Pierre-Yves Pichon
email: pichon@rgsdevelopment.nl

Pierre Berneron
email: berneron@rgsdevelopment.nl

Joshua Levinsky
email: j.levinsky@rug.nl

Arjan Burema
email: a.a.burema@rug.nl

Graeme Blake
email: g.r.blake@rug.nl

David Berthebaud
email: david.berthebaud@cnrs.fr

Stéphanie Gascoin
email: stephanie.gascoin@ensicaen.fr

Franck Gascoin
email: franck.gascoin@ensicaen.fr

Sylvie Hebert
email: sylvie.hebert@ensicaen.fr

Jonas Amtsfeld
email: jonas.amtsfeld@gmail.com

Tijmen Hommels
email: tijmenhommels@hotmail.com

Mark Huijben
email: m.huijben@utwente.nl

Johannes De Boor
email: johannes.deboor@dlr.de

Eckhard Müller
email: eckhard.mueller@dlr.de

Christelle Navone
email: christelle.navone@cea.fr

Axel Schönecker
email: schonecker@rgsdevelopment.nl

Stability and thermoelectric performance of doped higher manganese silicide materials solidified by RGS (ribbon growth on substrate) synthesis

Keywords: Thermoelectric materials, crystal growth, microstructure, crystal structure, electrical transport

Large scale deployment of thermoelectric devices requires that the thermoelectric materials have stable electrical, thermal and mechanical properties under the conditions of operation. In this study we examine the high temperature stability of higher manganese silicide (HMS) materials prepared by the RGS (ribbon growth on substrate) technique. In particular we characterize the effect of element substitution on the structural and electrical changes occurring at the hot side of temperatures of thermoelectric devices relevant to this material (600°C). Only by using suitable substitution (4% vanadium at the Mn site) can we obtain temperature-independent structural parameters in the range 20°C -600°C, a condition that results in stable electrical properties. Additionally, we show that 4% vanadium substitution at the Mn site offers the best thermoelectric figure of merit among the different compositions reported here with ZT max =0.52, a value comparable to the state of the art for HMS materials. Our analysis suggests that ionized impurity scattering is responsible for the better performance of this material.

Introduction

The higher manganese silicide (HMS, MnSi γ ) phases are the most silicon-rich materials of the Mn-Si alloys. HMS materials are promising candidates for the deployment of large scale, costeffective thermoelectric generators operating up to 600°C thanks to their low raw material cost and good thermoelectric performance. The thermoelectric figure of merit (ZT) characterizes the effectiveness of a material to transform a heat flow into electrical power. It is defined as ZT = S 2 σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity, and T is the absolute temperature. Competitive ZT values in the range 0.5-0.7 have been measured on doped HMS materials synthesized by different techniques, which makes them technologically relevant for integration into thermoelectric devices [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF][START_REF] Fedorov | Thermoelectrics of Transition Metal Silicides[END_REF][START_REF] Zhu | Compromise and Synergy in High-Efficiency Thermoelectric Materials[END_REF], possibly in combination with n-type silicides (SiGe alloys, Mg 2 (Si,Ge,Sn) [START_REF] De Boor | Recent progress in p-type thermoelectric magnesium silicide based solid solutions[END_REF][START_REF] Skomedal | Design, assembly and characterization of silicide-based thermoelectric modules[END_REF]). Recently, supersaturated HMS materials synthesized by melt spinning achieved significantly improved performance with ZT values of about 1 for p-type Re-doped HMS [START_REF] Yamamoto | Thermoelectric properties of supersaturated Re solid solution of higher manganese silicides[END_REF][START_REF] Ghodke | Effect of grain boundaries and partial substitution of transition metals on thermoelectric properties of higher manganese silicide[END_REF][START_REF] Ghodke | Enhanced Thermoelectric Properties of W-and Fe-Substituted MnSiγ[END_REF]. Until now most of the work on thermoelectric materials has focused on increasing ZT. However, an important condition for successful large-scale deployment of high temperature thermoelectric devices is the stability of the thermoelectric properties at the relevant temperature and atmospheric conditions. The first objective of this work is to systematically characterize the high temperature electrical stability of HMS materials produced by the Ribbon Growth on Substrate (RGS) production process. We aim at clarifying the relations between electrical stability, doping type and structural evolution under high temperature module operation conditions. In this article we also demonstrate a significant improvement of both electrical stability and ZT for vanadium-doped HMS associated with ionized impurity scattering of the charge carriers and subsequent superior electrical and thermal properties.

The HMS phases belong to the family of so-called chimney-ladder structures: a [Mn] 'chimney' subsystem and a [Si] 'ladder' subsystem having a common a-axis but different stacking periods in the c direction, hence different subsystem c-axis lengths c Mn and c Si . Examination of the crystal structure shows that γ = c Mn /c Si . If is an irrational number the structure is incommensurate and cannot be described using a single overall lattice parameter in the c direction: this motivates the structural characterization of HMS in terms of two separate subsystems or by the (3+1) dimensional superspace approach [START_REF] Miyazaki | Superspace Group Approach to the Crystal Structure of Thermoelectric Higher Manganese Silicides MnSiγ[END_REF]. More recently another approach was proposed to model the XRD spectrum of the HMS structure by including significant defects in the Si sublattice [START_REF] Akselrud | Disorder in the composite crystal structure of the manganese "disilicide" MnSi1.73 from powder X-ray diffraction data[END_REF]. The valence electron count ( ) concept is useful to describe the thermodynamic stability of chimney-ladder phases and to estimate the charge carrier density of these materials from the structural parameter γ [START_REF] Fredrickson | The Nowotny chimney ladder phases: Whence the 14 electron rule?[END_REF][START_REF] Fredrickson | The Nowotny chimney ladder phases: Following the cpseudo clue toward an explanation of the 14 electron rule[END_REF][START_REF] Kikuchi | High temperature X-ray diffraction study on incommensurate composite crystal MnSi -(3+1)-dimensional superspace approach[END_REF][START_REF] Miyazaki | Modulated crystal structure of chimney-ladder higher manganese silicides MnSiγ (γ∼1.74)[END_REF]. The VEC is the number of valence electrons per transition metal element (here Mn). For unsubstituted MnSi γ , VEC = 7 + 4γ. For the general case of substituted HMS it can be written as:

= -) + + -) + ) (1)
Here x and V Me are the proportion and number of valence electrons of the element Me that substitutes Mn (e.g., V V = 5); y and V s are the proportion and number of valence electrons of the element that substitutes Si (e.g., V Al = 3; V Ge = 4). Furthermore, the charge carrier density can be estimated by:

= ) (2)
In equation [START_REF] Fedorov | Thermoelectrics of Transition Metal Silicides[END_REF] is the volume of the Mn subcell. Here we consider only the case where VEC<14 (ptype materials). In general, chimney-ladder phases are stabilized for a VEC count of 14 [START_REF] Fredrickson | The Nowotny chimney ladder phases: Whence the 14 electron rule?[END_REF][START_REF] Fredrickson | The Nowotny chimney ladder phases: Following the cpseudo clue toward an explanation of the 14 electron rule[END_REF]. Therefore, according to equation [START_REF] Fedorov | Thermoelectrics of Transition Metal Silicides[END_REF] stable chimney ladder phases should be charge neutral: in fact thermodynamic stability relates to the opening of a bandgap around the chemical potential. For the HMS phase the stoichiometry Mn 4 Si 7 (γ = 1.75) should be preferred, however structural analysis has shown that compounds with lower γ are actually synthesized , conferring to this material an intrinsic ptype character. Kawasumi et al. identified Mn 15 Si 26 as the stoichiometry of undoped-HMS solidified by the Bridgman method [START_REF] Kawasumi | Crystal growth of manganese silicide, MnSi~1.73 and semiconducting properties of Mn15Si26[END_REF] and also measured a hole density of about 2 × 10 27 m -3 in the room temperature-to 600 K range [START_REF] Kawasumi | Crystal growth of manganese silicide, MnSi~1.73 and semiconducting properties of Mn15Si26[END_REF], as predicted by equation (2) ([p]=1.98 × 10 27 m -3 ). Early works identified Mn 15 Si 26 (γ = 1.733), Mn 11 Si 19 (γ = 1.727), and Mn 27 Si 47 (γ = 1.741)) as commensurate structures [START_REF] Kawasumi | Crystal growth of manganese silicide, MnSi~1.73 and semiconducting properties of Mn15Si26[END_REF][START_REF] De Ridder | The structure of defect manganese silicides[END_REF][START_REF] Ye | High-resolution electron microscopic study of manganese silicides MnSi2-x[END_REF], while more recent studies report intermediate γ values, interpreting these as either incommensurate, incorporating defects at the Si sites, or comprising domains of different γ values [START_REF] Miyazaki | Superspace Group Approach to the Crystal Structure of Thermoelectric Higher Manganese Silicides MnSiγ[END_REF][START_REF] Akselrud | Disorder in the composite crystal structure of the manganese "disilicide" MnSi1.73 from powder X-ray diffraction data[END_REF][START_REF] Vivès | Microstructure control and transport properties of incommensurate manganese silicide based alloys for thermoelectricity[END_REF][START_REF] Truong | Thermoelectric Properties of Higher Manganese Silicides[END_REF][START_REF] Hamada | Crystal Structure and Thermoelectric Properties of the Incommensurate Chimney-Ladder Compound VGeγ (γ ~1.82)[END_REF].

Several studies have shown that undoped HMS can undergo solid-solid phase transitions in the temperature range useful for thermoelectric generation. For example a comparative study of Differential Thermal Analysis (DTA), Differential Scanning Calorimetry (DSC) and High Temperature powder X-Ray Diffraction (HTXRD) showed that solid-solid phase transformations occur upon heating [START_REF] Allam | Phase transformations in Higher Manganese Silicides[END_REF]. These transitions are primarily due to a temperature-dependence of the γ ratio: another HTXRD study of undoped HMS showed that the expansion rates of the Si and Mn sublattices in the c direction are different upon heating. As a result γ increases and the structure expels Mn, resulting in MnSi precipitation in the form of layered precipitates parallel to the a-b crystallographic plane [START_REF] Kikuchi | High temperature X-ray diffraction study on incommensurate composite crystal MnSi -(3+1)-dimensional superspace approach[END_REF]. In this study the authors suggest that the long-term stability of the material may be compromised due to cracks occurring at the HMS-MnSi interface. Cracking issues in the a-b plane have been a general concern for HMS solidified from the liquid [START_REF] Aoyama | Effects of Ge Doping on Micromorphology of MnSi in MnSi ∼1.7 and on Their Thermoelectric Transport Properties[END_REF], the cause being the lattice mismatch between the HMS phase and the MnSi phase precipitated during cooling from the melting point [START_REF] Suvorova | Precipitates of MnSi cubic phase in tetragonal Mn4Si7 crystal[END_REF][START_REF] Orekhov | Study of doped higher manganese silicides crystals by transmission electron diffraction and electron backscatter diffraction[END_REF]. Finally, another HTXRD study showed that the addition of alloying elements at the Mn or Si site can significantly influence the relative expansion coefficient of the sublattices, i.e. the γ(T) characteristic. For example, in the case of Ge doping γ is stable between room temperature and 600 °C [START_REF] Truong | Thermoelectric Properties of Higher Manganese Silicides[END_REF]. This suggests that appropriate doping may stabilize the HMS phase in the temperature range of interest. Notably, above a critical Ge concentration the layered MnSi precipitates disappeared in crystals grown by the Czochralski technique [START_REF] Aoyama | Effects of Ge Doping on Micromorphology of MnSi in MnSi ∼1.7 and on Their Thermoelectric Transport Properties[END_REF].

