Dr Daniel Grande
email: grande@icmpe.cnrs.fr

Géraldine Rohman

Prof. F Ph Guérin

Oligoester-Derivatized (Semi-) Interpenetrating Polymer Networks as Nanostructured Precursors to Porous Materials with Tunable Porosity

Keywords: Aliphatic oligoesters, (Semi-)Interpenetrating Polymer Networks, Extraction, Hydrolysis, Porous materials, Structure-morphology relationships

Porous polymeric materials with tunable porosity can be engineered from oligoesterderivatized semi-Interpenetrating Polymer Networks (semi-IPNs) or IPNs, respectively composed of either uncrosslinked or crosslinked aliphatic oligoesters entangled in a stiff subnetwork. In this paper, miscellaneous polyester/poly(methyl methacrylate)-based semi-IPN and IPN systems are first prepared as precursors with varying structural parameters, especially the nature (i.e., poly(D,L-lactide), poly(-caprolactone)) and the molar mass (i.e, from 560 to 3,700 g.mol -1 ) of the oligoester precursor. (Nano)porous networks with defined porosity are then generated through two complementary routes. This original paper discusses the scope and limitations of both approaches and investigates the correlation between the structure and morphology of the generated networks and the porosity of the resulting porous materials. We demonstrate that the choice of the precursors with defined compatibility is of paramount significance in the length scale of phase separation associated with nanostructured networks aswell as in the porosity scale of (nano)porous materials derived therefrom. Indeed, we find that the quantitative extraction of uncrosslinked oligoesters from semi-IPNs allows for the elaboration of nanoporous networks with pore diameters lower than 150 nm, provided that a high miscibility between both partners in semi-IPN precursors is attained, i.e. when using the lower molar mass oligoester. Alternately, the total hydrolysis of the polyester subnetwork associated with IPNs offers more versatility, since nanoporous networks can be obtained with a pore size range of 20-150 nm, regardless of the oligoester nature and molar mass in IPN precursors.

Introduction

The design of functional porous polymeric materials has been the subject of widespread interest and intense research, as they are involved in a wide array of applications, e.g. monoliths for chromatographic techniques, separation membranes, interlayer dielectrics, high surface area catalytic supports, as well as size/shape-selective nanoreactors [1][2][3][4][5][6][7][8][9]. Besides the classical synthetic strategies that rely on the use of solvents or gases as porogens, original approaches with porogen templates, capable of inducing specific structural pores within the residual structures, have been developed [10,11]. These template-oriented routes are quite interesting, since a wide array of porous polymers with a well-defined porosity can be designed.

Resorting to (semi-)Interpenetrating Polymer Networks ((semi-)IPNs) as nanostructured precursors to engineer porous crosslinked materials has solely been studied by a few research teams [12][13][14][15][16][17][18][START_REF] Sperling | Interpenetrating Polymer Networks and Related Materials[END_REF]. While semi-IPNs are composed of uncrosslinked sub-chains entrapped in a polymer network, IPNs constitute an intimate combination of two independent sub-networks, at least one of which is synthesized in the immediate presence of the other [START_REF] Sperling | Comprehensive Polymer Science[END_REF][START_REF] Sperling | [END_REF][START_REF] Kim | IPNs Around the World: Science and Engineering[END_REF][START_REF] Athawale | [END_REF][START_REF] Thomas | Micro-and Nano-Structured Interpenetrating Polymer Networks: From Design to Applications[END_REF][START_REF] Dean | [END_REF]. Although IPNs do not generally lead to chain interpenetration at the molecular length scale, small domain sizes from tens to a few hundreds of nanometers can be obtained under synthetically controlled experimental conditions. The peculiar interlocking framework confers to IPNs a microphaseseparated co-continuous morphology leading to their unique properties. The IPN morphology essentially depends on the compatibility of each partner (i.e., thermodynamic factor) and the kinetics and mechanism associated with the formation of each sub-network (i.e., kinetic parameters). Nevertheless, if the phase morphology may be varied with several parameters, it has been reported that the phase continuity is controlled by the partner volume fractions and a co-continuous morphology is generally obtained with a 50/50 composition [START_REF] Sperling | [END_REF][START_REF] Kim | IPNs Around the World: Science and Engineering[END_REF][START_REF] Athawale | [END_REF]. Moreover, when IPNs are synthesized by the sequential method, i.e. when each sub-network is obtained in two consecutive steps, the first sub-network generally constitutes the most continuous phase and its cross-linking density is an important parameter to control the IPN morphology, while the crosslinking density of the second sub-network has no significant effect [26]. Consequently, the order of the sub-network formation is crucial as different phase morphologies and properties may be obtained. When arising from the combination of two partners that exhibit a contrasted degradability under specific conditions, such complex polymer structures are particularly interesting since nanoporous networks can be generated through selective degradation methods [12][13][14][15][16][17][18][START_REF] Sperling | Interpenetrating Polymer Networks and Related Materials[END_REF]. In this regard, IPNs based on a hydrolyzable polyester, such as poly(D,L-lactide) (PLA)

or poly(-caprolactone) (PCL), and a non-hydrolyzable polymer, such as poly(methyl methacrylate) (PMMA), can be considered as appropriate precursors.

Straightforward routes to porous cross-linked polymeric materials through the utilization of PLA/PMMA semi-IPNs or IPNs as precursors were previously developed [26,27]. Porous methacrylic networks were readily generated from the quantitative extraction of uncrosslinked PLA oligomers in semi-IPNs or they were engineered from the selective hydrolysis of PLA subnetwork in IPNs. The scope and limitations of both systems for the generation of (meso)porous materials were investigated. The effect of the cross-linker nature and the cross-linking density of the PMMA sub-network on the domain sizes in the (semi-)IPN precursors, and the correlation with the pore sizes distributions in the porous materials derived therefrom, were carefully studied.

Macro-to mesoporous networks were derived from semi-IPNs and the variation of pore sizes was attributed to the miscibility of both partners in semi-IPN precursors [27]. For IPN systems, the pore sizes were always smaller than 100 nm, regardless of the cross-linker nature and concentration, which showed that the cross-linking density of the PMMA sub-network and the compatibility between both sub-networks had a relatively small impact on phase separation in IPN precursors [28].

In light of the scarcity of studies on porous materials derived from (semi-) IPN systems, we decided to get a better insight into the correlation between the morphology of the (semi-)IPN precursors and the pore sizes of the resulting porous methacrylic networks, and notably on the impact of the molecular features of the first sub-network generated during IPN synthesis (i.e.

polyester partner). In the present paper, miscellaneous polyester/PMMA (semi-)IPNs with a 50/50 composition are prepared to ensure the co-continuity of each phase, and the effect of the nature and molar mass of the oligoester precursor is systematically investigated for the first time.

In this regard, poly(D,L-lactide) (PLA) or poly(-caprolactone) (PCL) oligomers are used with different molar masses. We particularly pay attention to the correlations between the structure and morphology of the (semi-)IPN precursors and the porosity of the resulting porous materials through various physico-chemical analyses, since the control of the precursor miscibility associated with both types of reference systems is of paramount significance for the design of nanoporous materials with defined pore sizes.

Experimental

Materials

Dihydroxy-telechelic PLA oligomers were synthesized by ring-opening polymerization of D,Llactide initiated by the ethylene glycol/tin (II) octanoate system, according to a literature method [29]. Dihydroxy-telechelic PCL oligomers were purchased from Aldrich. Dibutyltin dilaurate (DBTDL, Fluka) was used as received. was purified by recrystallization in methanol.

Preparation of Precursory Networks

In all experiments, a mold was devised by clamping together two glass plates separated by a 2 mm-thick silicone rubber gasket.

Polyester Single Networks

Polyester single networks were prepared with a (Oligoester + Desmodur  RU)/dichloromethane mass composition of 50/50 wt% and ratios of [NCO]0/[OH]0 and [DBTDL]0/[Oligoester]0 equal to 1.4 and 0.44, respectively. An example of the preparation of a PLA single network is given hereafter. 1g of PLA (Mn = 1,700 g.mol -1 ; 5.9×10 -4 mol) was dissolved in 0.91mL of dichloromethane (1.21g), and subsequently, 0.45mL of Desmodur  RU (0.21g; 5.6×10 -4 mol) and 0.15 mL of DBTDL (2.5×10 -4 mol) were added. The solution was then poured into the mold and kept at room temperature for 20h. Thereafter, the mold was heated to 65°C for 2h, and then to 110°C for 2 h (Fig. 1).

