Noémie Coudert

Clément Debrie

Jutta Rieger

Taco Nicolai

Olivier Colombani

Thermo-sensitive hydrogels of BAB triblock copolymers exhibiting gradually slower exchange dynamics and an unexpected critical reorganization temperature upon heating

Keywords: amphiphilic block copolymer, exchange dynamics, hydration, light scattering, poly(dimethylacrylamide), RAFT, rheology, poly(methoxyethyl acrylate), thermo-responsive hydrogel, triblock

BAB amphiphilic triblock copolymers comprising poly(methoxyethyl acrylate) (PMEA) B-blocks of variable degrees of polymerization (x = 50, 100 or 200) and a central poly(dimethyl acrylamide) (PDMAc) hydrophilic A-block with a degree of polymerization y = 400 were synthesized by RAFT polymerization and their self-assembly in water was studied by light scattering and rheology. The BAB triblocks form a transient network in aqueous solution consisting of hydrophobic B cores bridged by hydrophilic A blocks. The exchange of B blocks is fast at low temperature (10°C) and/or low x values because PMEA is not too hydrophobic. However, the PMEA blocks become more hydrophobic with increasing temperature, leading to a decrease of the exchange rate of the B blocks and to tunable thermo-thickening properties, opposite to a classical Arrhenius behavior. In contrast to many thermo-sensitive BAB triblocks that undergo an abrupt sol-gel transition above the critical solubility temperature of the B blocks, the hydrophobicity of PMEA gradually increases with T, leading to a progressive increase of the viscosity of the polymer dispersion. In addition, an unprecedented reorganization of the network was observed by rheology at a critical temperature leading to a further decrease of the exchange rate of the B blocks that is not fully reversible. These features were attributed to the progressive variation of the hydrophobic character and hydration of PMEA with temperature.

Introduction

Gels are solid-like materials consisting of two or more components [START_REF] Almdal | Towards a phenomenological definition of the term 'gel[END_REF] , the main constituent being a liquid which can be water (hydrogels), an organic solvent (organogels [START_REF] Kempe | Self-assembled liquid-crystalline gels designed from the bottom up[END_REF][START_REF] Spontak | Thermoplastic elastomers: fundamentals and applications[END_REF][START_REF] Mineart | Decoupling of Mechanical and Transport Properties in Organogels via Solvent Variation[END_REF][START_REF] Draper | Low-Molecular-Weight Gels: The State of the Art[END_REF][START_REF] Guenet | Physical Aspects of Organogelation: A Point of View[END_REF] ), an ionic liquid (ionogels [START_REF] Marr | Ionic liquid gel materials: applications in green and sustainable chemistry[END_REF][START_REF] Lodge | Mechanically Tunable, Readily Processable Ion Gels by Self-Assembly of Block Copolymers in Ionic Liquids[END_REF][START_REF] Ueki | Stimuli-responsive polymers in ionic liquids[END_REF] ) or in some cases both water and an organic solvent (organohydrogels [START_REF] Zhang | Bioinspired organohydrogels with heterostructures: Fabrications, performances, and applications[END_REF] ). They can find applications in various fields including the food industry [START_REF] Singh | Advances in edible oleogel technologies -A decade in review[END_REF][START_REF] Yang | Applications of mixed polysaccharide-protein systems in fabricating multi-structures of binary food gels-A review[END_REF][START_REF] Cao | Design principles of food gels[END_REF] , the health sector [START_REF] Jeong | Thermosensitive sol-gel reversible hydrogels[END_REF][START_REF] Peppas | Hydrogels in Biology and Medicine: From Molecular Principles to Bionanotechnology[END_REF][START_REF] Drury | Hydrogels for tissue engineering: scaffold design variables and applications[END_REF][START_REF] Liu | Functional Hydrogel Coatings[END_REF][START_REF] Dimitrov | Thermosensitive water-soluble copolymers with doubly responsive reversibly interacting entities[END_REF][START_REF] Tsitsilianis | Responsive reversible hydrogels from associative "smart" macromolecules[END_REF][START_REF] Chassenieux | Recent trends in pH/thermo-responsive self-assembling hydrogels: from polyions to peptides-based polymeric gelators[END_REF][START_REF] Moon | Temperature-responsive compounds as in situ gelling biomedical materials[END_REF][START_REF] Jeong | Thermosensitive sol-gel reversible hydrogels[END_REF][START_REF] Wei | Selfhealing gels based on constitutional dynamic chemistry and their potential applications[END_REF][START_REF] Ko | Recent progress of in situ formed gels for biomedical applications[END_REF] , coatings and sealants [START_REF] Wei | Selfhealing gels based on constitutional dynamic chemistry and their potential applications[END_REF] , energy [START_REF] Cheng | Gel Polymer Electrolytes for Electrochemical Energy Storage[END_REF][START_REF] Zhu | Recent advances in gel polymer electrolyte for high-performance lithium batteries[END_REF] storage, enhanced oil recovery [START_REF] Zhu | Polymer Gel Systems for Water Management in High-Temperature Petroleum Reservoirs: A Chemical Review[END_REF] , organic electronics [START_REF] Babu | Self-Assembled Gelators for Organic Electronics[END_REF] or catalysis and sustainable chemistry [START_REF] Marr | Ionic liquid gel materials: applications in green and sustainable chemistry[END_REF] for example. Many strategies [START_REF] Draper | Low-Molecular-Weight Gels: The State of the Art[END_REF][START_REF] Yang | Applications of mixed polysaccharide-protein systems in fabricating multi-structures of binary food gels-A review[END_REF][START_REF] Wei | Selfhealing gels based on constitutional dynamic chemistry and their potential applications[END_REF][START_REF] Tam | Recent advances in metallogels[END_REF][START_REF] Panja | Stimuli responsive dynamic transformations in supramolecular gels[END_REF][START_REF] Chivers | Shaping and structuring supramolecular gels[END_REF][START_REF] Lan | To gel or not to gel: correlating molecular gelation with solvent parameters[END_REF][START_REF] Li | Functional supramolecular gels based on pillar[n]arene macrocycles[END_REF][START_REF] Segarra-Maset | Control of molecular gelation by chemical stimuli[END_REF][START_REF] Noro | Design and properties of supramolecular polymer gels[END_REF][START_REF] Voorhaar | Supramolecular polymer networks: hydrogels and bulk materials[END_REF][START_REF] Peak | A review on tough and sticky hydrogels[END_REF][START_REF] Chen | Fundamentals of double network hydrogels[END_REF][START_REF] Farjami | An overview on preparation of emulsion-filled gels and emulsion particulate gels[END_REF] exist to form gels, but a very attractive one relies on the solution self-assembly of linear BAB triblock copolymers consisting of solvophobic lateral B blocks connected to a central solvophilic A block [START_REF] Spontak | Thermoplastic elastomers: fundamentals and applications[END_REF][START_REF] Chassenieux | Rheology of associative polymer solutions[END_REF][START_REF] Winnik | Associative polymers in aqueous solutions[END_REF] . Solvophobic cores containing several B blocks serve as physical cross-links bridged by the A blocks, resulting in a 3D-spanning network preventing or slowing down flow. One key advantage of this strategy is that tuning the solubility of the B blocks with an external stimulus affects the strength of the selfassembly between the B blocks, leading to stimuli-responsive materials. In this context, temperature-responsive hydrogels 18-22,42, and ionogels [START_REF] Lodge | Mechanically Tunable, Readily Processable Ion Gels by Self-Assembly of Block Copolymers in Ionic Liquids[END_REF] have been widely studied because the former class allows injectability [START_REF] Chassenieux | Recent trends in pH/thermo-responsive self-assembling hydrogels: from polyions to peptides-based polymeric gelators[END_REF] or controlled release of drugs [START_REF] Jeong | Thermosensitive sol-gel reversible hydrogels[END_REF] for biomedical applications, while the latter allows processability for applications in separation membranes, energy storage or electronics for example.

For ionogels, specific polymer-ion and cation-anion interactions allow tuning the solubility of the B blocks [START_REF] Ueki | Stimuli-responsive polymers in ionic liquids[END_REF][START_REF] Tamate | Block copolymer self-assembly in ionic liquids[END_REF] , leading either to B blocks exhibiting an Upper Critical Solubility Temperature (UCST) or a Lower Critical Solubility Temperature (LCST), resulting respectively in gel-sol or sol-gel transitions upon temperature increase. For hydrogels [START_REF] Jeong | Thermosensitive sol-gel reversible hydrogels[END_REF][START_REF] Dimitrov | Thermosensitive water-soluble copolymers with doubly responsive reversibly interacting entities[END_REF][START_REF] Tsitsilianis | Responsive reversible hydrogels from associative "smart" macromolecules[END_REF][START_REF] Jeong | Thermosensitive sol-gel reversible hydrogels[END_REF][START_REF] Taylor | Thermoresponsive Gels[END_REF] , hydrogen bonding of the B blocks with water is mainly responsible for the existence of UCST-type or LCST-type transitions.

