Noémie Janot

Pascal E Reiller

Gregory V Korshin

Marc F Benedetti
email: benedetti@ipgp.fr

Using spectrophotometric titrations to characterize humic acid reactivity at environmental concentrations

Keywords: Spectrophotometry, potentiometry, titration, humic acid, organic matter, sorption, salt effect BRIEFS

Acid-base spectrophotometric titrations of humic acid are performed to assess humic proton binding groups at environmental concentrations. An operational transfer function is proposed to link spectroscopic changes to site densities variations as determined by acid-base potentiometric titrations.

1/13

ABSTRACT. Potentiometric titration is a common method to characterize dissolved organic matter (DOM) reactivity. Due to the sensitivity of pH electrodes, it is necessary to work with very high DOM (>1 g/L) concentrations that are unrealistic compared to those found in natural waters (0.1 to 100 mg/ L). To obtain proton binding data for concentrations closer to environmental values, spectroscopic titration method is a viable alternative to traditional potentiometric titrations. Spectrophotometric titrations and UV-visible spectra of a diluted solution of purified Aldrich humic acid (5 mg DOC /L) are used to estimate changes in proton binding moieties as function of pH and ionic strength after calculation of differential absorbance spectra variations. After electrostatic correction of spectrophotometric data, there is a linear operational correlation between spectrophotometric and potentiometric data which can be used as a transfer function between the two properties. Spectrophotometric titrations are then used to determine the changes of humic acid protonation after adsorption onto -alumina.

Introduction

Speciation and migration of metals in the environment are partly controlled by their interactions with natural organic matter (NOM) and minerals in soils [START_REF] Mccarthy | Mobilization of transuranic radionuclides from disposal trenches by natural organic matter[END_REF][START_REF] Mccarthy | Lanthanide field tracers demonstrate enhanced transport of transuranic radionuclides by natural organic matter[END_REF]. In aquatic systems, whether an organic molecule partitions to mineral surfaces or remains dissolved determines in large its potential transport and susceptibility to degradation [START_REF] Aufdenkampe | Sorptive fractionation of dissolved organic nitrogen and amino acids onto fine sediments within the Amazon Basin[END_REF]. For instance, in major rivers of the world 90% of transported organic matter is either adsorbed to fine minerals or remains dissolved [START_REF] Meybeck | Carbon, Nitrogen, and Phosphorus transport by world rivers[END_REF][START_REF] Keil | Loss of organic matter from riverine particles in deltas[END_REF]. A better description of ternary metal-NOM-surface systems is needed to improve the understanding of the behavior of metals.

Due to its heterogeneous nature, the composition and chemical properties of NOM are modified during adsorption onto mineral oxides [START_REF] Gu | Adsorption and desorption of natural organic matter on iron oxide: Mechanisms and models[END_REF][START_REF] Hur | Molecular weight fractionation of humic substances by adsorption onto minerals[END_REF][START_REF] Hur | Effects of pH and phosphate on the adsorptive fractionation of purified Aldrich humic acid on kaolinite and hematite[END_REF][START_REF] Kaiser | Sorption of natural organic matter fractions to goethite (a-FeOOH): Effect of chemical composition as revealed by liquid-state C-13 NMR and wet-chemical analysis[END_REF][START_REF] Reiller | Sorption of Aldrich humic acid onto hematite: Insights into fractionation phenomena by electrospray ionization with quadrupole time-of-flight mass spectrometry[END_REF][START_REF] Claret | Fractionation of Suwannee River fulvic acid and Aldrich humic acids on α-Al2O3: spectroscopic evidence[END_REF][START_REF] Saito | Adsorption of humic acid on goethite: Isotherms, charge adjustments, and potential profiles[END_REF]. Previous investigations [START_REF] Davis | Adsorption of dissolved organics in lake water by Aluminum-oxide -Effect of molecular weight[END_REF][START_REF] Day | Adsorption of natural organic matter onto goethite[END_REF] suggest that the NOM fractions of higher molecular weight, greater aromatic and carboxyl functional groups content, and more hydrophobic show preferential adsorption onto mineral oxides. This leads to modeling difficulties of the ternary systems [START_REF] Vermeer | Metal ion adsorption to complexes of humic acid and metal oxides: Deviation from the additivity rule[END_REF][START_REF] Robertson | Humic substances in the global environment and implication on human health[END_REF]. A better knowledge of HS binding moieties modifications after partitioning on mineral surface is necessary to describe the behavior of metals in ternary systems.

Humic substances (HS), mainly composed of humic and fulvic acids are a prominent part of NOM, and are often used as surrogates of NOM.

One of the most accurate ways to quantify HS functional groups is potentiometric titration, generally performed at a high concentration, i.e., c > 500 mg HA /L, to obtain a signal significantly different from background electrolyte titrations. These solution conditions are often unrealistic when compared to concentrations of dissolved organic carbon (DOC) in natural waters, i.e., 0.1 to 50 mg DOC /L, and much greater than those of HS in the supernatant of NOM adsorption experiments [START_REF] Gu | Adsorption and desorption of natural organic matter on iron oxide: Mechanisms and models[END_REF][START_REF] Hur | Molecular weight fractionation of humic substances by adsorption onto minerals[END_REF][START_REF] Hur | Effects of pH and phosphate on the adsorptive fractionation of purified Aldrich humic acid on kaolinite and hematite[END_REF][START_REF] Kaiser | Sorption of natural organic matter fractions to goethite (a-FeOOH): Effect of chemical composition as revealed by liquid-state C-13 NMR and wet-chemical analysis[END_REF][START_REF] Reiller | Sorption of Aldrich humic acid onto hematite: Insights into fractionation phenomena by electrospray ionization with quadrupole time-of-flight mass spectrometry[END_REF][START_REF] Claret | Fractionation of Suwannee River fulvic acid and Aldrich humic acids on α-Al2O3: spectroscopic evidence[END_REF][START_REF] Saito | Adsorption of humic acid on goethite: Isotherms, charge adjustments, and potential profiles[END_REF]. It is necessary to consider an alternative technique to obtain proton binding data of NOM under realistic environmental concentrations.