PMMA Single Network

An example of the preparation of a single network with a MMA/DUDMA molar composition of 90/10 mol% is given hereafter. A mixture of MMA (0.9 g; 9×10 -3 mol), DUDMA (0.47 g; 10 -3 mol), and AIBN (0.033 g; 0.2×10 -3 mol, [AIBN]0/([MMA]0 + 2[DUDMA]0) = 0.02) was degassed under vacuum, poured under nitrogen into the mold. Then, the mixture was heated at 65°C for 2h, and cured at 110°C for 2h (Fig. 2).

Oligoester/PMMA Semi-IPNs

An example of the preparation of a semi-IPN with a PLA/PMMA mass composition of 50/50 wt% and a MMA/DUDMA molar composition of 90/10 mol% ([AIBN]0/([MMA]0 + 2[DUDMA]0) = 0.02) is given hereafter. 0.50g of PLA (Mn = 1,700 g.mol -1 ; 2.9×10 -4 mol), 0.33g of MMA (3.3×10 -3 mol), 0.17 g of DUDMA (3.6×10 -4 mol), and 12 mg of AIBN (7.3×10 -5 mol) were mixed, degassed under vacuum, and poured into the mold under nitrogen. The system was then heated to 65°C for 2h, and cured at 110°C for a 2h (Fig. 3).

Polyester/PMMA IPNs

An example of the preparation of an IPN with a PLA/PMMA mass composition of 50/50 wt%, is given hereafter. 1g of PLA (Mn = 1,700 g.mol -1 ; 5.9×10 -4 mol), 0.76 g of MMA (7.6×10 -3 mol), 0.40 g of DUDMA (8.5×10 -4 mol), and 27.7 mg of AIBN (1.7×10 -4 mol) were mixed and degassed under vacuum. Then, 0.45mL of Desmodur  RU (0.21 g; 5.6×10 -4 mol) and 0.15 mL of DBTDL (2.5×10 -4 mol) were added under nitrogen, and the solution was poured into the mold and kept at room temperature for 20h.. Finally, the system was heated to 65°C for 2h, and cured at 110°C for 2h (Fig. 4).

Other single polyester networks and (semi-)IPNs were synthesized in similar ways by changing the nature and/or the molar mass of the oligoester precursor.

Extraction of Networks and Formation of Porous Networks from Semi-IPNs

All networks and (semi-)IPNs were Soxhlet extracted with dichloromethane for 24h at 40 o C.

After extraction, the samples were dried under vacuum, weighed, and the sol fractions (mass percentages of extractables) were calculated. The extraction of linear oligoesters from semi-IPNs led to the formation of residual porous PMMA networks (Fig. 3).

Formation of Porous Networks by Partial Hydrolysis of IPNs

0.2 g of IPNs were immersed at 60°C in a mixture composed of 4 mL of a methylamine solution (pH = 13.6) and 4 mL of ethanol. After 24h, the residual networks were rinsed with deionized water up to neutral pH, and dried under vacuum. The mass loss (Δm) was assessed as follows (Equation 1):

∆m (wt%)=100×(m 0 -m d )/m 0 (1)
where m 0 and m d stand for the initial mass of the samples and their residual mass after vacuum drying, respectively.

The total hydrolysis of the polyester sub-network led to the formation of residual porous PMMA networks (Fig. 4).

Instrumentation

FTIR spectra were recorded between 4,000 and 450 cm -1 by averaging 32 consecutive scans with a resolution of 4cm -1 on a Bruker Tensor 27 DTGS spectrometer in Attenuated Total Reflection (ATR) mode.

DSC thermograms were recorded with a Perkin Elmer DSC7 calorimeter under nitrogen atmosphere. The analyses were carried out at a heating rate of 20°C.min -1 and the second run was performed after quenching. In order to avoid network degradation during the analysis, PMMA single networks and (semi-)IPNs were scanned twice from -100 to 200°C, while polyester single networks and oligoester precursors were scanned from -100 to 100°C and from -100 to 200°C

for the first and second scans, respectively. The Tg ranges were measured in the second run through the determination of the values associated with the intercepts of tangent to midpoint of the specific heat increment with "glassy"(lower limit, Tg,onset) and "viscous" baselines (upper limit, Tg,end), respectively.

1 H and 13 C spectra of sol fractions and hydrolysis products were recorded at room temperature using a Bruker Avance II spectrometer operating at a resonance frequency of 400 and 100 MHz, respectively. The sample concentration was 10 mg.mL -1 , and CDCl3 was used as the solvent and internal standard (7.27 ppm).

The Size Exclusion Chromatography (SEC) equipment comprised a Spectra Physics P100 pump, two PLgel 5 m mixed-C columns (Polymer Laboratories), and a Shodex RI 71 refractive index detector. Tetrahydrofuran (THF) was used as the eluent at a flow rate of 1 mL.min -1 , and polystyrene standards (Polymer Laboratories) were employed for calibration.

Scanning Electron Microscopy (SEM) analyses were performed with a LEO 1530 microscope equipped with a high-vacuum (10 -10 mmHg) Gemini column. The accelerating tensions ranged from 1 to 5 kV; two types of detectors (InLens and Secondary Electron) were used. Prior to analyses, the samples were cryofractured and coated with a Pd/Au alloy (4 nm) in a Cressington 208 HR sputter-coater.

Thermoporometry by DSC

The pore size and pore size distribution of the porous materials were determined through thermoporometry based on the melting temperature (Tm) depression of a liquid constrained within the pores [30][31][32]. To this purpose, the samples were immersed in ethanol for 2h, and then placed for 1h in ethanol/water mixtures of various compositions (70/30, 50/50, 30/70 vol%). After a 2 week immersion in pure water, the melting thermograms of wiped samples were recorded from -50 to 5°C at a heating rate of 1 °C.min -1 .

The pore size distribution was obtained by plotting dV/dR vs. the pore diameter (Dp) evaluated by using Equation 2 and 3, respectively [30][31][32]:

dV/ dR (cm 3 .nm -1 .g -1 ) = [(dq/dt)×(T m -T m0 ) 2 ] / [32.33×ρ×υ×m×ΔH(T)] (2)
D p (nm) = 2 × [0.68 -32.33/(T m -T m0 )] (3)
where Tm and Tm0 are the melting temperatures of confined and bulk water, respectively, and dq/dt, ρ, v, m and ΔH(T) are the heat flow recovered by DSC, the water density, the heating rate, the sample mass and the melting enthalpy of water, respectively. ΔH(T) was calculated from Equation 4 [30][31][32]:

ΔH(T) (J.g -1 ) = 332 + 1.39× (T m -T m0 ) + 0.155×(T m -T m0 ) 2 (4)

Determination of Density and Porosity Ratio Values

The samples were immersed in ethanol for 2h, and then placed for 1h in ethanol/water mixtures of various compositions (70/30, 50/50, 30/70 vol%). After a 2 week immersion in pure water, the wet mass was measured, and the mass swelling ratio (qw), the pore volume (Vpore), and the apparent density (dapp) were calculated from Equation 5, 6 and 7, respectively [33]:

q w = 𝑚 𝑤 /𝑚 𝑑 (5)
V pore (cm 3 .g -1 ) = (q w -1)/d s (6)

V pore = 1/d app -1/d true (7) where mw, md, ds and dtrue stand, respectively, for the samples wet mass , their mass after vacuum drying, the solvent density (water), and the true density of the PMMA matrix measured by helium pycnometry at 25°C by using A Micromeritics Accupyc 1330 equipment.

