Xiaoyan He

Daming Hu

Guang Yang
email: guangyang@shu.edu.cn

Frédéric Adamietz

Vincent Rodriguez

Marc Dussauze
email: marc.dussauze@u-bordeaux.fr

Evelyne Fargin

Alexandre Fargues

Thierry Cardinal
email: thierry.cardinal@icmcb.cnrs.fr

Guang Yang Acd

Frederic Adamietz

-Guang Yang

Microstructured SHG patterns on Sm2O3-doped borophosphate niobium glasses by laser-induced thermal poling

Keywords: Laser-induced thermal poling, Laser-induced heating, Microstructured SHG patterns

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

In regard to microphotonic devices, the initial material should be tunable in terms of the three-dimensional control of its linear as well as second-and third-order nonlinear optical responses at the micrometer scale [ [START_REF] Dussauze | Thermal poling of optical glasses: mechanisms and second-order optical properties[END_REF], [START_REF] Richardson | Glasses for photonic applications[END_REF], [START_REF] Lepicard | Demonstration of dimensional control and stabilization of second harmonic electro-optical response in chalcogenide glasses[END_REF], [START_REF] Xiao | Cylindrical vector beam-excited frequency-tunable second harmonic generation in a plasmonic octamer[END_REF], [START_REF] Zhou | Broadband mid-infrared second harmonic generation using epitaxial polydomain barium titanate thin films[END_REF], [START_REF] Rocco | Tuning the second-harmonic generation in AlGaAs nanodimers via non-radiative state optimization[END_REF], [START_REF] Xue | Soliton regulation in microcavities induced by fundamental-second-harmonic mode coupling[END_REF]]. Glasses with good optical properties and low production cost are promising materials for use in microphotonic device applications. However, their natural centrosymmetry must be modified to achieve second-order nonlinear (SONL) responses. Thermal poling is an efficient method to induce SONL responses in glassy materials. An efficient macroscopic electrostatic field (Estat) at the anodic surface of the glass is created through thermal poling. That is, an electric field-induced second harmonic generation (EFISHG) as χ 2 = 3•χ 3 •Estat is observed, where χ 2 and χ 3 are the second-and third-order nonlinear susceptibilities, respectively. However, thermal poling is normally macroscale (up to a few mm). Thus, to achieve practical applications of SONL properties in microphotonics, such as electro-optic switching and wavelength conversion, a micrometer scale (or even less) Estat is required for thermal-poled glass as an isotropic material [START_REF] Lepicard | Demonstration of dimensional control and stabilization of second harmonic electro-optical response in chalcogenide glasses[END_REF][START_REF] Lipovskii | 2D-structuring of glasses via thermal poling: a short review[END_REF]. Although a considerable amount of insightful research has been done on glasses, the results have still not been sufficient for use in practical applications.

Our previous work reported that microstructured SHG patterns could be obtained by thermal poling on borophosphate niobium (BPN) glasses with an initial patterned silver film [START_REF] Delestre | Towards secondharmonic generation micropatterning of glass surface[END_REF]. Furthermore, our previous work showed that there was a spatial distribution of the frozen electric field with Cs symmetry containing components along the Z and X directions. The electric field was modulated by the Ag + /Na + -exchange process during thermal poling. Brunkov and Lipovskii et al. revealed that the anode electrode pattern could be stamped on the sample surface by normal and effective thermal poling [ [START_REF] Lipovskii | Electric field imprinting of sub-micron patterns in glass-metal nanocomposites[END_REF], [START_REF] Brunkov | Submicron-resolved relief formation in poled glasses and glass-metal nanocomposites[END_REF], [START_REF] Brunkov | Submicron surface relief formation using thermal poling of glasses[END_REF], [START_REF] Lipovskii | Imprinting phase/amplitude patterns in glasses with thermal poling[END_REF]]. Moreover, Sokolv et al. created a model to calculate the contours of the electric potential and charge carriers [START_REF] Sokolov | Spatially periodical poling of silica glass[END_REF]. They explained that the electric potential or electric field affected the distribution of sodium ions in the nonlinear layer. However, some important optical properties, such as microstructured SHG patterns, are seldom reported. Our recent works showed that periodic microstructured SHG or gradient refractive index could be imprinted on BPN glass or other glasses with patterned Si and microstructured ITO as anode electrodes [3,[15], [START_REF] Dussauze | Accurate second harmonic generation microimprinting in glassy oxide materials[END_REF], [START_REF] Yang | Ultralow voltage imprinting in GeS2-Ga2S3-AgI glasses for visible to middle-infrared diffraction gratings[END_REF], [START_REF] Yang | Imprinting gradient refractive index micro-structure in GeS2-Ga2S3-KCl glass for broadband diffraction grating[END_REF]].

Another effective method for fabricating active glasses with microstructured SHG is to design new functional glass-crystal hybrid materials. Compared with the normal method of well-controlled heating treatments, laserinduced crystallization in glass has been increasingly studied because active crystals can be well patterned only in spatially selected positions. Komatsu's group has patterned many active crystals (such as LiNbO3 and β-BaB2O4) on the glass surface or inside glass through a continuous-wave (cw) Nd:YAG laser-written technique [START_REF] Komatsu | Laser patterning and characterization of optical active crystals in glasses[END_REF][START_REF] Shimada | Laser patterning of oriented LiNbO3 crystal particle arrays in NiO-doped lithium niobium silicate glasses[END_REF]. This technique simply utilized rare-earth atoms (such as Sm 3+ and Dy 3+ ) or transition metal atoms (Ni 2+ and Cu 2+ ) to absorb laser energy and then strong nonradiative lattice vibration induced enough local heating (laser-induced heating) to achieve crystallization. Therefore, we suppose it is possible to achieve microstructured SHG through special micropoling controlled by laser-induced heating at low laser powers.

In this work, a laser-induced thermal poling (LITP with an external electric field combined with laser-induced heating under certain preheating conditions) method is developed for fabricating microstructured SHG patterns. First, we study the laser-induced heating effect on a series of Sm2O3-doped BPN glasses. Then, we report the ability of this technique to write microstructured SHG on Sm2O3-doped BPN glass.

Experimental procedure

Sm2O3-doped sodium borophosphate niobium oxide glasses with a composition of (100-x)[0.58 (0.95NaPO3+0.05Na2B4O7)+0.42Nb2O5]+xSm2O3 (hereafter called xSmBPN, x = 1, 2 and 4) were prepared with the conventional melt quenching method. The sketch of the poling sandwich is shown in Fig. 1. The top part was the glass slide (SIGMA-ALDRICH, 578274 ALDRICH with a surface resistivity of 8-12 Ω/sq, an ITO coating thickness of 120-160 nm, a slide size of 75 mm × 25 mm × 1.1 mm and a transmittance of more than 83%) with the ITO on one side as the anode electrode, which was also previously coated with a thin silver line (with a width of 2-3 mm of silver conductive paint from RS 186-3600) on one cross-section side and on the top surfaces by ourselves to connect to a direct current source. The middle part was a xSmBPN glass with a thickness of 1 mm, and the bottom part was a silicon wafer as the cathode electrode. The effective transmittance of the cw laser power was approximately 80%. During the LITP process, first, the poling sandwich was preheated to a temperature of 125 °C or 160 °C in an ambient atmosphere. Next, a high voltage of 2.5 kV was applied. Then, a series of spots were irradiated by the cw laser at different laser powers (P = 1.40, 1.78, 2.20, 2.58, 2.84, 3.10, 3.26 and 3.40 W), different laser focus depths (D = 0, 5, 10, 15 and 20 μm) and fixed irradiation durations at each point (5 min). Finally, the sandwich was cooled to room temperature before the voltage was turned off. Absorption spectra were recorded using a double beam spectrophotometer (CARY 5000 UV-VIS-NIR, VARIAN, US) between 200 and 2000 nm for the serial xSmBPN glasses with a thickness of 1 mm. Laser-induced heating experiments were carried out by a homemade setup with the cw laser (at a wavelength of 1064 nm). The maximum laser power was 8 W. Laser-induced heating of the xSmBPN glasses was recorded by an IR thermal camera (FLIR A615, FLIR Systems Inc., US). Elemental concentration profiles of samples were analyzed by energy dispersive X-ray spectroscopy (EDS) integrated with an emission electron microprobe RX (CAMECA SX 100, CAMECA, France) and imaged with a scanning electron microscope (Bruker AXS, Bruker Inc., US). EDS tests were carried out on the sample surface whose effectively detected depth was controlled by the high voltage.

