Thierry Brotin

Patrick Berthault

Delphine Pitrat

Jean-Christophe Mulatier

Selective Capture of Thallium and Cesium by a Cryptophane Soluble at Neutral pH

We report in this article the synthesis of an asymmetrical cryptophane derivative (possessing only C3-symmetry) bearing three phenol groups and three other carboxylic acid functions, each of these groups on the aromatic rings. Thanks to isothermal titration calorimetry experiments, we show that this compound binds large monovalent cations, such as Cs + and Tl + with a binding constant significantly lower than its congeners bearing a larger number of phenol groups grafted on the benzene rings. However, higher selectivity for Cs + and Tl + was observed with this compound since it does not show any affinity for other alkali cations. More importantly, due to the greater solubility of this derivative in pure water, we show for the first time that effective thallium(I) complexation O O O HO HO OH O O O O O O COOH HOOC HOOC Tl + O O O O O O O O O O HOOC COOH COOH HOOC COOH COOH COOH HOOC HOOC 1 2 3 high affinity for Tl + no affinity for Tl + ?

takes place at neutral pH. This result demonstrates that cryptophane derivatives decorated with a higher number of phenol groups are promising host molecules for removing traces of thallium(I) from aqueous phases at neutral pH or above.

INTRODUCTION

Thallium is a heavy metal present in low concentration in the earth's crust and it can be found in a large variety of sulphur-containing minerals. [1][START_REF] Ahrens | The Abundance of Thallium in the Earth's Crust[END_REF][START_REF] Taylor | Abundance of the Chemical Elements in the Continental Crust: A new Table[END_REF] In this form this element does not constitute a particular threat for humans and eco-systems in general. However, when released into the environment (mainly as Tl(I)) as a result of human activities, this element poses a major threat to humans and all ecosystems. Indeed, this element is considered to be very toxic to human health, even at low concentrations. [START_REF] Zitko | Toxicity and Pollution Potential of Thallium[END_REF][5][START_REF] Maluszynski | Thallium in the Environment[END_REF] Its effects on humans and rodents are well documented: an acute exposure is usually fatal and a moderate thallium exposure can induce severe disorders. [START_REF] Zasukhina | Mutagenic Effect of Thallium and Mercury Salts on Rodent Cells with Different Repair Activities[END_REF][START_REF] Peter | Thallium : A Review of Public Health and Environmental Concerns[END_REF] Surprisingly, despite its high toxicity, this element has not received much attention compared to other heavy metals such as lead, mercury and cadmium.

Concentration of thallium in air, groundwater and soils has considerably increased during the 20 th century as a consequence of the human activities. Thallium pollution originates mainly from various types of human activities such as coal combustion, mineral extraction and cement industry. [9][START_REF] Saha | Thallium Toxicity : A growing concern[END_REF][START_REF] Lopez Anton | Thallium in Coal: Analysis and Environmental implications[END_REF][START_REF] Chen | Environmental Exposure and Flux of Thallium by Industrial Activities Utilizing Thallium-Bearing Pyrite[END_REF][START_REF] Karbowska | Presence of Thallium in the Environment : Sources of Contaminations, Distribution and Monitoring Methods[END_REF] All these activities have contributed to the dispersion of thallium in ecosystems, leading to air, groundwater and soil pollution. In addition, thallium has also been widely used as a rodenticide, which has also contributed to the release of thallium into the wild. [START_REF] Lisella | Toxicology of Rodenticides and their Relation to Human Health[END_REF][START_REF] Gratz | A Critical Review of Currently Used Single-Dose Rodenticides[END_REF][START_REF] Vyas | Rodenticide Incidents of Exposure and Adverse Effects on Non-Raptor Birds[END_REF] Countries such as the United States of America or China that rely heavily on coal industries as a source of energy are directly affected by thallium pollution, but many others are facing thallium pollution from mining activities, for example. [START_REF] Liu | Thallium Pollution in China and Removal Technologies for Waters: A review[END_REF][START_REF] Wang | Temporal Sedimentary Record of Thallium Pollution in an Urban Lake : An Emerging Thallium Pollution Source from Copper Metallurgy[END_REF][START_REF] Lin | Thallium Speciation in the Great lakes[END_REF][START_REF] Ghezzi | Groundwater and Potentially Toxic Elements in a Dismissed Mining Area : Thallium Contamination of Drinking Spring Water in the Apuan Alps (Tuscany, Italy)[END_REF][START_REF] Cheam | Thallium Contamination of Water in Canada[END_REF][START_REF] Gomez-Gonzalez | Thallium Occurrence and Partitioning in Soils and Sediments Affected by Mining Activities in Madrid Province (Spain)[END_REF] Different solutions have been proposed to extract Tl(I) from soil and groundwater. [START_REF] Twidwell | Potential Technologies for Removing Thallium from Mine and Process Wasterwater : An Annotation of the Literature[END_REF][START_REF] Memon | A Green and Economical Sorbent for Thallium Removal[END_REF][START_REF] Peter | Removal of Thallium from Aqueous Solutions by Modified Aspergillus Niger Biomass[END_REF][START_REF] Li | Efficient Removal of Thallium(I) from Wastewater Using Flower-Like Manganese Dioxide Coated magnetic Pyrite Cinder[END_REF][START_REF] Li | Removal and Recovery of Thallium from Aqueous Solutions via a Magnetitemediated Reversible Adsorption-Desorption Process[END_REF][START_REF] Li | Oxidation and Removal of Thallium and Organics from Wastewater Using a Zero-Valent-Iron-Based Fenton-Like Technique[END_REF][START_REF] Fu | Removal of Trace Thallium from Industrial Wastewater by Fe 0 -Electrocoagulation[END_REF] Among them, macrocyclic compounds with a good affinity for Tl(I) are assumed to be promising host derivatives for removing traces of Tl(I) in soil water. [START_REF] Zhao | Adsorptive Removal of Trace Thallium(I) from Wastewater : A Review and New Perspectives[END_REF] For instance, Calix[n]arene (n = 4 -6) and crown-ether derivatives show good affinity and selectivity for Tl(I). These molecules have been incorporated into various systems to detect traces of thallium in water, even in the presence of other cationic species. [START_REF] Talanova | Novel Fluorogenic Calix[4]arene-bis(crown-6-Ether) for Selective Recognition of Thallium(I)[END_REF][START_REF] Katsu | I)-Selective Membrane Electrodes Based on Calix[6]arene or Calix[END_REF][START_REF] Dong | Determination of Thallium and Cadmium on a Chemically Modified Electrode with Langmuir-Blodgett Film of p-Allylcalix[4]arene[END_REF][START_REF] Cheraghi | Voltammetric Sensing of Thallium at a Carbon Paste Electrode Modified with a Crown Ether[END_REF][START_REF] Chester | A Calixarene-Based Ion-Selective Electrode for Thallium(I) Detection[END_REF] More recently, another class of macrocyclic derivatives showing high affinity for Tl(I) in aqueous solution has emerged. [START_REF] Brotin | Water-Soluble Molecular Capsule for the Complexation of Cesium and Thallium Cations[END_REF][START_REF] Brotin | Influence of the Cavity Size of Water-Soluble Cryptophanes on Their Binding Properties for Cesium and Thallium Cations[END_REF][START_REF] Chapellet | Experimental and Theoretical Study of the Complexation of Cesium and Thallium Cations by a Water-Soluble Cryptophane[END_REF] These compounds are interesting because the number of host molecules that can bind Tl(I) in aqueous phase are rather limited and most of the studies reported in the literature have concerned macrocyclic compounds dissolved in organic solvents. [START_REF] Matthews | Thallium -Cation Complexation by Calix4tubes : 205 Tl NMR and X-ray Evidence[END_REF][START_REF] Roper | Selective Recognition of Thallium(I) by 1,3-Alternate Calix4arene-bis(crown-6 Ether) : A New Talent of the Known Ionophore[END_REF][START_REF] Cuc | Behavior of Cesium and Thallium Cations inside a Calixarene Cavity As Probed by Nuclear Spin Relaxation. Evidence of Cation-π Interactions in Water[END_REF][START_REF] Makrlik | Interaction of the Thallium Cation with 1,3-alternate-25,27-bis(1-octyloxy)calix4arene-crown-6 : Experimental and Theoritical Study[END_REF][START_REF] Haddadi | Cation- interaction in Complex Formation Between Tl + Ion and calix4crown-6 and Some calix4biscrown-6 Derivatives : Thallium-203 NMR, Proton NMR, and X-ray Evidence[END_REF][START_REF] Chester | The extraction of Thallium(I) and Silver(I) Ions with 1,3-Alternate Calix4arene Derivatives[END_REF] These derivatives also show good affinity for Cs + cations, but association constants have been shown to be generally an order of magnitude lower under the same experimental conditions. Anyway, studying comparatively the interaction of large cations such as Tl + and Cs + with these host molecules represents good challenge. This class of compounds can be defined as hollow-type macrocyclic compounds and they have been named cryptophane derivatives for simplicity. [START_REF] Brotin | Cryptophanes and their Complexes : Present and Future[END_REF] These derivatives are made of two cyclotribenzylene (CTB) caps connected together by three alkoxy linkers whose length and nature can be varied.