The porosity ratio P was then calculated by using Equation 8:

P = 1 -d app /d true (8) 3
Results and Discussion

Preparation of Semi-IPN Precursors and Investigation of Phase Separation

Various Oligoester/PMMA (50/50 wt%) semi-IPNs were prepared by bulk free-radical copolymerization of MMA and DUDMA with a composition of 90/10 mol%, in the presence of oligoesters of different natures and molar masses (Table 1). The radical polymerization occurred at 65°C and the cross-linking completion arose during the final curing at 110°C (Fig. 3), which was confirmed by the absence of the C=C absorption band of MMA and dimethacrylate monomers at 1,640 cm -1 in the FTIR spectra. In a previous study concerning the kinetics of network formation, it was shown that "soft" oligoesters behaved like a diluent toward the methacrylic copolymerization process which led to the complete conversion of C=C bonds before the curing process [START_REF] Dean | [END_REF]. Moreover, the kinetic process was not greatly affected by the variation of the polyester nature or molar mass (data not shown).

For (semi-)IPN-related materials [START_REF] Sperling | [END_REF][START_REF] Kim | IPNs Around the World: Science and Engineering[END_REF], the turbidity τ, which corresponds to the relative attenuation of light by the materials, accounts for the degree of chain interpenetration and allows for the determination of the microdomain size, provided the difference between the refractive indices of both partners is significant (Δn ≥ 0.02). Indeed, microdomain sizes are smaller than about150 nm when materials are transparent, while the opaque ones possess microdomain sizes higher than 150 nm [34]. Table 2 reports the different visual aspects observed for semi-IPNs before extraction. In the case of PLA-based semi-IPNs, the experimental nD 25 values measured for the PLA oligomer and a PMMA network were quite different (nD 25 PLA = 1.46, nD 25 PMMA = 1.49), and therefore the material turbidity can be used to evaluate the effect of the oligoester molar mass on the phase separation. It is noteworthy that the increase in the PLA molar mass led to an increase in the oligoester domain sizes, as semi-IPNs were transparent when the molar mass of the oligomer was equal to 570 g.mol -1 and opaque when the latter was equal to 3,700 g.mol -1 .

For PCL-based semi-IPNs, the nD 25 values of PMMA sample and PCL oligomer (nD 25 PCL = 1.49)

were quite identical, and it was consequently difficult to take into account the transparency of the samples. Nevertheless, there was clearly a phase separation when the samples were opaque.

Consequently, it was possible to conclude that PCL oligomers led to higher oligoester domain sizes compared to PLA oligomers with the same molar mass, as semi-IPNs were opaque with PCL 2,100 g.mol -1 and translucent for PLA 1,700 g.mol -1 .

Semi-IPN samples, before extraction,displayed single and fairly narrow glass transitionranges (Table 2).The Tg values were quite low but comprised between the Tg of corresponding oligoester (Table 1) andthat of PMMA single network (Table 3).Yet, theTg ranges of semi-IPNs did not match the valuescalculated from the Fox equation for miscible blends.For PLA-based semi-IPNs, the transparent aspect of the samples solely argued in favor of the absence ofphase separation at a length scale of a few hundreds ofnanometers. Moreover, the values of the heat capacity jump at theglass transition (Cp) decreasedwhen the molar mass of the PLA oligomers increased and became smaller than the values obtained for a 50/50 wt% physical blend constituted of PLAoligomer and PMMApreparedunder experimental conditions identical tothose employed for single network preparation (Cp = 0.33 J.g -1 .°C -1 ). This result also corroborated the conclusionsinferred from the visual observations concerning the increase in phase separation when using oligomers with higher molar masses. In the case of PCL oligomers, the values of Cp found for miscible blends were 0.18 and 0.28 J.g -1 .°C -1 for PCL 560 and 2,100 g.mol -1 , respectively. As a consequence, both PCL-containing semi-INPs exhibited a phase separation at the length scale of a few hundred nanometers. One more time, the phase separation was found higher for PCL-based semi-IPNs compared to PLA ones with the same molar mass as the differences between the values of Cp for semi-IPNs and those for miscible blends increased.

Finally, a decrease in the enthalpy of melting and inthe crystallinitydegree of PCL oligomers were observed in semi-IPNs as PMMA hindered the oligoester crystallization [34].

In a previous paper [START_REF] Thomas | Micro-and Nano-Structured Interpenetrating Polymer Networks: From Design to Applications[END_REF], we already related the dependence of domain size to the polymer-polymer miscibility in semi-IPN precursors, thanks to the calculation of PLA/PMMA interaction parameters () and critical interaction parameters (cr). We hypothesized that the domain sizes could be tuned by varying structural parameters through the variation of miscibility between the oligoester and the PMMA sub-network. In order to confirm this idea, we also evaluated these parameters in PLA/PMMA and PCL/PMMA semi-IPNsunder investigation, and we studied the effect of the variation of the oligoester molar mass. Because relatively weak interactions (van der Waals forces or hydrogen bonds) are involved in the systems under study, the values could be related to the Hildebrand solubility parameters of both partners using Equation9 [35][START_REF] Grulke | Polymer Handbook[END_REF][START_REF] Coleman | [END_REF][START_REF] Van Krevelen | Properties of Polymers[END_REF]:

( ) 2 2 1 m T R V  -    =  (9)
where Vm and Tare the reference molar volume andthe temperature, taken as 100 cm 3 .mol -1 and 298 K,respectively, Ris the gas constant, 1 is the solubilityparameter of oligoester, and 2 is the solubility parameter ofa methacrylic copolymer network.

1 was calculatedusing the group contribution method based on VanKrevelen's molar attraction constants: 29 1= 18.56± 0.15 MPa 1/2 for PLA and 1=17.94 ± 0.15 MPa 1/2 for PCL. 2 was calculatedusing an additive molar contribution relationship and was found to equal 20.76 ± 0.15 MPa 1/2 for a 90/10 mol% MMA/DUDMA network [26]. As a matter of fact, the values of were 0.19 ±0.05 and 032 ±0.07 for PLA/PMMA and PCL/PMMA semi-IPNs, respectively. As the  value was higher for PCL-based systems, it could be concluded that PCL oligomers led to less miscibility with the PMMA sub-network in semi-IPN precursors. To evaluate the influence of oligoester molar masson the miscibility of both semi-IPN partners, cr were estimated for thesystems considered. The cr values were calculated fromEquation 10 [35-38]: (10) where N1 and N2 are the polymerization degrees of oligoester and PMMA sub-networks, respectively. Whena polymer is cross-linked, Nis equal to infinity; hence,the latter equation could simply be expressed as follows(Equation 11):

1 cr N 2 1  =  (11)
Applying Equation12 to the PLA and PCL oligomers used in thisinvestigation, the value of crcould be calculated. Nevertheless, it should be stressed that these valuesare valid for systems withonly dispersive forces. According to Coleman's practicalguide to polymer miscibility [START_REF] Coleman | [END_REF],cr can be increased bysteps of 0.25 (cal.cm -3 ) 1/2 , depending on the strength ofthe potential intermolecular interactions present betweenthe polymeric components of biphasic systems.In DUDMA-based semi-IPNs,hydrogen bonding could potentially be established betweenthe urethane functions of DUDMA cross-linksand the main-chain ester groups of oligoester. We previously demonstrated that theextent of hydrogen bonding, so in turn the strength ofintermolecular interactions, could be increased withincreasing amounts of DUDMA [26].

Therefore, cr wasfurther increased depending on the DUDMA content.The initialcr values were estimated for each oligoesters using the reference molar volume of 57.7 cm 3 .mol -1 and 106.5 cm 3 .mol -1 for PLA and PCL, respectively. After the appropriate step increase for 10 mol% DUDMA-based systems [26],cr values were calculated and are given in Table 4. Consequently, these values showed that the miscibility decreased when the oligoester molar mass increased as crbecame smaller. Finally, the limits of miscibility could be predicted from the difference cr-.

Indeed, when the value of cr-> 0, the system can be considered to be miscible, while it is immiscible if cr-< 0. Therefore, 10 mol% DUDMA-based semi-IPNs containing PLA 570 g.mol -1 would not exhibit phase separation, while PLA 3,700 g.mol -1 or PCL 2,100 g.mol -1 -based systems should. At least, PLA 1,700 and PCL 560 g.mol -1 -based systemswere in the limit of phase separation as the values of cr-were around 0. To conclude, this theoretical approach may well account for the different behaviourstowards phase separation in semi-IPNs when varying the oligoester nature or molar mass. Indeed, thecalculation of oligoester/PMMA interaction parameters andthe comparison between and cr values corroborated the conclusions inferred from our previous results associated with DSC analysis and visual aspects.

