Aaliyah Z Dookhith

Nathaniel A Lynd

Costantino Creton

Gabriel E Sanoja

Controlling Architecture and Mechanical Properties of Polyether Networks with Organo-aluminum Catalysts

Soft materials can sustain large, elastic, and reversible deformations; finding widespread use as elastomers and hydrogels. These materials constitute 3-D polymer networks and are typically synthesized by cross-linking polymer chains or copolymerizing monomer and cross-linker.

Seminal investigations have enabled control over the network architecture by cross-linking chains of poly(dimethyl siloxane), poly(1,4-butadiene), or tetra-poly(ethylene glycol); but as soft materials become attractive for robotics, electronics and prosthetics, co-designing the network architecture, mechanical, and functional properties has become pressing. We investigate the relationship between reaction pathway, network architecture, and mechanical properties in poly(ethyl glycidyl ether) networks synthesized by epoxide ring opening polymerization with two organo-aluminum catalysts. The key result is that uncontrolled polymerizations yield loosely cross-linked, entangled, soft, and extensible networks; whereas more controlled polymerizations, instead, lead to highly cross-linked, stiff, and brittle networks. Such catalytic control over network architecture and mechanical properties could enable design of novel soft, tough, and functional materials.

INTRODUCTION

Soft materials form an integral part of society as engineering elastomers and biomedical hydrogels due to their ability to sustain large, elastic, and reversible deformations. These materials have been of major interest since the discovery of rubber vulcanization in the 19 th century, with numerous investigations focused on understanding the relationship between molecular structure and mechanical properties in elastomers like natural rubber, styrenebutadiene rubber, and filled rubber. [START_REF] Gent | Engineering with Rubber[END_REF] However, as soft materials find use in emerging applications like robotics, 2 electronics, [START_REF] Rogers | Materials and Mechanics for Stretchable Electronics[END_REF] and prosthetics, [START_REF] Minev | Electronic Dura Mater for Long-Term Multimodal Neural Interfaces[END_REF] challenges in attaining satisfactory mechanical and functional properties have spurred renewed interest in understanding their structure-property relationships. [START_REF] Creton | Fracture and Adhesion of Soft Materials: A Review[END_REF][START_REF] Creton | 50th Anniversary Perspective: Networks and Gels: Soft but Dynamic and Tough[END_REF][START_REF] Long | The Fracture of Highly Deformable Soft Materials: A Tale of Two Length Scales[END_REF][START_REF] Danielsen | Molecular Characterization of Polymer Networks[END_REF] Soft materials are constituted of polymer networks, 3-D arrangements of polymer chains interconnected through crosslinking points. Solids at the macroscopic scale, these materials have liquid-like segmental dynamics, and exhibit functional and mechanical properties dictated by the monomer-cross-linker chemistry and network architecture. Long-established molecular models on properties like elasticity, swelling, and fracture depict the network architecture as homogeneous; when in reality it is heterogeneous, [START_REF] Bastide | Large-Scale Heterogeneities in Randomly Cross-Linked Networks[END_REF] ill-defined, and pervaded by topological defects like dangling chains and loops. However, how these defects are formed during network synthesis remains abstract.

Polymer networks are typically synthesized by cross-linking polymer chains or copolymerizing monomer and cross-linker. Early investigations focused on controlling the network architecture by cross-linking poly(dimethyl siloxane) chains of narrow dispersity and welldefined molecular weight. The resulting materials enabled a better molecular understanding of mechanical properties like elasticity [START_REF] Mark | Model Networks of End-linked Polydimethylsiloxane Chains. I. Comparisons between Experimental and Theoretical Values of the Elastic Modulus and the Equilibrium Degree of Swelling[END_REF][START_REF] Gottlieb | Equilibrium Modulus of Model Poly(Dimethylsiloxane) Networks[END_REF][START_REF] Yoo | Effect of Network Structure on the Stress-Strain Behaviour of Endlinked PDMS Elastomers[END_REF] and fracture, [START_REF] Llorente | Model Networks of End-Linked Polydimethylsiloxane Chains -11. Use of Very Short Network Chains To Improve Ultimate Properties[END_REF][START_REF] Genesky | Toughness and Fracture Energy of PDMS Bimodal and Trimodal Networks with Widely Separated Precursor Molar Masses[END_REF] but their architectures proved to be heterogeneous based on small-angle scattering [START_REF] Mallam | Microscopic and Macroscopic Thermodynamic Observations in Swollen Poly(Dimethylsiloxane) Networks[END_REF][START_REF] Mendes | Small-Angle Neutron Scattering Study of End-Linked Gels[END_REF][START_REF] Seiffert | Scattering Perspectives on Nanostructural Inhomogeneity in Polymer Network Gels[END_REF] . Networks of poly(butadiene), [START_REF] Taylor | Rubber Networks Containing Unattached Macromolecules. VI. Stress Relaxation in End-Linked Polybutadiene with Unattached Linear Polybutadiene[END_REF][START_REF] Stadler | Linear Viscoelastic Rheology of Moderately Entangled Telechelic Polybutadiene Temporary Networks[END_REF] poly(urethane), [START_REF] Cristiano | An Experimental Investigation of Fracture by Cavitation of Model Elastomeric Networks[END_REF][START_REF] Cristiano | Fracture of Model Polyurethane Elastomeric Networks[END_REF] and poly(ethylene glycol) [START_REF] Sakai | Design and Fabrication of a High-Strength Hydrogel with Ideally Homogeneous Network Structure from Tetrahedron-like Macromonomers[END_REF] have been synthesized using a similar strategy, with the latter ones being the most homogeneous [START_REF] Matsunaga | Structure Characterization of Tetra-PEG Gel by Small-Angle Neutron Scattering[END_REF] and also affording refinement of molecular models on elasticity, [START_REF] Zhong | Quantifying the Impact of Molecular Defects on Polymer Network Elasticity[END_REF] swelling, [START_REF] Rebello | Adding the Effect of Topological Defects to the Flory-Rehner and Bray-Merrill Swelling Theories[END_REF] and fracture. [START_REF] Arora | Fracture of Polymer Networks Containing Topological Defects[END_REF] However, synthesizing polymer networks by cross-linking polymer chains requires multiple steps including, at the very least, the synthesis of polymer chains and post-cross-linking in the bulk or concentrated solution. As a result, this strategy can be time-intensive when co-designing the functional and mechanical properties of polymer networks by varying, for example, the chain composition.

Another strategy to synthesize polymer networks, instead, is to co-polymerize monomer and cross-linker, with tunability of the functional and mechanical properties afforded by the monomer-cross-linker reactivity, initiator efficiency, solvent quality, reaction temperature, and concentration. [START_REF] Anseth | Kinetic Gelation Model Predictions of Crosslinked Polymer Network Microstructure[END_REF][START_REF] Anseth | Mechanical Properties of Hydrogels and Their Experimental Determination[END_REF][START_REF] Elliott | Kinetics of Primary Cyclization Reactions in Cross-Linked Polymers: An Analytical and Numerical Approach to Heterogeneity in Network Formation[END_REF] The simplicity of this reaction makes it ubiquitous in academic and industrial laboratories. However, the lack of architectural control, relative to the synthesis of polymer networks by cross-linking polymer chains, limits its potential for molecular design. Controlled radical polymerizations like NMP, [START_REF] Ide | Nitroxide-Controlled Free-Radical Copolymerization of Vinyl and Divinyl Monomers. Evaluation of Pendant-Vinyl Reactivity[END_REF][START_REF] Ide | Nitroxide-Controlled Free-Radical Copolymerization of Vinyl and Divinyl Monomers. 2. Gelation[END_REF] ATRP, [START_REF] Bannister | Development of Branching in Living Radical Copolymerization of Vinyl and Divinyl Monomers[END_REF][START_REF] Gao | Effect of Cross-Linker Reactivity on Experimental Gel Points during ATRcP of Monomer and Cross-Linker[END_REF][START_REF] Gao | Synthesis of Polyacrylate Networks by ATRP: Parameters Influencing Experimental Gel Points[END_REF] and RAFT [START_REF] Liu | One-Pot Hyperbranched Polymer Synthesis Mediated by Reversible Addition Fragmentation Chain Transfer (RAFT) Polymerization[END_REF][START_REF] Vo | RAFT Synthesis of Branched Acrylic Copolymers[END_REF] have been used to synthesize polymer networks, and the recent review of Cuthbert et al. [START_REF] Cuthbert | STEM Gels by Controlled Radical Polymerization[END_REF] details post-synthetic strategies to functionalize latent active sites and spatio-temporally control material properties. These networks are presumably more homogeneous than analogues synthesized by free radical polymerization due to the reversible activation and deactivation of polymer chain ends during monomer and crosslinker co-polymerization, exhibiting delayed gelation and higher percolation thresholds. [START_REF] Ide | Nitroxide-Controlled Free-Radical Copolymerization of Vinyl and Divinyl Monomers. Evaluation of Pendant-Vinyl Reactivity[END_REF][START_REF] Ide | Nitroxide-Controlled Free-Radical Copolymerization of Vinyl and Divinyl Monomers. 2. Gelation[END_REF][START_REF] Gao | Effect of Cross-Linker Reactivity on Experimental Gel Points during ATRcP of Monomer and Cross-Linker[END_REF][START_REF] Gao | Synthesis of Functional Polymers with Controlled Architecture by CRP of Monomers in the Presence of Cross-Linkers: From Stars to Gels[END_REF] Yet, how such control over the network architecture ultimately affects the mechanical properties, particularly at large deformations, remains unknown.

Here, we restrict our scope to polyether networks; a class of materials widely used as polymer electrolytes, gas separation membranes, and artificial tissue scaffolds because of their oxygenrich backbone. [START_REF] Brocas | Polyether Synthesis: From Activated or Metal-Free Anionic Ring-Opening Polymerization of Epoxides to Functionalization[END_REF][START_REF] Klein | Aliphatic Polyethers: Classical Polymers for the 21st Century[END_REF][START_REF] Zhao | Designing Solid-State Electrolytes for Safe, Energy-Dense Batteries[END_REF] Polyethers result from the ring opening polymerization of epoxides and, despite the abundance of commercially available monomers, are mainly used as poly(ethylene glycol) or poly(propylene glycol) chains with restricted backbone functionality. We outline a relationship between the reaction pathway, network architecture, and mechanical properties in model networks synthesized by ring opening co-polymerization of ethyl glycidyl ether (EGE) monomer and 1,4-butanediol diglycidyl ether (BDGE) cross-linker using two different initiators/catalysts: a chelate of AlEt3 with acetylacetone and water, referred to as Vandenberg catalyst; and a chelate of AlEt3 with dimethylaminoethanol, referred to as Lynd catalyst. By evaluating the kinetics of co-polymerization by [START_REF] Gent | Engineering with Rubber[END_REF] H NMR spectroscopy and GPC, and the mechanical properties by rheology, uniaxial extension until failure, and single-edge notch crack propagation, we characterize the evolution of the network architecture with monomer conversion by fitting the molecular model of Rubinstein and Panyukov on non-linear elasticity of entangled and cross-linked networks. [START_REF] Rubinstein | Elasticity of Polymer Networks[END_REF] Finally, we provide insights on the role of network architecture on energy dissipation in the vicinity of the crack tip and fracture energy using the molecular model of Lake-and Thomas. [START_REF] Lake | The Strength of Highly Elastic Materials[END_REF]

EXPERIMENTAL SECTION

Materials. Unless otherwise specified, all chemicals were used as received. Air and moisturesensitive reactions, outside the glovebox, were carried out using standard Schlenk-line techniques. Ethyl glycidyl ether (EGE), 1,4-butanediol diglycidyl ether (BDGE), and 2 M butylmagnesium chloride in THF were sourced from TCI; acetyl acetone, anhydrous diethyl ether, 1.0 M triethylaluminum (AlEt3) in hexanes, and dimethylaminoethanol, from Millipore Sigma; methanol, and dichloromethane from VWR; deuterated chloroform from Cambridge Isotopes; and hydrochloric acid from Fischer. EGE (100 mL) was purified by stirring over butyl magnesium chloride (2.0 M in THF, 1 mL) for 1 h and distilling under vacuum. Caution! Butylmagnesium chloride is a pyrophoric and moisture-sensitive chemical and should be handled with appropriate care. Distilled EGE, acetyl acetone, and DI water were placed in dry septum-sealed bottles, sparged with N2 for 45 min, and transferred into a N2-filled glovebox.