Interestingly, they can also be decorated with different substituents, depending on the application wanted. In recent articles, we have shown that the presence of phenol groups grafted onto the benzene rings (Chart 1: compound 1) allows these molecules to bind Cs + and Tl + in aqueous solution with a very high efficacy. These host molecules are also able to recognize other alkali cations such as Rb + and K + but the association constants measured under the same conditions are several orders of magnitude lower than those observed for Tl + and Cs + . We concluded that the presence of phenol groups is mandatory to observe an efficient complexation of Tl + and Cs + and the introduction of other functionalities on the cryptophane skeleton leads to a lack of recognition. For instance, the replacement of all phenol functions by carboxylic acid groups led to a compound that do not show any affinity for Cs + and Tl + cations (Chart 1: compound 2).

The recognition process can be easily detected by several techniques such as isothermal titration experiments (ITC), 205 Tl NMR spectroscopy and 133 Cs NMR spectroscopy. To date, basic conditions were necessary to perform these experiments with cryptophane derivatives since these host molecules are strongly lipophilic and are consequently not soluble at neutral pH. Thus, the ability of new cryptophane derivatives to bind thallium and cesium cations at neutral pH remains to be determined. The demonstration of the ability of these molecules to bind the cesium and especially Tl(I) cations at neutral pH would be extremely interesting for future applications in environmental chemistry.

Recently, we have reported a synthetic procedure that allowed us to prepare in a single step new asymmetrical anti-cryptophane and syn-cryptophane derivatives with C3symmetry. [START_REF] Brotin | Synthesis of Cryptophane-B : Crystal Structure and Study of its Complex with Xenon[END_REF] Interestingly, these new derivatives possess reactive chemical functions that can be easily functionalized at latter stages to build-up new derivatives that could not otherwise be synthesized. Thus, from these compounds, it is possible to prepare cryptophane derivatives having different functionalities on each CTB units, such as compound 3, which has three phenol functions grafted on one CTB unit and three carboxylic acid functions grafted onto the other CTB unit (Chart 1: compound 3). From a structure point of view this compound can be seen as intermediate between compounds 1 and 2. Thus, the similarity of compound 3 with these two structures and their different affinity with respect to the cesium and the thallium cations prompted us to investigate the binding properties of compound 3 with these two species in more details.

We report in this paper the synthesis of compound 3 and we study its ability to bind thallium, cesium and other alkali cations in aqueous solution. Isothermal Titration Calorimetric experiments (ITC), 205 Tl and 133 Cs NMR spectroscopy have been used to study the binding process with these two cations. Due to the non-negligible solubility of compound 3 in pure water, it is possible for the first time to assess the thallium and cesium binding properties of a phenol-containing cryptophane at neutral pH.

CHART 1: Chemical structures of compounds 1-3 (a single enantiomer is show).

