Nonlinear Optical Contrast in Azobenzene-Based Self-Assembled

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Nonlinear Optical Contrast in Azobenzene-Based Self-assembled Monolayers Claire Tonnelé, Benoît Champagne, Luca Muccioli, and Frédéric Castet Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.9b01241 • Publication Date (Web): 13 May 2019 Downloaded from http://pubs.acs.org on May 14, 2019

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Chemistry of Materials

Nonlinear Optical Contrast in Azobenzene-Based Self-assembled Monolayers Claire Tonnelé,∗,† Benoit Champagne,∗,‡ Luca Muccioli,∗,¶ and Frédéric Castet∗,† Institut des Sciences Moléculaires (ISM, UMR CNRS 5255), University of Bordeaux, 351 Cours de la Libération, 33405 Talence, France, Unité de Chimie Physique Théorique et Structurale, Chemistry Department, Namur Institute of Structured Matter, University of Namur, Belgium, and Department of Industrial Chemistry "Toso Montanari", University of Bologna, Viale Risorgimento 4, 40136 Bologna, Italy E-mail: [email protected]; [email protected]; [email protected]; [email protected]

Abstract Conjugated organic photochromes like azobenzene derivatives can show remarkable nonlinear optical (NLO) properties and rapid responses, two essential requirements for the realization of optoelectronic switching devices. These applications also require the control of the molecular organization over the micrometric scale, which in principle can be achieved by arranging chromophore units in self-assembled monolayers (SAMs). To rationalize the interplay between the NLO responses of isolated molecules and those of photoresponsive materials, we implement here a computational approach combining ∗

To whom correspondence should be addressed Institut des Sciences Moléculaires (ISM, UMR CNRS 5255), University of Bordeaux, 351 Cours de la Libération, 33405 Talence, France ‡ Unité de Chimie Physique Théorique et Structurale, Chemistry Department, Namur Institute of Structured Matter, University of Namur, Belgium ¶ Department of Industrial Chemistry "Toso Montanari", University of Bologna, Viale Risorgimento 4, 40136 Bologna, Italy †

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molecular dynamics simulations and DFT calculations for predicting the NLO responses of azobenzene-based SAMs with different surface densities. We show that collective switching of the chromophores is indeed possible, even though trans→cis photoisomerization yields decrease when increasing the chromophore concentration. The magnitude of the second-order NLO response of trans SAMs is dominated by the component normal to the surface, which is considerably larger than the parallel one and significantly increases with the packing density. Photoswitching has the neat effect of halving the first hyperpolarizability, allowing for large NLO contrasts exploitable for storing and reading information in selected portions of the surface.

Introduction The design of photoresponsive materials allowing remote and reversible commutation of their electronic, magnetic or optical properties remains one of the greatest challenge for the development of optoelectronic and photonic devices. 1 In this context, photochromic materials that exhibit switchable second-order nonlinear optical (NLO) responses are of particular interest for optical data storage or chemical sensing applications. Indeed, since NLO responses are measured using low energy near-infrared wavelengths, they can be exploited to probe the electronic state of a light-responsive system without triggering uncontrolled photoconversions or photochemical side reactions. NLO switchable materials thus offer a unique way for designing molecular-scale memory devices with multiple storage and nondestructive readout capacity. 2–5 The suitability of a material for practical use in a photoresponsive NLO device is conditioned by two main requirements. The first is that constitutive molecules must exhibit a large first hyperpolarizability in at least one of their forms, as well as a sizable first hyperpolarizability contrast upon switching. Typical NLO photoswitches display a dipolar donoracceptor structure, whose electron conjugation can be altered upon light irradiation through different mechanisms: trans-cis isomerization (in azobenzenes), 6,7 intramolecular proton 2


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transfer (in anils), 8–10 and cyclization/ring-opening (in spiropyrans, 11 diarylethenes, 12,13 dithiazolylethenes, 14 dihydroazulenes, 15 oxazines, 16 oxazolidines, 17–22 and even Stenhouse adducts 23 ). The second requirement is that responsive molecules must adopt a non-centrosymmetric spatial organization that preserves or even enhances their gas phase switching ability and contrast. By constraining the alignment of the molecular units at controlled concentrations, surface coating with self-assembled monolayers (SAMs) constitutes a viable strategy for introducing NLO chromophores into a device in view of maximizing its macroscopic secondorder susceptibility. The realization of such two-dimensional (2D) functional materials has been recently demonstrated by Tegeder and coworkers, by anchoring azobenzene or fulgimide NLO switches at silicon or gold solid surfaces. 24–26 C12 -OSi(OH)2N N

