Caterina Dolce

Guillaume Mériguet
email: guillaume.meriguet@upmc.fr

Ionization of short weak polyelectrolytes: when size matters

The ionization of short weak polyelectrolytes in dilute solutions is investigated by 1 H Nuclear Magnetic Resonance (NMR). The increase of the pH of the medium causes both the ionization of the polyacids and, due to the intramolecular repulsions, the swelling of the chains. As a result, a noticeable effect of the pH change on the NMR chemical shift δ , and on the self-diffusion coefficient D is observed. The ionization of the polyelectrolyte occurs at higher pH as the length of the chain increases. The variation of the selfdiffusion coefficient with pH exhibits the opposite dependence on the length of the chain. However, no detectable effect of the length of the polyelectrolyte chain on the evolution of the chemical shift with pH is observed. These apparent contradictions are examined to clarify the impact of the chain length on the polyelectrolyte properties, and the counterion role in the ionization process.

Introduction

According to the nature of their ionic group and their behavior with pH , polyelectrolytes fall into two distinct categories: strong and weak polyelectrolytes. For strong polyelectrolytes, the distribution of charge is not sensitive to pH, whereas for weak polyelectrolytes the amount of charged sites varies as a function of pH. For weak polyelectrolytes, the charging process and the associated structural and dynamics outcomes have to be known and controlled in order to take advantage of the polyelectrolyte in its potential applications. For example, the modification of the state of charge of a polyelectrolyte makes it possible to tune its hydrophobicity, which is useful for the decolorization of dye solutions [START_REF] Jiang | Decolorization of anionic dye solutions using the hydrophobically modified polyelectrolytes containing beta-cyclodextrin moieties[END_REF]. Another example is the power conversion efficiency in polymer solar cells, which is governed by the protonated state of the conjugated polyelectrolytes [START_REF] Yi | Protonation process of conjugated polyelectrolytes on enhanced power conversion efficiency in the inverted polymer solar cells[END_REF].

Among weak polyelectrolytes, polyacrylic acid (PAA) has a specific interest since it is widely used in household and industry products as a scale inhibitor or thickening agent [START_REF] Brandrup | Polymer Handbook[END_REF][START_REF] Knappe | Poly(acrylic acid): A combined analysis with field-flow fractionation and SAXS[END_REF]. In addition, PAA can be seen as a model for natural organic polyacids which are at play in various environmental processes, such as the facilitated transport of heavy metals or radionuclide ions [START_REF] Roger | Characterization of humic substances and polyacrylic acid: A high precision conductimetry study[END_REF]. Furthermore, though a noticeable number of studies have been devoted to polyelectrolytes, especially PAA, the vast majority have so far focused on long chain polyelectrolytes since they are compatible with scaling approaches or infinitely long chain descriptions [START_REF] Laguecir | Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment[END_REF][START_REF] Schweins | Dilute solution behaviour of sodium polyacrylate chains in aqueous NaCl solutions[END_REF]. However, some applications use short chain polyelectrolytes [START_REF] Gonzalez | Flocculation efficiency of blends of short and long chain polyelectrolytes[END_REF][START_REF] Yu | Interaction of human serum albumin with short polyelectrolytes: a study by calorimetry and computer simulations[END_REF], for which the validity of the theoretical developments and scaling laws needs to be examined, especially for systems where the length of the chain is in the order of few persistence lengths.

The present work focuses on the ionization process of the sodium polyacrylate (PAANa) of different molecular weights. Beyond the evaluation of the ionization ratio α, the present work relies on two NMR observables to assess the consequences of the ionization and to investigate the infuence of the polyelectrolyte chain length. A recent study [START_REF] Swift | The pHresponsive behaviour of poly(acrylic acid) in aqueous solution is dependent on molar mass[END_REF] claims that the conformational transition with the pH does not occur for short chain polyacrylate (M n < 16.5 kDa). The present study aims at shedding some light on this debated transition starting from simple carboxylic acids up to short chain polyelectrolytes (N ∼ 100). We therefore intend to assess the influence of the molecular weight on the diffusion and evaluate the consequences of a pH change on the protonation, the self-diffusion, and the local environment via the NMR chemical shift.

To address these issues, we take advantage of the diffusion NMR technique [START_REF] Price | NMR Studies of Translational Motion: Principles and Applications[END_REF][START_REF] Scheler | NMR on polyelectrolytes[END_REF][START_REF] Callaghan | Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR[END_REF]. NMR is a versatile technique to study the conformation and structure of polymer chains [START_REF] Hatada | NMR Spectroscopy of Polymers[END_REF][START_REF] Saalwächter | Polymer Applications of NMR[END_REF]. NMR diffusion can quantify the mobility of polyelectrolytes [START_REF] Walderhaug | Self-diffusion in polymer systems studied by magnetic field-gradient spin-echo NMR methods[END_REF] and evaluate the association of ions or molecules [START_REF] Šarac | Salicylate isomer-specific effect on the micellization of dodecyltrimethylammonium chloride: large effects from small changes[END_REF][START_REF] Giesecke | Ion association in aqueous and non-aqueous solutions probed by diffusion and electrophoretic NMR[END_REF][START_REF] Hostnik | Influence of counterions on the conformation of conjugated polyelectrolytes: the case of poly(thiophen-3-ylacetic acid)[END_REF]. On the molecular scale, NMR gives insight to the variation of the spin environment, when the protonation state changes through the chemical shift [START_REF] Bezencon | pK(a) determination by H-1 NMR spectroscopy -An old methodology revisited[END_REF]. On a larger length scale (10-100 µm), the self-diffusion of the polyelectrolytes can be investigated using the Pulsed Field Gradient NMR (PFG-NMR) method. In contrast to fluorescence correlation spectroscopy (FCS), that measures the diffusion coefficients thanks to fluorescent moieties in the diffusing species [START_REF] Laguecir | Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment[END_REF][START_REF] Pristinski | Fluorescence correlation spectroscopy studies of diffusion of a weak polyelectrolyte in aqueous solutions[END_REF], NMR does not need the grafting of additional external species that might alter the dynamics [START_REF] Mcdonough | Fluorescent Labeling Can Alter Polymer Solution Dynamics[END_REF]. Furthermore, diffusion NMR is not affected by the limitations of the dynamic light scattering (DLS), from which diffusion coefficients can also be determined. DLS measures concentration fluctuations and hence collective (mutual) diffusion coefficients [START_REF] Sedlák | Structure and dynamics of polyelectrolyte solutions by light scattering[END_REF]. DLS is not suited for small molecule while diffusion NMR is a method of choice. Therefore, NMR is a powerful tool to determine the absolute value of the diffusion coefficient and to assess the effects of the medium [START_REF] Price | NMR Studies of Translational Motion: Principles and Applications[END_REF][START_REF] Callaghan | Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR[END_REF].

This paper is organised as follows. First, the samples and the methods used are presented in the experimental section. Secondly, the ionization of the polyectrolytes is determined with acid-base titration and the effect is shortly discussed together with the literature data. Thirdly, the effect of this ionization on the two NMR observables, the chemical shift and the self-diffusion coefficient, are investigated to understand the effects on the polyelectrolyte chain and the influence on the length of the polyelectrolyte.

Experimental section

Materials and methods

Four PAANa, [-CH 2 -CH(COONa)-] n , of different molecular weights (M = 2.1, 5.1, 8 and 15 kDa) were purchased from Sigma-Aldrich. The water content of the different products was accounted for during the preparation of the studied samples. NMR spectra and conductivity monitoring during dialysis show that the concentration of impurities is less than 2 %. Propionic acid (Alfa Aesar, 99%), glutaric acid (Alfa Aesar, 99%) and 1,3,5-pentanetricarboxylic acid (TCI, > 98%) were used for comparison. Unless otherwise stated, all experiments were performed at 298 K. The details of PAANa are reported in the Table 1. M is the approximate weight averaged molecular weight in Dalton given by the provider. M w , the weight-average molecular weight, and M n , the numberaverage molecular weight, were obtained from size exclusion chromatography (SEC) with an Ultimate 3000 RSLC system in aqueous solution of sodium nitrate (0.1 mol L -1 ) to minimize ionic effects. Shodex OH-pak 30 cm columns were used (802.5HQ, 804HQ, 806HQ and 807HQ) in series. 1 Structural features of PAANa with different molecular mass in kg mol -1 , M (label value from the provider). M w is the weight-average molecular weight, M n is the number-average molecular weight, N w is the weight averaged degree of polymerization, R h in nm is the hydrodynamic radius obtained from NMR measurements at pH ∼ 8, max in nm is the max end-to-end distance is obtained from monomers' number and length, and c in kg m -3 is the overlap concentration obtained from Equation 1.

