Feres Benabdallah

Catherine Elissalde

U-Chan Chung Seu

Dominique Michau

Angeline Poulon-Quintin

Marion Gayot

Pascale Garreta

Hamadi Khemakhem

Mario Maglione

U-Chan Chung

Structure-microstructure-property relationships in lead-free BCTZ piezoceramics processed by conventional sintering and spark plasma sintering

Keywords: Lead-free piezoceramics, Spark plasma sintering, ferroelectricity, piezoelectricity, defects

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

Introduction

For more than half a century, lead-based piezoelectrics such as PbZr1-xTixO3(PZT),Pb(Mg1/3Nb2/3)1-xTixO3 (PMN-PT) and Pb(Zn1/3Nb2/3)1-xTixO3 (PZN-PT) have dominated the area of actuator, sensor and transducer technology. These lead-based materials are commonly used with compositions near the morphotropic phase boundary (MPB) where the crystal structure changes abruptly and the electromechanical properties are maximized [START_REF] Setter | Piezoelectric Materials and Devices[END_REF][START_REF] Moulson | Electroceramics: Materials, Properties and Applications[END_REF][START_REF] Sebald | Morphotropic PMN-PT system investigated through comparison between ceramic and crystal[END_REF][START_REF] Park | Ultrahigh Strain and Piezoelectric Behavior in Relaxor Based Ferroelectric Single Crystals[END_REF].Over the last decade, environmental concerns have been strongly driving the need to replace the lead-based perovskites by equivalent or better performance lead-free piezoelectric materials [START_REF] Rödel | Transferring lead-free piezoelectric ceramics into application[END_REF][START_REF] Coondoo | Lead-free piezoelectrics: Current status and perspectives[END_REF]. Thus, two different approaches have been considered. The first one, the so-called 'compositional engineering approach', focuses on the enhancement of electro-mechanical properties by selecting compositions close to a region with structural instabilities such as polymorphic phase transition (PPT) or MPB [START_REF] Jaffe | Piezoelectric Ceramics[END_REF][START_REF] Budimir | Piezoelectric Anisotropy-Phase Transition Relations in Perovskite Single Crystals[END_REF][START_REF] Saito | Lead-free piezoceramics[END_REF][START_REF] Shrout | Lead-free piezoelectric ceramics: Alternatives for PZT?[END_REF]. The coexistence of different competing phases with equivalent free energies allows a 'softening' of the crystal lattice and an increased alignment of ferroelectric domains during poling (several equivalent polarization orientations at the nanoscale).This gives rise to high piezoelectric effect through polarization rotation or polarization extension mechanisms [START_REF] Damjanovic | A morphotropic phase boundary system based on polarization rotation and polarization extension[END_REF].The second approach is centered on the 'structurally engineered materials' by controlling the micro and/or nanoscale structure. It mainly relies on various structural engineering techniques such as grain size optimization, templated grain growth and domain engineering [START_REF] Park | Ultrahigh Strain and Piezoelectric Behavior in Relaxor Based Ferroelectric Single Crystals[END_REF][START_REF] Tani | Reactive-Templated Grain Growth Processing for Lead Free Piezoelectric Ceramics[END_REF][START_REF] Wada | Enhanced Piezoelectric Properties of Barium Titanate Single Crystals with Different Engineered-Domain Sizes[END_REF].

Few years ago, the first approach was successfully used to prepare novel perovskite-structured solid solutions (1-x)BaTi0.8Zr0.2O3-xBa0.7Ca0.3TiO3(BCTZ) with a surprisingly large electro-mechanical response surpassing that of the ultrasoft PZT-5H close to room temperature [START_REF] Liu | Large Piezoelectric Effect in Pb-Free Ceramics[END_REF]. The unusual properties of the Pb-free pseudo-binary system were attributed to the vanishing polarization anisotropy near a phase convergence region (a nearly spherical degeneration of the free energy surface related to structural instabilities) [START_REF] Keeble | Revised structural phase diagram of (Ba0.7Ca0.3TiO3)-(BaZr0.2Ti0.8O3)[END_REF]. Such discovery fostered many researchers to develop even-higher-performance BaTiO3-based materials. Indeed, a modified lead-free piezoelectric BCTZ with higher Curie temperature Tc and colossal piezoelectric activity was designed by increasing the Curie temperature of the two end members in the phase diagram [START_REF] Bao | A modified lead-free piezoelectric BZT-xBCT system with higher Tc[END_REF]. Moreover, <001> textured BCTZ ceramics ( BCTZ50, x=0.5) were synthesized by Ye et al. using templated-grain growth method.

The obtained materials were shown to exhibit higher piezoelectric constants and larger electromechanical coupling factors compared to those of randomly oriented BCTZ ceramics whilst Tc revealed an increase with the template content [START_REF] Ye | Structure and electrical properties of <001> textured (Ba0.85Ca0.15) (Ti0.9Zr0.1)O3 lead-free piezoelectric ceramics[END_REF].

In parallel to the extensive research of new lead free piezoelectrics, the current miniaturization trends in ceramic technology along with the growing consideration for production costs have compelled research efforts to process dense ferroelectric ceramics with both tailored grain sizes and optimal properties using non-conventional methods of synthesis (sol-gel, mechanosynthesis) and sintering such as hot pressing (HP) or spark plasma sintering (SPS). In the latter case, the sintering process allows obtaining high-density ceramics at lower temperatures and shorter processing times (typically a few minutes) compared to conventional sintering. As a result, grain coarsening can be limited. Interestingly, one can mention numerous achievements on the preparation of fine-grained ceramic materials (BaTiO3, Ba1-xSrxTiO3, BaTi1-xZrxO3, K0.5Na0.5NbO3(KNN), modified KNN, (1-x) Bi0.5Na0.5TiO3-x BaTiO3 (BNT-BT),…). Detailed studies have been thus presented elucidating the relationships between the crystallographic structure/grain sizes/domain configurations and their ferroelectric /piezoelectric properties [START_REF] Deng | Phase Transitions in Nanocrystalline Barium Titanate Ceramics Prepared by Spark Plasma Sintering[END_REF][START_REF] Deng | Ferroelectric properties of nanocrystalline barium titanate ceramics[END_REF][START_REF] Hungria | Dense, Fine-Grained Ba1-xSrxTiO3 Ceramics Prepared by the Combination of Mechanosynthesized Nanopowders and Spark Plasma Sintering[END_REF][START_REF] Li | Ferroelectric and Piezoelectric Properties of Fine-Grained Na0.5K0.5NbO3 Lead-Free Piezoelectric Ceramics Prepared by Spark Plasma Sintering[END_REF][START_REF] Shen | Electrical and Mechanical Properties of Fine-Grained Li/Ta-Modified (Na,K)NbO3-Based Piezoceramics Prepared by Spark Plasma Sintering[END_REF][START_REF] Cernea | Preparation and properties of nanocrystalline BNT-BTx piezoelectric ceramics by sol-gel and spark plasma sintering[END_REF][START_REF] Deluca | Investigation of the composition-dependent properties of BaTi 1-x Zrx O3 ceramics prepared by the modified Pechini method[END_REF]. However, few available data were reported in the literature emphasizing such correlations in the BCTZ solid solutions, when the grain size is reduced [START_REF] Hao | Correlation Between the Microstructure and Electrical Properties in High-Performance (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 Lead-Free Piezoelectric Ceramics[END_REF][START_REF] Tang | Effect of grain size on the electrical properties of (Ba,Ca)(Zr,Ti)O3 relaxor ferroelectric ceramics[END_REF].