Despite several literature reports on the HMS phases show the occurrence of a solid-solid reactions in the temperature range of interest for thermoelectric applications, very little information is available on the stability of the thermoelectric properties, and on their relations with the synthesis technique, the concentration of a particular substitution element, and the corresponding γ(T) characteristics. Most papers have reported the thermoelectric properties of as-synthesized materials, without demonstrating that the materials are thermodynamically and/or electrically stable. The motivation of this work is to bridge the gap between stability studies and performance studies of the HMS materials. In this framework, here we examine the effects of doping on the (micro)structural evolution of HMS and on the changes in thermoelectric properties at high temperatures. We study the effect on the thermoelectric properties of maintaining the materials at a temperature of 600°C in ambient atmosphere. Based on a review of the literature, we expected that synthesis techniques involving relatively fast cooling such as RGS (about 2 K/sec above 500 °C) may result in metastable γ after synthesis. Upon further high temperature exposure in devices this might result in MnSi precipitation, cracking, and changes in [p]. Therefore, we use HTXRD to characterize γ(T) in the room temperature-to 600°C range and to explain changes in the microstructure, in the charge carrier density and in the mobility upon aging. This work is reported in section 3.1.

Since the doping type and level are key parameters affecting the γ(T) characteristics, we chose a set of nominal compositions based on promising materials reported so far. Mn[Si 0.9955 Al 0.0045 ] 1.73 was chosen because of the good thermoelectric properties already reported [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF]. We selected Mn[Si 0.991 Ge 0.009 ] 1.73 because of the reported effects of Ge on γ(T) and MnSi precipitation [START_REF] Aoyama | Effects of Ge Doping on Micromorphology of MnSi in MnSi ∼1.7 and on Their Thermoelectric Transport Properties[END_REF][START_REF] Ivanova | Higher Manganese Silicide Based Materials[END_REF][START_REF] Zhou | Microstructure and thermoelectric properties of SiGe-added higher manganese silicides[END_REF]. Mn substitution by Re was also chosen because it yields a state of the art ZT value [START_REF] Yamamoto | Thermoelectric properties of supersaturated Re solid solution of higher manganese silicides[END_REF], but we opted for a lower doping amount of [Mn 0.97 Re 0.03 ]Si 1.73 to avoid Re silicide formation during synthesis with our RGS technique. The substitution of V for Mn above 2% was recently shown to suppress the formation of MnSi precipitates while highly disordered strained Si domains appeared instead [START_REF] Miyazaki | Crystal Structure and Thermoelectric Properties of Lightly Vanadium-Substituted Higher Manganese Silicides (Mn1-xVx)Siγ)[END_REF][START_REF] Miyazaki | Crystal structure and thermoelectric properties of lightly substituted higher manganese silicides[END_REF]. Therefore, we included [Mn 0.98 V 0.02 ]Si 1.73 and [Mn 0.96 V 0.04 ]Si 1.73 as nominal compositions. Throughout the following discussion the materials will be referred to by the percentage of substituted elements, such as '4%V-HMS' for [Mn 0.96 V 0.04 ]Si 1.73 . While characterising these materials we noticed that V-doped materials exhibit significantly different electrical properties compared to the others. A comparative analysis of the thermoelectric performance of the different materials is the subject of section 3.2.

Materials and methods

Synthesis

The materials were synthesized by solidification from the melt using the RGS process. This solidification technique consists in moving a flat mould band (kept at a temperature several hundred Celsius lower than the melting point) under the liquid melt, which is contained in a continuously refilled reservoir. The liquid is solidified at a growth rate between 0.1 and 1 mm.s -1 resulting in a sheet of typical thickness 0.5 mm grown on the mould. The solidified semiconductor sheet detaches upon cooling, can be transferred out of the process chamber and the mould can be reused. A detailed description of the process is given in [START_REF] Apel | Simulation of the crystallisation of silicon ribbons on substrate[END_REF][START_REF] Hahn | New crystalline silicon ribbon materials for photovoltaics[END_REF]. The solidification velocity is intermediate between that of large batch growth processes (the Czochralski, floating zone, directional solidification and Bridgman techniques have a solidification velocity of about 10 -5 -10 -4 m.s -1 ) and non-equilibrium processes such as spin casting with a solidification velocity of several m.s -1 . Therefore, RGS materials have unique (micro)structures and electrical properties. This process is interesting from a technological point of view as it allows for HMS thermoelectric legs of controlled dimensions to be produced in one step and at rates compatible with the large-scale deployment of thermoelectric generators.

Characterization

The stability of the materials was tested under two types of conditions. In a first series of tests the Seebeck coefficient and the electrical conductivity of as-solidified samples were measured as a function of time at 600 ˚C in inert gas (12 to 45 hours). Such measurements were done routinely at University of Groningen and selected samples were measured at CEA and University of Twente for confirmation. In a second series of tests the samples were subjected to annealing steps at 600 ˚C for 10 hours, then for 100 hours in air. These testing conditions are more relevant to practical applications since a thermoelectric material that is usable in oxidative environments opens the door to more costeffective module designs compared to, e.g. encapsulated module configurations. The Seebeck coefficient and electrical conductivity were measured at room temperature on each sample in the asgrown state, after 10 hours of annealing and after 10+100 hours of annealing. Additional samples were undergoing the same annealing sequence and were analysed by Hall measurements, microstructure analysis, HTXRD and thermoelectric performance evaluation. For all samples where the Seebeck coefficient and/or electrical conductivity were measured (including Hall samples), one surface of the RGS-cast HMS sheet samples was ground to reduce thickness inhomogeneities.

Note that our analysis plan allowed for cross-checking of the measurements performed at three different laboratories for the room temperature Seebeck coefficient and at four different laboratories for the electrical conductivity. We verified a posteriori that the error bars indeed overlap.

Stability: structure and microstructure

Samples on which the microstructure was studied were embedded in epoxy resin and polished (last step using a 1µm diamond suspension) for analysis by optical microscopy and Scanning Electron Microscopy (SEM). In order to reveal the presence of MnSi precipitates the polished cross-sections were submitted to a dilute HF etching step (HF:H2O=5:95, typically 10 s). SEM analysis was performed using a Hitachi SU70 electron microscope with an acceleration voltage of 15kV and a working distance of 15mm. Energy dispersive X-ray spectroscopy (EDX) was carried out on some samples to identify the different phases present and evaluate the composition homogeneity.

High resolution powder or bulk surface X-ray diffraction data were collected using a Bruker D8 Advance Vario 1 two-circle diffractometer (θ-2θ Bragg-Brentano mode) using Cu Kα radiation (λ=1.540598 Å) with a Ge (1 1 1) monochromator (Johansson type) and a Lynx Eye detector. Hightemperature experiments were carried out with an Anton Paar furnace HTK1200N; the temperature was regulated within ±3 K. Data were collected over the angular range 10 ≤ 2θ (°) ≤ 95 under air, measuring for 1 s at each angular increment of 0.0157° (1.5 h /scan). XRD patterns were recorded using the following temperature profile: a pattern at room temperature; one every 100 K from 373 K to 873 K (heating rate of 30 K/min); one every 100 K from 873 K to 373 K (cooling rate of 30 K/min); one at room temperature after cooling. The Le Bail method was employed to refine the lattice parameters and modulation vectors. Refinements were performed in the (3 + 1)-dimensional superspace group I41/amd(00g)00ss using the JANA2006 software package [START_REF] Petříček | Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA[END_REF].

Stability: thermoelectric properties

The Seebeck coefficient and electrical conductivity were measured simultaneously using a Linseis LSR-3 apparatus at the University of Groningen. To measure the Seebeck coefficient a temperature gradient of 30 K was applied across the sample and the induced voltage was measured at a constant current. The resistivity was measured using a four-point probe configuration where all contact points are aligned along a vertical line. To characterize the evolution of the electrical resistivity and Seebeck coefficient at elevated temperature, the samples were held at 600 ˚C for 14 hours under a protective helium atmosphere to prevent oxidation.

For the samples annealed in air at 600 ˚C the Seebeck coefficient and electrical conductivity were measured at room temperature on a custom-made test bench at RGS Development B.V. An HF dip was performed before the measurement to remove the oxide layer grown during the annealing step. The electrical conductivity was measured on a four-point probe system using an electrical current of 0.5 A over the (measured) sample cross-section area of approximately 0.4 x 15 mm 2 . The error of the electrical conductivity is estimated to be less than 8%, the highest error contribution coming from thickness variations. The Seebeck coefficient was evaluated by measuring the voltage drop generated by a temperature difference of 8 K around room temperature. The temperature difference was applied using commercially available Peltier elements and measured using type T thermocouples.

To evaluate the change in charge carrier density and mobility upon annealing, Hall measurements were carried out at CRISMAT labs on as-solidified samples and samples annealed for 10 hours at 600 ˚C in air. The measurements were performed in a PPMS system from Quantum Design, where the electrical contacts were soldered with indium on samples with a shape 5 × 5 × 0.4 mm. The carrier density was extracted from Hall effect measurements from 5 K to 300 K considering as a first approximation a simple single band model, to compare with the results from the literature [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF][START_REF] Miyazaki | Crystal structure and thermoelectric properties of lightly substituted higher manganese silicides[END_REF]. Electrical resistivity was measured using the van der Pauw geometry. Note that the measurements were performed in plane, and no noticeable anisotropy was detected during the Van der Pauw experiments. This is consistent with EBSD analysis which showed that the out of plane direction corresponds to the c axis direction. From both sets of measurements, the mobility could be extracted. For the resistivity the main source of error comes from the thickness determination, with a maximal error of ~ 8% except for the V-doped materials where the error is ~ 12% due to thinner solidified samples, and from the contact size and misalignment, estimated to be ~ 5%. The intrinsically high charge carrier density of HMS materials makes the measurement accuracy particularly sensitive to errors in the measurement of the slope of the Hall resistance curves R(H). All the carrier concentrations determined here are extracted from linear R(H) curves, the uncertainty in the linear least squares fit being less than 0.5%.

