Eris Sinoimeri

Victor Maia Fernandes

Jérôme Cognard

Jorge Fernando Brandão

Lenka Svecova

Ismaël Guillote

Isabelle Billard

Uncommon biphasic behaviour induced by very high metal ion concentrations in HCl/H 2 O/[P44414]Cl (tributyltetradecylphosphonium chloride) and HCl/H 2 O/Polyethene glycol-600 systems

In this work, the important role played by metal ions such as Fe(II/III), Cr(III) and Ni(II) in the formation and binodal behaviour of aqueous biphasic systems (ABS) composed of HCl and the ionic liquid, [P44414]Cl, or the polymer, PEG-600, is investigated. The concentration of metal ions used in this work exceeds several g/L for an industrial foreseen application. Experiments have also been carried out by varying the concentration of metal ions at different temperatures. Fe exhibits a totally different behaviour compared to Ni and Cr. In particular, the binodal curves in presence of the ionic liquid are far from the classical curves found in the literature, displaying an onion-shape form, while for Ni and Cr, the curves follow the classical trend. When any of the three metal ions is mixed with the polymer and HCl medium, only Fe(III) induces a biphasic system. Insights into the chemical driving forces at work are discussed.Introduction

In recent years, neutral Aqueous Biphasic Systems (ABS), composed of different polymer-polymer, polymer-salt or salt-salt combinations, plus water as the main protagonist, have been taken into consideration to selectively extract metal ions. In particular, the use of the [P44414]Cl (tri-butyl tetradecyl phosphonium chloride) ionic liquid (IL) or of the polyethene glycol (PEG) polymer for metal extraction has already been the subject of several papers. [1][START_REF] Billard | Ionic-liquid based aqueous biphasic systems: fundamentals and applications[END_REF][START_REF] Depuydt | [END_REF][4][5][6] The use of these compounds, more appropriately called biphasic inducers in these classical ABS, helps to make the process eco-sustainable. The [P44414]Cl hydrophilic ionic liquid (i) is less toxic than the respective hydrophobic IL 7 , (ii) can be used in much lower quantities than organic volatile solvents and (iii) the extraction kinetics is favored by its low viscosity. In regards to the PEG, this is an inexpensive, nontoxic, non-flammable compound which is commercially available in very large quantities. These systems are intrinsically much eco-friendlier than the classical liquid-liquid systems where organic solvents are used as main components and could thus be favorably considered by the industry. However, in order to comply with any industrial demand, extraction should proceed from highly loaded wastes, which is currently very rarely the case in the literature. Furthermore, most industrial wastes are highly acidic, which is not compatible with the most classical ABSs. Therefore, in the first step, we took advantage of the recently described Acidic Aqueous Biphasic Systems (AcABS) 8 loaded with very high concentrations of either Cr, Ni or Fe to perform fundamental studies in view of potential industrial applications. In this work, aqueous biphasic systems (ABS) are formed from solutions containing a single metal element, HCl as the acid, and using either [P44414]Cl or PEG as biphasic inducer. We focused on the influence of the metal, in particular on the contribution coming from the type of metal used and on its concentration. Furthermore, the influence of temperature has been taken into consideration for industrial needs. Finally, we reviewed past literature which proposed some possible explanations and we discussed these under the light of our experimental results.

Experimental Section Chemicals

Polyethene glycol with an average molecular weight of 600 (abbreviated as PEG-600) was acquired from Acros Organics. The ionic liquid tributyl tetradecyl phosphonium chloride, [P44414]Cl, was acquired from Interchim (Montluçon, France). The declared purity was > 95%. Some basic physicochemical properties of PEG-600 are reported in the supplementary materials. The hydrochloric acid, HCl, (37 wt% = 12 mol/L, in water) was acquired from Sigma-Aldrich. The following hydrated salts have been used: NiCl2.6H2O pure at 98% acquired from Rectapur, CrCl3.6H2O pure at 98% acquired from Fluka, FeCl2.4H2O pure at 98% and FeCl3.6H2O pure at 99% were acquired from Merck. All the chemicals were used without further purification. The water used in all experiments was passed through a Milli-Q apparatus purification system commercialized by Merck (18MΩ). AAS (Atomic Absorption Spectroscopy) single element standard solutions (1000 mg/L) were acquired from Perkin Elmer for Cr and from Chem-Lab for Fe and Ni.

Sample preparation

In order to investigate the effect of large amounts of metal ions onto the biphasic behaviours of the systems [P44414]Cl /HCl/H2O and PEG-600/HCl/H2O, aqueous acidic solutions of Ni(II), Cr(III), Fe(II) and Fe(III) have been prepared in HCl/H2O 37 wt%, at metal concentrations below their maximum solubilities, as described in Table 1. Weights have been measured with a balance (Precisa gravimeters AG ± 0.0001 g), and volumetric flasks have been used to prepare the solutions. a : estimated value for the chloride salt in HCl 37 wt%.

Each solution was left under stirring at 700-800 rpm with a magnet overnight, until total dissolution.

Electrospray Ionization-mass spectrometry measurements

The different species present in the various stock solutions were detected by Electrospray Ionization-Mass Spectrometry (ESI-MS) using Bruker Amazon Speed apparatus. The working temperature chosen for the experiments was 40°C.

Phase diagrams: Turbidity and battle ship methods

The binodal curves were obtained with two different methods: the traditional turbidity method 9 and a new method proposed by our research team, which will be referred to as the 'battle ship method' in the following.

For the turbidity method, it is more convenient to work with liquid aliquots of low viscosity. The IL or the polymer can be either solid or liquid. Therefore, in a first step, a small amount of water was added to either the IL or the polymer in order to ease their handling. Then a known mass of the moistured IL or polymer was poured into a beaker, constituting the initial limpid monophasic solution. Then, the acidic solution was added dropwise to the system, under stirring, until the appearance of turbidity, which indicated the biphasic state creation. The turbid appearance of the sample is due to the fact that the two phases are not fully separated yet. A known amount of water was then added to the system until the mixture became transparent again. As there was systematically a rise in temperature during the addition of water and/or the acidic solution, consistent with the exothermic behaviour of such mixtures, stabilisation of the temperature was checked before the addition of the following reagent. All the weights were determined using an analytical balance Precisa gravimeters AG, with an accuracy of ± 0.0001 g and the procedure was repeated several times to build the curve. Experiments were performed at a controlled temperature of T = (25 or 50 ±1) °C by the use of a thermostatic bath.

For the battle ship method, several samples were prepared in glass vials by mixing different amounts of polymer or IL, water and stock solutions of acid and metal salts. Then the temperature of the vials was controlled in the range 25 °C -50 °C by the use of a water bath. At the given temperature, a visual observation easily allowed sorting the samples as either monophasic or biphasic. The battle ship method was chosen because it allows obtaining data faster than the turbidity method, in particular, when the temperature investigation is required. By transporting all the samples from the bath at 25°C to another bath at 50°C, it was possible to define the biphasic or monophasic state of the samples, after leaving them 30 minutes in each bath. In the turbidity method case, it is necessary to perform a new experimental session if different temperature conditions are taken into account, so the time required to perform the turbidity experiments increases. Furthermore, another time-consuming aspect in the turbidity method is due to the waiting time between one drop and the following one in order to re-stabilize the temperature within the solution.

The uncertainty of the turbidity method is related to the ability of the operator to well-distinguish between the biphasic or the monophasic behaviour of the sample in the vicinity of the binodal curve. In particular, the uncertainty is even linked to the number of drops (1 or 2) to pass from one region to the other. For the battle ship method, the uncertainty is due to the reasonable number of samples prepared by the operator to confirm with exactitude the position of the binodal curve. The two methods have been proved to give coherent experimental results (see Figure 8).

System notation and graphical display

In the following, the prepared systems are noted as In order to compare data obtained with different metals and/or oxidation states, the 2D graphical display has been chosen, with IL or PEG-600 (in wt%) on the y-axis and HCl wt% on the x-axis. 10 The amount of water is the sum of ultra-pure water added, the water present in the hydrochloric acid, in the hydrated metal salts and in the IL or in the polymer. Compared to other components the quantity of metal ions in the IL-system is negligible (≤ 1%wt), while in the polymer system it ranges from 0% to 2 wt % (see suppl. materials).