RESULTS

Synthesis of compound 3:

A cryptophane (compound 4; C3-symmetry) of anti configuration bearing three phenol moieties and three benzyl groups has recently been reported in the literature. [START_REF] Brotin | Synthesis of Cryptophane-B : Crystal Structure and Study of its Complex with Xenon[END_REF] This new derivative offers many advantages as it allows different functionalities to be grafted onto the two CTB caps, thus extending the chemistry of these derivatives. For instance, this compound was used as a starting material to prepare the water-soluble cryptophane 3. It is noteworthy that compound 3 has recently been used as a pH sensor in combination with laser-polarized xenon NMR. [START_REF] Léonce | Accurate pH Sensing Using Hyperpolarized 129 Xe NMR Spectroscopy[END_REF] Two different strategies were tested to prepare cryptophane 3: the synthetic pathway 1, named the two-step approach, requires the use of two different protecting groups to protect both the phenol and the ester functions. In contrast, the synthetic pathway 2, named the one-step approach, uses the same protecting groups for both chemical functions. In the two-step approach, compound 4 was allowed to react with an excess of methylbromoacetate (5) rise to compound 6 in 90% yield. Thus, compound 6 possesses two orthogonal protective groups (three methyl and three benzyl groups) that can be easily removed at different stages of the synthesis. In contrast, in the one step-approach, methylbromoacetate (5) is replaced by its benzylbromoacetate analogue (7). Using the same methodology reported for 6, compound 8 was prepared in 80% yield by reacting compound 4 with an excess of 7. The introduction of six benzyl groups in compound 8 may be an advantage in preparing compound 3 in a single

step, but we found that compound 8 was more difficult to isolate due to its higher lipophilicity. Deprotection of the three benzyl ester groups of 7 was performed by hydrogenolysis with palladium on charcoal (Pd/C; 10%) as a catalyst in a mixture of CH2Cl2/MeOH. This gave compound 9 in 97 % yield. Unfortunately, the selective deprotection of the three methyl ester groups (synthetic pathway 1) performed in KOH/D2O in the presence of THF did not allow us to obtain the desired compound. Indeed, although we noticed that deprotection of the three ester functions took place, the 1 H NMR spectrum of the crude revealed a very complicated spectrum due to the presence of the imploded form in significant amounts. The presence of the imploded form makes therefore the synthetic pathway 1 useless since this peculiar conformation does not show any interesting binding properties. In addition, the presence of two stable conformations in solution (inflated and imploded) would complicate the interpretation of our results. In contrast, the hydrogenolysis reaction (synthetic pathway 2) performed with compound 8 with Pd/C in a CH2Cl2/MeOH mixture allowed us to obtain compound 3 with a good yield. In this example, compound 3 was recovered without any imploded form as shown by 1 H NMR spectroscopy. Compound 3 and 7-9 have been fully characterized by 1 H and [START_REF] Karbowska | Presence of Thallium in the Environment : Sources of Contaminations, Distribution and Monitoring Methods[END_REF] C NMR spectroscopy and HRMS (See Supporting Information S4-S11). Compound 3 was found very soluble in DMSO and in water under basic condition. Importantly, we also observed that this compound is also slightly soluble at neutral pH. 133 Cs and 205 Tl NMR spectroscopy: 133 Cs NMR spectroscopy of compound 3 in the presence of CsOH was recorded at 290 K in NaOH (0.1 M). In a previous article, Cryptophane 1 and some of its congeners were studied in basic aqueous solution because these molecules have a good solubility under these conditions. Thus, in the present study, compound 3 was first studied under the same conditions for comparison purposes. Indeed, the presence of a characteristic signal at a low frequency relative to free Cs + would be a good indication that compound 3 can accommodate this cation under the same conditions.

At this temperature, the NMR spectrum shows a single signal located near 0 ppm, which is characteristic of Cs + in the bulk. Another very broad signal, upfield shifted, can be detected with difficulties but at this temperature it is difficult to assign it to the Cs + @3 complex.

However, lowering the temperature to 285 K confirms this second 133 Cs NMR signal ( ~ -250 ppm). This signal is still broad but becomes sharper as the temperature decreases (see Figure 1). For instance, at 275 K, which is the lowest temperature that we could reach, the 133 Cs NMR spectrum reveals a sharp signal at -248.0 ppm, which is characteristic of the formation of the Cs + @3 complex, see Figure 1). 205 Tl NMR spectroscopy was found more difficult to achieve because the 205 Tl nucleus resonates at a frequency, which is too high for most of commercial broadband NMR probes, and too low to be detected by the 1 H channel. However, detection of this nucleus was made possible by using a homemade system (see experimental section). At room temperature, a sample of cryptophane 3 in NaOH in the presence of a small amount of thallium acetate revealed only a broad signal at 440 ppm. No other 205 Tl NMR signal was detected at lower frequency that could indicate the formation of the Tl + @3 complex at this temperature (see Supporting Information S12). Unfortunately, our homemade system does not allow us to record 205 Tl NMR spectra at even lower temperature. Anyway this result is consistent with that obtained with 133 Cs NMR spectroscopy, which shows no specific spectral signature for the 133 Cs@3 complex at room temperature.

Titration experiments: Isothermal titration calorimetry (ITC) appears to be the method of choice to measure accurately the association constants between compound 3 and cationic species in aqueous solution. In addition, all the parameters associated to this binding process can be easily determined or calculated from the enthalpogram. For instance, both the binding constant and the enthalpy of complexation H 0 can be measured from the ITC experiments.

In turn, the free enthalpy G 0 and entropy S 0 of complexation can be easily calculated from these data. ITC experiments were carried out under different conditions and the results are summarized in Table 1 and Table 2. Here again, for comparison purposes, compound 3 was first investigated under basic conditions. In LiOH (0. (See Supporting Information S19).

Higher association constants have been measured for the Tl + @3 complex. Decreasing the pH of the solution to pH = 9.2 (TRIS buffer) gives rise to a decrease of the binding constant K = 9300 M -1 (See Supporting Information S20). At pH = 7.12 and pH = 7.71 (HEPES buffer, 10 mM) the association constants measured are K = 5800 M -1 and 6700 M -1 , respectively (See Figure 2 and Supporting Information S21).

It is noteworthy that compound 3 does not show any affinity for other alkali cations such as K + and Rb + under the same conditions. For instance, an ITC experiment performed in LiOH (0.1 M) at 298 K does not reveal any specific interaction between host 3 and the K + cation (See Supporting Information S22). A similar result was obtained with the Rb + cation (See Supporting Information S23).