Thermoelectric performance

Samples were measured at DLR to evaluate their thermoelectric performance. The samples were polished before the measurements to decrease the surface roughness and improve the electrical contacts. The electrical conductivity σ and the Seebeck coefficient S of the samples were measured concurrently using a custom-built setup. Setup details and a detailed description of the data analysis for the Seebeck coefficient measurements can be found in published works [START_REF] De Boor | High-Temperature Measurement of Seebeck Coefficient and Electrical Conductivity[END_REF][START_REF] De Boor | Data analysis for Seebeck coefficient measurements[END_REF]. Due to the small thickness and the sometimes uneven surface, the uncertainty for the electrical conductivity is estimated to be 10%, while the uncertainty for the Seebeck coefficient is 5%. The measurement data were acquired both during heating up and during cooling down. The thermal diffusivity (α) of the samples was obtained using a Netzsch LFA 467HT apparatus. The density ρ was determined using Archimedes' method, while the heat capacity C P was measured using a Netzsch DSC 404. The thermal conductivity (κ) was obtained using the relation κ = αρC P and the measurement accuracy is estimated to be 10 %, the uncertainty stemming mainly from the C P measurement and the thickness sensitivity of the LFA measurement. Note that for practical reasons of sample geometry the conductivity (and Seebeck coefficient) are determined in-plane, while thermal conductivity is determined cross-plane. Therefore the ZT results reported here should be seen as best estimates, since one cannot exclude possible anisotropic effects.

Results and Discussion

Stability

Stability of the electrical properties

Figure1 shows measurements of the Seebeck coefficient and electrical conductivity as a function of time at 600˚C for 4%V-HMS, 0.9%Ge-HMS, 0.45%Al-HMS, and 3%Re-HMS. The measurements show that the electrical resistivity increases by between 6% and 20% during the 12 h of measurement time for the Ge, Al and Re doped samples. Note that for these samples the electrical resistivity still continues to increase at the end of the test. In contrast, the electrical resistivity of 4%V-HMS is found stable over time and does not vary within the measurement error. Changes in the Seebeck coefficient, if any, are at most 2% based on data analysis after noise filtering, which is relatively small compared to changes in the resistivity. Our data show that the 4%V-HMS has stable electrical properties at 600˚C, a typical hot-side thermoelectric module temperature. We confirmed this observation by measuring additional samples at different laboratories for up to 45 hours. Figure S1 in the supplementary information shows the evolution of the electrical properties of 4%V-HMS and 0.45%Al-HMS as a function of time. Figure 2 summarizes these results by showing a comparison of the high temperature power factor of different materials as-solidified and after 10 hours exposure to 600˚C.

Since we are interested in the material stability under atmospheric conditions, we also measured the changes of the room temperature electrical conductivity and Seebeck coefficient for samples that had undergone successive annealing for 10 h and 100 h in air at 600 ˚C. The effect of the two annealing steps on the room temperature electrical properties is shown in figure 3. Except for 4%V-HMS where the electrical properties do not change, the electrical conductivity of all materials (including 2%V-HMS) decreases by 20-25% after 10 + 100 hours of annealing, while the change in the Seebeck coefficient is relatively smaller. Figure 2 and figure 3 show that the decrease in electrical conductivity on annealing results in a significant reduction of the power factor S 2 σ, with the exception of 4%V-HMS. Note that the material with the highest power factor before thermal treatment is the Gedoped material but after annealing the V-doped materials have the best electrical properties. Additionally, we conclude that the testing atmosphere is likely not the most influential parameter to explain the changes in electrical properties, and that a minimum vanadium concentration is required to stabilize the electrical conductivity.

Structure and microstructure analysis

The purity of the 2%V-HMS, 4%V-HMS, and 0.45%Al-HMS materials and the absence of any significant volume fraction of secondary phases were checked by XRD measurements on powder samples derived from as-solidified materials. The XRD patterns are shown in figure 4 and demonstrate the absence of significant amounts of MnSi, Al-rich or V-rich phases. The variation of peak intensity is due to preferential orientation effects. All peaks could be indexed as HMS phase with superspace group I41/amd(00γ)00ss according to the composite structural model suggested by Miyazaki et al. [START_REF] Miyazaki | Preparation and Thermoelectric Properties of a Chimney-Ladder (Mn 1-x Fe x )Si γ (γ∼1.7) Solid Solution[END_REF]. According to research on the Mn-Si-Al system, excess Al-doping would result in the formation of Alrich phases with about 30at% Al (C40 or C54 phase) [START_REF] Krendelsberger | On the constitution of the system Al-Mn-Si[END_REF][START_REF] Yamamoto | Thermoelectric properties of Al-Mn-Si C40 phase containing small amount of W or Ta[END_REF], which are not observed in our case. This confirms that the chosen Al doping level is below the solubility limit as already demonstrated by Chen et al. [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF]. Similarly, we do not observe any signal from VSi 2 in 2%V-HMS and 4%V-HMS, which would be the case if we significantly exceeded the solubility limit of V in the HMS phase. However, Miyazaki et al. suggested that the solubility limit of V substituting Mn in HMS is 3% [START_REF] Miyazaki | Crystal Structure and Thermoelectric Properties of Lightly Vanadium-Substituted Higher Manganese Silicides (Mn1-xVx)Siγ)[END_REF]. As will be discussed later, small amounts of the MnSi phase are present in all materials but could not be detected by the XRD measurements because of their low volume fraction.

All materials (as-grown and annealed) presented in figure 3Figure were analysed by optical microscopy to search for the presence of MnSi. Some samples were also analysed by SEM-EDX to characterize the homogeneity of the dopant distribution in the HMS matrix and to identify secondary phases, if present. The microstructural changes of the 0.45%Al-HMS material are representative of that of the unstable materials (Re, Al, and Ge-doped), and therefore only the microstructure analysis of this material is reported here, as compared to that of the stable 4%V-HMS. A comparison of the optical microscopy features of the as-solidified and annealed materials is shown in figure 5. The MnSi phase is identified by different contrast to the bulk due to the effect of the MnSi etching step (this was confirmed by measuring a ratio [Si]:[Mn] = 1:1 using SEM-EDX). For both materials the presence of a small volume fraction of MnSi dendritic crystals at the surface contacting the mould is noticed. Because of the presence of a peritectic transformation it is expected that solidification starts first by MnSi nucleation at the mould surface and further by dendritic growth, and that later the HMS phase overgrows the MnSi dendrites in a melt slightly enriched in Si [START_REF] Kerr | Solidification of peritectic alloys[END_REF].

The main feature that distinguishes the as-solidified 4%V-HMS from the 0.45%Al-HMS material is the presence of MnSi layered precipitates in the latter, while these so-called striations are absent from 4%V-HMS. This observation confirms the general trend observed by other authors [START_REF] Miyazaki | Crystal Structure and Thermoelectric Properties of Lightly Vanadium-Substituted Higher Manganese Silicides (Mn1-xVx)Siγ)[END_REF] on melt-grown V-doped HMS materials, although in contrast to them we did observe a minor amount of striations also in the 2%V-HMS. For the Al-doped material the striation defects are concentrated in the centres of the grains and often absent close to the grain boundaries. Local analysis of the composition by EDX showed that the concentration of Al dopant corresponds to about 0.2% substitution of Si in the striated regions and up to more than 1% substitution closer to the grain boundaries, while the nominal substitution amount is 0.45%. Similarly, we observe that for the Ge-doped materials, higher [Ge] closer to grain boundaries is correlated with the absence of striations there, as also reported by other authors for Ge-doped arc-melted samples [START_REF] Vivès | Microstructure control and transport properties of incommensurate manganese silicide based alloys for thermoelectricity[END_REF]. As observed by Vives [START_REF] Vivès | Microstructure control and transport properties of incommensurate manganese silicide based alloys for thermoelectricity[END_REF], above a critical Ge or Al concentration MnSi striations do not precipitate during cooling after solidification. As will be discussed later, this is likely due to the stabilization effect of the substituted element on the γ(T) characteristic above a critical concentration. In our case the concentration gradients originate from dopant segregation during RGS solidification. Note that the presence of gradients in the concentration of substitution elements imply that our materials are electrically inhomogeneous in the as-solidified state.

The effect of annealing the samples in air at 600 °C for 10 hours is also shown in figure 5. We do not observe significant microstructural changes for the 4%V-HMS, whereas for all the other materials (including the 2%V-HMS), we observe a layer of MnSi at the grain boundaries, as revealed by the dark contrast in the optical microscopy images. Local SEM-EDX analysis confirmed that the stoichiometry of the grain boundary (GB) precipitates is approximately [Si]:[Mn] = 1:1. The morphology of the striation defects is also different after annealing: striations disappeared completely in some regions or broke down into discontinuous dotted lines. For the as-grown and annealed Aldoped materials, microcracks are often observed along the striations and for the annealed materials voids are present at the MnSi-rich grain boundaries (denoted as 'GB voids' in figure 5). Whether or not these voids are induced by the sample preparation procedure, in both cases we conclude that the interface between HMS and the MnSi phase is mechanically weak due to the significant lattice mismatch [START_REF] Suvorova | Precipitates of MnSi cubic phase in tetragonal Mn4Si7 crystal[END_REF][START_REF] Orekhov | Study of doped higher manganese silicides crystals by transmission electron diffraction and electron backscatter diffraction[END_REF][START_REF] Ivanova | Higher Manganese Silicide Based Materials[END_REF]. Finally it is worth mentioning that the striation defects have an orientation corresponding to a tilt of at most about 30˚ with the wafer plane. EBSD measurements confirmed a preferential orientation with the c-axis pointing out of wafer plane. This implies that any anisotropy in the thermoelectric properties, if present, should result in properties in plane different from cross plane. The 4%V-HMS material is the only one that does not show MnSi precipitation as striations or at grain boundaries in as-grown and annealed samples. This is also the only electrically stable material. We can thus correlate electrical stability with the absence of MnSi in this material. We are thus able to propose the following two hypotheses:

1 The formation of MnSi results in microcracks and lowers the charge carrier mobility.

2 The formation of MnSi is the result of structural changes (e.g, the γ ratio) in the HMS lattice, which also influences the charge carrier density via equations [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF] and [START_REF] Fedorov | Thermoelectrics of Transition Metal Silicides[END_REF].

High temperature structural characterization and Hall measurements

To clarify hypotheses 1 and 2 we first investigated how the structural parameters of assolidified 0.45%Al-HMS, 2%V-HMS and 4%V-HMS evolve between room temperature and 600 °C using HT-powder XRD on as-solidified materials. The samples are the same as for the measurements shown in figure 4. We chose the timescale of the HTXRD measurements and the exposure time at high temperature (total cycle time: 17 hours, time above 500 °C: 4.5 hours) to be a similar order of magnitude to the timescale over which changes in the electrical properties were measured (see figure 1). The complete set of unit cell parameters are plotted in the supplementary information (Figure S2). Figure 6 shows the evolution of γ as a function of temperature and measurement sequence. In essence, plotting γ(T) is equivalent to characterizing the position of the HMS phase in the temperaturecomposition phase diagram. Figure 6 demonstrates that the HMS phase composition for 0.45%Al-HMS and 2%V-HMS changes during the measurement: the HMS phase is enriched with Si upon heating above about 300 °C, primarily due to a negative expansion coefficient of the silicon sub-lattice in the c-direction during heating, i.e. the Si sub-cell contracts in the c-direction while the Mn subcell expands (see Figure S2, supplementary information). Upon cooling the expansion coefficient of both sub-lattices in the c-direction is similar, γ is stable and the HMS phase composition remains unchanged.

