O Isnard

M Guillot

V Paul-Boncour

A Hoser

Metamagnetic transitions in Y0.5Er0.5Fe2D4.2 deuteride studied by high magnetic field and neutron diffraction experiments

Keywords: Laves phase compound, deuteride, neutron diffraction, high magnetic field, Metamagnetic transitions

Metamagnetic transitions in Y0.5Er0.5Fe2D4.2 deuteride studied by high magnetic field and neutron diffraction experiments

V.

Introduction

Rare-earth (RE) and 3d transition metal (TM) intermetallic compounds present a wide range of interesting fundamental magnetic properties and they can be used in many various applications (permanent magnets, magnetic storage, magnetic refrigeration…) related to the coupling between the localized magnetism of the 4f electrons and the itinerant behavior of 3d bands. The direct 3d-3d interactions are larger than the 4f-4f and 4f-3d indirect interactions (RKKY interactions), but the last one is responsible for the nature of the coupling between the RE and TM moments. The sign of the 4f-3d interaction in the ground state depends on the nature of the rare earth: it is positive for light rare-earths (RE=Ce-Eu) and negative for heavy rareearth (RE=Gd-Tm). As a consequence, RE-TM intermetallic compounds with heavy rare-earth show an antiparallel coupling of the RE and TM moments in the ground state at low field and low temperature. A forced ferromagnetic alignment of the heavy RE moments with Fe or Co moments can be induced by the application of a high magnetic field. Such transitions have been studied in RE2Fe14B (RE= Tm and Er) [START_REF] Kido | High-field magnetization of R2FE14B compounds measured up to 55-T[END_REF][START_REF] Kato | Field-Induced Phase-Transitions In Ferrimagnetic R2Fe14B In Ultra-High Magnetic-Fields[END_REF], ErFe11Ti [START_REF] Kostyuchenko | High-field magnetic behavior and forced-ferromagnetic state in an ErFe11TiH single crystal[END_REF] single crystals, RE2TM17 intermetallics (RE= Er, Tm; TM=Fe, Co) [START_REF] Andreev | High-field magnetization study of a Tm2Co17 single crystal[END_REF][START_REF] Andreev | Magnetic and magnetoelastic anomalies of an Er2Co17 single crystal in high magnetic fields[END_REF][START_REF] Isnard | High magnetic field study of the Tm2Fe17 and Tm2Fe17D3.2 compounds[END_REF] using pulsed-field induction magnetometer. In Tm2Co17 a ferromagnetic state with Tm and Co moments parallel to the c-axis was observed above 50 T and with a transition field Btrans of 39 T [START_REF] Andreev | High-field magnetization study of a Tm2Co17 single crystal[END_REF]. In Tm2Fe17, two step-like transitions were observed at 41 and 54 T but the ferromagnetic alignment was far from being reached at 60 T [START_REF] Isnard | High magnetic field study of the Tm2Fe17 and Tm2Fe17D3.2 compounds[END_REF]. Hydrogen absorption has been used to decrease the transition magnetic field and even reach saturation. For example, a ferromagnetic state has been reached at only 57 T in Tm2Fe17H5 [START_REF] Tereshina | Forced-ferromagnetic state in a Tm2Fe17H5 single crystal[END_REF]. Indeed, H insertion induces a large cell volume increase and consequently a reduction of the RE-TM interactions and a lowering of Btrans. In TmFe2H3.4 a spin reorientation has been observed with Btrans≈ 10 T at 4.2 K, but the ferromagnetic state was reached at a saturation field BSat =100 T due to large Tm anisotropy [START_REF] Mushnikov | Magnetization process and magnetic structure of the TmFe2H3.4 hydride in ultrahigh magnetic fields up to 100 T[END_REF]. In [START_REF] Tereshina | Forced-ferromagnetic state in a Tm2Fe17H5 single crystal[END_REF], a linear decrease of the reduced exchange integral JRE-Fe versus the relative cell volume change (ΔV/V) was presented for selected RE2Fe17 hydrides, deuterides, carbides and nitrides and REFe2 hydrides. This decrease was found larger for the REFe2Hy Laves phase compounds which can absorb a significantly higher H content versus metal atom (H/M=1.1 for y=3.4) compared to RE2Fe17Hy hydrides (H/M= 0.26 for y =5).

Few results were reported for Er-Fe and Er-Co compounds (Er2Co17) but saturation could not be reached even at maximum applied fields [START_REF] Kostyuchenko | High-field magnetic behavior and forced-ferromagnetic state in an ErFe11TiH single crystal[END_REF][START_REF] Andreev | Magnetic and magnetoelastic anomalies of an Er2Co17 single crystal in high magnetic fields[END_REF].

We have recently observed a forced ferromagnetic transition in Y0.7Er0.3Fe2D4.2 at a Btrans of only 8T below 30 K [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF], which is even smaller than for TmFe2D3.4 (Btrans =10 T) [START_REF] Mushnikov | Magnetization process and magnetic structure of the TmFe2H3.4 hydride in ultrahigh magnetic fields up to 100 T[END_REF]. At 4.2 K and using continuous high magnetic field up to 35 T (isothermal conditions) the saturation magnetization reaches 6.3 µB (f.u.) -1 , close to the value expected for a ferromagnetic structure with parallel Fe and Er moments (6.5 µB).

At higher temperature Y0.7Er0.3Fe2D4.2 displays a second metamagnetic transition which has been related to the itinerant electron metamagnetic (IEM) behavior of the Fe sublattice. At low field Y0.7Er0.3Fe2D4.2 undergoes a ferromagnetic-antiferromagnetic (FM-AFM) transition at TM0 = 66 K. Above TM0, a field induced AFM-FM transition is observed, with a linear increase of BTrans versus applied field. As the Er moments order below TEr= 55 K (B=0), the Er sublattice should be paramagnetic above TM0. However, the increase of the magnetization curves above BTrans cannot be only explained by the sum of the ferromagnetic contribution of the Fe sublattice and the paramagnetic contribution of the Er atoms. To explain this observation, it has been assumed that Er moments parallel to the Fe moments are also induced above BTrans.

The first aim of this study is therefore to investigate the nature and the mechanism of the forced ferri-ferromagnetic transition, which was observed at low temperature in Y0.7Er0.3Fe2D4.2, by studying a compound with larger Er content. The second goal it is to observe more clearly the influence of the Er content on the FM-AFM transition and understand the behavior of the Er sublattice under applied field above TM0.

For this purpose, we have investigated the structural and magnetic properties of Y0.5Er0.5Fe2D4.2 deuteride using both high magnetic field measurements up to 35 T in isothermal conditions and neutron powder diffraction under applied field at different temperatures. These results will be presented and compared with those of Y1-xErxFe2D4.2 deuterides (x = 0, 0.3). A more general discussion will be performed about forced ferromagnetic transitions and IEM behavior in comparison with other RE-Fe(Co) systems displaying similar type of transition and discuss the influence of hydrogen insertion.

Experimental methods

The synthesis methods of the Y0.5Er0.5Fe2 intermetallic compound and corresponding deuterides are described in details in refs. [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF][START_REF] Leblond | Isotope effect on the thermodynamic and structural properties of Y1-yRyFe2(H,D)x compounds (R=Tb, Er, Lu; 4.0 < x([END_REF]. Two deuteride samples have been prepared by a Sievert method: a first one with a small mass of m=0.5 g (S1) and the second one with larger mass m=11.2 g for neutron diffraction experiments (S2). Both samples were quenched into liquid nitrogen after deuterium absorption to avoid deuterium release and slowly heated under air up to room temperature in order to passivize the surface and avoid further deuterium desorption. The average D content determined from volumetric method and change of mass after absorption was 4.25±0.10 D f.u .-1 .

The crystal structure of intermetallic and both deuterides was checked by powder X-ray diffraction (XRD) at room temperature on a D8 Bruker diffractometer (Cu Kα radiation). Y0.5Er0.5Fe2 was found to crystallize in the cubic C15 structure (Fd-3m space group) with a= 7.3182(1) Å (V=391.93 Å 3 ). The electron probe microanalysis (EPMA) confirms that this compound is single phase with an average composition Y0.52(6)Er0.48(6)Fe2.10(7) calculated over 200 points.

The magnetization measurements were performed using a conventional Physical Properties Measurement System (PPMS-9T) from Quantum Design operating with field up to 9 T. Additional high field magnetic measurements were performed in Grenoble High Magnetic Field Laboratory (GHMFL, Grenoble, France) in high continuous magnetic field up to 35 T.

The experimental procedures of the magnetic studies are detailed in [START_REF] Guillot | Magnetic properties of Y0.7Er0.3Fe2(H,D)4.2 compounds under continuous magnetic field up to 35 tesla[END_REF]. Isothermal variations MT(B) were then obtained. It is noted that after sweeping the field up and down at a given temperature the absence of remanent magnetization was checked before increasing temperature.

Neutron powder diffraction (NPD) patterns of Y0.5Er0.5Fe2D4.2 have been registered at 300 K on the high-resolution spectrometer 3T2 in the Laboratoire Léon Brillouin (LLB, CEA, Saclay, France) with a wavelength of 1.225 Å. Additional NPD measurements were performed with the D1B instrument at the Institut Laue Langevin (ILL, Grenoble, France) with temperature varying from 2 to 300 K. On the D1B instrument the diffraction patterns have been recorded over an angular range of 80° (2θ) starting at 3° and using a multidetector with a step width of 0.2° between each of the 400 3 He detection cells. In this configuration D1B is operating with a wavelength of  = 2.52 Å selected by a (002) Bragg reflection of a pyrolytic graphite monochromator, the take-off angle being 44.2° in 2. Due to the high flux available on the instrument, temperature evolution of the diffraction pattern has been recorded in situ during heating by recording the diffraction patterns every 3 K. The powder sample was introduced in vanadium cylindrical sample container.

NPD measurements have been also performed between 2 and 170 K in vertical magnetic field up to 10 T on E6 focusing diffractometer in Helmholtz Zentrum Berlin (HZB, Berlin, Germany). The powder sample introduced in an aluminum cylindrical sample container was frozen using deuterated alcohol to avoid preferred orientation of grains with the magnetic field.

The selected wavelength was 2.454 Å. The angular range was between 3 ° < 2 < 113 ° with a step width of 0.15 °.

All the XRD and NPD patterns were analysed using the Rietveld refinement method implemented in the Fullprof code [START_REF] Rodríguez-Carvajal | FULLPROF: A Program for Rietveld Refinment and Pattern Matching Analysis[END_REF].

