domain: sdu phys

text:
Holger Döring
email: holgerdoering@alumni.tu-berlin.de

A brief note on space-time spin

Keywords: spacetime-signature, spin-formalism, boole-algebra, rank, dual-system, spin-2-particle

Space-time signature can be derived via a simple sort of spin-formalism. This formalism is described in a short comment .It comes from a simple Boole-algebra.

Introduction:

In classical local flat spacetime of tangential space in Minkowski-type but also in description of GRT and gravity there is used a four-dimensional form of spacelike and timelike dimensions of signature in main diagonal-line of a fundamental tensor: s=(+1/ +1/+ 1/-1) or s=(-1 /-1/-1/+ 1) [1.],[2.], [3.]. Since in Minkowski-space covariant and contravariant vectorfields are indistinguishable, the choice of version is arbitrary there but in GRT there must be told, which form is used [4.], [5.], [6.].

2.Concrete modelling:

The imaginary, concrete model (analog to Maxwells methods) on which the problem is based consists of an electric circuit diagram of a lamp and two switches in a series construction. There are four possibilities:

3.Calculation:

Each state of the switches can be related to a defined form of spacetime-spin in a system: the different states are called SpIN and SpOUT.

1. ψ 1 ⇒⇐ ψ 2 means s=-1 , timelike state of spacetime: "SpIN-SpIN", 2. ψ 1 ⇐⇐ ψ 2 means s=1 , spacelike state of spacetime: "SpOUT-SpIN" , (1.a-1.d) 3. ψ 1 ⇒⇒ ψ 2 means s=1 , spacelike state of spacetime: "SpIN-SpOUT", 4. ψ 1 ⇐⇒ ψ 2 means s=1 . spacelike state of spacetime: "SpOUT-SpOUT".

The arrows explain the spacetime spin-state direction, however these will be interpreted. Remark: Instead of speaking of "up and down" like ordinary spin-system its here the meaning of "in and out" . This also can be written in a version of Diracs bracket-notation ⟨SpIN|SpOUT ⟩ or in formulation of QFTH with creation-and annihilation quantum operators a +1 , a -1 . Possibly these states can be connected to causal ingoings and outgoings of an fourevent in lightcone-or conoid-description. Furthermore this spin system confirms a simple form of a Boole-Algebra:

ψ 1 ∧ψ 2 =W ¬ψ 1 ∧ψ 2 =F ψ 1 ∧¬ψ 2 =F ¬ψ 1 ∧¬ψ 2 =F → 1∧1=1 1∧0=0 0∧1=0 0∧0=0 , (2.a-2.d)
where 1 means "SpIN" and 0 means "SpOUT".

This corresponds with the signature structure of (+1/-1 /-1/-1) of the local classical fourspacetime. The inverted analogon of signature s then can be constructed via an "or"-relation in Boole-algebra ( this means concrete a parallel-circuit of a lamp and two switches):

ψ 1 ∨ψ 2 =W ¬ψ 1 ∨ψ 2 =W ψ 1 ∨¬ψ 2 =W ¬ψ 1 ∨¬ψ 2 =F → 1∨1=1 0∨1=1 1∨0=1 0∨0=0 (3.a-3.d)
And this structure corresponds with signature-form s of (+1/ +1/+1 /-1) .

4.Spin-structure of spin-2-particles generates four-signature:

The classical signature s can be generated by structure of spin-1-particles (s1p) or spin-2particles (s2p). Since s1p are included in s2p, the situation is only discussed for s2p.The condition for s1p can be derived from this. Real spacetime is not really empty, in reality there is no flat spacetime, there are always gravitational vacuum-structures after model of GRT called vacuum-fluctuations, which span the basic ground structure of spacetime, not only for quantum systems but even in classical Einstein gravity. The following arrow-graph symbolizes the structure of a s2p in two dimensions, because it has to be invariant under rotations about 180 °≃π .

⟨ ← ↓ ↑ → ⟩ picture 1: 2-dimensional structure of a s2p.
Now two of them sp2 are coupled; the inner horizontal arrows represent the coupling structure. That's why they are shown larger now. But this is only screened for optics of the coupling now because for invariance after rotation about 180 °the opposite arrows have to be seen in the same size. So neglect the size by looking at the structures.It's only for optics, no "rotation variation of size ", although this meaning could be supposed in a later hypothesis if the forces are calculated. Explanation of rotations of spin-coupling: 4a) Normal "zero-state", both particles are in the same eypression. 4b) Left particle rotates about α=90 so the difference between the states is Δ α=90 °. 4c) Left s2p rotates about α=90 °clockwise and right s2p rotates about α=90 °clockwise.The difference now is still Δ α=90 °. 4d) Left s2p rotates about α=90 ° and right s2p doesn't rotate.The difference now is Δ α=180 °. So also the rotating difference can represent the spin-2-state but of course this rotating systems also can be represented by s1-particles as is said above.

Conclusion and Summary:

The structure of signature form s of real spacetime can be reduced to a form of spinning system, which gives the tension of the four-spacetime dimension system in a real simple dual quality of SpIN and SpOUT by coupling of two spin-2-particles ("gravitons"). That completeness of description may be one reason, why classical spacetime is a fourdimensional manifold and has no other dimension-number.

  This arrangement means signature of s=-1 . ⟨ → ↑ ↓ ← ⟩ ⋯ ⟨← ↓ ↑ →⟩ This arrangement means signature of s=1 . (4.a-4.d) ⟨ ← ↓ ↑ → ⟩ ⋯ ⟨→ ↑ ↓ ←⟩ This arrangement means signature of s=1 . ⟨ → ↑ ↓ ← ⟩ ⋯ ⟨→ ↑ ↓ ←⟩ This arrangement means signature of s=1 .


Yin Xu

Jérémy Dhainaut
email: jeremy.dhainaut@univ-lille.fr

Jean-Philippe Dacquin

Jean-François Lamonier

Hui Zhang

Sébastien Royer

On the role of cationic defects over the surface reactivity of manganite-based perovskites for low temperature catalytic oxidation of formaldehyde

Keywords: Perovskite, Lanthanum deficiency, Surface defects, Electronic structure regulation, Formaldehyde oxidation

Defect engineering in catalytic materials is a versatile strategy to fine-tune their performance towards oxidation reactions, and break the related bottlenecks. Herein, a series of La1-xMnO3 perovskite-based materials was designedly synthesized to investigate the effect of cation defects on their physico-chemical properties. Based on extensive characterizations and density function theory (DFT) calculations, it is demonstrated that La-deficiency could orderly induce oxygen vacancies and electronic structure regulation on perovskite, which prominently promotes the catalytic activity towards formaldehyde oxidation. The leading material (La0.6MnO3) could retain high activity for 63 hours, either under dry or humid air. In brief, this work unveils the feasibility of modulating the surface reactivity by modifying the electronic structure properties of lanthanum manganite perovskites following simple adjustment of the Asite cationic vacancies, and also highlights A-site deficient perovskite as a potentially efficient catalyst for environmental remediation.