However, in most studies on gels formed by the self-assembly of BAB triblock copolymers in solution, B-blocks exhibiting abrupt temperature-transition behaviors have been used, resulting in an on-off reversible transition from a low viscosity liquid to a non-flowing gel [START_REF] Lodge | Mechanically Tunable, Readily Processable Ion Gels by Self-Assembly of Block Copolymers in Ionic Liquids[END_REF][START_REF] Dimitrov | Thermosensitive water-soluble copolymers with doubly responsive reversibly interacting entities[END_REF][START_REF] Tsitsilianis | Responsive reversible hydrogels from associative "smart" macromolecules[END_REF][START_REF] Chassenieux | Recent trends in pH/thermo-responsive self-assembling hydrogels: from polyions to peptides-based polymeric gelators[END_REF] . This abrupt transition can be explained by the fact that the rheological properties of the physically cross-linked networks are controlled by the exchange time of the B blocks, the latter depending primarily on their solvophobic character [START_REF] Chassenieux | Rheology of associative polymer solutions[END_REF][START_REF] Annable | The rheology of solutions of associating polymers: Comparison of experimental behavior with transient network theory[END_REF][START_REF] Zinn | Telechelic Polymer Hydrogels: Relation between the Microscopic dynamics and Macroscopic Viscoelastic Response[END_REF][START_REF] Halperin | On micellar exchange: The Role of the Insertion Penalty[END_REF][START_REF] Nicolai | Dynamic polymeric micelles versus frozen nanoparticles formed by block copolymers[END_REF] . Hence, highly solvophobic B blocks lead to non-flowing gels because their exchange time is long compared to the experimental time window. Rarely, hydrogels have been obtained with moderately hydrophobic and thermo-responsive B blocks which become gradually more hydrophobic with increasing temperature [START_REF] Mistry | Rheological Behavior of Aqueous Micellar Solutions of a Triblock Copolymer of Ethylene Oxide and 1,2-Butylene Oxide: B10E410B10[END_REF][START_REF] Tsitsilianis | Thermoresponsive Hydrogels Based on Telechelic Polyelectrolytes: From Dynamic to "Frozen" Networks[END_REF][START_REF] Lauber | pH-and Thermoresponsive Self-Assembly of Cationic Triblock Copolymers with Controlled Dynamics[END_REF] . This does not result in an abrupt temperature-induced transition from a low viscosity aqueous solution to a nonflowing gel, but causes a gradual increase of the viscosity of the solution with increasing temperature. This behavior is opposite to the classical Arrhenius behavior causing a decrease of viscosity with increasing temperature [START_REF] Chassenieux | Rheology of associative polymer solutions[END_REF][START_REF] Halperin | On micellar exchange: The Role of the Insertion Penalty[END_REF][START_REF] Nicolai | Dynamic polymeric micelles versus frozen nanoparticles formed by block copolymers[END_REF][START_REF] Drozdov | Equilibrium Swelling of Biocompatible Thermo-Responsive Copolymer Gels[END_REF] . Hietala et al. [START_REF] Hietala | Thermoassociating Poly(Nisopropylacrylamide) A-B-A Stereoblock Copolymers[END_REF] prepared BAB triblock copolymers with a central atactic poly(N-isopropyl acrylamide) (PNIPAM) block, which remained hydrophilic below its LCST = 32°C, and lateral isotactic PNIPAM blocks, which did not exhibit any distinct LCST, but were partly hydrated at 5°C and dehydrated with increasing temperature. As a result, hydrogels exhibiting a thermo-thickening behavior were observed below 32°C: the viscosity of the solutions increased with increasing temperature, suggesting an increase of the exchange time of the B blocks with increasing temperature. Mistry et al. [START_REF] Mistry | Rheological Behavior of Aqueous Micellar Solutions of a Triblock Copolymer of Ethylene Oxide and 1,2-Butylene Oxide: B10E410B10[END_REF] studied BAB triblock copolymers with short poly(butylene oxide) (PBO) lateral B blocks (DPn = 10) and a long central poly(ethylene oxide) block. An increase of the rheological relaxation time with temperature was observed. The authors attributed the phenomenon to the dispersity of the PBO blocks. It seems however more reasonable to explain these results by an increase of the hydrophobic character of the PBO blocks with temperature as reported by Castelletto et al. [START_REF] Castelletto | Structure and rheology of aqueous micellar solutions and gels formed from an associative poly(oxybutylene)poly(oxyethylene)-poly(oxybutylene) triblock copolymer[END_REF] . More recently, Tsitsilianis et al. [START_REF] Tsitsilianis | Thermoresponsive Hydrogels Based on Telechelic Polyelectrolytes: From Dynamic to "Frozen" Networks[END_REF] and Lauber et al. [START_REF] Lauber | pH-and Thermoresponsive Self-Assembly of Cationic Triblock Copolymers with Controlled Dynamics[END_REF] studied BAB triblock copolymers with a central hydrophilic poly(dimethyl aminoethyl methacrylate) (PDMAEMA) block and lateral B blocks consisting of random copolymers of very hydrophobic n-butyl methacrylate and a rather hydrophilic and thermosensitive comonomer (respectively triethylene glycol methacrylate or DMAEMA). In both cases, the presence of the thermo-sensitive comonomer imparted temperature responsiveness to the triblocks, resulting in an increase of the exchange time of the B blocks with increasing temperature. The former was studied in view of preparing injectable hydrogels exhibiting sufficiently low viscosity at 5°C for injection, but becoming gels at body temperature. Another polymer architecture has been described by Podhajecka et al. [START_REF] Podhajecka | Synthesis and viscoelastic behavior of watersoluble polymers modified with strong hydrophobic side chains[END_REF] who studied poly(sodium acrylate)s grafted with moderately hydrophobic poly(tert-butyl acrylamide). These graft copolymers formed transient networks also exhibiting an increase in viscosity with increasing temperature. The small number of systems leading to gradual increase of the viscosity with T is probably due to the rarity of intrinsically moderately hydrophobic homopolymers that are able to dehydrate progressively with increasing temperature.

In these earlier studies, the effect of the length of the B blocks on the variation of the exchange time had not been investigated yet on such systems.

In this context, poly(methoxyethyl acrylate) (PMEA) is of interest. PMEA belongs to the poly(oligoethylene glycol (meth)acrylate) series [START_REF] Lutz | Point by Point Comparison of Two Thermosensitive Polymers Exhibiting a Similar LCST: Is the Age of Poly(NIPAM) Over?[END_REF][START_REF] Lutz | Thermo-Switchable Materials Prepared Using the OEGMA-Platform[END_REF][START_REF] Badi | Non-linear PEG-based thermoresponsive polymer systems[END_REF][START_REF] Vancoillie | Thermoresponsive poly(oligo ethylene glycol acrylates)[END_REF] , but contrary to other polymers of this series, PMEA is already hydrophobic at room temperature, because its LCST is close to 5°C. [START_REF] Hoogenboom | Copolymers of 2-hydroxyethylacrylate and 2-methoxyethyl acrylate by nitroxide mediated polymerization: kinetics, SEC-ESI-MS analysis and thermoresponsive properties[END_REF] Still, PMEA is significantly hydrated (~ 10 wt%) at room temperature [START_REF] Tanaka | Cold crystallization of water in hydrated poly(2-methoxyethyl acrylate) (PMEA)[END_REF][START_REF] Tanaka | Effect of water structure on blood compatibility-thermal analysis of water in poly(meth)acrylate[END_REF] . Contrary to the better known PNIPAM, which dehydrates abruptly at its LCST, PMEA dehydrates progressively with increasing temperature, making it potentially suitable to design thermo-responsive hydrogels exhibiting gradual increase of their exchange time with T. Chemical gels, homopolymers or block copolymers containing PMEA [START_REF] Mizoue | Association Behavior of Amphiphilic ABA Triblock Copolymer Composed of Poly(2-methoxyethyl acrylate) (A) and Poly(ethylene oxide) (B) in Aqueous Solution[END_REF][START_REF] Kurokawa | Antithrombogenic poly(2methoxyethyl acrylate) elastomer via triblock copolymerization with poly(methyl methacrylate)[END_REF] have been widely studied especially in view of the strong blood compatibility [START_REF] Tanaka | Cold crystallization of water in hydrated poly(2-methoxyethyl acrylate) (PMEA)[END_REF][START_REF] Tanaka | Effect of water structure on blood compatibility-thermal analysis of water in poly(meth)acrylate[END_REF][START_REF] Kurokawa | Antithrombogenic poly(2methoxyethyl acrylate) elastomer via triblock copolymerization with poly(methyl methacrylate)[END_REF][START_REF] Miwa | 2H-NMR and 13C-NMR Study of the Hydration Behavior of Poly(2-methoxyethyl acrylate), Poly(2-hydroxyethyl ethacrylate)and Poly(tetrahydrofurfuryl acrylate) in Relation30 to Their Blood Compatibility as Biomaterials[END_REF][START_REF] Bag | Impact of the Hydration States of Polymers on Their Hemocompatibility for Medical Applications: A Review[END_REF][START_REF] Sato | The Relationship Between Water Structure and Blood Compatibility in Poly(2-methoxyethyl Acrylate) (PMEA) Analogues[END_REF][START_REF] Haraguchi | Highly Protein-Resistant Coatings and Suspension Cell Culture Thereon from Amphiphilic Block Copolymers Prepared by RAFT Polymerization[END_REF][START_REF] Haraguchi | Antithrombogenic Properties of Amphiphilic Block Copolymer Coatings: Evaluation of Hemocompatibility Using Whole Blood[END_REF] of this polymer, which is attributed to its strong interaction with water 61,62,64- 75 , or for the design of self-assembled particles by Polymerization-Induced Self-assembly [START_REF] Mellot | Templated PISA: Driving Polymerization-Induced Self-Assembly towards Fibre Morphology[END_REF][START_REF] Sugihara | In situ nano-objects via RAFT aqueous dispersion polymerization of 2-methoxyethyl acrylate using poly(ethylene oxide) macromolecular chain transfer agent as steric stabilizer[END_REF] .

However, to the best of our knowledge, PMEA has so far not been used as B block in view of preparing transient networks exhibiting thermo-thickening properties. PMEA B-blocks of varying degrees of polymerization (x = 50, 100 or 200) and a central poly(dimethyl acrylamide) (PDMAc) hydrophilic A-block with y = 400. The polymers were prepared by Reversible Addition Fragmentation chain-Transfer (RAFT) radical polymerization and their self-assembly in aqueous solution was studied by light scattering and linear rheology.

We observed that the triblock copolymers not only exhibit the targeted progressive thermosensitivity leading to thermo-thickening hydrogels with gradually slower exchange dynamics, but that they also show an unprecedented transient network reorganization at a critical temperature that depends on the DPn of the B blocks.

