Zakaria Zoukal

Said Elhasri

Alain Carvalho

Marc Schmutz

Dominique Collin

Praveen K Vakayil

Ayyappanpillai Ajayaghosh

Jean-Michel Guenet

Vakayil K Praveen

Ayyapanpillai Ajayaghosh

HYBRID MATERIALS FROM POLY[VINYL CHLORIDE] AND ORGANOGELS

Keywords: PVC, organogels, gelation, hybrid materials, rheology, morphology

The making of hybrid materials from polymers and self-assembled systems may open up new horizon for imparting new properties to usual polymers without recourse to chemistry. Here it is again shown that preparation of such materials can be straightforwardly achieved by a physical SOL-GEL process with polyvinyl chloride (PVC), an extensively-used polymer, and oligo(pphenylenevinylene) organogelators (OPVOH), a molecule that forms organogels displaying optoelectronic properties (change of colour at the SOL-GEL transition). Low amounts of OPV with respect to PVC are used (ratio ~1/10 to ~1/30). Although the PVC structures form first, the thermodynamic of the OPVOH gelation is virtually not altered (same formation temperatures and same melting temperatures). It is observed that the organogel does pervade the polymer structures, which results in a noticeable strengthening of the mechanical properties. Thanks to the OPVOH opto-electronic properties, one may prepare, after appropriate solvent extraction, hybrid, porous material that may be used as a sensor for detecting in air or in water undesired molecules by alteration of the OPVOH scaffold. solvent

INTRODUCTION

Polyvinyl chloride, PVC, the third-most widely produced synthetic polymer, is currently experiencing a renewal with respect to environmental issues thanks to its recycling to a very large extent (see http://www.vinylplus.eu/resources/publications/progress-report). The continuous interest toward this polymer arises from two essential and unique properties, triboelectricity and flameretardant [START_REF] Gnanou | Organic and Physical Chemistry of Polymers[END_REF] . Although used for decades as one of the oldest synthesized polymer, PVC has still a future ahead before being superseded by polymers of equivalent properties produced by bioengineering. Attempting to impart new properties to this polymer remains a topic of interest.

PVC is basically an atactic polymer, which surprisingly produce thermoreversible gels of fibrillar morphology in a large variety of solvents 2-4 . This has been shown to arise from a low amount of long syndiotactic sequences that can crystallize [START_REF] Juijn | Crystallinity in atactic poly vinyl chloride Kolloid Z[END_REF][START_REF] Te Nijenhuis | Investigation of the aging process of a polyvinyl chloride gel by the measurement of its dynamic moduli[END_REF] . Because of the relatively small size of the chlorine atom, isolated iso or hetero defects along syndiotactic sequences do not hinder them from forming crystalline structures. PVC is at variance with other polymers such as polystyrene where the bulky phenyl group definitely impedes these defect-containing sequences to be accommodated into the crystal phase. Guenet and coworkers have further shown that the other types of sequences can form polymer-solvent complexes whose occurrence can account for the increase of the elastic modulus with gel aging [START_REF] Mutin | Physical gels from PVC: ageing and solvent effect on thermal behavior, swelling and compression modulus[END_REF][START_REF] Guenet | Polymer-solvent molecular compounds[END_REF][START_REF] Abied | Physical gels from PVC: molecular structure of pregels and gels by low angle neutron scattering[END_REF][START_REF] Lopez | Molecular structure by neutron scattering of thermoreversible gels from chemically-modified PVC[END_REF] . From its wet gels, fibrils are processed for the textile industry. The gel state also affords preparation of porous materials by proper removal of the solvent [START_REF] Daniel | Aerogels with a Microporous Crystalline Host Phase[END_REF] .

In a quite different domain of science, a wealth of self-assembling systems has been synthesized these past twenty years. In many cases the solutions of these molecules generate through a quench at low temperature fibrillar networks that are commonly designated as organogels or molecular gels [START_REF] Terech | Low molecular mass gelators of organic liquids and the properties of their gels[END_REF][START_REF] Terech | Editors Molecular Gels: Materials with Self-Assembled Fibrillar Networks[END_REF][START_REF] Liu | Soft Fibrillar Materials: Fabrication and Applications[END_REF][15][START_REF] Weiss | The past, present and future of molecular gels. What is the status of the field, and where is it going?[END_REF][START_REF] Guenet | thermodynamics, structure, solvent role and properties[END_REF][18] . Interestingly, these systems often bear a functional property (opto-electronic, magnetic,..).

The merging of these two separate domains of science can offer an original approach for preparing hybrid materials that involve a polymer and a self-assembling system, thus bringing unexpected functional properties to common polymers. Recent functional materials have been prepared in this way [19][START_REF] Lopez | Encapsulation of filaments of a self-assembling bicopper complex in polymer nanowires[END_REF][START_REF] Boulaoued | Guenet Hybrid fibrillar xerogel with unusual magnetic properties[END_REF][START_REF] Raj | Insulated Molecular Wires: Sheathing Semi-Conducting Polymers with Organic Nanotubes through Heterogeneous Nucleation[END_REF][START_REF] Bairi | A Co-assembled Gel of a Pyromellitic Dianhydride Derivative and Polyaniline with Optoelectronic and Photovoltaic Properties[END_REF][24] . Magnetic nanomaterials have been obtained by encapsulation of ferromagnetic filaments [START_REF] Lopez | Encapsulation of filaments of a self-assembling bicopper complex in polymer nanowires[END_REF][START_REF] Boulaoued | Guenet Hybrid fibrillar xerogel with unusual magnetic properties[END_REF] within polymer fibrils. Insulated nanowires from encapsulated poly(3-butylthiophene-2,5-diyl) (P3BT) fibrils by self-assembled nanotubes have been prepared in the same way [START_REF] Raj | Insulated Molecular Wires: Sheathing Semi-Conducting Polymers with Organic Nanotubes through Heterogeneous Nucleation[END_REF] .

In this paper we report on preliminary investigations aiming at extending the design of hybrid functional materials prepared from polymers and organogels to PVC which offers more potential for apllications. The organogelator used in this preliminary study is of the type oligo(pphenylenevinylene) molecule 15,[START_REF] George | Self-Assembled Nanotapes of Oligo(p-phenylene vinylene)s: Sol-Gel-Controlled Optical Properties in Fluorescent π-Electronic Gels[END_REF] , OPVOH (figure 1) whose organogels are well documented 15,19 .

As will be again shown the making process is simple, easy to implement, while no chemistry is required. Two solvents have been considered: benzyl alcohol (BA), a poor solvent to PVC, and bromobenzene, (BB), a good solvent to PVC. While OPVOH produces fibrillar organogels in both solvents, PVC exhibits differing morphologies. In this study the OPVOH concentration has been kept constant while the PVC content has been varied.

An interesting outcome of this study deals with the significant improvement of the gel mechanical properties in spite of the low amount of organogelator.

EXPERIMENTAL SECTION

Materials

The PVC used in the present study was supplied by Rhovyl SA. The weight average molecular weight as determined by SEC in THF at 25°C (universal calibration) is M w = 1.2x10 5 g/mol and the polydispersity index M w /M n =2.3. The fractions of triads were obtained by [START_REF] Terech | Editors Molecular Gels: Materials with Self-Assembled Fibrillar Networks[END_REF] C-NMR: syndio: 33%, iso: 18%, hetero: 49% [START_REF] Mutin | Physical gels from PVC: ageing and solvent effect on thermal behavior, swelling and compression modulus[END_REF] .

The fibrillar organogels are prepared from oligo(p-phenylenevinylene) with differing aliphatic side chains (R 12 = C 12 H 25 and R 16 = C 16 H 33 ) possessing two OH terminal groups (designated as OPVOH12 and OPVOH16 in what follows). The synthesis and properties of these molecules are extensively described in reference 24.

Bromobenzene (purity grade 99.5%) and benzyl alcohol (purity grade 99%) were purchased from SigmaAldrich and used as-received.

The preparation of the hybrid systems is quite straightforward: a mixture of PVC, organogelator and solvent is prepared at the desired concentration. Depending upon the PVC concentration and on the solvent, the system is heated up to 120-140°C in bromobenzene and 160-180°C in benzyl alcohol until a clear, homogeneous solution is obtained. Finally, the solution is quenched to low temperature (0°C down to -20°C) for producing the sample.

The PVC concentrations are ranging from 4.810 -2 g/cm 3 to 17.510 -2 g/cm 3 , while the OPVOH concentration is always kept constant at 0.4x10 -2 g/cm [START_REF] Alfrey | Some studies of plasticized polyvinylchloride[END_REF] (see SI Table S1).

Differential Scanning Calorimetry

The gel formation and melting were investigated by means of the DSC 8500 from Perkin Elmer.