Microstructured SHG patterns were measured in reflection mode by a modified confocal micro-Raman spectrometer (HR800, Horiba/Jobin Yvon, France). A picosecond pulsed laser at 1064 nm was applied for the microstructured SHG measurements. Measurements of the SHG response were carried out through two doughnut radial and azimuthal polarization geometries to probe the SHG component along the z-direction (perpendicular to the surface) and within the xy-direction (parallel to the surface), respectively. Before the detector, there was also a filter to separate the microstructured SHG signal polarization directions in the xydirection (parallel to the surface). These special polarizations were obtained by a polarization converter from Arcoptix. A microscope objective (Olympus, 100 × ) with a numerical aperture of 0.5 was used for SHG and Raman imaging. Finally, the microstructured SHG signal was recorded by a Peltier-cooled high-sensitivity CCD camera (Hamamatsu C4742-95).

Results and discussion

Laser-induced heating

Absorption spectra were obtained for the xSmBPN glasses with a thickness of 1 mm, as shown in Fig. 2. The absorption spectra indicate detailed assignments of the bands for excited states from the ground state 6 H5/2 of Sm 3+ ; these excited states are centered at 401, 473, 943, 1075, 1228, 1373, and 1478 nm corresponding to the optical transitions from 6 H5/2 to 4 F7/2, 4 I11/2, 6 F11/2, 6 F9/2, 6 F7/2, 6 F5/2+ 6 H15/2, and 6 F3/2+ 6 F1/2, respectively [START_REF] Lin | Spectral parameters and visible fluorescence of Sm 3+ in alkali-barium-bismuth-tellurite glass with high refractive index[END_REF][START_REF] Yang | Modified local environment and enhanced near-infrared luminescence of Sm 3+ in chalcohalide glasses[END_REF]. These spectra also show that the absorption coefficient α of the xSmBPN glasses increases with the Sm2O3 content. For example, the α at 1075 nm increases almost linearly from 1.31 to 2.30 and then to 4.15 cm -1 with the addition of Sm2O3 from 1% to 2% and then to 4%, respectively. Thus, it is obvious that the Sm 3+ ions are homogenously distributed in the BPN glass matrix, and samples with a higher content of Sm2O3 will easily reach a higher temperature due to their stronger absorption of laser power. Furthermore, glasses with strong absorption bands can be utilized to perform laser-induced heating or writing processes for all kinds of optical applications [START_REF] Komatsu | Laser patterning and characterization of optical active crystals in glasses[END_REF]. where A0 is the room temperature, A1 is the maximum temperature induced by laser irradiation, P0 is the effective laser power constant (for samples reaching a temperature close to their saturation temperature A1) and β is the dispersion parameter (0 ≤ β ≤ 1) to be used in the fitting procedure. A1 is related to the matrix glass and content of doped Sm2O3. The fitting results are shown in Table 1, and they reveal that there is the same onset at A0 = 25 °C when the laser power is at x = 0 W. Then, the local temperature increases with the samples at different ratios before finally reaching saturation temperatures of 261, 411, and 682 °C; thus, the A1 has a maximum up to 682 °C for the 4SmBPN glass. However, these saturation temperatures are extrapolated data at a very high laser power and are not reached in this study. In addition, P0 and β are almost unchanged with the changes in Sm2O3 content. From Fig. 3, we can also see that the local temperature of samples doped with 2% and 4% Sm2O3 easily reaches above 200 °C, which is attributed to their stronger absorption of laser energy and the subsequent stronger nonradiative transition (lattice vibration) of these samples compared with that of the 1SmBPN glass. As a result, temperatures above 200 °C are sufficient for special thermal poling, where the heating of thermal poling is controlled by laser-induced heating, as described in the next section.

To avoid damaging the sample surface by a high-power laser while effectively maintaining laser-induced heating, we can use a complementary technique named preheating. In regard to the preheating range, a threshold temperature as the onset temperature for normal poling should be considered. According to our previous report [START_REF] Dussauze | Large second-harmonic generation of thermally poled sodium borophosphate glasses[END_REF], the threshold voltage to perform poling for the Na10P8.5B1.5Nb15O65 composition (which is close to 55(95NaPO3-5Na2B4O7)-45Nb2O5) is approximately 1 kV, and the threshold temperature is approximately 200 °C. Thus, we chose a series of preheating cycles at 25, 75, 100, 125, 150, and 175 °C to investigate the effect of laser-induced heating. The detailed experimental temperatures vs laser power for the 4SmBPN glass at different preheating temperatures are shown in Fig. 4. We find that the local temperature increases almost linearly with the irradiation laser power for the six different preheating cycles, and their ratios are similar. Normal thermal poling can be performed with a total heating temperature equal to or above 200 °C. Therefore, the positions above the dashed line can be good conditions to perform LITP. In addition, the most enhanced temperature of the sample surface ΔT1 can be obtained by ΔT1 = Tij-T1j, where Tij is the temperature of the sample surface at a preheating temperature of Ti and a laser irradiation power of Pj; additionally, T1j is the temperature of the sample surface at room temperature and a laser irradiation power of Pj. Fig. 5 reveals that most of the ΔT1 values are lower than the enhanced temperature ΔT2, which is the difference between preheating and room temperature. This result can be due to preheating enhancing electron-phonon interactions at both the ground state and excited state of the absorption center for Sm 3+ ions [ [START_REF] Hsu | On the thermal broadening of zero-honon impurity lines in absorption and fluorescence spectra[END_REF], [START_REF] Mikhailik | One-and two-photon excited luminescence and band-gap assignment in CaWO4[END_REF], [START_REF] Kim | Temperature-dependent emission spectra of M2SiO4:Eu 2+ (M=Ca, Sr, Ba) phosphors for green and greenish white LEDs[END_REF]].

LITP

According to our previous report [START_REF] Dussauze | Large second-harmonic generation of thermally poled sodium borophosphate glasses[END_REF], the onset of the poling temperature for the 4SmBPN glass is approximately 160 °C at a poling voltage of 2.5 kV. Thus, to obtain a good signal-to-noise ratio of SHG on the laser irradiation spot positions of the 4SmBPN glass, preheating temperatures of 125 °C and 160 °C were chosen to ensure either no or a weak thermal poling effect, respectively, occurs with the glass matrix. Variations in the current curves over time at a fixed high voltage are shown in Fig. 6(a). With a preheating temperature of 160 °C, it is found that the current appears in a timely manner when laser irradiation is turned on and disappears then the laser is off. Moreover, the intensity of the current stabilization at a certain level with the laser is focused on a series of depths from 0 to 20 μm at the same laser power and increases from 0.039 to 0.078 mA as the laser power increases from 1.40 to 3.40 W. Compared with that of the preheating temperature of 160 °C, there is almost no current at a low preheating temperature of 125 °C. However, in Fig. 6(b), we can find that all spots show obvious topological deformation of the glassy surface after laser irradiation, and some are even damaged when the laser is focused on a series of depths between 0 and 10 μm. Notably, the spot positions are still glassy.