Material and methods

Synthesis of the PMEAx-b-PDMAc400-b-PMEAx triblock copolymers

The three PMEAx-b-PDMAc400-b-PMEAx with x = 50, 100 or 200 were prepared by RAFT polymerization as described in section 1 of the Supporting Information.

Preparation of aqueous polymer dispersions for light scattering and rheology

Aqueous polymer samples were prepared by directly dispersing the polymer powder in deionized water (Millipore, 18 M.cm) at room temperature. For samples at low polymer concentration (<10 g/L) macroscopic dissolution was achieved under stirring at room temperature overnight. The samples were then stored at least 24h in the fridge (~ 5°C) to make sure that equilibrium was reached. For higher polymer concentrations leading to highly viscous solutions or hydrogels, the samples were placed in an iced bath (~ 0°C) or in a fridge (~ 5°C) and regularly homogenized by manual shaking to speed up the dissolution process. Homogeneous samples were obtained after one to three days depending on the polymer concentration and x. They were stored in the fridge until use.

Static and Dynamic Light Scattering (SLS and DLS)

Light scattering measurements were done using ALV-CGS3 and ALV-CGS8 systems operating with vertically polarized He-Ne laser with a wavelength λ=633nm (ALV-GmbH, Germany) coupled with an ALV-5004 and ALV-5003 multi tau correlator system (ALV-GmbH, Germany) respectively. Samples were placed in a thermostated decalin bath that is quasi isorefractive of glass in order to lower reflections of light at the surface of the light scattering cells.

The measurements were done over a wide range of scattering wave vectors q = 6.8.10 4 -2.5. ) (with n = 1.33 the refractive index of the solvent that is water in the present investigation, and 𝜃 = 30-150° the angle of observation). Polymer solutions were studied by light scattering in a concentration range C = 0.1 to 3 g/L. The temperature was controlled between 10 and 50°C by a thermostatic bath to within ±0.2 °C. All solutions were filtered through Acrodisc GHP 0.45 µm pore size filters before measurement.

Dynamic Light Scattering (DLS).

The Siegert equation g2(t) = 1 + βg1²(t), where β is the spatial coherence factor, was used to determine the electric field autocorrelation function, g1(t), from the measured normalized autocorrelation function of the scattered light intensity, g2(t). The relaxation time (τ) distributions, A(τ), were extracted from g1(t) using the REPES [START_REF] Berne | Dynamic Light Scattering[END_REF][START_REF] Brown | Dynamic Light Scattering: The Method and Some Applications[END_REF] routine (equation 1).

𝑔 1 (𝑡) = ∫ 𝐴(𝜏) exp (- 𝑡 𝜏 ) 𝑑𝜏 equation (1)
In the concentration range investigated, a single relaxation mode was observed. The cooperative diffusion coefficient, D, was determined from the average relaxation rate : 𝐷 = 〈𝜏 -1 〉 𝑞 2 and is linked to the z-average hydrodynamic radius Rh of the solute using the Stokes-Einstein equation (equation

2)

.

𝑅 ℎ = 𝑘𝑇 6𝜋𝜂𝐷 equation (2)
With k = 1.38 × 10 -23 J/K Boltzmann's constant, η the solvent (water) viscosity which depends on temperature, T.

Static Light Scattering (SLS).

The Rayleigh ratio, Rθ, was calculated according to equation 3.

R θ = I solution (θ)-I solvent (θ) I toluene (θ) ( n solvent n toluene ) 2 R toluene equation (3)
where Isolution, Isolvent and Itoluene are the average intensities scattered respectively by the solution, the solvent, and the reference (toluene). The Rayleigh ratio of the reference is Rtoluene = 1.35 x 10 - 5 cm -1 , and the refractive indexes of the reference and the solvent (water) are respectively ntoluene = 1.496 and nsolvent = 1.333.

The apparent molar mass (Mapp) of the solute at concentration C was calculated from the Rayleigh ratio of the solution according to equation 4.

R θ = KCM app S(q) equation ( 4)

where S(q) is the structure factor and K a constant defined in equation 5.

K = 4π 2 n solvent 2 λ 4 N A ( ∂n ∂c ) 2 equation (5)
where ∂n/∂c is the specific refractive index increment of the solute and NA is Avogadro's number.

A refractive index increment ∂n/∂c = 0.15 mL/g was measured with a differential refractometer (Oprilab rEX -Wyatt Technology Corporation) at λ = 633 nm for one of the triblock copolymers with solutions at a concentration between 1 and 5 g/L.

In dilute solutions (C = 0.1-3 g/L), one single population of scatterers was observed by DLS for all x and T investigated (see data for x = 100 within the T-range of investigation Figure S4 SI).

Mapp exhibited no significant angular dependency, implying that S(q) ~ 1 and that the radius of gyration Rg of the scatterers was too small to be determined accurately (Rg < 20 nm). Moreover, Mapp (resp. Rapp) did not vary with C in this concentration range implying that it represented the true weight average molecular weight of the scatterers, Mw, (resp. true hydrodynamic radius, Rh)

with an uncertainty of about 10%.

The aggregation number, 𝑁 𝑎𝑔𝑔 , corresponding to the number of B blocks within the selfassembled structures, was determined as 𝑁 𝑎𝑔𝑔 = S1). The polymerization of DMAc was started in bulk at 60°C for 20 min to ensure the solubility of CTA1. Then, water was added and the polymerization was allowed to proceed at 70°C until 90% monomer conversion to reach the targeted degree of polymerization of the central PDMAc block. After purification by dialysis against water and freeze-drying, the bifunctional CTA-PDMAc400-CTA macroCTA was used to control the polymerization of MEA in ACN solution at 35°C. The [MEA]0/[macroCTA]0 ratio was adapted to reach the desired x value at around 30% conversion, where the reaction was stopped. Well-defined triblock copolymers

PMEAx-b-PDMAc400-b-PMEAx with the expected degrees of polymerization of the blocks and a rather low dispersity (Ɖ ~ 1.1-1.2) were eventually obtained (see details in section 1 of the Supporting Information and Table S2).

2. Characterization of the self-assembly in aqueous medium 2.1. Self-assembly at the nanometric scale. . The relaxation is caused by exchange of the B blocks among different hydrophobic cores [START_REF] Chassenieux | Rheology of associative polymer solutions[END_REF][START_REF] Annable | The rheology of solutions of associating polymers: Comparison of experimental behavior with transient network theory[END_REF][START_REF] Zinn | Telechelic Polymer Hydrogels: Relation between the Microscopic dynamics and Macroscopic Viscoelastic Response[END_REF] . The relaxation of the transient network is characterized by a distribution of relaxation times as was already observed for other BAB triblock copolymers and can be explained by the dispersity in length of the B blocks [START_REF] Chassenieux | Rheology of associative polymer solutions[END_REF][START_REF] Charbonneau | Controlling the Dynamics of Self-Assembled Triblock Copolymer Networks via the pH[END_REF][START_REF] Seitz | Self-Assembly and Stress Relaxation in Acrylic Triblock Copolymer Gels[END_REF][START_REF] Lund | Unraveling the equilibrium chain exchange kinetics of polymeric micelles using small-angle neutron scattering -architectural and topological effects[END_REF] .

For x = 50, 100 and 200, the same qualitative behavior was observed for all T < Tc and C > Cp investigated, allowing the construction of a single master curve (see Figure S8 SI) and implying that a transient network was formed with a similar relaxation mechanism independent of x and T.

Dependence of the percolation concentration on T and x. According to the theory of rubber elasticity [START_REF] Larson | The structure and Rheology of Complex fluids[END_REF] , the elastic modulus at the rubbery plateau (Ge, determined as described in the experimental part) is proportional to the number of elastically active chains in the network that is the number of BAB chains forming a bridge between two micellar cores connected to the network (equation 7).

𝐺 𝑒 = 𝑣. 𝑘. 𝑇 (equation 7)

with Ge in Pa,  the number concentration of elastically active chains (number of molecules.m -3 ), k Boltzmann's constant (m 2 .kg.s -2 .K -1 ) and T the absolute temperature (K). The evolution of Ge/Ge_ideal is qualitatively the same at different temperatures for x = 100 (Figure 3a, where Ge_ideal is defined in equation 6, see experimental part) and is consistent with the expected behavior of a transient polymer network: Ge increases with C above Cp as more and more chains become part of the network [START_REF] Chassenieux | Rheology of associative polymer solutions[END_REF][START_REF] Annable | The rheology of solutions of associating polymers: Comparison of experimental behavior with transient network theory[END_REF] . The fact that the curves on Figure 3a do not superimpose at different T values implies that Cp varies with T, which explains why a vertical shift was required to construct the master curves. By appropriately estimating Cp values, which depend on T, the evolution of Ge/Ge_ideal falls on a single curve as a function of C/Cp, see Figure 3b. The same qualitative behavior was also observed for x = 50 and 200 (Figure S9 in SI), allowing the determination of Cp in mol/L (Figure 4a) and g/L (Figure 4b) as a function of T for different x. For a given x, Cp increases with T (it reaches a plateau at 20°C for x = 100). However, for a given T, Cp does not follow a systematic trend with x (no matter if expressed in g/L or mol/L). One possible reason to explain the variations of Cp as a function of T and x could be that Nagg varies with these parameters. Increasing Nagg indeed decreases the molar concentration of physical cross-linking points, which may therefore increase Cp expressed in mol/L. However, this cannot explain the increase of Cp with T for x = 100 and x = 200 as Nagg hardly varies in the relevant T-range (Figure 1). In addition, at T = 15°C, Nagg ~ 12, 60, 140 for, respectively, x = 50, 100, 200, whereas the molar percolation concentration does not follow a monotonous variation with x (Cp = 2.10 -4 , 5. Quantitative evaluation of the exchange dynamics.

Within the investigated T-range, rincreases with increasing C for all x (Figure S10 in SI). This behavior is typical for self-assembling triblock copolymers and can be explained by the decrease of the percentage of defects in the network with increasing C, as discussed in the previous section.