Adjusting the grain size close to 1 µm in BaTiO3 ceramics allows to enhance permittivity and piezoelectric coefficient by increasing domain wall density [START_REF] Tan | Unfolding grain size effects in barium titanate ferroelectric ceramics[END_REF]. In addition, a controlled microstructure in terms of defects is also challenging regarding their impact on domain-wall contributions to the dielectric, elastic and piezoelectric properties. Such fine control of the microstructure is hardly achieved using conventionnal sintering as the high sintering temperature required to reach high density promotes grain growth and the long holding time can favor defects.

SPS is now well recognized as a very efficient technique to obtain highly densified nanostructured ferroelectric ceramics and this fast consolidation process was largely used to probe the influence of size effects on properties. In this context, in depth investigations of BCTZ piezoceramics with selected compositions and controlled grain size using advanced sintering technique are still required for a better understanding of the relationships between structure, microstructure and functional properties. We propose a comparative study of BCTZ ceramics (compositions x=0.32 and 0.5) processed by conventional sintering and SPS. The aim is to probe the impact of the microstructure on the dielectric, pyroelectric, ferroelectric and piezoelectric responses of BCTZ ceramics.

Structural defects induced by the SPS process were linked to a lower domain wall mobility which could explain the altered piezoelectric and ferroelectric performances of the BCTZ compositions sintered by SPS.

Experimental

The perovskite-structured BCTZ powders with a generic formula (1-x) BaTi0.8Zr0.2O3-xBa0.7Ca0.3TiO3 (x=0.32 and 0.5) were synthesized by conventional solid state reaction method using as starting chemicals, BaCO3 (99.95%), CaCO3 (99.5%), ZrO2 (99.99%) and TiO2 (99.9%). For each composition, the raw materials were weighed according to the stoichiometric formula and mixed by ball milling in alcohol using zirconia balls for 4h. After being dried, the mixtures were calcinated in oxygen atmosphere at 1350°C during 15h, then ball milled again to break the agglomerates. Two sintering methods were used to obtain dense BCTZ ceramics with different grain sizes and morphologies. For spark plasma sintering, the powders were loaded in a cylindrical graphite die with an inner diameter of 10 mm and heated under vacuum using an SPS apparatus (SYNTEX. INC, SPS-515S). The rapid heating was achieved owing to a pulsed direct electric current traversing the die. The temperature was raised at 50-100°C/min and kept at a constant value of 1300°C for 10 min. Afterwards, the sample was cooled to 600°C with a relatively low cooling rate of 35°C/min and then, to room temperature by shutting down the power supply. A constant pressure of 90 MPa was applied along the Z-axis of the graphite die during the whole sintering process. Finally, the SPS-processed samples were annealed in oxygen at 900-1000°C for 12 h in order to remove surface carbon contamination and to limit oxygen vacancies caused by the reducing conditions. For the conventional sintering, the powders were pressed into disks (= 8 mm, e= 1 mm) under a uniaxial pressure of 120 MPa and sintered at 1450°C for 4h under oxygen atmosphere.

Phase structure of the BCTZ powders and ceramics was identified by X-ray powder diffraction (XRD) using a PANalytical X'Pert MPD diffractometer with Cu Kα radiation of wavelength 1.54056 Å. The XRD patterns were recorded at room temperature with scan rates ranging from 0.02 to 0.008° and a counting time of 70s/step. The microstructures of the ceramic samples were observed using a scanning electron microscope (SEM, JEOL 6360 A) and a transmission electron microscope (TEM-FEG, JEOL-JEM-2200FS with an acceleration voltage of 200 kV). Fractures of SPS ceramics (BCTZ32) were thermally etched at 1200°C. The samples were introduced in the hot region of the tube furnace, kept at 1200°C during 1h and then quenched. BCTZ50 ceramics were chemically etched in HCL for 4h. The grain size of the sintered ceramics was evaluated by linear intercept method on scanning electron microscopy micrographs. The average grain size was evaluated for each sample based on at least 100 grains. Thin foils for TEM were prepared by mechanical polishing to a thickness of 80 μm and argon ion-beam polishing using a 691 Gatan Precision argon Ion Polishing System (PIPS, 5kV).

For electrical measurements, both sides of polished ceramic disks were sputter coated with gold electrodes. The temperature dependence of the dielectric constant and losses were measured at different frequencies (10 2 -10 5 Hz) using an LCR meter (Wayne Kerr 4300) connected to a hightemperature tube furnace. The polarization-electric field (P-E) hysteresis loops were recorded at room temperature based on a standard Sawyer-Tower circuit. Samples for pyroelectric and piezoelectric measurements were poled under various DC electric fields (≈10-15 kV/cm) during cooling from the ferroelectric-non ferroelectric phase transition temperature down to the lowtemperature region where a stable ferroelectric phase with rhombohedral symmetry was evidenced for both BCTZ compositions. The piezoelectric responses for the radial mode were determined at room temperature by the resonance-antiresonance method on the basis of IEEE standards [28]. The thermal variation of the pyroelectric current and the spontaneous polarization Ps was investigated for all samples by using a digital multimeter Keithley 2100.

Results and discussion

Microstructural characterizations

Scanning electron microscope (SEM) images of fracture surfaces illustrate the microstructural features of the BCTZ ceramics prepared by conventional and spark plasma sintering methods (Figs. 1a-f). All the samples are well densified with almost no noticeable large porosity. The bulk relative densities of BCTZ32 and BCTZ50 obtained by conventional sintering were found to be respectively 93% and 90%. Whatever the composition, both intergranular and intragranular fracture modes are observed. The inhomogeneity of the microstructures arises from exaggerated grain growth occurring at the high sintering temperature (1450°C) (Fig. 1a,1b). The average grain size and its standard deviation depend on the chemical composition of the ceramics, ranging between 10  4.0 m for BCTZ32 and 15  6 m for BCTZ50. In both compositions, few grains with a size 25-30 m are observed.

When the sintering temperature was decreased using SPS (150°C lower than for conventional sintering), the relative densities significantly increased and reached values close to 97% and 98% for BCTZ32 and BCTZ50 respectively. No further increase of the density was noticed when the pressure during SPS sintering is raised from 90 MPa to 110 MPa. SPS ceramics exhibit complex fractured surface with predominantly intragranular fracture mode. The grain size determination was possible only after revealing grain boundaries by thermal and chemical etching according to the samples. Whatever the composition, finer microstructures are observed compared to conventional sintering (Figs. 1c-f). The average grain size is 2  1 µm for BCTZ32 and decreased in the sub-micrometer range 0.8  0.4 µm for BCTZ50. The grains are mainly equiaxed and few spherical shaped grains can be distinguished among the smallest ones. As expected, the microstructural investigations confirm that enhanced kinetics during SPS allow to retain fine grain microstructure in BCTZ ceramics.

TEM micrographs of the BCTZ32 pellet sintered by SPS are shown in fig 2. The images reveal the existence of numerous isolated dislocations within some individual grains (located in a region ranging from 300 to 400nm close to the grain boundaries) witnessing of a plastic activity inside the grains.

Evidence of such defects clearly shows that SPS process performed under selected parameters of temperature and pressure, can induce thermo-mechanical solicitations at the top surface of grains during sintering leading to their plastic deformations.