Sample characterisations

Some samples being under a biphasic state at 25 °C were agitated and left overnight at 25 °C. Then the coexisting phases were carefully separated and weighed. The determination of the metal concentrations was carried out by Atomic Absorption Spectroscopy (AAS) using a Perkin Elmer Pinaacle 900F apparatus with an accuracy of ± 0.5%. The measurements were accomplished by calibration curves using mixed standard solutions. All calibration curves were based on six standards, including a blank. The calibration ranges were selected within 1 mg/L to 50 mg/L range (1 -4 -10 -25 -50 mg/L). Standard solutions for AAS analyses were prepared by diluting the commercial 1000 mg/L mixed element solution for each element in 250 mL flasks. The water content of the IL was determined by thermogravimetric analysis (TGA -Mettler Toledo, with an accuracy of 0.0025%) The initial water content in all IL samples was found to be less than 3% of the total mass. The water content of the polymer was determined by Karl-Fischer titration. It was found to be below 25 ppm.

Results

IL-based systems

Figure 1 displays the binodal curves obtained for several initial Cr(III) concentrations ranging from 0 to 15 g/L. The binodal curve of the system composed of [P44414]Cl/[HCl 37wt%]/H2O was compared with the previous one from Mogilireddy et al. 10 As can be seen in Figure 1, the two binodal curves obtained without Cr and performed with the same IL supplied by two different producers do not superimpose. This difference between the curves without metal ions is ascribed to the different providers (i.e. Cyphos® IL 167-Cytec 10 versus Interchim, this work). According to the literature, phosphonium based ILs are prepared by nucleophilic addition of tertiary phosphines to haloalkanes. 11,12 The used phosphines can contain several isomers and other impurities (such as phosphine oxides) that can then be found in the resulting IL 12 and depending on their quantity influence their extraction properties. In Figure 1 two different providers have been compared as the supplied products had different purities. The different level of impurities is probably responsible of binodal curves shifts, although no information on this particular phenomenon has been found in the literature. Fortunately, this observation did not impact the results of this study as only Interchim's product has been used in this work. In contrast, it has been checked that using different HCl providers (i.e. Fluka and Sigma Aldrich) does not induce discrepancies in the binodal determinations (see Figure S1, supplementary materials). The addition of Cr(III) to the solution leads to an increase in the biphasic domain of the system, shifting the binodal curve to the left side (i.e. lesser amount of HCl is needed to promote biphasic regime), while the shape of the curves does not show any significant change. The more pronounced is the initial Cr(III) concentration, the more are the curves shifted to the left and thus less HCl is necessary to induce the phase separation. The experimental points corresponding to Cr(III) are always on the left of the points corresponding to Ni(II) for the same concentration of metals. It seems, that chromium(III) has always a higher capacity than nickel(II) to induce the biphasic system. The experimental curves also show that as the metal concentrations are increased, the difference between the curves of the two metals is more significant. Molecular weight of Ni (58.69 g/mol) is slightly higher than the molecular weight of Cr (51.99 g/mol), so the difference is of ca. 11% and may explain part of the observed differences. However, this should induce a constant effect over the studied range of metal concentrations, which is not experimentally observed. Therefore, the difference cannot be solely ascribed to the difference of molar weight of the two studied components and other phenomena should be considered. Figure 4 and Figure 5 display, respectively, the binodal curves for the systems [P44414]Cl/[Fe(II)+HCl 37 wt%]/H2O and [P44414]Cl/[Fe(III)+HCl 37 wt%]/H2O obtained for several Fe concentrations. A rather particular behaviour is seen when Fe(II) or Fe(III) is used instead of Ni(II) or Cr(III). There is still an increase in the biphasic domain of the system when the Fe concentration is increased but there is also a substantial change in the shape of the curve as compared to curves obtained for Ni(II) or Cr(III).

In general, the binodal curves found in the literature are smooth decreasing curves, oriented from top left to bottom right. Curves presenting this kind of deformation have been scarcely reported in the literature. Two IL-based ABS binodal curves with this characteristic "onion shape" were reported by Neves et al. 13 and Mogilireddy et al. 10 However, in the former case the curves are deformed under the effect of the IL, namely by number of alkyl groups present at the cation, the cation side alkyl chain length and the presence of double bonds, aromatic rings and hydroxyl groups on this alkyl chain. In the latter case, the curves are deformed under the effect of the temperature of the system. By contrast, the deformation of the curves observed in Figure 4 and 5 is simply obtained by raising the Fe concentration in the solution at fixed temperature. Moreover, the elbow of these curves is oriented towards right in an opposite direction compared to Mogilireddy et al. 10 , whose curves were oriented towards left.

Regarding the repartition of different elements of the system, the Atomic Absorption Spectroscopy (AAS) analyses performed for systems comprising 25 wt% of HCl and 30 wt% of

Polymer-based systems

By using PEG-600 instead of the ionic liquid [P44414]Cl, no biphasic behaviour is observed for the system PEG-600/HCl 37 wt%/H2O whatever its composition, as ranges from 0 wt% to 99 wt% of PEG-600 and from 0 wt% to 37 wt% of HCl have been explored. Similarly, the systems PEG-600/[Me(x)+HCl 37wt%]/H2O with Fe(II), Ni(II) and Cr(III) are monophasic at 25 °C and at 50 °C, whatever the composition (see Table S19 in the supplementary materials for all the compositions investigated). As well as in the case of the IL-system, the binodal curves obtained for the polymer-system with Fe(III) at 50 °C (Figure 8) present a different shape compared to the classical binodal curves found in the literature. [14][15][16] The AAS analyses performed for systems comprising 25 wt% of HCl and 30 wt% of PEG-600 show that 50% of Fe(III) remains in the aqueous phase. The calculation was performed considering an arbitrary volume repartition of 95 wt% of upper phase (aqueous phase) and 5 wt% of lower phase (polymer phase) due to the difficulty to quantify the low amount of bottom phase obtained, starting from a total volume of 10 mL of sample. This is thus the second time in this article when the deformation of the binodal curve is linked to an extraction phenomenon.

Discussion

The effects of metal salts observed by us are very uncommon in the literature. To the best of our knowledge, only two papers have evidenced changes in the cloud point temperature of a system by addition of rather large amounts of a metal salt or an oxide: Rim et al. 17 evidenced the effect of large Cr(III) nitrate additions (from 0 to 10 g/L) in the cloud point of an aqueous/surfactant system while Fagnant and co-workers 18 got a decrease of the cloud point temperature by ca. 20 °C by adding up to 4 wt% of Nd2O3 in the HbetTf2N/H2O system. However, these two systems are somewhat different from the current work. Our data address several aspects of the impact of high metal ion concentrations onto the binodal curves for one phosphonium IL-based and one PEG-based ABS. Considering the different nature of [P44414]Cl and PEG-600, the latter being a neutral molecule while the former is formally a salt, we have divided the discussion into two parts, for these two different systems.

[P44414]Cl-based ABS

The fact that metal salts could be part of IL-based ABS is not new. As reviewed by Freire and co-workers 19 some examples with Ca(II) and Mg(II) can be found in literature. Moreover, ABS containing Al(III) salts 20 have also been described. Yin et al. investigated ABS composed of ILs and either Rb(I) or Cs(I) 21 . The amounts of metal salts in such systems are in the range of ca. 5 to 45 wt% and the ILs used belong mainly to the imidazolium family, although ILs constituted by phosphonium and pyridinium cations can also be found. IL-based ABS induced by Sr(II), Eu(III) and Cs(I) have also been the topic of molecular dynamic simulations 22 . However, these systems can only bear metal ions that are not liable to hydrolysis because their working pH is close to neutrality, so the variety of metal elements composing them is somehow limited. On the other hand, metal salts, introduced as traces in already formed ILs-based ABS, experience a partition between the upper and lower phases. This is in turn used to perform selective extraction, with numerous examples involving Sc(III) [START_REF] Depuydt | [END_REF] , Cr(VI) 23 , Ru(III) 24 , Co(II) versus Ni(II) 25 , Ag(I) versus Cd(II) 26 , and Cd(II) versus Co(II), Cu(II), Fe(III) and Zn(II) 27 . Again, imidazolium, phosphonium and ammonium ILs' families are the most studied. Similarly, these systems are not compatible with metal ions suffering hydrolysis. More recently, the extraction of metal ions, i.e. Pt(IV) and Fe(III), at the trace levels, has been performed in novel AcABS acidic ABS 8 (AcABS).

