL = 10 -4 ):

In such conditions, a clear black/white contrast in AFM phase images strongly suggests a full phase segregation of acid chains in nanoscale domains (Fig. 1c1). Given the average density of acid chains N acid = 0.23 /nm 2 (Fig. 4) and the coverage of n-domains  n = 0.08, a local acid chain density D n = N acid /  n = 2.9 /nm 2 is determined. The characteristic frequency of the CO band (~1712 cm -1 ) is nonetheless somewhat surprising (Fig. 7a) because the necessary structural chain distortions to form symmetric face-to-face acid dimers (expected frequency ~1710 cm -1 ) are impossible to meet the estimated high D n value. A likely explanation is that the interactions between the COOH dynamic dipoles, which decay as 1/(distance) [START_REF] Love | Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology[END_REF] , become significant at such high surface density. This point will be addressed in a forthcoming paper.

The origin of the above phase separation probably results from a structuration of the grafting solution. Molecular or supramolecular assembly of carboxylic acid chains in benzene [START_REF] Levy | Thermodynamics of aggregation of long chain carboxylic acids in benzene[END_REF] or in THF, [START_REF] Ruiz | Water-Induced Coacervation of Alkyl Carboxylic Acid Reverse Micelles: Phe ome o escriptio a d Pote tial for the Extractio of Organic Compounds[END_REF] at concentration at least down to the millimolar range was indeed reported and similar behavior may be anticipated for our mixed grafting solutions. Therefore, we propose that undecylenic acid molecules self-organize as reverse micelles when the acid chain concentration becomes close to the critical micellar concentration (cmc). The COOH groups are indeed likely confined in the micelle core because they are stabilized by H-bonding (see frequency 1711.5 -1712.5 cm -1 of the CO band in Fig. S6).  SOL = 10 -4 corresponds to an acid chain concentration of 0.5 mM which is close to reported cmc for non-ionic amphiphile molecules in non-polar solvents. [START_REF] Levy | Thermodynamics of aggregation of long chain carboxylic acids in benzene[END_REF][START_REF] Ruiz | Water-Induced Coacervation of Alkyl Carboxylic Acid Reverse Micelles: Phe ome o escriptio a d Pote tial for the Extractio of Organic Compounds[END_REF][START_REF] Correa | Nonaqueous Polar Solvents in Reverse Micelle Systems[END_REF] The following mechanism is then proposed for the formation of a mixed monolayer in very dilute conditions. The micelle concentration being in the µM range (see estimate below of the number of chains per micelle), the reverse micelles are progressively adsorbing as isolated entities on the H-terminated surface in the dark (Figure 8a). Upon UV illumination, the C=C ends of the acid chains, which are located at periphery of the reverse micelles, readily react with the hydrogenated Si surface. In other places, alkyl chains (the majority species in solution) are grafted simultaneously. An alkyl monolayer is therefore obtained with isolated nanoscale acid bilayer islands (Fig. 8b). The acid dimers are finally disrupted by mechanical cleaning, which leaves an atomically smooth surface with nanoscale acid-chain-rich islands (Fig. 8c). This scenario is not only consistent with AFM observations but also with the IR spectra recorded before and after the mechanical cleaning that indicate the removal of ~ 25-50% of acid chains (data not shown). A further argument in favor of this scenario is the close similarity between the diameter of the reverse micelles (see estimate below) and the domain size (8 nm in Fig. 1c1). According to the scheme in Fig. 8, the reverse micelles must contain about 300 acid chains because the dark domains are composed of ~150 acid chains (diameter ~ 8 nm and D n = 2.9 acid chains/nm 2 ) and the mechanical wiping removes about the same number of acid chains.

The micelle diameter is therefore given by the inner core diameter plus two times the chain length (1.1 nm). To estimate the inner core diameter, we consider a COOH packing of 4.5 nm -2 on the inner surface of the micelle (this is the density of a -COOH terminated SAM on Au(111)). This gives a core diameter of ~4.4 nm. The micelle diameter is therefore ~6.6 nm, which is very close to the domain size. This diameter is also matching well with the lateral dimension of the adsorbing entities in the dark (Fig. 6). The height of the latter appears however shallower (~1.5 nm) than 6.6 nm because of a reorganization of the micelle when it interacts with the hydrophobic H-Si(111) surface and/or because a mechanical deformation during AFM imaging.