Introduction

Perovskites might represent the most studied mixed-oxide structures, owing to their exceptional thermal stability, ionic conductivity, electronic structure, electron mobility, and redox behavior [START_REF] Hwang | Perovskites in catalysis and electrocatalysis[END_REF][START_REF] Royer | Perovskites as substitutes of noble metals for heterogeneous catalysis: dream or reality[END_REF]. Perovskite structures can be expressed with a general formula ABO3, where the A-site cation is 12-fold coordinated with oxygen, while the B-site cation is 6-fold coordinated with oxygen [START_REF] Royer | Perovskites as substitutes of noble metals for heterogeneous catalysis: dream or reality[END_REF]. As a benefit of a wide range of possible substitutions at both A and B sites, perovskites offer great flexibility allowing to tailor their physicochemical properties and better target specific applications. The B-site cations were found to play a primary role in altering the electronic structure of the perovskites, thus modifying the catalytic efficiency [START_REF] Hwang | Perovskites in catalysis and electrocatalysis[END_REF][START_REF] Royer | Perovskites as substitutes of noble metals for heterogeneous catalysis: dream or reality[END_REF][START_REF] Arandiyan | Defect engineering of oxide perovskites for catalysis and energy storage: synthesis of chemistry and materials science[END_REF]. In particular, manganese-based perovskites are emphasized as possible alternatives for noble metal-based catalysts (Pt, Rh, Pd), mainly due to their relatively low cost, good thermal stability at high temperature and ease of preparation [START_REF] Najjar | Development of Mn-based perovskite materials: Chemical structure and applications[END_REF]. For instance, lanthanum manganite perovskites (A = La; B = Mn) provide redox (Mn 4+ /Mn 3+ ) active centers to facilitate a wide variety of catalytic reactions [START_REF] Hwang | Perovskites in catalysis and electrocatalysis[END_REF][START_REF] Xu | La1-x(Sr, Na, K)xMnO3 perovskites for HCHO oxidation: The role of oxygen species on the catalytic mechanism[END_REF][START_REF] Yang | Lanthanum manganite-based perovskite as a catalyst for co-production of ethylene and hydrogen by ethane dehydrogenation[END_REF].

The catalytic activity of perovskites can be modulated by altering their crystallinity, morphology, microstructure or surface/interface chemical states. Different strategies were hence developed to improve the performance of stoichiometric perovskites, such as increasing the specific surface area, doping with transition metals or other lanthanides and rare earths, or modifying the crystal structures and morphologies [START_REF] Arandiyan | Defect engineering of oxide perovskites for catalysis and energy storage: synthesis of chemistry and materials science[END_REF][START_REF] Wang | Perovskite oxide catalysts for advanced oxidation reactions[END_REF]. Among these, doping is the most common and efficient strategy. For example, aliovalent substitutions on A-or B-sites using cations of different valences, like K + , Sr 2+ or Ce 4+ , were reported [START_REF] Xu | La1-x(Sr, Na, K)xMnO3 perovskites for HCHO oxidation: The role of oxygen species on the catalytic mechanism[END_REF][START_REF] Royer | Mechanism of stearic acid oxidation over nanocrystalline La1-xA′xBO3 (A′= Sr, Ce; B= Co, Mn): The role of oxygen mobility[END_REF]. To meet the criteria of electron neutrality, this substitution was suggested to either change the oxidation state of the transition metal cation (in Bposition) or introduce oxygen vacancies, facilitating oxygen transfer and thus increasing oxygen mobility.

As a kind of surface defects, oxygen vacancies have been widely reported to act as adsorption and active sites in heterogeneous catalytic reactions. However, cation vacancies are another kind of important defects, which have been often overlooked. For instance, as-prepared MnO2 often tends to exhibit Mn vacancies (with 2.8 ~ 11.1 mol%) [START_REF] Wang | Half-Metallicity in Single-layered manganese dioxide nanosheets by defect engineering[END_REF], and these vacancies can significantly change the electronic structure and photoconductivity of the material [START_REF] Kwon | Defect-induced photoconductivity in layered manganese oxides: A density functional theory study[END_REF]. Recently, cation vacancies have been also generated to promote the catalytic activity of perovskites in oxygen evolution reactions (OER) [START_REF] Xu | High-performance perovskite composite electrocatalysts enabled by controllable interface engineering[END_REF][START_REF] Xu | Recent advances in novel nanostructuring methods of perovskite electrocatalysts for energy-related applications[END_REF][START_REF] He | Recent advances in perovskite oxides for non-enzymatic electrochemical sensors: A review[END_REF]. For instance, a cation deficiency-promoted phase separation strategy was applied to prepare perovskite-based composites with significantly enhanced H2O oxidation performances owing to improved mobility of lattice oxygens as ionic oxygen species [START_REF] Xu | High-performance perovskite composite electrocatalysts enabled by controllable interface engineering[END_REF]. The SnCoFe perovskite hydroxide (SnCo0.9Fe0.1(OH)6) with Sn cation deficiency exhibited excellent OER activity due to the promoted exposure of active CoFe sites and improved conductivity [START_REF] Chen | Preferential cation vacancies in perovskite hydroxide for the oxygen evolution reaction[END_REF]. A-site deficiency in La-Ni and La-Fe perovskites also led to an enhanced OER activity, which has been attributed to the generated surface oxygen vacancies and improved metal-oxygen hybridization [START_REF] Zhu | Enhancing electrocatalytic activity of perovskite oxides by tuning cation deficiency for oxygen reduction and evolution reactions[END_REF][START_REF] Qiu | Understanding the enhancement mechanism of A site-deficient LaxNiO3 as an oxygen redox catalyst[END_REF].

Thus, cationic defects modulation in perovskite oxides is an effective strategy to modify their physical and chemical properties which should be further studied and applied to VOCs oxidation reactions.

While most of the research effort focused on stoichiometric lanthanum manganite perovskites with varying oxygen excess, commonly noted LaMnO3+δ, it should be noted that those structures are actually defective in both La and Mn positions [START_REF] Van Roosmalen | The defect chemistry of LaMnO3±δ: 2. Structural aspects of LaMnO3+δ[END_REF]. Thus, a more rigorous formula would be La1-xMn1-xO3. For instance, a δ value of 0.158 corresponds to ~5 % of La and Mn vacancies (La0.95Mn0.95O3), though the La/Mn vacancy ratio can also be controversial [START_REF] Alonso | Non-stoichiometry, structural defects and properties of LaMnO3+δ with high δ values (0.11 ≤ δ ≤ 0.29)[END_REF][START_REF] Dezanneau | Magnetic properties related to structure and complete composition analyses of nanocrystalline La1-xMn1-yO3 powders[END_REF]. In particular, a deficiency of A-site ions in the perovskite lattice (A1-xB1-yO3, with x > y) leads to self-(or vacancy-) doped perovskites [START_REF] Ulyanov | Hybridization of electronic states and magnetic properties of self-doped La1-xMnO3+δ (0≤ x≤ 0.15) perovskites: XANES study[END_REF]. The latter materials showed intriguing results in heterogeneous catalysis and especially in oxidation reactions [START_REF] Faye | Influence of lanthanum stoichiometry in La1-xFeO3-δ perovskites on their structure and catalytic performance in CH4 total oxidation[END_REF][START_REF] Chen | The influence of nonstoichiometry on LaMnO3 perovskite for catalytic NO oxidation[END_REF]. Formaldehyde (HCHO), as one of the dominating indoor air pollutants, is mainly emitted from various building materials and household products [START_REF] Fang | Indoor formaldehyde levels in residences, schools, and offices in China in the past 30 years: A systematic review[END_REF]. Long term exposure to HCHO may cause irritation of the eyes and of mucosa of the upper respiratory tract. In 2004, the International Agency for Research on Cancer (IARC) classified HCHO as carcinogenic for humans (Group 1) [START_REF] Arc | IARC classifies formaldehyde as carcinogenic to humans[END_REF]. Various conventional approaches such as adsorption, plasma technology, photocatalytic oxidation, and thermal catalytic oxidation have been applied for the removal of HCHO [START_REF] Ye | Room-temperature formaldehyde catalytic decomposition[END_REF][START_REF] Vellingiri | Advances in thermocatalytic and photocatalytic techniques for the room/low temperature oxidative removal of formaldehyde in air[END_REF].

