Zaifa Pan
email: panzaifa@zjut.edu.cn

Prof. B Victor Castaing

Liping L Yan

Lulu Zhang

Cong Zhang

Kang Shao

Yifan Zheng

Changkui Duan

Dr Jianhua Liu

Cyrille Richard

Bruno Viana
email: bruno.viana@chimie-paristech.fr

Prof L Z F P Pan

Dr K Zhang

Shao

Prof. Y F Zheng

Prof. C K Duan

Viana

Facilitating low energy activation in the near-infrared long-afterglow complex spinel Zn1+xGa2-2xSnxO4:Cr 3+ via band gap engineering and control of cation occupancy

Keywords: persistent luminescence, complex spinel, low energy activation, band gap engineering, cation occupancy control

scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

whereas the persistent excitation redshift facilitates the activation of the persistent luminescence by low energy radiation. Furthermore, it appears that increasing the rate of cation site-inversion in the spinel can lead to an optimum anti-site defect concentration for charge trapping. These results, which highlight the benefit of cation occupancy control for persistent luminescence properties, may be of further interest for the development of spinel materials with optimized optical properties.

1.Introduction

Persistent luminescent materials are attracting a great deal of attention in bio-imaging applications, because they feature an inherent advantage over conventional luminescent materials that require constant in situ excitation. [START_REF] Wu | Long Afterglow Phosphorescent Material[END_REF][START_REF] Li | Long Persistent Phosphors-from Fundamentals to Applications[END_REF][START_REF] Lécuyer | Chemically Engineered Persistent Luminescence Nanoprobes for Bioimaging[END_REF][START_REF] Liu | Imaging and Therapeutic Applications of Persistent Luminescence Nanomaterials[END_REF] This feature not only suppresses photodamage of biological tissue from external excitation light, but also reduces autofluorescence background, [START_REF] Frangioni | In vivo Near-infrared Fluorescence Imaging[END_REF] leading to ultrahigh signal-to-noise ratio. Furthermore, due to the deep penetration of near infrared (NIR) photons in bio-tissues, persistent luminescent materials with NIR emissions are particularly suitable for deep tissue imaging. [START_REF] Wu | Long Afterglow Phosphorescent Material[END_REF][START_REF] Li | Long Persistent Phosphors-from Fundamentals to Applications[END_REF][START_REF] Lécuyer | Chemically Engineered Persistent Luminescence Nanoprobes for Bioimaging[END_REF][START_REF] Liu | Imaging and Therapeutic Applications of Persistent Luminescence Nanomaterials[END_REF][START_REF] Frangioni | In vivo Near-infrared Fluorescence Imaging[END_REF][START_REF] Chermont | Nanoprobes with Near-Infrared Persistent Luminescence for in vivo Imaging[END_REF][START_REF] Bessière | ZnGa2O4:Cr 3+ : a New Red Long-lasting Phosphor with High Brightness[END_REF] Cr 3+ activated phosphors with the spinel structure are currently the most promising materials for such applications, due to the suitable afterglow wavelength of Cr 3+ (in the 650 -750 nm emission range) and the high concentrations of antisite defects that are supported by the spinel lattice.

The normal spinel ZnGa2O4:Cr 3+ was reported as a new bright red persistent luminescent phosphor in 2011. The potential of its deep red persistent luminescence for application in in vivo imaging was demonstrated using activation by visible light (orange/red LEDs). [START_REF] Bessière | ZnGa2O4:Cr 3+ : a New Red Long-lasting Phosphor with High Brightness[END_REF][START_REF] Maldiney | The in vivo Activation of Persistent Nanophosphors for Optical Imaging of Vascularization, Tumours and Grafted Cells[END_REF] It is reported that the afterglow originates mainly from distorted Cr 3+ and that antisite defects in the spinel lattice play a crucial role in the trapping mechanisms. However, the afterglow performance of ZnGa2O4:Cr 3+ is still too low for practical application. In the race for new persistent luminescent materials for in vivo applications, a considerable amount of research on the persistent emission and trap tuning by aliovalent substitution, [START_REF] Allix | Considerable Improvement of Long-Persistent Luminescence in Germanium and Tin Substituted ZnGa2O4[END_REF] co-doping [START_REF] Abdukayum | Functional Near Infrared-Emitting Cr 3+ /Pr 3+ Co-Doped Zinc Gallogermanate Persistent Luminescent Nanoparticles with Superlong Afterglow for in vivo Targeted Bioimaging[END_REF][START_REF] Liu | Phonon-Assisted Upconversion Charging in Zn3Ga2GeO8:Cr 3+ Near-Infrared Persistent Phosphor[END_REF][START_REF] Zhao | Fabrication and bioconjugation of B III and Cr III Co-doped ZnGa2O4 Persistent Luminescent Nanoparticles for Dual-Targeted Cancer Bioimaging[END_REF][START_REF] Castaing | Persistent Energy Transfer in ZGO:Cr 3+ ,Yb 3+ : A New Strategy to Design Nano Glass-Ceramics Featuring Deep Red and Near Infrared Persistent Luminescence[END_REF][START_REF] Zhuang | Enhancement of Red Persistent Luminescence in Cr 3+ -Doped ZnGa2O4 Phosphors by Bi2O3 Codoping[END_REF] and lattice modification of the spinel host is still in progress. [START_REF] Pan | Sunlight-activated Long-Persistent Luminescence in the Near-Infrared from Cr 3+ -Doped Zinc Gallogermanates[END_REF][START_REF] Shen | Effect of Cr on Long-Persistent Luminescence of Near-Infrared Phosphor Zn3Ga2Ge2O10:Cr 3+[END_REF][START_REF] Li | Long Persistent and Photo-Stimulated Luminescence in Cr 3+ -Doped Zn-Ga-Sn-O Phosphors for Deep and Reproducible Tissue Imaging[END_REF][START_REF] Li | Tailoring of the Trap Distribution and Crystal Field in Cr 3+ -Doped non-gallate Phosphors with Near-Infrared Long-Persistence Phosphorescence[END_REF] The red persistent luminescence of this spinel phosphor was improved considerably by the aliovalent substitution of gallium by germanium or tin, with a nominal composition Zn1+xGa2-2x(Ge/Sn)xO4(0 ≤ x ≤ 0.5). [START_REF] Allix | Considerable Improvement of Long-Persistent Luminescence in Germanium and Tin Substituted ZnGa2O4[END_REF] Such aliovalent substitutions (in this case the replacement of a trivalent cation by tetravalent one) induces distorted octahedral sites in the resulting spinel solid solutions, which are surrounded by octahedral Ge/Sn positive defects, and work as new efficient traps.

Similarly, the new partially Ge-substituted host, Zn3Ga2Ge2O10:0.5%Cr 3+ presents a great enhancement of the NIR persistent luminescence, which can glow for more than 360 hours and can be repeatedly charged by sunlight. [START_REF] Pan | Sunlight-activated Long-Persistent Luminescence in the Near-Infrared from Cr 3+ -Doped Zinc Gallogermanates[END_REF] New tin containing spinel host Zn3Ga2SnO8:0.5%Cr 3+ [START_REF] Li | Long Persistent and Photo-Stimulated Luminescence in Cr 3+ -Doped Zn-Ga-Sn-O Phosphors for Deep and Reproducible Tissue Imaging[END_REF] and Al doped non-gallate long-persistence phosphors Zn2-xAl2xSn1-xO4:0.2%Cr 3+ [START_REF] Li | Tailoring of the Trap Distribution and Crystal Field in Cr 3+ -Doped non-gallate Phosphors with Near-Infrared Long-Persistence Phosphorescence[END_REF] have also been designed. Both of these show remarkable long persistent luminescence properties with the potential for reproducible tissue imaging applications. Finally, a further enhancement of the persistent luminescence was obtained in Pr 3+ /Cr 3+ co-doped zinc gallogermanate Zn3Ga2Ge2O10:Cr 3+ ,Pr 3+ and applied to long-term in vivo targeted tumor imaging, after bioconjugation with the peptide c(RGDyK). [START_REF] Abdukayum | Functional Near Infrared-Emitting Cr 3+ /Pr 3+ Co-Doped Zinc Gallogermanate Persistent Luminescent Nanoparticles with Superlong Afterglow for in vivo Targeted Bioimaging[END_REF] Spinels are conventionally represented by the formula AB2O4, in which element A is a divalent cation occupying a four-coordinate tetrahedral site and B is a trivalent cation occupying a six-coordinate octahedral site. [START_REF] Sickafus | Structure of Spinel[END_REF][START_REF] Zerarga | Electronic and Optical Properties of Spinel Oxides ZnAl2O4, ZnGa2O4 and ZnIn2O4[END_REF] Consequently, a normal spinel can be described as (A)[B]2O4, where parentheses () and brackets [] denote tetrahedral and octahedral sites, respectively. In addition to the normal spinel structure, the valence state of the cations can be tetravalent and divalent, for example in TiMg2O4 and TiZn2O4 [START_REF] Cogle | Solid-Solution Formation, Electrical Properties and Zero-Resistance Behaviour in the Spinel System Mg2TiO4-MgTi2O4[END_REF][START_REF] Sun | Efficient Photocatalytic Hydrogen Production over Rh-Doped Inverse Spinel Zn2TiO4[END_REF] which are inverse spinels. In the inverse spinel structure, all the tetravalent cations (M) and half of the divalent cations (N) occupy octahedral sites, while the rest of the divalent cations (N) occupy tetrahedral sites. The general structure of inverse spinel compounds can be represented by the formula (N)[MN]O4.

It should be pointed out that intermediate occupancies (partial disordering of cations between the sites) are commonly observed with inverse cation distributions, which can be written as (A1-xBx)[A x ⁄2B1-x ⁄2]2O4. For instance, the ZnGa2O4 host contains ~3% antisite defects. [START_REF] Allix | Considerable Improvement of Long-Persistent Luminescence in Germanium and Tin Substituted ZnGa2O4[END_REF][START_REF] Li | Tailoring of the Trap Distribution and Crystal Field in Cr 3+ -Doped non-gallate Phosphors with Near-Infrared Long-Persistence Phosphorescence[END_REF] Thanks to their distinctive antisite defects, spinel compounds are the most important hosts for near infrared long afterglow luminescent materials. [START_REF] Bessière | ZnGa2O4:Cr 3+ : a New Red Long-lasting Phosphor with High Brightness[END_REF] It is expected that site inversion will be more abundant in these intermediate occupancy compounds than those of pure normal spinel hosts.

Because of this structural chemistry, new complex spinels designed with intermediate site occupancies have the potential to host high concentrations of antisite defects, leading to better afterglow properties. Hence, a series of near infrared afterglow materials, comprised of complex spinels with different ratios of spinel ZnGa2O4 and inverse spinel Zn2SnO4, were targeted and prepared by a high temperature solid state method. The crystal structures and cation site occupancies were characterized by X-ray powder diffraction (XRD), transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). The effects of the band gap and traps on the afterglow properties in different hosts were studied by PL and PLE spectra, persistent luminescence excitation spectra, thermoluminescence curves and photon counting imaging. This detailed optical characterization demonstrates that these new complex spinel persistent luminescence materials are more suitable for in vivo imaging through low energy activation. The evolution of the optical properties as a function of composition are discussed and illustrated with a series of schematic energy level diagrams.

