Evelyne Lampin
email: evelyne.lampin@isen.iemn.univ-lille1.fr

Catherine Priester

Christophe Krzeminski

Laurence Magaud

Graphene buffer layer on Si-terminated SiC : a multi-minima energy surface studied with an empirical interatomic potential

The atomistic structure of the graphene buffer layer on Si-terminated SiC is studied using a modified environment-dependent interatomic potential (EDIP). The investigation of equilibrium state by conjuguate gradients suffers from a complex multi-minima energy surface. A dedicated procedure is therefore presented to provide a suitable initial configuration on the way to the minimum. The result forms an hexagonal pattern with unsticked rods to release the misfit with the surface. The structure presents an agreement with the global pattern obtained by experiments and even with the details of an ab initio calculation.

I. INTRODUCTION

Graphene is an attractive alternative to silicon for high-mobility devices due to its unique electronic properties. The graphitisation of SiC by high-temperature annealing 1 is often seen as the most promising route to fabricate large layers of graphene. Although many experimental works were devoted to the refinement of the fabrication process, the graphitization mechanism remains poorly understood. In particular, the control of the sublimation of Si atoms during and after formation of the first graphene layer is a key step of the fabrication of larger and more regular layers 2 . ab initio calculations have shown that the first graphene layer, the so-called buffer layer, on the Si-terminated surface has not a graphenelike dispersion 3 and is strongly bonded to the substrate 4 , 5 . The experimental counterpart is not simple, in particular due to the high sensitivity to the preparation procedure 6 . Further understanding could be provided with molecular dynamics calculations that describe the evolution of an atomic system submitted to thermal annealing. Such calculations could only be carried out with rough approximations in the framework of ab initio descriptions and the use of an interatomic potential is therefore more adapted. We present in this study the results of calculations performed with a version of the environment-dependent interatomic potential (EDIP) modified for SiC by Lucas 7 . The equilibrium state of the buffer layer on SiC(0001) is studied. The difficulty to achieve convergence in this multi-minima energy surface is demonstrated, and a specific procedure is given to reach equilibrium. The configuration of minimal energy presents the symetries observed by experiments. Moreover, the details are compared to ab initio results. A good agreement is obtained and the optimum even presents an higher level of order. We therefore conclude on the ability of the potential to describe the graphitisation of SiC surface.

II. METHOD

In a first step, a model of graphene on SiC(0001) is constructed. For the sake of simplicity we consider a 3C-SiC substrate, but the system is perfectly equivalent to 4H-and 6H-SiC provided a planar SiC surface is considered (the equivalence does not hold in the case of a step for example). The lattices of graphene and SiC do not match. A low misfit is obtained for a (6 8 put in regard of a sheet of 13-hexagon wide honeycomb. The misfit, defined by the ratio :

√ 3 × 6 √ 3)R30 • supercell
13 × a graphene 6 √ 3 × a SiC (1)
is equal to 0.7 % experimentally and 3.0 % with the lattice parameters (a graphene , a SiC ) obtained at equilibrium using the interatomic potential presented hereafter. The graphene layer of the basic cell contains 338 atoms of C. The depth of the SiC substrate has to be high enough to absorb the strain generated by misfit. We choose to use 6 SiC bilayers, with a total of 1296 atoms, although the dependence of the results on the depth of the substrate will be tested in the last section of this article. The basic hexagonal cell is replicated twice along x and y to facilitate the visualization of the patterns formed by atoms in the buffer layer. Fig. 1 presents lateral and top views of the corresponding sytems of 6536 atoms.