This unusual activity at the nanoscale has not been detected for all grains of the ceramic probably due to the random orientation of the crystallites with respect to the SPS pressure axis. A more detailed study would be required to examine how the sizes and/or densities of dislocations change as a function of the operating parameters during the sintering process. For BCTZ50 sintered at 1450°C /4h, the powder pattern was indexed in the tetragonal symmetry with space group P4mm. Nevertheless, recent XRD investigations with synchrotron radiation have allowed to identify an intermediate ferroelectric phase (orthorhombic, Amm2 space group) extending over a relatively broad temperature range (260-300K) between two other ferroelectric phases of rhombohedral (R3m) and tetragonal (P4mm) symmetry [START_REF] Keeble | Revised structural phase diagram of (Ba0.7Ca0.3TiO3)-(BaZr0.2Ti0.8O3)[END_REF]. This result is consistent with the recent work of Zhang et al. highlighting the presence of a line of high-performance compositions in the BCTZ system undergoing a tetragonal -orthorhombic phase transition at room temperature [START_REF] Zhang | Correlation Between Piezoelectric Properties and Phase Coexistence in (Ba,Ca)(Ti,Zr)O3 Ceramics[END_REF]. The volume fractions of the coexisting phases and their lattice parameters in the case of BCTZ50 determined from Rietveld refined fits to the data at 300 K are listed in table I.

As for BCTZ32 prepared by conventional sintering, all the diffraction peaks of the powder pattern (using the standard XRD technique) were indexed in the cubic symmetry at 300K (Pm m space group, a=4.0206(2) Å, ). Full Rietveld refinements were performed as well using synchrotron radiation and the crystal structure was found to be cubic (a = 4.0216(9) Å,

). These results are not compatible with the piezoelectricity of the material at room temperature. However, it is worth noting that BCTZ32 is located in the vicinity of a 'phase convergence region' where a cubic non-ferroelectric phase merges with three ferroelectric phases of rhombohedral, orthorhombic and tetragonal symmetry without breaking the Gibbs phase rule in the BaTi0.8Zr0.2O3-Ba0.7Ca0.3TiO3 pseudo-binary phase diagram [START_REF] Keeble | Revised structural phase diagram of (Ba0.7Ca0.3TiO3)-(BaZr0.2Ti0.8O3)[END_REF]. Thus, it becomes difficult to provide evidence of such structural distortions away from the parent cubic structure.

Several structural evolutions have been observed for the samples sintered by SPS at 1300°C/90 MPa /10 min. First, the diffraction peaks for BCTZ50 ceramic are shifted to the higher diffraction angles revealing the shrinkage of the unit cell volume. Such behaviour attributed to an increase in the internal stress in the ceramic is less pronounced for BCTZ32. Furthermore, the splitting of (200)pc

Bragg reflection characteristic of a tetragonal lattice distortion (P4mm space group) in coarse-grained BCTZ50 sample is transformed into a broad single peak typical of a pseudo-cubic symmetry in finegrained one. This suggests a progressive reduction of the long range ferroelastic strain and the intrinsic unit cell polarization with decreasing grain size. Similar trends have been reported for the niobium-doped PZT ceramics by C. A. Randall et al. [START_REF] Randall | Intrinsic and Extrinsic Size Effects in Fine-Grained Morphotropic-Phase-Boundary Lead Zirconate Titanate Ceramics[END_REF].

The broadening of all diffraction profiles detected for the SPS processed samples can be correlated with the existence of microstrains which may originate from a spreading of dislocations within the individual grains as observed in TEM. In general, elastic fields resulting from structural defects could introduce a contribution to the width of each reflexion [START_REF] Stephens | Phenomenological model of anisotropic peak broadening in powder diffraction[END_REF].

Low-frequency impedance spectroscopy measurements

Figure 4 shows the temperature dependence of the dielectric constant r and loss tangent (tan of the BCTZ ceramics under investigation recorded at 10 kHz. For the SPS sintered samples, the relative dielectric permittivity drastically decreases at the phase transition temperature (Tm) which shifts to higher values for both compositions. This significant permittivity drop may be attributed to the increasing contribution of the non-ferroelectric low-permittivity grain boundaries as a consequence of the dielectric mixing(brick-wall model) [START_REF] Frey | The Role of Interfaces on an Apparent Grain Size Effect on the Dielectric Properties for Ferroelectric Barium Titanate Ceramics[END_REF][START_REF] Emelyanov | Grain-Boundary Effect on the Curie-Weiss Law of Ferroelectric Ceramics and Polycrystalline Thin Films: Calculation by Method of Effective Medium[END_REF].The dielectric constant peaks become much broader leading to a more pronounced diffuse phase transition (DPT) behaviour, already present in coarse grained ceramics. The dielectric permittivity is moderately rising at the low temperature regime while the loss tangent increases over the whole temperature range with decreasing grain sizes. This temperature dependence of dielectric properties is attributed to the contribution of extrinsic effects. The abnormal broadening of the dielectric peaks can be explained by an increase of To provide a clear description of the phase transition behaviour for SPS BCTZ samples, the temperature dependences of the dielectric constant and losses were measured at different frequencies ranging between 100 Hz-100 kHz. As shown in figure 5c, BCTZ50 exhibits a diffuse phase transition with a broad peak at the corresponding dielectric temperature (Tm), with no apparent shift of this maximum over the investigated range of frequency. On the other hand, BCTZ32 displays a strongly broadened dielectric anomaly at Tm which shifts to higher values with increasing frequency, thus suggesting the occurrence of a relaxor state (Fig. 5a).

The dielectric losses notably increase with increasing frequency at low temperature regime for both compositions (Figs. 5a-c).We ascribe the observed frequency dispersion of the dielectric response to the presence of additional extrinsic contributions to polarization processes associated with the dynamics of polar domains and randomly distributed defects . At high temperatures, the increase of tan at low frequency values is attributed to the thermal activated conductivity due to the motion of oxygen vacancies.

To further confirm the peculiar dielectric trends of BCTZ samples obtained by SPS process, we use the At this stage, one can gives emphasis to the close relationship between the structural/ microstructural features of the BCTZ ceramics and their dielectric responses. From Transmission electron microscope (TEM) and X-ray powder diffraction (XRD) analysis, it is clear that the spark plasma sintering process can induce structural disorder due to both grain size decrease and local strain field increase. As a result a gradual transformation is observed from ferroelectric DPT behaviour (conventional sintered BCTZ32) towards a proper relaxor state (SPS sintered BCTZ32).

However, we should underline that SPS may intensify the chemical disorder (compositional inhomogeneity) as well, for example through an increased density of Zr-rich clusters because of the fast sintering kinetics. These large compositional fluctuations are correlated to the fluctuation of the cell parameters and as a result, have pronounced effects on the dielectric properties of the perovskite system.

Ferroelectric and piezoelectric properties

The temperature dependence of the spontaneous polarization Ps is given for each SPS processed BCTZ ceramic in figure 6. It is clear that Ps decreases smoothly through the dynamic transition temperature Tm and retains finite values up to rather high temperatures because polar domains persist well above Tm. The latter physical picture is typical of a diffuse phase transition (BCTZ50) which may progressively be forced to merge into a relaxor state (BCTZ32) with a higher degree of chemical /structural disorder. These findings confirm that the already smooth temperature variation of the polarization reported in standard ceramics is even more softened in SPS ceramics [START_REF] Benabdallah | Linking large piezoelectric coefficients to highly flexible polarization of lead free BaTiO3-CaTiO3-BaZrO3 ceramics[END_REF].