DISCUSSION:

The recent synthesis of asymmetrical cryptophanes, such as compound 4, allows us to design new original cryptophane derivatives bearing different substituents positioned on each CTB unit. Thus, from the partially protected cryptophane 4 used as a starting material, we have been able to introduce specifically three protected carboxylic acid moieties on the same CTB unit whereas the second CTB unit can be decorated with other functionalities. It is noteworthy that this kind of cryptophane such as compound 3 could not be easily prepared with the previous strategies described in the literature. In this article two different synthetic pathways have been proposed to prepare this derivative. The two-step approach is interesting as it offers the opportunity to design different cryptophane derivatives by taking advantage of the presence of the three phenol functions. Unfortunately, as already observed in the past with cryptophane 3 congeners, the deprotection step performed under basic conditions may result in the formation of the imploded form in significant amount. This particular conformation can be easily identified by 1 H NMR spectroscopy as it gives rise to characteristic 1 H NMR signals and it decreases the molecular symmetry of the cryptophane, thus resulting in a very complex spectrum. As the host of interest is made of two different CTB units two different structures can be drawn for the imploded form of 3 (see supporting information S21). Of course, this result does not mean that basic conditions cannot be used for deprotection of methyl ester functions. For instance the well-known hexacarboxylate cryptophane is usually prepared in this way and the imploded form is usually absent or present only in a small proportion. [START_REF] Huber | Water soluble cryptophanes showing unprecedented affinity for xenon: candidates as NMR-based biosensors[END_REF] Our results show that the deprotection of ester groups under basic conditions is highly dependent on the structure of the cryptophane under study and that great attention must be paid to the experimental conditions used. This peculiar problem was also encountered recently with cryptophane derivatives having a slightly larger cavity. [START_REF] Baydoun | Synthesis of Cryptophane-223-Type Derivatives with Dual Functionalization[END_REF] In contrast, the one-step approach, that use milder conditions allow us to prepare compound 3 without formation of the imploded form. In addition, in this example, the hydrogenolysis of the benzyl moieties takes place in CH2Cl2, a solvent that can easily adapt to the host cavity and prevents host collapse.

Our results clearly show that compound 3 is able to recognize Cs + and Tl + cations in a large range of conditions. For instance, 133 Cs NMR spectroscopy reveals a specific spectral signature for the Cs + @3 complex at lower frequencies ( ~ -249 ppm at 275 K). It can be observed that this system resonates in the same spectral range as the Cs + @1 complex and its congeners, all of which exhibit a characteristic signature between -250 and -270 ppm. [START_REF] Brotin | High Affinity of Water-Soluble Cryptophanes for Cesium Cation[END_REF] This down-shifted NMR signature is the consequence of the strong shielding effect induced by the six aromatic rings surrounding the cesium cation. In contrast to compound 1, the 133 Cs NMR signal of the Cs + @3 complex is not clearly defined at room temperature but a clear NMR signature is observed at lower temperature for this complex. Temperature has an inverse effect on these two complexes. For instance, an increase of the temperature (up to 340 in basic water) results in a strong sharpening of the 133 Cs NMR signal of the Cs + @1 complex. Other water-soluble cryptophanes having very high affinity for Cs + show a similar behaviour. In contrast a sharpening of the 133 Cs NMR signal effect with temperature lowering has been observed with cryptophane derivatives showing lower affinity for Cs + , as observed with the Cs + @3 complex. [START_REF] Brotin | Influence of the Cavity Size of Water-Soluble Cryptophanes on Their Binding Properties for Cesium and Thallium Cations[END_REF] This result is supported by the isothermal titration calorimetry experiments that show a significant decrease of the association constant with respect to compound 1. For instance in LiOH (0.1 M) at 298 K an association constant K = 2.7x10 9 M -1 has been reported

for the Cs + @1 complex. In the same conditions the Cs + @3 complex shows an association constant lowered by several orders of magnitude, K = 11000 M -1 . This leads to a free enthalpy of complexation G 0 = -5.5 kcal mol -1 at 298 K. As this was suggested previously after study of different Cs + @cryptophane derivatives, the number of phenol groups grafted onto the cryptophane skeleton has a strong effect on the recognition of alkali cations by cryptophanes.

For instance, DFT calculation has revealed that coulombic interactions between cesium and the phenolate moiety play a key role in the stabilisation of the cryptophane complexes. [START_REF] Chapellet | Experimental and Theoretical Study of the Complexation of Cesium and Thallium Cations by a Water-Soluble Cryptophane[END_REF] Thus the removal of three phenol groups has a tremendous effect of the ability of 3 to bind alkali cations. For instance, we observed, in contrast to compound 1, that this compound is unable to accommodate Rb + in the same condition whereas compound 1 still shows a good affinity for this cation with an association constant K = 9.2x10 5 M -1 in LiOH (0.1 M). In NaOH (0.1 M) and KOH (0.1 M) slightly lower association constants have been measured in these two solvents leading to free enthalpy of complexation values G 0 = -5.5 and G 0 = -5.4 kcal mol - 1 , respectively (see Table 1 and Supporting Information S22). In these two solvents, an increase of the enthalpy of complexation is compensated by an increase of the negative entropic term S 0 .

Thanks to the introduction of three carboxylic moieties grafted onto the cryptophane skeleton compound 3 possesses a sufficient solubility in water to perform ITC experiments at neutral pH. Thus, in HEPES buffer (pH = 7.28), compound 3 shows a low affinity (K = 600 -700 M - 1 ) for Cs + at 298 K. This result has interesting consequences because it suggests that cryptophane 1 and its congeners having six phenol moieties can bind more efficiently Cs + at neutral pH. However, the solubility of these host molecules in water is not sufficient to measure the association constants by ITC experiments. Nevertheless, their integration into a polymer matrix or nanoparticles can easily be designed to promote their solubility in water.