Synthesis of IPN Precursors and Investigation of Microphase Separation

IPNs constituted of polyester and PMMA sub-networks (50/50 wt%) were synthesized by the in situ sequential method, i.e. by mixing all the precursors homogeneously, and then forming both networks via two successive and non-interfering cross-linking reactions. Hence, the polyestersub-network was first generated at room temperature for 20h by DBTDL-catalyzed cross-linking of dihydroxy-telechelic oligoesters(molecular characteristics described in Table 1)

with a pluriisocyanate, i.e.Desmodur  RU. Subsequently, the methacrylic sub-network was created at 65°C (2h) by AIBN-initiated free-radical copolymerization of MMA and DUDMA with a molar ratio of 90/10, and finally cured at 110°C for 2h to ensure a near completion of the cross-linking processes (Fig. 4) [27,[START_REF] Majdoub | [END_REF]40].Next, the IPN samples were extracted in a Soxhlet device with CH2Cl2 for 24h, and the amounts of soluble fractions are reported in Table 5.The soluble fractions were always below 14 wt% which matched with the sum of the corresponding polyester and PMMA single networks soluble fractions, except for PLA 3,700 g.mol -1 -based IPNs in which soluble fractions were very high. In the latter case, the SEC analysis of the soluble fractions showed that they were constituted in majority of PLA oligomer precursors (around 85%). DBTDL, PMMA oligomers, and only traces of residual methacrylates were also found by 1 H NMR. On the contrary, a high ratio of PMMA with molar mass ranging from 100 to 60,000 g.mol -1 was extracted from PLA 570 g.mol -1 -based IPNs, and a higher content of residual methacrylates was also found. However, the IRTF study of networks after extraction revealed that hydroxyl groups were still present in IPNs synthesized from oligoester with low molar mass which indicated that the cross-linking of polyester sub-network was not complete. The variations of the kinetic process of the polyester sub-network with the oligoester precursor molar masswerenot studied as the Lambert-Beer Law was not valid for low molar mass.

Concerning the PMMA-sub-network formation, we showed in a previous study [27] that the "soft" polyester sub-network acted as a diluent towards the methacrylic copolymerization process, preventing the reaction medium from attaining the glassy state as a solvent would have done it. However, as the free-radical polymerization proceeded, the Tg of the system increasedand the temperature of the reaction medium, i.e. 65°C, was around the Tg values of IPNs (Table 6). Therefore, the polymerization was considered to take place in a confined medium (into the polyester sub-network matrix) and was going to stop unless the temperature was increased to 110°C.We also found that the kinetic process was not greatly affected by the variation of the polyester nature or molar mass (data not shown).

Interestingly, all IPNs were transparent indicating that domain sizeswere always smaller than 150nm as the difference between the refractive indices ofboth sub-networkswas significant (n ≥ 0.02). Actually, theexperimental nD 25 values measured for the PLA and PCL sub-networks were equal to 1.51 and 1.53, respectively, while that for PMMA sub-network was equal to 1.49.Such visual observations showed that chain interpenetration of both polyester and PMMA sub-networks in the interlocking configuration of IPNs led to a significant decrease in the phase separation compared to the corresponding semi-IPN homologues. This was particularly true for systems with a higher degree of immiscibility like those with PLA 3,700 g.mol -1 and PCL 2,100 g.mol -1 as the semi-IPNs synthesized with these oligomers were opaque.

DSC analyses also confirmed the decrease in phase separation in IPNs (Table 6). Indeed, all IPNs displayed single glass transition ranges comprised between the Tg of corresponding polyester sub-networks and that of PMMA single network (see Table 3), which argued in favor of the absence of phase separation at a length scale of a few hundreds of nanometers. No melting temperatures were detected in PCL-based IPNs, as the oligoester cross-linking totally prevented PCL crystallization. Moreover, the values of the heat capacity jump at the glass transition (Cp)

were always equalor close to the expected Cpvalue of a 50/50 wt% physical blend theoretically constituted of polyester and PMMA networks(Cp,theoretical = 0.25 J.g -1 .°C -1 ), except for PCL 2,100 g.mol -1 -based IPNs. Nevertheless, the Cp values decreased when the oligoester precursor molar mass increasedshowing that the domain sizes were still higher for these systems,like in the case of semi-IPN systems. This was very clear when using PCL 2,100 g.mol -1 as the value of Cpwas equal to only 0.14 J.g -1 . o C -1 . This trend was also supportedby the increase inTg with the oligoester precursor molar mass.All these results confirmed that the phase separation in IPNs was mainly governed by the interpenetration created by the cross-linking of both partners, preventing any phase segregation at the nanoscopic scale [27,[START_REF] Majdoub | [END_REF]40].

Generation of Porous Networks from Semi-IPNs

Porous methacrylic networks were obtained by mere extraction of the un-crosslinked oligoesters from oligoester/PMMA (50/50 wt%) semi-IPNs (Fig. 3). One such extraction was performed with a good solvent of oligoesters at a temperature (40 o C) far below the Tg value of PMMA network to avoid the collapse of the residual porous structures [26,[41][42][43]. The amounts of soluble fractions are reported in Table 5. Regardless of the oligoester nature and molar mass, the extraction of linear oligomers was quantitative as indicated by extractable contents higher than or equal to 50 wt%. Furthermore, 1 H NMR and SEC analyses of the soluble fractions showed that they were constituted of more than 95% of oligoester precursor. No undesired grafting of PLA or PCL sub-chains onto PMMA sub-networks through transfer reactions was detected in the present systems. The total disappearance of the characteristicbands associated with ,-dihydroxyoligoester (hydroxyland carbonyl groups) in the FTIR spectra of semi-IPNs afterextraction confirmed the latter assertion. DSC analyses (Table 2) showed that the Tg and Cpvalues of semi-IPNs after extraction matched pretty well those of the correspondingsingle network (Table 3). This arose from thequantitative extraction of oligoesters. Nevertheless for PLA 3,700 g.mol -1based systems,Tg,onsetwas slightly lower than the value expected,probably due to a non quantitative extraction as shown also by anextractable content of 48 %.

The morphologiesof semi-IPNs after extraction were examinedby SEM (Fig. 5).The micrographs revealed highly porous structures, thus showing the effective role of oligoesters as template porogens. Pore sizes strongly depended on the oligoester nature and molar mass.

Indeed, pore diameters were as large as 450 nm for PLA-based systems and 1,000 nm for PCLbased-system homologues. Moreover, pore sizes clearly increased when increasing the oligoester molar mass (Table 7). The pore size distributions were also determined through DSC-based thermoporometry using water as the penetrant solvent. We already used this technique for the determination of pore size distributions in (semi-)IPNs which also gave complementary results compared to SEM analysis, as thermoporometry allows for the measurement ofthe smallerpore diameters (<200 nm) [26,27]. The pore size ranges are reported in Table 7 and pore size distributions are shown in Fig. 6a. Overall, the pore sizes obtained by SEM and those determined by thermoporometry were in reasonable agreement. Finally, the dependence of pore sizes in such porous materialsmirrored the differences observed in semi-IPNprecursors from visual aspects, DSC analysis, and polymer-polymer miscibility inferred from thecalculation of oligoester/PMMA interaction parameters.To conclude, the miscibility of both partners in semi-IPN systems is the most essential parameter controlling the pore size distribution after extraction.

Nanoporous structures with poressmaller than 150 nm could be engineeredwhen usinga PLA oligomer with amolar mass lower than around 2 000 g.mol -1 , while a PCL oligomer with the latter molar mass led to a porous structure with a very broad pore size distribution.