2.Experimental

Sample preparation

The complex spinels were designed as combinations of the normal spinel ZnGa2O4 and inverse spinel Zn2SnO4 with different ratios, as represented by the formula Zn1+xGa2-2xSnxO4 :Cr 3+ (x = 0.09, 0.11, 0.14, 0.20, 0.33, 0.5, 0.66 and 0.8, which we denote as ZGSO-2, ZGSO-3, …, and ZGSO-8). ZnGa2O4 (ZGO-1) and Zn2SnO4 (ZSO-9) were also prepared for comparison. The specific chemical composition of each sample is listed in Table 1. The doping content of activator Cr 3+ is 0.5 mol % versus Ga 3+ for all Ga containing samples and 0.5 mol % for the Zn2SnO4 sample. The powder samples were synthesized by a high-temperature solid-state method starting from binary oxide materials: ZnO (99.99%), Ga2O3 (99.99%), SnO2 (99.99%), and Cr2O3 (99.99%). These starting materials were weighed according to the stoichiometric ratio of the formula. The mixed powders were ground homogenously in an agate mortar, and then the mixtures were put into an alumina crucible. The alumina crucible was subsequently placed in a high temperature furnace at 1350 ℃ for 9 h in air to produce the final samples. After cooling to room temperature, the phosphors were ground to a fine powder. the peaks was also used to evaluate the reasonableness of the fitting results. The diffuse reflection spectra were measured with a Shimadzu UV-2700 UV-VIS-NIR spectrometer. A 365 nm LED (ThorLabs) was used as the excitation source for the photoluminescence spectra (PL), persistent luminescence (spectra and decays) and thermoluminescence. For the photoluminescence excitation (PLE), and persistent luminescence excitation spectra, the excitation was provided by an intense Xe plasma lamp (EQ-99X LDLS, Energetiq Inc.) coupled to a monochromator. For the persistent luminescence excitation measurements, the sample was placed in a fixed sample holder, and the afterglow spectrum was recorded 30 seconds after a 2 minute excitation. The sample was then heated at 300 °C for 5 minutes to thermally empty the traps, then the excitation wavelength was changed and the process reiterated. All the optical measurements above were recorded using a charge coupled device (CCD) camera (Roper Pixis 100) coupled to a visible 300 grooves per mm monochromator (Acton Spectra Pro, Princeton Instruments). The persistent luminescence decay comparison of all studied samples was recorded using a photon-counting device (Optima, Biospace Lab). The samples were arranged in a circle and excited simultaneously using LEDs.

3.Results and discussion

Crystal structure characterization

ZnGa2O4 has a normal spinel structure, as shown in Figure 1. Normal spinel structures usually belong to the cubic lattice system with two tetrahedral and four octahedral sites per formula unit. Even though there are about 3% antisite defects in the normal spinel lattice of ZnGa2O4, [START_REF] Allix | Considerable Improvement of Long-Persistent Luminescence in Germanium and Tin Substituted ZnGa2O4[END_REF] this situation evolves dramatically with cationic substitution. Indeed, Figure 1b shows that Zn 2+ ions occupy the tetrahedral sites and Ga 3+ ions occupy the octahedral sites, while Zn2SnO4 possesses an inverse spinel structure, where Zn 2+ ions occupy two different positions: half of these Zn 2+ ions occupy tetrahedral sites as in normal spinel structure, and the rest occupy the octahedral sites (along with the Sn 4+ ions). Both of these two materials are cubic close-packed oxides with space group Fd-3m. In the complex spinel combined by ZnGa2O4 and Zn2SnO4, the tetrahedral sites are expected to be filled by Zn 2+ ions, the octahedral sites are filled by the rest of the Zn 2+ ions and all of the Sn 4+ ions and Ga 3+

ions. It should be noted that site inversions are expected to be more abundant in this complex spinel than in the pure normal spinel ZnGa2O4 [START_REF] Allix | Considerable Improvement of Long-Persistent Luminescence in Germanium and Tin Substituted ZnGa2O4[END_REF] . The tetrahedral sites are expected to be filled by Zn 2+ ions, the octahedral sites are filled by the rest Zn 2+ ions and all the Sn 4+ ions and Ga 3+ ions.

A series of Cr 3+ doped long afterglow materials with a complex spinel (ZGSO) structure were synthesized by the systematic variation of molar ratios between

where λ is the Cu Kα X-ray wavelength (λ = 0.154178 nm), d is the distance between the two crystal planes and θ is diffraction angle. As shown in Figure 1, in the cations, and the octahedral sites are occupied by the remaining Zn 2+ cations and all of the tetravalent Sn 4+ and trivalent Ga 3+ cations. In other words, the complex spinel could be viewed as the substitution of 2Ga 3+ by a Zn 2+ -Sn 4+ cation pair. Because the sum of the ionic radii of two Ga 3+ cations (0.76 Å, CN = VI) is less than the sum of Zn 2+ (0.88 Å, CN = VI) and Sn 4+ (0.83 Å, CN = VI) [START_REF] Shannon | Effective Ionic Radii in Oxides and Fluorides[END_REF] , the cell volume of the complex spinel ZGSO and Zn2SnO4 are larger than those of ZnGa2O4. Hence, the d value increases, which results in diffraction peaks shifted to a lower angle.

Additionally, the XRD results also demonstrate that Cr 3+ has been doped into ZGSO without changing the crystal structure. Considering that the radius of Cr 3+ (0.755 Å) is close to that of Ga 3+ (0.76 Å), Cr 3+ is inclined to occupy the octahedral Ga 3+ sites. XPS studies of the complex spinel ZGSO-3 (Zn10Ga15.92SnO36:0.08Cr 3+ ) and the ZGO-1 (ZnGa2O4:Cr 3+ ) samples were carried out to confirm the coordination site occupancies of each cation. Figure 3A shows the XPS survey scan of ZGO-1 and the tetrahedral and the octahedral sites, in ZGSO-3. Since higher coordination number will result in higher binding energy, the highest binding energy shoulder should originate from Zn in the six coordinate octahedral sites [START_REF] Briggs | Handbook of X-ray Photoelectron Spectroscopy[END_REF] . The area of the peak with the higher binding energy is smaller than that of the peak with low binding energy, suggesting that the number of Zn atoms in the six coordinate octahedrons is smaller, which is consistent with our design principle. metallicity than Ga, the lower binding energy is related to the Zn-O bond and the higher binding energy is related to the Ga-O bond. [START_REF] Briggs | Handbook of X-ray Photoelectron Spectroscopy[END_REF]

Diffuse reflectance spectra and photoluminescence properties

Figure 5(a) shows the diffuse reflectance spectra of the complex spinels Zn1+xGa2-2xSnxO4:Cr 3+ , normal spinel ZnGa2O4:Cr 3+ and inverse spinel Zn2SnO4:Cr 3+ .

The spectra of all samples show two obvious absorption peaks, peaking for instance for the ZnGa2O4:Cr 3+ sample at 550 nm and 420 nm, which originate from the 4 A2( 4 F) → 4 T2( 4 F) and 4 A2( 4 F) → 4 T1( 4 F) transitions of Cr 3+ respectively. The observed

 1 13   1 3 1
shoulders at around 300 nm are due to the 4 A2( 4 F)→ 4 T1( 4 P) spin-allowed absorption peak of Cr 3+ , partially overlapping the band gap edge of ZnGa2O4. The band gap absorption edge originates from the O 2--Ga 3+ charge-transfer transition in the ZnGa2O4 host. [START_REF] Sharma | Interplay between Chromium Content and Lattice Disorder on Persistent Luminescence of ZnGa2O4:Cr 3+ for in vivo Imaging[END_REF] With the decrease of the ZnGa2O4 content, the three absorption peaks of Cr 3+ shift towards longer wavelengths, due to an increase of the crystal field splitting as the Sn content increases. The band gap absorption edge also shifts gradually towards the longer wavelength, indicating that the band gap becomes smaller when increasing the Zn2SnO4 content. In order to calculate the band gap energies and their variations for all the samples, we convert the diffuse reflectance R∞ into a Kubelka-Munk function F(R∞) as follows: [26] (2)

Then one plot (hνF(R∞)) [START_REF] Li | Long Persistent Phosphors-from Fundamentals to Applications[END_REF] with hν according to the equation proposed by Tauc: [START_REF] Tauc | Optical Properties and Electronic Structure of Amorphous Ge and Si[END_REF] (3

)
where hv is the photon energy, A represents a proportionality constant and Eg is the

    2 12 F R R R           2 g h F R A h E      
samples decrease gradually from 4.87 to 3.65 eV with increasing Zn2SnO4 content.

The measured band-gap energy of the ZnGa2O4 sample in this work is smaller than that reported for samples prepared via hydrothermal methods (5.07 eV), but larger than that reported for samples prepared by solid state methods (4.76 eV). [START_REF] Zhang | Full Color Emission in ZnGa2O4: Simultaneous Control of the Spherical Morphology, Luminescent, and Electric Properties via Hydrothermal Approach[END_REF] The latter tends to be smaller due to a Zn deficiency induced at high sintering temperatures [START_REF] Bessière | ZnGa2O4:Cr 3+ : a New Red Long-lasting Phosphor with High Brightness[END_REF] .

The value of the band gap of pure Zn2SnO4 agrees well with the one reported previously. [START_REF] Li | Long Persistent and Photo-Stimulated Luminescence in Cr 3+ -Doped Zn-Ga-Sn-O Phosphors for Deep and Reproducible Tissue Imaging[END_REF] Figure 6(a) presents the photoluminescence excitation (PLE) spectra of ZGSO, ZGO-1 and ZSO-9, monitoring their emission at 696 nm. The PLE spectra of all samples possess a strong band-to-band absorption and three excitation bands due to the 4 A2( 4 F)→ 4 T2( 4 F), 4 A2( 4 F)→ 4 T1( 4 F) and 4 A2( 4 F)→ 4 T1( 4 P) transitions of Cr 3+ , which are in agreement with the absorption bands in the diffuse reflectance spectra.

Taking the PLE spectrum of ZGSO3 as an example, it contains a strong and broad excitation band located at 272 nm, which can be attributed to the VB→CB transition of the host. The other peaks at 555 nm, 404 nm and the shoulder at 320 nm can be assigned as 4 A2( 4 F)→ 4 T2( 4 F), 4 A2( 4 F)→ 4 T1( 4 F) and 4 A2( 4 F)→ 4 T1( 4 P) transitions of Cr 3+ respectively. [START_REF] Li | Long Persistent and Photo-Stimulated Luminescence in Cr 3+ -Doped Zn-Ga-Sn-O Phosphors for Deep and Reproducible Tissue Imaging[END_REF][START_REF] Brito | Persistent Luminescence Mechanisms: Human Imagination at Work[END_REF] The VB→CB absorption feature is slightly red shifted from 274 nm to 292 nm and its intensity decreases with the increase of the inverse spinel Zn2SnO4 content. As shown in Figure 6(b) and Table 2, with the increase of the inverse spinel Zn2SnO4 content, the 4 A2( 4 F)→ 4 T2( 4 F) band shifts towards the red range (i.e. 550 nm for ZnGa2O4:Cr 3+ and 598 nm for Zn2SnO4:Cr 3+ ) with declining intensity. This is related to the decreasing crystal field strength of the solid solution as the proportion of inverse spinel increases. Hence, the energy levels of 4 T2( 4 F), 4 T1( 4 F) and 4 T1( 4 P) manifolds shift downwards, as presented in the d [START_REF] Lécuyer | Chemically Engineered Persistent Luminescence Nanoprobes for Bioimaging[END_REF] Tanabe-Sugano diagram presented Figure 7. For a more quantitative analysis, the crystal field strength Dq and the Racah parameters B can be estimated by the energy of various excitation peaks as follows : [START_REF] Chen | A Bifunctional Cr/Yb/Tm:Ca3Ga2Ge3O12 Phosphor with Near-Infrared Long-Lasting Phosphorescence and Upconversion Luminescence[END_REF] (4)

2 10 q D   (5)
where ν1 and ν2 are the energy corresponding to Cr 3+ ions [ 4 A2→ 4 T1] and [ 4 A2→ 4 T2] transitions, respectively. The obtained results are presented in Table 2 and marked in

Photoluminescence (PL):

In the previous section, we highlighted the evolution of the excited states energies (via the Tanabe-Sugano diagram) as a function of the compositional variation. In the following section, the evolution of the emission properties is presented. The normalized PL spectra are shown in Figure 8. For the ZnGa2O4:Cr 3+ (ZGO-1) reference compound, the expected Cr 3+ 2 E → 4 A2 PL spectrum is observed, and is composed of several sharp lines including the R1, R2, N1 and N2 lines, which are well reported and characteristic of chromium on the gallium octahedral site. [START_REF] Gourier | Origin of the Visible Light Induced Persistent Luminescence of Cr 3+ -Doped Zinc Gallate[END_REF][START_REF] Van Gorkom | Optical Spectra of Cr 3+ Pairs in the Spinel ZnGa2O4[END_REF] When Sn 4+ substitutes for Ga 3+ , several modifications of the PL spectra are observed.