Since Multi-Angle Light Scattering (MALS) was coupled with the SEC separation, no calibration standard sample was used. This characterization was performed by the Institute Charles Sadron (Strasbourg -France). N w is the weight averaged degree of polymerization obtained from molecular mass of polymer and of the monomer (M m ), N w = M w /M m [START_REF] Ise | Ordered structure in dilute solutions of ionic biopolymers. 2. Small-angle X-ray scattering study of sodium polyacrylate solution[END_REF][START_REF] Muroga | Investigation of local conformations of polyelectrolytes in aqueous solution by small-angle Xray scattering. 1. Local conformations of poly(sodium acrylates)[END_REF]. R h is the hydrodynamic radius obtained from NMR measurements at pH ∼ 8, using Stokes-Einstein equation R h = k B T /(6πηD) as also calculated by [START_REF] Saito | Determination of the size of a polystyrene nanosphere by the pulsed field gradient nuclear magnetic resonance method[END_REF]. Where k B is the Boltzmann constant, T is the temperature (T = 298 K) and η is the viscosity of the solvent at 298 K (10 % D 2 O and 90 % H 2 O, 930 µPa s) [START_REF] Kestin | Tables of the Dynamic and Kinematic Viscosity of Aqueous Nacl Solutions[END_REF]. The maximum end-toend distance max is calculated from monomers' number N w and length a, max = N w • a. The value of a was obtained from SAXS experiments (a = 0.252 nm) [START_REF] Ise | Ordered structure in dilute solutions of ionic biopolymers. 2. Small-angle X-ray scattering study of sodium polyacrylate solution[END_REF][START_REF] Muroga | Investigation of local conformations of polyelectrolytes in aqueous solution by small-angle Xray scattering. 1. Local conformations of poly(sodium acrylates)[END_REF]. c is the value of overlap or crossover concentration, specific of each mass, above which the entanglement occurs. Indeed, polyelectrolyte chains begin to overlap when the distance between them is in the order of their size. The geometrical definition of the overlap concentration depends on the conformation of the chain [START_REF] Teraoka | Polymer Solutions: An Introduction to Physical Properties[END_REF]. The radius of gyration is often used for coiled conformations, whereas the contour length is used for rod-like chains. In the present study, c , is estimated with the hydrodynamic radius R h , which is an indirect measure of the conformation:

c = M n N A (2R h ) 3 (1)
where N A is the Avogadro constant. The PAANa solutions were prepared at weight fraction of ∼ 1% in MilliQ water. The range of concentrations studied lies below the estimated c , as confirmed by the linear dependence of the self-diffusion on concentration (Figure S1 -Electronic Supplementary Material). Indeed when c > c , the expected concentration dependence would be a power law [START_REF] Cosgrove | The Critical Overlap Concentration Measured by Pulsed-Field Gradient Nuclear-Magnetic-Resonance Techniques[END_REF]. In this regime, the effect of inter-chain interactions is weak compared to the intra-chain interactions, and thus changes in diffusion can then mainly be ascribed to changes in conformation of the chain.

The pH was varied with NaOH (Chem-Lab) and HCl (Chem-Lab) solutions at 1.000 ± 0.002 mol L -1 . For NMR measurements, 500 µL of each solution and 100 µL of D 2 O (CEA-ORIS, isotopic content ≥ 99.8%) were transferred in a conventional 5 mm NMR tube.

Titration

Titration were performed with the titrator DT1200 from Dispersion Technology. Measurements were carried out at room temperature with 50 titrant doses, adjusted from 30 to 300 µL.

Samples were prepared at ∼ 1 wt% and diluted 10 times using MilliQ water, the final molarity of the polyelectrolyte units was around 0.01 mol L -1 . The initial pH of this system is ∼ 9. The titrant was HCl (0.1000 ± 0.0002 mol L -1 , Carl-Roth). The proportion of ionized sites, or deprotonation degree α, of the polyelectrolyte is calculated from the difference of the amounts of protons bound to the polyelectrolyte and those remaining in solution as measured by pH.

Nuclear Magnetic Resonance

NMR measurements were carried out on a Bruker Avance DRX 500 NMR spectrometer operating at 499.76 MHz for 1 H, with a maximal magnetic gradient field achievable of 57 × 10 -2 T m -1 . Data were recorded in 90% H 2 O -10% D 2 O mixture (residual HOD, peak at 4.7 ppm) for locking purpose. The sample temperature was controlled by a Bruker BCU and set to 298.0 K. 13 C experiments were also performed using the broadband channel of the BBO probe.

In an aqueous solution, the strong water signal would cover the polyelectrolyte signal and create a strong baseline distortion in the NMR spectra [START_REF] Majer | Accurate and absolute diffusion measurements of Rhodamine 6G in low-concentration aqueous solutions by the PGSE-WATERGATE sequence[END_REF]. To avoid this effect which limits the capacity to measure the diffusion coefficient in aqueous solutions, a low power presaturation pulse of water signal was used during the recycle delay. To obtain the diffusion coefficient, the pulsed field gradient (PFG) stimulated echo sequence BPP-LED (ledbpgppr2s Bruker sequence) with a water presaturation was used [START_REF] Price | Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. basic theory[END_REF][START_REF] Wu | An improved diffusionordered spectroscopy experiment incorporating bipolar-gradient pulses[END_REF].

The pulse gradient were sine-shaped and their duration δ was 5 ms. The diffusion delay ∆ was 0.200 s and the field gradient amplitude g was varied with 16 increments, from 2 % to 80 % of the maximum field gradient amplitude. To obtain each spectrum, sixteen measurements were averaged and for each sample four spectra were acquired.

The resultant signal intensity I(b), depends on the diffusion sensitivity factor b and on the diffusion coefficient D. The diffusion sensitivity factor is equal to b = γ 2 g 2 δ 2 (∆δ /3τ/2), where γ is the gyromagnetic ratio of the nucleus and τ (400 µs) is a delay for the gradient recovery. The value of the gradient was calibrated with the value of the self-diffusion coefficient of HOD in D 2 O [START_REF] Holz | Temperature-dependent selfdiffusion coefficients of water and six selected molecular liquids for calibration in accurate 1 H NMR PFG measurements[END_REF][START_REF] Holz | Calibration in Accurate Spin-Echo Self-Diffusion Measurements Using H-1 and Less-Common Nuclei[END_REF]. Furthermore, when using NMR experiments on polymer solutions, particular expedients have to be considered to analyze the signal. Polymer systems are generally characterized by a range of molecular weights [START_REF] Stepto | Dispersity in polymer science (IUPAC Recommendations 2009)[END_REF] that give rise to a distribution of molecular sizes and then a distribution of selfdiffusion coefficients. Therefore, due to the diffusion coefficient dispersity, at high b values the signal deviates from a simple single exponential and a mono-exponential fit leads to a significant underestimation of the average diffusion coefficient D . To fit the data satisfactorily, it is then necessary to take into account this departure [START_REF] Walderhaug | Self-diffusion in polymer systems studied by magnetic field-gradient spin-echo NMR methods[END_REF][START_REF] Hostnik | Influence of counterions on the conformation of conjugated polyelectrolytes: the case of poly(thiophen-3-ylacetic acid)[END_REF][START_REF] Callaghan | The size and shape of amylopectin: A study using pulsed-field gradient nuclear magnetic resonance[END_REF][START_REF] Håkansson | The influence of polymer molecular-weight distributions on pulsed field gradient nuclear magnetic resonance self-diffusion experiments[END_REF][START_REF] Oostwal | Chain self-diffusion in aqueous salt-free solutions of sodium poly(styrenesulfonate)[END_REF][START_REF] Roding | The gamma distribution model for pulsed-field gradient NMR studies of molecular-weight distributions of polymers[END_REF], using for example the following second order expansion:

I(b) I(b = 0) = ∞ 0 P(D) exp(-bD)dD (2) exp -b D + 1 2 b 2 D 2 -D 2 + • • • (3)
where the first cumulant D is the average diffusion coefficient, and the second D 2 -D 2 , gives access to the width of the distribution. Besides, the observed diffusion coefficient distribution might differ from the real diffusion coefficient distribution because of the relaxation effects during the application of the pulse sequence. A detailed analysis of this effect on the average diffusion coefficient would lie out of the scope for this paper, but this effect was quantified and was found to be of the order of the experimental uncertainty. The analysis of the decay was then fitted by equation 3 with the first and second cumulants as free parameters, but only the average diffusion coefficient D will be discussed further in the present work. The diffusion coefficients reported in the following, are an average of the diffusion coefficients of the CH and CH 2 peaks. A repeatability error of the 2% is associated to the diffusion coefficient.

