Wensen Wang

Nicolas Onofrio

Eddy Petit

Bonito Aristide Karamoko

Huali Wu

Jiefeng Liu

Ji Li

Kun Qi

Yang Zhang

Christel Gervais

Luc Lajaunie

Chrystelle Salameh

Philippe Miele

Zhiyuan Zeng

Damien Voiry

High Surface Area Functionalized Nanolaminated Membranes For Energy Efficient Nanofiltration And Desalination In Forward Osmosis

Stacking two-dimensional (2D) nanosheets into laminar membranes to create nanochannels has attracted widespread attention at fundamental and practical levels for separation technology. Constructing space-tunable and long-term stable sub-nanometer channels provide original systems for nanofluidic investigations and accurate molecular sieving. Here, we report a scalable strategy for the preparation of non-swelling covalently functionalized molybdenum disulfide (MoS2) membranes with tunable cohesion energy and interlayer space from 3.5 to 7.7 Å, depending on the nature of the functional groups attached to the MoS2 nanosheets. We evaluated the relationship between the capillary width, the surface chemistry, the stacking disorder and the sieving behaviors of the membranes in forwards osmosis (FO). By combining experimental investigations and numerical simulations, we identified that the functionalization with aryl groups induces the formation of a capillary width of 7.1 Å and interlayer stiffness as low as 5.6 eV Å - 2 , leading to controlled stacking defects. We report the fabrication of membranes up to 45 cm 2 , which demonstrate a salt rejection as high as 94.2% for a continuous operating time of 7 days. Our work presents a desalination strategy in FO with a specific energy consumption (SEC) of 4 × 10 -3 kWh m -3 , which compares favorably with commercial FO membranes.

Introduction

The construction of selectively permeable membranes with sub-nanometer channels has gained attention for artificial bionics and molecular sieving by taking advantage of the sub-nanometer size of the pores formed between two successive nanosheets. Two-dimensional nanolaminates are regarded from both fundamental and practical points of view as mimicking systems of the biological protein transport channels and building blocks of nanofiltration membranes [START_REF] Shen | Artificial channels for confined mass transport at the sub-nanometre scale[END_REF][START_REF] Werber | Materials for next-generation desalination and water purification membranes[END_REF] . In nanolaminated membranes, mass transport typically occurs within the physical gap between the layers defined as the interlayer space or the capillary width. The fabrication of 2D subnanometer channels with controlled dimensionality and chemistry of the interlayer space has therefore emerged as a mature topic in the field of 2D materials [START_REF] Wang | Two-dimensional nanochannel membranes for molecular and ionic separations[END_REF][START_REF] Kang | 2D laminar membranes for selective water and ion transport[END_REF][START_REF] Cheng | Two-dimensional-material membranes: Manipulating the transport pathway for molecular separation[END_REF] . The practical demonstration of nanolaminate membranes has not been achieved due to two main bottlenecks, which are (i) the intrinsic instability of the interlayer space and (ii) the difficulty in fabricating pinhole-free membranes on a large scale with controlled thickness [START_REF] Safaei | Progress and prospects of two-dimensional materials for membrane-based water desalination[END_REF][START_REF] Liu | Two-dimensional material membranes for critical separations[END_REF][START_REF] Cheng | Two-Dimensional Membranes: New Paradigms for High-Performance Separation Membranes[END_REF] . Currently, the most widely studied 2D building block of nanolaminate membranes is graphene oxide (GO), which forms free spaces of around 5 Å in dry condition. This allows a narrow molecular sieve size with sharp molecular cut-off for rejecting large molecules and ions at the expense of the water flux [START_REF] Joshi | Precise and ultrafast molecular sieving through graphene oxide membranes[END_REF] . Although the space size can be modulated by encapsulating GO membrane into epoxy under different humidity, the process is rather complex and prevents realistic applications [START_REF] Abraham | Tunable sieving of ions using graphene oxide membranes[END_REF] . Other strategies for controlling the pore size of the nanolaminates include ion coordination [START_REF] Chen | Ion sieving in graphene oxide membranes via cationic control of interlayer spacing[END_REF] , polymer intercalation [START_REF] Shen | Subnanometer two-dimensional graphene oxide channels for ultrafast gas sieving[END_REF] , crosslinking [START_REF] Hung | Cross-linking with diamine monomers to prepare composite graphene oxide-framework membranes with varying d-spacing[END_REF] . Inevitable swelling occurs in pristine GO membranes when it is operated in an aqueous solution, which dramatically increases the interlayer spacing, leading to a rapid degradation of the sieving performance [START_REF] Zheng | Swelling of graphene oxide membranes in aqueous solution: characterization of interlayer spacing and insight into water transport mechanisms[END_REF][START_REF] Su | Graphene oxide membranes: controlling their transport pathways[END_REF][START_REF] Han | A review of performance improvement strategies for graphene oxide-based and graphene-based membranes in water treatment[END_REF] .

Besides GO, MoS2 and MXene nanosheets are alternative building block candidates for the construction of 2D nanochannels [START_REF] Sun | Laminar MoS2 membranes for molecule separation[END_REF][START_REF] Guo | MoS2 membranes for organic solvent nanofiltration: stability and structural control[END_REF][START_REF] Ren | Charge-and size-selective ion sieving through Ti3C2Tx MXene membranes[END_REF][START_REF] Ding | A two-dimensional lamellar membrane: MXene nanosheet stacks[END_REF] . MoS2 laminated membranes have shown outstanding water permeation in reversed osmosis (RO) and the improved stability compared to GO and MXene membranes [START_REF] Wang | Ion sieving by a two-dimensional Ti3C2Tx alginate lamellar membrane with stable interlayer spacing[END_REF][START_REF] Kim | 2D nanosheets and their composite membranes for water, gas, and ion separation[END_REF] . Unfortunately, the molecular cutoff of MoS2 membranes depends on the presence of intercalated water molecules in the laminated structure [START_REF] Wang | Understanding the aqueous stability and filtration capability of MoS2 membranes[END_REF] . We have recently reported a facile strategy to modify the surface chemistry of the MoS2 nanosheets and tune the interlayer space [START_REF] Ries | Enhanced sieving from exfoliated MoS2 membranes via covalent functionalization[END_REF] . Although the vast majority of the efforts have focused on membranes for RO applications, forward osmosis (FO) is regarded as a strategy to reduce the energy footprint associated with water purification processes. To date, only few studies have however focused on the production and testing membranes with sizes greater than 1 cm 2 due to the difficulty in controlling the integrity of the membrane structures over large area (swelling, delamination, formation of pinholes) [START_REF] Ries | Enhanced sieving from exfoliated MoS2 membranes via covalent functionalization[END_REF][START_REF] Mei | Simultaneous Electrochemical Exfoliation and Covalent Functionalization of MoS2 Membrane for Ion Sieving[END_REF][START_REF] Chu | Precise ångström controlling the interlayer channel of MoS2 membranes by cation intercalation[END_REF] .

Here, using MoS2 nanosheets as building units, we adopted a chemical functionalization strategy to prepare FO membranes with controlled interlayer space and interlayer stiffness in order to tailor the interlayer space and the stacking disorder in the nanolaminated structure. The membranes are found to be resistant against swelling, while the interlayer space can be adjusted with ångström precision. We demonstrated the fabrication of membranes with thickness from 100 nm up to 1 µm and dimensions as large as 45 cm [START_REF] Werber | Materials for next-generation desalination and water purification membranes[END_REF] . The membranes achieved a water flux as high as 12

LMH with molecular cutoff of 180 Da and a salt rejection as high as 94.2%. When tested against desalination, the functionalized MoS2 FO membranes demonstrated superior salt rejection performance for 7 days without significant loss of the water flux compared with GO-based membranes and commercial polymer FO membranes. The nanofluidic behavior in various channels has been studied using physical characterizations and molecular dynamic simulations to unravel the size entanglements of the surface chemistry, the sub-nanometer interlayer space and the disorder of the stacking of the nanosheets in the laminated structure. We finally evaluated the energy consumption of our filtration system and found that the MoS2 nanolaminate membranes may allow for a lower electrical power consumption compared to commercial FO membranes thus opening avenues for practical applications of nanolaminate FO membranes.

Characterization of Nanolaminated MoS2 Membranes

Molybdenum disulfide nanosheets were exfoliated in water from a bulk crystal and further functionalized using alternatively organohalides or diazonium salts in order to covalently attach alkyl and aryl functional groups, respectively [START_REF] Eda | Photoluminescence from chemically exfoliated MoS2[END_REF] . Six types of molecules were selected offering different sizes and polarities. The functionalized MoS2 nanosheets were first observed using electron microscopy in order to confirm the presence of attached functional groups and the crystallinity of the nanosheets (Fig. 1a,b). The functionalized nanosheets were then characterized by performing Attenuated total reflectance Fourier-transformed infrared (ATR-FTIR), Raman and [START_REF] Hung | Cross-linking with diamine monomers to prepare composite graphene oxide-framework membranes with varying d-spacing[END_REF] The membranes were fabricated by vacuum filtering of the suspension of MoS2 nanosheets on a porous support and the membrane thickness was adjusted between 100 nm and 1 µm (Supplementary Figure 5). The ordered interstitial structure was confirmed by the cross-section view of one typical functionalized membrane using scanning electron microscopy (SEM) and X-ray diffraction (XRD) (Fig. 1c and Fig. 2c,d).