Fig. 6. (a) Variation of current with time at a voltage of 2.5 kV (black open square) and different preheating temperatures of 160 °C (blue open circular) and 125 °C (red open triangle). (b) Microscope image of 4SmBPN glass surface after poling process at a preheating of 125 °C. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

The effects of the LITP process on the implementation of second-order optical properties were characterized by SHG confocal microscopy in reflection mode. Radial and azimuthal incident polarizations have been utilized. They probe the longitudinal (noted I2ω⊥) and in-plane (noted I2ω//xy) SHG responses (check the reference in Figs.

6(b) and Fig. 7(a)), respectively. In regard to the sample poled at a preheating temperature of 160 °C, the difference in SHG intensity observed between the maximum at each edge and the background signal measured from the LITP spots is approximately one order of magnitude, as shown in Fig. 7(b). One possible reason is that the preheating temperature of 160 °C is enough to induce a certain SHG response on the 4SmBPN glass over the whole ITO anode under the present conditions, thereby showing a much stronger anode bonding strength between the ITO anode and 4SmBPN glass at the preheating temperature of 160 °C compared with that at 125 °C. Thus, we decreased the preheating temperature to 125 °C to achieve microscale thermal poling with a higher SHG intensity contrast than that at a preheating temperature of 160 °C. The concentration profiles of Na + on the surface of the xSmBPN glasses at the anode side were recorded by EDS, and the results are shown in Fig. 8. The results reveal that the Na + concentration profile of the 4SmBPN glass is almost totally depleted at particular spots (except for some effect in the upper-right angle of Fig. 8(a)), while the Na + concentration of the left area is unchanged. Furthermore, the linear analysis in Fig. 8(b) for spots irradiated at a laser focus depth (D) of 15 μm and a laser power (P) of 3.10 W shows a depleted depth up to 6 μm, and the Na + concentration on the edge of the spot varies sharply from 0 to 8 at% within a depth of less than 6 μm. The Na + concentration map in space nicely indicates that a 3-dimensional electric field probably appears along the Z direction and radial direction of the spot, similar to that in Ref. [START_REF] Dussauze | Accurate second harmonic generation microimprinting in glassy oxide materials[END_REF].

Typical microstructured SHG patterns of spot (15 μm, 3.10 W) are shown in Fig. 9, denoting an accurate spatial location of the SHG signal on the edges of each imprinted spot at a preheating temperature of 125 °C. Fig. 9(a,d) shows that the difference in intensity observed between the maximum at each edge and the background signal measured out of the imprinted spots is greater than two orders of magnitude. Notably, the in-plane SHG signal is null when the excitation polarization is parallel to the edge but is maximal when the excitation polarization is vertical to the edge in the configuration shown in Fig. 9(b andc). The respective locations of the longitudinal and in-plane SHG responses are well matched in regard to their intensity profiles (Fig. 9(e)). Both the longitudinal and in-plane SHG components are confined within a width of 5 μm. The longitudinal SHG response I2ω⊥ (Fig. 9(d)) shows two distinct maxima, whereas the in-plane SHG response I2ω//xy (Fig. 9(a)) has one maximum located between the two maxima of the longitudinal signals corresponding to the edge of the spots.

The origin of the SHG microstructures in the 4SmBPN glass correlates with both the microstructures promoted by local laser heating and the ITO microstructures. On the one hand, to clarify the large effect of LITP on both the location and geometry of SHG properties, we should consider the influence of side effects promoting the local field enhancement of the modified electrode because the laser caused some notable damage to the ITO electrode [START_REF] Dussauze | Accurate second harmonic generation microimprinting in glassy oxide materials[END_REF]. An undoped BPN glass was written by the cw laser with an ITO cover at 0 V and room temperature, as shown in Fig. 10. We found that both the ITO and undoped glass can be damaged by the focused laser even at spot of (0 μm, 1.78 W) which is observed in the form of a black spot. With an increasing laser focus depth in the glass surface, the damage to the ITO glass is alleviated and even disappears. This result means that the morphology of ITO can be modified by cw laser irradiation at room temperature due to the high laser powers ranging from 1.78 to 2.58 W through the ITO equaling an effective laser power range of 1.42-2.06 W. Compared with the undoped BPN glass, our 4SmBPN glass will more easily achieve the surface morphology of ITO with a strong absorption of the laser power at a preheating temperature of 125 °C because the 4SmBPN glass can reach a local temperature of 250-300 °C, as shown in Fig. 4. On the other hand, the laser simultaneously induced heating on the xSmBPN glasses. As in our above results, Sm 3+ in the xSmBPN glasses have strong absorption bands at approximately 1080 nm through ƒ-ƒ transitions ( 6 F9/2 → 6 H5/2) [START_REF] Honma | Nonlinear optical crystal-line writing in glass by yttrium aluminum garnet laser irradiation[END_REF]. Because the main relaxation is nonradiative, the absorbed laser energy is transformed into the lattice system as lattice vibrations through electron-phonon coupling. Next, the LITP effect can be achieved by irradiation with cw laser-induced local heating combined with the strong local electric field enhancement of the modified electrode. Then, sodium depletion zones are only formed at the laser-heated volume positions in Fig. 8 after LITP. Finally, we observe a similar SHG pattern or static field distribution at the border of the modified electrode as that on the BPN glasses by thermal poling using micropatterned electrodes [START_REF] Dussauze | Accurate second harmonic generation microimprinting in glassy oxide materials[END_REF]. However, sodium depletion is induced only within the heated volume, which provides an opposite composition profile compared to the "classical" thermal electrical imprinting process even with micropatterned electrodes.

The preheat and voltage steps were conducted before laser irradiation, but the profile of ITO was modified by laser irradiation within a few seconds or less, which is much shorter than the duration of laser-induced thermal poling (5 min at each point). Thus, we suggest that ITO electrodes should be previously microstructured by laser ablation before the poling process. According to our previous report [START_REF] Dussauze | Accurate second harmonic generation microimprinting in glassy oxide materials[END_REF], a sketch of the electrostatic model used to simulate the polarized glass at one edge of a structured electrode is shown in Fig. 11. The subanodic layer formed below the conductive electrode is defined at a depth of 2 μm and a negative anodic charge concentration ρanode = -2 × 10 3 C m -3 . To consider both the field enhancement and the lateral (or in-plane) poling effects at the electrode edges during LITP, we formed two regions with equal charge concentrations and sizes but with opposite signs (ρside1 = -ρside2 = -2 × 10 4 C m -3 ) [START_REF] Dussauze | Structural rearrangements and second-order optical response in the space charge layer of thermally poled sodium niobium borophosphate glasses[END_REF]. The longitudinal component of the electric field (Ez) has two main contributions in opposite directions along the edge of the electrode, whereas the main contribution of the in-plane electric field component is a maximum just at the border of the electrode (Exy). Thus, it is possible to infer the theoretical SHG responses (two maxima along the longitudinal direction and one maximum in the plane along the border of the electrode) expected from our qualitative electrostatic model. The good correlation observed between the theoretical microstructured SHG patterns and those of the experiment in Fig. 10 qualitatively proves the key importance of both charge accumulation and the in-plane poling contribution along electrode discontinuities. Furthermore, we tried thermal poling on undoped BPN sample at a condition of 125 °C and 2.5 kV for 0.5 h. The ITO and undoped BPN samples have a similar structure after LITP, but no enhanced microstructured SHG can be observed on the undoped BPN samples. This result is also an indication that Sm2O3 significantly affects the nonlinear optical response in the form of laser-induced heating with regard to what has been reported in Sm2O3-doped glasses [START_REF] Komatsu | Laser patterning and characterization of optical active crystals in glasses[END_REF]. Above all, the laser irradiation of the Sm2O3-doped BPN samples can first induce profile deformation of ITO into a microstructured electrode, while simultaneously providing enough energy in the form of heat to obtain an accurate and original sodium distribution in the heated volume. Thus, microstructured SHG spots or complex patterns are achieved after the LITP process.