3 Results and Discussion

Titration

The protonation of polyelectrolytes has been widely studied [START_REF] Borkovec | Ionization processes and proton binding in polyprotic systems: Small molecules, proteins, interfaces, and polyelectrolytes[END_REF] and will not be described in detail here. Only the main features of interest will be discussed as a reference for comparison with the properties measured by NMR. To assess the charge properties of the polyelectrolyte with pH, acid-base titrations of PAANa were carried out. In Figure 1, four PAANa with different lengths are shown together with the three carboxylic acids. All curves show a sigmoidal increase of the fraction of deprotonated sites α, with pH, in agreement with literature data [START_REF] Laguecir | Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment[END_REF][START_REF] Sadeghpour | Influence of alkali metal counterions on the charging behavior of poly(acrylic acid)[END_REF]. For a simple carboxylic acid (N = 1), the degree of ionization α can be described by the Henderson-Hasselbalch equation [START_REF] Henderson | Concerning the relationship between the strength of acids and their capacity to preserve neutrality[END_REF][START_REF] Hasselbalch | Die Berechnung der Wasserstoffzahl des blutes auf der freien und gebundenen Kohlensaure desselben, und die Sauerstoffbindung des Blutes als Funktion des Wasserstoffzahl[END_REF]: For polycarboxylic acids (N > 1), the slope of α vs pH decreases. For polyelectrolytes, the protonation is strongly influenced by the state of charge of nearby sites. As a result, even if a sigmoidal shape of the titration curve is obtained, the slope deviates from the Henderson-Hasselbalch behavior (equation 4). Several models can be used to describe this deviation: a smeared out charge model [START_REF] Borkovec | Ionization processes and proton binding in polyprotic systems: Small molecules, proteins, interfaces, and polyelectrolytes[END_REF], a Poisson-Boltzmann description [START_REF] Sadeghpour | Influence of alkali metal counterions on the charging behavior of poly(acrylic acid)[END_REF], a "neighbour effect" model [START_REF] Annenkov | Analysis of the potentiometric titration curves within the framework of the theory of the "neighbor effect[END_REF], or Monte-Carlo simulations either with implicit or explicit counterions [START_REF] Carnal | Influence of Explicit Ions on Titration Curves and Conformations of Flexible Polyelectrolytes: A Monte Carlo Study[END_REF][START_REF] Ullner | A Monte Carlo study of titrating polyelectrolytes[END_REF][START_REF] Ullner | Conformational properties and apparent dissociation constants of titrating polyelectrolytes: Monte Carlo simulation and scaling arguments[END_REF]. One even simpler approach is to consider the pH value for which half of the sites are ionized (α = 0.5, horizontal line in Figure 1), the midpoint of the ionization process, as an estimate of an effective pK, noted p α hereafter. The effect of the chain length is clearly noticeable in Figure 1. The observed p α increases with the length of the polyelectrolyte. This effect could be related to the difficulty to ionize high molecular weight polyelectrolytes, because of the increase of the electrostatic potential with M w [START_REF] Laguecir | Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment[END_REF][START_REF] Carnal | Influence of Explicit Ions on Titration Curves and Conformations of Flexible Polyelectrolytes: A Monte Carlo Study[END_REF]. These values are slightly lower than values of p α found by Laguecir et al. [START_REF] Laguecir | Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment[END_REF], certainly due to the difference in concentration and salinity between the samples. Ullner et al. [START_REF] Ullner | A Monte Carlo study of titrating polyelectrolytes[END_REF][START_REF] Ullner | Conformational properties and apparent dissociation constants of titrating polyelectrolytes: Monte Carlo simulation and scaling arguments[END_REF] have studied the phenomenon using Monte-Carlo simulations and a scaling approach, they have suggested the following law for the deviation from the noncharged pK:

pH = pK + log α 1 -α (4)
p α -pK a ∼ α 1 3 (ln N) 2 3 (5)
The deviations of p α values from the pK a of the propionic acid (N = 1), and equation 5 are reported in Figure S2 (Electronic Supplementary Material). A rather fair agreement between the data and Ullner relation is observed.

Nuclear Magnetic Resonance

In this section, 1 H NMR (500 MHz) was used to access information on the local environment via the chemical shift δ and on the self-diffusion via the measurement of the diffusion coefficient D.

Analysis of 1 H spectra

The 1 H NMR spectrum of PAANa 15 kDa is shown in Figure 2. Two families of peaks, corresponding to the two different types of hydrogens in the PAANa chain, has been identified. This assignment was confirmed by DEPT-135 and 13 C-1 H HSQC experiments where the number of hydrogen atoms attached to each carbon is determined unambiguously (data not shown). In Figure 2, the peak centered around 2.02 ppm at pH = 8.8 is associated to methine groups (CH) and the peak centered at 1.42 ppm is associated to methylene groups (CH 2 ). The splitting observed is due to the various configurations of the carboxylate groups with respect to the chain, i.e. the tacticity. The effects of pH on the 1 H NMR spectrum are reported in Figure 2. As seen in Figure 2, the chemical shift changes with the pH: δ decreases when the pH increases, because of the dependence on the protonation state of adjacent acidic or basic sites [START_REF] Borkovec | Ionization processes and proton binding in polyprotic systems: Small molecules, proteins, interfaces, and polyelectrolytes[END_REF].

In basic medium, the shielding of the magnetic field is higher because the protons are richer in electrons and a lower δ value is observed. This behavior has already been identified for protons located in the α position of small carboxylic acids [START_REF] Tynkkynen | From proton nuclear magnetic resonance spectra to ph. assessment of 1 H NMR pH indicator compound set for deuterium oxide solutions[END_REF]. The opposite trend is observed for 13 C, for which the chemical shift is seen to increase with the pH (Figure S3 -Electronic Supplementary Material), with a largest variation for the carboxyl carbon. This is in agreement with the previous results for small carboxylic acids [START_REF] Cistola | Ionization behavior of aqueous short-chain carboxylic acids: a carbon-13 NMR study[END_REF] or longer PAA chains [START_REF] Chang | Determination of the tacticity and analysis of the pH titration of poly(acrylic acid) by proton and carbon-13 NMR[END_REF]. The polarization of the C-H bond could be the cause of the two opposite evolutions of the chemical shifts of 13 C and 1 H [START_REF] Buckingham | Chemical Shifts in the Nuclear Magnetic Resonance Spectra of Molecules Containing Polar Groups[END_REF][START_REF] Schneider | Proton Magnetic Resonance Chemical Shift of Free (Gaseous) and Associated (Liquid) Hydride Molecules[END_REF], but an effect of conformational change cannot be disregarded at this stage [START_REF] Neal | Rapid and accurate calculation of protein 1 H, 13 C and 15 N chemical shifts[END_REF][START_REF] Platzer | pH-dependent random coil 1 H, 13 C, and 15 N chemical shifts of the ionizable amino acids: a guide for protein pK a measurements[END_REF].

To check the effect of the electrostatic interaction, the influence of added salt on the chemical shift has been examined. The moderate addition of salt (up to 1 mol L -1 ) has no noticeable effect on the chemical shift of the polyacrylate (Figure S4 left -Electronic Supplementary Material). However, up to 0.1 mol L -1 of added salt, a noticeable effect on the conformation is observed with a change of the diffusion coefficient (Figure S4 right -Electronic Supplementary Material). The effect of conformation on the chemical shift in the present case can then be considered as weak compared to the effect of bond polarization. To study the influence of the chain length, the spectra of polyelectrolytes of different molecular mass were acquired (2.1, 5.1, 8 and 15 kDa) together with the small carboxylic acids. For all molecules, the chemical shift decreases with increasing pH. In Figure 3, the chemical shifts δ of the protons in α position with respects to the carboxylate group (CH in PAA chain) as a function of pH are reported. Surprisingly, while small differences can be seen for the small carboxylic acids, the global variation of δ appears to be independent from the molecular mass for the PAA chains. All the data are well fitted with a unique sigmoidal curve (dotted curve in the Figure 3):

δ (pH) = δ acid + δ basic -δ acid 1 + exp p δ -pH k (6)
with a resulting midpoint p δ = 5.6 ± 0.1 and k = 0.81 ± 0.05. The decrease of this curve is slower than for the small carboxylic acids which follow closely the Henderson-Hasselbalch equation (k = 1/ ln 10 = 0.44). This departure from the Henderson-Hasselbalch equation suggests the existence of a charge regulation process during the deprotonation, as observed for the degree of ionization α.

If the chemical shift δ and the ionization degree α both exhibit a sigmoidal variation with pH, α shows a molecular mass dependence, not seen for δ . To explain this difference, we have to consider the physical origin of α and δ . The titration measures the macroscopic amount of protons exchanged in the solution, this number is directly related to the chain length and does not measure the counterion condensation. The NMR chemical shift δ , is a microscopic measure of how the magnetic field is shielded for the nucleus. As discussed before, it is correlated to the C-H bond polarization due to the local electric field. It depends indirectly on the number of sites deprotonated and on the amount of sodium ions condensed. As shown before, a significant fraction of the deprotonated sites is compensated by the sodium counterions.

