Manel Gritli
email: manel.gritli@yahoo.com

Hélène Cheap-Charpentier
email: helene.cheap-charpentier@epf.fr

Hubert Perrot
email: hubert.perrot@upmc.fr

Olivier Horner
email: olivier.horner@epf.fr

Ben Amor

Scaling inhibition by sol-gel phosphosilicate hybrid films: Influence of doping Cu 2+ and Zn 2+ cations

Keywords: Scale inhibition, zinc (II) cation, copper (II) cation, sol-gel coating, quartz crystal microbalance electrochemical quartz crystal microbalance, CA: chronoamperometry, QCM: quartz crystal microbalance, SEM: scanning electronic microscopy, XRD: X-Ray diffraction

In this work, the scaling protection performance of Zn 2+ and Cu 2+ , added to a phosphosilicate hybrid sol-gel coating and applied on both carbon and stainless steel surface, was evaluated for the first time in a solution containing initially 200 mg.L -1 of Ca 2+ (corresponding to a water hardness of 50 °F) at 30 °C. Inhibition efficiency was estimated using chronoamperometry (CA) and quartz crystal microbalance (QCM). Results showed that these smart coatings were efficient to protect steel surface against scaling phenomenon. The coatings containing the Cu 2+ inhibitor was the most effective of the systems tested. Moreover, CA and QCM measurements showed that the formation of calcium carbonate deposition on carbon steel decreased when the amount of zinc and copper ions added to the sol-gel film increased. Scanning electronic microscopy and X-ray diffraction results indicated that both cations included in the sol-gel film affected calcium carbonate nucleation by changing the morphology of CaCO3 crystals.

Introduction

The problems related to the scaling phenomena of industrial facilities in contact with waters become more massive and more insidious. These issues can, as already pointed in numerous scientific papers, lead to a decrease of the thermal efficiency of the circuit, an obstruction of pipes as well as the proliferation of living organisms [1][START_REF] Peronno | Study of the inhibition effect of two polymers on calcium carbonate formation by fast controlled precipitation method and quartz crystal microbalance[END_REF][START_REF] Ben Amor | Study of the effect of magnesium concentration on the deposit of allotropic forms of calcium carbonate and related carbon steel interface behavior[END_REF][START_REF] Ben Amor | Apport de la microbalance à quartz dans l'étude de l'influence des ions sulfate, chlorure et magnésium sur la cinétique d'entartrage[END_REF][START_REF] Ben Amor | Nucleation-growth process of calcium carbonate electrodeposition in artificial water-Influence of the sulfate ions[END_REF][START_REF] Cheap-Charpentier | Study of the influence of the supersaturation coefficient on scaling rate using the pre-calcified surface of a quartz crystal microbalance[END_REF][START_REF] Chhim | Performance of green antiscalants and their mixtures in controlled calcium carbonate precipitation conditions reproducing industrial cooling circuits[END_REF]. Thus, the economic losses associated with CaCO3 precipitation can be significant [START_REF] Macadam | Calcium carbonate scale control, effect of material and inhibitors[END_REF][START_REF] Touati | Sand filtres scaling by calcium carbonate precipitation during groundwater reverse osmosis desalination[END_REF][START_REF] Korchef | Effect of pH and temperature on calcium carbonate precipitation by CO2 removal from iron-rich water[END_REF]. To fight this phenomenon, several protection methods have been applied to preserve installations against scaling. These methods can be divided into two types: physical and chemical methods. Among the physical methods, magnetic treatments are generally used [START_REF] Al Helal | The influence of magnetic fields on calcium carbonate scale formation within monoethylene glycol solutions at regeneration conditions[END_REF]. Chemical methods are based on the use of organic molecules as anti-scalant in numerous situations to prevent scale precipitation [START_REF] Chaussemier | State of art of natural inhibitors of calcium carbonate scaling. A review article[END_REF][START_REF] Zahlan | Synthesis of poly (citric acid-co-glycerol) and its application as an inhibitor of CaCO3 deposition[END_REF]. Some synthetic and natural water-soluble polymers used as scaling inhibitors have been investigated and reported in literature [START_REF] Chaussemier | State of art of natural inhibitors of calcium carbonate scaling. A review article[END_REF][START_REF] Zahlan | Synthesis of poly (citric acid-co-glycerol) and its application as an inhibitor of CaCO3 deposition[END_REF][START_REF] Popuri | Development of green/biodegradable polymers for water scaling applications[END_REF][START_REF] Guangqing | Polyether copolymer as an environmentally friendly scale and corrosion inhibitor in seawater[END_REF][START_REF] Xu | Inhibition of calcium carbonate fouling on heat transfer surface using sodium carboxymethyl cellulose[END_REF]. However, many inhibitors showed up has a secondary effect, causing damages on the environment. Indeed, poly-phosphonates are very efficient but they can cause eutrophication when they are rejected in natural waters [START_REF] Camargo | Ecological and toxicological effects of inorganic nitrogen pollution in aquatic ecosystems: A global assessment[END_REF][START_REF] Belkin | The effect of coagulants and antiscalants discharged with seawater desalination brines on coastal microbial communities: A laboratory and in situ study from the southeastern Mediterranean[END_REF]. Thus, the scientific community began searching for environmentally friendly inhibitors (green inhibitors) derived from petrochemicals [START_REF] Popuri | Development of green/biodegradable polymers for water scaling applications[END_REF][START_REF] Guangqing | Polyether copolymer as an environmentally friendly scale and corrosion inhibitor in seawater[END_REF][START_REF] Xu | Inhibition of calcium carbonate fouling on heat transfer surface using sodium carboxymethyl cellulose[END_REF][START_REF] Camargo | Ecological and toxicological effects of inorganic nitrogen pollution in aquatic ecosystems: A global assessment[END_REF][START_REF] Belkin | The effect of coagulants and antiscalants discharged with seawater desalination brines on coastal microbial communities: A laboratory and in situ study from the southeastern Mediterranean[END_REF][START_REF] Thombre | Synthesis and biodegradability of polyaspartic acid: a critical review[END_REF][START_REF] Euvrad | Effects of carboylic polyelectrolytes on the growth of calcium carbonate[END_REF][START_REF] Quan | Experimental study on scale inhibition performance of a green scale inhibitor polyaspartic acid[END_REF][START_REF] Chen | Synthesis of modified polyaspartic acid and evaluation of its scale inhibition and dispersion capacity[END_REF], plant extracts [START_REF] Abdel-Gaber | Investigation of fig leaf extract as a novel environmentally friendly antiscalant for CaCO3 calcareous deposits[END_REF][START_REF] Abdel-Gaber | A natural extracts scale and corrosion inhibitor for steel surface in brine solution[END_REF][START_REF] Abdel-Gaber | Green anti-scalant for cooling water systems[END_REF][START_REF] Bonoli | Qualitative and semi quantitative analysis of phenolic compounds in extra virgin olive oils as a function of the ripening degree of olive fruits by different analytical techniques[END_REF][START_REF] Maciejewska | A typical calcium coordination number: physicochemical study, cytotoxicity, DFT calculations and in silico pharmacokinetic characteristics of calcium caffeates[END_REF][START_REF] Lee | Assessment of phenolics-enriched extract and fractions of olive leaves and their antioxidant activities[END_REF][START_REF] Woodward | Structure-function relationships of protein polysaccharide complexes: specific ion-binding properties[END_REF][START_REF] Belarbi | Inhibition of calcium carbonate precipitation by aqueous extracts of Paronychia argentea[END_REF][START_REF] Lourteau | Scale inhibition effect of Hylocereus undatus solution on calcium carbonate formation[END_REF][START_REF] Horner | Antiscalant properties of Herniaria glabra aqueous solution[END_REF][START_REF] Cheap-Charpentier | Antiscalant properties of Spergularia rubra and Parietaria officinalis aqueous solutions[END_REF] and chemical modified natural products from industrial process [START_REF] Qiang | Study on scale inhibition performances and interaction mechanisms of modified collagen[END_REF][START_REF] Zhang | A botanical polysaccharide extracted from abandoned corn stalks: modification and evaluation of its scale inhibition and dispersion performance[END_REF][START_REF] Yu | Evaluation of the structural morphology of starch-graftpoly (acrylic acid) on its scale-inhibition efficiency[END_REF]. Nevertheless, the compatibility with the water environment and the respect of the different safety rules are always questionable even if these products come from plants or similar. Alternate approach must be found in this context and smart films based on sol-gel technique can be examined [START_REF] Wang | Sol-gel coatings on metals for corrosion protection[END_REF]. Materials such as organic-inorganic hybrid compounds are one of the feasible solutions that enable protection from CaCO3 precipitation reactions during application. They constitute a new generation of multifunctional materials with useful properties and diverse applications. In addition, polymeric materials are characterized by their low weight to volume ratio, their excellent resistance to chemical attack, their eco-friendly properties and their low cost [START_REF] Rodič | The effect of copolymerisation on the performance of acrylate-based hybrid sol-gel coating for corrosion protection of AA2024-T3[END_REF]. Further modification of polymer matrix by doping with ions at low concentrations can proffer superior physical properties of such polymer.