The interactions between atoms are described by an empirical interatomic potential. Empirical interatomic potentials are developed for a specific domain of a material physics. It is generally difficult to estimate the range of validity of a given potential when it is applied to a different phenomenon for the first time 9 . Indeed one of the aim of this work is to confront the potential under study to ab initio calculations in order to validate its application to the study of graphene on SiC. The interatomic potential is a slightly modified version of EDIP 10 , 11 , 12 parametrised for C-C and Si-C interactions by Lucas 7 . Other classical interatomic potentials such as Tersoff 13 and Brenner 14 have also been adapted and parametrised for Si-C 15 , 16 , 17 , 18 , 19 . Tewary and Yang 20 have constructed a parametric interatomic potential but it is restricted to graphene (only C-C interations). As for the study of SiC graphitization, Tang et al. used Tersoff's potential in molecular dynamics simulation of the heating of Si-less layers on SiC 21 and of graphene nanoribbons 22 although the coordination of order 3 is not natural for a potential developed for diamond lattice. In the present study, the environment-dependent mathematical formulation of EDIP has been assumed to be an advantage for the modelisation of the bonding of graphene layer on the SiC surface including sp2 and sp3 bonds. The potential energy of a system of atoms at position r i is given by :

E = i E i , E i = j =i V 2 ( r i , r j , Z i ) + j =i k =i,k>i V 3 ( r i , r j , r k , Z i ).
(

The coordination number is :

Z i = m =i f (r im ), f (r) =        1, r < c exp α/ 1 -a-c r-c 3 ∆(r), c < r < a 0, r > a. (3)
The corrective function ∆(r) is added by Lucas 7 to avoid the second nearest neighbour Si-Si interactions in SiC to be accounted for. The function is equal to unity except if two Si atoms are interacting :

∆(r) =        1, r < c exp α/ 1 -a-c r-c 3 , c < r < a -δ 0, r > a -δ (4)
with δ = 0.3 Å. The two-body part is given by :

V 2 ( r i , r j , Z i ) = A B r ij ρ -exp(-βZ 2 i ) exp σ r ij -a ∆(r ij ). ( 5
)
The three-body term is made of radial and angular contributions : with u 1 = -0.165799, u 2 = 32.557, u 3 = 0.286198 and u 4 = 0.66. The parameter set is given in Tables I andII. The result is a potential able to describe Si-and C-based crystals and their defects. The only noticeable drawback, as in standard ab initio calculations, is that the Van der Waals interactions are poorly described. Therefore graphite could only be obtained by fixing the distance between two planes of graphene. Periodic boundary conditions are applied in the lateral directions x and y (see Fig. 1. The bottom SiC bilayer in the z direction is frozen to avoid reconstruction of the C-terminated surface. The relaxation is performed with the method of the conjugate gradients 23 until a precision of 10 -8 is reached on the total energy (tenths of µeV/atom) after tenths to hundreds of steps. The initial gap between graphene and the surface is set between 1.5 and 3 Å by step of 0.01 Å, the cutoff of the Si-C interactions being equal to 2.67 Å and the equilibrium Si-C distance to 1.91 Å. Three lateral locations of the graphene plane compared to the SiC surface are tested :

V 3 ( r i , r j , r k , Z i ) = exp γ r ij -a ∆(r ij ) exp γ r ik -a ∆(r ik )h(cos θ ijk , Z i ), h(l, Z) = λ (1 -exp[-Q(Z)(l + τ (Z)) 2 ]) + ηQ(Z)(l + τ (Z)) 2 , (6)
Q(Z) = Q 0 exp(-µZ), τ (Z) = u 1 + u 2 (u 3 e -u4Z -e -2u4Z ), Si-Si C-C Si-C a( Å)
• shift 1 : a C atom in graphene at the vertical of a Si surface atom • shift 2 : center of a graphene hexagon at the vertical of a Si surface atom

• shift 3 : middle of a C-C bond in graphene at the vertical of a Si surface atom.

III. RESULTS

The total energy after relaxation is presented in Fig. 2 as a function of the gap between the plane of graphene and the surface and for the three shifts. The second and third shifts, corresponding to an alignment on the center of an hexagon or on the middle of a bond, give exactly the same energy. Indeed these configurations should be equivalent. In the three cases, the result strongly depends on the initial gap. Above the Si-C cutoff radius of the interactions (2.67 Å), the energy does not depend on the initial gap as expected and corresponds to the sum of the independent contributions of the SiC substrate and of the plane of graphene. In the range [2.1-2.6] Å, the energy only slighlty evolves with the initial gap while there is a strong variation of the result when the graphene plane is set at less than 2.1 Å of the SiC surface. From one value of the gap to the neighboring one, the bonds between graphene and Si surface involve different atoms and this is enough to break bonds and form new ones. This is the explanation of the great dependence of the total energy on the initial gap of graphene, and the presence of multiminima in energy. The method of conjuguate gradient is obviously not able to allow the system to go out of a local minimum. The open question is therefore whether the absolute minima is found or not with this method.