Initially, the Cr 3+ emission lines broaden with increasing Sn 4+ content. This can be explained by the increased Cr 3+ nearest-neighbor disorder as the Sn 4+ content increases. In parallel, a large contribution appears in the deep red range between 700 nm and 900 nm and shifts towards higher wavelengths as the Sn 4+ content continues to increase. This broad band can be attributed to the Cr 3+ 4 T2 → 4 A2 emission as already reported in the literature for the zinc gallate host. [START_REF] Ueda | Ratiometric Optical Thermometry Using Deep Red Luminescence from 4 T2 and 2 E States of Cr 3+ in ZnGa2O4 Host[END_REF] Furthermore, the observed redshift is in good agreement with the crystal field evolution as determined by the excitation spectra.

Persistent luminescence:

In the previous paragraph, we demonstrated that the increase of the Sn 4+ content leads to a significant red shift of the Cr 3+ 4 T2 → 4 A2 emission. The purpose of the following part is to study what occurs to the persistent luminescence alongside the solid solution. The normalized persistent luminescence (AG-PL) spectra are presented in Figure 9 (a). As soon as Sn 4+ substitutes for Ga 3+ , the predominance of N2 increases and the R lines become barely distinguishable. In addition, the broad band contribution of the Cr 3+ 4 T2 → 4 A2 on the persistent luminescence spectra increases and shifts towards the near infrared range as the Sn 4+ content increases. However, the signal to noise ratio suggests that the persistent luminescence intensity of ZGSO-7, ZGSO-8 and ZSO-9 is lower compared to compounds with less Sn 4+ substitution. The persistent luminescence decay profiles, presented in Figure 9 (b) confirm that at some point, the increase of Sn 4+ content lowers the persistent luminescence intensity. Still, it can be observed that low Sn 4+ content compounds (ZGSO-2, ZGSO-3 and ZGSO-4) possess persistent luminescence intensities comparable and even better to the ZGO-1 reference material. Indeed, the ZGSO-2 and ZGSO-3 phosphors have higher performance and persistent luminescence intensity than ZGO-1 in the first minutes after stopping the UV excitation (for instance 55 s for ZGSO-3 and 123 s for ZGSO-2). The higher intensity and faster decay of the persistent emission of tin substituted zinc gallates suggests shallower traps compared to ZGO-1. The trap evolution in these materials will be further studied using thermoluminescence (TL).

Nevertheless this behavior should be very interesting for bioimaging applications. As demonstrated in Figure 6 (absorption and excitation spectra), both the band-to-band energy and the energies between the 4 A2 and the 4 T levels decrease with Sn 4+ content. In order to find out if the observed redshifts can be useful for charging the persistent luminescence, the persistent luminescence excitation spectra (also called AG-PLE) were recorded (see Figure 10). In this figure, the persistent luminescence excitation spectrum of the reference sample (ZGO-1) is compared to the ZGSO-4 and ZGSO-5 with intermediate dopant content. The ZGO-1 AG-PLE spectrum is composed of one intense band peaking at 320 nm and one weaker band centered around 600 nm. This is consistent with previous results obtained by Bessière et al [START_REF] Bessière | Storage of Visible Light for Long-Lasting Phosphorescence in Chromium-Doped Zinc Gallate[END_REF] in which the high energy band was associated with the charging through the bandgap with conduction band mixed with the 4 A2 → 4 T1 transition, whereas the low energy band was related to the charging through the 4 A2 → 4 T2 band triggered by a local electric field. [START_REF] Gourier | Origin of the Visible Light Induced Persistent Luminescence of Cr 3+ -Doped Zinc Gallate[END_REF] The ZGSO-4 and ZGSO-5 AG-PLE spectra are slightly different.

Although the high energy band is lower compared to the ZGO-1 material, an interesting red shift is found as the Sn 4+ content increases. This redshift is of major importance for persistent luminescence charging using blue LEDs which are less expensive and more powerful compared to UV sources. More interestingly, we observe that the low energy bands are not only shifted towards the deep red range but are also more intense when Sn 4+ is added. This is of major interest for persistent luminescence materials used for in vivo imaging. Indeed, the ZGSO-5 material will be the compound with the highest persistent luminescence intensity with deep red charging, which is an important requirement for in vivo charging and long-term bioimaging. [START_REF] Bessière | ZnGa2O4:Cr 3+ : a New Red Long-lasting Phosphor with High Brightness[END_REF] Figure 10: Persistent luminescence excitation spectra of ZGO-1, ZGSO-4 and ZGSO-5 samples.

In order to analyze the persistent luminescence decays (Figure 9) and the persistent luminescence excitation spectra (Figure 10) in more detail, a photon counting imaging camera was used to record the persistent luminescence intensity after several excitation modes. It is important to note that this system leads to an approximate maximal error of 10%. After 365 nm excitation (Figure 11 (a), (c) and (d)) it is notable that, with the exception of ZGSO-2 (in the 10 % error bar range), the persistent luminescence intensity decreases when Sn 4+ content increases. Moreover, the difference between integrated intensity after 25 min and 70 min is smaller for ZGO-1 than ZGSO-2 which corresponds to a slower persistent luminescence decay for ZGO-1. These results are in good agreement with the AG-PL and AG-PLE results previously presented. The procedure was repeated with 625 nm excitation (Figure 11 (b), (e) and (f)), an excitation wavelength with smaller energy at the edge of the first biological window where the transparency of the tissue starts to be efficient. It is found that the highest persistent luminescence intensity is obtained for a partially tin substituted compound, ZGSO-5, in good agreement with the AG-PLE measurements.

In a same way, the integrated intensity of the persistent luminescence was recorded after exposure to ambient laboratory light i.e. visible light charging (see Figure S1).

Again, the integrated intensity was found to increase from ZGO-1 to ZGSO-5 and then decreases at higher tin contents, in good agreement with the blue shift of the charging bands observed with AG-PLE results. The integrated intensity difference between 6 min and 17 min after 625 nm excitation is lower for ZGO-1 compared to ZGSO-5. This indicates that the trapping is more efficient for the ZGSO-5 tin partially substituted compound than ZGO-1 but that the trap depth should decrease with increasing tin content.

The following part of the paper is dedicated to the study of the evolution of the trap depths and trap distribution with Sn 4+ content by means of thermoluminescence. To highlight the great potential of ZGSO complex spinels for in vivo imaging, the persistent luminescence emission of three selected samples was carried out under a 7 mm thick raw pork slice (Figure 12 (a)). To demonstrate the possible in vivo activation of the persistent luminescence, the samples were excited with a 625 nm red LED through the raw pork slice. The samples were previously heated at 300 °C to ensure that no charges were trapped before charging with the red LED. After the red light charging through the raw pork slice, all the samples present persistent luminescence decays as presented on Figure 12 (b) and (c). The number of the persistent photons collected with the camera through the raw pork slice increase drastically from ZGO-1 reference spinel to ZGSO-5. Indeed, the number of photons collected for ZGSO-5 is 400 times higher compared to ZGO-1 reference material 90 s after stopping the excitation. This result is consistent with the increasing persistent luminescence charging using in the deep red range for partially tin substituted samples.

This strong increase of the collected persistent luminescence evidences the tremendous interest of the ZGSO-5 sample for possible in vivo bio-imaging.

Thermoluminescence:

The persistent luminescence decay curves of the different compounds have different slopes revealing an evolution of the persistent luminescence kinetics and an evolution of the trap depths. To study the trap positions of each compound, we performed thermoluminescence studies. From the normalized TL profiles (Figure 13 (a)), we observe that the trap depths decrease with the increase of Sn 4+ content. This is consistent with the steeper slopes of the decay profiles with higher Sn 4+ contents.

Moreover, the TL bands are broader when Sn 4+ substitutes for Ga 3+ . This can be related to the increasing number of SnGa° and ZnGa' defects. These two defects can act as electron and hole traps respectively. The TL glow curves (Figure S2) have been integrated to compare the persistent luminescence efficiency and the total trap capability (Figure 13 (b)). In order to compare the persistent luminescence efficiency, the profiles have been integrated between 298 and 313 K, which is the useful temperature range for applications. The persistent luminescence efficiency decreased all along the solid solution. To estimate the total trap capacity, the whole thermoluminescence spectra have been integrated, even in low temperature ranges (where the de-trapping occurs immediately after stopping the excitation) and at high temperature ranges (where at room temperatures the trapped charges cannot be de-trapped). Unlike the persistent luminescence efficiency, a small Sn 4+ content can improve the total charge trapping and the charging of the materials. This explains why the persistent luminescence profiles of ZGSO-2 and ZGSO-3 are higher than ZGO-1 at short times after stopping the excitation, and validates the interest in studying these compounds.

Discussion:

The optical results obtained from the materials mainly indicate the following evolutions with the tin substitution:

(i) A redshift of the main persistent luminescence excitation band;

(ii) A decrease in intensity of this main persistent luminescence excitation band;

(iii) A redshift of the persistent luminescence excitation band related to chromium bands;

(iv) An intensity increase of this persistent luminescence excitation band;

(v) A shift towards lower temperature of the thermoluminescence bands;

(vi) A broadening of the thermoluminescence bands;

(vii) An decrease intensity of the thermoluminescence signal (around RT)

In the following part we tentatively explain why these properties evolve in this way with the composition, and propose a set of schematic energy-level diagrams (as presented in Figure 14) to illustrate this interpretation.

The decrease of the band gap energy with the increase of Sn 4+ /Ga 3+ substitution can explain process (i). Indeed, a decrease of the band gap can lead to a decrease in the energy difference between the Cr 3+ ground state and the conduction band. This is observed through the shift of the main excitation band. This process is schematized in Figure 14 by the decreasing length of the dotted arrows and by the color going from violet to blue.

The crystal field strength variation, illustrated in the Tanabe-Sugano diagram, [(see Figure 7)] explains the decrease in the energy difference between the Cr 3+ 4 A2 and 4 T2 levels and the redshift of the low energy persistent excitation band [observation (iii)].