To assess the extent of this phenomenon, the Manning parameter ξ can be computed. The distance between neighbouring monomers is a = 0.252 nm [START_REF] Ise | Ordered structure in dilute solutions of ionic biopolymers. 2. Small-angle X-ray scattering study of sodium polyacrylate solution[END_REF][START_REF] Muroga | Investigation of local conformations of polyelectrolytes in aqueous solution by small-angle Xray scattering. 1. Local conformations of poly(sodium acrylates)[END_REF], . The Bjerrum length, B = e 2 /4πε 0 ε r k B T = 0.71 nm at 298 K, is the distance at which the electrostatic interaction between two elementary charges is equal to the thermal energy k B T . The Manning parameter ξ , that compares the two lengths [START_REF] Manning | Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I[END_REF], is defined as ξ = B /a = 2.84. Since ξ > 1, Coulomb interaction dominates over the thermal energy and the condensation of counterions occurs. The value of ξ 3 shows that the length of three repeating units is close to the Bjerrum length, and suggests then that 2/3 of the sites are compensated by the condensation of sodium counterions when the chain is completely deprotonated. This estimation is consistent with previous conductivity measurements [START_REF] Roger | Characterization of humic substances and polyacrylic acid: A high precision conductimetry study[END_REF] and 23 Na diffusion NMR experiments (Fig. S5 -Electronic Supplementary Material).

The counterion condensation decreases the electrostatic field and consequently the value of the transition midpoint observed for the chemical shift δ is lower than that for α, where the sodium condensation is not taken into account. Moreover, the length of the polyelectrolyte does not cause any noticeable changes, since the chemical shift is sensitive only to the local environment. The values of midpoints for δ (p δ ) and α (p α ) are closer for the shortest chain or even equal for the small carboxylic acid within the experimental uncertainty for which no significant condensation occurs. Conversely, the longer the chain, the higher is the deviation between the two midpoint values. The NMR chemical shifts should then be used with caution to determine the degree of deprotonation and the pK a for large molecules where ion condensation occurs. Fig. 4 Diffusion coefficient of PAANa (•) and small carboxylic acids (•) at pH = 6 as a function of molecular weight obtained by diffusion NMR. Data obtained by fluorescence correlation spectroscopy (×, [START_REF] Laguecir | Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment[END_REF]) and from the Polymer Handbook ( , [START_REF] Brandrup | Polymer Handbook[END_REF]) for a concentration of added salt of 10 mM of NaCl. Inset: effect of pH on the evolution of the diffusion coefficient with molecular weight.

Diffusion

So far, NMR has given information on the local environment, but NMR is also a powerful technique to study the diffusion of the polyelectrolytes on larger scale. To understand the variation of the self-diffusion with the molecular mass, the diffusion coefficients of PAANa as a function of the molecular weight at pH= 6, are reported in Figure 4 together with the values for the small carboxylic acids. The values for longer chains from the literature are also reported for comparison [START_REF] Brandrup | Polymer Handbook[END_REF][START_REF] Laguecir | Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment[END_REF] with a concentration of added salt of 10 mM of NaCl. All the data for the polymeric chains are well fitted with the expression D(M) ∝ M -ν with ν = 0.56, except the points corresponding to the small carboxylic acids that depart from this law certainly due to their too small size. The value of ν found is in agreement with the literature values determined by light scattering in a good solvent [START_REF] Schweins | Dilute solution behaviour of sodium polyacrylate chains in aqueous NaCl solutions[END_REF][START_REF] Reith | How does the chain extension of poly (acrylic acid) scale in aqueous solution? a combined study with light scattering and computer simulation[END_REF]. To understand the physical meaning of the value of ν found, it is compared with theoretical values for different conformations:

-0.3 is the ν value for a hard ellipsoid [START_REF] Callaghan | A pulsed field gradient NMR study of self-diffusion in a polydisperse polymer system: dextran in water[END_REF], -0.6 is the value for a random coil chain, -1.0 is the value for a rod-like particle [START_REF] Oostwal | Chain self-diffusion in aqueous salt-free solutions of sodium poly(styrenesulfonate)[END_REF].

The same analysis was carried out at pH = 2 and pH = 8 (see figure 4 -inset). At pH = 2, the exponent ν is equal to 0.49 ± 0.05 showing that the conformation is more compact at low pH. At pH = 8, the value of ν = 0.67 ± 0.05 found shows that the chain cannot be seen as a rigid rod and adopts a more flexible conformation. This last result is consistent with viscosimetric determination at low salt concentration [START_REF] Kulicke | Viscosimetric Determination of the Molar Mass[END_REF]. The evolution of the diffusion coefficients of PAANa 2.1, 5.1, 8 and 15 kDa as a function of pH are reported in Figure 5 together with data of PAANa 50 kDa (obtained by FCS) from the literature [START_REF] Laguecir | Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment[END_REF]. The diffusion coefficients decrease with a sigmoidal behavior since at high pH, the PAANa is fully charged and the electrostatic interaction is strong enough to stretch the polyelectrolyte chain. The observed increase of the hydrodynamic radius is also consistent with the evolution of the radius of gyration with the increase of the ionization degree α observed by Monte Carlo simulations [START_REF] Laguecir | Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment[END_REF][START_REF] Carnal | Influence of Explicit Ions on Titration Curves and Conformations of Flexible Polyelectrolytes: A Monte Carlo Study[END_REF]. Carnal et al. [START_REF] Carnal | Influence of Explicit Ions on Titration Curves and Conformations of Flexible Polyelectrolytes: A Monte Carlo Study[END_REF] have simulated using the Monte-Carlo simulation an isolated weak polyelectrolyte of 100 monomers at several pH values. At a high pH, they found that an extended structure is achieved to minimize the long-range electrostatic energy.

Moreover, as seen in Figure 5 (bottom), the relative variation of the diffusion coefficient with the pH is size-dependent. This variation increases with the molecular weight, from 26 % for the 2.1 kDa to 34 % for 15 kDa PAANa. This trend is also observed in the data of Swift et al. [START_REF] Swift | The pHresponsive behaviour of poly(acrylic acid) in aqueous solution is dependent on molar mass[END_REF] where the decrease of D, between acidic and basic conditions, varies from 50 to 75% while the mass varies from 17 kDa to 55 kDa. However, contrary to the results of Swift et al. [START_REF] Swift | The pHresponsive behaviour of poly(acrylic acid) in aqueous solution is dependent on molar mass[END_REF], the change of diffusion coefficient is even observed for low molecular weight PAANa (down to M w = 2.1 kDa). Actually, the small carboxylic acids also display a transition between acid and basic forms (Figure S6 -Electronic Supplementary Material) consistently with the results of Dunn et al. [START_REF] Dunn | The diffusion of monocarboxylic acids in aqueous solution at 25[END_REF]. For low molecular weight species, this change of diffusion could be ascribed to a change of solvation between the neutral and the charged species as suggested by Dunn et al. [START_REF] Dunn | The diffusion of monocarboxylic acids in aqueous solution at 25[END_REF]. For longer chains, this solvation phenomenon also occurs, but the main origin of the swelling is the electrostatic interactions as discussed before. The mass dependence of this swelling is consistent with the increase of the electrostatic potential with M w already discussed for the ionization of the chain ( §3.1). The size threshold (Mn < 16.5 kDa) suggested by Swift et al. [START_REF] Swift | The pHresponsive behaviour of poly(acrylic acid) in aqueous solution is dependent on molar mass[END_REF] does not seem justified since the conformational transition is seen whatever the size of the polyacrylate. However, the present study indeed proves that the extent of the transition in terms of expansion of the hydrodynamic radius is larger for longer chains.

To have a comprehensive view of the the ionization process for the different molecular weight, the data in Figure 5 are fitted with a sigmoidal curve and the midpoints obtained, p D , are compared with the previous midpoints versus the molecular weight (Figure 6). The comparison of the different midpoints (p D , p α and p δ ) points out the complex interplay between the different parameters under study. The constant value of the p δ proves the local character of δ , that is independent to the molecular weight. For small carboxylic acids, the same value of midpoints p is observed whatever the method. For longer chain polyelectrolytes, a departure is expected. The difference between p α and p δ was already discussed in §3.2.1. p D is found to be lower than the other two midpoints as it was already observed in the work of Pristinski et al. [START_REF] Pristinski | Fluorescence correlation spectroscopy studies of diffusion of a weak polyelectrolyte in aqueous solutions[END_REF], for a 72 kDa poly(methacrylic acid) PMAA. In the present case, this departure is found to increase with the molecular weight of the chain. The conformational change with the pH can be discussed in the light of the persistence length, which measure of how far a polymer chain persists in a given direction. In the case of polyelectrolytes, the persistence length P can be divided into a sum of two contributions: an intrinsic persistence length, due to the rigidity of the chain backbone and an electrostatic persistence length arising from the repulsion between neighbouring ionic sites [START_REF] Cranford | Variation of Weak Polyelectrolyte Persistence Length through an Electrostatic Contour Length[END_REF]. The persistence length of long chain PAANa (M w > 15 kDa) was determined by X-ray scattering measurements by Muroga et al. [START_REF] Muroga | Investigation of local conformations of polyelectrolytes in aqueous solution by small-angle Xray scattering. 1. Local conformations of poly(sodium acrylates)[END_REF]. P values ranging from 0.8 to 1.5 nm were found for α varying from 0.1 to 0.85, and for salinity up to 0.1 mol L -1 . Molecular dynamics simulations [START_REF] Cranford | Variation of Weak Polyelectrolyte Persistence Length through an Electrostatic Contour Length[END_REF] of a single and isolated PAA chain of 50 monomers gave values of P from 0.4 nm (α=0) to 1.3 nm (α=1) [START_REF] Cranford | Variation of Weak Polyelectrolyte Persistence Length through an Electrostatic Contour Length[END_REF]. For the studied polymeric chains, both the hydrodynamic radii R h and the max end-to-end distances max are of the order of few persistence lengths. As a result, they tend to behave as long chain polyelectrolytes but still exhibit slight deviations from this behaviour as the evolutions of the transition midpoints with the length show. The small carboxylic acids are significantly below the persistence length and does not follow the same scaling laws (Figure 4 for example).