The ferroelectric switching behaviour was investigated in terms of the polarization-versus electricfield hysteresis loops measured at 50 Hz and at room temperature. As shown in figure 7; the P-E loops recorded for the conventionally sintered ceramics are slim giving a small remanent polarization and a relatively low coercive field. The Pr and Ec values were found to be 3 C.cm -2 , 0.975 kV.cm -1 for BCTZ32 and 5.6 C.cm -2 , 2.75 kV cm -1 for BCTZ50. However, the SPS processed ceramics exhibit well saturated hysteresis loops and the measured ferroelectric responses are strongly weakened giving smaller Pr and higher Ec (2.8 C.cm -2 and 4 kV.cm -1 respectively for BCTZ50). Such polarization-field dependences with decreasing grain size appear to be a general trend for both Pb-based and Pb-free perovskite-structured solid solutions [START_REF] Randall | Intrinsic and Extrinsic Size Effects in Fine-Grained Morphotropic-Phase-Boundary Lead Zirconate Titanate Ceramics[END_REF][START_REF] Zuo | PMN-PT Ceramics Prepared By Spark Plasma Sintering[END_REF][START_REF] Wang | Fabrication and characterization of potassium-sodium niobate piezoelectric ceramics by spark-plasma-sintering method[END_REF][START_REF] Maiwa | Structure and properties of Ba(Zr0.2Ti0.8)O3 ceramics prepared by spark plasma sintering[END_REF].

The critical change in the ferroelectric switching characteristics can be interestingly explained using two different and complementary approaches. The first one involves the theory of D-E hysteresis loops based on the Avrami model proposed by Orihara [START_REF] Orihara | A Theory of D-E Hysteresis Loop Based on the Avrami Model[END_REF]: the proportion of grains contributing to polarization reversal mechanism is given by;

where Ga represents the grain anisotropy energy density and d is the grain size. Thus, it is well understood that this proportion decreases in fine grained ceramics leading to the drop of the ferroelectric properties.

The second approach, of great relevance for the ferroelectric materials, is related to the interaction of defects with domain walls. These defects are, generally, either intrinsic or induced by the addition of dopants. In this study, it is concluded that the existence of dislocations with a significant spatial extent and isolated charged defects (oxygen vacancies) in SPS ceramics acts as strong pinning centers to inhibit domain-wall mobility [START_REF] Chandrasekaran | Defect ordering and defect-domain-wall interactions in PbTiO3: A first-principles study[END_REF]. Moreover, when the grain size decreases, increasing the number of grain boundaries will systematically increase the pinning points for the moving walls. As a result, the macroscopic ferroelectric properties are affected as follow:

(1) The values of remanent and saturated polarization decline because of the reduction of the achievable domain alignment with the applied electric field.

(2) A drastic drop in the domain wall motion meaning that higher switching fields are required during the polarization reversal process. From the thermodynamic point of view, the structural defects locally modify the ferroelectric double-well potential depth resulting in higher barrier energy for the motion of the domain wall [START_REF] Chandrasekaran | Defect ordering and defect-domain-wall interactions in PbTiO3: A first-principles study[END_REF][START_REF] Rabe | Physics of ferroelectrics a modern perspective[END_REF].

The piezoelectric resonance measurements were performed at room temperature using an HP4194 A impedance analyzer on ceramic samples prepared in disc shapes Kp, the mechanical quality factor Qm can then be directly determined from the circuit parameters and the values of the parallel and series resonance frequencies (fp and fs) given by: Figure 8 shows the recorded spectra of the conductance G and the susceptance B around the radial vibration mode for poled BCTZ50 ceramic discs (both normal and SPS sintered samples) along with their corresponding admittance locus (G-B curves). The electrical behaviour of the free piezoelectric resonator was fully determined in accordance with the previously mentioned protocol.

The values of d31, Kp and Qm were found to be 197 pC/N, 0.45 and 77 respectively for normal sintered sample, whereas, the SPS processed one revealed inferior piezoelectric coefficients with values as low as d31= 43 pC/N, Kp=0.12 (Qmis raised to a value as high as 334). Similar trends were unambiguously disclosed for BCTZ32 composition, showing decreasing values of the electromechanical coefficients from about d31= 120 pC/N, Kp= 0.33 , Qm = 106 using the conventional sintering technique to 30 pC/N , 0.1 and 200 respectively using SPS.

Similarly to the dielectric and ferroelectric properties, it is understandable that the electromechanical responses should be correlated to the structural /microstructural features in BCTZ ceramics: the excellent piezoelectric properties obtained for conventionally sintered BCTZ50 ceramic originate from the different coexisting/competing phases (Amm2+P4mm)close to room temperature.

The material was shown to be quite 'soft' with respect to the electric field (easy paths for polarization rotation in anisotropically flattened free energy profile) and, even more importantly, with respect to the crystal lattice (large electrostrain obtained under small electric field) [START_REF] Xue | Elastic, piezoelectric, and dielectric properties of Ba(Zr0.2Ti0.8)O3-50(Ba0.7Ca0.3)TiO3 Pb-free ceramic at the morphotropic phase boundary[END_REF][START_REF] Praveen | Effect of poling process on piezoelectric properties of sol-gel derived BZT-BCT ceramics[END_REF].

These two effects go hand in hand leading to high piezoactivity due to faster domain wall motion under external stresses. Here, it is important to keep in mind the underlying structural mechanism stressing the key role of domain structures for the Pb-free Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 system: experimental evidences are presented showing that d33-maximum region is tied strictly to a nanometer-sized ferroelectric domains with a domain hierarchy in the 'morphotropic phase boundary, MPB' regime [START_REF] Gao | Microstructure basis for strong piezoelectricity in Pb-free Ba(Zr0.2Ti0.8)O3-(Ba0.7Ca0.3)TiO3 ceramics[END_REF]. In SPS ceramics, additional extrinsic effects arising from the existence of structural defects (dislocations) and point defects (oxygen vacancies) leading to local strain fields hinder the domain wall mobility and thus alter electromechanical efficiency.

Conclusions

Dense BCTZ ferroelectric ceramics of the pseudo-binary system (1-x)BaTi0.8Zr0.2O3-x Ba0.7Ca0.3TiO3(x=0.32, 0.5) have been successfully prepared using both conventional and spark plasma sintering techniques. The effects of their crystallographic structures along with microstructural characteristics on the corresponding dielectric, ferroelectric and piezoelectric properties have been studied in detail. Drastic changes have been evidenced when decreasing the grain size for the selected BCTZ compositions using SPS. This behaviour was in part explained by the existence of microstrains or more generally by a random distribution of defects generating random elastic fields.

In comparison with coarse BCTZ ceramics, the low-frequency dielectric measurements reveal a significant drop of the dielectric constant at the phase transition temperature in fine-grained samples. It was also shown that the SPS process leads to enhanced DPT behaviour which can gradually be transformed into a relaxor state in the case of BCTZ32. Such property tuning is systematically driven by structural disorder and composition fluctuations.

The improved ferroelectric and piezoelectric properties observed in conventional sintered BCTZ ceramics are linked to the different coexisting phases at the nanoscale near the room temperature.