Pore volumes of porous networks were obtained through mass swelling ratio in water and led to the determination of apparent density and porosity ratio values (Table 8). Porosity ratioswere all around 50 vol% which matched the expected values, taking into account the quantitative extraction of linear oligoesters from semi-IPNs with a 50/50 wt% oligoester/PMMA composition.As also seen in SEM micrographs, this strongly indicated that the porous networks were monolithic structures constituted of open pores or interconnected channels through which a fluid could circulate. Moreover, the porous samples were wrapped in apolyethylene film and placed in n-pentane (d20°C= 0.624): in such a low-density solvent, they did float,thus confirming apparent density as well as porosityratio values lower than or equal to values around 0.6.

Engineering Nanoporous Networks from IPNs

Porous networks were produced by an original approach through the total hydrolysis of the polyester sub-network associated with partially hydrolyzable polyester/PMMA (50/50 wt%) IPNs [27,[START_REF] Majdoub | [END_REF]40]. Advantage of the contrasted hydrolytic degradability of aliphatic polyesters and PMMA was thus taken. The degradation was conducted for 24 h at 60°C using a 50/50 vol% mixture of methylamine (pH = 13.6) and ethanol. It has to be stressed that the hydrolysis was performed at an intermediate temperature between the Tg of polyester single networks and that of PMMA single network to avoid the collapse of the residual porous methacrylic structures, while allowing for an efficient degradation of the polyester partner. The role of ethanol wasdual: (i)

increasing the hydrophilic behaviour of the methacrylic sub-network, thusenabling a better diffusion of the medium into the IPN structure [44,45], and (ii) increasing the diffusion rate of the degradation products outside the networkas ethanol is a good solvent of oligoesters. With these conditions, PLA-and PCL-based single networks were completely hydrolyzed after 5 min and 3.5 h, respectively, while no mass loss was detected for 10 mol% DUDMA-based single networks. Table 5 gives the mass losses obtained after hydrolysis of IPNs. Regardless of the oligoester precursor nature or molar mass, mass loss values close to 50 wt% were determined, which demonstrated a nearly quantitative degradation of the oligoester-derivatized subnetworkfrom polyester/PMMA (50/50 wt%) IPNs. Moreover, the total disappearance of the characteristic bands associated with polyester sub-networks (urethane and carbonyl groups) in the FTIR spectra of residual networks after hydrolysis confirmed their methacrylic structure.

Nevertheless, in comparison to the corresponding PMMA single network, the residual methacrylic networks, after IPN hydrolysis, exhibited a low intensity band from 3,700 cm -1 to 2,300 cm -1 and a band at 1,660 cm -1 . This showed the appearance of carboxylic acid groups due to the partial hydrolysis of ester groups of the PMMA sub-network. Furthermore, the Tg,onset values of IPNs after hydrolysis (see Table 6) were higherthan that of the corresponding PMMA single network (i.e., 118°C). As no mass loss was detected for thissingle network, it was possible to hypothesize that the partial hydrolysis of PMMA sub-network was essentially due to the hydrolysis of ester side groups in the PMMA sub-chains without degrading the main chain and cross-linking points.

The morphologies of typicalIPNs after hydrolysis were examined by SEM (Fig. 7).It was difficult to obtain images with a good resolution without degrading the materials during the SEM analysis. Nevertheless, it is noteworthy that the residual networks typically exhibitednanoporous structures with pore sizessmaller than 100 nm. With such materials, the thermoporometry technique was very useful to determine pore sizes and the pore size distributions. The pore size ranges thus obtained are reported in Table 7, and pore size distributions are shown in Fig. 6b.Pore sizes were always smaller than 150nm, and thisresult mirrored the observations made from visual aspectsof IPNprecursors. As expected, compared to semi-IPN analogues, the pore diameters were dramatically decreased due to the good chain interpenetration of both polyester and PMMA sub-networks in the interlocking framework of IPN precursors. Moreover, as already hypothesized from DSC analysis, the pore size increased with the oligoester precursor molar mass, but no differences were noticed between PLA-and PCL-based IPN precursors. This meant that domain sizes in IPNs were larger when the cross-linking density of the polyester subnetwork was smaller, regardless of the miscibility between PLA/PCL and PMMA. This result was in a good agreement with literature reports [START_REF] Dean | [END_REF]46,[START_REF] Hourston | Polymer37:3521. Table 7 Pore diameters of resulting porous networksafter extraction of semi-IPNs orhydrolysis of IPNs as determined by SEM and DSC-based thermoporometry Oligoester nature and molar mass Pore diameters Semi-IPNs IPNs SEM (nm) DSC (nm) DSC (nm) PLA[END_REF]. As a matter of fact, when synthesizing IPNs by the sequential method, the network first formed constitutes the most continuous phase, and its cross-linking density generally determines the final morphology of the system, while the cross-linking density of the second network has no significant effect.

Pore volumes of nanoporous networks were obtained through mass swelling measurements in water and led to the determination of the apparent density and the porosity ratio values (Table 8).Porosity ratios ranged from 33 to 42%, which was lower than expected values, taking into account the quantitative hydrolysis of polyester sub-network from polyester/PMMA (50/50 wt%) IPNs. This was probably due to a partial collapse of the resulting porous structures.

Porosity ratio increasedwith the oligoester precursor molar mass,due tolarger pore sizes.

Conclusions

This contribution highlights the effectiveness and versatility of using oligoester-

  ratios of [NCO]0/[OH]0 and [DBTDL]0/[Oligoester]0 equal to 1.4 and 0.44, respectively, and a MMA/DUDMA molar composition of 90/10 mol% ([AIBN]0/([MMA]0 + 2[DUDMA]0) = 0.02)

  derivatized semi-IPNs and IPNs as nanostructured precursors to porous networks with tunable porosity.Miscellaneous PLA-or PCL-containing methacrylic (semi-)IPNs were indeed prepared as model systems from corresponding oligomers with different molar masses, and the pore sizes of related porous materials could be correlated with the polyester domain sizes inferred from the physico-chemical analysis of the (semi-)IPN precursors. Even though the quantitative extraction of uncrosslinked oligoestersfrom semi-IPNs generally led to the formation of macroporous networks, the semi-IPN approach constituted a straightforward and effective route toward nanoporous networks provided the extent of miscibility between both semi-IPN partners was high, i.e. when using the lower molar mass oligoester and preferably PLA. Alternatively, the complete hydrolysis of the polyester sub-networkfrom IPNs afforded more versatility, since nanoporous networks were generally derived therefrom, regardless of the molecularfeatures associated with the oligoesters. The nanoporosity of residual porous networks could be attributed to the good degree of chain interpenetration associated with both sub-networks in IPN precursors arising from their peculiar interlocking framework. Still, pore sizes in nanoporous frameworks increased with increasing oligoester molar masses, as the extent of microphase separation in IPNs was larger when the crosslinking density of polyester sub-network decreased.Such complementary routes involving semi-IPN and IPN systems may provide a straightforward and facile means to tune the morphology associated with (nano-)porous polymeric materials. Moreover, the functionalization of the pore surface through the initial incorporation of functional monomers in the (semi-)IPNs precursors may allow for the development ofa large variety of applications mainly expected in the areas of separation techniques (chromatographic supports, selective membranes) and chemistry in confined media (nanoreactors, catalytic supports).

( 18 (

 18 Tm = 38 o C, Hm = 22.2 J.g -1 , Xc d = 16%) PCL 2,100 g.mol -Tm = 63 o C, Hm = 40.0 J.g -1 , Xc d = 30%) a o: opaque, tl: translucent, tr: transparent. b Tg = Tg,end -Tg,onset: range of temperatures in which the glass transition occurs as determined by DSC. c Cp = Cp,v -Cp,g: heat capacity jump at Tg as determined by DSC, where Cp is the heat capacity, the subscripts v and g refer to the "viscous" and "glassy" states, respectively. d crystallinity degree calculated with Hm0(100% crystallinePCL) = 135 J.g -1 .[Kweon HY, Yoo MK, Park IK, Kim TH, Lee HC, Lee HS, Oh JS, Akaike T, Cho CS (2003) Biomaterials 24:801]

a

  Experimental conditions: [DBTDL]0/[Oligoester]0=0,44 -[NCO]0/[OH]0 = 1,4 -MMA/DUDMA molar ratio: 90/10 -[AIBN]0/([MMA]0 + 2[DUDMA]0) = 0.02 -20h at room T (only for polyester single networks and IPNs)+ 2h at 65°C + 2h at 110°C.

Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 1 /Fig. 7

 12345617 Fig. 1 Preparation of polyester-based single networks

  4,4',4''-triisocyanato-triphenylmethane (Desmodur  RU; 1.25 mol.L -1 in dichloromethane solution) was provided by Bayer. Methyl methacrylate (MMA, Aldrich) was dried over CaH2, and distilled under vacuum prior to use. Diurethane dimethacrylate (DUDMA) were purchased from Aldrich and used as received. AIBN (Merck)

Table 1

 1 Molecular and thermal characteristics of oligoesters

		Mn a	Ð b	Tg c	Cp d	Tm	Hm	Xc e
	Nature
		(g.mol -1 )		(°C)	(J.g -1 .°C -1 )	(°C)	(J.g -1 )	(%)
	PLA	570	1.2	-20	0.57	-	-	-
		1,700	1.2	10	0.55	-	-	-
		3,700	1.4	25	0.61	-	-	-
	PCL	560	1.7	-80	0.16	36	46.1	34
		2,100	2.1	-70	0.35	65	89.7	66

a Molar mass as determined by

1

H NMR. b Polydispersity index as determined by SEC in THF with polystyrene standards for calibration. c Tgvalue as obtained at the midpoint. d Cp = Cp,v -Cp,g: heat capacity jump at Tg as determined by DSC, where Cp is the heat capacity, the subscripts v and g refer to the "viscous" and "glassy" states, respectively. e crystallinity degree calculated with Hm0(100 % crystalline PCL) = 135 J.g -1 .[Kweon HY, Yoo MK, Park IK, Kim TH, Lee HC, Lee HS, Oh JS, Akaike T, Cho CS (2003)

Biomaterials 24:801]

Table 2

 2 Visual aspect and DSC analysis of semi-IPNs before and after extraction

			Semi-IPNs before extraction	Semi-IPNs after extraction
	Oligoester nature
		Visual aspect a	Tg onset	Tg b	Cp c	Tg,onset	Tg b	Cp c
	and molar mass
			(°C)	(°C)	(J.g -1 .°C -1 )	(°C)	(°C)	(J.g -1 .°C -1 )
	PLA 570 g.mol -1	tr	-14	25	0.25	116	25	0.24
	PLA 1,700 g.mol -1	tl	25	18	0.23	116	27	0.19
	PLA 3,700 g.mol -1	o	39	13	0.19	106	31	0.23
	PCL 560 g.mol -1	tl	-70	40	0.05	112	31	0.17

Table 3

 3 DSC analysis of polyester and PMMA single networks

		Oligoester nature and	Tg,onset	Tg a	Cp b
		molar mass	(°C)	(°C)	(J.g -1 .°C -1 )
	Polyester single networks	PLA 570 g.mol -1	50	30	0.32
		PLA 1,700 g.mol -1	20	25	0.29
		PLA 3,700 g.mol -1	30	15	0.27
		PCL 560 g.mol -1	-5	25	0.28
		PCL 2,100 g.mol -1	-55	10	0.32
				(Tm = 50 °C, Hm = 4 J.g -1 )
	PMMA single network	-	118	19	0.16

a Tg = Tg,end -Tg,onset: range of temperatures in which the glass transition occurs as determined by DSC. b Cp = Cp,v -Cp,g: heat capacity jump at Tg as determined by DSC, where Cp is the heat capacity, the subscripts v and g refer to the "viscous" and "glassy" states, respectively.

Table 4

 4 Variations ofcrwith oligoester nature and molar massfor 10 mol% DUDMA-

	basedsystems
	Oligoester nature and
		cr
	molar mass
	PLA 570 g.mol -1	0.32 ± 5.10 -3
	PLA 1,700 g.mol -1	0.21 ± 5.10 -3
	PLA 3,700 g.mol -1	0.17 ± 5.10 -3
	PCL 560 g.mol -1	0.34 ± 5.10 -3
	PCL 2,100 g.mol -1	0.24 ± 5.10 -3

Table 5

 5 Soluble fractions associated with single networks and polyester/PMMA (50/50 wt%) (semi-)IPNsafter extraction as well asmass loss associated with polyester/PMMA (50/50 wt%) IPNs after hydrolysis a

		Soluble fractions after extraction (wt%)
						Mass loss
	Oligoester nature	Polyester
			PMMA single			(wt%) after
	and molar mass	single		Semi-IPNs	IPNs
			networks			IPN hydrolysis
		networks
	PLA 570 g.mol -1	9	-	53	11	46
	PLA 1,700 g.mol -1	6	-	51	10	47
	PLA 3,700 g.mol -1	5	-	48	23	48
	PCL 560 g.mol -1	11	-	50	11	48
	PCL 2,100 g.mol -1	12	-	56	14	49

Table 6

 6 DSC analysis of IPNs before and after hydrolysis Tg,end -Tg,onset: range of temperatures in which the glass transition occurs as determined by DSC. b Cp = Cp,v -Cp,g: heat capacity jump at Tg as determined by DSC, where Cp is the heat capacity, the subscripts v and g refer to the "viscous" and "glassy" states, respectively.

		IPNs before hydrolysis	IPNs after hydrolysis
	Oligoester nature
		Tg,onset	Tg a	Cp b	Tg,onset	Tg a	Cp b
	and molar mass
		(°C)	(°C)	(J.g -1 .°C -1 )	(°C)	(°C)	(J.g -1 .°C -1 )
	PLA 570 g.mol -1	58	35	0.26	122	23	0.21
	PLA 1,700 g.mol -1	45	46	0.22	128	16	0.15
	PLA 3,700 g.mol -1	45	49	0.22	126	19	0.21
	PCL 560 g.mol -1	38	32	0.23	121	15	0.19
	PCL 2,100 g.mol -1	-50	52	0.14	126	20	0.19

a Tg =

Table 8

 8 Pore volume (Vpore), apparent density (dapp), and porosity ratio (P) of resulting porousnetworks after extraction of semi-IPNs or hydrolysis of IPNs

			Semi-IPNs			IPNs
	Oligoester nature
		Vpore			Vpore
	and molar mass		dapp	P		dapp	P
		(cm 3 .g -1 )			(cm 3 .g -1 )
	PLA 570 g.mol -1	0.87	0.59	0.51	0.42	0.80	0.33
	PLA 1,700 g.mol -1	0.89	0.58	0.52	0.55	0.72	0.40
	PLA 3,700 g.mol -1	0.86	0.59	0.51	0.54	0.72	0.40
	PCL 560 g.mol -1	0.84	0.59	0.50	0.42	0.79	0.34
	PCL 2,100 g.mol -1	0.83	0.60	0.50	0.60	0.69	0.42

m (d)

The "Région Ile-de-France" is gratefully acknowledged for financial support through SESAME projects allowing for the purchase of SEM equipment. The authors are indebted to late Prof.

Conflict of interest statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.