Synthesis of Vandenberg Catalyst. The Vandenberg catalyst was prepared following a procedure reported by Beckingham et al. [START_REF] Beckingham | Simple and Accurate Determination of Reactivity Ratios Using a Nonterminal Model of Chain Copolymerization[END_REF] A dry septum-sealed bottle equipped with a Teflon stir bar was placed in a LN2 cold well located inside a N2-filled glovebox. Anhydrous diethyl ether (10 mL) and AlEt3 (1.0 M in hexanes, 10 mL, 10 mmol, 2 equivalents) were sequentially added with gastight syringes, and stirred for 30 min. Caution! AlEt3 is a pyrophoric and moisture-sensitive chemical and should be handled with appropriate care. Acetyl acetone (0.51 mL, 5 mmol, 1 equivalent) was then added with a gastight syringe, and the reaction stirred for another 2 h. Finally, DI water was added (0.09 mL, 5 mmol, 1 equivalent) with a gastight syringe, and the reaction allowed to stir overnight at room temperature.

Synthesis of Lynd Catalyst. The Lynd catalyst was prepared following a procedure reported by Rodriguez et al. [START_REF] Rodriguez | Ring-Opening Polymerization of Epoxides: Facile Pathway to Functional Polyethers via a Versatile Organoaluminum Initiator[END_REF] A dry septum-sealed bottle equipped with a Teflon stir bar was immersed in a LN2 cold well located inside a N2-filled glovebox. AlEt3 (1.0 M in hexanes, 12 mL, 12 mmol, 2.5 equivalents) and dimethylaminoethanol (0.445 mL, 4.4 mmol, 1 equivalent) were sequentially added with syringes, and stirred overnight while allowing the cold well to equilibrate at room temperature.

The Lynd catalyst was purified by recrystallizing three times from hexanes in the LN2 cold well to remove excess AlEt3, and then decanting and drying overnight under vacuum inside the glovebox.

Polymerization of Ethyl Glycidyl Ether (EGE): Linear Polymers. Linear polymers were synthesized in a N2-filled glovebox. EGE (99 mol%) and initiator/catalyst (1 mol%) were added to 20 mL scintillation vials and reacted on a hot plate equilibrated at 60 o C. Monomer conversion was monitored by 1 H NMR spectroscopy, with spectra collected on reaction aliquots (50 µL) dissolved in CDCl3 (600 µL) with a Bruker Avance 400 MHz spectrometer equilibrated at room temperature.

Linear polymers were terminated by dissolving the reaction mixture in dichloromethane (10 mL) and 0.1 M acidic methanol (500 µL), and purified by washing with DI water (3 x 20 mL) and separating the organic and aqueous phases via centrifugation for 10 min at 11,000 rpm and 21 o C. The organic phases were then concentrated by rotary evaporation at 45 o C, and the polymers dried overnight at room temperature under vacuum. Number-average molecular weights, Mn, and dispersities, Đ, were evaluated by Gel Permeation Chromatography by eluting polymer solutions, previously filtered with PTFE of 0.45 µm pore size, in Agilent PLgel 10 μm MIXED-B and 5 μm MIXED-C columns (200-10,000,000 g.mol -1 relative to polystyrene standards) using chloroform (50 ppm of amylene) at 0.5 mL.min -1 and 30 o C as the mobile phase.

Polymerization of Ethyl Glycidyl Ether (EGE):

Polymer Networks. Networks were synthesized via bulk polymerization of EGE. In a N2-filled glovebox; monomer EGE, cross-linker BDGE, and initiator/catalyst (1 mol%) were well-mixed in a 20 mL scintillation vial and subsequently transferred to a mold composed of two Teflon-covered glass plates sealed with a silicone spacer (≈ 0.1 cm thick). Polymerization was conducted in the glovebox antechamber for 6 days at 60 o C, and the resulting polymer networks transferred outside of the glovebox for termination and purification. Typical network dimensions were 8 x 4 x 0.1 cm 3 .

Polymer networks were terminated with a series of five washing steps. First, the networks were swollen in a solution of acidic methanol (0.1 M HCl) in DI water (40 mL, 90% v/v) for 2 h; and then swollen in methanol for 2 h (4 x 40 mL). The networks were allowed to dry first under ambient conditions for 4 h, and then under vacuum at room temperature overnight. Gel fractions were determined from the mass difference between the as-polymerized and terminated networks.

The aluminum concentration of Lynd-and Vandenberg-catalyzed networks at 10 mol% BDGE are respectively 7900 ppm and 100 ppm as measured by ICP-MS.

Rheology. Polymer networks were punch-cut into cylindrical specimens of 8 mm diameter and ≈ 1 mm thickness, and their rheological properties evaluated in a Discovery HR-2 rheometer equipped with stainless steel flat plates of 8 mm diameter.

Frequency sweeps from 0.1 rad.s -1 to 100 rad.s -1 at temperatures from 30 to 75 o C were performed within the linear viscoelastic regime at a strain of 1.00%. Time-Temperature-Superposition was used to construct master curves at a reference temperature of 30 o C, using vertical and horizontal shift factors.

Uniaxial Tension. Polymer networks were punch-cut into dog-bone shaped specimens of 20 mm gauge-length, 4 mm width, and ≈ 1 mm thickness. These were marked with two dots of white paint and subsequently deformed at a cross-head velocity of 0.06 mm.s -1 (0.003 s -1 ) with an Instron 34TM5 equipped with a 100 N load cell and a video extensometer. The resulting force-displacement curves were used to compute the engineering stress, N, and stretch,  Single-Edge-Notch Crack Propagation. Polymer networks were punch-cut into dog-bone shaped specimens of 20 mm gauge length, 4 mm width, and ≈ 1 mm thickness. These were cut with a fresh razor blade to introduce a crack of ≈ 1 mm length, marked with two dots of white paint, and deformed at a cross-head velocity of 0.06 mm.s -1 (0.003 s -1 ) with an Instron 34TM5 equipped with a 100 N load cell and a video extensometer. The resulting force-displacement curves were used to compute the engineering stress, N, and stretch, 

RESULTS AND DISCUSSION

Role of Initiator/Catalyst on the Reaction Pathway

We synthesized linear polymers by epoxide ring opening polymerization of ethyl glycidyl ether (EGE) using two different initiators/catalysts. Detailed synthetic conditions are provided in Materials and Methods, and reaction compositions and 1 H NMR spectra are summarized in the Supporting Information (SI, Table S1, Fig. S1). The Vandenberg and Lynd catalysts (Fig. 1A) lead to dramatically different rates and mechanisms of polymerization as evidenced by the evolution of monomer conversion with time (Fig. 1B), and distribution of molecular weights (Fig. 1C). Polymerization of EGE with the Vandenberg catalyst is fast and uncontrolled, achieving 95% conversion in 1 day, high molecular weight (Mn ≈ 100 kDa) and broad dispersity (Đ ~ 8.4); whereas polymerization with the Lynd catalyst, instead, is slow and controlled, achieving 95% conversion in 6 days, target molecular weight (Mn ≈ 10 kDa), and narrow dispersity (Đ ~ 1.6). These observations are consistent with previous investigations on epoxide ring opening polymerizations; where Vandenberg-catalyzed polymerizations have obscure initiating and catalytic species that derive from reaction of AlEt3 with acetylacetone and water, [START_REF] Vandenberg | Catalysis: A Key to Advances in Applied Polymer Science[END_REF][START_REF] Ferrier | Demystifying the Mechanism of Regioand Isoselective Epoxide Polymerization Using the Vandenberg Catalyst[END_REF] and Lynd-catalyzed polymerizations, instead, are controlled (i.e., living) with a well-defined mono(μ-alkoxo)bis(ethylaluminum) initiating species that derives from reaction of AlEt3 with dimethylaminoethanol. [START_REF] Rodriguez | Ring-Opening Polymerization of Epoxides: Facile Pathway to Functional Polyethers via a Versatile Organoaluminum Initiator[END_REF][START_REF] Ferrier | Four-Fold Increase in Epoxide Polymerization Rate with Change of Alkyl-Substitution on Mono-μ-Oxo-Dialuminum Initiators[END_REF][START_REF] Imbrogno | Decoupling Catalysis and Chain-Growth Functions of Mono(μ-Alkoxo)Bis(Alkylaluminums) in Epoxide Polymerization: Emergence of the N-Al Adduct Catalyst[END_REF] To further understand the reaction pathway; we assumed that Vandenberg-and Lynd-catalyzed polymerizations were equilibrium-limited, and estimated apparent rate constants using the following first-order rate equation:

𝑋-𝑋 𝑒 1-𝑋 𝑒 = 𝑒 -𝑘 𝑎𝑝𝑝 𝑡 (Eq. 1)
Where X, Xe, kapp, and t are respectively the monomer conversion, equilibrium conversion, apparent rate constant, and reaction time. Non-linear least-square regressions yield kapp ~ (10 -2 min -1 ) for the Vandenberg catalyst, and kapp ~ (10 -3 min -1 ) for the Lynd catalyst, where the symbol O() indicates order-of-magnitude. These apparent rate constants, kapp, are consistent with differences in the rate of polymerization (Fig. 1B), though we note that they are also proportional to the concentration of active chain ends, which is lower for Vandenberg-catalyzed polymerizations based on the higher Mn (Fig. 1C). Hence, it is likely that the difference in the propagation rate constants is more pronounced than that reflected in Fig. 1B. We attribute differences in the rate of polymerization to the energy of the transition state, as evaluated from the temperature-dependence of kapp using Eyring's equation:

ln ( 𝑘 𝑎𝑝𝑝 𝑇 ) = ln ( 𝑘 𝐵 ℎ ) + ∆𝑆 ‡ 𝑅 - ∆𝐻 ‡ 𝑅𝑇 (Eq.2)
Where T, kB, h, R, H ‡ , S ‡ are respectively the temperature, Boltzmann constant, Planck constant, universal gas constant, and standard enthalpy and entropy of activation (Fig. S2-S3).

Linear least-square regressions yield rather similar H ‡ ≈ 20 kcal.mol -1 for both catalysts and comparable to that reported by Ferrier et al. for analogous allyl glycidyl ether, [START_REF] Ferrier | Demystifying the Mechanism of Regioand Isoselective Epoxide Polymerization Using the Vandenberg Catalyst[END_REF] but a lower S ‡ for the Lynd catalyst (Table S2); suggesting that restrictions in the number of configurations explored by the transition state are key for attaining control over the rate of polymerization.

From a molecular point of view, it is possible that more adducts of monomer and propagating chain ends are present in the transition state of Lynd-catalyzed polymerizations, reducing the number of effective collisions that lead to chain propagation and transfer/exchange reactions.