Experimental Results

Crystal structure

The XRD analysis of Y0.5Er0.5Fe2D4.2 S1 and S2 samples at room temperature (RT) shows that the main phase has a monoclinic structure isostructural to that of YFe2D4.2. The S1 sample was found single phase compound, but the second S2 sample contained two additional cubic phases with smaller cell volume, corresponding to deuteride phases with smaller D content. The XRD results are reported in Table 1. The monoclinic cell is described in the Pc space group that has been previously determined by NPD measurements to fully describe the crystal structure of YFe2D4.2 taking into account the ordering of deuterium atoms [START_REF] Ropka | Deuterium ordering in Laves phases deuterides YFe2D4.2[END_REF]. This monoclinic structure corresponds to a distortion of the cubic structure of the pristine compound with a mean cell volume increase ΔV/V= 26.8% for Y0.5Er0.5Fe2D4.2.

The NPD pattern of S2 sample measured at 300 K on 3T2 was refined with the same monoclinic structure than YFe2D4.2 and Y0.7Er0.3Fe2D4.2 in Pc space group [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF][START_REF] Ropka | Deuterium ordering in Laves phases deuterides YFe2D4.2[END_REF] and two cubic phases with Fd-3m space group. The results of the refinement are given in Table 2 and the refined NPD pattern is presented in Fig. 1. The monoclinic b cell parameter has a particular behavior compared to the two other a and c parameters: it is expanded while the two others are contracted and it is doubled along the b axis compared to the values obtained by symmetry lowering starting from a cubic structure with the same cell volume expansion. The a, b, c and V cell parameters of the monoclinic structure in Y0.5Er0.5Fe2D4.2 are smaller than that of YFe2D4.2 as expected from the smaller radius of Er relative to Y. The monoclinic cell volume was reduced of 1.26 % compared to YFe2D4.2. The monoclinic angle  remains similar in both compounds. In the monoclinic phase there are 4 RE sites (with 0.5 Y and 0.5 Er on each RE site), 8 Fe sites and 18 deuterium sites. The deuterium atoms are located in 15 RE2Fe2 and 3 REFe3 (D11, D17 and D18) tetrahedral interstitial sites with occupancy factors ranging between 0.62 and 1. No D atom were observed in Fe4 sites which have smaller size. The total D content 4.04 D (f.u.) -1 is smaller than that refined for YFe2D4.2 but comparable to that of Y0.7Er0.3Fe2D4.2 (4.05 D (f.u.) -1 ). As in this monoclinic structure they are 96 available RE2Fe2 and 32 REFe3 tetrahedral interstitial sites, this means that 81 RE2Fe2 and 29 REFe3 remain empty. The existence of empty sites is partially explained by the repulsion between two D atoms closer than 2 Å. The lowering of symmetry in a monoclinic structure results from a minimization of the total energy compared to a disordered cubic structure and leads also to a displacement of the metal atoms to accommodate the presence of interstitial deuterium atoms. Some Fe-Fe interatomic distances are elongated whereas other are shortened.

The cell volumes of the two cubic phases in sample S2 are smaller than the monoclinic one and the number of D atoms located in RE2Fe2 sites smaller than in the monoclinic phase. This indicates a partial deuterium desorption from this sample despite our trial to avoid it. Rwp: 10.3 % Chi2: 6.5

Magnetic properties

Magnetic measurements

The magnetic properties of the two S1 and S2 samples are compared in Fig. 2

M (µ B (f.u.) -1 ) 4.2 K (a) 8.2 T 53 K 53 K 62 K 72 K 88 K 100 K 110 K 120 K 140 K 150 K M (µ B (f.u.) -1
) Between 62 and 150 K, the MT(B) curves present a metamagnetic behavior with a critical field shifted to larger values as T increases (Fig. 3(b)). The S shape of the corresponding Arrott-Below plots (Fig. 4) clearly indicates the first order character of both metamagnetic transitions occurring for T ≤ 28 K and 62 ≤ T ≤ 140 K respectively. The intermediate behavior observed at 38 and 53 K, also leads to cross the other curves at the critical field of c.a. 8.2T. In this temperature range the transition, if any, is no longer of first order since the S shape has disappeared in the Arrott-Below plots.

B (T) (b)
(µ B (f.u.) -1 ) 2 4.2 K 28 K 38 K 53 K 62 K 72 K 88 K 100 K 110 K 120 K 140 K 150 K (b) M 2 (µ B (f.u.) -1 ) 2 B/M (T/(µ B (f.u.) -1 ))
The transition fields BTrans are obtained at each temperature from the maximum of the dMT(B)/dB derivative and are compared to that of YFe2D4.2 deuteride in Fig. 5. Below 38 K, BTrans varies between 7 and 8.2 T for the Er containing compound. In this low temperature range, the Er and Fe sublattices form a ferrimagnet in the ground state. Increasing the field is expected to favor a ferromagnetic arrangement; therefore BTrans is assigned to such ferri to ferromagnetic transition. The occurrence of similar metamagnetic transition from ferrimagnetic towards a ferromagnetic state has been also reported in Y0.7Er0.3Fe2D4.2 [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF] .

Then above the temperature TM0=38 K, Btrans increases linearly versus temperature for the two compounds (x=0 and 0.5); TM0 values being obtained by an extrapolation of Btrans to zero field. Note that TM0 also corresponds to the maximum of the peak observed in the magnetization curve of Y0.5Er0.5FeD4.0 at 0.03 T. TM0 decreases versus the Er content and the dBtrans/dT slope is larger for the Er containing compound (0.24±0.01 T.K -1 ) than without Er (0.15 T.K -1 ). In this temperature range Btrans has been attributed to the transition from an AFM towards a FM state [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF] through an itinerant metamagnetic behavior of the Fe sublattice. The spontaneous magnetization (MSpont) was obtained by extrapolation of the linear part of the magnetization (above 1 T and below BTrans) as defined below and in ref [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF]:

MT (B) = MSpont(T) + χ(T).B (1)
The evolution of MSpont is displayed in Fig. 6(a) and is compared with that of YFe2D4.2. At 4.2 K, MSpont= 0.35 µB corresponds to 2.mFe-0.5.mEr with mFe= 1.82 µB (Fe atom) -1 and mEr=6.58 µB (Er atom) -1 assuming a collinear and antiparallel alignment of the Fe and Er moments. The mean Fe moment mFe was assumed to be the same than for YFe2D4.2 and it corresponds to half the magnetization obtained at BCross. The mean Er moment mEr is smaller than the free ion value (9 µB), but close to the value observed in Y0.7Er0.3Fe2D4.2 (mEr = 6.4 µB (Er atom) -1 ). The reduction of mEr compared to the free ion value can be attributed to a strong crystal field effect related to the Er environment. The increase of MSpont up to 40 K can be related to the decrease of mEr. Above TM0, MSpont is barely identical to the value obtained for YFe2D4.2. We conclude that, in this high temperature range, the Fe magnetic moments are in the same magnetic state for both compounds and that the Er contribution to the magnetization is very small. The saturation magnetization (MSat) has been extrapolated at high field using the 1/B 2 ferromagnetic approach law above 15 T:

MT (B) = MSat(T )(1 -bM/B 2 ) (2)
MSat of Y0.5Er0.5Fe2D4.2 is significantly larger than that of YFe2D4.2 in all the temperature range. Assuming that the difference between the two deuterides is related to the Er moments parallel to the Fe ones, mEr= 8.3 µB (Er atom) -1 at 4.2 K. This value is larger than that estimated at low field but remains smaller than the Er free ion value. The observation of the MT(B) curves in Fig. 3(a) shows that the saturation is still not reached at 35 T due to the large Er anisotropy indicating that a higher magnetic field will be necessary to reach a saturated ferromagnetic state. Interestingly, one can notice that MSpont slightly increases versus temperature whereas MSat decreases above 50 K for Er containing compound. In spite of these opposite evolutions both reflect the same thermally activated reduction of the Er magnetic moment in the ferri (or AFM) and field-induced ferromagnetic regime respectively.

Neutron diffraction

Magnetic structures at B=0 T

The temperature dependence of the NPD patterns measured from 2 to 300 K on D1B

spectrometer is presented as a 3D plot in Fig. 7. This plot shows the existence of magnetic peaks related to three magnetic ranges: a ferrimagnetic structure at low temperature, an intermediate AFM structure between TM0 and TN and a paramagnetic state above TN. NPD patterns representative of each magnetic range (T= 2, 75 and 208 K) are displayed in Fig. 8. A 2 K, three main magnetic peaks are observed: an intense peak (noted NF) at Q = 1.35 Å -1 , which contains the nuclear and the magnetic contributions of both Er and Fe moments, and two small peaks labelled Er1 and Er2 at Q = 2.195 and 2.296 Å -1 respectively, which are only due to the Er magnetic moments. The magnetic peak indexation are reported in Fig. 8. At 75 K, we observe a large peak at Q = 0.26 Å -1 (referred to as AF) and a smaller one at Q = 1.14 Å -1 which both belong to the AFM structure, whereas the intensity of the large NF peak has decreased, and the two magnetic Er1 and Er2 peaks are no more visible. Then at 208 K, only peaks belonging to the crystal structure are seeable.

In Fig. 9, the thermal variation of the intensity of the three main magnetic peaks (NF, Er1 and AF), allows to determine the magnetic ordering temperatures: the Er sublattice orders at TER=50 K, the AFM structure appears at TAF=40K (close to TM0= 38 K) and disappears at TN=115 K with a maximum at 74 K. As TEr is higher than TM0, this means that a transition occurs between a ferrimagnetic order (Ferri) towards an AFM structure between 38 and 50 K. The cell volume (bottom of Fig. 9) decreases sharply (ΔV/V= -0.87 %) between 38 and 55 K with an inflexion point at 45 K, then is almost constant in the AFM range between 55 and 115 K. The linear increase of the cell volume above 115 K-in the paramagnetic range-is related to the thermal expansion with a coefficient αV=1/V0 dV/dT= 2.67(4)10 -5 K -1 and V0=