Az11 -OSi(OH)2-

O

AZO

ALK

Figure 1: C12 and Az11 molecular structures, and definition of the ALK and AZO moieties of Az11. In complement to chemical engineering, the rational design of NLO devices and optimization of their performances can also benefit from the development of computational strategies that provide a microscopic description of the relationships linking the interfacial molecular organization to the NLO response. To this aim, we recently implemented a sequential computational approach combining molecular dynamics (MD) simulations and density functional theory (DFT) calculations to evaluate the second-order NLO responses of SAMs based on indolino–oxazolidine photoswitches. 27 Here we extend this strategy to investigate the morphologies and NLO responses of azobenzene-based SAMs grafted onto an amorphous SiO2 surface, and composed of unsubstituted and chromophore-functionalized alkyl chains, referred to as C12 and Az11, respectively (Figure 1). In MD simulations, the trans-cis 3


isomerization process is triggered by means of an iterative process using distinct torsional profiles for the ground and first excited states of the Az11 derivatives. 28 The resulting morphologies in the two switching states are characterized both in terms of structural order and of their NLO responses, which are compared to recent polarization-resolved second-harmonic generation (SHG) experiments. 24 The impact of electrostatic intermolecular interactions on the NLO responses is then discussed.

Computational methods Simulation details MD simulations were carried out using the NAMD software. 29 Oxygen and silicon atoms from the amorphous silica substrate were described using the Clay Force Field (FF). 30 C12 and Az11 molecules were modeled using a modified version of the General AMBER Force Field. 31 For both trans and cis Az11 conformers, ESP-fitted atomic charges 32 as well as torsional potential parameters were derived from M06/6-311G(d) DFT calculations (see the Supporting Information, SI). In addition, distinct torsional force field parameters for the ground (S0 ) and excited (S1 ) states of Az11 were derived by employing Ph-N=N-Ph torsional potentials calculated at the CASPT2 ab initio level, 33 with the methodology reported in Ref. 34. Additionally, the FF bond equilibrium distances were modified to ensure close reproduction of the DFT bond lengths (with a mean absolute error of 0.006 Å for both trans and cis conformers, see SI), a fundamental requirement for utilizing FF geometries in quantum chemical calculations of NLO properties, since those are strictly linked to the accurate description of bond lengths and bond length alternation. 35–37

Preparation of trans-Az11 SAMs SAMs were produced following the successive steps illustrated in Figure S4. A 52.044×51.119 Å2 surface of amorphous silica was first prepared, using the methodology reported in Ref. 4


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27. Then, a vertical C12 molecule was replicated 11 × 11 = 121 times in a regular lattice to generate a SAM with coverage of 4.55 molecules/nm2 , a typical value for closely packed alkylsiloxane SAMs. 38 To simulate the formation of Si-O single bonds between the C12 molecules and the surface, one hydroxyl hydrogen was removed and specific Lennard-Jones interaction was added between the corresponding hydroxyl oxygen and silicon atoms of the surface. 39 The slab of C12 molecules was then placed on top of the SiO2 surface and equilibrated at T = 300 K and constant volume for about 70 ns. Observables for this SAM were then calculated from a 10 ns-long production run. From the final C12 SAM structure, the position of grafting oxygens was frozen and transAz11 SAMs of increasing chromophore concentrations were generated by substituting C12 molecules with trans-Az11 conformers in the 1:2, 3:4 and 1:1 Az11:(Az11+C12) ratios, yielding three samples designated hereafter as (1:2)trans (composed by 60 Az11 and 61 C12 molecules), (3:4)trans (91 and 30), and (1:1)trans (121 and 0), respectively. All trans samples were annealed at 400 K for 60 ns, and subsequently cooled down at 300 K for 30 ns before a 10 ns production run was performed.

Preparation of cis-Az11 SAMs The iterative photoisomerization procedure described in Ref. 28 was applied to obtain the cis SAMs morphologies. This procedure considers solely the torsional mechanism, and uses distinct force field parameterizations for the S0 and S1 states of Az11 photochromes. In a first step (step A in Figure S5-S6), the S0 → S1 photoexcitation is simulated by replacing, for all molecules in trans conformation, the S0 force field by the one optimized for S1 . The molecular geometries subsequently relax within the S1 potential energy surface for 1 ns. In a second step (step B in Figure S5-S6), the FF parameterization is turned back to the ground state potential for 200 ps. The molecular geometries can then evolve either towards their cis conformation, or come back to their initial minimum-energy trans form. For each molecule reaching the cis conformation, the atomic charges adapted for the starting trans geometry 5



are substituted by the ones calculated for the cis conformer. This procedure is then iterated for all unswitched trans molecules until convergence. Convergence is attained when i) the whole monolayer has switched to cis or ii) 10 consecutive unsuccessful iterations (i.e. without any switching) are obtained. Further details regarding the procedure are provided in SI.

