L Barbier
email: lucile.barbier@espci.fr

M Protat
email: mprotat@hotmail.com

P Pipart

A Marcellan
email: alba.marcellan@espci.fr

Y Tran

D Hourdet

Sol/gel transition of thermoresponsive Hyaluronan: from liquids to elastic and sticky materials

Keywords: Hyaluronan, hydrogel, tissue engineering, thermo-responsive polymers, gelation

Thermoassociating copolymers were prepared by grafting temperature responsive poly(Nisopropylacrylamide-stat-N-tert-butylacrylamide) telomers onto hyaluronan. By varying the composition of LCST side chains, from 50 to 100 wt% of NIPAM units, it is shown that the sol/gel transition of entangled solutions can be accurately controlled in the range of 10 to 35 °C with an abrupt transition and reversible properties. Complementary experiments, performed by DSC and NMR, demonstrate the close relationship between thermoassociation of LCST grafts, forming microdomains of low mobility, and macroscopic properties. Moreover, by performing tack experiments during heating we demonstrate that hyaluronan formulations abruptly switch from a weak adhesive viscous behavior to an elastic adhesive profile in the gel regime. As LCST side-chains form concentrated micro-domains of low mobility, physical gels can resist to dissociation above their sol/gel transition for relatively long periods when immersed in excess physiological medium. The thermoassociative behavior of these copolymers, whose properties can be finely tuned in order to form sticky gels at body temperature, clearly demonstrates their potential in biomedical applications such as injectable gels for drug delivery or tissue engineering.

Introduction

Thermo-responsive polymers have attracted considerable attention during the last 30 years as they can be easily used to design smart macromolecular architectures able to reversibly selfassemble in aqueous media. In this context, and depending on the application, the transition temperature (Tas) and the extent of the phase separation (from micro to macro) are two relevant parameters that are directly related to the macromolecular design.

Concerning the association temperature, the adequate responsive trigger can be easily selected from the wide list of polymers having a Lower Critical Solution Temperature (LCST) in water like N-substituted poly(acrylamide)s, poly(N-vinyl amide)s, poly(oxazoline)s, poly(ether)s, or poly(oligo(ethylene glycol)methacrylate) (POEGMA) [START_REF] Aseyev | Non-ionic Thermoresponsive Polymers in Water. Self Organized Nanostructures of Amphiphilic Block Copolymers Ii[END_REF]. This non exhaustive selection is clearly limitless if we consider the possibility to tune the "LCST" of a macromolecular chain by introducing more hydrophilic or hydrophobic comonomers [START_REF] Durand | Thermoassociative graft copolymers based on poly(Nisopropylacrylamide): Relation between the chemical structure and the rheological properties[END_REF][START_REF] Liu | Lower critical solution temperatures of N-substituted acrylamide copolymers in aqueous solutions[END_REF]. Once chosen the LCST trigger, the self-assembling remains the central feature as it tightly correlates the macromolecular architecture to the macroscopic properties.

During the 80's, there were a lot of theoretical and experimental works on LCST hydrogels and particularly on poly(N-isopropylacrylamide) [PNIPAM], concerning the swelling/collapse behavior induced by temperature or other external parameters like salt, pH, added surfactant or co-solvent [START_REF] Irie | Stimuli-Responsive Poly(N-Isopropylacrylamide) -Photoinduced and Chemical-Induced Phase-Transitions[END_REF][START_REF] Kokufuta | Effects of Surfactants on the Phase-Transition of Poly(N-Isopropylacrylamide) Gel[END_REF][START_REF] Shibayama | pH and salt concentration dependence of the microstructure of poly(N-isopropylacrylamide-coacrylic acid) gels[END_REF][START_REF] Suzuki | Phase-Transition in Gels of Submillimeter Size Induced by Interaction with Stimuli[END_REF][START_REF] Zhang | Super-Absorbency and Phase-Transition of Gels in Physiological Salt-Solutions[END_REF]. In this case, similar to the coil/globule transition of a single macromolecule, researchers at that time were mainly interested in the volume transition of polymeric materials and to a lesser extent in the mechanical transition induced in isochoric conditions [START_REF] Shibayama | Phase-Separation Induced Mechanical Transition of Poly(N-Isopropylacrylamide) Water Isochore Gels[END_REF]. With respect to solutions, it is often necessary to maintain the integrity of the formulation and to avoid a macroscopic phase separation at high temperature. For that purpose, the responsive polymer has to be introduced sequentially within the water-soluble structure in order to stabilize the phase separation at a microscopic level. This concept of thermo-associating or thermo-thickening copolymers, initially developed with cellulosic derivatives [START_REF] Desbrieres | Thermogelation of methylcellulose: rheological considerations[END_REF][START_REF] Heymann | Studies on sol-gel transformations. I. The inverse sol-gel transformation of methylcellulose in water[END_REF][START_REF] Suto | Lyotropic liquid-crystalline solutions of hydroxypropyl cellulose in water -effect of salts on the turbidity and viscometric behavior[END_REF], have been expanded since with synthetic block copolymers of poly(ethylene oxide) [PEO] and poly(propylene oxide)

[PPO] [START_REF] Brown | Triblock copolymers in aqueous-solution studied by static and dynamic light-scattering and oscillatory shear measurements -influence of relative block sizes[END_REF][START_REF] Mortensen | Phase-behavior of poly(propylene oxide) poly(ethylene oxide) poly(propylene oxide) triblock copolymer melt and aqueoussolutions[END_REF] (pluronics) and then explicitly rationalized with graft copolymers tailored with LCST side-chains [START_REF] Bromberg | Scaling of rheological properties of hydrogels from associating polymers[END_REF][START_REF] Hourdet | Reversible gelation of aqueous polymer solutions induced by responsive stickers[END_REF][START_REF] Hourdet | Smallangle neutron scattering study of microphase separation in thermoassociative copolymers[END_REF][START_REF] Hourdet | Reversible thermothickening of aqueous polymer-solutions[END_REF]. When responsive sequences and water-soluble counterparts are well-balanced within the macromolecular architecture, a physical network can be formed and remain stable without syneresis, even at high temperature, provided that the concentration is high enough to allow percolation through the whole volume of the solution. These responsive copolymers are of great interest as they provide technological responses for complex fluids which require improved rheological properties above a given temperature. This situation typically concerns a wide range of industrial formulations like suspensions, coatings [START_REF] Yeung | Polymers which exhibit thermothickening properties and process making same[END_REF], cosmetics [START_REF] L'alloret | Polymer comprising water-soluble units and LCST units, and aqueous composition comprising same[END_REF], drilling fluids [START_REF] Maroy | Thermoviscosifying polymers, their synthesis and their uses in particular in the oil industry[END_REF] but also biomedical applications [START_REF] Bellotti | Injectable thermoresponsive hydrogels as drug delivery system for the treatment of central nervous system disorders: A review[END_REF][START_REF] Thambi | Stimuli-Sensitive Injectable Hydrogels Based on Polysaccharides and Their Biomedical Applications[END_REF].

In this field, the concept of injectable hydrogels, that are liquid solutions able to form gel at body temperature, is a crucial issue for specific applications. For instance, the possibility to easily inject active molecules initially embedded into liquid formulations able to form gels spontaneously in contact with physiological surfaces, like buccal [START_REF] Zeng | Cyanine derivative as a suitable marker for thermosensitive in situ gelling delivery systems: In vitro and in vivo validation of a sustained buccal drug delivery[END_REF], ocular [START_REF] Destruel | In vitro and in vivo evaluation of in situ gelling systems for sustained topical ophthalmic delivery: state of the art and beyond[END_REF], vaginal [START_REF] Bouttier | Characterization and in vitro evaluation of a vaginal gel containing Lactobacillus crispatus for the prevention of gonorrhea[END_REF], rectal [START_REF] Koffi | Modulation of the rheological and mucoadhesive properties of thermosensitive poloxamer-based hydrogels intended for the rectal administration of quinine[END_REF], nasal [START_REF] Cao | Potential application of injectable chitosan hydrogel treated with siRNA in chronic rhinosinusitis therapy[END_REF] or gastrointestinal mucosa [START_REF] Miura | The feasibility of a novel injectable hydrogel for protecting artificial gastrointestinal ulcers after endoscopic resection: an animal pilot study[END_REF], or to protect these surfaces, is clearly a hot topic in drug delivery. In this framework, pluronics, also known as poloxamers, which are FDA approved polymers able to transit from sol to gel in the vicinity of body temperature, are often used as injectable hydrogels Nevertheless they are usually formulated with other polymer, generally polysaccharides, as pluronics exhibit weak mucoadhesive properties [START_REF] Koffi | Modulation of the rheological and mucoadhesive properties of thermosensitive poloxamer-based hydrogels intended for the rectal administration of quinine[END_REF][START_REF] Smart | The basics and underlying mechanisms of mucoadhesion[END_REF].