493.38Å 3 . All three a, b, c parameters show a sharp decrease above TM0 (Fig. 10), with relative contractions of -0.33 % for a, -0.26 % for b and -0.31% for c. There is a very small variation of the monoclinic angle β near TM0 indicating that the monoclinic distortion is not changed. This cell parameter contraction has been attributed to the magnetostrictive effect related to the Ferri-AFM transition. In Y0.7Er0.3Fe2D4.2 the cell contraction was much more pronounced in the (a, A quantitative analysis of the magnetic structure of Y0.5Er0.5Fe2D4.2 was undertaken by refining the NPD pattern measured at 10 K on 3T2. In a first attempt the NPD pattern was refined taking into account only the nuclear contribution of the three phases (one monoclinic and two cubic phases) with the deuterium positions and occupation factors refined at 300 K and a collinear ferrimagnetic structure for the Y0.5Er0.5Fe2D4 monoclinic phase. This magnetic structure was described as in ref [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF], with the same mean Er (Fe) moment mEr (mFe) for all Er (Fe) atoms. The refined Er and Fe moments were respectively mEr =7.53 [START_REF] Paul-Boncour | Percheron-Guégan, Structural study of the pseudobinary Y(Ni,Cu)2 system[END_REF] µB and mFe=2.51(6) µB, corresponding to larger values than estimated from the magnetic measurements (mEr=6.58 µB and mFe= 1.82 µB). In a second step, a magnetic structure was added for the main cubic phase (a =7.8939 Å at 300 K and 7.8889 Å at 10 K). This allows to obtain mEr=6.43 [START_REF] Paul-Boncour | Percheron-Guégan, Structural study of the pseudobinary Y(Ni,Cu)2 system[END_REF] µB and mFe=1.92( 6) µB for the main monoclinic phase, values similar to those deduced from magnetic measurements. However, attempt to determine the magnetic structure of the cubic phase Y0.5Er0.5Fe2D3.2 assuming also a collinear ferrimagnetic structure did not permit to get precisely the Er and Fe moments in such secondary phases. Adding a magnetic contribution to the second cubic phase Y0.5Er0.5Fe2D1.6 did not improve the NPD pattern refinement nor modify the results for the monoclinic magnetic structure. Two main reasons for this being the low content of the secondary phases and the already large number of refined parameters. In addition, for the same reasons, it was not possible to perform a quantitative analysis of the antiferromagnetic structure using the NPD pattern measured at 75 K on D1B which has a limited Q range (0.5-3 Å -1 ). Nevertheless, as Y0.5Er0.5Fe2D4.0 is isostructural to Y0.7Er0.3Fe2D4.0 and the low temperature diffraction patterns present similar magnetic peaks, it is also reasonable to assume similar collinear ferrimagnetic and antiferromagnetic structures for this compound.

Neutron diffraction experiments versus applied field

The evolution of the NPD patterns at 2 K was measured between 0 and 12 T. The main observations are a field-induced decrease of the NF line intensity and a variation of the Er1 and Er2 intensities. A plot of selected patterns between 0 and 12 T is shown in Fig. 11, whereas the variation of the NF and Er1 peak intensities versus field is displayed in Fig. 12(a). The main NF peak decreases continuously versus field with an inflexion point at 7.4 T, i.e. close to the transition field determined with the magnetization curve at 4.2 K (BTrans= 7 T). The Er1 peak intensity decreases down to a minima at 6 T and increases after. The variation of the Er2 peak intensity is more difficult to observe due to its weaker intensity leading to a low signal/noise ratio). A small peak intensity decrease is however observed as the field varies from 0 to 3T, but then the intensity remains constant within the error bars. These results can be interpreted, through appropriate simulations, to a decrease of the mean Er moment magnitude, but not to a full demagnetization which would imply the disappearance of the Er1 and Er2 peaks. On the other hand, if the ferri-ferromagnetic transition was only due to a rotation of the Er moment, the intensity of the Er2 peak should increase when that of Er1 decrease, which is not the case.

It is also important to notice, that there is no significant variation of the Bragg peak position, meaning that the cell volume do not varies under applied field. Intensity (arb. units)

Q (Å -1 ) NF Er1 (a)
Er2 Intensity (arb. units) The evolution of the NF and Er1 peak intensity at 10 T versus temperature is similar (Fig. 12(b)), with a progressive intensity decrease reaching a constant value above 40 K. It can be attributed to the reduction of the Er magnetic moment, as already observed at zero field.

Q (Å -1 ) B(T) 0 3 6 9 12 Er1 (b)
The NPD patterns were measured versus applied field at T= 50, 55, 65 and 75 K, i.e. above TM0=38 K. The variation of the NF peak intensity is presented in Fig. 13 (top). At low field, the compound is antiferromagnetic as a weak AF peak is observed in the patterns. At 75 K, were this AF peak is more visible, a smooth decrease of its intensity is observed between 0 and 6 T. The transition is therefore characterized by simultaneous variation of two Bragg peak intensities versus field: a decrease of the AF peak and an increase of the NF peak. Additionally, the magnetic field which triggers the increase of the NF Bragg peak intensity is shifted to higher values upon increasing temperature (see Fig. 13). These shifts are in agreement with Btrans variation versus T, as observed in the magnetization curves (Fig. 5). This clearly confirms that this metamagnetic transition corresponds to the AFM-FM transition. Therefore, the progressive NF peak intensity change at BTrans can be attributed to both the rotation of half of the Fe magnetic moments (from AFM to FM) and a contribution of a field-induced Er magnetic moment component parallel to the Fe moments. This change of the Er moment results from the field experienced at the Er position which is the sum of the applied magnetic field and the molecular field produced by the Fe sublattice in the ferromagnetic state.

In addition, the expansion of the interplanar distances of the NF peak (dNF) is observed as the magnetic field increases follows the NF intensity variation (Fig. 13). It confirms the existence of a magnetostrictive effect at the AFM-FM transition as previously observed for YFe2D4.2 and Y0.7Er0.3Fe2D4.2 [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF][START_REF] Paul-Boncour | Interplay between crystal and magnetic structures in YFe2(HαD1-α)4.2 compounds studied by neutron diffraction[END_REF]. The relative distance variation ΔdNF/dNF = 0.35 % is comparable to the thermal contraction observed for the a cell parameter (0.31 %). As the NF peak is indexed with (100) miller indices, this indicated that the magnetostrictive effect induced either by temperature or applied field is of the same order of magnitude.

Discussion

This study has shown the existence of two different types of metamagnetic transitions in Y0.5Er0.5Fe2D4: the first one at low temperature which is observed only for Er containing compounds and the second one observed in all Y1-xErxFe2D4.2 compounds including x=0. Both transitions present a first order character but have different physical origin, and therefore will be discussed separately below. It will then be followed by a more general conclusion.

Low temperature metamagnetic transition (T ≤ 38K)

In the ground state and below 38 K, the Er and Fe sublattices form a ferrimagnetic structure. A metamagnetic transition occurs at a transition field Btrans= 7.5±0.5 T, which remains almost constant between 4.2 and 38 K. This transition has been related to a change from a ferrimagnetic towards a ferromagnetic structure, i.e. from an antiparallel towards a parallel alignment of both Er and Fe moments. At low field the mean Er moment is 6.4 µB/Er atom only, its reduction compared to the Er 3+ free ion value can be attributed to a crystal field effect. At high magnetic field the Er moment becomes larger (mEr=8.3 µB (Er atom) -1 ). This ferriferromagnetic transition originates from the application of a magnetic field surpassing the Er-Fe interaction, and occurs at a relatively low field (7.5 (5) T) compared to other compounds in the literature. Indeed, in heavy rare-earth containing RE2TM17 compounds the transition fields required to induce a ferromagnetic alignment ranges between 40-50 T [START_REF] Andreev | Magnetic and magnetoelastic anomalies of an Er2Co17 single crystal in high magnetic fields[END_REF][START_REF] Isnard | High magnetic field study of the Tm2Fe17 and Tm2Fe17D3.2 compounds[END_REF][START_REF] Isnard | High magnetic field study of the Dy2Fe17Hx compounds with x=0-3.8[END_REF]. Hydrogen absorption yields an increase of the interatomic distances between the Er and Fe atoms and therefore a decrease of the strength of the Er-Fe exchange interaction. According to Tereshina et al. [START_REF] Tereshina | Forced-ferromagnetic state in a Tm2Fe17H5 single crystal[END_REF], the reduced exchange integral JRE-Fe(y)/JRE-Fe(0) decreased linearly with the relative cell volume (ΔV/V) and a larger reduction was found in REFe2 hydrides (RE=Tm, Er, Ho) compared to those of RE2Fe17 hydrides, as they absorb larger H/RE hydrogen content. For example in Tm2Fe17Hy, the transition from ferrimagnetic to ferromagnetic state at 4.2 K occurs between 30 and 57 T, [START_REF] Isnard | High magnetic field study of the Tm2Fe17 and Tm2Fe17D3.2 compounds[END_REF][START_REF] Tereshina | Forced-ferromagnetic state in a Tm2Fe17H5 single crystal[END_REF] whereas in the corresponding alloy the magnetization increases in four steps and the saturation is not reached at 74 T [START_REF] Isnard | High magnetic field study of the Tm2Fe17 and Tm2Fe17D3.2 compounds[END_REF]. In rhombohedral TmFe2H3.4, BTrans was only 10 T at 4.2 K and the ferromagnetic state was reached at 100 T, due to a strong anisotropy of the Tm sublattice [START_REF] Mushnikov | Magnetization process and magnetic structure of the TmFe2H3.4 hydride in ultrahigh magnetic fields up to 100 T[END_REF]. The cell volume of Tm2Fe17Hy decreases of only 4.2 %, and that of TmFe2H3.4 of 24.1 %. Consequently, the reduction of the molecular field coefficient can be estimated to be 20 % in Tm2Fe17Hy and 62 % in TmFe2H3.4. As in Y0.5Er0.5Fe2D4.2, the cell volume increase reaches 26.7 %, a large reduction of the JEr-Fe exchange interaction is therefore expected. Interestingly this transition field observed in Y0.5Er0.5Fe2D4.2 is not very sensitive to the Er content as it remains close to that observed in Y0.7Er0.3Fe2D4.2.

The transition from the ferrimagnetic to ferromagnetic state can occur through different ways: a demagnetization of the RE moments as proposed in [START_REF] Andreev | High-field magnetization study of a Tm2Co17 single crystal[END_REF][START_REF] Isnard | High magnetic field study of the Tm2Fe17 and Tm2Fe17D3.2 compounds[END_REF] or a rotation with constant magnetic moment magnitude [START_REF] Isnard | High magnetic field study of the Gd-Co exchange interactions in GdCo12B6[END_REF]. The MT(B) curves of Y0.5Er0.5Fe2D4.1 cross at a value corresponding to 2.mFe suggesting a demagnetization of the Er sublattice with a minimum around 8 T. In addition, the previous NPD results in Y0.7Er0.3Fe2D4.1 isotype, have suggested a demagnetization process of the Er moment, but the Er1 and Er2 peak intensities were small and it was difficult to fully conclude owing the low signal/noise ratio [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF].