Our study differs markedly from these previous works for two main reasons: i) the presence of HCl does prevent hydrolysis of the metal ions; ii) the metal ions, present in large amounts, can be regarded as modifiers of the original ABS composed of [P44414]Cl, HCl (at 37 wt%) and H2O, and not as trace level solutes. First, the addition of Ni(II) and Cr(III) salt, at 25 °C, leads to an enlargement of the biphasic area, in comparison with the system in the absence of metal ions (Figure 1 and Figure 2). This effect is metal concentration-dependent, being more significant above ca. 1 g/L of metal ion, increases with concentration and is more pronounced for Cr in comparison to Ni (Erreur ! Source du renvoi introuvable.). Second, one of the striking results of this work is the change in the shape of the binodal curves upon Fe(II) or Fe(III) addition (Figure 4 and Figure 5), which tends to disappear at a higher temperature (see Figure 6). At 25 °C, the effect of Fe(II) or Fe(III) addition onto the shape of the binodal curves is different from that observed for Ni(II) or Cr(III) (this work) or Na(I) 28 . It is evident that the physico-chemical mechanisms behind the effects of the salts in the phase demixing cannot be solely ascribed to the oxidation state of the metal and are far more complex. Data displayed in Figure 4 and Figure 5 evidence a rather unusual phenomenon as soon as Fe ions are added to the system. In the absence of Fe ions, the sample (point A, Figure 5) is monophasic. Adding increasing amounts of pure IL to this sample will move the point towards a pure IL composition (reached upon infinite addition of pure IL only), along the arrow and the sample will remain in a monophasic state whatever the amount of added IL. By contrast, in case Fe(III) ions are added in HCl at 2.5 g/L, point A corresponds to a biphasic region and by addition of pure IL amounts, the sample will change from biphasic to monophasic along the arrow at ca. 15 wt% of HCl and 15 wt% of IL. Increasing the amount of Fe(III) ions will modify the values at which the sample will turn monophasic, stressing the complexity of the phenomena involved in such biphasic/monophasic behaviour. There is another aspect of the binodal curves in the presence of Fe(III) ions that can be deduced from the plots in Figure 5. Extrapolations of the three binodal curves converge towards an equivalent point on the x-axis, corresponding to the chemical composition of ca.2 wt% HCl and no IL (see dashed-dotted lines in Figure 5). However, such an intersection with the x-axis is chemically impossible, as it would mean that a sample composed of water and, for example, 5 wt% of HCl in water would be biphasic, which is not the case. Similar reasoning leads to the conclusion that the binodal curves cannot cross the y-axis either. As the binodal curves cannot present a critical point as for the gas-liquid equilibrium, the only possibility to extend any of the binodal curves in Figure 5 in a chemically meaningful way is to have an onion-shaped curve as experimentally observed in Figure 6 for [Fe(II)] = 20 g/L at T = 25°C. In this case, starting from a monophasic sample composition corresponding to point B, adding increasing amounts of pure IL will first turn the sample to a biphasic state (C) and in a second step, back to a monophasic state (D), along the arrow B, C, D. See another comment in supplementary materials (Figure S2).Furthermore, considering the contribution of metal ions as a function of the acid concentration (in wt%), the binodal curves for the systems containing Ni(II) and Cr(III) are parallel, while for Fe(II) and Fe(III), the curves do not present a parallel tendency. This can be confirmed by plotting HCl concentration at the binodal curve as a function of metal concentration at different IL wt% (20/30/40). The plots are straight lines with slopes almost identical for Ni and Cr, while slopes differ markedly for Fe(III) and Fe(II) (see Figure S2 of the supplementary materials). works have been devoted to the empirical fitting of classical binodal curves. 29 These empirical expressions have already been shown to be irrelevant for the fitting of onion-shaped curves as those evidenced in this work 10 . On a more theoretical aspect, several papers have dealt with the formation mechanism of IL-based ABS. Some explanations focus on entropic reasons while others put the emphasis on Gibbs free energy. Recently, Schaeffer and co-workers 30 suggested an explanation for the ABS formation in the [P44414]Cl/HCl/H2O system and the effect of NaCl addition based on the comparison of entropy of hydration of NaCl and HCl. Using dynamic molecular simulations and experimental data, they supported the idea that the phenomenon is related to a competition for the water molecules between Na + , [P44414] + and H3O + , together with the relative interactions occurring between all these ions. For these authors, [P44414]Cl forms micelles, the size of which is increased by the presence of Na + . By contrast, the presence of H3O + has no direct effect on the micelles size but impacts micelles interactions, bringing water molecules to the micelles and thus being unfavourable to ABS formation. Due to these different interactions arising from NaCl or HCl addition, the system [P44414]Cl/HCl/H2O is less prone to ABS formation than ABS containing other chloride salts, in particular, NaCl. Indeed, Schaeffer et al. 1 proposed to use a mixture of NaCl and HCl instead of a pure AcABS only with HCl. In this way, the metal extraction efficiency is preserved and a lower amount of HCl is used. To summarise, additions of NaCl induce a shift of the binodal curve of the system [P44414]Cl/HCl/H2O to the left, with no change in the shape of its binodal, while keeping a reasonable amount of HCl allows extraction of metal ions prone to hydrolysis. In our work, chloride salts of Ni(II), Cr(III), Fe(II) and Fe(III) were used instead of Na(I). Based on literature data 31 , the order of conventional standard molar entropies of hydration of the studied ions (ΔhydrSi°conv, at 25°C and expressed in JK -1 mol -1 ) is as follows: Na(I) >> Ni(II) ≥ Fe(II) > Cr(III) ≥ Fe(III). As suggested by Schaeffer et al. 1 , the purpose of our work was to extend the range of chloride salts and to evaluate their effect on the phase separation. However, as demonstrated in Erreur ! Source du renvoi introuvable., at the same concentration the ABS formation is favoured in the case of Cr compared to Ni. Moreover, the unusual shape of Fe containing system is not well explained by this parameter either and hydration entropy parameter fails thus to explain our experimental results. For example, the binodal curve of the system with 5 g/L of Fe(III) is an almost vertical linear curve (see Figure 5), which crosses the onion-shaped binodal curve of the Fe(II)-based ABS (Figure 4). It is important to note that the ΔhydrSi°conv values for Ni(II) and Fe(II) are very similar (-307 JK -1 mol -1 for Ni(II) and -318 JK -1 mol -1 for Fe(II)), as well as both Cr(III) and Fe(III) ions (-448 JK -1 mol -1 for Cr(III) and -490 JK -1 mol -1 for Fe(III)), but the shapes of the corresponding binodal curves are fully distinct, either between Ni(II) and Fe(II) or between Cr(III) and Fe(III). These differences in the shape of respective binodal curves indicate that ΔhydrSi°conv is not the only parameter to be considered. The second type of explanation for the ABS formation is related to the Gibbs free energy of hydration of ions (ΔhydrG°). Marcus et al. 32 determined the ΔhydrG° of a wide range of ions and the concept of the hydration of metal ions. In 2007, Bridges and co-workers 33 formed salt/salt ABS composed of K3PO4, K2CO3, (NH4)2SO4, and hydrophilic imidazolium-, pyridinium-, phosphonium-based ILs. They demonstrated that, like in the polymer-salt ABS, the salting-out strength of the highly charged inorganic salts (i.e. water-ion interaction stronger than water-water interactions) follows the Hoffmeister series which can be related to the ions' Gibbs free energy of hydration (ΔhydrG°). The molar Gibbs energy of hydration of the studied ions (ΔG * hydr.) differs (Ni 2+ = -1980; Cr 3+ = -4010; Fe 2+ = -1840; Fe 3+ = -4265, all expressed in kJmol -1 ) and the values follow the order: Fe(II) > Ni(II) > Cr(III) > Fe(III). The order of this series is identical to the one of the series based on entropy considerations, except for Ni(II) and Fe(II), which are inverted. As a consequence, the points raised above (shape of the binodal curves and atypical behaviour of Fe(II) versus Fe(III)) remain unexplained, and thus the conclusion is that Gibbs free energy considerations are not sufficient to explain our whole data set. Apart from the ΔhydrSi°conv or Gibbs free energy possible involvement in the formation of ABS, the chloride ion is another important partner in the systems under study which role should not be minimized. Onghena et al. 25 worked with [P44414]Cl/NaCl/H2O while Gras et al. 8 used [P44414]Cl/HCl/H2O, both of them to separate Co(II) and Ni(II). These two studies pinpoint the decisive effect of Co(II)-Cl -complexation and anionic species formation for its extraction to the IL-rich upper phase via an anion exchange, while Ni remains in the aqueous phase as a cation due to its limited coordination with chloride anions. In these works, the concentrations of Co and Ni were in the traces range 8 or ca. 1 g/kg 25 , to be compared to our maximum value equal to ca. 12.5 g/kg. We have also used chloride salt and can thus confirm, that the increased concentration of Ni used in our work does not affect the observed results, which are similar to the previous ones, i.e. Ni remains in the lower aqueous phase and is not extracted. Therefore, one possible additional phenomenon at work in the formation of [P44414]Cl/[Me(x)+HCl 37 wt%]/H2O ABS is the complexation of metals with chloride and evolution of their chemical speciation caused by concentration and temperature changes of the system. Values for the first complexation constant, K1, for various metal ions and several temperatures can be found in the literature. [START_REF] Sillén | Stability constants of metal-ion constants[END_REF] Unfortunately, there's a lack of reliable data related to the chloride systems, namely when the influence of increasing temperature is looked for. We have only been able to found these values for perchlorate based systems: For Fe(III) in 1 mol/L HClO4, values range from K1 = 0.36 (14.3-16.3 °C); 0.46 (25 °C); 0.49 (30.1 °C) until 0.68 (44.3 °C). The K1 increases with the temperature, which can be correlated with the enlargement of the biphasic region, i.e. when the temperature was changed from 25 to 50 °C. However, the involved physico-chemical phenomenon related to this correlation is not clear. As a consequence of the formation of FeCl4 -, the new compound [P44414][FeCl4] is thus theoretically formed, although there is no proof yet that the two ions are associated. Other iron-containing ILs, based on dialkylimidazolium cations, have been shown to display a thermomorphic behaviour in pure water, with a Lower Critical Solution Temperature (LCST) [START_REF] Xie | [END_REF] . To the best of our knowledge, a LCST behaviour for [P44414][FeCl4] has not been reported but could be involved in the change of the binodals we observed. Similarly, considering Cr(III) in 4.4 mol/L HClO4 medium, following values evidence an increase in K1: K1 = -0.62 (30 °C); -0.42 (46.3 °C); -0.19 (63.5 °C) until 0.16 (95.4 °C). Finally, comparing the chloride complexation constants of Cr(III) and Ni(II) in almost identical media (K1 for Cr(III) = 0.18 measured in 1 mol/L NaClO4 medium and K1 of Ni(II) = -0.25 measured in 1.5 mol/L NaClO4 medium), it is observed that it also correlates with the ability of Cr(III) to display a larger biphasic area than Ni(II) (Figure 2). However, as highlighted previously, the involved physico-chemical phenomenon remains unclear. Moreover, the difference in complexation constants do not explain the particular shape of binodal curves for iron containing systems. The deformation may be related to the extraction phenomenon, but it should be further investigated. These comparisons are thus only limited ones and are not substantiated by a deeper theoretical approach.