In tissue regeneration, the possibility to inject liquid formulations containing cells or drugs that will switch to gel in physiological conditions without any chemical reaction is clearly a challenging topic. In this context, responsive hydrogels also need to mimic the chemical and physical environments of the extracellular matrix (ECM) and natural polymers like proteins (collagen, gelatin, fibrin) or polysaccharides (carboxymethylcellulose, chitosan, alginate and hyaluronan) are very good candidates for these applications [START_REF] Boateng | Wound Healing Dressings and Drug Delivery Systems: A Review[END_REF][START_REF] Malafaya | Natural-origin polymers as carriers and scaffolds for biomolecules and delivery in tissue engineering applications[END_REF].

In this context, the use of PNIPAM derivatives as LCST triggers, is very common and versatile as the incorporation of more hydrophobic monomer, such as NtBAM [START_REF] Iatridi | Injectable self-assembling hydrogel from alginate grafted by P(N-isopropylacrylamide-co-N-tert-butylacrylamide) random copolymers[END_REF][START_REF] Muramatsu | Poly(Nisopropylacrylamide-co-N-tert-butylacrylamide)-grafted hyaluronan as an injectable and self-assembling scaffold for cartilage tissue engineering[END_REF][START_REF] Safakas | Alginate-g-PNIPAM-Based Thermo/Shear-Responsive Injectable Hydrogels: Tailoring the Rheological Properties by Adjusting the LCST of the Grafting Chains[END_REF], or more hydrophilic one such as acrylamide [START_REF] Durand | Thermoassociative graft copolymers based on poly(Nisopropylacrylamide): Relation between the chemical structure and the rheological properties[END_REF], allows fine control of the association temperature below or above 32 °C, respectively. Among previous biopolymers, hyaluronic acid (HA), that is one of the main component of ECM in connective, epithelial and neural tissues, clearly appears as a standard and various covalent structures coupling HA to LCST polymers have been developed during the last decade. Different chemistries have been used for this purpose, generally involving covalent coupling between HA and end-functionalized LCST chains [START_REF] D'este | Single step synthesis and characterization of thermoresponsive hyaluronan hydrogels[END_REF][START_REF] Ekerdt | Thermoreversible Hyaluronic Acid-PNIPAAm Hydrogel Systems for 3D Stem Cell Culture[END_REF][START_REF] Ha | Preparation of thermo-responsive and injectable hydrogels based on hyaluronic acid and poly(Nisopropylacrylamide) and their drug release behaviors[END_REF][START_REF] Mortisen | Tailoring Thermoreversible Hyaluronan Hydrogels by "Click" Chemistry and RAFT Polymerization for Cell and Drug Therapy[END_REF][START_REF] Muramatsu | Poly(Nisopropylacrylamide-co-N-tert-butylacrylamide)-grafted hyaluronan as an injectable and self-assembling scaffold for cartilage tissue engineering[END_REF], or graft polymerization on modified HA [START_REF] Ohya | Thermoresponsive artificial extracellular matrix for tissue engineering: Hyaluronic acid bioconjugated with poly(N-isopropylacrylamide) grafts[END_REF][START_REF] Pitarresi | New hyaluronic acid based brush copolymers synthesized by atom transfer radical polymerization[END_REF], and various architectures based on HA grafted with PNIPAM, PEGMA [START_REF] Pitarresi | New hyaluronic acid based brush copolymers synthesized by atom transfer radical polymerization[END_REF], poloxamers [START_REF] Ramya | Characterizing the yielding processes in pluronic-hyaluronic acid thermoreversible gelling systems using oscillatory rheology[END_REF] or statistic copolymers of ethylene oxide and propylene oxide [START_REF] D'este | Single step synthesis and characterization of thermoresponsive hyaluronan hydrogels[END_REF] have been designed with a wide panel of thermo-thickening properties and applications like differentiation of human mesenchymal stem cells, cartilage regeneration [START_REF] Muramatsu | Poly(Nisopropylacrylamide-co-N-tert-butylacrylamide)-grafted hyaluronan as an injectable and self-assembling scaffold for cartilage tissue engineering[END_REF] (repair) or cell-based therapy in disc repair [START_REF] D'este | Evaluation of an injectable thermoresponsive hyaluronan hydrogel in a rabbit osteochondral defect model[END_REF][START_REF] Peroglio | Thermoreversible hyaluronan-based hydrogel supports in vitro and ex vivo disc-like differentiation of human mesenchymal stem cells[END_REF]Marianna Peroglio et al., 2012;[START_REF] Rosenzweig | Thermoreversible hyaluronan-hydrogel and autologous nucleus pulposus cell delivery regenerates human intervertebral discs in an ex vivo, physiological organ culture model[END_REF].

Depending on the application, a wide range of specifications are required such as 1) low viscosity below body temperature to inject the formulation, 2) sol/gel transition just below body temperature with thermodynamic and kinetic control of the phase transition, 3) specific gel properties including elastic modulus, deformability, adhesiveness, swelling and stability in physiological environment and 4) biocompatibility and biodegradability.

In this context, our main motivation was to develop a comprehensive study of injectable hydrogels based on hyaluronan grafted with different LCST side-chains in order to investigate their impact on the association behavior and the gel properties. To this end, we designed 3 graft copolymers of similar topology (see Scheme 1) starting from a long Hyaluronan backbone and shorter side chains (about one tenth of the Hyaluronan molar mass).

HA-g-P100

HA-g-P75 HA-g-P50 Scheme 1. Schematic representation of graft copolymers designed from the same Hyaluronan backbone (HA) and different LCST side-chains (Px) of similar molar masses. The sidechains, Px, were prepared by copolymerization between N-isopropylacrylamide (NIPAM) and N-tert-butylacrylamide (NtBAM), with x corresponding to the weight fraction of NIPAM.

By synthesizing these copolymers with equivalent mass fractions of backbone and side chains, this design makes it possible to obtain graft copolymers with a sufficient number of responsive grafts capable of developing efficient associative properties. For that purpose, we prepare a series of LCST copolymers by copolymerization of NIPAM with N-tert-butylacrylamide (NtBAM) in order to tune the transition temperature below body temperature, typically between 10 and 30 °C.

After grafting the LCST polymer onto the hyaluronan backbone, we will investigate the effect of grafting on the transition temperature (Tas) and the influence of polymer concentration on the sol/gel transition with respect to the regime of concentration. The viscoelastic behavior will be discussed in relation to current theories on associating polymers. Gel properties will be explored further, either beyond the linear regime by probing the adhesive behavior in the course of the transition, but also in long term experiments to investigate their swelling properties as well as their stability under physiological conditions.

Experimental section

Reagents and solvents

N-isopropylacrylamide (NIPAM, Aldrich), N-tert-butylacrylamide (NtBAM, Aldrich), cysteamine hydrochloride (AET, Sigma), potassium peroxodisulfate (KPS, Acros), 1-[3dimethylaminopropyl]-3-ethylcarbodiimide hydrochloride (EDC, 98%, Acros), Nhydroxysuccinimide (NHS, 98%, Aldrich) were used as received without further purification.

Water was purified with a Millipore system combining inverse osmosis membrane (Milli RO)

and ion exchange resins (Milli Q).

Polymer precursors

Hyaluronan backbone.

A Hyaluronan sample (HA) was purchased from Soliance (France). The number average molar mass, characterized by Size Exclusion Chromatography, was Mn = 200 kg/mol with a dispersity of molar masses Ð  2.