However, we note that this molecular picture remains hypothetical and requires further experimental and theoretical investigation.

The initiator/catalyst plays a key role in the rate of polymerization, molecular weight, and dispersity of the linear polymers, which is ultimately reflected in the bulk viscoelastic properties as measured by the storage G' and loss G" moduli (Fig. 2, with strain sweeps at 10 rad.s -1 in Fig. S4). Vandenberg-catalyzed polymers exhibit G' ≈ G" and a crossover at ω ≈ 2 rad.s -1 ; whereas Lynd-catalyzed polymers, instead, exhibit G" ≫ G' and Maxwell-like scaling G' ~ ω 2 and G" ~ ω. This observation indicates that Vandenberg-catalyzed polymers are viscoelastic and able to dissipate elastic energy like entangled melts when subject to small deformations (i.e., Mn/Me ≈ 3.5, estimating an entanglement molecular weight, Me ≈ 30 kDa, from rubber elasticity theory.

Details of this estimation are summarized in the SI); whereas Lynd-catalyzed polymers, instead, are low-molecular weight liquids that readily flow (i.e., Mn/Me ≈ 0.35).

Role of the Reaction Pathway on the Network Architecture and Mechanical Properties

We synthesized polymer networks through epoxide ring opening polymerization of EGE monomer and 1,4-butanediol diglycidyl ether (BDGE) cross-linker. Detailed synthetic conditions are provided in the Materials and Methods section and summarized in the SI (Table S3), but they differ both in the choice of initiator/catalyst and cross-linker concentration (Table 1). [START_REF] Gao | Synthesis of Functional Polymers with Controlled Architecture by CRP of Monomers in the Presence of Cross-Linkers: From Stars to Gels[END_REF] where the extent of reaction at the critical point, pc, is given by:

𝑝 𝑐 = √ [𝑀 * ] 𝑡 2[𝑋] 0 1 Ð (Eq. 3)
Where [M*]t, [X0], and Ð are respectively the instantaneous concentration of polymer chain ends during polymerization, the initial concentration of cross-linker, and the dispersity of the polymer chains that would result from monomer polymerization in the absence of cross-linker.

These quantities can be estimated from the GPC traces of the linear polymers (Fig. 1C) and the composition of the reaction mixture (Table S3-S4). The Flory-Stockmayer model on gelation is overly simplistic because it neglects the defective architecture of polymer networks; but it unveils, in our viewpoint, the right qualitative picture. Lynd-catalyzed networks percolate at higher cross-linker concentrations than Vandenberg-catalyzed networks because of the higher instantaneous concentration and lower dispersity of the propagating chains during co-polymerization (i.e., pc Vandenberg /pc Lynd ≈ 0.14). In other words, percolation at higher cross-linker concentrations is a natural consequence of the reaction pathway that procures control over the rate of polymerization. This effect of the reaction pathway and initiator/catalyst on network percolation is also evident in the bulk mechanical properties of the gel fraction of polyether networks (i.e., after extracting the sol fraction with organic solvent and drying in vacuum overnight. GPC trace of the sol fraction in Fig. S5). Although both catalysts lead to rubbery and thermally stable materials with Tg ≈ -55 o C and Td ≈ 400 o C (Fig. S6-S7), Vandenberg-catalyzed networks physically appear softer and tackier than their Lynd-catalyzed analogues (Fig. 3A). This observation is also reflected in the viscoelastic properties, as measured by the storage G' and loss G" moduli (Fig. 3B). Vandenberg-catalyzed networks exhibit G' ≈ 0. To further understand the role of reaction pathway on the network architecture and mechanical properties, we evaluated the mechanical properties by uniaxial elongation until failure (Fig. 3C).

Vandenberg-catalyzed networks are soft, extensible, and rather insensitive to the nominal concentration of BDGE cross-linker, x; whereas Lynd-catalyzed networks, instead, are stiffer, with a Young's modulus, E, that progressively increases with x. This observation agrees with the viscoelastic response of Vandenberg-catalyzed networks, indirectly suggesting the presence of entanglements within the network architecture. The density of these entanglements, as well as that of elastically active chains, can be quantified by fitting the stress-stretch curves with the molecular model of Rubinstein and Panyukov on non-linear elasticity of entangled polymer networks (Fig. S7-S8). [START_REF] Rubinstein | Elasticity of Polymer Networks[END_REF] According to this model, the engineering stress in uniaxial tension, N, is given by: 𝜎 𝑁 = (𝜈 𝑥 + 𝜈 𝑒 0.74𝜆+0.61𝜆 -0.5 -0.35

)𝑘 𝐵 𝑇 (𝜆 -1 𝜆 2 )(Eq. 4)

Where , x, and e are respectively the stretch, and the density of elastic chains and entanglements. Non-linear least square regressions reveal some important effects of the reaction pathway and initiator/catalyst on the network architecture (Fig. 3D). First, the Vandenberg catalyst leads to inefficient chemical cross-linking, likely because the reaction of a BDGE pendant epoxy moiety with a propagating chain end is limited by the entangled polymer dynamics rather than the reaction rate constant. Second, the Vandenberg catalyst leads to networks with similar densities of chemical cross-links and entanglements. And finally, control over the rate of polymerization, as attained with the Lynd catalyst, translates into effective chemical cross-linking and an increase in the modulus E with the density of elastically active chains, x.

The molecular picture that results from our observations is summarized in Scheme 1.

Vandenberg polymerizations lead to networks that are loosely cross-linked and entangled, whereas Lynd polymerizations, instead, yield networks that are highly cross-linked and that, a priori, appear untangled. This difference in mesoscopic heterogeneities is like that depicted for networks synthesized by controlled and free radical polymerizations; [START_REF] Ide | Nitroxide-Controlled Free-Radical Copolymerization of Vinyl and Divinyl Monomers. Evaluation of Pendant-Vinyl Reactivity[END_REF][START_REF] Ide | Nitroxide-Controlled Free-Radical Copolymerization of Vinyl and Divinyl Monomers. 2. Gelation[END_REF][START_REF] Gao | Effect of Cross-Linker Reactivity on Experimental Gel Points during ATRcP of Monomer and Cross-Linker[END_REF][START_REF] Gao | Synthesis of Polyacrylate Networks by ATRP: Parameters Influencing Experimental Gel Points[END_REF][START_REF] Gao | Synthesis of Functional Polymers with Controlled Architecture by CRP of Monomers in the Presence of Cross-Linkers: From Stars to Gels[END_REF] though we highlight, in addition, the effect of reaction pathway on the density of elastically active chains and entanglements. Also, we note that such control over the network architecture through the initiator/catalyst is probably related to the reactivity of the monomer and the cross-linker during polymerization, as measured by their reactivity ratios. However, this information remains experimentally inaccessible in EGE networks due to the inability to discern spectroscopic signals from EGE monomer and BDGE cross-linker during polymerization. The initiator/catalyst serves to tailor the network architecture and linear mechanical properties like the modulus, but also non-linear ones like the fracture toughness. We fractured Vandenbergand Lynd-catalyzed networks by single-edge-notch crack propagation, and estimated their critical energy release rate, Gc, following Greensmith's method (Fig. S10-S12 and Table S5). [START_REF] Greensmith | Rupture of Rubber. X. The Change in Stored Energy on Making a Small Cut in a Test Piece Held in Simple Extension[END_REF] Irrespective of the nominal concentration of BDGE cross-linker, x, Vandenberg-catalyzed networks are tougher and more resistant to crack propagation than their Lynd-catalyzed analogues. This observation is consistent with the ability of Vandenberg-catalyzed networks to dissipate energy by molecular friction during untangling of polymer chains. Lynd-catalyzed networks, instead, are more elastic and mainly able to dissipate energy by network chain scission. Insights on the role of bond scission and molecular friction on energy dissipation can be gained by considering the critical energy release, Gc, within the molecular model of Lake and Thomas. [START_REF] Lake | The Strength of Highly Elastic Materials[END_REF] According to this model, the minimum (i.e., threshold) energy dissipated upon creation of an interface, G0, is that required to break a monolayer of stretched elastic polymer chains, and given by: 𝒢 0 = 𝑈 𝑏 𝑁 𝑥 ∑ 𝑥 (Eq. 5)

where Ub, Nx, and x are respectively the energy of a covalent bond (i.e., typically 350 kJ.mol -1 but recently revised by Wang et al. to 60 kJ.mol -1 based on a probabilistic view of bond scission [START_REF] Wang | Quantitative Adjustment to the Molecular Energy Parameter in the Lake-Thomas Theory of Polymer Fracture Energy[END_REF] ), the number of covalent bonds between crosslinks, and the areal density of elastic polymer chains. However, it is worth noting that Nx and x are coupled through:

∑ 𝑥 ≈ 𝜈 𝑥 〈𝑅 0 〉 1 2 2 ≈ 𝜈 𝑥 (𝐶 ∞ 𝑁 𝑥 ) 1 2𝑙 0 2 (Eq. 6)
Where 〈𝑅 0 〉 1 [START_REF] Martinez | Soft Actuators and Robots That Are Resistant to Mechanical Damage[END_REF] is the average end-to-end distance of an elastic polymer chain, C∞ the characteristic ratio of EGE (i.e., 7.46 based on molecular dynamic simulations, and comparable to that of analogous polyacetal), and l0 the average length of a C-C and C-O bond (i.e., 1.48 Å). As a result, the threshold energy, G0, is related to the density of elastic chains, x, by:

𝒢 0 = 𝑈 𝑏 𝑁 𝑥 𝜈 𝑥 (𝐶 ∞ 𝑁 𝑥 ) 1 2𝑙 0 2 ≈ 𝑈 𝑏 𝑙 0 𝐶 ∞ 1/2 2 ( 𝜌𝑁 𝐴 𝑀 0 ) 3/2 𝜈 𝑥 -1/2 (Eq. 7)
Where , M0, and NA are respectively the density of the polymer network, molar mass of the monomer, and Avogadro's number. Eq. 7 unveils a trade-off between the threshold fracture energy, G0, and the density of elastic polymer chains, x, which has been experimentally validated in conventional elastomers [START_REF] Bhowmick | Threshold Fracture of Elastomers[END_REF] and tetra-poly(ethylene glycol) hydrogels [START_REF] Akagi | Fracture Energy of Polymer Gels with Controlled Network Structures[END_REF] under conditions where molecular friction is suppressed like high temperature or high solvent concentration. Lynd-catalyzed networks are elastic and predominantly dissipate energy by chain scission, leading to better agreement between the critical energy release rate, Gc, and the threshold energy, G0 (Fig. 4B). Vandenberg-catalyzed networks, instead, are viscoelastic and able to dissipate a notable amount of energy by molecular friction, yielding marked deviations of Gc from G0. This difference in dissipation mechanism is also reflected in the fracture surfaces (Fig. S13); which are smoother for viscoelastic, Vandenberg-catalyzed networks as in synthetic elastomers like styrene-butadiene rubber. [START_REF] Tsunoda | Effect of Materials Variables on the Tear Behaviour of a Non-Crystallizing Elastomer[END_REF] However, we note that Vandenberg-catalyzed networks are also more blunted than Lynd-catalyzed networks at the critical point (Fig. 4A), indicating that they are also subject to larger deformations ahead of the crack tip (i.e., see elasto-adhesive length in Fig. S14, and crack-tip opening displacement at the onset of crack propagation in Fig. S15). Slootman et al., recently argued that such stretch concentration because of molecular friction also increases the local probability of bond scission, coupling the mechanisms of energy dissipation that control fracture in polymer networks. [START_REF] Slootman | Quantifying Rate-and Temperature-Dependent Molecular Damage in Elastomer Fracture[END_REF] Hence, it is possible for the critical energy release rate, Gc, of Vandenberg-catalyzed networks to notably deviate from the Lake and Thomas threshold energy, G0, not only because of viscoelastic dissipation but also molecular damage.

