Benoit Caprin

Guadalupe Viñado-Buil

Guillaume Sudre

Xavier P Morelle

Fernande Da Cruz-Boisson

Aurélia Charlot
email: aurelia.charlot@insa-lyon.fr

Etienne Fleury

κ-carrageenan associated with Fructose/Glycerol/Water LTTM: towards natural thermosensitive physical gels

Keywords: κ-carrageenan, Low Transition Temperature Mixture, organogels, thermosensitivity

κ-carrageenan was combined to a natural Low Transition Temperature Mixture (LTTM) composed of fructose, glycerol, and water in a 1:1:5 molar ratio (FGW) to generate fully biobased physical gels through a simple method. The resulting gels can be easily prepared under various shapes. As for their hydrogel analogues, the rheological characterization of FGWbased samples evidenced a thermosensitive gelation, attributed to the formation of aggregated H-bonded helices composed of κ-carrageenan chains. FGW-based gels exhibit gel-sol transition temperature (Tg/s) higher than the one of hydrogels with recoverable and reversible viscoelastic properties upon successive heating/cooling cycles. SAXS analysis revealed a more extended conformation of chains in FGW that leads to more physical cross-linking junction zones within the materials. Such peculiar spatial internal organization provides a mechanical reinforcement demonstrated by compression tests. In conclusion, the use of FGW solvent allows for designing κ-carrageenan physical gels with enhanced thermal and mechanical properties.

Introduction

In the context of sustainable development, polysaccharides remain a powerful and tantalising resource for biomass valorisation since they can be used to generate eco-friendly materials. In this context, such natural polymers have been combined with Deep Eutectic Solvents (DES), just through a simple mixture, usefully exploited to obtain fully biobased and biosafe materials with relevant and tunable properties. [START_REF] Tomé | Emerging Ionic Soft Materials Based on Deep Eutectic Solvents. The journal of physical chemistry[END_REF] The interest is to benefit from the unique attributes synergistically provided by the combination of natural polymers (reduced environmental impact, renewable origin, non-toxicity…) with DES solvents, more specifically their biosafe properties, their organized character and the large versatility they provide in terms of final macromolecular structure. The preparation of these novel solvents is simple since DES come from the mixture of two (or more) H-bonded low-cost molecules. When no eutectic can be clearly identified, such mixtures are classified as low transition temperature mixtures (LTTM).

In particular, natural deep eutectic solvents (NaDES) can be conceived from biobased and biosafe precursors. For instance, guar gum, a vegetal galactomannan, was combined to various choline chloride (ChCl)-based DES and physical gels with elastic behavior and relevant ionic transport properties were formed from ChCl-Urea/guar mixtures. [START_REF] Depoorter | Fully Biosourced Materials from Combination of Choline Chloride-Based Deep Eutectic Solvents and Guar Gum[END_REF] Xanthan gum was also described as a potential gelator of ChCl-based DES. [START_REF] Zeng | Highly biodegradable, thermostable eutectogels prepared by gelation of natural deep eutectic solvents using xanthan gum:Preparation and characterization[END_REF] The authors proved that the addition of water was required to obtain physical gels. It is also reported that xanthan gum NaDES-based gels exhibit a larger thermal operating window compared to hydrogels due to the involvement of water in the supramolecular structure of the NaDES. [START_REF] Xia | Novel Biocompatible Polysaccharide-Based Eutectogels with Tunable Rheological, Thermal, and Mechanical Properties: The Role of Water[END_REF] Despite of the prominent interest to explore LTTM in the polysaccharide field, the design of materials including carrageenans has not been reported yet. Carrageenans, linear sulfated polysaccharides, are mainly extracted from red algae (Rhodophyceae). Carrageenan chains consist of D-galactopyranose units alternately linked by α-1,3 and β-1,4 glycosidic bonds. The repeating units are most often disaccharides and are generally distinguished by their degree of sulfation and by the presence or absence of a 3,6-anhydro bridge on the β-1,4-linked galactose unit. The three mostly studied carrageenans are κ, ι and λ-carrageenan. κ-carrageenan is particularly interesting since it not only finds applications in food, cosmetic and pharmaceutical industries but it leads to hard gels in aqueous medium. [START_REF] Zia | A review on synthesis, properties and applications of natural polymer based carrageenan blends and composites[END_REF] It is accepted that the gelation of κ-carrageenan in water is achieved by a two-step thermo-dependent mechanism. Upon cooling, a coil-to-helix transition occurs, followed by the aggregation of helices, resulting in a gelation. [START_REF] Yuguchi | Structural characteristics of carrageenan gels: temperature and concentration dependence[END_REF] This gelation has been investigated by rheological and micro differential scanning calorimetry, which allowed to determine the thermal transitions : from solution to gel (Ts/g) and from gel to solution (Tg/s). [START_REF] Liu | Thermoreversible gelation and viscoelasticity of κ-carrageenan hydrogels[END_REF] The influence of the nature of the solvent on the thermal transitions was also examined by Yang et al. by additions of sucrose or ethanol in water solutions. [START_REF] Yang | Characterisation of rheology and microstructures of κ-carrageenan in ethanol-water mixtures[END_REF][START_REF] Yang | Effects of sucrose addition on the rheology and microstructure of κcarrageenan gel[END_REF] Their investigation emphasized that the nanostructure of gels was affected by the solvent.

In this context, we propose herein a new study dealing with the association of κ-carrageenan and a novel green solvent, namely a neutral low transition temperature mixture, composed of bio-sourced and non-toxic molecules: Fructose (F), Glycerol (G), and Water (W). Indeed, we recently reported by means of DSC, rheology, and NMR spectroscopy, that FGW in 1:1:5 molar ratio (subsequently named FGW) behaves as a cooperatively H-bonded supramolecular structure leading to a stable solvent identified as LTTM exhibiting a unique and low Tg, and an outstanding microbiological stability. [START_REF] Caprin | Scrutiny of the supramolecular structure of bio-sourced fructose/glycerol/water ternary mixtures:Towards green low transition temperature mixtures[END_REF] Moreover, this composition was industrially implemented to efficiently extract bioactives substances from plants for cosmetic applications. [START_REF] Caprin | Chapter Twelve -The use of NADES to support innovation in the cosmetic industry[END_REF] Due to its appealing advantages in terms of structuration, polarity, and ability to develop synergetic interactions between its compounds, we pursue as statement of hypothesis that FGW constitutes a well-suited solvent to generate, when mixed with κ-carrageenan, soft materials with improved thermo-reversible properties, and reinforced mechanical behavior, compared to water-based systems.

In this work, we evidence for the first time the straightforward formation of physical gels based on the incorporation of κ-carrageenan in FGW. In particular, we successively investigate (i) their physico-chemical properties through thermal analysis, (ii) use rheological measurements to characterize the formation of gels and to underpin the thermal dependence of the gelation mechanism, (iii) use small angle X-ray scattering experiments to elucidate their internal structure, and (iv) perform compression tests in order to validate their mechanical response. The properties of the analogous κ-carrageenan hydrogels were systematically analyzed and compared with our novel system, in order to gain insight into the role of FGW solvent in the structuration of the gels, which is shown to dictate the final properties. To the best of our knowledge, this is the first study dealing with soft materials resulting from κ-carrageenan and a fully biobased LTTM.

Experimental Materials

Fructose (powder, M=180.16 g/mol, purity > 99%) provided by Danisco and glycerol (liquid at 25°C, M=92.09 g/mol, purity > 99.5%) acquired from Oleon were used without any further purification. Deionized water (18 MΩ.cm) obtained from a Veolia Aquadem TM system was used as the third component to obtain FGW LTTM according to the recently described method. [START_REF] Caprin | Scrutiny of the supramolecular structure of bio-sourced fructose/glycerol/water ternary mixtures:Towards green low transition temperature mixtures[END_REF] κ-carrageenan was provided by Roth and was used without any further purification.

Its water uptake (≈7wt%) and thermal decomposition temperature (≈250°C) were measured by thermogravimetric analysis (Figure S1). Its molar mass determined by Size Exclusion Chromatography is Mw ≈ 6.0 x 10 5 g/mol with a dispersity of 1.3 (Figure S2). Elementary analysis conducted by Inductively Coupled Plasma -Atomic Emission Spectrometry (ICP-AES) confirms that the counter ion of the κ-carrageenan used is potassium since equivalent molar quantities of sulfur and potassium were obtained (data not shown). The structure of the κ-carrageenan was confirmed by [START_REF] Tomé | Emerging Ionic Soft Materials Based on Deep Eutectic Solvents. The journal of physical chemistry[END_REF] H NMR analysis (Figure S3).