Amino-terminated P(NIPAM-stat-NTBAM)

The synthesis of functional chains was carried out by telomerization, which allows controlling the polymer end-group as well as its molar mass. The same protocol detailed in reference (Durand & Hourdet, 1999) was applied for the three copolymers taking care that the reaction takes place below or around 5 °C under nitrogen atmosphere. As NtBAM is less soluble in water than NIPAM, its copolymerization was carried out in more dilute conditions (see Table 1). The synthesis of cotelomers can be summarized as follows in the case of PNIPAM: in a three necked flask, 15.3 g of NIPAM (135 mmol) was dissolved in 135 mL of water and the solution was deoxygenated for 1 h with nitrogen bubbling in an iced bath. Redox initiators, KPS (0.37 g; 1.35 mmol) and AET, HCl (0.31 g; 2.7 mmol), were separately dissolved in 10 mL and 5 mL of water, respectively, before addition to the monomer solution. The reaction was allowed to proceed at low temperature, below 5 °C in order to avoid phase separation of the copolymer. After 4 hours, an appropriate amount of sodium hydroxide was added to neutralize ammonium end-groups and the polymer was recovered by dialysis against pure water and freeze-dried. Three PNIPAM copolymers were prepared in these conditions, with an initial weight feed of NIPAM (x) of 100, 75 and 50 wt% (see Table 1). The copolymers will be named Px, with x the weight percentage of NIPAM in the copolymer. The synthesis yield after dialysis was between 65-85 wt% for all the reactions. Composition and molar mass of the copolymers were obtained by titration, 1 H NMR and SEC.

Grafting reaction

The coupling reaction between carboxyl groups of HA and terminal amine of PNIPAM derivatives was carried out in cold water using EDC/NHS as coupling reagents, following the procedure already reported for other synthetic and natural polymers (Durand & Hourdet, 1999;[START_REF] Guo | Cold and Hot Gelling of Alginate-graft-PNIPAM: a Schizophrenic Behavior Induced by Potassium Salts[END_REF][START_REF] Karakasyan | Synthesis and rheological properties of responsive thickeners based on polysaccharide architectures[END_REF]. A schematic representation of the reaction process is given in Scheme S1 in supporting information. The same procedure has been followed for all the copolymers except the concentration of polymers which has been slightly reduced for the grafting of P50 and P75 in order to avoid interchain coupling initially observed during the grafting of P100 (see Table 2). A typical reaction can be summarized as follows for the grafting of PNIPAM onto HA. In a reaction vessel equipped with a magnetic stirrer, 6 g of HA was initially dissolved under stirring in 200 mL of water for at least 24 hours at room temperature. 6 g of PNIPAM was separately dissolved in 100 mL of cold water in order to get a homogeneous solution and the pH was adjusted around 5-6 with hydrogen chloride (1 mol/L). After cooling the HA solution in an iced bath at T = 2-3 °C, the solution of PNIPAM was slowly added and the pH was controlled again and adjusted to pH 5 to 6, if necessary, while adjusting the total amount of water to 350 mL before reaction. After one hour of mixing under stirring below 10 °C, a series of 5 daily feeds of NHS/EDC, initially dissolved separately in 5 mL of water, were added into the reaction vessel and the reaction was let to proceed for at least 24 hours after the last feed. In these conditions, the total molar ratio EDC/COOH  1 with a fixed molar ratio EDC/NHS = 1.6. The polymer solution was then purified by dialysis initially against sodium chloride 0.1 mol/L, to remove the large excess of positively charged EDC, and then against pure water before freeze drying. The total feed conditions and the yield of the synthesis are given in Table 2.

Size Exclusion Chromatography (SEC)

Hyaluronan precursor (HA) and homoPNIPAM (P100) have been characterized by SEC using a Waters system equipped with three Shodex OH-pak columns equilibrated at T = 20°C in aqueous solution (NaNO3 0.5 mol/L). A triple detection "viscometry/light scattering/refractometry" allows an absolute characterization of the molar masses after an initial calibration of the columns with PEO standards. The two other PNIPAM copolymers (P50 and P75) were characterized similarly by SEC in THF.

Preparation of copolymer solutions

All studies were performed in the semi-dilute regime, either in pure water or in physiological conditions using phosphate buffer saline (PBS) solutions. For each solution, copolymer and solvent were weighted, mixed and let to dissolve under magnetic stirring in a cold bath until homogenous solutions were obtained. Then, samples were stored between 1 to 5 days in the fridge prior to analysis. Polymer concentrations are given in weight percentage (wt%).

Linear rheology

Viscoelastic properties of graft copolymers in aqueous solutions were studied in the semi-dilute regime using a stress-controlled rheometer (Haake RS600) equipped with a cone/plate sanded geometry (diameter 35 mm, angle 2°, truncature 103 m). Experiments were performed in the linear viscoelastic regime which was determined for each sample after various stress sweep and frequency sweep experiments performed at different temperatures: 10, 37 and 60 °C (see Figure S2). A particular care was taken to avoid drying of the sample by using a homemade cover which prevents from water evaporation during experiment. Temperature scanning experiments were performed at constant frequency (1 Hz) and shear stress (2 Pa) by applying consecutive heating and cooling scans at 2°C.min -1 with a high power Peltier system that provided fast and accurate adjustment of the temperature. In these conditions, storage (G') and loss (G″) moduli (see Figure S3) as well as complex viscosity (*) were recorded between 2-10 and 50-60°C according to the sample. Reproducibility was verified for each experiment.

Probe Tack Test.

Probe tack experiments were adapted from the original work of Vahdati et al. (Vahdati, Ducouret, Creton, & Hourdet, 2020a) using a DHR-3 rheometer (TA Instruments). Using stainless steel surface as simple model, tack tests were performed between a top flat sand-blasted probe ( 2 0 0 4 r a 

 with r0 = 10 mm), attached to the axial load cell of the rheometer, and a bottom sandblasted plate mounted on the Peltier temperature control system. Initially set at low temperature, a precise volume of liquid polymer solution has been carefully deposited with a micropipette on the bottom plate and the probe was then brought into intimate contact by squeezing the solution to the initial thickness (h0 = 400 µm). The layer was then heated rapidly to the target temperature, followed by a 10 min standing time to make sure that temperature is homogeneous across the sample. The axial force (F) required to detach the probe at a constant debonding rate (v = 100 µm.s -1 ) was recorded as a function of time (t) or displacement (h). Finally, nominal stress (σ=F/a0) was plotted versus nominal strain (ε=(h-h0)/h0) and work of adhesion (Wadh) was calculated from the product of the initial thickness and the area under nominal stress-strain curves up to failure:

   max 0 0 ) (     d h W adh .
All the probe tack tests were performed at least twice.

Swelling experiments

In order to get information about the stability of physical gels in aqueous environments, swelling experiments were carried out with HA-g-P100 and HA-g-P50 in the gel state. After thermal equilibration during 15 minutes at T = 37 °C for HA-g-P50 (or 50 °C for HA-g-P100) in a plastic syringe, a piece of cylindrical gel was weighted (m0= mp,0/wp), with mp,0 the initial mass of polymer in the piece of gel and wp the initial weight fraction of polymer, before being immersed in a large excess of water or PBS solution also at 37 °C (or 50 °C). The sample was then weighted as a function of time (mt) and then finally dried in order to estimate the fraction of extractable:

  0 , , 0 , p t p p ext m m m w  
, with mp,t the mass of polymer in the dried sample.

Differential Scanning Calorimetry

The phase transition of PNIPAM copolymers in aqueous solution was investigated by Differential Scanning Calorimetry using a DSC Q200 from TA instrument. Polymer solutions (about 80 mg), equilibrated with a reference filled with the same quantity of solvent, were submitted to temperature cycles between -5 o C and 60 o C. Heating and cooling rates were fixed at 2 o C.min -1 similarly as the rates used in rheology experiments.

Injectability

For proof of concept, injectability tests were performed by injecting HA-g-P100 and HA-g-P50 solutions, initially stored below their gelation temperature, into a PBS solution thermostated either below or above the gel point. In order to visually follow the evolution of the solution injected into the PBS bath, Rhodamine B was initially mixed with the polymer solution (C = 0.01 wt%). In the case of HA-g-P100 the injection force as a function of flow rate was also determined using a specific setup mounted on an Instron machine (see supporting information).