Three heating and cooling rates were used, namely 5°C/min, 10°C/min and 15°C/min. The temperature range was from -20°C to 150°C. The formation and melting temperatures were determined after extrapolation to 0°C/min. The associated enthalpies were determined from the spectra obtained at 10°C/min. Samples were prepared as described above. About 30 mg of the mixture were then transferred to stainless steel pans that were hermetically sealed by means of an o-ring. The weight of the sample was checked after completion of the different cycles in order to evaluate any solvent loss.

Turbidity determination

Turbidity in the samples prepared from benzyl alcohol was determined by means of an optical setup that allows measurement of the light intensity transmitted through the sample when temperature is decreased. Basically, a collimated and attenuated monochromatic beam (λ = 632.8 nm) from a HeNe laser (Melles Griot 05-LHP-151) was shined onto a 5 mm-thick cuvette containing the sample, while the transmitted light was collected onto a CCD camera (Retiga 2000R). The samples were heated at 150°C, and then cooled at room temperature at a rate of about 1.4-1.5°C/min.

Scanning Electron Microscopy

The system PVC/BB has been observed by cryo-SEM technique. A piece of the gel was placed on a cryo-holder and quickly plunged into a nitrogen slush in the cryo preparation chamber of a Quorum PT 3010 machine. Subsequently, the sample is transferred under vacuum into the chamber attached to the microscope. There, the frozen sample is coated with a thin Pt layer (by sputter deposition) and fractured with a razor blade. A slight etching at -100°C is performed to render the morphology more visible. The sample is eventually transferred in the FEG-cryoSEM (Hitachi SU8010) and observed at 1keV at -150°C. The images were taken with the SE-in lens detector. The system PVC/BA has been observed at room temperature after subsequent drying under vacuum by conventional scanning electron microscopy (Hitachi SU8010) at 1 keV.

Rheology

The real and imaginary parts of the complex shear modulus were measured with a stress-controlled rheometer (Haake, Mars III) operating in the oscillatory mode. Two types of measurements cells were chosen: plate-plate type (35 or 60 mm diameter) was used for measuring the elastic modulus G' as a function frequency and of PVC concentration, whereas determination of the gelation temperature in bromobenzene at constant frequency was achieved by means of a double Couette cell (DG41, Haake). The temperature in the Couette cell was regulated by an external bath (Haake F3) and that in the plate-plate cells by Peltier elements embedded in one of the plates. For all shear measurements the applied stresses were lower than 5×10 -2 Pa to ensure that the measurements were carried out in the linear response regime. The gap in the Couette cell was ∼400 μm and the thickness of the samples was ranging between 400 and 800 μm in the plate-plate set-up.

RESULTS AND DISCUSSION

Mapping out a temperature-concentration phase diagram for PVC systems turns out to be impossible from differential scanning calorimetry (DSC) investigations. The low amount of syndiotactic sequences together with their large length distribution results in the spreading of the exotherms and endotherms over a large range of temperature. Although several papers had reported observations of melting endotherms these were chiefly artefactual. Geil and coworkers have shown that the DSC endotherm systematically disappears on the second heating [START_REF] Yang | Morphology and properties of PVC/solvent gels[END_REF] . This received further support by Mutin and Guenet who showed that the artefactual enthalpy arose from a mechanical effect [START_REF] Mutin | Physical gels from PVC: ageing and solvent effect on thermal behavior, swelling and compression modulus[END_REF] .

Figure 2:

Visual aspect ) at room temperature of the gels in bromobenzene (left) and the systems in benzyl alcohol (right (gel for OPVOH, phase separated system for PVC, and gel for the hybrid system). While solvent release occurs in PVC/benzyl alcohol, thus forming two macroscopic phases, it no longer occurs in PVC/OPVOH/benzyl alcohol. In all cases C PVC = 4.810 -2 g/cm [START_REF] Alfrey | Some studies of plasticized polyvinylchloride[END_REF] , C OPVOH = 410 -3 g/cm [START_REF] Alfrey | Some studies of plasticized polyvinylchloride[END_REF] .

In the aim of overcoming this drawback, the onset of "structures" formation of PVC was determined by turbidimetry observation for the PVC/benzyl alcohol system (SI figure S1, turbidimetry vs temperature) and rheology experiments for the PVC/bromobenzene gels (SI figure S2, G' and G" vs temperature). As will be apparent in what follows, rheology is not appropriate for the systems in benzyl alcohol. Conversely, turbidity measurement are not appropriate for the PVC/bromobenzene gels as the refractive indices are virtually identical (n D = 1.565 for bromobenzene, and n D = 1.55 for PVC).

Conversely, the formation and melting of OPVOH organogels can be detected by DSC experiments as their associated enthalpies are large enough.

Gels in bromobenzene

A transparent gel is produced with the system PVC/BB which does not undergo any noticeable PVC/BB morphology consists of a fibrillar network resembling a knitwear structure with a mesh size in the range 80-100 nm (figure 4a). This morphology confirms former observations by Yang and Geil. [START_REF] George | Self-Assembled Nanotapes of Oligo(p-phenylene vinylene)s: Sol-Gel-Controlled Optical Properties in Fluorescent π-Electronic Gels[END_REF] . OPVOHs molecules form gels in bromobenzene that consist of an assembly of more or less straight fibrils (figure 4b) of cross-sections in the range 80-100 nm.

. The formation and melting temperatures of the OPVOH gels at C OPV = 0.4x10 -2 g/cm 3 as determined by DSC are T gel = 42°C with T m = 404°C for OPVOH16/BB, and T gel = -102°C with T m = 404°C for OPVOH12/BB. The low values of the formation and melting enthalpies suggest that not all the OPVOH molecules participate in the formation of the gel scaffold, a subsequent fraction still remaining in the SOL state. Indeed, the enthalpies values for the pure OPVOHs are H OPVOH12 = 78 J/g and H OPVOH16 = 101 J/g, which should give H= 0.31 to 0.4 J/g Determination of the gel formation temperatures of the binary systems therefore show that the PVC network forms well before the OPVOHs molecules can organize. As a result, in the ternary systems, the OPVOHs fibrils are forced to grow in a medium filled with subsequent "obstacles". In addition, the available space for a fibril to grow, namely determined by the PVC gel mesh size, is about the same order of magnitude as their cross-sections.

In the case of the ternary system PVC/OPVOH/BB, a gel is also produced where the OPVOH molecules are homogeneously dispersed (figure 2 left). That OPVOH molecules have undergone some degree of organization is confirmed by the occurrence of melting endotherms and formation exotherms (see SI Figure S3, DSC traces). The associated temperatures are not significantly altered in spite of the presence of the PVC network (figure 3 and see SI Table S1). There is no clear tendency as to whether the corresponding enthalpies depend upon the PVC content.

The typical morphology of these ternary gels is basically similar to that of the binary system although the network appears somewhat looser (figure 4c). The organogel fibrils cannot be distinguished. That the OPVOH fibrils grow within a network of rather small mesh size may possibly alter the original organogel morphology. S2, G' vs PVC concentration). The typical behavior observed for these ternary systems is reported in figure 5 together with the behavior of the corresponding binary gels.

The intermingling of the OPVOH organogel with the PVC physical network results in a conspicuous increase of the elastic modulus at low PVC concentrations, which gradually vanishes at higher PVC concentrations. Clearly, a rather strong reinforcement of the PVC gel mechanical properties occurs with a relatively low amount of OPVOH.

The model by Takayanagi et al. 27 and by Zhang and Rochas 28 derived for mixed gels of compatible biopolymers may be considered in the present case. In this model the shear modulus of the hybrid gel is simply the sum of the moduli of each component:

(1) 𝐺 ′ ℎ𝑦𝑏 = 𝐺 ′ 𝑂𝑃𝑉 + 𝐺 ′ 𝑃𝑉𝐶 (𝐶)

As we have determined experimentally at -20°C, namely:

𝐺 ′ 𝑃𝑉𝐶 (𝐶) (Pa)
(2) 𝐺 ′ 𝑃𝑉𝐶 (𝐶) = 9.26𝑥10 6 𝐶 3.17 increasing the temperature from -20°C to 10°C entails partial melting of both networks the decrease seen for is expected (see SI figure S5, and table S2).

𝐺 ′ 𝑂𝑃𝑉

The shear modulus of the OPVOH organogel has been measured at a concentration of C OPVOH = 410 -3 g/cm 3 at the same temperatures in order to test the validity of the above approach. The same experimental protocol, namely heating at the same temperature and cooling at the same rate, was applied to all the samples. The OPVOH organogel is made up with rigid objects, the fibrils, whose elasticity is of enthalpic nature [START_REF] Guenet | thermodynamics, structure, solvent role and properties[END_REF] . The shear modulus of the network is then a combination of the intrinsic (bending) modulus of its constituting fibrils e and of the number of physical cross-links per unit volume, the latter being expressed through the concentration of elastic material . For straight fibrils it is written [START_REF] Zhang | Interactions between agarose and κ-carrageenans in aqueous solutions[END_REF][START_REF] Guenet | Polymer-solvent molecular compounds[END_REF] :

(4) 𝐺 ′ ~ 𝑒𝜑 2
Since the OPVOH concentration is rather low, this suggests that the OPVOH fibrils have a very high intrinsic modulus.

