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

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. [1][2][3][4][5][6][7][8][9] 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. 5,10 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. 4,11 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. 12 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. 10 Recent reports about low frequency phonons in nanocrystals [13][14][15][16][17] 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. 13,15,18 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 19 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. 15,16 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. [20][21][22] We demonstrated previously 15 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. 15,16 The lumped mass effect is accounted for with the following equation, whose roots give the resonance frequencies of the NPL across the thickness: 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.

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 6 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. 23 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. 20,24 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. 15 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).  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][26][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. [25][26][27] 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. 5 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  ligands. In this spectrum, an intense asymmetric peak at 203 cm -1 , and a band around 275 cm -1 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). [28][29][30] The second band has already been observed 5 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. Due to the preparation method, the NPLs surface is almost completely covered with carboxylates 35 , 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. 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. 40 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  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 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 20 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.
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.