Among them, mild temperature catalytic oxidation (< 100 °C) is considered as an attractive technology for HCHO abatement. It overcomes the disadvantages of relatively short adsorbents lifetime, additional apparatus and operating costs of plasma technology and photocatalytic oxidation.

Currently, noble metal-based catalysts (i.e. Pt, Pd, Rh, Au and Ag-doped materials) present the highest catalytic activities in HCHO oxidation [START_REF] Chen | Unravelling the critical role of silanol in Pt/SiO2 for room temperature HCHO oxidation: An experimental and DFT study[END_REF][START_REF] Ye | Synergy between platinum and gold nanoparticles in oxygen activation for enhanced roomtemperature formaldehyde oxidation[END_REF]. However, their high cost limits real-life applications, and transition metal oxide-based catalysts would be preferred [START_REF] Zhang | Catalytic oxidation of formaldehyde over manganese oxides with different crystal structures[END_REF][START_REF] Wang | Room-temperature oxidation of formaldehyde by layered manganese oxide: effect of water[END_REF][START_REF] Wang | The effect of manganese vacancy in birnessite-type MnO2 on room-temperature oxidation of formaldehyde in air[END_REF][START_REF] Selvakumar | Reaction of formaldehyde over birnessite catalyst: A combined XPS and ToF-SIMS study[END_REF]. In particular MnOx-based materials are under extensive investigation, as they show the best catalytic activity among transition metal oxides. Surprisingly, Mn-based perovskites have been scarcely reported for HCHO oxidation though they have been applied to a wide range of volatile organic compounds (VOCs) [START_REF] Xu | La1-x(Sr, Na, K)xMnO3 perovskites for HCHO oxidation: The role of oxygen species on the catalytic mechanism[END_REF][START_REF] Ding | Understanding A-site tuning effect on formaldehyde catalytic oxidation over La-Mn perovskite catalysts[END_REF]. In this work, a series of lanthanum manganite perovskite-based materials was prepared. The molar concentration of lanthanum was modulated during the synthesis, resulting in materials having La1-xMnO3 as a general formula (with x = 0, 0.1, 0.2, 0.3 and 0.4). This series was extensively characterized and tested for the mild oxidation of HCHO.

By combining extensive characterization, density function theory (DFT) calculations, and catalytic results, better understanding of the influence of cationic vacancies on the catalytic performances of perovskite-based materials is provided herein.

Experimental

Synthesis of catalysts

A series of manganese-based La1-xMnO3 perovskite materials (with x = 0, 0.1, 0.2, 0.3 and 0.4) was prepared following the citrate complexation method described in more details in a previous work [START_REF] Xu | Hierarchical porous ε-MnO2 from perovskite precursor: Application to the formaldehyde total oxidation[END_REF]. Briefly, the La1-xMnO3 catalysts were prepared starting from the following molar ratio of reagents: (1-x) La(NO3)3•6H2O (≥ 99.0 %, Sigma-Aldrich) : 1 Mn(NO3)2•4H2O (97.0 %, Aldrich) : (2-x) C6H8O7 (+99.5 %, Alfa Aesar).

All reagents were dissolved in distilled water, and the resulting homogeneous solutions were kept under stirring at room temperature overnight. Excess water was eliminated by rotary evaporation, resulting in gels which were further thermally treated under air over two steps: 180 °C for 1 h (3 °C min -1 ), and 700 °C for 8 h (2 °C min -1 ) excepted in the case of La0.7MnO3 and La0.6MnO3, for which the second temperature step was adjusted at 750 °C to obtain fully crystalline perovskite phases. The reason will be discussed in section 3.1. The reference Mn3O4 was prepared in the same way, with no addition of lanthanum nitrate (x = 1). The gel was thermally treated at 1000 °C for 4 h (2 °C min -1 ) [START_REF] Dezanneau | Magnetic properties related to structure and complete composition analyses of nanocrystalline La1-xMn1-yO3 powders[END_REF].

HCHO catalytic oxidation

Formaldehyde (HCHO) oxidation was performed in a fixed bed reactor (internal diameter = 8 mm), loaded with 0.20 g of the catalyst. Catalyst activation was performed in situ at 300 °C for 1 h under 20 vol% O2/He, with a flow rate of 100 mL•min -1 .

Gaseous formaldehyde was produced from paraformaldehyde in a permeation tube placed in a permeation chamber (Dynacalibrator, VICI Metronics, Inc.) and kept at 100 °C. The reacting gas containing 100 ppm of HCHO in 20 vol% O2/He was flowed through the fixed bed reactor and its temperature was controlled by applying a temperature decrease rate of 0.5 °C min -1 from 300 to 100 °C, and of 0.2 °C min -1 from 100 to 25 °C. The total flow rate was 100 mL min -1 , corresponding to a gas hourly space velocity (GHSV) of 30 L gcat -1 h -1 . The effluent gas was monitored online by a gas chromatograph (GC, Varian) equipped with a thermal conductivity detector.

Separations were performed using two columns: one CP-Sil 5 CB column channel (8 m) for HCHO analysis, and one COX column channel (1 m) for CO2 analysis.

The HCHO oxidation into CO2 was expressed as HCHO conversion, while HCHO elimination refers to the removal efficiency of HCHO. They were calculated using the following equations, respectively:

HCHO conversion (into CO2) = [CO 2 ] 𝑡 [HCHO] 0 (1) HCHO elimination = [HCHO] 0 -[HCHO] 𝑡 [HCHO] 0 (2)
where [HCHO]t and [CO2]t are their concentration at time t as monitored by GC, and

[HCHO]0 is the initial HCHO concentration (100 ppm).

During the stability test, a fresh catalyst was first activated as indicated before (300 °C, 1 h under 20 vol% O2/He, 100 mL min -1 ). Then the reacting gas (100 ppm HCHO in 20 vol% O2/He, 100 mL min -1 ) was passed through the catalyst bed at T50 reaction temperature (corresponding to 50 % HCHO conversion) for 63 h.

Characterization

X-ray diffraction patterns (XRD) were collected on a Bruker D8 Advanced AXS diffractometer equipped with Cu Kα1 monochromatic radiation source (λ = 1.5418 Å) and operated at 40 kV and 30 mA. X-ray diffractograms in the 10°-80° region were recorded with a 0.02° step size (step time = 1 s). Scherrer equation (d = Kλ/(βcosθ)) was performed at an identified diffraction peak which does not overlap with crystalline impurities, where d is the mean crystallite size (nm), K is a dimensionless shape factor (0.9), λ is the X-ray wavelength (0.15418 nm), β is the full width at half maximum (FWHM, in radians), and θ is the Bragg angle (in radians). Following the thermal treatment of the material series at 1000 °C, their powder diffraction patterns were measured (2θ scan = 10-90 °, 2θ step size = 0.03, integration time = 3 s/step) and analyzed by Rietveld refinement using the Jana2006 freeware. As the starting model, we used a reference structure with a similar chemical composition, La0.945Mn0.945O3 (COD database, card number 1531526). In the structure refinement, cell parameters, sample shift, thermal parameters, and lanthanum and oxygen sites occupancies were considered variable parameters. A Pseudo-Voigt shape function was used to fit the peak shape. In situ XRD experiments were performed by first depositing the samples on a kanthal sample holder and XRD patterns were collected every 50 °C from room temperature to 1123 °C, under a gas mixture composed of 3% H2 diluted in He (50 mL min -1 ) and after 30 min of sample stabilization at the desired temperature. After recording the XRD pattern at 1123 °C, the sample was cooled down to 30 °C for a last diffractogram recording.