In the present study, the variation of Er1 contribution versus applied field is more clearly According to previous studies on YFe2D4.2 (x=0) this transition is related to the IEM behavior of the Fe sublattice. In these previous works [START_REF] Paul-Boncour | High field induced magnetic transitions in the Y0.7Er0.3Fe2D4.2 deuteride[END_REF][START_REF] Paul-Boncour | Interplay between crystal and magnetic structures in YFe2(HαD1-α)4.2 compounds studied by neutron diffraction[END_REF], the AFM structure has been described as the alternance of two ferromagnetic layers with Fe moments perpendicular to the monoclinic b axis and in opposite direction to each other, separated by a row of non-magnetic Fe atoms. As in the monoclinic cell there are 8 different Fe sites with different number of neighboring H atoms, it was shown that one Fe atom which is surrounded by 4.7 D neighbor atoms loses its magnetic moment at TM0 and form a nonmagnetic Fe row perpendicular to the b axis. Such non-magnetic Fe atoms are found to be located at the Fe7 position (Table 2). Then the shortest Fe-Fe distance between the 6 Fe atoms surrounding the Fe7 atoms becomes larger (> 4.7Å) and the coupling between their magnetic moments negative. Similar Fe sublattice behavior is therefore expected in the case of Y0.5Er0.5Fe2D4.2. The remaining question is then how the Er moments behaves at this AFM-FM transition. At low field the spontaneous magnetization above TM0 is very close for Y0.5Er0.5Fe2D4.2 and YFe2D4.2 which suggests that the Er moments do not contribute to the magnetization. Additionally no Er peaks are observed in the NPD pattern in the AFM range, indicating that the Er moment are not ordered in the AFM structure.

In Y0.5Er0.5Fe2D4.2 the IEM transition field BTrans increases linearly versus the temperature up to 150 K, with a slope dB/dT =0.24±0.01 T.K -1 . Similar linear increase of BTrans has also been observed in Hf0.825Ta0.175Fe2 Laves phase which displays also an FM-AFM transition with TM0= 195±0.05 K and dB/dT =0.13±0.01 T.K -1 [START_REF] Diop | Large magnetovolume effects due to transition from ferromagnetic to antiferromagnetic state in Hf0.825Ta0.175Fe2 intermetallic compound[END_REF][START_REF] Diop | Neutron diffraction study of the itinerantelectron metamagnetic Hf0.825Ta0.175Fe2 compound[END_REF].

For temperatures close to TM0 the Ferri-AFM transition is abrupt and is accompanied by a cell volume increase. When T increases, the change of magnetic order occurs in a broader range of temperature. According to NPD studies on Y0.5Er0.5Fe2D4.2, the Néel temperature at zero applied field is TN =115 K, but metamagnetic behavior is still observed up to 150 K, indicating that paramagnetic-ferromagnetic transitions are taking place above TN (Figs. 3 and4).

The shape of the magnetization curves indicates that the ferromagnetic state is not fully reached at 35 T, but that a field-induced component of the Er magnetic moment aligned parallel to the Fe sublattice should be considered to explain the evolution of the saturation magnetization. Above Btrans the combination of the molecular field and the applied magnetic field should be sufficient to induce an Er moment parallel to the Fe moments.

Another feature of this metamagnetic transition is the sensitivity of TM0 to the cell volume variation upon Er for Y substitution. Indeed, taking into account previous results on Y0.7Er0.3Fe2D4.2, TM0 decrease versus the cell volume of the deuterides with a slope dTM0/dV= 7.7 K Å -1 . This Er/Y substitution effect is comparable in magnitude but smaller than the 12.7 K Å -1 value reported for YFe2(H,D)4.2 compounds [START_REF] Paul-Boncour | Giant isotopic effect on the itinerant electron metamagnetism in YFe2(HyD1-y)4.2[END_REF] where the cell volume increase linearly upon H for D substitution. The influence of the applied pressure on TM0 was examined for YFe2D4.2 and YFe2H4.2 [START_REF] Isnard | On the origin of the giant isotopic effect of hydrogen on the magnetic properties of YFe2A4.2 (A = H, D): A high pressure study[END_REF][START_REF] Isnard | Pressure-induced changes in the structural and magnetic properties of YFe2D4.2[END_REF]. Different dTM0/dV slopes were obtained for the deuteride and the hydride, but they converged towards a critical volume VC= 501.7 Å 3 , below which the ferromagnetic ground state was suppressed. The stabilization of an AFM ground state by applying an external pressure of few tent of GPa has been observed in other Fe rich compounds like RE2Fe17 compounds (RE= Y, Lu and Ce) [START_REF] Medvedeva | High pressure effect on magnetic properties and volume anomalies of Ce2Fe17[END_REF][START_REF] Kamarád | Magnetization and neutron diffraction studies of Lu2Fe17 under high pressure[END_REF]. Er for Y substitution in YFe2D4.2 can be considered as a chemical pressure effect, and it can be expected that the ferrimagnetic state will be suppressed for larger Er content. Nevertheless, the critical cell volume should be lower than for YFe2(H,D)4.2 under pressure, as the cell volume of Y0.5Er0.5Fe2D4.2 (V=496.6(3) Å 3 ) is already smaller than VC and a linear extrapolation of TM0=f(V) yields 492 Å 3 . This means that the influence of Er for Y substitution on TM0 in not a pure chemical pressure effect, and that the magnetic contribution of Er influence also the stability of the ferrimagnetic state.

Such relationship between magnetic ordering temperature and unit cell volume has been observed in other systems presenting IEM effect, like in La(Fe,Si)13Hy [START_REF] Fujieda | Giant isotropic magnetostriction of itinerant-electron metamagnetic La(Fe0.88Si0.12)13Hy[END_REF][START_REF] Fujita | Influence on hydrogenation on the electronic structure and the itinerant-electron metamagnetic transition in a strong magnetocaloric compound La(Fe0.88Si0.12)13[END_REF] compounds.

This relationship can be a consequence of a change of the density of state at the Fermi level induced by unit cell volume expansion and possible modifications of the splitting of the minority and majority band and/or the curvature of the Landau d band.

Conclusions

Combining magnetic field measurements with neutron powder diffraction, this experimental study on Y0.5Er0.5Fe2D4.2 has showed the existence of two different types of first order metamagnetic transitions depending on the temperature range. The first one observed at low temperature is explained by a forced ferrimagnetic to ferromagnetic transition with a fieldinduced reorientation of the Er moment parallel to the Fe one. The transition field is not very sensitive to the temperature, and its low value (7-8T) compared to that of other Fe rich intermetallics is attributed to the significant weakening of the Er-Fe exchange interaction due to the 27 % cell volume expansion induced by the 4 D atom f.u. -1 insertion. This study confirms the earlier results on Y0.7Er0.3Fe2D4.2 and is in agreement with the assumption that strong reduction of the RE-Fe interaction occurs upon H insertion.

Then, above TM0=38K, a second AFM-FM metamagnetic transition is observed for Y0.5Er0.5Fe2D4.2. This transition is related to the IEM behavior of the Fe sublattice, with a linear variation of Btrans versus temperature. TM0 and Btrans are very sensitive to the Er content and the significant unit cell volume change. It can be attributed to a strong magnetoelastic coupling.

The cell volume contraction observed at TM0 confirms the itinerant character of the Fe moment.

At larger applied magnetic fields (> Btrans), an Er moment is induced and forced to align parallel to the Fe magnetic moment.

Further studies will be performed in order to have a more systematic overview of the influence of Er content and of the (H,D) isotope effect on the magnetic properties of Y1-xErxFe2(H,D)4.2 compound. It will be also planned to investigate the influence of the nature of the substituted rare-earth element on both metamagnetic transitions. Indeed the strong lowering of the RE-Fe interactions by a large hydrogen content insertion, will allow to study the forced ferri-ferromagnetic transitions for heavy RE ranging from Gd to Tm.

Fig. 1 :

 1 Fig. 1: Refined NPD pattern of Y0.5Er0.5Fe2D4.2 (sample S2) measured in 3T2 at 300 K (λ= 1.225 Å). Refinement with one monoclinic and two cubic phases. (Q = 4 sinƟ /).

Fig. 2 :

 2 Fig. 2 : Thermomagnetization curves of the Y0.5Er0.5FeD4 samples under different applied magnetic fields: a) comparison of S1 and S2 under 0.03T; b) Evolution of the magnetization curves under different applied field for sample S1 in main part and sample S2 in Inset.

Fig. 3 :

 3 Fig. 3: Magnetization curves of the Y0.5Er0.5Fe2D4.0 compound (S2) under high magnetic field up to 35 T between 4.2 and 53 K (a) and 53K to 150 K (b).

2

 2

Fig. 4 :

 4 Fig. 4: Arrott-Belov curves of the Y0.5Er0.5Fe2D4.0 S2 compound measured under high magnetic field (35 T) between 4.2 and 38 K (a) and 53 K to 150 K (b).

Fig. 5 :

 5 Fig. 5: Transition field BTrans versus temperature for Y1-xErxFeD4.2 compounds (x=0, 0.5).

Fig. 6 :

 6 Fig. 6: Temperature evolution of the spontaneous magnetization MSpont (a) and of the saturation magnetization MSat (b) for the Y1-xErxFeD4.2 deuterides (x=0, 0.5).

Msat

  is almost constant up to 53 K, then a progressive decrease is observed. The saturation magnetization of YFe2D4.2 is large (close to 4µB/f.u.) and corresponds to the field induced ferromagnetic coupling of the Fe magnetic moments. The larger value of MSat of Y0.5Er0.5Fe2D4.2 as compared to that of YFe2D4.2 indicates that an Er moment component parallel to the Fe magnetization should be induced by the applied magnetic field thus contributing to the total magnetization. Up to 50K, MSat of Y0.5Er0.5Fe2D4.2 remains constant at about 8µB/f.u. in spite of the temperature increase. Then above 50K, as can be seen from Fig.6(b), the MSat of Y0.5Er0.5Fe2D4.2 and YFe2D4.2 present different behaviors. The first compound exhibits a MSat decrease versus temperature whereas for the second one, featuring the Fe sublattice only, MSat remains almost constant. The MSat difference is consequently attributed to the Er sublattice magnetization and its temperature dependence reflects the Er moment decrease versus temperature. At 150K, we estimate the field induced ferromagnetic component of the Er moment to 5.7µB/Er atom against 1.75µB/Fe atom.

Fig. 7 :

 7 Fig. 7: Temperature evolution of the NPD patterns of Y0.5Er0.5Fe2D4.2 (sample S2) recorded every 3 K between 2 and 300 K, as measured on the D1B diffractometer (λ= 2.52 Å).

Fig. 8 :

 8 Fig. 8: NPD patterns of Y0.5Er0.5Fe2D4.2 (sample S2) at T=2, 75 and 208 K measured on D1B (Q = 4 sin /; λ= 2.52 Å).

Fig. 9 :

 9 Fig. 9: Temperature dependence of (top) the intensities of AF, NF and Er1 Bragg peaks and (bottom) cell volume of Y0.5Er0.5Fe2D4.2 in zero applied field for the S2 sample. TM0 and TN positions are marked with dotted line as guide for eyes.

c)Fig 10 .

 10 Fig 10. Cell parameters variation versus temperature. The positions of TM0 and TN are indicated by arrows.

Fig. 11 .