Preparation of the samples

The preparation is based on two main steps. The first step corresponds to the dispersion of κcarrageenan into FGW at room temperature (RT), under slow mechanical stirring. RT allows to limit the water evaporation that can disturb the H-bonds of FGW. For concentration of polysaccharide higher than 15 g/L, the volume of liquid and the height of the rotor were adjusted to ensure an efficient stirring while preventing the formation of bubbles in these highly viscous solutions. The water content of κ-carrageenan was considered for the calculation of the total amount of polysaccharide. The resulting turbid κ-carrageenan/FGW mixture was stirred for 30 min. The second step consists in the thermal induced gelation. The mixture was gently poured into a cylindrical recipient to prevent the formation of bubbles. The recipient was then capped and put in a temperature-controlled oven at 80°C for 3 h, in which the sample progressively became transparent. The thermal induced gelation process of κ-carrageenan occurred during the cooling phase down to RT. The as-formed FGW-gels were pushed out of the recipient and transparent cylindrical samples were finally obtained as illustrated in Figure 1. The same procedure was applied to generate hydrogels by replacing FGW solvent by deionized water. By convenience, the carrageenan concentration is usually discussed in mass fractions (wt%) in the literature. However, in this study the concentration is expressed in g/L as FGW is denser than water (d = 1.3).

Characterizations

Differential scanning calorimetry (DSC)

DSC analyses were carried out on a DSC-Q22 device (TA Instruments). Samples were placed in aluminium hermetic pans at room temperature. Thermal analyses were performed under nitrogen flow (50mL/min) and samples were submitted to 4 temperature cycles with a ramp rate of 10°C/min: 1) from 25°C down to -140°C; 2) from -140°C up to 100°C; 3) from 100°C down to -140°C; 4) from -140°C up to 25°C. The glass transition temperature (Tg) was determined from the second heating ramp and the midpoint of the thermal transition was considered. The melting temperature (Tm) value of hydrogels was collected from the first heating run and the maximum of the thermal transition was considered.

Rheology

The shear viscosity (η) measurements were carried out on a DHR2 controlled stress rheometer (TA Instruments) operating in flow mode and using two different geometries according to the viscosity of the mixtures: i) an aluminium cone/plate geometry (diameter 40 mm, angle 2°, gap 52 µm) for viscosities higher than 2 Pa.s and ii) an aluminium concentric cylinders geometry (bob diameter x length : 28.03 x 42.11 mm, cup diameter 30.36 mm) for viscosities lower than 2 Pa.s. The temperature was precisely controlled by a high-power Peltier system. Dynamic viscoelastic properties were determined with the same rheometer using a plate/plate geometry (diameter 40 mm, gap 460 µm). All dynamic rheological data were checked as a function of strain amplitude to ensure that the measurements were performed in the linear domain.

Typically, the applied strain during the dynamical measurements was settled at 1%. Temperature sweep on gels was realized in the same conditions (F=1Hz, strain=1%). The samples were carefully loaded on the Peltier plate regulated at 20°C and covered with a homemade cover to prevent evaporation. The temperature was then increased by a controlled temperature ramp to a maximum temperature depending on the analysed sample (see discussion part). Then, the temperature was decreased with the same ramp to examine the reversibility with temperature. For the highest concentrations of κ-carrageenan in FGW, multiples thermal cycles (heating and cooling) were performed. All rheological data were processed with Trios, TA instruments software.

Small angle X-ray scattering analysis (SAXS)

SAXS measurements were performed at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) on D2AM beamline. Samples were placed between 250 µm Kapton foils stuck on 1.6-mm-thick washers. Measurements were performed on samples equilibrated at either 20°C or 80°C. The incident photon energy E was set to 17.000 keV (ΔE/E= 10 -4 ). The SAXS intensity was collected using a 2D D5 detector which was placed at a sample-to-detector distance of D = 1.57 m, leading to a q-range from 0.01 to 0.2 Å -1 . The two-dimensional data were obtained by considering the detector geometry and its flat field response. The position of the direct beam was determined with attenuators. The q-calibration was performed thanks to a silver behenate standard. The corrected two-dimensional data were averaged azimuthally to obtain intensity vs scattering vector q (q = (4π/λ)•sin(θ), where 2θ is the scattering angle and λ is the incident wavelength). Finally, the scattering data were corrected for the scattering from the empty cell (Kapton windows) and normalized by the thickness and attenuation of the samples. The contribution from the solvent (FGW or Water) was subtracted.

Compression tests

Compression measurements were performed on a double-column Instron universal testing machine at room temperature with a 500 N load cell. The cylindrical gel samples (12 mm height, 20 mm diameter) were set on the lower plate and compressed by the upper plate. The compression was conducted at a constant rate of 1 mm/min to obtain engineering stress -engineering strain curves. The compression experiments were conducted in three replicates for each gel system.

Results and Discussion

Preparation of the samples

Based on the literature dealing with κ-carrageenan hydrogels [START_REF] Mangione | Thermoreversible gelation of κ-Carrageenan: relation between conformational transition and aggregation[END_REF] , the gels formed with the ternary biobased FGW mixture, or deionized water as solvent were prepared according to a straightforward method described in experimental section ( §2.2). At high κ-carrageenan concentration (C = 26.5 g/L = 2 wt% in FGW and 2.65 wt% in water), transparent soft materials with a macroscopically gel-like behavior were obtained without further processing (see picture in Figure 1). The resulting FGW-gels can be easily prepared under various shapes.

Comparatively to hydrogels, FGW-gels appear less slippery, less prone to syneresis, and exhibit a better long-lasting physical stability without FGW exudation with time. This good dimensional stability can be ascribed to favorable and strong enough interactions (mainly Hbonds) between polysaccharide chains and FGW solvent (see vide-infra). Another crucial point is that FGW-based gels display an excellent microbiological stability compared to its hydrogel analogues. To conclude, an easy-to-implement and robust preparation protocol was used to obtain fully biobased gels based on polysaccharide and this natural LTTM mixture. As recently described, the solvent FGW, classified as a natural LTTM, is characterized by a single and low glass transition temperature (Tg) at -80°C. [START_REF] Caprin | Scrutiny of the supramolecular structure of bio-sourced fructose/glycerol/water ternary mixtures:Towards green low transition temperature mixtures[END_REF] DSC analyses were then applied to evaluate the impact of κ-carrageenan addition on FGW thermal properties. Examples of thermogram are given in Figure S4, for a gel prepared in FGW, in comparison with the corresponding hydrogel. It appears that during the heating cycles, the hydrogel presents at 7°C a thermal event attributed to the melting of iced water when temperature varies from -140°C to 100°C, whereas the FGW-gel only exhibits a Tg at -79°C, related to the Tg of FGW. The presence of such unique Tg value reflects the monophasic character of the mixture and shows that polysaccharide chains do not deeply disturb the intrinsic organization of FGW solvent. We can note that no other thermal transition can be clearly identified in these DSC thermograms.

Interestingly, the DSC analysis shows that the FGW-based samples are not subjected to any phase transition related to water, which extends their operating temperature range.

Rheological characterization

Rheological properties of κ-carrageenan-based systems were investigated. Firstly, the evolution of viscosity with shear rate, in water and in FGW, was examined at low concentrations (C < 12 g/L) (Figure S5). No macroscopical gel-behavior is observed either in water or in FGW. For C < 5 g/L, the aqueous solutions exhibit a Newtonian plateau. A shear-thinning behavior is observed for larger concentrations. Conversely, FGW-based mixtures display a shear-thinning behavior even at low concentrations (0.6 g/L). At this concentration, the viscosity of FGW sample is two decades higher than the water-based one. This can be attributed first to the intrinsically higher viscosity of FGW, but also to the formation of peculiar interactions between the κ-carrageenan chains and/or a different chain conformation in FGW. To gain more insights into the rheological behavior of samples based on higher chains concentrations, the frequency dependence of G' and G'' was examined in water and in FGW at 20°C for various ranges of concentrations (C from 8.1 to 26.5 g/L in water, and from 6.6 to 26.5 g/L in FGW) (Figure 2 A and B, respectively). Regarding the aqueous samples, at C = 8.1 g/L, G' is higher than G'' within the entire detected frequency range, but the moduli remain sensitive to the frequency, by following a relatively close frequency dependence (G' and G'' ∝ f 0.4 ) which is typical of a transition towards a solidlike behavior. [START_REF] Richter | Recent Gelation Studies on Irreversible and Reversible Systems with Dynamic Light Scattering and Rheology -A Concise Summary[END_REF] For higher concentrations, the samples behave as physical gels as G' is significantly larger (about one order of magnitude) than G'' with no strong variation of both moduli with frequency. G' reaches ∼ 5000 Pa at C = 26.5 g/L (Figure 2A), which is consistent with values reported in the literature (2000 and 7000 Pa for 20 and 30 g/L, respectively). [START_REF] Liu | Thermoreversible gelation and viscoelasticity of κ-carrageenan hydrogels[END_REF] For FGW-based samples, the viscoelastic response is different. The gel point (G' ∝ G'' ∝ f 0.4 ) was observed to occur at higher concentration (C = 10.5 g/L). Above this concentration, physical gels, characterized by a high G'/G'' ratio are obtained and the previous "weak gels", as classified by Clark & Ross-Murphy, shift to more cohesive gels when the polysaccharide concentration increases. [START_REF] Clark | Structural and mechanical properties of biopolymer gels[END_REF] It is well accepted in the literature that the gelation of κ-carrageenan in water results from the formation of double-stranded helices laterally arranged in aggregates. [START_REF] Yuguchi | Structural characteristics of carrageenan gels: temperature and concentration dependence[END_REF] From this comparison of the viscoelastic properties, it appears that the critical κ-carrageenan concentration required for the aggregation of helices to occur is higher in FGW than in water.