Note that the structure of these cryptophanes has recently been modified in order to facilitate the grafting of these molecules onto polymers or other solid matrices for instance. [START_REF] Chapellet | Synthesis of Cryptophanes with Two Different Reaction Sites: Chemical Platforms for Xenon Biosensing[END_REF] As observed with all cryptophane derivatives bearing phenol groups, compound 3 exhibits a larger affinity for Tl + than for Cs + in the same experimental conditions. This affinity is at least an order of magnitude higher than the one observed for Cs + . Compared to cesium, the better affinity of thallium for water-soluble cryptophanes has been verified with different systems. DFT calculations have clearly established that thallium interacts more strongly with the CTB units of cryptophanes than cesium. [START_REF] Chapellet | Experimental and Theoretical Study of the Complexation of Cesium and Thallium Cations by a Water-Soluble Cryptophane[END_REF] Here again, in LiOH (0.1 M) at 298 K, the association constant K = 4.2x10 5 M -1 between host 3 and thallium is significantly larger than the one measured with cesium. This leads to a measured free enthalpy of complexation G 0 = -7.7 kcal mol -1 (Table 2 and Supporting Information S22). As observed with the Cs + @3 complex the large enthalpy of complexation H 0 = -12.0 kcal mol -1 is compensated by a large negative entropic term TS 0 = -4.3 kcal mol -1 . Interestingly, these values are not affected by a change of the experimental conditions since similar K, H 0 and TS 0 values are obtained in NaOH and KOH solutions. Indeed, contrary to what is observed with host 1, the K + cation does not show any affinity for host 3. Thus, compound 3 has lower affinity for both thallium and cesium but it presents a better selectivity since other alkali cations such as K + or Rb + are not recognized by this host.

Lowering the pH of the solution (pH = 9.2; TRIS buffer) results in a decrease of the association constant K ~ 8000 M -1 (G 0 = -5.3 kcal mol -1 at 298 K). At this pH value, which is of the same order of magnitude as the pK value of a phenolic function, the proportion of phenolate function decreases significantly, resulting in both a reduction of the coulombic interaction with thallium and of the electron density of the benzene rings. At lower pH value (HEPES buffer, pH = 7.12) the same trend is observed and an association constant K ~ 6000 M -1 between Tl + and host 3 has been measured, suggesting that recognition of thallium is still effective at a neutral pH. It should be mentioned that an increase in the number of phenol groups on a cryptophane skeleton would result in higher association constants for thallium recognition at neutral pH. Thus, the integration of these derivatives into solid matrix (polymer, nanoparticles) would certainly be very useful to build-up new materials for the extraction of traces of thallium of aqueous phases contaminated with thallium.

CONCLUSION

In this article we report the synthesis of a water-soluble cryptophane bearing two different functionalities onto the benzene rings: three phenol and three carboxylic acid moieties. We show that only Cs + and Tl + cations are well recognized by this new host over a large pH range. Compared to the other cryptophane studied so far, compound 3 shows a better selectivity since other alkali cations do not show any affinity for this host. The association constants measured with compound 3 are somewhat lower than the association constants observed with compound 1 that possesses six phenol functions. For the first time we have assessed the ability of a water-soluble cryptophane derivative to bind Tl + at neutral pH, thanks to the higher solubility of compound 3 in these conditions. Thus, we have demonstrated that this compound shows a moderate affinity for Tl + at neutral pH (pH = 7.12) despite the presence of only three phenol groups in its structure. This important result suggests therefore that water-cryptophane possessing a larger number of phenol groups grafted onto the benzene rings are able to bind + in pure water with a great efficacy. A modification of the structure of these cryptophanes to improve their solubility in water or their incorporation into polymer matrix can be envisaged to prepare efficient materials for removing traces of thallium(I) in aqueous phase. Thus, cryptophane derivatives can find applications in environmental chemistry in solving problems related to water pollution by traces of thallium (I).

EXPERIMENTAL DETAILS

Synthesis of cryptophane 3:

Hydrogen gas was bubbled at room temperature into a solution of compound 8 (0.31 g, 0.2 mmol) and Pd/C (10%) in a mixture of CH2Cl2 (8 mL) in methanol (6 mL). The reaction was stirred overnight at room temperature. The black mixture was then filtered over celite. The desired product was then extracted with a NaOH (0.5 M) solution (75 mL). The aqueous phase was washed once with CH2Cl2 and then cooled into ice.

Acidification with HCl gives rise to compound a white product. The solid was collected on frit washed with water and dried in air. The solid was then finally washed with diethyl ether to

SCHEME 1 :

 1 SCHEME 1: synthesis of cryptophane 3 according to two different synthetic routes.

Figure 1 :

 1 Figure 1: 133 Cs NMR spectroscopy of 3 in the presence of CsOH in NaOH (0.1 M) recorded at several temperature (290, 285, 280, 275 K). Left signal: free Cs + in the bulk. Right signal: Cs + @3 complex.

  1 M), host 3 binds moderately Cs + with a binding constant K = 11000 M -1 at 298 K (see Supporting Information S13). A change of the base used to prepare the solution (NaOH and KOH) leads to a small decrease of the binding constant and binding constants. Binding constants K = 8700 M -1 and 8300 M -1 have been obtained at 298 K in NaOH (0.1 M) and KOH (0.1 M), respectively (see Supporting Information S14-S15). Interestingly, higher binding constants have been measured with thallium. For instance, at 298 K a binding constant K = 4.2x10 5 M -1 has been measured for this cation in LiOH (0.1 M) (Figure2). A change of the nature of the basic solution does not significantly modify the binding constant since K = 3.93x10 5 M -1 and 3.53x10 5 M -1 have been measured respectively in NaOH (0.1 M) and KOH (0.1 M), respectively (See Supporting Information S16-S17).Interestingly, the moderate solubility of compound 3 allows us for the first time to investigate the binding properties of cesium and thallium at neutral pH. In order to avoid any change of the pH of the solution upon slight addition of the analyte, these experiments have been performed in the presence of a HEPES buffer. Thus, an ITC experiment performed in HEPES (10 mM; pH = 7.28) with compound 3 in the presence of Cs + gives rise to a moderate binding constant K = 650 M -1 at 298 K (See Supporting Information S18). Lowering the temperature to 288 K leads to a slight increase of this constant K ~ 1250 M -1 (HEPES, 10 mM; pH = 7.18)

Figure 2 :

 2 Figure 2: Isothermal Titration Experiments recorded at 298 K of compound 3 in the presence of TlOAc. a) Calorimetric titration of 3 in LiOH/H2O at 298 K. The host solution (c = 0.08 mM) was placed into the calorimeter cell (1.4 mL) and 28 successive aliquots (10 L) of TlOAc solution (c= 0.99 mM) were added at 3 min intervals. Stoichiometry n = 1.04. b) Calorimetric titration of 3 in HEPES buffer (10 mM; pH = 7.12) at 298