The use of eco-friendly sol-gel coatings to prevent scale inhibition can constitute an emerging area of applications such as it is the case in the corrosion domain [START_REF] Zheng | Inorganic-organic sol-gel hybrid coatings for corrosion protection of metals[END_REF][START_REF] Catauro | Corrosion behavior and mechanical properties of bioactive sol-gel coatings on titanium implants[END_REF][START_REF] Roussi | Anticorrosion and nanomechanical performance of hybrid organo-silicate coatings integrating corrosion inhibitors[END_REF][START_REF] Figueira | Hybrid sol-gel coating for corrosion protection of hot-dip galvanized steel in alkaline medium[END_REF][START_REF] Mrad | Corrosion prevention of AA2024-T3 alloy with a polyaniline/poly (γ-glycidoxypropyltrimethoxysilane) bi-layer coating: Comparative study with polyaniline monolayer feature[END_REF][START_REF] Mrad | Effect of AA2024-T3 surface pretreatment on the physicochemical properties and the corrosion performance of poly (γglycidoxypropyltrimethoxysilane) sol-gel coating[END_REF][START_REF] Del Olmo | Hybrid sol-gel coatings applied on anodized AA2024-T3 for active corrosion protection[END_REF]. In a similar manner, sol-gel hybrid coatings for metal protection against scaling phenomenon appears as an interesting field of research. Indeed, it is an attractive technique used to synthesize hybrid materials with various composition that allow to entrap molecules in an inorganic glassy matrix [START_REF] Roussi | Anticorrosion and nanomechanical performance of hybrid organo-silicate coatings integrating corrosion inhibitors[END_REF][START_REF] Suárez-Vega | Properties of hybrid sol-gel coatings with the incorporation of lanthanum 4-hydroxy cinnamate as corrosion inhibitor on carbon steel with different surface finishes[END_REF]. The properties of these sol-gel coatings are strongly dependent on their processing conditions, pH, temperature and molar ratio of precursors [START_REF] Figueira | Hybrid sol-gel coating for corrosion protection of hot-dip galvanized steel in alkaline medium[END_REF][START_REF] Figueira | Hybrid sol-gel coatings for corrosion mitigation: A critical review[END_REF]. Silica hybrid sol-gel coatings are particularly studied and employed for corrosion protection due to their interesting properties, such as hydrophobicity and good adhesion to metallic substrates [START_REF] Lakshmi | Silica-alumina based sol-gel coating containing cerium oxide nanofibers as a potent alternative to conversion coating for AA2024 alloy[END_REF]. The use of precursors containing non-hydrolysable bonds allows the organic network to bind directly to the inorganic network in the structure. Thus, hybrid sol-gel coatings can have the combined properties of both organic and inorganic functions [START_REF] Mrad | Corrosion prevention of AA2024-T3 alloy with a polyaniline/poly (γ-glycidoxypropyltrimethoxysilane) bi-layer coating: Comparative study with polyaniline monolayer feature[END_REF][START_REF] Mrad | Effect of AA2024-T3 surface pretreatment on the physicochemical properties and the corrosion performance of poly (γglycidoxypropyltrimethoxysilane) sol-gel coating[END_REF]. The nature of the organic function (phenyl function, epoxy function, vinyl function and methacrylate function) influences the properties of the network [START_REF] Zheng | Inorganic-organic sol-gel hybrid coatings for corrosion protection of metals[END_REF][START_REF] Santana | Silica-based hybrid coatings for corrosion protection of carbon steel. Part I: Effect of pretreatment with phosphoric acid[END_REF]. The integration of phosphate or phosphonate groups in the sol-gel network has been published in several works [START_REF] Khramov | Sol-gel coating with phosphonate functionalities for surface modification of magnesium alloys[END_REF][START_REF] Kannan | Synthesis and characterization of methacrylate phosphor-silicate hybrid for thin film applications[END_REF][START_REF] Kannan | Electrochemical performance of sol-gel derived photo-silicate-methacrylate hybrid coating[END_REF]. The outcomes proved a good adhesion to the metallic surface of the film containing phosphorus groups. Santana et al. [START_REF] Santana | Silica-based hybrid coatings for corrosion protection of carbon steel. Part I: Effect of pretreatment with phosphoric acid[END_REF] studied the effect of the pre-treatment of the carbon steel surface with a phosphoric acid solution before applying a hybrid sol-gel film. SEM images showed that the pre-treatment step produces a rougher surface than that of untreated steel. This roughness results in better adhesion of the sol-gel film to the treated steel substrate. The microstructure of the film obtained by the sol-gel process depends on the pH of the solution [START_REF] Mrad | Corrosion prevention of AA2024-T3 alloy with a polyaniline/poly (γ-glycidoxypropyltrimethoxysilane) bi-layer coating: Comparative study with polyaniline monolayer feature[END_REF][START_REF] Mrad | Effect of AA2024-T3 surface pretreatment on the physicochemical properties and the corrosion performance of poly (γglycidoxypropyltrimethoxysilane) sol-gel coating[END_REF]. Therefore, an acid catalysis leads to the formation of longitudinal fibers and an increase in the condensation generated while a basic catalysis leads to clusters formation characterized by a spherical shape [START_REF] Xiao | Microstructure control of nanoporous silica thin film prepared by sol-gel process[END_REF]. Under acidic conditions, the cation H3O + facilitates the substitution of the OR groups and therefore hydrolysis. With basic catalysts, the OH -anion is attracted towards the electronegative metal (M) and favours the formation of M-O-M bond by condensation [START_REF] Chiang | Preparation, characterization and properties of novolac-type phenolic/SiO2 hybrid organic-inorganic nanocomposite materials by sol-gel method[END_REF][START_REF] Bonino | Les revêtements sol-gel pour l'anticorrosion[END_REF]. According to Phan et al. [START_REF] Phan | E ects of sol-gel process parameters on the anticorrosive performance of phospohosilicate hybrid coatings for carbon steel: structural and electrochemical studies[END_REF], adding phosphoric acid H3PO4 provides the most resistant hybrid coating. A denser network with a greater number of Si-O-P bonds promotes good adhesion to the metallic surface. The formation mechanism is given in [START_REF] Phan | E ects of sol-gel process parameters on the anticorrosive performance of phospohosilicate hybrid coatings for carbon steel: structural and electrochemical studies[END_REF] and these authors have used this coating to study the corrosion of a metallic surface.