Results and Discussion

Synthesis and characterization of LCST precursors

As shown in Table 3, the three syntheses performed with various compositions of NIPAM/NtBAM, keeping constant telogen (and persulfate)/monomer ratios, give rise to copolymer chains with similar number average molar masses (Mn = 15-20 kg/mol) and moderate dispersity (Ð = 1.2-1.6). Moreover, final compositions of the copolymer are almost identical to those of the initial feed ratio as it could be expected since the monomer reactivity ratios are rather close and copolymerization is almost quantitative. This was studied in more detail by [START_REF] Gibbons | Nitroxide-mediated controlled statistical copolymerizations of N-isopropylacrylamide with N-tertbutylacrylamide[END_REF] who demonstrate that the NIPAM-NtBAM copolymer composition remained similar to the feed ratios regardless of polymerization processes (conventional or controlled) and experimental conditions such as solvent, temperature or conversion. Thermal properties of copolymers have been studied by DSC as the phase separation process of all these LCST copolymers displays a clear endotherm during the heating process corresponding to the reorganization of interactions between monomer units and water molecules.

Here, analyses were performed in PBS solution which does not really impact the association temperature as the salting out remains weak in these conditions. As reported in Figure 1 Thermograms of a P100 solution prepared in PBS (C = 2 wt%). Ton () and Tmax/heat () denote, respectively, the onset temperature and the temperature at the maximum of the endotherm during heating. Tmax/cool () denotes the maximum of the exotherm during cooling. Heating and cooling rates = 2 °C.min -1 By cooling, the remixing of the two phases starts below 38 °C with a maximum of the exotherm located at 31.0 °C. This hysteresis mainly originates from kinetic effect at this rate of cooling, here 2 °C/min, as the PNIPAM chains phase separate into highly concentrated domains of low mobility due to the proximity of their glass transition. This hysteresis can be reduced, even eliminated, when applying much slower sweeping rate, typically below 1 °C/min. The comparison between the 3 LCST Px polymers in Figure 2 highlights the impact of the hydrophobic modification of the copolymer with a decrease of the transition temperature Tmax,heat (see also Table 4) with the increasing fraction of hydrophobic NtBAM. At the same time, the hysteresis that can be estimated by the difference between the maxima observed during heating and cooling steps increases from around 6 °C, 10 °C and above for x = 100, 75 and 50. These characteristic temperatures are in perfect agreement with those reported by Hoffman et al. [START_REF] Hoffman | Really smart bioconjugates of smart polymers and receptor proteins[END_REF] who have explored NIPAM-NtBAM copolymers over a much broader range of composition going from 100-0 to 30-70 (in mol%). Upon heating, the end of the transition, which can be appreciated from the endotherm, is around 50 °C for P100 but the transition is already achieved at 40 and 30 °C for P75 and P50, respectively. For these two copolymers, and especially for the last one (P50), this means that it possible to fully achieve the phase separation process in physiological conditions, which is not the case for P100.

Synthesis and characterization of graft copolymers

For all the coupling reactions, which were carried out in water, the pH is a key parameter for the formation of amide bonds as it results from a compromise between successive reactions which involve: 1) the reaction of EDC/NHS with carboxyl groups to form O-acylisourea, NHS activated ester or anhydride at pH = 3.5-5 and 2) the amide formation between previous intermediates and non-ionized amines which prevail at higher pH [START_REF] Nakajima | Mechanism of amide formation by carbodiimide for bioconjugation in aqueous-media[END_REF][START_REF] Staros | Enhancement by Nhydroxysulfosuccinimide of water-soluble carbodiimide-mediated coupling reactions[END_REF]) (see Scheme 1 in supporting information). Obviously the ionization equilibrium depends on the pKa of the amine, but generally it comes that pH=5 is a good compromise between the above mentioned requirements. The grafting reaction proceeding in water, we have also to consider the thermodynamic properties of LCST polymeric grafts. As mentioned previously, the solubility of these precursors varies with their composition but they are all soluble in water below 10 °C and the reactions were consequently performed in an iced bath at T = 2-5 °C in order to work in homogeneous conditions and to promote the random distribution of LCST grafts along the polysaccharide backbone. The characterization of the copolymers by 1 H NMR (see supporting information Table S1 and Figure S1) shows that the coupling reactions are almost quantitative as the composition of the copolymers roughly corresponds to the feed polymer ratio. The lower weight fraction of HA into the copolymer (45 wt%) compared to the feed ratio (50 wt%) is attributed to the higher level of hydration of HA powder (compared to dry Px) which was not taken into account in the initial weighing of compounds. Even if the copolymer solutions (HAg-Px) becomes opalescent above their transition temperature, highlighting the presence of residual ungrafted LCST side chains, we can reasonably assume that most of the LCST sidechains have been effectively grafted onto the HA backbone. If we consider the initial number average molar mass of the precursors, these grafting ratio correspond to about 12 and 16 LCST grafts per HA backbone for P100 and P50-P75 respectively. As shown in Table 2, the yield after purification is around 80 % for most of the coupling reactions except for HA-g-P100 which has been treated in basic conditions (pH=13) at the end of the reaction. Indeed, after several additions of coupling reagent the reaction medium has shown a weak gel-like behavior that was attributed to either the formation of ester bonds between carboxyl and hydroxyl groups of hyaluronic chains [START_REF] Neises | 4-Dialkylaminopyridines as Acylation Catalysts .5. Simple Method for Esterification of Carboxylic-Acids[END_REF] or to anhydride bridges between hyaluronan chains [START_REF] Hermanson | Modification with synthetic polymers[END_REF]. The formation of such covalent bonds, that we have already observed when adding large amounts of EDC/NHS to alginate solutions for instance, can be readily hydrolyzed in basic medium.

Thermoresponsive behavior of modified Hyaluronans

DSC and NMR analyses

As shown by DSC in Figure 3, the incorporation of P100 side chains onto the hyaluronic backbone does not apparently modify the thermodynamic behavior of the LCST polymer as the phase transition takes place on a similar temperature range whether the PNIPAM chains are grafted or not. Endotherms of homoPNIPAM (P100) and HA-g-P100 solutions prepared in PBS at different concentrations.

Heating rate = 2 °C.min -1 P100 at 2 wt% () and HA-g-P100 at 1.5 wt% (), 3 wt% () and 5 wt% ()

While the transition temperatures are similar, the main difference arises from the transition enthalpy, expressed in kJ per mol of NIPAM unit, which is almost two times lower for the graft copolymer compared to the homoPNIPAM precursor (see Table 4). This behavior that has been observed with a lot of similar systems [START_REF] Karakasyan | Synthesis and rheological properties of responsive thickeners based on polysaccharide architectures[END_REF][START_REF] Vahdati | Topology-Specific Injectable Sticky Hydrogels[END_REF]) can be explained by considering that the transition enthalpy is correlated to the effective balance between disruption (water-amide) and reformation (water-water and amide-amide) of hydrogen bonds. The lower energy observed for the aggregation of PNIPAM chains covalently bound to the hyaluronic backbone could be related to (1) the energy barrier against the association process due to the steric hindrance imposed by the water-soluble backbone and/or (2)

to the formation of smaller and/or less dehydrated PNIPAM aggregates at high temperature. As shown in Figure S4, in supplementary information, as well as in Table 4, the same conclusions hold for the two other copolymers grafted with P75 and P50. Complementary experiments were carried out by 1 H NMR with the copolymer HA-g-P50 to investigate the aggregation process of LCST side-chains as a function of temperature. From the series of NMR spectra obtained between 4 and 45 °C with a copolymer solution at 1.5 wt% in D2O (Figure 4), we can see that the signals of methyl protons of NIPAM and NtBAM units, observed at about 1.1 and 1.3 ppm respectively, as well as the methanetriyl proton of NIPAM at about 3.9 ppm, show a dramatic decrease above 10 °C. Conversely, the proton signal of the hyaluronan cycle remains almost unaffected by the temperature change as clearly highlighted in Figure 4b where the normalized area of protons signals has been plotted as a function of temperature. At 45 °C, the remaining proton signals of LCST side-chains is less than 10% from the value determined at 4 °C, below the transition temperature. This feature, that has been reported with PNIPAM copolymers [START_REF] Guo | Influence of topology of LCST-based graft copolymers on responsive assembling in aqueous media[END_REF] and gels [START_REF] Sun | 1H NMR studies of poly(Nisopropylacrylamide) gels near the phase transition[END_REF], can be assigned to the formation of a solid-like rich-polymer phase with highly reduced mobility. As shown in

Viscoelastic properties in the linear regime

Strongly coupled to the thermodynamic properties, the viscoelastic behavior of semi-dilute solutions of HA-g-Px nicely mirror the microphase separation giving rise to the formation of physical crosslinks. A representative example is given in Figure 5 with a 5 wt% HA-g-P100 solution, where variations of dynamic moduli (G' and G") have been plotted as a function of temperature, for a given frequency (1 Hz), or as a function of the frequency at three different temperatures. After an initial decrease of the viscoelastic properties with increasing temperature, which follows the classical Arrhenius dependence, both G' and G" sharply increase at about 4). This sol/gel transition, which takes place between 30 and 40°C with the crossover of dynamic moduli, is then followed by a weaker temperature dependence above 40°C, in the gel regime. In Figure 5B, the corresponding frequency dependences clearly underline the sol/gel transition starting from a viscous liquid state at low temperature, here 10°C (G' 2 and G"), and reaching an elastic gel state at high temperature (60°C) with almost no frequency dependence for both dynamic moduli.