Quantum chemical calculations of NLO properties The static and dynamic components of the molecular first hyperpolarizability tensor (β) were evaluated using the time-dependent DFT (TD-DFT) method at the M06-2X/6-311+G(d) level for individual molecular structures extracted from trans and cis-Az11 SAMs at regular time intervals along the MD trajectories. Owing to its substantial amount (54%) of long-range Hartree-Fock exchange, the M06-2X exchange-correlation functional (XCF) 40 was demonstrated to perform well for calculating the first hyperpolarizabilities of conjugated organic dyes in their equilibrium geometries. 23,41–44 The choice of the M06-2X XCF for evaluating the variations of the NLO responses with respect to dynamical geometry fluctuations was also substantiated by a cross-validation with calculation performed with the range-separated CAM-B3LYP functional on a representative set of molecular structures (see Tables S3-S4). Frequency-dependent calculations were carried out using an incident wavelength of 800 nm (¯hω=0.057 a.u.), typical of Ti:sapphire laser systems. Preliminary investigations were first conducted to define the relevant molecular fragments that must be considered in NLO calculations, i.e. the truncation offering the best compromise between accuracy and computational cost. These benchmarks led to the conclusion that, in addition to the azobenzene photoresponsive unit, the -(CH2 )10 CH3 alkyl chain has to be explicitly included, while the terminal Si(OH)2 O- anchoring unit can be omitted. They also demonstrated the consistency between first hyperpolarizability values calculated using DFT- and FF-optimized geometries, proving the reliability of the force field parameterization (see SI for details). A total of 10 MD frames were then used to sample the multiple geometrical conformations 6


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adopted by the Az11 photoswitches within the trans and cis SAMs at various coverages (i.e. a total of 610, 910 and 1210 molecular geometries for (1:2), (3:4) and (1:1) SAMs, respectively). The interfacial NLO responses were analyzed by considering the components and norm of the first hyperpolarizability vector, defined as follows:

βi =

1X (βijj + βjij + βjji ) 3 j

(1)

q βx2 + βy2 + βz2

(2)

β=

The anisotropy of the NLO response was also characterized as the ratio between the normal (z) and in-plane (x, y) contributions of the first hyperpolarizability vector:

aβ = p

|βz | βx2 + βy2

(3)

With this definition, a perfectly isotropic NLO system for which βx = βy = βz is characterized √ by an anisotropy ratio of 1/ 2. Larger values reveal the predominance of the β-component normal to the surface plane, resulting from the molecular alignment within the SAMs. The average SAM anisotropy was calculated as the average of the molecular anisotropies. All quantum chemical calculations were performed using the Gaussian09 package. 45 β values are reported assuming a Taylor series expansion of the induced dipole with respect to the applied electric field (T convention), 46,47 and are given in atomic units (1 au of β = 3.6310−42 m4 V−1 = 3.2063 × 10−53 C3 m3 J−2 = 8.641 × 10−33 esu).

Results and discussion Structure of Az11 SAMs We start our discussion by characterizing the morphologies of SAMs before and after switching, in terms of positional and orientational order. Not surprisingly, the photoswitching was 7



not successful in the maximal (1:1) density sample, for which photoisomerization is completely suppressed due to steric effects, as previously observed for tightly-packed azobenzeneterminated SAMs. 48–51 On the contrary, photoisomerization yields of 95% and 59% were respectively obtained for SAMs of (1:2) and (3:4) relative coverage (see Figure S7). In the following, these two systems are referred to as (1:2)cis and (3:4)cis, respectively, though they contain a fraction of azobenzenes still adopting trans conformation. We also treat separately, in the analysis of structural observables, the alkyl chains of Az11 (ALK) from the terminal azobenzene units (AZO), as defined in Figure 1. This distinction is useful since in all Az11 SAMs, for which characteristic snapshots are reported in Figure 2, alkyl chains exhibit the hexagonal crystalline packing typical of alkylsiloxane SAMs. 38 This peculiar ordering is evidenced by the hexagonal pattern of the 2D radial distribution functions (RDFs), which measure the probability that the center of mass of a molecule occupies a given position in the (x, y) plane with respect to the center of mass of a reference central molecule. 2D RDFs also show that the hexagonal structure of the ALK sublayer is neither affected by the concentration of the Az11 chromophores nor by their isomerization (Figure 2, bottom panels). In line with previous reports for H- and azideterminated alkylsiloxane SAMs, 27,52 the C12 and all Az11 SAMs share the same lattice parameter (d = 5.02 Å) and paracrystallinity parameter 53 (σd /d ≈ 0.1), as also illustrated by 1D RDFs in Figures S9 and S10. Furthermore, the 2D RDFs of all samples evidence that the hexagonal order is at least partially transferred to the azobenzene moieties in the top-half sublayer, which is however consistently more disordered than the aliphatic sublayer. The sample at maximum (1:1) coverage deserves further discussion: here the azobenzene moieties assume a herringbone disposition (c.f. the corresponding top view snapshot in Figure 2) which is not perfectly compatible with the hexagonal cell of the alkyl portion of the molecules. This mismatch seems to give rise to defects on the herringbone lattice of the AZO upper portion of the SAM, and to a distortion of the hexagonal lattice of the lowermost section, as indicated by the asymmetric peaks in the corresponding RDF. It is worth noting