The electron paramagnetic resonance (EPR) spectra were measured on a Bruker (MiniScope MS 5000) spectrometer with a center field of 350 mT, a microwave power of 0.1 mW and a microwave frequency of 9.48 GHz.

Nitrogen sorption measurements were performed at -196 °C on a Micromeritics

TriStar II Plus apparatus. Samples were degassed at 150 °C during 6 h prior analysis. Specific surface areas (SBET) were calculated according to the Brunauer-Emmett-Teller (BET) method.

Morphological properties and elemental mapping of the samples were evaluated on a field-emission scanning electron microscope (SEM-FEG Hitachi SU-70) with an energy dispersive spectrometer (EDS) microanalysis (EDAX Genesis).

X-ray Photoelectron Spectroscopy (XPS) was performed on a AXIS Ultra DLD spectrometer (Kratos Analytical) with a monochromatic Al Kα X-ray source (1486.6 eV). High resolution spectra were collected with a constant pass energy (PE = 20 eV) and the binding energy (BE) was calibrated with the adventitious carbon (BE(C1s) = 284.8 eV). Quantification and spectral decomposition were processed using CasaXPS software.

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) analyses were performed on a TOF.SIMS 5 spectrometer (ION TOF GmbH) equipped with a pulsed bismuth liquid metal ion gun as source of primary ions. Bi3 + clusters (25 keV, 0.3 pA current) were used to improve molecular information in the spectra. The analyzed sample area was 500×500 μm 2 for spectral analyses with 128x128 pixels and 150 scans.

Temperature programmed reductions (TPR) were carried out on about 60 mg of unpretreated sample under 5 vol% H2/Ar gas flow (50 mL min -1 ) with a heating rate of 10 °C min -1 up to 1000 °C using a Micromeritics Autochem II 2920 apparatus. The same apparatus was used for O2 temperature-programmed desorption experiments (TPD) and coupled with mass spectrometry. The catalysts (50 mg) were in situ preactivated under 5 vol% O2 diluted in He and submitted to the following conditions: 30 mL/min He, temperature from 40 °C to 1000 °C with a ramp of 10 °C/min. The outlet gases O2 (m/z = 32) were identified using a mass spectrometer. The amount of O2 desorbed from the catalyst was quantified from calibrated pulses (1 μmol).

Stoichiometry of La and Mn in the solids were monitored by inductively coupled plasma-optical emission spectroscopy (ICP-OES) (Agilent Technologies 700 Series spectrometer). Before analysis, the solids were dissolved in a concentrated HCl/HNO3 mixture.

The DFT calculations were carried out using the Vienna Ab-initio Simulation Package (VASP) with the frozen-core all-electron projector-augment-wave (PAW) method. The Perdew-Burke-Ernzerhof (PBE) of generalized gradient approximation (GGA) was adopted to describe the exchange and correlation potential. The cutoff energy for the plane-wave basis set was set to 450 eV. The 2×1 LaMnO3 (001) slab has 2-layers atoms, and a vacuum region of 15 Å above them was used to ensure the decoupling between neighboring systems. For the geometry optimization, the atoms in the bottom layer of slab were fixed to their bulk positions. The geometry optimizations were performed until the forces on each ion was reduced below 0.01 eV/Å, and the S1). As reported in the literature [START_REF] Dezanneau | Magnetic properties related to structure and complete composition analyses of nanocrystalline La1-xMn1-yO3 powders[END_REF][START_REF] Markovich | Magnetic properties of nanocrystalline La1-xMnO3+δ manganites: size effects[END_REF][START_REF] Shelke | Influence of the calcination temperature on the combustion synthesized perovskite LaMnO3 compound[END_REF], manganese oxide phases MnOx usually form in lanthanum-deficient perovskites. In order to verify this point, La0.6MnO3 was further calcined at 1000 °C during 4 h and the related XRD pattern is given in Figure S2. A secondary crystalline phase, Mn3O4, is unambiguously observed, verifying the presence of amorphous manganese oxide (MnxOy) phase at 700 °C. To obtain more detailed analysis of their crystalline composition, all samples were thermally treated at 1000 °C and the related XRD patterns are given in Figure S3. Following the semi-quantitative analysis of their crystalline composition, it appears that all solids contain La2O3, La(OH)3, and Mn3O4 in various proportions, with more Mn3O4 formed following further La-deficiency as indicated in Table S1. Furthermore, Rietveld refinement was performed on these XRD patterns (Figure S3) and the calculated lattice parameters are given in Table S1. It appears that all perovskites present a similar composition LaxMnO3 with a slight deficiency in lanthanum (x = 0.89-0.92), as shown by Gao et al [START_REF] Gao | Preparation and characterization of the nonstoichiometric La-Mn perovskites[END_REF]. Thus, it can be concluded that all catalysts thermally treated at 700-750 °C are actually composed of LaxMnO3 perovskite (x = 0.9 ± 0.02) decorated with amorphous LaxOy(OH)z and MnxOy species. The presence of the latter have a great influence over the surface redox properties of the perovskites as determined hereafter.

As seen in Table 1, the crystallite size of the samples decreased from 26 to 19 nm with the decrease of the La/Mn ratio, when applying the Scherrer equation to the (024) plane (2θ = 46.9°) [START_REF] Xu | Hierarchical porous ε-MnO2 from perovskite precursor: Application to the formaldehyde total oxidation[END_REF]. The textural properties are also presented in Table 1. As expected for perovskite materials, all catalysts have relatively low specific surface areas (from 18 to 24 m 2 g -1 ) due to high temperature calcination and lack of significant internal porosity in the aggregates. The surface morphology of La0.6MnO3 was visualized by FEG-SEM. As shown in Figure S4, this sample is composed of agglomerated small particles with an irregular morphology and forming large macropores, which is very similar to reference LaMnO3 perovskite [START_REF] Xu | Hierarchical porous ε-MnO2 from perovskite precursor: Application to the formaldehyde total oxidation[END_REF]. EDS mapping of the sample further shows that La, Mn and O elements are homogeneously distributed on the surface (Figure 1), while EDS spectra allow to evaluate the La/Mn atomic ratio to be 0.50 instead of 0.60 (Figure S5), which could be attributed to the presence of extra-framework Mn species. Moreover, the O/Mn atomic ratio is found be 2.32, much lower than the expected stoichiometry for a reference perovskite and supporting the presence of single oxide species (MnO or Mn3O4) at the surface.