 11 Fig. 11. Neutron powder diffraction patterns of Y0.5Er0.5Fe2D4.2 recorded at 2 K under various magnetic fields on the E6 (BENSC) spectrometer (λ = 2.454 Å). Inset (a) zoom on NF peak. (b) zoom on Er1 and Er2 peaks.

Fig 12 :

 12 Fig 12: Variations of the NF and Er1 peak intensities of the Y0.5Er0.5Fe2D4.2 deuteride versus applied magnetic field at 2K (a) and versus temperature under 10 T (b). The inset of Fig 12(a) corresponds to a zoom on Er1 and Er2 peaks at selected temperatures.

Fig. 13 :

 13 Fig. 13: Evolution of the NF peak intensity (top) and of the interplanar dNF distance (bottom) for Y0.5Er0.5Fe2 D4.2 deuteride at 50, 55, 65 and 75 K.

  seen in the NPD patterns thanks to its larger Er content. All the NPD patterns measured at 2 K indicates the absence of additional Bragg peaks and shows a field dependence of the NF and Er1 peak intensities. The field evolution of the NPD patterns reveals a progressive decrease of the Er contribution down to about 6 T and an increase above with an Er moment parallel to that of Fe as confirmed by magnetic measurements. Although the Er demagnetization is not complete at Btrans -there is still an Er contribution in the NPD patternsthis Ferri-Ferro transition occurs through a possible reduction of the Er moment.4.2 High temperature metamagnetic transition (T>38K)The NPD pattern analysis at zero field, indicates that the Er sublattice orders below TEr = 50 K (Figs 9 and 12) whereas the AF line appears above 40 K, which means that there is a small temperature range were the ferrimagnetic structure (Er moments coupled antiparallel to all Fe moments) coexists with the antiferromagnetic structure (AFM dominated by the Fe magnetic moments). The metamagnetic behavior observed above TM0= 38 K, corresponds therefore to a transition from an AFM to a FM state.

Table 1 :

 1 Cell parameters of YFe2D4.2 and Y0.5Er0.5Fe2D4.2 deuterides S1 and S2 at 293 K.

	Compounds	S.G.	a (Å)	b (Å)	c (Å)		V (Å 3 )	Wt
								%
	YFe2D4.2	Pc	5.507(1)	11.472(2)	9.428(1)	122.354(1) 502.96(9) 100
	Y0.5Er0.5Fe2D4.2	Pc	5.4825(2) 11.4286(4) 9.3894(3)  496.94(2) 100
	S1
	Y0.5Er0.5Fe2D4.2	Pc	5.4875(3) 11.4126(6) 9.3943(4) 122.429(2) 496.57(2) 77(1)
	S2
		Fd-3m 7.9028(7)				493.57(8) 17(1)
		Fd-3m 7.5757(4)				434.77(4)	6(1)

Table 2 :

 2 Results of the refinement of Y0.5Er0.5Fe2D4.2 NPD pattern measured on 3T2 at 300 K. The Debye Waller factors were constrained to the same values for Y/Er, Fe and D atoms respectively. The Y and Er atoms were located on the same sites with an occupancy ratio 0.5:0.5 in agreement with the chemical analysis.

	Atom	x	y	z	B (Å 2 )	Nocc
	Y1, Er1	0.140	0.119	0.869	0.83( 5)	1
	Y2, Er2	0.873	0.372	0.636		1
	Y3, Er3	0.112	0.375	0.362		1
	Y4, Er4	0.880	0.121	0.132		1
	Fe1	0.492	0.127	0.488	0.77( 3)	1
	Fe2	0.029	0.128	0.515		1
	Fe3	0.503	0.243	0.256		1
	Fe4	0.505	0.244	0.751		1
	Fe5	0.008	0.374	-0.005		1
	Fe6	0.494	0.494	0.240		1
	Fe7	0.479	0.992	0.737		1
	Fe8	0.508	0.382	0.001		1
	D1	0.553(15)	0.618(5)	0.846(8)	1.58(11)	0.71(9)
	D2	0.446(15)	0.628(4)	0.134(6)		0.77(9)
	D3	0.497(11)	0.137(5)	0.154(7)		0.62(10)
	D4	0.868(8)	0.274(3)	0.826(5)		1.00(8)
	D5	0.133(9)	0.004(3)	0.635(4)		1.00(8)
	D6	0.118(8)	0.277(4)	0.155(5)		0.97(10)
	D7	0.175(8)	0.777(4)	0.168(5)		1.00(9)
	D8	0.872(9)	0.467(4)	0.840 (5)		0.97(9)
	D9	0.871(7)	0.975(4)	0.838(5)		1.00(9)
	D10	0.279 (10)	0.466(4)	0.807(5)		0.81(9)
	D11	0.647(8)	0.135(3)	0.721(4)		0.96(9)
	D12	0.772(9)	0.740(3)	0.786(5)		0.74(8)
	D13	0.563(7)	0.237(3)	0.939(4)		1.00(8)
	D14	0.169(8)	0.838 (3)	0.904(4)		1.00(9)
	D15	0.826(8)	0.567(3)	0.596(5)		0.82(9)
	D16	0.499(7)	0.974(3)	0.427(4)		1.00(8)
	D17	0.291(10)	0.525(4)	0.531(5)		0.79(9)
	D18	0.732(8)	0.193(3)	0.466(4)		0.91(8)
		Space group Cell parameters V (Å 3 )	D/f.u.	wt%
	Mono	P 1 C 1	a=5.4822(2) Å	495.63 (3)	4.04(4)	79.3(1.5)
			b=11.4136(5) Å
			c=9.3839(3) Å
			β=122.424(3)°
	Cub 1	Fd-3m	a= 7.8939(6) Å	491.90 (7)	3.2(2)	17.2(8)
	Cub 2	Fd-3m	a= 7.5642(8) Å	432.81(8)	1.6(4)	3.5(4)
		RBragg :5.7% Rp: 10%

ACKNOWLEDGMENTS

The authors thank the Institut Laue Langevin (ILL, Grenoble, France), the Laboratoire Léon Brillouin (LLB, Saclay, France) and the Grenoble High Magnetic Field Laboratory (GHMFL, Grenoble, France), as well as the Helmholtz Zentrum Berlin (Berlin, Germany) for the allocated beam time to perform the experiments. This research project at HZB has been supported by the European Commission under the 6th Framework Program through the Key Action: Strengthening the European Research Area, Research Infrastructures. Contract n°: RII3-CT-2003-505925 (NMI3).


Damien Thomasson

Fernande Boisson

Emmanuel Girard-Reydet

Françoise Méchin

Françoise Mechin
email: fmechin@insa-lyon.fr

Hydroxylated hyperbranched polyesters as crosslinking agents for polyurethane networks: Partial modification of the OH chain ends

Keywords: hyperbranched polyesters, chemical modification, modification degree, urethane, hydrogen bonds

come

Introduction

Macromolecules with a compact architecture can be of great interest as additives or as building blocks in novel polymeric materials. Among them, hyperbranched polymers represent an important part of the family of dendritic and multibranched polymers [1,2] . While dendrimers have perfect, monodisperse structures built around a core moiety with a branching point in every repeating unit, hyperbranched polymers are polydisperse and include some linear units in their molecular structure. However, these differences are not large enough to suppress some of their typical dendritic polymer characteristics. Similarly to dendrimers, hyperbranched polymers were shown to exhibit much lower solution viscosities than linear polymers due to the lack of entanglements and to their very low intrinsic viscosities, which result from their packed structure [3][4][5][6] . They also often possess very high solubilities compared to those of linear polymers, as a result of the large number of peripheral terminal functional groups available per macromolecule. These attractive properties allow to blend large amounts of hyperbranched polymers with thermoplastics [7][8][9][10] , but also with thermosetting precursors [11][12][13] without increasing too much their viscosity, and even sometimes lowering it.

The properties of hyperbranched polymers in blends are indeed strongly determined by the nature of their terminal groups [14][15][16][17] . For example solubility, which mainly depends on endgroup structure, may be regulated by the partial or total chemical modification of the "terminal" groups. Due to the irregularities of hyperbranched polymers in their molecular architecture, these functional groups can be located not only in the periphery, as in perfect dendrimers, but also inside the globular branched structure; even the terminal functional groups of dendritic macromolecules can fold back to the inside [18] . Nevertheless, several authors could show that nearly all functional groups were accessible for small reagents [19,20] , which easily allows a quite total modification of functionalized hyperbranched polymers. Some hyperbranched oligomers and polymers are now commercially available on a large scale and among them, hydroxylated hyperbranched polyesters based on bis(methylol)propionic acid, bis(MPA), have been the subject of numerous studies dealing either with their synthesis [21][22][23][24][25] or their characterization [26][27][28][29] . Their relatively well-known structure, together with their medium to high hydroxyl functionality, could make them good candidates as original precursors for new polymer materials. Our group has been working for many years on the synthesis of segmented polyurethanes and of polyurethane or polyurethane acrylate networks [30][31][32] , most of which are obtained from the reaction of hydroxylated compounds with diisocyanate-terminated prepolymers based on a macrodiol and excess diisocyanate [32][33][34] . Therefore the use of the above hyperbranched polyesters as specific crosslinking agents for such materials seemed to us a very promising way of synthesizing new polyurethane networks with a controlled architecture, as described in Figure 1. For such a purpose, the hyperbranched units obviously have at first to be miscible in bulk with the other precursors, namely the macrodiol and the diisocyanate. Unfortunately this is not the case for most macrodiols (α,ω-dihydroxy polyesters, polyethers, polyolefines…), nor for commonly used diisocyanates. Consequently, a partial endcapping of the hydroxyl groups of the hyperbranched component by a monofunctional aromatic isocyanate was implemented with the aim of achieving crosslinking agents with tunable functionalities and miscibilities.

Experimental

• reagents A commercial fourth-generation hyperbranched hydroxy-functional polyester based on bis(methylol)propionic acid, bis(MPA) (Boltorn H40, HB40, Perstorp AB) and on a tetrafunctional core (pentaethoxylated pentaerythritol) was used without purification throughout this study. To illustrate the possible defects in the molecule architecture, a typical chemical structure of a lower "generation" is shown in Figure 2. As modifier and titrating agent, respectively, p-tolyl isocyanate (pTI) and p-toluenesulfonyl isocyanate (tosyl isocyanate, TOS), both from Aldrich, were used as received, as well as di-n-butylamine (Fluka) and the solvent, anhydrous THF (water < 0.02 %) from SDS.