Conclusions

The conformation and the self-diffusion of low molecular mass polyelectrolytes in a dilute regime at different pH, concentrations, and salt concentrations have been investigated using NMR. The small chains investigated in the present study appear to follow the same scaling law for the diffusion coefficient as longer chains studied in the literature and differ from simple carboxylic acids. The diffusion coefficient decreases with the molecular weight with a powerlaw dependence D(M) ∝ M -ν . The data compare well with the literature values at pH 6. At higher pH, the higher slope indicates that the conformation adopted tends towards a flexible rod when the polyelectrolyte is fully charged. Conversely, the chain is more compact at low pH values.

The charging process of the chain, governed by pH of the solution, has a noticeable effect on the chemical shift δ and the diffusion coefficient D. While simple carboxylic acids are well described by the Henderson-Hasselbalch equation, the latter equation fails unambiguously for the evolution of the same quantities measured for the polyelectrolytes. Furthermore, as the length of the chain increases, the deprotonation degree α, the chemical shift δ and the diffusion coefficient D give rise to significant differences not observed for the simple carboxylic acids. Whereas the chemical shift δ has a variation with pH independent of the chain length, α and D display opposite molecular weight dependences. The different molecular weight dependence between δ and α, is related to the different role of the condensation of counterions for the two quantities. The diffusion coefficient shows the swelling of the chain with the ionization. Furthermore, the change of diffusion with the ionization is found to be dependent on the length of the chain. For longer chains, the onset of the diffusion coefficient modification appears at lower pH and the relative decrease of the diffusion coefficient is larger. The present study shows that even short polyelectrolytes singularly differ from simple carboxylic acids and tend to behave like long chain polyelectrolytes. Finally, their ionization process and its effect on diffusion cannot be easily derived by a single parameter study, since several phenomena are at play.

Fig. 1

 1 Fig. 1 Fraction of deprotonated sites α as a function of pH. Titration for different molecules: propionic acid (N = 1, +), glutaric acid (N = 2, ), 1,3,5-pentanetricarboxylic acid (N = 3, * ), 2.1 kDa (N = 22, ), 5.1 kDa (N = 54, ×), 8 kDa (N = 85, ), 15 kDa (N = 160, •). The dashed line marks α = 0.5.

Fig. 2 1

 2 Fig. 2 1 H NMR (500 MHz) spectra of PAANa 15 kDa at pH = 8.8 (solid line) and pH = 2.8 (dashed line).

Fig. 3

 3 Fig. 3 Chemical shift δ (ppm) versus pH value for α-protons: propionic acid (N = 1, +), glutaric acid (N = 2, ), 1,3,5pentanetricarboxylic acid (N = 3, * ), 2.1 kDa (N = 22, ), 5.1 kDa (N = 54, ×), 8 kDa (N = 85, ), 15 kDa (N = 160, •).

Fig. 5

 5 Fig. 5 Top: Diffusion coefficient and hydrodynamic radius versus pH for different molecular mass of PAANa: 2.1 kDa (N = 22, ), 5.1 kDa (N = 54, ×), 8 kDa (N = 85, ) and 15 kDa (N = 160, •). The data of the PAANa 50 kDa (obtained by FCS) come from the literature [6] (N = 700, ). Bottom: same data normalized by the diffusion coefficient at pH ∼ 2.

Fig. 6

 6 Fig.6Inflection points of the previous measurements as a function of pH, versus the degree of polymerization. p D is related to the diffusion coefficient in Figure5( ); p α to α in Figure1 (•); p δ is the midpoint for the chemical shift in Figure3 ().

Acknowledgements The authors thank Dr. Isabelle Correia (UPMC -Sorbonne Universités) for the NMR facilities and technical assistance and B. Ancian for fruitful discussions and UPMC for funding.

Funding

This study was funded by UPMC.

Conflict of interest

The authors declare no conflict of interest.


Mathilde Koskas

Sophie Derrot

cataloguing legal deposit ebooks at the National Library of France

Keywords: ebooks, legal deposit, national bibliography, automated metadata retrieval, cataloguing standards

French law on digital legal deposit covers websites and online content as well as ebooks. It imposes no obligation to produce a bibliography in the traditional form, indexing being sufficient. But despite their innovative characteristics, ebooks are still books, and their bibliographic metadata is closer to that of printed materials than to the indexation of web archives. To set up a complete ebook deposit workflow, the Bibliothèque nationale de France (BnF) benefits from its experience with digital documents and its tradition of legal deposit. This paper aims to present the questions that it faces when dealing with the cataloguing of ebooks and the management of their metadata, and the solutions that are emerging.

Legal deposit was established in 1537 in France and it has followed the development of the national intellectual production and the various media used to disseminate it ever since.

Through a 2006 law on legal deposit of digital content, the Bibliothèque nationale de France has the legal mission of collecting online content as well as printed books. For a long time, this online content has been mostly in the form of websites, but since 2012, the BnF has been working on a specific legal deposit for ebooks. The nature of ebooks is dual, between electronic documents and traditional books, and their status is ambiguous, as the debate within the European Union about their tax rate reveals. Such a legal deposit falls within the 2006 law, but the workflow which allows a better treatment by the BnF and an easier way for publishers to deposit their documents is very close to the traditional legal deposit for printed books. The major issue is that the digital legal deposit law differs on several points from that on printed legal deposit: there is no obligation of comprehensiveness or of producing a national bibliography. These differences have to be kept in mind because they draw a line between the treatment of ebooks and that of printed books.

The dematerialisation of the legal deposit process began with the possibility for publishers to fill in their mandatory declaration online, thanks to a dedicated Extranet. More recently, they have also been able to mandate their distributor to send a metadata flow that acts as that declaration. The next step is the processing of ebooks and their metadata arriving at the BnF through an automatic process. To achieve this new evolution of legal deposit, the BnF has to adopt a position on important bibliographic questions and to resolve tensions between the bibliographic theory and the organisation of such an institution. In many ways, the postulate of a proximity with printed books has its limits, which we must take into account when we decide how best to create and disseminate bibliographic records for ebooks.

Working with publishers' metadata

The project of a legal deposit of ebooks began in mid-2012, with a dialogue with our partners from the publishing world, the Syndicat national de l'édition (French Publishers Association). This first phase was important because the ebook market was quite unknown to the BnF in many of its dimensions: how many ebooks are published per year? What formats are the most common? How does the publishing and commercialisation workflow work? All these questions were crucial to the organisation of a viable legal deposit. One of the first questions we faced during these meetings was that of metadata: how does the information about an ebook go from the author and publisher to the final seller and consumer? As our knowledge of the workflow increased, we realised that some of the main actors add metadata during the process and that the need of a standardised way to transport metadata has therefore preexisted the BnF demand.

The standard widely used within the publishing world (in France and worldwide) is one of the ONIX 1 standards, dedicated to books. ONIX for Books was originally developed by EDItEUR and is maintained today by this company and an international steering committee 2 . It is designed to support computer-to-computer communication, in XML language. An ONIX file can describe printed books as well as electronic books, and can express bibliographic, technical and commercial metadata thanks to a great variety of fields precisely described in an up-to-date documentation available online. Within the French ebook market, the ONIX file describing an ebook is created by the distributor based on the information supplied by the publisher.

The BnF already has experience of processing distributors' ONIX files for printed books.

Since late 2014, publishers have the possibility to make their mandatory legal deposit declaration directly through an ONIX flow provided by their distributors to the BnF. Books are sent separately and when they arrive at the BnF, their digital declarations are checked and then automatically transferred to the cataloguing application for treatment by the cataloguers.

After this last step, some specific metadata created by the BnF (RAMEAU indexing for example) can be sent automatically to the publishers who need it, to complete their own database. This experience was very helpful in the implementation of the ebook legal deposit workflow.

All of our partners use ONIX 3.0 files to transfer ebooks metadata from the distributor to the online sellers. They provided us with samples from their production, so we could have an idea of the quality of these ONIX files. Meanwhile, we conducted a reflection on the form that an ebook record should take within the BnF's General Catalogue 3 . We compared the information from both sources and thus made an ideal ONIX model, with mandatory, optional or wished fields. This model was sent to our partners; it tends to evolve according to the ongoing reflection on the subject and the information provided by distributors.

Samples of the BnF ONIX model, concerning the ebook format and its title: 3 . The BnF already buys ebooks (and access to ebooks). However they are not described within the General Catalogue but within a specific application dedicated to "Electronic resources", such as databases or e-journals.

