Adelina-Antonia Andelescu

Benoît Heinrich

Maria Angela Spirache

Massimo Emilie Voirin

La Deda

Giuseppe Di Maio

Elisabeta I Szerb

Bertrand Donnio

Otilia Costisor

Playing with Pt II and Zn II Coordination to Obtain Luminescent Metallomesogens

Keywords: isotropic liquid, [c] Onset peaks, [d] Decomposition before melting, [e] POM observations, [f] Broad transition

Blue-green luminescent terpyridine-containing Pt II and Zn II complexes are reported. Equipped with lipophilic gallate units, which act as monodentate ancillary coordinating ligands and/or as anions, they display low-temperature mesomorphic properties (lamello-columnar and hexagonal mesophases for Pt II and Zn II complexes, respectively). The mesomorphic properties were investigated by polarised optical microscopy, differential scanning calorimetry, thermogravimetric analysis and X-ray scattering of bulk materials and oriented thin films. The model of self-assembly into the lamello-columnar phase of the Pt II complex has been described in detail. The optical properties of the complexes were investigated in the liquid and condensed liquid crystalline states, highlighting the delicate balance between the role of the metal in determining the type of excited state responsible for the emission, and the role of the ancillary ligand in driving intermolecular interactions for proper mesophase formation.

Pt_1

155 Dec [d] Pt_2 303 Cr 37.1 (-) [e,f] M+Colhex∼100-155 (-) Iso Iso 140.0 (-) [e,f] Iso+Colhex 84.9 (-8.5) M+Colhex 18.5 (-70.6) Cr Cr 39.2 (74.7) M+Colhex 89.3 (8.3) [f] Iso+Colhex 155 (-) Iso Pt_3 280 Cr 170 (-) [e] Iso Pt_4 285 LamColr 65-135 (11.6) [f] LamCol 255 (-) [e] Iso Zn_1 246 Cr 243 (-) [e] Iso Zn_2 309 Colhex 101 (2.2) Iso Iso 108 (-2.0) Colhex  [a] Significant weight loss (5 %) from degradation from the TGA trace. [b] Determined on first cooling and second heating (for mesomorphous compounds), and only first heating for the other: Cr, crystalline phase; Colhex, hexagonal columnar mesophase; LamCol, lamellar columnar mesophase; LamColr, lamellar columnar mesophase with rectangular symmetry; Iso,

Introduction

Luminescent d-block metallomesogens are promising functional materials for practical applications.

They have mainly been investigated in terms of obtaining polarised emission to be used as backlighting in displays,1-4 but also some studies concerning their use as stimuli responsive materials for sensing5, 6 or security inks,7 or high-hole mobility materials for electroluminescent devices8 have been reported. Despite recent progress with square-planar Pt II and octahedral Ir III complexes, which are considered among the best emitters, there is still considerable work to be done to control the phase type and transition temperatures or to improve the luminescence in the mesophase.9 In fact, only a few studies on the mesophases of luminescent liquid-crystalline transition metal complexes have been carried out, with, just to cite non-exhaustively, the contributions of Bruce et al. on Ir III ,8,[10][11][12], 15 on Au I , Gimenénez et al. on Ag I[16] and Zn II ,17 Cârcu et al. on Pd II ,[18][19][20] and Pucci, Crispini and Ghedini et al. on Ru II ,23 Ag I ,24-26 Ir III[27] and Zn II[28,29] complexes. For practical applications, technological and economic issues have to be taken into account, such as thermal and optical stabilities, availability and cost of the precursors and straightforward syntheses. Lately, some ionic Pt II complexes with terpyridine (tpy) or functionalised terpyridine ligands were showed to be good candidates for obtaining luminescent supramolecular assemblies both in liquid crystalline phases and gels, [30][31][32][33] owing to the extended aromatic region that favours π-π stacking and short Pt⋅⋅⋅Pt distances. [34] However, no study has demonstrated the retention of luminescence properties in the mesomorphic ranges of the bulk Pt II terpyridine-based complexes yet.

In this context, our interest in luminescent d-block metallomesogens [24,27,[35][36][37] prompted us to synthesise some luminescent Pt II coordination complexes. They were prepared by a versatile and straightforward synthesis, which permits facile molecular engineering by using anions of different coordination strengths and dimensions, including non-coordinating medium sized BF4, weakly coordinating bulky lipophilic benzoate and small and strongly coordinating Cl (Scheme 1). This strategy represents an easy way to induce liquid crystallinity in Pt II complexes by avoiding the several steps necessary to precisely functionalise the ligands. To explore the role of the metal cation, the same strategy was extended to Zn II complexes, but owing to the different electronic configuration only neutral penta-coordinated species were obtained. Scheme 1 Synthesis of Pt II and Zn II complexes: i) MeOH, ΔT, 1.5 h; ii) CHCl3/MeOH 1:1, r.t., 2 h; iii) CHCl3/MeOH 1:1, r.t., 1 h; iv) CHCl3/acetone 1:5, r.t., 2 h; v) MeOH/CHCl3, r.t., 1.5 h; vi) CHCl3, r.t., 2 h.

In this study, we designed and synthesised tpy-containing Pt II and Zn II complexes by using this simple concept. Initially, the straight, non-functionalised 2,2′:6′,2"-terpyridine ligand was used, but the low solubility of the Pt II chloro chloride (analogues of Pt_1 in Scheme 1) and Zn II dichloro (analogues of Zn_1) derivatives prevented the acceptable progress of the successive steps.

Therefore, the ligand was functionalised with a long alkyl chain through an ether linkage (ligand L).

The methyl ester group at the end of the chain is important for future applications of the complexes, as it allows derivatisation potentially to link the complexes onto functionalised metallic and/or oxide nanoparticles or mesoporous silica structures for theranostic purposes, in particular.

Of the three lipophilic complexes (i.e., Pt_2, Pt_4, Zn_2 in Scheme 1), two were found to be mesomorphous, displaying room-temperature lamello-columnar (Pt_4, LamColr and LamCol) and hexagonal columnar (Zn_2, Colhex) phases, whereas Pt_2 was found to be thermally unstable and to dissociate rapidly (see below). The thermal behaviour and liquid-crystalline self-assemblies were fully characterised by polarised optical microscopy (POM), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and small-and wide-angle X-ray scattering (S/WAXS) of bulk materials, combined with grazing incidence wide-angle X-ray scattering (GIWAXS) on oriented thin films. Accurate structural and photophysical investigations in different solvents and condensed states were carried out, in an attempt to determine structure-property relationships. In particular, of capital interest was the investigation of the influence of the mesophase organization on the emitting states.

Results and Discussion

Synthesis and spectroscopic characterisation

Ligand L (tpy) was obtained from 2,6-bis-(2′-pyridyl)-4-pyridone [38] by etherification with methyl 11bromoundecanoate [39] (see the Supporting Information). Complex Pt_1, synthesised by a slight modification of a method described in the literature for similar derivatives, [40] was used as precursor for both Pt_2 and Pt_3 ionic complexes: Pt_2 was obtained by reacting Pt_1 with 2 moles of the silver(I) salt of 3,4,5-tridodecyloxybenzoate, [41] whereas Pt_3 was obtained by metathesis reaction by using an excess of NH4BF4. The intermediate coordination strength of the benzoate unit gives the possibility for this anion to act as both counter anion and as coordinating ligand on Pt II , when no other competitor is present (complex Pt_2), or exclusively as a ligand in the presence of a noncoordinating anion like BF4 (complex Pt_4).

The reaction of the tpy ligand L with ZnCl2 afforded the neutral complex Zn_1, with the metal centre penta-coordinated by the tridentate terpyridine and two monodentate chlorine ligands. Although Zn II can be forced to accommodate a square-planar geometry with salicyldimine Schiff base [42,43] or porphyrin [44] ligands, without steric constraints, it prefers tetrahedral or higher number coordination geometries. We tried to obtain analogue ionic Zn II complexes but all attempts failed and only the neutral Zn_2 complex was obtained with two benzoate ligands saturating the coordination sphere of the Zn II metal centre. The proposed chemical structures of the ligand and its Pt II and Zn II complexes are supported by IR and accurate 1D and 2D NMR spectroscopy. The ionic character of the Pt II complexes was evidenced in solution by conductivity measurements. [45] The complexes were obtained as yellow (Pt II species) or white (Zn II species) powder or waxy solids and were dried for several days under high-pressure vacuum and then equilibrated under air. All Pt II complexes were hygroscopic; the presence of water molecules being evidenced both by IR spectroscopy (strong broad band centred at 3400 cm -1 ) and by TGA experiments (Figures SI-1 to SI-7 in the Supporting Information) and elemental analysis.