In particular, super-bridges relax more rapidly than one single elastically active chain [START_REF] Annable | The rheology of solutions of associating polymers: Comparison of experimental behavior with transient network theory[END_REF][START_REF] Charbonneau | Controlling the Dynamics of Self-Assembled Triblock Copolymer Networks via the pH[END_REF] . As a consequence, the relaxation time measured by rheology gives a correct estimation of the exchange dynamics of the B blocks only for C >> Cp where defects become negligible. Figure 5 compares the dependence of ron temperature at C = 100 g/L, i.e. at C >> Cp, for the three x values. For a given temperature, the relaxation time strongly increases with x, in agreement with the fact that longer B blocks exchange more slowly. Indeed, longer B blocks are less mobile and exhibit a larger surface of contact with water, thereby increasing the energy barrier for unimer exchange and thus the exchange time [START_REF] Chassenieux | Rheology of associative polymer solutions[END_REF][START_REF] Zinn | Telechelic Polymer Hydrogels: Relation between the Microscopic dynamics and Macroscopic Viscoelastic Response[END_REF][START_REF] Halperin | On micellar exchange: The Role of the Insertion Penalty[END_REF][START_REF] Nicolai | Dynamic polymeric micelles versus frozen nanoparticles formed by block copolymers[END_REF] . In addition, for a given x value, rincreases strongly with increasing temperature. This key result is opposite to the expected behavior in case of a simple thermalactivation process (Arrhenius law), for which r should decrease with T as explained in the introduction. This behavior implies that the energy barrier for the exchange of B blocks increases with T, which means that the PMEA block becomes less mobile/more hydrophobic with increasing T. We hypothesize that the increase of the exchange time with T is due to a decrease of the hydration of the PMEA block. Many studies have been conducted to determine the interaction of water with PMEA and how this affects the crystallization of water. However, these studies were mostly conducted at temperatures below 0°C [START_REF] Tanaka | Cold crystallization of water in hydrated poly(2-methoxyethyl acrylate) (PMEA)[END_REF][START_REF] Tanaka | Effect of water structure on blood compatibility-thermal analysis of water in poly(meth)acrylate[END_REF][START_REF] Miwa | 2H-NMR and 13C-NMR Study of the Hydration Behavior of Poly(2-methoxyethyl acrylate), Poly(2-hydroxyethyl ethacrylate)and Poly(tetrahydrofurfuryl acrylate) in Relation30 to Their Blood Compatibility as Biomaterials[END_REF][START_REF] Morita | Hydration Structure of Poly(2-methoxyethyl acrylate): Comparison with a 2-Methoxyethyl Acetate Model Monomer[END_REF][START_REF] Morita | Time-Resolved In Situ ATR-IR Observations of the Process of Sorption of Water into a Poly(2-methoxyethyl acrylate) Film[END_REF][START_REF] Gemmei-Ide | Recrystallization of Water in Non-Water-Soluble (Meth)Acrylate Polymers Is Not Rare and Is Not Devitrification[END_REF][START_REF] Gemmei-Ide | Recrystallization of Water in a Non-Water-Soluble Polymer Examined by Fourier Transform Infrared Spectroscopy: Poly(2-methoxyethylacrylate) with Low Water Content[END_REF] . PMEA being water-insoluble at room temperature, the evolution of its hydration with temperature above 0°C has seldom been studied.

Mochizuki et al. [START_REF] Mochizuki | Water structure of poly(2methoxyethyl acrylate) observed by nuclear magnetic resonance spectroscopy[END_REF] performed a 2 D NMR study revealing that PMEA still contains about 10 wt% water between 15 and 45°C and that the water is heterogeneously distributed within the polymer.

Hou et al. [START_REF] Hou | On the abnormal ''forced hydration'' behavior of P(MEA-co-OEGA) aqueous solutions during phase transition from infrared spectroscopic insights[END_REF] prepared statistical copolymers consisting of 90 mol% MEA and 10 mol% oligo (ethylene glycol)acrylate (OEGA 480 containing 8-9 ethylene oxide units per monomer) and observed a progressive, rather than abrupt, decrease of the hydration of the copolymer with increasing temperature. Similarly, it was observed [START_REF] Hou | Exploring the Volume Phase Transition Behavior of POEGA-and PNIPAM-Based Core-Shell Nanogels from Infrared-Spectral Insights[END_REF] that nanogels of P(MEA-co-OEGA480) shrink in water with increasing temperature due to water expulsion. Interestingly, for this kind of nanogels, the evolution of the shrinkage with temperature was progressive rather than critical [START_REF] Drozdov | Equilibrium Swelling of Biocompatible Thermo-Responsive Copolymer Gels[END_REF][START_REF] Hou | Microgels with Linear Thermosensitivity in a Wide Temperature Range[END_REF][START_REF] Liu | Development of thermosensitive copolymers of poly(2-methoxyethyl acrylate-co-poly(ethylene glycol) methyl ether acrylate) and their nanogels synthesized by RAFT dispersion polymerization in water[END_REF] , suggesting a gradual rather than abrupt variation of the hydrophobic character/hydration. These results, although they were not conducted with pure PMEA, agree with the gradual increase of the relaxation time observed in our study for the PMEAx-b-PDMAc400-b-PMEAx triblock copolymers. We stress that this behavior is very different from that of poly(Nisopropyl acrylamide) which abruptly dehydrates at its LCST, causing a critical sol-gel transition at the LCST.

Considering that the variation of the hydration of the PMEA blocks most probably explains the evolution of the exchange time of the B blocks with T, we compared the behavior of PMEA100-b-PDMAc400-b-PMEA100 in D2O and H2O. D2O-D2O interactions have been reported by Schvartzman et al. [START_REF] Schvartzman-Cohen | An isotopic effect in self-assembly of amphiphilic block copolymers: the role of hydrogen bonds[END_REF] to be stronger than H2O-H2O interactions, which should make D2O a poorer solvent for neutral polymers solubilized by hydrogen bonding with water. The authors consistently observed an increase of micelle aggregation number in D2O compared to H2O for PEO-b-PPO-b-PEO triblock copolymers. Surprisingly though, chemically cross-linked nanogels of P(MEA-co-OEGA 480) containing 90 mol% of MEA swelled more in D2O than in H2O according to Hou et al. [START_REF] Hou | Exploring the Volume Phase Transition Behavior of POEGA-and PNIPAM-Based Core-Shell Nanogels from Infrared-Spectral Insights[END_REF] ; which is in disagreement with the findings by Schvartzman et al. Additionally, the variation of the swelling of these nanogels with temperature was steeper in D2O than in H2O.

Light scattering experiments conducted with PMEA100-b-PDMAc400-b-PMEA100 at 3 g/L and 20°C showed that Rh was not significantly different in H2O and D2O (23 nm in H2O vs. 25 nm in D2O), but that Nagg was slightly larger in D2O (45) than in H2O (37). Rheological experiments (Figure 6) showed longer relaxation times in D2O than in H2O, whereas Ge was unaffected.

Moreover, the evolution of these parameters with T is identical. Our results are thus consistent with those of Schvartzman et al. [START_REF] Schvartzman-Cohen | An isotopic effect in self-assembly of amphiphilic block copolymers: the role of hydrogen bonds[END_REF] suggesting that PMEA is less hydrated in D2O than in H2O, causing an increase of the extent of aggregation and of the exchange time of the B blocks.

Evidence for a critical reorganization temperature Tc

As briefly mentioned in the beginning of section 2.2, the transient network was found to reorganize above a critical temperature Tc, which varied with x. A typical rheological signature is presented in Figure 7 for x = 100 at 50 g/L and f=1Hz. Upon heating the aqueous dispersion from 10 to 30°C (< Tc), G' and G'' varied only during the first 20s required to reach the target temperature and then remained constant even for long periods of time (data not shown), implying no specific behavior. Up to 30°C, the rheological properties were moreover reversible: full recovery was observed by heating from 10 to 30°C and shortly after cooling back down to 10°C (see Figure S11 in SI). On the contrary, upon heating from 10 to 50°C (> Tc), which takes about 1 minute, an abrupt drop of G' and G'' was observed after ~30 s followed by a subsequent increase after 2 min (Figure 7 and Figure S12). Moreover, G' and G'' slowly continued to evolve with time afterwards even for days (data not shown). After cooling back from 50 to 10°C, which takes about 10 minutes, the initial rheological properties of the system at 10°C are not recovered (see SI Figure S13). The variations of Ge and r after returning back to 10°C were moreover not reproducible. In some cases, applying a strong shear (30s at 100 rad/s, for a few minutes) helped recovering partially the initial properties (see SI Figure S14), but in other cases even shearing was not efficient (see SI Figure S13). for T=50°C. Lines are guides to the eyes. Notice that heating was done at a very fast rate so that the temperature was already higher than 10°C at the time of the first measurement.

Upon heating a sample from 10°C to a temperature T > Tc, the larger the difference between T and Tc, the larger the decrease of G' and G" and the slower the subsequent increase of G' and G'' (see Figures 7 andS12 for representative examples). Qualitatively, the behavior is the same at different concentrations and different x, but quantitative differences are observed (see SI Figures There is no abrupt variation of Nagg close to Tc at steady-state (Figure 1). Moreover, no significant dynamic variation of Nagg was observed by SLS during the time-span of the transition at Tc after heating PMEA100-b-PDMAc400-b-PMEA100 from 10 to 50°C (data not shown). It follows that the molar concentration of micelles hardly changes close to Tc both at steady-state and over time. Therefore, the abrupt decrease of G' and G'' at Tc cannot be explained by an abrupt variation of the number of elastically active chains. It is therefore probably caused by many of the bridging chains becoming temporarily more dynamic at Tc, so that they can relax rapidly and are able to reorganize. The subsequent increase of G' and G'' implies that the system probably becomes again less dynamic. However, Figure 9 shows that if the same experiment is conducted at f = 0.1 or 10

Hz instead of 1 Hz, the behavior is qualitatively similar. It follows that when Tc is crossed, the number of elastically active chains does not vary, but some of them become so dynamic that they relax even at 0.1 Hz, causing an abrupt decrease of G', allowing the network to reorganize. The temperature at which this phenomenon occurs depends on x and the speed of the reorganization decreases with increasing temperature above Tc. According to those findings, we speculate that the transition is initiated when the dehydration of the core has reached a critical value during heating.

