domain: spi phys chim

text:
Mathieu Fèvre
email: mathieu.fevre@onera.fr

Juan M Sanchez

Ross J R Stewart

Jean Sébastien Mérot

Frédéric Fossard

Yann Le Bouar

Katsushi Tanaka

Hiroshi Numakura

Guy Schmerber

Véronique Pierron-Bohnes

J.-M Sanchez

J R Stewart

J.-S Mérot

Investigations of the Co-Pt alloy phase diagram with neutron diffuse scattering, inverse cluster variation method and Monte Carlo simulations

Keywords: numbers: 61.12.Ex, 64.60.De, 64.60.Cn, 75.50.Cc, 81.30.Bx

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

Understanding the mechanisms governing the phase stability of alloys is essential to predict the modification of their bulk physical properties by surface or confined effects.

This has important consequences especially in catalysis, optic, plasmonic or magnetic based applications. In all generality, in metals, transformation temperatures can be sustained by different effects such as chemical, elastic, electronic or magnetic interactions and couplings.

Identifying the major contributions which must be incorporated in models to reproduce the thermodynamics of alloys is therefore important. For the Co-Pt system, this task has not been fully completed yet. At the present time, an accurate description of the concentrationtemperature phase diagram of the Co-Pt system by atomistic approaches is still absent.

In the solid state, Co 1-x Pt x alloys exhibit three ordered phases with the classical AuCu (L1 0 ) and AuCu 3 (L1 2 ) ordered structures around the CoPt, CoPt 3 and Co 3 Pt compositions. Order-disorder transitions take place at temperatures close to 1100 K, 1000 K, and 830 K respectively 1-3 . The difference of 170 K between the ordering temperatures of the Co 3 Pt and the CoPt 3 phases cannot be explained by lattice mismatch ( 10%) and elastic moduli differences ( 20%) between α-cobalt and platinum. It was suggested by Monte Carlo simulation that in binary A-B alloys of the face centered cubic (FCC) structure the order-disorder transition temperature of AB 3 is higher than that of A 3 B when the atom species B is smaller in size 4 . However, the trend is the opposite in the Co-Pt system 1,5 .

In this system, the Curie temperature decreases rapidly 6 from T CM = 1400 K at x = 0 to T CM = 0 K at x = 1.0. The ordering transition occurs in the ferromagnetic domain for the Co 3 Pt phase and in the paramagnetic domain for the CoPt and CoPt 3 phases. The importance of magnetism in the formation energies of Co-Pt has been demonstrated using ab initio electronic structure calculations 7,8 .

Phase stability and thermodynamics of substitutional binary alloys have been extensively studied on rigid lattices using phenomenological approaches such as lattice gas models coupled to statistical mechanics methods. This consists in describing the internal energy of the alloy by occupational degrees of freedom, related to chemical species, interacting through an Ising-like Hamiltonian which is expressed as a sum of pair and higher order multiplet interactions (triplets, quadruplets, ...). In the general perturbation method, the ordering energy is written as a perturbation development with respect to a reference state corre-sponding to the random alloy. For phase diagram calculations in transitions metal alloys with ordering on a fcc lattice, it has been shown using tight-binding calculations that (i) the pair approximation is valid provided their concentration dependence is taken into account 9,[START_REF] Ducastelle | Order and Phase Stability in Alloys, Cohesion and structure[END_REF] , (ii) the magnitude of the effective pair interaction (EPI) follow the hierarchy

| Ṽ1 | >> | Ṽ2 , Ṽ3 , Ṽ4 | >> | Ṽ5 , Ṽ6 , • • • |,
where Ṽi is the EPI related to i th nearest neighbor sites.

A useful consequence of describing binary alloys in terms of EPI rely on the fact that, providing that chemical effects can be separated from other contributions (elastic, magnetic, ...), they can be determined quite simply using diffuse X-ray or neutrons scattering experiments.

The pair interaction approximation therefore provides a framework where outcomes arising from experiments and first principles calculations can be confronted or combined. However, due to its simplicity, this approach suffers from several general limitations : (i) the described model is relevant when chemical effects are the driving force of the phase stability. For the L1 0 -A1 transition, this condition is fulfilled since the primary order parameter is related to chemical ordering whereas the deformation of the unit cell is a secondary order parameter 11 , (ii) EPI are determined for a given alloy composition. The formalism is in principle not relevant if the phase transition involves two-phase domains where the concentrations related to the coexisting phases significantly differ from the concentration corresponding to the disordered state.

At the CoPt composition, the derivation of EPI from the formation energy of stable and metastable phases led to a transition temperature which was about half of the measured one 12 . This suggests that some effects not taken into account in the ab initio calculations and in the cluster expansion (CE) formalism 13 prevent the accurate prediction of the transition temperature. This could be the contributions of the vibrational free energy 14 or electronic excitations 15 .

The short-and long-range orders (SRO and LRO) developing in the disordered state close to solid-solid phase transitions have been investigated using neutron and X-ray diffuse scattering experiments near the Co 3 Pt and CoPt 3 compositions 5,16 . The EPI calculated with the Inverse Cluster Variation Method 17 (ICVM) exhibit an important composition dependence of the nearest neighbor pair interaction energy. As the measurements on Co 3 Pt were carried out in the ferromagnetic domain whereas those on CoPt 3 were made in the paramagnetic domain, this behavior could be attributed to the effect of magnetism. Similar measurements at the CoPt composition could answer this question. The Monte Carlo simulations performed on a rigid face centered cubic (FCC) lattice with the derived EPI succeeded in reproducing the experimental ordering temperatures. This shows that effective pair interactions determined from diffuse scattering measurements on Co-Pt alloys can be used as quantitative data for developing atomic interaction potentials -implemented on-or off-lattices -capable of describing accurately the main features of the alloy phase diagram (ordering temperatures, asymmetry, compositions related to congruent transformations). This step is the basis for studies devoted to precipitation kinetics 18,19 or surface and interface phase stability [20][21][22] for example.

Semi-empirical atomic interaction potentials were also employed to study the Co-Pt system. Due to the great interest associated with the use of nanoalloys with the L1 0 structure in high density recording media, the CoPt composition was intensively investigated. In most parametrizations of the tight-binding formalism within the second moment approximation of the electronic density (TB-SMA), the ordering temperature is below the measured one (within a 15%-50% interval) [23][24][25][26] . A recent calibration provides better results since the ordering temperature of the CoPt and CoPt 3 phases were in good agreement with experiments 22 . However, the asymmetry of the phase diagram with respect to the equiatomic composition was not reproduced. Indeed, the transition temperature of the Co 3 Pt phase is also close to T = 1000 K instead of T = 830 K. The Embedded Atom Model (EAM) was not more successful 27 . Encouraging results have been provided by a Modified EAM (MEAM) model, which successfully reproduces the asymmetry between the L1 2 structures with deviations of 7-8% from experimental values 28 . The ordering temperature of the L1 0 phase is however 12% lower than in measurements and 100 K lower than the one related to the CoPt 3 phase. With the objectives of (i) determining if the strong concentration dependence of Ṽ1 is related to the sample magnetic state at the measured temperatures, (ii) acquiring quantitative data on the SRO developing at temperatures close to the ordering temperature, (iii) providing interaction energy for developing reliable atomic potentials, we have carried out neutron diffuse scattering measurements on CoPt single crystals. EPI are deduced within the ICVM. Monte Carlo simulations are performed to calculate transition temperatures, SRO, LRO, and phase equilibria related to the measured and reported EPI for the Co-Pt system.

II. NEUTRON DIFFUSE SCATTERING MEASUREMENTS A. Experimental details

A CoPt single crystal of equiatomic composition was grown using the Bridgman technique from a polycrystalline ingot prepared by arc melting of 4N metals under an argon atmosphere. The crystal bar was homogenized with a 168 hours heat treatment at 1373 K under secondary vacuum ended by air quench. Three cuboidal specimen with dimensions close to 4.5 mm × 4.5 mm × 4.5 mm and faces oriented parallel to a (001) (for two of them) and 110-type (for the other four) crystallographic planes were then shaped with the spark erosion technique.

To minimize absorption and multiple scattering effects, the three samples were stacked up for the neutron measurements. After the first measurements at T ds = 1203 K and T ds = 1423 K with horizontal (001) faces ((001) diffraction plane), each sample was rotated by 90 degrees to switch to the (110) diffraction plane.

Diffuse scattering measurements were performed with the D7 time-of-flight spectrometer of the Institut Laue-Langevin (ILL) using an unpolarized neutron flux with an incident wavelength of λ = 3.02 Å. The 4-slits chopper rotation frequency was 133 Hz. The samples were wrapped in a niobium foil fixed on a high temperature boron nitride holder in a high temperature furnace mounted on a ω-rotation stage (the furnace rotation axis is vertical).

The scattered intensity was recorded with four banks of 16 3 He-gas detectors covering the diffraction angles, 2θ, from -80 • to 145 • with a step of about 3 • . The ω sample rotation extended on 180 • with a 2 • step at T ds = 1203 K and a 4 • step at T ds = 1423 K. The incident beam was monitored from its diffusion by a niobium foil. Signals with the empty furnace and with an absorber (a Gd rod with the same width and place as the sample) were registered at the two temperatures in order to correct the signal from instrumental background. Measurements with a vanadium rod was also made in the same geometries at room temperature to calibrate the detectors.

A time-of-flight (TOF) analysis was performed to separate the elastic signal from the phonon and magnetic inelastic contributions, which are quite important at the investigated temperatures. The elastic intensity was modeled by a trapezoid convoluted by a Gaussian shape adjusted on the signal measured on the vanadium reference sample at T = 300 K (Fig. 1). The elastic line-width was close to 2.2 meV. Inelastic and quasi-elastic scattering (phonons) were modeled by Gaussian functions. For further analysis, we only considered spectra where elastic and inelastic contributions were well-separated. Moreover, spectra where a high elastic signal was originating from the high temperature chamber (detected The intensities deduced from the TOF spectra were corrected for instrumental background, detector efficiency, dynamic atomic displacements (Debye-Waller attenuation), multiple scattering and sample absorption with the procedures reported by Kentzinger et al. 16 .