The vanishing polarization anisotropy near a so-called 'phase convergence region', the lattice softening and the consequent high domain sensitivity to external stresses are considered as the main features of the (1-x)BaTi0.8Zr0.2O3-x Ba0.7Ca0.3TiO3solid solutions processed using conventional sintering method. These colossal responses go down in SPS ceramics due to the lower domain mobility resulting from the existence of microstructural defects. Our main conclusion is that the BCTZ compositions investigation display large piezoelectric coefficients because their polarization is highly sensitive to moderate external stress. This is why their ferroelectric properties are affected by the microstructural distortions resulting from the SPS sintering while other ferroelectric materials like pure BaTiO3 require much stronger disturbances. In terms of apparent size effects, we have evidenced large changes in the ferroelectric properties for average grain sizes ranging between ≈ 0.8-2 m, while shorter length scale (≈ 100 nm) should be reached in the case of pure BaTiO3 [START_REF] Curecheriu | Grain Size-Dependent Properties of Dense Nanocrystalline Barium Titanate Ceramics[END_REF].

  Room temperature XRD patterns of polycrystalline BCTZ (x=0.32 and 0.5) prepared using both sintering methods are shown in fig.(3-a,3-b). All samples have single-phase perovskite structure within the sensitivity of the XRD technique. However, one should emphasize the distinct structural trends for different processing conditions.

  both compositional fluctuations and strain resulting from the change in microstructure of the SPS ceramics compared to the conventional ones. Such interpretation is well supported by the work of Wu et al. reporting the peak width at two-third maximum dielectric constant as a linear function of the compositional fluctuations [34]. Besides, it is important to underline that the sequence corresponding to rhombohedral-orthorhombic (R-O) and orthorhombic-tetragonal (O-T) phase transitions is no longer obvious in SPS processed BCTZ50 ceramics due to the increase of the diffuse character of the permittivity maximum (Fig 4a and inset of Fig 4b).

modified

  Curie-Weiss law proposed by K. Uchino and Nomura[START_REF] Uchino | Critical Exponents of the Dielectric Constants in Diffused Phase Transition Crystals[END_REF]:where rm is the maximum value of dielectric constant at the phase transition temperature Tm, is the degree of diffuseness, and C is the Curie-like constant. The limiting values = 1 and = 2 correspond to the case of normal ferroelectric and ideal relaxor ferroelectric respectively. Figures5b and 5dshow the plots of ln ( ) as a function of ln at 100 kHz in the temperature range . A linear (power-law) relationship is obvious for all compositions. The fitted values are 1.98 and 1.64 for BCTZ32 and BCTZ50 respectively (while it is found to be 1.73 and 1.53 for ceramics with the same compositions obtained by conventional sintering). Such increased values reflect a strengthening of the relaxor character from standard to SPS sintering and from BCTZ50 to BCTZ32.

  . The complex admittance (inverse of the impedance Z) of the resonator was recorded as a function of the frequency across the first resonance (the fundamental resonance) corresponding to the radial vibration mode. The experimentally obtained data of the real (conductance G) and imaginary (susceptance B) components of the admittance were then fitted to the theoretical spectra generated from the admittance equation of an equivalent circuit model [a Van Dyke model with real circuit parameters: C0, R0 (for the static branch) and C, L, R (for the motional branch)]. This model is recommended by the IEEE standard on piezoelectricity [28,43-46]. The use of a nonlinear least-squares fit to the equivalent circuit model allows us to find the values of the circuit constants C0, R0, R, L and C. The material constants such as the transverse piezoelectric coefficient d31, the electro-mechanical coupling factor

Fig. 1 .

 1 Fig. 1. Scanning electron microscope (SEM) micrographs of fracture surfaces: (a) BCTZ32 (x = 0.32) and (b) BCTZ50 (x = 0.5) ceramics sintered at 1450 °C/4 h/O2; (c, e) BCTZ32 (d, f) BCTZ50 sintered at 1300 °C/90 MPa/10 min using spark plasma sintering (after thermal and chemical etching respectively).

Fig. 2 .

 2 Fig. 2. Transmission electron microscopy (TEM) images of SPS processed BCTZ ceramic (x = 0.32,1300 °C/90 MPa/10 min): the images correspond to the surfaces of thin plates explored perpendicular to the SPS pressing direction. The presence of numerous dislocations within some individual grains is noticed close to grain boundaries. This finding proves that the use of selected parameters during the SPS process can provoke both nonrecoverable and irreversible plastic deformations on grain surfaces.

Fig. 3 .

 3 Fig. 3. Standard X-ray diffraction patterns of BCTZ ceramics prepared under different sintering conditions: (a) BCTZ32, (b) BCTZ50. Inset: zoom on the diffraction profiles around 2 ≈ 45°.

Fig. 4 .

 4 Fig. 4. Temperature dependence of the dielectric properties of BCTZ ceramics prepared under different sintering conditions: the conventional sintering was done at 1450 °C/4 h in oxygen atmosphere and the spark plasma sintering performed at 1300 °C/90 MPa/10 min. (a) The relative dielectric permittivity and (b) loss tangent (tan δ) recorded at 10 kHz. Inset: focus on the well defined R-O and O-T phase transitions in conventionally sintered BCTZ50 which disappear in the SPS processed ceramic.

Fig. 5 .

 5 Fig. 5. (a, c) Temperature dependence of the dielectric constant ϵr and loss tangent (tan δ) for SPS processed BCTZ32 and BCTZ50, respectively. The measurements were recorded at different frequencies ranging between 10 2 and 10 5 Hz. (b, d): ln (1/ϵr -1/ϵrm) as a function of ln (T -Tm) for the BCTZ ceramics prepared using SPS at 100 kHz (T > Tm) . The values of γ calculated from the slope of the graphs reflect the increase of the relaxor features from BCTZ50 (γ = 1.64) to BCTZ32 (x = 0.32) (γ = 1.98).

Fig. 6 .Fig. 7 .

 67 Fig. 6. Temperature dependence of the spontaneous polarization Ps in BCTZ ceramics (x = 0.32 and 0.5) processed by SPS.

Acknowledgment

F. Benabdallah and co-authors are all grateful for financial support by the French National Center for Scientific Research (CNRS) and the ministry of higher education and scientific research of Tunisia. We thank also Annie Simon for fruitful discussions, Sonia Gomez for SEM observations and Eric Lebraud for XRD measurements. The authors acknowledge PLACAMAT (UMS 3626 CNRS-University Bordeaux) for technical support.


Ana Carolina

M Ecoscia

Nida Sheibat-Othman

Timothy F L Mckenna
email: timothy.mckenna@univ-lyon1.fr

Ana Carolina Mendez

Emulsion polymerisation of Vinylidene Fluoride: Effects of Mixing and Reaction Conditions on the Initial Rate of Polymerisation

INTRODUCTION

Polyvinylidene fluoride (PVDF) is a polymer made commercially via a free-radical suspension or emulsion polymerisation process. Since the distribution of free radicals, as well as the reactor conditions are not the same in the 2 types of processes, they each produce polymers with a different set of physical propertie. [1] The emulsion polymerisation of vinylidene fluoride (VDF) is the focus of the current paper. Despite the usefulness and industrial importance of this polymer, very few academic studies are available in the open literature on the kinetics and particle formation process during VDF polymerisation. [1] The emulsion polymerisation of PVDF is more complicated than many other emulsion polymerisation processes because the monomer is typically either a gas or a supercritical fluid, and thus much lighter than the continuous phase (water) in the reactor under the polymerisation conditions of interest. In semi-batch processes typical of commercial production, the constant monomer pressure characteristic in industrial production means that the reaction rate is exactly equal to the flux of monomer into particles, which is determined by the stirring rate. Therefore, the polymer particles are always "starved", and not necessarily saturated, meaning that mass transfer can potentially limit the rate of polymerisation and eventually the macromolecular properties. These particularities are of course not limited to PVDF homo-and copolymerisations; products such as ethylene-vinyl acetate or others where one or more of the monomers is significantly lighter than the reaction medium will also share certain of these challenges.