Compared to pristine MoS2 nanolaminates, which display an intense (002) peak at ~14.2°, the peaks of functionalized membranes shift to lower angles corresponding to an increased interlayer space between the nanosheets. The capillary width was estimated by subtracting 6.15 Å corresponding to the Mo-Mo distance between two successive layers of MoS2 in a bulk crystal. We obtained capillary width of 3.6 Å, 4.8 Å, 5.3 Å, 6.9 Å, 6.5 Å, and 7.1 Å for C2-, C3-, Ace-, Ben-, C3OH-and Arylfunctionalized MoS2, respectively. Our XRD analyses therefore suggest that the interlayer spacing can be fine-tuned to ångström accuracy by employing different sizes of functional groups. To visually observe the increase of the interlayer space, we measured the evolution of the membrane thickness before and after functionalization (Fig. 2e and Supplementary Figure 6). The thickness determined from our SEM crosssection analyses increases linearly with the d-space distance measured from XRD.

The structural stability of MoS2 nanolaminates in aqueous solution was examined by successive ex-situ XRD measurement at increased soaking time in water as well as in saline solutions (Supplementary Figure 789). As shown in Figure 2f, the interlayer space of hydrophobic nanochannel is found virtually stable in water for over 100 hours with a swelling of only 8.6%, outperforming GO and MXene membranes (Supplementary Note 2). Our results indicate that stacking functionalized MoS2 nanosheets into membranes forms stable nanochannels with finely tunable interlayer space and long-term stability. The changes of surface wettability after MoS2 functionalization were also examined by water contact angle (WCA) measurements (Fig. 2g and Supplementary Figure 10, 11). Compared to pristine membranes, increased WCA values were obtained in the case of hydrophobic groups grafted on the MoS2, whereas hydrophilic groups caused a decrease in the WCA. The measurements of the WCA brings direct evidence of the role of the surface chemistry to change the physical and chemical behavior of the membranes.

Ionic and Water Transport in Functionalized MoS2 Membranes

We first sought to evaluate the transport of the monovalent ions: Li + , Na + and K + across the functionalized MoS2 membranes using a custom-made U-shape cell, where the two-compartments are filled with an electrolyte solution and DI water, used as permeate and feed solutions, respectively. We found that compared to water, the transport of Na + is more sensitive to the height of the 2D capillary, and shows an exponential dependence with the capillary width (Fig. 3a and Supplementary Figure 12). The inhibition of Na + transport with decreasing channel size arises from steric hindrance of the pore. The permeation rate for Na + decreased by 20 folds as the capillary width decreased from 7.6 Å to 3.6 Å compared to 3 folds for water. In aqueous solution, Na + , Cl -and SO4 2-have hydration shells with diameters of 7.16 Å, 6.64 Å and 7.58 Å, respectively [START_REF] Nightingale | Phenomenological theory of ion solvation. Effective radii of hydrated ions[END_REF] . This suggests that to enter inside a narrower channel, the ions will necessarily strip more water molecules, which requires additional energy. It is worth noting that the evolution of the permeation rates of Na + with the capillary width, i.e. the slopes in the middle and right panels of Figure 3a, is independent from the nature of the counter ions (Cl -or SO4 2-). While the faster permeance of Na + (about 3 times) in the case of NaCl compared to Na2SO4 is attributed to the larger value of hydration energy for SO4 2-: -1330 kJ mol -1 compared to -420 kJ mol -1 and -350 kJ mol -1 for Na + and Cl -, respectively [START_REF] Teychené | Investigation of ions hydration using molecular modeling[END_REF] . We also found slightly higher permeance rates for Mg 2+ compared to Na + despite larger ionic radius. This is attributed to the Gibbs-Donnan effect due to the presence of remaining excess of charges on the functionalized MoS2 nanolaminates, as confirmed by our zeta potential measurements (Supplementary Table 1). Remarkably, our results also indicated a stricter dependence of the permeance with the capillary width, which is attributed to the larger hydrated radius and hydration energy of the Mg ions.

The application of hydrostatic pressure in reverse osmosis conditions is known to affect the structure of the capillaries in the nanolaminated structure [START_REF] Wei | Declining flux and narrowing nanochannels under wrinkles of compacted graphene oxide nanofiltration membranes[END_REF][START_REF] Morelos-Gomez | Effective NaCl and dye rejection of hybrid graphene oxide/graphene layered membranes[END_REF] . Conversely, by operating in FO, we were able to precisely examine the influence of nanochannel structure and surface chemistry on water permeation. We first evaluated the water permeation across the functionalized MoS2 membranes with different interlayer spaces under forward osmosis (FO) operation. Concentrated KCl (3M) and deionized (DI) water were used as draw and feed solutions, respectively. Figure 3b shows the water flux across the functionalized membranes with increasing stacking sequence from 160 layers up to 1600 layers in forward osmosis conditions. While pristine membranes were found impermeable [START_REF] Wang | Understanding the aqueous stability and filtration capability of MoS2 membranes[END_REF][START_REF] Hoenig | Controlling the Structure of MoS2 Membranes via Covalent Functionalization with Molecular Spacers[END_REF] (Supplementary Note 3), water permeated through all the functionalized MoS2 nanolaminates, demonstrating the benefit of functionalization for the diffusion of water. The water flux quickly increased with the decrease of stacking layers due to the shortened pathway for water molecules. We found the highest flux of ~12 L h -1 m -2 (LHM) in the case of Aryl-functionalized membrane with a stacking of 160 layers. This flux is higher than the typical flux for forward osmosis, which is 5~10 LHM [START_REF] Abraham | Tunable sieving of ions using graphene oxide membranes[END_REF][START_REF] Chekli | A comprehensive review of hybrid forward osmosis systems: Performance, applications and future prospects[END_REF] .

We then sought to discriminate the contribution of the capillary width and the surface chemistry of the nanosheets on the water flux. For a fixed number of MoS2 nanosheets in the nanolaminate, the water flux showed a nearly linear relationship with the capillary width with a ≈3-fold increase when the capillary width increased from 3.6 Å to 7.6 Å. This confirms a size-dependent mass transfer process (Supplementary Figure 14,15 and Supplementary Note 4). We extracted the different slopes values for the functionalized membranes when increasing the number of MoS2 nanosheets from 160 to 1600. The evolution of the water flux in LMH Å -1 with the number of MoS2 nanosheets revealed an exponential decrease tendency (Fig. 3b,inset). According to the curve fitting, our results predict a flux larger than 100 LMH from a nanolaminate membrane with a capillary width of 7 Å and a stacking sequence of 8 layers of MoS2, corresponding to a thickness of ≈ 10 nm. To better understand the mechanism of water permeation through the size-varied nanochannel, we estimated the activation energy of water permeation [START_REF] Wang | PBI) nanofiltration hollow fiber membranes applied in forward osmosis process[END_REF] and found a linear decrease with capillary width (Fig. 3c,d and Supplementary Note 5). Hydrophobic ethyl-functionalized membrane with the narrowest channel demonstrated the highest transmembrane energy barriers for water permeation in line with the fact that the membrane exhibits the lowest water flux. With the increase of capillary width, the energy barriers rapidly and continuously decrease, leading to improved water flux. Remarkably, we note that the activation energy of water permeation is less affected by the nature of the functional groups (Supplementary Figure 16). The results clearly point out the role of the sub-nanometer interlayer distance for controlling the energy barriers and the water permeance under FO filtration.

It is also worth noting that the Aryl-functionalized membranes showed the highest flux for all thicknesses, while it had moderate energy barriers suggesting that the energy barrier is not the only parameter governing water diffusion in nanolaminates.

To elucidate the origin of the apparent high-water flux in Aryl-functionalized MoS2 membranes, we examined the structure of the nanolaminates by comparing the fullheight at half-maximum (FWHM) of (002) XRD peaks. The FHWM of the diffraction peaks is known to be a good indicator of the degree of disorder of a crystal and has been used by extension to qualitatively assess the disorder in 2D nanolaminates [START_REF] Ries | Enhanced sieving from exfoliated MoS2 membranes via covalent functionalization[END_REF][START_REF] Lu | Relating selectivity and separation performance of lamellar twodimensional molybdenum disulfide (MoS2) membranes to nanosheet stacking behavior[END_REF] . The FO membranes made of Aryl-functionalized MoS2 exhibit the largest FWHM at 1.74° ± 0.03°, indicating a large variation of capillary width of 1.57 Å (Supplementary Figure 17). For comparison, the variation of the capillary width of the corresponding pristine MoS2 membranes is of only 0.40 Å. The XRD analyses thus suggest a less ordered stacking compared to the other functionalized membranes. A less ordered structure is therefore likely to bring minor tortuosity, leading to a reduced effective path length for water transport, thereby facilitating the water permeation [START_REF] Lu | Relating selectivity and separation performance of lamellar twodimensional molybdenum disulfide (MoS2) membranes to nanosheet stacking behavior[END_REF] . To further gauge the influence of the stacking disorder on the water diffusion in the nanolaminate, we plotted the water permeance as a function of capillary width and width variation for nanolaminates with 400 and 1600 nanosheets (Figs. 3e,f). We observed that for the thinnest membranes corresponding to a stacking number of 400, the water permeance is controlled by the capillary width, while for thicker laminates the permeance is mainly controlled by the variation in the capillary width. The reduction of the diffusion pathway caused by the decrease of membrane tortuosity is negligible for the thinnest laminates. As the transport pathway increases for thicker membranes, the effect of the tortuosity on the diffusion becomes significant. In light of these results, we identify different behaviors of the nanolaminate FO membranes as the number of two dimensional capillaries increases, which is characterized by a transition from a sizecontrolled diffusion for the thinnest membranes to disorder-controlled diffusion of the water molecules. Our investigations suggest that the control of both the interlayer space and the stacking disorder in Aryl-functionalized MoS2 nanolaminates is responsible for the superior water flux in FO, making this membrane a relevant candidate for the realization of practical FO filtration.