The systems in benzyl alcohol

The system PVC/BA separates into two phases when rapidly quenched to 0°C (see figure 2), where the polymer-rich phase is of the gel-like type. Turbidimetry experiments (SI figure S1) further show that a liquid-liquid phase separation is involved [START_REF] Mutin | Physical gels from PVC: ageing and solvent effect on thermal behavior, swelling and compression modulus[END_REF] as ascertained by the observation of a miscibility gap delimited by a binodal curve in the temperature-concentration phase diagram (figure 3 right).

The location of the binodal curve at high temperature further confirms that benzyl alcohol is a very poor solvent to PVC. Morphological investigations by scanning electron microscopy (SEM) reveal an array of spherical objects of the "meat-ball" type of about 1 µm diameter, that are more or less connected so as to form a network in the early stage of the phase separation (figures 6a). Yet, this system is not strictly speaking a gel but rather a transient network that eventually collapses in the course of time [START_REF] Guenet | thermodynamics, structure, solvent role and properties[END_REF] , resulting in the formation of two macroscopically-separated phases (figure 2). As the PVC balls are frozen in by a low degree of crystallinity 7 they do not fuse into a continuous, structureless polymer-rich phase as would do an amorphous polymer.

OPVOHs molecules form gels in BA of typical fibrillar morphology (figure 6b). The mesh size rather lies in the micron range in the concentration domain considered in this study (C OPV =0.4x10 -2 g/cm 3 ), while the fibrils possess cross-sections in the range 100-500 nm that are significantly larger than those of OPVOH/BB gels. The formation and melting temperatures of the gels at C OPV = 0.4x10 -2 g/cm [START_REF] Alfrey | Some studies of plasticized polyvinylchloride[END_REF] as determined by DSC are T gel = 453°C and T m = 745°C. The ternary system PVC/OPVOH/BA does not display any noticeable solvent release unlike the binary system PVC/BA figure 2. Also, no macroscopic phase separation between the PVC and OPVOH components occurs in the course of time as the yellow colour remains homogeneous throughout.

The occurrence of the OPVOHs gels formation and melting within the ternary system has been determined by DSC (see SI Figure S3). Data reported in the temperature-concentration phase diagram of figure 3 right reveal that the gel formation temperatures of both OPVOHs are virtually unaltered by the presence of the PVC structures, nor are the melting temperatures (detailed values are given in SI table S1). Only the corresponding enthalpies seem to decrease with the increasing amount of PVC. This may imply that a lesser amount of OPVOH molecules form the organogel scaffold (the gel phase) while a significant part remains dissolved (the sol phase). This would further suggest that all happens as if the presence of PVC improved the solvent quality towards OPVOH. Yet, the low values measured for the enthalpies do not allow one to draw unquestionable conclusions on this point. SEM observations unveil that the PVC "meat-balls" are actually imprisoned in the OPVOH gel (figures 6c and 6d). This outcome accounts for the absence of solvent release for the aged ternary systems. Evidently, the presence of existing PVC structures has virtually no influence on the thermodynamic of the gelation process of OPVOH molecules, nor has it on the final organogel morphology. A difference can, however, be observed between OPVOH12 and OPVOH16 gels.

OPVOH12 fibrils interact extensively with the PVC balls by wrapping them unlike OPVOH16 fibrils. The reason is presently not clear but most probably related to the length of the paraffinic moieties.

CONCLUDING REMARKS

In this paper we show that a hybrid material made up with PVC and an organogelator can be straightforwardly prepared by a simple process which consists in cooling homogeneous, ternary solutions. This achievement is made possible thanks to two essential properties: i) PVC and the organogelator are compatible in solutions at elevated temperature, and ii) the organogel formation is not impeded by the presence of the existing PVC structures. In the case of PVC/bromobenzene gels it is observed that the gel mechanical properties are dramatically improved by incorporation of a low amount of organogelator. In the case of PVC/benzyl alcohol, the pervading organogel prevents the collapse of the transient network, which to some extent is also an improvement of the mechanical properties.

The present outcomes further strengthen recent studies that have established the principle of functionalizing polymers with organogelators [19][START_REF] Lopez | Encapsulation of filaments of a self-assembling bicopper complex in polymer nanowires[END_REF][START_REF] Boulaoued | Guenet Hybrid fibrillar xerogel with unusual magnetic properties[END_REF][START_REF] Raj | Insulated Molecular Wires: Sheathing Semi-Conducting Polymers with Organic Nanotubes through Heterogeneous Nucleation[END_REF][START_REF] Bairi | A Co-assembled Gel of a Pyromellitic Dianhydride Derivative and Polyaniline with Optoelectronic and Photovoltaic Properties[END_REF][24] . Imparting a functional property to PVC without any additional chemistry is therefore feasible. Here, OPVOH possesses opto-electronic properties, which results in a change of colour (sup. Info. S7, change of colour at the SOL-GEL transition) at the melting of the organogel fibrils while the PVC network remains unaltered 15,19 . After appropriate drying the porous material could be used as a sensor for detecting in air or in water undesired molecules that are capable of dissolving or even slightly altering the OPVOH scaffold. This is but one example of possible applications.

Corresponding

Figure 1 :

 1 Figure 1: Chemical structure of OPVOH12 (left) and OPVOH16 (right) 24 .

  syneresis 7 as shown in figure 2. As aforementioned, transparency arises from the nearly identical refractive indices.

Figure 3 :

 3 Figure 3: Structures formation temperatures vs concentration in bromobenzene (left), and in benzyl alcohol (right), () PVC/bromobenzene as determined by rheology, () PVC/benzyl alcohol as determined by turbidimetry , () OPVOH12 and () OPVOH16 in the ternary systems as determined by DSC.

Figure 4 :

 4 Figure 4: SEM micrographs typical of (a) PVC/bromobenzene gels, C PVC = 4.810 -2 g/cm 3 ; (b) OPVOH16/bromobenzene, C OPVOH = 410 -3 g/cm 3 ; (c) PVC/OPVOH16/bromobenzene gels, C PVC = 4.810 -2 g/cm 3 , C OPVOH = 410 -3 g/cm 3 .

Figure 5 :

 5 Figure 5: Variation of the elastic modulus G' as determined at frequency= 1Hz and at T= -20°C (left) and T= 10°C (right) for PVC/bromobenzene gels (, ) and PVC/OPVOH16/bromobenzene gels (,).

  𝐺 ′ 𝑃𝑉𝐶 (𝐶) = 4.62𝑥10 6 𝐶 3.0 𝑃𝑉𝐶 The fit yields = 2217660 Pa at T= -20°C and = 1090700 Pa at T= +10°C. Since 𝐺 ′ 𝑂𝑃𝑉 𝐺 ′ 𝑂𝑃𝑉

For

  T= -20°C and T= 10°C it is found = 2239 Pa and = 981 Pa, respectively (see SI table 𝐺 ′ 𝑂𝑃𝑉 𝐺 ′ 𝑂𝑃𝑉 S2, and figure S6, G' vs PVC concentration). These values are in excellent agreement with those obtained from the theoretical fit which supports the assumption of combining linearly the modulus of each component.

Figure 6 :

 6 Figure 6: SEM micrographs typical of: (a) PVC/benzyl alcohol, C PVC = 4.810 -2 g/cm 3 ; (b) OPVOH/benzyl alcohol, C OPVOH = 410 -3 g/cm 3 ; (c) PVC/OPVOH12/benzyl alcohol, C PVC = 4.810 - 2 g/cm 3 , C OPVOH = 410 -3 g/cm 3 ; (d) PVC/OPVOH16/benzyl alcohol, C PVC = 4.810 -2 g/cm 3 , C OPVOH = 410 -3 g/cm 3 .

  Author jean-michel.guenet@ics-cnrs.unistra.fr; ORCID 0000-0002-3829-8303 Author Contributions This article is part of Z.Z. thesis. M.S. and A.C. performed the SEM investigations, A.A and V.K.P. provided the OPV molecules, D. C. carried out the rheological part and the turbidimetry measurements, S.E. and J.M.G. supervised the work. Notes The authors declare no competing financial interest Acknowledgments: The authors are indebted to C. Saettel for the DSC investigations.

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R2D2 spherical TPC: first energy resolution results

Spherical gaseous time projection chamber detectors, known also as spherical proportional counters, are widely used today for the search of rare phenomena such as weakly interacting massive particles. In principle such a detector exhibits a number of essential features for the search of neutrinoless double beta decay (ββ0ν). A ton scale experiment using a spherical gaseous time projection chamber could cover a region of parameter space relevant for the inverted mass hierarchy in just a few years of data taking. In this context, the first point to be addressed, and the major goal of the R2D2 R&D effort, is the energy resolution. The first results of the prototype, filled with argon at pressures varying from 0.2 to 1.1 bar, yielded an energy resolution as good as 1.1% FWHM for 5.3 MeV α tracks having ranges from 3 to 15 cm. This is a milestone that paves the way for further studies with xenon gas, and the possible use of this technology for ββ0ν searches.