Finally, it is also interesting to note that Vandenberg-catalyzed networks exhibit dramatic differences in critical energy release rate, Gc, despite having similar densities of elastically active chains and entanglements (i.e., elastic modulus and strain softening in Fig. 2C). This observation indicates that refined descriptions of the network architecture are necessary to understand energy dissipation and fracture. The molecular model of Rubinstein and Panyukov describes the nonlinear behavior of entangled polymer networks up to moderate strains but the region ahead of the crack tip, instead, is subject to large strains because the polymer chains extend near their limiting extensibility. Vandenberg-catalyzed networks synthesized with higher nominal concentrations of cross-linker strain harden at lower strains, suggesting that they are composed of less extensible chains and able to dissipate less energy by network chain scission (Fig. 2C, Fig. S16, and Table S6). In addition, these networks have a lower viscoelastic dissipation factor, tan(), at the characteristic frequency of crack propagation, indicating that they also dissipate less energy by molecular friction (Fig. S17 and Table S6). Hence, increasing the nominal concentration of A typical strategy to tune the architecture and mechanical properties of polymer networks is to vary the nominal concentration of cross-linker in the polymerization. However, polymerization with the Vandenberg catalyst results in networks with an elastic modulus insensitive to the crosslinker concentration, whereas polymerization with the Lynd catalyst does not afford percolated networks at cross-linker concentrations below 3 mol%. As a result, tailoring the reaction pathway through the choice of organo-aluminum catalyst widens the range of synthetically accessible elastic moduli, affording additional leverage over the architecture and mechanical properties of polyether networks. Nonetheless, it is worth noting that neither the Vandenberg nor the Lynd catalyst is, in absolute terms, fast or controlled, suggesting that novel initiator/catalysts for epoxide ring-opening polymerization could serve to improve the mechanical properties of polyether networks.

Effective cross-linking is attained through Lynd polymerizations, but the amount of energy dissipated upon fracture is still more than that required to break a monolayer of elastic polymer chains. Other soft materials like tetra-poly(ethylene glycol) hydrogels [START_REF] Akagi | Fracture Energy of Polymer Gels with Controlled Network Structures[END_REF] and olefin-based elastomers [START_REF] Bhowmick | Threshold Fracture of Elastomers[END_REF] have fracture energies that approach the threshold energy in regimes where viscoelastic dissipation is negligible. As such, it is likely that our polymer networks synthesized by Lynd polymerizations, though highly cross-linked and elastic, still contain trapped entanglements and viscoelastic dissipation ahead of the crack tip.

Network architectures that result from Vandenberg polymerizations have similar densities of elastic chains and entanglements, as well as an elastic modulus and strain softening that are insensitive to the nominal concentration of cross-linker during polymerization. However, these materials exhibit dramatic differences in their resistance to crack propagation, suggesting that descriptions of the network architecture beyond that afforded by the mean-field model of Rubinstein and Panyukov might be necessary to understand energy dissipation and fracture. In this regard, combinations of experiments and theory like those recently undertaken by Arora et al. [START_REF] Arora | Fracture of Polymer Networks Containing Topological Defects[END_REF] , Lin et al. [START_REF] Lin | Fracture and Fatigue of Ideal Polymer Networks[END_REF] , and Barney et al. 57 might prove useful to understand how the load-bearing capacity of chemical cross-links, entanglements, and topological defects evolves as polymer chains deform, untangle, and fully extend before failure.

Controlling the reaction pathway with organo-aluminum catalysts affords polyether networks that are elastic at low strains but able to dissipate energy primarily by bond scission above a critical strain in the vicinity of the crack tip. Such fundamental understanding of the mechanical properties serves to molecularly design soft, tough, and durable materials for engineering applications (e.g., tires and dampers), energy conversion and storage devices (e.g., wearable electronics, ion gels), and medicine (e.g., soft prosthetics).

Figure 1 .

 1 Figure 1. Polymerization of EGE with Lynd and Vandenberg catalysts. (A) Chemical structures of the Lynd and Vandenberg catalysts. (B) Evolution of monomer conversion with time demonstrates drastic differences in the rate of polymerization. (C) GPC traces unveil that Lynd-catalyzed polymerizations are controlled, attaining target molecular weight (dashed) and narrow dispersity, whereas Vandenberg-catalyzed polymerizations, instead, are uncontrolled.

Figure 2 .

 2 Figure 2. Linear Viscoelastic Properties of PEGE. Storage (■) and loss (□) moduli illustrate that polymers synthesized with the Vandenberg catalyst are more viscoelastic (i.e., G' ≈ G" or tan() ≈ 1 ) at T = 25 o C than those synthesized with the Lynd catalyst.The initiator/catalyst inherently dictates the reaction pathway to convert monomer into

Figure 3 .

 3 Figure 3. Mechanical Properties of EGE Networks. (A) Pictures of EGE10 networks after bending. Clearly, Lynd-catalyzed networks readily crack upon bending whereas Vandenberg-catalyzed networks appear pristine. (B) Linear viscoelastic properties of EGE networks. Storage (■) and loss (□) moduli illustrate that networks synthesized with the Vandenberg catalyst are softer and more viscoelastic (i.e., frequency dependent G") at T = 30 o C than those synthesized with the Lynd catalyst. (C) Stressstretch curves of EGE networks. Vandenberg-catalyzed networks are soft, extensible, and rather insensitive to the nominal concentration of BDGE cross-linker, x; whereas Lynd-catalyzed networks, instead, are stiff, with a Young's modulus, E, that progressively increases with x. (D) Densities of elastically active chains and entanglements. Vandenberg-catalyzed networks are loosely cross-linked and entangled, whereas Lynd-catalyzed networks, instead, are highly cross-linked and, a priori, untangled.

Scheme 1 .

 1 Scheme 1. Evolution of network architecture with monomer conversion. Vandenberg polymerizations yield networks with similar densities of entanglements and chemical cross-links, whereas Lynd polymerizations, instead, yield more homogeneous networks pervaded by elastic chains.

Figure 4 .

 4 Figure 4. Fracture Properties of EGE Networks. (A) Pictures of EGE10 at the critical stretch for crack propagation. Vandenberg-catalyzed networks have crack-tip opening displacement,  ~ O(1 mm), whereas Lynd-catalyzed networks, instead, have  ~ O(0.1 mm) (Fig. S13-14). (B) Critical energy release rate, Gc, of EGE networks. Lynd-catalyzed networks exhibit better agreement with the Lake and Thomas model on fracture in terms of the scaling with x.

Table 1 . Composition and mechanical properties of polymer networks.

 1 The nominal concentration of BDGE cross-linker during the polymerization x, density of elastically active chains x, density of entanglements e, Young's modulus E, and fracture energy Gc.

	Catalyst	x mol% BDGE	x (10 24 m -3 ) e (10 24 m -3 )	E (MPa)	Gc (J.m -2 )
		3	45	12	0.7	58
	Lynd	5	150	0.82	1.6	36
		10	290	0	3.3	12
		3	15	6.4	0.3	130
	Vandenberg	5	17	8.1	0.3	90
		10	18	5.8	0.3	55
	Lynd-catalyzed networks require a higher cross-linker concentration, x = 3 mol%, than

Vandenberg-catalyzed networks to gel (Table

S3

), indirectly suggesting that the percolation threshold of EGE networks is affected by the reaction pathway and initiator/catalyst. A similar observation was interpreted by

Gao et

al. in networks synthesized by controlled radical polymerization within the molecular model of Flory and Stockmayer on gelation,

  yield loosely cross-linked, entangled, soft, and extensible networks; whereas slow and controlled polymerization with the Lynd catalyst, a chelate of AlEt3 with dimethylaminoethanol, instead, result in highly cross-linked, stiff, and brittle networks. This trade-off between stiffness and elasticity at low deformations (i.e., high modulus and negligible energy dissipation), and resistance to crack propagation (i.e., high toughness) is characteristic of polymer networks that rely on molecular friction to dissipate energy in the vicinity of the crack tip.

	CONCLUDING REMARKS
	Polymer networks synthesized by epoxide ring opening polymerization provide novel insights
	on the role of reaction pathway on network architecture and mechanical properties. Fast and
	uncontrolled polymerizations with the Vandenberg catalyst, a chelate of AlEt3 with acetylacetone
	and water,
	cross-linker in Vandenberg-catalyzed networks compromises energy dissipation both by
	molecular damage and friction, resulting in less resistance to crack propagation as measured by
	the critical energy release rate, Gc.

This work was funded by The University of Texas at Austin. C.C. acknowledges support from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Program (Grant Agreement N o 695351 -CHEMECH). N.A.L. acknowledges support for synthesis from the National Science Foundation (CHE-2004167) and the Welch Foundation (F-1904). ACKNOWLEDGEMENTS A.Z.D. and G.E.S. acknowledge support and guidance from Dr. Adrianne Rosales.

Data and Materials Availability. All data needed to evaluate the conclusions are present in the paper and/or the Supporting Information, as well as in the Texas Data Repository.

Funding Sources

Notes

The authors declare no competing financial interest.

Mech


Justine Fouillé

Thi Lan

Huong Nguyen

Baptiste Alix

Brett Becker

Matthieu Rochard

Hélène De Ribaupierre
email: deribaupierreh@cardiff.ac.uk

Laurent D'orazio
email: laurent.dorazio@univ-rennes1.fr

Brett

ASSIST: Outil pour l'extraction et l'analyse statistique d'articles

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

Introduction

Publier ou périr illustre assez bien la pression que ressentent les chercheurs pour réussir une carrière universitaire. Les chercheurs sont ainsi encouragés à promouvoir leurs progrès en rédigeant des articles en les soumettant à des ateliers, des symposiums, des conférences ou des revues, au niveau national ou international.

Des études ont récemment démontré qu'il y a moins d'auteures que d'auteurs dans le domaine de la recherche scientifique1 . Cependant, il n'existe pas encore de système fournissant des données concrètes pour le prouver, permettant par exemple de connaître la proportion de femmes pour un domaine donné (par exemple la médecine ou l'informatique), un sous-domaine (les bases de données ou l'interaction humaine par exemple), un domaine de recherche (comme l'intégration de données ou l'optimisation des requêtes), ou selon les différents évènements et selon leur classement (A*, A, B, C ou non classé). Il est donc impossible de voir l'évolution de la place des femmes au cours du temps.

Plusieurs plateformes existent pour analyser certains aspects des publications scientifiques telles que Scopus 2 , altmetric 3 , Plumx 4 , Dimensions 5 . Ces plateformes portent soit sur les performances des scientifiques (comme le h-index), soit sur les réseaux de citations des articles, soit sur le classement de la revue (comme les facteurs d'impact). Des solutions telles que Core 6 regroupent les articles en libre accès de différentes ressources et proposent une API pour accéder au texte brut des articles. Cependant, à notre connaissance, il n'existe pas de plateforme ouverte permettant de rassembler et d'analyser les données contenues dans les articles scientifiques. Un cas d'utilisation possible de cette plateforme que nous présentons est d'analyser l'évolution de la place des femmes au sein de la communauté scientifique.