Mechanical properties of MoS2 membranes from MD simulations

The stacking order of the nanolaminate membranes is directly related to the mechanical properties of the layers. Therefore, to get further insight on the atomic origin of the superior water flux of Aryl-functionalized membranes observed above, we performed classical MD simulations of the interaction between functionalized layers (details in the Methods section). Mechanical properties including surface energy and interlayer stiffness can be evaluated by fitting the potential energy of two functionalized layers as a function of interlayer distance, as depicted in Figure 4a. Here we use a simple 3parameters Morse function to fit the potential energy. Our calculations predict surface energies (De) of 24, 9 and 6 meV/ Å 2 , and interlayer stiffnesses (ke) of 113.7, 11.1 and 5.6 eV/ Å 2 for pristine, Ben-and Aryl-functionalized MoS2, respectively (see Fig. 4b andc). We obtained capillary width (δ=d0-6.15, Fig. 4d) of 0.3, 7.4 and 7.8 Å for pristine, Ben-and Aryl-functionalized MoS2, respectively, in good agreements with those measured from experiment (0.05, 6.9 and 7.1 Å, Fig. 2d). As expected, functionalization leads to larger interlayer spacing, smaller surface energy as well as smaller interlayer stiffness. Interestingly, we found that for Aryl-functionalized MoS2, both the surface energy and the interlayer stiffness are about 50 % smaller than for Ben-MoS2. The small surface energy and the softness of Aryl-MoS2 layers can be appreciated by the small depth and the flat bottom of the potential well, respectively (Fig. 4a). The combination of small surface energy and interlayer stiffness leads to an increase of stacking defects, which contributes to the broadening of the diffraction peaks measured experimentally. We also performed simulations with a lower extent of functional groups and found that the mechanical properties were only slightly affected, while the capillary width decreased significantly (Supplementary Table 2). Our molecular analysis suggests a direct connection between surface chemistry of the nanosheets and the macroscopic nanofluidic properties of the membranes and it provides a framework for future screening of efficient functional groups for water filtration and desalination.

Forward Osmosis Nanofiltration

To demonstrate the potential of the functionalized MoS2 membranes, the molecular sieving performance for micropollutants and salt were further evaluated. Four typical micropollutants, a preservative (benzoic acid, BA), a psychoactive drug (caffeine), a common drug (diclofenac sodium, DF) and an organic dye (phthalocyanine), with varied Stoke diameter from ~5.64 Å up to ~14 Å (Supplementary Table 3), were selected and the rejection was measured using high performance liquid chromatography.

Rejections of over 90% for all the micropollutants in functionalized membranes were measured, suggesting excellent separation performance in FO. Particularly, the C2functionalized membrane with the narrowest channel presented the perfect repulsion of ≈ 100% for the four selected micropollutants. Figure 5a shows that the membrane rejection improves with the increase of the molecular weight of the micropollutants in line with the size-limited diffusion as the primary sieving mechanism (Supplementary Note 6). When comparing the evolution of the rejection of the micropollutant with the capillary width, we observe a sharp molecular cut-off of the FO MoS2 membranes (Fig. 5b,c). This behavior highlights the importance of controlling the interlayer space and further evidences the absence of pinholes. To benchmark the performance of the functionalized MoS2 membranes, we also estimated the separation performance of the graphene oxide (GO) nanolaminates and a commercial polymeric FO membrane (Cellulose Triacetate, CTA) under the same conditions. As shown in Figure 5d, the CTA membrane exhibited both a reduced flux and rejection for the smaller contaminants. We determined a rejection of less than 80% for benzoic acid (BA) in agreement with previous reports from the literature [START_REF] Alturki | Performance of a novel osmotic membrane bioreactor (OMBR) system: flux stability and removal of trace organics[END_REF] . Both the rejection and the water permeance rapidly increase when filtering large molecules. This behavior is surprisingly the opposite to those of both GO and MoS2 FO membranes, which showed a decreased rejection and an increased flux for the smaller micropollutants. The decreased performance for sieving out the smallest molecules hints for a rapid fouling due to the blocking of the one-dimensional nanopores of the polymer membranes.

Conversely, nanolaminates exhibit a fouling for the largest molecules due to the deposition of the rejected molecules on the surface of the membranes, while the 2D capillaries are not obstructed (Supplementary Figure 18). The surface fouling of the nanolaminate can however be mitigated by operating under tangential crossflow filtration (as described later in the article). GO membranes also exhibited a poor rejection of 65% for the smallest molecules of BA which is attributed to the large capillary width due to swelling. Overall, owing to the tailored and stable interlayer space, the Aryl-functionalized MoS2 membranes exhibited superior performance both in rejection and flux than GO and commercial polymer membranes.

To properly estimate the molecular weight cutoff (MWCO) of the MoS2 membranes, we evaluated the rejection performance of the nanolaminates for small neutral compounds: PEG 200 and D-Glucose. As show in Figure 6a-c, all the functionalized MoS2 membranes exhibited high separation performance with rejection greater than 92%, demonstrating excellent cutoff for PEGs and sugar molecules (Supplementary Note 7).

We then examined the performance of the Aryl-functionalized MoS2 membranes towards desalination under realistic conditions. FO nanolaminated membranes were prepared by vacuum filtration with sizes up to 45 cm 2 and a stacking of 400 layers, corresponding to a thickness of ≈ 550 nm. We studied the pure water permeance of the planar 45 cm 2 Aryl-functionalized membranes by employing a 2M sucrose as draw solution. A stable water flux of 1.3 LMH was achieved under constant flow conditions at room temperature for a period of 7 days (Supplementary Figure 19). The desalination performance of the functionalized MoS2 membranes was further evaluated on a pilotscale tangential flow filtration cell under the forward osmosis operation using 0.1 M NaCl as the feed solution (Fig. 6d). A water flux greater than 1.6 LMH was achieved and was largely stable over a 7-day period, whereas salt rejection was maintained at greater than ≈ 94.2% and peaked at 96%. These robust desalination properties are attributed to the control of the interlayer distance from the grafted functional groups and the low interlayer stiffness. Remarkably, the interlayer space after 7 days of continuous operation was almost identical to that of the as-prepared membranes (Supplementary Figure 20). We note that the performance is slightly lower than those obtained using smaller membranes, which demonstrated a water flux of 4.37 LMH with a NaCl rejection of 93.9% suggesting that further improvements can be achieved. We also evaluated the performance of GO membranes and obtained a poor salt rejection of less than 50 % due to the large capillary width of 12.8 Å in line with the literature (Supplementary Figure 8) [START_REF] Abraham | Tunable sieving of ions using graphene oxide membranes[END_REF] . Importantly, the GO membrane could only run for one day and then rapidly delaminated upon the application of the tangential flow which highlights their intrinsic instability in water [START_REF] Andreeva | Two-dimensional adaptive membranes with programmable water and ionic channels[END_REF] . Besides, commercial CTA polymer membranes exhibited a rejection of around 89.1% with an average flux of 1.25 LMH when tested under the same conditions-consistent with previous reports [START_REF] Al-Aibi | Evaluation of draw solution effectiveness in a forward osmosis process[END_REF][START_REF] Li | Cellulose triacetate forward osmosis membranes: preparation and characterization[END_REF] . Compared with other 2D laminar membranes, the functionalized MoS2 membranes exhibit a higher water flux and superior salt rejection, exceeding the latest upper bound of stateof-the-art 2D laminar membranes (Fig. 6e). Importantly the desalination performance is not significantly affected by the upscaling process and the Aryl-functionalized MoS2 membranes clearly outperform the best desalination performance from the literature under forward osmosis operation (Fig. 6f). We finally evaluated the specific energy consumption (SEC) of our FO system (Supplementary Note 8). Under a flow rate of 3.75 mL min -1 (1.65 cm s -1 ), the FO system recovered 148 mL of water in 20 h, corresponding to a SEC of 0.004 kWh m -3 . This value is lower than previous reports for flat-sheet CTA membranes, which exhibit SECs of 0.008 kWh m -3 and 0.02 KWh m -3 , respectively [START_REF] Zou | Enhancing wastewater reuse by forward osmosis with self-diluted commercial fertilizers as draw solutes[END_REF][START_REF] Lambrechts | Performance and energy consumption evaluation of a fertiliser drawn forward osmosis (FDFO) system for water recovery from brackish water[END_REF] . Although additional processing of the draw solution is requested to obtain potable water, the present FO system shows a clear reduction of the energy footprint compared to the other water recovery approaches such as traditional RO filtration (1.5-2.5 kWh m -3 ) [START_REF] Al-Karaghouli | Energy consumption and water production cost of conventional and renewable-energy-powered desalination processes[END_REF][START_REF] Shannon | Science and technology for water purification in the coming decades[END_REF] , thermal distillation technology (16.3-27.3 kWh m -3 ) [START_REF] Al-Karaghouli | Energy consumption and water production cost of conventional and renewable-energy-powered desalination processes[END_REF] , and self-supplied FO with thermolytic ammonium bicarbonate (0.1 kWh m -3 ) [START_REF] Qin | Self-supplied ammonium bicarbonate draw solute for achieving wastewater treatment and recovery in a microbial electrolysis cell-forward osmosiscoupled system[END_REF] .