Kikuchi et al. [START_REF] Kikuchi | High temperature X-ray diffraction study on incommensurate composite crystal MnSi -(3+1)-dimensional superspace approach[END_REF] showed that the expansion coefficient of the Si sublattice in the c-direction is higher than that of the Mn sublattice in the temperature range 500-900 °C. This results in the HMS phase becoming more Si-rich upon cooling (see Figure 6) and is in fact the driving force for the formation of MnSi striation precipitates during the cooling of melt-grown HMS crystals as observed by several authors [START_REF] Kawasumi | Crystal growth of manganese silicide, MnSi~1.73 and semiconducting properties of Mn15Si26[END_REF][START_REF] Vivès | Microstructure control and transport properties of incommensurate manganese silicide based alloys for thermoelectricity[END_REF][START_REF] Kojima | Crystal growth of Mn15Si26[END_REF]. We observe MnSi striation precipitates in our as-solidified 0.45%Al-HMS and 2%V-HMS materials, therefore we expect that the γ(T) for these materials is similar in shape to that of Kikuchi et al. [START_REF] Kikuchi | High temperature X-ray diffraction study on incommensurate composite crystal MnSi -(3+1)-dimensional superspace approach[END_REF] above 600 °C. However, in our case these materials are likely not stabilized due to the fast cooling rate between the solidification temperature and room temperature in the RGS process (of the order of 2 °K/s). Thus, during synthesis the HMS phase relaxes only partially upon cooling and γ is kinetically 'locked' to values lower than the thermodynamically stable value. During the XRD measurement and the annealing tests, the HMS phase stabilizes to higher γ values. This explains the changes in MnSi striation morphology and the appearance of MnSi at grain boundaries (Figure 5) for the samples that had a similar exposure time at high temperature. In the 4%V-HMS material, the absence of MnSi striation precipitates suggests that the composition of the HMS phase solidified at high temperature is stable down to room temperature. This is supported by the temperature-independent γ(T) characteristic. These measurements clearly show that stable HMS thermoelectric materials can be obtained by avoiding structural changes between the synthesis temperature and the temperature range of operation in a module. In other words the two sub-lattices should have the same expansion coefficient along the c axis and γ should be independent of temperature. The manipulation of γ(T) can be achieved by adding substitution elements [START_REF] Truong | Thermoelectric Properties of Higher Manganese Silicides[END_REF][START_REF] Hamada | Crystal Structure and Thermoelectric Properties of the Incommensurate Chimney-Ladder Compound VGeγ (γ ~1.82)[END_REF], and we have shown that this approach can be used to stabilize the HMS phase over the room temperature-to-600 °C range. One may further generalise to state that the use of substitution elements that shifts γ to (lower) values close to that at the synthesis temperature helps to prevent the precipitation of MnSi striations. We believe that this also explains the success of using Ge as a substitution element reported by several researchers, although in our case large [Ge] gradients most likely prevent sufficiently high substitution in the intra-grain regions such that MnSi still precipitates [START_REF] Vivès | Microstructure control and transport properties of incommensurate manganese silicide based alloys for thermoelectricity[END_REF][START_REF] Truong | Thermoelectric Properties of Higher Manganese Silicides[END_REF][START_REF] Ivanova | Higher Manganese Silicide Based Materials[END_REF][START_REF] Zhou | Microstructure and thermoelectric properties of SiGe-added higher manganese silicides[END_REF].

To examine the relations between changes in the structure and the electrical resistivity, considering as a first approximation a simple single band model, we compared the room temperature charge carrier density estimated by equations [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF] and [START_REF] Fedorov | Thermoelectrics of Transition Metal Silicides[END_REF] with that measured by the Hall technique, before and after annealing. The results are summarized in Figure 7, which compares the Hall carrier density measured at room temperature on as-solidified materials and on samples annealed for 10 hours at 600 °C in air with the carrier density estimated from the VEC model using the compositions determined from room temperature powder XRD data at the beginning and end of the measurement cycle (data from the samples in Figure 6). In equation ( 1) we use the nominal substitution levels x and y with the assumption that the solubility limit is not exceeded, as confirmed by the absence of aluminium or vanadium silicides (XRD data, Figure 4). Our Hall concentration data fits very well with that recently published by Miyazaki et al. for V-doped samples [START_REF] Hamada | Crystal Structure and Thermoelectric Properties of the Incommensurate Chimney-Ladder Compound VGeγ (γ ~1.82)[END_REF] and with that of Chen et al. for the Al-doped samples [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF]. Figure 7 shows a good correlation between the measured change in carrier density and that predicted by the VEC model. This implies that the structural changes occurring during annealing result in a reduction of the charge carrier density by 20-30%, which is of the same order of magnitude as the decrease in electrical conductivity shown in Figure 3. Thus, the charge carrier mobility was not significantly influenced by the annealing step, and microcrack formation and/or development are likely not responsible for the change in the electrical properties (hypothesis 1). Additional if cracks would appear or develop during annealing one would not expect quantitatively reproducible measurements of the resistivity change. Instead, our measurements support hypothesis 2, i.e. the reduction of the electrical resistivity is the result of loss of charge carriers due to structural changes.

As a final remark we note that in a rigid band picture the reduction in charge carrier density upon annealing will shift the electrochemical potential towards the gap and with that also the Seebeck coefficient is expected to significantly increase (see Appendix). However this is not the case in our measurements. This observation is consistent with the measurements of Chen et al., where Al doping increased the charge carrier density by up to 20% but the Seebeck coefficient was only weakly affected [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF]. We take this as a clear hint on a change of the band structure close to the gap withchanging carrier density. With increased V content we observe a better accordance of the transport properties to a model with higher effective mass which points to flatter bands and, with that a weaker change of the electrochemical potential with carrier density. Clearly, more research is needed to study the effects of the carrier concentration and of the crystal structure ( value) on the band structure and occupancy close to the chemical potential and understand how these parameters influence the Seebeck coefficient of HMS materials.

Thermoelectric performance

We now focus on the thermoelectric performance of the HMS materials. Based on the results discussed in the previous section we chose to compare the thermoelectric properties of the materials after annealing for 10 hours at 600°C in air in order to reduce the effect of high temperature instabilities and compare the materials on a fairer basis. The low temperature Hall measurements and the high temperature thermoelectric properties are reported in figure 8. Note that the Hall data, the high temperature resistivity and Seebeck coefficient data reported in figure 8, and the electrical properties reported in figure 1 and figure 3 agree within measurement error even though different measurement setups were used. Despite our efforts to reduce the instabilities by pre-annealing, the electrical resistivity data between room temperature and 700°C clearly show that the electrical properties are not stabilized for all materials: the resistivity still increases during the measurement for Ge and Al-doped HMS. This is consistent with our observation that the resistivity still increases after 10 hours at 600 °C (figure 1 and figure 3) for these materials. However, the 3%Re-HMS show a resistivity decrease during the measurement: this contradicts our data in figure 1 and figure 3. The hysteresis behavior of the resistivity of this material could be related to a slow kinetics of γ change following the temperature-time profile of the measurement with a delay. If for 2%V-HMS γ(T) behaves qualitatively as the undoped sample of Kikuchi et al. [START_REF] Kikuchi | High temperature X-ray diffraction study on incommensurate composite crystal MnSi -(3+1)-dimensional superspace approach[END_REF] above 600 °C (figure 6), delayed γ changes would result in a hysteresis in the carrier density (hence in the resistivity) consistent with the measurement. The 4%V-HMS is stable during the high temperature measurements, which is consistent with the stability study.

Figure 8 shows that the V-doped HMS samples have significantly different electrical properties to the Al, Ge and Re-doped materials. The higher hole concentration of 2%V and 4%V HMS compared to the other materials is the result of the stability of V in the structure, while the other materials seem to stabilize at a carrier concentration of about 1.64 × 10 27 m -3 at 300 K (figure 8). Perhaps unexpected is the observation that the carrier concentration of the V-doped HMS materials increases with increasing temperature: unless very close to 0 K p-type thermoelectric materials typically possess a filled valence band and one does not expect this behaviour. This may be the result of impurity levels in the band gap. The Hall measurements also show a significantly lower charge carrier mobility for the V-doped materials, and a different temperature dependence. The Al, Ge and Re-doped materials all have the typical temperature dependence µ L ∝ T -1.5 demonstrating that latticephonon scattering is the dominant limiting factor for carrier transport, as also concluded from measurements on undoped or lightly doped HMS materials by other authors [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF][START_REF] Fedorov | Thermoelectrics of Transition Metal Silicides[END_REF]. The mobility of the V-doped materials is nearly an order of magnitude lower and varies with temperature as µ ∝ T -0.5 . Contrary to the Al, Ge and Re-doped materials for which the resistivity vanishes when the temperature tends to 0 K (confirming the phonon-limiting behaviour of the electrical transport), the resistivity of the V-doped materials remains significant at temperatures close to 0 K. Overall the temperature dependence of the Seebeck coefficient and of the electrical resistivity is significantly less strong for the V-doped materials. This is precisely the nearly temperature-independent resistivity that confers the superior figure of merit for the 4%V-HMS material. Finally we note that the charge carrier concentration and mobility of the Ge and V-doped samples have comparable value as that of arcmelted samples with similar substitution levels recently published by Miyazaki et al. [START_REF] Hamada | Crystal Structure and Thermoelectric Properties of the Incommensurate Chimney-Ladder Compound VGeγ (γ ~1.82)[END_REF]. The lower mobility of V-doped HMS materials, their different temperature dependence and higher charge carrier density suggests that ionized impurity scattering is an additional limitation to the transport properties of these materials compared to the Al, Ge, and Re-doped materials. In general, the scattering time dominates the temperature dependence of the mobility (µ(T) ∝ (e/m) τ(T) where e and m are the electron charge and mass, respectively). The scattering time for ionized impurities scales as τ i ∝ T 1.5 , and that of phonons as τ L ∝ T - 1.5 . When both effects occur simultaneously the total scattering time τ will follow Matthiessen's rule as:

= + (3)
Equation ( 3) implies that in the case of mixed scattering the temperature exponent of τ varies between -1.5 and 1.5, which is the case for the V-doped samples. Based on these observations we choose to use the mixed scattering single parabolic band model of Fistul to describe the behaviour of the V-doped materials [START_REF] Fistul | Heavily Doped Semiconductors[END_REF]. The mobility depends on both the scattering time for acoustic vibrations τ L = τ 0L ε -1/2 and the scattering time for ionized impurities τ i = τ 0i ε 3/2 where ε is the reduced carrier energy. Using equation (3) the total scattering time can be written as τ = τ oL ε 3/2 / ( ε 2 + a 2 ) , where the scattering index a = √ τ oL / τ oi is a measure of the strength of ionized impurity scattering relative to acoustic phonon scattering. In this framework the electrical properties can be written as follows:

! ", $) = %& ' * ) ) *+ * ), -.) * ) /, 0 * ", $) (4)
", $) = , -1 0 ",$) 0 * ",$) -23 (5)
= & 4

)' * , -.