For concentrations above 20 g/L, the storage moduli in both solvents are quite similar with a G' value slightly higher in FGW, compared to water (Figure 2B). These striking similarities regarding the overall viscoelastic response suggest similar gelation mechanism in the two solvents. It is well known that the rheological properties of κ-carrageenan hydrogels are thermally sensitive. [START_REF] Liu | Thermoreversible gelation and viscoelasticity of κ-carrageenan hydrogels[END_REF][START_REF] Mangione | K(+) and Na(+) effects on the gelation properties of kappa-Carrageenan[END_REF] Consequently, the evolution of G' and G'' as a function of temperature upon successive heating-cooling sweep was evaluated. Additionally, the influence of the polysaccharide concentration on these transition regions was also examined. From the rheological data at 20°C, a concentration in κ-carrageenan of 20.5 g/L was selected to study the temperature dependence of G' and G'' (Figure 3). Focusing on the hydrogel case, upon heating from 20 °C up to 80 °C (dark blue squares, Figure 3), G' is higher than G'' at 20 °C (as previously shown, see Figure 2A) but in the temperature range between 35 °C and 55 °C, G' and G'' sharply decrease of around 3 decades and 1.5 decade, respectively. G'' becomes greater than G' for T > 48 °C, indicating a liquid-like behavior. This substantial decrease of both moduli has been ascribed to the thermal-induced dissociation of the helices-based aggregates [START_REF] Rochas | Mechanism of gel formation in k-carrageenan[END_REF] through the progressive disruption of hydrogen bonds by temperature increase, causing the breakage of the network. The temperature corresponding to the G', G'' crossover point, indicator of the gel-solution transition temperature (Tg/s), was determined to be 48 °C which is consistent with the literature. [START_REF] Liu | Thermoreversible gelation and viscoelasticity of κ-carrageenan hydrogels[END_REF] The viscoelastic response of the hydrogel was then monitored upon an immediate cooling after the first heating ramp. Back at low temperatures, pronounced differences in the G' and G'' values between the heating and cooling ramp emerge, which come from water evaporation during the analysis.

Literature reported thermal hysteresis phenomenon ascribed to a different kinetic organization of the polysaccharide helices during heating and cooling, resulting in two different thermal transition temperatures. [START_REF] Ueda | Observation of the Molecular Weight Change during the Helix-Coil TransiMon of κ-Carrageenan Measured by the SEC-LALLS Method[END_REF] 3 emphasizes a quite small thermal hysteresis of 3 °C, as a value of Ts/g of 51 °C was recorded (light blue squares). This hysteresis is lower than the one described in bibliography, which can reasonably be explained by an overestimation of Ts/g value due to water evaporation. The FGW-gel, at similar concentration, was analyzed following the same thermal procedure. As shown by Figure 3, differences in the thermal behavior are observed. Firstly, the decrease of G' and G'' of the FGW-gel upon the heating ramp is less acute (two decades against three decades in water for G'). Secondly, the decrease of the moduli spreads over a larger range of temperature, with a smooth decrease from 35 °C to 52 °C followed by a more pronounced one from 52 °C up to 80 °C. Thirdly, the FGW-gel exhibits a better solvent retention propensity: after the two temperature cycles, G' and G'' are perfectly superimposed, and the initial viscoelastic properties are fully recovered (Figure 3 red and green data points at low temperature). The Tg/s of 74 °C of the FGW-gel, determined upon the heating sweep is noticeably higher than in water, and a significant hysteresis (9 °C) appears with a Ts/g identified at 65 °C. The Ts/g values of κ-carrageenan hydrogels are known to decrease while increasing the temperature rate and increase with increasing concentration. [START_REF] Liu | Thermoreversible gelation and viscoelasticity of κ-carrageenan hydrogels[END_REF] Thus, we analyzed two FGW-gels (C = 20.5 and 26.5 g/L), at various temperature ramps (1, 2 and 10 °C/min) (Table 1). The global expected trend is observed, but some small discrepancies appear for these values measured from the crossover of G' and G''. To complete these data, we also conducted another approach to determine the gelation temperature, based on the divergence of the complex viscosity (η*) during the cooling ramp, method described in detail by Liu et al. for hydrogels (Figure S6). The resulting Ts/g values are quite lower than the ones collected from the crossover method, probably due to the pronounced dispersive character of the thermal transitions within the FGW gels. Interestingly, this series of data better fits with the expected effect of concentration and temperature rate. Finally, irrespective of the employed method, Ts/g of FGW-gels are higher than the ones measured for the hydrogels. Thus, a higher temperature is required in FGW to allow both the dissociation of helices aggregates and the helix-to-coil transition. Indeed, the high viscosity of FGW solvent, compared to water, requires a more substantial temperature input to impart a sufficient motion of polysaccharide chains. Additionally, a FGW-gel (C = 26.5 g/L) was subjected to several heating/cooling cycles at 10 °C/min between 40 and 100 °C. These cycles were applied either successively (Figure S7A), or after different waiting times between each cycle (Figure S7B). Figure S7 highlights a complete reversibility of the viscoelastic properties, which underpins that the kinetics of the thermal-induced disorganization / reorganization of the cross-linked zones is rapid and confirms the high solvent retention with temperature for FGW gels, compared to hydrogels.

Determination of

Nanostructure of the materials

SAXS measurements were performed to obtain further structural information on the different gels. FGW-gels and hydrogels, at two different chain concentrations (C = 8.1 and 20.5 g/L)

were analyzed at 20°C (Figure 4). These concentrations were selected so that the resulting mixtures exhibit different viscoelastic behaviors. Below a polysaccharide concentration of 10 g/L, viscoelastic liquids were obtained in FGW while "weak" gels started to be formed in water.

Conversely, for C > 20 g/L and at 20 °C (T < Tg/s), physically crosslinked gels characterized by G' much higher than G'' are generated (see Figure 3). Figure 4A shows the corresponding SAXS patterns (I(q) vs q) of these samples. All four SAXS profiles presented in Figure 4A can be divided in three parts as a function of the wavevector. For q < 0.3 nm -1 , I(q) scales with q -1 in water (Figure 4A1). This decrease of the scattering intensity is indicative of the presence of rod-like monodispersed structures [START_REF] Hollamby | Practical applications of small-angle neutron scattering[END_REF] , which corroborates the well-accepted gelation mechanism of κ-carrageenan in water that results from the formation of laterally arranged double-stranded helices. Thus, the physical 3D network can be described as made of bound cylinders crosslinks. [START_REF] Yuguchi | Structural characteristics of carrageenan gels: temperature and concentration dependence[END_REF] In FGW at 8.1 g/L of κ-carrageenan, the intensity is somewhat constant in this q-region, which seems consistent with the fact that this sample is still a viscous liquid composed of only dissolved polysaccharide chains (i.e. no bound cylinder crosslinks present yet). In contrast, at 20.5 g/L in FGW, the intensity decreases with a variation of q -1 in a shorter region (0.1 nm -1 < q <0.3 nm -1 ) and the slope is steeper at lower qvalues; this result suggests that cylinders are still implied in the structure of the gel, but another structure at larger length scales is also expected.

Then, when q is comprised between 0.3 and 0.7 nm -1 , scattering patterns are characterized by a broad peak. In the case when water is the solvent, it corresponds to the polyelectrolyte peak of κ-carrageenan. [START_REF] Yuguchi | Structural characteristics of carrageenan gels: temperature and concentration dependence[END_REF] The peak position qmax is related to the correlation length between chains.

As expected, the position of the polyelectrolyte peak is directly linked to the concentration of κ-carrageenan. It is also observed that the polyelectrolyte peak becomes wider when the concentration increases. Nonetheless, by adding progressive amounts of sucrose in 2 wt% κcarrageenan hydrogels, Yang et al reported that the polyelectrolyte peak vanished for 30 wt% of sucrose. The authors argued that H-bonds between the polysaccharide and the sucrose overcame the electrostatic repulsion interactions between κ-carrageenan chains. [START_REF] Yang | Effects of sucrose addition on the rheology and microstructure of κcarrageenan gel[END_REF] In the present study, the continuous phase (FGW) is composed of 50 wt% of fructose and ∼25 wt% of glycerol and water. Despite the important number of available OH groups of the polysaccharide for developing H-bonds, a structure peak is still observed at q-values close to those of the polyelectrolyte peak observed for water-based systems. As fructose is strongly H-bonded to glycerol and water, it is less accessible to form H-bonds with the polysaccharide, as reported by Yang et al. for hydrogels containing sucrose.

Finally, when q becomes larger than 0.7 nm -1 , the decrease of the signal can be assigned to the propensity of the solvent to dissolve polysaccharide free chains. In this region, I(q) scales with q -2 for water while the exponent is higher for FGW (∼q -1.3 ). This suggests that the LTTM is a better solvent than water for the κ-carrageenan chains.