Introduction

Determining the nature of neutrino has now become a necessity in the field of particle physics, and in the related domains of astrophysics or cosmology. The neutrino could be a Majorana particle (i.e. its own anti-particle) or a Dirac particle (neutrino and anti-neutrino are distinct particles) and the most sensitive way to elucidate this property is to look for neutrinoless double beta (ββ0ν) decay forbidden by the SM [START_REF] Doi | Neutrinoless modes of double beta decay[END_REF][START_REF] Pascoli | The Absolute neutrino mass scale, neutrino mass spectrum, majorana CP-violation and neutrinoless double-beta decay[END_REF]. Such a process requires that the neutrino is a Majorana particle, and an observation would clarify its nature and would provide the most sensitive laboratory technique for measuring the neutrino mass. Furthermore, the observation of ββ0ν decay would have consequences on cosmology on our understanding of the creation of matter at the beginning of the Universe: a Majorana neutrino is mandatory in the theoretical models including a lepto-genesis phase to explain the baryon asymmetry in the Universe.

The experimental search is based on the detection of the two electrons emitted in the decay and on the reconstruction of their kinetic energy. In case of a ββ0ν decay, the kinematics of the two body reaction foresees that the sum of the energy of the electrons must be equal to the transition energy Q ββ . Such a peak has to be identified and distinguished from the background issued by natural radioactivity and from the energy tail of the allowed ββ2ν decay. For this, high energy resolution, low radioactivity materials and isotopes with high Q ββ must be privileged in order to operate in a region of interest (ROI) with higher energy compared to natural radioactivity. Nowadays the theory fails to predict the best target and the expected half-life for ββ0ν decay. There is a large panel of experimental detection techniques for rare searches, which are usually based on a pure calorimetric approach with a large target mass, and on the use of low radioactive materials. Some of them benefit, in addition, from an excellent energy resolution and/or low threshold and/or tracking. The typical experimental techniques used for ββ0ν decay search exploit: germanium semiconductors such as GERDA [START_REF] Agostini | Improved Limit on Neutrinoless Double-β Decay of 76 Ge from GERDA Phase II[END_REF], bolometers such as CUORE [START_REF] Alduino | First Results from CUORE: A Search for Lepton Number Violation via 0νββ Decay of 130 Te[END_REF], gaseous or liquid TPC such as EXO-200 [START_REF] Albert | Search for Neutrinoless Double-Beta Decay with the Upgraded EXO-200 Detector[END_REF], tracking-colorimetry technique such as SuperNEMO [START_REF] Arnold | Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO[END_REF], and liquid scintillators such as KamLAND-Zen [START_REF] Gando | Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen[END_REF], which achieved the best sensitivity on the effective neutrino mass m ββ of 65 -165 meV depending on the nuclear matrix elements [START_REF] Engel | Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review[END_REF]. For a comprehensive review of the different experimental searches see Ref. [START_REF] Dell'oro | Neutrinoless double beta decay: 2015 review[END_REF]. Despite the different techniques used, the sensitivity of almost all experiments is limited by background (in particular coming from radon contamination), which reduces the advantage given by an increase of the target mass.

Driven by the need of large detectors with zero background to improve the sensitivity on ββ0ν decay search, the Rare Decays with Radial Detector (R2D2) R&D effort aims at the development of a new concept of detector based on spherical gaseous time projection chambers (TPC) also called spherical proportional counters (SPC). The low detection threshold capability of the SPC, down to a single ionisation electron, has been demonstrated [START_REF] Gerbier | NEWS: a new spherical gaz detector for very light WIMP detection[END_REF]. For this reason they are today used for the search of light weakly interacting massive particles (WIMPs) as dark matter candidate by the NEWS-G collaboration [START_REF] Gerbier | NEWS : a new spherical gas detector for very low mass WIMP detection[END_REF][START_REF] Arnaud | First results from the NEWS-G direct dark matter search experiment at the LSM[END_REF]. Experimentally, there are strong similarities between searches for light dark matter candidates and searches for ββ0ν decays: only few events per year are expected for detectors using targets of several tens or hundreds kg and several years of taking data. The challenge is to drastically reduce background coming from the natural radioactivity, and to reach unprecedented level of radio-purity in the detector material.

A spherical high pressure gas TPC is a detector which reduces the impact of radioactivity the most effective way, limiting the detector material. Inside the sphere the only mechanical parts are constituted by the central anode and its supporting rod. Furthermore, such a detector meets the two additional requirements needed in ββ0ν decays search: a large mass and a good energy resolution. A large isotope mass can be contained in a small volume: a sphere of 1 m radius could contain 1 ton of 136 Xe at a pressure of 40 bar. Concerning energy resolution, high pressure gas TPC could in principle achieve a sub-percent energy resolution at the relevant Q ββ , which was demonstrated so far in ionization mode up to 60 bar [START_REF] Bolotnikov | The spectroscopic properties of high-pressure xenon[END_REF]. Assuming an energy resolution of 1% FWHM at the xenon Q ββ of 2.458 MeV, the sensitivity of a detector filled with 136 Xe at a pressure of 40 bars was investigated [START_REF] Meregaglia | Study of a spherical Xenon gas TPC for neutrinoless double beta detection[END_REF], and the obtained results are indeed the origin of the R2D2 R&D effort. A detector of 200 kg of 136 Xe could reach values of effective neutrino mass in the range 35 -70 meV, improving the current world best sensitivity by a factor of two [START_REF] Gando | Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen[END_REF], whereas a ton scale detector could cover the inverted mass hierarchy region, measuring a neutrino effective mass of the order of 10 meV. The sensitivity of the proposed detector is shown in Fig. 1 as a function of its mass, for one year of data taking, assuming the parameters (i.e. background, energy resolution and signal efficiency) of Ref. [START_REF] Meregaglia | Study of a spherical Xenon gas TPC for neutrinoless double beta detection[END_REF].

The perspective to achieve an excellent energy resolution at the per-cent level and to develop a tracking capability inside the gas, the simplicity of the detector with only one readout channel, and the very low material budget induced by its very simple mechanical structure, make the proposed technology ideal to search for ββ0ν decays. The path to a final ton scale detector to explore the inverted mass hierarchy region involves several intermediate steps to validate the different detector features, the first one being the possibility to reach an energy resolution of 1% FWHM at 2.458 MeV. To validate this critical point a prototype, conceived and built at CENBG, has been filled and then operated with 98% argon + 2% methane in order to verify all the technical aspects and to fully characterise the detector response. The experimental search is based on the detection and measurement of the sum of the kinetic energies of emitted electrons which must be equal to the Q-value of the transition, Q 2 , if the electrons are the only light p in the final state, as happens for example in the case of light neutrino exchange mechanism. Therefore, the sen of the experiments will depend on their capability to distinguish this process from the background dominated ambient natural radioactivity and by the allowed 2⌫2 decay. Huge e↵orts have been made in these last dec improve the particle identification and the energy resolution of the detectors. In parallel, production and sele radiopure materials as well as new anti-radon strategies continue to be developed. The detectors must also be accommodate large isotope masses, today typically of the order of few tens or hundreds of kilograms, depen the experimental approach. Investigating di↵erent isotopes is also part of the strategy in a context where the predictions are not reliable enough yet.

Most of the 0⌫2 experiments exploit a homogeneous approach, i.e. the detector coincides with the enhancing the e ciency for the collection of the electrons emitted in the decay. It is the case for the germ semiconductors (GERDA, MAJORANA, LEGEND), bolometers (CUORE, CUPID, AMoRE), gaseous or liqu (NEXT, PANDA-X-III, EXO-200, nEXO), crystals at ambient temperature (COBRA, CANDLES, AUROR liquid scintillators (KamLAND-Zen, SNO+). This last technology reached the best sensitivity on m -65 165 meV depending on the nuclear matrix elements -with the KamLAND-Zen experiment exploiting 1 of liquid scintillator loaded with xenon-136 (350 kg). A di↵erent approach consists in separating the source detector. The loss of e ciency is compensated by the better topological reconstruction of the single electrons could be very appealing in case of discovery. The NEMO detectors are the only ones to have proven the tec feasibility with a gaseous tracker volume surrounded by a scintillator calorimeter. The already measured or e sensitivities of most of the projects are given in Figure 2.

SuperNEMO

The SuperNEMO detector capitalizes on a unique tracker/calorimeter detection technique ("tracko-calo") wh successfully operated with the NEMO-3 experiment (running from 2003-2011 at the LSM underground laborato This technology has been initiated in the 1980's in France playing an important role in the development, expl and management of the successive NEMO projects.