The first indication of the dual coordination mode of the benzoate group in the case of the Pt_2 complex was evidenced by the COO -stretching frequencies, different from the frequencies of the alkyl chain methanoate (νas=1740 cm -1 ). Indeed, for the benzoate the asymmetrical stretching (νas) is around 1635 cm -1 , and the symmetrical stretching (νs) for the ionic band appears at 1555 cm -1 (Pt_2) and at 1340 cm -1 for a coordinated bond (Pt_2 and Pt_4), giving a separation (Δ) of 80 and 295 cm -1 , respectively (Figure 1). [46] Moreover, for Pt_4, the characteristic band of the BF4 -counter ion appears centred at 1062 cm -1 (Figure 1). The IR spectra of the Zn II derivative Zn_2 (Figure SI_1, in the Supporting Information) contain only the stretching COO -vibrations corresponding to the coordinated specie (Δ≈250 cm -1 ). The chemical shifts of the aromatic protons were assigned on the basis of accurate 1D and 2D NMR investigations (Tables SI-1 to SI-6 in the Supporting Information). In the cases of Pt_2 and Pt_4, the aromatic protons belonging to the benzoate groups have different chemical shifts when coordinated to the metal centre as a monodentate ligand or ensure the neutrality of the complex as a negatively charged ion (Figure 2). In particular, for the coordinated benzoate, the aromatic protons are less shielded, shifting to higher frequencies. Thermal and mesomorphic behaviour (POM, TGA, DSC)

The thermal behaviour was first investigated by POM, TGA and DSC. The complexes without the benzoate group (Pt_1, Pt_3 and Zn_1 in Scheme 1) were obtained as amorphous or crystalline solids with high melting points, and, as expected, deprived of liquid crystalline properties owing to the absence of aliphatic chains. The introduction of lipophilic gallate units as monodentate ligands (Pt_4 and Zn_2 in Scheme 1) or as both ligand and counter anion (Pt_2 in Scheme 1) resulted in the drastic lowering of the melting points for all and in the induction of mesomorphism for the former ones (Table 1).

The thermal behaviour of the platinum complex with two gallate groups, Pt_2, is rather peculiar and complicated, and requires some precision. During the first heating, a first broad, endothermic event is detected at around 37 °C by DSC, and a texture characteristic of a hexagonal (Colhex) phase is easily recognised by POM (Figure 3 and Figure SI-9 in the Supporting Information). On further heating, above 90 °C, phase co-existence is observed (between Colhex phase and isotropic liquid), and the birefringence persists until the sample fully clears at 155 °C, at which temperature no more birefringence is seen. This very broad transition, spreading over several tens of degrees Celsius, was not detected by DSC. On cooling, the isotropic liquid and the Colhex phase were found to coexist again until a transition was detected at around 85 °C by DSC, where two phases eventually co-exist. It is important to note that this transition was not seen by POM and that no textural change was evidenced either. On further cooling, the compound partly crystallises. This singular phenomenon is reversible on successive thermal cycles, and suggests the partial dissociation of one gallate group during the first thermal treatment, as later confirmed by S/WAXS. 1 H NMR and IR spectroscopy measurements performed on Pt_2 after one cycle of heating and cooling indeed confirmed the dissociation of the ionic gallate (see Figures SI-18 and SI-19 in the Supporting Information). This lack of thermal stability therefore precludes any conclusive remarks on its supramolecular behaviour.

Table 1. Thermal behaviour of Pt II and Zn II complexes. [a] Thermal properties: mesophases, [b] transition temperatures [c] [°C] and enthalpies (ΔH [kJ mol -1 ]) Characterisation of the mesophases by small-and wide-angle X-ray scattering (S/WAXS)

Complex Tdec 5 % [°C]

Combined with S/WAXS investigation, lamello-columnar phases were eventually confirmed for Pt_4 from room temperature up to 255 °C, whereas a hexagonal mesophase was confirmed for Zn_2. The S/WAXS patterns, recorded for both samples at various temperatures, revealed several sharp and intense reflections in the small-angle range characteristic of the various twodimensional arrangements of mesogenic columns separated in space by a molten aliphatic continuum (Figure 4). For Zn_2, up to four reflections in the ratio 1:√3:2:√7 were observed, unambiguously characterising a hexagonal p6mm lattice. The numerous sharp reflections of Pt_4 could be indexed according to a p2mg rectangular lattice, with the arrangement of columns into a rectangular symmetry. In the large-angle region, a broad and diffuse scattering signal, emerging from undifferentiated lateral distances between the aliphatic chains and the gallate groups, respectively, hch+hgal, was systematically present and confirmed the fluid and liquid crystalline nature of all mesophases: these average lateral distances give rise to scattering maxima hgal and hch, which are not resolved from the large scattering contribution hch from the molten chains in the periphery of the columns. An additional signal is observed for Pt_4, hπ, arising from the stacking distances between successive tpy-platinum complexes into columns: this signal is rather sharp, suggesting a regular stacking of the complex along the columns. This signal is not present for the zinc complex, indicating that the stacking is completely undifferentiated from the broad scattering, hch+hgal. For this latter complex, another scattering maximum with a two-core ) and with a chain packing ratio, [47] qch, slightly above unity (Table 2). The stacking distance of the tpy rings is indeed 3.2945 Å at 25 °C in the single-crystal structure CSD-TPYZNC [48] of the dichloro-terpyridyl-zinc(II) complex, thus is nearly the same as in the frozen Colhex state of Zn_2. The qch value around 1.1 corresponds to almost stretched chains, favouring the formation of sharp nanosegregation interfaces with piled cores and thus columnar mesomorphism.

Table 2. Mesophase parameters of complex Zn_2.

Phase T [a]

Vmol ρ

[ b] a A[Z] [c]
hmol [d] χVch Acore [e] Dcyl [f] Sch,cyl [g] qch,cyl [h] Colhex [e] χVch, calculated aliphatic volume fraction; Acore=(1-χVch)×(A/Z), cross-sectional area of columnar cores (Å 2 ). [f] Dcyl=√(4/π Acore), diameter (Å) of equivalent cylinder of cross-sectional area Acore. [g] Sch,cyl=πDcyl×hmol/nch: cylinder area per chain (Å 2 ), nch=7, the number of chains per molecule. [h] qch=Sch,cyl/σch, chain packing ratio, σch=21.2 (Å 2 ), the cross-sectional area of a molten chain at 20 °C.

For the LamColr, the glide line coincides with the b-axis, along which column rows and counter ions compactly self-assemble into layers (Figure 5). The sequence of column layers and of intermediate molten chain layers along the a-axis generates a lamellar periodicity, dlam, giving a very strong firstorder reflection (1 0) and reflections series (h l) that extend to high h. In the thin-film pattern, the b- Figure 5 Left: model of terpyridyl-platinum complex moieties and gallate units, as reconstructed from single-crystal structures CSD-RAXFIH [49] and CSD-IJUMEG. [50] Right: schematic representation of the likely molecular organization in the LamColr mesophase of p2mg symmetry.

Columns of stacked complexes and BF4 -counter ions arrange in staggered rows; gallate units and molten alkyl chains (not represented) fill the gaps between successive staggered rows. The a-axis coincides with a lamellar periodicity dlam, maintained after heating in the LamCol mesophase, whereas the rectangular long-range lattice is suppressed by thermal fluctuations allowing successive column rows to move laterally one to another.

Terpyridyl-platinum complexes stack into columns that self-assemble with counter ions into layers alternating with aliphatic chains. At low temperature, the rings are nearly orthogonal to layers (hmol≈hπ), and the chains stretch onto the layer normal (qch≈1); the superimposition of layers defines a rectangular lattice of one-lamella and two-column periodicity (Table 3). At higher temperature, fluctuations of ring orientations out of the lamellar plane are enhanced (⟨ψ⟩≫0), which causes elongation of columns (hmol>hπ) and lateral expansion of lamellae (higher Amol and qch), which in turn affects the regularity of π-stacking (lower ξ). The columnar superstructure finally vanishes in the following lamello-columnar mesophase (LamCol), which preserves the long-range correlated lamellar structure and a local-range ribbon periodicity from average lateral distances between piled complexes (D). Table 3. Mesophase parameters of complex Pt_4.

Phase T [a]

Vmol ρ [b]

a b A[Z] dlam[NL] [c] D[ξ] [d]

Amol Sch [e] qch [f] Dcol Scol [g] hmol hπ

[ξ] [h] ψ [i]

Photophysical characterisation

The photophysical properties of the complexes have been investigated in DMSO solution for Pt_1, Pt_3, Pt_4, in CH2Cl2 solution for Pt_2, Zn_1, Zn_2 and in the solid state for all samples.

The results are summarised in Table 4 and Table 5.

Table 4. Photophysical properties of the complexes in solution at room temperature.

Sample Absorption, λmax [nm] (ϵ [M

-1 cm -1 ]) Emission λmax [nm] Quantum yield, Φ [%] Lifetime τ [ns]
Pt_1 [a] 286 (24 780), 305 (13 330), 320 ( 13 All Pt II complexes present a pale-yellow colour in diluted solutions and absorb in the UV region with weak bands in the visible region of the electromagnetic spectra (Figure 6 The emission quantum yields measured in air-equilibrated solution at room temperature are low and range from 0.2 to 1.7 %. The emission intensity decay has been fitted with a mono-exponential function giving lifetime values between 251 and 397 ns (Table 4).

Platinum tpy complexes are well known to form aggregates through metal⋅⋅⋅metal/π⋅⋅⋅π interactions, [51][52][53][54] which give rise to various excited states. The combined effect of the counter ion nature, the solution concentration and the solvent polarity modulates the photophysical properties of these complexes. On this basis, the 459 nm (Pt_1) and 455 nm (Pt_3) absorption bands in the first spectral region above identified, are attributed to a metal-metal-to-ligand charge transfer In the Supporting Information (Figure SI-21), the absorption spectra of platinum complexes at different concentrations are reported. It can be seen that as the concentration increases, the ratio between the bands attributed to the intermolecular interactions and those attributed to transitions on the single molecule, tends to grow, which is evidence for aggregation in solution.