HS solutions are colored and absorb UV and visible light. UV-Visible spectra of HS solutions, even though they tend to be rather featureless [START_REF] Maccarthy | Humic Substances in soil, sediment and water. Geochemistry, isolation, and characterisation[END_REF], may help to characterize HS sorption-fractionation processes [START_REF] Claret | Fractionation of Suwannee River fulvic acid and Aldrich humic acids on α-Al2O3: spectroscopic evidence[END_REF][START_REF] Korshin | Monitoring the properties of natural organic matter through UV spectroscopy: A consistent theory[END_REF]. Subtle changes in HS spectra induced by varying physico-chemical conditions have been used in differential absorbance spectroscopy to characterize HS [START_REF] Ghosh | UV and visible absorption spectroscopic inverstigations in relation to macromolecular characteristics of humic substances[END_REF][START_REF] Korshin | Use of differential spectroscopy to evaluate the structure and reactivity of humics[END_REF], and to inter- between variations of sample charge and solution absorbance. Previous studies have pointed to the importance of HS conformations that are affected by ionic strength on spectroscopic measurements [START_REF] Del Vecchio | On the origin of the optical properties of humic substances[END_REF][START_REF] Conte | Conformational arrangement of dissolved humic substances. Influence of solution composition on association of humic molecules[END_REF]. Variations of molar extinction coefficients and chromism effect [START_REF] Vekshin | Screening hypochromism in chromophore stacks[END_REF] depend both on chemical parameters of the solution and the HS studied. These variations must be accounted when relating potentiometric and spectrophotometric measurements.

Hereafter, spectrophotometric titrations at different ionic strengths were used to examine the deprotonation of purified Aldrich humic acid. The results were compared with those obtained from potentiometric titrations, in order to validate the spectroscopic method to characterize humic acid reactivity in solutions under environmental conditions and to determine a relationship between results of both methods for this humic acid. A spectrophotometric titration of a supernatant from a HS sorption experiment on α-alumina was also performed under environmentally realistic conditions to test the methodology and to probe the acido-basic properties variation.

Materials and methods

Preparation of samples

Commercial Aldrich humic acid was purified (PAHA) according to ref. [START_REF] Kim | Characterization of humic and fulvic acids from Gorleben groundwater[END_REF]. Stock suspension at 2.5 g DOC /L was prepared by diluting PAHA in NaOH (pH around 10) to completely dissolve the sample. In this work, concentrations of PAHA solutions, noted in g/L, always correspond to g DOC /L. Alumina (α-Al 2 O 3 ) was purchased from Interchim (pure 99.99%, size fraction 200-500 nm). The solid was washed thrice with carbonate-free NaOH and thrice with Millipore water before drying and storage at room temperature under N 2 atmosphere according to ref. [START_REF] Alliot | Sorption of aqueous carbonic, acetic, and oxalic acids onto α-alumina[END_REF].

Potentiometric titrations

All titrations were performed using a computercontrolled system under N 2 atmosphere, in a thermostated vessel (25°C) equipped with a magnetic stirrer, at a HA concentration equal to 0.5 g/L.

Ionic strength (I) was fixed using NaClO 4 (0.01, 0.1, and 0.5 mol/L). The quoted ionic strengths are the initial values before the addition of any titrant.

In data analyses, actual I was calculated for every data point, accounting both background electrolyte

Results and Discussion

Potentiometric titrations

Results of PAHA titrations are shown in Figure S1 of the Supporting Information (SI), together with the fits obtained by the NICA-Donnan model [START_REF] Kinniburgh | Ion binding to natural organic matter: Competition, heterogeneity, stoichiometry and thermodynamic consistency[END_REF]. In this model, the median affinities constants The optimization of NICA-Donnan parameters for the titration curves was calculated using ECOSAT and FIT software [START_REF] Keizer | A computer program for the Calculation of Chemical Speciation and Transport in Soil-Water Systems (ECOSAT 4.7)[END_REF][START_REF] Kinniburgh | FIT Non-linear Optimization Algorithm and User Manual[END_REF]. Modeling parameters are given in Table 1, together with the ones used by Vermeer [START_REF] Vermeer | Metal ion adsorption to complexes of humic acid and metal oxides: Deviation from the additivity rule[END_REF] and Milne et al. [START_REF] Milne | Generic NICA-Donnan model parameters for proton binding by humic substances[END_REF] for Aldrich humic acid. Differences between modeling of the same humic acid used in several studies can be due to (i) range of I studied, (ii) differ-4/13 dx.doi.org/10.1021/es1012142 ences of the background electrolyte used, and (iii) differences in the stock and purification procedure.

(log K i ),
Our parameters are however within the range of those obtained previously.

Spectrophotometric titrations

PAHA absorbance spectra (see insert in Figure 1) show a broad and featureless shape characteristic of HS absorbance spectra throughout the pH range [START_REF] Maccarthy | Humic Substances in soil, sediment and water. Geochemistry, isolation, and characterisation[END_REF]. The absorbance is increasing with the 5/13 [START_REF] Dryer | In situ examination of the protonation behavior of fulvic acids using differential absorbance spectroscopy[END_REF].

The solution at pH≈11 absorbs around 10% more than the same solution at pH≈3. Differential absorbance spectra were calculated using the following equation

 A pH (λ)= 1 l cell [ A pH (λ) DOC - A pH ref (λ ) DOC ref ] (1)
where l cell is the cell length (cm), DOC and The spectrum recorded at the lowest pH value, i.e., pH ref ≈3, is used as a reference to examine the evolution of differential spectra throughout the en-tire pH range, according to ref. [START_REF] Dryer | In situ examination of the protonation behavior of fulvic acids using differential absorbance spectroscopy[END_REF]. Specific features appear in the differential spectra when the solution pH was increased from 3.5 to 10.9 (see Figure 1), such as the large band centered at 370 nm and the peak centered at 270 nm. This latter peak corresponds to the UV region where the -* electron transition occurs for example for phenolic substances and polycyclic aromatic hydrocarbons [START_REF] Chin | Molecular weight, polydispersity, and spectroscopic properties of aquatic humic substances[END_REF], and so become more important with the deprotonation of the aromatic moieties of PAHA.

The broad band at 370 nm and higher wavelengths is similar to the feature observed in the pH-differential spectra of Suwannee River fulvic acid [START_REF] Dryer | In situ examination of the protonation behavior of fulvic acids using differential absorbance spectroscopy[END_REF].

This feature appears to be specific to humic species and can be hypothesized to be associated with inter-chromophore interactions, in accord with observation made in prior publications [START_REF] Del Vecchio | On the origin of the optical properties of humic substances[END_REF].