Overall this work presents a robust and scalable method to prepare stable nanolaminated membranes with tunable sieving performance and high water permeance in FO filtration. The structure of the functionalized MoS2 membranes can be precisely adjusted over a large range of interlayer spaces using alkyl and aryl groups which offers ångström-precision for the 2D nanochannels. Using this approach, we elucidated the contributions from the surface chemistry, the interlayer space and the stacking tortuosity on the behavior of FO nanolaminate membranes. Our functionalized membranes exhibit excellent water purification performance compared with the GO and commercial membranes. In particular, we identified Aryl-functionalized MoS2 membranes as promising candidates for FO application and demonstrated its scalability up to 45 cm 2 .

Methods

Preparation of single-layer MoS2 nanosheets.

The single-layer MoS2 nanosheets were obtained by exfoliating the bulk MoS2 powder using the lithium intercalation method.

Typically, 400 mg MoS2 powder and 4 mL n-butyllithium were mixed up in hexane solution and the mixture was stirred at 65°C for 48 h under argon protection. After that, the intercalated powders were collected by vacuum filtration and washed with excessive hexane to remove the unreacted reagent. Then the Li-intercalated powder was added to the water for exfoliation and the process was accelerated by the sonication. After one-hour sonication, the solution was further centrifuged two times at 10,000 g to strip the lithium cations from the nanosheets. In the end, the supernatant containing the singlelayer MoS2 nanosheets was collected after centrifugation twice at 1,400 g for 30 min.

Covalent functionalization of single-layer MoS2 nanosheets. The single-layer MoS2

nanosheets were modified in solution by reacting with organohalide reagents and diazonium. Six different molecules were selected: iodoethane, 1-iodopropane, ethyl iodoacetate, (2-iodoethyl) benzene, 3-iodo-1-propanol, and 4-bromobenzenediazonium.

First, dimethyl sulfoxide (DMSO) was added to the MoS2 solution to achieve a volume ratio of 3:2. Then the organohalide reagents or diazonium were directly added to the mixture to react for 48h. The excessive organohalide reagents with ten times fold in molar ratio than MoS2 was added. While the charged diazonium with the same molar amount as MoS2 was separately added several times to avoid the electrostatic quench and aggregation. Finally, the functionalized MoS2 solutions were obtained.

Preparation of functionalized MoS2 membranes. Vacuum filtration was employed to

prepare the laminated membranes using diluted functionalized MoS2 solution. Briefly, a certain amount of MoS2 solution was filtered on Nylon filter paper with a pore size of 220 nm. To improve the uniformity of the nanolaminate, polyethersulfone (PES, 50 nm pore size) was used to prepare membranes larger than 10 cm 2 . After filtration, the membranes were carefully washed 3 times to remove the unreacted reagents. The prepared membranes were dried at room temperature over 24 h.

Water permeation through nanolaminated MoS2 membranes.

The pure water flux of nanolaminated MoS2 membranes was measured using the forward osmosis devices, which consist of two compartments filled with equal volumes (40 mL) of salt solution (3 M KCl) and pure water. The MoS2 membranes were placed in the middle to separate those two compartments. The volume of salt solution as a draw solution would increase due to the passed water. Based on the increased volume (ΔV) with permeation time (Δt), the water flux could be calculated following the equation:

𝐽 𝑤 = 𝛥𝑉 𝐴𝛥𝑡 (2)
Where the A is the effective membrane area (1.13 cm 2 ).

Ionic permeation through the nanolaminated MoS2 membranes. The Na + /Mg 2+ permeation through the 400-layer stacked membranes was measured using two Teflonmade compartments, which were filled with the same volume of DI water and 1 M NaCl/MgCl2 or 0.5 M Na2SO4 solution, respectively. Magnetic stirring was used all the time to eliminate possible concentration gradients around the membranes. The conductivity of the feed side was recorded as a function of permeation time. According to the measured conductivity, the salt concentration of feed side could be calculated using the following equation:

∁= 𝜅 𝛬 𝑚 (3)
where C denotes the salt concentration, κ presents the measured conductivity and Λm is the molar conductivity (NaCl: 126.4 S cm 2 mol -1 , MgCl2: 258.6 S cm 2 mol -1 , Na2SO4:

259.8 S cm 2 mol -1 ) [START_REF] Horvath | Handbook of aqueous electrolyte solutions[END_REF] . The salt permeation rate (J) was calculated by:

𝐽 = 𝑉𝐶 𝐴𝑡 ( 4
)
where V is the solution volume in the feed side (200 mL), C is the calculated concentration from equation (3), A is the surface area of the membrane and t is the permeation time.

Water purification and rejection evaluations. The water purification performances of the membranes were measured using the same apparatus as for the water permeation measurements. However, the draw side and feed side were filled with 2 M sucrose solution and 50 mM micropollutant solution (except for the dye solution, which was 3.3 mM), respectively. The two sides were constantly stirred to avoid the concentration polarization. The draw side solution was collected after 20 h and the concentration of micropollutant in sucrose solution was quantitatively analyzed by High-Performance Liquid Chromatography-Ultraviolet (HPLC-UV). The flux was calculated by equation

(2) and the rejection was evaluated by the following equation:

𝑅 (%) = 𝐶 𝐹 -𝐶 𝑃 𝐶 𝐹 × 100 (5)
Where CF and CP denote the concentration of the feed and permeate solutions, respectively. Unlike the reverse osmosis experiments, the permeated solution in forward osmosis system was diluted by the draw solution. The real concentration of the permeated solution was calculated using the following equation to eliminate the dilution effects:

𝐶 𝑝 = 𝐶 𝐷 × 𝑉 𝐷 𝑉 𝑃 (6)
Where CD and VD are the measured micropollutant concentration in the draw side and the volume of the draw solution. The VP presents the volume of permeated solution, which is the increased volume in the draw side.

Water desalination in tangential cross-flow filtration cell. We used the tangential cross-flow filtration cell to estimate the water desalination performance of membranes in long-term operation. The membranes with large surfaces prepared on the polyethersulfone (PES) substrates were installed in the middle of the pilot-scale forward filtration unit to separate the flowing draw and feed solution. The draw and feed tank were filled with 2 M sucrose solution and 0.58 wt.% NaCl solution, respectively. A peristaltic pump was utilized to provide a constant flow rate of 3.75 mL min -1 . Two balances were used to monitor the mass changes of draw and feed tank and the recorded data was further used to calculate the flux. The solutions in the tank were refreshed every 20 h. At the same time, the sucrose solution was collected and the salt concentration was analyzed by Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES). According to the increased mass and salt concentration in draw side, the salt rejection could be calculated using equations ( 5) and (6).

Molecular dynamics simulations parameter. Molecular dynamics simulations have been performed with the LAMMPS package [START_REF] Plimpton | Fast parallel algorithms for short-range molecular dynamics[END_REF] and the OPLS interatomic potential [START_REF] Jorgensen | Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids[END_REF] .

To describe Mo-S interactions, we use the potential proposed by Blankschtein [START_REF] Sresht | Quantitative modeling of MoS2-solvent interfaces: predicting contact angles and exfoliation performance using molecular dynamics[END_REF] . We developed OPLS parameters (harmonic bonds, harmonic angles and dihedrals) for S-C interactions between fixed MoS2 and various organic functional groups. We used a Monte Carlo procedure (similar to that presented in Ref. Correspondence and requests for materials should be addressed to D.V.

(damien.voiry@umontpellier.fr). after immersing the membranes in water for a long time (Supplementary Figure 7). e-f,

The plotted water permeance of membranes with different stacking numbers (400 layers in e and 1600 layers in f) as a function of capillary width and width variation (Supplementary Figure 17). The permeation rates were normalized by the permeance of Aryl-functionalized MoS2 membranes. All vertical error bars correspond to SD and based on at least five independent measurements.

  C nuclear magnetic resonance ( 13 C NMR) spectroscopies as well as thermogravimetric analysis (TGA) (Supplementary Note 1). Figures 2a, b show the chemical shifts of functionalized MoS2 nanosheets compared with those of the pristine organohalide or diazonium salt reagents. The 13 C signals of the aliphatic carbon (α-C) at -3.7 ppm 28 and 115.3 ppm 29 for ethyl iodoacetate and 4-bromobenzenediazonium respectively disappear after functionalization and are shifted around 46 ppm and 126 ppm. The significant perturbation of the α-C chemical shifts suggests a new chemical environment, which is attributed to the formation of S-C bonds.