In between, like at 37°C, the formulation passes through intermediate states pointing out the existence of a gel point. In our case, the gelation temperature (Tgel) is defined by the crossover of dynamic moduli determined at fixed frequency, here f = 1 Hz, that is very close in this case to the body temperature (see Table 4). This transition is sharp and fully reversible with little hysteresis as already pointed out from the thermodynamic properties of the grafts.

B

In order to analyse the rheological behavior, viscoelastic data have been replotted by using the complex viscosity (η*) as a single parameter (see Figure 6). Indeed, 𝜂 * = √(𝐺′ 𝜔 ⁄ ) 2 + (𝐺" 𝜔 ⁄ ) 2 can be identified to the Newtonian viscosity in the sol regime (*  0, for G" >> G'), while it scales with the plateau modulus (G0) in the gel regime for G' >> G" : *  G0/, with  = 6.28 rad/s in our experimental conditions. As shown in Figure 6, the association of PNIPAM sidechains above their transition temperature gives rise to abrupt changes of * leading to a large variation of viscosity. As the complex viscosity inversely scales with the frequency in the gel regime, *  G0/, a second y-axis has also been added on the right to highlight the values of the elastic modulus which is constant, at least in the frequency window explored. By comparison with these dynamic experiments carried out at low deformation in the linear regime, the steady state shear viscosity (𝜂 𝛾̇) was analysed in similar condition (𝛾̇= 6.28 𝑠 -1 ). While the equivalence 𝜂 𝛾̇= 𝜂 𝜔 is well observed below Tgel the steady state shear viscosity starts to diverge in the high temperature range, above 40°C (see SI Figure S5). Even if the empirical Cox-Merz rule (𝜂 𝜔 * = 𝜂 𝛾̇) has been found to hold for polymer melts, and concentrated or semi-dilute solutions, this relation generally fails with colloidal or gelled systems due to a larger loss of structure at high deformations [START_REF] Alhadithi | The relationship between the linear (oscillatory) and nonlinear (steady-state) flow properties of a series of polymer and colloidal systems[END_REF]. This loss of viscoelastic properties under shear is nevertheless reversible and the gel material demonstrate self-healing properties with time at high temperature or by applying a cooling/heating cycle as shown in 4), and a shift of the rheological properties towards higher values. Comparatively, the association temperature can be readily controlled through the thermodynamic properties of LCST side-chains. As shown in Figure 7 and Table 4 (see also Figure S3), the association and gelation temperature can be lowered by 15 or 25°C by using the less hydrophilic grafts, P75 and P50, respectively.

Taking into account the whole set of rheological data, several points are worth discussing. First, the solutions of HA-g-P50 display a large hysteresis in the transition zone between heating and cooling steps. This hysteresis, already pointed out by DSC with the P50 precursor, is related to slow dynamics of these polymers above their transition temperature due to the higher content of bulky and hydrophobic t-butyl groups. Such behavior has already been reported by Tsitsilianis and coworkers [START_REF] Safakas | Alginate-g-PNIPAM-Based Thermo/Shear-Responsive Injectable Hydrogels: Tailoring the Rheological Properties by Adjusting the LCST of the Grafting Chains[END_REF] in the case of alginates grafted with P(NIPAM-co-NtBAM) side chains of various compositions. The other point is related to the lower viscosity of HA-g-P100 solutions compared to those of other grafted hyaluronan below the transition temperature, like at 6°C for instance as reported in Table 4. As mentioned in the synthesis section, some ester crosslinks can be formed during grafting performed in excess of carbodiimide and this has been observed in particular in the case of HAg-P100 which has been treated with sodium hydroxide (pH  13) to hydrolyze these interchain ester bounds. Although, hyaluronan is quite resistant to hydrolysis we can nevertheless assume that either some additional chain breakage happened during the hydrolysis of HA-g-P100, or conversely that some interchain crosslinks occurred during the grafting process of the two other samples, increasing consequently the average molar mass. If we assume, as we will see below, that all the solutions were studied in the semi-dilute entangled regime, where the viscosity strongly increases theoretically with the molar mass as 𝜂~𝑀 3.4 , the decrease of viscosity between HA-g-P100 and HA-g-P75 or HA-g-P50 corresponds to a decrease of the molar mass ratio by a factor 1.5 or 1.3-1.4, respectively. This statement concerning the entangled regime is clearly highlighted in Figure 8 by plotting the Newtonian viscosity determined at 6 °C, in the sol regime, versus the concentration. Indeed, the 3 series of polymer solutions follow a similar scaling relation 𝜂~𝐶 𝛼 , with 𝛼 = 3.5 ± 0.2 in rather good agreement with theoretical predictions for semi-dilute entangled neutral polymer solutions in athermal solvent or flexible polyelectrolytes in the high-salt limit (𝜂~𝐶 15/4 ). [START_REF] Colby | Structure and linear viscoelasticity of flexible polymer solutions: comparison of polyelectrolyte and neutral polymer solutions[END_REF] This is typically the case with HA-g-PX solutions in PBS containing more added salt ions than counterions and similar results (𝜂~𝐶 4.0±0.2 ) have been reported by [START_REF] Milas | Comparative rheological behavior of hyaluronan from bacterial and animal sources with cross-linked hyaluronan (hylan) in aqueous solution[END_REF] as well as by Krause et al [START_REF] Krause | Rheology of sodium hyaluronate under physiological conditions[END_REF]. Moreover, if we consider that the entanglement concentration of polymer solutions (Ce) is typically reached for 𝜂 ≅ 30. 𝜂 𝑠𝑜𝑙𝑣𝑒𝑛𝑡 [START_REF] Krause | Rheology of sodium hyaluronate under physiological conditions[END_REF][START_REF] Milas | Comparative rheological behavior of hyaluronan from bacterial and animal sources with cross-linked hyaluronan (hylan) in aqueous solution[END_REF], which is clearly below all the solutions investigated at C  1.5 wt% (see Table 5), we can extrapolate this critical concentration at Ce=0.03 Pa.s from the plot =f(C) in Figure 8A. This gives Ce = 1.24, 0.85 and 1.03 wt% for the 3 hyaluronic samples grafted with P100, P75 and P50, respectively.

Under the hypothesis of athermal solvent, the concentration dependence of the viscosity can be interestingly reduced either by using the overlap concentration (C * ) or the entanglement concentration (Ce) which are proportional in these conditions (Michael Rubinstein & Colby, 2007). As shown in Figure 8B, the plot of the viscosity versus the reduced concentration (C/Ce)

gives rise to a single relation in good agreement with the theory. At 50 °C, in the gel regime, the elastic modulus scales as 𝐺~𝐶 2 . Such "quadratic" dependence of the modulus with the concentration is relatively common well above the percolation threshold,

and it has been widely reported experimentally for many macromolecular physical network and in particular for thermoassociating polymers showing either gelation upon cooling (gelatin, carrageenan, agarose)(A. H. [START_REF] Clark | Kinetics of biopolymer gelation-Implications of a cascade theory description for the concentration, molecular weight, and temperature dependences of the shear modulus and gel time[END_REF]Allan H. Clark & Ross-Murphy, 1985;[START_REF] Rochas | Relation between the molecular structure and mechanical properties of carrageenan gels[END_REF] or upon heating like Bovine Serum Albumine(Allan H. [START_REF] Clark | The concentration dependence of biopolymer gel modulus[END_REF] and methylcellulose [START_REF] Arvidson | Interplay of Phase Separation and Thermoreversible Gelation in Aqueous Methylcellulose Solutions[END_REF].