The corrected intensity is referred to as I exp . In the following, intensities are expressed in Laue units (LU), which is defined by: 1

LU = N x(1 -x)(b Co -b Pt ) 2 , with b Co = 2.49±0.02
fm and b Pt =9.60±0.01 fm, the Co and Pt nuclear coherent scattering lengths, N the number of atoms in the sample and x the concentration of Pt. In a fully disordered alloy, I exp is constant and equal to 1 LU.

B. Experimental results

The intensity maps measured at T ds = 1423 K and T ds = 1203 K for the (001) and ( 110 As expected the diffuse intensity decreases with increasing temperature. The maps show the symmetries expected in a cubic lattice in the two investigated planes. The displacements are small because, in the intensity maps, there is neither a significant shift of the maxima positions from the superstructure positions, nor an asymmetry of the peaks, nor a detectable difference between (100)-, (110)-, and (120)-type superstructure peaks.

III. DATA ANALYSIS A. Short-range-order parameters

The corrected intensities were then used to determine the Warren-Cowley short-range order parameters defined as:

α p = α p = 1 -P A(B) (r p )/c A , (1)
where P A(B) (r p ) is the probability to have an A atom on the site r p = a 2 (l, m, n), knowing that there is a B atom at the origin. p stands for the integers (l, m, n) and p for the number of the shell occupied by site (lmn) and its equivalents by symmetry. A positive (respectively negative) α p value corresponds to an attractive (respectively repulsive) chemical interaction between the central atom and the atoms of the same species in the p-th shell.

The separation of the contributions related to the chemical SRO and the static atomic displacements was achieved using the Borie and Sparks 29 formulation. The method, adapted when small displacements occur, consists in writing the modulated intensity as a sum of a term associated with the correlations between chemical species and terms related to static displacements. In CoPt 3 16 and Co 3-Pt 1+ alloys 5 , the first order term in the displacement expansion was sufficient to have a good description of the scattered intensity in spite of a 13% atomic size mismatch between cobalt and platinum. Local distortions may be indeed small even for large atomic size differences. In this study, the measured intensities were thus also described using the first order development in the displacements u p at lattice site r p :

I exp (q) = I SRO (q) + I D1 (q) + I cst , (2)
where q is the scattering vector, I cst is a constant term related to incoherent scattering, whereas I SRO and I D1 are the short-range order and displacement contributions, cross sections per atom in Laue units given by:

I SRO (q) = p>0 α p cos(q • r p ) = α(q) (3)
I D1 (q) = 3 i=1 h i Q i (q), (4)
where {h i } are the coordinates of the scattering vector in 2π/a units (RLU). The quantities Q i (q) are related to the Fourier transform of the first-order displacement parameters γ i p :

Q i (q) = p γ i p sin(q.r p ) (5)
In an equiatomic alloy, the displacement parameters γ i p are defined by :

γ i p = - 2π a τ,τ b τ b τ ∆b 2 ρ 2,p (τ τ ) ∆u τ τ p,i , (6)
where ∆u τ τ p,i is the average relative displacement between atoms of type τ and τ (i.e. In Eq. 2, the q-independent term has the following form :

I cst = 1 + I nucl + I para , (7)
where the first term on the right-hand side, unity, is the SRO contribution when r p = 0, the second term is the incoherent nuclear scattering arising from isotopic and nuclear spin disorder and the last term is related to the incoherent cross section due to magnetic moments of electrons in the paramagnetic phase. The last two contributions are calculated respectively with incoherent nuclear scattering cross sections and magnetic moments reported for Co and Pt atoms. For the sake of readability, the calculations are detailed in Appendix B. I cst is found equal to 3.14±0.33 LU assuming that Co atoms hold their room temperature moments and 2.55±0.14 LU assuming that they have zero magnetic moments. The Pt moment is assumed to disappear in the paramagnetic phase.

A least-squares procedure was used to reproduce the corrected data with Eq. 2 using sets of SRO parameters α p and first order displacement parameters γ i p . After an analysis of the sensitivity to the number of p shells in Eqs. 3 and 4, the best results were obtained with N SRO = 20 and N D1 = 7 for both temperatures investigated. The corresponding values are reported in Appendix A (Tab. II and Tab. III). I cst was 2.992±0.010 LU at T ds = 1203 K and 2.962±0.015 at T ds = 1423 K. The paramagnetic moments thus do not change significantly between the two temperatures and are equal to 1.52±0.06 µ B on average. The paramagnetic state so pertains to a situation where Co atoms hold their room temperature moments (within experimental uncertainties 30 ).

The contributions to the diffuse intensity calculated with the obtained SRO and first order displacement parameters are represented in Fig. 3 for measurements at T ds = 1423 K and T ds = 1203 K. I SRO presents all symmetries of a cubic reciprocal space (mirrors, rotation and translation symmetries); I D1 presents the mirrors including O, the origin in the reciprocal space, and π/4 (only in (001) plane) and π/2 rotations around O due to the h i term in Eq. (4). Only the top-right quarters of the simulated maps are shown as they can be extended taking into account the symmetry planes including O. Note that the scales are different for I D1 that is much smaller in amplitude than I SRO and presents changes of sign. The γ i p values are lower than 0.07, which is consistent with the hypothesis of small displacements amplitudes assumed in the Borie and Spark formalism 29 . They are also of the same order of magnitude as those measured for a CoPt 3 alloy 16 . The agreement between experimental and simulated intensities is assessed by analyzing profiles going through four superstructure reflections, which are associated with SRO parameters of the alloy (dashed lines in Fig. 2). The intensity profiles related to measurements at T ds = 1423 K and at T ds = 1203 K are represented in Fig. 4. Experimental data correspond to symbols with error bars and calculations to colored lines whose thickness indicates the uncertainty resulting from the data processing. For T ds = 1423 K, the intensity at the maxima is satisfyingly reproduced with N SRO = 20 (Fig. 4a). For T ds = 1203 K, increasing N SRO from 20 to 30 allows to increase the intensity at the maxima and to reach the experimental error bars, but it strongly increases the uncertainty on the resulting values (Fig. 4b). In addition, the first SRO parameters are not sensitive to the variation of N SRO . Therefore, twenty parameters were used to describe the short-range order in the CoPt alloy. Since measurements were performed about 100 K above the ordering temperature, the difficulty T Ṽ1 -Ṽ4 (K) 1085±87 1005±48 480 1120

T Ṽ1 -Ṽ6 (K) a 1095±95 1025±65 480 1120
a with Ṽ5 = 0 to fully match measurements with simulations for T ds = 1203 K is probably inherent to some pre-transitional effects.

B. EPI from inverse cluster variation method

The next step was to determine the effective pair interactions (EPI) from the experimental values of SRO parameters α(r p ). This was performed with the ICVM previously used to fit SRO data for CoPt 3 in [16] and for Fe 0.804 V 0.196 in [31]. The Hamiltonian of the system was described by:

H({p i }) = 1 2 N i,j =i=1 Ṽ (r ij ) σ i σ j , (8)
with Ṽ = (V CoCo + V PtPt -2V CoPt )/4, the EPI which depend on the distance r ij = r p between atoms located in a fixed FCC lattice. σ i = ±1, is the spin variable related to the occupation of the atomic site i. In the C-O approximation, the farthest pairs considered are the sixth neighbor pairs. Nevertheless, the fifth neighbor pairs are excluded since they do not belong to the maximum clusters, the face-centered cube and the 13-point cubo-octahedron [START_REF] Finel | Statics and Dynamics of Alloy Phase Transformations[END_REF] .

However, it can be assumed that they have a weak contribution to the alloy stability since the amplitude of SRO parameters decrease in the following order: second, first, fourth, sixth, fifth, and third (Tab. II in Appendix A). The EPI obtained from our measurements are listed in the upper part of Tab. I (ICVM) as well as those reported in the literature 12,22 and based on rigid FCC lattice calculations. The values determined from the neutron diffuse scattering measurements significantly differ from those obtained from the cluster expansion approach (CE) and the tight-binding Ising model (TBIM). The repercussions on transition temperatures and short-range order are discussed in Sec. IV.

C. Monte Carlo calculations (MC)

With the aim of determining the order-disorder (OD) temperatures and the SRO parameters, the EPI obtained from the ICVM and those reported in the literature were used as input parameters of Monte Carlo simulations carried out on a rigid FCC lattice with periodic boundary conditions. The calculations were carried out with 20 × 20 × 20 unit cells of 4 atoms. The initial configuration of the Markov chain consisted in a random solid solution.

The thermodynamics of the binary alloy was described with the Hamiltonian of Eq. 8. A detailed description of the code and the methodologies developed to determine phase diagrams of binary alloys in different thermodynamic ensembles were provided in previous papers 4, 33 .

To calculate the alloy phase diagram, the Monte Carlo simulations were performed in the semi-grand canonical (N, ∆µ, V, T ) ensemble where the total number of atoms N , the alloy chemical potential ∆µ, the volume of the simulation V and the temperature T are fixed quantities. The Metropolis algorithm 34 is applied to changes of atomic species on single sites (Co ↔ Pt flipping mechanism). The composition was thus not conserved during the Markov chain. The advantage of the semi-grand canonical thermodynamic ensemble is that only single phases take place in the simulation, thus avoiding artificial effects caused by interfaces between ordered and disordered phases. The ordering state of the alloy is monitored as a function of the composition and the temperature with a LRO parameter defined within the concentration wave representation 2, [START_REF] Khachaturyan | Theory of Structural Transformations in Solids[END_REF] . The order-disorder temperatures corresponding to all the EPI sets are reported in Tab. I (T OD ). The temperature dependence of the LRO parameter calculated for the EPI determined at T ds = 1203 K and at T ds = 1423 K exhibits a similar behavior (Fig. 5): the two curves are superimposed in the disorder state and the discontinuity of the order parameter at the transition is the signature of a first order transformation. The amplitude of the discontinuity is 0.23 for the highest temperature and 0.16 for the lowest. This hierarchy tends to consolidate the fact that the transition is weakened by some pre-transitional effects. The transition temperature depends on the interaction cutoff distance (Fig. 6). For EPI determined at T ds = 1423 K (filled symbols), a 500 K jump is indeed observed when interactions farther than the third neighbors are considered. Weak effects are observed between the second and the third, or between the fourth and the sixth interaction distances. For the EPI determined at T when these two temperatures are not distinguishable.