Table 1 :

 1 thermodynamic parameters of complexation K, H 0 , TH 0 and G 0 for the Cs + @3 complex recorded at 298 K in various solvents. The values reported have been obtained from isothermal titration (ITC) experiments.

	a: HEPES buffer (10 mM; pH = 7.28).
	Solvents	K (M -1 )	H 0 (kcal/mol)	TS 0 (kcal/mol)	G 0 (kcal/mol)
	LiOH (0.1 M)	11000	-8.2	-2.7	-5.5
	NaOH (0.1 M)	8700	-10.7	-5.3	-5.4
	KOH (0.1 M)	8300	-9.6	-4.3	-5.3
	HEPES a	640	-6.2	-2.4	-3.9

Table 2 :

 2 thermodynamic parameters of complexation K, H 0 , TH 0 and G 0 for the Tl

	Solvents	K (M -1 )	H 0 (kcal/mol)	TS 0 (kcal/mol)	G 0 (kcal/mol)
	LiOH (0.1 M)	4.2 10 5	-12.0	-4.3	-7.7
	NaOH (0.1 M)	3.93 10 5	-11.5	-3.8	-7.7
	KOH (0.1 M)	3.53 10 5	-11.5	-3.9	-7.6
	TRIS buffer a	9300 a	-7.8	-2.5	-5.3
	HEPES buffer b	5750 c	-7.2	-2.1	-5.1

+ @3 complex recorded at 298 K in various solvents. The values reported have been obtained from isothermal titration (ITC) experiments. a: TRIS buffer (10 mM; pH = 9.2). b: HEPES buffer (10 mM; pH = 7.28). c: another experiment performed at pH = 7.71 gives rise to a binding constant K = 6700 M -1 (see Supporting Information S21).

  Merck silica gel 60 (0.040-0.063 mm). Analytical thin layer chromatography (TLC) was performed on MERCK silica gel TLC plates F-254. The solvents were distilled prior to use: DMF and CH2Cl2 from CaH2, THF from Na/benzophenone and pyridine from KOH. Filtration and evaporation of the solvent gave compound 8 as an oily product. This product was first subjected to column chromatography on silica gel (eluent: CH2Cl2/Acetone: 95/5). The evaporation of the solvents gave compound 8 as a yellow oily product. A second column chromatography on silica gel (CH2Cl2 then CH2Cl2/Acetone: 99/1; 97/3 and 96/4) allows us to recover compound 8 (0.34 g; 80 %) as a clean product after evaporation of the solvents. Compound 8 was isolated as a white glassy product. 1 H NMR (CDCl3, 300 MHz):  7.50 -7.20 (m, 30H), 6.71 (s, 3H), 6.69 (s, 3H), 6.62 (s, 3H), 6.59 (s, 3H), 5.05 (m, 6H), 4.91 (m, 6H), 4.48 (d, 3H, J = 13.5 Hz), 4.45 (d, 3H, J = 13.5 Hz), 4.34 (m, 6H), 4.25 -4.05 (m, 12H), 3.27 (d, 3H, J = 13.5 Hz), 3.245 (d, 3H, J = 13.5 Hz).13 C{ 1 H} NMR (CDCl3, 75.5 MHz)  168.8, 149.0, 147.9, 147.7, 147.3, 137.4, 135.3, 134.2, 134.0, 133.6, 132.5, 128.7, 128.5, 127.9, 127.6, 122.0, 120.7, 119.7, 117.5, 71.8, 69.4, 69.2, 67.7, 66.7, 36.0. HRMS (ESI-TOF) m/z [M+H + ] calcd for C96H85O18 1525.5747, found 1525.5730. Hydrogen gas was bubbled at room temperature into a solution of compound 6 (0.09 g, 0.07 mmol) and Pd/C (10%) in a mixture of CH2Cl2 (4 mL) in methanol (3 mL). The reaction was stirred for 16 hours at room temperature under a hydrogen atmosphere. The black solid was then filtered on celite. The solid was washed several times with CH2Cl2 and few drops of DMF to ensure that extraction is complete. The organic layer was then evaporated under reduce pressure to give a residue, which was purified on silica gel (CH2Cl2/acetone: 90/10). Evaporation of the solvents gives compound 9 (0.055 g, 80 %) as a white glassy product, which was collected on a frit and washed with diethyl ether. 1 H NMR (CDCl3, 300 MHz):  8.36 (s, 3H), 6.80 (s, 3H), 6.75 (s, 3H), 6.57 (s, 3H), 6.53 (s, 3H), 4.69 (m, 6H), 4.49 (d, 3H, J = 13.5 Hz), 4.41 (d, 3H, J = 13.5 Hz), 4.30 -4.00 (m, 12H), 3.78 (s, 9H), 3.28 (d, 3H J = 13.5 Hz), 3.155 (d, 3H, J = 13.5 Hz). 13 C{ 1 H} NMR (CDCl3, 75.5 MHz)  169.9, 146.9, 146.1, 145.7, 144.2, 133.6, 133.0, 132.6, 130.0, 119.4, 118.9, 117.8, 116.0, 68.2, 68, 65.8, 51.7, 35.0, 34.8. HRMS (ESI-TOF) m/z [M+H + ] calcd for C57H55O18 1027.3383, found 1027.3387.