Moreover, we studied in more details the structure of the graphene plane and its bonding to the surface for the two gaps that give a low energy in the configuration of shift 1, i. e. an alignment of a C in graphene on a Si at the an order 6 could be expected, and the structure is surprisingly not regular in Fig. 3. Clearly, the minimisation does not seem achieved. The two figures however evidence the complexity of the energy surface, since the topologies of the graphene layer are so different with total energies almost equal (difference of 0.007%). Therefore we decided to refine the construction of the initial structure to facilitate the relaxation. Indeed, it seems obvious that the multiple possible binding of some of the C atoms of the graphene layer to the Si of the surface is too difficult to handle by the procedure of conjuguate gradients. Since the choice of the initial configuration is of primary importance, 3 initial structures have been specifically built as illustrated in Figs. 5 to 7 In these structures, the graphene layer is no longer planar, but the C atoms are set at 3 different heights z. The C atoms initially close to a Si at the surface are set at the lower z to strengthen the bonds, their immediate surrounding to an intermediate z and the remaining atom to a higher z. By varying the initial mean gap between graphene and the surface, the layer is more or less blue, i.e. more or less sticked to the SiC surface. Fig. 5 corresponds to a mean gap of 2.55 Å, Fig. 6 to 2.58 Å and Fig. 7 to 2.62 Å. A cross view of the system shown on Fig. 5 is also given in Fig. 8 and evidences the slight separation along z of the three levels.

After relaxation, the graphene sheet presents a pronounced buckling of magnitude typically equal to 1.5 Å (Fig. 9). The energy obtained with the three 3-levels systems is smaller than the minimum obtained using a planar sheet as a starting point (Fig. 2). The most stable structure is obtained using the highly-sticked system presented in Fig.

5.

A color map of the positions along z of the C atoms in graphene is given in Fig. 10 for the corresponding system. Low regions form circular and triangular patterns separated by rods at higher z. These rods are necessary to release the misfit of 3.0 % between the graphene sheet and the substrate. The duplication of the elementary pattern results in the formation of an hexagonal structure formed of a central disk surrounded by six triangles separated by rods distributed in a six-branch star. The cross view shown in Fig. 9 suggests that the C atoms in these rods are not bonded to the surface, an assumption that will be discussed in the next section. By comparing the initial structure (Fig. 5) to the relaxed one, we guess that the half rods already present initially extend to form complete rods during the relaxation.

IV. DISCUSSION

The result presented in Fig. 10 has several interesting features. First, it has the lowest energy ever found in our various calculations. Moreover, the structure presents a high level of order, in particular compared to solutions such as

ab initio

Empirical potential Interatomic interations GGA 24 (code VASP 25 )

Modified version of EDIP the one presented in Fig. 3. The symetry level is also the highest, and the (6

√ 3 × 6 √
3)R30 • and (6 × 6) periodicities already observed by scanning tunneling microscopy 6 are visible in Fig. 10. This solution presents all the features expected for the equilibrium state.

The gap between the SiC surface and the graphene layer, defined in this case as the distance between the upper Si atom of the surface and the lower C of the graphene, is equal to 1.68 Å. This gap is smaller than the equilibrium distance of the Si-C bond with EDIP, i. e. 1.91 Å, which is due to the formation of leaning connections between atoms that are not at the vertical of each other. The higher C atoms in graphene are at z = 3.17 Å, a value to compare to the cutoff radius of the Si-C interactions with EDIP equal to 2.67 Å. As foreseen in the previous section, the C atoms in the rods are indeed not bonded to the surface, their location is only fixed by sp2 interactions with their neighbours in the buffer layer. The amplitude of graphene buckling is equal to 1.50 Å. The energy per C atom in graphene is equal to -7.42 eV. This value is lower than the cohesive energy in graphite (-7.38 eV), which is due to the formations of Si-C bonds. Moreover, the impact of the substrate thickness, which could be important due to the stress of the bonded graphene in misfit has been studied. The test has been performed on the energy per graphene atom since the total number of atom is not constant. It has been obtained a variation of only 0.0056% from 4 to 6 SiC bilayers, and 0.0005 % from 6 to 15 bilayers. Obviously 4 SiC bilayers are enough to absorb the strain.