Today the collaboration consists of 21 laboratories from 9 countries (France, Czech Republic, Finland, Russia, Slovakia, UK, Ukraine, US) including 6 IN2P3 laboratories: CENBG, CPPM, LAL, LAPP, LPC-C LSM.

The full SuperNEMO detector has been designed to hold 100 kg of double-beta decay isotope (seleniu baseline) to reach a sensitivity of the order of 10 26 years to the half-life of decay, corresponding to a 50-1 e↵ective Majorana neutrino mass (Figure 2, points SN-Se and SN-Nd for 100 kg of selenium-82 and neodyn respectively).

SuperNEMO is a detector with multi-observables that allows full topological reconstruction of events r in a powerful background rejection. A background index b ⇠ 8 ⇥10 5 counts/(keV.kg.y) is expected in th of interest. The topological reconstruction and the kinematic information on individual particles (single 2 Figure 1. Expected sensitivity for neutrinoless double beta decay search using a SPC in terms of its mass assuming the parameters of Ref. [START_REF] Meregaglia | Study of a spherical Xenon gas TPC for neutrinoless double beta detection[END_REF] for one year of operation (left). The width of the blue band is due to the uncertainty on the nuclear matrix elements which are used to convert the limit on the lifetime to the limit on the effective mass. The allowed regions for the effective neutrino mass m ββ as a function of the lightest neutrino mass for normal and inverted hierarchy are also shown (right) with the same vertical scale for a direct comparison.

Despite the final experiment will use xenon as gas to fill the detector, operating the detector with argon represents an efficient and cost-effective manner to access all the technical aspects of the detector while optimizing the xenon recuperation system. Indeed argon is wasted at each filling whereas xenon is quite expensive and needs to be recovered and possibly purified at each filling. In addition the energy resolution should be intrinsically better in xenon since the number of electrons produced for a given deposited energy is higher with respect to argon [START_REF] Weiss | Energy required to produce one ion pair in several noble gases[END_REF], making the energy resolution obtained with argon a conservative limit. To exploit the most the particular electrostatic topology of the spherical TPC, and achieve the best possible performances, intensive use of signal processing techniques becomes also critical. The signal treatment is fundamental to extrapolate information on the events, such as the track direction, from the specific features of the waveforms. The comparison of the data taken with the prototype with the simulated ones is important to validate this point and confirm our understanding of the detector response.

In this paper we report on measurements carried out with α sources, in particular to evaluate the energy resolution for long penetrating α tracks inside the detector. A detailed data-simulation comparison and signal treatment analysis are also presented showing a deep understanding of the detector response.

R2Dsetup

Detector description

The R2D2 setup consists of a 20 cm radius sphere for a volume of approximately 33.5 L which could contain about 7.9 kg of xenon at a pressure of 40 bars. Given that high-radiopurity is not critical at this stage of the investigations, aluminium was chosen for the detector construction. Such a choice was driven by the in-house capabilities of CENBG of machining aluminium allowing for cost containment. The detector was built starting from two cylindrical blocks of aluminium which were machined in order to form two semi-spheres inside, and then bolted together as shown in the mechanical drawing in Fig 2.

The anode at a positive high voltage, leading to the drift of the ionisation electrons and their subsequent amplification to form the observed signal, is located at the centre of the grounded sphere. The sensor [START_REF] Katsioulas | A sparkless resistive glass correction electrode for the spherical proportional counter[END_REF] (i.e. the central anode) consists of a 2 mm diameter stainless steel sphere connected to an insulated wire of 150 µm diameter, which is held in place by a supporting grounded rod. More details on the detector working principle and on the sensor itself can be found in Ref. [START_REF] Gerbier | NEWS : a new spherical gas detector for very low mass WIMP detection[END_REF][START_REF] Savvidis | Low energy recoil detection with a spherical proportional counter[END_REF][START_REF] Giomataris | A Novel large-volume Spherical Detector with Proportional Amplification read-out[END_REF].

Electronics play a critical role in the detector operation since the requirements in terms of low noise, and immunity to radio frequency interferences (RFI), to achieve a good energy resolution are relatively stringent. Details on the specific developments are given in Sec. 2.2, whereas the main elements of the electronic chain are listed below:

• HV splitter. The HV cable connecting the sensor to the power supply is also used to extract the signal: to separate the signal a dedicated splitter box has been prepared at CENBG.

• Preamplifier. A preamplifier for impedance matching, shaping and amplification of the signal is needed before passing it to the acquisition card. For that we used a custom made low noise resistive feedback charge sensitive preamplifier, with an adapted frequency bandwidth, conceived at CENBG in the framework of the OWEN project [19].

• HV power supply. HV power supply can be an important source of detector instability and a possible source of noise. We used a commercial CAEN power supply DT8034 [20]

R f C f Q sensor HV Vo (t) polarization T1 JFET (a)
The layout of the preamp (Figure 5) has been optimize capacitance. The pinout is pin compatible with the CREM reference. In order to polarize the sensor, the preamplifier is couple described in the simplified circuit above. A noise measureme conditions. For comparison, with the high voltage filter, the e the CREMAT CR-110 is 856e -and 566e -for the OWEN pre with a current monitor at the level of 0.5 nA and a voltage ripple below 10 mV.

• DAQ. The DAQ is done using a CALI card developed for, and widely used by spherical gaseous detectors such as NEWS-G experiment [START_REF] Gerbier | NEWS : a new spherical gas detector for very low mass WIMP detection[END_REF], read by the SAMBA acquisition software [START_REF] Armengaud | Performance of the EDELWEISS-III experiment for direct dark matter searches[END_REF].

Custom electronics

A charge sensitive preamplifier was developed at CENBG in the framework of the OWEN (Optimal Waveform recognition Electronic Node) project [19]. This circuit integrates the current signal coming from the sensor on the feedback capacitance C f , then it generates an output voltage signal which is proportional to the original input charge Q registered by the central anode. The output voltage signal slowly decreases according to the time constant τ . As shown by the equivalent circuit (see Fig. 3(a)), the relation between the output voltage pulse V o (t) and the decay time constant τ is given by:

V o (t) = - Q C f e -t/τ . (2.1)
From equation 2.1, it can be seen that the signal charge pulses Q collected by the sensor are converted into voltage pulses with amplitude

V o (0) = -Q/C f and τ = R f × C f .
In our case the value of the feedback capacitor C f is 1.5 pF and the one of the feedback resistor R f is 100 MΩ. The architecture of the preamplifier is based on the established design by T.V. Blalock [START_REF]Instrumentation électronique en physique nucléaire (mesures de temps et d'énergie)[END_REF]. Usually, the preamplifier uses a Field Effect Transistor (FET) as an input element associated with a bipolar transistor to form a cascode. In order to improve the gain bandwidth product (GBW), a transistor T1 used as a current amplifier is inserted between the FET and the bipolar transistors as shown in Fig. 3(a). The layout of the preamplifier shown in Fig. 3(b) has been optimized in terms of noise, frequency bandwidth, and parasitic capacitance. The pinout is pin compatible with the CREMAT CR-110-R2 [23], which was used for the first tests on detector stability. In order to polarize the sensor, the preamplifier is coupled to a high voltage filter shown in the dashed box of Fig. 3(a).

To evaluate the performance of the preamplifier, a noise measurement was carried out. The full specifications of the OWEN preamplifier can be found in Tab. 1. The HV splitter was based on an existing one developed for the SEDINE [START_REF] Fard | Background reduction of a spherical gaseous detector[END_REF] detector and an optimization for the R2D2 detector is foreseen for a possible further reduction of the electronic noise.

The gain of the CREMAT preamplificator is 1.4 V/pC whereas for the OWEN preamplifier a gain of 0.75 V/pC was measured. This difference is due to an additional amplification stage which was avoided in the OWEN preamplifier. The OWEN preamplifier meets the low noise requirements needed by the R2D2 detector and it was therefore chosen as baseline option.

In addition, the OWEN preamplifier has the advantage of having customizable parameters allowing for a better matching between the filter and the preamplifier bandwidth acceptance.

Operation

For a good detector performance, contamination of the gas volume with electronegative impurities has to be minimised. In particular the presence of oxygen would result in a loss of signal radially dependent, degrading the achievable energy resolution. The ArP2 mixture (i.e. 98% Ar and 2% CH 4 ) is extremely pure with a contamination at the level of 1 ppm, which is sufficient for our detector as demonstrated by the results presented in this paper. The detector has been heated for several weeks at 80 • C in order to reduce the material outgassing during operation, and it is systematically pumped to a vacuum at the level of 10 -6 mbar before each filling. The limiting factor comes from the oxygen contamination in the gas: a vacuum of 10 -6 mbar corresponds to a purity of 5 ppb at 1 bar, negligible with respect to the gas contamination at the level of 1 ppm. The system leakage was also measured with an helium leak tester and no leak was observed at the level of 5 × 10 -9 mbar/s. The main contribution to vacuum loss is therefore due to outgassing of materials and a value of 2 × 10 -6 mbar/s was measured. Such a value is acceptable in this R&D phase assuring a good detector stability for several weeks. To test the detector response and resolution, a radioactive α source was used. Although the final experiment will observe electrons, at pressures below 10 bar it is very difficult to contain them in the small detector volume, therefore α particles were used despite their ionisation quenching [START_REF] Lindhard | Integral equations governing radiation effects[END_REF].