	compound 6 (0.097 g, 90 %) as a white crystalline solid. 1 H NMR (CDCl3, 300 MHz):  7.51
	-7.28 (m, 30H) 6.80 (s, 3H), 6.78 (s, 3H), 6.71 (s, 6H), 4.97 (m, 6H), 4.525 (d, 6H, J = 13.5
	Hz), 4.32 (s, 6H), 4.28 -4.16 (m, 12H) 3.62 (s, 9H), 3.375 (d, 3H, J = 13.5 Hz), 3.355 (d, 3H,
	Mass spectra (HRMS) were performed by the Centre de Spectrométrie de Masse, University of Lyon. Analyses were performed with a hybrid quadrupole-time of flight mass spectrometer, microToF QII equipped with an Electrospray ion source. Data Analysis® 4.0 was used for instrument control, data collection, and data treatment. HRMS analyses were performed in full scan MS with a mass range from 50 to 2000 Da at an acquisition rate of 1 Hz. Transfer parameters were: RF Funnel 1, 200 V; RF Funnel 2, 200 V; hexapole, 50 V; transfer time, 70 μs and PrePulse storage time, 1 μs Before each acquisition batch, external calibration of the instrument was performed with a sodium formate clusters solution. 1 H and 13 C NMR spectra were recorded at 300 and 75.5 MHz, respectively. Chemical shifts are with great care. NMR Experiments. 133 Cs NMR spectra (65.587 MHz) were recorded on a 11.7 T Bruker Avance spectrometer using a 5 mm probehead. A solution of CsNO3 was used as a chemical shift reference (0 ppm). An interscan delay of 1s was applied. The 205 Tl NMR experiments were performed on a 11.7 T Bruker Avance spectrometer using an 8 mm microimaging (Micro-5) probehead basis equipped with a homebuilt 205 Tl/ 1 H insert. A solution of thallium nitrate was used as a chemical shift reference (0 ppm), and comparison was made with a solution of thallium acetate. For the 205 Tl NMR spectrum of 3, an interscan delay of 1.2 s was applied. The FID was apodized by an exponential window of 200 Hz before Fourier transformation. EXPERIMENTAL PROCEDURE Synthesis of cryptophane 6: methylbromoacetate (95 L) was added to a mixture of cryptophane 4 (0.09 g, 0.083 mmol), cesium carbonate (0.163 g, 0.5 mmol) in DMF (3 mL) under an argon atmosphere. The mixture was heated to 60°C (oil bath) for 16 hours. Then, the mixture was poured into a biphasic solution of CH2Cl2 (10 mL) and water (10 mL). The product was extracted twice with CH2Cl2. Then, the combined organic layers were washed once with water and dried over Na2SO4. Filtration and evaporation of the solvent gave a solid residue, which was subjected to column chromatography on silica gel (CH2Cl2/acetone: 134.2, 134.0, 133.7, 132.5, 128.5, 127.9, 127.6, 121.8, 120.9, 119.5, 117.5, 71.8, 68.4, 69.3, 67.5, 51.8, 36.1. HRMS (ESI-TOF) m/z [M+H + ] calcd for C78H73O18, 1297.4791, found 1297.4799. Synthesis of cryptophane 8: benzylbromoacetate (0.4 mL) was added under argon to a mixture of cesium carbonate (0.36 g, 1.1 mmol), cryptophane 4 (0.3 g, 0.28 mmol) in DMF (6 referenced to Me4Si ( CAUTION: thallium salts are highly toxic. Thallium salts such as TlOAc must be handled J = 13.5 Hz). 13 C{ 1 H} NMR (CDCl3, 75.5 MHz)  169.3, 149.0, 148.0, 147.8, 147.3, 137.5, Synthesis of cryptophane 9:
	90/10). Compound 6 was isolated as a white glassy product. Filtration on a frit gives

1

H,

[START_REF] Karbowska | Presence of Thallium in the Environment : Sources of Contaminations, Distribution and Monitoring Methods[END_REF]

C). Column chromatographic separations were carried out over mL). The mixture heated overnight at 60°C (oil bath) under an argon atmosphere. Then, after cooling, the mixture was poured in a mixture of CH2Cl2 (20 mL) and water (20 ml). The aqueous layer was extracted twice with CH2Cl2 (2 x 20 mL). The combined organic layers were then washed with water to remove DMF. The organic layer was dried over sodium sulphate.

ACKNOWLEDGEMENTS

The CNRS and the CEA are acknowledged for financial support. The authors thank Kévin Chighine for the building of the 205 Tl insert.

AUTHOR INFORMATION

Corresponding author *E-mail: thierry.brotin@ens-lyon.fr ORCID Thierry Brotin: 0000-0001-9746-4706 Patrick Berthault: 0000-0003-4008-2912

Notes

The authors declare no competing financial interest.


Johann Faouzi
email: johann.faouzi@icm-institute.org

Hicham Janati
email: hicham.janati@inria.fr

pyts: A Python Package for Time Series Classification

Keywords: time series, classification, machine learning, python

pyts is an open-source Python package for time series classification. This versatile toolbox provides implementations of many algorithms published in the literature, preprocessing functionalities, and data set loading utilities. pyts relies on the standard scientific Python packages numpy, scipy, scikit-learn, joblib, and numba, and is distributed under the BSD-3-Clause license. Documentation contains installation instructions, a detailed user guide, a full API description, and concrete self-contained examples.

Introduction

A time series is a sequence of values indexed in chronological order. Given their structured nature, they are very common in many real-world applications. With the increasing availability of sensors and the development of Internet of things devices, the amount of time series data and the number of applications is continuously growing. Applications can be found in a virtually unlimited number of fields ranging from finance and econometrics [START_REF] Perron | The great crash, the oil price shock, and the unit root hypothesis[END_REF] to geology with earthquake prediction [START_REF] Amei | Time series analysis for predicting the occurrences of large scale earthquakes[END_REF], and climate science with weather forecasting [START_REF] Agrawal | An application of time series analysis for weather forecasting[END_REF].

In machine learning, exploiting the structural patterns of the data in order to assign a certain label to a new observation is known as classification. Classifying time series data can solve several real-world problems including disease detection using electrocardiogram data [START_REF] Olszewski | Generalized Feature Extraction for Structural Pattern Recognition in Time-Series Data[END_REF], household device classification to reduce carbon footprint, and image classification [START_REF] Ratanamahatana | Three myths about dynamic time warping data mining[END_REF]. However, standard machine learning classification is not always well suited for time series because of the possibly high correlation between back-to-back time points. One typical example is the Naive Bayes algorithm, which assumes a conditional independence between each feature given the class the time series belongs to. For this reason, algorithms dedicated to time series classification have been developed such as bag-of-words models, shapelet-based approaches and modifications to standard tree-based algorithms.

In this paper we present pyts, a Python package for time series classification. To the best of our knowledge, among several Python packages for time series analysis, pyts is the only Python package entirely dedicated to time series classification. The following sections describe the project development, the dependencies, the API design, a comparison to related Python packages and future works.