Emission spectra recorded from solid samples at room temperature (Figure 6 c) have the same structure as those collected in solution under the same conditions. All show a redshift with respect to the solutions, but more accentuated for the complexes that bind chlorine (Pt_1 and Pt_3, which emit with a maximum at 676 and 690 nm, respectively) than for those that bind benzoate (Pt_2 and Pt_4, which emit with a maximum at 650 and 660 nm, respectively). Emission quantum yields and lifetimes in the condensed phase undergo a significant variation with respect to the values recorded in solution for Pt_2 and Pt_4, but this variation is much more consistent for Pt_1 and Pt_3 (see Table 4 andTable 5). In fact, the complexes bearing chlorine in solid samples show a redshifted emission maximum and an enhancement of the luminescence intensity with respect to the solution, whereas for the complexes with benzoate ligand these differences are smaller. This behaviour reflects the different origin of the emitting state for the two classes of compounds: for Pt_1 and Pt_3, the small steric hindrance of chlorine reinforces the Pt-Pt interaction in the solid, giving rise to an MMLCT excited state. On the contrary, the bulky benzoate group in Pt_2 and Pt_4 does not allow a Pt-Pt interaction, whereas weak π-π interactions on the tpy ligands give rise to the formation of excimers, similarly to the solution.

The photophysical behaviour of Pt_2 and Pt_4 was explored by changing the temperature. Both samples continue to emit during the heating and cooling cycles between 30 and 160 °C, retaining their emission maxima exhibited in the solid sample, that is, 650 nm and 660 nm for Pt_2 and Pt_4, respectively. The emission quantum yields have been measured at various temperatures (Table 6 andTable 7). For Pt_2, two heating/cooling cycles have been recorded, interspersed with cooling in the freezer (at -20 °C) for 30 min. For Pt_4, three cycles have been performed; between the end of the second cycle and the start of third cycle, the sample was cooled in the fridge (at 4 °C) for 2 h.

Table 6. Quantum yields for Pt_2 by varying the temperature; emission maximum λmax=650 nm.

First cycle Second cycle

Heating Cooling Heating Cooling Generally, the quantum yield decreases as the temperature increases, owing to thermal agitation, which favours the non-radiative deactivation pathway. For Pt_4, the experimental data follow this trend, after an initial steeper decrease on first heating, related to the development of the LamColr structure with the softening of the sample. Values on cooling and second heating stabilise around 0.5 % in this phase and decrease to 0.2 % in the less-ordered LamCol phase, prior to dropping to below 0.1 % in the isotropic liquid state. This rational dependence upon structure contrasts with findings for the Pt_2 sample, which shows an increase in the quantum yield during the first cycle, whereas from the beginning of the second cycle, the emission quantum yield is higher than the value measured in the solid. This peculiar behaviour can be rationalised by considering that on heating Pt_2 during the first cycle eliminates one gallate unit and the metal centres are getting closer, which explains the increase of luminescence by Pt-Pt interactions. The absorption spectra of Zn_1 and Zn_2 complexes recorded in CH2Cl2 solution (Figure 7 a)

T [°C] Φ [%] T [°C] Φ [%] T [°C] Φ [%] T [°C] Φ [%] 30
show a series of bands (Table 4) in the UV portion of the electromagnetic spectrum, all originating from tpy LC transitions. [55][56] In particular, for Zn_2, these transitions overlap with those localised on the benzoate ligand, giving rise to a broad band below 300 nm. Interestingly, by comparing the absorption spectra of the zinc complexes with that of the tpy ligand (see Figure SI-20 in the Supporting Information), it can be noted that in this last one the bands above 300 nm are very low in intensity, whereas in the absorption spectra of the complexes, these bands have an intensity comparable with those of the other bands. This different spectral behaviour is due to the different symmetry of the free and zincbonded terpyridine; the free tpy shows the nitrogen atoms of the lateral pyridines both facing the opposite side with respect to the nitrogen atom of the central pyridine, [56] whereas when the tpy binds a zinc ion all the nitrogen atoms are facing the same side. Both complexes are fluorescent, showing an asymmetric emission band at 365 nm (with a vibronic shoulder at 386 nm) for Zn_1, and at 379 nm (and a long tail extending towards the green spectral range) for Zn_2 (Figure 7 a).

The luminescence intensity is quite high, with an emission quantum yield of 6.4 % for Zn_1 and 24.5 % for Zn_2; time-resolved measurements give a mono-exponential decay of the excited states, with lifetimes of, respectively, 1.2 and 2.7 ns (Table 4). By comparing the photophysical properties of the two zinc complexes, it is evident that the substitution of the two chlorine atoms with two electron-donor benzoate groups involves a lowering of the energy of the emitting state, an increase of the Stokes shift and, above all, a considerable increase in the emission quantum yield. 4) with those measured in the condensed state (Table 5), the emission maximum remains almost unchanged (365 vs. 360 nm, respectively), whereas the quantum yield doubles from 6.4 % to 15.8 %, and the lifetime increases from 1.2 ns to 78.5 ns. This behaviour is attributable to the reduction of non-radiative de-excitation pathways that occurs in the solid phase, where the vibronic modes of the single molecule are somewhat reduced.

If we compare the behaviour of Zn_2 in solution (Table 4) with the pristine condensed phase (Table 5), we first notice a consistent redshift of the emission band (379 nm in solution vs. 450 nm in condensed phase), a drastic reduction of the quantum yield from 24.5 % to 7.1 % and different kinetics of the excited-state decay: mono-exponential in solution (with a lifetime of 2.7 ns) and multi-exponential in the pristine condensed phase, with a relevant percentage of short lifetimes (Table 5). The effect of temperature variation on the photophysical properties of Zn_2 is reported in Table 8. The temperature increase (both during the first and the second heating/ cooling cycle) involves a redshift of the emission band and a decrease of quantum yield. As found for Pt_4, trends are reversible by decreasing the temperature, but the initial higher values are never restored in relation

Conclusion

Luminescent metallomesogens are promising functional materials for various display applications.

Although considered as an emerging and growing field of research, there are still relatively few reported examples of square-planar Pt II and octahedral Ir III complexes being considered as outstanding emitters. This leaves space for the design of new metal-ligand systems to control the phase type, transition temperatures and thermal stability as well as to improve their luminescence in the mesophases.

The use of lipophilic gallate units is shown to be a good strategy in inducing low-temperature liquid crystalline properties in terpyridine-based Pt II and Zn II coordination complexes by an elegant and straightforward synthetic approach. The tpy ligand also was functionalised with a long alkyl chain, which ends with a methyl ester group, allowing further functionality derivatisation.

Only one Zn complex (Zn_2) and one thermally stable Pt complex (Pt_4) exhibited mesomorphic properties, the latter forming an original LamColr mesophase of p2mg symmetry, for which selfassembly and a structural model were proposed and discussed.

The photophysical properties of the complexes were investigated in solution and in the condensed state. In this work, we have highlighted the role of the metal in determining the type of excited state responsible for the emission, and the role of the ancillary ligand in driving intermolecular interactions. In the case of a d-block open-shell metal, such as platinum, we have studied the role of metal-metal interactions in the formation of excited states involving the metal centre, and the steric hindrance of the ancillary ligands in directing such interactions. For Pt_1 and Pt_3 the small steric hindrance of chlorine allows a Pt-Pt interaction (already present in solution and more strongly reinforced in the solid), giving rise to an MMLCT excited state in the mesophase. On the contrary, the bulky benzoate group of Pt_2 and Pt_4 does not allow a Pt-Pt interaction, whereas weak π-π interactions on the tpy ligands give rise to the formation of excimers, similarly to the solution.

Instead, in the case of a closed-shell metal such as zinc, the excited states are typically located on the ligand, so any variation of the intermolecular interactions (different in solutions rather than in the various condensed phases), which modifies the distances between the ligands of neighbouring complexes, entails a variation of the emission wavelength.

Finally, the presence of a metal centre, providing the optical properties tuning, requires great attention during molecular design, as the excited electronic states responsible for the luminescence can be modified by the supramolecular interactions that occur in the mesophase. The gallate unit, although beneficial for inducing room-temperature mesomorphism for both metal centres, is detrimental for the luminescence of the Pt II complexes, whereas it is more favourable for the synthesis of luminescent Zn II complexes. However, whereas in solution the Zn_2 complex is a good emitter, in columnar mesomorphic organisation its luminescence decreases. The great sensitivity of the metal centre with respect to its molecular environment is a potentially good property, which will be further exploited in sensing applications.

Figure 1

 1 Figure 1 IR spectra of Pt II complexes Pt_1, Pt_2 and Pt_4, showing the two types of carboxylate coordination m odes.

Figure 2 1 H

 21 Figure 2 1 H NMR spectra of ligand L, Pt_2 and Pt_4, showing the different chemical shifts of the aromatic proton belonging to the benzoate when they are coordinated or ionic.