However, its exact nature remains to be ascertained. [START_REF] Vekshin | Screening hypochromism in chromophore stacks[END_REF]. This is consistent with previous observations that humic molecules tend to undergo aggregation at higher ionic strength, when the electrostatic double layer is more compressed [START_REF] Conte | Conformational arrangement of dissolved humic substances. Influence of solution composition on association of humic molecules[END_REF][START_REF] Duval | Humic substances are soft and permeable: evidence from their electrophoretic mobilities[END_REF].

6/13

Modeling

To model the data, NICA parameters (m i , log (

The only optimized parameters are A 1 (λ), and A 2 (λ), which represent the maximum change of absorbance of two mains groups of chromophores of low and high affinity for protons. These values depend on the chosen wavelength for modeling, here 270 nm. For sake of clarity, they will be henceforth denoted as A 1 and A 2 instead of A 1 (270nm) and A 2 (270nm). S1).

8/13 dx.doi.org/10.1021/es1012142

ΔA pH ( λ )= | A 1 ( λ) ( K1 [H + ] D ) m 1 1+( K1 [ H + ] D ) m 1 -A 1 (λ) ( K 1 [H + ] D ref ) m 1 1+( K1 [ H + ] Dref ) m 1 | + | A 2 ( λ) ( K2 [H + ] D ) m 2 1+( K2 [H + ] D ) m 2 -A 2 (λ) ( K 2 [H + ] D ref ) m 2 1+( K 2 [H + ] D ref ) m 2 |

Comparison of methods

Modeling of potentiometric and spectrophotometric titration curves gave the same distribution of binding sites as seen in Table S1. In both cases, around 51% of signal was due to low affinity-type groups, and 49% to high affinity-type groups.

An additional correction was needed to account for the effect of I on the spectroscopic signal in addition to the Donnan correction. Data at low I were corrected to include results at the higher electrolyte concentration (0.5 mol/L NaClO 4 ), for which the effects of counter ions in the double layer was minimal and had less influence on the solution absorptivity. In the range of I studied here

This correction, suitable in the range of I studied in this study, was then applied to the differential absorbance values:

( A) I ,corr =f I ( A) I ( 4
)
The corrected titration curves plotted against [H + ] D collapsed rather well into a single titration curve independent from ionic strength like for the Master Curve of potentiometric titrations, as shown in Figure 3. dx.doi.org/10.1021/es1012142 (see Figure S3). The charge of non-sorbed PAHA Q R20 was calculated from corrected spectrophotometric titration curve using the linear Q vs. A corr equation obtained previously.

The NICA-Donnan parameters for PAHA fraction generated in the adsorption experiment were optimized using FIT and ECOSAT software [START_REF] Keizer | A computer program for the Calculation of Chemical Speciation and Transport in Soil-Water Systems (ECOSAT 4.7)[END_REF][START_REF] Kinniburgh | FIT Non-linear Optimization Algorithm and User Manual[END_REF] and given in Table 1.

Within this approach, it appears that there is no need to greatly modify the heterogeneity parameters m i before and after sorption, but a shift of the median affinity constants towards higher pH is required for the non-sorbed sample.

During the retention experiment, carried out at pH 6, around 61% of sites of non-sorbed PAHA are deprotonated: 52% of low affinity-type sites and 9% of high affinity-type sites. The former should have been more attracted by the surface than the latter. The modeling suggests a general loss of 50% of low affinity-type sites and 17% of high affinity-type sites after contact with the oxide. This suggests, within the validity limit of the transfer function, that fractions of PAHA molecules that have stayed on the surface contained mostly all of ionized low affinity-type sites and a greater proportion of high-affinity sites than their ionized proportion. Low affinity-type sites are not only composed of aliphatic but also of benzoic including hydroxybenzoic compounds [START_REF] Moulin | Direct characterization of iodine covalently bound to fulvic acids by electrospray mass spectrometry[END_REF][START_REF] These | Determination of molecular formulas and structural regularities of low molecular weight fulvic acids by size-exclusion chromatography with electrospray ionization quadrupole time-of-flight mass spectrometry[END_REF], and the sorption data of HS and of phthalic [START_REF] Gu | Adsorption and desorption of different organic-matter fractions on iron-oxide[END_REF][START_REF] Ali | Competitive sorption of simple organic acids and sulfate on goethite[END_REF] or hydroxybenzoic acids [START_REF] Davis | Effect of adsorbed complexing ligands on trace-metal uptake by hydrous oxides[END_REF][START_REF] Evanko | Influence of structural features on sorption of NOM-analogue organic acids to goethite[END_REF] on iron and aluminum (oxy)hydroxide extend largely after the pK of their first carboxylic function as it is the case for HS [START_REF] Varadachari | Complexation of humic substances with oxides of iron and aluminum[END_REF][START_REF] Meier | Fractionation of aquatic natural organic matter upon sorption to goethite and kaolinite[END_REF][START_REF] Reiller | Retention behaviour of humic substances onto mineral surfaces and consequences upon thorium (IV) mobility: case of iron oxides[END_REF]. One can thus understand that high-affinity-type sites are proportionally overrepresented on the surface as it was evidenced by Claret et al. [START_REF] Claret | Fractionation of Suwannee River fulvic acid and Aldrich humic acids on α-Al2O3: spectroscopic evidence[END_REF].