To gain more insight into the dimensions of junction zones at the origin of the formation of the physically cross-linked gels, cross-sectional Guinier plots (ln(q.I(q)) vs q²) were performed.

Such representation has often been used in studies reporting the nanostructure of carrageenan hydrogels. Scattering from a long rod with a cross-sectional radius of gyration Rg is given by the Guinier approximation as q.I(q) ≈ exp(-q².Rg²/2). [START_REF] Glatter | Small angle X-ray scattering[END_REF] Rg can thus be evaluated from the linear region in cross-sectional Guinier plots (qRg < 1). Figure 4B shows the cross-sectional Guinier plots obtained in water and in FGW for the two different studied κ-carrageenan concentrations (8.1 and 20.5 g/L). On the one hand, in the case of water, a linear region appears after the peak due to the electrostatic interactions at lower q values. The cross-sectional radius of gyration obtained are equivalent for the two concentrations (1.08 nm and 1.1 nm) (Figure 4B1), which is line with the values reported by Yang et al. This result indicates that the number of rods distributed in the aqueous phase increases, but the average diameter of the helices aggregates remains constant. On the other hand, Figure 4B2 shows the cross-sectional Guinier plots obtained in FGW. As discussed before, only rare aggregates may be present in the solution of lowest concentration. Thus, no Rg value can be determined in this case. Conversely, the Guinier plot for the FGW gel at C =20.5 g/L yields a cross-sectional radius of 0.95 nm. SAXS profiles were also investigated at 80°C for all samples, the Guinier plots obtained at this temperature for C = 20.5 g/L (data not shown) present the same profile that for the lower concentration in FGW (Figure 4B2) suggesting the disappearance of aggregates induced by the temperature increase. This is consistent with rheological measurements and the thermo-reversible behavior of κ-carrageenan gels (Figure 3). Eventually, it appears once again that the gelation mechanism resulting from the formation of laterally arranged double-stranded helices is quite similar between FGW and water solvents, leading to rod-like structure with similar size. Since the structure peak of the polysaccharide is broader in FGW, the distribution of interaction lengths is less dispersed in space in the case of water. We thus propose, in Figure 5, the following schematic representation of the internal organization of the hydrogel and FGW gels, mainly based on SAXS investigation but corroborated by the observed rheological behavior. In both gels, gelation is obtained, at low temperature and for sufficient polysaccharide concentration, when κ-carrageenan chains start forming rod-like aggregates acting like physical crosslinks.

These physically bounded cylinders (schematized in blue in Figure 5) are made of an aggregate of double-stranded helices. [START_REF] Yuguchi | Structural characteristics of carrageenan gels: temperature and concentration dependence[END_REF] In the case of water-based gels, these aggregates are slightly larger in diameter than for FGW-based gels, with probably one extra double-stranded helix. Another difference between the two systems raises from the interactions between the solvent and the free κ-carrageenan chains, while in the case of hydrogels the chains are more coiled up; in the case of FGW, being a better solvent for κ-carrageenan chains that leads to a more extended network with more H-bonds between the solvent and chains, despite an apparently less homogeneous distribution of interactions lengths. With this overall structural picture, and considering a same concentration κ-carrageenan chains, the FGW-based gel should lead to a better-connected network with more physical junctions (as the physical aggregates in the hydrogel case involved more κ-carrageenan helices) and stronger solvent-chain interactions (i.e. strongly H-bonded solvent).

Mechanical properties

It was reported that κ-carrageenan forms rigid and brittle hydrogels. When the water phase is modified or another solvent than water is used to obtain κ-carrageenan gels, small deformation tests are used to discuss the viscoelastic behavior of such mixtures. However, the mechanical response to large deformation is scarcely described. Herein, we submitted gels obtained in FGW and in water (26.5 g/L) to compression tests in order to reach the large strain response (see 2. to the stress at which the gel ruptures. When samples are subjected to small strain (< 20 %), the mechanical response of hydrogel and FGW-gel are similar. This is consistent with the rheological measurements performed at small strains (see Figure 2, C = 26.5 g/L): the storage modulus values obtained in both solvents are comparable. Then, for larger strains, the nonlinear elastic regime of gels appears. The slope values for both solvents are relatively equivalent indicating a similar strain-hardening capacity, underlining a relatively analogous physically crosslinked gel structure. However, the range of stress supported by the FGW-gel is significantly higher than that of the hydrogel. In other words, the stress at fracture obtained in FGW (0.50 MPa) is almost twice bigger than that of the hydrogel (0.26 MPa) (Figure 6B).

Concomitantly, a higher strain at break is also reported for the FGW-gel compared to the hydrogel, respectively around 65% and 50%, based on triplicate measurements (Figure 6C).

For the hydrogel, the values of stress/strain at break are consistent with a previous study that reported a fracture stress of around 0.2 MPa for a 2% κ-carrageenan hydrogel. [START_REF] Cairns | Comparative studies of the mechanical properties of mixed gels formed by kappa carrageenan and tara gum or carob gum[END_REF] In the case of FGW, despite the high compression ratio, the gel hardly exudes (compared to water), highlighting again the good solvent retention ability of the system. As the assumption of constant volume being almost respected the true stress-true strain curves are given in Figure S8. Figure S8 shows that the true strain of the FGW-gel presents a slight inflexion at large strains indicating a propensity to shear localization before rupture.

Thus, with a very simple preparation method, the FGW mixture proposed in this study appears as an interesting alternative to develop fully biobased gels with enhanced mechanical properties compared to hydrogels. Better properties may arise in the future for FGW-gels as Cairns et al.

also studied the addition of carob gum to obtain tougher κ-carrageenan hydrogels which were better able to withstand mechanical stress.

Conclusion

In conclusion, we were able to develop fully biosourced physical gels through the incorporation of κ-carrageenan chains in FGW solvent, via an eco-friendly experimental approach. As hypothesized in the introduction, FGW-based gels present improved properties compared to their aqueous analogous. Indeed, the gels exhibit promising thermal behavior with an extended operating temperature range compared to hydrogels. Even if the study of the nanostructure and the rheological characterizations evidenced a similar gelation mechanism of κ-carrageenan in both solvents, the transition temperatures Tg/s of the FGW-gels are higher than the ones obtained in water, and the initial viscoelastic properties are fully recovered after multiple heating and cooling cycles which is a key advantage compared to hydrogels. The supramolecular FGW structuration offers a better solvent retention and contributes to the formation of additional Hbonds within the gel. This peculiar spatial structuration provides a mechanical response improvement demonstrated by compression tests. Finally, we validate through this study, that the enhanced properties of these FGW-based gels result from the formation of synergetic interactions between this peculiar LTTM solvent and κ-carrageenan polymer chains. These soft materials, never reported in literature so far, are expected to find applicative uses in green and sustainable soft material technologies.

Figure 1 .

 1 Figure 1. Illustration of the two steps procedure of κ-carrageenan/FGW gels: 1) dispersion of κ-carrageenan at room temperature, 2) heating at 80°C for 3h, and gelation by cooling down to RT. The same procedure was applied to obtain hydrogels. 3) Picture of the κ-carrageenan/FGW gel.

Figure 2 .

 2 Figure 2. Frequency-dependence of G′ (filled symbols) and G′′ (open symbols) at different concentrations (C in g/L) of κ-carrageenan in water in blue (A) and in FGW in red (B) at 20°C

Figure 3 .

 3 Figure 3. Evolution of the storage G′ (filled symbols) and loss G′′ (open symbols) moduli as a function of temperature during a heating (1) and cooling (2) rate (2°C/min), C = 20.5 g/L of κcarrageenan in FGW (red and green symbols) and in water (blue and light blue symbols). The thermal transitions directly indicated in the figure correspond to the crossover point of G' and G''.

Figure

Figure 4 .

 4 Figure 4. A. SAXS patterns at 20 °C of κ-carrageenan at 8.1 and 20.5 g/L in water (A1) and in FGW (A2). B. Cross-sectional Guinier plots of the SAXS patterns in water (B1) and in FGW (B2) and graphical exploitation to determine the average cross-sectional radius (Rg) of rods composed of aggregates of κ-carrageenan helices.

Figure 5 .

 5 Figure 5. Illustration of the suggested organizations obtained in water-based gel and in FGWbased gel.

3 . 4

 34 Compression tests).

Figure 6

 6 Figure 6 regroups the engineering stress -engineering strain curves obtained. As shown in this Figure, samples are progressively deformed until a maximum stress is reached, corresponding

Figure 6 .

 6 Figure 6. (A) Engineering stress -strain curves obtained through compression tests at room temperature with a compression rate of 1 mm/min for 26.5 g/L gels in water (blue line) and in FGW (red line). (i) to (v) Pictures of the FGW-gel during compression test are shown to illustrate its ability to reach large compressive deformation. (B) Average stress at break and (C) average strain at break for both solvents-based gels (measurements were performed in triplicate).

Table 1 .

 1 Comparison between two methods for the determination of Ts/g value for two

	Ts/g (°C)

concentrations of κ-carrageenan in FGW (C = 20.5 and 26.5 g/L) at three different temperature ramps (1, 2 and 10 °C/min). All experiments were performed at a fixed frequency of 1 Hz with a constant strain of 1%.