Figure 3

 3 Figure 3 POM textures (top) of the Pt_2 sample at 35 °C on first cooling, of Pt_4 at 175 °C on second cooling, and of Zn_2 at 80 and 20 °C, respectively, on cooling. DSC traces (bottom) of Pt_4 and Zn_2.

  periodicity (hch+hgal+hπ)/2 was distinguished, in relation to the change of in-plane orientation between successive cores. The S/WAXS patterns recorded at various temperatures for complex Pt_2 unfortunately confirmed the erratic behaviour owing to the dissociation of the ionic gallate and the co-existence of two or more species, making the phase identification impossible (Figure SI-13 in the Supporting Information).

Figure 4

 4 Figure 4 Representative S/WAXS (top) and GIWAXS (bottom) patterns of Pt_4 (in the lowtemperature LamColr phase) and Zn_2 (in the Colhex). In the thin-film pattern, the b-axis and hπ scattering lie in the equatorial plane and lamellae are thus parallel to the substrate (see text). The profile analysis of the strip-like hπ scattering further reveals that complexes fluctuate out of the lamellar plane by roughly 10°.

  axis and hπ scattering lie in the equatorial plane and lamellae are thus parallel to the substrate. The profile analysis of the strip-like hπ scattering further reveals that complexes fluctuate out of the lamellar plane by roughly 10° (Figure 4, bottom right).

  a). The spectra show a well-resolved structure with numerous peaks, which can be grouped in three main regions: lowest intensity bands in the 450-500 nm range; medium-intensity peaks in the 370-400 nm region; highintensity bands below 350 nm. Although the spectral shape is almost unvaried on changing the counter ion or the ancillary ligand, the ϵ values are different.

Figure 6

 6 Figure 6 (a) Absorption spectra of Pt II complexes in DMSO (Pt_1, Pt_3, Pt_4) or CH2Cl2 (Pt_2) solutions. (b) Emission spectra of Pt II complexes in DMSO (Pt_1, Pt_3, Pt_4) or CH2Cl2 (Pt_2) solutions at room temperature. Concentrations are reported in Table 4. (c) Emission spectra of Pt II complexes in condensed phase at room temperature.

(

  MMLCT) excited state, indicative of Pt-Pt dimerization in Pt_1 and Pt_3, both bearing the chlorine ancillary ligand. When this ligand is replaced by a benzoate, as in the case of Pt_2 and Pt_4, the bands at 459 and 469 nm, respectively, are attributed to a π-π* transition of the tpy-tpy bound dimer, the Pt-Pt interaction being hampered by the steric hindrance of the gallate ligand. The absorption bands in the second spectral region (superimposable in the DMSO-dissolved complexes, and slightly redshifted in the CH2Cl2-dissolved compounds) are due to a metal-to-ligand charge transfer (d-π* MLCT) transition from Pt II to the tpy ligand. Finally, the bands in the third region are attributed to a ligand-centred (π-π*LC) transition on the tpy ligand. Pt_1 and Pt_3 show an emission band at 620 and 615 nm, respectively, owing to the 3 MMLCT deactivation.The Pt_2 and Pt_4 broad, unstructured emission band (peaked at 600 and 650 nm, respectively) is ascribed to an excimeric emission, which accounts for the large Stokes shift observed for Pt_4 compared with Pt_1 and Pt_3; the blueshift observed for Pt_2 emission is ascribed to the different solvent in which the compound has been dissolved. This different aspect of the emission spectra of the complexes bearing a chlorine as an ancillary ligand (Pt_1 and Pt_3) compared with those that bind a gallate (Pt_2 and Pt_4), confirms the different attribution of the lowest excited state, that is, an MMLCT in the case of the first pair, and an excimer (formed by means of π-π interactions between the aromatic rings of tpy) in the case of the second pair.

Figure 7

 7 Figure 7 (a) Absorption (continuous line) and emission (dashed line) spectra of Zn II complexes in CH2Cl2 solutions at room temperature. (b) Emission spectra of Zn II in the pristine condensed states at room temperature.

  to the structural changes on first heating. The columnar structure of the Zn complex is indeed initially disordered, with only average distances between irregularly arranged columns (Figure SI-16 in the Supporting Information), and the regular hexagonal arrangement only develops with the softening of the sample on first heating. Such a transformation clearly creates interactions between the compounds, which stabilise the excited state, as indicated by the redshift of the emission band, whereas the quantum yield decreases owing to the non-radiative deactivation increase triggered by the high temperature.

  Temperature of the measurement (°C). [b]Vmol, calculated molecular volume (Å 3 ); ρ, density (g cm-3 ). [c] a, b, A=a×b, Z: lattice parameters (Å), lattice area (Å 2 ) and number of columns per lattice; dlam, NL: lamellar periodicity (Å) and number of molecular layers per lamella (LamColr: dlam=a) (for LamColr only). [d] D, ξ: average distance between columns from scattering maximum (Å) and associated correlation length (Å, Scherrer equation with K=0.9) (for LamCol only). [e] Amol=Vmol/(dlam/NL) molecular area (Å 2 ); Sch=Amol/2: area per chain in the lamellar plane (Å 2 ). [f] qch=Sch/σch, chain packing ratio, σch=21.2 Å 2 at T=20 °C, being the cross-sectional area of a molten chain.[g]

								Dcol: distance
	between columns in the lamellar plane (Å) (LamColr: Dcol=b/2; Lamcol: Dcol=D); Scol =Dcol×(dlam/NL): cross-
	sectional area of a column (Å 2 ). [h] hmol=Vmol/Scol: molecular slice thickness (Å); hπ, ξ: distance
	between stacked complexes from scattering maximum (Å) and associated correlation length (Å,
	Scherrer equation with K=0.9). [i] ψ=acos(hπ/hmol): mean out of plane tilt angle of stacked complexes
	(°).
	LamColr	1820	41.20	44.2	1.04	12.55	3.52	9
	20	1.28	25.11	22.1		517	3.48
			1035[2]				[90]
			41.20[1]
			-
	LamColr	1880	40.60	46.3	1.05	12.58	3.68	17
	70	1.24	25.16	23.1		511	3.51
			1022[2]				[70]
			41.60[1]
			-
	LamCol	1960	-	53.2	1.15	12.5	4.24	33
	140	1.19	36.90[1]	26.6		462	3.54
			12.5[60]				[40]
	LamCol	2010	-	57.1	1.20	12.2	4.68
	180	1.16	35.17[1]	28.6		429	3.56
			12.2[60]				[25]



[a]

Table 5 .

 5 Photophysical properties of the complexes in the condensed state at room temperature.

	940), 334



Table 7 .

 7 Quantum yields for Pt_4 by varying the temperature; emission maximum λmax=660 nm.

	First cycle			Second cycle
	Heating		Cooling		Heating			Cooling
	T [°C] Φ [%] T [°C] Φ [%]	T [°C]	Φ [%]	T [°C]	Φ [%]
	30	1.80	150	0.07	30	0.56	150	0.11
	50	1.29	100	0.17	50	0.45	100	0.19
	100	0.50	50	0.41	100	0.22	50	0.41
	150	0.08	30	0.56	150	0.11	30	0.57
	160	0.06			160	0.08

Table 8 .

 8 Emission maximum and quantum yields for Zn_2 by varying the temperature. Emission maximum varies with temperature.

	First cycle
	Heating			Cooling
	T [°C]	λmax [nm] Φ	T [°C]	λmax [nm]	Φ
	30	450	7.1	80	497	1.92
	80	478	4.97	30	478	2.98
	140 (isotropic)	507	0.71

Second cycle Heating Cooling T [°C] λmax [nm] Φ T [°C] λmax [nm] Φ

	30	478	2.98	80	493	1.63
	80	500	1.35	30	482	3.27
	140 (isotropic)	509	0.50

Acknowledgements

This research was partially supported by Regione Calabria (POR Calabria FESR 2014/2020-Azione 1.2.2) through the MERAVIGLIE project. M.L.D. and G.D.M. are grateful to Dr. Angela Candreva for her collaboration in spectral acquisition. We thank the Pohang Accelerator Laboratory (PAL) for giving us the opportunity to perform the GIWAXS measurements, MEST and POSTECH for supporting these experiments, Dr. Hyungju Ahn for adjustments and help, and other colleagues from the 9A USAXS beamline for assistance. E.V., B.D. and B.H. thank the CNRS and University of Strasbourg for support. A.A.A., M.A.S., E.I.Sz. and O.C. acknowledge the Romanian Academy, Program 4. A.A.A. is grateful for an "Ion Heliade Radulescu" mobility scholarship.


Marion A Hurier

Maxime Wierez-Kien

Cecilia Mzayek

Bertrand Donnio

Jean-Louis Gallani

Mircea V Rastei

Nonlinear Phase Imaging of Gold Nanoparticles Embedded in Organic Thin Films

The phase detection in the dynamic mode of the atomic force microscopes is a known technique for mapping nanoscale surface heterogeneities. We present here an additional functionality of this technique, which allows high-resolution imaging of embedded inorganic nanoparticles with diameter and interparticle distances of a few nanometers. The method is based on a highly nonlinear tip-sample interaction occurring markedly above the nanoparticles, giving thus a high phase contrast between zones with and without nanoparticles. A relationship between the tip-sample interaction strength and the phase signal is established in experiments and from calculations conducted with the model developed by Haviland et al. [ Soft Matter 2016, 12, 619], which is based on solving a combined equation of motion for both the cantilever and surface while taking into account the time-varying interaction forces. The nonlinear phase behavior at the origin of the subnanometer spatial resolution is found by numerical analyses to be the result of a local mechanical stiffening of the zone containing nanoparticles, which is enhanced by 2 orders of magnitude or more.