4 . These values refer to code-lists attached to the standard. Thanks to the ONIX format, the BnF and all its partners have a common way to handle metadata. The ONIX file describing an ebook is mandatory for the legal deposit of that ebook.

Both metadata and ebook files will be uploaded to the BnF sFTP platform by the distributor.

The automatic treatment begins by checks (presence of both files, format compliance checks of EPUB, PDF and ONIX files) and once the files are certified to be well-formed and matching the BnF's requirements, the metadata is converted for the next step, cataloguing.

Organisation of the cataloguing workflow

The aim of this agreement with the publishers was to fit a workflow by which metadata enters automatically the cataloguing channel of the library. The BnF already has experience dealing with ONIX files describing printed books, as mentioned earlier. This work is intellectually still quite close to the traditional method: printed books arrive in the usual way and are handled by cataloguers and the ebooks workflow is quite similar in terms of the treatment of metadata.

As it arrives on the BnF server, the metadata sent by the distributor is controlled both automatically (compliance with the ONIX format but also compliance with the BnF model) and manually. This manual procedure is still under construction, but librarians will have to check whether the incoming ebook comes under our definition of a book or should be sent to one of the BnF's other legal deposit sections (periodicals, maps, music, audiovisual, prints and photographs) to receive the proper bibliographic treatment. After this first step, the ONIX file is converted into an INTERMARC record in the same way whether it describes a printed or an electronic book. The result of this conversion is a rather full basis for a bibliographic record, already mentioning a majority of the needed information (title, contributors, publisher, etc.). The cataloguers then have to check this information and enrich the record to reference level, the highest-quality level of description, as defined by French cataloguing rules, with all authorities, indexing and correct bibliographic description.

The organisation of the cataloguing of ebooks is still in its prefiguration stage, but the major elements are already in place. A taskforce of five cataloguers and a coordinator was created in the unit of the library which already catalogues all the printed books arriving to the legal deposit. As an integral part of this unit, they must be able to catalogue printed books as well as ebooks. During the experimental phase of the project, only a few cataloguers will work with ebooks, defining new ways of working. But the aim is to spread this expertise and to make every cataloguer of this unit able to deal with both ebooks and printed books.

To prepare the arrival of ebooks within the workflow of this unit, a large training and communication program was put in place: several general and specific information sessions took place for both the dedicated taskforce and the rest of the unit. Cataloguers were mostly very positive and keen on information about the project. Formation sessions are also planned between the newcomers and the existing team, so the knowledge about cataloguing at the BnF can be directly shared between experts. Several working groups were created on subjects related to the arrival of ebooks in the unit: cataloguing, training and communication. Dynamic communication media were created internally, namely thematic "digital coffee sessions" and an internal monthly newsletter dedicated to the project. The new cataloguers are fully involved in these initiatives and it made their integration within the unit easier.

The aim of this training and communication program was to help the whole cataloguing team to make this new object and working principles their own. However, the cataloguing of the first ebooks to arrive will be assigned only to those in the taskforce; it will enable us to study and experiment a new way of working and answer questions like what kind of work station these cataloguers need (e.g. two screens or a single, larger one). As the whole workflow is automated, the cataloguers can access the ebooks only when they are available in the digital library, after the preservation step 6 . So their work on the record really finishes and closes the process. Thus they will have the possibility to catalogue with the book "in hand" -or, more precisely, before their eyes. But some questions remain open, such as the suitability of the public interface of the digital library to a consultation in order to catalogue.

We have already learned from our first experience: the taskforce's offices have been brought

closer to those of the rest of the unit and they take part in technical tests. Working sessions are organised on the reading interface and they make remarks which are taken in account for further developments. A "virtual book cart" was created to enable us to distribute incoming ebooks thematically for cataloguing and indexing (mirroring the organisation we have for printed books), to access the ebook and do all the management operations we would do with shelves and book carts in the physical world. The thematic distribution is based on the metadata from the publishers' ONIX, namely the CLIL subject classification system 7 (now aligned with THEMA). Due to its very practical use, the virtual book cart was first developed as a very simple interface, which will evolve as needed.

Besides these very pragmatic points, we had to think on an almost conceptual subject: the definition of an ebook's bibliographic record. This definition determined the mapping of the conversion from the publishers' to the library metadata and thus the information the cataloguers will have to deal with.

What could an ebook record within the catalogue of the BnF be like? To help answer this question, a specific working group on the bibliographic aspects was created from the beginning of the project, to study the needs of the ebooks workflow in this matter. Establishing the bibliographical context has indeed been useful to support other aspects of the project (human resources for cataloguing or preservation, for example). This working group still meets regularly, to follow evolutions on the subject.

The people participating in this working group reflect the complexity of the nature of ebooks: members of the Legal Deposit department (leader of the project and department of the cataloguers of deposited books), the Audiovisual department (which takes care of the legal deposit of multimedia documents) and the Digital and Bibliographic Information department (which is in charge of metadata consistency and standards compliance).

To define what an ebook record could be, this group had to face ontological questions: should the bibliographical description of an ebook be closer to that of a printed monograph or of an electronic document? One of the major elements of context was that these ebooks will be treated by cataloguers who deal with printed monographs. For the time being, the decision was made to treat these documents more as books than as electronic documents.

Once this choice had been made, the next question was how to integrate new metadata in the BnF model. On the one hand, some information doesn't yet exist within the General Catalogue of the library (a file's format and its versions, for example). On the other hand, some bibliographical uses already exist to describe the very diverse collection of the BnF and had to be taken into account: for instance, the notion of the weight of a document is declared in a specific field of our format, but that field is currently used to record the weight of a coin or medal, so another field had to be found for the "weight" of a file (its size).

Meanwhile, this reflection on the ideal ebook record allows innovations that are a driving force for printed books. For instance, when working with the publishers on the ONIX data model, we asked them to provide us with the European Article Numbering (EAN) of other versions of the same book, a field that exists in ONIX (<RelatedProduct>). Thanks to this information, a link is created between the different records during the automated conversion of ONIX into MARC records, if the catalogue already holds a record with the said EAN. The same will also be possible with authority records for authors, by means of the International Standard Name Identifiers (ISNI). Using the links between records for the same book in different formats, it will then be possible to retrieve all the relevant information, ranging from the original title to the link(s) to authority records and to the content type, from the most complete record to automatically enrich the other one(s). Depending on which version of the book is deposited and catalogued first, this means not only that a record created for a printed book can be used to enrich a record for a PDF or an EPUB, but that the reverse will also be possible.

Example of an ebook record in UNIMARC format with information retrieved from a printed book record: Consequently, records of different levels of completeness and standard compliance will coexist within the catalogue. It is a common situation, but it will be particularly intricate because it won't be a simple case of printed and electronic books having different quality records. Some ebooks will have richer records because of the data retrieved from a pre-existing printed book record, and the reverse might be true too. Thus, the very process will induce such a symbiosis between records that we won't be able (should we want it) to separate workflows for printed and electronic books.

The overlap also exists in terms of standards: the French standard applicable to ebooks is NF Z 44-082 Catalogage des documents électroniques, which dates back to 1999. It only gives indications about recording the specific characteristics of electronic documents, the rest of the resource being described under the specifications of the relevant standard (printed books, maps, serials, etc.). Of course, that standard, which predates the rise of ebooks, is now outdated. That is another point we had to take into account to devise the cataloguing framework for ebooks.

"Within a catalogue and beyond" 8

Our first response to the question "How do we let ebooks into the catalogue?" was expressed in terms of format, because it is how we catalogue, in a most concrete way. But the answer lies with standards.

There is no set of standards specifically dedicated to ebooks in France today. The rules are derived from those for printed books and for electronic material, both French cataloguing rules and ISBD. The issue of updating French cataloguing rules is broader than that of ebooks, especially in the global context of switching to RDA. France has had a working group on the adoption of the latter cataloguing rules since 2010. In late 2014, both national bibliographic agencies 9 decided on a policy of converging towards RDA: adopting as much of the code as possible, without compromising our national practices where they are richer or more conform to FRBR than RDA currently is.

Under approach, with general rules that encompass all types of documents, could be useful toward a convergence of records.

For instance, inside the National Library, parallel to our project on the legal deposit of ebooks, there is a distinct project for ebooks coming into the collections by other acquisition modes, and the Audiovisual department also handles digital documents. We share the need to describe system details for an electronic resource. We worked on the in-house INTERMARC format while discussing at a national level on RDA-FR. As fast answers are needed for these projects, the standard is discussed and the format updated in very quick succession, with to and fros because, contrary to the way standards tend to be written, the use cases happen almost simultaneously and we can put our questions directly to those who write them. That is how the INTERMARC field 257 evolved over the course of one year. It used to be specific to the audiovisual collections, to describe the type and size of an electronic resource and had only three subfields, for size, type and linking words. During the past year, we added eight subfields, cancelled one and completely changed the field's structure, so as to use it for every type of electronic resource. It took months, because it was not a case of creating a new field just for one purpose, but taking an existing one and evolving it to the point where it could be used for all types of documents and cataloguing practices.