Conclusion

We demonstrated LITP could be considered a laser writing process governing the implementation and geometry of SONL properties at the micrometer scale for glass materials. Preheating allowed the xSmBPN (x ≥ 2) glass surfaces to reach above 200 °C with low-power laser irradiation. However, preheating also decreased the efficiency of laser-induced heating due to enhancing the electron-phonon interactions at both the ground state and excited state of the absorption center. Furthermore, the LITP could induce a microstructured electrode, while simultaneously providing enough energy to achieve local electric field enhancement effects. This enhanced local electric field of the microstructured electrode along with laser-induced heating were the main factors affecting the geometry and strength of the electric field. Therefore, LITP could be a potential method to fabricate optical materials with an accurate microstructured design of second-order optical properties.

Declaration of competing interest:

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .

 1 Fig. 1. Sketch of the laser-induced thermal poling setup.

Fig. 2 .

 2 Fig. 2. Optical absorption spectra of xSmBPN glasses at room temperature.

Fig. 3 .

 3 Fig. 3. Experimental temperature vs laser power for xSmBPN glasses with a 10 × -0.5NA air objective at room temperature. The dash line is a guide at a preheating temperature of 200 °C.

Fig. 3

 3 Fig.3shows the experimental temperature vs laser power for the xSmBPN glasses under a 10 × -0.5NA air objective. It appears that the local temperature of the three xSmBPN glasses increases with laser power. The variation in the enhanced temperature is in good agreement with that of α. Then, they were well fitted by the stretched exponential function (Kohlrausch law) shown below [[START_REF] Krecmer | Reversible nanocontraction and dilatation in a solid induced by polarized light[END_REF],[START_REF] Ren | In-situ measurement of reversible photodarkening in ion-conducting chalcohalide glass[END_REF],[START_REF] Yan | Millisecond kinetics of photo-darkening/bleaching in xGe45Se55-(1-x)As45Se55 chalcogenide amorphous films[END_REF]]:

Fig. 4 .

 4 Fig. 4. Experimental temperature vs laser power for 4SmBPN glass at different preheating temperatures and a 10 × -0.5NA air objective. The dash line is a guide at a preheating temperature of 200 °C.

Fig. 5 .

 5 Fig. 5. Variation of sample's surface temperature (ΔT1) vs enhanced preheating (ΔT2) for 4SmBPN glass under different laser power and a 10 × -0.5NA air objective. The dash line is a guide for slope equaling to 1.

Fig. 7 .

 7 Fig. 7. Microscope image (a) and microstructured SHG pattern (b) of 4SmBPN glass surface after LITP at a preheating temperature of 160 °C. The SHG pattern was detected by a radial donut laser in Y-direction and with a scanning interval of 1.5 μm.

Fig. 8 .

 8 Fig. 8. (a) Sodium distributions of 4SmBPN glass after LITP under a condition of 125 °C and 2.5 kV for 0.5 h and (b) linear sodium concentration distributions across center of spot (3.10 W, 15 μm) detected with different effective testing depths: 10 kV (1 μm), 20 kV (4 μm), 30 kV (6 μm).

Fig. 9 .

 9 Fig. 9. Microstructured SHG pattern of 4SmBPN glass at spot (15 μm, 3.10 W) detected by azimuthal donut (a-c) laser inplane and radial donut (d) laser in longitudinal direction under a scanning interval of 0.5 μm. (e) Overlap of microstructured SHG of (a) and (d).

Fig. 10 .

 10 Fig. 10. Microscope image of an undoped BPN glass (a) written by a cw laser with an ITO (b) as a cover.

Fig. 11 .

 11 Fig. 11. A schematic of the electrostatic model of field enhancement and lateral poling effects at one electrode edge.

Acknowledgements: This work is supported by the National Natural Science Foundation of China (No. 52072231, 51602187), and the Young Eastern Scholars Program 2015 (No. QD2015028) supported by Shanghai Municipal Education Commission (China).


Quentin Martinet

Justine Baronnier

Adrien Girard

Tristan Albaret

Lucien Saviot

Alain Mermet

Benjamin Abecassis

Jérémie Margueritat

Benoît Mahler

Ligand-dependent nano-mechanical properties of CdSe nanoplatelets: calibrating nanobalances for ligands affinity monitoring

Keywords: Nanoplatelets, low frequency Raman spectroscopy, Nanomechanics, Nanobalance

The influence of ligands on the low frequency vibration of different thicknesses cadmium selenide colloidal nanoplatelets is investigated using resonant low frequency Raman scattering.

The strong vibration frequency shifts induced by ligand modifications as well as the sharp spectral linewidths make low frequency Raman scattering a tool of choice to follow ligand exchange as well as the nano-mechanical properties of the NPLs, as evidenced by a carboxylate to thiolate exchange study. Apart from their molecular weight, the nature of the ligands, such as the sulfur to metal bond of thiols, induces a modification of the NPLs as a whole, increasing the thickness by one monolayer. Moreover, as the weight of the ligands increases, the discrepancy between the massload model and the experimental measurements increase. These effects are all the more important when the number of layers is small and can only be explained by a modification of the longitudinal sound velocity. This modification takes its origin in a change of lattice structure of the NPLs, that reflects on its elastic properties. These nanobalances are finally used to characterize ligands affinity with the surface using binary thiols mixtures, illustrating the potential of low frequency Raman scattering to finely characterize nanocrystals surfaces.

Introduction

Vibrations in nanostructures are a powerful tool to study and characterize colloidal nanocrystals and heterostructures, especially quantum dots. The frequency of optical phonons is characteristic of the bonds in the material composing the nanocrystal, and is sensitive to their local environment. [START_REF] Kelley | Resonance Raman spectra of wurtzite and zincblende CdSe nanocrystals[END_REF][START_REF] Baker | Resonance Raman and photoluminescence excitation profiles and excited-state dynamics in CdSe nanocrystals[END_REF][3][START_REF] Lin | Electron-Phonon Coupling in CdSe/CdS Core/Shell Quantum Dots[END_REF][START_REF] Grenland | Resonance Raman Investigation of the Interaction between Aromatic Dithiocarbamate Ligands and CdSe Quantum Dots[END_REF][START_REF] Mork | Temperature dependence of acoustic vibrations of CdSe and CdSe-CdS core-shell nanocrystals measured by low-frequency Raman spectroscopy[END_REF][START_REF] Maddux | Weak Exciton-Phonon Coupling in CdSe Nanoplatelets from Quantitative Resonance Raman Intensity Analysis[END_REF][START_REF] Paillard | Strain characterization of strained silicon on insulator wafers[END_REF][START_REF] Cazayous | Strain and composition in self-assembled SiGe islands by Raman spectroscopy[END_REF] Raman spectroscopy can therefore be an efficient tool to probe several features such as local defects, deformations induced by strain, as well as nanoscale alloying. [START_REF] Grenland | Resonance Raman Investigation of the Interaction between Aromatic Dithiocarbamate Ligands and CdSe Quantum Dots[END_REF][START_REF] Miscuglio | Confined Acoustic Phonons in Colloidal Nanorod Heterostructures Investigated by Nonresonant Raman Spectroscopy and Finite Elements Simulations[END_REF] Furthermore, a careful analysis of Raman spectra of heterostructured nanocrystals can reveal in detail the nature of the heterostructure, the presence of sharp interfaces, interfacial alloying and electron-phonon coupling. [START_REF] Lin | Electron-Phonon Coupling in CdSe/CdS Core/Shell Quantum Dots[END_REF][START_REF] Mukherjee | Measuring and Predicting the Internal Structure of Semiconductor Nanocrystals through Raman Spectroscopy[END_REF] Phonons usually scrutinized in these cases are optical phonons, at frequencies higher than 100 cm -1 .