α p = ρ p -y 2 1 -y 2 , (9)

IV. DISCUSSION

Neutron diffuse scattering measurements were carried out at two temperatures close to the order-disorder transition of the CoPt alloy. The main outcome is the determination of the effective pair interactions (EPI) which reproduce (i) the short-range order developing close to the transition as well as (ii) the experimental ordering temperature, T OD . The temperature sensitivity of the EPI allowed to evaluate (i) the reliability of the results, and

(ii) the presence of magnetic or pre-transitional effects. The analysis of the constant term of the diffuse scattering cross section resulted in the estimate of the average magnetic moment in the paramagnetic regime. Using Monte Carlo simulations, the phase stability of the alloy at and around to the equiatomic composition and the uncertainties related to the data analysis were investigated. The importance of interactions up to the fourth atomic neighbor shell was pointed out. In order to evaluate the stability of these approaches to predict accurately the SRO state and the order-disorder temperature at the CoPt composition, the EPI obtained at high temperature were confronted to those arising from theoretical studies based on the cluster expansion (CE) and the tight-binding Ising model (TBIM). By considering all the diffuse scattering measurements carried out for the Co-Pt system 5,16 , we obtain the concentration dependence of the EPI providing the basis for the development of reliable atomic interaction potentials that can reproduce the composition-temperature phase diagram of the Co-Pt alloy (such EPI were still missing at present). We now discuss all these aspects based on the results presented above.

Temperature effects. The neutron diffuse scattering measurements were carried out at temperatures 383 K and 603 K higher than the Curie temperature of the alloy (T CM = 820 K in the disordered A1-CoPt 6 ). In this high temperature range, magnetic correlations were expected to be negligible and the EPI should correspond to the mean field limit, thus being temperature independent [START_REF] Pierron-Bohnes | [END_REF] . This is verified in this study; differences were not more than a few meV between the two measurement temperatures (Fig. 7a). Such variations were of the order of the usual accuracy provided by the measurement technique and by the hypotheses made in the data analysis 16 . The temperature dependence of the EPI mainly affected the SRO parameters related to the shells farther than the fourth atomic neighbor distance with relative deviations in the 22%-44% interval (Fig. 7b). Moreover, the deduced ordering temperature (T OD , see Tab. I) is close to the experimental one (1098 K). A 10% difference (100 K) was observed between the two measurement temperatures. Since the accuracy of the ordering temperature determination is close to 90 K, it is not possible to affirm that this difference is inherent to some physical effects.

The q-independent term of the diffuse scattering intensity differed by about 1% between the two investigated temperatures. Therefore, the average paramagnetic moment of 1.52±0.06 µ B , determined from the measurements, was not significantly modified by temperature.

Importance of interactions. Starting from the EPI determined up to the sixth neighbor shell, the influence of the interaction distance on the ordering temperature and the shortrange order close to the transition was investigated with Monte Carlo simulations. Considering the interaction between sixth neighbors (sites at the ends of the body diagonal of the cubic unit cell) increases the ordering temperature by 53% in comparison to the situation where interactions up to the second or up to the third neighbors are considered (Fig. 6a). A good agreement with the experimental temperature was obtained only in calculations which use interactions farther than the third neighbor shell. The discontinuity of the LRO parameter at the transition temperature followed the behavior found at the ordering temperature: a value of 0.43±0.01 was calculated when interactions up to the third neighbor shell were considered and a value of 0.23±0.01 was calculated when considering interactions up to the fourth and sixth atomic distances. The SRO parameters calculated with interactions up to the second and third neighbor shells were similar due to the weak value of Ṽ3 and strongly differed from the SRO parameters calculated with interaction up to the sixth neighbor shell in terms of amplitude and sign (Fig. 6b). When EPI related to the fourth neighbor shell were included, the SRO parameters of the two sets were equal for distances up to the eighth neighbors. Farther, SRO parameters related to interactions up to the fourth neighbor shell exhibited non zero values (Fig. 6b).

Reliability of the reported EPI. The EPI measured in this study can be compared to those reported in the literature for the CoPt alloy. Fig. 7(a) represents the EPI calculated by Chepulskii et al. 12 using the cluster expansion approach (CE) and those deduced by Lopes et al. 22 within a tight-binding Ising model (TBIM). The corresponding ordering temperature and SRO parameters are provided in Tab. I and in Fig. 7(b) respectively. EPI obtained from the CE were rather close to those measured in this study. However, the SRO parameters and the ordering temperature (450 K) were not in good agreement with experimental results.

This shows that some missing contributions play a significant role in the thermodynamics of CoPt alloys (e.g., vibrational free energy 14 , electronic excitations 15 ). EPI obtained from TBIM are strongly different from the EPI derived in this study but the SRO parameters are in good qualitative agreement. For the first neighbor shells, relative errors are indeed in the 10%-25% interval depending on the temperature. 41% and 102% discrepancies are, however, observed for α 2 at 1203 K and α 3 at 1423 K. As expected, the ordering temperature is equal to the measured. Indeed, this was a constrain in the determination of EPI 22 . The relatively good description by the TBIM EPI of SRO developing close to the ordering temperature has to be pointed out because the transition temperature is the only information directly related to the high temperature thermodynamics which was included in the fitting procedure. those at x = 0.5. For the sake of readability, the EPI measured at T ds = 1423 K are shifted in composition by ∆c = 0.03. Red lines are quadratic fits to the EPI measured in the previous studies 5,16 . For the CoPt alloy, the EPI measured at T ds = 1203 K follow quite well the fits. The calculated ordering temperature is, however, 75 K below the experimental one. The EPI measured at 1423 K deviate by a few meV from the quadratic behavior. The transition temperature is nevertheless equal to the experimental one. This is consistent with the formation enthalpy of the L1 0 structure, which writes:

Concentration

∆E L1 0 = -16 Ṽ1 -32 Ṽ3 -32 Ṽ5 , (10)
for interactions up to the sixth atomic shell. Assuming that Ṽ5 is zero, ∆E L1 0 is -226±23 meV.atom -1 for T ds = 1203 K and -240±31 meV.atom -1 for T ds = 1423 K.

In Fig. 9, the EPI determined in the paramagnetic state for the Co 0.5 Pt 0.5 alloy do not exhibit a singular behavior with respect to those determined in the ferromagnetic state for the compositions Co 0.75 Pt 0.25 and Co 0.65 Pt 0.35 . The drop in the composition dependence of Ṽ1 is therefore not caused by the change of the magnetic state at the measurement temperature.

At high temperatures, in the chemically disordered state (A1 structure), the average magnetic moment of the CoPt alloy was estimated to be 1.52±0.06 µ B and temperature independent. This value is close to the magnetic moment of ferromagnetic cobalt (1.76±0.26 µ B ) obtained from X-ray magnetic circular dichroism (XMCD) measurements at room temperature and ab initio calculations 30 . It is also in agreement with the Curie-Weiss-type behavior observed in the ordered and disordered states [START_REF] Sanchez | [END_REF] , as expected from the fact that pure cobalt is a strong ferromagnet. The magnetic moment of cobalt is therefore only weakly modified by temperature (0 K< T < 1423 K), by the magnetic state (ferromagnetic/paramagnetic), and by the chemical order (L1 0 /A 1 ). This induces that the concentration dependence of the measured EPI is not related to some magnetic moment variations. (symbols in Fig. 9). Red hatched regions are ordered/disordered two-phase domains calculated using a quadratic composition dependence of EPI (line in Fig. 9)

74, 62, and 62 days, respectively. The order-disorder transition temperature determined by transmission electron microscope observations was estimated in the 830 K-843 K range, in agreement with the reported values by Inden et al. [START_REF] Inden | Mater. Res. Soc. Symp. Proc[END_REF] and Capitan et al. 5 (Appendix D).

The order-disorder transition temperatures calculated from the data provided by all the diffuse scattering measurements are also superimposed in Fig. 10 (blue circles). The errors bars, close to 125 K, have been estimated from the uncertainties related to the EPI determi-nation 16 . A good agreement between experimental and calculated ordering temperatures is obtained, notwithstanding the accuracy of the EPI determination and the simplicity of the model. Magnetic, elastic effects as well as electronic entropy are indeed neglected in such a rigid lattice approach.

For the sake of comparison, the phase diagram calculated with the quadratic composition dependence of EPI (Fig. 9) is superimposed (red lines) to the experimental phase diagram.

This approximation leads to a qualitative description of the phase stability only. The ordering temperatures, asymmetry of the phase diagram, compositions related to congruent transformations are not fully reproduced.

V. CONCLUSION

The phase stability of the CoPt alloy was investigated close to its order-disorder transition temperature (T OD = 1100 K) using neutron diffuse scattering experiments. The effective pair interactions (EPI) obtained from measurements carried out at 1423 K and 1203 K indicate that, provided the accuracy of the technique and the hypotheses made in the data analysis, the EPI belong to the mean field limit, thus being temperature independent. Temperature mainly affects atomic shells farther than the fourth neighbor distance yielding a 100 K variation of the calculated order-disorder transition temperature. The comparison of EPI with those reported in the literature within the cluster expansion 12 and the tight binding Ising model 22 shows that the TBIM EPI provide a relatively good description of the alloy thermodynamics at temperatures close to ordering temperature (short-range order and temperature of phase transformation), even if they strongly differ from the EPI determined in this study. Cowley parameters α p are calculated with Eq. 9. The results related to the different EPI sets are listed up to the eleventh atomic shell in Tab. IV for the Co 0.5 Pt 0.5 alloy.

FIG. 1

 1 FIG. 1. (Color online) Typical neutron time-of-flight spectrum recorded at T ds = 1423 K in the CoPt sample. Circles correspond to experimental data and lines to the separation of elastic and inelastic contributions: in cyan: elastic contribution = a trapeze (in dark blue) convoluted by a gaussian (in green); in blue: quasi-elastic phonon; in orange (respectively magenta): high-(respectively low-) energy phonon; in red: sum of all contributions. The channel width is 7.32 µs and the elastic line-width is close to 2.2(9) meV.