  pret titration data of fulvic acids in dilute solution, e.g., 5 mg DOC /L[START_REF] Dryer | In situ examination of the protonation behavior of fulvic acids using differential absorbance spectroscopy[END_REF].These spectrophotometric titrations allow examining the evolution of absorbance spectra with changes in pH. HS light-absorbing functional groups, or chromophores, are deemed to typically contain conjugated double bonds and aromatic rings. The deprotonation of chromophores at increasing pH causes modification of the chromophores' absorbance spectra and/or formation of new absorbing centers and leads to a progressive modification of their absorbance properties. In contrast, potentiometric titrations determine the development of the sample charge within the pH range. So far, no attempt has been made to directly link the evolution of NOM absorbance signal to the change in charge with changes in pH. The aim of this study is to investigate the possible link between these two phenomena, even an operational one. The functional groups determined by potentiometry are composed of, bound to, or in close vicinity of the HS molecules chromophores. It seemed then possible to find a transfer function 2/13 dx.doi.org/10.1021/es1012142

  ions and free H + and OH -. The pH values of the solutions were controlled during titrations by addition of 0.1 mol/L HClO 4 and NaOH solutions. Base titrant (titrisol for 0.1 mol/L solution) was prepared with degassed Millipore water. The pH values were recorded with two pH Metrohm 6.0133.100 glass electrodes and a single Metrohm 6.0733.100 reference electrode. The reference electrode was connected to the reaction vessel via an electrolyte bridge filled with NaCl at the background electrolyte concentration to prevent KClO 4 precipitation in the system. The pH electrodes were calibrated by performing a blank titration of the background electrolyte prior to the sample titration. The aqueous suspension was purged with N 2 at pH=3 for 4 hours. The suspension was then titrated by adding small volumes of titrant and pH was recorded as a function of the titrant volume added to the suspension. After each addition, a drift criterion for pH was used (mV/min< 0.05) and a maximum time of 15 minutes was set for acquiring each data point. A similar procedure was followed for the blank solution titration. Three 3/13 dx.doi.org/10.1021/es1012142 forward and backward titrations were done to eliminate the hysteresis effect (27). Absorbance measurements Absorbance titrations. After potentiometric titrations, solutions were diluted in background electrolyte to obtain 100 ml of solution at a concentration of 5 mg/L in a thermostated vessel at 25°C. After acid addition (pH 3), the solution was N 2 -purged for 1 hour. The pH was increased by addition of NaOH at 0.01 or 0.1 mol/L. Absorbance spectra were recorded in a 5 cm quartz cuvette at circa 0.5 pH intervals between pH 3 and 11 using a Thermo Evolution 600 UV/ Visible spectrophotometer between 190 and 600 nm. UV/Visible spectra were recorded at room temperature (25±4°C). It was checked that variations of temperature between 15 and 35°C had no influence on solution absorption (data not shown). The final data were corrected for dilution effects due to acid or base additions. Influence of ionic strength on solution absorbance. To study the influence of I on absorbance of the solution, 500mL of a 5 mg/L PAHA solution at I=5 mmol/L NaClO 4 was made, and acidified with HClO 4 (0.1mol/L) to pH 3. 50 mL-aliquots from this solution were sampled and weighted solid NaClO 4 was added in each sample to obtain solutions with electrolyte concentrations of 0.01, 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5mol/L Na-ClO 4 . The pH values were adjusted if needed, and absorbance spectra were recorded. Adsorption experiment Three solutions of 10 g/L α-Al 2 O 3 and 100 mg/L PAHA, I=0.1 mol/L NaClO 4 and adjusted to pH 6, were made in 10.4 ml polycarbonate Beckman centrifugation tubes (41121703). After 5 days of equilibration, the solutions were ultra-centrifuged at 60,000 rpm for 2 hours. The supernatants were mixed and the solution was diluted in 0.1mol/L NaClO 4 to obtain a 100-mL solution of 5 mg/L, which was then titrated using the spectrophotometric method previously described. PAHA concentration in the supernatant was measured using Shimadzu TOC-VCSH analyzer and was 26.5% of the initial content of PAHA.

  and the heterogeneity of distribution (m i ) for the two main types of binding sites of humic acid (low-affinity, or so-called carboxylic, and high-affinity of so called phenolic groups) are fitted. The electrostatic parameters are obtained using the Master Curve procedure (27), optimizing the Donnan parameter b in order to merge the original curves. The pH values were corrected for concentrations of protons using Davies equation (29).

Figure 1 .

 1 Figure 1. Differential absorbance spectra of PAHA in 0.1 mol/L NaClO 4 (pH ref =2.9). The original absorbance spectra are shown in the insert.

  DOC ref (mg/L) are the dilution-corrected concentrations of DOC in the solution at the pH of interest and at the chosen reference pH, respectively. A(λ) and A(λ) are the absorbance values measured at a given wavelength λ at the pH of interest and at the reference pH, respectively.

Figure 2 .Figure 2

 22 Figure 2. DOC-normalized absorbance spectra of PAHA solutions (~5 mg/L) at pH 3, I = 0.005 -0.5 mol/L NaClO 4 .

Figure 3 .

 3 Figure 3. Original and corrected spectrophotometric titration curves of PAHA at I = 0.01 (◊), 0.1 (□), and 0.5 (4 ) mol/L NaClO 4 . Results are plotted against the concentration of protons in the Donnan gel [H 3 O + ] D . The close symbols are the original data. The open symbols are the data corrected from electrostatic component (0.5 mol/L being the reference for correction, both curves are stacked). The lines are the Master Curve from the potentiometric titrations (on the right axis).

  K i ) of PAHA obtained by potentiometric titrations were used. The electrostatic effects were accounted by the Donnan model, using the concentration of protons into the Donnan gel at given pH [H + ] D and at the reference pH [H + ] Dref . The absorbance titration curves were modeled using the following equation, derived from the NICA equation:

  Figure S2 represents the titration curve with the respective influence of the two main groups of chromophores, and the result of modeling for the experiment at 0.1mol/L NaClO 4 . As shown in Figure 4, the overall maximum change of absorbance by the two main groups of chromophores increased linearly with logI, with parameters of linear regression being dependent on modeling wavelength. The conformation of humic acid, which changes with the concentration of electrolyte ions, had an influence on the absorbance of these solutions. But the proportion of the two mains groups of chromophores did not change significantly: within uncertainties and remained the same for all of the ionic strength studied (Table

Figure 4 .

 4 Figure 4. Comparison of the evolution of maximal absorbance A 1 +A 2 as a function of logI.The continuous line is the result of the linear regression and the dotted ones the statistical envelope (A 1 +A 2 ) ± s(A 1 +A 2 ).

( 0 .

 0 01 to 0.5 mol/L) there is a linear relationship between the sum of maximal change of absorbance of both types of groups (A 1 +A 2 ) and logI as shown in Figure 4: A 1 +A 2 = c log(I) + d, with c = 5.27±1.02 and d = 17.33±1.30. The correction factor f I was calculated from this linear regression. f I = c log (0.5)+d c log (I )+d

Figure 5 13 Figure 5 .Al 2 O 3 .

 513523 Figure 5 shows charge versus electrostatic-corrected differential absorbance values at 270 nm for the same concentrations of protons and the three ionic strengths. There is a linear relationship between both properties. The linear regression of Q

Figure 6 .