+ ) 5 * ) 6 ) ") (6) 7 =
) *' * /, 0 * ",$) 6

) ")

0 8 ", $) = 9 : 8 ;< = : ")

: ) >$ ) ) >;< = : ") ) ?@ A / (8)
Here F 1/2 (η) is the Fermi integral of order ½. η, m*, k B , h are the reduced Fermi energy, the density of states effective mass, Boltzmann coefficient and Planck constant respectively. It is assumed that the density of states effective mass is equal to the mobility effective mass. This model is an extension of the more commonly used single parabolic band model where only acoustic phonon scattering is considered [START_REF] May | Introduction to Modeling Thermoelectric Transport at High Temperatures[END_REF] (limiting case a = 0). This mixed scattering model has also been used by several authors to describe the superior properties of highly substituted skutterudites [START_REF] Wang | On Intensifying Carrier Impurity Scattering to Enhance Thermoelectric Performance in Cr-Doped Ce y Co 4 Sb 12[END_REF][START_REF] Dyck | Thermoelectric properties of the ntype filled skutterudite Ba0.3Co4Sb12 doped with Ni[END_REF]. We solved the set of equations [4]- [START_REF] Ghodke | Effect of grain boundaries and partial substitution of transition metals on thermoelectric properties of higher manganese silicide[END_REF] numerically for two sets of { m* ; a }to illustrate the differences between the 4%V-HMS and the Re, Ge and Al substituted materials. We assumed that [p] is temperatureindependent and chose the value measured at room temperature to estimate η T) (equation ( 6)). First, we fit the model to the data of the Re, Ge and Al-doped samples using a = 0 (τ i → ∞ negligible ionized impurity scattering) and [p] = 1.64 × 10 27 m -3 (as measured at room temperature). Using the Seebeck coefficient data and equation [START_REF] Skomedal | Design, assembly and characterization of silicide-based thermoelectric modules[END_REF] we obtain m* = 7.5 m 0 from equation ( 6), a value similar to that previously published [START_REF] Chen | Effects of (Al,Ge) double doping on the thermoelectric properties of higher manganese silicides[END_REF]. τ oL is estimated by fitting the mobility data, resulting in τ = τ oL = 19.2 fs at room temperature. The same value of τ oL is used for V-doped samples since there is a priori no reason that phonon scattering affects the electrical transport properties differently for V-doped samples and Al, Ge and Re-doped materials. However, to reproduce the specific features of the data of Vdoped HMS it is necessary to introduce ionized impurity scattering (i.e. D > 0). Using m* = 10.5 m 0 and a (300K) = 4.3 ( τ i (300K) = 1 fs ), the model reproduces the room temperature data of 4%V-HMS well. Figure 8 shows that the essential differences between the V-doped samples and the Al, Ge and Re-doped samples are well described by introducing ionized impurity scattering. Especially the significant differences in the temperature dependence of the mobility, the low temperature resistivity data and the high temperature Seebeck coefficient data (at temperatures below about 450°C) are well reproduced: the mobility scales as µ ∝ T -0.5 , the resistivity does not vanish towards 0 K, and the temperature dependence of S(T) is less pronounced. However, while the model qualitatively predicts that the resistivity of V-doped materials becomes lower than that of the other samples at high temperature, there is a significant discrepancy between the values predicted by the model and the measurements.

The thermal conductivity of 4%V-HMS is significantly lower than that of the other samples. Since this material also has a lower electrical resistivity, the electrical contribution to the thermal conductivity should be higher: this means that the lattice contribution to the thermal conductivity overcompensates the higher electrical contribution. Although this effect should be studied in more detail, we hypothesize that this may be the result of an alloy scattering effect. Overall, the significantly higher ZT of 4%V-HMS is the result of the improved power factor and lower thermal conductivity. ZT max =0.52 is estimated for this material. Most importantly, this material is also stable at high temperature, in contrast to the Al, Ge, Re-doped samples and the 2%V-HMS material.

Conclusions

On the basis that the performance of thermoelectric materials should remain stable under relevant device temperature conditions, we have used several procedures to measure the structural and thermoelectric stability of HMS materials substituted with different elements. We demonstrate that most HMS materials prepared by the RGS technique have a temperature-dependent γ factor and are structurally and electrically unstable at 600°C. Specifically, structural changes result in the formation of MnSi precipitates and reduction of the charge carrier concentration of a magnitude comparable with the electrical conductivity decrease. Therefore we conclude that the structural changes are responsible for the unstability. By substituting 4% of Mn by V the γ factor then becomes temperature independent in the range of interest, resulting in the prevention of MnSi precipitate formation and stable electrical properties when exposed to 600°C for up to 45 h. As a topic for future research, it would be interesting to confirm the structural stability of this material up to the melting point.

The 4%V-HMS material also exhibits the highest ZT. This is in part due to its thermal stability, but also because ionized impurity scattering effects mitigate the reduction of the Seebeck coefficient due to the higher charge carrier concentration. In combination with a lowered thermal conductivity, the estimated ZT of this material reaches state-of-the-art values. • Thermoelectric alloys MnSi ~1.74 were solidified by a new synthesis technique • Long-term high temperature stability is characterized • Al, Ge and Re doped materials are neither structurally nor electrically stable • 4% V substitution stabilizes the (micro)structure and electrical properties • Vanadium-doped higher manganese silicide reaches state-of-the art ZT=0.52

Figures and captions

Figure

  Figure 1. (Color Online) Seebeck coefficient and electrical resistivity as a function of time at high temperature (600 ˚C) in inert gas (measurements Uni Groningen). The samples were as-solidified prior to the measurement.

  Figure 1. (Color Online) Seebeck coefficient and electrical resistivity as a function of time at high temperature (600 ˚C) in inert gas (measurements Uni Groningen). The samples were as-solidified prior to the measurement.

Figure 2 .

 2 Figure 2. (Color Online) Seebeck coefficient and electrical conductivity of as-grown materials (points at start of arrows) and materials after 10 h annealing at 600°C (points at end of arrows). The curved lines are power factor isolines. Uni Groningen data are taken from Figure 1, CEA and Uni Twente data are taken from Supplementary information -Figure S1. DLR data (after 10 h) are taken from figure 8 (average between temperature ramp up and ramp down).

Figure 3 .

 3 Figure 3. (Color Online) Seebeck coefficient and electrical conductivity of as-grown materials (points at start of arrows) and materials annealed for 10 h (second points along arrows) and 100 h (points at ends of arrows) in air at 600°C. The curved lines are power factor isolines. Each data point corresponds to the average of 3 to 5 replicated measurements. The 3 measurement points for 4%V-HMS overlap within the measurement error.

Figure 4 .

 4 Figure 4. Room temperature XRD measurements of as-solidified (a) 2%V-HMS, (b) 0.45%Al-HMS, and (c) 4%V-HMS.

Figure 5 .

 5 Figure 5. (Color Online) Optical microscopy images of polished cross sections of 0.45%Al-HMS (upper set) and 4%V-HMS (lower set). The solidification direction is from bottom to top on all images. Pictures are taken under polarized light at low magnification (top) and high magnification (bottom -regions corresponding to the black inset frames above). As-solidified samples are shown on the left and annealed samples (10 h at 600 °C in air) on the right. All cross sections were submitted to a MnSi etch to reveal the presence of the MnSi phase.

Figure 6 .

 6 Figure 6. (Color Online) γ(T) structural parameter for as-solidified HMS materials measured by HTXRD. The arrows show the evolution of γ upon heating (↑) and cooling(↓). The data of Kikuchi et al.[13] for undoped HMS prepared by arc melting is shown for comparison and discussion purposes.

Figure 7 .

 7 Figure 7. (Color Online) Effect of annealing on the charge carrier density of 0.45%Al-HMS, 2%V-HMS, and 4%V-HMS. Hall measurements (vertical axis) are compared to the carrier density estimated from the VEC model (horizontal axis). The straight line corresponds to y=x.

Figure 8 .

 8 Figure 8. (Color Online) Low temperature (left) and high temperature (right) thermoelectric properties of HMS materials produced by the RGS process containing different substitution elements. All materials were annealed for 10 hours at 600 °C in air prior to the measurements. Materials doped with Ge, Al and Re have not reached a stable state after this thermal treatment. The coloured arrows in the high temperature resistivity plots show the data acquisition sequence during heating and cooling. Dashed black lines are model results for different effective masses m* and scattering parameters a at 300 K.

Acknowledgements

This work is partly financially supported by Rijksdienst voor Ondernemend Nederland (RVO) under project HEAT (ID: IK14062).

The authors would like to thank Przemyslaw Blaschkewitz for his help with the measurement of transport properties done at DLR.

Appendix

For example, taking the Hall carrier concentration data for 0.45%Al-HMS (figure 7) and using the single parabolic band model at 300K (equations ( 4)-( 8) with a = 0, m* = 7.5 m 0 ), one finds that the carrier concentration change during the 10 h annealing step corresponds to a decrease in electrical conductivity from 90 × 10 4 S/m to 70 × 10 4 S/m (-22% -note that the absolute values fit the data of figure 3 fairly well) and to an increase of the Seebeck coefficient from 83µV/K to 101µV/K (+22%, whereas measurements show a change from 110 µV/K to 100µV/K, i.e. -9%).

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:


Minh-Quan Le

Jean-Christophe Gimel

Xavier Garric

Thao-Quyen Nguyen-Pham

Cédric Paniagua

Jérémie Riou

Marie-Claire Venier-Julienne
email: marie-claire.venier@univ-angers.fr

MODULATION OF PROTEIN RELEASE FROM PENTA-BLOCK COPOLYMER MICROSPHERES

Keywords: protein sustained release, penta-block copolymer, microsphere, microencapsulation, release modulation PLGA, poly(D,L-lactic-co-glycolic acid), PLA, Polylactic acid, MS, microsphere, PEO, poly(ethylene oxyde), PPO, poly(propylene oxyde), scanning electron microscopy, DSC, differential scanning calorimetry, Tg, glass transition temperature, EE, encapsulation efficiency, BSA, Bovine serum albumin, IQR, interquartile range, PEO, polyethylene oxyde

Releasing a protein according to a zero-order profile without protein denaturation during the polymeric microparticle degradation process is very challenging. The aim of the current study was to develop protein-loaded microspheres with new PLGA based pentablock copolymers for a linear sustained protein release. Lysozyme was chosen as model protein and 40 µm microspheres were prepared using the solid-in-oil-in-water solvent extraction/evaporation process. Two types of PLGA-P188-PLGA penta-block copolymers were synthetized with two PLGA-segments molecular weight (20 kDa or 40 kDa). The resulting microspheres (50P20-MS and 50P40-MS) had the same size, an encapsulation efficiency around 50-60% but different porosities. Their protein release profiles were complementary: linear but non complete for 50P40-MS, non linear but complete for 50P20-MS. Two strategies, polymer blending and microsphere mixing, were considered to match the release to the desired profile. The (1:1) microsphere mixture was successful. It induced a bi-phasic release with a moderate initial burst (around 15%) followed by a nearly complete linear release for 8 weeks. This study highlighted the potential of this penta-block polymer where the PEO block mass ratio influence clearly the Tg and consequently the microsphere structure and the release behavior at 37°C. The (1:1) mixture was a starting point but could be finely tuned to control the protein release.