• OH modification reaction HB40 is not miscible with pTI, and therefore the chemical modification of the OH groups was carried out in solution. HB40 was at first carefully dried, then dissolved in anhydrous THF (concentration: 0.5 g/mL). The desired amount of pTI was then added and the mixture was allowed to react under argon at room temperature; no catalyst was used in order not to perturb the future syntheses of polyurethane networks. The reaction was run until total disappearance of the isocyanate peak (2270 cm -1 ) using FTIR spectrometry. The modified product was then recovered by THF evaporation (precipitation in a non-solvent was avoided, since it inevitably would have led to a partition between smaller and larger HB molecules), and thorough drying. The resulting samples were named after their actually measured modification degree (i.e. HBpTI19 refers to HB40, modified by pTI using an initial ratio NCO/OH = 0.25, and for which 19% of the OH groups were finally found to be turned into urethane groups).

• OH titration

A general procedure was established for the chemical determination of OH functions for crude and modified HB polyesters. It consisted in a titration by a strongly reactive isocyanate (TOS), followed by neutralization of the excess isocyanate by an aliphatic amine and backtitration with hydrochloric acid. In a first stage, the samples were thoroughly dried under a vacuum, and then dissolved in anhydrous THF (~ 0.5 mol OH /L). After that, the same volume of a 1N solution of TOS in THF was added and the mixture was reacted for 2h. Another same volume of a 2N solution of di-n-butylamine was then added and the mixture reacted for 1 more hour. After diluting with acetone (co-solvent), the excess amine was finally back-titrated by a 1N HCl aqueous solution. The hydroxyl number was obtained with respect to the titration of a blank solution.

• physico-chemical analysis -1 H and 13 C NMR were used to determine the average modification degree (OH conversion, t m ) and the microstructure of the HB polymers. Spectra were recorded in DMSO-d6 with a 5 mm-QNP probe at 67°C on a Bruker DRX 400 spectrometer operating at 400 MHz for 1 H and 100.6 MHz for 13 C. Inversegate (ig) decoupling proton was used under appropriate conditions (70° rf pulse; 11.4 s recycle time) to obtain accurate relative values for the integrations of all carbon peaks.

-Differential Scanning Calorimetry (DSC) analysis of the samples was carried out on ~10 mg samples in aluminum pans, using a Mettler DSC30 apparatus. The heating rate was 10°C/min under argon atmosphere. Thermogravimetric analysis, TGA, was run under the same conditions (but the atmosphere: nitrogen or helium) on a TGA2950 apparatus from TA Instruments.

-Rheological measurements were carried out with the help of a RDA II spectrometer (Rheometrics). Samples (1-1.5 mm-thick) were placed between parallel circular plates (diameter: 50 mm). For thermomechanical measurements, the strain was set at 1.5% and the heating rate at 3°C/min (ω = 1, 10 or 100 rad/s). Isothermal rheological analysis was run at 110°C with a 10% strain, i.e. in the linear domain for all the samples.

-Finally, Wide-Angle X-ray diffraction (WAXS) measurements were performed on a Siemens D500 diffractometer with a Brentano-Bragg geometry (40 kV, 30 mA, λ = 1.54Å), at room temperature.

Results and discussion

Characterization of the microstructure of the initial HB40

Commercial HB polyesters from Perstorp have already been used in several studies for which they were quite completely characterized, especially recently by Žagar et al. [26][27][28][29] .

However some of these measurements were carried out once again in this work to have a better insight of the specific lot used in this study, but most of all for comparison purposes (between crude and modified samples). A good knowledge of the chemical microstructure of the HB polyester was indeed particularly important in order to understand how it could be influenced by its chemical modification afterwards. Therefore the pristine HB40 was at first fully characterized by 1 H and 13 C NMR. Both spectra shown in Figure 3 are in good agreement with the structure depicted in Figure 2 as well as with former analyses of bis(MPA)-based HB polyesters [21] . Dendritic, D, linear, L and terminal, T units can be distinguished both by 1 H NMR using the methyl signal at 1.0-1.4 ppm and by 13 C NMR using either the carbonyl peaks [171-175 ppm], or that of the quaternary carbons, Cq, [45-51 ppm].

In the case of 1 H NMR, trifluoroacetic acid, TFA, can also be added in order to isolate the broad peaks associated with labile protons (OH groups, but also residual water [27] ). These 3 particular areas of the NMR spectra are presented in Figure 4. Using appropriate conditions (see experimental section), it is possible to compare quantitatively the relative areas of C=O and Cq peaks with each other. For the relative proportions of D, L and T units, comparable values from the 3 types of data are indeed obtained, as summarized in Table 1. Numerous linear units are detected, meaning that HB40 bears about 48% terminal OHs and 52% linear OHs. From these data, it is possible to estimate a degree of branching, DB, using the definitions given either by Frechet:

T L D T D DB Frechet + + + = (1)
or Frey:

L D 2 D 2 DB Frey + = (2)
Both series of values are reported in Table 1. The main difference lies in the fact that DB Frechet takes into account the linear propagation as a branching direction and thus overestimates DB for small molecules, whereas both definitions merge for higher molar masses. Here average values of DB Frechet ~ 0.44 (DB Frey ~ 0.38) are found, quite consistently with the results obtained by Žagar et al. on similar samples (DB Frey = 0.367 [26] ). A value of DB = 0.50 would have been expected if all OH groups were equireactive in the bis(MPA) (AB 2 ) polyesterification reaction. A lower DB suggests that the terminal hydroxyls might have a higher reactivity in the original polyesterification. Finally, the average number of OH groups per constitutional repeating units, n CRU , can be estimated from the ratio

L T 2 L T D L T 2 + = + + + (since D +T + L = 1)
. The average value lies around 1.08 ± 0.04.

Theoretically, for a 4 th generation dendritic polymer based on a tetrafunctional core this value should be written as a function of the number average functionality, f n , and degree of polymerization, DP n :

n CRU = z/N CRU = f n /DP n ( 3
)
where z stands for the number of reactive groups per molecule and N CRU for the total number of CRU per molecule. More precisely in this case (dendrimer based on AB fB monomer, core with functionality f c and generation G):

z = f c f B G and N CRU = 1 1 G B c B f f f   -   -   or n CRU = ( 1) 1 G B B G B f f f - - = 1.067 (G = 4, f B = 2) (4)
The value found experimentally, although not so different, is thus slightly higher. NMR can also give some information on DP n . According to Burgath et al. [35] , for a polycondensation involving an AB m -type monomer and a core with B functionalities, DP n can be calculated by:

( ) ( ) ( 2) ( ) ( ) ( 2) c c n c c N B N AB f N DP N B N AB f N + - - = - - - (5)
where

N(B) = number of B functions, N(AB) = number of A-B bonds, N c = number of core
molecules with a functionality f c . In this work these parameters can be related to the 1 H NMR integrations, I, of the various CH 3 peaks (for methyl groups born by D, L or T units, and therefore linked either to a CH 2 OR or CH 2 OH group). The integrations can be written as:

I(CH 2 OH) = 4 3 I(CH 3 ) T + 2 3 I(CH 3 ) L ( 6
)
I(CH 2 OR) = 4 3 I(CH 3 ) D + 2 3 I(CH 3 ) L (7) I(CH 2 OH) is directly proportional to N(B) -(f c -2)N c
, and I(CH 2 OR) to N(AB) with the same proportionality factor. Therefore DP n can be written as:

3 3 3 3 3 3 3 3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) D L T tot n T D T D

I CH I CH I CH I CH DP I CH I CH I CH I CH

+ + = = - - (8)
It is clear that a small variation in these integrations could induce a large error for DP n values. Taking into account the most accurate measurements (i.e. those obtained in the presence of TFA), the value obtained for DP n is 22.7, thus (as expected) much less than the theoretical value of 60 for a perfect 4 th generation dendrimer. On another lot of HB40, Žagar et al. [26] obtained values in the same range, DP n = 22.4 -23.8, using CH 2 OR and OH signals and taking into account the presence of some labile protons. In contrast the very low value given by Burgath [35] , DP n = 9.2, can most probably be attributed to the fact that these labile protons were not considered when calculating the various peak integrations.

An estimation of the number average molar mass can finally be deduced from the value of OH/molecule). This would lead to M n ~ 2990 g/mol. In another laboratory, the molar mass of the same HB40 sample was measured by SEC-MALLS at M n = 2930 g/mol [36] . Knowing the initial OH equivalent weight (Eq OH = 8.4 mol/kg) this would correspond to a value of f n ~ 24.6 OH/molecule. Both analyses, NMR and SEC-MALLS, are thus in very good agreement.

DP n using M n = DP n M CRU + M c + f n (M CRU =

Estimation of the modification degree, t m (OH conversion)

After completion of the modification reaction and drying steps, thermogravimetric analysis (TGA) was performed at first on the modified samples in order to check the absence of any residual isocyanate (T eb (pTI) = 70-72°C/10 torr or ~195°C/760 torr) or solvent. The results obtained for various modification degrees are shown in Figure 5. By checking with a coupled FTIR spectrometer, a slight loss of volatile compounds (mainly water and THF, but in any case lower than 0.5 wt%) was indeed observed up to 170°C; after that, the well-known thermal reversibility of the urethane bonds [37][38] starts to interfere, with some pTI being evolved:

OH + N=C=O O-C-NH- -CH 3 CH 3 O ~170°C inversion temperature

Scheme 1

Traces of p-toluidine could also be identified in this temperature range. It is clear from Figure 5 that the weight loss observed between 180 and 270°C is directly proportional to the amount of pTI used for the chemical modification. Since no residual isocyanate bond was detectable by FTIR in the initial material, pTI can only be produced through the thermal decomposition of urethane bonds. Above 275°C, the products detected correspond mainly to the degradation of the HB polyester architecture itself. Moreover the various phenomena are always observed at the same temperatures, whatever the initial modification degree. This modification degree, t m , reflects the proportion of OH groups initially present in the HB molecules that have been converted to urethane groups by reaction with pTI. t m can thus be expressed as a function of the initial and final number average functionalities, f n :

) HB ( f ) HB ( f ) HB ( f t n mod n n m - = (9)
Two different techniques, chemical titration and 1 H and 13 C NMR, were used and compared for the determination of t m . The amount of modified OH groups was at first estimated by chemical titration. In this case the measurement directly leads to an OH equivalent weight, or number of OH groups per kg of the sample, Eq OH . Consequently, the increment in molar mass induced by the presence of new p-tolyl urethane end groups must be taken into account in order to calculate t m , which is given by the following equation:

) M 10 ) HB ( Eq 1 )( HB ( Eq ) HB ( Eq ) HB ( Eq t pTI 3 mod OH OH mod OH OH m ⋅ ⋅ + - = - ( 10
)
where Eq OH are the measured numbers of moles of OH groups/kg for the various samples and M pTI stands for the molar mass of pTI in grams (133.15 g/mol).