The shift towards low temperature of the TL bands (v) may be explained either by the decrease of the bandgap energy or by the decrease of the crystal field as de-trapping is assumed to occur through the band gap and the chromium excited bands. [START_REF] Gourier | Origin of the Visible Light Induced Persistent Luminescence of Cr 3+ -Doped Zinc Gallate[END_REF][START_REF] Bessière | Storage of Visible Light for Long-Lasting Phosphorescence in Chromium-Doped Zinc Gallate[END_REF] The decrease in intensity of the persistent excitation band in the UV/blue range (ii) reveals the decreases of the useful traps when persistent luminescence is required.

The lowering of the trap depths observed with TL may explain this decrease. In Figure 14, the useful and ineffective traps are presented in green and red respectively.

This decrease of the relevant traps is consistent with the decrease of the thermoluminescence signal around room temperature (vii), yet the total TL glow curve is higher for ZGSO-2 and ZGSO-4 than for ZGO-1, which indicates a higher total storage capability.

The trapping processes have been linked to the antisite defects stabilized in the local environment of Cr 3+ , [START_REF] Gourier | Origin of the Visible Light Induced Persistent Luminescence of Cr 3+ -Doped Zinc Gallate[END_REF][START_REF] De Vos | First-Principles Study of Antisite Defect Configurations in ZnGa2O4 :Cr Persistent Phosphors[END_REF] and 71 Ga NMR studies have previously shown that the antisite content first increases and then decreases with Ga 3+ /Sn 4+ substitution. [START_REF] Maldiney | The in vivo Activation of Persistent Nanophosphors for Optical Imaging of Vascularization, Tumours and Grafted Cells[END_REF] These results can explain the first increase of the total storage capability (from ZGO-1 to ZGSO-2) followed by its decrease along the solid solution.

The TL peak broadening (vi) can be linked to the defect distribution, particularly to the antisite defects, which increases with tin content.

Finally, the increasing charging efficiency through the Cr 3+ bands (iv) is observed from ZGO-1 to ZGSO-5. It could be linked to an increase of the local electric field brought by the antisite defects around Cr 3+ . The evolution of the surrounding local environment of Cr 3+ with Sn 4+ substitution for Ga 3+ is clearly observed in the EPR spectra (see Figure S3). This evolution is schematized by the yellow "lighting" arrow in Figure 14.

Conclusions

Pure spinel phases can be obtained through a solid solution approach to combine the normal and inverse spinel structures. In the complex spinel, the tetrahedral sites are filled by Zn 2+ divalent cations, and the octahedral sites are occupied by the remaining Zn 2+ cations together with all the tetravalent Sn 4+ cations and the trivalent Ga 3+ cations. Gallium substitution by tin appears as a good strategy to redshift both the large chromium excitation and emission bands, which is due to the variation in crystal field strength. The tin substitution is easily performed and makes only small modifications to the structural and crystalline properties, but has a comparatively large influence on the optical properties. While increasing the tin concentration, the trap depths slightly decrease which increases the persistent luminescence decay rate, but this is associated with a large increase of the total storage capability. Indeed with tin substitution, compounds have higher total storage capacity compared to ZnGa2O4:Cr 3+ .

Since persistent emission is redshifted into the deep red region, this could be a useful way to tune the emission in the biological window and manage diffusion problems. More interestingly, persistent luminescence excitation bands are also redshifted and strongly enhanced in the blue and orange/red ranges. Therefore, the activation of persistent luminescence toward the visible range instead of the UV range is much easier for the Zn1.33Ga1.34Sn0.33O4:Cr 3+ compared to ZnGa2O4:Cr 3+ . In addition to this redshift, the low energy charging band also appears more intense for Zn1.33Ga1.34Sn0.33O4:Cr 3+ compared to ZnGa2O4:Cr 3+ . This is of major interest for the further development of persistent luminescence materials suitable for in vivo imaging as their re-activation through the living tissues will be more efficient.

Table of content:

New complex spinel with tin substitution Zn1+xGa2-2xSnxO4:Cr 3+ was synthesized with a large increase of the total light storage capability. Both the persistent luminescence excitation and emission spectra of the optimized complex spinel samples are redshifted, which is of interests for easier deep tissues penetration and facilitates the low energy activation.

Figure 1 .

 1 Figure 1. (a) The crystal structure of the normal spinel ZnGa2O4. The blue spheres represent Zn, red spheres represent O, and yellow spheres represent Ga. (b) Polyhedral view of a complex spinel.

2 .

 2 ZnGa2O4 and Zn2SnO4 end members. These samples form a solid solution whose diffraction patterns are consistent with the standard pattern of ZnGa2O4 (PDF No.086-0413), as shown in Figure All of the samples are phase-pure, indicating that complex spinel structures can be obtained through this solid solution approach which combines the normal and inversed spinel structures. In addition, the diffraction peaks of the samples are very sharp and intense, confirming a high degree of crystallinity. As shown in Figure2, with the decrease of the ZnGa2O4 content, the diffraction peaks of ZGSO shift to a lower angle and become gradually closer to the diffraction peaks of Zn2SnO4 (PDF No.074-2184), indicating that the unit cell volumes of the samples are between that of the ZnGa2O4 and Zn2SnO4 spinels. This phenomenon can be explained with Bragg's equation,

  -2xSnxO4 :Cr 3+ , the tetrahedral sites are filled by divalent Zn 2+

Figure 2 .

 2 Figure 2. XRD patterns of complex spinel ZGSO, the standard data for ZnGa2O4 (PDF No.086-0413) and Zn2SnO4 (PDF No.074-2184).

4 PDF

 4 No.074-2184 high resolution spectra of Zn 2p, O 1s, Zn LMM and Ga 3d; Figure 3B shows the XPS survey scan of ZGSO-3. In Figure 3(a1), the binding energies of 1021.4 eV and 1044.5 eV for Zn 2p peaks can be attributed to the 2p3/2 and 2p1/2 states of Zn 2+ in tetrahedral coordination, respectively. Comparing with Figure 3(a1), the binding energies of Zn 2p in Figure 3(b1) are 1021.2 eV and 1044.3 eV, which show no obvious shift. However, the Zn 2p3/2 peak of ZGSO-3 is broader and can be fitted with two peaks (1021.2 eV and 1023.4 eV), indicating that Zn occupies two sites, i.e. the

Figure 3 (

 3 a3) and (b3) show the Auger lines of Zn in the ZGO-1 and ZGSO-3 samples.Figure 3(a2) shows the high resolution spectra of O 1s of ZGO-1, which can be fitted as three peaks. The highest binding energy originates from the adsorbed oxygen, and the other peaks correspond to the two chemical states of O. As Zn has weaker electronegativity and stronger

Figure 3 (

 3 b2) shows the high resolution O 1s spectra of ZGSO-3, which can be fitted as four peaks. In comparison with Figure 3(a2), there are additional peaks caused by Sn in the host. Due to the higher electronegativity of Sn compared to those of Ga and Zn, the highest binding energy is related to the Sn-O bond. The high resolution Ga 3d spectra, which overlap with O 2s and Sn 4d, are shown in Figures 3(a4) and (b4) respectively. The binding energy of Ga 3d in ZGSO-3 (19.5 eV) appears to be lower than that of Ga 3d in ZGO-1 (20.0 eV). This could be due to the accommodation of Sn in the octahedral sites and the higher electron cloud density for the octahedral Ga environment.

Figure 4

 4 Figure 4 shows the high resolution transmission electron microscopy data obtained from a sample of ZGSO-3. As shown in Figure 4(a), the sample exhibits clear lattice fringes, confirming the high degree of crystallinity observed by PXRD. The main d-spacings were measured as 0.295 nm and 0.191 nm, which corresponds to the (220) and (331) Miller planes respectively, as obtained by PXRD. The SAED

Figure 4 .

 4 Figure 4. (a) HRTEM images, (b) SAED image, and (c) element distribution mapping of ZGSO-3.

Figure 5 .

 5 Figure 5. (a) The diffuse reflectance spectra and (b) (hνF(R∞)) 2 -hν plots of ZGSO-X, ZGO-1 and ZSO-9. The band-gap energy for each sample was estimated from the intercept of the fitted dashed line with (hνF(R∞)) 2 = 0.

  band gap energy value. The band-gap energy values can be estimated from the intercepts of fitted straight lines with the (hνF(R∞)) 2 = 0 horizontal line in the obtained graph, as shown in Figure 5(b). It is found that the band-gap energy values of the

Figure 7

 7 Figure 7 with vertical lines.

Figure 6 .

 6 Figure 6. (a) PLE spectra of all ZGSO samples, including ZGO-1 and ZSO-9. (b) The normalized PLE spectra ranging from 480 to 680 nm for all samples.

Figure 7 .

 7 Figure 7. Tanabe-Sugano diagram of Cr 3+ with d 3 electron configuration in the complex spinel samples ZGSO-X, ZGO-1 and ZSO-9.

Figure 8 :

 8 Figure 8: (a) Normalized PL spectra of the ZGO-1, ZGSO-X and ZSO-9 samples. (b) PL emission spectra of the samples with highlighted N2 line and 4 T2 → 4 A2 emission band. For all measurements, a 365 nm LED was used as excitation source.

Figure 9 :

 9 Figure 9: (a) Normalized persistent luminescence spectra of ZGO-1, ZGSO-X and ZSO-9 samples recorded 1 min after 365 nm excitation for 5 min. (b) Persistent luminescence decays of the same samples using the same excitation conditions.

Figure 11 :

 11 Figure 11: Pictures of the samples using photon counting system (a) 25 min after UV (365 nm) excitation and (b) 6 min after 625 nm excitation. The diagrams represent the persistent luminescence intensity integrated during 3 min (c) 25 min after 365 nm, (d) 70 min after 365 nm, (e) 6 min after 625 nm and (f) 17 min after 625 nm excitation.

Figure 12 :

 12 Figure 12: (a) Picture of the raw pork slice used for the measurements. (b) Persistent luminescence decays of ZGO-1 (black triangles), ZGSO-2 (red dots) and ZGSO-5 (blue squares) recorded 90 s after 2 minutes of 625 nm excitation through the raw pork slice. (c) Pictures of the samples under the raw pork slice using the photon counting system.

Figure 13 :

 13 Figure 13: (a) Thermoluminescence glow curves of selected samples after UV excitation during 5 minutes at 14 K. (b) TL integrated intensity around RT relative to ZGO-1, representing the persistent luminescence efficiency at room temperature. Inset, total TL integrated intensity relative to ZGSO-2, representing the total storage capacity of the persistent phosphors.

Figure 14 :

 14 Figure 14: Schematic representation of the energy diagram evolution to model the evolution of the luminescence properties with the material composition. In this scheme, the trapping through the charge transfer from Cr 3+ to the conduction band is represented by dotted arrows.The decreasing energy required for this process is schematized by the decreasing size and the color shift of the arrows from violet to blue. The trapping through the chromium bands is represented by the red solid arrows and their required energies are schematized by their size and tint. The local electric field that triggers the charging through chromium bands is represented by the yellow "lighting" arrows. Its efficiency is schematized by the arrows thickness. The red part of the traps represents traps that are not involved in the persistent luminescence process (traps that are too deep or too shallow for instance) whereas the green part represents the "useful" part when bioimaging applications are envisioned.