The present result obtained with the EDIP empirical potential is afterwards compared to the result of an ab initio calculation 4 (Table III). The structure is duplicated and a color map is applied to visualize the variations in height of the C in graphene as in Fig. 10. The result is presented in Fig. 11. The structure is less ordered, and an elementary pattern does not clearly stand out, although the hexagonal structure is undoubtly appearent at a larger scale. The rods are smaller and the low regions are not so regular but circular forms and quasi triangular ones can be distinguished. The difficulty to find the minimum is probably here again at the origin of the irregularities of the structure, but the pattern globally corresponds to the result of the EDIP calculation. The atomic positions along z and the corresponding Fourier transforms are drawn at larger scale in Fig. 12. The Fourier transforms evidence some particular features in common (hexagon at 0.3 Å-1 for the 6×6-SiC modulation and 0.7 Å-1 for a local symmetry of the more or less circular grains at low z) and the higher level of symmetry obtained with the present minimisation (second hexagon at 0.3 Å-1 coming from the 30 • -rotated 6×6-SiC periodicity and central hexagon at 0.2 Å-1 due to the (6 √ 3 × 6 √ 3)R30 • elementary pattern, at least more intense in the present calculation). The buckling amplitude of the graphene layer is equal to 1.2 Å to be compared to 1.5 Å for EDIP, for respectively 0.7 and 3.0 % of graphene-SiC misfit. The space between graphene and the surface is equal to 1.8 Å, versus 1.7 Å for EDIP.

The global agreement of the two calculations leads us to the conclusion that this empirical potential is perfectly suited for the study of graphene on SiC. The level of order of the superstructure is even more pronounced, due to the methodology developed to find the minimum despite an empirical physical description of atomic interactions. If in this case, ab initio calculations were still affordable, the use of an empirical description will be essential to study larger systems with surface steps or perform molecular dynamics simulations at a given temperature in order to investigate the mechanism of Si sublimation that results in the formation of graphene.

V. CONCLUSION

In conclusion, the bonding of the graphene buffer layer to the Si-terminated surface of SiC has been studied using a modified version of the interatomic potential EDIP. The difficulty to find the equilibrium configuration has been emphasized, and a dedicated procedure has been developed in order to produce a starting configuration on the way to the minimum. The result presents high level of order and symmetry, with an hexagonal pattern formed of sticked circular and triangular regions and unbonded rods to release the misfit. The structure is coherent with the result obtained using an ab initio description and presents all the symetries identified in experiments. The physical description is therefore validated for further study on the graphitization process.

FIG. 1 :

 1 FIG. 1: Lateral (left) and top (right) views of the atomic system under study. The C atoms are colored in orange, the Si in grey. The delimitations of the basic cell are shown on the right view.

FIG. 3 :FIG. 4 :

 34 FIG. 3: Color map of the position of the C atoms in graphene along z (black dots). Initial gap set to 1.63 Å. Blue (red) means near (far from) the SiC surface. Light crosses indicate the position of the Si atoms of the surface. FIG. 4: Same figure than Fig. 3 but for an initial gap of 2.26 Å.

FIG. 5 :FIG. 6 :

 56 FIG. 5: Strongly sticked three-level structure of the graphene layer. Blue dots are for C atoms closed to the surface, red dots for those far from the surface and green ones for intermediate values of z. Mean gap equal to 2.55 Å. FIG. 6: Moderately sticked three-level structure of the graphene layer. Mean gap equal to 2.58 Å. Same color code than in Fig. 5.

FIG. 10 :

 10 FIG. 10: Color map of the positions along z of the C atoms (black dots) in graphene. Most stable configuration. Blue (red) means near (far from) the SiC surface. Light crosses indicate the position of the Si atoms of the surface.