ICP and XPS analysis

To go further in details on the elemental composition and chemical states, bulk (ICP-OES) and surface (XPS) analyses were conducted and the related quantitative elemental compositions including La/Mn, Mn/O and La/O atomic ratios are summarized in Table 2. The XPS spectra for La 3d and Mn 2p, and Mn 3s and O 1s core levels are given in Figures S6 and2, respectively. Within experimental and apparatus errors, the determined atomic ratios of La/Mn by ICP follow closely the La/Mn ratios in the initial solutions. According to XPS, a slight deficiency of La (La0.9MnO3 and La0.8MnO3) in the perovskite structure induces a strong decrease of both La/O (from 1.06:3 to 0.52:3) and Mn/O (from 0.95:3 to 0.71:3) surface atomic ratios, suggesting that La-deficiency resulted in the formation of both La and Mn cationic vacancies (VLa and VMn) at the surface. Further La-deficiency (La0.7MnO3 and La0.6MnO3) does not further change significantly the La/O surface atomic ratio (0.56:3 to 0.51:3), however the Mn/O surface atomic ratio dramatically increases from 0.71:3 to 1.21:3. Moreover, La/Mn atomic ratios as determined by XPS are systematically lower than by ICP for La-deficient perovskites, all pointing to surface enrichment in manganese as framework cations and extra-framework oxides.

High-resolution Mn 3s XPS spectra can be observed in Figure 2a. The average oxidation state (AOS) of the surface Mn was determined by the binding energies of the doublet separation of Mn 3s (△Es) following the correlation: AOS (Mn) = 8.956 -1.126 × △Es [START_REF] Yang | Catalytic removal of gaseous unintentional POPs on manganese oxide octahedral molecular sieves[END_REF]. For the stoichiometric LaMnO3, the AOS (Mn) is about 3.42 (Table 2), in agreement with a mixture of Mn 4+/3+ with Mn 3+ as the predominant cation. La0.9MnO3 and La0.8MnO3 present similar AOS (Mn) of 3.40 and 3.41, respectively. Further Ladeficiency led to a more marked decrease of the AOS (Mn) towards 3.36 and 3.33 for La0.7MnO3 and La0.6MnO3, respectively. Assuming constant AOS (Mn) of perovskite, this confirms the presence of Mn-oxide phase with Mn valency ≤ 3 for these last two samples.

Figure 2b displays the XPS spectra in the O1s region for all samples. Three peaks can be observed around 529.3, 531.1, and 532.8 eV, representing the surface lattice oxygen (O 2-, denoted as Olatt), the surface adsorbed oxygen species (such as O2 2-or O - belonging to defect-oxides and OH groups, denoted Oads), and molecular water adsorbed on the surface (denoted Ow), respectively [START_REF] Xu | Hierarchical porous ε-MnO2 from perovskite precursor: Application to the formaldehyde total oxidation[END_REF].

Table 2 also presents the proportion of the different oxygen species. The fraction of surface adsorbed oxygen species initially increases slightly with the deficiency in lanthanum. These Oads species are usually linked to surface oxygen vacancies (VO) [START_REF] Deng | Strontium-doped lanthanum cobaltite and manganite: highly active catalysts for toluene complete oxidation[END_REF], the former being highly mobile, while the latter provides sites for adsorption, activation and migration of oxygen species. Further La-deficiency leads to a marked decrease of Oads fraction, along with an increase in the fraction of surface lattice oxygen Olatt. Some previous works reported that Oads plays a major role in the oxidation of HCHO [START_REF] Wang | Room-temperature oxidation of formaldehyde by layered manganese oxide: effect of water[END_REF][START_REF] Zhang | Alkalimetal-promoted Pt/TiO2 opens a more efficient pathway to formaldehyde oxidation at ambient temperatures[END_REF], while others pointed out that Olatt is mainly responsible for the catalytic activity in HCHO oxidation [START_REF] Zhang | Catalytic oxidation of formaldehyde over manganese oxides with different crystal structures[END_REF][START_REF] Santos | The role of lattice oxygen on the activity of manganese oxides towards the oxidation of volatile organic compounds[END_REF]. Most likely, both oxygen species can play a key role in oxidation reactions, depending on the reaction conditions leading to either a suprafacial or an intrafacial oxidation mechanism.

Defects analysis and theoretical calculations

In order to estimate the content of anionic vacancies in the different materials, solid-state EPR and Raman spectra were obtained to complete XPS analysis. As seen in Figure 3, all samples exhibit a signal at a g-value of 2.002, which is attributed to unpaired electrons trapped by the oxygen vacancies. Most surprisingly, the EPR signal of the La1-xMnO3 samples linearly increases with increasing the deficiency of La up to x = 0.3 (Figure 3, insert), implying that the amount of oxygen vacancies on the catalyst could be precisely modulated by simply adjusting the ratio of A site : B site cations.

However, it should be noted that further deficiency in A-site cations (La0.6MnO3) causes a drastic decrease in the amount of oxygen vacancies. This might indicate that, if the amount of oxygen vacancies exceeds a threshold value, the structure would partially collapse with the formation of a new external phase (i.e. MnxOy) in addition to the perovskite phase.

The existence of defects is further confirmed by Raman spectroscopy (Figure S7).

Raman bands around 490 and 610 cm -1 , respectively associated to bending-and stretching-like vibrations of the MnO6 octahedra [START_REF] Granado | Orderdisorder in the Jahn-Teller transition of LaMnO3: A Raman scattering study[END_REF], might reflect the extension and compression of Mn-O bond pairs, correlated with Jahn-Teller distortion [START_REF] Granado | Orderdisorder in the Jahn-Teller transition of LaMnO3: A Raman scattering study[END_REF][START_REF] Teng | Catalytic behavior of hydrothermally synthesized La0.5Sr0.5MnO3 single-crystal cubes in the oxidation of CO and CH4[END_REF]. As observed, the large band from 300 to 700 cm -1 in La0.8MnO3 is more intense and broader than the dual bands in LaMnO3 centered at 490 and 610 cm -1 . This indicates higher distortion of MnO6 octahedra by the Jahn-Teller effect and consequently, the presence of more oxygen vacancies [START_REF] Wang | Evaluation of Fe substitution in perovskite LaMnO3 for the production of high purity syngas and hydrogen[END_REF]. These results are consistent with EPR spectra. As expected, the reduction of lattice oxygen results in the generation of coordinatively unsaturated metal centers, as well as lattice dislocation and disordered local structure, all leading to electrostatic repulsion between positively charged oxygen vacancies and Mn 3+ cations, and the subsequent lattice distortion/expansion. Of note, La0.6MnO3 spectrum does not show a similar large band, in line with EPR observations showing the presence of few oxygen vacancies. In contrast, a new band at 642 cm -1 appears, assigned to Mn-O stretching mode of MnxOy species [START_REF] Yu | Catalytic combustion of chlorobenzene over Mn-Ce-La-O mixed oxide catalysts[END_REF]. Importantly, this redshift corresponds to a weakening of Mn-O bonds [START_REF] Huang | Superior performance of α@ β-MnO2 for the toluene oxidation: Active interface and oxygen vacancy[END_REF], and thus higher lattice oxygen activity in line with the increase of Olatt/Otot observed by XPS.

To understand the origin of oxygen defects and their role in the catalytic activity enhancement of La-deficient perovskites, density function theory (DFT) calculations were performed to study the oxygen vacancy formation energy (EOV) and the density of states (DOS), respectively. A LaMnO3 crystal with Mn-terminated (001) surface was chosen as our calculation model, due to the facts that it is the most stable surface, and the redox active Mn atoms are expected to be the main active sites for catalytic oxidation [START_REF] Wang | Oxygen reduction activity on perovskite oxide surfaces: a comparative first-principles study of LaMnO3, LaFeO3, and LaCrO3[END_REF].

Models of stoichiometric and La-deficient (La1-xMnO3, with x slightly inferior to 0.1) perovskite surfaces, with and without oxygen vacancy, are shown in Figure 4.