PMEA 100 -b-PDMAc 400 -b-PMEA 100

Step Time (min)

Conclusion

PMEAx-b-PDMAc400-b-PMEAx triblock copolymers form in aqueous solution small micelles at low concentrations and transient hydrogels above a critical percolation concentration.

Unexpectedly, an abrupt reorganization of the transient networks was observed above a critical temperature, Tc. The reorganization was characterized by an abrupt decrease of G' and G'' shortly after reaching Tc, followed by their recovery after a few minutes. This phenomenon was caused by a large fraction of elastically active chains becoming transiently very dynamic. The transition might be initiated by dehydration during heating, but further investigation is required to understand the origin of the process on a molecular level. From a more practical point of view, this unprecedented reorganization phenomenon causes strong variations of the elastic modulus and relaxation time of the network, which are not reproducible and most often irreversible even upon application of a strong shear to rejuvenate the network. This critical temperature decreases with increasing PMEA block length.

Below Tc, the behavior of the transient network is perfectly reproducible and the exchange time of the PMEA blocks between micellar cores could be determined by rheology. As expected, the exchange time increases for longer PMEA blocks, because the latter are less mobile and more hydrophobic. More originally, the exchange time increases strongly with increasing temperature, which is opposite to the classical arrhenian behavior and means that the activation energy increases with increasing temperature. A key result is that the variation of the exchange time with T is progressive (rather than abrupt as for PNIPAM which exhibits a critical sol-gel transition at its LCST), allowing fine-tuning of the rheological properties of the network with T. These results are attributed to the gradual dehydration of the thermo-sensitive PMEA-block with increasing temperature.

These findings are not only relevant to design thermo-thickening hydrogels based on PMEA, but they may also shed light on applications where PMEA is used, notably the design of bloodcompatible hydrogels or the synthesis of self-assembled particles consisting of a PMEA core by Polymerization Induced Self-Assembly.

10 5 𝑐𝑚 - 1

 51 defined as 𝑞 =

Scheme 1 .

 1 Scheme 1. Synthesis route for the PMEAx-b-PDMAc400-b-PMEAx triblock copolymers obtained

For x = 50 ,Figure 1 . 2 . 2 .Figure 2 .

 501222 Figures 1a)and b) present the evolution of the aggregation number Nagg (extracted from Mw, see

Figure 3

 3 Figure 3. a) Ge/Ge_ideal as a function of the polymer concentration (g/L) at different temperatures

Figure 4

 4 Figure 4. a) Cp in mol/L and b) Cp in g/L as a function of temperature (°C) determined for the three

Figure 5 .

 5 Figure 5. Relaxation time (s) as a function of temperature (°C), for the three triblock copolymers,

Figure 6

 6 Figure 6. a) Relaxation time (s) as function of temperature (°C); b) elastic modulus (Pa) as function

Figure 7 .

 7 Figure 7. Time dependence of the storage (opened symbols) and loss moduli (filled symbols) while

  S15 and S16). The amplitude of the variation of G' and G'' during restructuration of the network increases with increasing C (Figure8), whereas Tc decreases with increasing x. Tc was found to be between 40-50°C for x = 50, 30-40°C for x = 100 and 12-15°C for x = 200 (see details in SI, section 2.3.).

Figure 8 .

 8 Figure 8. Time dependence of the storage (filled symbols) and loss moduli (opened symbols) while

Figure 9 .

 9 Figure 9. Time dependence of the elastic modulus (Pa) while heating above Tc (10 to 50°C) at

and 3.10 -4 mol/L for x =

[START_REF] Tsitsilianis | Thermoresponsive Hydrogels Based on Telechelic Polyelectrolytes: From Dynamic to "Frozen" Networks[END_REF], 100 and 200 respectively). The evolution of Cp with T and x therefore does not seem to be related to the extent of aggregation of the micelles, as was already reported for other BAB triblock copolymers[START_REF] Charbonneau | Controlling the Dynamics of Self-Assembled Triblock Copolymer Networks via the pH[END_REF] .

ACKNOWLEDGMENT

This work has been funded by the Agence Nationale de la Recherche in the framework of the DYNAMIC-PISA ANR project (ANR-19-CE06-0002-01). The authors thank François Stoffelbach for his scientific support and help, Lazhar Benyahia and Cyrille Dechance for their help and support for the rheological measurements.

Funding Sources

This work has been funded by the Agence Nationale de la Recherche in the framework of the DYNAMIC-PISA ANR project (ANR-19-CE06-0002-01).

ASSOCIATED CONTENT

Supporting Information.

This material is available free of charge via the Internet at http://pubs.acs.org.

1. Synthesis of the PMEAx-b-PDMAc400-b-PMEAx triblock copolymers; 2. Additional characterizations of the self-assembly in aqueous medium.

AUTHOR INFORMATION

Corresponding Author

*E-mail: olivier.colombani@univ-lemans.fr

Notes

The authors declare no competing financial interest.


Muhammed P U Haris

Jianxing Xia

Samrana Kazim

Zuzanna Molenda

Lionel Hirsch

Thierry Buffeteau

Dario M Bassani

Mohammad Khaja Nazeeruddin

Shahzada Ahmad
email: shahzada.ahmad@bcmaterials.net

Probing proton diffusion as a guide to environmental stability in powder-engineered FAPbI3 and CsFAPbI3 perovskites

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

INTRODUCTION

In the emerging solar cells category, a monumental research focus has been given to the field of perovskite solar cells (PSCs) in the last decade. [START_REF] Kim | Lead Iodide Perovskite Sensitized All-Solid-State Submicron Thin Film Mesoscopic Solar Cell with Efficiency Exceeding 9%[END_REF] The first reported methylammonium lead triiodide (MAPbI 3 ) based PSCs showed competitive results, which was followed by compositional engineering of the perovskites to harvest more solar energy, in terms of higher photo-current and open-circuit voltage engineering through the materials composition variation. [START_REF] Pellet | Mixed-Organic-Cation Perovskite Photovoltaics for Enhanced Solar-Light Harvesting[END_REF] However, the concern of volatility of methylammonium (MA) in the former, and phase segregation in the latter, led to the renaissance of formamidinium lead triiodide (FAPbI 3 ) for solar cell fabrication. [START_REF] Koh | Formamidinium-Containing Metal-Halide: An Alternative Material for Near-IR Absorption Perovskite Solar Cells[END_REF][START_REF] Juarez-Perez | Degradation Mechanism and Relative Stability of Methylammonium Halide Based Perovskites Analyzed on the Basis of Acid-Base Theory[END_REF][START_REF] Zheng | Unraveling the Water Degradation Mechanism of CH 3 NH 3 PbI 3[END_REF] Among other merits, such as favorable lower bandgap for improved light harvesting, long-term thermal stability due to the higher activation energy for thermal degradation, and improved bulk stability due to the self-healing property of formamidinium ion, [START_REF] Ceratti | The pursuit of stability in halide perovskites: the monovalent cation and the key for surface and bulk self-healing[END_REF] their switching of photo-active (α-phase) to photoinactive (δ-phase, yellow) phase compromises reliability issues under operational conditions. [START_REF] Binek | Stabilization of the Trigonal High-Temperature Phase of Formamidinium Lead Iodide[END_REF] The phase transition to the thermodynamically stable δ-phase is initiated through the lattice strain relaxation and further accelerated by diverse environmental forces. [START_REF] Moloney | Strain Engineering in Halide Perovskites[END_REF] To overcome such grievances, various strategies such as compositional, [START_REF] Jena | Halide Perovskite Photovoltaics: Background, Status, and Future Prospects[END_REF][START_REF] Wang | Over 24% efficient MA-free CsxFA1-xPbX3 perovskite solar cells[END_REF] additive, [START_REF] Liu | A Review on Additives for Halide Perovskite Solar Cells[END_REF] dimensionalities, [START_REF] Kim | A review on two-dimensional (2D) and 2D-3D multidimensional perovskite solar cells: Perovskites structures, stability, and photovoltaic performances[END_REF] passivation [START_REF] Kim | Review of Novel Passivation Techniques for Efficient and Stable Perovskite Solar Cells[END_REF] and process engineering, [START_REF] Haris | Low-Temperature-Processed Perovskite Solar Cells Fabricated from Presynthesized CsFAPbI 3 Powder[END_REF][START_REF] Sánchez | Thermally controlled growth of photoactive FAPbI 3 films for highly stable perovskite solar cells[END_REF][START_REF] Li | Sequential vacuum-evaporated perovskite solar cells with more than 24% efficiency[END_REF] have been adopted by the research community, to deliver significant advancements in terms of power conversion efficiencies (PCE) and phase stability for FAPbI 3 -based PSCs. The engineering of composition, in particular, the multi-cation combination (MA, Cs + , and Rb + with FA) with different halide anions emerged as a path to fabricate efficient PSCs. Recent investigations at the localized level (nanostructure) revealed that the triple cation perovskites show a tilted octahedral formation which boosted the phase stability. However, further studies suggested that phase stability is restricted only to the macroscopic level and the inhomogeneously-tilted octahedra accelerate the phase segregation followed by the creation of deep traps and photo-generation pathways. [START_REF] Doherty | Stabilized tilted-octahedra halide perovskites inhibit local formation of performance-limiting phases[END_REF] Owing to the substantial advancement made in MAPbI 3 based PSCs, rational choice of additives and passivation successfully addressed the phase instability issue, and the PCE skyrocketed through strain engineering. Methylene diammonium dichloride has been introduced as an additive and their employment along with smaller Cs + mitigated the lattice strain and achieved higher efficiency of 24.4% and the PSCs maintained >80% of their initial PCE after 1300 h in the dark at 85 °C. [START_REF] Kim | Impact of strain relaxation on performance of α-formamidinium lead iodide perovskite solar cells[END_REF] In addition to the high PCEs, reliability is critical for PSCs to enter the commercialization endeavor of PSCs, while the PV market relies broadly on operational costs. Moisture or humidity is the main factor for degradation while other environmental scenarios such as heat, light, and combinations of factors alleviate this. [START_REF] Boyd | Understanding Degradation Mechanisms and Improving Stability of Perovskite Photovoltaics[END_REF][START_REF] Holzhey | A full overview of international standards assessing the long-term stability of perovskite solar cells[END_REF][START_REF] Haris | Substance and shadow of formamidinium lead triiodide based solar cells[END_REF][START_REF] Zhang | Degradation pathways in perovskite solar cells and how to meet international standards[END_REF][START_REF] Ho | Grain Transformation and Degradation Mechanism of Formamidinium and Cesium Lead Iodide Perovskite under Humidity and Light[END_REF] Moisture-induced degradation accelerates intrinsic instability. With the herald, building abound FAPbI 3 as a material of choice, a direct, rapid, and reliable approach is paramount to investigating and developing fast and efficient screening of materials. Water ingress into the perovskite layer may proceed through i) mono-, di-hydrate formations, ii) strong waterorganic amine interaction induced degradation through the weakening of cation-PbI 6 interaction, and iii) protonation of iodide to form hydroiodic acid leaving PbI 2 behind as the final decomposition product. [START_REF] Boyd | Understanding Degradation Mechanisms and Improving Stability of Perovskite Photovoltaics[END_REF] Understanding the reaction kinetics and mechanistic origin are pivotal to designing robust perovskite-based absorbers. Ion diffusion into the perovskite grains occurred as a result of ion migration at grain boundaries and in the bulk, this negatively affects the overall device performance. [START_REF] Walsh | Taking Control of Ion Transport in Halide Perovskite Solar Cells[END_REF][START_REF] Yang | Enhancing Ion Migration in Grain Boundaries of Hybrid Organic-Inorganic Perovskites by Chlorine[END_REF] Quantifying experimental approaches to monitor water uptake will be beneficial, although current techniques such as TOF-SIMS [START_REF] Harvey | Probing Perovskite Inhomogeneity beyond the Surface: TOF-SIMS Analysis of Halide Perovskite Photovoltaic Devices[END_REF] do not apply to hydrogen species (H + , H 0 , and H -1 ), it can be studied by neutron scattering experiments. [START_REF] Braun | Experimental neutron scattering evidence for proton polaron in hydrated metal oxide proton conductors[END_REF] However, this requires access to large-scale radiation facilities and planning. The development of experimental techniques for tracking the migration of hydrogen species is of significance to deciphering the stability of designed materials.