FIG. 2 .

 2 FIG. 2. Corrected intensity in CoPt at T ds = 1423 K : (a) (001) and (b) (110) diffraction planes and at T ds = 1203 K : (c) (001) and (d) (110) diffraction planes. q xy is the vector along the [1 10] direction in reciprocal lattice units (RLU). The dashed line in (a) indicates the location of the intensity profile shown in Fig. 4.

  ) reciprocal lattice planes are shown in Fig. 2. The white areas correspond to domains where no measurement could be done or to excluded regions where a precise determination of the diffuse intensity was not possible due to the sample or the furnace Bragg peaks, or due to too large inelastic contributions. Some diffuse intensity maxima are clearly observed around the superstructure positions -(100) and equivalents -revealing a strong short-range order. I exp is modulated at T ds = 1203 K (respectively T ds = 1423 K) between 2.1±0.4 LU (respectively 1.85±0.35 LU) for the lowest values and 10.2±1.1 LU (respectively 6.7±0.7 LU) for the highest values. The relative error bars are 9% at the superstructure peaks and below 20% in the lowest-intensity ranges.

  Co and Pt) separated by r p . ρ 2,p (τ τ ) is the probability of finding atoms τ and τ at a distance r p . It is equal to (1 + α p )/4 and (1 -α p )/4 for homochemical (CoCo or PtPt) and heterochemical (CoPt) pairs, respectively. ∆b is the usual contrast factor: ∆b = b Co -b Pt .

FIG. 3 .

 3 FIG. 3. Simulated intensities in the (001) and (110) planes in CoPt at T ds = 1423 K and T ds = 1203 K : (a)-(b), (g)-(h) total intensity, (c)-(d), (i)-(j) short-range order contribution (I SRO ), and (e)-(f), (k)-(l) first order displacement contribution (I D1 ). Note that the intensity scales differ between (a) to (d) and (e) or (f) as well as between (g) to (j) and (k) or (l).

FIG. 4 .

 4 FIG. 4. Experimental (black bullets) and simulated intensities (taking into account the cumulated error bars by an area) along the q x = 1 RLU line in CoPt (a) at T ds = 1423 K (violet area: N SRO = 20). N D1 = 7 and (b) at T ds = 1203 K (violet area: N SRO = 20 and green area :N SRO = 30)

FIG. 5 .

 5 FIG. 5. Temperature dependence (5 K step size) of the CoPt alloy long-range order (LRO) parameter calculated near the transition for the two EPI sets determined in this study (see Tab. I). L1 0 and A1 are respectively the ordered and the disordered structures.

FIG. 6 .

 6 FIG. 6. (a) CoPt order-disorder temperature as a function of the EPI cutoff distance. Distances are given as neighbor shell numbers (p) and interatomic distance coordinates (r p ) in a/2 unit (bottom and top axes, respectively). The experimental transition temperature of the alloy is indicated by the dashed line. (b) SRO parameters as a function of the distance for four EPI cutoff distances.

  ds = 1203 K (open symbols), the transition temperature increases with the interaction distance up to the fourth neighbor shell and then stabilizes at temperatures close to 1000 K. Monte Carlo calculations thus show that interactions up to the fourth neighbor atomic shell are required to reproduce the experimental order-disorder transition temperature. The effects of the accuracy of EPI on the transition temperature have been assessed with Monte Carlo simulations. The ordering temperature variations are close to ±90 K and ±60 K for the two sets of EPI (see Tab. I), which is consistent with the used formalism 16 .To calculate SRO parameters, the Monte Carlo simulations were performed in the canonical (N Co , N Pt , V, T ) ensemble where the number of cobalt N Co and platinum N Pt atoms, the volume of the simulation V and the temperature T are fixed quantities. The Metropolis algorithm34 is applied to exchanges between particles to reproduce chemical correlations (Co ↔ Pt swapping mechanism). The composition is thus conserved. The initial configuration is equilibrated by 5 × 10 5 swapping attempts per atomic site before computing the Warren-Cowley parameters with the following equation:

  with y = 2N Pt /N -1 and ρ p , the configurational average of the spin variable product σ n σ m where the atomic site m is located in the p-th neighbor shell of the atomic site n. The values of α p are calculated every 100 Monte Carlo step (MCS), where a MCS consists in N swapping attempts. The mean value and the standard deviation were finally determined from 1000 values of α p . The results related to the different EPI sets are represented up to the eleventh atomic shell in Fig.7(b) and the numerical values are listed in Appendix C (Tab. I) for the sake of readability. This analysis of these results is provided in the following section.

FIG. 7 .

 7 FIG. 7. (a) Effective pair interactions and related (b) SRO parameters as a function of p, the atomic neighbor shell number, in the CoPt alloy.

  FIG. 9. Composition dependence of effective pair interactions (EPI) determined from diffuse scattering and ICVM in the Co-Pt system. Red lines are guidelines (parabolic fits). Data corresponding to T ds = 1423K are displaced by ∆c = 0.03 for the sake of clarity. Filled symbols correspond to measurements in the ferromagnetic state, open symbols to measurements in the paramagnetic state.

  Phase diagram. Phase stabilities in the Co-Pt system have been experimentally investigated by various techniques: X-ray diffraction, electronic microscopy, and electrical resistivity measurements 1,37,39 . The resulting phase diagram is represented in Fig.10by black lines and dots. The Co-rich domain has not been studied extensively because of the slow atomic diffusion at temperatures close to T OD , the transition temperature. For cross-checking purposes, three samples with the Co 0.75 Pt 0.25 composition were sealed in quartz tubes, one in each, homogenized for 48 h at 1273 K and then annealed at 823 K, 830 K, and 843 K for

FIG. 10 .

 10 FIG. 10. Experimental phase diagram of the Co-Pt system from the work of Inden et al. 37 , Leroux et al. 1 and Le Bouar et al. 39 , in black. Blue open circles are the phase boundaries derivedfrom Monte Carlo calculations using the EPI determined from diffuse scattering experiments5,16,40

  FIG. 11. TEM observations. Selected area electron diffraction (SAED) pattern recorded in the [001] zone axis of a Co 0.75 Pt 0.25 sample (a) at T = 830 K, (b) at T = 843 K. Insets: intensity profiles associated with the dashed boxes.

Appendix D :

 : Transmission electron microscope observations of the Co 0.75 Pt 0.25 alloy Co 0.75 Pt 0.25 φ3 mm × 250 µm annealed discs were mechanically thinned to 50 µm using 1200, 2400 and 4000 paper-grit and then diamond suspensions (3 µm and 1 µm). The specimens were then ion-polished with a GATAN Precision Ion Polishing System (PIPS) in dual beam mode. Finally, observations were carried out in a FEI CM20 transmission electron microscope operating at 200 kV. Diffraction patterns acquired along [001] zone axis in samples annealed at T a = 830 K and T a = 843 K are represented in Fig. 11. Lines profiles, represented in the insets, reveal that the intensity ratio between the superstructure peaks related to the L1 2 phase and the (200) fundamental peak related to solid solution is 15% for T a = 830 K and 2% for T a = 843 K.

T

  Ṽ1 -Ṽ4 (K) 1085(87) 1005(48) 480 1120 T Ṽ1 -Ṽ6 (K) a 1095(95) 1025(65) 005(1) -0.010(1) 0.003(1) -0.010(1) 8 0.007(2) 0.034(2) 0.005(3) 0.020(3) 9 -0.005(1) 0.001(1) -0.002(1) -0.013(1) 10 0.002(1) -0.001(1) -0.001(1) 0.017(2)

TABLE I .

 I EPI ( Ṽi ) obtained from neutron diffuse scattering measurements at T ds = 1423 K and T ds = 1203 K in the Co 0.5 Pt 0.5 alloy using ICVM. Order-disorder temperatures (T OD ) are calculated using Monte Carlo simulations. Results arising from EPI reported in the literature are also listed in the last two columns.

		ICVM	ICVM CE TBIM
		1423 K	1203 K [12]	[22]
	Ṽ1 (meV) 14.88±1.00 12.56±0.67 10.35 34.5
	Ṽ2 (meV)	-4.85±0.65 -7.32±0.47 -4.75	8
	Ṽ3 (meV)	0.07±0.48 0.78±0.39 4.35	8
	Ṽ4 (meV)	-3.00±0.35 -1.26±0.16 2.8	0
	Ṽ6 (meV)	-0.05±0.24 -0.22±0.14	0	0
		ordering temperature (T OD )

TABLE III .

 III The determined EPI complete those already measured for the Co 0.75 Pt 0.25 , the Co 0.65 Pt 0.35 , and the Co 0.25 Pt 0.75 compositions.5,16 Their composition dependence shows that the EPI determined in the paramagnetic state for the Co 0.5 Pt 0.5 alloy do not significantly differ from those determined in the ferromagnetic state for Co 0.75 Pt 0.25 and Co 0.65 Pt 0.35 . The drop in the composition dependence of EPI related to the first neighbor atomic shell is therefore not caused by the change of the magnetic state at the measurement temperature. First order displacement parameters (γ β p ) obtained from neutron diffuse scattering measurements at T ds = 1203 K and 1423 K in the Co 0.5 Pt 0.5 alloy.

	p l m n α T ds =1203K p	α T ds =1423K p
	1 1 1 0 -0.1078(21) -0.1002(19)
	2 2 0 0	0.1568(19)	0.1102(20)
	3 2 1 1 -0.0230(13) -0.0091(11)
	4 2 2 0	0.0788(12)	0.0619(12)
	5 3 1 0 -0.0250(10) -0.0171(10)
	6 2 2 2	0.0464(13)	0.0272(13)
	7 3 2 1	-0.0099(6)	-0.0046(6)
	8 4 0 0	0.0339(15)	0.0071(18)
	9 3 3 0	0.0014(10)	0.0049(11)
	10 4 1 1	-0.0011(7)	0.0016(8)
	11 4 2 0	0.0244(8)	0.0120(9)
	12 3 3 2	-0.0013(9)	0.0024(9)
	13 4 2 2	0.0159(7)	0.0025(8)
	14 4 3 1	-0.0051(5)	-0.0024(5)
	15 5 1 0	-0.0101(9)	-0.0053(9)
	16 5 2 1	-0.0050(6)	-0.0009(6)
	17 4 4 0	0.0139(10)	0.0068(11)
	18 4 3 3	-0.0020(9)	0.0004(8)
	19 5 3 0	-0.0035(7)	-0.0006(8)
	20 4 4 2	0.0094(8)	0.0041(8)

Transmission electron microscope observations carried out on several annealed Co 0.75 Pt 0.25 samples confirmed that the order-disorder transition takes place in the 830 K-843 K tem-

TABLE IV .