Acknowledgements

This project has received funding from Gattefossé. The authors are also thankful to Agnès Crepet (IMP, Université Claude Bernard Lyon 1) for her valuable help to obtain and process Size Exclusion Chromatography and to all technical support received at IMP lab to achieve this work. The authors also acknowledge the D2AM beamline staff at ESRF and are in debt of Isabelle Morfin (LIPhy, Grenoble) for the setup of the beamline and the initial data treatment.

Conflicts of interest

There are no conflicts to declare.

Supporting Information

The supporting information part, available online, contains additional polysaccharide characterizations (TGA, SEC and NMR), and complementary physico-chemical analysis of the gels: thermal properties (DSC), rheological and mechanical properties.

Graphical Abstract

Fully biosourced physical gels with enhanced mechanical properties were obtained through an eco-friendly and simple experimental route

For Table of Contents Only


domain: phys chim

text:
Paul Cochard-Marchewka
email: paul.cochard-marchewka@espci.psl.eu

Nicolas Bremond

Jean Baudry

Droplet-based microfluidic platform for viscosity measurement over extended concentration range †

Rheology of concentrated protein solutions is crucial for the understanding of macromolecular crowding dynamics as well as the formulation of protein therapeutics. The cost and scarcity of most protein samples prevents wide-scale rheological studies as conventional viscosity measurement methods require large sample volume. There is a growing need for a precise and robust viscosity measurement tool that minimizes consumption and simplifies the handling of highly concentrated protein solutions. This objective is achieved by combining microfluidics and microrheology : we developed a specific microsystem to study the viscosity of aqueous solutions at high concentrations. The PDMS chip allows in-situ production, storing and monitoring of water-in-oil nanoliter droplets. We perform precise viscosity measurements inside individual droplets by particle-tracking microrheology of fluorescent probes. Pervaporation of water through a PDMS membrane induces aqueous droplet shrinking, concentrating the sample up to 150 times, thus allowing viscosity measurements along an extended concentration range in just one experiment. The methodology is precisely validated by studying the viscosity of sucrose sucrose solutions. Two model proteins are also studied with sample consumption reduced to as little as 1 µL of diluted solution, showcasing the viability of our approach for the study of biopharmaceuticals.

Introduction

In vitro studies often focus on the interaction of selected macromolecules in dilute systems, far from the reality of a highly concentrated and heterogeneous in vivo environment 1 . Most cells contain 20-30% of macromolecules in volume. Intracellular protein concentration is in the range 200-300 g.L -1 , regardless of the type of cell, adding to an environment already packed with RNA (75-150g.L -1 ) 2 .

High-concentration experiments are necessary to better understand intracellular physics 3 , to characterize protein behavior in intra or extracellular mediums 4,5 or study enzymatic reactions 6,7 for example. In the case of biopharmaceutics, most notably monoclonal antibodies (mAbs), high-concentration viscosity characterization a crucial step in the formulation process 8 , as well as an important research field 9 . Biopharmaceutics sometimes need to be formulated at concentrations above 100 mg.mL -1 . At such high concentrations, mAb-mAb interactions can cause a rapid, sequence-dependent 10 increase in viscosity 11 . For these formulation problems, and because viscosity represents a macroscopic measurement of protein-protein interactions 12 , the rheology of protein solutions is an important experimental field, often limited by the high sample volumes required by standard characterization experiments 13 .

By allowing the handling and analysis of fluid samples at the microscopic scale, microfluidics 14 represent a great stride in the search for a low sample consumption, with uses in analytical chemistry and biology.

In addition, droplet-based microfluidics, that relies on the production, manipulation and analysis of individual nanoliter compartments 15 , allows rapid screening of the parameters space, while limiting costly protein consumption.

The ability to precisely characterize reduced volumes is crucial for the rheological study of scarce samples such as proteins. As such, several in-chip viscosity measurement techniques have been recently developed 16 . Microrheology is an efficient way to measure viscosities inside microfluidic samples. Initially developed to measure viscosities within cells 17 , microrheology relies on the tracking of colloidal probes whose passive or active motion can be linked to the medium's properties 18 . It has since been successfully applied to microfluidic protein samples 13 as well as millifluidic droplets 19 .

In addition to manipulation and sorting of droplets, microdevices have been designed to modify the concentration of the medium inside the droplets by dialysis. Removing water from the droplets, either through osmosis, pervaporation or dilution in the continuous phase, induces aqueous shrinking 20 , effectively con-centrating the solutes. The reduced required sample size and the precise control over in-droplet concentration proves useful for analyte detection 21 . Protein crystallization is a costly and trial-anderror based process that is likewise greatly simplified by the use of micro-devices 22,23 .

We designed a device able to combine some of the aforementioned techniques, offering a simple and reliable platform for investigating viscous features of various hydrophilic compounds.

The accuracy and reliability of our approach were validated by studying samples of tabulated viscosity, pure water and sucrose solutions. The study of two model proteins showcased the efficiency of our method to characterize protein samples with minimal sample consumption. Our approach requires as low as 1 µL of dilute samples to perform full viscosity characterization of a given solute, as a step-emulsification geometry allows on-demand droplet production. Pervaporation-induced shrinking allows indroplet concentration by a factor of 125 while viscosity is continuously measured by particle-tracking microrheology. Initially developed to explore a 1-200 mPa.s viscosity range, corresponding to the viscosity range of biopharmaceutics, our method proved capable of accurate measurements on a 1 mPa.s-5 Pa. range.

Material and Methods

Microfluidic device

The 3-layer microfluidic device was obtained through soft litography 24 . For each layer, a quartz/chromium photolitography mask was printed by direct laser exposure (µPG 101, Heidelberg Instruments). A multi-layer master was fabricated by exposing epoxy photoresist (SU-8, Kayaku Advanced Materials) with a mask aligner (MJB4, Süss MicroTec). The design of the 3 separate layers is visible in figure 1 of the supplementary information.

Samples

Sucrose (179949), Bovine Serum Albumine (A7906) and Lysozyme from chicken egg white (L4919) were purchased from Merck KGaA. All samples were prepared with ultra-pure water (Milli-Q, Merck KGaA), and filtrated through 0.2 µm PTFE syringe filters (VWR).

Droplet production and manipulation

Novec 7500 (3M, η N7500 ≈ 1.2 mPa.s) or Fomblin Y06/6 (Solvay, η Y 06 ≈ 89 mPa.s) fluorinated oils were used as continuous phase, mixed with RAN-008 fluorosurfactant (RAN Biotechnologies) at a 0.2% w/w concentration. A 2-channel syringe pump (Nemesys, Cetoni GmbH) was used to inject both the continuous and dispered phases. A peristaltic pump (Sci-Q 323, Watson Marlow) produced the air flow used for droplet shrinking.

Fluorescent probes

500nm-diameter yellow-green fluorescent probes (FluoSpheres™ , ThermoFisher Scientific, F8813) were encapsulated in the droplets at an initial solid volume fraction of φ i = 4 • 10 -7 , corresponding to ≈6 particles per nanoliter or ≈90 particles per droplet. The probes were tracked with an inverted microscope (Axio Observer 7, Zeiss) mounted with a 40x objective (EC Plan-Neofluar NA 0.75, Zeiss), a multicolor LED light source (Zeiss Colibri 7) and a CMOS camera (ORCA-Flash4.0 LT C11440, Hamamatsu Photonics). The probes were imaged in the droplet's equatorial plane, localized by autofocusing on the droplet's edge. For each acquisition, a continuous 1000-images fluorescence timelapse was performed with an exposure time τ = 100 ms. The camera was used in streaming mode, with a delay between two images equal to the exposure time (∆t = τ = 100 ms). One batch of tracers was grafted with -PEG chains (Amine-PEG, M w = 20 kDa, Rapp Polymer) following Garting & Stradner's protocol 25 . The type of tracers used will be specified in the subsequent results. The hydrodynamic radius of the probes was determined through dynamic light scattering (ZetaSizer Ultra, Malvern Panalytical).

Particle detection & tracking

Post-acquisition data analysis, mainly particle detection & tracking, diffusion coefficient estimation and droplet volume measurement, was performed with a custom-made MATLAB script. The .czi files and their metadatas were read with the Bio-Formats toolbox 26 (Open Microscopy). The particles' positions were detected on each of the 1000 frames of the time-lapse. After thresholding to reduce background noise, a first peak detection was performed to roughly localize the brightest spots of the image. Then, a centroid fit was used to localize the center of the tracers with sub-pixel accuracy 27 (10 nm typical accuracy for fixed particles).