Thus, whatever the explanation for ABS formation as discussed above, none of these can fully explain our data sets. Further computational studies would be very important in revealing the main mechanisms behind their phase separation, in particular, why Fe containing systems display binodal curves of a very different shape as compared to Ni and Cr containing systems characterized by more traditional curve shapes.

PEG-based ABS

Regarding PEG 600 based systems, our data showed that PEG-600/HCl 37 wt%/H2O system is never biphasic, neither at 25 °C nor at 50 °C. Four metal salts were added as adjuvants to verify whether these elements can induce the phase separation. Although the addition of Fe(II), Ni(II) and Cr(III) salts did not induce the formation of a biphasic region, interestingly Fe(III) acted as a biphasic inducer (see Figure 7). Our data have already pinpointed Fe(III) as specific IL-based ABS modifier (owing to the shape of the binodal curves Figure 5) and this ion is also peculiar in the case of PEG-based ABS. However, one can notice differences between the PEG-based and IL-based systems involving Fe(III) ions as far as the temperature is concerned. Actually, as T increases from 25°C to 50°C, the onion shape behaviour becomes more obvious for the IL-based systems (Figure 5). As already discussed for the IL-based systems, these data cannot be described by using traditional empirical models, owing to the onion shape of the binodal curves. This remark is also valid for the Setschenow equation (Ni et al. 36 ), another empirical function that is nevertheless related to some physicochemical parameters of the system and has been proposed for the mutual solubility of an electrolyte and a polymer. By contrast to the IL-based ABS, one can find many works devoted to PEG-based ABS and the possible reasons behind the formation of the biphasic state or its absence, as in the case of PEG-600/[HCl 37 wt%]/H2O. Among the proposed hypotheses can be cited those referring to the changes in the hydration of the polymer or to the existence of strong interactions between multivalent cations, particularly metal ones, and ether oxygens of PEG and will be discussed below under the light of our data. First, the absence of biphasic state for mixtures of PEG-600, HCl and water should be explained. Huddleston et al 37 stated that the formation of a biphasic regime by dissolving water-soluble polymer and inorganic salts results from the competition for hydration between the polymer and the salts. This is dependent on the relative hydrophobicity of the polymer (based on polymer type or average molecular weight) and the salting-out strength of the inorganic salt ions, i.e. ions' Gibbs free energies of hydration 38 . Water is the main component in this system and PEG-600 is highly hydrophilic, interacting actively with 2 or 3 water molecules per each ethylene oxide (EO) unit. As most ionic species, Cl -anions are also highly water-soluble. Therefore, to induce a phase demixing, the salt should exhibit a salting-out aptitude enough to dehydrate, at least partially, the PEG-600. Although hydrogen chloride (HCl) when dissolved in water behaves as a strong electrolyte, its preferential hydration is not strong enough to dehydrate and expel the hydrophilic PEG-600 to another incompatible phase. Thus, all compounds are remaining dissolved in a monophasic aqueous solution. Additionally, as demonstrated by Tomé et al. 39 , it has also to be considered that Cl - anions can establish an equivalent of hydrogen bonds with the -OH end group of the PEG polymers, favouring their mutual solubility in water. Therefore, in addition to the water solvation of the ether groups of the oxygen chain, the formation of ABS when mixing aqueous solutions of PEG and chloride-based salts is also a result of the ability of the PEG terminal groups to preferably interact with water or the chloride anion (Pereira et al. 40 ). Second, the biphasic inducing property of Fe(III) should be examined, together with the inefficiency to do so of the other metal ions tested in our work. As already discussed for the IL-based data, it is known that the complexation constant 33 of Fe-Cl is higher than the Ni-Cl or the Cr-Cl complexation constants. The charge density [START_REF] Rayner-Canham | Descriptive inorganic chemistry: Fifth edition[END_REF] of the metal ions is also quite different (Ni 2+ = 82; Cr 3+ = 261; Fe 2+ = 181; Fe 3+ = 349, all expressed in C mm -3 ) and follows the order: Ni<Fe(II)<Cr(III)<Fe(III). If the behaviour is influenced by the charge density, then the ABS formation "ability" would follow this order (in both cases, i.e. IL and PEG), which is not the case. Moreover, it does not explain the iron case particularities. Finally, the molar Gibbs energy of hydration of ions (ΔG * hydr.) values already given in the previous section differ markedly for the studied ions, whereas very close values are ascribed in the literature for Ni and Fe(II) and then again for Cr(III) and Fe(III). So if the biphasic behaviour and partition phenomenon were governed solely by this parameter, one could expect that Ni and Fe(II) will behave similarly and then again Cr(III) and trivalent iron, which is clearly not the case. To go a step further, one has to recall that the formation of a biphasic state imposes electro-neutrality to both the upper (PEG and iron-rich) and lower phases. From the electrospray ionization -mass spectrometry (ESI-MS) analyses, the main species present in the acidic solution of Fe(III) and HCl (37 wt% = 12 mol/L) is [Fe(III)Cl4] -(Figure S3 supp. materials). This implies that the [Fe(III)Cl4] -species, which is responsible for the biphasic formation, is accompanied by a positively charged species during the phase separation. In our system, the only available cation is the H + . Therefore, one has to consider at the same time the ability of H + and [FeCl4] -to be trapped in the PEG-rich phase. Regarding the cationic moiety, Sartori et al. [START_REF] Sartori | [END_REF] described PEG's ability to absorb ions from solutions containing an alkali-metal cation (Li + , Na + , Rb + , K + and Cs + ) and a series of anions including Cl -. Furthermore, they showed that the polymer strongly interacts with the cations they examined. This leads to the formation of a positively charged surroundings that "attracts the anions (…) to the vicinity of the PEG molecule" [START_REF] Sartori | [END_REF] . Although H + was not studied in the work of Sartori et al., it is reasonable to assume that the proton plays the role of an alkali metal cation in our system. However, this first hypothesis does not exclude the strong contribution of the anion to the system partition. Bulgariu et al. 43 suggested that chloride anionic species based on Zn(II), Hg(II) and Cd(II) are ''fixed'' by the O-groups present in the ether chain of the PEG by ionic forces. It could thus be envisioned that the same phenomenon occurs with [Fe(III)Cl4] -. As shown in Figure 10, the chemical structure that can be proposed is the intramolecular bonding between two polymer chains of PEG that are connected via the water molecules.