In parallel, various theoretical models have been developed to describe the concentration dependence of elastic properties. This is the case for gelation theories based on the pioneering works of Flory [START_REF] Flory | Molecular Size Distribution in Three Dimensional Polymers. I. Gelation 1[END_REF] and Stockmayer [START_REF] Stockmayer | Theory of Molecular Size Distribution and Gel Formation in Branched-Chain Polymers[END_REF], further extended by Hermans [START_REF] Hermans | Investigation of the elastic properties of the particle network in gelled solutions of hydrocolloids. I. Carboxymethyl cellulose[END_REF] and Clark et al(Allan H. Clark & Ross-Murphy, 1985). Using different assumptions, they show that well above the percolation threshold (C0), the shear modulus can be described by a scaling relation 𝐺~𝐶 𝛿 with  = 2 in the case of bimolecular interactions or cascade theory taking into account a large number of functional group per chain.

A similar quadratic dependence can also be predicted for biphasic copolymer solutions above their transition temperature by analogy with nanocomposites. In this case, the shear modulus of nanocomposites (Gc) can be described by the following expression [START_REF] Soyarslan | Effective elastic properties of 3D stochastic bicontinuous composites[END_REF]:

𝐺 𝑐 = 𝐺 1 + (𝐺 2 -𝐺 1 )𝜙 2 2
with Gi and i, the shear modulus and volume fraction of the soft (i = 1) and hard (i = 2) phases and 𝐺 𝑐 ≅ 𝐺 2 𝜙 2 2 when 𝐺 1 ≪ 𝐺 2 .

Last but not least, similar scaling relations have been well established for entangled solutions of polymers, associating polymers or loosely crosslinked chemical hydrogels: 𝐺~𝐶 𝛽 with = 9/4 in athermal solvents [START_REF] Leibler | Dynamics of reversible networks[END_REF][START_REF] Obukhov | Network Modulus and Superelasticity[END_REF]Michael Rubinstein & Colby, 2007; M. [START_REF] Rubinstein | Dynamics of entangled solutions of associating polymers[END_REF].

As shown in Figure 8B, both the viscosity at low temperature and the elastic modulus at high temperature can be reduced for the 3 grafted hyaluronans by using the entanglement concentration. Although this is not expressly considered in the previous models, the normalization of G' as 𝐺′~(𝐶/𝐶 𝑒 ) 2 , leading to 𝐺′~𝐶 2 𝑀 3/2 with 𝐶 𝑒 ~𝑀-3/4 , means that the molecular weight of the polymer chain and its level of entanglement really matter in the final elastic properties of the thermoassociating polymers.

Swelling properties of physical gels

Since the lifetime of the association does not allow to access the dynamics of physical gels their swelling properties were investigated to highlight their long term behavior in the gel state. For that purpose, a 5 wt% solution of HA-g-P50 was initially prepared in PBS at T = 5°C, below the transition temperature. The solution was then introduced into a syringe and heated at 37°C for 15 minutes in an oven. Then, a piece of the cylindrical gel was poured into a closed container filled with a large excess of PBS at 37°C and stored in the oven; the macroscopic gel being regularly weighted with time during 6 days. Gel swelling is calculated as 𝑄 = 𝑚 𝑡 𝑚 0 ⁄ with mt the weight of the swollen gel at time t and m0 the initial weight of polymer in the gel. As shown in Figure 9, the physically crosslinked formulation swells moderately in PBS and reach equilibrium after 1 day: from Q0 = 20 to Qe = 50 (or C0 = 5 wt% to Ce = 2.0 wt%). Swelling behavior in the gel state of hyaluronan formulations prepared at 5 wt% in PBS:

 HA-g-P100 (Q0 = 20); T = 50 °C  HA-g-P50 (Q0 = 20); T = 37 °C Throughout the swelling experiment, the swollen network keeps its cylindrical shape and at the end of the study, after drying overnight at 60°C, the polymer loss was shown to be less than 20 wt%. This simple experiment proves that the physical crosslinks formed between LCST side chains are rather strong or more precisely that their dynamics is very slow as most the chains remain connected even after almost 1 week in PBS solution. A similar study was carried out with a 5 wt% HA-g-P100 gel prepared at 50°C in PBS following the same procedure. The results gathered in Figure 9 clearly highlight a higher level of swelling for HA-g-P100 compared to the previous sample that can be ascribed to a lower level of physical crosslinks: 𝐺′ 50°𝐶 = 930 𝑃𝑎 for HA-g-P100 against 𝐺′ 37°𝐶 = 1760 𝑃𝑎 for HA-g-P50 at the same initial concentration of 5 wt% (Q0 = 20). Moreover, if the level of extractible is around 10 wt% after 2 hours, it reaches 35 wt% after 2 days. Even if the results of this swelling study remains qualitative, they clearly underline the very low dynamics of the physical associations which make these gels strong, robust and stable. The lifetime of the whole network in wet environments unquestionably depends on external parameters such as temperature, ionic strength and pH. However other parameters, like the level of entanglements which impact the connectivity, also play a role in the swelling and disruption of the hydrogel.

Adhesive properties of thermoresponsive Hyaluronan.

Adhesive properties of hyaluronan formulations were studied as a function of temperature using a DHR-3 rheometer. In the tack configuration, the liquid sample, in the sol state, was initially confined (h 0 = 400 µm) between two flat sand-blasted plates; the probe one at the top ( 2 0 0 4 r a   with r0 = 10 mm), and the bottom one being mounted on a Peltier temperature control system. The formulation was then equilibrated at a given temperature for 10 minutes before starting the experiment performed at a constant debonding rate v = 100 µm.s -1 , corresponding to 𝜆 ̇= 0.25 s -1 in our conditions. As shown in Figure 10 for the formulation of HA-g-P100 at 5 wt% in PBS, the stress-strain profiles are strongly modified upon heating starting from a viscous response at low temperature up to a viscoelastic one above the transition. Theoretical fits have been added in supporting information (Figure S6) in order to model the theoretical capillary (cap), viscous () and elastic (G) contributions given by the following relations [START_REF] Shull | Deformation behavior of thin, compliant layers under tensile loading conditions[END_REF]:

σ cap = 2γ h 0 (ϵ+1) [1] σ η = 3ηλ (ϵ+1) 2 (1+ 1 2 (a 0 h 0 ⁄ ) 2 (ϵ+1) 3 ) [2] σ G =3Gε (1+ 1 2 (a 0 h 0 ⁄ ) 2 ) [3]
where  is the surface energy of water (= 72 mN/m in the range T = 30-40 °C) and ε is the nominal strain equal to (h-h0)/h0.

For that purpose, we have used the complex viscosity at low temperature and the elastic modulus at high temperature. At low temperature, below and within the transition zone (T = 32 and 37°C), the - curves correspond mostly to a viscous liquid behavior with an initial maximum stress at = 0 dominated by capillary forces at 32°C (𝜎 𝑚𝑎𝑥 = 2𝛾 ℎ 0 ≅ 350 𝑃𝑎 ⁄

) and viscosity at 37°C (σ max ≅(3 2 ⁄ )ηλ ̇(a 0 h 0 ⁄ ) 2 ≅ 235𝜂 ≅ 680 𝑃𝑎). Then the stress decays rapidly versus deformation with forces below the experimental resolution making difficult to accurately define the strain at break and to calculate the work of adhesion. Well above the transition threshold, for T = 42°C and 46°C, the formulation becomes predominantly elastic and the initial part of the stress-strain curve can be fitted reasonably well with equation [3] which highlights the effect of the confinement over mechanical properties. Then the curve reaches a maximum stress which coincides with the occurrence of fingering instabilities in the periphery of the hydrogels as reported by Vahdati et al. with similar grafted copolymers [START_REF] Vahdati | Topology-Specific Injectable Sticky Hydrogels[END_REF]. This phenomenon, that has been widely described in the literature for confined layers of various fluids(Ben Amar, Bonn, [START_REF] Amar | Fingering instabilities in adhesive failure[END_REF][START_REF] Biggins | Fluid-driven fingering instability of a confined elastic meniscus[END_REF][START_REF] Nase | Dynamic evolution of fingering patterns in a lifted Hele-Shaw cell[END_REF], also holds for soft elastic solids where fingering instabilities maximize the compliance of the layer. As discussed by [START_REF] Shull | Deformation behavior of thin, compliant layers under tensile loading conditions[END_REF], bulk fingering is expected in confined layers of soft elastic solids for high level of confinement a0/h0 > 1 and relatively large ratios of atmospheric pressure to Young's modulus (P0/E >> 1) which prevents the formation of internal cavities. These finger-like instabilities can propagate along the interface, when adhesion is weak, or in the bulk when adhesion is strong. Temperature dependence of the adhesive behavior of HA-g-P100 prepared at 5 wt% in PBS: T = 32 °C (), 37 °C (), 42 °C (), 46 °C (), 50 °C () and 55 °C ().