A Crocker-Grier algorithm 28 was then used to build particular trajectories. For each of the detected trajectory, a (∆x n , ∆y n ) n∈[1,N i ] matrix of particular displacement was obtained, with N i the length of the i trajectory. We only considered continuous trajectory longer than 100 frames. An average of 30 trajectories were detected per acquisition, with a typical length of 300 frames. A covariance-based estimator (CVE) was used to estimate diffusion coefficients from trajectory data. Recently developed by Christian L. Vestergaard 29 , this regression-free estimator provides unparalleled accuracy compared with the standard MSD or MLE-based estimators, given our experimental parameters. From the displacement matrix, the diffusion coefficient for a given trajectory is estimated as:

D i = ⟨(∆x n ) 2 ⟩ + ⟨(∆y n ) 2 ⟩ 4∆t + ⟨∆x n ∆x n+1 ⟩ + ⟨∆y n ∆y n+1 ⟩ 2∆t (1)
The Stokes-Einstein law was then used to estimate the dynamic viscosity associated with each trajectory:

η i = k B T 6πr D i (2)
with k B the Boltzmann constant, T the temperature and r the probe radius. The estimated global measured viscosity η was obtained as the average of the estimates provided for each trajectory, weighted by the trajectory length:

η = ∑ T i=1 N i η i ∑ T i=1 N i (3)
Correlation assessment between the measured viscosity and vari-ous experimental parameters was performed by calculation of the Spearman's rank correlation coefficient ρ on statistically significant data sets. Spearman's correlation measures rank correlation, with extreme values of ρ = ±1 indicating the variables are perfectly monotone functions of each other. The p-value indicates the statistical significance of any correlation between the variables. We adopted the common convention that the correlation is only statistically significant for p-values lower than 0.05 30 .

Droplet volume measurement

In-chip concentration monitoring was performed through droplet volume measurement.

Edge detection of the spherical droplets was performed by circular Hough transform 31 on brightfield images. The detected droplet radius gave access to their volume, and in turn to the solute's in-droplet concentration as the sample's initial concentration was known.

We estimate the error on droplet volume measurement to be <5% in the vast majority of the cases. This estimation is detailed in the supplementary information. In particular, edge detection was validated with optical models 32 .

Concentration

Samples of known initial mass concentration c 0 were prepared. This concentration is defined as:

c 0 = m s V T (4)
With m s the mass of solute and V T the solution's total volume.

At any given time, volume measurement gave access to the indroplet mass concentration:

c(t) = c 0 r(t) (5)
With r(t) = V 0 V (t) the droplet's shrinking ratio. For sucrose samples, the results were expressed in terms of mass fraction. The mass fraction of a solution is defined as:

c w/w = m s m T (6)
With m T the total mass of the solution.

To perform the conversion between c and c w/w , the partial specific volume of sucrose 33,34 (v=0.62 mL.g -1 ) was taken into account. The mass fraction inside the droplet was expressed as:

c w/w (t) = r(t)m s m w + [v + (1 -v)r(t)]m s (7)
With m s and m w the masses of solute and water in the initial solution.

Protein samples of known initial mass concentration c 0 were studied. The results were expressed in terms of effective volume fraction, defined as 35 :

φ eff = k 0 × c (8)
with c the mass concentration and k 0 the voluminosity of the pro-teins, defined as:

k 0 = 4 3 π N A M w R 3 S (9)
with N A the Avogadro constant, M w the protein's molar mass and R S their Stokes radius. The values of R bsa S = 3.5 nm and R lys S = 2 nm were considered for BSA 36 and Lysozyme 37 respectively.

Results and Discussion

Results

Device operation

Figure 1 shows schematic view of the whole chip, as well as a detailed view of its rheological section.

The first section of the chip is a dropmaker. The use of a step-emulsification geometry allows on-demand production of droplets 38,39 by bursts of 10-20 droplets corresponding to 150-300 nL of sample. This geometry, combined with a syringe pumpbased injection technique, allowed us to perform successful experiments using as little as 1 µL of diluted solution. A detailed view of the dropmaker and its dimensions is visible in figure 2 of the supplementary information. A movie showing the production of a droplet burst is visible in the electronic supplementary information.

Once produced, droplets are stored in a selection chamber, just upstream of the main channel. Precise flow control allows to individually select and load droplets in cylindrical wells located above the main channel. The wells have a 300 µm diameter and a 300 µm depth. Flow control is achieved by precise tuning of the differential height between the inlet and the outlet, see figure 3 of the supplementary information. The loading is gravitational, as the water droplets are lighter than the fluorinated continuous phase (∆ρ = 614 kg.m -3 in the case of Novec 7500). By shielding the droplets from residual flow in the main channel, the wells allow stabilization of the droplets, essential for MPT microrheology. Once loading is complete, droplet shrinking is achieved by water pervaporation through the 200 µm PDMS membrane between the main and lateral channels 22,23 . Air flow in the lateral channel keeps the humidity gradient constant and is imposed by a peristaltic pump.

Experimentally, the shrinking speed as a function of membrane thickness behaves as described by previously established pervaporation models 20 . Depending on the solute, the shrinking speed can then be adjusted by changing either the membrane's width or the humidity of the air flow. In our case, a 200 µm-wide membrane minimizes the experiment time while ensuring homogeneity of the droplet's content 40 .

Validation of particle-tracking microrheology

To assess the accuracy of our particle-tracking microrheology method, we first measured the viscosity of pure water without any droplet shrinking. On 3 droplets of distinct radius, a serie of 20 successive time-lapses was performed. The results, reported in table 1, showcase the accuracy and the repeatability of our measurements, with an average relative standard-deviation (RSD) of around 3%. Additionally, these experiments allowed us to evaluate the correlation between measured viscosity and particular position. Figure 2 displays the heatmap of viscosities measured in the equatorial plane of a pure water droplet. Each point corresponds to the mean particle position for a given detected trajectory. The variations in measured viscosity do not correlate with the particles position in the equatorial plane. To study the influence of the shrinking process we monitored the viscosity of shrinking water droplets, whose viscosity remains constant regardless of shrink. Figure 3 shows the combined results of 4 distinct shrinking experiments. These experiments tend to indicate that the shrinking process has no significant effect on particular diffusion until lower droplet radii under 30 µm.

Step-emulsification dropmaker

Characterization of the accessible range

To demonstrate the range of our experimental approach, we then measured the viscosity of sucrose solutions. Sucrose presents a good solubility in water, allowing the study of a wide concentration range. Over this range, its viscosity continuously increases, covering 4 decades (1 mPa.s -10 Pa.s), making sucrose a compound of choice to assess both the concentration and viscosity ranges accessible to our approach. Sucrose viscosity has been tabulated with high precision 41 , and as such it has been previously used as a calibration agent for microrheology 13 .

Starting from dilute solutions (5% w/w), droplet shrinking allowed us to reach concentrations as high as 80% w/w. Figure 4 shows a good comparison between the experimental relative viscosity profile of sucrose and the tabulated values. Relative viscosity is defined as:

η rel = η η 0 ( 10
)
with η 0 the dynamic viscosity of the solvent, in our case water.

20 experiments were conducted, with varying initial concen- trations and droplet radii. To estimate the precision of these experiments, we performed a linear interpolation between our data and the tabulated values before measuring the distance between the two curves. On the target 1-200 mPa.s range, the average relative error was around 3%. The measured viscosities compare well with the tabulated until around 1.7 Pa.s corresponding to 75% w/w. Above this value, in the 75-80% range, viscosities as high as 18 Pa.s were measured. While these values have no tabulated value to compare with, they qualitatively match the general trend of sucrose's viscosity curve.

For viscosities above 200 mPa.s, a more viscous fluorinated oil was used as the continuous phase to prevent noise caused by droplet movement (see 3.2.3).

Proteins

Finally, we applied our approach to the study of two model proteins dissolved in pure water: Bovine Serum Albumin and Lysozyme. For these experiments, the fluorescent probes were grafted with -PEG polymer chains, allowing the particles to remain stable regardless of the studied protein's charge. With this steric stabilization 25 , the same probes can be used to work with either negatively charged proteins, such as BSA, or positively charged ones, such as Lysozyme. With the use of a syringe pumpbased injection system, we were able to conduct these experiments using as little as 1 µL of diluted initial solutions, demonstrating our approach's contribution to the reduction of sample consumption. For these two model proteins, all concentrations give a viscosity within our approach's measuring range. shows the relative viscosity (cf equation (10)) profile for the two proteins.

Discussion

Influence of droplet interface

One of the novelties of our approach is the use of MPT microrheology in microfluidic droplets. The Stokes-Einstein law (equation (2)) relies on the hypothesis of free diffusion. In reality, the liquid-liquid interface at the edge of the droplet will affect the diffusion of the probes 42 . The rigidity of the surfactant-covered interface 43,44 will induce an increase of the particle's drag at its vicinity, that will in turn results in a decrease of the particle's diffusion coefficient and an increase of viscosity measured through the Stokes-Einstein equation. The influence of the interface is anisotropic, whether the particle is experiencing diffusion normal or parallel to the interface 45 . Previous instances of indroplet microrheology have been performed in millifluidic-sized droplets 19 , where particle tracking could be performed at a distance where any influence from the interface was negligible. For bigger droplets, the interface can be approximated as plane, and the diffusion coefficient decrease can be calculated [START_REF] Happel | Low Reynolds Number Hydrodynamics[END_REF] . For example, a particle experiencing normal diffusion at 5 µm of the interface will display a 5% diffusion coefficient decrease. At 100 µm, the diffusion coefficient decrease drops to just 0.3%.