8


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that a herringbone packing was also experimentally detected for the same SAM on Au(111), 54 even if in our case we do not observe domains with different orientations, probably because of finite size effects and periodic boundary conditions. Overall, the very similar molecular ordering found between Az11/Au(111) and Az11/SiO2 interfaces suggests that the nature of the substrate underneath the organic SAM does not have a significant influence on the spatial organization of the C12 molecules onto which the azobenzene units are grafted. (1:2)trans

(1:2)cis

(3:4)trans

(3:4)cis

(1:1)trans

Figure 2: Lateral and vertical views of the different samples (first and second rows), and two dimensional radial distributions functions of AZO (third row) and ALK (fourth row) portions of the SAMs. From the left to the right: (1:2)trans, (1:2)cis, (3:4)trans, (3:4)cis and (1:1)trans SAMs. The snapshots in Figure 2 also show that molecules assume the expected upright arrangement, with alkyl chains slightly tilted with respect to the surface normal, and azobenzene 9



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Table 1: Average values of thickness (Å), RMS surface roughness (Å) and nematic order parameter S and tilt angle (θ, ◦ ) of the AZO and ALK portions of the C12 and Az11 SAMs at different surface coverages and conformations. thickness roughness SALK SAZO θALK θAZO

C12 (1:2)trans 18.4 24.5 0.97 2.19 / 0.865 / 0.114 / 14 ± 7 / 41 ± 16

(3:4)trans 26.3 1.40 0.897 0.658 18 ± 7 33 ± 11

(1:1)trans 28.1 1.22 0.928 0.958 18 ± 6 18 ± 5

(1:2)cis (3:4)cis 23.6 26.1 1.26 1.46 0.854 0.873 0.058 0.388 15 ± 7 16 ± 7 38 ± 17 28 ± 14

groups more variedly oriented; the corresponding ensemble-averaged tilt angles, together with SAM thickness, roughness and nematic order parameter S, are reported in Table 1. The latter measures the degree of orientational order, and is calculated as the h 32 cos2 φ − 21 i average, where φ is the angle between the long molecular axis and the direction of maximum alignment. 52 The orientational order is always high for the ALK part of the SAMs (SALK ∼ 0.9), while it is clearly coverage and conformation dependent in the AZO portion, with more densely packed samples and trans conformation leading to higher order. In particular with decreasing chromophore coverage, the azobenzene moieties, becoming less densely packed, adopt more tilted conformations and progressively lie down with random orientation, as confirmed by the increase of the tilt angle and by the low SAZO values. The decrease of the azobenzene tilt with increasing coverage also induces a slight augmentation of the trans SAMs thickness, while isomerization causes the latter to reduce, even if the effect is weak (see Table 1). The interplay between molecular orientation, density of azobenzene units and photoisomerization can be better rationalized by inspecting the distributions of the tilt angles shown in Figure 3, where again we distinguish the alkyl and azobenzene moieties, and also analyze distinctly the orientational distributions of the two azobenzene phenyl rings. The distributions of the tilt angle cosines for the ALK segment is almost unimodal for all samples and peaked at values slightly off from the normal direction (cos θ = 1), corresponding to the tilt angles of 14-18◦ reported in Table 1. The same behavior is observed for the AZO segments of 10


P(cos θ)

20 15

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ALK (1:2)trans (1:2)cis (3:4)trans (3:4)cis (1:1)trans

P(cos θ)

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(1:2) (1:2)

6.0

P(cos θPh) P(cos θPh)

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6.0 6.0 Ph1−trans Ph1−trans Ph1−cis Ph1−cis 5.0 5.0 Ph2−trans Ph2−trans 4.0 4.0 Ph2−cis Ph2−cis

7.0 5.0 4.0

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(3:4) Ph1−trans Ph1−cis Ph2−trans Ph2−cis

Ph2

N N

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0.0 0.0 0.0 0.6 −1.0 −1.0 −0.6 −0.6 −0.2 −0.20 00.2 0.2 0.6 0.6 1.0 1.0 −1.0 −0.6 −0.2 0 0.2 tilt angle (cos θPh) tilttiltangle angle(cos (cosθPh θPh ))

1.0

O

Figure 3: Top: Normalized distributions of tilt angles θALK of all Az11 SAMs (left) and θAZO of trans SAMs (right) characterizing the global orientation of ALK and AZO parts of the molecule with respect to the surface normal. Bottom: Normalized distributions of the tilt angles of azobenzene phenyl groups. Note that the peak at low θP h2 values in the (3:4)cis SAM corresponds to molecules remaining in trans conformation.