Lower frequency vibrations also exist and are characteristic of deformations of the nanocrystal as a whole. They are related to propagative acoustic phonons in the bulk material whose velocity, the sound velocity, is directly related to the physical properties of the material, namely its mass density and elastic constants. For small enough sizes, the vibrations are confined inside the nanocrystals and some of them can inelastically scatter light which manifest as peaks in the lowfrequency Raman spectra. They are known as Lamb modes. [START_REF] Lamb | On the Vibrations of an Elastic Sphere[END_REF] Their frequencies depend on the physical properties of the material as in the case of the acoustic waves, but also on the shape, size and environment of the nanocrystal. They can therefore provide crucial information about the shape of heterostructures in a non-destructive manner, as demonstrated in the case of dot-in-rods CdSe/CdS nanocrystals. [START_REF] Miscuglio | Confined Acoustic Phonons in Colloidal Nanorod Heterostructures Investigated by Nonresonant Raman Spectroscopy and Finite Elements Simulations[END_REF] Recent reports about low frequency phonons in nanocrystals [START_REF] Mork | Modulation of Low-Frequency Acoustic Vibrations in Semiconductor Nanocrystals through Choice of Surface Ligand[END_REF][START_REF] Morgan | Transient Absorption Spectroscopy of CdSe Nanoplatelets[END_REF][START_REF] Girard | The mass load effect on the resonant acoustic frequencies of colloidal semiconductor nanoplatelets[END_REF][START_REF] Girard | Environmental effects on the natural vibrations of nanoplatelets: a high pressure study[END_REF][START_REF] Poyser | Coherent Acoustic Phonons in Colloidal Semiconductor Nanocrystal Superlattices[END_REF] measured through diverse techniques (pump-probe, Raman) have also shown the importance of the surface energy of the nano-object. Indeed, controlling the surface states is crucial to control electron-phonon interactions occurring at nanocrystals surfaces. However, if the effect of the ligands on the electronic properties has been widely investigated, the mechanisms involved in the modifications of the phonon's frequencies are still unclear, especially in the case of the Lamb modes. This is due to two main reasons. First, the size of the nano-object must be small to observe a measurable effect of the ligands. [START_REF] Mork | Modulation of Low-Frequency Acoustic Vibrations in Semiconductor Nanocrystals through Choice of Surface Ligand[END_REF][START_REF] Girard | The mass load effect on the resonant acoustic frequencies of colloidal semiconductor nanoplatelets[END_REF][START_REF] Martinet | Performances of the Lamb Model to Describe the Vibrations of Gold Quantum-Sized Clusters[END_REF] Second, studying small nanoparticles requires to study assemblies of nanoparticles presenting a small size and shape dispersion. Indeed, the width of the measured low frequency Raman peak is rapidly enlarged with these morphology parameters dispersion [START_REF] Bachelier | Size dispersion effects on the low-frequency Raman scattering of quasispherical silver nanoparticles: Experiment and theory[END_REF] and the effect of the ligands might be obscured. We have shown that nanoplatelets (NPLs) of CdS and CdSe are ideal objects to investigate this effect. [START_REF] Girard | The mass load effect on the resonant acoustic frequencies of colloidal semiconductor nanoplatelets[END_REF][START_REF] Girard | Environmental effects on the natural vibrations of nanoplatelets: a high pressure study[END_REF] Their thicknesses are perfectly controlled at the atomic scale from 3 to 5 atomic layers (0.9 nm to 1.5 nm in case of CdSe), and due to their lateral dimensions which is much larger than their thickness, only the breathing vibration of the thickness is measured, making them model nano-objects with negligible size dispersion. Moreover, in these 2D systems, the ligands nature can be easily modified through standard ligands exchange procedures. [START_REF] Mahler | Core/Shell Colloidal Semiconductor Nanoplatelets[END_REF][START_REF] Antanovich | A strain-induced exciton transition energy shift in CdSe nanoplatelets: the impact of an organic ligand shell[END_REF][START_REF] Vasiliev | Spontaneous Folding of CdTe Nanosheets Induced by Ligand Exchange[END_REF] We demonstrated previously [START_REF] Girard | The mass load effect on the resonant acoustic frequencies of colloidal semiconductor nanoplatelets[END_REF] that in the framework of continuum elasticity, the frequency of the breathing vibration of a free CdSe NPL depends on its density and elastic constant ( in the case of cubic structure) according to (1) where is the thickness of the NPL expressed as a function of the lattice parameter and , i.e. the longitudinal speed of sound in the NPL. The presence of the native ligands can be taken into account through the inertial mass load they induce. [START_REF] Girard | The mass load effect on the resonant acoustic frequencies of colloidal semiconductor nanoplatelets[END_REF][START_REF] Girard | Environmental effects on the natural vibrations of nanoplatelets: a high pressure study[END_REF] The lumped mass effect is accounted for with the following equation, whose roots give the resonance frequencies of the NPL across the thickness:

(

) 2
where  is the surface mass density of the ligands and  the volume mass density of the NPL.

The magnitude of this effect is driven by the ratio of the masses between the ligands and the NPL (σ/ρ factor).

In this article, we demonstrate that other parameters play a role in the change of frequency and that an improved model is required. We show that the breathing vibration of NPLs also depends on the structural modification of the NPLs induced by the presence of ligands at their surfaces.

This provides a new mean to control phonons in such nanostructures but also a new tool to characterize ligand induced modification of their lattice structure. This latter effect is all the more important when the NPLs are thin, i.e. when the proportion of atoms close to the surface is large. Significant deviations from the mass-load model are reported. They are explained by the modification of the NPL structure as a function of ligand nature, which impacts on the mechanical properties of the NPLs. The fine characterization of this modification allows to calibrate the NPLs vibration frequency as a function of the molecular weight on their surface using the experimental measurements, and the ability of these calibrated nanobalances is demonstrated by studying the relative binding affinities of different thiol ligands at the NPL surface.