 IV EPI ( Ṽi ) and SRO parameters (α p ) obtained from neutron diffuse scattering measurements at T ds = 1423 K and 1203 K in the CoPt alloy using ICVM. Order-disorder temperatures (T OD ) were calculated using Monte Carlo simulations. Results arising from EPI reported in the literature are also listed in the last two columns.

		ICVM	ICVM	CE	TBIM
		1423 K	1203 K	[12]	[22]
	Ṽ1 (meV) 14.88(100) 12.56(67)	10.35	34.5
	Ṽ2 (meV)	-4.85(65) -7.32(47)	-4.75	8
	Ṽ3 (meV)	0.07(48) 0.78(39)	4.35	8
	Ṽ4 (meV)	-3.00(35) -1.26(16)	2.8	0
	Ṽ6 (meV)	-0.05(24) -0.22(14)	0	0
		order-disorder temperature (T OD )

TABLE V .

 V EPI ( Ṽi ) reported from diffuse scattering measurements in the Co-Pt system. Orderdisorder temperatures (T M C ) calculated using Monte Carlo simulations are compared to measured ones (T exp ). Co 0.75 Pt 0.25 Co 0.65 Pt 0.35 Co 0.25 Pt 0.75

		[5]	[5]	[16]
	Ṽ1 (meV)	13.81	13.52	3.76(70)
	Ṽ2 (meV)	-6.21	-7.15	-7.73(107)
	Ṽ3 (meV)	1.31	0.87	1.11(43)
	Ṽ4 (meV)	-0.73	-0.24	-3.17(76)
	Ṽ6 (meV)	0.51	0.08	-0.29(80)
		order-disorder temperature
	T exp (K)	830		996
	T M C (K)	837	861	1002(104)

-0.012(1) -0.024(1) 0.003(1) -0.006(1)

ACKNOWLEDGMENTS

The authors acknowledge A. Finel for helpful discussions on neutron diffuse scattering analysis with the ICVM approach and the French-German ANR-DFG MAGIKID project for some support.

perature interval. The synthesis of the experimental and numerical studies devoted to the Co-Pt phase stability show that the simulation of its phase diagram is not yet satisfactory.

Improvements would imply to incorporate both magnetic and elastic effects, which are usually neglected in rigid lattice approaches 8 .

Appendix A: SRO and first order displacements parameters obtained from the data processing The measured intensities are described using the first order development in the atomic displacements (Eqs. 2-4). A least-squares procedure was used to reproduce the corrected data using sets of SRO parameters α p and first order displacement parameters γ i p . The best results were obtained with N SRO = 20 and N D1 = 7 for both of the investigated temperatures.

The corresponding values of α p and γ i p are given in Tab. II and Tab. III, respectively, for the two measurement temperatures.

Appendix B: Derivation of the q-independent contribution in neutron diffuse scattering

The incoherent cross sections found in the tables correspond to the contributions due to isotopic distribution and to nuclear moments: σ tab inc (Co) = 4.8 ± 0.3 barn and σ tab inc (Pt) = 0.13 ± 0.11 barn. Using a rule of mixtures, we get σ tab inc (CoPt) = 2.465 ± 0.205 barn and I tab inc (CoPt) = 1.55 ± 0.14 Laue units (LU).

In the paramagnetic state, a supplementary contribution has to be added: the incoherent cross section due to the average paramagnetic quadratic magnetic moments M 2 µ on species µ. Assuming g = 2 (neglecting the spin-orbit coupling), it can be written as [START_REF] Marshall | Theory of thermal neutron scattering[END_REF] :

where N µ is the number of µ atoms, m e and e the electron mass and charge, c the speed of light and γ the neutron gyromagnetic ratio. We can assume that F (q), the magnetic form factor, is constant in the investigated q-range: ( γe 2 2mec 2 ) 2 F (q) 2 ≈ 72.65 mbarn.sr -1 .atom -1 . The magnetic moments in CoPt have been measured using X-ray magnetic circular dichroism (XMCD) at 300 K by Grange et al. 30 : µ Co = 1.76 ± 0.26 µ B and µ Pt = 0.35 ± 0.05 µ B (we assume a 0.15 relative error bar, typical for XMCD). As the Pt moment is induced by a polarization of its electronic bands by the average Co moment, the Pt moments disappear at the Curie temperature. We thus obtain an upper limit for the paramagnetic incoherent contribution per atom: I para = 0.59 ± 0.19 LU. The value of the constant term in the experimental data is finally: I cst = 1 + I nucl + I para = 3.14 ± 0.33 LU assuming that Co atoms keep their 300 K moment and I cst = 2.55 ± 0.14 LU assuming that all Co moments disappear. • To calculate SRO parameters, the Monte Carlo simulations are performed in the canonical (N Co , N Pt , V, T ) ensemble where the number of cobalt and platinum atoms, N Co and N Pt , the volume of the simulation V and the temperature T are fixed quantities. The Warren-


Clara Jiménez Saelices

Maud Save

Isabelle Capron

Synthesis of Latex Stabilized by Unmodified Cellulose Nanocrystals: Role of Monomers on Particle Size

Cellulose nanocrystals (CNCs) are sustainable rod-shaped nanoparticles able to adsorb at oil-water interfaces to produce highly stable Pickering emulsions with enhanced mechanical properties. Polymerization of the CNC-stabilized monomer droplets is investigated in details to elucidate the synthesis mechanism of both micro-and nanoparticles of latex in relationship with the initial sizes of the droplets. It is shown in this study that unmodified CNCs, used as sole stabilizer, are efficient to produce both monomer-in-water Pickering emulsion and nanocomposite latex particles with controlled dimensions. For the initial liquid emulsion of styrene, two populations of droplets were observed: micrometric droplets with diameters that decrease down to 5 μm with increasing CNC concentrations, and nanometric droplets with a diameter distribution ranging from 500 nm to 2 μm for all CNC concentrations. It leads to two distinct populations of polystyrene latex particles by polymerization in aqueous dispersed media, i.e. microparticles of 5-18 µm and nanoparticles with an average diameter below 1 µm. The polymerization of various monomers, i.e. styrene, lauryl methacrylate, isobornyl Acrylate, butyl methacrylate, methyl methacrylate, in the presence of different initiators highlighted that the solubility of the monomer in the aqueous continuous phase is the key parameter to tune the size distribution of the latex particles. Nanocomposite CNCstabilized waterborne latexes were prepared from polymer with different glass transition temperatures.