Based on energy minimization, the EOV of a perfect LaMnO3 plane is 3.203 eV, which is higher than that of a La1-xMnO3 plane (2.724 eV). Lower EOV evidences that Ladeficiency effectively promotes the formation of oxygen vacancies, confirming the result of solid EPR experiments. In addition, the length of two Mn-O bonds (IMn-O1, IMn-O2) were further calculated in the stoichiometric LaMnO3 (Figure 4a) and in the Ladeficient La1-xMnO3 with oxygen vacancy (Figure 4d). Interestingly, IMn-O1 and IMn-O2 are significantly extended from 1.837 and 1.987 to 2.002 and 2.043 Å, respectively, by introducing La and O vacancies. The stretched Mn-O bonds should result in higher lattice oxygen reactivity.

As mentioned above, it is assumed that introducing La defects into LaMnO3 would lead to partial reduction of Mn 4+ to Mn 3+ . That is, unpaired electrons would fill empty eg orbitals to move from the t2g 3 eg 0 to the t2g 3 eg 1 electronic configurations. Such eg orbital occupation can cause a spin hole in oxygen via exchange interactions [START_REF] Du | A-site cationic defects induced electronic structure regulation of LaMnO3 perovskite boosts oxygen electrode reactions in aprotic lithium-oxygen batteries[END_REF].

Consequently, the eg electrons would become delocalized and produce a spin channel connecting the Mn cations to the O anions, further creating an unimpeded spin route to accelerate charge transfers and thus redox reactions.

To support this viewpoint, the DOS patterns, which are intuitive evidence of the variation of electronic structure, were simulated via DFT. As observed in Figure 5a-b, the d-band center of Mn 3d is calculated at -1.434 and -1.382 eV for LaMnO3 and La1-xMnO3, respectively. Hence, in the presence of La vacancy, the d-band center shifted towards Fermi level (EF) as a result of the increase of antibonding states [START_REF] Abild-Pedersen | Scaling properties of adsorption energies for hydrogen-containing molecules on transition-metal surfaces[END_REF]. It is considered that antibonding electrons with high energy are unstable, thus resulting in eg orbital electrons being more active for redox reactions. Similarly, as illustrated in Figure 5c-d, the p-band center of O 2p also shifted towards EF level: from -3.938 to -3.824 eV for LaMnO3 and La1-xMnO3, respectively. This can be interpreted as the lattice oxygen becoming more favorable thermodynamically to participate in redox mechanism. Both Mn 3d and O 2p state shifts indicate that charge transfers between Mn and O-related adsorbates (i.e. O 2-and O2 2-) would accelerate in La-deficient La0.9 perovskites, facilitating the oxidation of Mn species.

Based on these observations, it is assumed that the electronic structure of Mn-O bands can be modulated by introducing La vacancies, which would affect the catalytic activity of perovskites in redox reactions.

Low temperature redox studies

The H2-TPR tests were performed to investigate the reducibility of the series of catalysts and related data are shown in Figure 6 and Table 3, respectively. For LaMnO3, the main peak is centered at 371 °C, with a shoulder at 448 °C which can be assigned to the reduction of Mn 4+ into Mn 3+ as well as a part of Mn 3+ ions into Mn 2+ , respectively.

From 600 °C, an additional intense peak corresponds to the reduction of the remaining Mn 3+ to Mn 2+ . The calculated total H2 consumption is 2.66 mmol/g, fitting with the total reduction of Mn ions (Mn 3+ and Mn 4+ ) constituting a stoichiometric LaMnO3.15 perovskite into Mn 2+ .

The main peak for the three less La-deficient perovskites (La0.9MnO3 to La0.7MnO3) is centered on a similar temperature from 370 °C to 379 °C. In contrast, the main peak for La0.6MnO3 is shifted towards higher temperature (395 °C), which can be attributed to the presence of manganese oxide [START_REF] Stobbe | The reduction and oxidation behaviour of manganese oxides[END_REF]. A small shoulder (Figure 6, area highlighted in yellow) is observed at low temperature (~ 255 °C) for all samples. It is most likely due to the removal of surface reactive oxygen species. The corresponding initial H2 consumption rates of the first reduction shoulder (before occurrence of phase transformation) have been calculated, and the results are indicated in Figure S8. This rate increases with decreasing the La/Mn ratio and indicates that partial deficiency in A-site (La 3+ ) cations, along with the formation of Mn3O4 species from La0.7MnO3, promote the low temperature reducibility of the LaMnO3-based catalysts, probably through increasing the concentration of surface oxygen reactive species (such as O2 2-, O -, and OH groups), with expected beneficial influence over HCHO oxidation.

To get more insights into the reduction mechanism, in-situ temperature-controlled XRD under H2 flow was conducted on La0.6MnO3 to evidence the progressive Mn 4+ reduction process. XRD patterns in the range of 25 to 800 °C are shown in Figure 7.

Small peaks attributed to La2O3 and MnO are observed from 25 °C under reducing conditions. Such a low temperature further reveals the presence of surface reactive species including LaxOy(OH)z and MnxOy, knowing that the latter can be reduced into MnO at low temperature [START_REF] Stobbe | The reduction and oxidation behaviour of manganese oxides[END_REF]. Furthermore, the diffraction peaks attributed to the LaMnO3 crystalline phase started to decrease in intensity from 200 °C, confirming the facilitated reduction of Mn 4+ composing the perovskite phase in this A-deficient composition. On the other hand, the intensities of La2O3 and MnO reflections gradually increase with increasing the temperature of reduction. From 600 °C under reductive conditions, the perovskite phase almost disappears from the XRD patterns, indicating its complete reduction which correlate well with TPR results (Figure 6). O2-TPD tests were carried out to estimate both the surface and bulk oxygens reactivity. As indicated in Figure S9, three regions (III, II, I) respectively refer to the release of bulk lattice oxygen (Olatt, above 750 °C); the desorption of β oxygen species (β-O2, at T = 440 -750 °C) attributed to the reduction of bulk Mn(IV) species by the outward diffusion of oxygen species; and α oxygen species including weakly adsorbed surface oxygen species and some active oxygen species from the subsurface lattice (O2 -) (α-O2, at T = 100 -440 °C). Strikingly, compared with LaMnO3 and La0.8MnO3, La0.6MnO3 has more surface active oxygen species and especially more easily-released lattice oxygen species (0.21 and 0.41 versus 0.88 mmol of desorbed O2 per gram, respectively). In line with the above discussion, their increased concentration is directly related to the presence of abundant amorphous MnxOy species. These weakly bonded oxygen atoms are expected to participate in oxidation reactions.

Catalytic activity

The catalysts performance towards formaldehyde (HCHO) oxidation into CO2 is shown in Figure 8a, and the related data are given in Table 4. In line with the observations made, the conversion efficiency increases with increasing the Ladeficiency, even with the presence of Mn3O4 species on the surface of La0.7MnO3 and La0.6MnO3. The T50 (defined as the temperature needed to convers 50 % of HCHO into CO2) is lowered from 145 °C (LaMnO3) to 128 °C with the best catalyst of this series, La0.6MnO3. Mn3O4 (which may not be the manganese oxide present at the surface of the perovskites at 750 °C) itself is poorly active, as seen on Figure S10, with a T50 of 205 °C. The apparent activation energies (Ea) were also calculated from the Arrhenius plots given on Figure 8b. Ea decreases from 96.4 kJ/mol (LaMnO3) to 43.7 kJ/mol (La0.6MnO3), within the range of A-site substituted perovskites [START_REF] Ding | Understanding A-site tuning effect on formaldehyde catalytic oxidation over La-Mn perovskite catalysts[END_REF] and most supported noble metal catalysts [START_REF] Chen | The active sites of supported silver particle catalysts in formaldehyde oxidation[END_REF][START_REF] Chen | A novel redox precipitation to synthesize Au-doped α-MnO2 with High Dispersion toward low-temperature oxidation of formaldehyde[END_REF].