A 210 Po source producing a single α of 5.3 MeV with an activity of 4 Bq was used, allowing to quickly evaluate the detector gain. The main drawback of such a source is the electric field distortion due to the source itself and its support (see schematic drawing in Fig. 4(a)).

Although the source is on the outer surface to minimise potential perturbation of the electric field, a weak distortion could still be present being more relevant for short alpha particle tracks i.e. at high pressure. Furthermore some α particles lose part of the energy in the source support yielding a low energy tail which slightly spoils the gaussian peak we want to measure as explained in Sec. 5.2. The detector is sensitive to acoustic and electronic noise as well as to temperature variations. To work in the best available condition, the R2D2 prototype was installed at the PRISNA facility [26] at CENBG, where the temperature is kept constant within 1 degree and human activity is reduced the most. All the electronic devices have been grounded to a large metallic plate on which the detector is hosted, and all commercial power supplies have been replaced with laboratory power supplies to reduce the electronic noise. To reduce vibrational noise impacting the baseline stability, and therefore the resolution, the sensor supporting rod has been mechanically decoupled from the rest of the detector through a joint as shown in Fig. 4(b). A sizable impact on the noise reduction at low frequencies was observed (factor of about 2 at 60 Hz) and for the next detector upgrade a dedicated system to reduce vibration on the central sensor will be developed.

Simulation

The framework presented in Ref. [START_REF] Katsioulas | Development of a Simulation Framework for Spherical Proportional Counters[END_REF] has been used to simulate the experimental set-up, combining Geant4, a toolkit for the simulation of particle interactions with matter [START_REF] Allison | Recent developments in Geant4[END_REF], and Garfield++, a toolkit for the detailed simulation of gaseous particle detectors [START_REF] Veenhof | GARFIELD, recent developments[END_REF][START_REF] Schindler | Garfield++ user guide[END_REF]. Garfield++ interfaces to Heed, for particle interactions [START_REF] Smirnov | Modeling of ionization produced by fast charged particles in gases[END_REF], and Magboltz, for modelling electron transport parameters in gases [START_REF] Biagi | Monte Carlo simulation of electron drift and diffusion in counting gases under the influence of electric and magnetic fields[END_REF]. The electric field in the detector is described using the ANSYS finite element software [START_REF] Ansys R | Academic research mechanical[END_REF]. The electron transport parameters in the gas mixture, crucial input to the simulation, are estimated using Magboltz. In Fig. 5, the drift velocity, as well as the longitudinal and transverse diffusion coefficients are presented for the two gas pressures considered in this study i.e. 200 mbar and 1.1 bar.

The gain of the gas mixture is typically governed by the Townsend coefficient, however, in gas mixtures like Ar:CH 4 the Penning effect is observed. The methane ionisation potential is lower than the ionisation potential of argon, and potential ionisations of the latter may lead to ionisation of the former. In the calculations a transfer probability of 15% [START_REF] Sahin | Penning transfer in argon-based gas mixtures[END_REF] was used. Electro-negative molecules, like O 2 , tend to attach electrons, which subsequently do not contribute to the signal formation. The attachment coefficient for ArP2 at 200 mbar with different levels of O 2 contamination are presented in Fig. 6. The presence of methane in the gas mixture leads to attachment in regions with large electric field values, whereas oxygen results in attachment in regions with low magnitudes of the electric field, which, due to the 1/r 2 radial dependence of the electric field, cover the vast majority of the gas volume. The probability of an electron to give an avalanche is shown in Fig. 7(a) as a function of the electron initial position for different levels of impurities at 200 mbar with anode voltage at 720 V. The corresponding probability for ArP2 at 1.1 bar with anode voltage at 2000 V is shown in Fig. 7(b). From these results it is evident that minimising the amount of impurities is of paramount importance.

The comparison of the simulated signal to registered waveforms (see Fig. 9 in Sec. 4) shows a good agreement. This simulation can therefore be used to investigate the properties of the events. In Sec. 4 several variables extracted from the signal waveforms are presented and used to extract events properties such as α direction or mean distance from the anode. Those variables are benchmarked with the simulation to validate the obtained distributions, confirming our correct understanding of the detector behaviour. the case of point-like energy deposits [START_REF] Arnaud | First results from the NEWS-G direct dark matter search experiment at the LSM[END_REF][START_REF] Arnaud | Precision laser-based measurements of the single electron response of spherical proportional counters for the NEWS-G light dark matter search experiment[END_REF].

The mean drift time to the anode of primary electrons (PEs) produced in the initial ionization of the gas depends on their production point in the detector volume. For detectors larger than ∼ 10 cm in radius, due to the electric field dependence of 1/r 2 (where r is the distance from the central anode), the drift time can be as large as tens of µs (even much larger if low voltages are applied to the anode). Along the drift, electrons are also subject to a Gaussian diffusion whose standard deviation increases as r 3 . Both mechanisms entangle and introduce a significant temporal dispersion, even for electrons produced at the same time. When the electrons reach the high field region, approximately 1 mm from the sensor, the avalanche produces the ions which slowly drift towards the cathode, reaching the detector surface in times as long as few seconds. Since their velocity decreases while travelling in a weakening electric field, they induce less and less signal, and the stronger part of the ionic current is produced in the first hundreds of µs of this displacement. Combined with the bandwidth of our electronics (i.e. < 100 MHz), the ionic contribution becomes then the dominant current which is integrated by the resistive feedback charge sensitive amplifier. Merged with the time constant (RC = 150 µs) of the amplifier, all these effects lead to a significant ballistic deficit. The maximum amplitude of the signal no longer faithfully reflects the deposited energy, and its rise time no longer depends entirely on the initial location of the event. To correct for this bias, the raw waveform (or voltage pulses) of the amplifier has been deconvoluted assuming a simple exponential decay i.e. e -t/RC for its impulse response.

The processing chain for extracting our observables starts recording the raw amplifier waveform S(i) of 4166 samples digitized at a sampling frequency f e of 2.08 MHz with a transient located at 50% of the waveform length. A baseline correction to zero is applied to the raw signal before applying the deconvolution algorithm. In order to attenuate a part of the radio-frequency interference captured during the readout process, several types of composite filtering can be used [START_REF] Smith | The Scientist and EngineerâĂŹs Guide to Digital Signal Processing[END_REF][START_REF] Lyons | Understanding Digital Signal Processing[END_REF] depending of the observed level on noise (see fig. 8).

Finally, before computing the deconvoluted waveform, the raw one is renormalized by the impulse response of the amplifier following:

S(i) = S(i)/(RC/te) (4.1)
where te is the sampling period (te = 1/f e) and RC/te = n=∞ n=0 e (-n * te/RC) . As a cross check, the computation of the deconvoluted signal has been performed both in the frequency domain and directly in the temporal domain [START_REF] Jordanov | Deconvolution of pulses from a detector-amplifier configuration[END_REF][START_REF] Nahman | Deconvolution of time domain waveforms in the presence of noise[END_REF]. For each raw and deconvoluted waveform, an amplitude threshold is determined at 3 standard deviations from the noise calculated using the first part of each waveform in the interval of sample [0 -1750]. The first sample crossing the thresholds is kept as a starting marker for the determination of the observables described below. The variables related to signal amplitude or integral are given in DAQ units (ADU) whereas the temporal ones are given in µs. Usually, 3 observables can be extracted from the raw signal of the integrator, as shown in Fig. 9(a):

• The integral of the transient, Ct, which correspond to the area of the transient defined in the sample interval [threshold marker -4166].

• The rise time of the transient, Rt, defined as the duration of the sample interval [threshold marker -sample of the maximum].

• The maximum amplitude, Ma, of the raw signal.

For the deconvoluted signal, which corresponds to the initial induced current, 4 primary observables can be declined in order to describe the great variety of shapes:

• The integral of the transient, Qt, calculated as the area of the transient for the sample interval [threshold marker -4166]. This quantity, which must be equal to Ct, makes it possible to verify the accuracy of the calculation of the deconvoluted signal.

• The total duration of the transient, Dt, defined as the time over threshold. It enables to estimate the signal width, without the long tail of the total ion train.

• The full width at half maximum, Dh, which is dedicated to evaluating the width of the current distribution, in particular with respect to Dt.

• The maximum amplitude Ad, of the deconvoluted signal.

From these direct observables, 2 additional quantities, of composite natures, were also derived to further characterize the shape of the current signal:

• The peak time Pt, giving the sample location of the signal maximum as a percentage of Dt, using : Pt (%) = Pt (s) × 100 / Dt (s). It indicates the location of the maximum of signal in unit of Dt, and gives the direction of the track relative to the anode as shown in Fig. 10.