Results

A. Nanobalance calibration

In order to characterize the sensitivity of the breathing vibration of the NPLs to the mass of the ligands present on its surface, we prepared CdSe NPLs with a 5 monolayers thickness. After synthesis, the surface of the NPLs is covered with oleic acid ligands (OA, molecular weight:

282.46 g.mol -1 ) and the black curves on figures 1a and 1b show the corresponding UV-Visible absorption and low frequency Raman spectra respectively. The initial absorption spectrum shows two peaks at 515 and 550 nm that are the typical signature of the exciton confinement in a 5 monolayer NPL with oleic acid ligands. [START_REF] Ithurria | Continuous Transition from 3D to 1D Confinement Observed during the Formation of CdSe Nanoplatelets[END_REF] After ligand exchange by alkyl-thiols (see material and methods), the excitonic energy is reduced, which results in a red shift of the excitons peaks to 536 and 567 nm respectively, confirming that the ligand exchange is complete. [START_REF] Mahler | Core/Shell Colloidal Semiconductor Nanoplatelets[END_REF][START_REF] Tschirner | Interfacial Alloying in CdSe/CdS Heteronanocrystals: A Raman Spectroscopy Analysis[END_REF] The length of the thiol chain, varied to modify the mass of the ligands from 146.29 g.mol -1 for octanethiol (OT), to 286.56 g.mol -1 for octadecanethiol (ODT), does not influence significantly the energy of the exciton. To measure the vibration frequency as a function of the ligand molecular weight, the measurements must be performed in close resonance with the lower energy exciton peak. [START_REF] Girard | The mass load effect on the resonant acoustic frequencies of colloidal semiconductor nanoplatelets[END_REF] In such condition a strong luminescence background overwhelming the Raman signal is observed, and a low concentration of copper ions are introduced in the NPLs in order to quench part of the luminescence (see methods section). Figure 1b shows the variation of the breathing vibration frequency as a function of the thiol ligand molecular weight. An increase of the ligand molecular weight induces a down-shift of the frequency (from 28.7 cm -1 to 23.5 cm -1 ), as predicted in our previous work. [START_REF] Girard | The mass load effect on the resonant acoustic frequencies of colloidal semiconductor nanoplatelets[END_REF] However, the vibration frequencies measured for OA and ODT whose masses are almost the same (see methods section), are significantly different: 25.7 cm -1 and 23.5 cm -1 respectively. This behavior is reported in figure 1c, where the experimental results (hexagonal dots) are compared with the mass-load model [START_REF] Girard | The mass load effect on the resonant acoustic frequencies of colloidal semiconductor nanoplatelets[END_REF] for 5 monolayers and 6 monolayers thick NPLs. Surprisingly, the measured frequency shifts as a function of thiol molecular weights are in good agreement with the model only if we consider 6ML NPLs while they are in between 5 and 6 monolayers for OA ligands.

The influence of thiol ligands at the surface of CdSe nanocrystals has already been investigated.

This type of ligands induces a red-shift of the lowest excitonic transition of CdSe nanocrystals, 25- 27 as shown in Figure 1a for our NPLs. This shift has first been interpreted as a decrease of the quantum confinement of the hole due to the presence of the ligands. [START_REF] Frederick | Optical Properties of Strongly Coupled Quantum Dot-Ligand Systems[END_REF][START_REF] Teunis | Effects of Surface-Passivating Ligands and Ultrasmall CdSe Nanocrystal Size on the Delocalization of Exciton Confinement[END_REF][START_REF] Jin | Enhanced Rate of Radiative Decay in CdSe Quantum Dots upon Adsorption of an Exciton-Delocalizing Ligand[END_REF] But this effect can also be explained if one considers that the sulfur atoms of the thiol ligands are forming a shell around the CdSe nanoplatelets thus increasing slightly its effective thickness. Then it is the delocalization of the exciton that induces a red-shift of the excitonic peak. [START_REF] Grenland | Resonance Raman Investigation of the Interaction between Aromatic Dithiocarbamate Ligands and CdSe Quantum Dots[END_REF] In the case of NPLs, considering that the sulfur atoms coming from the thiol ligands are part of the lattice structure, half a monolayer is added on each side of the NPLs, increasing the total thickness by one monolayer. If we consider this hypothesis with the mass load model, the agreement with the experimental measurements is significantly improved for thiol molecules as shown in Figure 1c.

The presence of this sulfide layer is supported by the Raman spectra at higher frequency (between 200 and 300 cm -1 ) where the longitudinal optical phonons of CdS and CdSe manifest. are observed. The first peak corresponds to the CdSe LO phonon. The broadening of the peak with respect to bulk CdSe LO phonon is explained by the increasing role of surface optical phonons (at lower frequency) and by the spatial confinement that induces scattering from phonons (higher frequency). [START_REF] Lu | Raman analysis of CdSe/CdS core-shell quantum dots with different CdS shell thickness[END_REF][START_REF] Dzhagan | Resonant Raman scattering study of CdSe nanocrystals passivated with CdS and ZnS[END_REF][START_REF] Dzhagan | Morphology-induced phonon spectra of CdSe/CdS nanoplatelets: core/shell vs. core-crown[END_REF] The second band has already been observed [START_REF] Grenland | Resonance Raman Investigation of the Interaction between Aromatic Dithiocarbamate Ligands and CdSe Quantum Dots[END_REF][START_REF] Tschirner | Interfacial Alloying in CdSe/CdS Heteronanocrystals: A Raman Spectroscopy Analysis[END_REF][START_REF] Dzhagan | Resonant Raman scattering study of CdSe nanocrystals passivated with CdS and ZnS[END_REF][START_REF] Dzhagan | Morphology-induced phonon spectra of CdSe/CdS nanoplatelets: core/shell vs. core-crown[END_REF][START_REF] Dzhagan | Vibrational spectroscopy of compound semiconductor nanocrystals[END_REF][START_REF] Dzhagan | The influence of pyridine ligand onto the structure and phonon spectra of CdSe nanocrystals[END_REF] when performing resonant Raman measurement on CdSe QDs plus CdS or elemental S. It was assigned to the presence of sulfur atoms that form CdS bonds whose LO phonon frequency depends on the thickness of the CdS layer. For a single monolayer the frequency of this CdS-like LO phonon is around 270 cm -1 . The difference in frequency between the CdSe LO phonon and the CdS-like LO phonon can be used to estimate the quantity of Se atoms with respect S atoms. [START_REF] Azhniuk | Resonant Raman studies of compositional and size dispersion of CdS 1-x Se x nanocrystals in a glass matrix[END_REF] Here a difference of 72 cm -1 is measured which approximately corresponds to 80% of Se and 20% of S atoms. This is the expected ratio if we consider NPLs of 5MLs with half monolayer of sulfur on each sides. Unfortunately, this band was not observed on all samples due to the luminescence background but the effect of the sulfur bonds is also clearly evidenced at low frequency when considering the breathing vibration mode of the NPLs.

Indeed, the origin of this vibration mode at low frequency has also been discussed by A. I.

Lebedev in ref. 34. In this publication the author uses first-principle calculations and modeling of the Raman spectra to determine the origin of this vibrational peak. CdSe NPLs of different thicknesses (2 to 6 MLs) are modeled with a fluorine atoms layer compensating the cadmium atoms surface charge for the calculations. Vibration modes with a displacement out of plane, qualified as quasi-Lamb, are calculated but their frequencies are not in good agreement with our experimental frequencies for NPLs covered with OA. However, it is interesting to note that fluorine atoms are placed in the vacant selenium positions, and that the wave confinement calculated in 34 is defined on the thickness of the plate plus the two layers of fluorine atoms.

These theoretical frequencies are therefore obtained for a bare platelet of CdSe with an additional layer of fluorine atoms and must be compared to the Lamb model of a bare NPL with the same thickness. When considering this additional monolayer, a good agreement between the approach in ref 34 and the Lamb model is observed. These results thus confirm that the sulfur atom constituting the thiol group is involved in a molecular bond with the cadmium atoms present at the surface of the NPLs.

This influence of the binding group explains why the NPLs with OA ligands do not follow the same behavior as the NPLs with thiol ligands. However, in the case of OA, there is still a discrepancy between the mass-load model for 5 monolayers and the experimental measurement.