  51) to optimize OPLS parameters against a training set of density functional theory calculations, as developed in the Supplementary file. Molecular models consist of 2 layers of T' MoS2 replicated 8 and 14 times in the x and y directions, starting from the rectangular unit cell.Functionalization was achieved by randomly grafting functional groups to S atoms until the fraction of 20% groups/S was reached. In order to obtain good statistics on the data points corresponding to the potential energy surface shown in Figure4, we scanned 4 times successively the interlayer distance (back and forth). One potential energy surface corresponds therefore to 8 times (4 times back and forth) 300 interlayer distances. At each interlayer distance, the functional groups were randomized by performing 10 ps of NVT simulation at 600 K followed by an energy minimization. We used high temperature MD to provide efficient randomization of the functional groups at each interlayer distances. Although our force field could be used with a larger timestep, we chose a timestep of 0.5 fs in order to properly integrate the equations of motion in the rough conditions of the simulations. online version of the paper.

Figure 1 |

 1 Figure 1 | Characterizations of the functionalized MoS2 nanosheets. a, High-angle annular dark-field (HAADF) STEM image of 4-bromobenzenediazonium salt functionalized MoS2 nanosheets and the corresponding EDX mapping for elements Br (in red) and S (in blue). The elemental mapping of Br in the functionalized MoS2 nanosheets shows that the aryl groups are homogeneously grafted on the nanosheets surface. b, HRTEM images of MoS2 nanosheets functionalized with aryl groups. The vertically aligned nanosheets form an interlayer spacing of ~13.2 Å, in line with the XRD measurements. Meanwhile, the crystalline nature of the basal plane of Aryl-MoS2 nanosheets is confirmed by the diffraction pattern (inset). c, The SEM cross-section view of laminated membrane prepared by vacuum filtration of Aryl-MoS2 nanosheets suspension. The highly aligned nanosheets in the vertical direction form 2D capillaries.

Figure 2 |

 2 Figure 2 | Characterization of the functionalized MoS2 membranes. a and b, 13 C CP MAS NMR spectra of the Ace-functionalized (a, bottom) and Aryl-functionalized (b, bottom) MoS2 nanosheets. 13 C NMR spectra of pure chemical reagents namely ethyl iodoacetate (a, top, solution) and 4-bromobenzenediazonium (b, top, solid-state) were also recorded for comparison. The color dots are used to point out the positions of carbon atoms in different chemical environments. c, Schematic illustration of the separation process of stacked functionalized MoS2 membranes with varied capillary width for water purification and desalination. The values marked in the nanochannels represent the effective layer space in aqueous solution through which water molecules can shuttle. Atom color codes: Mo, pink; S, yellow; C, cyan; H, white; O, red; Br, magenta; Na + , blue; Cl -, green; Micropollutant, ice-blue; water, transparent gray. d, X-

Figure 3 |

 3 Figure 3 | Water permeation and ionic transport. a, The Na + /Mg 2+ permeation rates and water flux measured by using 400-layer stacked membranes at room temperature. 1 M NaCl/MgCl2 or 0.5 M Na2SO4 were employed to provide the high ionic strengths (1 M Na + /Mg 2+ ) for diffusion. The Na + /Mg 2+ permeation rate depends exponentially on the capillary width while the water flux varies linearly. Error bars are omitted for clarity. The dotted lines are best fits. b, Water flux of functionalized MoS2 membranes with different stacking layers measured at room temperature under forward osmosis, where 3M KCl and DI water were used as the draw and feed solution, respectively. Inset: the water permeance as a function of membrane thickness. The red curve is the best fit. c, Temperature dependence of water permeation of 400-layer stacked membranes. Solid lines are best fits to Arrhenius activation energies. d, Activation energy of water permeation for the functionalized MoS2 membranes as a function of capillary width. The activation energy varied linearly with capillary width. The dotted line is the best fit. Horizontal error bars represent the average half-height of the XRD peaks measured

Figure 4 |

 4 Figure 4 | Mechanical properties of functionalized MoS2 nanosheets. a, Potential energy as a function of interlayer separation. To obtain reliable data and statistics, the potential energy surface was scanned 4 times back and forth, as described in the Methods section. Dots correspond to averaged data points and some error bars are displayed (one error bar every 10 averaged data points). Lines correspond to Morse fits

Figure 5 |

 5 Figure 5 | Water purification performance of the functionalized MoS2 membranes. a, Trace organic contaminants rejection measured with 400-layer stacked functionalized MoS2 membranes at 30℃ under forward osmosis, where the 2 M sucrose and 50 mM contaminants (3.3 mM for dye) were used as draw and feed solution. The rejection is plotted as a function of the molecular weight of contaminants. Vertical error bars represent SD of at least five independent measurements. The insets show the molecular structure of contaminants and the gray, white, red, blue, green and yellow balls denote C, H, O, N, Cl and S, respectively. b and c, Evolution of the rejection for the benzoic acid (b) and caffeine (c) with the capillary width of membranes. The dotted lines represent the effective hydrodynamic diameter of contaminant molecules (Stokes diameter). The rejection sharply decreases after the capillary width of membranes are larger than the effective diameter of the micropollutants, showing size-selective sieving. The solid gray lines are guides to the eyes. d, Comparison of the water purification performance from the functionalized MoS2 membranes with GO and commercial FO membrane (CTA). Each symbol represents the average flux and rejection calculated from at least five independent measurements and the error bars are omitted for clarity. The complete test data of all functionalized MoS2 membranes are shown in Supplementary Figure 18.

Figure 6 | 1 M

 61 Figure 6 | Molecular weight cut-off and water desalination performance of the functionalized MoS2 membranes. Evolution of the rejection for the PEG-238 (a), PEG-282 (b) and D-Glucose (c) with the capillary width of membranes. The rejection was measured with 400-layer stacked functionalized MoS2 membranes at 30 ℃ under forward osmosis, where the 2 M sucrose/50 mM PEG 200 and 0.92 M Na2SO4/50 mM D-Glucose were used as draw/feed solution, respectively. Error bars correspond to SD of at least five independent measurements. The dotted lines represent the effective hydrodynamic diameter of PEG and D-Glucose (Stokes diameter). And the solid gray lines are guides to the eyes. d, The desalination performance of Aryl-functionalized MoS2 membrane and the comparison with GO and commercial FO membrane. The measurements were conducted in a tangential cross-flow cell using 2 M sucrose and 0.1 M NaCl as draw and feed solution. The GO membrane could only be run for one day

Table 5 .

 5 f, Comparison of effective membrane area measured in our work with previously reported membranes.

	662

Acknowledgments

This research study was supported by the French National Agency (ANR, program 2D-MEMBA -ANR-21-CE09-0034-01). D.V., K.Q., and H. W. acknowledge funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 804320). W.W., J.Liu and J.Li acknowledge PhD scholarship from the China Scholarship Council (CSC). C.S. acknowledged funding from the French National Agency (ANR, JCJC program, MONOMEANR-20-CE08-0009). K.Q. and Y.Z. acknowledge financial support from the China Postdoctoral Science Foundation (2018M633127) and the Natural Science Foundation of Guangdong Province (2018A030310602). J.Li acknowledge financial support by the National Natural Science Foundation of China (21808134). The French Région Ile de France -SESAME program is acknowledged for financial support (700 MHz NMR spectrometer). This work was granted access to the HPC resources of IDRIS under the allocation 2021-2022-A0110913046 and 097535 made by GENCI. L.L. acknowledges funding from the Andalusian regional government (FEDER-UCA-18-106613), the European Union's Horizon 2020 research and innovation program

Data availability

The data that support the plots within this paper and other findings of this study are available from FigShare (https://doi.org/10.6084/m9.figshare.21901638.v1).

Author Contributions

Competing financial interests

The authors declare no competing financial interests.

Additional Information

Supplementary information and chemical compound information are available in the


domain: sdv sde

text:
Beth A Reinke
email: e-reinke@neiu.edu

Hugo Cayuela

Fredric J Janzen

Jean-François Lemaître

Jean-Michel Gaillard

A Michelle Lawing

Ditte John B Iverson

Marie Christiansen

Iñigo Martínez-Solano

Gregorio Sánchez-Montes

Jean- Michel Gaillard

Ditte G Christiansen

Iñigo Martínez- Solano

Jorge Gutiérrez-Rodríguez

Francis L Rose

Nicola Nelson

Susan Keall

Alain J Crivelli

Theodoros Nazirides

Annegret Grimm-Seyfarth

Klaus Henle

Emiliano Mori

Gaëtan Guiller

Rebecca Homan

Anthony Olivier

Erin Muths

Blake R Hossack

Xavier Bonnet

David S Pilliod

Marieke Lettink

Tony Whitaker

Benedikt R Schmidt

Michael G Gardner

Marc Cheylan

Françoise Poitevin

Ana Golubović

Ljiljana Tomović

Dragan Arsovski

Richard A Griffiths

Jan W Arntzen

Jean-Pierre Baron

Jean-François Le Galliard

Thomas Tully

Luca Luiselli

Massimo Capula

Lorenzo Rugiero

Rebecca Mccaffery

Lisa A Eby

Venetia Briggs-Gonzalez

Frank Mazzotti

David Pearson

Brad A Lambert

David M Green

Nathalie Jreidini

Claudio Angelini

Graham Pyke

Jean-Marc Thirion

Pierre Joly

Jean-Paul Léna

Tony Tucker

Col Limpus

Pauline Priol

Aurélien Besnard

Pauline Bernard

Kristin Stanford

Richard King

Justin Garwood

Jaime Bosch

Franco Souza

Jaime Bertoluci

Shirley Famelli

Kurt Grossenbacher

Omar Lenzi

Kathleen Matthews

Sylvain Boitaud

Deanna H Olson

Tim S Jessop

Graeme Gillespie

Jean Clobert

Murielle Richard

Andrés Valenzuela-Sánchez

Gary M Fellers

Patrick M Kleeman

Brian J Halstead

Evan H Campbell Grant

Phillip G Byrne

Thierry Frétey

Bernard Le Garff

Pauline Levionnois

John C Maerz

Julian Pichenot

Kurtuluş Olgun

Nazan Üzüm

Aziz Avcı

Claude Miaud

Johan Elmberg

Gregory P Brown

Richard Shine

Nathan F Bendik

Lisa O'donnell

Courtney L Davis

Michael J Lannoo

Rochelle M Stiles

Robert M Cox

Aaron M Reedy

Daniel A Warner

Eric Bonnaire

Kristine Grayson

Roberto Ramos-Targarona

Eyup Baskale

David Muñoz

John Measey

F Andre De Villiers

Will Selman

Victor Ronget

Anne M Bronikowski

David A W Miller

Diverse aging rates in ectothermic tetrapods provide insights for the evolution of aging and longevity