I Fossard

Chen W Florea

M Foldyna

P Roca

I Cabarrocas

A Lpicm

J Tang

J.-L Maurice
email: jean-luc.maurice@polytechnique.edu

F Fossard

I Florea

W Chen

E V Johnson

L Yu

Cabarrocas

Natural occurrence of the diamond hexagonal structure in silicon nanowires grown by a plasma-assisted vapour-liquid-solid method

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

Introduction

In standard (pressure, temperature) conditions, silicon has a diamond cubic (dc, Fd-3m) crystalline structure. Its properties such as the bandgap, carrier mobility and absorption are specific to that structure. The diamond cubic arrangement is a face-centred cubic (fcc) structure with a two-atom motif. It is one close-packed stacking arrangement, called polytype 3C, of which there are many other polytypes. Most of these polytypes have hexagonal symmetry P6 3 /mmc; they correspond to hexagonal close packed (hcp) phases. In silicon, these polytypes are thus possible and would present other electronic band structures with different band gaps. The calculated band structure of the diamond hexagonal 2H polytype of Si indicates that it would have a smaller band gap that would become direct in nanowires 1 or under strain 2 . Interestingly, it would provide a higher absorption of the solar spectrum 1,2 . In silicon, these polytypes are metastable and are not present in the phase diagram [3][4][5] . Names for the diamond hexagonal phase include 2H, dh, hd and lonsdaleite; the term "wurtzite", which is often found in the literature, is actually for cases where the two atoms of the motif are different (e.g. GaN). The first report of the 2H polytype was in 1963 by Wentorf et al 6 . These authors obtained the 2H phase by applying a series of high pressure (~15 to 16 GPa) and high temperature (200°C to 1000°C) treatments to diamond cubic crystalline Si. In the literature, there are many theoretical predictions of such hexagonal Si phase [7][8][9][10][11] , but few examples of experimental evidence [12][13][14] , in addition to some examples for Ge or SiGe 15,16 . It is quite remarkable that apart from the cases where it is obtained by the use of an epitaxial template 14,16 , the 2H polytype occurs in cases where a shear stress has been applied 12,13,15 . Other reports show that 2H SiNWs can be grown directly 17-20 . However, the proofs in these reports are given by transmission electron microscopy (TEM) analyses carried out in such a way that cubic Si multiple twinning would exhibit a very similar contrast 21,22 . Therefore, there remains a lingering uncertainty about whether these objects are truly hexagonal, and therefore about the very possibility of directly growing this metastable phase in nanowires.

The difference between the types of stacking of close packed planes (which defines polytypism) is only directly visible in one type of zone axis: [110] 3C / 2H . Any other zone axis will give ambiguous results. In this paper, we present TEM characterizations in the 2H zone axis, in cases where cubic multiple twinning cannot be mistaken for diamond hexagonal stacking. This work is thus the first unambiguous demonstration of the natural ‡ occurrence of the metastable diamond hexagonal structure. The 2H phase appears to be quite stable: it remained after 5 months in air, and after annealing at 700°C.

Experimental details

Silicon nanowires were grown through a plasma-assisted vapour-liquid-solid (VLS) method using a Sn catalyst 23,24 . In order to observe the crystallinity of the SiNWs without any transfer process, they were grown directly on carbon-coated TEM grids. First, a Cu grid was attached to a piece of ZnO:Al coated Corning glass using silver paste (Fig. 1a). Then a 1-nm thick Sn film was thermally evaporated on top. The substrate was then loaded into a standard plasma-enhanced chemical vapour deposition (PECVD) reactor to perform the SiNW growth. During the growth, the gas pressure, substrate temperature, radio frequency (RF) plasma power density and the growth duration were 133 Pa, 400°C, 17 mW/cm 2 and 2 min, respectively. After the growth, the sample was first analysed by scanning electron microscopy (SEM) (Fig. 1). Then the Cu TEM grid was removed from the substrate and loaded into a TEM microscope for high-resolution imaging. The SEM equipment was a Hitachi S-4800, and the TEM instruments were a Jeol 2010F with a point-to-point resolution of 0.23 nm, and a Zeiss Libra 200 FE, with a point-to-point resolution of 0.24 nm. In situ annealing was performed in the latter, using a Gatan heating holder, with plateaus at 230°C (51 min) 240°C (25 min), 470°C (25 min), 600°C (9 min) and 700°C (5 min). The acceleration voltage was 15 kV for the SEM, and 200 kV for both the TEMs.

Results

All the observed hexagonal SiNWs were grown directly on the Cu TEM grid. During the TEM observations, we found seven nanowires oriented close to a [110] 3C /[1-210] 2H zone axis, the only orientation where 2H characterisation can be done. those seven, five contained significant sections having the 2H structure. These five NWs are the subjects of the following analysis.

A high resolution TEM image (HRTEM) of a SiNW grown on the Cu TEM grid is shown in Fig. 2a. It has been recorded in the [110] 3C /[1-210] 2H zone axis, so that the stacking sequence of the (111) 3C /(0002) 2H close-packed planes is directly visible. In order to strengthen this direct evidence, HRTEM simulations were carried out using the JEMS package 25 . The thickness in these simulations was taken approximately equal to the crystalline SiNW core diameter: 4.6 nm; the best fit between the experimental and simulated images was obtained with a defocus of 60 nm (Scherzer defocus was 54 nm); in this case, each dark dot corresponds to two columns of Si atoms, as shown in Figs. 2c and2e. The enlarged Fig. 2b shows the top part of this NW. It can be seen that the dark dots have a translational symmetry with a periodicity of six along the vertical direction. This structure is consistent with the 6H polytype, and shows good agreement with the simulated 6H Si structure shown in Fig. 2c. The enlarged Fig. 2d shows the bottom part of this NW; it can be seen that the dark dots are now almost aligned in the vertical direction. In fact these dots have a translational symmetry with a periodicity of 2 along the vertical direction, consistent with a 2H polytype 3 , and it also shows good agreement with the simulated 2H structure shown in Fig. 2e. The amorphous contrast at the NW surface indicates the presence of an oxide shell.

The pure 2H structure has also been observed in other nanowires grown in the same batch. Figure 3 In figure 4, the NW has a diamond cubic phase near its base and a 2H phase at its top. In the cubic part, there is a twin plane, as shown in the schematic on the right of Fig. 4. The first layer of the 2H part may have a twin relation with the cubic part. There is a ~3° misorientation between the actual orientation of the 2H part and what would be expected from a perfect twin orientation. This switching from the diamond cubic phase to the 2H polytype would indicate that the latter was energetically favourable at this stage of growth, under the precise growth conditions that were present. order to study the stability of the hexagonal SiNWs, we have kept the SiNW sample under standard ambient temperature and pressure conditions for 5 months before further TEM observation. Figure 5a shows the TEM image of such a SiNW. This NW has a diameter around 8 nm at its base and a length of ~90 nm. The enlarged Fig. 5b shows the crystallinity of the NW. It can be seen that a thick (~3 nm) amorphous SiOx has developed at the surface of this NW, but the core part has kept a 2H crystalline structure. Aligning the zone axis was delicate as the nanowire moved under electron beam excitation. Thus, the electron diffraction pattern (EDP) recorded in selected area mode (65 nm) lacks several spots (fig. 5c); however, it clearly exhibits 2H diffraction spots that cannot be interpreted as originating from cubic stacking. This shows that the 2H phase in such thin nanowires is stable under standard atmosphere conditions.

The thermal stability of 2H SiNW was also studied. After acquiring the HRTEM image of the NW in Fig. 5a, the temperature of the TEM grid holder has been increased to anneal the NW and determine the temperature up to which the 2H phase is stable. Figure 5d shows the NW after 30 minutes of annealing at 230°C. This is the same NW as the one shown in Fig. 5a. The NW has started to bend; however, a FFT of the enlargement shown in Fig. 5e still reveals the presence of 2H spots, indicating that the phase is stable up to that temperature. Unfortunately, the [1-210] zone axis is lost after further bending induced by electron irradiation, which stops the observation of the phase at higher temperatures. However, we were able to record, at room temperature, the image of another nanowire, which had not been irradiated during in situ annealing (fig. 5g-i). That nanowire had thus undergone the whole annealing cycle up to 700°C (see experimental section). The FFT of its core (fig. 5i) still exhibits 2H spots. This nanowire must have kept its 2H polytype up to 700°C or, alternatively, it must have recovered it upon cooling. Either explanation demonstrates that the 2H phase is relatively robust in such objects and benefits from a significant stability domain.

In the following, we extract as much quantitative data as possible from the TEM measurements. Table I summarises the geometrical properties of the 2H nanowires and shows their d 10-10 interplanar spacings and the angles between their (0002) and (10-10) planes, as measured in FFTs and diffraction patterns. A total of twenty-two measurements were performed on the five nanowires.