Figure S1 :

 S1 Figure S1: (a) Picture of the samples with photon counting 5 min after ambient lab light exposition (b) the diagram represent the persistent luminescence intensity integrated during 3 min 5 min after ambient lab light exposition.

Figure S2 :

 S2 Figure S2: Thermoluminescence glow curves of selected samples recorded after UV excitation during 5 minutes at 14 K.

Table 1 .

 1 Chemical compositions of complex spinels with different ratios of ZnGa2O4 and

	Zn2SnO4.
	Samples	ZnGa2O4 :Zn2SnO4	Zn1+xGa2-2xSnxO4 :Cr 3+
	ZGO-1	1:0	x = 0
	ZGSO-2	10:1	x = 0.09
	ZGSO-3	8:1	x = 0.11
	ZGSO-4	6:1	x = 0.14
	ZGSO-5	2:1	x = 0.33
	ZGSO-6	1:1	x = 0.5

  Zn LMM peaks and two Sn 3d peaks, with Sn 3d3/2 at high binding energy (494.5 eV) and Sn 3d5/2 at low binding energy (486.0 eV).

	of ZGSO-3.
		Intensity (cps)	(A)	Ga 2p 3/2 Ga 2p 1/2		Zn 2p 1/2 Zn 2p 3/2		O 1S		Zn lmm	Ga 3d
		1400		1200		1000	800 Binding Energy (eV) 600	400	200	0
			(a1)					Zn 2p	(a2)	[GaO]		O 1S
		Intensity (cps)			Zn 2p 1/2	Zn 2p 3/2			Intensity (cps)				[ZnO]
					23.1	1021.4
					1040 Binding Energy (eV) 1030	1020		534	532 Binding Energy (eV) 530	528	526
			(a3)					Zn LMM	(a4)			Ga 3d
		Intensity (cps)		Zn LMM					Intensity (cps)		O 2s	20.0	Ga 3d
			995	990	985	980	975	970		26	24	22	20	18	16	14
					Binding Energy(eV)					Binding Energy (eV)
	Intensity (cps)	Intensity (cps)	(B)		Ga 2p 1/2	Zn 2p Ga 2p 3/2 1/2 Zn 2p 3/2		O 1S	Sn 3d 3/2 Sn 3d 5/2	Ga 3d
		1400		1200		1000	800 Binding Energy (eV) 600		400	200	0
			(b1)				Zn 2p	(b2)	[GaO]	O 1s
		Intensity (cps)			[ZnO6]	[ZnO4]	Intensity (cps)	[SnO]		[ZnO]
						23.1	1021.2
			1045 1040 1035 1030 1025 1020 1015	536	534	532	530	528	526
					Binding Energy (eV)					Binding Energy (eV)
			(b3)	Zn LMM			Sn 3d	(b4)			Ga 3d
		Intensity (cps)			Sn 3d 3/2	Sn 3d 5/2	Intensity (cps)	Sn 4d		O 2S	19.5	Ga 3d
						8.5	486.0
			500	495	490	485	480	28	26	24	22	20	18	16
					Binding Energy (eV)					Binding Energy (eV)

Figure 3(b3) shows the high resolution Sn 3d and Zn Auger spectra, which can be fitted by

Figure 3. (A) XPS survey scan and high-resolution Zn 2p, O 1s, Zn LMM and Ga 3d XPS spectra of ZnGa2O4, (B) XPS survey scan and high-resolution Zn 2p, O 1s, Ga 3d and Sn 3d XPS spectra

Table 2 .

 2 Peak position of PLE and estimated crystal field parameters of Cr 3+ in the complex spinel

	samples ZGSO, ZGO-1 and ZSO-9.
		4 A2→ 4 T1 [nm] 4 A2→ 4 T2 [nm]	Dq [cm -1 ]	B [cm -1 ]	Dq/B
	ZGO-1	403	550	1818	645	2.818
	ZGSO-2	404	553	1808	651	2.778
	ZGSO-3	405	557	1795	661	2.717
	ZGSO-4	406	558	1792	657	2.726
	ZGSO-5	410	568	1761	670	2.626
	ZGSO-6	412	575	1739	686	2.537
	ZGSO-7	417	580	1724	669	2.577
	ZGSO-8	421	589	1698	677	2.508
	ZSO-9	425	598	1672	685	2.442

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Project No. 10804099, 21804119), Key projects of Zhejiang Natural Science Foundation (Project No. LZ18B050002).

Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff)) Published online: ((will be filled in by the editorial staff))

In the above figure the effect of the Cr 3+ surrounding by Sn 4+ substitution for Ga 3+ is clearly observable.


Pierre Vialar

Pascal Merzeau

Suzanne Giasson
email: suzanne.giasson@umontreal.ca

Carlos Drummond
email: drummond@crpp-bordeaux.cnrs.fr

Compliant Surfaces under Shear: Elastohydrodynamic Lift Force

In this work we have investigated the behavior under shear and compression of mica surfaces coated with poly (N-isopropylacrylamide) cationic microgels. We have observed the emergence of velocity dependent, shear-induced normal forces, which can be large enough to entrain a fluid film that separates the surfaces out of contact, driving the dynamic system from conditions of boundary to hydrodynamic lubrication. By implementing a feedback-loop control on the surface separation, we were able to quantify the magnitude of the lift force as a function of the surface separation and driving speed. Our results illustrate how elastohydrodynamic effects can play an important role in the lubrication of compliant surfaces, providing pathways for control of friction and wear.

INTRODUCTION

Surface Forces govern the outcome of a significant number of physical processes; colloidal stability, adhesion, wettability, boundary lubrication or capillarity can all be better described if the different surface forces involved are correctly taken into account. Modern experimental studies of interaction between solids dates back to the 1920s, when Tomlinson investigated the interaction between orthogonal metal filaments. [START_REF] Tomlinson | Molecular Cohesion[END_REF] Later, efforts headed by Overbeek and Derjaguin led to the development of reliable techniques for measuring the distance-dependent force between surfaces of quartz or glass. [START_REF] Overbeek | London-van Der Waals Attraction between Macroscopic Objects[END_REF][START_REF] Rabinovich | Direct Measurements of Long-Range Surface Forces in Gas and Liquid Media[END_REF] These earlier technical developments were constrained by the difficulty of manufacturing sufficiently smooth and clean substrates, a significant problem at small surface separations. As a solution to this problem, the use of mica as a substrate for surface force experiments was suggested by Bailey and Courtney-Pratt. [START_REF] Bailey | The Area of Real Contact and the Shear Strength of Monomolecular Layers of a Boundary Lubricant[END_REF] Mica can be cleaved to produce macroscopic, molecularly smooth surfaces, ideal for measuring surface forces at small separations and evaluating theoretical developments. Based on the use of this substrate, a remarkable body of work was accomplished, leading to the development of the Surface Forces Apparatus, SFA, by Tabor, Winterton and Israelachvili. [START_REF] Bailey | The Area of Real Contact and the Shear Strength of Monomolecular Layers of a Boundary Lubricant[END_REF][START_REF] Israelachvili | The Measurement of Van Der Waals Dispersion Forces in the Range 1.5 to 130 Nm[END_REF] The technique was later developed to allow measurement in different liquid and gaseous environments. [START_REF] Israelachvili | Measurement of Forces between Two Mica Surfaces in Aqueous Electrolyte Solutions in the Range 0-100 Nm[END_REF] It was initially proposed to use multiple beam interferometry (MBI) to determine the actual separation between the surfaces D with subnanometric resolution. Israelachvili developed simple analytical expressions to calculate the thickness and refractive index of a film confined between mica surfaces. [START_REF] Israelachvili | Thin Film Studies Using Multiple-Beam Interferometry[END_REF] This information is central for the quantitative description of surface forces, placing the SFA at the leading-edge in techniques of surface force measurement.

Different strategies have been developed for measuring normal interaction forces in the SFA. In the quasi-static approach originally used by Israelachvili and coworkers, one of the surfaces is attached to a loading spring (KN, Fig. 1). When the system is at mechanical equilibrium, surface forces (if present) are balanced by the elastic force of the spring. To measure the static force of interaction between the surfaces, FN, the separation between the other surface and the distal spring end (T, in Fig. 1) is changed in steps. After this movement, any difference between the variation of T and the change in surface separation determined by MBI, D, signals a deflection of the normal spring, from which the change in the normal interaction force can be readily calculated if KN is known. This procedure might be limited by mechanical instabilities if the absolute value of the variation of the force with separation, dFN/dD, is larger than KN. Derjaguin and co-workers proposed the use of a feedback technique, applying and additional force (e.g. magnetic) to maintain the spring undeflected at all times [START_REF] Rabinovich | Direct Measurements of Long-Range Surface Forces in Gas and Liquid Media[END_REF] eliminating the mechanical instability. Several implementations of this idea have been reported. [START_REF] Tonck | Measurements of Intermolecular Forces and the Rheology of Dodecane between Alumina Surfaces[END_REF][START_REF] Stewart | Force Feedback Surface Force Apparatus: Principles of Operation[END_REF][START_REF] Parker | Force Feedback Measurements of Surface Forces[END_REF] Static surface forces have been rationalized in terms of different contributions (e.g. electrostatic, dispersive, hydrophobic or steric). But equilibrium forces are only one aspect of the interactions governing the properties of many systems of interest. Under out-of-equilibrium conditions, or in presence of changing conditions, the scenario may be more involved. For instance, considerable efforts have been carried out to study of the interaction between contacting surfaces in relative motion (tribology). In a typical nanotribology experiment with the SFA, the surfaces are brought to a certain separation D. Then, a lateral displacement between the surfaces is imposed at a given velocity V, and the tangential force induced by this displacement is measured. In these dynamic studies the response of the system to a changing environment can influence the boundaries (e.g., the value of D or the shape of the surfaces) in ways that may depend on the specifics of the experimental setup. These changes complicate the process of separating intrinsic aspects of the system under study from the measuring device, and make it more difficult to compare results from different laboratories using different techniques or experimental setups. In addition, theoretical developments are often built considering unchanging contact geometry, or assuming that the surface separation remains unaffected sufficiently far from the contact zone, effectively assuming that the surfaces are fixed in an infinitely stiff housing. This may facilitate the task of modelling, but is often not accurately reproduced in practical circumstances. For instance, in many biotribological problems the rubbing surfaces are attached to compliant or deformable supports, with multiple degrees of freedom. In the case of force measuring devices, a spring of finite calibrated stiffness is commonly used to apply the external load L, by balancing the elastic spring force with the surface forces. If there is a temporal evolution of these forces, the spring deflection (and the relative position of the surfaces) will change accordingly.

The SFA allows a direct determination of the geometry of the contact in real-time based on MBI. Few decades ago, it was a demanding and time consuming task to obtain accurate measurements. Nowadays, fast and sensitive cameras, computers, and fast algorithms allow precise determination of the geometry in real time. The fast determination of the contact geometry, unique to the SFA technique, together with faster an accurate piezoelectric-based nano-positioners, makes it possible to compensate some of the changes that may appear in dynamic experiments. Thus, instead of working at constant applied load (or pressure), the applied load can be continuously changed in response to possible changes in surface separation, allowing to operate the system at constant separation between the surfaces, with sub-nanometric resolution. This method may improve our understanding of the dynamic response of interacting surfaces under changing conditions, like applied shear or external fields (e.g. electric or magnetic field).