FIG. 11 :

 11 FIG. 11: Color map of the positions along z of the C atoms (black dots) in graphene. Result of the ab initio calculation presented in Ref. 4. Blue (red) means near (far from) the SiC surface.

TABLE I :

 I Two-body parameters of the EDIP potential used in the present work 12 , 7 .

			3.1213820 2.2918049 2.6746212
		c( Å) 2.5609104 1.5698566 2.0050591
		α	3.1083847 1.1268088 2.1175967
		A(eV) 7.9821730 11.6773355 9.6545591
		B( Å) 1.5075463 0.9612016 1.2037674
		ρ	1.2085196 2.8779528 2.0432362
		β	0.0070975 0.0255960 0.0163467
		σ( Å) 0.5774108 0.7103453 0.6404382
		γ( Å) 1.1247945 1.2258251 1.1742237
		Si-Si-Si	C-C-C	Si-SiC	C-SiC	Si-CC
				or -CSi	or -CSi	or C-SiSi
	λ(eV) 1.4533108 1.7800184 1.5349877 1.6983415 1.6166646
	η	0.2523244 0.8115872 0.3921401 0.6717715 0.5319558
	Q0 312.1341346 417.5476826 338.4875216 391.1942956 364.8409086
	µ	0.6966326 0.6122148 0.6755281 0.6333192 0.6544237

TABLE II :

 II Three-body parameters of the EDIP potential used in the present work 12 , 7 .

TABLE III :

 III Main features of the ab initio and empirical potential calculations.

			7
	Misfit graphene/SiC	0.7%	3.0 %
	Basic cell	1310 atoms, 4 SiC bilayers, 6536 atoms, 6 SiC bilayers,
	characteristics	H-passivation at bottom	frozen atoms at bottom
	Convergence	Residual forces	Variation in energy
	criterium	< 15 meV/ Å	< tenths of µeV/atom
	Number of steps		Tenths to
	for relaxation		hundreds


A Bergeret

N Binda

A Crespy

for mica flakes in propylene/ ethylene copolymer composites

Keywords: Mica, propylene/ ethylene copolymer, comp尔ite, epoxy resin, 业ilane, surface treatment粤 curing agent, mechanical properties

Epoxy resins as surface treatments

INTRODUCTION

Fillers are often used for the improvement of certain properties of polymers (stiffness, compressive strenght, dimensional邓tability, high temperat11re properties, and others) in order to meet the requirements of specific applications. Among these fillers, mica is a well known and abundantly found mineral having great potential as a mineral filler fo「polymers. Neve11heless, these fillers are chemically inert towards a polyolefine matrix. Thus, to reach optimum performance the interactions between 、 the polymer matrix and the filler must be adjusted. Several types of coupling agents and adhesion promoters are usually used. Among these coupling agents, the silanes and other silicon-containing compounds are the most conunonly used because they seem to perform best [ 1-9]. Indeed, 叮o whom correspondence should be addressed. E-mail: abergere@ensm-ales.fr surface treatment with silicon-containing coupling agents appears to change the free energy of a mica surface by interacting physically and/ or chemically, thereby i ?1 p � oving _ the we!t � bilit � _ with _ the � ly � lefin � mat : ix and t � e _ deaggl � � � ration of the fi ne mica particles. Many investigations have been carried out which suggest that silane compounds of different functionality (amine [7][8][9], vinyl [START_REF] Chiang | [END_REF]6], epoxy [ 7], etc.) create both (i) strong chemical bonds and a monolayer which results in stiff and brittle materials and (ii) a diffuse interlayer which offers more advantageous properties such as a relatively high impact resistance. These authors also tried to evaluate the influence of different parameters (i.e. the hydrophobic character of the silane, the crosslinking of the siloxane structure, the thermal stability of the silane, etc.) on the mechanical performance.

Another class of coupling agent often used to treat mica particles includes zirconate- [ 7 ] and titanate- [START_REF] Trotignon | [END_REF]8,9] based agents.These yield lower modulus and ultimate strength than those treated with silane but much higher than untreated ones. Malik [8] assumed that the titanate agent should behave as a lubricating agent. Titanate appears to cause a breakdown of the aggregates in response to the applied stress resulting in an increase in elongation whereas the silane agent should increase the adhesion between the mica and the polymer matrix resulting in an increase in modulus as well as strength. Moreover, through f r acture observations, Xavier et al. [9] speculated that the intertacial adhesion between titanate-treated mica and polypropylene is poor although the fonner had developed a transcrystalline interphase with polypropylene. An altering of the plastic zone in front of the crack was also observed by these authors.