Based on the characterization conducted, this catalytic improvement can be attributed to the cumulated effect of several factors: Figure S11 shows the linear decrease of Ea with decreasing the La/Mn ratio (in the bulk and on the surface) and the Mn average valence. Additionally, more oxygen vacancies (Ovac) should decrease Ea to some extent, as discussed. However, herein La0.6MnO3 both presents the lowest Ea and Ovac, highlighting the prevalent role of surface-active oxygen species (i.e. Oads). Hence, two different stages occur: (1) Initially, at La/Mn atomic ratios above 0.7, the catalysts provide more cation vacancies (VLa and VMn) at the surface, compared with the stoichiometric LaMnO3. Their presence likely induces the formation of unsaturated oxygen species and further facilitates the formation of surface-active Oads species [START_REF] Wang | The effect of manganese vacancy in birnessite-type MnO2 on room-temperature oxidation of formaldehyde in air[END_REF], as confirmed by XPS and TPR analyses. All mentioned factors would lead to a moderate improvement of the catalysts performance towards HCHO oxidation. (2) Further decreasing the La/Mn ratio from 0.7 promotes the formation of MnxOy species at the surface of the perovskite. Their presence has a clear effect on the reactivity, by increasing the relative content of surface oxygen species [START_REF] Santos | The role of lattice oxygen on the activity of manganese oxides towards the oxidation of volatile organic compounds[END_REF], as shown by TPR.

Moreover, it has been reported that MnOx species are able to mineralize few ppm of HCHO from 25 °C under 25-30% of relative humidity over long periods [START_REF] Zheng | Advances of manganese-oxides-based catalysts for indoor formaldehyde removal[END_REF]. In particular, VMn cationic vacancy is considered to enhance the lattice oxygen reactivity and mobility, and lower the formation energy of oxygen vacancies. Besides, the decrease of Mn(AOS) involves the generation of oxygen vacancies to some degree.

Active lattice oxygens are expected to play a major role in HCHO oxidation. It should be noted that the activity is well-correlated to the low-temperature reducibility of the catalysts. This result implies that surface oxygen species in La-deficient samples, which are the most reducible, have a predominant contribution over the global oxidation activity. In brief, the catalytic oxidation of HCHO herein may be considered as a function of the surface-and lattice-active oxygen species, and low-temperature reducibility of the catalysts (weaker Mn-O bonds).

Stability test and Moisture effect

Figure 9 illustrates the HCHO conversion into CO2 and HCHO elimination under dry air over La0.6MnO3 at T50. As seen, the catalyst maintains a relatively stable activity performance, however with an overtime decrease for both yields of about -20 % after 63 hours.

To investigate the possible changes of surface properties related to these lowered performances, La0.6MnO3 was again characterized after test. The XRD pattern (Figure S12a) of the spent catalyst appears unchanged. However, the TPR profile as displayed in Figure S12b reveals a lower consumption of H2 below 600 °C (2.22 mmol/g) than the as-made La0.6MnO3 (2.81 mmol/g), implying that Mn species with lower valence state are present in the spent catalysts. Moreover, the onset temperature of reduction is shifted towards a higher temperature (225 °C instead of 147 °C), implying that less surface adsorbed oxygen species are present. Additionally, a shoulder (marked as red star in Figure S12b) can be clearly observed at 465 °C. O2-TPD profile (Figure S9) also shows a lower oxygen desorption peak in the spent catalyst. All H2-TPR and O2-TPD data suggest that the La0.6MnO3 catalyst reducibility is decreased after the catalytic test, in line with a decline of its overtime catalytic activity. Similarly, a slight change of the surface AOS (Mn) from 3.33 to 3.24, can be observed by XPS in the Mn 3s region (Figure S13a), which is in good agreement with TPR hydrogen consumed evolution.

XPS spectra in the O1s region of the catalyst before and after reaction are shown in Figure S13b. After test, the relative content of lattice oxygen species (Olatt) decreased considerably, from 67.7 % to 55.1 %. This correlates with the observed global manganese reduction following Olatt consumption during HCHO oxidation. Besides, the relative contents of surface adsorbed oxygen species (Oads) and surface water (Ow) increased, which is attributed to the formation of surface oxygen species (mainly surface -OH groups) and the adsorption of water formed during the decomposition of formate species (HCOO -ads) [START_REF] Quiroz | Total oxidation of formaldehyde over MnOx-CeO2 catalysts: The effect of acid treatment[END_REF], an intermediate product of HCHO oxidation. This phenomenon would counterbalance up to some point the decrease of Oads and Olatt, and thus sustain the activity over long periods.

Of note, and as reported before [START_REF] Xu | La1-x(Sr, Na, K)xMnO3 perovskites for HCHO oxidation: The role of oxygen species on the catalytic mechanism[END_REF][START_REF] Selvakumar | Reaction of formaldehyde over birnessite catalyst: A combined XPS and ToF-SIMS study[END_REF], a contribution named CF emerged around 288.6 eV on the XPS spectrum in the C 1s region of the spent catalyst, which refers to the presence of formate and HCHO species on the surface. Its low intensity implies that these species transform or desorb faster over La0.6MnO3. This observation was confirmed by the ToF-SIMS spectra displayed in Figure S14, showing four times more fragments attributed to HCHO intermediates (based on CO3 -) on the surface of LaMnO3 than on the surface of La0.6MnO3.

Mild temperature catalytic oxidation is known to be greatly affected by moisture, the presence of which is unavoidable in most practical applications. We recently reported that a controlled moisture is not only beneficial to the desorption of carbonate adsorbed on the active sites, but it also facilitates the regeneration of surface -OH groups, greatly enhancing the activity of La1-xA' xMnO3 catalysts [START_REF] Xu | La1-x(Sr, Na, K)xMnO3 perovskites for HCHO oxidation: The role of oxygen species on the catalytic mechanism[END_REF]. Here the catalytic activity of La0.6MnO3 under humid conditions (relative humidity (RH) = 46 % at room temperature) was evaluated and the results are shown in Figure 10. As can be seen, the presence of H2O greatly improves the overtime catalytic activity of La0.6MnO3, with constant HCHO elimination and conversion yields up to 63 hours at T50. In a typical HCHO oxidation process, HCHO is first adsorbed on the catalyst surface, and then oxidized by surface active oxygen species (O * : O2 -, O -, -OH) into formate species (Eqs. 3 and 4) [START_REF] Wang | Room-temperature oxidation of formaldehyde by layered manganese oxide: effect of water[END_REF][START_REF] Wang | The effect of manganese vacancy in birnessite-type MnO2 on room-temperature oxidation of formaldehyde in air[END_REF]. Further oxidation of formate by O * generates carbonate species (Eq. 5) and finally CO2 (Eqs. 6 and 7) [START_REF] Wang | Room-temperature oxidation of formaldehyde by layered manganese oxide: effect of water[END_REF][START_REF] Wang | A nonoxide catalyst system study: Alkali metal-promoted Pt/AC catalyst for formaldehyde oxidation at ambient temperature[END_REF]. The consumed O * can be regenerated by the complex migration from surface Olatt to oxygen vacancies with the continuous dissociation of molecular oxygen, while the transfer from gas-phase oxygen to surface Olatt can be completed via the oxygen transfer mechanism (Eqs. 8-10) [START_REF] Wang | Room-temperature oxidation of formaldehyde by layered manganese oxide: effect of water[END_REF]. Additionally, surface -OH groups can be also replenished via the reaction between O * and water (Eq. 11). Thus, in the presence of moisture, the catalytic cycle is looped.