Dans cet article, nous présentons notre application Web, AXIS, pour Article eXtraction and statIstical AnalysiS. L'objectif est de dresser un portrait de l'évolution du monde de la recherche et de mettre en évidence les différences de genre dans ce domaine. AXIS permet donc de centraliser plusieurs sources bibliographiques et d'analyser les métadonnées des articles scientifiques. Les données concernant les articles (titre, liste des auteurs, références, citations, éditeur, origine...) sont donc récupérées depuis de multiples Interfaces de Programmation d'Applications ou API (DBLP, Core, etc.) pour varier les sources d'informations. Le sexe des auteurs est déterminé par leur prénom. L'application permet ensuite d'établir des statistiques sur le nombre d'auteurs par genre ou encore par évènement.

La structure de cet article est la suivante. Dans un premier temps, nous présentons comment nous améliorons les analyses faites avec les articles. Nous avons développé de nouvelles fonctionnalités permettant des analyses plus précises comme le nombre d'auteures selon les années chez un éditeur. Nous avons également développé un nuage de mots-clés pour chaque article qui affiche les principaux thèmes qu'il aborde. Pour finir, nous montrons comment pour résoudre le problème de récupération de données, nous avons changé le système de récupération des données des API.

Motivation

Les données bibliographiques extraites d'articles scientifiques ont plusieurs finalités. Les auteurs dans Di [START_REF] Di Iorio | Exploring scholarly papers through citations[END_REF]; [START_REF] West | The role of gender in scholarly authorship[END_REF] proposent une liste des différentes tâches possibles sur les bibliographies selon les différentes classes d'utilisateurs. Dans cet article, nous aborderons deux tâches (construire une bibliographie et analyser l'impact d'un chercheur) et développerons la dernière en une nouvelle tâche (analyser l'évolution du paysage des publications et le nombre de femmes). Ce qui suit n'est pas une liste exhaustive de tous les outils et recherches possibles qui sont disponibles pour accomplir ces tâches, mais ceux qui sont souvent utilisés par les scientifiques pour accomplir ces tâches.

L'utilisateur souhaite constituer une bibliographie sur un sujet donné. Par exemple, l'utilisateur souhaite constituer une bibliographie sur le thème des "nanopublications" et obtenir toutes les publications pertinentes sur ce sujet. Des outils tels que Google Scholar 7 pourraient 2. https ://www.scopus.com/home.uri 3. https ://www.altmetric.com 4. https ://plumanalytics.com/ 5. https ://www.dimensions.ai 6. https ://core.ac.uk 7. scholar.google.com les aider à démarrer leur tâche. Les nanopublications étant un terme très spécifique, le résultat de la requête dans google Scholar ne sera que de 973 résultats. Si le scientifique veut explorer l'ensemble complet des résultats, cela lui prendra déjà un certain temps. Cependant, une étude montre que les scientifiques n'explorent souvent pas tous les résultats [START_REF] Renear | Strategic reading, ontologies, and the future of scientific publishing[END_REF]. La tâche devient déjà plus délicate pour le scientifique puisque le premier article présenté à l'utilisateur est un article qui compte 286 citations. L'utilisateur souhaite-t-il explorer toutes les citations de cet article, ou seulement un sous-ensemble de celles-ci ? Et ce n'est que pour la première publication présentée au scientifique. Google Scholar offre une certaine possibilité de filtrage, comme la recherche parmi les 286 citations du premier article, mais n'offre pas la possibilité de filtrer à un niveau plus profond ou de rechercher tous les articles qui auraient pu être cités couramment par l'ensemble des 973 des articles. L'utilisateur commencera à étudier article par article, et regardera les différentes listes de citations, ouvrira les articles qui lui semblent intéressants, et cherchera les références ou les citations de ces articles. La tâche devient très longue et difficile car le nombre d'articles croît de manière exponentielle. Le scientifique pourrait alors changer pour un outil qui pourrait être plus approprié, et proposer plus de filtrage tel que Microsoft Academic 8 . L'interface vous permet de suivre un peu plus longtemps le fil des citations, mais si le scientifique souhaite télécharger un lot d'articles connexes, ce n'est pas possible non plus. De plus, il n'est pas possible de donner le nombre d'itérations que le scientifique souhaite réaliser dans sa recherche. A noter, que l'écosystème est dynamique. Ainsi Microsoft Academdic a été désactivé en décembre 2021.

La deuxième tâche consiste à analyser l'impact d'un scientifique. Cela se fait souvent par le nombre de citations sur les publications de l'auteur, ou de nouvelles métriques comme la popularité de cet article sur les réseaux sociaux (Tweeter, ResearchGate, etc). Plusieurs outils peuvent aider à accomplir cette tâche tels que Web Of Science 9 , Google Scholar, Microsoft Academic, PlumX 10 , Altmetric 11 , Sci2Tool 12 . La plupart de ces outils ne donnent qu'une vue partielle de l'impact d'un scientifique et utiliseront différentes méthodes. Par exemple, Google Scholar semble compter dans le h-index du scientifique les auto-citations, quand d'autres outils comme WebOfScience ne comptent que les publications qui leur sont accessibles. Le chercheur qui veut analyser son propre impact ou l'impact de quelqu'un d'autre naviguera (lorsqu'il y aura accès) à travers différents sites Web et rassemblera les différentes informations pour pouvoir avoir une vue complète.

La troisième tâche consiste à analyser la participation des différentes minorités à la science. De nombreuses recherches montrent que le pourcentage d'auteures est inférieur à celui des hommes [START_REF] Danell | Career prospects for female university researchers have not improved[END_REF], cependant cette recherche est souvent effectuée de manière très manuelle, où le scientifique va collecter un sous-ensemble de données bibliographiques et analyser le pourcentage d'auteures de ce sous-ensemble. Cela prend beaucoup de temps et, en plus, ne montre qu'une vision très restreinte de la situation dans son ensemble. La comparaison entre les différents domaines de recherche est difficile, et pour pouvoir analyser à plus grande échelle, les données doivent être disponibles et traitées de manière automatique. Cette tâche présente plusieurs défis. Premièrement, toutes les données ne sont pas librement disponibles ; deuxièmement, toutes les données ne sont pas situées aux mêmes endroits ; et troisièmement, 8. academic.microsoft.com 9. https ://app.webofknowledge.com 10. https ://plumanalytics.com 11. https ://www.altmetric.com 12. https ://sci2.cns.iu.edu/user/index.php certaines données doivent être déduites, telles que le sexe de l'auteur, car elles ne sont pas disponibles à partir des données de publication elles-mêmes.

Aperçu

Notre proposition, Article Extractions and Statistical Analysis (AXIS), se compose de deux fonctionnalités principales : (1) Gestion de données (Extraction et traitement de données) qui récupère les articles et répond aux requêtes d'articles pour les utilisateurs ; (2) Analyse de données permettra à l'utilisateur de collecter des statistiques sur les articles stockés et de les afficher.

4 Gestion de données Pour chaque article son titre, date de publication, résumé, DOI 13 et le texte complet sont collectés. Pour les auteurs : leurs nom, genre, position (premier auteur, deuxième auteur...) et affiliation sont également stockés. Enfin, l'origine de l'article (une conférence ou une revue) ainsi que les citations de l'article et les références faites par l'article sont également collectées.

Une fois les articles récupérés, une application de définition du genre (telle que gender.io) permettra à la base de données d'associer un genre au nom de chaque auteur.

Difficultés

Les principales difficultés sont premièrement de gérer les différents formats des informations envoyées par ces API. Certains d'entre eux utilisent XML, d'autres JSON ou encore Bibtex. Une façon d'éviter ce problème consiste à n'utiliser que des API qui utilisent le même format ou peuvent renvoyer des formats différents. Une deuxième façon consiste à convertir les données dans un format unique une fois qu'elles sont reçues.

Le manque de DOI pour les articles plus anciens peut également poser un problème pour la récupération des citations et des références et donc des API alternatives peuvent être nécessaires. Les homonymes posent un autre problème car de nombreux auteurs pourraient partager le même nom et l'objectif sera de les distinguer. Une autre perspective sera de considérer le changement de prénom ou de nom au cours de la carrière de l'auteur.

Même si ce ne sera pas la réponse ultime à ces défis, nous pouvons utiliser l'identifiant ORCID d'un auteur. Actuellement, aucune des API qui ont été choisies ne renvoient l'identifiant ORCID de l'auteur, mais on peut imaginer que ce sera bientôt le cas, étant donné que son utilisation tend à augmenter. le sexe est inconnu. Cela permet de récupérer des données brutes à utiliser dans diverses analyses. Grâce à cette fonctionnalité, il est possible de comparer le nombre d'auteurs par genre d'une année sur l'autre ou de plusieurs éditeurs une année donnée.

Nuage de mots clés

Le but du nuage de mots clés d'afficher les mots-clés d'un article scientifique mais aussi de récupérer ceux qui correspondent à ce mot-clé. Cela permet à l'utilisateur de visualiser les différents sujets qui correspondent à un terme spécifique. Cette fonctionnalité permet de découvrir de nouveaux articles scientifiques en proposant une liste d'articles correspondant au mot clé sélectionné par l'utilisateur. Ce nuage permettrait aussi de savoir sur quels sujets les femmes publient le plus. On aurait donc des statistiques encore plus précises que la proportion d'auteures dans un domaine.

Difficultés

Il y a plusieurs aspects qui peuvent influencer les statistiques, en particulier pour le sexe. Tout d'abord, il n'est pas toujours possible d'attribuer un genre à un nom. Pour cette raison, un seuil de probabilité de 85% de genderize.io a été décidé. Il semble préférable de construire des statistiques sur moins de données, plutôt que de construire sur de fausses données. Dans certains cas, il est également difficile de déterminer le sexe des auteurs, puisqu'ils ne fournissent que l'initiale du prénom.

Conclusion

Cet article présente AXIS, une plateforme s'appuyant sur plusieurs API pour rassembler et stocker de grandes quantités de publications scientifiques. Cette plateforme devrait aider le jeune chercheur à déterminer une bibliographie de manière beaucoup plus simple, car le processus récursif permettra à l'utilisateur de rassembler une liste précise et exhaustive de publications scientifiques.

Cette plateforme aidera également les scientifiques intéressés par l'analyse du paysage des publications scientifiques à avoir une vision plus complète ensemble de données à analyser.

De plus, la grande quantité de données permet l'analyse des statistiques et l'étude des tendances dans la communauté scientifique. Faciliter l'accès aux vastes quantités d'informations disponibles est primordial.

Avec les grandes quantités de données viennent cependant différentes contraintes telles que la contrainte des homonymes. Il est fort probable que parmi les auteurs insérés dans la base de données, certains porteront le même nom. Il n'existe actuellement aucun moyen de les distinguer. De plus, si un auteur change de nom, il sera enregistré comme deux personnes différentes. De plus, la plateforme n'analyse pour le moment que le sexe des auteurs en utilisant le prénom de l'auteur, cette manière d'analyser le sexe des auteurs conduira certainement à l'exclusion d'autres minorités, et devrait être investiguée plus avant.

Cette plateforme pourrait être très utile pour mener de nouvelles recherches dans le domaine de la scientométrie, ou simplement pour référencer un grand nombre d'articles scientifiques et leurs auteurs.

4. 1

 1 FIG. 1 -Diagramme des flux de données

Dans cet article, nous ne considérons que les femmes et les hommes, et des recherches supplémentaires devraient être menées pour inclure tout le monde.