As it is summarized above, many compounds were applied as scaling inhibitors. All of them were added to the studied water while the metallic surface treatments such as sol-gel coating process, were mainly applied to protect metal against corrosion. To our knowledge, no investigations on the scaling inhibition via sol-gel doped coatings on steel surface in pure carbonic solution have been performed to date. The present investigation shows the first attempt to synthesize a sol-gel film on a surface and doped with metallic ions to prevent scale formation.

In this work, hybrid sol-gel coatings were deposed on both carbon steel and stainless steel from 3-[(methacryloyloxy)propyl] trimethoxysilane (MEMO) and bis-[2-(methacryloyloxy) ethyl] phosphate (BMEP) via sol-gel process (Fig. 1). The experimental procedure is similar to that adopted by Phan et al. [START_REF] Phan | E ects of sol-gel process parameters on the anticorrosive performance of phospohosilicate hybrid coatings for carbon steel: structural and electrochemical studies[END_REF]. To improve their anti-scaling properties, deposited coatings were doped by Cu 2+ and Zn 2+ cations. Chronoamperometry (CA) and quartz crystal microbalance (QCM) methods were performed to evaluate the scaling inhibition efficiency of these layers.

To complete the information about the composition and the morphology of the doped sol-gel coatings, scanning electron microscopy (SEM) observations and X-ray diffraction (XRD) analysis were done to link the layer properties to the electrochemical and gravimetric characterizations.