Introduction

Cellulose is the most widespread biopolymer on earth. It is present in a wide variety of plants where it mainly acts as a reinforcement material. The supramolecular structure of this polysaccharide is not uniform. Cellulose contains both crystalline phases and disordered domains that are generally considered to be amorphous. These amorphous regions are considered to be structural defects in the microfibrils and can be removed by acid hydrolysis to prepare highly crystalline particles called cellulose nanocrystals (CNCs). Sulfuric acid hydrolysis is typically used to isolate CNCs; 1 grafting anionic sulfate half ester groups (OSO3 -), the negative charges at the surface are responsible for colloidal stability in water by electrostatic repulsion. [2][3][4][5][6][7][8] CNCs from wood are rigid, rod-shaped nanoparticles with a length of 150-200 nm and a width of 3-20 nm. 9 They are associated with a very high aspect ratio (around 30), high axial elastic modulus (150 GPa), high specific surface (200-300 m 2. g -1 ) and low density (1.6 g . cm -3 ). [10][11][12] CNCs are renewable and toxicity studies have shown them to be harmless. 13 In recent years there has been a growing interest to combine the outstanding properties of CNCs produced from renewable resources with the properties of synthetic polymers. 14,15 The colloidal dispersions of submicronic polymer particles produced by polymerization in aqueous dispersed media are known as waterborne latex particles. Waterborne latexes are used in many applications, including adhesives, paints, paper coating, printing inks, rubber products, cement reinforcement, as well as in medical industry. [16][17][18] They can be produced by different heterophase polymerization processes like emulsion polymerization, miniemulsion polymerization, dispersion polymerization or suspension polymerization. [19][20][START_REF] Kawaguchi | Polymer Particles[END_REF] From an engineering viewpoint, a water-based continuous phase favors heat transfer of the exothermic polymerization reaction and facilitates polymer recovery from the reactor as a fluid aqueous colloidal dispersion. The process is also environmentally benign, meeting one of the green chemistry requirements concerning the decrease of volatile organic compounds (VOC's). Emulsion polymerization commonly involves the use of surfactants or polar co-monomers to stabilize the growing polymer particles and to prevent the monomer droplets from coalescence. However, excess surfactants can have a negative impact on the material properties and the environment because they remain in the latex after polymerization. To limit this drawback, polymer scientists have investigated surfactant-free emulsion polymerization, where the charges of the initiator or comonomer play the role of a stabilizer. [START_REF] Ceska | [END_REF][23][24] Nonetheless, the low solid content is a limitation of these techniques. Molecular surfactants have also been replaced with macromonomers or amphiphilic copolymers, [25][26][27][28][29] but the high number of steps required for the synthesis of these stabilizing polymers is a Please do not adjust margins Please do not adjust margins limitation for such systems. Since the early studies carried out at the beginning of the 2000s, 30,31 the use of reactive hydrophilic polymers able to simultaneously act as both control agents and macroinitiators or macromolecular chain transfer agents proved to be very efficient to produce stable monodispersed latex particles via surfactant-free emulsion or dispersion polymerization. [32][33][34][35] A wide variety of synthetic and biosourced hydrophilic reactive polymers have been investigated for the synthesis of polymer colloids with various morphologies by polymerization-induced self-assembly (PISA), including functionalized polysaccharides that have proved to be efficient reactive stabilizers. [36][37][38] Another promising alternative for replacing molecular surfactants is to use colloidal particles as stabilizers. Amphiphilic particles can be used to stabilize emulsion droplets, creating the so-called Pickering emulsions. 39,40 Compared to conventional emulsions, a low fraction of colloidal particles is required to produce Pickering emulsions with higher stability because the adsorption energy is several orders larger than with surfactants. 41 Colloidal particles form a solid armor around the droplet that avoids their coalescence by steric repulsion. A large variety of nanoparticles has been successfully used to stabilize emulsion droplets and generate nanocomposite latex via different heterophase polymerization techniques. 35,42 Silica, Laponite clay, magnetite, zinc oxide, titanium and graphene oxide are examples of commercially-available inorganic nanoparticles used in Pickering emulsions. [43][44][45][46][47][48] There has been a growing interest in recent years in the use of biobased nanocelluloses as Pickering emulsifiers. [49][50][51][52][53] It has been shown that CNCs can effectively stabilize oil-water interfaces by strong adsorption along the less polar (200) crystalline plan. 54 CNCs have been incorporated into polymerization processes to design nanocomposite latexes in order to improve the mechanical properties of the polymer. 55 In the early studies, CNCs were used in combination with surfactants and were anchored at the interface either by coupling agents [56][57][58] or by electrostatic interactions with surfactants. 59,60 CNCs were therefore not directly involved in the stabilization of monomer droplets or latex particles. Recent studies have shown that modified CNCs can be used to stabilize latexes. For example, heterogeneously modified CNCs with hydrophobic alkyl chains were used to stabilize polystyrene (PS) latex with micrometric diameters. 61 Kedzior et al. produced CNC nanocomposite latexes with a double morphology composed of micrometric polymer particles decorated with nanometric ones. 62 They used methyl-cellulose (MC)-coated CNCs to stabilize poly(methyl methacrylate) (PMMA) latex particles via microsuspension polymerization. The presence of polymer nanoparticles was explained by the excess of methyl cellulose chains, which implies the stabilization by methyl cellulose alone. Zhang et al. used CNCs hydrophobically modified with different alkyl-amines to stabilize emulsions with droplet sizes of only a few hundred nanometers, leading to nanometric latexes by polymerization of styrene. 63 Using acetylated CNCs, Werner et al. showed that polymerization of styrene in aqueous dispersed media produced a mixture of micrometric and nanometric polystyrene latex particles from an initial liquid emulsion composed of droplets in the micrometer range. 64 This study presents for the first time the use of unmodified CNCs as the sole stabilizer of both monomer-in-water Pickering emulsions and final nanocomposite latex particles synthesized by polymerization in aqueous dispersed media. In order to shed light on the production of stable latex particles of different sizes (latex microparticles and latex nanoparticles), we investigated in detail the emulsification and polymerization processes according to various experimental parameters. We first studied the surface charge of CNCs and the viscosity ratio between continuous and dispersed phases. Subsequently, a range of monomers (and initiators) with various limits of solubility in water were used to investigate the role of monomers on the droplet size and on the nucleation and growth of latex particles. A novel range CNC-based nanocomposite waterborne latex is targeted with polymers of a wide range of glass transition temperatures.

Experimental Section

Materials. The cotton cellulose nanocrystals (CNCs) were obtained from Whatman filters (grade 20 Chr). Commercial CNCs (c-CNCs) were provided by the University of Maine (Orono, ME, USA) in the form of aqueous suspensions at 12 wt%. c-CNCs were diluted, sonicated and intensively dialyzed for ten days before use. Hexadecane and the initiators, azobisisobutyronitrile (AIBN) and 4,4′-Azobis(4-cyanovaleric acid) (ACPA), were acquired from Sigma Aldrich and used without further purification. The monomers (Styrene (S), Lauryl Methacrylate (LMA), Isobornyl Acrylate (iBoA), Butyl Methacrylate (BMA), Methyl Methacrylate (MMA)) were provided by Sigma Aldrich (> 99%) and were passed through an alumina column before use to remove the inhibitors. Table S1 shows the density, solubility in water, viscosity and surface tension of the selected monomers. Water was purified with the Milli-Q reagent system (18.2 MΩ cm Millipore Milli-Q purification system). CNC preparation. Cellulose nanocrystals (CNCs) were prepared from cotton linters according to the method of Revol et al. 5 with minor modifications. Briefly, 50 25 g of filters were dispersed in water and then hydrolyzed with sulfuric acid at 58% at 70°C under stirring for 20 min. After hydrolysis, the suspension was washed by centrifugation, dialyzed to neutrality against Milli-Q water for 2 weeks, and deionized using mixed bed resin (TMD-8, Sigma Aldrich). The final dispersion was sonicated for 10 min, filtered through a 0.45 µm filter, and stored at 4°C. CNC characterization. The CNCs and the c-CNCs were visualized by Transmission Electron Microscopy (TEM) using a JEOL JEM-1230 TEM at 80 kV. The suspensions were deposited on a freshly glow-discharged carbon-coated copper grid (Electron Microscopy Sciences, UK) and negative staining was performed using phosphotungstic acid (1% w/v, adjusted to pH 6 with NaOH and filtered at 0.1 µm). The grids were dried at room temperature. The average length and width of the nanocelluloses were analyzed from 100 images using Image J (Figure 1).

Please do not adjust margins

Please do not adjust margins

The surface charge density of CNCs and c-CNCs was measured by conductometric titration using an automated Metrohm 905 Titrando controlled by a computer with TIAMO software (Metrohm, Switzerland). The sulfate contents of suspensions (Figure 1) were titrated with NaOH. The degree of substitution of sulfate groups was calculated on the basis of the following equation:

𝑑 𝑠 = (𝑉 𝑒𝑞 • 𝐶 𝑁𝑎𝑂𝐻 • 𝑀 𝑤 )/𝑚 where Veq is the volume of NaOH in mL at the equivalent point, CNaOH is the concentration (mol/L), Mw is the molar mass and m is the weight of titrated cellulose. The surface charge density was calculated by dividing the degree of substitution by the surface area of CNC.