Analyse de donnéesAprès avoir recueilli beaucoup de données, il est possible de les analyser et de découvrir des informations intéressantes. En croisant une ou plusieurs sources de données, il sera possible d'obtenir des statistiques variées.5.1 VisualisationEn utilisant les données stockées dans la base de données, des statistiques peuvent être calculées de différentes dimensions : le sexe de l'auteur, la position de l'auteur sur l'article, le nombre de citations, le nombre d'auto-citations, le nombre de références, les éditeurs, l'origine de l'article et la date de publication. Cette rubrique permet d'analyser différentes problématiques concernant le champ de la recherche scientifique et notamment la place des femmes dans celui-ci. L'utilisateur peut afficher le nombre d'auteurs par sexe par année pour un éditeur ou une conférence préalablement choisi. Le résultat est affiché sous forme de tableau avec le nombre total d'articles, le nombre d'auteures, le nombre d'auteurs et le nombre d'auteurs dont 13. Un identifiant d'objet numérique est un identifiant persistant ou un descripteur utilisé pour identifier des objets unique, normalisé par l'Organisation internationale de normalisation

Summary

There are fewer female authors than male authors in the field of scientific research. However, there is not yet a system that provides a way to analyze the data that is available, and to backup that claim. This paper illustrates the upgrade of a tool previously made, in order to make it more efficient and add new features. Such new features are the keywords cloud or the new statistical functionality. Sources, references and other information on the article will be displayed for each articles retrieved. Genders of the authors will be determined using a database linking first names to genders, to be able to get accurate statistics on a large number of gathered articles.


Paula Araujo Gomes

Jean-Baptiste D'espinose De Lacaillerie
email: jean-baptiste.despinose@espci.fr

Bruno Lartiges

Martin Maliet

Valérie Molinier

Nicolas Passade-Boupat

Nicolas Sanson
email: nicolas.sanson@espci.fr

¶ Jean-Baptiste D'espinose De Lacaillerie

Microalgae as Soft Permeable Particles

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

Introduction

In recent years, microalgae have garnered increasing attention because of their various biotechnological applications, particularly for biofuel production, water treatment, and greenhouse gas emission mitigation [START_REF] Luiten | Realizing the promises of marine biotechnology[END_REF][START_REF] Garrido-Cardenas | Microalgae research worldwide[END_REF] . Despite the promising uses of these microorganisms, the harvesting step's high energy cost is currently a limiting factor in microalgae production [START_REF] Lam | Current status and challenges on microalgaebased carbon capture[END_REF] .

Microalgae harvesting may include two steps: a pre-concentration of the algae culture followed by a dewatering process consisting of separating the cells from the aqueous medium [START_REF] Vandamme | Flocculation as a low-cost method for harvesting microalgae for bulk biomass production[END_REF] .

To achieve this, several methods such as centrifugation, sedimentation, filtration, flotation, and coagulation/flocculation exist with their relative advantages and disadvantages [START_REF] Kumar | Microalgae harvesting techniques: updates and recent technological interventions[END_REF] . For instance, centrifugation is a high-efficiency harvesting method, however, it is too expensive for large-scale applications [START_REF] Najjar | Harvesting of microalgae by centrifugation for biodiesel production: A review[END_REF] . In order to achieve cost-efficiency in large-scale production, a lowcost concentration method such as flocculation can be implemented before a less demanding physical separation [START_REF] Branyikova | Harvesting of microalgae by flocculation[END_REF] .

Microalgae are microscopic organisms possessing a layer of extracellular polymeric substances (EPS) at their surface which governs, among other things, the physicochemical prop-erties of microalgae in aqueous media [START_REF] Xiao | Overview of microalgal extracellular polymeric substances (EPS) and their applications[END_REF] and consequently their dispersion state, their interfacial behavior, and their adhesion [START_REF] Zeng | How Interfacial Properties Affect Adhesion: An Analysis from the Interactions between Microalgal Cells and Solid Substrates[END_REF][START_REF] Zhang | Cell Surface Energy Affects the Structure of Microalgal Biofilm[END_REF] . Therefore, a better understanding of algae surface physics is particularly interesting to enhance cell-cell adhesion, thus favoring flocculation.

Conceptually, microalgae can be seen as micrometer sized particles having a non-permeable core surrounded by a charged polyelectrolyte layer in an electrolyte solution. Classically, the electrical properties of colloidal particles are modeled assuming they are non-permeable to electrolyte ions and flow, i.e., hard particles, and these properties are expressed in terms of zeta potential. However, as described above, bioparticles such as microalgae or bacterial cells possess permeable charged EPS layers on their surface [START_REF] Ohshima | On the electrophoretic mobility of biological cells[END_REF] . Therefore, accounting for their electrical properties through the values of zeta potential is not suitable.

Over the years, numerous studies investigated hard particles surrounded by a permeable polyelectrolyte layer, called soft particles [START_REF] Ohshima | Electrophoresis of soft particles[END_REF][START_REF] Saville | Electrokinetic Properties of Fuzzy Colloidal Particles[END_REF][START_REF] Hill | Electrophoresis of spherical polymer-coated colloidal particles[END_REF][START_REF] López-García | Numerical study of colloidal suspensions of soft spherical particles using the network method: 1. DC electrophoretic mobility[END_REF] . A schematic representation of a soft charged particle can be seen in Figure 1. A significant contribution to describing the electrokinetic behavior of a soft particle was made by Ohshima [START_REF] Ohshima | On the electrophoretic mobility of biological cells[END_REF][START_REF] Ohshima | Electrophoresis of soft particles[END_REF] , whose model is the most widely accepted. In short, the soft particle theory is based on the Poisson-Boltzmann equation for the electric potential distribution, the Navier-Stokes equation for the liquid flow, and, to account for the polyelectrolyte layer contribution, a Debye-Bueche model is used [START_REF] Duval | Progress in electrohydrodynamics of soft microbial particle interphases[END_REF][START_REF] Ashrafizadeh | Electrophoresis of spherical soft particles in electrolyte solutions: A review[END_REF] . General ex- pressions can be written from the soft particle theory to predict electrophoretic mobility, but they can only be solved numerically. However, within given sets of approximations, analytic solutions can be derived and applied in many relevant cases [START_REF] Ohshima | Electrophoresis of soft particles[END_REF][START_REF] Ohshima | Electrophoresis of soft particles: Analytic approximations[END_REF][START_REF] Maurya | Electrophoresis of composite soft particles with differentiated core and shell permeabilities to ions and fluid flow[END_REF][START_REF] Ohshima | Approximate analytic expressions for the electrophoretic mobility of spherical soft particles[END_REF] .

This soft particle formalism has already been applied to many particles 21 such as synthetic microgels [START_REF] Fernández-Nieves | Electrophoresis of ionic microgel particles: From charged hard spheres to polyelectrolyte-like behavior[END_REF][START_REF] Daly | Temperature-dependent electrophoretic mobility and hydrodynamic radius measurements of poly (N -isopropylacrylamide) microgel particles: structural insights[END_REF] , humic substances [START_REF] Duval | Humic Substances Are Soft and Permeable: Evidence from Their Electrophoretic Mobilities[END_REF] , natural latex particles [START_REF] Makino | Surface Structure of Latex Particles Covered with Temperature-Sensitive Hydrogel Layers[END_REF][START_REF] Ho | Surface Structure of Natural Rubber Latex Particles from Electrophoretic Mobility Data[END_REF] , yeast [START_REF] Karreman | The stress response protein Hsp12p increases the flexibility of the yeast Saccharomyces cerevisiae cell wall[END_REF][START_REF] Shamrock | The role of the heat shock protein Hsp12p in the dynamic response of Saccharomyces cerevisiae to the addition of Congo red[END_REF] and bacteria [START_REF] Gaboriaud | Coupled Electrostatic, Hydrodynamic, and Mechanical Properties of Bacterial Interfaces in Aqueous Media[END_REF][START_REF] Sonohara | Difference in surface properties between Escherichia coli and Staphylococcus aureus as revealed by electrophoretic mobility measurements[END_REF] .

To the best of our knowledge, there is no study reporting the application of the soft particle theory to microalgae yet. Therefore, the purpose of this study is to evaluate the applicability of soft particle theory to describe the electrostatic behavior of unicellular microalgae. To that effect, the electrokinetic behavior of different microalgae was assessed experimentally and compared to the predictions of the soft particle theory considering their cell's surface structure. Three species were considered: one freshwater species, Chlorella vulgaris (C. vulgaris), and two seawater ones, Nannochloropsis oculata (N. oculata) and Tetraselmis suecica (T. suecica). Then, the charge density of the polyelectrolyte layer (ZN ) and hydrodynamic softness (λ shell ) of each microalga was evaluated by fitting the data to the soft particle predictions. To validate the applicability of the surface properties obtained by considering the microalgae as soft colloids, the confidence interval of estimated parameters was calculated.

Finally, the extracted parameters, charge density and penetration length, combined with transmission electron microscopy (TEM) observations provided detailed insights into the algae cells' surfaces and consequently a better understanding of their behavior in suspension.

Materials and Methods

Microalgal Strains

C. vulgaris (CA104), N. oculata (CA101), and T. suecica (CA106) in the exponential growth phase were obtained from Greensea culture collection at Mèze, France. The cultures were stored in the dark at 4 °C in the refrigerator and used within 3 weeks of receipt.

Electrophoretic Mobility

For electrophoretic mobility measurements, the cells were centrifuged at 20 °C for 20 min under 3000×g, washed, and resuspended in KNO 3 solutions with adjusted ionic strengths in the range of 1-200 mM with a final cell concentration of approximately 10 7 cells/mL. The cell concentration was estimated using a Neubauer counting chamber (Blaubrand, Germany) with a depth of 0.1 mm. Cell integrity was evaluated before and after centrifugation with an optical inverted microscope in transmitted light (Zeiss Axio Observer A1).

The electrophoretic mobility was measured as a function of the ionic strength of the suspensions using a Zetasizer Nano ZS (Malvern, UK) at 20 °C. The suspensions were put into a folded capillary cell (model DTS1070, Malvern, UK) with a syringe to prevent the formation of air bubbles. Experiments were repeated ten times for each suspension, the average values and standard deviations were then calculated and reported in the appropriate figures.

Transmission Electron Microscopy

Transmission electron micrographs of microalgae ultrathin sections were taken with a JEOL JEM-1400 HC microscope equipped with a Gatan Orius SC1000B CCD camera. For the preparing of the ultrathin sections, the algae suspensions were first centrifuged at 280×g for 5 min. The supernatant was collected to prepare a 2.5% glutaraldehyde/2% paraformaldehyde solution that was used to fix the microalgae pellet at ambient temperature for 2 hours.

The samples were then washed once with the supernatant and twice with water, before being chemically fixed with 1% osmium tetroxide for 1 hour, the excess fixative being removed by water washing. The microalgae pellet was then embedded in agarose (2%) and the consolidated sample, placed in an Eppendorf cone, was dehydrated in ascending ethanol series (25, 50, 70 and 90% for 15 min and three times in 100% for 30 min). The microalgae pellet in ethanol was then gradually infiltrated in epoxy resin (25, 50 and 75% for 1 h, and twice in 100% for 12 h) and polymerized in molds at 60 °C for 48 h. The ultrathin sections (80 nm thick), cut using an ultra-microtome fitted with a diamond knife (Leica UCT), were collected on Formvar-covered copper grids (Mesh 200) and stained with UranyLess to enhance contrast.