These measurements were carried out on numerous samples prepared at various times during this study. All the values obtained for t m are reported as a function of the initially expected modification degree (i.e. the NCO/OH ratio used for the modification reaction) in Figure 6. The results are quite reproducible, but it is also clear that the value obtained for t m is systematically lower than expected, and that the discrepancy is all the more pronounced as higher amounts of isocyanate were used. Part of this reagent (15-20%) thus seems to have been lost in some side reaction. Although the reactions had been carried out using as dry as possible conditions, HB polyesters have been shown to be easily hydrated, especially on carbonyl sites, and the complete removal of water is difficult [27] . The most probable reaction would thus be the reaction of pTI with moisture, leading first to p-toluidine (I) and finally to a substituted urea (II):

N=C=O + H 2 O CH 3 N-C-OH CH 3 O NH 2 + CO 2 CH 3 NH 2 CH 3 N=C=O CH 3 + NH-C-NH CH 3 CH 3 O (I) (II)

Scheme 2

Such species should not interfere with the chemical titration. Therefore the number of OH groups detected should be the actual one, provided that every hydroxyl function (whatever its position in the HB molecule, terminal or linear) is able to react with the titrating agent, tosylisocyanate. In the case of the non-modified HB40, a value of Eq OH equal to the theoretical value associated with the ideal dendrimeric structure, i.e. 8.4 mol OH /kg, was indeed found.

Of course, more information could be extracted from NMR data, and the above hypotheses could be confirmed. After modification of part of the OH groups by pTI, new pseudo-dendritic and pseudo-linear units are generated, and 13 C NMR can be as useful in detecting these units as in the case of the starting HB polyester [21] . All the units that can be found in a partially pTI-modified HB molecule are depicted in Figure 7. D i , L i and T i are the initial dendritic, linear and terminal units, respectively; whereas L u is a new linear unit created by the reaction of a T i unit with one pTI; and D 1u and D 2u arise from the reaction of one pTI with L i , or of two pTI with T i (i.e. 1 pTI with L u ), respectively. Using NMR L i and L u , or D i , D 1u and D 2u cannot be entirely separated, but it is still possible to evaluate the global amounts of D, T and L units.

In Figure 8 is presented the variation in the 1 H NMR spectra of the HB sample modified with 50%pTI. After this modification, new peaks can be detected around 2.2 ppm (CH 3 bound to the aromatic ring) and between 7.0 and 7.3 ppm (aromatic protons), but from these spectra it is not possible to tell whether pTI has indeed reacted with HB40 or not.

The 13 C spectrum of the same sample is shown in Figure 9. The various corresponding integrations are displayed in Table 2. The modified HB displays new C=O peaks between 152.7 and 153.4 ppm, that can be attributed to urethane or urea groups. Aromatic carbons appear between 118.5 and 137.3 ppm, whereas the methyl group originating from pTI can be found at 20.2 ppm. A quantitative analysis of this last resonance allows to calculate the total amount of pTI-derived units with respect to HB (represented by the CH 3 of the D, T and L units), and thus to indirectly verify the amount of pTI that was initially added to HB40 (since the product was recovered by evaporation, see below). But it is also possible to go more into details: 3 types of carbonyl groups are indeed detectable, as well as several signals in the aromatic region that can be attributed to 2 different types of aromatic rings. After synthesizing the symmetrical urea (II) derived from pTI, it was possible to confirm that this compound was indeed present in the pTI-modified HB samples and could account for these multiple peaks.

As stated before, the chemical modification of HB also induces a change in the peaks associated with quaternary carbons, Cq, carbonyls, C=O, and methyl groups of the HB constitutional repeating units (CRU). This evolution is particularly visible in the Cq area of HB40, HBpTI19 and HBpTI40 depicted in

D = D i + D 1u + D 2u (13) it is possible to estimate the relative number of OH groups per CRU, equal to L+2T. The proportion of converted OH groups, t m , is thus given by:

40 HB mod HB m ) T 2 L ( ) T 2 L ( 1 t + + - = (14)
Another possible way to estimate t m is to use the urethane carbonyl area since the peaks associated with C=O (urethane) and C=O (urea) are well separated, provided that a quantitative comparison of their integrations is possible. This was obtained by using an inversegate sequence with suppression of the NOE, and a delay of 10.72 s between 2 impulsions (pulse angle: 70°). Under such conditions t m , which can also be considered as the urethane yield (proportion of initial OH groups that were used to produce urethanes), can be directly evaluated as:

40 HB urethane m ) T 2 L ( ) O C ( t + = = (15)
Finally, as the creation of 1 urea molecule (II) requires 2 pTI, the relative amount of isocyanate consumed by water, or urea yield, is equal to:

40 HB urea ) T 2 L ( ) O C ( 2 % urea + = = (16)
Whereas the total amount of pTI initially added to the HB polyester (pTI/OH 0 ) can be verified from the integration of the aromatic methyl groups:

40 HB phenyl 3 0 0 ) T 2 L ( ) CH ( ] OH [ ] pTI [ + = (17)
As shown in Table 2, this last value is obviously very close to the initially expected modification degrees (12.5, 25 or 50%), but also to the sum (t m + urea%), which proves that all pTI molecules were consumed either in the modification of a hydroxyl end group or in the creation of a urea molecule (II). Moreover, both methods for the determination of t m (equations 14 and 15) lead to very similar results, which confirms the hypotheses made about L u , D 1u and D 2u and validates the previous various estimations. But most important is the fact that the values of t m found by 13 C NMR are also consistent with the results obtained by chemical titration. This result allows to use titration, an easy and immediate technique, rather than the more complicated and rather time-consuming NMR as a systematic method to determine the modification degrees, t m .

Relative reactivities of "linear" and "terminal" hydroxyls

Moreover, additional information can still be obtained from the NMR measurements, concerning the relative reactivities of the different types of OH groups (terminal, T, or linear, L). If the reaction between NCO and OH groups occurred statistically, t m would be equal to the probability of finding 1 reacted OH group, whereas (1-t m ) would be the probability of finding 1 non-reacted OH. Therefore during the chemical modification with a final conversion equal to t m , an initial T unit could lead either to a final L u unit with a probability 2*T i *t m *(1t m ), or to a final D 2u unit with a probability T i *t m *t m , whereas an initial L unit could lead to a final D 1u unit with a probability L i *t m . If all these OH functions were equireactive, the final relative amounts of the 3 types of units D stat , L stat and T stat after chemical modification (t m ) could thus be directly written as a function of t m :

D stat = D i +t m L i + t m 2 T i (18)
L stat = L i + 2t m (1-t m )T i -t m L i (19)
T stat = T i -2t m (1-t m )T i -t m 2 T i (20)
(with D i + L i + T i = D stat + L stat + T stat , and

OH stat = L stat + 2T stat = OH i (1-t m ) = (L i + 2T i )(1-t m ))
In Figure 11, these statistical results were plotted together with the actual values of D, L and T found for crude HB40 and for 3 modified samples. It appears that for every modified HB polymer, the real values of D and T are smaller than what would be expected for equireactive OH groups, whereas higher amounts of L units are systematically obtained as compared to the statistical values. This result proves that OH groups are indeed not equireactive, and more precisely that T-type hydroxyls are more reactive towards pTI than Ltype hydroxyls. This is also consistent with the low degree of branching found for these hyperbranched polymers (see above), with again unexpectedly high amounts of linear units in their structure: whatever the reaction (esterification or addition of an isocyanate), the latter seem to display a lower reactivity, maybe because of a better accessibility for terminal OHs.

This has been explained in the literature in terms of a screening effect that would be most important for inner linear hydroxyls [39] . Also the reactivity of OH groups can be more or less affected by their ability to create hydrogen bonds; terminal OHs are more likely to be involved in hydrogen bonds with other hydroxyls, or even to remain free, whereas linear OHs inside the HB molecules are most probably linked to neighboring carbonyl groups. It has indeed been shown that these latter units were mainly responsible for the creation of ordered domains [29] ; this could also account for a lower chemical reactivity.

As a result, the initial proportion of linear and terminal OHs (respectively 52/48 for the non modified HB polymer) becomes more and more unbalanced as the modification degree increases: HBpTI19 has 30% OH T for 70% OH L , and HBpTI40 only 12% OH T for 88% OH L .

Therefore more and more modified HB samples will probably become less and less reactive.

Effect of chemical modification on thermal and rheological behavior

The thermal behavior of crude and modified HB polyesters was studied by Differential Scanning Calorimetry, DSC. Figure 12 shows the first and second runs obtained for all the samples. In the first scan (up to 140°C), a strong endothermic phenomenon is visible above the glass transition, around 70°C for HB40, as well as for the samples with the lowest modification degrees (HBpTI4 and HBpTI8). This endotherm is most probably associated with hydrogen bonds involving OH groups [27,29] that would induce a pseudo-crystallization phenomenon, and would thus logically tend to disappear for the most modified samples. The second runs were obtained immediately after fast cooling (rate ~ 50°C/min); and show two different phenomena. The first one, once again above Tg and between 50 and 100°C, is clearly visible for non-or little-modified samples and disappears for higher values of t m . In contrast, a new endothermic peak appears around 200°C for strongly modified samples that could not be detected for the others. Consequently, it would be logical to attribute the first peak to the ordering/disordering of domains formed by hydrogen bonds between OH groups, whereas the second peak would be due to the "melting" of quasi-crystalline domains formed by ordered aromatic urethane groups, linked by strong hydrogen bonds in a similar way as the hard segments found in segmented polyurethanes [30] . This hypothesis was confirmed by a WAXS analysis of the same samples, as shown in Figure 13. The spectrum obtained for crude HB40 displays only a broad peak centered on 2θ ≈ 17.5°; whereas strongly modified samples display new sharp peaks at 2θ = 6.5°, 20° and 26.5°, corresponding to characteristic lengths, d, equal to 13.8, 4.4 and 3.4 Å, respectively. In this same figure was also represented the WAXS spectrum of the model diurethane obtained by reacting bis(methylol)propionic acid (the base monomer of our HB polyester) with pTI:

HOCH 2 -C-CH 2 OH COOH CH 3 + 2 NCO CH 3 NH-C- CH 3 CH 3 O-CH 2 -C-CH 2 -O-C-NH COOH CH 3 O O

Scheme 3

This partially crystalline material displays the same diffraction peak at d = 13.8 Å. This peak can consequently be related to a partial crystallization of the 4-methyl phenyl urethane chain ends in the modified samples, provided that the modification degree is high enough to allow the presence of a sufficient amount of urethane groups.

Moreover, the second DSC scans also allow the determination of the glass transition temperature of the pristine and modified HB polyesters. The values obtained for numerous samples are represented as a function of t m in Figure 14. It is clear from this curve, as well as from Figure 12 that Tg increases linearly with the modification degree. In the literature, other chemical modifications of HB chain ends have been performed and resulted in variable effects on the glass transition temperature of the modified materials, but showing generally that Tg of HB polymers is mostly affected by the polarity of terminal groups [21,40] . For example using increasing amounts of long aliphatic chains induced a regular decrease in Tg [41] . In contrast, in this work the creation of new rigid units, replacing rather weak hydrogen bonds between OH end groups by stronger bonds between urethanes results in an overall lower mobility for the ends of the branches of the HB molecule and therefore in an increase in Tg, just like it could be observed for a linear telechelic oligomer endcapped with a monoisocyanate [42] .