The polymerisation of VDF in supercritical carbon dioxide, at temperatures from 50 to 80°C and pressures that can exceed 3.05  10 4 kPa has been discussed in the literature. [ 2 , 3 , 4 , 5 , 6 ] Unfortunately, the difference in reaction and process conditions make it very difficult to extrapolate any of the kinetic interpretations to emulsion polymerisation. Apostolo et al. [ 7 ] presented an experimental and modelling study of the copolymerisation of VDF with hexafluoropropylene with a particular focus on the evolution of the molecular weight distribution (MWD). They showed that adding ethyl acetate as a chain transfer agent (CTA) reduced the average molecular weight as expected, but also decreased the degree of long-chain branching. They did not discuss the eventual impact of the CTA on the polymerisation rate. Certain patents [8,[START_REF] Greuel | A[END_REF] and a recent paper from our group [START_REF] Stefanichen Monteiro | [END_REF] suggest that some CTA commonly used in the emulsion polymerisation of VDF (in particular ethyl acetate -EA) have a strong impact not only on the average molecular weight, but increasing CTA concentrations can slow down, or totally inhibit the polymerisation reaction.

It is clear that more work needs to be done if we are to better understand key aspects of this industrially important polymer. The objective of this work is to contribute to better understanding of how process parameters like agitation can influence the initial reaction rate, what influences the particle formation process and the polymerisations during the emulsion homopolymerisation of VDF at high pressure; broadly to capture most of the important features that control this system.

EXPERIMENTAL

Vinylidene fluoride monomer (VDF) was kindly supplied by Arkema (Pierre Bénite, France) and used without further purification. Polymerisation was initiated with Potassium persulfate (99 %, Sigma Aldrich); the emulsion was stabilized by a proprietary anionic surfactant with a critical micelle concentration between 8-12 g/L and a parking area a s (the surface area occupied by a molecule of surfactant) on the order of 25 Å 2 . Ethyl acetate (ACS grade, Carlo Erba Reagent) was used as chain transfer agent (CTA). Sodium acetate (99 %, Sigma Aldrich) was used as buffer. Parafin wax was used to reduce sticking of the latex on the wall (see reference [1] for a discussion on the role of the wax.) All reagents were employed as received. The Molecular Weight Distribution was measured using the Size Exclusion Chromatography, equipped with three porous columns -two columns of 1000 Å and one column of 30 Å -of Polyester copolymer (Gram columns, PSS). A mixture of Dimethyl sulfoxide (DMSO) with sodium nitrate (NaNO3) previously filtered was used as solvent. The latex samples were first dried and then solutions of around 5 mg/mL were prepared and maintained at 55 °C to ensure the complete dissolution. When the samples were completely dissolved, solutions were filtered using nylon filter of 0.45 μm porous size. The retention time and the molecular mass of the injected PVDF were obtained using the PMMA calibration. The calibration curve was constructed using three samples of PMMA, the minimum molecular weight was 831 Da and the maximum was 1,430,000 Da A schema of the reactor set-up is shown in Figure 1. Polymerizations were performed in an unbaffled 4 L jacketed 316 Stainless steel autoclave described elsewhere [10,11]. 2 dip tubes (one to feed liquid components, and one to house the thermocouple) serve to interrupt the internal flow. The internal reactor diameter is 0.101 m. The bottom of the reactor has a truncated cone form of height 0.009 m and a diameter varying from 0.08 to 0.014 m. The inlet and outlet temperatures of the jacket were measured and used to follow the rate of polymerization by calorimetry. [11] The reactor temperature was regulated by a Proportional Integral Derivative (PID) controller. The volume of liquid in the reactor varies between 210 -3 (initial volume of water) and 2.510 -3 m -3 (final volume of latex reported) during the reaction. Note that the objective of the current paper is to demonstrate the impact that mass transfer limitations can have on the polymerization rate and polymer properties when the monomer is significantly lighter than the continuous phase.

Deionized water, surfactant, and wax were added to the reactor in an initial step. The feed line was then shut and the reactor heated to increase the temperature to 83°C under agitation. During the heating step, the reactor was peruged with nitrogen to remove residual oxygen. CTA and monomer were introduced in subsequent steps with a syringe pump (500HL Syringe Pump, Isco). VDF was fed into the reactor via a refridgerated feedline, and entered the feed pump at 10-20°C. A Coriolis mass flowmeter (Optimass 3000, Khrone) was used to monitor the inlet feed rate, which also provided a redundant measure of the reaction rate.

The rate of agitation was reduced at the end of the polymerization, and the reactor was cooled by reducing the temperature in the external jacket. The residual VDF was removed by gentle degassing. The final latex was removed via a valve at the bottom of the reactor under nitrogen purge. Reference values of the levels of reactive components used in the runs are based non the range given in Table 1: 8800 kPa (88 bars) VDF; wax = 2.4 g/L; EA = 3.3 g/L; Salt = 0.06 g/L; surfactant 1.5 g/L; and KPS = 0.09 g/L. The reference agitation speed was set at 550 rpm or 400 rpm, depending on the agitation system, as described below. All polymerisations will use these reference values unless otherwise stated. We will look at the impact of varying the EA, surfactant, KPS, stirring rate and impeller type in the following sections. Surfactant (anionic, proprietary) << CMC -Note: all concentrations are given in grams of active material per litre of pure water.

RESULTS AND DISCUSSION

Influence of Agitation on the Reaction

As discussed by Mendez Ecoscia et al. [1] , it is expected that the agitation can have an impact not only only latex coagulation, but also on the reaction rate in polymerisations where the monomer is significantly lighter than the continuous reaction as is the case here. To this end we investigated the influence of 2 different agitation systems and the agitation speed on the polymerisation rate. These are shown in Figure 2. With the initial Setup S1, the mixing system consists of a central shaft and 4 pitched six-blade turbine impellers (45°) with a 5 cm diameter; one at the bottom of the shaft 8 cm from the reactor bottom and the other 3 impellers at 8 cm intervals above. Agitator setup S2 is similar, but the 45° pitched 5 cm impeller at the bottom was replaced by a 4-blade A315 hydrofoil with a diameter of 8 cm, while keeping the 3 of the previous turbines at 8 cm intervals above it. Given that we are working at surfactant concentrations well below the CMC it was important to use a low shear agitator like the hydrofoil, in order to avoid shear-induced particle coagulation. [START_REF] Manikowski | [END_REF] Several batch polymerisations were run to explore the impact of the agitation system and speed on the polymerisation rate and the reactor temperature. The results are shown in Figure 3 for the original S1 configuration, where it can be seen that the agitation rate has a strong impact on the rate of batch polymerisation (Figure 3a), and on the ability to control the reactor temperature (Figure 3c). At the fastest agitation speed, 650 rpm, the rate of polymerisation (R p ) was significantly higher than for the other runs. Under these conditions, R p increases very rapidly,

Pitched

Blade Turbines Hydrofoil reaching a maximum approximately 18 minutes after the beginning of the reaction. The subsequent decrease in the reaction rate is due to the disappearance of monomer in the batch mode as shown by the pressure drop (Figure 3b). The reactor temperature also rises very quickly and becomes controllable again only when R p diminishes. Therefore, despite the fact that the reactor side heat transfer coefficient is expected to be higher under higher agitation speeds (see Figure 5 below), it is difficult to control the reactor temperature at agitation rates much higher than 600 rpm. Finally, the particle size distributions from these experiments (Figure 3d) show no signs of noticeable agglomeration at the different stirring rates. Figure 4 shows that using the hydrofoil (S2) leads to significantly higher rates than when S1 was used. It should be noted that different levels of initiator were used in the experiments shown in Figures 3 and4, but it is reasonable that the lower initiator concentrations used in Figure 4 would lead to lower polymerisation rates, and that the general trends in terms of how S1 and S2 impact the polymerisation can translate from one figure to the next.