• The ionization density Di = Qt / Dh, which aims to quantify, in another way, the temporal distribution of the PEs upon their arrival at the anode. Although not formally demonstrated in this work, this observable seems to be particularly sensitive to the average distance of the trace to the cathode (several other combinations of primary observables -such as Ad/Qt, Ma/Rt, Ct/Rt, etc. -seem to provide similar information). In Fig. 9(b) a simulated pulse produced by a 5.3 MeV α particle is shown to be compared to the real signal of Fig. 9(a). In the example both the current and voltage pulses are shown, equivalent to the deconvoluted and raw signals, respectively. Typical 2D distributions are presented in Fig. 11 and compared to the usual representation, rise time versus maximum amplitude (Ma, Rt) (see Fig. 12), historically used for analyzing the output signals of the charge integrator [START_REF] Brossard | Spherical proportional counters; development, improvement and understanding[END_REF]. As it can be seen in Fig. 12, with the 210 Po source, the ballistic deficit induces a significant spreading of the source spot. The combination of Ma and Rt observables does not provide a correct interpretation of the energy deposited. This is no longer the case using Ct and Qt. The data can be compared directly to the expected 2D distributions obtained with the simulation and the agreement is very good (see Fig. 11) both in terms of pattern and on the absolute time scale. Such an agreement could be reached after including the electronic noise in the simulation. Some characteristics of long tracks can be inferred from the introduced observables. In this context, the peak time Pt allows in addition to estimate the direction of the track relative to the anode. Indeed, for a track subject to a significant energy deposit at its end (Bragg peak), the deconvoluted signal must show a peak corresponding to this deposit. Therefore, a track pointing towards the anode will present a maximum close to the beginning of the signal, leading to a Pt in the range (0% < Pt < 50%). This corresponds to typical configurations of the tracks labeled 1, 2 and 3 in Fig. 10. Tracks pointing towards the cathode will present instead a maximum in the second part of the signal (50% > Pt > 100%). This is indeed confirmed by the simulation results of Fig. 11(d) where the direction of tracks is represented by the colour scale: the colour indicates the initial zenithal direction of the α particle, where cos θ = -1 denotes an α particle emitted directly towards the anode (see Fig. 4(a) for a graphical explanation). Given the overall signal formation mechanism, for uniform primary ionizations, interpretation of Pt is more complex. For a deposit developing perpendicular to the radius, both ends of the track have identical radial distances to the anode. The maximum of the signal will be approximatively located halfway along the track (at the minimum impact parameter point relative to anode). Consequently, since the deconvoluted signal will have a bell-like shape, Pt should be around 50%. Such a situation is represented by track labeled as 4 in Fig. 10, which corresponds to an α-particle stopped in the cathode before losing all its energy in the gas. Considering instead other directions, the uniform ionization will lead to a similar Pt for the two orientations (towards the anode or the cathode), with a value of slightly less than 50%. These cases point out the limit of this simple model. A more intuitive interpretation can be deduced from the observable Di shown in Fig. 11(d) and Fig. 11(f). Indeed, compared to the simulation results indexing the direction of the track, the experimental distribution of the events reasonably suggests that the Di observable could be related to the average distance from the track to the cathode. The main features of the presented detector understanding were checked by locating in the 3-dimensional space (Qt, Dt, Rt) the events produced by a 210 Po source positioned on the internal surface of the cathode. As shown in Fig. 13, the triplet of observables (Qt, Dt, Rt), extracted from the deconvoluted waveform, significantly improves the classification of interacting events inside the detector as well as the interpretation of the data.

Results

Detector stability

Initially, the detector stability over time was studied to understand how the possible oxygen increase due to leakage/outgassing would impact the gain. The 210 Po α source was used, placed at the bottom the sphere at a distance of 20 cm from the central sensor as explained in Sec. 2.3.

To disentangle detector effects from changes due to the temperature or to the electronics response variations, in each run a pulse (delta shape) was injected in the test-in input of the preamplifier with a generator at a frequency of 0.5Hz. This allows not only to evaluate possible gain variations due to electronics or external conditions, but also to control the impact of the noise on the energy resolution. The first few hours after switching on the HV were discarded to allow the detector to reach a stability regime and then we took runs of 30 minutes. One of the output of the DAQ is the integral of the signal in ADU: this was converted into equivalent reconstructed energy assuming a linear scale using as anchor point in the conversion the 5.305 MeV α peak of the 210 Po source as shown in Fig. 14. These two peaks are fitted with Gaussian functions to find the mean and its error, and those values were monitored over two weeks. Note that these runs were not good for energy resolution measurements and the width of the Gaussians are quite large. This is due to the fact that a commercial CREMAT preamplifier CR-110-R2 [23] was used in the electronic chain with the addition of two diodes to avoid damaging the preamplifier on possible discharges of the sensor. No discharges were observed and the preamplifier was eventually replaced by OWEN one (see Sec. 2.2) with the advantage of having the protection diodes integrated and a reduction on the baseline fluctuation.

The time variation of the signal integral is seen in Fig. 15. The generator pulses are rather stable as expected (blue line), nonetheless for the first two days an increase of the signal value is observed. We expected to reach a signal stability more rapidly since the temperature of the electronics should normally be stable in a few hours. The cause of such an electronic gain change might therefore be a different one, probably related to external and electronic noise. The same signal increase at the beginning of the run is observed for α signals (red line). The use of a pulse generator allows us to disentangle the real variations of the detector gain since we can correct for the electronic gain eliminating such variations. We multiplied the integral value for a factor corresponding to the gain changes of the generator:

S c (t) = S(t) × G(t 0 ) G(t)
where S c (t) is the corrected source integral at a time t, S(t) is the original source integral at a time t, and G(t) and G(t 0 ) the generator signal at a time t and at the beginning of the run (t 0 ) respectively. We see that once the signal is corrected we observe a gain loss in time as expected and the loss amounts to about 0.05% of the signal per hour. Such a small loss can be corrected offline and allows for a good quality data taking for periods of weeks. In addition it could be avoided reducing the leaks and materials outgassing and recirculating the gas through an oxygen removal cartridge.

Energy resolution

To compute the energy resolution we used the OWEN preamplifier to have the smallest possible noise. Fluctuation of the baseline would indeed directly affect the energy reconstructed which is computed integrating the signal waveform subtracting the baseline. We obtained a baseline noise (i.e. RMS variation of baseline of a single event in 1 ms before the trigger) of about 8.2 ADU and an RMS on the baseline value (i.e. RMS of the mean baseline value of all the events) of 13.1 ADU (without the RC × f e normalisation).

With the obtained noise we achieved a width on the reconstructed pulse generator signal which corresponds to an intrinsic energy resolution of 0.5% FWHM at the α peak. Such a spread is driven by the electronic chain (preamplifier, DAQ, HV) and could eventually be the ultimate limiting factor. One of the goals of the OWEN project is indeed to develop a custom low noise readout in order to reduce the most the contribution of the electronics. The resolution of the α events is of course much worse since we have to account for the smearing due to the source itself (estimated to about 0.4%), and for possible inhomogeneities on the central anode (i.e. different gain depending on the starting point of the ionization electrons).

The signal treatment presented in Sec. 4 was applied to the registered waveforms of a run taken at 1.1 bar with a voltage of 2000 V on the central anode. To have a cleaner sample and eliminate tracks hitting the cathode, signals with a width at half maximum smaller than 65 µs are excluded as it can be seen in Fig. 16, where the low energy tail would be removed with the applied cut. The reconstructed charge Qt, converted into visible energy as done in Sec. 5.1, shows a resolution of 1.2% FWHM as presented in Fig. 17(a), where we excluded from the fit the remaining low energy shoulder due to tracks hitting the source support. Such a tail is anyway intrinsic to the source itself (i.e. deposited Po on silver support): despite the Po has been deposited on the silver surface a Geant4 simulation showed the existence of such an energy loss for α particles crossing very tiny amounts of material at the level of 100 nm. This means that the deposit itself could screen some alphas emitted more in the core of the Po source producing the observed tail at energies lower than the expected alpha emission one.

One important point to assess is to make sure that the energy resolution is not degraded going from point-like energy depositions to long tracks, which would be the case for the electrons emitted in the ββ decays. At 1.1 bar, α signals are not point-like energy deposits but rather tracks of 3-4 cm. To further study this point, a run at 200 mbar with a HV of 720 V was taken where the α tracks have a mean length of about 15 cm. The high voltage was tuned in order to have almost the same gain as in the run at 1.1 bar. The obtained energy resolution is 1.1% FWHM, which is better than the resolution obtained at 1.1 bar, demonstrating that the resolution is not degraded when tracks are long. Results for such a run are shown in Fig. 17(b). The possible explanation for the improvement at low pressure is that longer tracks are less affected by electric field distortions around the source support. In additions such tracks reach regions closer to the central sensor and are therefore less affected by electronegative impurities as detailed in Sec. 3. If we subtract quadratically to the resolution the contribution due to the electronics and the source (i.e. 0.6% overall) we obtain 0.97% which is not far from the ultimate detector requirement (i.e. 1% at 2.458 MeV). Further improvements will come from a more homogeneous and spherical sensor and from a reduction of the baseline fluctuation affecting the signal integral. Note that, for ArP2, the expected intrinsic energy resolution due to stochastic fluctuation of the number of generated electrons-ion pairs is expected to be 0.24%.