Emulsion and latex preparation and characterization

The Pickering emulsions were prepared by mixing an aqueous dispersion of CNCs and an organic phase at a 10/90 O/W volume fraction. For all the emulsions, the aqueous phase with 50 mM NaCl consisted of CNCs dispersed at concentrations between 0.2 and 2.3 wt% based on the styrene. This ionic strength was chosen to limit repulsions due to charged groups present at the surface. An oil soluble initiator (AIBN) was added to the monomer phase before emulsification (ratio: 100:1 w/w). When required, a water soluble initiator (ACPA) was also added to the aqueous phase before emulsification (50:50 molar fractions of both initiators). The emulsions were prepared by sonication with an ultrasonic device with a dipping titanium probe close to the surface (amplitude 2 corresponds to 4 W/mL applied power) for 45 s, using intermittent pulses. The resulting emulsion was polymerized at 70°C without stirring for 48 h. The kinetics of polymerization for monomers used in this work is shown in Figure S1. At low CNC concentrations, the emulsions require a stabilization time before polymerization. If the polymerization is carried out before the stabilization of the droplets, neckless-like aggregates of droplets that polymerize during the coalescence stage are obtained (Figure S2). The emulsions were systematically kept for 48 hours in order to polymerize stable emulsions. In the case of emulsions prepared with high concentrations of CNC, this stabilization time does not affect the droplet diameters (Figure S3) and remains constant for months at 20°C. The average droplet diameters and diameter distribution before polymerization, and the average polymer particle size and size distribution after polymerization were measured by laser light scattering particle size analysis using a Horiba LA-960 (Kyoto, Japan). Calibration with water was carried out before each measurement. The diameter was expressed as the surface mean diameter D(3,2) (the Sauter diameter). The emulsions were all visualized by transmission optical microscopy (BX51 Olympus microscope). Image analysis was used to measure the droplet diameters of the styrene-in-water emulsions. The number average droplet diameter, Dn, of the emulsions was measured from the microscopic images using ImageJ software. Scanning electron microscopy (SEM) was used in order to visualize the formed latex. When there was more than one particle population, the latex dispersion was centrifuged several times for 2 min at 10000 g in order to separate the populations. The dried polymer particles were metallized with gold and visualized with a JEOL 6400F instrument. The CNC-stabilized Pickering emulsions were prepared using an aqueous suspension of CNC at concentrations between 0.2 and 2.3 wt%, based on the styrene. The transmission optical micrographs of styrene-in-water emulsions stabilized with increasing concentrations of CNCs are shown in Figure 2. For all emulsions, two very distinct populations of droplets were observed: droplets with diameters greater than 1 µm, and droplets with diameters smaller than 1 µm (Figure 2). For the purpose of clarity, the term 'micrometric droplet' is used in this study for droplets with diameters greater than 1 µm, whereas the term 'nanometric droplet' describes droplets with diameters of less than 1 µm. Micrometric droplet size decreases with increasing CNC concentration. This concentration dependence on the diameter, previously reported for hexadecane-in-water emulsions, 50 is known as the principle of limited coalescence. 65 The micrometric droplet diameter is then controlled by the amount of CNC. Regarding nanometric droplets, no dependence of the concentration on the diameter was observed. The average droplet diameter (Dn) of the styrene nanometric droplets was approximately 600 nm for all the emulsions, regardless of CNC concentration (Figure S4). Moreover, the nanometric droplets seem to be predominant compared to the micrometric droplets and represent a nonnegligible volume (Figure 2). Photographs of the emulsions before and after polymerization are shown in Figure 3. Before polymerization (Figure 3a), styrene micrometric droplets cream because styrene density (d = 0.906 g.cm-3) is lower than water. Moreover, an increasing volume of cream is clearly observed by increasing the CNC concentration, whereas the initial volume of styrene is unchanged. Increasing the amount of CNCs allows the stabilization of a larger interface. Consequently, a greater number of smaller size droplets are formed, filling a larger emulsion volume. In addition, since CNCs are surrounded by a layer of water, it leads to more hydration layers, thus immobilizing more water between the droplets. These two phenomena result in an increase in the cream volume with the concentration of CNCs (Figure 3a).50, 66 For all concentrations, the aqueous phase located below the creaming layer has a cloudy optical aspect, even after centrifugation. This is due to the presence of the nanometric droplets of styrene visualized by optical microscopy (Figure 2) that are not submitted to gravity. Please do not adjust margins Please do not adjust margins In a second step, the styrene polymerization is initiated by the hydrophobic AIBN initiator at 70°C. Two distinct populations of polystyrene particles are measured: one with D [3,2] average particle diameters between 5 and 18 µm (called microparticles) and a smaller one below 1 µm (called nanoparticles) (Figure 3c). A sedimentation of the microparticles is observed because of the higher density of polystyrene (d = 1.04 g . cm -3 ) compared to water (Figure 3b). Similarly to the former emulsions, the volume of the sedimented microparticles increases with increasing CNC concentration. In addition, the top aqueous phase is still cloudy suggesting the presence of polystyrene nanoparticles that are not submitted to gravity. The polystyrene microparticles reveal a CNC concentration dependence on the diameter. The D [3,2] average diameter decreased, from 18 µm down to 6 µm for CNC concentration of 0.9 wt% (Figure 3c). Above this concentration the ability of CNCs to cooperative orientation induces a densification of the CNC layer at the interface of individual droplets without diameter variation. 54 In contrast, the polystyrene nanoparticles show no dependency with CNC concentration with a D [3,2] average diameter of polystyrene nanoparticles approximately 300 nm for all CNC concentrations (Figure 3c). However, it should be noticed that the CNC concentration influences the amount of nanoparticles. When increasing content of CNCs is added, more nanoparticles are observed by a very clear increase in the relative granulometry peak area without noticeable modification of the average particle diameter (Figure S5). Another remarkable aspect is that, after polymerization, the resulting polystyrene nanoparticles (D[3,2] = ~300 nm) are smaller than the initial styrene nanometric droplets (Dn = 600 nm). The latex dispersion and the organization of CNCs at the interface were both analyzed by the visualization of detailed surfaces with scanning electron microscopy (SEM). In order to separate the two populations of polystyrene particles, the final latex dispersion was centrifuged. SEM images of the polystyrene microparticles are shown in Figure 4. The comparison of microparticles produced at two CNC concentrations shows that the microparticle diameters decrease from 10 µm to 5 µm with increasing CNC concentrations from 0.5 to 2 wt% based on styrene. Moreover, a scan of the surface of the microparticles shows that, increasing the amount of CNC introduced, the nanocrystals are densely organized along the surface of the micrometric beads (Figure 4b and Figure 4d). SEM observation of polystyrene nanoparticles with diameters ranging from 100 to 600 nm is displayed in Figure 5. A much lower surface coverage is observed compared to microparticles. However, the presence of CNCs strongly adhering to and curved along the nanoparticle surface was clearly revealed, confirming the assumption that the styrene nanometric droplets were effectively stabilized by the CNCs. The polystyrene nanoparticles exhibit average diameters of between 100 and Please do not adjust margins Please do not adjust margins 400 nm, sizes close to the CNC length, which suggests an impressive bending of CNCs. The plastic deformation limits of CNCs were studied in a simulation study done by Chen et al. 67 They demonstrated that CNCs are able to bend up to a critical bending angle of approximately 60° with a greater elastic limit displacement along the (200) crystalline plane. This assumption makes it possible to hypothesize the stabilization of these nanolatexes. In previous studies, 50,51 a detailed characterization of hexadecane-in-water emulsions stabilized by unmodified CNCs showed that it was not possible to stabilize droplets smaller than 5 µm, even using ultra high shear like ultrasonication. Submicrometer droplets (D[3,2] = 300 nm) could be obtained only by repeated passes through a high-pressure homogenizer, 53 for which high-energy consumption is required. To better understand the presence of nanometric droplets in the emulsions and the presence of polystyrene nanoparticles after polymerization, several parameters were investigated. We first investigated the effect of the viscosity ratio between both phases. In contrast to hexadecane (3.5 mPa . s), styrene viscosity (0.763 mPa . s) is lower than water viscosity (1 mPa . s). The low viscosity of the dispersed phase compared to the continuous phase could result in a better deformation, which would make the stabilization of smaller droplets possible. In order to confirm this hypothesis, hexadecane-in-water emulsions were prepared with a continuous aqueous phase of higher viscosity by adding dextran to reverse the viscosity ratio between the continuous and the dispersed phase. The droplet size distributions of the resulting emulsions are represented in Figure 6 for the different viscosities. All of the curves are superimposed with the same average droplet diameter of 5 µm for the investigated viscosity ratios. Even when the continuous phase presents a viscosity three times greater than the one of the dispersed phase, it is not possible to stabilize smaller nanometric droplets. Similarly to the viscosity ratio, the variation in surface charge density showed no modification in the formation of nanometric droplets when comparing CNCs at 0.2 and 0.6 e . nm -2 (Figure S6). Please do not adjust margins Please do not adjust margins Since the adjustment of viscosity or the surface charge density of CNCs has no effect on the droplet size of hexadecane-inwater emulsion, the presence of small droplets in styrene-inwater emulsions might be ascribed to a higher concentration limit of solubility in water. In order to investigate the effect of this parameter, the next part of this study is devoted to the polymerization in aqueous dispersed media of different monomers with various limits of solubility in water.

Results and Discussion

Synthesis of polystyrene latex stabilized by cellulose nanocrystals: characterization of the initial emulsion and final polymer particles

Role of the monomer on droplet and particle sizes

Unlike hexadecane, which is completely non-soluble in water, styrene has a solubility of 0.05 g . L -1 in water (Table 1). It is known that the solubility limit of styrene in water allows the nucleation of emulsion polymerization in the aqueous phase and the further polymerization step by diffusion of monomers through the continuous phase from monomer droplets to the growing particles. 68 This ability to diffuse through the water could explain the presence of stable nanometric droplets without a high coverage of CNCs. To verify this hypothesis, the styrene was replaced by other monomers with different values of water solubility (Table 1). The same procedure was carried out for the preparation of emulsions stabilized with CNCs and their subsequent polymerization. The resulting monomer-in-water emulsions were visualized by optical microscopy and compared to hexadecane-in-water emulsions for a concentration of CNC of 2.3 wt% (Figure 7). The D [3,2] average droplet diameter of emulsions and the D [3,2] average particle diameter of latex dispersions are represented in Figure 8. We first analyzed the liquid monomer-in-water emulsions. Similarly to hexadecane, lauryl methacrylate (LMA) is insoluble in water, while isobornyl acrylate (iBoA) shows solubility in water ranging between lauryl methacrylate and styrene (Table 1). For these both monomers, CNC stabilized only micrometric liquid droplets with D [3,2] average diameter of 5 µm, in the absence of nanometric droplets (Figure 7 and Figure 8). Concerning styrene emulsions, the measurement by granulometry corroborates the results obtained by microscopy since two populations of droplets are observed: (i) a population of nanometric droplets with a diameter distribution ranging from 500 nm to 2 μm for all CNC concentrations; and and (ii) a second distribution of micrometric droplets for which the diameter decreases with CNC concentration and reaches a minimum value of 5 μm for the highest CNC concentrations (Figure 7 and Figure 8). Please do not adjust margins

Please do not adjust margins

The n-butyl methacrylate (BMA) is associated with a water solubility limit that is four times higher than styrene (Figure 8). BMA also forms emulsions with two populations of droplets (Figure 7). The granulometric characterization showed one population of droplets with diameters greater than 20 μm and another with diameters of around 1 μm (Figure 8). However, the resulting systems are unstable and the continuous and dispersed phases can mix over several hours. Finally, the water solubility of methyl methacrylate (MMA) is too high, preventing the formation of any emulsions in similar experimental conditions. The size distribution of monomer droplet is thus related to the level of the concentration limit of water solubility Please do not adjust margins Please do not adjust margins of the monomer dispersed phase. When the monomer is completely insoluble in water, like in emulsions prepared with LMA or iBoA, only micrometric droplets were produced using direct sonication. Sonication produces a much larger area of the monomer/water interface than can potentially be covered by the CNCs. When sonication is stopped, the partially unprotected droplets coalesce. This coalescence results in a decrease of the oil/water interface and stops as soon as the interface is sufficiently covered. However, in the case of partial solubility in water, like with styrene, the monomer is able to diffuse through the continuous phase and thus allows the formation of nanometric droplets. The steric repulsion between CNCs avoids the coalescence of both the droplets and nanometric droplets. These results slightly differ from those reported by Zhang et al. 63 who chemically modified CNCs to increase their hydrophobicity and used them to stabilize styrene droplets of a few hundred nanometers. The authors justified the stabilization by the reduction of the interfacial tension between the styrene and the water phase due to CNC surface modification. The waterborne latex particles were formed by polymerization of the initial emulsions by different heterogeneous polymerization mechanisms according to the water solubility of the monomers. In the case of LMA, the polymerization initiated by hydrophobic AIBN mainly occurs via a suspension polymerization process. The nucleation of suspension polymerization takes place in the monomer droplets, and the solid particles are the exact replicas of the LMA emulsion droplets (Figure 8). The SEM analysis of PLMA particles was not possible since the glass transition temperature of the polymer is too low (Tg = -65°C), preventing formation of a solid bead for imaging. It should be observed that granulometry did not reveal the concomitant formation of PLMA nanoparticles in the final latex. In the case of the iBoA polymerization, the polymer microparticles were the replica of the micrometric droplets with a diameter of 5 µm, suggesting also a suspension polymerization mechanism initiated by the hydrophobic AIBN initiator. However, a second population of polymer nanoparticles appeared for the highest concentration of CNCs (2.3 wt%) (Figure 8). These nanoparticles were produced during the iBoA polymerization, and SEM images of P(iBoA) nanoparticles confirmed the presence of CNCs at their surface (Figure S7). The presence of both P(iBoA) microparticles and nanoparticles suggests a concomitant suspension and emulsion polymerization mechanism. The iBoA micrometric droplets were nucleated by the hydrophobic radical fragment of AIBN for suspension polymerization, leading to the production of microparticles. The formation of nanoparticles by emulsion polymerization is possible by diffusion of iBoA across the water phase towards the polymer nuclei formed by the water-soluble fraction of AIBN radical fragments. In fact, previous investigation of the emulsion polymerization initiated by the hydrophobic AIBN initiator revealed that nucleation from the fragment of AIBN in water can occur despite its low concentration in water. 68 In order to confirm the hypothesis of an emulsion polymerization mechanism, an iBoA-in-water emulsion was prepared using a mix of water-soluble/oil-soluble initiators (50:50 molar fractions of both initiators). The hydrophobic initiator (AIBN) was dispersed in the oil phase, whereas the water soluble initiator (4,4′-Azobis(4-cyanovaleric acid) (ACPA)) was dispersed in the aqueous phase. It should be noted that only the distribution of micrometric iBoA droplets ( 5 µm) was observed before polymerization. Figure 9 shows the overlay of the diameter distribution of the P(iBoA) latex particles synthesized using either both AIBN and ACPA initiators or AIBN initiators alone. When a water-soluble initiator was dissolved in the aqueous phase, more nanoparticles were Please do not adjust margins Please do not adjust margins produced, confirming their formation by an emulsion polymerization mechanism based on a nucleation in the water phase and a diffusion of monomer from the droplets towards the growing polymer nanoparticles. Concerning styrene, the presence of both PS microparticles and nanoparticles implies, as in the case of iBoA, concomitant suspension and emulsion polymerization mechanism. PS microparticles were synthesized by a suspension polymerization mechanism initiated by the hydrophobic AIBN initiator, whereas PS nanoparticles were produced by emulsion polymerization. The population of PS nanoparticles exhibits an average diameter of 300 nm for all CNC concentrations, which is clearly lower than the diameter of the nanometric styrene droplets (0.5-2 µm). The reduction in particle size with respect to the droplet size (see Table 1 and Figure 8) confirms the diffusion of styrene from the droplets towards the growing PS nanoparticles during the polymerization process. Furthermore, the fraction of PS nanoparticles is enhanced with increasing the concentration of CNC, leading to larger PS specific surface. In summary, the emulsion polymerization mechanism, based on a nucleation in the water phase, is possible if the solubility of monomers in water allows their diffusion across the continuous phase. In the case of n-butyl methacrylate (BMA) monomer with higher limit concentration of solubility in water (Table 1), the polymerization was possible only for the highest concentration of CNCs (2.3 wt%) (Figure 8). After polymerization, only PBMA microparticles were observed as the replica of the BMA droplets, suggesting a suspension polymerization mechanism initiated by the hydrophobic AIBN initiator.