The stress-strain curves are averages based on triplicates. The work of adhesion (Wadh) is proportional to the area under the stress strain curve.

At higher temperatures T= 50 and 55°C, the initial slope of the curve is well described by equation [3]. Nevertheless, there is an increasing deviation from the theoretical behavior with increasing strain that can be ascribed to a more progressive development of the fingering instabilities giving rise to a more rounded shape of the tack curve.

These instabilities, which appear around the peak in nominal stress at the adhesive-air interface for  < 0.1, grow into the bulk, moving from the edge of the confined layer toward the center as the probe is pulled up, and lead to a large drop in stress. Upon stretching, the confined hydrogel layer continually softens as shown by the regular decrease in the nominal stress which becomes negligible beyond  = 1. As described by Vahdati et al. with poly(N,N-dimethylacrylamide) (PDMA) grafted with PNIPAM side chains, the softening behavior can be attributed to the pullout under strain of PNIPAM grafts from hydrophobic domains bridging hydrophilic backbones [START_REF] Vahdati | Topology-Specific Injectable Sticky Hydrogels[END_REF]. From these curves, the work of adhesion (Wadh) can be calculated by multiplying the area under the nominal stress-strain curve up to failure by the initial thickness:

   max 0 0 ) (     d h W adh
. As shown in the inset of Figure 10, the work of adhesion follows the general trend of the thermo-thickening behavior with a large increase of adhesive properties correlated to the sol/gel transition. The maximum values obtained for such formulations at 5 wt%, around 1 J/m 2 , are far below usual pressure sensitive adhesive (PSA) but we have to consider that here the formulation contains 95 wt% of water.

In the case of the HA-g-P50 formulation studied in the gel regime (T = 25 °C), the stress-strain curve given in Figure 11 displays an initial slope at low strain ( < 0.1) which is similar to that of HA-g-P100 studied at 55 °C. This result is in agreement with their close elastic modulus which were determined under the same conditions: 1200 and 1140 Pa, respectively. Nevertheless, one can observe clear differences between these two samples with: (i) a much higher resistance to deformation with a maximum stress at 40 kPa for HA-g-P50, compared to 18 kPa for HA-g-P100, (ii) an abrupt decrease of the stress for  > 0,07 followed by a second peak stress of low amplitude and a pseudo plateau which extends up to  = 1.2-1.4 giving rise to a higher work of adhesion (Wadh  2 J.m -2 ) compared to HA-g-P100 (Wadh  0.9 J.m -2 ).

These features, which highlight a greater elastic contribution of HA-g-P50 during deformation, can be attributed to a stronger cohesion of P50 domains, compared to P100 ones, thus offering a greater resistance to the pull out of LCST grafts under strain from hydrophobic domains bridging hydrophilic backbones. Moreover, it can be assumed that the higher level of entanglement of HA-g-P50 chains also contributes to the reinforcement of viscoelastic properties at large deformations.

Injectability

For a proof of concept, injectability tests were performed by injecting HA-g-P100 and HA-g-P50 solutions (C=5 wt%), initially stored below their gelation temperatures, into a PBS bath thermostated either below or above the gel point. The tests were carried out with syringes of 1 mL (Rs = 2.3 mm) equipped with 35G needle (Rn = 0.13 mm ; Ln = 12.7 mm) commonly used in cases of self-injection.

In the case of HA-g-P100, which exhibits a sol/gel transition at 35 °C, the viscous solution at room temperature is rapidly dispersed when injected into the PBS bath at 20 °C and leads to a fast release of Rhodamine (see Video 1 in supplementary information). Conversely, when the same solution is injected into the PBS bath at 37 °C, just above the gelation point, one can observe the instantaneous formation of an extruded gel filament which remains stable and greatly slows down the Rhodamine release.

In the case of HA-g-P100, the injection force was also measured as a function of injection rate using a specific setup mounted on an Instron machine (see Figure S7 in supporting information).

By increasing the injection rate between 10 and 200 mm/min, corresponding to flow rates between 0.18 and 3.7 mL/min, the force increases from 2.2 N to 5.7 N (see Figure S8 in supporting information) but remains well below the limit of 12 N which is considered by patients as a boundary condition for an easy injection. [START_REF] Robinson | Filling the Gap: A Correlation between Objective and Subjective Measures of Injectability[END_REF] In the case of the solution of HA-g-P50 (C=5 wt%), which displays a gelation temperature at 10 °C, the tests were performed by hand at 5 and 20 °C (see Video 2 in supporting information) and similar behaviors were observed with rapid dissolution at 5 °C and formation of a stable gel filament at 20 °C. Nevertheless, these tests remain qualitative because in the first case (T<Tgel) the syringe must be immersed in the PBS bath equilibrated with ice at 5° C to avoid gelation before the injection. This particular situation is observed during the test carried out in the PBS bath at 20°C, when the syringe is not thermostated below 10°C ; this leading to very high injection forces.

This general comparison between the two copolymers, highlights the impact of the physicochemical parameters playing a key role on gelation and injection properties. The size of the macromolecular backbone indeed directly impacts the viscosity and the injectability at low temperature but this can be controlled with the copolymer concentration. By decreasing the gelation temperature, it is possible to form gels that are more stable under physiological conditions, but in this case the injection must be carried out at low temperature. This can be considered for example in the case of tissue engineering by introducing stem cells into a liquid matrix at low temperature before letting them proliferate and differentiate under physiological conditions. In the case of direct introduction or injection into the human body, the gelation temperature must remain above room temperature to avoid gelation before introduction. In this case an important point to consider is the sharpness of the transition which is closely dependent on the thermodynamic properties of the reactive stickers.

Conclusions

The grafting of LCST side-chains onto water-soluble backbones is a versatile method for the preparation of responsive copolymers with orchestrable sol/gel transition properties. In this context, the use of poly(N-alkylacrylamide)s characterized by a phase transition close to body temperature are triggers of choice for the development of applications in bioengineering. Starting from PNIPAM responsive polymers, the incorporation of a hydrophobic comonomer, NtBAM, allows easy adjustment of the transition temperature below 35 °C. The introduction of increasing amounts of NtBAM decreases the transition temperature in aqueous medium but also the dynamics of the aggregates as revealed by the increase in hysteresis during the cooling step. Once grafted onto the hyaluronan backbone, LCST side-chains begin to self-associate into microdomains at temperatures similar to those of the ungrafted chains. The main difference comes from the lower transition enthalpy of the grafts which underlines a less effective dehydration process (breaking of water/monomer hydrogen bonds in favor of monomer/monomer interactions). In the semi-dilute entangled regime, the formulations exhibit a clear sol/gel transition with a large increase of their viscoelastic properties. In the gel regime, the elastic properties are controlled by the responsive stickers which serve as physical crosslinks but also by the molar mass of the copolymer which impacts the level of entanglement of the network. The formation of elastic gels is also coupled with a strong increase in adhesion properties and a very good resistance to dissolution when immersed in an excess of solvent above Tgel.

If the structure/properties relationships are considered, it is interesting to discuss separately the role of responsive grafts on the one hand and of the water-soluble backbone on the other hand.

When choosing a LCST trigger, there are at least 3 main characteristics to consider:

1) The transition temperature. It can easily be adjusted by modifying the hydrophilic/hydrophobic balance of the LCST chain. Nevertheless, the dependence of the transition temperature on the concentration, which can vary greatly from one polymer to another, is also important to consider if precise control of the transition zone is sought.

2) The sharpness of the transition. It is essentially based on the phase diagram of the LCST polymer in the solvent considered, i.e. on the variation of the concentration of polymer-rich and solvent-rich phases with temperature.

3) The dynamics of LCST microdomains forming crosslinks. It depends on polymer hydrophobicity but also on how far is the polymer-rich phase from its glass transition. This will strongly influence the lifetime of the association and of the entire polymer network.