INTRODUCTION

During the past two decades, there has been a great interest in controlled release of drugs particularly for therapeutic proteins. Proteins are usually injected so it is crucial to reduce the frequency of the injections, to increase the confort and patient compliance [START_REF] Patel | Recent Advances in Protein and Peptide Drug Delivery: A Special Emphasis on Polymeric Nanoparticles[END_REF][2] [START_REF] Dipak | Delivery of Therapeutic Proteins[END_REF].

Many approaches have been proposed to carry and deliver protein following continuous and sustained manners. Among those, protein encapsulation in microspheres using biodegradable and biocompatible polymers such as poly(D,L lactide-co-glycolide) (PLGA) [START_REF] Pagels | Polymeric nanoparticles and microparticles for the delivery of peptides, biologics, and soluble therapeutics[END_REF] were often used to control the release over several weeks. However protein sustained delivery from PLGA-based microspheres (MS) is still a challenge due to the variety of protein native structures, their instability particularly during the polymer degradation [START_REF] Mohammadi-Samani | PLGA micro and nanoparticles in delivery of peptides and proteins; problems and approaches[END_REF], and their very low diffusivity into PLGA matrixes [START_REF] Fredenberg | Measurement of protein diffusion through poly(D,L-lactide-Co-glycolide)[END_REF]. To limit this drawback, a central hydrophilic segment such as poly(ethylene oxyde) (PEO) was polymerized with PLGA to obtain a polymer triblock [START_REF] Kissel | ABA-triblock copolymers from biodegradable polyester Ablocks and hydrophilic poly(ethylene oxide) B-blocks as a candidate for in situ forming hydrogel delivery systems for proteins[END_REF][8] [START_REF] Feng | Effects of drug and polymer molecular weight on drug release from PLGA-mPEG microspheres[END_REF][10] [START_REF] Patel | PEG-PLGA based large porous particles for pulmonary delivery of a highly soluble drug, low molecular weight heparin[END_REF]. The protein release from A-B-A type triblock was enhanced as the presence of hydrophilic segments in multi-block copolymers facilitated the microsphere swelling during the release and provided protein diffusion pathways [START_REF] Kissel | ABA-triblock copolymers from biodegradable polyester Ablocks and hydrophilic poly(ethylene oxide) B-blocks as a candidate for in situ forming hydrogel delivery systems for proteins[END_REF] [START_REF] Buske | Influence of PEG in PEG-PLGA microspheres on particle properties and protein release[END_REF]. But an incomplete release was still observed due to the degradation of the entrapped protein into the microsphere core [START_REF] Tran | Protein-loaded PLGA-PEG-PLGA microspheres: A tool for cell therapy[END_REF]. In addition, it was shown that by adding free poloxamer in the formulation, the protein degradation [Ref to add] and its adsorption on PLGA were reduced [START_REF] Giteau | Reversible protein precipitation to ensure stability during encapsulation within PLGA microspheres[END_REF] [START_REF] Paillard-Giteau | Effect of various additives and polymers on lysozyme release from PLGA microspheres prepared by an s/o/w emulsion technique[END_REF]. In that respect, to modulate both the hydrophilic/hydrophobic balance of the polymer and improve the protein stability, a penta-block was synthetized by copolymerizing PLGA with amphiphilic triblock polymers such as poloxamers [START_REF] Le | Penta-block copolymer microspheres: Impact of polymer characteristics and process parameters on protein release[END_REF] [START_REF] Morille | New PLGA-P188-PLGA matrix enhances TGF-beta3 release from pharmacologically active microcarriers and promotes chondrogenesis of mesenchymal stem cells[END_REF].

In the literature, many efforts have been made to develop different strategies to modulate the protein release profile. Most of them relied on polymer blend strategies [START_REF] Liggins | Paclitaxel-loaded poly(L-lactic acid) microspheres 3: blending low and high molecular weight polymers to control morphology and drug release[END_REF][19] [START_REF] Liu | Highly bioactive, bevacizumab-loaded, sustained-release PLGA/PCADK microspheres for intravitreal therapy in ocular diseases[END_REF] [START_REF] Gu | Prediction of dexamethasone release from PLGA microspheres prepared with polymer blends using a design of experiment approach[END_REF], whereas the strategy of mixing different types of PLGA-based microspheres was rarely addressed. Nevertheless, releasing a protein according to a zeroorder profile without protein denaturation during the polymer degradation process is still very challenging.

The aim of the current study was to modulate the protein release from the penta-block copolymer microspheres. Lysozyme was chosen as a model protein [START_REF] Van Der Walle | An overview of the field of peptide and protein delivery[END_REF] and 40 µm microspheres were prepared using the solid-in-oil-in-water (S/O/W) solvent extraction/evaporation process [START_REF] Le | Penta-block copolymer microspheres: Impact of polymer characteristics and process parameters on protein release[END_REF]. Penta-block copolymers were synthetized with two PLGA-segments molecular weight (20 kDa or 40 kDa). Various strategies (i.e. polymer blending, microsphere mixing) were also considered to modify the release profile while maintaining the completion of the protein release over 8 weeks. The proposal of a strategy to achieve a complete active protein release from microspheres with the desired profile was the main contribution of this study.

MATERIALS AND METHODS

Materials

Lysozyme (chicken egg white) and its substrate Micrococcus lysodeikticus, glycofurol, dimethylformamide (DMF), methylene chloride (DCM), acetone, and trizmabase (Tris) were purchased from Sigma-Aldrich (Saint-Quentin Fallavier, France). Poloxamer (P188, Pluronic ® F68) was obtained from BASF (Levallois-Perret, France). D,L-lactide and glycolide were purchased from Corbion (Gorinchem, The Netherlands). Polyvinyl alcohol (Mowiol ® 4-88) was supplied by Kuraray Specialities Europe (Frankfurt, Germany). Tin(II) 2-ethylhexanoate (Sn(Oct) 2 , 95%), dichloromethane (DCM), diethyl ether, tetrahydrofuran (THF), chloroform (CHCl 3 ) were purchased from Sigma-Aldrich (St-Quentin Fallavier, France).

The poloxamer 188 (P188) is a commercial tri-block copolymer of PEO and poly(propylene oxyde) (PPO) with general formula HO(C 2 H 4 O) 80 (C 3 H 6 O) 27 (C 2 H 4 O) 80 H [START_REF] Rowe | Handbook of Pharmaceutical Excipients[END_REF]. Two penta-block copolymers (named 50P20 and 50P40) were synthesized by ringopening polymerization of D,L lactide and glycolide from P188 as initiator. Typically, 5g of P188 and various amounts of D,L-lactide and glycolide (respectively 25 and 20.1 g for the 50P40 and 13 and 10.1 g for the 50P20) were introduced into two flasks, then were vacuum dried for 24h. Tin (II)-2 ethylhexanoate (0.1% of the number of hydroxyl functions of P188) was added in dried polymerization flasks. After degassing, the flask was sealed under vacuum and polymerization was carried out at 130°C for 5 days. The copolymers were recovered by dissolution in dichloromethane and precipitated in cold ethanol. The precipitated copolymers were filtered and dried under reduced pressure up to constant weight. The composition of copolymers was investigated by nuclear magnetic resonance spectroscopy (1H-NMR spectroscopy) at room temperature with an AMX300 Bruker  spectrometer (300 MHz), using DMSO as a solvent and trimethylsilane as the internal standard. The dispersity (Ð) was determined by size exclusion chromatography (SEC, Shimadzu  , Japan) using two mixed medium columns PLgel 5 µm MIXED-C (300 × 7.8 mm), a Shimadzu  RI detector 20-A and a Shimadzu  UV detector SPD-20A (270 nm) (40°C thermostatic analysis cells). Tetrahydrofuran (THF) was the mobile phase with 1 mL/mn flow at 30°C (column temperature).

The general formula of the resulting penta-block copolymer is (PLGA-PEO-PPO-PEO-PLGA). The PLGA segments contained 25% D-lactic units, 25% L-lactic units and 50% glycolic units. The penta-block copolymer 50P40 was composed of one central segment of P188 (Mn=8,400 g/mol) and two segments of PLGA (Mn=40,000 g/mol each) at the ends, the copolymer average molecular mass (Mn) was 88,400 g/mol (Ð=1.72). The penta-block copolymer 50P20 was composed of one central segment of P188 (Mn=8,400 g/mol) and two segments of PLGA (Mn=20,000 g/mol each) at the ends, the copolymer average molecular mass was (Mn) 48,400 g/mol (Ð=1.51).

Microsphere preparation 2.2.1. Preparation of 50P40-MS or 50P20-MS

Copolymer microspheres (50P40-MS and 50P20-MS) were prepared as described previously (called thereafter the standard procedure) [START_REF] Tran | Protein-loaded PLGA-PEG-PLGA microspheres: A tool for cell therapy[END_REF]. The theoretical protein loading was 0.6% (w/w). Briefly, lysozyme and P188 (ratio lysozyme/P188 1/10 (w/w)) were dissolved in water. Then 3.12 g of glycofurol were introduced in the solution to form a suspension. After an incubation at 4°C for 30 min, the nanoprecipitated protein was recovered by centrifugation (10,000 g, 4°C, 30 min). The precipitated protein was dispersed in 2 mL solution of dichloromethane/acetone 3/1 (v/v) containing 150 mg of penta-block copolymer. The suspension was emulsified in 90 mL PVA (6% w/v) at 1°C and mechanically stirred at 1,000 rpm for 1 min in a glass vessel (4.5 cm inside diameter) with a dual wall to control the temperature. 100 mL of cold deionized water were then added and the emulsion was stirred for 10 min more. Then, the emulsion was poured into a second glass vessel (10 cm inside diameter, with a dual wall) containing 500 mL of deionized water (1°C) and stirred continuously at 550 rpm during 20 min to extract the solvent. In all steps, an overhead stirrer with a 4 blades propeller was used (Heidolph  RZR 2041, Schwabach, Germany). Finally, microspheres were recovered by filtration on a 5 μm filter (HVLP type, Millipore SA, Guyancourt, France), washed, freeze-dried and stored at -20°C.

Preparation of microspheres using polymer blend

The formulation process was similar to the standard procedure describe above. The mixture of lysozyme and P188 was nanoprecipitated in glycofurol using the same protocol. In this case, a physical blend of 50P40 and 50P20 copolymers (with a weight ratio 1/1) was dissolved in DCM/acetone (3/1, v/v). The nanoprecipitated protein was dispersed in a 2 mL solvent mixture containing 150 mg of the copolymer blend. Later on, the emulsification and solvent extraction/evaporation steps were performed using the standard procedure described above.