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

Abstract:

Comparative studies of mortality in the wild are necessary to understand the evolution of aging, yet ectothermic tetrapods are under-represented in this comparative landscape despite their suitability for testing evolutionary hypotheses. We present a study of aging rates and longevity across wild tetrapod ectotherms, utilizing data from 107 populations (77 species) of reptiles and amphibians. We test hypotheses of how thermoregulatory mode, temperature, protective phenotypes, and pace of life-history contribute to aging. Controlling for phylogeny and body size, ectotherms display a higher diversity of aging rates than endotherms, and include phylogenetically-widespread evidence of negligible aging. Protective phenotypes and life-history strategies further explain macroevolutionary patterns of aging. By adding ectothermic tetrapods, our comparative analyses enhance our understanding of the evolution of aging.

One-Sentence Summary: Aging rates are highly variable among ectothermic tetrapods in the wild, ranging from negligible aging to fast aging rates, and aging rates decrease in species with protective phenotypes (e.g., armor, venom) and slow-paced life histories.

Main Text:

Comparative studies of animal aging rates in the wild are critical for assessing the potential limits of longevity and understanding ecological and evolutionary factors shaping variation in aging strategies [START_REF] Jones | Diversity of ageing across the tree of life[END_REF][START_REF] Bronikowski | Aging in the natural world: Comparative data reveal similar mortality patterns across primates[END_REF][START_REF] Healy | Animal life history is shaped by the pace of life and the distribution of age-specific mortality and reproduction[END_REF]. Demographic indicators of aging include adult longevity and whether, and at what rate, age-specific mortality accelerates with advancing adult age. Previous comparative studies have provided important insights regarding the evolution of demographic aging in the endothermic tetrapods (birds and mammals; e.g., 2-6). However, ectotherms hold most of the records for animal longevity, and comprise 26 of the 30 known records for vertebrate species with maximum longevity estimated to be over 100 years [START_REF] De Magalhães | A database of vertebrate longevity records and their relation to other life-history traits[END_REF][START_REF] Berkel | Analysis of longevity in Chordata identifies species with exceptional longevity among taxa and points to the evolution of longer lifespans[END_REF][START_REF] Stark | Cold and isolated ectotherms: Drivers of reptilian longevity[END_REF][START_REF] Stark | Cold and dark captivity: Drivers of amphibian longevity[END_REF] (tetrapod examples include Galapagos tortoises, eastern box turtles, European pond turtles, and Proteus salamanders). Additionally, some ectothermic tetrapods may exhibit low or even negligible (sensu 12) mortality and reproductive aging [START_REF] Jones | Diversity of ageing across the tree of life[END_REF][START_REF] Congdon | Testing hypotheses of aging in long-lived painted turtles (Chrysemys picta)[END_REF][START_REF] Congdon | Hypotheses of aging in a long-lived vertebrate, Blanding's turtle (Emydoidea blandingii)[END_REF][START_REF] Cayuela | Slow life-history strategies are associated with negligible actuarial senescence in western Palaearctic salamanders[END_REF][START_REF] Reinke | Joint estimation of growth and survival from mark-recapture data to improve estimates of senescence in wild populations[END_REF][START_REF] Warner | Decades of field data reveal that turtles senesce in the wild[END_REF][START_REF] Sparkman | An empirical test of evolutionary theories for reproductive senescence and reproductive effort in the garter snake Thamnophis elegans[END_REF]. Understanding whether, and how, natural selection has shaped mortality trajectories and longevity requires phylogenetically-controlled tests to determine whether these species-specific results are anomalies that evolved in specific lineages of ectotherms, or if they are common and repeated evolutionary outcomes. Recent advances in contrasting endotherm and ectotherm longevity have contributed to a phylogenetic perspective on lifespan [START_REF] Stark | Cold and isolated ectotherms: Drivers of reptilian longevity[END_REF][START_REF] Stark | Cold and dark captivity: Drivers of amphibian longevity[END_REF], but often use maximum longevity as their metric, which is not based on the age-specific mortality trajectory and is strongly influenced by sample size, so can lead to inaccurate conclusions [START_REF] Ronget | Assessing ageing patterns for comparative analyses of mortality curves: Going beyond the use of maximum longevity[END_REF][START_REF] Moorad | A comparative assessment of univariate longevity measures using zoological animal records[END_REF]. Additionally, the lack of comparative analyses of aging rates in ectothermic tetrapods is a major gap in our knowledge [START_REF] Hoekstra | The untapped potential of reptile biodiversity for understanding how and why animals age[END_REF]. A comprehensive analysis of aging across ectothermic tetrapods requires decades of field-based population-level research, international collaborations, and powerful quantitative tools. Integrating these efforts across studies and taxa allows for using data from ectotherms to test evolutionary hypotheses of aging [START_REF] Hoekstra | The untapped potential of reptile biodiversity for understanding how and why animals age[END_REF], and for a phylogenetic understanding of the evolution of aging across tetrapods.

The evolutionary genetics of aging result from age-specific mutation-selection balance trajectories where mutations have age-specific effects that may be strictly deleterious in later adult stages or ages, and/or beneficial earlier (i.e., antagonistically pleiotropic, 22). Hypotheses for how natural selection and the environment interact to shape this balance were first formulated by Medawar [START_REF] Medawar | An unsolved problem of biology[END_REF], and further developed by Hamilton (24) and others [START_REF] Bronikowski | Testing evolutionary theories of aging in wild populations[END_REF][START_REF] Williams | The shaping of senescence in the wild[END_REF][START_REF] Ricklefs | Evolutionary Theories of Aging : Confirmation of a Fundamental Prediction , with Implications for the Genetic Basis and Evolution of Life Span[END_REF]. In ectotherms, body temperature varies with the environment and, because metabolism responds to temperature, ectothermic metabolism and cellular processes downregulate in cold temperatures, allowing for extended periods of brumation and aestivation. In addition, after controlling for body size, ectotherms have lower resting metabolic rates than endotherms [START_REF] Gardner | The relationship between genome size and metabolic rate in extant vertebrates[END_REF]. Accordingly, the Thermoregulatory Mode Hypothesis predicts that ectothermic lineages have evolved lower aging rates and greater longevities than their similarly-sized endothermic counterparts [START_REF] Flouris | Links between thermoregulation and aging in endotherms and ectotherms[END_REF][START_REF] Stark | No evidence for the 'rate-of-living' theory across the tetrapod tree of life[END_REF].

Layered on top of metabolic mode, environmental temperature itself is expected to be a strong driver of mortality in ectotherms, impacting both the evolution and the plasticity of aging through metabolic mechanisms [START_REF] Stark | Cold and isolated ectotherms: Drivers of reptilian longevity[END_REF][START_REF] Munch | Latitudinal variation in lifespan within species is explained by the metabolic theory of ecology[END_REF][START_REF] Cayuela | Thermal conditions predict intraspecific variation in senescence rate in frogs and toads[END_REF], but see 33). Within many endothermic species, individuals with lower body temperatures have been found to live longer and age slower than those with higher body temperatures [START_REF] Flouris | Links between thermoregulation and aging in endotherms and ectotherms[END_REF][START_REF] Keil | Being cool: how body temperature influences ageing and longevity[END_REF], but across species, this pattern is less clear [START_REF] De Magalhães | An analysis of the relationship between metabolism, developmental schedules, and longevity using phylogenetic independent contrasts[END_REF].

Similarly, ectotherms in cooler climates may also exhibit longer lifespans compared to those in warmer climates (10, 11; Temperature Hypothesis, hereafter).

Phenotypes that alter age-specific mutation-selection trajectories would be expected to result in the evolution of altered rates of aging [START_REF] Hamilton | The moulding of senescence by natural selection[END_REF], provided genetic variation exists [START_REF] Ricklefs | Evolutionary Theories of Aging : Confirmation of a Fundamental Prediction , with Implications for the Genetic Basis and Evolution of Life Span[END_REF][START_REF] Williams | Pleiotropy , Natural Selection , and the Evolution of Senescence[END_REF].