 6 Figure 6. Differential absorbance spectra of PAHA in 0.1 mol/L NaClO 4 after fractionation onto a-Al 2 O 3 (R=10mg/g).

Table 1 .

 1 NICA-Donnan modeling parameters for PAHA potentiometric titration and calculated charge from absorbance measurements after retention experiment.

		log K 1	m 1	Q 1	log K 2	m 2	Q 2	Q 0	b
	HH18 (32)	3.76	0.55	2.94	8.07	0.24	2.40		0.69
	HH24 (32)	2.87	0.89	2.31	8.00 (fixed)	0.14	5.34		0.25
	PAHA (44)	4.03	0.44	3.74	8.48	0.53	1.30
	this study	2.66	0.81	3.24	6.90	0.29	2.88	0.60	0.4
	PAHA after fractionation onto α-Al 2 O 3 (R=10mg/g)	2.90	0.85	1.61	8.00	0.25	2.37	0.29	0.4

Acknowledgment. This work was financed through the MRISQ (DEN/DISN/AvC) project of CEA. This is IPGP contribution 3049.


Tristan Haute

Camille Kelbel

François Briatte

Giulia Sandri
email: giulia.sandri@univ-catholille.fr

Down with Covid: patterns of electoral turnout in the 2020 French local elections

Keywords: COVID-19, voting, local elections, socioeconomic variables, France

This article contributes to the ongoing research effort assessing the effects of the COVID-19 crisis on turnout in the municipal elections held in France in March and June 2020. Holding the election in pandemic times caused turnout to drop significantly, but unevenly so across the electorate. We use both aggregate electoral results at the polling station level and individual-level data drawn from a survey we conducted between June and July 2020 3 . If fear of contagion partly explains voters' abstention, this article highlights the contradictory effects of the pandemic on the socioeconomic determinants of voter turnout. On the one hand, the variation in turnout levels by age, which usually is quite significant in France, has considerably decreased in 2020. On the other hand, the differences in turnout levels according to the voters' economic and social status have been reinforced during the pandemic. This analysis of local individual data shows that the health crisis has generated important consequences also on the patterns of social inequalities in political representation.

Introduction

The COVID-19 pandemic has caused the rescheduling of elections in many political systems. However, while 71 countries across the world decided to postpone national or subnational elections between February and August 2020, at least 60 other countries have held elections in the same period 4 . This unprecedented event offers an interesting setting for measuring the impact of a global public health crisis on voting behavior. Recent and preliminary studies have started exploiting that opportunity, and have shown that the pandemic has caused either a rally-round-the-flag effect, with massive electoral support for incumbents [START_REF] Leininger | Voting at the Dawn of a Global Pandemic[END_REF][START_REF] Neihouser | Élections municipales: ce que révèle l'analyse du premier tour de mars 2020[END_REF], or massive abstention [START_REF] Brouard | Participation aux élections municipales 2020 en métropole: l'effet du Covid-19[END_REF].

In France, the first round of the municipal elections was maintained on March 15 despite the start of strict confinement measures a few days earlier. Only 44.7% of registered voters went to the polls compared to 63.6% in 2014, allowing to designate in that first round 30,125 mayors (out of 34,968). The next day, the government proclaimed the general lockdown and decided to postpone the second round of the elections, which only took place in late June. Turnout then only reached 41.6% in the remaining 4,843 communes while the average turnout rate in the second round in 2014 was of 62.1%. This drop in turnout in 2020, although impressive, is also part of a continuous decline of turnout in local elections in France, that started in 1989 [START_REF] Jaffré | L'abstention aux élections municipales depuis l'après-guerre (1947-2014)[END_REF] with 2014 already marking a historically low point before.

This situation creates both an unprecedented context and a quasi-experimental setting for testing the impact of crises on electoral turnout, a topic on which we know relatively and comparatively little. If health crises cause a decrease in electoral turnout, what about the other determinants of turnout that are generally pointed out to explain such declines?

The overarching theoretical issue raised by the COVID-19 context is whether we should expect (different types of) crises to have any sort of effect on turnout. In a rational choice perspective, there are little incentives to go to the polls as individual voters have only marginal effects on the results [START_REF] Blais | To Vote or Not to Vote: The Merits and Limits of Rational Choice Theory[END_REF]. Thus, adding a further obstacle -or, to stick to the vocabulary, increasing the cost of voting (since going to the polls under a pandemic is likely to be seen as more risky, uncertain, or simply more complicated) -should lead to a decreased turnout.

Drawing more on the tradition of the social-psychological models of political engagement, some have objected that difficult times are propitious for a surge of the sense of civic duty [START_REF] Uhlaner | Relational Goods and Participation: Incorporating Sociability into a Theory of Rational Action[END_REF]. In other words, the main triggers of the vote in terms of resources and motivations, be them their socioeconomic situation, political efficacy, or values and norms [START_REF] Brady | Beyond SES: A Resource Model of Political Participation[END_REF], are unlikely to be negatively affected in the short-term, even to the contrary. If such is the case, then external shocks should lead to more turnout at the individual level, but mostly among those that display a more acute sense of civic duty. Along the same lines but somewhat contradictorily, famous empirical studies more specifically focusing on the act of voting have shown that social pressure -i.e. being praised for upholding a social norm -and social contacts [START_REF] Gerber | Social Pressure and Voter Turnout: Evidence from a Large-Scale Field Experiment[END_REF] are likely to enhance political participation, something potential voters have been arguably less subject to in recent months.

The current coronavirus sanitary crisis is specific mostly in two respects. At the macro level, it constitutes an external shock. There are only a few empirical actual works linking external events to electoral behavior and more specifically to participation patterns. Some isolated works have studied the impact of natural phenomena such as weather conditions or extreme climate events on turnout. Somewhat unsurprisingly, heavy showers have thus been found to lead to the demobilization of voters [START_REF] Arnold | Only Conservatives are Voting in the Rain: Evidence from German Local and State Elections[END_REF], albeit with varying effects depending on the national setting in which they occurred (Persson, Sundell, and Öhrvall 2014) or on sense of civic duty [START_REF] Knack | Does Rain Help the Republicans? Theory and Evidence on Turnout and the Vote[END_REF]). In the case of massive floods, however, Bodet and his colleagues (2016) find no effect on voter turnout in their indepth study on the Calgary case. Yet another type of external shock that may shed some light on current events are terrorist attacks. Although vote choices are impacted, especially if elections are held closely after, their punctual nature has seemingly made their impact on turnout negligible (Berrebi and Klor 2008, 289-290).