One such technique is polarization-modulated infrared reflection-absorption spectroscopy (PM-IRRAS), [START_REF] Sadhu | Observing the Migration of Hydrogen Species in Hybrid Perovskite Materials through D/H Isotope Exchange[END_REF] which can track the migration of hydrogen species in MAPbI 3 by registering the difference in the vibrational frequency of X-H vs X-D bonds during isotope exchange processes, where X is a heavier element such as carbon, oxygen, or nitrogen. [START_REF] Sadhu | Observing the Migration of Hydrogen Species in Hybrid Perovskite Materials through D/H Isotope Exchange[END_REF] Alternatively, the H / D composition of the material can also be determined using NMR spectroscopy after the dissolution of the material. [START_REF] Ceratti | Eppur si Muove: Proton Diffusion in Halide Perovskite Single Crystals[END_REF] As an extension of this work, we employ transmission infrared (IR) spectroscopy using a sealed cell to follow the isotope exchange under controlled conditions. We show that this is a particularly suitable technique as it allows direct probing of local environmental effects, such as relative humidity, on the migration of hydrogen species. Additionally, we have opted for powder-engineered perovskites as the choice of material owing to i) achieving the highest PCEs and reproducibility over their conventional counterpart, [START_REF] Zhang | CH3 NH3 PbI3 and HC(NH2 )2 PbI3 Powders Synthesized from Low-Grade PbI2 : Single Precursor for High-Efficiency Perovskite Solar Cells[END_REF][START_REF] Jeong | Pseudo-halide anion engineering for α-FAPbI 3 perovskite solar cells[END_REF][START_REF] Haris | Microstrain and Urbach Energy Relaxation in FAPbI 3 -Based Solar Cells through Powder Engineering and Perfluoroalkyl Phosphate Ionic Liquid Additives[END_REF] ii) reduction in the microstrain and Urbach energy values for perovskite layers fabricated from the powder engineering process, indicating mitigated structural and electronic disorders. [START_REF] Haris | Microstrain and Urbach Energy Relaxation in FAPbI 3 -Based Solar Cells through Powder Engineering and Perfluoroalkyl Phosphate Ionic Liquid Additives[END_REF] Additionally, the powder methodology, would overcome the Pb impurities issue from the Pb precursors and elimnate the error in the weighing of the precursors. The indirect assessment of the protection against moisture induced by surface modification of the powderengineered α-FAPbI 3 and α-CsFAPbI 3 can be obtained by simply monitoring the rate of hydrogen exchange within the active layer in the presence of ambient moisture. This knowledge can be used to predict the material´s propensity towards moisture-induced defect formation. Optimization of such process and materials design rule will suppress the non-radiative recombination of photo-generated charge carriers, paving way for higher fill factor and the V OC in PSCs. With this in hand, we further improve the performance of powder-engineered PSCs with promising fluorinated ionic liquids as an additive.

RESULTS AND DISCUSSION

Preparation and characterization of thin films

Hereafter we use the term ῾FAPbI 3 from -powder' and ῾FAPbI 3 from α-powder' for FAPbI 3 thin films fabricated from the pre-synthesized -phase and α-phase powders respectively. The synthesis of -phase and α-phase powders are detailed in the experimental section, briefly -phase powder was precipitated by stirring lead iodide (PbI 2 ) with the formamidinium iodide containing acetonitrile solution at room temperature. The α-FAPbI 3 powder was realized by annealing the -phase powder at 150 °C. Thin films of the perovskites were prepared by spin-coating precursor solutions onto a 2 mm thick BaF 2 disk (20 mm diameter). Upon annealing to 150 °C for 30 min, both FAPbI 3 , ie FAPbI 3 from -, and α-powders, gave dark brown films with identical UV-vis spectra. Scanning probe microscopy (SPM) images (Fig. S1) were collected on each sample to determine grain size.

Proton diffusion studies

The samples were placed in a home-built spectroscopic cell that hermetically seals the BaF 2 substrate inside a controlled environment. After measuring the transmission IR spectrum at t = 0, a saturated solution of K 2 CO 3 in D 2 O is injected into the cell to maintain the relative humidity fixed at 43%. Successive IR spectra are then taken to determine the proportion of H / D exchange taking place in the material over time.

The spectral variation during the H / D exchange for the FAPbI 3 from the α-powder sample is shown in Figure 1A in the 1850-1250 cm -1 region. At t=0, the IR spectrum exhibits three main bands at 1712, 1613, and 1352 cm -1 , with strong, weak, and medium intensities, respectively. The 1712 and 1352 cm -1 bands are coupled modes involving CN, NH 2, and CH vibrations; the 1712 cm -1 mode is dominated by the CN (50%) and NH 2 (40%) components whereas the 1352 cm -1 mode is dominated by the CH (72%) component. The 1613 cm -1 mode is pure NH 2 vibration. [START_REF] Kucharska | Vibrational properties and DFT calculations of formamidine-templated Co and Fe formates[END_REF] Upon D 2 O exposition, the 1712 and 1352 cm -1 bands decreased in favor of the increase of the 1681 and 1336 cm -1 bands, respectively, whereas the decrease of the NH 2 band at 1613 cm -1 mode is associated with the increase of the ND 2 band at 1393 cm -1 (Figure 1A). It is important to note that only the H in the NH 2 fragment will exchange with D 2 O. The H / D exchange for the -FAPbI 3 sample can be followed by either the spectral variation of the pure NH 2 mode or by the sum of the spectral variation of the two bands related to the coupled modes involving CN, NH 2, and CH vibrations.

Both were found to give identical kinetic profiles but, due to the weaker intensity of the NH 2 mode, the spectral vibration of the coupled modes of CN and CH were selected.

The variations in the spectral data are related to the exchange of the labile N-H protons in FAPbI 3 by deuterium, which causes a shift of the vibration to lower frequencies due to its higher mass. This is a complex process that we can decompose into 3 steps: (i) dissociation of D 2 O on the surface of the substrate, (ii) diffusion of D + into the sample, and (iii) H / D substitution in the formamidinium cation. Both the dissociation of D 2 O and isotopic substitution are expected to be fast with respect to ion diffusion in the solid, which should therefore be rate-limiting. The diffusion of a species in a solid follows Fink's law stating that the rate of diffusion of a species is proportional to the concentration gradient of that species. The exact solutions of Fink's law depend on the experimental conditions. For the diffusion in nano-crystalline perovskite thin films, we have evidenced that highdiffusivity pathways between grains are important in determining the diffusion rate. Indeed, the measured diffusion rates are relatively insensitive to sample thickness in agreement with a model in which diffusion occurs rapidly around the grains, and more slowly inside. [START_REF] Buffeteau | Comment on "Eppur si Muove: Proton Diffusion in Halide Perovskite Single Crystals": Eppur Non si Muove: A Critical Evaluation of Proton Diffusion in Halide Perovskite Single Crystals[END_REF] The individual grains can be modeled as spheres of radius R, and the bulk sample's H / D exchange is obtained by integrating over the thickness of the sample (eq 1):

(1)

Where m(t) is the fraction of total deuterium present at time t, M is the intensity of the signal for the deuterated species present, D is the diffusion constant, and R is the radius of the sphere approximating the grain size or lattice domain.