Introduction

Many research fields require a simple technique for nondestructive subsurface imaging of inorganic nanoparticles. [START_REF] Krieg | Atomic Force Microscopy-Based Mechanobiology[END_REF][START_REF] Behzadi | Cellular Uptake of Nanoparticles: Journey inside the Cell[END_REF][START_REF] Tan | Plasmonic Light Trapping in Thin-Film Silicon Solar Cells with Improved Self-Assembled Silver Nanoparticles[END_REF][START_REF] Corbierre | Gold Nanoparticle/Polymer Nanocomposites: Dispersion of Nanoparticles as a Function of Capping Agent Molecular Weight and Grafting Density[END_REF] In this respect, several advanced techniques based on ultrasound [START_REF] Kolosov | Nonlinear Detection of Ultrasonic Vibrations in an Atomic Force Microscope[END_REF][START_REF] Angeloni | Identification of Nanoparticles and Nanosystems in Biological Matrices with Scanning Probe Microscopy[END_REF][START_REF] Van Es | Mapping Buried Nanostructures Using Subsurface Ultrasonic Resonance Force Microscopy[END_REF] or heterodyne [START_REF] Cuberes | Heterodyne Force Microscopy of PMMA/Rubber Nanocomposites: Nanomapping of Viscoelastic Response at Ultrasonic Frequencies[END_REF][START_REF] Verbiest | A Subsurface Add-on for Standard Atomic Force Microscopes[END_REF][START_REF] Verbiest | Beating Beats Mixing in Heterodyne Detection Schemes[END_REF] force detection demonstrated exceptional lateral resolution at the nanometer scale. [START_REF] Verbiest | Cantilever Dynamics in Heterodyne Force Microscopy[END_REF][START_REF] Verbiest | Subsurface Contrast Due to Friction in Heterodyne Force Microscopy[END_REF] These techniques, implemented in some custom-built atomic force microscopes, represent significant advancements in subsurface imaging and tomography, but their use by the broader community unfortunately is hindered by added/intrinsic complexity. [START_REF] Garcia | The Emergence of Multifrequency Force Microscopy[END_REF] On the other hand, the possibility of measuring the phase of the cantilever oscillation with respect to the excitation phase at a fixed driving frequency has been implemented very early [START_REF] Albrecht | Frequency Modulation Detection Using High-Q Cantilevers for Enhanced Force Microscope Sensitivity[END_REF][START_REF] Leclère | Microdomain Morphology Analysis of Block Copolymers by Atomic Force Microscopy with Phase Detection Imaging[END_REF][START_REF] Tamayo | Effects of Elastic and Inelastic Interactions on Phase Contrast Images in Tapping-Mode Scanning Force Microscopy[END_REF][START_REF] Rabe | Vibrations of Free and Surface-coupled Atomic Force Microscope Cantilevers: Theory and Experiment[END_REF] in all atomic force microscopes working in dynamic mode. The phase shift method, which has been successfully used for imaging surface heterogeneities [START_REF] Martínez | Measuring Phase Shifts and Energy Dissipation with Amplitude Modulation Atomic Force Microscopy[END_REF][START_REF] Claesson | From Force Curves to Surface Nanomechanical Properties[END_REF][START_REF] Huang | Local Surface Mechanical Properties of PDMS-Silica Nanocomposite Probed with Intermodulation AFM[END_REF] or for a local measurement of conservative and dissipative nanoscale forces, [START_REF] García | Dynamic Atomic Force Microscopy Methods[END_REF][START_REF] Platz | Interaction Imaging with Amplitude-Dependence Force Spectroscopy[END_REF][START_REF] Farrell | Conservative and Dissipative Force Imaging of Switchable Rotaxanes with Frequency-Modulation Atomic Force Microscopy[END_REF][START_REF] Cleveland | Energy Dissipation in Tapping-Mode Atomic Force Microscopy[END_REF] has in turn the drawback of probing sample characteristics only in regions near the surface, i.e. at a maximum depth of a few nanometers, according for instance to the DMT (Derjaguin, Muller and Toporov) model. [START_REF] Garcia | Identification of Nanoscale Dissipation Processes by Dynamic Atomic Force Microscopy[END_REF] Moreover, the phase shift signals have demonstrated large instabilities and fluctuations even for relatively weak surface heterogeneities. [START_REF] Sugawara | Elimination of Instabilities in Phase Shift Curves in Phase-Modulation Atomic Force Microscopy in Constant-Amplitude Mode[END_REF] Such unwanted phase instabilities are often caused by finite imaging bandwidths of the cantilever sensor or intrinsically by cantilevers with low spring constants. [START_REF] Paulo | Tip-Surface Forces, Amplitude, and Energy Dissipation in Amplitude-Modulation (Tapping Mode) Force Microscopy[END_REF][START_REF] Schirmeisen | Dynamic Modes of Atomic Force Microscopy[END_REF] Indeed, looking beyond the force gradient approximation introduced by Mertz et al., [START_REF] Mertz | Regulation of a Microcantilever Response by Force Feedback[END_REF] it was shown that the amplitude and phase signals may present discontinuities due to nonlinear tip-surface interactions. [START_REF] Sugawara | Elimination of Instabilities in Phase Shift Curves in Phase-Modulation Atomic Force Microscopy in Constant-Amplitude Mode[END_REF][START_REF] García | Attractive and Repulsive Tip-Sample Interaction Regimes in Tapping-Mode Atomic Force Microscopy[END_REF][START_REF] Nony | Nonlinear Dynamical Properties of an Oscillating Tip-Cantilever System in the Tapping Mode[END_REF] Since then, the phase shift was recognized as an ample and stable imaging tool only for weak enough tip-sample interactions, which are distance dependent, that ensure a rather constant cantilever spring constant (linear response approximation). This is critical not only for amplitude-modulation (AM) imaging mode, [START_REF] Martin | Atomic Force Microscope-Force Mapping and Profiling on a Sub 100-Å Scale[END_REF][START_REF] Giles | Noncontact Force Microscopy in Liquids[END_REF][START_REF] Hansma | Tapping Mode Atomic Force Microscopy in Liquids[END_REF][START_REF] Putman | Tapping Mode Atomic Force Microscopy in Liquid[END_REF] where the cantilever is externally driven at a constant excitation and frequency, but also for frequency-modulation (FM) mode when the excitation frequency is permanently adjusted by an external electronic device or by changing the probe-sample distance. [START_REF] Albrecht | Frequency Modulation Detection Using High-Q Cantilevers for Enhanced Force Microscope Sensitivity[END_REF][START_REF] Sugawara | Elimination of Instabilities in Phase Shift Curves in Phase-Modulation Atomic Force Microscopy in Constant-Amplitude Mode[END_REF] The situation is even more challenging when adhesion [START_REF] Brandsch | On the Factors Affecting the Contrast of Height and Phase Images in Tapping Mode Atomic Force Microscopy[END_REF][START_REF] Yablon | Quantitative Viscoelastic Mapping of Polyolefin Blends with Contact Resonance Atomic Force Microscopy[END_REF] and viscosity [START_REF] Yablon | Quantitative Viscoelastic Mapping of Polyolefin Blends with Contact Resonance Atomic Force Microscopy[END_REF] are considered, their effects being increasingly important when soft molecular surfaces are investigated. [START_REF] Thorén | Modeling and Measuring Viscoelasticity with Dynamic Atomic Force Microscopy[END_REF][START_REF] Killgore | Viscoelastic Property Mapping with Contact Resonance Force Microscopy[END_REF][START_REF] Haviland | Probing Viscoelastic Response of Soft Material Surfaces at the Nanoscale[END_REF] Molecular films containing metal nanoparticles are crucial for applications in fields such as optics, energy production and storage, microelectronics, information technologies, etc. The interesting aspect related to the use of organic matrices is the possibility they offer to preserve some of the intrinsic properties of the incorporated nanoparticles and, moreover, to specifically tune the overall material response through a controlled adjustment of the particle nature and interparticle separation. [START_REF] Ye | Structural Diversity in Binary Superlattices Self-Assembled from Polymer-Grafted Nanocrystals[END_REF][START_REF] Bell | The Impact of Nanoscience on Heterogeneous Catalysis[END_REF] Such functionalities can be achieved by modifying the nature of the capping organic molecules which govern the growth of precise nanoparticle networks having various organizational structures and lattice constants. [START_REF] Boles | Many-Body Effects in Nanocrystal Superlattices: Departure from Sphere Packing Explains Stability of Binary Phases[END_REF][START_REF] Malassis | Dendronization-Induced Phase-Transfer, Stabilization and Self-Assembly of Large Colloidal Au Nanoparticles[END_REF][START_REF] Diroll | Polycatenar Ligand Control of the Synthesis and Self-Assembly of Colloidal Nanocrystals[END_REF] ) Having the possibility to easily and readily image and characterize these systems at the nanometer scale is of critical importance for checking the structure-property relationship. The fact that the nanoparticles are embedded in an organic matrix precludes or strongly hampers the use of techniques such as electron microscopy.