Materials and methods

Scaling solution

The synthetic carbonically pure water, containing initially 200 mg. L -1 of Ca 2+ (water hardness of 50 °F), was prepared by dissolving calcium carbonate (CaCO3) powder (VWR AnalaR NORMAPUR, 99.7% purity) in bi-distilled water. To dissolve calcium carbonate, carbon dioxide CO2 gas was introduced in the solution for 24 h with moderate magnetic stirring (450 rpm). After the total dissolution of the solid, the pH of the solution was in the range of 5.5 -5.7. The synthetic water was then filtered using a filter with a porosity of 0.45 μm to remove impurities.

Doping solution

Suitable amounts of solutions of analytical grade ZnCl2 (Merck, 98 % purity) and CuCl2-2H2O (Acros Organics, 99 % purity) were prepared for doping coatings tests. For the doping process, metallic cations molar quantities ranged from 10 -5 to 10 -3 mol.

Sol-gel coating solution

The sol-gel coating process was applied using 3-[(methacryloyloxy)propyl] trimethoxysilane (MEMO) and bis [2-(methacryloyloxy) ethyl] phosphate (BMEP) precursors from Sigma-Aldrich and ethanol provided by VWR. All compounds were used without any further purification and chemical formulas are given in Fig. 1.

Metallic substrate and covered QCM resonators

Two different metallic substrates were used in this study. The first one is carbon steel with a chemical composition (in wt %) of 0.28 % C, 0.28 % Si, 1.25 % Mn, 0.03 % P, 0.16 % Cr, 0.15 % N, 0.07 % Ni, 0.009 % Mo and Fe balance. The carbon steel working electrode, 0.2 cm 2 of active area, was embedded in inert resin, polished with silicon carbide paper up to 1200 grade before each experiment. A rotating disk electrode (Tacussel model EDI 101) was used with a rotation speed () which was fixed at 500 rpm. The second substrate is based on stainless steel AISI 316L (Fe/Cr18/Ni10/MO3) sheet (Good fellow, reference FF210320). Thin stainless steel 316L films were prepared on quartz resonators surface using a commercial RF magnetron sputtering system (Pfeiffer PLS500) from 316L steel disc target of 50 mm diameter. More precisely, stainless steel was deposited on the gold electrode (0.2 cm 2 ) of the resonators (9 MHz, AWS Sensors, Spain) to perform QCM-based analysis.

Sol-gel coating 2.5.1. Pre-treatment of the surface

The pre-treatment of the electrode surface was carried out by crystalline phosphating process with a commercial solution Decorrdal 47-15-1 (Klüthe). It is a mixture of ethanol (molar fraction between 50 and 75%) and sodium 3-nitrobenzenesulphonate C6H4NNaO5S (molar fraction between 50 and 75% and molecular weight 225.15 g.mol -1 ). Crystalline phosphating process, recommended by Klüthe, reduces the flaking surface by forming a phosphateconverting layer that constitutes a base for bonding the coatings, making the surface rougher and improving the adhesion of the coating on the metallic surface [START_REF] Phan | E ects of sol-gel process parameters on the anticorrosive performance of phospohosilicate hybrid coatings for carbon steel: structural and electrochemical studies[END_REF].

The surfaces of 316L steel and carbon steel were pre-treated with a Decorrdal 47-15-1 commercial solution for 5 min at a temperature of 40 °C. The increase in temperature is more favourable to phosphating, which eliminates the presence of iron oxide on the steel surface.

Sol-gel preparation

The sol-gel process is based on the hydrolysis and condensation reactions of silicons alcoxydes Si(OR)n in solution (sol) allowing to achieve an infinite viscosity network (gel), where n is the oxidation state and OR is an alkoxy group with R an alkyl chain [START_REF] Wang | Sol-gel coatings on metals for corrosion protection[END_REF]. The most often used precursors for this type of application are tetra-functional silicon alkoxides of formula Si(OR)4 [START_REF] Livage | Les procédés sol-gel, de l'art feu à la chimie douce[END_REF]. Herein, the sol-gel preparation was done in two stages: hydrolysis (the synthesis of "sol") following by the condensation (the formation of "gel"). The mechanism was well detailed by Phan et al. [START_REF] Phan | E ects of sol-gel process parameters on the anticorrosive performance of phospohosilicate hybrid coatings for carbon steel: structural and electrochemical studies[END_REF]. Hydrolysis of MEMO in aqueous medium took place via Si-OCH3 methoxysilane groups according three successive reactions:

R-Si(OCH3)3 + H2O  R-Si(OCH3)2(OH) + CH3OH (1) R(Si(OCH3)2(OH) + H2O  R-Si(OCH3)(OH)2 + CH3OH (2) R(Si(OCH3)(OH)2 + H2O  R-Si(OH)3 + CH3OH (3)
Then, condensation reactions occurred according the following reactions:

R-Si(OH)3 + R-Si(OH)3  R-(OH)2Si -O -Si(OH)2-R + H2O (4) R-Si(OCH3)3 + R-Si(OH)3  R-(OCH3)3Si -O -Si(OH)2-R + CH3OH (5)
The sol-gel procedures used in this work are schematised in Fig. 2. In a first step, MEMO is hydrolysed in an ethanol/water mixture with MEMO/ethanol/water molar ratio of 1/2/3 (corresponding to the volumes 2.85/1.4/0.65 mL) and then, by stirring at room temperature during 3h. This selected duration makes it possible to obtain a complete hydrolysis. Ca 2+ and Zn 2+ cations were injected in the ethanol solution at the beginning with different molar amounts ranged from 10 -5 mol to 10 -3 mol. Then, 0.3 mL of BMEP was added to the above solution in order to obtain MEMO/BMEP molar ratio of 10/1 (10Si-1P). This mixture was stirred vigorously at 65 °C for 1 hour, diluted with 1.61 mL of ethanol to obtain a mass concentration of 80% of sol-gel in ethanol. Afterwards, the mixture was stirred for at least 15 min until complete dissolution. The methoxy-silane groups of MEMO precursor are capable to form an inorganic network Si-O-Si through sol-gel reactions and a polymerizable methacrylate group capable of producing an organic network. The BMEP precursor containing the functional P-OH group allows the coating to have good adhesion and a better-condensed inorganic network by forming strong Fe-O-P bonds with metallic substrates and Si-O-P bonds with a silica network [START_REF] Phan | E ects of sol-gel process parameters on the anticorrosive performance of phospohosilicate hybrid coatings for carbon steel: structural and electrochemical studies[END_REF][START_REF] Kirtay | Preparation of hybrid silica sol-gel coatings on mild steel surfaces and evaluation of their corrosion resistance[END_REF]. The obtained sol-gel films were deposited on polished carbon steel and stainless steel substrates deposited on the gold electrode of a quartz resonator using a micropipette (2 μL). The film is maintained at room temperature for 5 min, then, dried at 80 °C for 20 h, and finally at 120 °C for 2 h in an oven.

Scaling study techniques 2.6.1. Quartz crystal microbalance (QCM)

The piezoelectric properties of the quartz crystal correlate the frequency change and the mass change deposited on the active surface of quartz crystal according to the Sauerbrey equation [1,[START_REF] Gritli | Scale inhibition properties of Cu 2+ and Zn 2+ cations in hard water by using a pre-calcified quartz crystal microbalance[END_REF]:

∆ 2 ∆ (6)
where Δf and Δm are the frequency change and the mass change deposited on the electrode surface, respectively, fo is the quartz resonance frequency, , the quartz density, , the quartz shear modulus and S, the active surface of the quartz given by the shape of one of the gold electrodes. In a typical QCM set-up, the working electrode is made of a 0.2 cm 2 gold disc deposited in a 9 MHz AT cut quartz crystal resonator. Typically, the theoretical sensitivity using Eq. 6 is around 1 ng/Hz. The gold surface of the quartz was previously covered with a layer of stainless steel 316L covered by a sol-gel film as described in the previous paragraph.

During the QCM test, a volume of 400 ml of the studied synthetic water (carbonically pure solutions containing 200 mg.L -1 of Ca 2+ , corresponding to 50 °F) was transferred to a Teflon container placed in a thermostated bath at 30 °C. CO2 degassing was achieved by magnetic stirring at 850 rpm. The degassing of the solution was blocked by stopping the stirring and closing the opening of the beaker lid in order to block its level of supersaturation corresponding to a pH of 7.9. Then, a peristaltic pump was used to transfer the solution in the QCM cell. The QCM setup was monitored by a lab-made software, allowing the recording of the frequency changes as a function of time. At the end, mass variations over time can be estimated using Eq.

6. Details of this methodology were already given in other works [1,[START_REF] Cheap-Charpentier | Study of the influence of the supersaturation coefficient on scaling rate using the pre-calcified surface of a quartz crystal microbalance[END_REF].

Chronoamperometry (CA)

CA was used to investigate the scaling process under different conditions [START_REF] Ben Amor | Nucleation-growth process of calcium carbonate electrodeposition in artificial water-Influence of the sulfate ions[END_REF][START_REF] Lédion | Détermination du caractère incrustant d'une eau par un essai d'entartrage accéléré[END_REF]. During measurement, the current was recorded as a function of time at a fixed scaling optimal potential of -1 V/SCE [START_REF] Lédion | Détermination du caractère incrustant d'une eau par un essai d'entartrage accéléré[END_REF]. Experiments were carried out in a classical three electrodes cell. A saturated calomel electrode (SCE) was used as a reference electrode. The carbon steel with and without sol-gel coating acted as a working electrode. The counter electrode was a large platinum grid.

Surface characterizations 2.7.1. SEM observations

After each experiment, the morphology of calcium carbonate crystals deposited on both carbon steel and stainless steel with and without sol-gel coating during the QCM and CA experiments was analysed using scanning electronic microscopy (SEM). The SEM pictures were obtained on a SEM-FEG Zeiss Ultra55 microscope model. SEM-EDS spectra were recorded using a Quanta 250 FEG (Field Emission Gun) model accompanied by an EDS detector for elemental composition measurement, at an accelerating voltage of 10 kV, keeping the magnifications up to 1,000.000 and 1 nm resolution.

X-ray diffraction analysis

The XRD spectra were recorded with 2θ angle in the range of 20-80° with an X-ray diffractometer type X-Empyrean Panalytical employing Cu-Kα radiation (λ=1.54 Å).

Intensities of the diffraction peaks at 104 (2= 29.5°), 221 (2= 46°) and 110 (2= 25°) were used to quantify the calcite, aragonite and vaterite crystallographic forms, respectively. The calculation of the molar fraction of each variety was reported elsewhere [START_REF] Gritli | Scale inhibition properties of Cu 2+ and Zn 2+ cations in hard water by using a pre-calcified quartz crystal microbalance[END_REF].