Once again, it is important to pay attention to the control of the reactor temperature. The setpoint for these experiments was 83°C, and for high polymerisation rates, and in particular at 550 rpm, Figure 4c and Figure 4d show that small temperature excursions are observed at the beginning of the reaction for both S1 and S2. For S2, the reaction rate is at least twice as high at peak values, but the improved quality of mixing implies that the heat transfer coefficient is much better for S2 than for S1. The approach described by Mendez-Ecoscia et al. [1] was employed to estimate the lumped heat exchange coefficient U for these experiments, and it can be seen from Figure 5 that S2 at 550 rpm offers much higher values of U than S1 at 550 rpm (but at 350 rpm, U is similar for both S1 and S2). There is clearly a trade-off between enhanced polymerisations rates and the ability to remove the heat due to the high reaction rate. The higher rates observed at higher stirring speeds are most likely attributable to enhanced mass transfer from monomer "bubbles" to the aqueous phase. If the aqueous concentration of VDF is below its saturation limit, and consequently the concentration of VDF in particles is lower than its saturation value, it is possible that higher stirring rates will lead to an increase in these quantities.

In order to understand how the agitation rate impacted mass transfer during the polymerizations, a series of measurements were realized, based on the dynamic technique reported by Chaudhari et al. [ 22 ] , to evaluate the gas-liquid mass transfer coefficient k L a for agitator S2 at 83°C. Specifically, in absence of chemical reaction, we assumed that the variation of the monomer absorption into the aqueous phase and polymer particles is directly related to the evolution of the pressure as a function of time. The general operating protocol consists in the following steps:

1. A charge composed of deionized water (or PVDF latex at a given solids content) was added into the reactor and the agitation was set on. The PVDF latex was produced in batch mode and has a crystallinity of approximately 48 wt%.

2. The liquid was degassed with nitrogen until the desired temperature was reached.

3. Monomer was added into the reactor via the diaphragm pump, and the inlet mass was monitored. 5. The reactor pressure was measured every 10 seconds until equilibrium is reached 6. Steps 3-5 were repeated.

Figure 6 shows a typical profile of the pressure versus time. Note that pressure drop can only be seen clearly and reproducibly when the pressure is lower than 4000 kPa (40 bars), so all data treatments were carried out at a pressure of 2500 kPa (25 bars). In principle, the mass transfer coefficient should independent of the pressure, since of the pressure on the flux from the gas phase bubbles to the liquid should be accounted for in the driving force shown in Equation ( 1):

(

where is total diffusive flux of the component A (here gas) out of the "bubbles", is the liquid mass transfer coefficient of A, is the mass transfer area, is the interfacial concentration, and is the bulk concentration. Figure 7a shows an example of the monomer pressure drop during the batch absorption. The following assumptions were made in order to estimate the mass transfer coefficients: (i) the volumes of the liquid and gas phases remain invariable during the experiments; (ii) the monomer heat transfer rate is faster than monomer mass transport, (iii) pressure variation is due to gas absorption (i.e.

). Then, the mass balance of the gas inside the reactor can be expressed as [23,24,25] :

where is the mass transfer area per unit volume, is the initial pressure baseline (registered just before adding the monomer) resulting from the mass of water in the vapor phase and remaining nitrogen, is the pressure at any given time t, is the pressure at a given time t and is the final pressure obtained when the mass transfer equilibrium is reached, and H e is the Henry coefficient. As shown in Figure 7b, a linear fit to the variation slope of versus time can be used to compute the mass transport coefficient since:

(SM1. 3)
Figure 8a shows the influence of the agitation on the monomer mass transport coefficient, and the characteristic mass transfer time is shown in Figure 8b. As expected the mass transport coefficient increases as the rate of agitation increases, as a consequence of the bigger generated area of monomer "bubbles". The evolution of the mass transfer coefficient with agitation speed shows similar tendencies to other studies, for instance in a Fischer-Tropsch system. 25 Typically, reactions were carried out at 400 (for agitator S2) in semi-batch mode and 550 rpm (for agitator S1) in batch mode. At these stirring speeds we can see that at 2-3 minutes are required to attain the monomer mass transfer equilibrium at 30 bar, whereas at lower agitation rates, the characteristic mass transfer time is quite slow. If one considers the evolution of the weight average molecular weight (M w ) seen in Figure 9, the almost linear dependence of M w on the rate of agitation, coupled with the k L a data in Erreur ! Source du renvoi introuvable. strongly suggests that at lower stirring speeds the particles are in fact starved of monomer. The only difference between these experiments is the stirring speed and a drift in the temperature of a few degrees. The stirring speed itself should not directly influence the molecular weight of course. And while the temperature might be a factor, higher temperatures noted at the higher stirring speeds would decrease, not increase, the molecular weight. Particle size information cannot be reported here, but we can affirm that as was seen for the batch experiments (Figure 3d) no agglomeration was detected in any of these experiments.

There is no evidence that a change in diameter occurred that could provoke large enough changes in the average number of radicals per particle to explain the observed differences in. The only reasonable explanation for the higher molecular weight is an increase in the monomer concentration at higher agitation rates (explained nicely by the higher mass transfer rates shown above). In order to ensure that the rate of reaction is reasonably high but that the temperature is controllable, and to maintain the same conditions of mass transfer so as to be able to understand the impact of the other process parameters, in the following sections, it was decided to work under constant stirring rate depending on the agitation system used: In the experiments with agitator S1, we chose to work at a stirring rate of 550 rpm, and with S2 at an agitation rate of 400 rpm, unless otherwise stated.

Process parameters and particle growth

In ideal free radical polymerisations, it is usually assumed that the chain transfer agent controls the molecular weight of the produced polymer without affecting the rate of polymerisation. This is based on the implicit assumption that free radicals created by a chain transfer event to CTA have essentially the same reactivity as free radicals created by the reaction of an initiator fragment and the monomer. However, as discussed by Monteiro et al. [START_REF] Stefanichen Monteiro | [END_REF] , ethyl acetate, the CTA used in this work (and presumably most compounds containing a labile hydrogen), shows a degradative effect on the polymerisation rate. A series of batch and semi-batch experiments were run to investigate this effect. The different species concentrations remained at the reference values, except for that of the EA (CTA), which was varied from 0 to 13.5 g/L. The recipes are given in Table 2. Note that batch reactions were done with agitator setup S1 at 550 rpm, while semi-batch polymerisations were done with S2 at 400 rpm. The rate of polymerisation is plotted as a function of the solids content (SC, i.e. the weight fraction of polymer per unit volume of latex) in Figure 10. One can see the impact of the level of EA on the polymerisation, as well as that of the agitation system. The degradative effect of ethyl acetate on the reaction rate discussed by Monteiro et al. [START_REF] Stefanichen Monteiro | [END_REF] is observed in both batch and semibatch reactions. The slope of Rp slightly tends to decrease with the increase of the concentration of CTA, but it remains positive. As batch reactions were done with agitator setup S1 (at 550 rpm), while semi-batch polymerisations were done with S2 (at 400 rpm), a higher reaction rate is obtained in semi-batch experiments since the beginning of the reaction Figure 10. Effect of different levels of ethyl acetate on the rate of polymerisation of VDF in (a) batch polymerisations (adapted from reference [10]) and (b) semi-batch polymerisations.