Carboxy-terminated butadiene (CTB) and carboxy-terminated butadiene-acrylo nitrite _ copolymer ( _ CTB _ �!_ have also _ been us � d as � ouplin � age � ts _ for mka-p � ly propylene composites [IO]. According to the authors, these lead to composites which give the highest yield strengths and elastic moduli compared to a chlorosilane agent. Moreover, Trotignon et al. [START_REF] Tro | 1igi1on[END_REF] have shown that coating mica with silane and chloroparaffin gave similar tensile properties. But the use of the later treatment may involve changes in the material colour. Finally, Chun and Woodhams [12] suggested that chlorinated waxes may tend to decompose at processing temperature and to evolve coITosive gas. Therefore, they proposed to modify polypropylene with the addition of I to 5% carboxylated polypropylene. This material may substitute for silane coupling agents.

Nevertheless, silane agents seem to give the best mechanical properties (tensile and impact) according to previous studies. But their disadvantage is their relatively high price which has an unfavourable impact on commercial applications. The「e fore, this study describes attempts to find another coupling agent for mica reinforced composites that will be more comn1ercially viable.

A new surface treatment based on an epoxy resin was used because of its low price compared to a silane coating. A previous study [ 13] using a combination of an epoxy prepolymer and various aminimide curing agents had already been carried out. The results give evidence for (i) the same increase in tensile strength with these epoxy systems comp釭ed to unfilled matrix as when silane coupling treatments are used, and for ( ii) the importance of the choice of the curing agent used to harden the epoxy resin. That is the reason why the present work will attempt to use different curing agents which are well known and commercially used compared to aminimide curing agents which require a particular chemical synthesis [ 14 ) . Previous studies [START_REF] Bergeret | Ew: Cm!f on Macromolecular Physics. Surf</(心 (md l/1/«rf,IC('s m PolIII1erS (/I1d Compo[END_REF][START_REF] Binda | Proc. lnrern. Cml}: 011 Filled Polymers and Fillers (Eur硕1/ers'97)[END_REF] have already reported preliminary results with curing agents of different flex伽lity levels. In this paper, the influence of the nature of the curing agent will also be studied and moreover the influence of various parameters will be investigated: (i ) the deposition process (dry or wet process) used to modify the mica surface; (ii) the ratio bet\veen the epoxy prepolymer and the curing agent ; ( iii ) the amount of coating added to mica p articles ; and ( iv) the curing temperature of the epoxy resin.

EXPERIMENTAL PROCEDURE

Materials

The polymer used was a propylene/ethylene copolymer (called PP/PE ) supplied by Appryl Co., France under the trade mark 3150MN5 Muscovite mica flakes ( Micarvor 80, Kaolins d'Arvor Co., France) with an aver age particle size of 48 µ, m were used in this study. It is a layered aluminosilicate mineral with silicon-oxygen tetrahedral layers linked to gibbsite Al(OH h octahe dral layers. Each sheet is su•ongly negatively charged due to the substitution of some aluminium atoms by silicon ones in the tetrahedral layer. These charges are balanced by cations ( mostly potassium) located between the sheets. Unlike silica, there are no surface silanol groups on mica.

Mica flakes were coated by a combination of an epoxy prepolymer (Epikote 828, Shell Co., France ) and different curing agents. A triethylenetetramine ( Prolabo Co., France ) called TETA and two polyetheramines (Texaco Chemical Co., France ) with two (called PEA2 ) or three (called PEA3) amine groups were used as curing agents. A silane coupling agent (PCIA/PCIB in the ratio 3 / l ) supplied by Osi Co., France, was also used as a surface modifier for the mica flakes

Su rf ace treatment o f mica fl akes

The mica flakes were coated with Epikote 828 and the curing agent<; using either a dry process or a wet process ( parameter I).