The anionic iron species interacts then with the oxygens present within the polymer. It is important to underline that the interaction between Fe and O is not based on a covalent bond but is rather an ionic interaction due to the differences in the electronegativities of the two atoms. This is supported by the ESI-MS results that showed the absence of a stable covalent bond between the PEG and the metal ions (Figure S4 Supplementary materials). In this sense the schematic view, as displayed in Figure 10 is in line with the comment of Sartori and co-workers [START_REF] Sartori | [END_REF] , who pinpointed that "the anions remain mainly outside the polymer coil". Furthermore, it seems that in a high concentrated HCl medium, the structure of the Fe(III) is an equilibrium between an octahedral (Figure 10-C) and a tetrahedral structure (Figure 10-D) 44 .

Conclusions

In the absence of metal ions, the mixture [P44414]Cl/[HCl 37 wt%]/H2O is an ABS, while the corresponding system with PEG-600 instead of IL is not. In this work, we investigate the impact of 4 different types of metal ions: Fe(II)/(III), Ni(II) and Cr(III) onto the behaviour of these mixtures. In the case of IL, it was possible to obtain a biphasic system with all four different metal ions. The peculiarity these systems lies in the particular onion shape form that presents the binodal curve of the system with Fe(II)/(III). Regarding PEG-600-based systems, only Fe(III) can induce a biphasic system in the presence of HCl, and also in this case the binodal curve has an atypical shape. As far as the efficiency of the extraction of these systems is concerned, 80 wt% of Fe(II) and 100 wt% of Fe(III) are extracted in the IL phase, while 50 wt% of Fe(III) is extracted in the polymer phase, considering the difficulty to determine the distribution of metal ions for the PEG-600 systems, due to the small remaining volume of the polymer phase. The investigation of the influence of factors such as the presence of metals and the temperature on the binodal curves of ABS is important at the fundamental level for the understanding of these systems. In particular, close to the elbow of the onion-shaped binodal curve, addition of PEG will turn the system from monophasic to biphasic and finally back to monophasic for rather small amounts of polymer. This means that the sample is susceptible to small concentration changes and this could be an interesting experimental and theoretical point to study in the near future. On another hand, these investigations have also a very pronounced practical aspect, given the high potential for industrial use of this knowledge. There are many industrial aqueous liquid wastes that contain a very high concentration of iron. Our work demonstrates that there is a very cheap and efficient way to significantly reduce the amount of iron ions in these wastes by adding PEG polymer. A clear advantage is that the more concentrated the iron is, the lower amount of PEG is required to remove this element from its solution. Once iron is extracted, it should be easier to recover the other minor but valuable elements possibly present, either by traditional means (electrodeposition, precipitation etc.) or by inducing the formation of another ABS system. Furthermore, it is already known 45 that increasing the molecular weight of the polyethene glycol, the hydrophobicity of the polymer increases, so this is another parameter to play with. Work on these lines is currently under progress in our laboratory.

Figure 1

 1 Figure 1 Binodal curves of the systems: [P44414]Cl/[HCl 37 wt%]/H2O (IL= Cytec) (▲) 10 ; [P44414]Cl/[HCl 37 wt%]/H2O (IL= Interchim) -this work (Δ); [P44414]Cl/[Cr(III)+HCl 37 wt%]/H2O -[Cr(III)] = 2.5 g/L (•); [P44414]Cl /[Cr(III)+HCl 37 wt%]/H2O -[Cr(III)] = 5 g/L (○); [P44414]Cl/[Cr(III)+HCl 37 wt%]/H2O -[Cr(III)] = 10 g/L (■); [P44414]Cl/[Cr(III)+HCl 37 wt%]/H2O -[Cr(III)] = 15 g/L (□) at 25°C.

Figure 2

 2 displays the binodal curves obtained for several initial Ni(II) concentrations ranging from 0 to 15 g/L.The same behaviour is observed for both Cr(III) and Ni(II) containing systems, i.e. an increase in the concentration of metals in the solution leads to a growth of the biphasic domain of the system. However, when comparing identical concentrations of Ni(II) and Cr(III) in the same graph, as shown in Erreur ! Source du renvoi introuvable. for 5 g/L and 15 g/L, it is relevant to notice significant differences in the increase of the binodal region when Ni(II) is changed to Cr(III).

Figure 2

 2 Figure 2 Binodal curves of the system: [P44414]Cl/ [HCl 37wt%]/H2O -[Me(x)] = 0 g/L (Δ); [P44414]Cl/[Ni(II)+HCl 37 wt%]/H2O -[Ni(II)] = 2.5 g/L (•); [P44414]Cl/[Ni(II)+HCl 37 wt%]/H2O -[Ni(II)] = 5 g/L (○); [P44414]Cl /[Ni(II)+HCl 37 wt%]/H2O -[Ni(II)] = 10 g/L (■); [P44414]C /[Ni(II)+HCl 37 wt%]/H2O -[Ni(II)] = 15 g/L (□) at 25°C.

Figure 4

 4 Figure 4 Binodal curves of the system [P44414]Cl/[Fe(II)+HCl 37 wt%]/H2O at: [Fe(II)] = 0 g/L (Δ), [Fe(II)] = 1 g/L (■), [Fe(II)] = 10 g/L (□) and [Fe(II)] = 15 g/L (•) at 25°C. Dashed lines (---) are only a guide for the eye.

Figure 3

 3 Figure 3 Binodal curves of the systems: [P44414]Cl/[HCl 37 wt%]/H2O, [Me]= 0 g/L (Δ); [P44414]Cl/[Ni(II)+HCl 37 wt%]/H2O at 5 g/L (■) or 15 g/L (□) of Ni(II); [P44414]Cl/[Cr(III)+HCl 37 wt%]/H2O at 5 g/L (•) or 15 g/L (○) of Cr(III) at 25°C.

  [P44414]Cl show that 80% of Fe(II) and 100% of Fe(III) are extracted in the IL-rich phase (upper phase) while Ni(II) and Cr(III) are not extracted. One can thus wonder whether the binodal curves deformation is related or not to the metals' extraction. Finally, Figure 6 (obtained via the battleship method explained in the Experimental section) highlights the influence of the temperature in the system [P44414]Cl/[Fe(II)+HCl 37wt%]/H2O at [Fe(II)] = 20 g/L. The biphasic area significantly increases as T is increased from 25 °C to 50 °C.

Figure 6 Figure 5 A

 65 Figure 6 Phase diagram obtained with the battle ship method for the system [P44414] Cl/[Fe(II)+HCl 37wt%]/H2O -[Fe(II)] = 20 g/L. Monophasic samples at both T = 25 °C and 50 °C (■), biphasic samples at both T = 25 °C and T = 50 °C (▲)and samples that become biphasic passing from 25 °C to 50 °C (○). Experimental points B, C, D. The arrow () indicates the displacement direction of the point B, C, D increasing the wt% of IL (see text). Dashed lines (---) are only a guide for the eye.

Figure 9

 9 Figure 9 compares binodal curves of the system PEG-600/[Fe(III)+ HCl 37wt%]/H2O ([Fe(III)] = 10 g/L and 40 g/L) obtained at T = 25 °C and T = 50°C (Please note that only a small portion of the binodal curve from Figure 8 -triangles -is shown in Figure 9 -empty squares). These results evidence, independently of [Fe(III)] concentration, a widening of the biphasic area when the temperature increases.

Figure 8

 8 Figure 8 Phase diagram obtained by battle ship and turbidity method for the system PEG-600/[Fe(III)+HCl 37wt%]/H2O -[Fe(III)] = 40 g/L at 50°C. Monophasic region (•), biphasic region (○), binodal curve obtained by the turbidity method (Δ). The dashed line (---) is only a guide for the eye.

Figure 9

 9 Figure 9 Binodal curves obtained by turbidity method for the system PEG-600/[Fe(III)+HCl 37wt%]/H2O -[Fe(III)] = 40 g/L at 50°C (□) and at 25°C (■) and for the systems PEG-600/[Fe(III)+HCl 37wt%]/H2O -[Fe(III)] = 10 g/L at 50°C (○) and at 25°C (•).

Figure 7

 7 Figure 7 Phase diagram obtained by turbidity method for the systems PEG-600/[Fe(III)+HCl 37wt%]/H2O -[Fe(III)] = 10 g/L (•) and 40 g/L (○) at 25 °C.