At the micro level, however, the current crisis may have a direct impact especially since it touches upon health. We know little about health and voting, except perhaps precisely that at the individual level poor health impedes turnout, or at least motivation to take part [START_REF] Denny | Analysing the Relationship Between Voter Turnout and Health in Ireland[END_REF][START_REF] Mattila | Healthy Voting: The Effect of Self-Reported Health on Turnout in 30 Countries[END_REF][START_REF] Gollust | The Bodies Politic: Chronic Health Conditions and Voter Turnout in 2008 Elections[END_REF][START_REF] Pacheco | Incorporating Health into Studies of Political Behavior[END_REF], with arguments ranging from the time-consuming nature of taking care of one's own condition to ill people displaying lower levels of political efficacy.

There are few studies to date that have studied the impact of the current health and sanitary crisis upon elections and they have produced mixed results. In the case of France, some, however, have observed that the higher the turnout in a municipality, the greater the excess mortality due to COVID-19 [START_REF] Bertoli | Turnout in the Municipal Elections of March 2020 and Excess Mortality During the COVID-19 Epidemic in France[END_REF]. Along the same lines, [START_REF] Zeitoun | Reciprocal Association Between Participation to a National Election and the Epidemic Spread of COVID-19 in France: Nationwide Observational and Dynamic Modeling Study[END_REF] have shown that the greater the risk of epidemics on the territory of a municipality, the lower the abstention. By contrast, basing their analysis on the first round and data collected at the aggregate level on almost 10,000 municipalities, [START_REF] Brouard | Participation aux élections municipales 2020 en métropole: l'effet du Covid-19[END_REF] evidenced that the more a department is affected by the COVID-19 pandemic, the more abstention has increased compared to the 2014 elections (based on several different public health indicators that they use as a proxy for the perceived risk). Similar results are drawn by [START_REF] Noury | How Does COVID-19 Affect Electoral Participation? Evidence from the French Municipal Elections[END_REF].

Likewise, according to the survey conducted at the local level we used in this article, a significant proportion of voters (42.1% in the first round, 35.9% in the second round) declared that they would not have abstained if the health crisis had not taken place. The health dimension alone is however insufficient to explain the overall low levels of turnout and in particular its decline between the first and the second round. The Brouard and McAvay study (2020) carries several specific insights on this issue. On the one hand, it shows that higher proportions of older voters (over 65 years of age) in a municipality led to lower turnout rates in 2020 compared to their 2014 levels. On the other hand, the sociodemographic characteristics of the municipalities are associated with significant variations in abstention; the more the proportion of high school graduates has increased, the less abstention followed a similar path.

More generally, previous studies on the relationships between voter turnout and traditional sociodemographic variables (gender, age, socio-professional category, level of education) have concluded until recently that higher shares of abstainers are to be found in the ranks of the youngest voters or the members of the working class. This is especially true of France, where the so-called "heavy variables" or main socioeconomic features of the electorate (age, education level and socio-5 There are 63 additional polling stations whose boundaries were changed between 2014 and 2020 and that are not included in the current analysis.

6

The research team consists of the authors of this article as well as Marie Neihouser and Felix-Christopher von Nostitz (Université Catholique de Lille, ESPOL).

professional situation) have almost invariably been found to preserve their discriminatory power in determining turnout [START_REF] Braconnier | The Heavy Variables Are Still Alive and Kicking. The Drop in Voter Turnout and the Increase in Electoral Disparities in Spring 2017[END_REF].

Overall, this article examines the social determinants of electoral turnout in times of crisis. Based on the case of the 2020 municipal elections in France and comparing the profile of voters with other ballots, we consider whether the drop in turnout, which we assume to be largely related to the health crisis, is affecting all voters in the same way. In other words, have social inequalities in electoral participation, which are highly prevalent in France, been maintained, reduced or reinforced under the effect of the health crisis?

Materials and methods

This article combines data both at aggregate (electoral results at the polling station level) and at individual levels (original survey data) on a specific case study, namely the metropolitan area of Lille, which is composed of 95 different municipalities and which represents as such the fourth largest French city (1,146,320 inhabitants in 2017). The case study is selected because of its sociodemographic characteristics: the metropolitan area is mostly urban, with high population density, and is structured by strong social inequalities (Collectif Degeyter 2017) which traditionally affect political dynamics, especially at the electoral level [START_REF] Rivière | Studying Electoral Cleavages from the Intra-Regional to the Infra-Urban Scale. The Case of the 2010 Regional Election in Nord-Pas de Calais[END_REF].

At the aggregate level, we compared the turnout rates at the 2014 and 2020 municipal electionscalculated at the level of the 658 polling stations 5 of the Lille metropolitan area -with demographic data from the electoral listings and with socioeconomic data from the population census (see Table 1).

The comparison between population census data and electoral listings data required a reapportion procedure. We carried it out using the "spReapportion" R package [START_REF] Gombin | spReapportion: Reapportion Data from One Geography to Another[END_REF], due to the fact that sub-municipal census data are not available at the polling station level, but only at the level of the socalled "IRIS" statistical units (Ilots regroupés pour l'information statistique), a territorial unit of the same order of magnitude. For each election, we then calculated the correlation between turnout rates and several socio-economic variables related to eligible voters and local residents, including age, education attainment and occupational status.

At the individual level, we use original opinion poll data from the "PELMEL" ("Participation ÉLectorale dans la MEtropole Lilloise" -Electoral participation in the Lille metropolitan area) surveys. This survey was carried out online by two research centers (ESPOL and CERAPS) 6 and a polling institute, Dynata France, based on a sample of 863 respondents, representative of the population of the Lille metropolitan area aged 18 and over. The sample was selected according to age and gender population quotas, and we used the "icarus" R package [START_REF] Rebecq | Icarus: An R Package for Calibration in Survey Sampling[END_REF] to compute poststratification weights in order to match the marginal distribution of the sample to known population margins, using levels of educational attainment and vote choices in the first round of the 2017 presidential election.