Strategy of batch mixing following the preparation of microspheres

The 50P40-MS and 50P20-MS were prepared separately following the standard procedure.

Then, equal amounts of 50P40-MS and 50P20-MS (15 mg) were suspended in 1 mL of water. The mixture was gently mixed using the vortex prior to be freeze-dried. The resulting microsphere mixture (50P40-MS/50P20-MS 1/1, w/w) was stored at -20°C for further study.

Microsphere characterization 2.3.1. Microsphere morphology and mean size

The microsphere mean size was measured using a Coulter ® Multisizer (Coultronics, Margency, France). Microspheres were dispersed in an isotonic saline solution prior to be analyzed (Isoton  II solution, Coultronics, Margency, France).

Microsphere surface morphology was observed using scanning electron microscopy -SEM (JSM 6310F, JEOL, Paris, France). Freeze-dried microspheres were mounted onto metal stubs using double-sided adhesive tape, vacuum-coated with a film of carbon using a MED 020 (Bal-Tec, Balzers, Lichtenstein) before being analyzed. The microsphere internal morphology was studied using the following process [START_REF] Le | Penta-block copolymer microspheres: Impact of polymer characteristics and process parameters on protein release[END_REF]. An appropriate amount of microspheres was dispersed into 1 mL of Tissue-Tek ® (Sakura Finetek, USA) and freezed (-20°C, 1 hour). Resulting blocks were cut into slices (20 µm-thickness) at -15°C using a micro-cutting device (Leica, Nanterre, France). Slices were rinsed three times with cold water (1°C) before being freeze-dried. Samples were then analyzed by SEM as described above.

Glass transition temperature of the copolymers

To measure the glass transition of raw copolymers and microspheres, differential scanning calorimetry (DSC) analysis was carried out. DSC measurements were performed under nitrogen on a Perkin-Elmer Instrument DSC 6000 thermal analyzer. Samples were subject to a first heating ramp from -50°C to 200°C (10°C/min), followed by a cooling step (10°C/min) and finally a second heating ramp from -50°C to 200°C (10°C/min) was performed to measure the glass transition temperature (Tg).

Protein encapsulation efficiency

The amount of entrapped lysozyme was determined by dissolving 5 mg of microspheres in 0.9 mL DMF in a silanized glass tube at room temperature under agitation (1 hour). Then, 3 mL of a Tris solution (Tris 0.05 M buffer and 0.09% w/v NaCl, pH 7.4) was added and the agitation was carried on for 1 hour more. The resulting solution was introduced into a Micrococcus lysodeikticus test for active lysozyme quantification as described previously [START_REF] Le | Penta-block copolymer microspheres: Impact of polymer characteristics and process parameters on protein release[END_REF]. The protein encapsulation efficiency (EE) was determined in triplicate.

In vitro release of active lysozyme from microspheres

5 mg of lysozyme-loaded microspheres were dispersed in 375 µL of buffer solution (Tris 0.05 M buffer, pH 7.4, containing 0.1% w/v BSA and 0.09% w/v NaCl) [START_REF] Aubert-Pouëssel | A novel in vitro delivery system for assessing the biological integrity of protein upon release from PLGA microspheres[END_REF] using 1.5 mL polyethylene microtubes (Eppendorf type). The suspension was incubated in a water bath at 37°C and oscillated on a rack at 125 rpm. At defined time intervals, tubes were removed and centrifuged for 5 min at 3,000 g. The supernatant was collected, tested for active lysozyme quantification and replaced by fresh buffer. Release profiles were determined on at least 3 different microsphere batches and for each one, at least 3 experiments were carried out.

To investigate the effect of the release temperature on the microsphere morphology, release tests were carried out in a similar way but the water bath was controlled at 22°C or placed in a 4°C cold chamber.

Microsphere morphology change during the release test

15 mg of lysozyme-loaded microspheres were dispersed into 1,050 µL of buffer solution (Tris 0.05 M buffer, pH 7.4, containing 0.1% w/v BSA and 0.09% w/v NaCl) in 1.5 mL polyethylene microtubes (Eppendorf type). The suspension was incubated in a water bath at 37°C and oscillated on a rack at 125 rpm. After a defined duration, tubes were centrifuged for 5 min at 3,000 g. The supernatant was removed and the remaining particles were washed 3 times with cold water (1°C) before being freeze-dried. For microsphere cross-sectional observations, microspheres were cut and analysed with SEM as described above.

Statistical Analysis

The quantitative variables were described using the mean +/-95% confident interval when variable distribution was normal, and otherwise using median and Inter-Quartile Range.

Both batches and samples were taken into account to assess the global variability of the process. In view of the observation, a non-parametric Mann-Whitney test was performed when necessary.

RESULTS AND DISCUSSION

Glass transition temperature

The glass transition temperature (Tg) of raw copolymers (table 1) was 24.3°C for 50P40 and 9.6°C for 50P20. Both values were smaller than the ones reported in the literature for bulk PLGA where Tg varies from around 50°C for 40kDa to around 40°C for 20kDa PLGA [START_REF] Omelczuk | The Influence of Polymer Glass Transition Temperature and Molecular Weight on Drug Release from Tablets Containing Poly(DL-lactic Acid)[END_REF]. In a previous study, it was shown that when PLGA blocks were copolymerized with a central PEO blocks, the resulting triblock Tg decreased noticeably as the relative amount of the hydrophilic block was increased [START_REF] Tran | Protein-loaded PLGA-PEG-PLGA microspheres: A tool for cell therapy[END_REF]. This was also observed in the present study where the relative amount of PEO increased from 9.5% (w/w) in 50P40 to 17% (w/w) in 50P20. Decreases of Tg were mainly due to plasticizing effects provided by the PEO block [START_REF] Santovena | Structural properties of biodegradable polyesters and rheological behaviour of their dispersions and films[END_REF].

Besides, Tg values of uncharged lyophilized microspheres were very closed to those of raw copolymers. It is known from the literature that the surfactant, especially PVA due to its hydroxyl groups [START_REF] Rouse | Physical ageing and thermal analysis of PLGA microspheres encapsulating protein or DNA[END_REF], and residual solvents like DCM [START_REF] Vay | A detailed view of microparticle formation by in-process monitoring of the glass transition temperature[END_REF] can significantly impact Tg values. Then, it can be assumed a good elimination of PVA and residual solvents during the process.

On the other hand, the co-encapsulated poloxamer lowered the Tg values of microspheres, the effect being more pronounced for 50P20-MS where Tg fell from 9.1°C to 5.5°C.

Incorporating the lysozyme enhanced these phenomena. Plasticizing effects of additives like pegylated compounds or proteins have been widely reported in the literature [START_REF] Fredenberg | The mechanisms of drug release in poly(lactic-co-glycolic acid)-based drug delivery systems--a review[END_REF] [START_REF] Wang | Controlled release of sirolimus from a multilayered PLGA stent matrix[END_REF].

These observations were important to explain the morphology of microspheres formulated at 1°C and their behaviors during the protein release process at 37°C. In this work, Tg were measured on dry (lyophilized) products. But it is known that hydrated products, especially porous ones, display lower Tg [START_REF] Passerini | An investigation into the effects of residual water on the glass transition temperature of polylactide microspheres using modulated temperature DSC[END_REF]. Any how it was reasonable to assume that hydration should not modify our conclusions as the Tg of hydrated 50P20-MS should still be lower than the one of hydrated 50P40-MS.

[Table 1] Glass transition temperatures of different copolymers.

Morphology, mean size and encapsulation efficiency

Both types of microspheres were formulated below the glass transition temperature of their constitutive copolymer. For 50P40, the microsphere formation took place at 5% below Tg. They exhibited smooth surface with no visible pores. Their internal structure was porous with closed small pores distributed uniformly in the volume (Figure 1A). For 50P20, the microsphere formation took place at 1% below Tg. They were highly porous with numerous interconnected pores visible on the surface as well as in the interior (Figure 1B).

During the solvent/cosolvent extraction step, the phase separation occurs into the initial polymer solution droplets with coexisting polymer rich and polymer poor phases. The further removal of solvent induces the glass transition in the polymer rich phase, and the microsphere solidification comes to an end. The phase transition kinetics becomes arrested as the glassy state is reached in the dense polymer phase while the polymer poor phase will form the future pores in the microsphere structure. The competition between the ongoing phase separation and the appearance of the glassy state has been described and modeled in the literature [START_REF] Li | Kinetic and thermodynamic modeling of the formation of polymeric microspheres using solvent extraction/evaporation method[END_REF][33] and could explain the structural differences observed. 50P40-MS reached the glassy state faster than 50P20-MS and consequently developed less porous structures compared to 50P20-MS.

The median particle size and the interquartile range [IQR] of 50P40-MS were respectively 39.0 µm [38.7, 41.2] and 38.3 µm [37.6, 41.5] for 50P20-MS (Figure 1C). Encapsulation efficiency (EE) values ranged from 52 to 61% regardless the copolymers used (Figure 1C). Both types of microspheres were not significantly different considering their size (p = 0.4681) and their encapsulation efficiency (p = 0.6501). This result may be due to a statistical lack of power (the sampling was too small) or to the absence of real differences in the size or EE of 50P20-MS and 50P40-MS.

The rather low encapsulation yield can be attributed to the leakage of the protein into the external aqueous phase during the microparticle formation [START_REF] Fu | Effects of formulation factors on encapsulation efficiency and release behaviour in vitro of huperzine A-PLGA microspheres[END_REF] [START_REF] Luan | Key parameters affecting the initial release (burst) and encapsulation efficiency of peptide-containing poly(lactide-co-glycolide) microparticles[END_REF].

Protein release profiles

Drug release from PLGA-based microspheres can follow mono-, bi-or tri-phasic profiles depending on various factors including the hydrophilic balance or their morphology [START_REF] Fredenberg | The mechanisms of drug release in poly(lactic-co-glycolic acid)-based drug delivery systems--a review[END_REF].

Polymer characteristics (Tg), porosity and mean particle size are recognized as critical factors for the protein release profile from PLGA-based microspheres [START_REF] Siepmann | Effect of the size of biodegradable microparticles on drug release: experiment and theory[END_REF] [START_REF] Klose | How porosity and size affect the drug release mechanisms from PLGA-based microparticles[END_REF]. In the present study, the microsphere diameter was kept constant to avoid its impact on the profile. The active protein release from 50P40-MS (dense surface/porous interior; Figure 1A) was carried out during 8 weeks and compare to 50P20-MS (porous surface/porous interior; Figure 1B).

[Figure 2] Average protein release profiles from microspheres of copolymer 50P20 (triangles) and copolymer 50P40 (squares). Error bars represent 95% confident intervals of mean values (n=24 for 50P20 and n=10 for 50P40). The dashed line is a guide to the eyes, it figures out the ideal desired profile.