Monolayer structure and origin of invariable composition at intermediate dilution

At intermediate dilution, the striking result is that the monolayer composition stays quasi invariant over a very wide range of composition of the grafting solution: Γ SURF = 0.3 -0.4 while 10 -3 ≤ Γ SOL ≤ 0.1. The phenomenon is strongly correlated with (i) the presence of a large excess of matter left on the as-grafted surface, even after multiple rinsing in hot solvents; (ii) the formation of acid chain-rich µ-and n-domains on the AFM phase images and (iii) a lower interaction between COOH groups as evidenced by the shift of the CO IR bands, from 1714.8 cm -1 to 1717.2 cm -1 , and its broadening (Fig. 7b).

As mentioned above, dark domains in AFM phase images suggest strong segregation. To check this hypothesis, we will estimate the density of acid chains D µ,n in µ-and n-domains. Full segregation means that N acid = D µ  µ + D n  n , where N acid is given in Fig. 4 and  µ is given by Fig. 3. For the purpose of illustration, we consider the median value  n ~0.35 to determine D µ,n .

In a restricted subrange (10 -3 ≤ Γ SOL ≤ 5.10 -3 ) where the contribution of µ-domains is negligible, N acid = D n  n ~ 0.65 / nm 2 which yields D n ~1.8 /nm 2 . For Γ SOL between 5.10 -3 and 10 -1 and keeping D n  n ~ 0.65 /nm 2 , a postulated value of D µ ~1.7 /nm 2 insures that the calculated N acid value reaches the experimentally determined one for all the investigated  SOL values (see open squares in Fig. 7b). The acid-chain domains are therefore significantly less densely packed than a pure acid monolayer (2.4 /nm 2 ) or the nanoscale domain at extreme dilution (2.9 /nm 2 ) and this is coherent with two observations: (i) the surface roughness is enhanced inside the µ-domains (see Fig. S4) and (ii) the acid groups are in weaker interaction (f CO ~ 1717 cm -1 , see Fig. 7a). A full segregation at µm and a few 10 nm length scales appears therefore to capture the major experimental results. However, one cannot totally exclude a minor segregation at a shorter length scale since a density of 0.1 /nm 2 outside dark domains is calculated if D µ,n is taken 10% smaller than the above values.

The origin of the different length scales of segregation may be explained by extrapolating the mechanism described in Fig. 8. The surface density of the reverse micelles progressively increases with increasing  SOL and surface saturation is reached around  SOL = 10 -2 . The corresponding surface density of acid chains is ~10 acid chains / nm 2 (Fig. 5) or ~0.03 reverse micelles / nm 2 (there are 300 molecules / micelle, see above). These values suggest that some interpenetration of adsorbed micelles takes place, or that the lipophilic character of the hydrogenated surface induces a fusion of the micelles to form bigger supramolecular structures. [START_REF] Ruiz | Water-Induced Coacervation of Alkyl Carboxylic Acid Reverse Micelles: Phe ome o escriptio a d Pote tial for the Extractio of Organic Compounds[END_REF][START_REF] Correa | Nonaqueous Polar Solvents in Reverse Micelle Systems[END_REF] Upon UV irradiation, the chains belonging to these structures are again grafted preferentially on the H-Si surface in agreement with the AFM observations after partial removal of the extra material left upon grafting (supplementary information Fig. S7). The IR data in Fig. S2 provide also strong evidence that some photochemical reactions occur in parallel in the solution phase next to the surface since the IR band related to C=C (expected at ~1640 cm -1 ) is missing in the removed product and esters are also forming (see shoulder around 1735 cm -1 in the CO IR band in Fig. S2). Such a reticulation of chains explains well the strong difficulties to clean the as grafted surfaces in this range of dilution. It could be favored by a dense packing of acid chains in the surface vicinity. [START_REF] Rossignol | Atmospheric photochemistry at a fatty acid-coated air-water interface[END_REF]

Conclusion

The composition and the structure of mixed acid/decyl monolayers covalently grafted on oxidefree silicon surfaces by hydrosylilation have been investigated. Monolayers prepared with a high concentration of acid molecules in solution are homogenous on the nm scale, in perfect agreement with our previous work. Upon dilution of undecylenic acid in decene, the results demonstrate that the mixed monolayers are phase separated whereas statistical mixing was anticipated from simple considerations based on the irreversibility of the grafting reaction.

Exploring extreme dilutions was a decisive step to build a scenario and demonstrate that the phase separation is induced by a structuration of the solution. The nanoscale domains result in fact from the adsorption of individual reverse micelles composed of acid chains with their COOH groups inside the core of the micelle. This approach might be used for monolayer templating strategies.