Project Development

Code quality. The package comes up with a lot of unit tests, leading to 97% code coverage for the release of version 0.10. Moreover, analysis tools such as PEP8 and Flake8 are used and LGTM 1 gives the package an A+ grade for code quality.

Continuous integration. In order to ensure new code integration and backward compatibility, continuous integration is performed on all supported platforms.

Collaborative development. The package is hosted on GitHub, which allows for collaboration between the developers and any contributor, discussion on eventual issues, and feature requests.

Documentation.

A detailed documentation is hosted on Read the Docs with installation instructions, a comprehensive user guide, the whole API documentation and numerous examples.

Dependencies

NumPy: the base N-dimensional array package. numpy [START_REF] Van Der Walt | The numpy array: A structure for efficient numerical computation[END_REF] provides among other things a powerful N-dimensional array object, linear algebra operations, Fourier transform, and random number capabilities.

SciPy: the fundamental library for scientific computing. scipy [START_REF] Jones | Scipy: Open source scientific tools for python[END_REF] contains mathematical algorithms, statistical tools, sparse matrices, and convenience functions built on top of numpy.

Scikit-learn: machine learning in Python. scikit-learn [START_REF] Pedregosa | Scikit-learn: Machine learning in python[END_REF]) is a versatile toolbox for data mining and data analysis consisting of many machine learning algorithms and utility tools.

Joblib: running Python functions as pipeline jobs. joblib is a set of tools to provide lightweight pipelining in Python, such as transparent disk-caching of functions and simple parallel computing.

Numba: a high performance Python compiler. numba [START_REF] Lam | Numba: A LLVM-based python JIT compiler[END_REF] translates Python functions to optimized machine code at run time using the LLVM compiler library. Numbacompiled numerical algorithms in Python can reach the speeds of C or FORTRAN.

API Design

As illustrated in Listing 1, the pyts API is inspired by the scikit-learn API and is designed to be compatible with scikit-learn tools such as cross validation, model selection, Listing 1: Code snippet illustrating pyts's intuitive API on a classification example. and pipelines. All transformers have three main methods: fit derives statistics on the data set if applicable, transform computes the transformation with the learned statistics, and fit transform is an optimized version of fit followed by transform when possible. All classifiers have two main methods: fit learns statistics from the data set and predict derives predicted classes.

Assumptions on Input Data

One important challenge with time series is their number of time points. A data set of equallength time series consists of time series that all have the same number of time points. A data set of varying-length time series consists of time series that may have different numbers of time points. For computational efficiency, most algorithms implemented in pyts can only deal with data sets of equal-length time series. One exception is our implementation of Dynamic Time Warping [START_REF] Sakoe | Dynamic programming algorithm optimization for spoken word recognition[END_REF] and its variants.

Data sets of univariate and multivariate are both supported, being represented as twodimensional arrays and three-dimensional arrays respectively.

Comparison to Related Software

pyts is not the only Python package providing tools for time series classification. sktime [START_REF] Lning | sktime: A unified interface for machine learning with time series[END_REF] and tslearn [START_REF] Tavenard | tslearn: A machine learning toolkit dedicated to time-series data[END_REF] are dedicated to time series analysis in general, while tsfresh [START_REF] Christ | Time series feature extraction on basis of scalable hypothesis tests (tsfresh -a python package)[END_REF], cesium [START_REF] Naul | cesium: Open-source platform for time-series inference[END_REF] and seglearn [START_REF] Burns | Seglearn: A python package for learning sequences and time series[END_REF] are focused on extracting statistics-based features from time series. Table 1 provides an extensive comparison of available algorithms for time series classification in these packages. sktime and pyts stand out with their numbers of implementations of algorithms published in the literature. sktime provides more tree-based algorithms, while pyts is more focused on dictionary-based and image-based models.

In order to provide users confidence in our implementations, we also track the predictive performance of our implementations on some data sets and compare them to the results published in the literature. Table 2 highlights the accuracy scores on the test set for the BOSS transformer [START_REF] Schäfer | The BOSS is concerned with time series classification in the presence of noise[END_REF] followed by a one-nearest neighbor classifier with the BOSS metric [START_REF] Schäfer | The BOSS is concerned with time series classification in the presence of noise[END_REF] on several data sets.

Conclusion

The pyts Python package is a versatile toolbox for time series classification, providing implementations of several algorithms published in the literature, preprocessing tools, and data set loading utilities. A detailed documentation and concrete examples illustrate the use of the functionalities made available. Future works include better support for data sets of unequal-length time series and multivariate time series.

1

  from pyts . classification import BOSSVS 2 from pyts . datasets import load_gunpoint 3 4 # Load the GunPoint data set 5 X_train , X_test , y_train , y_test = load_gunpoint ( return_X_y = True ) the classifier on the training set 11 clf . fit ( X_train , y_train ) 12 13 # Compute the accuracy on the test set 14 accuracy = clf . score ( X_test , y_test ) 15 16 # Print accuracy 17 print ( accuracy ) 18 0.98

Table 1 :

 1 Availability of several algorithms for time series classification published in the literature. Packages (versions): pyts (0.10.0), sktime (0.3.1), tslearn (0.2.5), seglearn (1.1.0), tsfresh (0.13.0), cesium (0.9.10).

	Algorithms	pyts sktime tslearn seglearn tsfresh cesium
	Feature Extraction
	Dynamic Time Warping
	Support Vector Machine
	Learning Shapelet
	Shapelet Transform
	SAX-VSM
	BOSS
	BOSSVS
	WEASEL
	WEASEL+MUSE
	Recurrence Plot
	Gramian Angular Field
	Markov Transition Field
	Time Series Forest
	Proximity Forest
	Elastic Ensemble
	RISE
	Adiac ECG200 GunPoint MiddlePhalanxTW Plane
	(Schäfer, 2015) 0.765	0.870	1.000	0.526	1.000
	pyts	0.752	0.870	1.000	0.526	1.000

Table 2 :

 2 Accuracy scores on the test set for the BOSS transformer followed by a one-nearest neighbor classifier with the BOSS metric on several data sets.

can be downloaded from https://github.com/johannfaouzi/