These measurements depend on the equipment used, and variations of -4% to +6% were observed with respect to the mean. Even with the same microscope, variations between different magnifications in imaging mode and between imaging and diffraction modes reached 3% on the same object, due to different calibrations and varying departures from the exact . Thus we decided to normalise all measurements to this reference value, so that only d 10-10 varies in table I. We estimate the relative measurement error for d 10-10 to be within +/-0.3%. Quite remarkably, measurements performed in the two differently oriented regions ([0002] and ) the NW in fig. 3 exhibited no difference in parameters, suggesting that the surface geometry (and the pressure applied by surface tension) played no role. We also measured the angle between these two families of planes. This angle varied slightly from one measurement to the next on the same object, probably due to the rapidly varying orientation with respect to the beam, and because of the elongation of the spots perpendicular to the wire axis. Therefore, we estimate the uncertainty to be about +/-1.5°. Except for a value of 85° in the case of the NW of fig. 5a-f, all measurements were equal within that margin of error to 90°. We attribute the value of 85° to the bending of that particular NW, as its crystalline core was only 2 nm in diameter (see fig. 5a-b). All the angles were arbitrarily taken < 90° because one cannot differentiate 10-10 from -1010.

The theoretical bulk values for 2H Si in Table 1 were derived using the crystal parameters calculated by Rödl et al. I are quite close to these values: the average measured d 10- 10 /d 0002 ratio is 1.3 % greater than the theoretical value for 2H Si, and (neglecting the 85° of the NW of fig. 5a-f) the average angle is only 1.2% off. These results show that indeed, the nanowires presented here possess the 2H hexagonal structure, either partly or completely.

Finally, given the importance of the exact composition of the catalyst and of the impurity content in the silicon, we have performed energy-filtered TEM and energy-dispersive X-ray microanalysis (EDX) on some of the NWs. However, the chemical analysis of such small objects is difficult. To get a significant signal from Cu, the energy-filtered TEM method an energetic electron dose that destroyed the NWs, making the analysis impossible. EDX, on the other hand, delivered an intense Cu signal everywhere on the objects grown on the Cu grid, and even on the carbon membrane in between the grid bars. We therefore have no real information on the presence of Cu in the catalysts or in the NWs. The presence of Sn (and also O) was confirmed by EDX in the catalyst particles (see Supplementary information).

Discussion

The presence of this hexagonal metastable structure obliges us to confront some critical questions: what is creating it and/or what is stabilizing it? Three candidates could be invoked as an answer: (i) the influence of foreign atoms, (ii) kinetic effects during growth and (iii) size effects. We address each of these possible answers in the following.

(i) As we cannot exclude the presence of Cu in the catalyst, we grew (larger) NWs with Cu as sole catalyst, to check whether or not this element could promote the 2H structure in the same growth conditions. However, we found no 2H regions whatsoever in the NWs grown under such conditions. We therefore have no solid proof that Cu is a key factor in producing the 2H phase. On the other hand, Sn from the catalyst droplets may be present in significant concentrations in the nanowires, as was positively confirmed by atom probe tomography 26 . As a matter of fact, we have shown in previous work that during the plasma-assisted VLS growth of silicon nanowires using Sn as catalyst, a wetting layer should form around the wires in order to stabilize the drop and allow NW growth 24 . The (larger) NWs in that work, although cubic, included a very high density of twins. The presence of such wetting layer around the growing nanowire could play a crucial role in stabilizing the hexagonal structure.

(ii) As the 2H polytype was shown to form kinetically in GaAs nanowires 27 , it could form in the same way in SiNWs. However, if efficient, this mechanism would also deliver the 2H structure in larger nanowires, a phenomenon which we have never observed.

(iii) Finally, at these scales, size effects could play a predominant role. The surface-to-volume ratio is increased in small objects, which has consequences that could present themselves in two ways: (a) the surface tension from the sidewalls becomes significant and will exert a strongly anisotropic stress on the nanowire structure that could somehow mimic the cases where anisotropic stress is at the origin of the formation of this phase, and (b) the hexagonal phase would have atomic surface structures with lower energy, so that the global (surface + volume) free energy would be lower 28 . Indeed, two teams have separately calculated that the 2H phase would be favoured in small nanowires oriented in the [0002] direction 28,29 . However, our own data show no structural difference between the two orientations of the NW presented in fig. 3. Moreover, the fact that we observe the 2H phase in NWs covered by an amorphous layer (be it thin or thick) tends to indicate that any pristine surface structure plays a minor role. The exact surface structure that develops during growth remains to be determined; in particular, the wetting by the catalyst postulated earlier 24 could have a significant contribution. However here, the NW of fig. 3 has a length of more than 60 nm with orientation, which must be stabilised by some other means than those proposed by Akiyama et al. 28 .

Finally, among the parameters that differentiate the present from previous experiments, we would like to highlight the use of Sn as catalyst in a plasma environment. Calculations by Akiyama et al. underlined the effect of the surface atomic configuration (associated in their paper with a varying coverage by hydrogen 28), which could switch the phase from cubic to hexagonal and vice versa. Tin, by wetting the NW surfaces 24 , would change their contribution to the global free energy balance. In small NWs with high surface-to-volume ratios, this could switch the equilibrium towards the 2H hexagonal metastable phase.

Conclusions

In this paper, we have presented TEM images and diffraction patterns acquired in the [110] 3C / 2H zone axis of VLS grown silicon nanowires, which cannot be interpreted as the result of a cubic stacking configuration. These are the first unambiguous TEM observations of the 2H hexagonal Si phase in as-grown SiNWs. These nanowires differ from those usually studied essentially by their small diameter (<5 nm) and the fact that we use plasma-assisted CVD and Sn as catalyst for their growth. The hexagonal structure appears to be stable, over time in standard ambient temperature and pressure, and upon annealing at 700 °C in vacuum.

  FIG. 1. a) SEM image of TEM grid; b) detail of (a); c) SiNWs grown on sidewall of Cu TEM grid.

FIG. 4 .

 4 FIG. 4. Switch from twinned cubic phase to 2H phase, associated with a change in growth direction. The schematic shows that the relationship between the two phases is close to epitaxial. FIG. 5. (a-f) 2H SiNW that has been kept in standard atmosphere condition for 5 months. a) TEM image, b) enlargement of red square in (a), c) selected area (65 nm) EDP. d) Same SiNW after 30 minutes of annealing at 230°C. e) Enlargement of red square in (d); f) FFT of the image in e). (g-i) Similar nanowire but not irradiated during heating, having been additionally annealed in situ up to 700°C for 5 min (image recorded at room temperature after cooling). h) Enlargement of red square in (g); i) FFT of the image in (h).

2 :

 2 a = 0.3828 nm, c = 06325 nm. The experimental values in Table

  zone axis. The averaged d 0002 was 0.3143 nm, quite close to the bulk value d 0002 = 0.3162 nm calculated by Rödl et al. for unstressed 2H-Si 2

Table I :

 I Properties as measured by TEM for the NWs shown in figs. 2 to 5, compared to theoretical values In previous experimental works, other authors prepared SiNWs of similar sizes with CVD and using Au 30 or Ag 31 as catalysts, and found them to possess only the cubic structure. The fact that these NWs were not oriented in the [111]/[0002] direction for which calculations have predicted the 2H phase 1,28,29 makes them compatible with those calculations.

					2 . See measurement
	errors in text.
	Nano wire	Length (nm)	Crystalline diameter (nm)	Per-cent 2H	d 10-10 (nm)	d 10-10 /d 0002 Ratio	(10-10) -(0002) Angle (°)
	Fig2	65	3.3	40	0.337 1.069	88.8
	Fig3	95	4	100	0.339 1.076	89.1
	Fig4	100	4	70	0.340 1.078	89.5
	Fig5a-f 90	2	100	0.336 1.064	85.0
	Fig5g-i 60	3	50?	0.343 1.088	88.4
	Theoretical bulk 2H Si, ref. 2		0.335 1.061	90

Acknowledgements

This work was partly supported by the French National Research Agency (ANR) through the projects Solarium (ANR-14-CE05-0025), Platofil (ANR-14-CE26-0020) and the TEMPOS Equipex (ANR-10-EQPX-50), pole NanoMAX. We acknowledge the Centre interdiscipinaire de microscopie électronique de l'X (CIMEX) and Pierre-Eugène Coulon for providing TEM equipment in perfect working order at Ecole polytechnique. Jian Tang thanks the "French Ministry for Higher Education and Research" for his PhD funding.

Notes and references ‡ i.e. with no stress applied other than that of the SiNWs' own surfaces.