At intermediate dilution, full segregation occurs again but at various length scales (µm and a few 10 of nm) according to a process governed by a complex structuration of the grafting solution, in the bulk volume and at interfaces where some reticulation occurs. This scenario explains that the acid-chain fraction on the surface stays quasi constant over a wide range of dilution and that the excess matter left on the as grafted surface is insoluble and must be mechanically removed.

Supporting information:

This material is available free of charge via the Internet at http://pubs.acs.org. It presents AFM observations of the sample at different stages of cleaning and compares the topography inside

  Figures 1a1, c1 and 2a1-b1 show phase images recorded simultaneously with the

Figure 3

 3 Figure 3 presents a plot of the µ-domain coverage as a function of Γ SOL . The grey shaded

Figures:Figure 1 :

 1 Figures:

Figure 2 :

 2 Figure 2: AFM topography and phase images of mixed monolayers grafted on Si(111) from dilute acid solutions  SOL of 0.1 and 0.01, as indicated above the topographic images). Samples were rinsed in hot solvents and a mechanical cleaning was applied to remove a large excess of matter left after grafting (see text). The inset in image (b) is an image of the same sample at a larger magnification outside the dark domains. The surfaces are imaged after specific rinsing and cleaning (see text). Complementary observations are given in Supplementary Information (Fig. S1, S4).

Figure 3 :

 3 Figure 3: Surface coverage of the dark domains observed on the phase images (Figs.1 and 2) as a function of the acid-chain fraction in solution SOL . The gray shaded region corresponds to µdomains and the red data point corresponds to the dark domains at extreme dilution (see Fig.1c1). No domain is observed above 0.1 (Fig.1a1).

Figure 4 :

 4 Figure 4: FTIR characterizations of cleaned mixed monolayers grafted in solutions containing a variable content of acid molecules. (a-b) Narrow FTIR spectra in the CO range (1600-1800 cm - 1 ) and CH range (2800-3000 cm -1 ):  SOL = 10 -4 to 1 from bottom to top. (c) Surface density (left y-axis) of acid-chains (full squares) and total chains (acid+decyl) (open circles) as a function of the acid-molecule fraction  SOL in solution. The dashed line is a guide to eye. The acid-chain fraction in the monolayer  SURF is shown as open squares (right y-axis).

Figure 5 :

 5 Figure 5: Adsorption experiment on H-Si(111) exposed to a mixed solution in the dark, i.e., no grafting is occurring. Surface density of acid chains is plotted as a function of the acid-molecule fraction in solution  SOL . The log-log scale highlights that adsorption begins at very low  SOL . The data points are derived from in-situ FTIR measurement using a custom cell sketched in the inset. See text and supplementary information, Fig. S6, for details.

Figure 6 :

 6 Figure 6: AFM images of H-terminated Si(111) surfaces exposed in the dark and at room temperature to grafting solutions with variable acid fractions  SOL (Z range = 3 nm for all images). All spots in (b-d) are ~1.5 nm mean high while they are only 0.4 nm high in (a). See text. Each surface was exposed for 20 min to the grafting solution and rinsed in boiling dichloromethane for 5 min.

Figure 7 :

 7 Figure 7: (a) Variations of the frequency (f CO ) and width (fwhm) of the CO IR band as a function of the acid-molecule fraction in solution  SOL . f CO and fwhm are measured in the spectra shown in Fig. 4a. (b) Experimental density of acid chains (black squares) as a function of  SOL and plots of the normalized numbers of acid chains in µ-domains N µ (blue) and in n-domains N n (red) and sum (open squares). These plots have been calculated, with  n = 0.35, D µ = 1.7 /nm 2 and D n = 1.8 /nm 2 (hypothesis of full segregation condition : N µ + N n ~ N acid ). See text for details. The shaded area underlines the region where the contribution of µ-domains to the total acid surface density is not negligible. The symbols at  SOL = 10 -4 correspond to the dark domains observed in Fig. 1c1.

Figure 8 :

 8 Figure 8: Schematic grafting mechanism at extreme dilution of the mixed solution ( SOL = 10 -4 ). (a) Reverse micelles formed in solution are adsorbing on the H-terminated surface in the dark. (b) Upon UV illumination grafting occurs and the resulting monolayer consists of an alkyl monolayer with isolated bilayer islands composed of acid chains. (c) The dimers are disrupted by additional mechanical cleaning, which leaves an atomically smooth surface. This mechanism explains the observations in Figs. 1b-1c-.

and outside the dark phase domains. Full range IR spectra of the samples are presented as a complement to the narrow spectra presented in the main manuscript. Raw data corresponding to adsorption experiments are also presented.