HCHOads + 2O * → HCOO -ads + -OH

HCHOads + O * → HCOO -ads + H + (4)

HCOO -ads + O * → HCO3 -ads (5)
HCO3 -ads + OH -→ CO3 2-ads + H2O

HCO3 -ads + H + → H2CO3 ads → CO2 + H2O (7)

Mn 4+ -(O 2-)-Mn 4+ → Mn 3+ -(□)-Mn 3+ + O * /O2 (8)
Mn 4+ -( O 2-)-Mn 4+ + O * + HCHO → Mn 3+ -(□)-Mn 3+ + CO2 + H2O

Mn 3+ -(□)-Mn 3+ + O2 →Mn 4+ -(O 2-)-Mn 4+ + O * (10)

H2O + O * → 2 -OH (11)
"□" represents oxygen vacancies.

Under the studied conditions and as reported in the case of manganese oxide [START_REF] Wang | Room-temperature oxidation of formaldehyde by layered manganese oxide: effect of water[END_REF],

moisture regenerates the surface hydroxyl groups and further limits the accumulation of formate or carbonate species on the surface of La0.6MnO3. In turns, it facilitates the activation of H2O and chemisorbed oxygen, therefore resulting in stable long-term oxidation performance.

Conclusions

This work correlates the La-deficiency level of La1-xMnO3 perovskite-based materials and their catalytic activity for HCHO oxidation. Hence the material with the lowest La/Mn ratio, La0.6MnO3, presented the highest activity with a T50 of 128 °C (against 145 °C for LaMnO3) along with an apparent activation energy (Ea) of 43.7 kJ/mol (against 96.4 kJ/mol for LaMnO3). This improvement in activity was attributed to more reducible and active surface adsorbed oxygen species. Especially, highly reducible MnxOy species are formed besides the main perovskite phase when the La/Mn atomic ratio was below 0.8, and the resulting materials displayed improved HCHO oxidation performances owing to the enhanced reactivity and mobility of lattice oxygens, as well as the low-temperature reducibility of the metal oxide species.

Moreover, under the presence of moisture, the catalytic performance of La0.6MnO3 was completely retained (100 % HCHO elimination and 50 % HCHO conversion into CO2) for up to 63 hours at T50 which is an important characteristic in view of practical applications. Therefore, these results contribute to the development of low-cost and high-efficiency materials for indoor pollution control. Efforts should now be directed towards lowering its temperature of catalytic activity, meaning providing active oxygens at lower temperatures, for practical use. 25 °C red.

★ △ △ △ ★ ■ ■ △ △ △ △ ★ ■ △ △ △ ■ △ ■ △ △ △ ■ △ La 2 O 3 2 theta /°

  Monkhorst-Pack k-point sampling was set to 1×3×1. The resulting structures were then used to calculate the electronic structures, and the k-point sampling was increased to 3×5×1. The formation energies of O-vacancy were calculated by the following formula: Eform = E(vacancy) -E(pure) + ) O (  ; where E(vacancy) and E(pure) are the total energies of O-vacancy and pure LaMnO3(001), respectively. ) O (  is the chemical potential of atomic O. 3 Results and Discussion 3.1 Crystal phase structure XRD patterns of as-synthesized samples are shown in Figure S1. The first three samples (LaMnO3, La0.9MnO3, La0.8MnO3) present the typical diffraction pattern of lanthanum manganite perovskite (JCPDS 50-0298) with characteristic peaks at 2θ = 23.0°, 32.5°, 40.1°, 46.9°, 58.1°, 68.6° and 77.8°. However, the diffractograms of La0.7MnO3 and La0.6MnO3 annealed at 700 °C display a broad hump around 29°, attributed to the presence of an amorphous phase (Figure S2, insert). This hump disappears following calcination at 750 °C (Figure

Figure 1

 1 Figure1EDS mapping of La, Mn, and O on the surface of La0.6MnO3.

Figure 2

 2 Figure 2 XPS spectra of (a) Mn 3s and (b) O 1s of the La1-xMnO3 series (x = 0 to 0.4).

Figure 3

 3 Figure 3 EPR spectra of the La1-xMnO3 series (x = 0 to 0.4). Inset: linear relationship

Figure 4

 4 Figure 4 Side view of perovskite (001) surfaces: (a) LaMnO3, (b) La1-xMnO3, (c)

Figure 5

 5 Figure 5 Calculated (a, b) d-band centers of Mn and (c, d) p-band centers of O on

Figure 6

 6 Figure 6 H2-TPR profiles of the La1-xMnO3 series (x = 0 to 0.4).

Figure 7

 7 Figure 7 XRD patterns of La0.6MnO3 during in-situ temperature-programmed

Figure 8

 8 Figure 8 HCHO catalytic oxidation over the La1-xMnO3 series (x = 0 to 0.4): (a) HCHO

Figure 9

 9 Figure 9Overtime HCHO conversion over La0.6MnO3 under dry conditions at T50 =

Figure 10

 10 Figure 10Overtime HCHO conversion over La0.6MnO3 under humid conditions at T50

Figure 1 Figure 2

 12 Figure 1

  Figure 8

Table 1

 1 Textural and structural properties of the La1-xMnO3 series (x = 0 to 0.4).

	Samples	Crystalline phases a	SBET (m 2 /g)	d (nm)
	LaMnO3	LMO	18	26
	La0.9MnO3	LMO	22	24
	La0.8MnO3	LMO	20	23
	La0.7MnO3	LMO/MnxOy	24	21
	La0.6MnO3	LMO/MnxOy	22	19
	a As identified by X-ray diffraction.

Table 3

 3 H2 consumption deduced from the H2-TPR for the La1-xMnO3 series (x = 0 to 0.4).

		Tmax reduction peaks (°C)	H2 consumption (mmol/g)
	Samples	t1	t2	peak 1	peak 2	Total
	LaMnO3	371	818	1.52	1.14	2.66
	La0.9MnO3	377	806	1.83	1.06	2.89
	La0.8MnO3	370	830	1.71	1.34	3.05
	La0.7MnO3	379	803	2.11	1.10	3.21
	La0.6MnO3	395	766	2.81	0.58	3.39

Acknowledgments

The CNRS, the Chevreul Institute (FR 2638), the Ministère de l'Enseignement Supérieur et de la Recherche, the Région Hauts-de-France, the FEDER, the National Natural Science Foundation of China (Grant No. 22006034) and the Hubei Provincial Natural Science Foundation of China (Grant No. 2020CFB485) are acknowledged for supporting this work. Yin Xu acknowledges the China Scholarship Council (No. 201606270079) for the financial support for the PhD program. The authors acknowledge Dr. Pardis Simon (UCCS) for XPS, Dr. Nicolas Nuns (IMEC) for ToF-SIMS, and Mr Olivier Gardoll (UCCS) for O2-TPD characterizations.

Figure 5

Table 2 Relative surface abundances of the elements constituting the La1-xMnO3 series (x = 0 to 0.4).