To illustrate the potential of this method, in this work we studied the response of a compliant microgel-based coating under compression and shear, to investigate the coupling between normal and tangential motion and forces. Understanding of the tribology of compliant surfaces may be crucial in a number of different circumstances, from engineering (e.g. rubber seals or tires performance in wet roads) to many aspects of biotribology (e.g. ocular tribology or mammalian joints). The impact of surface compliance in surface forces can be recognized at two different levels. Under static or quasi-static conditions, surface deformation induced by surface forces increases with surface compliance, with important consequences in the way these forces are measured and analyzed. [START_REF] Hughes | Implications of Elastic Deformation on the Direct Measurement of Surface Forces[END_REF][START_REF] Parker | Deformation of Surfaces Due to Surface Forces[END_REF][START_REF] Attard | Deformation and Adhesion of Elastic Bodies in Contact[END_REF][START_REF] Barthel | Surface Deformation, Spring Stiffness and the Measurement of Solvation Forces[END_REF] It has been recently reported how the surface deformation generated by a long range repulsive force may hinder the minimum approach between interacting surfaces, limiting the growth of tangential forces. [START_REF] Vialar | Interaction between Compliant Surfaces: How Soft Surfaces Can Reduce Friction[END_REF] Surface compliance may also have significant effects in dynamic studies; hydrodynamic forces originated by the relative motion of the surfaces may generate significant surface deformation, changing the boundary conditions of the problem. Thus, understanding the behavior of the system requires solving the coupled hydrodynamic and elasticity problems, taking into account the general force balance of the global system. This last factor requires considering the effect of the stiffness of the measuring/loading springs.

Important effects of surface compliance on dynamic surface forces studies has been documented. For the case of approaching surfaces (narrowing gaps), Leroy and coworkers showed how surface deformation engendered by the dynamic fluid pressure -a consequence of squeeze flow between moving surfaces-must be considered in the analysis of hydrodynamic interactions, even for very small deformations. [START_REF] Leroy | Hydrodynamic Interactions for the Measurement of Thin Film Elastic Properties[END_REF][START_REF] Leroy | Hydrodynamic Interaction between a Spherical Particle and an Elastic Surface: A Gentle Probe for Soft Thin Films[END_REF] Wang and coworkers investigated how elastohydrodynamic deformation may prevent the contact of approaching compliant surfaces, and discussed the influence of the viscoelastic properties of the walls on the system behavior. [START_REF] Wang | Out-of-Contact Elastohydrodynamic Deformation Due to Lubrication Forces[END_REF] A study of the influence of substrate elastic deformation on hydrodynamic and pull-off forces was recently reported by Kaveh and coworkers. [START_REF] Kaveh | Hydrodynamic Force between a Sphere and a Soft, Elastic Surface[END_REF] Elastohydrodynamic effects in laterally moving surfaces have been widely investigated; a historical account of elastohydrodynamic lubrication (EHL) studies was reported by Dowson. [START_REF] Dowson | Elastohydrodynamic and Micro-Elastohydrodynamic Lubrication[END_REF] Different regimes of behavior in EHL can be identified, which depend on the geometry and the viscoelastic properties of both the lubricant and the confining surfaces. [START_REF] Johnson | Regimes of Elastohydrodynamic Lubrication[END_REF] Earlier studies investigated non-conformal contact between stiff surfaces. In this condition large pressures can be readily achieved in common operational conditions, often generating an important increase in lubricant viscosity (piezoviscous effect) and hydrodynamic forces. These forces can produce significant elastic deformation of the surfaces hindering surface contact, reducing friction and wear. The daunting multiphysics problem involving the coupling between hydrodynamic and elasticity was addressed by different groups, combining theoretical and numerical methods. [START_REF] Dowson | Elastohydrodynamic and Micro-Elastohydrodynamic Lubrication[END_REF] Significantly, a number of correlations involving viscoelastic properties of lubricant (viscosity) and confining surfaces (elastic modulus), and operational conditions, were proposed to successfully describe the behavior of the lubricant film thickness in EHL. Interestingly, in this regime the behavior of the system is much more sensitive to the piezoviscous properties of the lubricant than to the elastic properties of the walls.

The behavior of the system is substantially modified for the case of very compliant surfaces. In this scenario (soft EHL), surfaces can be severely deformed under load and large pressures are out of reach, so the lubricant viscosity remains constant; thus, correlations found for hard EHL do not apply. A number of theoretical studies of soft EHL have been reported. A perturbative approach to describe the limiting case of small surface deformations for different geometrical configurations was developed by Sekimoto and Leibler, [START_REF] Sekimoto | A Mechanism for Shear Thickening of Polymer-Bearing Surfaces: Elasto-Hydrodynamic Coupling[END_REF] Skotheim and Mahadevan, 23,[START_REF] Skotheim | Soft Lubrication: The Elastohydrodynamics of Nonconforming and Conforming Contacts[END_REF] and others. 25,[START_REF] Urzay | The Elastohydrodynamic Force on a Sphere near a Soft Wall[END_REF] Pandey and coworkers 25 discussed the possible influence of the viscoelastic properties of the solid on soft EHL. Snoeijer and coworkers investigate the limit of large loads in soft EHL. [START_REF] Snoeijer | Similarity Theory of Lubricated Hertzian Contacts[END_REF] The influence of EH effects on the motion of particles nearby deformable wall has also been discussed. [START_REF] Salez | Elastohydrodynamics of a Sliding, Spinning and Sedimenting Cylinder near a Soft Wall[END_REF][START_REF] Saintyves | Self-Sustained Lift and Low Friction via Soft Lubrication[END_REF] Most of these studies have aimed to develop strategies to solve the combined hydrodynamic and elasticity problems, obtaining solutions for the resulting contact geometry and the magnitude of the shearinduced normal ('lift') force, due to the coupling between normal and tangential motions. On the experimental side most efforts in soft-EHL have been conducted to characterize the lubricant film thickness and the geometry of the contact in dynamic conditions. On the contrary, a small number of studies have investigated elastohydrodynamic EH lift effects. Saintyves and coworkers studied the motion of small cylinders along a soft inclined wall; [START_REF] Saintyves | Self-Sustained Lift and Low Friction via Soft Lubrication[END_REF] Davies and coworkers studied moving microbeads close to compliant walls. [START_REF] Davies | Elastohydrodynamic Lift at a Soft Wall[END_REF] In both cases, the significant effect of EH lift force on the motion was evidenced. Even more scarce are studies of EH lift on loaded contacts. Sekimoto and Leibler [START_REF] Sekimoto | A Mechanism for Shear Thickening of Polymer-Bearing Surfaces: Elasto-Hydrodynamic Coupling[END_REF] suggested that the normal force increase observed by Klein and coworkers 32 in a study of confined polymer brushes under shear can in fact be interpreted in terms of EH coupling. Indications of EH lift force in surfaces lubricated by compliant polyelectrolyte coatings were also reported by Bouchet et al. [START_REF] Bouchet | Experimental Study and Modeling of Boundary Lubricant Polyelectrolyte Films[END_REF] We report here the results of an experimental study of the lubrication behavior of mica surfaces coated with dense layers of thermoresponsive cationic microgels. The main novelty of the work was to explore the emergence of shear-induced lift forces under conditions of controlled surface separation (instead of constant applied load), providing a more accurate procedure to quantify these forces.

EXPERIMENTAL SECTION

Materials

N-Isopropylacrylamide (NIPAM), N,NMethylenebisacrylamide (MBA), aminoethyl methacrylate hydrochloride (AEMH) and 2,2′-Azobis(2-methylpropionamidine) dihydrochloride (V50) were obtained from Sigma Aldrich, and used as received.

Microgel preparation

Microgels were synthesized by batch radical polymerization following the protocol described previously [START_REF] López-León | Cationic and Anionic Poly( N -Isopropylacrylamide) Based Submicron Gel Particles: Electrokinetic Properties and Colloidal Stability[END_REF] . For the data reported in this work, the monomers NIPAM, MBA (crosslinking agent) and AEMH (aminated monomer which provides charged sites to electrostatically stabilize the microgels in water) were diluted in Milli-Q grade water (Millipore) in mass proportion 90.3/5/2.5 (1g NIPAM/50 ml). The solution was heated at 75 C and deoxygenated under nitrogen for 1 hour. In parallel, the initiator V50 was diluted in water (1g/100 ml), heated at 70 C and deoxygenated for 10 minutes. After dissolution, the initiator solution was added to the monomer solution (2.1 gr V50/90.3 gr NIPAM), and the reaction was pursued at 75 C under continuous nitrogen flow for 4 hours. Then, the microgel dispersion was cooled down to room temperature and purified by dialysis against deionized water during 3 days, replacing the aqueous bath three times each day. Following this procedure, microgel particles of 96 nm hydrodynamic radius at 25C (in 1mM NaNO3) were obtained. The mean hydrodynamic radius decreased to 81nm at 35 C and 69 nm at 40 C, as determined by dynamic light scattering (Malvern Zetasizer), evidencing the thermoresponsive character of the pNIPAM-based microgel. At room temperature, pNIPAM microgels are largely swollen with water; water volume fractions in hydrated microgel particles can exceed 0.9. [START_REF] Yang | Concentration Dependent Phase Behavior and Collapse Dynamics of PNIPAM Microgel by Dielectric Relaxation[END_REF] Microgel coating. The copolymerization of a fraction of cationic monomers (AEMH) in the microgels triggers electrostatically driven adsorption of the microgel on the negatively charged mica surfaces. [START_REF] Pérez-Fuentes | Anions Make the Difference: Insights from the Interaction of Big Cations and Anions with Poly(N-Isopropylacrylamide) Chains and Microgels[END_REF] Microgel adsorption was carried out during two weeks at 25 C, after an initial stage of 2 days at 35C, in order to maximize the adsorption density microgels and the resistance of the protective coating to compression and shear. After adsorption, the microgel solution was replaced in the SFA with a 1mM NaNO3 solution, to minimize electrostatic repulsion between the irreversibly adsorbed microgels. A typical AFM micrograph of the microgel-coated mica (measured ex-situ, in dry air, after the SFA experiments) is presented in the inset of the Figure 2. As can be observed in this image, a large density of physisorbed particles was present on the surfaces. We have quantified a mean value of 26 particles/µm 2 , which corresponds to a surface coverage of ca. 75% for the swollen particles (T=25 C), signaling the high density achieved in the long microgel adsorption times implemented in this work.

Surface Forces Apparatus

We investigated the normal and friction forces between mica surfaces coated by poly (Nisopropylacrylamide) pNIPAM-based cationic microgel by using a Surface Forces Apparatus (SFA) modified for nanotribological studies. This technique [START_REF] Israelachvili | Recent Advances in the Surface Forces Apparatus (SFA) Technique[END_REF] is commonly used to measure the interaction between mica surfaces glued on silica lenses in crossed-cylinder configuration, which is equivalent to sphere-on-a-plate if the surface separation D is much smaller than the radii of curvature of the surfaces, R. The zero separation (D=0) reported in this work is determined from the thickness of the mica surfaces measured in adhesive contact in air, and corresponds to micamica contact.