Here, we experimentally and numerically investigate the formation of AFM phase images on samples composed of gold nanoparticles (NPs) embedded in soft organic films, namely, Au NPs capped with oleylamine ligands. We evidence an abrupt transition from a linear to nonlinear tip-sample interaction, exploited here for subnanometer high-resolution imaging. Working in AM-AFM mode, we identify a set of oscillation and excitation amplitudes that permit a very fine-tuning of the tip-sample interaction. We reveal that small variations in the oscillation amplitude generate rapid and substantial amplifications of the phase-shift signal, triggered by nonlinear effects. A precise control of the excitation amplitude then allows one to image subsurface NPs, which are otherwise difficult to resolve in topographic images, demonstrating that the phase shift method in AM-AFM mode still has an imaging interest. This also works in vacuum conditions where the high oscillation quality factor of the cantilever significantly reduces the frequency bandwidth used for detection.

Experimental Details

The measurements were performed at atmospheric pressure and occasionally under high vacuum (10 -6 Torr). Under vacuum conditions, the main conclusions of the study remain true, although spatial resolution is sometimes increased because of the higher mechanical quality factor. Nevertheless, we choose to present here only results obtained under ambient conditions. The substrates used for sample deposition were silicon wafers covered with a 2-4 nm thick oxide layer. Some excess of organic ligands was removed by rinsing with ethanol and deionized water and N2 drying prior to imaging. We used a modified atomic force microscope (Enviroscope) from Bruker, which is controlled by Nanoscope V electronics. An automatic gain control (AGC) was used to keep the oscillation amplitude of the cantilever at a fixed value. AFM probes of a spring constant of 40 N/m (resonant frequency of about 320 kHz) were employed; the tips were natively oxidized Si tips with an apex radius smaller than 10 nm. The samples were prepared outside the AFM microscope in ambient conditions and then transferred in the microscope.

The samples consisted of gold NPs incorporated in organic molecular films, as schematically shown for a single NP in Figure 1. The NPs have been chemically synthesized following the procedure of Peng et al. [START_REF] Peng | A Facile Synthesis of Monodisperse Au Nanoparticles and Their Catalysis of CO Oxidation[END_REF] The average diameter of the particles is 8.0 nm with a distribution width of about ±1 nm. The particles are coated with oleylamine, a weak ligand that does not strongly bind to gold unlike, e.g. alkanethiols. There is a need of an excess ligand to be present in the diluted liquid suspension for stability reasons. These ligands are not bound to the NPs and have the possibility of assembling on the surface during the spin-coated deposition. As seen below, this excess of organic ligands in the deposition suspension induces the formation of molecular films, which hide the NPs below the surface. An exact value of the thickness of the molecular film is not easily measurable, as the spin coating does not produce abrupt deposition edges. The film structure appears rather isotropic without evidence of an inner molecular organization. A few intentional scratches made on the film revealed a molecular thickness varying from a few nanometers up to about 30 nm, depending on the exact sample area. As a consequence, the standard AFM tapping mode is unable to clearly distinguish the subsurface localization of NPs. It is worth noting that upon deposition on surfaces such a situation is encountered for most of the weakly bound organic ligands used for the synthesis and stabilization of the nanoparticles. The precise depth of the NP with respect to the molecular surface is hence difficult to evaluate. However, the oscillation amplitude variations, as well as the numerical calculations presented below, suggest that NPs are rather close to the film surface, conceivably in the first few nanometers.

Phase Signal Formation

In tapping mode, the AM-AFM operates by constantly driving the cantilever near its mechanical resonance. The cantilever holder-sample distance is adjusted so that, for each cantilever oscillation, the tip can enter in repulsive interaction with the sample surface (contact regime). [START_REF] Martínez | Measuring Phase Shifts and Energy Dissipation with Amplitude Modulation Atomic Force Microscopy[END_REF][START_REF] García | Attractive and Repulsive Tip-Sample Interaction Regimes in Tapping-Mode Atomic Force Microscopy[END_REF] Depending on the cantilever/tip and surface elastic properties, the phase of the cantilever oscillation, and to some extent the amplitude, changes because the tip is pushed back by the surface, as depicted in Figure 1. This mechanical reaction of the surface is more or less delayed with respect to the initial oscillation, depending on the local elastic properties of the probed zone. As a general rule, the stiffer the surface, the stronger and quicker is the surface back-action on the cantilever oscillation. This effect has been exploited for imaging the heterogeneity of the mechanical properties of the molecular surfaces, particularly when adhesion forces (attractive interactions) were small as compared with the cantilever restoring force (see eq 1 hereafter). This is because the oscillation amplitude is large enough to enable the tip to oscillate in both attractive and repulsive regimes. As depicted in Figure 1, an embedded metal NP is also expected to impact the surface back-action on the tip because of its inertial mass and viscosity within the organic film. We will see below that above the NPs the repulsive interactions increase significantly, inducing a transition toward nonlinear phase responses, an effect that depends on the oscillation amplitude. It is perhaps important to note that the technique presented here is at variance with the magnetic force microscopy performed on partially or fully embedded magnetic nanoparticles, where phase shifts are induced by the far longer-range magnetostatic interactions. [START_REF] Kim | High-Density Ordered Arrays of CoPt 3 Nanoparticles with Individually Addressable Out-of-Plane Magnetization[END_REF][START_REF] Rastei | Nanoscale Hysteresis Loop of Individual Co Dots by Field-Dependent Magnetic Force Microscopy[END_REF][START_REF] Krivcov | Magnetic Force Microscopy of in a Polymer Matrix Embedded Single Magnetic Nanoparticles[END_REF] Figure 1. Schematic view of amplitude and phase changes when a tapping tip passes above an inorganic nanoparticle embedded in a soft organic molecular film. Amplitude and phase changes are accompanied by displacements of the mechanical resonance frequency of the cantilever (not shown).

Results and Discussion

An example of a phase image in both linear and nonlinear regimes on the same surface area is shown in Figure 2. It can be seen that the phase image from Figure 2a shows only little information about the location and organization of the NPs. Instead, increasing the tip-surface interaction by reducing the amplitude set point translates into a significant and abrupt contrast enhancement. The phase stability is also notably ameliorated, meaning that the tipsurface interaction is more homogeneous from oscillation to oscillation. Importantly, the lateral spatial resolution is remarkably enhanced, allowing not only the localization of the NPs within the aggregates below the surface but also their organization and to some extent an estimation of the particle sizes. In order to gain insight into the enhancement mechanism of the spatial resolution in phase images, we show in Figure 3a a tapping mode image acquired simultaneously with the phase image from Figure 3b. As seen, the topographic image reveals only a few details about the subsurface NPs; it would be impossible to locate precisely the NPs within the organic film or to count them. On the contrary, this information is readily accessible in the corresponding phase image acquired in the nonlinear regime. It is nevertheless important to recall that in phase images quantitative spatial information is however available only in the surface plane (x,y plane) and not on the z-axis. As a consequence, phase images are particularly valuable for revealing interparticle distances and organization. The profiles shown in Figure 3c,d, traced along the small lines from (a) and (b), provide additional information, namely, that an aggregate of NPs is seen in the topographic image only as a small surface protrusion, which has a significantly lower height than a nanoparticle diameter, an effect induced by the molecular film.

The phase line profile in Figure 3d shows that interparticle distances as small as 10 nm can easily be resolved in phase images. The maximum achievable spatial resolution depends on the exact scanning parameters, but a simple estimation performed on areas containing individual embedded NPs or defects reveals a spatial resolution higher than one nanometer, as shown hereafter.

Along this line, we show in Figure 4 a series of four phase images acquired for increasing values of cantilever drive amplitude (DA). First, it is seen that upon changing the DA value by 10 mV (from 375 mV to 385 mV) that the phase signal is enhanced by about 20°. This expresses the large sensitivity of the phase response triggered by the nonlinear tip-surface interaction above the NP. Second, the image acquired at 385 mV shows a remarkable abrupt phase variation in less than a 1 nm lateral scan, which is relevant for estimating the lateral resolution. To emphasize even better the lateral resolution, we show in Figure 5 phase profiles for different DA values, corresponding to the horizontal scan above the center of the NP from Figure 4. Each profile corresponds to a DA value from 370 mV to 385 mV using a step of 1 mV. The oscillation amplitudes associated with the DA values are also indicated. At 370 mV and free oscillation amplitude (A0) of 34.5 nm, the phase signal remains around -6° when scanning across the NP (Figure 5, green line). Upon increasing the DA toward 385 mV (A0 = 36 nm), the tip-surface interaction is gradually increased. At 385 mV (Figure 5, upper red curve), the phase signal exhibits a sharp increase at the NP edge, which measures about 0.6 nm. The phase signal is still not saturated, presenting instead a roof-like shape at the center of the NP, which is expected if one considers a phase dynamics reflecting the local stiffness of a finite indented area defined by the size of the tip apex. Considering that the molecular film has an identical surface nature above and near the NP, adhesion effects can hardly explain such a behavior (Figure 5). On the contrary, an increase of the surface stiffness may induce an abrupt enhancement of the surface reaction when the tip starts scanning above the NP, as we will see quantitatively in the simulations section. The linear to nonlinear transition is conveniently revealed by plotting the evolution of the phase shift as a function of the variation of oscillation amplitude (Figure 6), where the zero value indicates the initial amplitude set point. If the tip-surface interaction (toward positive values of amplitude variation) is progressively increased, the phase signal switches to a nonlinear behavior when the tip is located above the NP, whereas it remains linear if the tip stays above the molecular organic film. The amplitude variation is calculated here as the difference between the initial free oscillation amplitude (the one chosen before to approach the tip) and the corresponding free oscillation amplitude that results from subsequent modifications of the DA value. The amplitude variation is consequently a good representation of the sign and magnitude of the tapping force, as quantitatively described in refs [START_REF] Paulo | Tip-Surface Forces, Amplitude, and Energy Dissipation in Amplitude-Modulation (Tapping Mode) Force Microscopy[END_REF][START_REF] García | Attractive and Repulsive Tip-Sample Interaction Regimes in Tapping-Mode Atomic Force Microscopy[END_REF] . Figure 6. Phase shift evolution when approaching an individual subsurface NP. Each curve corresponds to a fixed lateral distance with respect to the center of the NP. The amplitude variation results from the change of the driving amplitude, which alters the tip-surface interaction and consequently the resonance oscillation frequency of the cantilever. Positive amplitude variation values mean larger oscillation amplitudes. The thick dark-blue line is an average of all curves taken on the NPs, whereas the thick light-blue line is an average of the curves acquired on the organic film when approaching the NP.