In a previous work of Werner et al. 64 , the authors studied the preparation of latexes using acetylated CNCs. They ascribed the production of polystyrene nanoparticles, concomitantly to the production of microparticles, to the extrusion of styrene monomer from the droplets and its polymerization in the continuous water phase initiated by isolated CNCs acting as nucleation sites. We showed that, in our case, nanometric droplets are already present in the starting styrene-in-water emulsion. The authors also suggested that the extrusion was due to incomplete coverage of the droplets that could be avoided by aggregation conditions such as the addition of salt. However, in this study, polystyrene nanoparticles were produced on a large range of coverage of the emulsion droplets, and notably above the limited coalescence domain in the presence of salt, and styrene nanoparticles can even be Please do not adjust margins Please do not adjust margins prepared in the higher coverage conditions. Furthermore, CNCs were identified as nucleation sites in the aqueous phase, whereas we previously confirmed the absence of CNCs in the aqueous phase by titration for emulsions prepared under similar conditions. 50,51 In this study, we highlighted that droplets can be prepared from a large range of monomers, leading to latex particles made of polymers of a wide range of glass transition temperatures (Tg, PLMA  -65 °C, Tg, PBMA  20 °C, Tg, PiBoA, PS  100 °C). [START_REF] Brandrup | Polymer handbook[END_REF] We revealed the clear impact of the limit concentration of water solubility of the monomer on the process of particle formation for their polymerization in aqueous dispersed media. (1) The more hydrophobic monomer, LMA, is not able to diffuse through the water phase and thus produces polymer microparticles by suspension polymerization as replicas of the initial micrometric droplets. (2) In the case of monomers with intermediate limit solubility in water, like iBoA, only micrometric droplets are obtained (like LMA). However particle formation takes place through two polymerization mechanisms: microparticles were obtained by suspension polymerization, and nanoparticles were produced by emulsion polymerization. The emulsion polymerization mechanism is possible due to the partial solubility of the monomer in water that allows its diffusion through the continuous phase and its nucleation induced by the fraction of AIBN that can be dissolved in water. 68 (3) Monomers with partial solubility in water, like styrene, allow the stabilization of emulsions with initial micro and nanometric droplets. The two concomitant mechanisms of suspension and emulsion polymerization produce microparticles and nanoparticles from the emulsion droplets. ( 4) By increasing again the solubility in water, like for BMA monomer, unstable liquid emulsion containing only large monomer droplets can be processed, leading to the formation of large PBMA particles with diameter far above 1 µm, in the absence of nanoparticles.

(5) For very polar monomers, like MMA, associated with a high solubility in water, the formation of emulsions is even not possible.

Conclusions

This study reports the efficiency of unmodified CNCs to act as stabilizer of both monomer-in-water Pickering emulsion and nanocomposite latex particles with controlled dimensions. Styrene-in-water emulsions have two populations of droplets: (i) micrometric droplets with diameters that decrease with CNC concentration and that reach a minimum value of 5 μm for the highest CNC concentrations and (ii) nanometric droplets with a diameter distribution ranging from 500 nm to 2 μm for all CNC concentrations. The polymerization of the initial styrene-inwater Pickering emulsions produced waterborne polystyrene latexes through two concomitant mechanisms: (i) microparticles were obtained by suspension polymerization mechanism initiated by the hydrophobic AIBN initiator and (ii) nanoparticles were produced by emulsion polymerization mechanism initiated by polymer nuclei formed by the watersoluble fraction of AIBN radical fragments.

Through the polymerization of a range of vinylic monomers (LMA, iBoA, S and BMA), we confirmed that the balance between the micro-and nanoparticles of latex are driven by the ability of the monomer to diffuse across the water phase related to its limit concentration of solubility in water. We therefore demonstrated that the solubility of the monomer in water is a key parameter for designing Pickering polymer nanoparticles. Furthermore, CNC efficiently stabilize such interface and increasing the concentration of CNC allows the stabilization of a larger number of styrene droplets, which results in a larger fraction of nanoparticles. The range of waterborne latex (PLMA, PiBoA, PS, PBMA) with various glass transition temperatures and final particle sizes produced by surfactant-free polymerization in aqueous dispersed media from unmodified CNCs offers new perspectives to design CNC-reinforced polymer materials.

Figure 1 .

 1 Figure 1. CNC Characterization

Figure 3 .

 3 Figure 3. Photographs of (a) styrene-in-water emulsions and (b) polystyrene latex particles after polymerization, for increasing CNC concentrations ranging from 0.2 to 2.3 wt%, based on the styrene. (c) D[3,2] average diameters of the two coexisting populations of polystyrene latex as a function of CNC content.

Figure 2

 2 Figure 2 Optical microscopy images of styrene-in-water emulsions before polymerization showing two populations of droplets. The scale bar is 50 µm.

Figure 4 .

 4 Figure 4. SEM images of microparticles polymerized from emulsions stabilized by CNCs at (a, b) 0.5 wt% and (c, d) 2 wt% based on the styrene.

Figure 5 .

 5 Figure 5. Representative SEM images of polystyrene nanoparticles stabilized by CNCs.

Figure 6 .

 6 Figure 6. Droplet size distributions of emulsions stabilized with CNC at 2 wt%, based on hexadecane (3.5 mPa . s) with different aqueous phase viscosities. Optical microscopy images of emulsions. The scale bar is 50 µm.

Figure 7 .

 7 Figure 7. Optical microscopic images of emulsions of (a, b) hexadecane, (c, d) lauryl methacrylate, (e, f) isobornyl acrylate, (g, h) styrene and (i, j) butyl methacrylate in water stabilized by CNC at 0.5 wt% (left part) and 2.3 wt% (right part), based on the monomer content. The scale bar is 50 µm.

Figure 8 .Figure 9 .

 89 Figure 8. Droplet diameter distributions of monomer-in-water emulsions (top row) and particle size distributions of the polymerized emulsions (bottom row) for CNCs at three concentrations: 0.5 wt% (plain lines), 1 wt% (dashed lines), 2.3 wt% (dotted lines)

Table 1 .

 1 Monomer solubility in water, size of the droplets, initiator used size of the solid particles formed and their nomenclature and polymerization mechanisms.

	Monomer	Solubility in water (g . L -1 )	D[3,2]drop	Initiator	D[3,2]particle	Name of latex particle	Polymerization process
	LMA	Insoluble	5 µm	AIBN	5 µm	Microparticle	Suspension polymerization
					5-7 µm	Microparticle	Suspension polymerization
	iBoA	0.02	5-7 µm	AIBN
					300 nm (minor population)	Nanoparticle	Emulsion polymerization
				AIBN	5-7 µm	Microparticle	Suspension polymerization
	iBoA	0.02	5-7 µm	+
				ACPA	300 nm (major population)	Nanoparticle	Emulsion polymerization
	Styrene	0.05	5-7 µm	AIBN	5-7 µm	Microparticle	Suspension polymerization

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 3

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 7

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 9

Acknowledgements

This work was carried out within the framework of the French National Research Agency (ANR Project CE08 2015). We gratefully acknowledge Emilie Perrin and Joëlle Davy (INRA, Nantes, France) for their excellent technical assistance for TEM and SEM visualizations, as well as Nicolas Stephant (Institut des Matériaux Jean Rouxel, Université de Nantes) for access to the SEM equipment. We are equally grateful to Geneviève Llamas (INRA, Nantes, France) for her support in laser scattering particle size analysis and Matthieu Tetart for the preparation of samples.

Conflicts of interest

There are no conflicts to declare