Experiences like this made us realise early on that one of the biggest hurdles we librarians face is the nature of ebooks. We tend to see them as books first and foremost, and are tempted to deal with them as we do with printed legal deposit material: create reference-level records for all ebooks, and publish them in the National Bibliography. In terms of display, should records be displayed in the books section of the bibliography, mixed with printed books, with only a dedicated title index? In terms of IT developments it would be the quickest and simplest solution. It might be a temporary one though, until a new section of the bibliography or a new website for the whole publication can be created. If we decide on updating the current website, what form would it be better for it to take? Once we have (potentially) several versions of the same title, a "FRBR" display might be considered. A look at the other websites the BnF uses to display metadata would be the first step of that particular study.

Conclusion

Once we look past the first impulse of doing just the same as we have "always" done, we must ask ourselves what service is expected from us. With ebooks, the context of legal deposit changes: ebooks carry with them formatted and standardised metadata. Even if the standards are not those we librarians use, we are provided with more than basic records that already provide a service to users. But is it the service we need to provide? At this point, it looks like a very good step in the right direction, but with still some way to go to be quite up to standards. So how do we close this gap? Automation will be a great help, retrieving data to have the same level of description between records for the same title, but it has its limits. That is where human intervention is necessary. This human intervention will probably be necessary during the early phase of the treatment as well, to control the incoming ebooks and their metadata. We are still in the testing phase, but we now deal with real metadata provided by our publisher partners. Our reflection gains from observing these metadata in our cataloguing environment. New questions come out almost every week and we need to think creatively, which makes the building of ebooks cataloguing very stimulating.

This project is highlighting the convergence of questions libraries are confronted with: the adoption of RDA, the revision of standards, the automation of cataloguing. To answer these questions, we have to take a more holistic view of our activity, transcending the library's sometimes rigid structure.

  -item collection, retailed as separate parts

  elements of the Title (200), Original title (454), Author(s) (200$g, 700, 702) and Summary (330) fields come from the printed book record. The following fields, when present, can also be retrieved: Dissertation note, Uniform title, General note, Reproduction note, With note, Audience characteristics, Subject access fields and Summary, as well as part of the Control field.

  the new name "Bibliographic transition", the group is now tasked with updating French standards into what we call RDA-FR. As it is a very long process, parts of the new standard are published and gradually replace the corresponding parts of French standards. It means that we are currently working with two standards at the same time. But RDA's consolidated 8 . International Federation of Library Associations and Institutions, Barbara Tillett and Ana Lupe Cristán, IFLA cataloguing principles: The Statement of International Cataloguing Principles (ICP) and its glossary : in 20 languages (München: K.G.Saur, 2009). [http://www.ifla.org/files/assets/cataloguing/icp/icp_2009-en.pdf] 9 . The Agence bibliographique de l'enseignement supérieur = Bibliographic Agency for University Libraries (ABES), and the Bibliothèque nationale de France.

  However it is not what the law tell us. Ebooks fall within the scope of the law on digital legal deposit, which was created with the web in mind. It means no obligation for the National Library of instituting a comprehensive legal deposit for ebooks, or of publishing a national bibliography. But our whole reflection on ebooks led us to emphasise the convergences rather than the differences between printed and electronic books, and to create a descriptive model closer to printed books than the web. Furthermore, we know that there is a need for a comprehensive, open national register or database for ebooks, with reference-level, trustworthy records; this was expressed in the Lescure report to the minister of Culture in 2013 10 . The commercial database Electre began providing metadata for ebooks lately. But the BnF has a unique position of observer of the publishing world, both printed and digital. Moreover, the very principle of producing individual records for ebooks in the library's catalogue seems an argument in favour of taking the next step and publishing them in the French National Bibliography.In terms of quality, the National Library is a service provider to a national community, especially through the National Bibliography, which, unlike the General Catalogue, traditionally holds only records of the highest quality. But the Guidelines for bibliographies in the electronic age11 have identified the problem and accepted that, with ebooks, different levels of description are acceptable. It remains for us to determine what level of description to adopt, bearing in mind that our process makes the records for ebooks and printed books tightly interdependent.

	The question of course is how?

ONIX (ONline Information eXchange): "one member of a family of XML-based international standards intended to support computer-to-computer communication between parties involved in creating, distributing, licensing or otherwise making available intellectual property in published form, whether physical or digital." http://www.editeur.org/74/FAQs/#q1

. http://www.editeur.org/8/ONIx/

. Pierre Lescure, Contributions aux politiques culturelles à l'ère numérique (Rapport à la ministre de la Culture, 2013). [http://www.ladocumentationfrancaise.fr/rapports-publics/134000278/index.shtml]

. Maja Žumer (ed.), National bibliographies in the digital age: guidance and new directions (München: Saur, 2009). [http://public.eblib.com/choice/publicfullrecord.aspx?p=454007]


Ahlem Bouhlel

Christophe Curti

Omar Khoumeri

Patrice Vanelle

M ; Koley

M ; Schnuerch

M. D. Mihovilovic

) Romero

M ; Harrak

Y ; Basset

J ; Orue

J A ; Pujol

Efficient one-pot double Buchwald-Hartwig coupling reaction on 5-phenyl-4phenylsulfonyl-2,3-dihydrofuran derivatives

Keywords: One-pot, Double Buchwald-Hartwig coupling, Manganese(III) acetate, Microwave

We report a new and efficient method of conducting a one-pot double Buchwald-Hartwig coupling reaction on 2,3-dihydrofuran derivatives bearing two bromine atoms. This rapid and convenient synthesis allows us to access a great variety of original mixed dicoupled compounds. The strategy appears promising for combinatorial chemistry and pharmacomodulation studies.

In view of our interest in anti-infectious drug discovery, 1 we have recently explored the antileishmaniasis potential of some diamidoximes. Several diamidoximes presenting a 2,3dihydrofuran heterocyclic scaffold and obtained via a single Buchwald-Hartwig coupling reaction (Scheme 1) showed interesting antiparasitic activities. 2 These promising results encouraged us to synthesize a series of dicyano-derivatives using various aminobenzonitriles so as to perform a double Buchwald-Hartwig reaction. Our earlier results had shown that Buchwald-Hartwig amination realized on the sulfone moiety led to better yields. 2 Thus, we were able to use this difference in reactivity to carry out a onepot double Buchwald-Hartwig reaction.

Since Buchwald-Hartwig's discovery, the amination reaction has successfully been applied to heteroaryl substrates, such as pyridines, quinolines, thiophenes, thiazoles, indoles, 1,3,5-triazines, or pyrimidines. 3 Moreover, C-N crosscoupling reaction on dihalogenated compounds has been fairly thoroughly investigated, as reported in the literature. 4 However, there have been few examples of efficiently modulating simple aryl scaffolds, particularly with products containing a sulfone moiety. 5 To our knowledge, very few one-pot Buchwad-Hartwig coupling reactions have been conducted. One of these is reported as a tandem inter-and intramolecular Buchwald-Hartwig amination; 6 while others include an intramolecular domino process, 7 or a double amination on the same aryl halide followed by an intermolecular Heck reaction. 8 Herein, we report a study allowing a convenient one-pot double Buchwald-Hartwig coupling reaction using three aminobenzonitriles differing from the cyano position (ortho, meta, or para) and a 2,3-dihydrofuran derivative bearing two bromine atoms. The combination of these aminobenzonitriles involved in C-N cross coupling reactions allowed us to access several dissymmetric dicoupled products.

The required starting material, 5-(4-bromophenyl)-4-(4bromophenylsulfonyl)-2,2-diphenyl-2,3-dihydrofuran (2), was synthesized in two steps (see Scheme 2). Firstly, the ketosulfone 1 was obtained by using a previously reported microwave irradiated method. 9 In the second step, the ketosulfone 1 was converted into the desired 2,3-dihydrofuran derivative 2 under microwave irradiation, via a manganese(III) acetate-based oxidative cyclization between compound 1 and 1,1-diphenylethene. 10 Thus, we obtained our key-substrate, a double aryl halide (2), to be used in conducting the Buchwald-Hartwig coupling reaction. First of all, the reaction of 5-(4-bromophenyl)-4-(4bromophenylsulfonyl)-2,2-diphenyl-2,3-dihydrofuran (2) with 2-aminobenzonitrile was conducted with only one equivalent of amine. We obtained a mixture of monocoupled 3, 11 dicoupled 4aa, [START_REF]General procedure for the first step optimization: Into a two-necked flask containing 25 mL of dry and degazed toluene, under inert atmosphere were added compound 2 (0.5 g[END_REF] and unreacted 2 products (Scheme 3).