Results and discussion

Scaling inhibition on sol-gel coating carbon steel electrode

Comparison between a bare electrode and a sol-gel coating electrode

Firstly, experiments were carried out by chronoamperometry in order to verify if the sol-gel film could prevent the formation of CaCO3 on the electrode. The scaling inhibition of the solgel film was studied on a carbon steel electrode using chronoamperometry and compared to a bare electrode. Measurements were carried out using a classical rotating disk electrode in a solution containing initially Ca 2+ ions at a concentration of 200 mg.L -1 (50 °F). A cathodic potential of -1 V/SCE was applied during the accelerated scaling test to induce the CaCO3 electrochemical precipitation [1][START_REF] Peronno | Study of the inhibition effect of two polymers on calcium carbonate formation by fast controlled precipitation method and quartz crystal microbalance[END_REF][START_REF] Ben Amor | Study of the effect of magnesium concentration on the deposit of allotropic forms of calcium carbonate and related carbon steel interface behavior[END_REF][START_REF] Cheap-Charpentier | Study of the influence of the supersaturation coefficient on scaling rate using the pre-calcified surface of a quartz crystal microbalance[END_REF]. The current was normalized by I0, which is the current value at the maximum of the curve. This current-time coordinate system was adopted by Barchiche et al. [START_REF] Barchiche | Role of sulphate ions on the formation of calcareous deposits on steel in artificial seawater; the formation of Green Rust compounds during cathodic protection[END_REF] to facilitate the comparison between results. The chronoamperometric curves performed with a bare carbon steel electrode and a carbon steel electrode covered by a sol-gel film are presented in Fig. 3. The two-recorded curves of Fig. 3 show a similar evolution.

Firstly, an increase of the normalized current is related to the reduction of atmospheric oxides formed on the active area of the working electrode before immersion [START_REF] Ben Amor | Nucleation-growth process of calcium carbonate electrodeposition in artificial water-Influence of the sulfate ions[END_REF]. Then, a rapid decrease of I/I0 was observed and attributed to a fast kinetics of CaCO3 deposition on the electrode [START_REF] Ben Amor | Study of the effect of magnesium concentration on the deposit of allotropic forms of calcium carbonate and related carbon steel interface behavior[END_REF].

The scaling time parameter (ts) can be obtained from chronoamperometric curve (Table 1). As indicated in Fig. 3, this parameter represents the time needed to lower the current to a stable value corresponding to the plateau current [START_REF] Garcia | Study of the scale inhibition by HEDP in a channel flow cell using a quartz crystal microbalance[END_REF]. For the bare electrode, the ts value is 38 min and the I/I0 value of the plateau is around 0.19 meaning that the electrode surface was totally covered by an isolating layer of CaCO3. When the carbon steel electrode was coated by a solgel film, the I/I0 value of the plateau is obtained more quickly and is higher (0.41) than for a bare carbon steel electrode. This first result shows that the sol-gel film is porous as the O2 can be reduced on the electrode and acts as a barrier against the formation of CaCO3 on the electrode. For the coating doped with 10 -5 mol of Cu 2+ (blue curve in Fig. 4(a)), the first increase of the normalized current was not really observed compared to the undoped coating. Then, I/I0 rapidly decreased to reach a nearly constant value indicating that the formation of CaCO3 on the surface of the coating was stopped after about 40 min of immersion that correspond to the scaling time.

Scaling on doped sol-gel film coating carbon steel electrode

However, the plateau current was higher than that of undoped coating, which means that Cu 2+ ions prevented slightly the CaCO3 formation. For the coating doped with 10 -4 mol of Cu 2+

(green curve in Fig. 4(a)), the current did not decrease over time so the scaling process was inhibited during the whole experiment. The scaling time (ts) was undefined. Indeed, practically no variation of the I/I0 value was observed during 120 min of experiment which shows that the kinetics of CaCO3 precipitation was extremely slow. For a sol-gel film containing 10 -4 mol of Cu 2+ , the formation of CaCO3 is considered as completely inhibited. cations. Their shapes were similar to that observed for the coating doped with 10 -5 mol of Cu 2+

(blue curve in Fig. 4(a)). The initial decrease of the normalized current was followed by a plateau of different I/I0 values depending on the Zn 2+ doping cation amount. The scaling time values were mentioned in Table 1. Higher is the amount of the doping Zn 2+ , higher is the scaling time. Comparing the effect of doping cations, it seems that the inhibitory effect of the film doped with copper ions is more pronounced than that doped with zinc ions. Indeed, the values of scaling time mentioned in Table 1 show that ts is undefined for 10 -4 mol of Cu while it is equal to 51 min for the same amount of Zn 2+ .

These results obtained by chronoamperometry showed that doping the sol-gel-film with metallic ions prevented the formation of CaCO3 on the metallic surface of the electrode. The sol-gel film with Cu 2+ shows a greater inhibition effect than that with Zn 2+ .

Sol-gel coating on stainless steel 316L through QCM tool

In order to assess the inhibiting effect of the metallic cations included in the sol-gel film, the quartz crystal microbalance (QCM) was used to quantify the mass of CaCO3 nuclei deposited when the electrode was covered by this coating.

The studied solution was prepared by fast controlled precipitation (FCP) in order to bring the solution to a given sursaturation coefficient [START_REF] Cheap-Charpentier | Study of the influence of the supersaturation coefficient on scaling rate using the pre-calcified surface of a quartz crystal microbalance[END_REF]. This method allowed forming calcium carbonate nuclei before precipitation in solution.

Undoped sol-gel film

The mass variations of the CaCO3 nuclei deposited on stainless steel sol-gel coating electrode (without and with doping cations) were recorded vs. immersion time in synthetic pure carbonic solution containing initially 200 mg.L -1 of Ca 2+ (water hardness of 50 °F) at a sursaturation coefficient of 32.