As mentioned above, the vibrations of the N-H(D) and C-H are strongly coupled. Because of this, it is not possible to individually discriminate between the partially deuterated species as is the case for MAPbI 3 , where the sequential transformation of CH 3 NH 3 + → CH 3 NH 2 D + → CH 3 NHD 2 + → CH 3 ND 3 + can be resolved. Furthermore, the contribution of the C-H vibrators (which do not undergo isotope exchange) should be deducted from the overall signals to obtain exclusively the changes resulting from the N-H to N-D exchange. To simplify this, we identified the vibration at vibrations at 1712 cm -1 , 1681 cm -1 , 1352 cm -1 , and 1336 cm-1 to be exclusively (or nearly so) due to N-H / D vibrators. For these bands, the loss of the N-H contribution (at 1712 cm -1 and 1352 cm -1 ) is fully compensated by the grow-in of the N-D species (at 1681 cm -1 and 1336 cm -1 ) as shown in Figure 1B, C) as shown in Figure 2A. From this, it is possible to verify that the loss of H can be precisely quantified from the sum of the intensities of the vibrations at 1712 cm -1 and 1352 cm -1 . The data may then be fitted to eq(1) using a value of R corresponding to the average grain size (Table 1)

determined by SPM and surface SEM images for each sample (Figure S1).

The results for the analysis of the diffusion of D + into thin films of FAPbI 3 or CsFAPbI 3 exposed to D 2 O are summarized in Table 1. The diffusion constants were determined using the corresponding average grain size for each sample as derived from the analysis of the AFM and SEM images (Figure S1). Overall, the diffusion coefficients are smaller than that previously determined for APbI 3 (D = 1.5 × 10 -15 s.cm -2 ). As expected, FAPbI 3 films prepared from either α-powder or -powder gave nearly identical results, in agreement with the observation that the nature of the precursor material does not affect the properties of the post-annealed active layer. It can also be seen that the rate of diffusion of protons into CsFAPbI 3 from α-powder is only one-fifth that of FAPbI 3 . Interestingly, the proton diffusion rate constants are greatest for MAPbI 3 and the smallest for CsFAPbI 3 , with MAPbI 3 > FAPbI 3 > CsFAPbI 3 . This is also the same order that is generally observed for the propensity towards damage by ambient moisture in halide perovskite materials, and we may speculate that the propensity of lead halide perovskite materials towards damage by moisture is related to the proton diffusion rate for the material. A similar observation was earlier made from the comparison of MAPI active layers in the absence of different adlayers capable of reducing moisture degradation. In this case, the rate of isotope substitution was found to be slowest for those adlayers offering the greatest protection. [START_REF] Sadhu | Observing the Migration of Hydrogen Species in Hybrid Perovskite Materials through D/H Isotope Exchange[END_REF] We also note that the fit of the experimental data for the CsFAPbI 3 from the α-powder sample shows some deviation from eq(1) which may reflect intra-grain inhomogeneity due to the partial substitution of FA by Cs + .

Though reports appear to suggest a performance enhancement in powder-engineered FAPbI 3

PSCs, [START_REF] Haris | Low-Temperature-Processed Perovskite Solar Cells Fabricated from Presynthesized CsFAPbI 3 Powder[END_REF][START_REF] Zhang | CH3 NH3 PbI3 and HC(NH2 )2 PbI3 Powders Synthesized from Low-Grade PbI2 : Single Precursor for High-Efficiency Perovskite Solar Cells[END_REF][START_REF] Jeong | Pseudo-halide anion engineering for α-FAPbI 3 perovskite solar cells[END_REF][START_REF] Haris | Microstrain and Urbach Energy Relaxation in FAPbI 3 -Based Solar Cells through Powder Engineering and Perfluoroalkyl Phosphate Ionic Liquid Additives[END_REF] the reason for intrinsic stability remains undiscovered to an extent. While comparing the conventional and powder engineering methods, we speculate that the precursor solution step acts as a Y-junction in the perovskite fabrication process and their investigations are crucial. It has been suggested that the perovskite precursor solution is a low-viscous solution that comprises polyiodide plumbates which drive the nucleation and crystallization upon further spin coating and annealing. [START_REF] Jung | Perovskite precursor solution chemistry: from fundamentals to photovoltaic applications[END_REF] To unravel the different scenarios between conventional (c-FAPbI 3 ) and powder engineering (α-FAPbI 3 ) methods, we probed the corresponding FAPbI 3 precursor solutions using proton nuclear magnetic resonance spectroscopy. With the presence of PbI 2 , the protons attached to two nitrogen atoms showed fast resonances which lead to the peak broadening (Figure 3). A slight peak broadening of -CH protons was also visible in the powder method than in the conventional counterpart. Arguably, such observations are attributed to the difference in the local protonic environment in the precursor solution which in turn impacts the photo-physical properties of the corresponding perovskite thin films.

Fabrication and analysis of PSCs

The photovoltaic performances of the PSCs employing FAPbI 3 and CsFAPbI 3 from α-powders were probed in an FTO/c-TiO 2 /m-TiO 2 /SnO 2 /Perovskite/Spiro-OMeTAD/Au device structure (Figure 4A).

Expectedly, [START_REF] Lee | Formamidinium and Cesium Hybridization for Photo-and Moisture-Stable Perovskite Solar Cell[END_REF][START_REF] Salado | The role of Cs+ inclusion in formamidinium lead triiodide-based perovskite solar cell[END_REF] the CsFAPbI 3 based PSCs exhibit a higher PCE of 19.2% as compared to 18.8% for FAPbI 3 based PSCs, and the steady-state efficiency of 19.14% (Figure 4B,C) is measured for CsFAPbI 3 .

To suppress the inhibition of ionic migration and a further improvement in the performance of PSCs, we adopted doping by ionic liquids, this will also reduce the ionic migration within the CsFAPbI 3 perovskite thin-film. We employed, the 1,3-bis(cyanomethyl)imidazolium bis(trifluoromethylsulfonyl)imide (IL) [START_REF] Gao | Engineering long-term stability into perovskite solar cells via application of a multi-functional TFSI-based ionic liquid[END_REF] as an additive into perovskite. The ionic liquid additivisation improved the crystallization of the perovskite layer and yielded an improvement in the thickness from 530 nm to 580 nm (Figure S2) as a result of the controlled crystallization process. The improved crystallization of perovskite film may attribute to the changing of surface tension within the precursor and the coordination between ionic liquid and PbI 2 . [START_REF] Wang | Water-Soluble Triazolium Ionic-Liquid-Induced Surface Self-Assembly to Enhance the Stability and Efficiency of Perovskite Solar Cells[END_REF][START_REF] Wang | Ionic Liquid Stabilized Perovskite Solar Modules with Power Conversion Efficiency Exceeding 20%[END_REF] Figure 4D exhibits the J-V curves of PSCs based on various concentrations of IL doping. At the doping concentration of 0.7 mol%, the PCE of the PSCs improved to 20.55% (Table 2, Figure S3), while under similar conditions the reference CsFAPbI 3 -based PSCs measured 19.27% in the same batch. The steady-state efficiency of the devices was compared (Figure 4E), and the PSC doped with IL displayed 20.38% PCE after 130 s of continuous illumination, further we noted that the PCE is close to the value derived from the J-V curve, and under the similar condition the CsFAPbI 3 based PSCs measured a PCE of 19.13%. Furthermore, the integrated current density (J SC ) from the incident photon to current efficiency (IPCE) (Figure 4F) over the spectral range from 350 to 900 nm to measure the veracity of the J SC of the J-V curves. The integrated J SC of PSCs based on references and doped with IL respectively achieved 22.86 and 22.81 mA cm -2 which is close to the short-circuit current density (J SC ) value from the J-V curves with a slight loss of 7%. We attribute these slight variations to the difference in the light source of J-V and IPCE used.

We performed the Time-Resolved Photoluminescence (TRPL) measurements (Figure 4G) of pristine and IL-doped CsFAPbI 3 on a structure of glass/perovskite to deduce the carrier lifetime of perovskite film, as well as the decay times. The data are fitted by a mono-exponential model at a long decay regime with τ components which indicated recombination. [START_REF] Stolterfoht | Visualization and suppression of interfacial recombination for high-efficiency large-area pin perovskite solar cells[END_REF] On the additivisation of CsFAPbI 3 film with IL, the decay time (τ) of TRPL increased from 516.1 to 614 ns indicating the reduced recombination of photogenerated electrons and hole, which is attributed to the passivation of trap states by the ionic liquid. [START_REF] Gao | Engineering long-term stability into perovskite solar cells via application of a multi-functional TFSI-based ionic liquid[END_REF] To conclude, here we employed transmission IR spectroscopy and demonstrated the suitability in allowing the tracking of local environment scenarios against the humidity and made quantification of ion migration to unravel the material´s intrinsic properties for device improvement. We noted the proton diffusion rate constants follow the order of APbI 3 > FAPbI 3 > CsFAPbI 3, and are lowest for CsFAPbI 3 . The majority of techniques fall short to probe hydrogen species migration, our report reveals guidelines for deciphering the H + migration and diffusion coefficient to increase the photostability of perovskites. The incorporation of Cs not only pushes the performance but also significantly reduces the diffusion coefficient by five times in FAPbI 3 . The development of such a protocol is an effective and rapid means to screen the viability of the material for perovskite solar cells technology and assess the fundamental limit of the materials to understand the local environment for reliability in a range of emerging semiconductors. We modeled the rate of H/D exchange employing first-order kinetics to elucidate numerical parameters that can be directly correlated to probe the effectiveness of surface modification on environmental exposure.

Experimental procedures

Synthesis of FAPbI 3 α-phase powder

The δ-phase powder was annealed in a tube furnace at 150 °C for 1 hour in an inert atmosphere to obtain a black α-phase powder. This black powder was kept in the glove box for further use.