11


the (1:1)trans SAM, while at lower coverage the chromophores can assume a much broader range of tilt angles. The observation of the orientation of each phenyl group is particularly useful for understanding the morphology changes upon isomerization at (1:2) and (3:4) coverages. Before switching, for both systems the two phenyl groups are parallel in the elongated trans conformer, and θP h1 and θP h2 consequently present very similar distributions. While a rather uniform orientation of the lower phenyl is obtained at coverage (3:4), the bimodal distribution of θP h1 observed for the (1:2)trans sample is associated with θ1 values of ∼60◦ (see Figure S11). Upon photoisomerization, the lowermost phenyl assumes a more vertical orientation and the distribution correspondingly becomes more peaked in the cos θ = 1 region. In contrast, instead of the uniform upward orientation found in the trans systems, the distribution of θP h2 becomes very broad in cis SAMs, and extend over a range of about 120◦ , even including a few molecules with the terminal phenyl group pointing down towards the surface. In the following paragraph, we shall see how this drastic change in morphology can affect the nonlinear optical response of the SAMs.

Nonlinear optical properties of Az11 SAMs trans-Az11 SAMs at different relative coverages We start the analysis of NLO properties by discussing the static and dynamic first hyperpolarizabilities (β and βz ) of molecular structures extracted from full trans SAMs. At this stage, we ignore the electronic interactions between adjacent chromophores and assume that the total response is the sum of the individual contributions of molecules forming the monolayer. Owing to dynamical geometry fluctuations and steric interactions, the second-order NLO responses of Az11 molecules are spread over a broad range of values, as reflected in the standard deviation of their distributions (see Figure 4 and Table 2). Whereas the average 12


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0 0

1

2

3

4

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Figure 4: Distributions of the static (left) and dynamic (right) values of β (top), βz (middle) and NLO anisotropy aβ (bottom), for trans-Az11 SAMs at different surface coverages.

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β values are hardly impacted by the relative coverage (top panels of Figure 4) and remain similar to the first hyperpolarizability computed on the optimized Az11 molecule in gas phase (with a maximum difference of 5%, see Figure S12 and Table S2), βz significantly increases with the packing density, as expected by the decrease of the molecular tilt with respect to the z direction. Meanwhile, the dispersion of βz values decreases, consistently with the progressive straightening and more ordered packing of the molecules on the surface (vide infra). As a consequence, the anisotropy factor aβ increases with chromophore concentration, with a particularly significant enhancement for the (1:1) sample. The comparison between static and dynamic NLO responses (left and right panels in Figure 4) shows that, independently of the surface coverage, frequency dispersion effects enhance three-four times the average first hyperpolarizability and its normal component, as well as their disorder (expressed in terms of ratio between average values and standard deviations). Reversely, frequency dispersion barely affects the average NLO anisotropy and spread of aβ values. The average dynamic anisotropy factors computed for the various relative coverages are in qualitative agreement with polarization-resolved SHG measurements on trans-Az11 SAMs reported by Schulze et al., 24 which evidenced that the second-order susceptibility perpendicular to the interface is larger than the parallel one. However, as a result of dynamical fluctuations in the geometries of the molecules and in their orientations with respect to the surface, the haβ i values are smaller than the estimate of ∼ 4 provided by ab initio calculations for the case of an isolated rigid Az11 molecule. 24

Switching of the NLO responses As already discussed, one of the main requirements for the realization of a photoresponsive NLO material is to exhibit a significant variation of its second-order response upon illumination. Indeed, the distributions of the dynamic and static first hyperpolarizabilities of structures extracted from cis SAMs are markedly shifted to lower values upon trans→cis