Regarding the water-soluble backbone, the two main characteristics are its hydrophilicity and its molar mass. In the case of copolymers characterized by a high level of modification, as is the case in the present study, the backbone must be very soluble in water in order to avoid macrophase separation above the transition temperature. The molar mass, and therefore the level of chain entanglement, is also important as it improves the elastic properties in the linear regime. At large deformations, which have been little studied so far, we believe this may be a critical parameter because the deformation and flow of the main chain by reptation requires the dissociation of LCST stickers and the longer the chain, the greater the number of grafted stickers will slow down its reptation.

If we look at the literature dealing with thermoassociative copolymers it appears that the nature of responsive grafts critically influences the association temperature as well as the dynamics of the physical network. This has been shown for example with various polymeric backbones, such as poly(sodium acrylate){Durand, 2000 #408}{Podhajecka, 2007 #391} or alginates{Safakas, 2021 #484}, by modifying the hydrophilic/hydrophobic balance of the side-chains. From our expertise on thermoassociating polymers, it appears that for a given LCST side-chain, the main parameters controlling the viscoelastic properties in the semi-dilute entangled regime are the level of entanglement of the copolymer chain (C/Ce) and the weight fraction of LCST grafts. All these points are important and deserve to be studied in more details in future investigations in order to properly control all of the properties sought in applications relating to injectable hydrogels.

  Figure1

Figure 2

 2 Figure 2

  Figure 3

Figure 4 ,Figure 4 .

 44 Figure4, the peaks of hyaluronic backbone are still observable at high temperature although the

  the beginning of the association process which closely corresponds to the transition temperature of PNIPAM side-chains determined by DSC (see Table

Figure 5 .

 5 Figure 5. (A) Variation of viscoelastic moduli (G':  and G" ) of HA-g-P100 in PBS (Cp = 5 wt%; f = 1Hz) upon heating (close symbols) and cooling (open symbols), (B) Frequency dependence of the same formulation at 3 different temperatures : 10, 37 and 60°C.

  Figure 6. (A)Temperature dependence of complex viscosity (*) of HA-g-P100 solutions prepared in PBS at C = 1.5 wt% (); 3 wt% () and 5 wt% (). The viscoelastic analysis has been performed at fixed frequency (f = 1 Hz or = 6.28 rad/s). The corresponding scale for the elastic modulus reported on the right axis (G0  6.28*), is valid only in the gel regime; typically above 40 °C for the 3 polymer solutions. The dashed line corresponds to the Arrhenius fit of * versus temperature in the sol regime (𝜂 𝑠𝑜𝑙 * ). (B) Temperature dependence of the relative viscosity: (𝜂 𝑟𝑒𝑙 = 𝜂 * 𝜂 𝑠𝑜𝑙

Figure 7 .

 7 Figure 7. Temperature dependence of the complex viscosity (*) of HA-g-P75 and HA-g-P50 solutions prepared in PBS at C = 1.5 wt% (); 3 wt% () and 5 wt% (). The viscoelastic analysis has been performed at fixed frequency (f = 1 Hz or = 6.28 rad/s upon heating (close symbols) and cooling (open symbols). The corresponding scale for the elastic modulus reported on the right axis (G0  6.28*), is valid only in the gel regime. The dashed line corresponds to the Arrhenius fit of * versus temperature in the sol regime (𝜂 𝑠𝑜𝑙 * ).

Figure 8

 8 Figure 8 (A) Concentration dependence of Newtonian viscosity (T = 6 °C; open symbols) and elastic modulus (T = 50 °C; filled symbols) of HA-g-Px solutions in PBS; with x = 100 (), 75 () and 50 (). (B) The same data are plotted versus the relative concentration normalized with Ce, the entanglement concentration.

  Figure 9

  Figure 10

  Figure11

Table 1 .

 1 Synthesis of amino-terminated P(NIPAM-co-NtBAM)

	Telomers	a [NIPAM]/[NtBAM] Molar ratio Weight ratio	b [M]0=[Monomer] [AET]/[M]0 [KPS]/[M]0 mol.L -1 Molar ratio Molar ratio
	P100	100/0	100/0	0.90	0.02	0.01
	P75	77/23	75/25	0.26	0.02	0.01
	P50	53/47	50/50	0.13	0.02	0.01
	a [NIPAM]/[NtBAM] is the monomer feed ratio and b [M]0 is the total monomer concentration.

Table 2 .

 2 Synthesis of thermo-responsive Hyaluronan : HA-g-Px.

	Copolymer Grafts (g) HA (g) EDC (g) NHS (g) Water (g) Yield (%) *
	HA-g-P100 P100	6	6	3.5	1.3	400	54
	HA-g-P75	P75	1	1	1.3	0.5	175	80
	HA-g-P50	P50	1.5	1.5	1.3	0.5	150	83
	* After dialysis
	2.4. 1 H NMR
	Hyaluronan precursors and their derivatives were characterized by 1 H NMR in D2O (~2 wt%)
	with a Bruker Avance 400 MHz spectrometer, while LCST copolymers were studied in CDCl3
	(see Figure S1 in supporting information). For advanced analyses of the temperature-responsive
	self-assembling behavior of HA-g-PNIPAM50, NMR experiments were performed on a Bruker
	Avance III HD spectrometer operating at 700 MHz for 1 H, using a standard 5 mm broadband
	smart probe. Temperature control was achieved by a Bruker BCU II unit and a build in
	temperature control unit. The following experimental conditions were employed for the variable
	temperature experiments: 32 transients, 45° flip angle, 2.5 sec acquisition time, 2 sec relaxation
	delay. The sample was allowed to equilibrate for about 10 minutes at each temperature. The 1 H
	chemical shifts were referred to residual HOD peak at each temperature [30].

Table 3 .

 3 Characteristics of LCST precursors

	Grafts	Mn (g/mol) a	Ð	NIPAM/NtBAM Weight Composition b Tmax,heat (°C) c
	P100	19 500	1.2 a	100/0	36.8
	P75	15 500	1.6 a	75/25	25.6
	P50	14 800	1.6 a	50/50	14.3
	(a) number average molar mass (Mn) and dispersity of molar masses (Ð) obtained from SEC;
	(b) weight composition of NIPAM and NtBAM comonomers in the copolymer calculated from
	1 H NMR; (c) temperature at the maximum of the endothermic peak (Tmax,heat) determined by
	DSC with LCST precursors in PBS solutions (2 wt%).

Table 4 .

 4 Association characteristics of grafted Hyaluronan and their precursors

				DSC*			Rheology*
	Polymer	C wt%	H kJ/mol	Tas (°C)	Tmax (°C)	Tas (°C)	Tgel (°C)	6°C (mPa.s)	G50°C (Pa)
	P100	2.0	6.5	33.4	36.8
	HA-g-P100	1.5	2.5	34.9	39.6	34.1	37.1	59	81
	HA-g-P100	3.0	2.9	33.9	38.0	33.7	36.2	464	346
	HA-g-P100	5.0	3.1	33.5	37.6	32.1	35.2	3080	928
	P75	2.0	5.4	21.5	25.6
	HA-g-P75	1.5	3.7	22.6	26.9	18.2	24.7	210	252
	HA-g-P75	3.0	3.8	21.7	25.8	19.1	23.1	1960	951
	HA-g-P75	5.0	4.3	21.1	25.7	18.7	19.2	12370	2382
	P50	2.0	8.8	10.7	14.3
	HA-g-P50	1.5	5.1	11.6	15.4	10.7	12.7	136	176
	HA-g-P50	3.0	6.1	11.0	14.9	9.7	12.3	1110	462
	HA-g-P50	5.0	6.0	10.0	14.0	8.7	10.3	11400	2038
		* All data were determined during the heating step

Acknowledgements

Lucile Barbier and Marine Protat contributed equally to this work. The authors gratefully acknowledge the financial support from CNRS, ESPCI Paris and Sorbonne University for the PhD funding of Lucile Barbier (Doctoral School on Materials Science ED397) and the Master funding of Marine Protat (Appel à Projets Convergence Sorbonne University). The authors also thank Dr. G. Ducouret from the SIMM lab. for technical advice on performing rheological measurements and Dr. P. R. Rajamohanan from NCL Pune (India) for carrying out temperature NMR experiments.