Synthesis of CsFAPbI 3 α-phase powder

Acetonitrile solution containing CsI and FAI in a 1:9 ratio was used in this case and the rest procedure is the same as the above for FAPbI 3 α-phase powder

Film and device fabrication

The chemically etched FTO glass was cleaned with a detergent solution, acetone, and ethanol. For

Material and thin-film characterizations

For the TRPL measurements, samples were excited with a 408-nm pulsed laser (MDL 300, PicoQuant) with 40 µm•cm -2 pulse energy density (pulse width 180 ps). a Determined using eq(1) according to the average grain size R obtained from AFM and SEM analysis of the samples.

  the compact TiO 2 (C-TiO 2 ) layer, TAA solution in ethanol (0.2 mL of TAA in 6 mL of anhydrous ethanol) was sprayed at 450 °C and heated for 1 h. The mesoporous TiO 2 (m-TiO 2 , 30-NRT) was diluted at ethanol with a ratio of 1:10 and coated on the C-TiO 2 substrate at a speed of 3000 rpm for 20 s with a ramp-up of 2000 rpm s -1 finally heating at 500 ℃ for 60 min. The SnCl 4 layer was dissolved in deionized water at a concentration of 12 μL/mL and spin-coating on the m-TiO 2 layer at a speed of 3000 rpm for 20 s with a ramp-up of 2000 rpm s -1 finally heating at 190 ℃ for 60 min, and then perovskite solutions were formulated by dissolving 1.4 M α-FAPbI 3 or CsFAPbI 3 powder in DMSO/DMF mixed solvent with a ratio of 1:8, 20 mg MACl was also added to the perovskite solution. In the additivated perovskites, the ionic liquid was added in varying concentrations of IL into the perovskite precursors. All the perovskite solutions were filtered through a PTFE filter with a 450 nm pore size. The perovskite layers are fabricated by spin-coating at 1000 rpm for 10 s and 5000 rpm for 30 s, respectively. Then, 200 µL of chlorobenzene was dropped in 10 s at 5000 rpm.Perovskite films were annealed at 150 °C for 15 min. The HTM solution was prepared by dissolving 75 mg of Spiro-OMeTAD (Merck) with additives in 1 mL of chlorobenzene and film fabricated by spin-coating at 4000 rpm for 30 s. As additives, 18 µL of Li-bis(trifluoromethanesulfonyl) imide from the stock solution (520 mg in 1 mL of acetonitrile), 13 µL of FK209 [tris(2-(1H-pyrazol-1-yl)-4-tert-butylpyridine)-cobalt(III) tris(bis (trifluoromethylsulfonyl)imide) (375 mg in 1 mL of acetonitrile), and 30 µL of 4-tert-butylpyridine were added. Finally, the deposition of the 70 nm thick Au electrode by thermal evaporation on the Spiro-OMeTAD.

  [START_REF] Kim | Lead Iodide Perovskite Sensitized All-Solid-State Submicron Thin Film Mesoscopic Solar Cell with Efficiency Exceeding 9%[END_REF] H-NMR spectra were recorded using a Varian Mercury 400 MHz spectrometer in DMSO-d6 solvent at 25 °C. The crosssectional and surface SEM images were acquired from a Hitachi S-4800 SEM machine. SPM images were acquired with the help of Autoprobe CP-Research microscope (VEECO) after the IR experiments. Transmission IR experiments were performed on a ThermoNicolet Nexus 670 FTIR spectrometer at a resolution of 4 cm -1 .Device characterizationsCurrent-voltage characteristics were recorded by applying an external potential bias to the cell while recording the generated photocurrent with a digital source meter (Keithley Model 2400). The light source was a 450 W xenon lamp (Oriel) equipped with a SchottK113 Tempax sunlight filter (Praezisions Glas & Optik GmbH) to match the emission spectrum of the lamp to the AM 1.5G standard. Before each measurement, the exact light intensity was determined using a calibrated Si reference diode equipped with an infrared cutoff filter (KG-3, Schott). The cells were masked with the active area of 0.09 cm 2 to fix the active area and reduce the influence of the scattered light on the small device. IPCE spectra were recorded as functions of wavelength under a constant white light bias of ≈10 mW•cm -2 supplied by an array of white light emitting diodes. The excitation beam coming from a 300 W xenon lamp (ILC Technology) was focused through a Gemini-180 double monochromator (Jobin Yvon Ltd) and chopped at ≈2 Hz. The signal was recorded using a Model SR830 DSP Lock-In Amplifier (Stanford Research Systems).

Figure 1 .

 1 Figure 1. Spectral variation during the H / D exchange (A) Evolution of the transmission IR spectra of a film (200µm thick) prepared from -FAPbI 3 exposed to 43% RH D 2 O (t = 0 to 100 h) and (B and C) Zoom of differential absorption spectra (Abs t -Abs t = 0 ). The presence of isosbestic points is visible in both the absolute (top) and differential (bottom) absorption spectra.

Figure 2 .

 2 Figure 2. Relative H/D composition (A) Relative hydrogen (blue symbols) and deuterium (red symbols) composition of thin films of FAPbI 3 exposed to D 2 O (RH = 43%) at room temperature determined from vibrations assigned to pure N-H or N-D modes. Solid black lines are the best fit for eq(1), (B) Comparison of the proportion of hydrogen present in thin films prepared from FAPbI 3 from αpowder (blue symbols), FAPbI 3 from -powder (green symbols), and CsFAPbI 3 (red symbols), as determined from the sum of the vibrations at 1712 cm -1 and 1352 cm -1 , exposed to D 2 O (RH = 43%) at room temperature. Solid black lines are the best fit for eq(1).

Figure 3 . 1 H

 31 Figure 3. 1 H-NMR characterization of precursor solutions (A) Solution 1 H-NMR spectra of FAI, conventional-FAPbI 3 and α-FAPbI 3 in DMSO-D 6 solvent at 25°C , the FA cation structure has been given in the inset; (B and C) Zoom-in view of Solution 1 H-NMR spectra of, (B) -NH 2 protons and, (C) -CH protons in all the three solutions.

Figure 4 .

 4 Figure 4. Scheme, and electro-optical analysis of perovskites and solar cells

Table 2 . Photovoltaic parameters of the devices based on pristine FAPbI 3, CsFAPbI 3, and IL doped CsFAPbI 3 based solar cells.

 2

	Perovskites		J SC (mA cm -2 )	V OC (mV)	FF (%)	PCE (%)
	FAPbI 3	Max	24.22	1022	76.2	18.85
		Average	23.51±0.71	993±29	74.5±1.7	17.40±1.45
	CsFAPbI 3	Max	24.38	1036	76.3	19.27
		Average	23.78±0.6	1011±25	74.4±1.9	17.90±1.37
	CsFAPbI 3 +IL 0.5 %	Max	24.36	1054	77.2	19.82
		Average	23.80±0.56	1004±50	75.2±2	18.00±1.82
	CsFAPbI 3 + IL 0.7 %	Max	24.36	1072	78.7	20.55
		Average	23.43±0.93	1036±36	76.9±2.1	18.63±1.92
	CsFAPbI 3 + IL 1 %	Max	24.40	1043	76.8	19.54
		Average	23.78±0.62	1015±28	75.7±1.1	18.16±1.38

Table 3 . Fitting parameters of mono-exponential decay function in TRPL measurements of CsFAPbI 3 perovskite in pristine form and with 0.7 mol% IL doping.

 3

	Film	τ (ns)
	Glass/CsFAPbI 3	516.1
	Glass/ CsFAPbI 3 + 0.7 %	614

ACKNOWLEDGMENTS

This work received funding from the European Union H2020 Programme under a European Research Council Consolidator grant [MOLEMAT, 726360]. Support from the Spanish Ministry of Science and Innovation (PID2019-111774RB-100/AEI/10.13039/501100011033 and INTERACTION {PID2021-129085OB-I00}) and the French ANR (ANR-18-CE05-0021) is also acknowledged. The authors are grateful to Mr. Julien Hunel for assistance with the SPM instrumentation.

Resource availability

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Shahzada Ahmad (shahzada.ahamad@bcmaterials.net).

Materials availability

This study did not generate new unique materials.

Data and code availability

This study did not generate datasets.

Chemical materials

Titanium diisopropoxide bis(acetylacetonate) (TAA), 4-tert-butylpyridine (tbp), tin(IV) chloride pentahydrate, bis(trifluoromethane) sulfonamide lithium salt, and [tris(2-(1H-pyrazol-1-yl)-4-tertbutylpyridine)-cobalt(III) tris(bis(trifluoromethylsulfonyl)imide)] (FK209), chlorobenzene (CB), dimethylsulphoxide (DMSO), dimethylformamide (DMF), methylammonium hydrochloride (MACl) were supplied from Sigma-Aldrich. lead iodide (PbI 2 ) and cesium iodide (CsI) was purchased from TCI. 2,2ʹ,7,7ʹ-Tetrakis(N, N-di-4-methoxyphenylamine)-9,9ʹ-spirobifluorene (spiro-OMeTAD) was purchased from Merck. 30-NRT was purchased from GreatCell. All of the purchased chemicals were used as received without further purification.

Synthesis of FAPbI 3 δ-phase powder

The δ-phase powder was synthesized by using the room temperature precipitation method. The 10.7 mmol FAI (synthesized from formamidine acetate 1 ) was dissolved in 100 ml of acetonitrile (HPLC grade, Alfa Aesar) by stirring, then 8.3 mmol of PbI 2 (99%) was added to the stirring solution and allowed the stirring to continue for 24 hours. The derived yellow powders were filtered and washed thoroughly (5-6 times) with acetonitrile and finally with diethyl ether to remove any residual PbI 2 and FAI. The yellow product was then dried under a continuous vacuum for another 24

DECLARATION OF INTERESTS

The authors declare no competing interests.