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Table 2: Average values and standard deviations (σ) of the static (λ = ∞) and dynamic (λ = 800 nm) first hyperpolarizabilities (β and βz , in a.u.) and anisotropy factors (aβ ) of Az11 molecules extracted from trans SAMs at various relative coverages. λ=∞ (1:2)trans (3:4)trans (1:1)trans λ = 800 nm (1:2)trans (3:4)trans (1:1)trans

hβz i ± σβz hβi ± σβ −2268 ± 609 3001 ± 494 −2531 ± 442 3021 ± 392 −2975 ± 378 3157 ± 389 hβz i ± σβz hβi ± σβ −8044 ± 2915 10842 ± 2976 −8864 ± 2627 10667 ± 2875 −10839 ± 2918 11533 ± 3081

haβ i ± σaβ 1.92 ± 3.15 2.01 ± 1.91 3.15 ± 1.08 haβ i ± σaβ 1.75 ± 2.11 1.89 ± 1.38 3.01 ± 0.92

isomerization. Since the molecular switching is incomplete (95% and 59% at (1:2) and (3:4) coverage, respectively), the distributions of β are now bimodal, with the minor peak (at larger β values) corresponding to Az11 molecules in trans conformation, and the major one to switched cis conformers (Figure 5 and S13, respectively). As reported in Table 3, the average static β reduces to 1600 a.u. for chromophores in cis conformation, versus around 3100 a.u. for unswitched molecules. Frequency dispersion effects enhance the β and βz responses of trans conformers by a factor ∼ 3.7, while the enhancement is smaller (∼ 2.7) for cis conformers. Moreover, as already observed in alltrans SAMs, the out-of-plane first hyperpolarizability βz is more sensitive to the chromophore concentration than the β norm. The influence of geometrical distortions of the azobenzene moiety on the NLO properties of the Az11 chromophores in (1:2)trans and (1:2)cis SAMs were further analyzed in terms of correlations between the θP h1 and θP h2 tilt angles and β (see Figures S17-S19). For the unswitched system, the β values do not show any evident correlation with the angles, while the normal component βz becomes increasingly negative with the decrease of the two angles, in line with the associated progressive straightening of the molecules on the surface. On the contrary, no apparent correlation with the tilt angles is found for β and βz in the cis SAM. To enable a direct comparison with experimental NLO contrasts, the variation of the second-order NLO response occurring upon photoisomerization has to be evaluated by com-

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7

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Figure 5: Distributions of the dynamic values of β (top), βz (middle) and NLO anisotropy aβ (bottom), for trans- and cis-SAMs of (1:2) (left) and (3:4) (right) relative coverage.

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paring the first hyperpolarizability of the all-trans SAMs (Table 2), and that of the photoisomerized SAMs considered as a whole, i.e. including both cis and trans conformers. It turns out that for the (1:2) coverage, the dynamic βz contrast reaches 2.22, while it is reduced to 1.41 for the (3:4) coverage, as a consequence of the smaller amount of molecules that have effectively switched to the cis conformation. Although a quantitative comparison is not appropriate since the experimental surface coverage is not exactly known, the ∼ 30% variation of the first hyperpolarizability we obtain for the (3:4) sample compares well with the change of 16% observed in the normal SHG intensity for Az11 SAMs. 24 This slight overestimation of the experimental contrast can be partly ascribed to the background NLO response of non-functionalized C12 units, neglected in our calculations. This signal is in fact present and constant in both trans and cis samples, thus reducing the measured NLO contrast. On the other hand, the average dynamic anisotropy ratios haβ i computed for the transSAMs (1.75 and 1.88 for (1:2) and (3:4) relative coverages, respectively), are smaller than those computed for the cis-SAMs (2.77 and 3.34). These values are correlated to the θP h1 tilt (Figure S20), with large aβ associated to a more vertical orientation of the lowermost phenyl ring. The trans−→cis photoswitching results in a sharper distribution of θP h1 , which is shifted towards lower angles (Figure 3) in the cis-SAMs, and associated in turn with an even larger haβ i. Note that, for the cis-SAM, these large anisotropy values correspond to tilt angle values θP h1 close to 0◦ and θP h2 comprised between 60◦ and 120◦ , and that an opposite behavior of the anisotropy upon switching has been measured by Tegeder and collaborators, 24 i. e. smaller anisotropies for the cis-SAM.

Effect of intermolecular electrostatic interactions The NLO response values reported so far refer to single molecules without any inclusion of polarization and intermolecular couplings, effects that could be instead relevant for densely packed Az11 SAMs where both H- and J-aggregation might occur. 48,55 In the following, we

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Table 3: Averaged values and standard deviations (σ) of the static (λ = ∞) and dynamic (λ = 800 nm) first hyperpolarizabilities (β and normal βz component, in a.u.) and anisotropy factors (aβ ) of Az11 molecules, extracted from SAMs of (1:2) and (3:4) relative coverage after photoisomerization (all ). The same quantities are also reported by considering independently the fraction of switched (cis) and unswitched (trans) molecules. (1:2)cis