Normal forces were measured from the deflection of a double cantilever springs attached to the surfaces. The static normal interaction FN was determined by displacing the position of the spring attached to the lower surface using a nanopositioner (P-753.2CD, Physik Instruments), and measuring the actual variation in the separation between the surfaces by MBI, as described above. The difference between both quantities indicates a variation in spring deflection, used to calculate FN. We have implemented the method described by Heuberger and coworkers for fast D calculation. [START_REF] Heuberger | The Extended Surface Forces Apparatus. Part I. Fast Spectral Correlation Interferometry[END_REF] To measure the dynamic normal (lift) force, constant speed, V, cyclic (back-andforth) lateral motion between the surfaces was imposed by using voltage-driven bimorph strips attached to the lower surface. [START_REF] Luengo | Thin Film Rheology and Tribology of Confined Polymer Melts: Contrasts with Bulk Properties[END_REF] For the measurements carried out at constant gap thickness, we have incorporated a feedback control loop based on the measured mica-mica separation at the point of closest approach (PCA) determined in static conditions. As the microgels are highly hydrated [START_REF] Yang | Concentration Dependent Phase Behavior and Collapse Dynamics of PNIPAM Microgel by Dielectric Relaxation[END_REF] there is a very small refractive index contrast with the aqueous environment. Thus, the MBI technique doesn't allow us to determine if spatial changes in coating thickness are occurring within the contact region as a consequence of a possible variation in the degree of swelling of the confined microgels. Due to variable microgel deformation in the contact (due to non-uniform pressure) the PCA in static conditions may not coincide with the closest approach between the coating layers under shear.

RESULTS AND DISCUSSION

Normal forces. Equilibrium interactions

Typical equilibrium (quasi-static) normal interaction force profiles between mica surfaces coated with physisorbed microgel immersed in 1mM NaNO3 bath are presented in Figure 2. As described before, the reported distance is referred to the mica-mica contact measured in dry air; the mica surfaces were kept inside the SFA in an aqueous environment at all times, during and after microgel adsorption. The force profiles were measured slowly approaching the surfaces towards each other, in steps of the position T of 5 nm. The surfaces were kept at rest 20 seconds between two experimental points, to assure the data were obtained at equilibrium. A long-range, repulsive interaction exponentially decreasing with the distance between the surfaces was observed, due to the steric interaction between the adsorbed particles. As expected, the range of the interaction is strongly dependent on microgel swelling, determined by the temperature. Thus, while at T=25 C the onset of repulsive interaction was observed with the mica surfaces about 400 nm apart, it was reduced to about 250 nm at T=35 C. The distance at the onset of repulsion, Donset, can be related to the temperature-dependent effective thickness of the microgel coating by Hs = Donset/2. Nevertheless, it is important to keep in mind that there is a certain degree of polydispersity in the microgels, which are porous, hydrated objects adsorbed as independent entities. In this sense, there is a large degree of uncertainty on the definition of Hs.

The system under study is a multilayer system, with layers (glue, mica and microgel) of different elastic properties. By increasing the applied pressure (increasing the normal load L), the different layers will deform; the compliant microgels will be compressed and shrunk between the mica surfaces; as the contact is non-conformal, this deformation will be a function of the position in the contact region. Likewise, the glue under the mica will deform under pressure, which is also spatially variant, from a maximum value at the point of closest approach to ambient pressure outside of the contact region. The long-range repulsive force due to the compression of the microgel coating must be taken into account to describe the contact mechanics of the system, and to correctly interpret the surface force measurements. [START_REF] Hughes | Implications of Elastic Deformation on the Direct Measurement of Surface Forces[END_REF][START_REF] Parker | Deformation of Surfaces Due to Surface Forces[END_REF][START_REF] Attard | Deformation and Adhesion of Elastic Bodies in Contact[END_REF][START_REF] Barthel | Surface Deformation, Spring Stiffness and the Measurement of Solvation Forces[END_REF] It has been recently described how this long range repulsive force, together with the mechanics of the contact, may have important consequences on the behavior of this system under compression and shear. [START_REF] Vialar | Interaction between Compliant Surfaces: How Soft Surfaces Can Reduce Friction[END_REF]

Normal forces: draining

The normal interaction force profiles presented in Figure 2 were measured in quasi-static conditions, allowing the surfaces and microgel coating to reach equilibrium steady-state for each experimental point. The scenario in dynamic (out-of-equilibrium) conditions can be substantially different. In particular, some transient opposition to the surface motion appears due to the viscous resistance to fluid flow perpendicular to the applied pressure during draining, as water must flow out of the compressed microgels (microgel are porous and hydrated in the absence of stress). This flow, which involves transport of water molecules over tens of nanometers, depends on the size of the system. A poroelastic time can be defined, characterizing the migration time of water molecules across the contact region. This poroelastic time depends on the contact size and can be as long as few hours for sizes of the order of few centimeters, as extensively discussed by several groups. [START_REF] Kalcioglu | From Macro-to Microscale Poroelastic Characterization of Polymeric Hydrogels via Indentation[END_REF][START_REF] Delavoipière | Friction of Poroelastic Contacts with Thin Hydrogel Films[END_REF] To evaluate the typical poroelastic time of our system, we have studied the response of the system to large T displacements (ca. 1 µm) at different velocities. Typical results are presented in Figure 3. At slow speeds and large separations the surfaces approached at the same rate as the imposed normal velocity; closer in, the approach slows down due to the emergence of the steric interaction force. Nevertheless, the deviation from linearity maps the contribution of the static interaction force, indicating that the repulsive hydrodynamic interaction is not significant. For the fastest change of T investigated (1.3 µm/s), D is quickly reduced, reaching separations below 130 nm (the thinnest film investigated in dynamic conditions below) in less than 1 sec, and the steady-state separation in few seconds. These results evidence a small viscous resistance to the imposed displacement, even in the cases of strong microgel compression, suggesting that the characteristic poroelastic time is shorter than 1 s (the temporal resolution of our experimental setup) for D>130 nm. This short time is due in part to the small size of the contact investigated (few tens of microns) but mainly to the rapid response of the microgels, due to its submicrometric size. The fast swellingshrinking time of pNIPAM-based microgels have been discussed before. [START_REF] Keidel | Time-Resolved Structural Evolution during the Collapse of Responsive Hydrogels: The Microgel-to-Particle Transition[END_REF]

Tangential motion

The lateral relative motion of the surfaces breaks the radial symmetry of the problem and pushes the system to out-of-equilibrium conditions. The possibility of continuous, real-time monitoring of the contact geometry allows to achieve a better understanding of the dynamical system. We investigated the behavior under shear of the microgel-coated mica in two different settings. First, an initial external normal load L was imposed using the loading spring, and then the position T remained unchanged. In a second set of experiments, the response of the system to the applied shear was investigated under constant mica-mica separation by implementing the feedback control loop described above, changing the position of T to regulate the applied normal force. The results reported in this communication are related to the coupling between normal and lateral motion (shear-induced lift force), seemingly due to elastohydrodynamic effects.

From our experimental setup, we can not explore the detailed behavior of the microgel particles under shear. In particular, we are not able to determine if sliding or rolling motion of the particles is occurring inside the contact region. However, no evidence of shear-induced wear or irreversible changes was detected in any of the contacts investigated. Thus, no noticeable changes were observed in the normal interaction force profiles measured before and after shear.

Shear-induced lift force: constant position of distal spring end, T

Typical results for the shear-induced variation of the separation of the point of closest approach between the surfaces at different values of V are presented in Figure 4. In general, a strong Vdependent variation of the PCA was observed at all surface separations below ca. 300 nm, further appart than the supposed contact between the microgel layers in the static approach. This dilation, which is necessarily accompanied by the compression of the loading spring, was more significant at higher temperatures. Thus, as the hydrodynamic size (and hydration degree) of the microgels decreased (T=35 C), the shear-induced lift force, Flift, increased. This important point will be addressed below. The position of T remains unchanged during the surface displacement; thus, the variation in separation (D) implies further deflection of the normal spring, i.e., a change in Fspring (which in static conditions is identified as the normal load, L). In static conditions, a non-zero elastic Fspring is balanced by steric contact forces. On the contrary, when D increases upon surface motion, fluid is entrained between the moving surfaces; the steady-state Fspring is balanced by elastohydrodynamic forces if a fluid film is present between the surfaces. This is the case at large separations, when the microgels are out of contact; but even at conditions of static contact between the microgels (non-zero static load L), the fact that under dynamic conditions Fspring increases significantly, strongly suggests that a fluid film is being developed between the surfaces due to hydrodynamic effects. Under this scenario, the system transits from boundary to hydrodynamic lubrication. In the conditions of low Reynolds number investigated in this work, Stokes equation applies. It has often been discussed that as a consequence of the reversibility of Stokes flow, no hydrodynamic normal force can be generated in the symmetric geometry investigated in this work (sphere-on-a-plate contact). [START_REF] Skotheim | Soft Lubrication: The Elastohydrodynamics of Nonconforming and Conforming Contacts[END_REF][START_REF] Sekimoto | A Mechanism for Shear Thickening of Polymer-Bearing Surfaces: Elasto-Hydrodynamic Coupling[END_REF][START_REF] Hooke | Elastohydrodynamic Lubrication of Soft, Highly Deformed Contacts[END_REF] This scenario changes when elastic deformation of the walls breaks the symmetry of the contact: growing deformation of the boundaries engenders a greater asymmetry of the pressure distribution in the contact region, leading to a non-null lift force between the rubbing surfaces.

We can use the value of D to obtain an estimation of Flift, which is a continuously increasing function of V. However, several factors must be taken into account. First, the microgel coating changes during an experiment due the changing degree of confinement. This variation will modify the extent of swelling and in consequence the elastic properties of the coating. Second, the varying mica-mica separation will make it difficult to precisely define the applied shear rate. Third, as the normal spring deflection is changing during the experiment, both the applied load and D vary. In addition, as Flift is a function of the experimental conditions (V and D), D will be a function of the stiffness of the experimental setup (i.e., the spring constant of the apparatus). All these factors will complicate the modelling and theoretical description of the system under study, and the comparison between results of different laboratories.

Shear-induced lift force: constant separation D

For the reasons mentioned above, we have implemented a feed-back system to allow a precise control of the distance D between the mica surfaces, by varying the position T. Using MBI as described above, the distance between the mica surfaces (at the PCA) can be controlled with an accuracy of 0.1 nm. As D remains unchanged, T can be directly used to calculate the velocitydependent Flift in controlled conditions of D and nominal shear rate (V/D).

Typical experimental traces are presented in Figure 5. The applied velocity was abruptly changed at regular intervals, as indicated. As described before, each time V was augmented the separation between the surfaces raised. However, by applying the adequate correction to the position T, the separation between the mica surfaces at steady-state was kept at a fixed value. After D reaches the set-point, T can be translated in a changing spring deflection, allowing to readily quantify the velocity-dependent lift force under better controlled conditions than in the preceding case. Due to the limited range of lateral displacement of our setup, a reciprocating motion was applied during the experiments. However, by testing different combinations of shear amplitude and frequency, it was established that the driving speed V is the main variable determining the shear-induced Flift.

As it is necessary to increase Fspring to maintain a constant gap, the average pressure inside the contact increases under shear, which compresses further the microgel coating (compared with the initial static condition). The compression of the microgel coating at constant D strongly suggests the emergence of a lubricant fluid film between the surfaces at sufficiently large V. Thus, while in static conditions Fspring is balanced by surface forces, under motion the enhanced Fspring is balanced by repulsive forces of hydrodynamic origin: if full fluid film conditions are assumed, the entire load is carried by it and Fspring is equivalent to Flift, an integration of the liquid film pressure in the contact area.