The excellent energy resolution is an important milestone in the R2D2 project demonstrating that the energy resolution of the spherical TPC detector is not affected by long tracks. This is a crucial condition for the final goal of the project i.e. the search of the ββ0ν process where long electron tracks have to be measured.

Future improvements

The R&D roadmap foresees measurements at high pressure to see if and how the gain changes since the proposed detector for ββ0ν decay search is expected to be filled with xenon at 40 bar. The actual prototype allowed for a first evaluation of the energy resolution at low pressure with argon, however the device is not certified to be operated at high pressure. A sphere certified to allow for measurements up to 40 bars is under conception. Another important point to control and improve is the uniformity of the electric field. The measurements presented in this paper are taken in the lower half of the sphere, where no field distortions should be present other than the possible one due to the α source support. However, the presence of the rod holding the central sensor results into a deformation of the electric field lines. A possible solution under study at CEA is to apply a degraded high voltage along it in order to have an homogenous electric field. In addition to test the whole volume of the detector without introducing any field distortion the possible use of a 220 Rn source is under study. A point that has to be kept in mind is that the final detector should be operated with xenon gas therefore the energy resolution should be assessed in the same condition. This was not done so far since operating with argon is cheaper and we can afford throwing it away after each filling, which is not the case when running with xenon. For this reason a recuperation system based on cryogenic pumping using liquid nitrogen is under preparation at CPPM. Gas purity is another critical item to be addressed when moving to xenon since the drift velocity of electrons is about two orders of magnitude smaller with respect to argon, and the probability of a signal reduction due to oxygen or electronegative impurities is much higher. For this reason we foresee to flush the xenon gas through an oxygen capture cartridge to further reduce the oxygen contamination and a recirculation system is under construction to systematically purify the gas between runs. Finally operating the detector at high pressure implies a very high voltage on the anode. A possible use of the detector in ionisation mode instead of the presented proportional mode is under discussion, however in order to mitigate the problem of the high voltage a dedicated multi-anode central sensor called "ACHINOS" is under test at CEA [START_REF] Giganon | A multiball read-out for the spherical proportional counter[END_REF][START_REF] Giomataris | A resistive ACHINOS multi-anode structure with DLC coating for spherical proportional counters[END_REF]. Such a sensor would have the additional advantage of allowing a possible coarse tracking. For what concerns the electronics possible upgrades could come from an optimized high voltage filter to reduce the electronic noise as explained in Sec. 2.2, and from the possibility of performing a multi-channel readout as needed by the ACHINOS sensor.

Conclusions

R2D2 is an R&D project aiming at a ton scale spherical xenon TPC for the search of the ββ0ν process. The first prototype was built at CENBG with the main goal of demonstrating that an energy resolution at the level of 1% FWHM can be achieved at 2.458 MeV i.e. at the Q ββ of 136 Xe. First tests were carried out with argon allowing to understand the detector response. Signal shape analysis showed that the main characteristics of the ionization track (distance and direction relative to the anode) can be obtained. The developed methods could also apply to cylindrical proportional counters. A resolution at the level of 1.1% was achieved with α's at 5.3 MeV. We also demonstrated that the energy resolution is not degraded going from point-like energy deposits to long particle tracks. This is critical in the search of the ββ0ν process where electrons tracks of several centimeters should be reconstructed. This first step is an important achievement for the R2D2 project paving the way for xenon measurements expected in a near future. The technical improvements discussed in Sec. 6, together with the fact that intrinsic resolution of xenon should be better with respect to argon, given the higher number of electrons per unit deposited energy, should allow to gain the waited factor of 1.5 and meet the requirements for the final detector. possible applications in industry". In addition we thank the CNRS International Emergency

Figure 1 :

 1 Figure 1: Allowed regions for the e↵ective Majorana mass as a function of the lightest neutrino mass, m1 for normal (cyan, HN) and m3 for inverted ordering (blue, HI). The oscillation parameters are varied within 3 ranges while the M CP phases are treated as free parameters. The horizontal band is the excluded region of the e↵ective Majorana mass pa by current neutrinoless double-beta decay measurement, while the vertical band is the excluded region of the mass cosmological observations.

Figure 2 .

 2 Figure 2. Actual realisation (a) and mechanical drawing (b) of the R2D2 detector. The two hemispheres can be seen as well as the pressure gauge, the HV connectors on top of the detector, and the large valve at the bottom to allow for the insertion of a radioactive source.

Figure 5 :

 5 Figure 5: OWEN Charge Sensitive Preampli

Figure 6a :Figure 3 .

 6a3 Figure 6a: Baseline noise measurement (CREMAT on left

Figure 4 .

 4 Figure 4. (a) 210 Po α source setup. The colour code represents the initial direction of the emitted α-particles which corresponds to the one used in the plots showing the output of the simulation. (b) Schematic drawing of the experimental setup showing the central sensor support and the 210 Po α source.

Figure 5 .

 5 Figure 5. Electron transport parameters ((a) drift velocity, (b) transverse and (c) longitudinal diffusion coefficients) as a function of the electric field in Ar:CH 4 98%:2% as estimated by Magboltz at 200 mbar and 1.1 bar.

Figure 6 .

 6 Figure 6. Attachment coefficient as a function of electric field in ArP2 for different level of O 2 contamination at 200 mbar.

Figure 7 .

 7 Figure 7. The survival probability of an electron as a function of its initial position for different levels of O 2 contaminations: (a) for ArP2 at 200 mbar and an anode voltage of 720 V, and (b) for the same gas mixture at a pressure of 1.1 bar and anode voltage of 2000 V.

Figure 8 .

 8 Figure 8. Average amplitude of the waveforms versus the frequency before filtering (blue), for the front parts of waveforms not containing a transient (orange), and after filtering (green).

Figure 9 .Figure 10 .

 910 Figure 9. (a) Real pulse with definition of observables used for the raw signal and for the deconvoluted one. (b) Example simulated pulses, showing both the current and voltage signals.

Figure 11 .Figure 12 .Figure 13 .

 111213 Figure 11. Example of 2D representation of events for different observables for data at 200 mbar and 720 V (Dt vs Qt Pt vs Qt (c), Di vs Qt (e)) and corresponding simulation (Dt vs Qt (b), Pt vs Qt (d), Di vs Qt (f )). For the data the colour stands for the number of event in the bin whereas for the simulation the color indicates the original α direction: cos θ = -1 for tracks going towards the central anode and cos θ = 0 for tracks emitted orthogonally to the radial direction. The figures were made with about 2000 events corresponding to about half an hour of data taking.

Figure 14 .

 14 Figure 14. Example of the signal integral output for a run with 201 Po source. The low energy shoulder due to the source support is clearly seen.

Figure 15 .

 15 Figure 15. Time variation of the integral for generator pulses (blue line), α signal (red line) and α signals corrected according to the generator pulse value (green line).

Figure 16 .

 16 Figure 16. Two dimensional plot of signal width at half maximum Dh versus the measured charge Qt of the 5.3 MeV α signal at 1.1 bar and 2000 V.

Figure 17 .

 17 Figure 17. Integral of the 5.3 MeV α signal at 1.1 bar and 2000 V (a) and at 200 mbar and 720 V (b).The Gaussian fit in red shows an energy resolution of 1.2% FWHM and 1.1% FWHM respectively.

Table 1 .

 1 Full specification of the OWEN preamplifier.

	Gain	0.75 V/pC
	Customizable gain	Yes
	Feedback C f	1.5 pF
	Feedback R f	100 MΩ
	Decay time	150 µs
	Baseline noise	920 µV pp
	Risetime	93 ns
	SNR	1868
	Linearity	1 fC to 2 pC
	Cost	20 euro

Signal treatmentSignal formation in SPC is subject to three main effects which make the analysis of long tracks more complicated with respect to the conventional treatment already established in

Acknowledgments

The authors would like to thank the IdEx Bordeaux 2019 Emergence program for the OWEN grant for the "Development of a custom made electronics for a single channel time projection chamber detector aiming at the discovery of neutrinoless double beta decays, and for Action (IEA) for the "E-ACHINOS" grant supporting the collaboration between CENBG and Birmingham University. We thank the CENBG technical staff. We thank M. Chapellier for providing the Po source and for useful discussions. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no 841261. K. Nikolopoulos acknowledges support by the European Research Council (ERC) grant agreement no 714893.