It is useful to take a quick look at the impact of the amount of surfactant added to the reactor. First of all, as the amount of surfactant used is significantly lower than the CMC, homogeneous coagulative nucleation is the only possible means of forming particles. As one would expect, increasing the surfactant concentration leads to a higher polymerisation rate in the batch and semi-batch experiments as shown in Figure 11. It is interesting to note that regardless of the surfactant concentration used, the rate of polymerization remains constant in the batch experiments in Figure 11a, and continues to increase during this initial phase of the semibtach polymerizations in Figure 11b. All of the experiments show a very rapid increase in the rate at the beginning of the experiment, followed by a more gentle phase afterwards. This is true for both batch and semi-btach experiments. However the increase in the batch experiments is less remarkable, undoubtedly because the monomer concentration decreases monotonically (see above.) At constant pressure, the rate continues to increase. Since the rate of this type of nucleation depends on the monomer, initiator, and surfactant concentrations in the aqueous phase, there is no reason for this process to not continue throughout the entire polymerization if these quantities do not change. This is true of the monomer and (more or less) initiator concentrations. These results suggest that the homogenous-coagualtive nucelation mechansim by which the particles are formed continues throughout the polymerisation, and that surfactant concentrations as low as 0.75 g/L are enough to stabilise the latex at least to a solids content of 15 wt%. However the free surfactant levels will diminish as polymer accumulates in the reactor, meaning that we can stabilize more particles earlier in the polymerization than we can at the later stages. (left) Batch polymerizations (using S1); (right) semi-batch polymerizations (using S2)

The impact of the amount of initiator injected in semi-batch polymerisations can be seen in Figure 12. Again, as expected an increased initial concentration of initiator leads to an increased rate of polymerisation. Also, as with the surfactant experiments presented in Figure 11, the rate of polymerisation continues to increase monotonically right after a very rapid increase in the rate at the start of the polymerisation. Figure 12. Impact of the injection protocol of initiator on the semi-batch polymerisation rate as a function of the solids content. Experimental conditions: 1.5 g/L of surfactant, 0.06 g/L of buffer, 3.2 g/L of EA.

Conclusions

In the experiments presented in this work, all particles are generated by homogeneous coagulative nucleation since the quantity of surfactant used is lower than the CMC. The first step in this process is the growth and precipitation of oligo-radicals/dissolved chains in water. The rate of growth is a direct function of the availability of monomer in the aqueous phase, which in turn will depend on the pressure, temperature and the monomer solubility, as well as on the rate of agitation. The results show that the agitation rate has a strong impact on the initial rate of polymerisation, and on the ability to control the reactor temperature. It was shown that agitation conditions that lead to a high gas-liquid mass transfer coefficient also lead to higher rates of polymerization, and higher average molecular weights. This is most likely due to a greater availability of monomer for both the particle nucleation process, and possibly the propagation step in the polymer particles. As expected, the quantity of surfactant used has an impact on the initial rate of polymerization as well as it is expected that this will lead to a higher number of particles. From the continuous increase of the reaction rate with time, it may be deduced that particle nucleation continues, but certainly in parallel to continuous particle coagulation.

l d ia p h r a g m p u m p C0 1 E q u i p m e n t Li s tFigure 1 .

 11 Figure 1. Reactor setup for VDF polymerisation.

Figure 2 .

 2 Figure 2. Different impellers considered in the current work, and configuration of the agitation system. S1 consisted of 4 pitched blades arranged as shown. With S2 the bottom pitched blade was replaced by the hydrofoil.

Figure 3 .Figure 4 .

 34 Figure 3. Impact of the agitation speed of batch polymerisations stirred with agitation setup S1 on: (a) the on the rate of polymerisation estimated by pressure drop in the reactor; (b) the pressure; (c) reactor temperature; (d) the particle size distribution. Set point temperature 85°C, initial pressure 8300 kPa (83 bars). Experimental conditions: 1.5 g/L of surfactant, 0.32 g/L of KPS, 0.06 g/L of buffer.

Figure 5 .

 5 Figure 5. Overall heat transfer coefficient U for the different agitation setups and stirring rates for the experiments shown in Figure 4.

4 .

 4 Injection of monomer was stopped.

Figure 6 .

 6 Figure 6. Example of raw data: Evolution of the reactor pressure at 83 °C, obtained at 400 rpm and 13,8%wt of solids content.

Figure 7 .

 7 Figure 7. Example of a) monomer pressure drop during batch absorption and b) data analysis, collected at 550 rpm and 13.8%wt of solids content.

Figure 8 .

 8 Figure 8. (a) Gas (supercritical fluid)-liquid mass transfer coefficient k L a as a function of stirring speed for agitator S1. (b) the equivalent mass transfer time at 83 °C. Solid content 13.8 wt%.

Figure 9 .

 9 Figure 9. Evolution of M w as a function of stirring speed for agitator system S1. Set point temperature 85°C, initial pressure 8300 kPa (83 bars). Experimental conditions: 1.5 g/L of surfactant, 0.32 g/L of KPS, 0.06 g/L of buffer. No CTA.

Figure 11 .

 11 Figure 11. Impact of the surfactant concentration on the evolution of the polymerisation rate. (left) Batch polymerizations (using S1); (right) semi-batch polymerizations (using S2)

Table 1 .

 1 Range of literature values for PVDF emulsion polymerisation formulations.

	Parameter	Value	Reference
	Maximum VDF Pressure	8800 KPa (88 bars)	[12]
	Parafin wax	0-6 g/L	[13,14,15,16,17]
	Temperature	80-85°C	[12,13,18]
	CTA -Ethyl acetate	1.2-24 g/L	[12Erreur !
			Signet non
			défini.,19]
	KPS	0.005-0.5 g/L	[20]

Table 2 .

 2 Recipes of the batch (R16, R17, 19, R20) and semi-batch (S11, S12, S20) polymerisations performed at different concentrations of EA. Batch reactions done with agitator setup S1 at 550 rpm. Semi-batch polymerisations done with S2 at 400 rpm.

	Run	Surfactant (g•L water -1 )	KPS (g•L water	-1 )	Salt (g•L water	-1 )	EA (g•L water	-1 )	Wax (g)
			Batch polymerisations
	R16	1.5	0.09		0.06		0.0		2.4
	R17	1.6	0.09		0.06		13.5		2.3
	R19	1.5	0.09		0.06		6.8		2.3
	R20	1.5	0.09		0.06		3.3		1.9
			Semi-batch polymerisations
	S11	1.4	0.09		0.06		6.9		3.0
	S12	1.4	0.09		0.06		13.2		2.2
	S20	1.5	0.09		0.06		3.3		2.3
	S10*	1.4	0.09		0.06		3.3		2.5
	*reproducibility test

ACKNOWLEDGEMENTS

The authors are grateful for financial support by ANR Scale-up project (ANR-12-RMNP-0016).