Figure 2 shows release profiles for both 50P40-MS and 50P20-MS. Lysozyme release from 50P40-MS complied with a bi-phasic profile with a moderate burst (11.2% ± 1.3% released after 24 hours). The release was then sustained and linear until Day 56 but the cumulated amount was 53.8% ± 6.2% only. Despite a highly porous surface and a porous internal structure, 50P20-MS exhibited a biphasic protein release with also a moderate burst after 24 hours (15.2% ± 1.1%), followed by a sustained and complete release (ending-up with 93.4% ± 3.1% of active lysozyme released) but not linear as emphasized by the dashed line in figure 2.

For protein loaded microspheres, a bi-phasic release profile is commonly achieved with porous microspheres [START_REF] Klose | How porosity and size affect the drug release mechanisms from PLGA-based microparticles[END_REF] [START_REF] Boukari | Physicomechanical properties of sintered scaffolds formed from porous and protein-loaded poly(DL-lactic-co-glycolic acid) microspheres for potential use in bone tissue engineering[END_REF] or with microspheres having non-porous surface but porous internal structure [START_REF] D'aurizio | Preparation and characterization of poly(lacticco-glycolic acid) microspheres loaded with a labile antiparkinson prodrug[END_REF]. The mechanism of drug release from PLGA is impacted by both the diffusion process and the polymer erosion [START_REF] Sackett | Mathematical modeling of polymer erosion: Consequences for drug delivery[END_REF] [START_REF] Ford | Mathematical modeling of drug delivery from autocatalytically degradable PLGA microspheres--a review[END_REF]. However, due to the very low diffusion coefficient of a protein embedded in a PLGA matrix, its transport through the pores was proposed as the main release mechanism [START_REF] Fredenberg | Measurement of protein diffusion through poly(D,L-lactide-Co-glycolide)[END_REF].

Microsphere size and morphology change during the release test

To clarify involved mechanisms, particle sizes and morphologies were monitored during the release (Figure 3 and Figure 4). After 2 days, 50P40-MS showed the appearance of few pores on their surface with an increase of the pore density in the peripheral structure (Figure 4-A2). These morphology changes were along with a 12% size increase (Figure 3). This phenomena was more marked on Day 10 with a stabilised size until Day 28 (Figure 4-A3).

[Figure 3] Evolution of microsphere mean sizes as a function of the release time for 50P20 (triangles) and 50P40 (squares). Error bars represent 95% confident intervals of the mean value (n=6 for 50P20 and 50P40).

A delayed polymer degradation and erosion were previously observed for porous PLGAbased microspheres and have been explained by facilitated interchanges between the internal environment and the external buffer medium. This reduced the acidification and autocatalysis phenomena [START_REF] Klose | PLGA-based drug delivery systems: importance of the type of drug and device geometry[END_REF] [START_REF] Ford | Derivation of an Analytical Solution to a Reaction-Diffusion Model for Autocatalytic Degradation and Erosion in Polymer Microspheres[END_REF] prolonging the drug release duration [START_REF] Berkland | Macromolecule release from monodisperse PLG microspheres: control of release rates and investigation of release mechanism[END_REF].

[Figure 4] Morphological changes of 50P40-MS (left column) and 50P20-MS (right column) during the release test (white scale bars represent 10 µm). After Day 28 MS could not be observed by SEM.

The active protein release was incomplete and a plateau around 54% was observed from Day 56 up to Day 70 (data not shown, n= 3). This phenomenon has already been observed for 60 µm PLGA-PEG-PLGA microspheres and it was demonstrated that the protein was entrapped and degradated within the dense microsphere core [START_REF] Tran | Protein-loaded PLGA-PEG-PLGA microspheres: A tool for cell therapy[END_REF].

The scenario was totally different for 50P20-MS which contained a higher amount of hydrophilic segments than 50P40-MS (17% vs 9.5% w/w respectively) with a lower Tg (3.5°C vs 15.9°C respectively, see Table 1).

The 50P20-MS size decreased continuously from the beginning to Day 28 (Figure 3). It appeared clearly from the SEM images that a pore-closing process occurred during the first 2 days. It was accompanied by a complete reorganization of the internal structure.

Microsphere structure became homogeneous with no visible pores neither on the surface nor in the interior. This phenomenon could explain the reduced burst while a significant one is classically expected for microsphere showing an initial porous surface [START_REF] Zheng | Effects of additives and processing parameters on the initial burst release of protein from poly(lactic-co-glycolic acid) microspheres[END_REF] [START_REF] Huang | Quantitative three-dimensional analysis of poly (lactic-co-glycolic acid) microsphere using hard X-ray nano-tomography revealed correlation between structural parameters and drug burst release[END_REF].

From Day 10, microspheres were no longer spherical and became brittle due to the polymer degradation/erosion.

To explain the drastic change observed at Day 2 for 50P20-MS, their morphology was investigated for various temperature of the release media, 3°C, 22°C, 37°C (Figure 5). These temperatures corresponded to three different relative distances to the dry microsphere Tg (-0.2%, + 6.7%, + 12,1% respectively). From figure 5, it was clearly evidenced that no reorganisation occurred at 3°C. A moderate one can be seen at 22°C and a complete one with, a pore closing process, was observed at 37°C. This demonstrated that the mobility of the polymer chains was a key parameter to explain this reorganization. with a moderate burst but a non constant release rate (See the ideal expected profile in figure 2), while 50P40-MS had a constante rate after a moderate burst, but did not achieve a complete release (54 ± 7%).

Both kinds of delivery system were good candidates for further optimizations using combination strategies. Indeed, a complete protein release with a moderate burst and a constant rate could ideally be wanted for some given therapeutic applications.

Adjustment of protein release profile

We have tried to design an optimal protein delivery system using two strategies: either a polymer blending or a microsphere mixing.

Release profile from polymer blending microspheres

The mean size (39.9 ± 3.4 µm) and encapsulation yield (45.9 ± 1.9%) (n=3) of microsphere from polymer blending (hereafter called blend-microspheres) were rather similar to those of 50P40-MS and 50P20-MS. Blend-microspheres exhibited numerous pores on the surface and in the internal structure (Figure 6-A1). Regarding the release of the protein (Figure 6-A2), the initial burst (20.4 ± 1.0%) was higher than previously observed. Then the subsequent protein release was rather linear from Day 1 to Day 42 (R 2 = 0.9026) and reached a plateau (69.1 ± 4.9% on Day 56). This kind of strategy has already been used with more or less success for PLA and PLGA microspheres [START_REF] Liggins | Paclitaxel-loaded poly(L-lactic acid) microspheres 3: blending low and high molecular weight polymers to control morphology and drug release[END_REF] [START_REF] Gu | Prediction of dexamethasone release from PLGA microspheres prepared with polymer blends using a design of experiment approach[END_REF].

In the present study, the polymer blend strategy was not an improvement.

Release profile from a mixture of microspheres

Concerning the microsphere mixing strategy, SEM picture (Figure 6 -B1) clearly revealed the two different types of microspheres (hereafter called Mix-microspheres). The initial burst was not significantly modified (15.2 ± 4.0%). Then the subsequent protein release was linear from Day 1 to Day 49 (R 2 = 0.9915) and reached a plateau (82.3 ± 2.6% on Day 56) (Figure 6 -B2). This was an improvement in the protein release control compared to the non linear profile of 50P20-MS.

Hickey and co-workers [START_REF] Hickey | Dexamethasone/PLGA microspheres for continuous delivery of an anti-inflammatory drug for implantable medical devices[END_REF] developed PLGA-MS for continuous delivery of dexamethasone over a month. Authors proposed to use a physical mixture of fresh and predegraded PLGA-MS. The resultant mixture exhibited an interesting profile with a moderated initial burst (from 15% to 20%) followed by a linear release but end up at around 60% after Day 3. Duvvuri and co-workers [START_REF] Duvvuri | Controlled delivery of ganciclovir to the retina with drug-loaded Poly(d,L-lactide-co-glycolide) (PLGA) microspheres dispersed in PLGA-PEG-PLGA Gel: a novel intravitreal delivery system for the treatment of cytomegalovirus retinitis[END_REF] prepared a physical mixture of two types of microspheres (containing ganciclovir) and dispersed the mixture into a thermogelling polymer. The resultant mixture exhibited an intermediate release profile compared to individual ones. In spite of a nearly 100% ganciclovir released after 25 days, the profile was tri-phasic with an initial massive burst. Herein, we successfully prepared a mixture of protein-loaded microspheres with the desired release profile: bi-phasic with a moderate burst, followed by a nearly complete linear release. The current achievement could be considered as a promising protein sustained release system.

CONCLUSION

The protein release profile from penta-block copolymer microspheres was successfully modulated using a mixture strategy based on 50P20-MS and 50P40-MS. Both had the same size, a moderate burst and complementary profiles (linear but non complete for 50P40-MS; non linear but complete for 50P20-MS) The microsphere mixture (1/1, w/w) induced a bi-phasic protein release profile with a moderate initial release followed by a nearly complete linear protein release over 8 weeks. This study highlighted the potential of this kind of penta-block polymers where the mass ratio of PEO blocks influenced clearly the Tg and consequently the release behavior at 37°C associated with the microsphere mixture strategy. The 1:1 mass ratio was used as a starting point but could be finely tune to control the protein release.

[Figure 1 ]

 1 Characterisation of MS produced using copolymers: (A) external/internal structure of 50P40-MS; (B) external/internal structure of 50P20-MS. In both cases, white scale bars represents 10 µm; (C) particle mean size (n=5) and encapsulation efficiency (n=5 for 50P40-MS and n=10 for 50P20-MS) as function of copolymers. Grey plot aims to compare the distribution of both interest variable as function of copolymers types. The boxes indicate the 75 th percentile (upper horizontal line), median (black bold horizontal line), and the 25 th (lower horizontal line) percentiles of the distribution. Surrounding the boxed (shaded area) on each side is a rotated kernel density plot.

[Figure 5 ]

 5 Internal structure at day 2 of 50P20-MS incubated into the release medium at different temperature : (A): 3°C; (B): 22°C; (C): 37°C. White scale bars represent 10 µm. 50P20-MS have shown a nearly complete active protein release after 8 weeks (93 ± 3%)

[Figure 6 ]

 6 (A1) Initial morphology of blend-MS (white scale bars represent 10 µm); (A2) average protein release profile from microspheres of a copolymer blend 50P20 and 50P40 (see text for details). Error bars represent 95% confident intervals of mean values (n=13); (B1) Initial morphology of mix-MS, porous particles represent 50P20-MS while non-porous surface particles correspond to 50P40-MS (white scale bar represents 10 µm); (B2) Average protein release profile from a mixture of microspheres of copolymer 50P20 and 50P40 (see text for details). Error bars represent 95% confident intervals of mean values (n=8). The red straight line represents a linear fit to the data (R 2 = 0.9795) from Day 1 to Day 56.

Acknowledgements

Polymer synthesis and characterizations (NMR and DSC) were performed using Synbio3 platform supported by GIS IBISA and ITMO Cancer (Montpellier, France). The authors would also like to thank the "Service Commun d'Imagerie et de Microscopie d'Angers" for SEM analysis.

Declaration of Interest

The authors declare no conflict of interest.