The important number of acquisitions performed on pure water droplets without shrinking (see figure 2) provided us with a data set statistically significant enough to perform correlation assessment. With a correlation coefficient of ρ = 0.017, and a p-value of 0.59 no correlation was found between the particle's position relative to the center of the droplet. For these droplets (figure 2 was obtained with a 140 µm-radius droplet), the interface seems to have no influence on particular diffusion. This results can be interpreted as such: not only the area where the effects of the interface are sizable is a small fraction of the area of the equatorial plane for bigger droplets but in addition the probes will diffuse in and out of this area during the acquisition, as the characteristic diffusion length is l c = √ D∆t ≈ 7 µm for probes diffusing in water during a 30 s time frame, corresponding to the average trajectory length.

This result might not hold for smaller droplets, as the area in the vicinity of the interface will increase in size relative to the equatorial plane, and as the increased confinement will prevent the probes from diffusing in and out of this area. Our goal of individual droplet manipulation, and our aim to continuously concentrate samples by droplet shrinking mandates us to work with droplets of reduced radius (R < 50 µm), a range previously unexplored. Additionally, at smaller radii the droplet's interface can no longer be considered as a plane. We monitored the viscosity of shrinking water droplets (see figure 3). For droplets under 30 µm in radius there is an increase in measured viscosity, potentially due to restrained diffusion caused by the droplet's interface.

We could only perform those experiments at the lowest bound of our viscosity range, the viscosity of pure water. Indeed water is the only compound whose viscosity is constant regardless of droplet shrinking. However, we studied the viscosity of sucrose solutions with various initial concentrations and initial droplet radii. The repeatability and continuity of the measured viscosities for more than 20 experiments tend to indicate that given our experimental conditions, the droplet's interface has no effect on the measured viscosity.

In-droplet homogeneity

By averaging the measured viscosity over all the detected trajectories, multi-particle tracking relies on the assumption that the viscosity is constant across the droplet's equatorial plan. Inhomogeneity of the solutes inside the droplet could jeopardize this assumption. Depending on the shrink speed and on the solute's diffusion coefficient, an accumulation of solute could occur at the droplet's interface. As developed in previous studies 40 , a colloidal suspension in a shrinking droplet can be considered homogeneous at Pe << 1, with Pe the Péclet number defined as:

Pe = Rv D (11)
R is the droplet radius, v is the speed of the interface shrinking towards the center of the droplet, and D is the solute's diffusion coefficient. This condition is met for our experiments, with a maximum value at Pe max ≈ 0.06. Moreover, individual particle tracking in the equatorial plane revealed no evidence of any recirculation flow that could have indicated diffusion cause by solute gradient. Finally, it is important to remind that the shrinking speed can be tuned by changing our setup's PDMS membrane width. Should any solute inhomogeneity appear, one could easily tune the shrinking speed to reduce Pe.

Influence of droplet movement

As the spherical droplet is not confined by the cylindrical well, it will experience Brownian diffusion itself. We defined the ratio κ, comparing the characteristic Brownian diffusion lengths of the fluorescent probes and of the droplet itself:

κ = √ 2D∆t √ 2D d ∆t = √ D √ D d ( 12
)
with D d the diffusion coefficient of the droplet. Both D and D d can be expressed by the Stokes-Einstein law (equation ( 2), and equation ( 12) simplifies as:

κ = η c η R r (13)
with R the droplet's radius, r the probe's radius and η c the viscosity of the continuous phase. As the droplet shrinks its radius will decrease and, with the exception of pure water, in-droplet viscosity will increase as the sample is concentrated. Decreasing droplet radius will induce an increase of droplet movement, and increasing in-droplet viscosity will decrease probe movement. For low values of R and high values of η, droplet movement will be in the same order of magnitude as probe movement, lowering the precision of MPT microrheology. Two factors will then define the upper viscosity limit measurable by our approach: the precision of particle-tracking and droplet movement. A rough estimate of the maximum measurable viscosity can be calculated by placing the limit at κ = 1. The maximum viscosity η max d can then be defined as:

η max d = η c R r (14)
It is important to note that this value is likely to be underestimated, as the diffusion of the droplet is hindered its contact with the top of the well. Some sucrose experiments were conducted with Novec 7500 as a continuous phase, a fluorinated oil with relatively low viscosity. At high viscosities (η> 300 mPa.s) and low radii (R<30 µm), some experiments displayed a plateau, seemingly indicating that the maximum measurable viscosity had been reached (data from these experiments is visible in the supplementary information). Moreover, the plateau was in the vicinity of the estimate provided by equation (14). Derived from equation ( 14), two solutions allow to push this limit and extend the viscosity range. The first is to increase the droplet radius R, thus limiting its movement. However, the drawback of this approach is the limitation of the maximum shrink factor. The second approach, which we have retained, is to increase η c , the viscosity of the continuous phase. By using Fomblin Y06 (η Y 06 = 89 mPa.s), equation ( 14) estimates a limit of 4.8 Pa.s for R = 20 µm, much higher than the 0.1 Pa.s estimated for Novec 7500 (η N7500 = 1.2 mPa.s). Using a more viscous continuous phase did not present any additional difficulties in the operation of the device. With Fomblin Y06, no plateau behavior was observed, even for viscosities above 5 Pa.s (see figure 4). Working with a more viscous continuous phase is an easy experimental approach to solving the issue of droplet movement.

It is also worth mentioning that particle-tracking on a fluctuating substrate is a well-studied problem, and that other more complex approaches such as two-point microrheology [START_REF] Crocker | [END_REF]48 are also available to cancel the noise caused by droplet movement.

Precision of particle tracking microrheology

To assess the precision of our MPT method, we took two values into account: the average relative error ⟨ | η-η| η ⟩ and the relative standard-deviation (RSD)

σ ( η)
⟨ η⟩ . The first value reflects any bias of our estimation, while the second quantifies its precision. For water, a slight bias was observed, as the viscosity was consistently underestimated. Such a bias can be linked with an error on the probes hydrodynamic radius, or on the measured temperature, both leading to a systematic error on the measured viscosity (see equation ( 2)). To limit the influence of this bias, the measured viscosities are expressed in terms of relative viscosity η rel (see equation (10)).

For both water and sucrose, a 3% RSD on the viscosity was consistently observed. Several factors explain this value. First, the standard deviation of the CVE estimator can be quantified as 29 :

σ ( D) = ⟨ D⟩ 6 + 4ε + 2ε 2 N + 4(1 + ε) 2 N 2 (15)
where ε = 1 SNR 2 -1 3 is linked to the signal-to-noise ratio of the particle tracking and N is the number of detected positions. The signal-to-noise ration is defined as SNR = √ D∆t σ , the ratio between the characteristic length of particular diffusion and the localization error. Both the experimental parameters of our optical acquisition method and our choice of particles were guided by the optimization of the SNR, with necessary compromises. For example, because our camera is in streaming mode, the shutter speed is equal to the interval between two consecutives images, τ = ∆t. Increasing the exposure time τ then results in an increased particular diffusion length, thus improving the SNR. However as the exposure time increases, motion blur will eventually cause the localization error σ to increase as well. The same conflicting effects guides the choice of fluorescent probes. As the diffusion coefficient is inversely proportional to the probe's radius, the characteristic diffusion length can be increased by decreasing the probe's radius. However, as probe fluorescence is proportional to probe volume, decreasing their radius will also result in a increased localization error, affecting the SNR. For any microrheology experiment, each of these experimental parameters has to be optimized to find the best compromise for the SNR. In our case, droplet shrinking brings an additional layer of complexity. As particular diffusion is inversely proportional to viscosity, it is easy to see that optimal values of τ and r will depend on the viscosity of the medium. Our choice of parameters (τ = 100 ms and r = 250 nm) provides high SNR values on a wide range (η ∈ [1 mPa.s, 1 Pa.s]). In the case of water, and more broadly for viscosities below 10 mPa.s, equation ( 15) can be simplified as 29 :

σ ( D) ⟨ D⟩ ≈ √ 5 √ N ( 16
)
For the experiments presented in table 1, an average of ⟨N⟩ ≈ 7800 positions were detected at each acquisition, giving an approximate RSD of ≈ 2.5%, an estimation in adequation with the experimental value of 3%.

Another source of error is the uncertainty on the radius of the fluorescent probes. Once the diffusion coefficient estimated, particle radius r is involved in the calculation of the viscosity η (see equation ( 2)). A polydispersity of σ p ≈ 14% in diameter was measured by dynamic light scattering. The RSD caused by particle polydispersity can be estimated as:

σ ( D) ⟨ D⟩ = σ p √ P ( 17
)
where P is the number of distinct particles tracked during a given acquisition. With an average of ⟨P⟩ ≈ 20 distinct particles tracked, polydispersity-linked error is estimated as δ ≈ 2.5% for our experiments. These results show that in our experimental conditions two main factors limit the precision of MPT microrheology: the number of measured particular positions and the number of individual particles.