To analyze which factors robustly determine electoral behavior in our survey, we estimate two logistic regression models, using voting in the first round of the municipal elections of 2020 and voting in the first round of the presidential election of 2017 as dependent variables. The predictors included in the models are gender, age, level of education, current or last occupation, and interest in politics (at the local level for the municipal election, at the national level for the presidential election).

Figure 1 shows the estimated coefficients of both models, the full results of which are listed in Table 2 along with voting rates per predictor.

Results

Observing the relationships between voter turnout and traditional sociodemographic variables (gender, age, socio-professional category, level of education), and taking into consideration the specificities of French social context, two major results appear in 2020 municipal elections. On the one hand, the participation gaps based on the age of voters have narrowed in 2020 compared to previous elections, although seniors are still among the most active participants. On the other hand, however, differences in turnout according to economic and social status have stayed the same, or even increased, due to the sanitary context.

Comparing the profile of voters reveals a narrowing of participation gaps by age in 2020 (see Table 1). According to our survey, voters aged 18-29 in 2020 who were also eligible to vote in 2017 participated significantly less than their elders in the first round of the presidential election (65.2% vs 78.7% of all respondents) (Table 2). For the first round of the 2020 municipal election, however, the difference in turnout was smaller and not statistically significant. Nevertheless, the oldest voters -i.e. those aged 45 and over -are still the most likely to participate in any given election.

Similarly, an analysis at the level of polling stations in the Lille metropolitan area (Table 1) reveals that turnout is positively correlated with the average age of voters in a polling station, whether in the first or second round of the 2020 municipal elections (+0.39 for both rounds). However, this relationship was much stronger in 2014 (coefficients of +0.52 in the first round and +0.59 in the second round). Therefore, while the decline in turnout concerns all age categories, it is more significant among seniors. Some of them, who are more "at risk", may have given up participating for fear of contamination. Nonetheless, inequalities in turnout based on age have not disappeared, as young people remain more marginalized from electoral practice than their elders do. While age-related disparities in turnout narrowed between 2014 and 2020, those related to socioeconomic status appear to have remained constant in 2020, or have even increased.

Comparing the profile of voters between the 2017 presidential election and the 2020 municipal elections may indicate a weakening of social inequalities in turnout. For example, university graduates voted significantly more in the first round of the 2017 presidential election (90.5%) than all respondents (78.7%), a difference not found in the first round of the 2020 municipal elections (64.3% vs 60.1%). However, if education has often been pointed out as the single most significant factor influencing one's propensity to go to the polls and to participate politically, it should be remembered that, in municipal elections in France, differences in turnout according to socio-professional position or level of education are traditionally smaller than in national elections. This is notably because geographical mobility, which particularly concerns university graduates and managers, does not favor their participation in local elections as shown previously by [START_REF] Héran | La double élection de 1995: exclusion sociale et stratégie d'abstention[END_REF].

Furthermore, some of the social groups with relatively lower participation in the 2017 presidential election appear to be still disengaged from the voting process in the first round of the 2020 elections. This is the case for people whose current or last employment contract was non-permanent: only 55.1% of them voted in the first round of the 2020 municipal elections compared to 60.1% of all respondents. The same is true for respondents who have never worked, with only 27.7% of them having voted in the first round of the 2020 municipal elections (see Table 2). These results confirm that socioeconomic status strongly affects political participation in general and electoral participation in particular. Note: Point estimates show the log-odds of the models summarized in Table 2, with 95% confidence intervals.

Baseline categories are being male, aged 45-59, with high school education, on permanent employment, with some interest in either local or national politics, for the municipal and presidential models respectively. Source: PELMEL survey, 2020. Polling station level analyses lead to similar conclusions. In Table 1, the turnout in a polling station is much more correlated to the share of university graduates in 2020 than in 2014 (+0.42 in the first round of 2020 vs +0.28 in the first round of 2014) or to the share of managers (coefficients of +0.40 in the first round of 2020 vs +0.24 in the first round of 2014). Other relationships appear also to be slightly less important in 2020 than in 2014. However, Table 1 reveals stable relationships over time.

For example, whatever the ballot considered, turnout at a polling station is always negatively correlated with the share of unemployed or inactive people, and to that of immigrants or social housing tenants. Conversely, it is always positively correlated with the share of intermediate professions, self-employed workers and homeowners.

At the meso-level, social or group processes may further separate a large part of the population from polling stations. Voting is above all part of collective dynamics -family, professional and interpersonal -and cannot be dissociated from reference groups and since more recently also from social media. It is these more or less diffuse influences that "activate" the civic norm in variable ways in precise contexts. Voting or not voting thus also depends on the state of the collective organization of the social group (or class) and its mobilization [START_REF] Braconnier | La démocratie de l'abstention[END_REF].

Finally, an interest in politics, which is known to be socially determined -because those who display a higher level of political interest are more often found among the ranks of the most educated, betteroff citizens -but is a variable in itself, seem to still go hand in hand with greater electoral mobilization. Respondents who were very interested or somewhat interested in politics overwhelmingly voted in the first round of the 2020 municipal elections (82.5% and 67.8% respectively), as they did in the first round of the 2017 presidential elections (88.7% and 83.4% respectively). Conversely, the majority of those not at all interested in politics remained on the sidelines in both 2020 (34.2%) and 2017 (53.3%). Finally, in 2020, individuals with little interest in politics were barely more mobilized than those with no interest at all (44.9% vs 34.2%), while in 2017 they were almost as mobilized as individuals with a fair interest in politics (77.7% vs 83.4%) (see Table 2). The public health crisis therefore primarily demobilized the citizens least interested in politics, and this holds even if one controls for various other socio-economic factors, as reflected in the predicted probabilities shown in Figures 2 and3.

Figure 2. Predicted probabilities of voting in municipal elections (2020) by age, education, and interest in politics.

Note: Point estimates show the predicted probabilities of the models summarized in Table 2, with 95% confidence intervals. The main facets of each plot show the varying effects of (from left to right, decreasing) interest in politics. Source: PELMEL survey, 2020.

Discussion

The COVID-19 pandemic had a major impact on the ballots held during the ensuing health crisis. In France, it contributed to an increase in abstention between the 2014 and 2020 municipal elections. Above all, it also had an impact on the inequalities traditionally observed in terms of turnout. In particular, the 2020 municipal elections saw a narrowing of the participation gap according to the age of voters, probably due to the higher mortality risk associated with COVID-19 among the elderly.