Rheological measurements were also performed on the pristine HB40 and on modified samples at 110°C, i.e. above both their glass transition and the first phenomenon detected by DSC. Under these conditions all of them, even those with the highest modification degrees, display a newtonian behavior (Figure 15). This means that no entanglement exists between the different HB molecules in the liquid state, even after a partial modification of the chain ends by a short, rigid moiety. Moreover this result also suggests that the interactions between urethane groups mentioned just above, and responsible for the endotherm at 200°C, would rather be intramolecular and not intermolecular, otherwise the newtonian character would be altered below this temperature. This could be due both to the linear character of a great part of the initial OH groups and to a tendancy of the chain ends to fold back inside the molecule.

The values obtained for the complex viscosity, η*, nevertheless increase with increasing t m , presumably simply as a consequence of the non-negligible increase in molar mass. More precisely, using the average molar mass measured by SEC-MALLS at M n = 2930 g/mol and the corresponding number average functionality, f n OH ~ 24.6 OH/molecule [36] , with t m = 64%

M n would increase up to about 5030 g/mol. Indeed, hyperbranched polymers usually display an increase in their zero-shear viscosity with increasing generation and molar mass [4] .

Concerning Boltorn  hyperbranched polyesters, their hydrodynamic radius was shown to scale as R h ~ M 0.39 [5] . Moreover in a work on the rheological behavior of dendritic polymers, Sendijarevic showed that for a series of dendrimers with the same architecture, for a given generation the nature of the chain ends also had a very important effect on the viscosity [4] .

Other measurements were also carried out using temperature (20-150°C) and frequency

(1, 10, 100 rad.s -1 ) sweeps. Only one α relaxation was detected in the G" and tanδ spectra, in agreement with the microcalorimetric studies. Another interesting feature is the rheological behavior of these samples at high temperature, as depicted in Figure 16. Three samples (pristine HB40, and samples with t m = 19 or 40%) were characterized at three different frequencies (ω = 1, 10 and 100 rad.s -1 ). The overall behavior can be seen in Figure 16a. At low temperature, η* depends mainly on the pulsation as the samples are in the glassy state, whatever their modification degree. When increasing temperature, these three groups of curves progressively diverge as the samples find themselves above their Tg; at such temperatures three new groups of curves are formed when the curves associated with a particular value of t m merge: above Tg and up to about 110°C, η* depends only on t m , whatever the frequency, consistently with their newtonian behavior already depicted in Figure 15. But at even higher temperature, a new phenomenon occurs that is more easily seen in Figure 16b. Whereas pristine HB40 keeps its newtonian behavior up to 160°C (blue curves), this character is lost for modified samples above 110-120°C, with an increase in viscosity observed especially for lower frequencies. No special phenomenon was detected by TGA in this temperature range (see Figure 5); moreover, a new chemical titration of the hydroxyl functions was carried out on the samples after these rheological measurements and revealed that the OH equivalent weights were exactly the same as before the experiment (for example before the experiment Eq OH (HBpTI40) = 3.52 mol/kg, after the experiment 3.51 mol/kg); therefore no side reaction inducing molecular coupling (such as etherification between two OH chain ends) must have occurred. In the same way, no difference could be observed in the size exclusion chromatograms of the samples before and after the measurement. Finally a DSC analysis of these samples was performed. After a first scan up to 150°C to eliminate all low-temperature phenomena, they were cooled back to room temperature (-50°C/min) and heated up again to 250°C at 10°C/min. Figure 17 displays the curves obtained for HBpTI40 before and after the rheological analysis. For the latter sample, Tg is slightly higher (44°C instead of 42°C), but the endotherms are also detected at higher temperature. Therefore the loss of newtonian behavior might be due to a better ordering of the already existing tolyl urethane domains, together with the establishment of new intermolecular interactions between tolyl urethane (end)groups. They could be favored by the slow increase (3°C/min) in temperature as it approaches that of the "melting" of such ordered domains, observed above ~ 150°C in the DSC traces recorded at 10°C/min. In a similar way, at high temperature segmented polyurethanes often display successive endotherms associated first with the micromixing of soft and hard domains, and slightly above with the melting of microcrystalline hard segments [43][44][45][46] . Annealing at increasing temperature (between 120 and 200°C) has often been shown to induce a better ordering of the domains and thus to result in an increase in the intermediate endotherm temperature; the same kind of phenomenon could be observed in this work.

Conclusions

A commercial hyperbranched polyester with multiple hydroxyl functional groups, HB40, was partially endcapped using p-tolylisocyanate, pTI, in order to obtain potential crosslinkers that would be miscible with usual polyurethane precursors (macrodiol and diisocyanate). The final microstructure of the modified samples was then characterized with the help of 1 H and 13 C NMR and the results compared with those of a chemical titration. The latter proved to be sufficient for a first approximation of the OH conversion or modification degree, t m . However NMR allows a more precise determination of t m , and also the estimation of the amount of pTI lost in a side reaction with moisture leading to non-reactive urea molecules.

Moreover, the use of NMR proved that OH groups belonging to linear bis(MPA) units were less reactive than those born by terminal bis(MPA) units, thus inducing a progressive decrease in the reactivity of increasingly modified samples that obviously bear increasing proportions of linear units.

This chemical modification was also shown to induce an overall increase in the Tg of these hyperbranched oligomers, as well as the creation of partially ordered domains between urethane groups for the samples with the highest modification degrees. The modified samples seem to be stable up to quite a high temperature, however their newtonian behavior tends to be altered by long annealing above 110-120°C, suggesting additional intermolecular associating phenomena. All these important parameters will have to be considered for the synthesis of the polyurethane networks, that will be described in a coming paper.

Figure captions

  115 g/mol, M c [molar mass of the core moiety, pentaethoxylated pentaerythritol] ~ 352 g/mol and according to eq. 3 f n = n CRU DP n ~ 24.5

Figure 10 .

 10 With increasing modification, a decrease in the intensity of T signals, as well as the appearance of new peaks in the L and D areas, are clearly visible. By comparing the global relative integrations of the 3 areas, i.e.: T = T i (11) L = L i + L u (with D + L +T = 1)

  1 H, 1.0-1.4 ppm) with TFA C=O ( 13 C, ig, 171-175 ppm) Cq ( 13 C, ig, 45-51 ppm)

Figure 1 :Figure 2 :Figure 3 : 1 HFigure 4 :Figure 5 :Figure 6 :Figure 7 :

 12314567 Figure 1: Ideal reaction scheme for the synthesis of well-defined polyurethane networks based on hyperbranched crosslinking agents Figure 2: Typical structure of a third-generation hyperbranched polyester based on bis(MPA) Figure 3: 1 H and 13 C NMR spectra of the fourth-generation hyperbranched polyester (HB40, Boltorn™ H40); s = protonated residue of DMSO-d6 Figure 4: Determination of D, L and T units by NMR. a) 1 H, CH 3 ; b) 13 C, Cq; c) 13 C, C=O Figure 5: Thermogravimetric analysis of pristine HB40 ( ) and of HB40 modified with various proportions of pTI; : 8%; : 19%; : 40% Figure 6: Actual modification degree, t m , obtained as a function of the expected value (initial [NCO]/[OH] ratio) Figure 7: Various D, L and T units in a partially pTI-modified HB polyester sample

Figure 8 : 1 HFigure 9 :Figure 10 :Figure 11 :Figure 12 :

 819101112 Figure 8: 1 H NMR spectrum of HB40 modified with 50% pTI (t m = 40%); s = protonated residue of DMSO-d6 Figure 9: 13 C NMR spectrum of HB40 modified with 50% pTI (t m = 40%) Figure 10: Cq area in the 13 C NMR spectra of a) pristine HB40; b) HBpTI19; c) HBpTI40 Figure 11: Variation of the proportion of D, L and T units with tm; (…, open symbols): all OHs equireactive; (, full symbols): experimental values Figure 12: DSC curves for pristine and variously modified HB40 samples: : pristine HB40; : HBpTI4; : HBpTI8; : HBpTI19; : HBpTI40; a) first scans; b) second scans after rapid cooling (-50°C/min).

Figure 13 :

 13 Figure 13: WAXS analysis of pristine HB40 and of two pTI-modified samples; comparison with pTI-modified bis(MPA).

Figure 14 :

 14 Figure 14: Glass transition temperature of the variously modified HB samples (from second DSC scans) as a function of their measured modification degree, t m .

Figure 15 :

 15 Figure 15: Complex viscosity of pristine HB40 and of 3 modified samples at 110°C.

Figure 16 :

 16 Figure 16: Complex viscosity of pristine and modified HB40 during a temperature scan (3°C/min) from room temperature up to 150°C; : HB40; : HBpTI19; : HBpTI40; clear color: 1 rad.s -1 ; medium color: 10 rad.s -1 ; dark color: 100 rad.s -1 .

Figure 17 :

 17 Figure 17: DSC analysis (second scan, after a first scan from -30°C to 150°C at 10°C/min and fast cooling) of HBpTI40: ( ) before rheological characterization; ( ) after rheological characterization.

  Figure 1

Table 2 :

 2 NMR analysis of HB40 and of 3 increasingly modified samples, and various values deduced from peak integrations

	Sample	Expected tm (%)	D (Cq)	L (Cq)	T (Cq)	average number of OH/CRU (L+2T)	C=O urethane	C=O urea	CH 3 phenyl	t m from D, L, T (%)	t m from C=O	t m from titration	urea yield %	t m (mean value) + u%	pTI / initial OH (from CH 3 phenyl)
	HB40	0	0.178	0.552	0.265	1.083	0	0	0	0	0	0	0	0	0
	HBpTI9	12.5	0.209	0.597	0.194	0.985	0.109	0.017	0.154	9.6	10.0	8.7	3.1	12.9	14.2
	HBpTI19	25	0.252	0.613	0.136	0.885	0.177	0.031	0.251	18.7	16.3	19.0	5.7	23.2	23.2
	HBpTI40	50	0.351	0.604	0.045	0.694	0.414	0.051	0.536	36.3	38.0	40.5	9.4	46.6	49.5

Acknowledgements

This work was initially undertaken within the framework of a European Copernicus Program on "Environmentally friendly crosslinked polyurethane materials from precursors of compact architecture". Fruitful discussion with all the participants, and especially the help of Prof. M.

Žigon and Dr E. Žagar for SEC-MALLS measurements, is gratefully acknowledged.