O S R 1 R 2 O O H N HON NH 2 H 2 N NOH R 1 = Me, Ph R 2 = Bn, Ph O S R 1 R 2 O O NC Br Buchwald-Hartwig reaction O S R 1 R 2 O O H N CN NC NH 2 OH.HCl KOtBu NH 2 CN

Scheme 1: Synthesis of amidoximes

The presence of one monocoupling product (3) revealed a difference in reactivity between the two brominated positions. This difference can be attributed to the electron-attracting effect of the sulfonyl group. Indeed, in the oxidative addition step, Pd(0) acts as a nucleophile and preferentially attacks the most electron-deficient position. [START_REF] Schröter | [END_REF] The position on which the first coupling reaction took place was confirmed by X-ray diffraction analysis of compound 3 (2-{4-[2-(4-bromophenyl)-5,5-diphenyl-4,5-dihydrofuran-3-ylsulfonyl]phenylamino}benzonitrile, Fig. 1). 13 In order to optimize the one-pot double Buchwald-Hartwig reaction, we started by investigating the conditions most likely to lead to a majority of monocoupled product in the first step. The study, realized with 2-aminobenzonitrile, examined various parameters (Table 1).

We began with two catalyst systems and different bases (Entries 1-6). We noted that the combined use of Pd(OAc) 2 /BINAP and Cs 2 CO 3 appeared to be the best reactive combination. 14 Then, studies to optimize the temperature were undertaken (Entries 1, 7-10). We noted that yields of monocoupled product 3 increased from rt to 70°C, but decreased on reaching 100°C, favoring the dicoupled product.

Concerning the equivalent number of amine (Entries 1, 11, 14, 16), it appeared that 1.4 equivalent of amine led to the best yield of monocoupled product. Indeed, we observed some selectivity of monosubstituted product (41% of monocoupled vs 17% of dicoupled product). Moreover, as shown in Table 1, the use of three equivalents of amine led to complete consumption of the starting material, and we obtained, as expected, a majority of double-coupled product 4 (67%). This last result (Entry 16) is considered at the time when the second amine was added. Next, we explored the compound produced by the sequential double Buchwald-Hartwig coupling reaction. First, we kept the same catalyst system and the same base, which were the most efficient. Then, in order to maximize double coupling product, we increased the amount of amine and the temperature. The first attempt was performed at 100°C, using 3 equivalents of the second aminobenzonitrile. This second coupling reaction was improved by the use of crown ether. When we tested the influence of crown ether on coupling reactions with the optimized parameters, we observed a significant rate enhancement when stoechiometric amount 18-Crown-6 was added to the reaction mixture (Entries 13, 15, 17).

As reported in the literature, crown ether can facilitate the exchange of the halide with amine in the intermediate palladium complex, resulting in the overall reaction rate acceleration. 15 These optimizations enabled us to carry out the one-pot double sequential Buchwald-Hartwig coupling reaction. We used a combination of three aminobenzonitriles on compound 2, which permitted us to obtain several dissymmetric dicoupled products (4ab, 4ac, 4ba, 4bc, 4ca, 4cb) (Scheme 4, Table 2). Moreover, we were able here to synthesize three compounds per reaction at the same time. The method therefore offers great promise for future pharmacomodulation studies. In summary, we have developed a novel and efficient method for a one-pot sequential double Buchwald-Hartwig coupling reaction on 2,3-dihydrofuran derivatives. We show that by controlling the amount of amine and the temperature, it is possible to synthesize dissymmetric dicoupled products with rather good global coupling yields.

This strategy can now be exploited with various amines, allowing access to a wide range of dihydrofuran derivatives. It should contribute to a combinatorial chemistry approach, of value in pharmacomodulation studies.

Scheme 2 : 2 Scheme 3 :Figure 1 :

 2231 Scheme 2: Synthesis of 5-(4-bromophenyl)-4-(4-bromophenylsulfonyl)-2,2-diphenyl-2,3-dihydrofuran 2

Scheme 4 :

 4 Scheme 4: Reaction of 2 in the one-pot double sequential Buchwald-Hartwig coupling reaction with 2-aminobenzonitrile and 3-aminobenzonitrile

Table 1 :

 1 Survey of Buchwald-Hartwig reaction conditions 1.2 eq. base for 1 eq. aminec Reaction in dry toluene, under argon atmosphere, during 12h, yields for isolated products based on compound 2 d Crown ether in catalytic amount e Crown ether in stoichiometric amount.

	Entry	Amine nbr equivalent	Catalyst a	Base b	Temperature	yield c 2 %	yield c 3 %	yield c 4aa %
	1	0.8	Pd(OAc)2/ BINAP	Cs2CO3	70	41	26	13
	2	0.8	Pd(PPh3)4	Cs2CO3	70	82	7	0
	3	0.8	Pd(OAc)2/ BINAP	K2CO3	70	100	0	0
	4	0.8	Pd(OAc)2/ BINAP	Na2CO3	70	100	0	0
	5	0.8	Pd(OAc)2/ BINAP	K3PO4	70	100	0	0
	6	0.8	Pd(OAc)2/ BINAP	KOtBu	70	60	10	0
	7	0.8	Pd(OAc)2/ BINAP	Cs2CO3	r.t.	100	0	0
	8	0.8	Pd(OAc)2/ BINAP	Cs2CO3	40	83	8	8
	9	0.8	Pd(OAc)2/ BINAP	Cs2CO3	50	50	25	8
	10	0.8	Pd(OAc)2/ BINAP	Cs2CO3	100	10	32	19
	11	1	Pd(OAc)2/ BINAP	Cs2CO3	70	40	29	8
	12 d	1	Pd(OAc)2/ BINAP	Cs2CO3	70	35	23	12
	13 e	1	Pd(OAc)2/ BINAP	Cs2CO3	70	25	37	20
	14	1.4	Pd(OAc)2/ BINAP	Cs2CO3	70	28	41	17
	15 e	1.4	Pd(OAc)2/ BINAP	Cs2CO3	70	5	42	31
	16	3	Pd(OAc)2/ BINAP	Cs2CO3	70	5	18	67
	17 e	3	Pd(OAc)2/ BINAP	Cs2CO3	70	0	16	71
	a 4 mol%

b

Table 2 :

 2 Synthesis of dicoupled products[START_REF]General procedure for one pot double sequential Buchwald-Hartwig coupling reaction: into a two-necked flask containing 50 mL of dry and degazed toluene, under inert atmosphere were added compound 2 (1 g, 1.68 mmol), corresponding first aminobenezonitrile (0.278 g, 2.35 mmol), palladium acetate (0.015 g, 0.07 mmol), BINAP (0.042 g, 0.07 mmol), and cesium carbonate (0.552 g, 2.86 mmol). The reaction mixture was stirred at 70°C from 12h. Then were added the second aminobenzonitrile (0.595 g, 5.04 mmol), crown ether (1.33 g, 5.04 mmol), palladium acetate (0.015 g, 0.07 mmol), BINAP (0.042 g, 0.07 mmol), and cesium carbonate (1.17 g, 6.05 mmol). The reaction mixture was stirred at 100°C from 3h, and monitored by TLC. Solvent evaporation gave a crude mixture which was solubilized in dichloromethane and filtered through Celite in order to remove inorganic salts. The mixture was purified by column chromatography (Dichloromethane/Petrolum Ether/DiethyEther: 6.5/3/0.5) and products obtained were recrystallized from isopropanol. 3-(4-{2-[4-(3-cyanophenylamino)phenyl]-5,5-diphenyl-4,5-dihydrofuran-3-ylsulfonyl}phenylamino)benzonitrile (4bb): white solid, mp 188°C. 1 H NMR (DMSO-d6, 200 MHz):  3.78[END_REF]

	Entry a	First Amine		Second Amine	Total coupling yield %	Dicoupled of 1rst Amine Product/ yield b (%)	Dissymmetric Product / Yield b (%)	Dicoupled of 2nd Amine Product/ yield b (%)
		NC			CN
	1	H 2 N		H 2 N		83	4aa (31)	4ab (35)	4bb (17)
		NC
	2	H 2 N		H 2 N	CN	86	4aa (20)	4ac (32)	4cc( 34)
		CN	NC
	3	H 2 N		H 2 N		71	4bb (14)	4ba (36)	4aa (21)
		CN
	4	H 2 N		H 2 N	CN	47	4bb (11)	4bc (21)	4cc (15)
				NC
	5	H 2 N	CN	H 2 N		72	4cc (16)	4ca (21)	4aa (37)
					CN
	6	H 2 N	CN	H 2 N		47	4cc (7)	4cb (34)	4bb (6)
	a 4 mol% Pd (OAc)2, 4 mol% BINAP, 2.86 mmol Cs2CO3 , 2.35 mmol of first aminobenzonitrile in dry toluene under argon atmosphere at 70°C for
	12 h; then, 4 mol% Pd(OAc)2, 4 mol% BINAP, 6.05 mmol Cs2CO3, 5.04 mmol of second aminobenzonitrile, 5.04 mmol crown ether are added at
	100°C

b

yields for isolated products based on compound 2.

Acknowledgments

This work was supported by the Centre National de le Recherche Scientifique and the Université de la Méditerranée. We would like to express our thanks to Dr V. Remusat for RMN spectra recording.