Note however that, after the tip-surface approach, the oscillation amplitude at the drive frequency is reduced in our case to about 80% of the free oscillation amplitude because of the tip-surface interaction. This implies that for null or slightly negative amplitude variation (Figure 6), the tip is still oscillating in both repulsive and attractive regimes (once per period). In any case, the plot from Figure 6 noticeably highlights the fact that, as the tapping force is increased, the phase dynamics above the NP exhibits a linear to nonlinear transition. It is important to recall now that, from the point of view of phase dynamics, a negative phase shift means an averaged attractive interaction whereas a positive shift means a repulsive interaction. On the organic film, the attractive interaction monotonically increases when the cantilever amplitude is increased, suggesting a monotonic enhancement of the attractive force. On the NP, the behavior is similar up to an amplitude variation of about -0.2 nm, when the repulsive forces start compensating the attraction force. Thus, at an amplitude variation of 0.6 nm, the repulsive force dominates and the phase shift transforms into positive values.

Per se, a nonlinear phase shift means that the phase response of the cantilever is not a linear function of the cantilever resonant frequency anymore. In other words, the phase of the cantilever oscillation does not change synchronously with the resonant frequency. Our automatic feedback loop adjusts the height of the cantilever holder in order to keep the amplitude constant. This means that the resonant frequency of the cantilever under the influence of the surface is not controlled. In any case, the nonlinearity observed on the NP in Figure 6 not only indicates that the phase presents a nonlinear behavior but also shows that the overall sign of the tip-surface interaction changed from attractive to repulsive.

In order to better understand the tip-sample interaction, we show in Figure 7 approachretract curves acquired above an embedded NP and over the organic layer. The force curves on the NP were vertically shifted for clarity. The first major difference between the two cases is observed in the approach force curves [Figure 7a]. As indicated by the green arrows, the total force acting on the tip changes the slope (repulsive forces start to dominate) at two different positions of the vertical displacement. Then, the repulsive force above the NP presents a rather smooth increase as can be seen between the green and black dashed arrows. This interval, where a repulsive interaction is progressively built up, is sensibly larger on the NP than on the organic layer. Afterward, the force follows a typical behavior of a tip in contact with a hard incompressible surface, which is likely the substrate surface; i.e. the slope of this last part is basically the spring constant of the cantilever. It is important to mention that the vertical displacement corresponds to the extension of the cantilever holder, which is not exactly the tip-apex displacement because of the cantilever deformation. The retract curves are reminiscent of the approach curves, although there is a clear hysteretic behavior (energy dissipation) in both cases, but it is slightly larger on the NP. The behavior seen in the force curves is confirmed by amplitude [Figure 7b] and phase [Figure 7c] signals acquired simultaneously with the curves from Figure 7a. The tip vertical positions where the phase signal changes sign in the approach curves [inset to Figure 7c] are indicated by solid black arrows. The earlier sign reversal of the phase on the NP again indicates a stiffening above the NP. It is, however, worth noting that the amplitude and phase curves depicted in Figure 7 can only be used here as additional information on the variation of the interaction force as a function of distance and cannot be directly linked with the phase variation from Figure 6 where the drive amplitude was continuously changed. Nonetheless, the fact that the tip experiences an earlier repulsion regime on the NP than on the organic film is in agreement with the change of the sign of the phase shift in Figure 7, speaking indeed in the favor of a stiffer local area at the NP location, which is the main driving force for contrast formation in our images. visualization. The force signal was acquired by measuring the average deflection of the cantilever. The free oscillation amplitude was 32 nm. In each case, there are two consecutive approach-retract curves taken at the same location, revealing a good reversibility after the indentation process. Black arrows show tip vertical positions where the phase signal changes the sign, as seen in the inset (zoom) from (c). Green arrows show tip vertical positions where the oscillation amplitude vanished.

To further assess this larger stiffness induced by the presence of NPs, we numerically evaluated the phase dynamics of the cantilever by using a recent model developed by Haviland et al., which is based on solving the dynamics of the cantilever and of the surface by the following equations of motions: [START_REF] Haviland | Probing Viscoelastic Response of Soft Material Surfaces at the Nanoscale[END_REF] (1)

(2)
where m is the mass of the AFM probe, z is the out-of-plane coordinate, ω0 is the cantilever's angular resonance frequency, and Q is the oscillation quality factor. In eq 2, ηs is the surface damping (viscosity) and k is the mechanical stiffness. Equation 1 describes the dynamics of the cantilever under the influence of the surface forces Fts(s, s). The instantaneous tip-surface separation s is a function of s0, which is the tip-surface distance when the tip is at equilibrium, and of velocity s. Negative s values correspond to tip indentation into the surface. The distance s between the tip and surface is s = s0 + z -ds, where ds is the instantaneous tipsurface separation, which partly changes because of the surface deformation.

The tip-surface interaction force Fts(s, s) reads: [START_REF] Haviland | Probing Viscoelastic Response of Soft Material Surfaces at the Nanoscale[END_REF] Fts(s, s) = Fcon(s) -[ηis]s<0, where Fcon(s) is the conservative force and the second term represents the dissipative part of the interaction with ηi being the interaction viscosity, existing only when the tip is in noncontact with the surface. Thus, the conservative force is [START_REF] Haviland | Probing Viscoelastic Response of Soft Material Surfaces at the Nanoscale[END_REF] (3) for s > 0 and (4) for s < 0, i.e., when the tip indents the surface. In eqs 3 and 4, Fadh is the adhesion force at s = 0, R is the tip radius, a0 is the interatomic distance, and E* is the reduced Young modulus.

Using the above equations, we numerically evaluate the effect of different sample stiffnesses, i.e., various ks values. It is worth noting that a small tip radius R as used here triggers deviations from standard models of contact mechanics, [START_REF] Butt | Force Measurements with the Atomic Force Microscope: Technique, Interpretation and Applications[END_REF] because of nanoscale elastocapillary effects. [START_REF] Style | Surface Tension and Contact with Soft Elastic Solids[END_REF][START_REF] Butt | Forces between a Stiff and a Soft Surface[END_REF] These effects are intrinsically captured in the model described above. (40,38) The results shown in Figure 8 correspond to the simulated phase of the cantilever with respect to the driving phase, as also experimentally measured. The curves in Figure 8 are for various sample stiffness ks values, which were found by several numerical tests to be able to approach the experimental results from Figure 6 (see blue curve for instance). For a rather soft sample (ks = 0.001 N/m), the cantilever phase is only slightly affected by the presence of the sample. On the other hand, by progressively increasing ks to 0.15 N/m, the phase signal becomes very similar to the one measured experimentally (Figure 7). In particular, it is seen that, in the first 1 nm of amplitude variation (starting from zero), the phase signal rises for the blue curve (ks = 0.15 N/m) up to about 12°, a value that can also be found in the experimental phase variation in Figure 7. It is also worth noting that these stiffness values are representative for the whole local zone probed by the tip, as the film thickness as well as the localization of the NPs within the film are not parameters explicitly taken into account into the model. We can nevertheless conclude from our numerical analyzes that the presence of a NP enhances the sample stiffness by more than 2 orders of magnitude. In addition, our simulations reveal that the surface elastically recovers after each tip oscillation, although the full local relaxation is delayed as compared to the tip trajectory (see insets, Figure 8), which is expected for a cantilever with a spring constant far larger than the surface stiffness.