(3:4)cis

(1:2)cis

(3:4)cis

λ=∞ all trans (5%) cis (95%) all trans (41%) cis (59%) λ = 800 nm all trans (5%) cis (95%) all trans (41%) cis (59%)

hβz i ± σβz hβi ± σβ −1308 ± 436 1574 ± 485 −2231 ± 468 3122 ± 457 −1261 ± 378 1494 ± 326 −1935 ± 792 2189 ± 817 −2742 ± 531 3073 ± 412 −1383 ± 337 1585 ± 327 hβz i ± σβz hβi ± σβ −3629 ± 1865 4442 ± 2314 −8198 ± 2799 11550 ± 3379 −3393 ± 1459 4075 ± 1519 −6284 ± 4113 7136 ± 4370 −9999 ± 3887 11235 ± 3858 −3746 ± 1509 4335 ± 1627

haβ i ± σaβ 2.89 ± 3.63 1.08 ± 0.31 2.98 ± 3.70 3.36 ± 4.15 3.31 ± 3.98 3.39 ± 4.26 haβ i ± σaβ 2.77 ± 3.19 1.06 ± 0.31 2.86 ± 3.25 3.34 ± 5.71 3.33 ± 5.92 3.35 ± 5.57

develop an attempt to evaluate the electrostatic contribution of these environment effects on the molecular second-order NLO responses of the (1:2) SAM, which is the sample that displays the largest isomerization yield. To this end, the electrostatic environment of individual Az11 chromophores was modeled with a set of point charges (PC) replacing the atoms of the surrounding molecules, namely the ESP atomic charges used in the force field. In order to assess the convergence of the NLO properties, the first hyperpolarizability (βenv ) and NLO anisotropy (aβ,env ) of Az11 molecules extracted from a same MD frame were first calculated using increasingly large PC environments. The size of the environment was defined using a cutoff radius rn (Å) = (d + 2.0) × n, with n = 1 − 5 and d=5.02 Å being the lattice parameter of the C12 SAM (see Figure 6, bottom left); all neighbors located at distances r < rn of the central molecule (with distances r evaluated between the centers of mass of the ALK moieties) were included. The PC-embedded NLO responses (referred to as βenv and aβ,env ) are systematically compared to those obtained for the isolated molecules (i.e. n = 0) considered in the pre-

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vious sections. Electrostatic interactions induce significant variations of the dynamic NLO responses with respect to those of isolated chromophores. These variations evolve smoothly with rn and show saturation for n = 5, as indicated by the βenv /βisol and aβ,env /aβ,isol ratios reported in Tables S5-S6 and Figure S21. For this environment size, we then extended the NLO calculations to all the molecular structures considered in the previous section. The results of these calculations are condensed in Table 4 which reports the average first hyperpolarizabilities and anisotropy factors of PC-embedded Az11 molecules, while their statistical distributions are compared to those of the isolated molecules in Figure 6. Depolarization effects due to the PC environment induce a decrease of the normal βz component compared to the isolated molecule. Owing to the polar alignment of the molecules on the surface, the local fields created on the reference molecule by the point charges reduce its donor-acceptor character, and lead to βenv values smaller than βisol . Noticeably, the magnitude of this lowering is similar for both trans and cis conformations, thus resulting in quasi unchanged contrasts compared to those calculated for isolated molecules. On the contrary, anisotropy variations due to electrostatic effects have opposite trends for the two isomers. As shown in Tables S5-S6, the average anisotropy factor of trans molecules slightly increases from 1.75 to 1.81 when accounting for the electrostatic environment), while it more markedly decreases (from 2.77 to 2.40) in the case of cis molecules. The non symmetrical impact of the point-charge embedding partially reconciles our predictions with experimental observations 24 regarding the relative amplitudes of normal and in-plane β components, although contrary to SHG measurements, we still obtain a larger anisotropy for the cis sample. A possible source of discrepancy is intrinsic to the plane-polarized experimental set-up. Indeed, given that the angle of the incident probe with respect to the surface plane is 45◦ , the susceptibility measured using a p-polarized beam is not purely perpendicular to the surface (i.e. parallel to the z axis considered in the calculations), but incorporates contributions arising from in-plane components (along x and y axes). A second origin is that the area probed experimentally is much larger than the size of the simulation

19



Page 20 of 32

box and may contain separated domains with different tilts of the SAM forming molecules with respect to the laser beam. The total in-plane response can then decrease, with respect to the one of the monodomain studied here, since it will be given by a summation of βx and βy components of different sign and magnitude. Theoretical investigations on larger systems would be necessary for clarifying this issue. Table 4: Averaged values and standard deviations (σ) of the static (λ = ∞) and dynamic (λ = 800 nm) first hyperpolarizabilities (β and normal βz component, in a.u.) and anisotropy factors (aβ ) of PC-embedded Az11 molecules extracted from (1:2)trans and (1:2)cis SAMs. The trans/cis contrasts are reported in the last column, and compared to those calculated for isolated molecules (in parentheses). λ=∞ (1:2)trans (1:2)cis hβi ± σβ 2200 ± 704 1174 ± 402 −1614 ± 693 −893 ± 375 hβz i ± σβz 1.79 ± 2.55 2.27 ± 2.87 haβ i ± σaβ λ = 800 nm (1:2)trans (1:2)cis hβi ± σβ 7703 ± 3675 3380 ± 1722 −5620 ± 3166 −2609 ± 1450 hβz i ± σβz haβ i ± σaβ 1.81 ± 2.42 2.40 ± 3.22