Firstly, a comparison of the CaCO3 mass variation deposited was carried out by QCM when the electrode was covered or not covered by a sol-gel film. The gravimetric curves for a bare stainless steel electrode and for the undoped coating electrode obtained by QCM are presented in Fig. 5. For the bare stainless steel electrode, the mass of CaCO3 increases progressively with the immersion time without reaching a constant value, even after 120 min of immersion (black curve in Fig. 5). However, the mass variation (m) of CaCO3 deposited on sol-gel coating stainless steel electrode is different. As it can be observed from the red curve in Fig. 5, an initial increase of the m was clearly recorded for 50 min of immersion. Afterwards, m reached a steady state value about 42 µg.cm -2 . This mass variation means that the active metallic surface was reduced and the progression of scaling process was stopped. In addition, no loss of mass has been observed for the sol-gel coating electrode which means that the film is adherent on the electrode surface. QCM is a suitable technic to control the film adhesion on the electrode surface. Indeed, if the coating leaves the surface of the QCM or is no longer in contact, there is a discontinuity in the propagation of the ultrasonic wave that can be detected immediately thanks to the very high sensitivity of the QCM. Covering stainless steel working electrode with a phosphosilicate hybrid coating promotes an important reduction of the mass of CaCO3 deposit, proving that the sol-gel coating prevents the formation of calcium carbonate on the metallic surface, even without doping cations. and scaling rate (Vs) were extrapolated from the gravimetric curves as defined by Tlili et al. [START_REF] Tlili | Study of Electrochemical Deposition of CaCO3 by In Situ Raman Spectroscopy[END_REF]. The corresponding values are given in Table 2. The increase of Cu 2+ doping cation amount influences mainly the scaling rate (Vs) that was reduced from 2.21 µg cm -2 min -1 (undoped film) to 0.15 µg cm -2 min -1 for the film doped with 10 -4 mol of Cu 2+ . The values of TN and TS for doped system are higher than that of the undoped system.

Sol-gel film doped with metallic ions

The effect of Zn 2+ doping cations on the anti-scaling properties of the sol-gel phosphosilicate hybrid coating was also studied by QCM. Four amounts of Zn 2+ cations ranged from 10 -5 mol to 10 -2 mol were also examined. The extrapolated scaling parameters are also added to the Table 2 and the corresponding recorded gravimetric curves are shown in Fig. 6(b). The increasing amounts of Zn 2+ cations in the sol-gel film progressively inhibit the formation of scale on the surface of the sol-gel phospohosilicate hybrid coating. The mass of calcium carbonate decreases from 42 µg.cm -2 to 7 µg.cm -2 . The Vs value (Table 2) decreases from 1.46 µg -1 cm -2 min -1 to 0.39 µg.cm -2 .min -1 when Zn 2+ molar quantity increases from 10 -5 mol to 10 -3 mol. The value of TN seems to be independent of the doping process while the values of TS for doped system are higher than those characteristic of scaling on undoped coating (Table 2).

Zn 2+ doping cations, as well as Cu 2+ , improved the anti-scaling effect of the studied sol-gel film.

However, these results confirmed that Cu 2+ ions are more efficient than Zn 2+ ions towards scale deposition. Indeed, for a sol-gel film doped with Cu 2+ and Zn 2+ at 10 -4 mol, the amount of CaCO3 deposits was 4.5 µg.cm -2 and 13 µg.cm -2 respectively (Fig. 6). This difference corroborates the result obtained by chronoamperometry for carbon steel, confirming the antiscaling properties of the studied sol-gel coating.

The inhibition effect of cations was assumed to be due to the weak release of the ions in the solution. Indeed, some experiments were carried out by spectrophotometry UV-Vis (data not shown here) in order to detect the presence of cations in the solution. The results showed that a very small quantity of cations was released from the sol-gel film towards the solution. As a consequence, the scaling inhibition is mainly related to an interfacial effect.

SEM micrographs and XRD analysis on 316L stainless steel

SEM images of the sol-gel film and CaCO3 formed on the surface of 316L stainless steel, under different experimental conditions (undoped and doped with ions), are shown in Fig. 7 and Fig. 8 for Cu 2+ and Zn 2+ respectively. The molar fractions of vaterite, aragonite and calcite calculated from XRD spectra are presented in Table 3. 3. Doping the sol-gel coating with 10 -2 mol of Zn 2+ lead to the aragonite formation (Fig. 8(d) and Table 3). The presence of these CaCO3 crystallographic forms was also confirmed by X-ray diffraction analysis (Fig. 8 (e) to (h)). XRD spectra were also recorded on coating doped with different amounts of Zn 2+ cation. Results are in agreement with SEM observations (Fig. 8(a) to (d)). For 10 -5 mol to 10 -3 mol of doping Zn 2+ cation, vaterite and calcite were the constituents of the CaCO3 deposit (Fig. 8(e) to (g) and Table 3). With 10 -2 mol of doping Zn 2+ , X-ray analysis (Fig. 8(h) and Table 3) showed the presence of aragonite.

The molar fractions of observed crystalline varieties formed on sol gel coating stainless steel electrode (Table 3) were estimated using the calculation method described in a previous paper [START_REF] Gritli | Scale inhibition properties of Cu 2+ and Zn 2+ cations in hard water by using a pre-calcified quartz crystal microbalance[END_REF]. The calculated values shown in Table 3 are dependent on the doping cations amount indicating the inhibiting role of this added ions on the scaling process and the CaCO3 structure.