Theory Soft Particle Theory

The Helmholtz-Smoluchowski equation (Equation ( 1)) is generally used to calculate from mobility measurements the potential at the shear plane surrounding the flowing particle, i.e., the zeta potential (ζ) [START_REF] Masliyah | Electrokinetic and colloid transport phenomena[END_REF] . The absolute values of the particle's surface potential and the ζ potential differ theoretically, but in practice, they are often considered the same since they differ only slightly and the latter can be conveniently determined for hard particles from electrophoretic mobility measurements through:

µ = ζ ϵ 0 ϵ r η ( 1
)
where µ is the electrophoretic mobility, ϵ the vacuum permittivity, ϵ r the dimensionless relative permittivity of the medium, and η the viscosity of the medium. This equation is valid only if the diffuse layer's thickness is small compared to the particle size, i.e., κa ≫ 1, where κ is the Debye-Hückel parameter which is a function of the ionic strength and a is the particle radius. Furthermore, this equation was first developed to describe hard particles (non-deformable and non-permeable). Conversely, when the particle contains an outer shell permeable to electroosmotic flow (flow of electrolytes relative to a charged surface/particle due to an applied field [START_REF] Masliyah | Electrokinetic and colloid transport phenomena[END_REF] ) and ions, i.e., in the case of a soft particle, the ζ potential cannot be strictly defined by Equation (1) anymore.

There is a fundamental difference in electrokinetic behavior between hard and soft particles: at high ionic strength, the electrophoretic mobility of a hard particle goes to zero whereas that of a soft particle reaches a non-zero plateau [START_REF] Dukhin | Electrophoresis of soft particles at high electrolyte concentrations: An interpretation by the Henry theory[END_REF] . Indeed, under high salt concentration conditions, the electric double layer is compressed, resulting in the screening of surface charges by solute ions, leading to zero mobility for hard particles. By contrast, the electrophoretic mobility of a soft particle originates from two phenomena: (i) the electric double layer, as for hard particles, and (ii) the electroosmotic flow within a permeable polyelectrolyte shell. The latter is responsible for a non-zero plateau value at high ionic strength [START_REF] Duval | Progress in electrohydrodynamics of soft microbial particle interphases[END_REF][START_REF] Dukhin | Electrophoresis of soft particles at high electrolyte concentrations: An interpretation by the Henry theory[END_REF] .

The soft particle theory developed by Ohshima attempts to explain the electrokinetic behavior of soft colloidal particles. The main assumptions [START_REF] Ohshima | Electrophoresis of soft particles: Analytic approximations[END_REF][START_REF] De Kerchove | Relevance of electrokinetic theory for "soft" particles to bacterial cells: implications for bacterial adhesion[END_REF] of this model are: (i) the Reynolds number of the liquid inside and outside the polymeric shell is small enough to neglect the inertial term of the Navier-Stokes equation; (ii) the applied electrical field is weak, thus, the particle velocity is proportional to the electrical field; (iii) the slipping plane is situated on the particle core surface; (iv) the particle core is impermeable to ions meanwhile the polyelectrolyte outer shell is permeable; (v) the charged groups are completely dissociated (no pH dependency) and uniformly distributed in the polyelectrolyte layer [START_REF] Duval | Progress in electrohydrodynamics of soft microbial particle interphases[END_REF][START_REF] Duval | Analysis of the Interfacial Properties of Fibrillated and Nonfibrillated Oral Streptococcal Strains from Electrophoretic Mobility and Titration Measurements: Evidence for the Shortcomings of the 'Classical Soft-Particle Approach[END_REF] ;

(vi) the relative permittivity inside and outside the polymeric shell are equal.

In the case of biological cells, Ohshima and Kondo 11 , through simplifications and new assumptions, reduced the initial complex set of equations describing the electrophoretic mobility to the following analytical expression:

µ = ϵ 0 ϵ r η ψ 0 /κ m + ψ D /λ shell 1/κ m + 1/λ shell + ZeN ηλ 2 shell ( 2
)
where ψ D , and ψ 0 are the Donnan and surface potentials respectively (Figure 2), κ m is the Debye-Hückel parameter of the polyelectrolyte layer, Z the valence of charged groups in the polymer shell, e the elementary charge, N the density of charged groups in the permeable polyelectrolyte shell and λ shell the softness parameter of the polyelectrolyte layer. ψ D , ψ 0 , and κ m are given by Equations (3-5):

ψ D = kT ze ln ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ZN 2zn ∞ + {( ZN 2zn ∞ ) 2 + 1} 1/2 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (3)
ψ 0 = ψ D + 2n ∞ kT ZeN ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 1 -{( ZN 2zn ∞ ) 2 + 1} 1/2 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (4)
κ m = κ [1 + ( ZN 2zn ∞ ) 2 ] 1/4 ( 5
)
where k is the Boltzmann constant, T the temperature, z, and n ∞ are the valence, and the bulk concentration of the symmetrical electrolyte respectively. ψ D , ψ 0 , and κ m are functions of the ionic strength and consequently, the first term of Equation ( 2) tends to zero at high salt concentration, but the second term is constant. Therefore, this model can predict the non-zero plateau observed at high ionic strength as [START_REF] Ohshima | Electrophoresis of soft particles[END_REF][START_REF] Makino | Soft particle analysis of electrokinetics of biological cells and their model systems[END_REF] : remains applicable for sufficiently high ionic strengths where polarization/relaxation effects are indeed negligible and the Debye-Hückel approximation is valid.

µ plateau ∼ ZeN ηλ 2 shell (6)
On the other hand, some studies applied numerical solutions with fewer assumptions to successfully fit the experimental data at several ionic strengths [START_REF] Gaboriaud | Coupled Electrostatic, Hydrodynamic, and Mechanical Properties of Bacterial Interfaces in Aqueous Media[END_REF][START_REF] Duval | Electrophoresis of Diffuse Soft Particles[END_REF][START_REF] Pagnout | What do luminescent bacterial metal-sensors probe? Insights from confrontation between experiments and flux-based theory[END_REF] . For instance, Pagnout et al. [START_REF] Pagnout | What do luminescent bacterial metal-sensors probe? Insights from confrontation between experiments and flux-based theory[END_REF] studied the electrophoresis of Escherichia coli bacteria with different surface structures. The authors correlated the electrokinetic measurements with analytical and rigorous numerical resolutions of the electrohydrodynamics of soft diffuse particles, i.e., taking into account the swelling process of the polyelectrolyte layer and the non-linear Poisson-Boltzmann equation with full integration of double layer polarization/relaxation [START_REF] Duval | Electrophoresis of Diffuse Soft Particles[END_REF] .

Electrostatic Interaction

In order to evaluate the colloidal stability of microalgae suspensions in light of soft particle theory, we must analyze the electrostatic forces at play. Ohshima 38 derived an expression of electrostatic energy between two spherical particles with the help of Derjaguin's approximation, which can be applied to both hard and soft particles. This expression is given by:

V (H) = 4πa 1 a 2 a 1 + a 2 ϵ 0 ϵ r ψ eff1 ψ eff2 e -κH (7)
where H is the distance between the two particles, a 1 and a 2 are the radius of spheres 1 and 2, and ψ eff1 and ψ eff2 are the effective surface potentials of spheres 1 and 2. Equation ( 7) is obtained using a linear superposition approximation (LSA) method.

According to Equation ( 7), the electrostatic energy is proportional to the particle's surface potential. If the charges of the particles are of the same sign, the electrostatic interaction is repulsive. Therefore, by comparing the effective ζ potential (Equation ( 1)) to the surface potential obtained using the soft particle theory (Equation ( 4)), it is possible to evaluate the difference between the predicted electrostatic repulsion using the approach of hard or soft particles.

In summary, Equation ( 7) represents a limiting case for soft particles where: (i) ψ D represents the potential deep inside the polyelectrolyte layer, i.e., λ

-1
shell is much smaller than the thickness of the polymer shell d (λ shell d ≫ 1); (ii) The Debye-Hückel's approximation is valid, i.e., low charged interface and low potential conditions; (iii) Derjaguin's integration is applicable, i.e., the particle size is much greater than the Debye Length, κ -1 ; (iv) LSA is valid, i.e., the particles are far apart (κH ≫ 1); (v) The particles are assumed to be surrounded by an homogeneous shell [START_REF] Duval | Electrostatic interactions between diffuse soft multi-layered (bio) particles: beyond Debye-Hückel approximation and Deryagin formulation[END_REF][START_REF] Ohshima | Electrostatic interaction of soft particles[END_REF] . This equation represents an analytical solution of the electrostatic forces between soft particles, Duval et al. [START_REF] Duval | Electrostatic interactions between diffuse soft multi-layered (bio) particles: beyond Debye-Hückel approximation and Deryagin formulation[END_REF] developed numerical resolutions with fewer assumptions.

Results and Discussion

Electrokinetic Behavior

The electrophoretic mobility of the three different microalgae species was measured as a function of ionic strength (KNO 3 ) and the results are reported in Figure 3. All three microalgae show negative values of electrophoretic mobility, reflecting, as expected, the overall negative surface charge of those microorganisms. In all cases, when salt concentration increases, the mobility becomes less negative due to the screening of the diffusive double layer.

However, the mobility does not go to zero, even at high ionic strength. On the contrary, the mobility tends to a non-zero plateau (better observed in linear scale, Figure S1), a behavior typical of soft particles (Equation ( 6)) [START_REF] De Kerchove | Relevance of electrokinetic theory for "soft" particles to bacterial cells: implications for bacterial adhesion[END_REF] . These results thus suggest that these microorganisms carry a charged and permeable polyelectrolyte type layer. According to Equation (2), the residual finite mobility should only depend on the fixed charged density and the flow permeability of the outer shell.

A typical value for the ionic strength of see water (see for example ASTM standard D1141-98(2013) artificial seawater [START_REF]Standard Practice for the Preparation of Substitute Ocean Water ; Standard[END_REF] ) is approximately 700 mM (vertical blue line in Figure 3). However, due to the degradation of the electrodes from the capillary cell at higher ionic strengths, mobility measurements were made only on samples with ionic strength below 200 mM. Since a plateau was found from approximately 150 mM, it can be expected that the electrophoretic mobility at see water ionic strengths is equal to the plateau value for each microalgae species.

To obey the criteria of κd ≫ 1 assumed in the derivation of Equation ( 2), the quantitative analysis was restricted to salt concentrations greater than 10 mM. Nonlinear least-squares minimization using the Levenberg-Marquardt algorithm implemented by LMFIT Python package [START_REF] Newville | Non-linear least-square minimization and curve-fitting for Python[END_REF] was used to fit the experimental data to Equation (2) (dashed lines in Figure 3). The quantities ZN and λ -1

shell obtained for each microalga from the best fit are listed in Table 1, these results are comparable with the values for others microorganisms [START_REF] Duval | Progress in electrohydrodynamics of soft microbial particle interphases[END_REF][START_REF] Louie | Parameter Identifiability in Application of Soft Particle Electrokinetic Theory To Determine Polymer and Polyelectrolyte Coating Thicknesses on Colloids[END_REF] . At low salt concentrations, the mobility of microalgae does not fit the model well, as can be seen in Figure 3. Many studies observed similar deviation in other soft particles at low ionic strength. This observation was attributed to polarization/relaxation of the electric double layer that is neglected in Equation ( 2), to the non-homogeneous fixed charges distribution within the polyelectrolyte layer and to the high electric potentials experimented at low ionic strength (i.e., Debye-Hückel's approximation is not valid) [START_REF] Gaboriaud | Coupled Electrostatic, Hydrodynamic, and Mechanical Properties of Bacterial Interfaces in Aqueous Media[END_REF][START_REF] Sonohara | Difference in surface properties between Escherichia coli and Staphylococcus aureus as revealed by electrophoretic mobility measurements[END_REF][START_REF] De Kerchove | Relevance of electrokinetic theory for "soft" particles to bacterial cells: implications for bacterial adhesion[END_REF][START_REF] Vouriot | Electrophoresis as a simple method to detect deleterious actions of engineered nanoparticles on living cells[END_REF] .