Figure 10

 10 Figure 10 Mechanism of PEG extraction of Fe(III). 10-A: inter-chain connection proposed by Bulgariu et al. 42 ; 10-B: Fe(III) connection with the ether group of the polymer; 10-C: octahedral structure of the species (Fe(III)Cl4)-; 10-D: tetrahedral structure of the species (Fe(III)Cl4)-; Adapted from ref. Bulgariu et al. 42 .

Table 1

 1 Concentrations of the metal ions in HCl 37wt% used for the binodal curves determinations and estimated maximum solubility limits.

		Ni(II)	Cr(III)	Fe(II)	Fe(III)
	Metal
	concentration in 37%wt HCl	2.5 -15	2.5 -15	1 -20	2.5 -40
	(g/L)
	Maximum
	solubility	40	50	90	75
	(g/L) a at 50°C

  [P44414]Cl /[Me(x)+HCl 37wt%]/H2O or PEG-600/[Me(x)+HCl 37wt%]/H2O, where Me stands for the metal of interest and x is the corresponding oxidation state. This notation highlights the fact that [P44414]Cl or PEG-600 and, in some cases, ultra-pure water, were added to a stock solution containing a metal salt dissolved in 37 wt% HCl/H2O (cf Table1). The systems in the absence of metals are noted [P44414]Cl/[HCl 37 wt%]/H2O and PEG-600/[HCl 37 wt%]/H2O. Following a previous publication 10 , the reference systems noted [P44414]Cl/[HCl 37 wt%]/H2O and PEG-600/[HCl 37 wt%]/H2O are called quaternary systems, as the number of different species is equal to four: (H + , Cl -, [P44414]

+ , H2O) or (H + , Cl -, PEG-600, H2O) respectively. Adding a chloride metal salt then only increases the number of species by one unit (either Ni(II), Cr(III), Fe(II), Fe(III)) and consequently, the systems [P44414]Cl/[Me(x)+HCl 37wt%]/H2O or PEG-600/[Me(x)+HCl 37wt%/]/H2O, will be called quinary systems.

Acknowledgements

The authors would like to thank Aperam for the financial support to this work. E.S. thanks the financial support of ANRT. E.S. is also very keen to thank Laure Fort, Rodolphe Gueret and Amélie Durand from the Molecular Chemistry Department of Grenoble for their contribution to the ESI-MS' analyses.

Conflicts of interest

There are no conflicts to declare.


Adrien Thibaud

Julien Fasson

Fabrice Arnal

Renaud Sallantin

Emmanuel Dubois
email: emmanuel.dubois@cnes.fr

Emmanuel Chaput

Cooperative Congestion Control in NDN

Keywords: ICN, NDN, QoE, Max-min fairness, Multipath flows, Congestion Control

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

I. INTRODUCTION

A new approach, the Information Centric Network paradigm (ICN), has recently emerged and defines a network layer that is content-oriented instead of location-oriented. Among the ICN architectures, Named Data Networking (NDN) [START_REF] Zhan | Named data networking[END_REF] seems promising and increasingly draws the attention of the research community. NDN uses the mechanisms that made the success of HTTP, CDN (Content Delivery Network) and P2P (Peer-to-Peer network) directly as a basis for the network layer. NDN is a receiver-driven architecture. As in HTTP with its GET message, the user (or the consumer in the NDN terminology) sends an Interest message requesting a piece of data. Multiple producers (as in P2P) and multiple paths might be available and used, but everything is transparent from the end-users point of view. Furthermore, each forwarding node is able to opportunistically cache contents and extra nodes might be set to cache the most popular content at strategical places (as in CDN). NDN design also integrates security: a data packet is intrinsically secured and does not depend on the end points. It thus can be reused for multiple users, facilitating the caching and multicasting of contents.

The challenge of this architecture is to design a more compliant network with user needs through a data-oriented approach. We consider here a network where multipaths are common and that is potentially overloaded (i.e. the global consumers need is above the network capacity). Indeed, as pictured in Fig. 1, consumer A can retrieve its requested Fig. 1: Illustrative network topology content through two different paths. But the network capacity is not able to satisfy consumers A and B simultaneously.

Given this context, our goal is to maximize the Quality of Experience (QoE) of all the users. In this paper, we only consider content-oriented applications that need a targeted rate. The QoE is evaluated through the received rate of the users. A user is increasingly satisfied with the rate he gets (capped by its personal objective rate). The competition of multiple users on the network rises a fairness problem. In our example in Fig. 1, the consumer A is in competition with the consumer B on the R1-R3 path, while the other path could have sufficient unused bandwidth to satisfy consumer A without bothering other users on the congested path. Ultimately, we search to distribute the flows of the users with a fairness concern, through all the paths available and with regards to the resources constraints.

Therefore, the problem can be seen as a joint congestion and fairness problem. In classical IP networks, two methods are used to handle this issue: an end-to-end one and a hopby-hop one. The best known example of the first method is TCP. The intelligence of this approach is located in the sender. The receiver only sends acknowledgment that are used by the sender to evaluate the network congestion level. The goal of the sender is to reach the best rate possible, possibly in an aggressive way. The second method is implemented through AQM solutions (Active Queue Management). For this approach, the intelligence is located in every node on the network. The nodes are able to detect when a congestion occurs and take action to avoid it. On the one hand, end-to-end methods cannot efficiently evaluate congestion phenomenon and tend to increase the rate of the user in order to increase their QoE, and on the other hand, hop-by-hop methods tend to decrease it in order to reduce the congestion. Even if those two kinds of method sometimes implement opposite actions, they actually cohabit in the Internet and have shown some efficiency. We thus believe that a NDN based solution should take the best of these two schemes. However, we think that they should be implemented in a single framework in order to be more consistent and thus, hopefully, effective. Furthermore, multipath retrieving is not natively handled in IP. MPTCP is the TCP solution for multipath, but it only works when one of the ends is multi-homed (with Fig. 1 example, MPTCP would not be feasible).

NDN provides the opportunity to manage multipath delivery on the network level and we are convinced that such a feature should be used in our framework. In this paper, we propose a new solution, Cooperative Congestion Control (CCC), that tackles these joint problems (congestion and fairness) in a more cooperative and effective way. CCC is based on a per node approach where the main elements are: a two ways cooperation between nodes, a local supervision of the output queues and a smart utilization of the multipath possibilities. Combined, these three principles can support a fair distribution of the flows.

The remaining sections of this paper are organized as follows. In Section II, we survey the related work. Then, Section III, we study the theoretical problem. Section IV presents the principles of CCC and how we implement it. In Section V, we present the evaluations of our solution. Lastly, the paper is concluded in Section VI.

II. RELATED WORKS

In term of congestion control, they are two main families of solutions: the end-to-end and the hop-by-hop type of solutions. A third and hybrid solution has quickly emerged since it allows to take advantage of NDN natural hop-by-hop processing while maintaining an end-to-end control like in IP with TCPlike protocols. All the solutions presented here are compared with our proposition in Sec. V.

Interest Control Protocol [START_REF] Carofiglio | Icp: Design and evaluation of an interest control protocol for content-centric networking[END_REF] (ICP) is the best known solution for congestion control, since it is an adaptation of TCP behavior for NDN. It is receiver-driven as well as an end-toend solution. The consumer handles a congestion window for the content to be retrieved. The size of this window evolves using an Additive Increase Multiplicative Decrease mechanism (AIMD). When a Data packet arrives at the consumer, it additively increases the size of the congestion window. This additive increase corresponds to the congestion avoidance phase of legacy TCP: the congestion window increases of one in a round-trip time (RTT). When congestion is detected by a timeout, the consumer decreases the window multiplicatively (divided by two here). The Retransmission Timeout (RTO) in ICP is computed as the mean between the minimum and the maximum of the measured RTTs.

A Practical Congestion Control Scheme [START_REF] Schneider | A practical congestion control scheme for named data networking[END_REF] (PCON) is an hybrid solution that defines how consumer sends its requests (end-to-end) and how nodes in the network handle Data and Interests (hop-by-hop). The end-to-end part is based on a congestion window at the consumer side whereas the hopby-hop part is a forwarding strategy on each NDN nodes. We respectively name them PCON-CS and PCON-FS in this paper. PCON-FS uses the CoDel approach [START_REF] Nichols | Controlled Delay Active Queue Management[END_REF] to detect the congestion: the nodes measure the sojourn time of each packet in their queue. If the minimum detected over a given period is higher than a threshold, the interface is considered as congested. The interface marks Data packets rather than dropping them in order to trigger an explicit adaptation from the upstream nodes. With the marks it receives, the traffic is progressively load balanced on the other available paths. The PCON-CS consumer has the same behavior as ICP: a congestion avoidance phase and the RTO computation from RFC 6298 [START_REF] Sargent | Computing TCP's Retransmission Timer[END_REF]. In addition, a marked Data is considered as a congestion notification and triggers a multiplicative decrease.