For example, species with phenotypes that reduce mortality risk are expected to have lower rates of aging than those without (21) (the so-called Protective Phenotypes Hypothesis). Previous work shows that ectothermic tetrapods, such as amphibians, with chemical protection mechanisms can live longer than those without, though how this trait (and any associated behavior) affects the rate of aging remains unknown [START_REF] Stark | Cold and dark captivity: Drivers of amphibian longevity[END_REF][START_REF] Blanco | Maximum longevities of chemically protected and nonprotected fishes, reptiles, and amphibians support evolutionary hypotheses of aging[END_REF][START_REF] Hossie | Species with a chemical defence, but not chemical offence, live longer[END_REF]. Tetrapod ectotherms are wellsuited for enabling direct comparisons of the rates of aging among species with and without phenotypes that have such physical or chemical protections. Within reptiles, diverse traits may confer protection from predation and/or environmental stressors, including turtle shells, crocodilian armor, and snake venom (even if such traits are exaptations sensu 39). Similarly, in amphibians, many species produce toxic or unpalatable secretions [START_REF] Daly | The chemistry of poisons in amphibian skin[END_REF]. Despite these characteristics, the Protective Phenotypes Hypothesis has not been tested across ectothermic tetrapods using robust aging metrics (but see 10, 11, 37 for analyses using maximum longevities) Aging and longevity may co-evolve through direct or indirect selection on life-history traits that are genetically correlated (3). Under antagonistic pleiotropy, genes that confer higher fitness in early life relative to late life will increase in frequency in populations that are skewed toward younger age classes [START_REF] Hamilton | The moulding of senescence by natural selection[END_REF]. Because many ectothermic tetrapods have indeterminate growth and fecundity [START_REF] Hota | Growth in Amphibians[END_REF][START_REF] Castanet | Age Estimation and Longevity in Reptiles[END_REF], life-history theory predicts that such species should have stronger selection against deleterious late-age mutations relative to species with determinate growth and fecundity [START_REF] Hoekstra | The untapped potential of reptile biodiversity for understanding how and why animals age[END_REF]. Indeed, any species in which individuals from older age classes contribute more to population growth (e.g., fecundity, behavior) relative to other species should have concomitant slower aging. Thus, the aging rate may evolve from genetic covariation among life-history traits, such as annual fecundity, age of first reproduction, and annual survival. This results in a slowfast continuum of life histories [START_REF] Stearns | The influence of size and phylogeny on patterns of covariation among lifehistory traits in the mammals[END_REF][START_REF] Read | Life history differences among the eutherian radiations[END_REF][START_REF] Gaillard | Encyclopedia of Evolutionary Biology[END_REF][START_REF] Promislow | Senescence in natural populations of mammals: A comparative study[END_REF] that should match slow vs. fast aging rates (the Slow-Fast Continuum Hypothesis). For example, fast aging, expected to be correlated with a short reproductive lifespan, should evolve in a correlated manner with fast pace of life, and vice versa [START_REF] Stearns | The influence of size and phylogeny on patterns of covariation among lifehistory traits in the mammals[END_REF][START_REF] Dammhahn | Pace-of-life syndromes: a framework for the adaptive integration of behaviour, physiology and life history[END_REF]. Therefore, the existence of a strong positive covariation among life-history traits (e.g., [START_REF] Calder | Size, function, and life history[END_REF] predicts that the aging rate should covary with age of first reproduction (negatively) and with annual fecundity (positively) such that species that mature relatively early or that allocate relatively more energy to reproduction early in life display faster aging and shorter longevities [START_REF] Gaillard | Encyclopedia of Evolutionary Biology[END_REF][START_REF] Kirkwood | The evolution of senescence in the tree of life[END_REF][START_REF] Scharf | Late bloomers and baby boomers: Ecological drivers of longevity in squamates and the tuatara[END_REF].

We applied comparative phylogenetic methods to tetrapod mark-recapture data to analyze variation within ectotherm demographic aging and longevity in the wild, to compare aging and longevity to endotherms, and to address the following four distinct but not mutuallyexclusive hypotheses: i) Thermoregulatory Mode, ii) Temperature, iii) Protective Phenotypes, and iv) Slow-Fast Continuum. We analyzed long-term capture-recapture data collected in the amphibians and non-avian reptiles. We present the first comprehensive comparative analysis of patterns of aging across these ectotherms and estimate both the rate of aging (computed as the slope of the relative rate of increasing age-specific mortality derived from the Gompertz model-b1) and longevity (computed as the number of years after the age of first reproduction until 95% of adults in a given cohort have died, as opposed to the age of the longest-lived individual). Specifically, we test: i) whether ectotherms consistently age more slowly and live longer than endotherms, ii) whether annual mean, minimum, or maximum environmental temperature experienced by a population covaries with rate of aging and longevity, iii) whether species with protective phenotypes (either physical or chemical) age slower and live longer than those without physical or chemical protections, and iv) whether the rate of aging and longevity strongly covary with other biological traits such as age at first reproduction and annual fecundity.

Aging in ectothermic tetrapods

All orders represented by the 77 reptile and amphibian species for which age-specific estimates of mortality could be estimated had at least one species with negligible aging (b1 ~ 0; S1). When corrected for body size and phylogeny (Table S2), crocodilians, tuatara, and salamanders were similarly slow in aging (crocodilians: mean b1 = 0.14 ± 0.06, tuatara: 0.005, and salamanders: 0.18 ± 0.05) in comparison to squamates (mean b1 = 0.55 ± 0. S1-S2, Data S1), again when corrected for the potential confounding effects of body size and phylogeny.

Thermoregulatory Mode Hypothesis

Controlling for phylogeny and body size, across tetrapods, aging rate and longevity did not differ between ectotherms and endotherms (Table 1, for ectotherms and 1.15 for endotherms), and had the greatest longevities (Cv=0.37 for ectotherms and 0.32 for endotherms; Fig S1). The aging patterns of ectotherms were thus more diverse, rather than slower than those reported in endotherms. Indeed, the ectotherm variance in aging rate was significantly greater than the endotherm variance (F106/118 = 5.49, p=<0.001), although the variance in longevities was not statistically different (F106/118 =1.31, p=0.16). As expected, there was a negative relationship between aging rate and longevity in both groups, with faster aging rates corresponding to shorter longevity, but the slope of the relationship was more steeply negative in ectotherms than in endotherms (Table 1, S3).

Temperature Hypothesis

Within ectotherms, the rate of aging increased with mean temperature in reptiles, but decreased with mean temperature in amphibians (Table 2, Fig S3). Models using minimum and maximum temperatures instead of mean showed the same patterns (Table S4).

Protective Phenotypes Hypothesis

We considered three categories of protection: physical (armor and shells), chemical (venom and skin toxins), and neither physical nor chemical (Fig S4). Within ectothermic tetrapods, species with physical or chemical protection aged slower than species with neither physical nor chemical protection (mean b1 ±SE; physical: 0.05 ± 0.01, chemical:0.29 ± 0.06, neither: 0.47 ± 0.07). Species with physical protection lived longer than those with no protection and those with chemical protection (mean years ± SD; physical: 36 ± 5, neither:10 ± 3, chemical:11 ± 1, Table S5, Data S1).

Slow-fast Continuum Hypothesis

We examined relationships between both the age of first reproduction and annual fecundity and rate of aging and longevity. As expected under the slow-fast continuum hypothesis, the rate of aging was negatively associated with the log age of first reproduction, and positively associated with the log annual fecundity (Table 2). However, because class (i.e., reptile or amphibian) influenced these relationships, we further investigated these associations within class. This analysis revealed a class-dependent structure of the slow-fast continuum results. A decreasing rate of aging with increasing age of first reproduction structured the life history variation in reptiles, whereas an increasing rate of aging with increasing annual fecundity structured the life history variation in amphibians (Table S6, Fig 4A -4B). In both amphibians and reptiles, longevity was positively associated with the age of first reproduction, as expected under the slow-fast continuum hypothesis (Table 2, Fig. 4C). However, longevity was not related to annual fecundity in either class (Table S6, Fig 4D). Importantly, all of these results were still true when we restricted the analyses to the best quality datasets (i.e., >25% of known-age individuals monitored and study length equal to or longer than the median longevity), demonstrating that variable data quality among populations has no detectable influence (Table S8).

Discussion

We found greater variation in aging rates and longevities across wild ectothermic tetrapods than in birds and mammals. Our study thus demonstrates that the parameter space for aging rates and longevities is much larger in ectotherms than previously thought. Turtles, crocodilians, and salamanders have remarkably low aging rates and extended longevities for their size. Most turtles have physical protection (bony shells), as well as a relatively slow pace of life, which both contribute to the negligible aging and exceptional longevity. Future work that focuses on turtles with soft shells (versus rigid, as in this study) may help disentangle causes of slow turtle aging. While turtle aging rates are low overall, they are surprisingly variable. For example, in Chrysemys picta, age at maturity, longevity, and aging rates vary significantly among populations (8, 11, 12, this study). Our analyses thus provide clear evidence that ectotherms have a remarkable diversity of aging rates and longevities and add to the growing literature on ectotherm longevity (e.g., [START_REF] Stark | Cold and isolated ectotherms: Drivers of reptilian longevity[END_REF][START_REF] Stark | Cold and dark captivity: Drivers of amphibian longevity[END_REF]. Within ectotherms, rates of aging ranged from -0.013 to 2.0, corresponding to a continuum from negligible aging to fast aging. Ectotherm longevity (measured here as the age when 95% of adults have died) ranged from 1 year to 137 years. For comparison, primate aging rates are between 0.04 -0.50 (longevity: 4 -84 years), with a human aging rate of about 0.1(longevity:100 years; 2). The overall mammalian rates of aging ranged from 0.03 to 1.2, with a single high value observed in eastern moles (Scalopus aquaticus) representing an outlier (Fig S1). Although negligible aging was not observed in the mammals included in our sample, it has been identified in naked mole-rats [START_REF] Ruby | Naked mole-rat mortality rates defy gompertzian laws by not increasing with age[END_REF]. One notable group of vertebrates missing from our comparisons is fishes, which themselves have highly variable aging rates and longevities and contain species of great interest to aging biology (e.g., rock fish, bigmouth buffalo, and short-lived poeciliids) [START_REF] Mangel | Age and longevity in fish, with consideration of the ferox trout[END_REF][START_REF] Sauer | No evidence of physiological declines with age in an extremely long-lived fish[END_REF][START_REF] Reznick | Effect of extrinsic mortality on the evolution of senescence in guppies[END_REF][START_REF] Kolora | Origins and evolution of extreme life span in Pacific Ocean rockfishes[END_REF].