The molar fractions of vaterite and calcite decreased when the molar quantities of ions increased. It can be noted the appearance of aragonite for a sol-gel film doped with 10 -2 mol of Zn 2+ at a molar fraction of 24% (Table 3). The inhibition effect of Cu 2+ and Zn 2+ cations added to the coating hybrid structure was demonstrated as it was the case when they were injected in solution as soluble scaling inhibitor [START_REF] Gritli | Scale inhibition properties of Cu 2+ and Zn 2+ cations in hard water by using a pre-calcified quartz crystal microbalance[END_REF][START_REF] Gutjahr | Studies of the growth and dissolution kinetics of the CaCO3 polymorphs calcite and aragonite, II. The influence of divalent cation additives on the growth and dissolution rates[END_REF][START_REF] Ras | Influence of copper and zinc on the power furring of encrusting water[END_REF][START_REF] Zeppenfeld | Prevention of CaCO3 scale formation by trace amounts of copper (II) in comparison to zinc (II)[END_REF]. Gritli et al. [START_REF] Gritli | Scale inhibition properties of Cu 2+ and Zn 2+ cations in hard water by using a pre-calcified quartz crystal microbalance[END_REF] have demonstrated by FCP a total efficiency of Cu 2+ and Zn 2+ in solution for a concentration of 5 and 4 mg.L -1 respectively.

Other authors [START_REF] Ras | Influence of copper and zinc on the power furring of encrusting water[END_REF] have determined with the same technique lower concentrations for the inhibition of CaCO3 formation (0.5 mg.L -1 of Cu 2+ and 0.15 mg.L -1 of Zn 2+ ). Zeppenfeld [START_REF] Zeppenfeld | Prevention of CaCO3 scale formation by trace amounts of copper (II) in comparison to zinc (II)[END_REF] have showed an inhibition efficiency at about 90% for a concentration superior at 2 mg.L -1 of Cu 2+ . To conclude this part, the doped sol-gel film acts as an antiscaling barrier.

Conclusion

The present study was devoted to investigate the anti-scaling performance of a sol-gel phosphosilicate hybrid coating doped with copper or zinc cations deposited onto two different metals, largely used in the water domain, stainless 316L steel and carbon steel. The outcomes allow the following conclusions to be drawn:

1. An hybrid doped sol-gel phosphosilicate coating was successfully applied onto stainless and carbon steel surfaces. The anti-scaling proprieties of this film was demonstrated under different experimental conditions.

2. The different techniques of investigations (QCM and CA) confirmed that doping the hybrid coating with Cu 2+ and Zn 2+ cations delayed the scaling process proving the scaling inhibiting performance of this doped film in synthetic water containing initially 200 mg.L -1 of Ca 2+ (water hardness of 50 °F).

3. Crystalline form of CaCO3 appeared at the studied interface. They were mainly influenced by the amount of Zn 2+ and Cu 2+ doping cations that are included in the different films.

4. Surface analysis techniques (SEM and X-ray diffraction) supported investigations and confirmed the anti-scaling properties of the doped coatings.

Fig. 4

 4 Fig. 4 regroups the chronoamperometric curves recorded during scaling tests on the doped coating carbon steel electrode polarised at -1 V/SCE for the two doping cations (Cu 2+ and Zn 2+ ).

Fig. 4 (

 4 Fig. 4(b) shows the chronoamperometric curves for scaling tests on coating doped with Zn 2+

Fig. 6 (

 6 Fig.6(a) presents the variation of the mass change of calcium carbonate deposited on sol-gel coating stainless steel electrode without and with doping Cu 2+ cations. The obtained curves show an important decrease of the deposit of CaCO3 on the doped sol-gel coating with the increase of cations quantities. Comparing to the undoped system, the steady state was reached faster leading to a decrease of CaCO3 deposit mass. For instance, when the sol-gel film was doped with 10 -5 mol of Cu 2+ (red curve in Fig.6(a)), the mass change reached a steady value of 13.8 µg.cm -2 . Doping progressively the film with Cu 2+ ions (from 10 -5 mol and 10 -4 mol of Cu 2+ added during the preparation of the film) reduces the amount of CaCO3 deposited to 13.8 µg.cm -2 and 4.5 µg.cm -2 , respectively. The mass change decrease is very important compared

Fig. 7a shows

  Fig.7ashows the presence of small CaCO3 crystals formed on the sol-gel coating without doping cations covering the surface of the stainless steel 316L electrode. The shapes of the crystals are difficult to identify. However, the presence of calcite has been confirmed by XRD analysis as shown in Fig.7(d), which revealed characteristic peaks of this crystalline variety.When the sol-gel coating was doped with 10 -5 and 10 -4 mol of Cu 2+ (Figs. 7(b) and (c) respectively), SEM images show that the deposit was mainly formed by circular crystal typical of vaterite[START_REF] Ben Amor | Nucleation-growth process of calcium carbonate electrodeposition in artificial water-Influence of the sulfate ions[END_REF][START_REF] Cheap-Charpentier | Study of the influence of the supersaturation coefficient on scaling rate using the pre-calcified surface of a quartz crystal microbalance[END_REF], which is confirmed by XRD analysis (Fig.7(e) and (f)). In addition, the presence of Cu 2+ ions decreased the number of CaCO3 crystals deposited on the doped sol-gel film. On the film doped with Cu 2+ , XRD analysis (Fig.7(e)) confirmed the presence of both calcite and vaterite as observed in the SEM images of Fig.7(b).The morphology of CaCO3 scale formed on the surface of the hybrid coating doped with Zn 2+ are shown in Fig.8. When the sol-gel film is doped with 10 -5 mol of Zn 2+ , vaterite form is observed (Fig.8(a)) which is confirmed by the XRD spectrum in Fig.8(e). Calcite appear when the doping cations rises to 10 -4 to 10 -3 mol, as it can be observed in the Fig.8(b) and (c) and Table3. Doping the sol-gel coating with 10 -2 mol of Zn 2+ lead to the aragonite formation (Fig.

Acknowledgements

This work was supported by PHC-Utique program 18G1218 (MES-DGRS Tunisia), 39229 TA (Campus France), Erasmus Plus program and the Islamic Development Bank (BID). The authors thank Françoise Pillier, Cyrille Bazin and Axel Desnoyers de Marbaix (LISE) for technical assistance.