Multipath-aware ICN Rate-based Congestion Control [START_REF] Mahdian | Mircc: Multipath-aware icn rate-based congestion control[END_REF] (MIRCC) has similar goals than CCC. It targets to achieve a max-min fairness using the network at its full capacity. For this purpose, the authors propose an adaptation of RCP [START_REF] Dukkipati | Rate Control Protocol (Rcp): Congestion Control to Make Flows Complete Quickly[END_REF] for NDN with multipath compatibility. Their algorithm is partially distributed: every node computes two stamping rates (as in RCP but with a second for multipath support) and each consumer chooses the paths it wants to use and at which rate (with the help of the two stamping rate). As opposed to our solution, MIRCC puts a lot of intelligence in the consumers and less in the nodes.

III. MODEL

In this part, we search the theoretical optimal solution for our problem. For this purpose, we define a model where we compute the fairest flow distribution on the considered network. This will help us to analyze our simulation results. We split our approach in two steps. In the first step, we maximize the throughput of the users and thus their QoE. In the second step, we distribute this throughput fairly to satisfy as many users as possible. Indeed, we prefer an average satisfaction for each user than to have a few users with the maximum QoE and some users with the worst. These two parts represent one optimization problem each and are described in the following sub-sections.

A. Maximum Multi-Commodity Flow problem

The first part is an adaptation of the common Maximum Multi-Commodity Flow problem [START_REF] Hu | Multi-commodity network flows[END_REF]. It can be formulated with the following objective:

max k F k (1)
and the following constraints:

k f k i,j - k f k j,i =    F k i = s k 0 i = s k , t k,l -F k,l i = t k,l , (2)
∀(i, j) ∈ E, ∀l = 1, . . . , L k , ∀k = 1, . . . , K k f k i,j ≤ u i,j , ∀(i, j) ∈ E ( 3
)
where K is the number of competing flow on our network, F k is the total size of the kth flow, L k is the number of nodes providing the kth flow, E is the set of edges of the network, s k is the node requesting the kth flow, t k,l is the lth node providing the kth flow, F k,l is the size of the lth path of the kth flow, f k i,j is the size of the kth flow on the edge (i,j) (i and j are vertices of the network) and u i,j is the capacity of this same edge. (2) represents the flow conservation constraints while (3) represents the capacity constraints. Furthermore, we suppose that our users have explicit rate objectives:

F k ≤ F k obj , ∀k = 1, . . . , K (4)
where F k obj is the objective size of the kth flow. The solution of this optimization problem gives the maximum aggregate throughput for all users and can be formulated as a new constraint:

k F k = z * (5)
where z * is the solution found. We thus define a new version of the optimization problem aiming to optimize fairness.

B. Fairness concern

Despite the fact that the aggregate throughput is maximized, the rate distribution might not be fair. Indeed, one user may have a very good throughput and penalizing another user at the same time. A fair share may decrease reasonably the QoE of this user and increase significantly the one of the unsatisfied users. It is therefore necessary to search for the fairest distribution, but without changing the optimal objective we found in the previous formulation. We decide to use the max-min fairness because it allows our users to get the maximum fair share possible without limiting them to get more if available. The second part of our model is then formulated with this new objective:

max t (6)
and these new constraints:

F k -t ≥ 0, ∀k = 1, .., K (7)
where t represents the minimum of the F k , through the Eq. [START_REF] Dukkipati | Rate Control Protocol (Rcp): Congestion Control to Make Flows Complete Quickly[END_REF]. Solving the optimization problem presented by ( 6) as objective and ( 2), ( 3), ( 4), ( 5) and ( 7) as constraints gives one of the possible fairest distributions and the minimum size each flow should have in order to have an optimal distribution. Both optimization problems can be solved using the simplex algorithm.

IV. COOPERATIVE CONGESTION CONTROL A. Principles

The algorithm we propose, Cooperative Congestion Control (CCC), defines a cooperative way to distribute the concurrent flows on a network. It works on a per node approach and aims at avoiding the congestion and using the multipath capacity of NDN efficiently. Our purpose is to give each flow the QoS it needs while preserving the network resources. To do so we will Our solution is based on three main principles: (i) a cooperation between nodes that takes the form of the exchange of applications objectives and networks constraints, (ii) a queue supervision to estimate its state and (iii) a smart decision making upon those pieces of information to allocate bandwidth to flows.

B. Node behavior

Fig. 2 represents a NDN node with one flow. Interests arrive from the Consumer side and are distributed on the n available paths (Upstream). On the reverse direction, Data arrive from the Producers and are sent to the Consumer (Downstream). Our solution is based on the control of the interests pace (Interests per second) on the upstream, in order to offer the compliant downstream data rate. On the Fig. 2, Interests arrive at the incoming pace p i on the interface 0 of our node. The p o,k (k = 1, . . . , n) represents the outgoing pace of Interest through the path k. With the size of the Data packet of the flow, our algorithm is able to estimate the rate induced by the transmission pace of Interests.

For each flow it manages, a node receives a pacing objective, p i _obj, from its neighbor on the consumer side and a constraint on this pacing, p i _max, from its neighbors on each producer side. The objective represents the application needs and tends to increase the rate allocated to the flow. The constraint represents the network limitation and tends to restraint the rate allocated to the flow. This represents the cooperation part of the algorithm. Each node has to respect the pace constraint and tries to satisfy the pace objective it receives. Then, it has to send its own constraint and objectives.

A node receives an objective for a flow p i _obj and can distribute it among the multiple output interfaces (p o,k _obj, k = 1, . . . , n). Eq. 8 represents the conservation of the objective through a node. No objective is created anywhere on the network. Thus, at a global scale, the sum of the received objective by all the producers is equal to the initial objective emitted by the consumer.

p i _obj = n k=1 p o,k _obj (8)
On the downstream, nodes receive n incoming constraints for a flow (p i,k _max, k = 1, . . . , n) and send their own outgoing constraint p o _max such as :

p o _max ≤ n k=1 p i,k _max (9)
Eq. 9 represents the aggregation of the incoming constraints.

It is not an equality because some local issue may reduce the outgoing constraint p o _max. On our scheme, Consumers and Producers network layer also uses CCC. As a result, the application stack has to follow the constraints and creates objective that satisfies their user needs.

The local issue represents a misuse of the bandwidth by the node. For this problem, nodes set up a supervision of theirs downstream output interfaces (here interface 0 in Fig. 2). This allows nodes to estimate if congestion is happening or if unused bandwidth is remaining. Depending of the case, a node may reduce the constraints for each active flow or distribute the available bandwidth. Nodes have to respect Eq. 9 even when a constraint is increased, i.e. an outgoing constraint cannot be increased more than the aggregate incoming constraints. With this mechanism, NDN nodes try to reach the objective of each flow. Such a behavior may be unfair, so we need to implement a fairness algorithm. Furthermore, if all the active flows are satisfied and there is still some unused bandwidth, nodes are allowed to increase the outgoing constraints above their incoming objective. This permits the previous node to have more opportunities to balance its traffic.

Indeed, nodes have n output interfaces for the considered flow and they have to choose how to use them efficiently. Interests arrive at the incoming pace p i and nodes have to determine the outgoing pace for all n output interfaces (p o,k , k = 1, . . . , n). The only restrictions are the received constraints:

p o,k ≤ p i,k _max, k = 1, . . . , n (10)
Finally, when an Interest arrives, nodes have to choose which output interface to use. Each output interface eventually paces Interests with their outgoing pace p o,k .

C. Algorithm

The overall behavior of each node implementing is the following:

• the node receives pacing objectives (p i _obj) and use an "Objective distribution" algorithm to compute the outgoing objectives (p o,k _obj, ∀k) ; • it forwards Interest based on a pacing policy enforced by the "Load balancing" algorithm ; • pacing is updated by a couple of "Pace increase" and "Pace decrease" algorithms ; • these algorithms are triggered by a "Queue supervision" algorithm which is fed by a "Queue status" algorithm and a bandwidth estimation (Eq. 12). As a consequence an effective CCC implementation consists in six sub-algorithms. We describe here a very straightforward implementation for each of them.