Due to the preparation method, the NPLs surface is almost completely covered with carboxylates [START_REF] Singh | Colloidal CdSe Nanoplatelets, A Model for Surface Chemistry/Optoelectronic Property Relations in Semiconductor Nanocrystals[END_REF] , that is a mixture of oleate and acetate ligands (in unknow proportions). The overall molecular weight to be taken into account should then be lower and may lead to a better agreement with the mass-load model. Moreover, one could expect that the oxygen atoms of the carboxylic function of OA might also be involved in the structure of the NPLs. To understand this behavior, thinner NPLs with thicknesses of 3 and 4 monolayers were synthesized with OA native ligands, and we carried out the same study with thiol ligand exchange. This model is based on several hypotheses: the first one is the surface coverage. To calculate the surface mass density of the ligands at the surface of the NPLs, we considered that each surface cadmium atom is linked to one ligand (surface density: 5.4 ligands. nm -2 ). This is an overestimation because the typical values deduced by NMR are between 5.3 and 4.6 ligands.nm -2 for OA ligands . [START_REF] Singh | Colloidal CdSe Nanoplatelets, A Model for Surface Chemistry/Optoelectronic Property Relations in Semiconductor Nanocrystals[END_REF][START_REF] Fritzinger | Utilizing Self-Exchange To Address the Binding of Carboxylic Acid Ligands to CdSe Quantum Dots[END_REF] The effect of a lower surface covering results in an increase of the frequency shifts (Figure S1 of Supplementary Materials) which is not the experimental behavior.

One would expect a different surface covering for thiol ligands, but thiol molecules have a greater affinity with nanoplatelets than OA, and therefore one can expect at least the same surface covering. Finally, while the surface covering of CdSe nanoplatelets with thiol molecules has not been measured, the surface covering of thiol molecules on gold surfaces has been extensively studied showing that the alkane chain length does not affect the covering. [START_REF] Djebaili | Atomistic simulations of the surface coverage of large gold nanocrystals[END_REF][START_REF] Hinterwirth | Quantifying thiol ligand density of self-assembled monolayers on gold nanoparticles by inductively coupled plasma-mass spectrometry[END_REF][START_REF] Smith | Ligand density quantification on colloidal inorganic nanoparticles[END_REF] These works also highlights the fact that the geometric effect can induce an increase in surface covering. In what follows, a fixed surface density of 5.4 ligands.nm -2 is therefore considered whatever the nature of the ligand.

The other parameter that can be modified is the value of the sound velocity of the CdSe nanoplatelet, that is related to its elastic and structural properties. In our model we used the bulk value of CdSe considering the zinc-blende structure of the NPLs: the lattice parameter a = 0.608 nm and the theoretical estimated elastic constant C = C 11 = 88 GPa, giving a longitudinal sound velocity of 3945 m.s -1 . [START_REF] Girard | The mass load effect on the resonant acoustic frequencies of colloidal semiconductor nanoplatelets[END_REF][START_REF] Girard | Environmental effects on the natural vibrations of nanoplatelets: a high pressure study[END_REF] These value were deduced from the bulk material considering a zincblende structure, but it is an estimation. In particular, several works have shown that the NPLs crystalline structure is slightly different from zinc-blende structure. The TEM images (figure 3) of the NPLs clearly show that ligands strongly impact their morphology. They induce a winding of the NPLs whose amplitude varies with the thiol ligand length. This behavior is unexpected and might be related to steric hindrance. Moreover, the nature of the bond between the molecule and the surface is also probably important to control the winding, but further experiments with different ligands of well-known steric hindrance and functional type should be performed to answer more specifically this question. Be it as it may, the TEM images shows a clear dependency of the winding radius as a function of the thiol length.

We performed PXRD measurements on our samples to determine the in-plane and out-of-plane lattice parameters (diffractograms in Supporting Information). Figure 3a confirms that the crystalline structure of the NPLs is more accurately described as pseudotetragonal, due to the differences between in-plane and out-of-plane lattice parameters. [START_REF] Chen | Structure Identification of Two-Dimensional Colloidal Semiconductor Nanocrystals with Atomic Flat Basal Planes[END_REF] The measured in-plane lattice parameter is slightly smaller (1%) than the out-of-plane parameter. Moreover, the in-plane and out-of-plane lattice parameters decrease slightly as a function of the alkyl chain length. It has to be noticed that due to the nano 2D nature of the sample, the peaks observed on the PXRD diffractograms and corresponding to the out-of-plane lattice parameter are difficult to fit and more precise PXRD measurements may be needed to refine the accuracy of the in plane and out of plane lattice parameters. Yet Figure 3a thus confirms that a modification of the lattice parameters and thus of the unit cell depends on the thiol chain length. This structure modification, from cubic to tetragonal, implies to take C 33 as elastic parameter along the c-axis of the NPLs (i.e. along the thickness), instead of C 11 . Unfortunately, the elasticity of such structure at the nanoscale is poorly characterized and no value of C 33 is reported, a fortiori as a function of ligand mass. Therefore, we rely on an empirical dependence of C 33 as a function of ligand mass to calibrate our nanobalances. Thus, by fitting the experimental data with our mass load model considering the modification of the lattice parameter (and density ) (see Supporting Information) we can deduce, for the 4MLs NPLs, the dependency of the elastic parameter as a function of the ligand mass ; where GPa and M is the molecular weight in g/mol. This dependency is used in figure 3b to calibrate the behavior of our nanobalances. Although the linear dependency of the elastic parameter as a function of the unit cell deformation (and thus on the molecular weight) is expected, should be replaced by the value of the elastic constant of a bare NPLs of 4MLs. Unfortunately, this value is not yet available. In addition, this dependence is extracted from the experimental data considering a surface covering of 100%. This is a strong assumption which also means that the potential structural deformation of NPLs is potentially greater than we expected. Anyway, the nanobalances are simply calibrated using the experimental data and the unique unknow quantity is the surface covering which is considered constant regardless of the nature of the ligands to determine the difference in binding affinity between OT and ODT.

B. Using the nanobalance effect to monitor the binding of ligands

In the previous part of the article, the study of the frequency shifts gave us insight about mechanical property variations of the nanoplatelets grafted with ligands of different chain length and binding groups that must be considered to calibrate the nanobalances. It has been possible to obtain an experimental relationship linking the frequency vibration of the NPL to the molecular weight of the ligands attached to the surface in the case of linear alkanethiols. We will now explore the possibility to use the NPL as a nanobalance that can allow to precisely analyze the composition of surface ligands in more complex cases where other techniques are not sensitive.

As we establish this relationship for linear alkanethiols we will consider the following equilibrium of binding between octanethiol and octadecanethiol at the surface of the nanoplatelets:

Cd NPL -octadecanethiolate + OT ⇌ Cd NPL -octanethiolate + ODT

The equilibrium constant K is simply expressed by:

We are expecting K to be near a value of 1, as the differences between the two considered ligands only reside in their chain length that shouldn't greatly modify their affinity towards the NPL cadmium surface cations. The experiment simply consists in mixing 3ML NPLs bearing their native carboxylate ligands with a large excess of an ODT:OT binary mixture of varying ratios. The measured spectra are shown as supplementary materials (figure S4) and figure 4 show the measured frequencies as a function of the molecular weight and ODT fraction. The ligand exchange is let to proceed at 65°C for 72h as described in the experimental section. Considering that the thiols are in large excess compared to the native carboxylates and that their affinity for the NPL surface is much higher, the observed equilibrium is practically the one noted above. If we call x the fraction of ODT in solution and y the fraction of ODT at the surface of the NPLs, the equilibrium can be written as:

Considering that the excess of free ligands is very large, y is then determined using the low frequency Raman measurement followed by the calculation of the average molar mass of ligands needed to reach this frequency according to the calibration curve (figure 3b). The results presented in figure 4 show a clear deviation to the linear case (K=1 green line), and the experimental values can be fitted reasonably well using our simple equilibrium model with a K = 2.7. This simple competitive binding experiment unambiguously demonstrate that OT has a higher affinity than ODT for the NPL surface cadmium ions and allow us to quantify the affinity difference. This result also allows to determine the energy difference between Cd-OT and Cd-ODT molecular bonds at the NPL surface. If we consider that:

It is possible to determine the energy difference since:

We measured which gives an energy differences of kJ/mol. These results clearly show that the vibrations of nanoplatelets are a really sensitive signature of their structure as well as their surface ligands. Being able to disentangle these effects give access to a sensitive way to probe their mechanical properties and to follow their surface modifications.