Conclusion

We developed an integrated platform, allowing viscosity characterization of aqueous solutes on an extended concentration range, starting from reduced volumes of dilute samples. Droplet shrinking, induced by water pervaporation through the microfluidic device, allows continuous concentration up to 150-fold of the solute throughout the experiment, while particle-tracking microrheology allows continuous viscosity measurement.

The use of the CVE estimator, along with a wide spectrum error sources quantification effort provides precise viscosity measurement on the 1-200 mPa.s initial range of interest, as well as an extension of this range up to viscosities above 5 Pa.s. Furthermore, the study of sucrose revealed our method's ability to easily reach extremely high concentrations, well above sucrose solubility in water of around 67%. The homogeneity brought by the small volume of the studied droplets and the absence of liquid-solid or liquid-gas interface greatly reduces nucleation, and the small volumes of the droplet increases the mean nucleation time 49 (∝ 1/V ), allowing to probe supersaturated solutions without the crystallization-linked complications or the complexity of sample preparation encountered in macroscopic experiments 50 . However, the liquid-liquid interface of the droplets still presents a potential risk: protein adsorption/desorption at the water-oil interface during the shrinking process could affect the bulk protein concentration. Our experiments were performed with droplets of various initial volumes and with solutions of various initial concentrations. The fact that our results overlap into a continuous viscosity curve attests that in our case this potential effect does not noticeably impact bulk protein concentration, but it could become significant for studies with very low initial protein concentrations.

Because it relies on volume measurement to access concentration, our approach provides results based on mass concentration. This presents no obstacle for protein rheology, as results are by convention expressed in effective volume fraction. Some industrial application such as biopharmaceutics formulation might require conversion to mass fraction. As mentioned for the study of sucrose, the knowledge of the solute's partial specific volume is necessary to perform this conversion. This should not be an obstacle either, even for previously unstudied biopharmaceuticals, as the partial specific volume of proteins has been shown to be constant inside broad families 51 . For monoclonal antibodies specifically, representing the vast majority of biopharmaceutics, a constant value of v = 0.73 g.mL -1 is considered 52 .

The presence of excipients or buffer media might limit the concentration range accessible to our device. As droplet shrinking induces sample concentration, any buffer or additive will get concentrated by the same factor, potentially affecting the sample's viscous behavior. It remains possible to study these kind of samples by dividing the viscosity curve in 2 or 3 distinct segments, and by adjusting the initial excipient concentration to avoid any interference. Even if this approach diminishes the convenience of plotting the entire curve in a single experiment, our device remains a cost-effective and time-efficient method for the study of biopharmaceuticals. Solvent conditions, most notably pH and ionic strength, can affect the viscous behavior of protein solutions. As such, the vast majority of available studies on the viscosity of proteins are performed in controlled solvent conditions. To fully validate the use of our approach for the study of protein solutions, additional experiments will be required with controlled solvent conditions and further purification. Without these additional steps, it is not yet possible to compare our data with previous work on the viscosity of BSA 53 and lysozyme 54 .

Showcasing the growing interest around this field, an device similar to ours was recently developed 55 with the aim of studying monoclonal antibodies in the future. Based on the same principle, this other work relies on a different microfluidic device, where the droplet are confined during the whole shrinking process. It is an advantage, as it eliminates the potential noise caused by droplet motion and thus does not require the use of more viscous continuous phase. By design, this other device relies on water pervaporation through the body of the microfluidic chip, whereas our device's lateral channel allow faster pervaporation and thus significantly shorten experiment times: from 24h to 3h, an 8-fold improvement. With such experiment times, we did not encounter any probe sedimentation issues and our device does not require the use of a rotator. Further reduction of the experiment time can be achieved by thining the membrane between the main and lateral channel, as we found out the droplet's shrinking time was roughly proportional to the membrane's thickness. The device presented in this article has a 200 µm membrane, but we were able to produce devices with membrane thicknesses as low as 20µm. However, one should keep in mind that increasing the droplet's shrinking speed might jeopardize in-droplet homogeneity, as previously discussed in 3.2.2.

Regardless of the device used, we highly recommend the use of Vestergaard's covariance-based estimator. It increases microrheology's precision, decreases the required number of particles and allows the quantification of the error made during particle tracking. Being regression-free, it is also significantly faster. The choice of this algorithm allowed us to expand our dynamic range 10-fold compared to the previous approach 55 and to measure viscosities 10 times higher. We are able to work with smaller droplets, increasing the maximum shrinking factor (150 compared to 30 in the previous work) and allowing our device to work with smaller protein samples ( 10 µg for our approach compared to 1 mg in the previous work). Increasing the maximum viscosity might not be useful for protein rheology but can find applications in other fields, such as polymer rheology. The precision of viscos-ity measurement and the maximum measurable viscosity could be increased by improving the imaging setup for particle tracking. By using a triggered camera, one could reduce the exposure time τ and increase the interval between two consecutive images ∆t, which would decrease motion blur and increase diffusion lengths. Using a more powerful light source (for example by using a laser instead of LEDs) and / or increasing the probe's fluorescence could result in increased precision. It would allow to further reduce the exposure time, increase the magnification and decrease the probe's radius.

Understanding the behavior of concentrated protein solutions is crucial, as most biological media present high macromolecular concentrations, and as protein's collective behavior is linked with biological phenomena such as degenerative diseases 56 . By greatly simplifying the precise study of high-viscosity samples of highly concentrated proteins, our device could be an important tool in this effort.

Conflicts of interest

There are no conflicts to declare.

Acknowledgments

This research received funding from BPIFrance under the "Investissement d'Avenir" framework (CELLIGO project). This work also received the support of "Institut Pierre-Gilles de Gennes" (laboratoire d'excellence, "Investissements d'Avenir" program ANR-10-IDEX-0001-02 PSL, ANR-10-EQPX-34 and ANR-10-LABX-31. Special thanks to Kevin Phan at IPGG who has been of great help during prototyping.

Notes and references

Fig. 1

 1 Fig. 1 Overview of the microfluidic device's architecture and of the droplet shrinking process. (a) Schematic, perspective view of the microfluidic device. The step-emulsification geometry allows on-demand production of droplets following injection of the continuous phase (fluorinated oil) and dispersed phase (aqueous solution). After production, droplets are briefly stored in a selection chamber before being individually selected and loaded into the rheological section. (Scale bar: 2000 µm) (b) Schematic, perspective view of the rheological section. Between the selection chambers, the main channel narrows to reach a width of 400 µm. Above the main channel, 7 cylindrical wells of 300 µm diameter serve as traps, as the lighter water droplets tend to rise in the wells. Separated by a 200 µm PDMS membrane, the lateral channel surrounds the rheological section. Air flow through the lateral channel maintains a humidity gradient between the dry air and the water droplets, inducing water pervaporation through the PDMS membrane and thus droplet shrinking. (Scale bar: 1000 µm) (c) Brightfield microscopy images of a water droplet at different shrinking stages. (40×, scale bar: 50 µm) (d) Measured droplet volume as a function of time. Continuous droplet shrinking is monitored via edge detection of the spherical droplet. The points corresponding to the 3 images shown in (c) are indicated.

Fig. 2

 2 Fig.2Measured viscosity heatmap on the equatorial plane of a pure water droplet. The position of each point corresponds to the mean particular position for each of the 996 trajectories tracked. The point's color codes for the measured viscosity, and its size codes for the trajectory length. The red circles corresponds to the position of the droplet's edge. These data have been obtained on a total of 20 acquisitions performed on a 140 µm radius water droplet (droplet 2 in table1).

Fig. 3

 3 Fig. 3 Measured viscosities for shrinking pure water droplets. Combined data from 4 distinct shrinking experiments, corresponding to a total of 197 acquisitions. Each points corresponds to one acquisition, with colors coding for the 4 different shrinking droplets. For lower droplet radii (R < 30 µm), an increase of measured viscosity η seem to indicate an influence of the droplet's interface on particular diffusion. The two dashed lines represent the confidence interval for MPT estimated from the acquisitions on fixed-radius droplets (table1).

Fig. 4

 4 Fig.4Relative viscosity as a function of mass fraction for aqueous sucrose solutions, comparing microrheology in shrinking droplet results (△) and tabulated data 41 (solid line). Two distinct experiments are reproduced here, with initial sucrose mass fraction of 5% and 40% respectively. For clarity, only 1 out of 5 data points have been reproduced. A similar figure with all measured data points is available in supplementary information.

Fig. 5

 5 Fig. 5 Relative viscosities for bovine serum albumin (BSA) △ and lysozyme (•) in pure water.

Table 1

 1 Measured viscosities in pure water droplets, without shrinking. On each of the 3 droplets, a serie of 20 successive time-lapses were recorded. The measured viscosities η are to be compared with the tabulated value of 0.89 mPa.s for water at 25°C.

	Experiment	1	2	3
	Droplet radius (µm)	95	140	62
	Mean viscosity ⟨ η⟩ (mPa.s)	0.88	0.85	0.87
	Relative error ⟨	| η-η| η ⟩	1%	4.5%	2%
	RSD	σ ( η) ⟨ η⟩		2.8% 2.9% 3.4%

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