First, Interests carry the objective of the flow. When a node receives it, it does not know if it is the global objective of the consumer or if it is only a part of it. The only requirement of the node is the conservation of the objective (Eq. 8) and thus have to distribute it when multiple path are available: For this first implementation, we decide to assign an equal part of the received objective to each output interface:

p o,k _obj = p i _obj n , ∀k (11)
With the objective distribution, the nodes try to encourage the use of multipath. But the load balancing is done by the pace distribution (Algo. 2) and driven by the received constraints.

Algorithm 2 Load balancing

Input: pace_to_distribute while pace_to_distribute is not null do Get an output interfaces not full (p o,k ≤ p i,k_max ) Increase its output pace to its constraint (with respect to residual pace_to_distribute) Update the pace_to_distribute end while It is used to distribute the incoming pace p i and to distribute a potential overflow to an output interface (when a new constraint p i,k _max is received and is below the current output pace p o,k ). Indeed, when a more restrictive constraint arrives, the Eq. 10 may not be respected. The output pace is then decreased to the new constraint and the overflow has to be distributed among the other output interface. If it is not possible, it is Eq. 9 that may not be respected. The outgoing constraint is then updated to respect the aggregation property.

For downstream and as for Interests, Data piggyback the constraint of its flow. The nodes have to do the aggregation of the constraints. They just have to ensure that the outgoing constraint respects the Eq. 9.

The nodes also set up a local supervision on each of their output interfaces (Algo. 3).

Algorithm 3 Queue supervision

Get queue status (Algo. 4) if congestion then Reduce the pace of each active flow (Algo. 5) else Evaluate available bandwidth (Eq. 12) Distribute it equally between active flow (Algo. 6) end if

They use a drop-based mechanism to detect congestion (Algo. 4): if some packets on the emission queue are dropped during the supervision period, the queue is considered as congested. The supervision is done periodically. Algorithm 4 Queue status if at least one packet dropped then Return True end if Return False If a congestion is detected, the nodes need to decrease the constraint of its active flows. The outgoing constraint of each flow is then set to 90% of the current incoming pace of Interests (as described in Algo. 5). The overall estimation of the link use is thus reduce by ten percent. If the bandwidth estimation is below the capacity of the link, the nodes can distribute the available bandwidth with Algo. 6.

Algorithm 6 Pace augmentation

Input: available_bandwidth Input: constraint of active flows for each active flow do Give an equal part of the available bandwidth end for

The single aspect of fairness of these algorithms is to manage each flow equally. Indeed, Algo. 5 and Algo. 6 have an obvious impact on the fairness of the flows distribution. But all six of these algorithms play a role in the fairness balance and with interdependence between each other. The relative simplicity of the proposed algorithms allows to reduce this interdependency and thus to analyze the performance the overall framework. In future works, we will study the use of advanced implementations in order to enhanced the fairness of our solution or propose multiple kinds of fairness.

V. EVALUATIONS

We have implemented CCC on the ndnSIM simulator [START_REF] Mastorakis | ndnSIM 2: An updated NDN simulator for NS-3[END_REF]. All the codes and environment parameters are available 1 in order to be able to reproduce our results. We have chosen two scenarios to evaluate our solution.

The first scenario is illustrated on the Fig. 1. Both consumers have larger rate objectives than the network can offer. Each content size is 400 Mbytes and is split in chunks of 8400 bytes. The consumer A begins its request at t = 0s while the consumer B begins at t = 10s. In this scenario, we compare our solution to ICP and PCON. As depicted in our previous work [START_REF] Thibaud | An analysis of NDN Congestion Control challenges[END_REF], we choose ICP as the end-to-end algorithm with PCON-FS as the hop-by-hop forwarding strategy and PCON-CS as the end-to-end algorithm with Dynamic Request Forwarding [START_REF] Carofiglio | Optimal multipath congestion control and request forwarding in informationcentric networks[END_REF] (DRF) as the hop-by-hop forwarding strategy.

The optimal fair distribution found with the model of Sec. III is also included. It represents the minimum rate each flow should reach in order to have a global max-min fairness. Fig. 3 shows the results of this scenario. Sub-figure 3a represents the rate of the flow A. When the flow is alone, it should theoretically reach 100Mbps as pictured by the optimal curve. However, the rate obtained by CCC is below the optimal curve. Indeed, 100Mbps is the level 2 link capacity while we trace the level 3 rate. Therefore, the difference is due to the overhead of the layer 2. At t = 10s, the second flow begins and the max-min fair rate (the optimal curve) drops to 50Mbps for each flow. Our solution is very stable in comparison to ICP and PCON. Indeed, our consumer never has to blindly increase its Interests transmission rate since the network explicitly notifies the procedure to follow. The convergence time is also very short: approximately one supervision period to reallocate the bandwidth and a few supervision periods to decrease the congested link below its capacity. Therefore, the completion time of both consumers is lower with our solution. It successfully uses the network resources with no oscillation and with a fast convergence when new flows appear or old flows disappear. In term of fairness, our solution has the same performance than the combination "ICP + PCON-FS" and the "PCON-CS + DRF". It achieves a local, per link, max-min fairness: during the competition, both flows get half the bandwidth of the congestion link (R1-R3). The global fairness is not reached since the flow B is above the max-min fair rate computed by our model.

The second scenario is done on the Abilene topology of Fig. 4 as used in [START_REF] Carofiglio | Optimal multipath congestion control and request forwarding in informationcentric networks[END_REF]. This topology represents a bigger and more realistic network. The figure shows how the routing tables are filled. We conduct the same experimentation as in [START_REF] Mahdian | Mircc: Multipath-aware icn rate-based congestion control[END_REF] and compare it to the results with MIRCC. Consumer arrival time follows a Poisson process with mean 3 seconds. It is randomly set on the nodes 11, 13, 14, 15, 17, 18, 20 or 21 and requests randomly a content among /amazon, /google and /warner. Each content size is 9Mbytes and is chunked in 5000 pieces.

Fig. 5 presents the completion times of MIRCC and CCC solutions. Our solution does not handle requests coming from multiple interfaces yet. This is why there is no result for four consumers (C20 for /google, C18 for /amazon, C17 for /amazon and C11 for /warner). We plan to add this feature in future work. However, our proposition successfully retrieves each content faster that the MIRCC solution. This scenario also demonstrates that CCC is functional on a large scale simulation.

VI. CONCLUSIONS

In this paper, we have described the problem of multi-flow fair distribution on a limited network and its theoretical model. Then, we have proposed a solution, Cooperative Congestion Control, based on NDN that tackles this difficult challenge through a comprehensive set of algorithms. It works in a distributed way: consumers, producers and nodes exchange objectives and constraints for each flow, measure local utilization of each link and use these pieces of information to allocate fairly the rate of the active flows. The implementation of each algorithm can be changed independently and we have first defined simple algorithms in order to demonstrate the efficiency of our design. Our solution successfully uses the multipath capacity of NDN and maximizes the rate and QoE of the users. Our local queue supervision ensures a rapid reallocation of flows. It provides a fast convergence time when a flow appears and disappears. Simulation results show that we can achieve local link max-min fairness: each active flow gets a fair share of the link bandwidth. This is the case for each link. As future works, we plan to study the performance of different Fig. 5: CCC/MIRCC comparison on the Abilene topology implementations for CCC sub-algorithms. A key issue is the fairness of the system. We have shown that CCC is fair at the link level. A global fairness is a much more challenging objective and involves several of these algorithms.

Fig. 2 :

 2 Fig.2: Node context use both pacing (i.e. delay between consecutive transmission within the same flow) and multipath (i.e. the use of different available paths for the same flow). Our solution is based on three main principles: (i) a cooperation between nodes that takes the form of the exchange of applications objectives and networks constraints, (ii) a queue supervision to estimate its state and (iii) a smart decision making upon those pieces of information to allocate bandwidth to flows.

Algorithm 1

 1 Objective distribution Require: p i _obj = n k=1 p o,k _obj Ensure: p i _obj = n k=1 p o,k _obj for all output interface do Set the outgoing objective at an equal share of the received objective end for

Algorithm 5

 5 Pace reduction for each active flow do Reduce outgoing constraint by ten percent end for If no congestion is detected, the nodes compute the current estimation of the link use : bandwidth_estimation = f lowF p F o _max * data_size F (12)

Fig. 3 :

 3 Fig. 3: Comparison between CCC, ICP and PCON

Fig. 4 :

 4 Fig.4: Topology abilene[START_REF] Carofiglio | Optimal multipath congestion control and request forwarding in informationcentric networks[END_REF]