However, the age-related differences in voter turnout did not entirely disappear. This suggests that abstention is a phenomenon determined by a multiplicity of factors. Moreover, these elections also saw a worsening of inequalities in turnout by social and economic status, while interest in politics remains a highly predictive variable. Our results seem thus to confirm previous findings showing that, in case of natural events, the ensuing electoral demobilization affects voters differently according to both their sense of civic duty and their partisan preference, which is itself very much socially situated -even though these relationships are not verified in all national contexts.

Considering abstention is a necessary prerequisite for any analysis of election results and the impact of COVID-19 on these. Indeed, both the massive level of abstention and the possible changes in its characteristics, which are highly dependent on local contexts and particularly on the spread of the virus during the first round, have undeniably impacted electoral outcomes. The low level of mobilization may have favored the re-election of well-established outgoing teams, while the greater than usual demobilization of voters least interested in politics and belonging to disadvantaged social groups may have eroded the performance of certain parties, both on the far right and on the left.

Figure 1 .

 1 Figure 1. Comparison of log-odds of voting in the municipal (2020) and presidential (2017) elections.

Figure 3 .

 3 Figure 3. Predicted probabilities of voting in presidential (2017) election by age, education and interest in politics.

Table 1 .

 1 Correlation matrix of municipal election vote rates and sociodemographic characteristics, Lille metropolitan area.

	% Vote in Round 1 in 2020 +0.39 +0.42 -0.41 +0.40 +0.52 % of self-employed +0.45 Mean voter age % of university graduates % with no high school diploma % of managers % of intermediate professions % of unemployed -0.63 % of inactive -0.49 (nonworking) % of homeowners +0.46 % of social housing -0.51 tenants % of immigrants -0.61 N (polling stations) 658	% Vote in Round 2 in 2020 +0.39 +0.32 -0.28 +0.33 +0.38 +0.36 -0.60 -0.56 +0.44 -0.54 -0.57 285	% Vote in Round 1 in 2014 +0.52 +0.28 -0.31 +0.24 +0.57 +0.41 -0.75 -0.55 +0.68 -0.56 -0.73 658	% Vote in Round 2 in 2014 +0.59 +0.20 +0.17 +0.15 +0.47 +0.42 -0.74 -0.57 +0.70 -0.49 -0.72 359

Note: All Pearson correlation coefficients above at are statistically significant at p < 0.01. The unit of analysis is polling station areas located in the Lille metropolitan area as of 1 January 2020. In order to match them with population census data, we only observe polling station areas with identical boundaries in 2014 and 2020. Not all stations are used during the second round, hence the lower sample size for those.

Source: French Ministry of the Interior for the vote rates, electoral listings by the Préfecture du Nord for polling stations, and French Census by INSEE for the sociodemographic data, which are from 2016.

Table 2 .

 2 Survey-weighted logistic regression models of voting in the municipal (2020) and presidential (2017) elections The dependent variable is voting in one of the elections. Baseline categories are marked as "ref". Both models are estimated on survey-weighted observations using the "survey" R package[START_REF] Lumley | Survey: Analysis of Complex Survey Samples[END_REF], with pseudo-R2 statistics computed using the Nagelkerke method[START_REF] Lumley | Pseudo-R2 Statistics Under Complex Sampling[END_REF]. Design-based standard errors for the log-odds are shown in brackets. Two-tailed p-values: ***p < 0.001, **p < 0.01, *p < 0.05. Source: PELMEL survey, 2020. The "survey" R package fits weighted logistic regression models by maximizing the Horvitz-Thompson estimator of the population loglikelihood, which means that they do not have a pseudo log-likelihood[START_REF] Lumley | Survey: Analysis of Complex Survey Samples[END_REF].

	Variable Gender Age Educational attainment Occupation (current or last) Interest in politics Constant N ( respondents ) (Full sample) Male Female 18-29 30-44 45-59 60+ Less than high school High school Higher education Permanent Non-permanent Never worked Self-employed A lot Some Little None Akaike Information Criterion Pseudo-R 2	% Voted in municipal election 2020, Round 1 60.1 60.7 59.5 53.8 51.1 62.7 69.1 56.9 59.6 64.3 65.8 55.1 27.7 68.4 82.5 67.8 44.9 34.2 699	Log-odds (SE) ref 0.12 (0.21) 0.22 (0.33) -0.53* ref 0.29 (0.31) -0. 24 (0.26) ref -0.09 (0.26) ref -0.43 (0.28) -1.61* ** (0.39) 0.04 (0.38) 0.82** (0.31) ref -1.02* ** (0.25) -1.39* ** (0.35) 1.20** * (0.30) 699 838.48 0.24	Odds ratio ref 1.13 1.24 0.59* ref 1.33 0.66 ref 0.92 ref 0.65 0.20** * 1.04 2.27** Ref 0.36** * 0.25** 3.34** *	% Voted in presidential election 2017, Round 1 78.7 77.0 80.0 65.2 74.7 80.6 86.6 70.6 77.5 90.5 84.1 71.5 55.5 73.9 88.7 83.4 77.7 53.3 659	Log-odds (SE) ref 0.53 (0.31) -0.92* (0.43) -0.61 (0.41) ref 0.60 (0.47) -0.62 (0.36) Ref 1.01** (0.37) Ref -0.42 (0.36) -1.09* (0.49) -0.84 (0.62) 0.49 (0.47) Ref -0.43 (0.42) -1.40** (0.38) 1.85*** (0.48) 659 604.24 0.27	Odds ratio ref 1.70 0.40* 0.54 Ref 1.82 0.54 Ref 2.75** Ref 0.66 0.33* 0.43 1.62 ref 0.65 0.25*** 6.39***
	Note:

Acknowledgements

We thank Marie Neihouser and Felix-Christopher von Nostitz (Université Catholique de Lille, ESPOL) for their contribution to the PELMEL survey, as well as Cécile Rodrigues and Thomas Soubiran (CNRS, CERAPS) for providing geographic data used in our analysis. We also thank the CRÉMI (Collectif de Recherche sur les Élections Municipales et Intercommunales) for inspiring us to work on this topic.

This work was supported by the Lille Center for European Research on Administration, Politics and Society (CERAPS, Université de Lille / CNRS / Sciences Po Lille), and by the European School of Political and Social Sciences (