Since the first demonstration of phase imaging for resolving surface heterogeneity, [START_REF] Magonov | Phase Imaging and Stiffness in Tapping-Mode Atomic Force Microscopy[END_REF] the technique has been successfully exploited for various and very diverse purposes, [START_REF] Martínez | Measuring Phase Shifts and Energy Dissipation with Amplitude Modulation Atomic Force Microscopy[END_REF][START_REF] García | Nanoscale Compositional Mapping with Gentle Forces[END_REF][START_REF] Forchheimer | Model-Based Extraction of Material Properties in Multifrequency Atomic Force Microscopy[END_REF] including for the imaging of embedded NPs. [START_REF] Tetard | Imaging Nanoparticles in Cells by Nanomechanical Holography[END_REF][START_REF] Tetard | Elastic Phase Response of Silica Nanoparticles Buried in Soft Matter[END_REF][START_REF] Ebeling | Visualizing the Subsurface of Soft Matter: Simultaneous Topographical Imaging, Depth Modulation, and Compositional Mapping with Triple Frequency Atomic Force Microscopy[END_REF][START_REF] Yao | Visualization of Au Nanoparticles Buried in a Polymer Matrix by Scanning Thermal Noise Microscopy[END_REF] We showed here that the phase contrast of embedded NPs presents a nonlinear behavior as compared to the softer organic film. In other words, the phase sign does not change precisely at the new resonance frequency triggered by the tip-surface interaction, which is by definition a nonlinear behavior. As schematically shown in Figure 1, when the tip scans above a NP, the repulsive response of the sample is strong enough to push back the tip well before its oscillation is completed. This significantly advances the oscillation phase with respect to the cantilever mechanical shaking, translated into a bright contrast (positive phase shifts) above the NP in phase images (see Figure 5). For weak tip-sample interactions, the phase changes are small, showing only weak and linear variations when the drive amplitude is increased. Despite these variations being small, they are nevertheless easily measurable by the microscope lock-in electronics.

In general, for strong repulsive interactions, there can be two scenarios, depending on the tip size (adhesion scales with tip size) and, importantly, cantilever stiffness. To better describe the impact of these two parameters, let us first briefly recall the main differences between amplitude and phase variations when used for imaging. It is important to recognize that in AM-AFM tapping mode the amplitude modification of the cantilever is constantly surveyed by the feedback loop, which role is to keep the tip at the user-imposed set point value. This is achieved by a permanent readjustment of the cantilever holder-sample distance, providing the topography. The cantilever phase shift is expected to be driven by the amount of dissipation energy through inelastic tip-surface interactions, [START_REF] Martínez | Measuring Phase Shifts and Energy Dissipation with Amplitude Modulation Atomic Force Microscopy[END_REF] which in turn depends on the local probed area. The large phase variation measured above the NPs can therefore be linked to large modifications in the amount of energy transferred by the tip to the sample. It is also important to remark that the amplitude is measured by averaging over a time interval, which usually consists of at least hundreds of oscillation periods, whereas the phase signal can be measured a bit faster. As a matter of fact, the phase is generally used to recover the amplitude. This, along with the fact that the phase acquisition does not require the operation of the feedback loop, is why the lateral resolution in phase images is generally higher, but as shown all along this work, this is not the sole advantage.

In order to track the phase changes during scanning, it is necessary to have some degree of coherence between consecutive oscillations; although for the typical lateral-scan speeds used in standard AFM imaging (some hundreds of ms per scan line), there is enough time per pixel to average over thousands of oscillations. The more dissimilar the oscillations are, the less resolved is the pixel-to-pixel average value, translating in a poor spatial resolution. This effect strongly depends on cantilever stiffness and surface adhesion force. The surface adhesion force scales in turn with the tip-apex size, increasing in a quadratic way with the tip-apex radius. Surface adhesion thus impedes the tip, at each oscillation, to freely detach from the surface, therefore also being very relevant for phase changes, as seen in the eq 4 through the tip radius R. This interferes with the local out-of-plane surface stiffness and, consequently, with the molecular volume probed by the tip, which is different on zones with or without NPs. Now, let us consider that the surface adhesion is constant all over the surface, which in the case of deeply embedded NPs is a rather good approximation. Hence, as the surface is able to retain the tip attached until the potential energy of the cantilever oscillation breaks the contact, abrupt phase changes will appear, translating in strong phase variations or instabilities. Importantly, such a process is a statistical process, first because of the finite temperature and second because the tip-surface contact is not identical for each oscillation. In this last process, the surface relaxations, which depend on the surface viscosity, may also play a relevant role, as also quantified in the numerical simulations via ηs. These last aspects are increasingly important when soft cantilevers are used, as they are less able to detach the tip from the surface as fast as the oscillation proceeds. Choosing the right cantilever stiffness is therefore a necessary condition for stable phase imaging. Coupling this requirement with the surface adhesion force previously discussed brings us to the conclusion that, the stronger the surface adhesion, the stronger the cantilever stiffness should be in order to avoid instabilities. It should also be remembered that this depends on the tip size, meaning that an initially sharp tip may provide good results and, progressively, as it becomes blunter, instabilities may appear, as very often encountered experimentally. These aspects are implicitly captured by the analytical model introduced by Haviland et al. [START_REF] Haviland | Probing Viscoelastic Response of Soft Material Surfaces at the Nanoscale[END_REF] and used here to reproduce our experimental results. The only free parameter in our case was the surface stiffness, which we find exalted by more than 2 orders of magnitude above an embedded NP. All the other parameters needed to solve the equations were considered known and kept constant.

As fundamentally pointed out in a recent work conducted by scanning thermal noise microscopy by Yao et al., [START_REF] Yao | Visualization of Au Nanoparticles Buried in a Polymer Matrix by Scanning Thermal Noise Microscopy[END_REF] the variation of surface stiffness and damping introduced by the presence of embedded nanoparticles in a soft polymer is indeed a key ingredient for subsurface imaging, as our findings also revealed. Their method further brings additional understanding in the subsurface imaging mechanism, but it has the disadvantage of requiring extremely long acquisition times for one image (>5 h). This is because a thermal noise spectrum is needed for each pixel of the image and because the frequency resolution in a noise spectrum scales with the total acquisition time of the cantilever fluctuation. An interesting aspect of the technique presented in ref [START_REF] Yao | Visualization of Au Nanoparticles Buried in a Polymer Matrix by Scanning Thermal Noise Microscopy[END_REF] is that it can easily be implemented with techniques that involve a cantilever excitation, like the phase method presented here, in order to conduct point spectroscopy in a thermal noise regime at specific locations. This can be achieved by a temporary stopping of the cantilever excitation, i.e. the time to acquire a thermal noise spectrum. Such a combined technique would afford the possibility for one to obtain additional information otherwise hidden by spurious peaks and skewness induced by the nonlinear interactions.

Conclusion

We have shown that a conventional atomic force microscope can be conveniently set to image hard nanoparticulate structures embedded in a soft organic matrix, like oleyamine. A little tweaking of the scan parameters allows very good imaging of the sample with high lateral resolution, the only cost being the loss of precise measurement along the vertical direction to the surface. As an example, we have shown how the packing of 8 nm gold nanoparticles becomes clearly visible while the usual topographic image only returns blurred contours of the clusters. This technique allows the imaging of materials that would be hardly or more costly imaged by other microscopy techniques. Composite materials made of nanoparticles dispersed in polymer melts or small molecules are nowadays more and more present in research and technology, like in organic photocells, plasmonic materials, bioactive materials, and energy storage and production, to cite but a few. It is of obvious importance to be able to probe the quality of the NP dispersion within the matrix, and the suggested procedure makes it quite easy to perform.

Figure 2 .

 2 Figure 2. Phase images (600 × 900 nm 2 ) acquired in standard tapping mode over the same area with the same tip. The excitation amplitude of the cantilever (drive amplitude DA) was 330 mV. The amplitude set point was 380 mV in (a) and 360 mV in (b). Between the two images, there is a transition from a linear to nonlinear phase response, which is induced here by reducing the oscillation amplitude set point.

Figure 3 .

 3 Figure 3. (a) Height (topographic) image (300 × 300 nm 2 ) acquired simultaneously with the phase image from (b). The lines are showing the location of the profiles from (c) and (d), respectively. (c) Height profile revealing the weak degree of the NP resolution. (d) Phase profile showing the increased lateral resolution with respect to the topographic data.

Figure 4 .

 4 Figure 4. Phase images (18 × 18 nm 2 ) recorded above an individual embedded NP recorded for increasing values of drive amplitude (values in upper right corner). The images emphasize the lateral resolution and the high phase sensitivity near the linear to nonlinear transition.

Figure 5 .

 5 Figure 5. Phase profiles acquired across a single nanoparticle for different drive amplitudes near the linear to nonlinear transition.

Figure 7 .

 7 Figure 7. (a) Approach-retract force curves acquired on top of an embedded NP and on the organic film. (b, c) Corresponding amplitude and phase signals acquired simultaneously with the force curves. Force and amplitude data for the NP were vertically shifted for a better

Figure 8 .

 8 Figure 8. Simulated phase shift for increasing values of sample stiffness. The large phase variation for ks = 0.15 N/m shows a phase variation very close to the experimental results for Figure 6. Insets are instantaneous cantilever and surface amplitudes.

Acknowledgments

We thank N. Beyer for technical assistance. This work is supported by ANR METABIP (12 BS10 003 01), ANR OH-RISQUE SMARAGD (14 OHRI 0008 01), and EOARD (FA8655-13-1-3001) and partially by ANR-11-LABX-0058-NIE within the Investissement d'Avenir program ANR-10-IDEX-0002-02.

Notes

The authors declare no competing financial interest.