20


trans/cis 1.87 (1.91) 1.81 (1.73) 0.79 (0.66) trans/cis 2.28 (2.44) 2.15 (2.22) 0.75 (0.63)

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60

60

transenv cisenv transisol cisisol

40 30 20 10 0


50

Probability (%)

50

Probability (%)

40 30 20 10

0

5

10 15 3 β (10 a.u.)

20

0

25

5

0

−5 −10 −15 3 βz (10 a.u.)

40

n=1 n=2

30

−25

25 20 15 10

n=3

5

n=4

0 0

n=5

−20


35

Probability (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

2

3 4 5 anisotropy

6

7

8

Figure 6: Distributions of the dynamic values of β (top left), βz (top right) and NLO anisotropy aβ (bottom right) of Az11 molecules extracted from the (1:2)trans- and (1:2)cisSAMs, considered isolated (isol ) or within a point charge embedding (env ). Bottom left: Color representation of the successive shells of molecular neighbors (n = 1 − 5) used for defining the point-charge electrostatic surrounding in NLO calculations.

21



Conclusions A computational approach encompassing classical molecular dynamics simulations and DFT calculations was applied to investigate the morphology and second-order nonlinear optical responses of photoswitchable azobenzene-based self-assembled monolayers grafted on silica. Simulations of the trans SAMs revealed that the hexagonal organization and herringbone pattern, present at full chromophore coverage, fades out as the concentration of azobenzene units decreases. The light-induced trans-cis isomerization of the azobenzene chromophores produces substantial disordering in the morphology of the azobenzene groups, while the alkyl portion of the SAMs is in practice unaffected. Photoisomerization yields of 95% and 59% were respectively obtained for SAMs of (1:2) and (3:4) relative coverage, while no switching was achieved at the highest (1:1) density. The sequential MD-QM scheme captures the impact of dynamical geometry fluctuations and steric interactions on the molecular first hyperpolarizability, often neglected in computational studies. For trans isomers, calculations showed that the average first hyperpolarizability component normal to the surface plane significantly increases with the packing density. Additionally, the anisotropy factors computed at different chromophore concentrations indicate that the β-component perpendicular to the interface is larger than the parallel contribution, consistently with previously reported SHG measurements. Calculations also evidenced that the βz (trans)/βz (cis) contrast observed upon photoisomerization of the SAMs strongly depends on the chromophore concentration, which drives the yield of molecules that eventually switch to the cis conformation. The computed variations of the normal first hyperpolarizability βz range between 30% and 50% depending on the relative surface coverage, in qualitative agreement with experimental reports. Finally, although calculations performed on isolated molecules provide reasonable estimates of first hyperpolarizability contrasts, we showed that electrostatic embedding induces substantial variations in the anisotropy of the molecular NLO response of densely packed aggregates. This observation suggests that more sophisticated schemes including mutual 22


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polarization effects and intermolecular electronic couplings should be developed to enable reliable comparison with polarization-resolved SHG experiments and to establish design rules for optimizing the performances of NLO materials.

Acknowledgement C.T. thanks Dr D. Przyrembel (Free University of Berlin) for helpful exchanges. This work was carried out in the frame of the Centre of Excellence LAPHIA (Investments for the future: Programme IdEx Bordeaux − LAPHIA (ANR-10-IDEX-03-02). It was also supported by funds from the M-ERA.NET project MODIGLIANI (ANR-15-MERA-0002-01). Computer time was provided by the Pôle Modélisation HPC facilities of the Institut des Sciences Moléculaires, co-funded by the Nouvelle Aquitaine region, as well as by the MCIA (Mésocentre de Calcul Intensif Aquitain) resources of the Université de Bordeaux and of the Université de Pau et des Pays de l’Adour. We gratefully thank P. Aurel for his technical support.

Supporting Information Available Details on: Force field parameterization; Preparation of the SAM samples; Morphology of the SAMs; NLO calculations; Relationships between geometrical structures and NLO responses; Effect of intermolecular electrostatic interactions. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Klajn, R.; Weinelt, M. Tailoring the properties of surface-immobilized azobenzenes by monolayer dilution and surface curvature. Langmuir 2015, 31, 1048–1057.

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Nonlinear Optical Contrast in Azobenzene-Based Self-Assembled

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