All the characteristic hydrodynamic penetration length values in the outer shell (λ

-1 shell )
found by fitting experimental data to Equation (2) ranged from one to two nanometers for the three microalgae species studied (Table 1). Concerning the permeable layer charge concentration, N. oculata and T. suecica exhibit a higher charge concentration than C.

vulgaris (Table 1). Moreover, N. oculata and C. vulgaris have a slightly lower penetration length (λ

-1
shell ) reflecting a possibly less permeable surface than T. suecica.

Confidence Interval

In order to investigate the significance of values obtained from the best fit, the confidence interval of parameters ZN and λ shell were estimated using the LMFIT Python package.

Results are shown in Table S1 in the Supplementary Information. LMFIT uses the F-test to obtain these confidence intervals. It compares the null model (the best fit found) with an alternative model, where one of the parameters is fixed to a specific value [START_REF] Newville | Non-linear least-square minimization and curve-fitting for Python[END_REF] .

Table S1 shows the best-fit values for the parameters, and parameter values that are at the varying confidence levels given by steps in σ (standard deviation), from 1-σ (68.27% confidence) to 3-σ (99.73% confidence). The errors are asymmetric; this is due to the complexity of the model used which comes from Equation (2).

Plots of the confidence region are shown in Figure 4; they have an elongated and curved shape. The surfaces reveal a small darker area corresponding to a high confidence level.

From Table S1 and Figure 4, it can be observed that the fit is in general more sensitive to variations of λ

Surface Potential

As mentioned in the introduction, the use of zeta potential to quantify the charge of microalgae is physically inappropriate. Indeed, using Equation ( 4), it is possible to estimate the outer surface potential of microalgae at different ionic strengths. Figure 5 compares these values to the apparent zeta potential calculated from the Helmholtz-Smoluchowski Equation (1). It can be observed that the surface potentials of N. oculata and T. suecica have approximately the same value at all probed ionic strength. This is because the surface potential calculated from Equation (4) only depends on the ionic strength and the polyelectrolyte layer's charge density ZN , and this latter value is similar for these two microalgae (Table 1). At high ionic strength, ψ 0 tends to zero for all three algal strains: this behavior can be attributed to the suppression of the surface potential due to the compression of the electric double layer [START_REF] De Kerchove | Relevance of electrokinetic theory for "soft" particles to bacterial cells: implications for bacterial adhesion[END_REF] . By contrast, the non-zero electrophoretic mobility at high ionic strength imposes to consider non-zero apparent ζ potential, an unrealistic occurrence under such conditions where the Debye length tends to zero.

As seen in Figure 5, the absolute values of the outer surface potential (ψ 0 ) of microalgae, The outer surface potentials, ψ 0 , were determined from the fitting of the measured electrophoretic mobilities to Ohshima's theory (Equation ( 2)). The apparent zeta potentials, ζ, were calculated from the measured electrophoretic mobilities using the Helmholtz-Smoluchowski Equation (1).

Error bars correspond to standard deviations.

obtained applying Ohshima's formalism, are smaller than the absolute value of the ζ potential, obtained following the Helmholtz-Smoluchowski equation. This indicates that the electrostatic force is smaller using ψ 0 as the effective surface potential in Equation ( 7) than using ζ [START_REF] Morisaki | The effect of motility and cell-surface polymers on bacterial attachment[END_REF][START_REF] Hori | Bacterial adhesion: From mechanism to control[END_REF] . In other words, the expected electrostatic repulsion between cells is notably smaller than that usually expected when simply considering ζ potentials that do not take into account the soft character of microalgae [START_REF] Zhang | Cell Surface Energy Affects the Structure of Microalgal Biofilm[END_REF][START_REF] Ozkan | Physico-chemical surface properties of microalgae[END_REF] . In other words, the electrostatic contribution to the colloidal stability of microalgae cells in suspension might be less important than expected from ζ potentials measurements.

Microalgae Morphology

In complement to the electrophoretic mobility measurements, the surface morphology of microalgae was investigated under optical and TEM microscopy. The results are shown in Figure 6. Chlorella vulgaris has a spherical to ellipsoidal shape, with a mean diameter of 4 µm in the growth phase (Figure 6a). Its cell wall is composed of electron-dense layers with short fibers which protrude from the outer layer (Figures 6d and6g). The microalgae's cell wall varies according to the cell growth stage and environmental conditions [START_REF] Safi | Morphology, composition, production, processing and applications of Chlorella vulgaris: A review[END_REF] . By measuring the thickness of the new daughter cell wall at different growth phases, Yamamoto et al.

48

classified C. vulgaris as an early type species, meaning that synthesis of the daughter cell wall begins at the early growth phase. This implies that the cell wall of C. vulgaris is thinner initially and gets thicker at the beginning of the growth phase due the formation of a daughter cell wall between the mother cell wall and the plasma membrane [START_REF] Baudelet | A new insight into cell walls of Chlorophyta[END_REF] . The cell wall thickness of C. vulgaris cells observed by TEM (Figure 6g) is between 50 and 150 nm, which may correspond to a combination of mother and daughter cell walls. Most interestingly, a layer of EPS extending away from the surface is apparent with a thickness in the range of 10 nm.

Nannochloropsis oculata is a small green spherical or oval cell measuring around 2 µm in diameter (Figures 6b and6e). As shown by TEM (Figure 6h), the N. oculata cell wall is composed of two layers and extensions protruding from the outer surface, with a cell wall thickness varying from 30-100 nm. The bilayer of the genus Nannochloropsis is composed of an inner cellulose layer and an outer algaenan layer [START_REF] Scholz | Ultrastructure and composition of the Nannochloropsis gaditana cell wall[END_REF] . A layer of EPS is also observed, albeit less evident than in the Chlorella vulgaris case.

(a) (b) (c) (d) (e) (f ) (g) (h) (i)
Tetraselmis suecica has an elongated shape and is 10-20 µm in length. It is a flagellated species, however, it was verified by optical microscopy that these cells lost their flagella during the centrifugation step of the samples preparation for electrophoretic mobility measurements (Figure 6c). From TEM micrographs (Figures 6f and6i), it is possible to observe a three-layer outer structure composed of a median electron-translucent layer between two electron-dense layers with fibers extending from outer layer. This structure can be attributed to the mother (outer layer) and daughter (inner layer) cell walls of T. suecica. When the mother cell wall breaks, the release of daughter cells occurs [START_REF] Abiusi | Growth, photosynthetic efficiency, and biochemical composition of Tetraselmis suecica F&M-M33 grown with LEDs of different colors[END_REF] . Daughter and mother cell wall thicknesses vary from 20-90 nm. Once again, a layer of EPS extend from the cells surfaces.

For all three species investigated, fiber structures were identified in the outermost surface layer corresponding to EPS layer. This EPS layer thicknesses observed on the TEM images (Figures 6g to 6i) were in few tens of nanometers and can be identified with the permeable shell evidenced from electrokinetics considerations. This results along with the estimated hydrodynamic penetration lengths (λ -1

shell in Table 1) are in accordance with Equation ( 2) assumption that λ shell d ≫ 1.

TEM has potential artifacts from sample preparation, therefore the dimensions obtained from TEM micrographs are not necessarily exact, but they remain representative of what occurs in suspension and of the actual state of the microalgae cells under investigation.

Conclusion

In the present work, we studied the electrostatic behavior of three microalgae species:

C. vulgaris, N. oculata, and T. suecica in solution as a function of the ionic strength using electrophoretic experiments. The variation of electrophoretic mobility with ionic strength was adjusted to the soft particle theory, confirming the soft nature of these microorganisms characterized by having an outer permeable layer. It transpired that the ζ potential is not a pertinent parameter to describe algal cell electrokinetic behavior and cannot be used to assess surface charge potential. An important consequence is that electrostatic phenomena might contribute less than usually expected to the colloidal stability of microalgae and that the balance between repulsive electrostatic and attractive hydrophobic interactions 52,53 should be reconsidered using the soft particle theory. The role of the charges within the extracellular polymeric substances' corona around the microalgae cell walls is then essential in controlling their flocculation and adhesion, [START_REF] Chen | Enhanced Secretions of Algal Cell-Adhesion Molecules and Metal Ion-Binding Exoproteins Promote Self-Flocculation of Chlorella sp. Cultivated in Municipal Wastewater[END_REF][START_REF] Demir | Nanoscale Evidence Unravels Microalgae Flocculation Mechanism Induced by Chitosan[END_REF] but cannot be comprehended solely through the measurement of an effective ζ potential. This study is thus a starting point for a better understanding of the colloidal behavior of microalgae in their natural environment or for devising new ways to improve microalgae harvesting, reducing overall energy consumption during microalgae production.

Figure 1 :

 1 Figure 1: Schematic representation of a soft charged particle with total radius b composed of a hard core of radius a and a permeable charged polymeric layer of thickness d.

Figure 2 : 1 shell 1 shell

 211 Figure 2: Schematic representation of the electric potential distribution of a soft particle. The particle is constituted of an impermeable non-charged core surrounded by a soft polyelectrolyte layer. In the present case, according to Equation (2), the polyelectrolyte layer d is thicker than the Debye length 1/κ.

Figure 3 :

 3 Figure 3: Electrophoretic mobility as a function of solution ionic strength (KNO 3 ) for three microalgae species: C. vulgaris, N. oculata, and T. suecica. The markers represent the average experimental mobility measurements, error bars correspond to standard deviations and the dashed line is a fit of experimental data at a high salt concentration to Equation (2). The vertical blue line corresponds approximately to the ionic strength of seawater.

- 1 shell

 1 than to variations in ZN .

Figure 4 :

 4 Figure 4: Confidence intervals obtained using LMFIT Python package for the charge density of the polymeric layer, ZN , and the hydrodynamic penetration length, λ -1 shell , for three microalgae

Figure 5 :

 5 Figure 5: Surface potential (filled markers), ψ 0 , and zeta potential, ζ (open markers) as a function of ionic strength of three microalgae species: C. vulgaris ( ), N. oculata (▲), and T. suecica (◆).

Figure 6 :

 6 Figure 6: Light microscopic micrographs at 20X magnification of (a) C. vulgaris, (b) N. oculata and (c) T. suecica suspensions after sample preparation for electrophoretic mobility measurements at 1 mM KNO 3 . Transmission electron micrographs of (d)-(g) C. vulgaris, (e)-(h) N. oculata and (f )-(i) T. suecica.

Table 1 :

 1 Values of charge density ZN (in mM) and hydrodynamic penetration length λ

	-1 shell (in

Acknowledgement

BL thanks Vanessa Soldan (METI) for precious help with resin embedding of microalgae.

The authors are thankful to Jérôme F. L. Duval (LIEC, Nancy, France) for helpful discussion about soft particle theory.

Funding Sources

This study was supported by TotalEnergies OneTech (Lacq, France). PAG's doctoral thesis is funded by TotalEnergies OneTech through a CIFRE ANRT fellowship N°2021/0655.

Supporting Information Available

Electrophoretic mobility as a function of ionic strength in linear scale (Figure SI-1) and confidence intervals obtained by LMFIT (Table SI-1).

Author Information

Notes

The authors declare no competing financial interest.