In conclusion, we have here demonstrated the sensitivity of the breathing vibration mode of CdSe NPLs to ligands molecular weight. By carefully considering the real thickness of the NPLs, we highlight that for relatively thick (6MLs) NPLs this breathing mode depends on the ligands molecular weight and follows the behavior predicted by the mass-load model we previously developed. However, when reducing the number of layers to potentially increase the breathing mode sensitivity to ligands weight variations, we observed that other effects must be considered. At this scale, the structure of the whole NPL is impacted by the surface modifications induced by the ligands. This results in a modification of the NPL mechanical properties that strongly depend on the nature of the ligands. To understand the dependency of the mechanical properties of the NPL plus ligands system further experimental and theoretical investigations must be performed.

Nevertheless, we were able to calibrate the nanobalances based on the relationship between the NPL vibration frequency and the molecular weight of ligands of the same type (alkyl chains), which was deduced experimentally. This calibration has finally been applied to monitor the competitive binding at the surface of 3ML NPLs between thiols of different chain length.

Although the development of more comprehensive models is still needed, the ability to obtain information on the structural properties by simply using inelastic light scattering spectroscopy opens new routes to investigate the physical-chemistry of the interfaces, and the effect of surface treatments on nano-objects. Finally, these results open a route to develop a new class of labelfree sensors based on a nanoplatelet acting as a nanobalance probed through inelastic light scattering.

Methods

Chemicals:

1-octadecene (ODE, 90%), oleic acid (90%) and 1-octylamine (99%) were purchased from Alfa Aesar. 1-octanethiol (OT, 98.5%), 1-octadecanethiol (ODT, 98%), 1-dodecanethiol (DDT, 98%), 1-hexadecanethiol (HDT, 95%), trioctylphosphine (TOP, 97%), tetrakis(acetonitrile)copper(I) Ligand exchange:

The ligand exchange protocol is adapted from ref [START_REF] Mahler | Core/Shell Colloidal Semiconductor Nanoplatelets[END_REF]. Typically, 200 μL of the as-synthetized NPLs in hexane are mixed with 2 mL hexane and 1 mmol alkanethiol (octanethiol, dodecanethiol, hexadecanethiol or octadecanethiol). The mixture is then placed in an oven at 65 °C for 72 h to allow for a complete ligand exchange to occur. After exchange, the NPLs are washed trice by precipitation with ethanol, centrifugation and dispersion by sonication in 5 mL hexane.

Copper doping:

A stock solution of tetrakis(acetonitrile)copper(I) hexafluorophosphate, [MeCN] 4 Cu I PF 6 , at 1 x 10 -4 M in ethanol is used to dope the NPLs. The stock solution of copper (I) ions is directly added to NPLs in hexane at a ratio of 1 Cu for 1000 Cd, and the mixture is heated at 65°C for 1h.

Excess ions are then discarded by precipitation in ethanol, centrifugation and dispersion in hexane. This copper doping allows to quench part of the luminescence in order to observe the Raman scattering signal.

Absorption spectra: Absorbance spectra have been recorded using an AvaSpec-ULS2048 fiber optic spectrometer equipped with an AvaLight balanced Deuterium-Halogen lightsource.

PXRD: Powder X-ray diffraction (PXRD) patterns were recorded on a PANalytical Empyrean diffractometer (Cu Kα radiation). Samples were prepared by drying on a low background silicon substrate.

Raman spectroscopy: Resonant Raman spectra were obtained using Labram HR and Renishaw microspectrometers equipped with ultra-low frequency notch filters. The spectra were acquired using different laser lines (532, 633, and 660nm) depending on the thicknesses of the NPls and thus on the energy of the excitons. A long working distance x50 objective was used and each time the laser power was fixed to avoid any damage on the sample for several hours (typical: 10 mW). Several spectra were acquired on different positions of the same samples and were used to extract the frequencies using a gaussian fitting method.

Figure 1 :

 1 Figure 1: a. Optical absorption spectra of 5ML NPLs as a function of the ligand type (from top

Figure 1 .

 1 Figure 1.d shows the Raman spectrum measured on the sample of NPLs covered with OT

Figure 2 :

 2 Figure 2: a. Measured frequencies of NPLs vibration modes as a function of thiol molecular

Figure 3 :

 3 Figure 3: Top. TEM images of the NPLs (3+1MLs) morphology as a function of the ligand. a.

Figure 4 :

 4 Figure 4: Competitive binding between octanethiol and octadecanethiol on 3ML CdSe NPLs

  [START_REF] Antanovich | A strain-induced exciton transition energy shift in CdSe nanoplatelets: the impact of an organic ligand shell[END_REF][START_REF] Chen | Structure Identification of Two-Dimensional Colloidal Semiconductor Nanocrystals with Atomic Flat Basal Planes[END_REF]

ACKNOWLEDGMENT

This work was partially supported by the ANR NanoVip project, Grant ANR.13.JS10.0002 of the French Agence National de la Recherche, the Fédération André Marie Ampère 2013 (FRAMA) and the Programme Avenir Lyon Saint-Etienne from Université de Lyon in the framework "Investissements d'Avenir" (ANR-11-IDEX-0007). L.S. acknowledges support by EUR-EIPHI Graduate School (contract ANR-17-EURE-0002). The authors declare no competing financial interest. We thank the Consortium Lyon St-Etienne de Microscopie (CLYM) for access to the microscope platform TEM characterizations, and the spectroscopy platform CECOMO at Villeurbanne for the access to the LABRAM-HR spectrometer.

85 mL ODE and 1.02g Cd(myr) 2 are introduced in a 250 mL three-neck flask and degassed 1h under vacuum at 100°C. Under Argon, 72 mg Se powder dispersed in 5 mL ODE is introduced in the flask. The temperature of the setup is set to 240°C and 300 mg Cd(Acetate) 2 is introduced in the flask at 205°C. The reaction mixture is annealed at 240°C for 12 minutes resulting in the formation of 4 MLs CdSe NPLs. At the end of the reaction, 6 mL oleic acid is added before the solution is let to cool down to room temperature. NPLs are isolated from the reaction mixture by precipitation using a hexane/ethanol mixture and centrifugation; they are then dispersed in hexane and precipitated one more time by addition of ethanol. The final product is dispersed in hexane for storage, adjusting the solution volume to obtain an optical density of 1.5 at 350 nm when diluted 15 times. 5MLs CdSe NPLs synthesis: 56 mL ODE and 680 mg Cd(myr) 2 are introduced in a 250 mL three-neck flask and degassed 1h under vacuum at 100°C. The temperature of the solution is raised to 250°C under Argon flux and 48 mg of Se powder dispersed in 2ML ODE is swiftly injected at this temperature. Immediately after injection, 480 mg Cd(Acetate) 2 is introduced in the flask. The reaction mixture is annealed at the same temperature for 15 minutes resulting in the formation of 5 MLs CdSe NPLs. At the end of the reaction, 10 mL oleic acid is added before the solution is let to cool down to room temperature. NPLs are isolated from the reaction mixture by centrifugation; they are then dispersed in hexane and precipitated one more time by addition of ethanol. The final product is dispersed in hexane for storage, adjusting the solution volume to obtain an optical density of 1.5 at 350 nm when diluted 15 times.