It is apparent that this method allows a clearer description of the system under study. However, one point of warning is in order. The lift force measured is a macroscopic value that integrates the contribution of the whole contact area. However, as mentioned before, the shear-induced pressure is a function of the position in the contact. Thus, it produces a deformation of the microgel coating, which is a function of the position in the contact region. Even though we are imposing the closest separation between the mica surfaces, the distance between the microgel coatings is not constant, due to the position-dependent microgel deformation. In other words, we are able to control the separation between the mica surfaces; not the separation between the deformable microgel coating layers.

Typical results for the shear-induced variation in Fspring (calculated as T.KN) as function of the surface velocity V for different inter-surface distances are presented in Figure 6. As can be observed in the figure, the measured lift force increases significantly with driving speed (nearly proportional to the square of V), and decreases with the gap between the surfaces. From our definition of coating thickness based in the normal interaction force profile, HS, the microgel coatings are in static contact for separations smaller than 250 nm. However, to maintain a constant gap while shearing, Fspring (and the mean gap pressure) must be augmented, which reduces the effective microgel thickness, as illustrated by the schema in the inset of Fig. 6. We can not measure directly the thickness of the microgel coating by MBI because it is highly hydrated, with little contrast of refractive index with the aqueous environment. A crude estimate of the dynamic microgel film thickness Hlk can be obtained from the static force profile (Fig. 2), making Hlk equal to half of the separation expected for an applied normal force corresponding the dynamic Fspring. Under this assumption the thickness of the fluid film developed under shear, h0, can be approximated as h0= D-2.Hlk.

The evolution of the measured forces with the mica-mica distance is presented in Figure 7. In Fig. 7a we compare the static normal force with the dynamic variation of Fspring at the fastest V investigated (V=9.6 µm/s). As can be observed in the Figure, the shear-induced variation in Fspring (Fspring) is larger than the static interaction force for large gaps, but this difference is reduced at shorter separations. However, Fspring can not be directly equated to the dynamic lift force: as mentioned before, if a fluid film is completely developed between the surfaces, the repulsive steric force will not be present. In the absence of this steric force, Fspring will be entirely balanced by the hydrodynamic lift force (Flift = Fspring). The lift force determined by this method as a function of the liquid gap h0 determined as described in the previous paragraph is presented in Figure 7b. As can be observed in the figure, the measured lift force decreases quickly with the thickness of the fluid gap, as expected for EH effects. The validity of the EH origin of the observed lift force could be further evaluated by comparing the evolution of the measured force on the different operational variables with theoretical predictions. Describing the dynamic system of a lubricated, compliant, point contact requires solving the coupled non-linear equations of hydrodynamic and elasticity, a very challenging problem due to the non-local effects introduced by the elastic deformation. We are not aware of any exact theoretical description for the full analytical description of this problem. Sekimoto and Leibler [START_REF] Sekimoto | A Mechanism for Shear Thickening of Polymer-Bearing Surfaces: Elasto-Hydrodynamic Coupling[END_REF] and Skotheim and Mahadevan 23,[START_REF] Skotheim | Soft Lubrication: The Elastohydrodynamics of Nonconforming and Conforming Contacts[END_REF] used a perturbation approach to develop analytical expressions for the EH lift force in the scenario of small deformations. For a sphereplane lubricated contact of a thin poroelastic layer on a rigid substrate, they proposed:

𝐹 𝑙𝑖𝑓𝑡 = 𝜇 2 𝑉 2 𝐻 𝑙 𝑅 2 (2𝐺+𝜆)ℎ 0 3 (1)
where µ is the fluid viscosity, and G and  are the shear modulus and the Lamé's first parameter of the thin layer. As this expression is valid in the limit of small deformations, it does not apply strictly to the system investigated here, in particular in the regime of large compressions. Nevertheless, we can compare it with our experimental results. As can be observed in Figure 6, the measured Flift data grows following a square dependence on V, in agreement with the previous expression. On the contrary, it clearly decays more slowly than the third power of the estimated thickness of the lubricant film (the prediction of eq. 1), as can be observed in Figure 7. One identifiable reason for this discrepancy comes from the fact that the elastic shear modulus of the microgel and its thickness are both strongly affected on the degree of swelling. Thus, the factor (2G+) in the denominator and Hl in the numerator of (1) are not independent of D. As a first approximation, one can consider the microgel coating thickness Hl as the minimum between Hs and half of the mica-mica separation before shear. It can also be assumed that the shear modulus is proportional to the density of network strands per unit volume, [START_REF] Rubinstein | Polymer Physics[END_REF] which is inversely proportional to Hl. As can be observed in Figure 8, by scaling the measured Flift data by Hs/Hl 2 , a reasonably agreement with an inverse cubic power law of h0 is obtained, as predicted by equation 1.

A more rigorous test to the description provided by eq. 1 comes from the direct calculation of microgel shear modulus from the experimental data. We obtains values of (2G+) ca. 1 Pa, which appears unreasonably low: direct measurements of the modulus of similar microgel systems are typically of the order of few kPa. [START_REF] Voudouris | Micromechanics of Temperature Sensitive Microgels: Dip in the Poisson Ratio near the LCST[END_REF] Several reasons could be at the origin of this discrepancy. First, the actual viscosity of the lubricant film is unknown; we have considered this film to be a layer of water, but it is probably more adequate to picture it as a solution of pNIPAM pendant chains. Indeed, it has been shown that the internal microstructure of common microgels, and in particular their degree of cross-linking, is often non-homogeneous. [START_REF] Stieger | Small-Angle Neutron Scattering Study of Structural Changes in Temperature Sensitive Microgel Colloids[END_REF][START_REF] Conley | Jamming and Overpacking Fuzzy Microgels: Deformation, Interpenetration, and Compression[END_REF] By using neutron scattering experiments, Stieger and coworkers showed that the crosslinking density of pNIPAM microgels decreases radially in the particle; thus, it is probably a more accurate image to consider the microgel layer as an elastic core decorated with a layer of dangling pNIPAM chains. Other reasons for calculating unrealistically low values of G could be the overestimation of the values of h0 (from values of D and Flift measured under dynamic conditions) or the large microgel deformation used in this work: large strains were applied in most of the test reported, which is beyond the range of validity of eq. 1, developed for small perturbations. Nevertheless, we obtained small G values even for the cases of none or small compression of the microgel layer (D/2 ≥ Hs).

Another point of discrepancy between our experimental results and the model described by eq. 1 is the behavior observed at different temperatures. We found a significantly enhanced Flift at higher temperatures (Fig. 4), when the swelling degree of the microgels is clearly reduced (cf. Fig 2). However, if eq. 1 holds, the opposite is expected, as the shear modulus of the microgel significantly decreases in the more hydrated state. [START_REF] Voudouris | Micromechanics of Temperature Sensitive Microgels: Dip in the Poisson Ratio near the LCST[END_REF] This apparent inconsistency may be partially due to the permeability of the microgel coating. Salez and Mahadevan 28 argued that for short poroelastic times (compared with the lubrication time scale) this element can be taken into account by including a (1-) factor in equation 1 (where  is the fluid volume fraction in the porous layer), implying an effective stiffening due to the presence of the fluid. This stiffening would be more significant at lower temperatures, when the degree of swelling of the microgel coating increases. Another important element missing in the description of Skotheim and Mahadevan is the influence of wall viscoelasticity. 23,[START_REF] Skotheim | Soft Lubrication: The Elastohydrodynamics of Nonconforming and Conforming Contacts[END_REF] As described by Pandey and coworkers 25 , the rheological properties of the walls can modify the behavior of the system; in particular, smaller Flift values should be expected for viscoelastic boundaries than for purely elastic system due to the dissipative contribution of the wall loss modulus.

Another remaining question of this study is the actual existence of a fluid lubricant film between the surfaces under compression and shear. There is no doubt that it will be present at large separations (D > Hs), but it may not be the case under an applied normal load. Working on macroscopic hydrogels, Chateauminois and coworkers 41 found that the system behavior was dominated by the long poroelastic times, and did not observe the formation of a lubricant film, reducing the influence of EH effects. On the contrary, in the present study the poroelastic time was short related to the typical excitation time (≈A 1/2 /V) due to the small size of the contact and the microgels; we observed the emergence of a lift force due to the coupling between normal and tangential motion: when the mechanical system was left to evolve freely, we observed a significant increase of the gap between the surfaces. Thus, our results strongly suggests that under shear the load bearing ability in the system progressively shifts from steric forces (surfaces in contact; boundary lubrication) to hydrodynamic forces of EH origin with increasing driving velocities, with a lubricant film separating the rubbing surfaces. This transit could be responsible for the bell-shaped response of friction vs. V (with a maximum value) often observed in lubrication studies of macromolecular coatings. [START_REF] Bouchet | Experimental Study and Modeling of Boundary Lubricant Polyelectrolyte Films[END_REF]

CONCLUSIONS

We have shown that shearing of surfaces coated by compliant microgel layers can generate a lift force of elastohydrodynamic origin, triggering the entrainment of a fully developed fluid film at large enough speeds, minimizing the contact between the opposite surfaces. After fluid film formation the system transits from boundary to hydrodynamic modes of lubrication, which is likely to trigger significant friction and wear reduction.

By using a feedback loop to fix the surface separation, we have been able to accurately determine the lift force, and to investigate its dependence on driving speed and surface separation. The scaling of the lift with these variables can be reasonably described by perturbative models developed to describe small dynamic deformation of the compliant coating.

Figure 1 .

 1 Figure 1. Schematic of the mechanism of the Surface Forces Apparatus. Two mica surfaces are glued on cylindrical lenses of radius R with their axis crossed. The distance D between the surfaces is measured by MBI. A normal force (Fspring) is applied between the surfaces using the normal spring (KN), by displacing the distal position T. This force determines the position D. The point of contact grows to a circular contact area A under load. The reciprocating tangential motion between the surfaces at a speed V is imposed by using piezoelectric actuators. The tangential force between the surfaces is determined from the deflection of the tangential spring Kf

Figure 2 .

 2 Figure 2. Normal interaction force measured during quasi-static approach (normalized by the nondeformed radius of curvature of the surfaces) vs. surface separation D between mica surfaces coated with a self-assembled layer of cationic pNIPAM microgels immersed in a solution of 1 mM NaNO3. Black squares: T=35 C. Open circles: T=25 C. The stars signal the onset of repulsive force, which can be identified as twice the thickness of the unperturbed microgel coating (Hs). Inset: 5 µm x 5 µm AFM tapping mode height micrograph measured in air (ex-situ) of a dried microgel-coated mica surface, after the SFA experiments.

Figure 3 .

 3 Figure 3. Liquid film draining: variation of the mica-mica distance at the PCA. An inward displacement of T of 1.3 µm was imposed at t=20 s at different speeds. Black squares: 1.3 µm/s. Red circles: 0.13 µm/s. Blue triangles: 0.013 µm/s. T=25C.

Figure 4 .

 4 Figure 4. Shear-induced variation of the mica-mica distance at the PCA under static conditions. Black squares: T=35 C. Open circles: T=25 C. The driving velocity V was modified at periodic intervals, as specified. The distal point of the loading spring T remains in a fixed position.

Figure 5 .Figure 6 .Figure 7 .Figure 8 .

 5678 Figure 5. Feedback loop control. The distal point of the loading spring is displaced to maintain the target value of the mica-mica distance at the PCA. Black line: applied driving speed V. Blue line: measured absolute mica-mica distance, D. Red line: relative position of the distal point of the loading spring, T. T=35 C

ACKNOWLEDGMENT

The authors are indebted to Dr. T. Salez for stimulating discussions and suggestions on the manuscript.