In addition to expanding the domain for aging research and gaining insights into ectotherm aging, we used novel data to test four hypotheses on the evolution of aging in a comparative framework. Our test of the Thermoregulatory Mode Hypothesis revealed that, contrary to the expectation, ectotherms did not have slower rates of aging (Adjusted R 2 =0.05, p=0.26) or longer lifespans (Adjusted R 2 =0.20, p=0.64) than similar-sized endotherms.

However, thermoregulatory mode does appear to modulate the relationship between aging rate and longevity (when phylogenetically and body-mass controlled: Adjusted R 2 =0. [START_REF] Hossie | Species with a chemical defence, but not chemical offence, live longer[END_REF] 2).

Moreover, this interaction corresponded to the same directionalities when we tested for a relationship with minimum or maximum environmental temperature (Table S4). We found no association between longevity and mean, minimum, or maximum environmental temperature.

Because temperature is a proximate mediator of cellular and biochemical processes, it is also likely a driver of local adaptation among populations -and plasticity within individuals -for phenotypes related to aging and longevity (31, reviewed in 56). Temperature increases ectotherm metabolic rate (or at least the length of the active season) and putatively hastens accumulation of molecular damage via multiple processes such as free radical production, telomere attrition, secretion of cytokines from senescent cells, and DNA damage [START_REF] Burraco | Climate change and ageing in ectotherms[END_REF]. For example, in garter snakes and at least one frog species, thermal differences among populations have been hypothesized to be an agent of selection for life-history divergence, including aging [START_REF] Cayuela | Genomic signatures of thermal adaptation are associated with clinal shifts of life history in a broadly distributed frog[END_REF][START_REF] Miller | Sociality, Hierarchy, Health: Comparative Biodemography: A Collection of Papers[END_REF].

Laboratory experiments that raise ectotherms under different thermal regimes can directly test for the proximate effect of temperature on aging (e.g., 58), and are necessary to tease apart how temperature might influence the evolution of aging. Whether and how global warming will impact the evolution of aging rates remains unknown, but will become especially important to understand for making management and conservation decisions to avoid species extinctions.

Our analyses also support the Protective Phenotypes Hypothesis within ectothermic tetrapods. Species with physically protective phenotypes, such as armor, spines, or shells, aged more slowly and lived much longer for their size than those without protective phenotypes (Table S5). Though species with chemical protection have greater maximum longevities than those without [START_REF] Hossie | Species with a chemical defence, but not chemical offence, live longer[END_REF][START_REF] Blanco | Environmental-induced acquisition of nuptial plumage expression: a role of denaturation of feather carotenoproteins?[END_REF], we provide here the first evidence that metrics describing the adult mortality trajectory are linked to these protective phenotypes. This result may explain uniquely slow rates of aging in turtles, coupled with extended longevities. Salamanders also aged slowly relative to other tetrapod ectotherms. We were unable to include behaviors such as fossorial lifestyles or seasonal activity, that may function as behavioral protections by reducing predation risk, with a consequence of low mortality rates (3, though see 11 which found that microhabitat preference, including fossorial behavior, did not influence maximum longevity). Moreover, many salamanders have regenerative capabilities that could contribute to slowing aging through greater damage repair efficiency [START_REF] Cayuela | Slow life-history strategies are associated with negligible actuarial senescence in western Palaearctic salamanders[END_REF][START_REF] Mccusker | The axolotl model for regeneration and aging research: A mini-review[END_REF][START_REF] Morrison | Salamander limb regeneration involves the activation of a multipotent skeletal muscle satellite cell population[END_REF].

Lastly, we document that the slow-fast continuum of life histories is strongly involved in shaping aging. Both rates of aging and longevities were associated with other biological traits (e.g., age at first reproduction and annual fecundity) in reptiles and amphibians. Earlier age at first reproduction in reptiles was correlated with faster aging rates (Table 2, Fig 4). A similar pattern has been documented in birds and mammals, where an earlier age at first reproduction corresponded to an earlier age at the onset of senescence [START_REF] Péron | Age at the onset of senescence in birds and mammals is predicted by early-life performance[END_REF][START_REF] Lemaitre | Polyandry has no detectable mortality cost in female mammals[END_REF]. Amphibian species with S2). S7).

Fig 1 ,

 1 Fig 1, Data S1). Notably, turtles had slow rates of aging (mean b1 ± SE= 0.04 ± 0.01), with a

  14) and frogs (mean b1 ± SE = 0.41 ± 0.06; Fig 2, Data S1). Turtles and tuatara exhibited greater longevity (95% of adult lifespan) than most other ectothermic tetrapods, with mean longevities of 39 (± SE 6) and 137 years, respectively, compared to crocodilians (21 years ± 5), squamates (12 years ± 2), frogs (8 years ± 0.6), and salamanders (10 years ± 1; Table

Fig 3 ,

 3 see Fig S1 for raw values by class). Ectotherms ranged well above and below the known aging rates for endotherms (Cv= 1.40

  Fig 3C). The negative association between rate of aging and longevity varied considerably among mammals, birds, reptiles, and amphibians, when considered by taxonomic class (Fig S2; Table

  , Fig 3C). We found mixed support for the Temperature Hypothesis as it relates to rate of aging (in agreement with Stark and colleagues' work on maximum longevity; 10, 11); mean environmental temperature interacted with class such that the rate of aging increased with temperature in reptiles, but decreased with temperature in amphibians (Fig S3, Table

Fig. 1 .

 1 Fig. 1. Tetrapod ectotherms and their measures of aging. The rate of aging is the Gompertz

Fig. 2 .

 2 Fig. 2. Measures of rates of aging and longevity across ectotherms. Letters denote statistical

  Bars show +/-1 SE. Points are uncorrected values for visualization. The rate of aging here is the mortality slope derived from a Gompertz model. Longevity is the number of years from the age of first reproduction at which 95% of the individuals in a population have died. Green denotes reptiles and purple denotes amphibians.

Fig. 3 Fig 4 .

 34 Fig. 3. Comparison between 481

Acknowledgments: Please see supplemental information for study-specific acknowledgements, contact information, and funding. This manuscript is contribution #805 of the USGS Amphibian Research and Monitoring Initiative. Any use of trade, firm, and product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

Funding: National Institutes of Health Grant R01AG049416 (AMB, FJJ, DAWM)

Data and materials availability: Data and code used for these analyses are available in Dryad (#TBD). Individual mark-recapture datasets can be obtained by contacting specific dataset owners (see Data S1).

higher annual fecundities, and therefore greater annual reproductive allocation, had faster rates of aging, which has also been found in birds and mammals, and supports Hamilton's original prediction [START_REF] Hamilton | The moulding of senescence by natural selection[END_REF]. Earlier age of first reproduction was also associated with shorter longevity in both amphibians and reptiles (Fig 4). Heralded as a key component of the life-history portfolio [START_REF] Ricklefs | Life-history connections to rates of aging in terrestrial vertebrates[END_REF][START_REF] Charnov | Reproductive constraints and the evolution of life histories with indeterminate growth[END_REF], this positive relationship between age at first reproduction and adult longevity is thus robust across tetrapod ectotherms as well. These results are congruent with patterns detected in endothermic vertebrates (4) and fit into an existing evolutionary framework of genetic correlations underlying relationships among life-history traits, including aging and longevity.

Further work on the quantitative genetic and genomic bases of aging and longevity are necessary to test broadly whether the phenotypic associations are underlain by genetic correlations.

The evolution of aging rates and longevity has seemingly multiple determinants from the genetic architecture of life-history traits to morphological adaptations, yielding complex aging patterns across free-ranging tetrapods [START_REF] Jones | Diversity of ageing across the tree of life[END_REF]. Long-term studies of species from wild populations are necessary for understanding such complexity in the natural context in which aging evolved [START_REF] Reinke | What Have Long-Term Field Studies Taught Us About Population Dynamics?[END_REF], and enable the use of more accurate aging metrics. Our compilation of long-term field studies clarifies mechanisms underlying the evolution of aging rate in tetrapod vertebrates, highlighting links among protective phenotypes, life-history tactics, and aging variation in the wild.

Author

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S7

Tables S1 to S8 References (67-89) Data S1