In the dry process, the epoxy prepolymer and the curing agent were dissolved in 900 ml of ethanol in a fixed epoxy prepolymer/curing agent ratio (parameter 2). This ethanol solution was then introduced in a mixer apparatus ( Drais) which already contained 3 kg of mica flakes. After continuous stirring, mica flakes were dried in an oven at 60 °C over J 2 h. Two different amounts of surface modifier ( Epikote 828 + curing agent ) added to the mica flakes were chosen (parameter 3). In the wet process, a fixed ratio of epoxy prepolymer and of each curing agent were also dissolved in ethanol but in a greater quantity (5 1). The mica flakes (3 kg) were then immersed in the ethanol solution with continuous stining and first partially dried under vacuum at room temperature during 2 h. Finally, ethanol was totally evaporated under a ventilated hood over 12 h.

In both processes, surface-modified mica flakes encapsulated by epoxy prepoly mer with the curing agent were obtained. Then these surface-modified mica flakes were subjected to different curing profiles (parameter 4). A coating layer adhering tightly to the mica surface was thus obtained

The mica flakes were also dry-coated by a combination of two silane coupling agents called PCIA/PClB. The same experimental procedure described above was used. But after the ethanol evaporation, no curing step was applied, so as to give a surface-coated mica with the silane-based coupling agent.

Composite specimens elaboration

These differently modified fillers were incorporated with the PP /PE copolymer through an extrusion process (twin screw extruder Clextral BC2 l). Filler content was about 40 wt%. Then compounds were molded through an injection process (Sandretto trademark) using a damping force of 90 tons. A composite reinforced by untreated mica flakes was also extruded and molded.

TECHNIQUES

Tensile and impact measurements

Young's modulus, yield stress and strain, ultimate stress and strain measurements were perfonned in tensile mode on an Adame! Lhomargy DY26 testing machine. The experimental procedure as well as the sample dimensions were defined accord ing to the International Norm ISO 527 standard method. Afterwards, ultimate stress values were not reported because they follow the same evolution as yield stress values.

Charpy impact resilience was measured on unnotched samples by means of a Zwick 5102 apparatus according to the International Norm ISO 75 standard method.

Impact direction was parallel to the thickness of the sample and the initial energy was 4 J.

In all cases, ten specimens per sample were tested and the measured values were averaged.

HDT (heat deflection temperaJure) measurements

The HDT measurements were carried out using a MIE-JPS apparatus according to the International Nonn ISO 75 standard method with a loading of 3.27 N and with a heating rate of 2 °C/min.

Wettability measurements

The wettability index of mineral powders was measured according to Stevens' method [START_REF] Stevens | Je11nen-Burtholomeussen R[END_REF]. The experimental procedure consisted in the preparation of isopropa nol/water mixtures of different surface tensions. The surface tension (E s , mJ/m勺 is correlated to the isopropanol content ('1; 心 propanol, ml) used to prepare I 00 ml solution through the following equation: Es = -11.34 In Visopropanol + 68.97

( l )

Wettab山ty of powders is measured by sieving the powder upon the isopropanol/ water mixtures of various surface tensions. Then the wettability index is the surface tension value of the solution which wets this powder. It is ea<;ier to see whether a powder is wetted or not when some methylene blue is added to the solution.

RESULTS AND DISCUSSION

Influence o

f the amount of coating 4.1.J. Wettab血y measurements. The influence of the amount of coating was studied tlu•ough wettability measurements, only in the case of the TETA curing agent and according to the experimental procedure described above. These tests allowed the quality of the encapsulation of the mica fl akes by the epoxy resin to be estimated. Indeed, the more efficient the mica encapsulation, the more hydrophobic the mica smface and the lower the wettab山ty index.

Before any wettability tests, the curing profile of the epoxy prepolymer by the TETA curing agent has been optimized by using a Differential Scanning Calorimeter (DSC92, Setaram Co., France). The TETA curing agent was mixed with the epoxy prepolymer at an epoxy prepolymer/ curing agent ratio of 9/ l. Then the thermogram was recorded over the temperature range 30-250 °C at a heating rate of I0 °C/min (Fig. I). Three heating treatments corresponding to different temperatures and times in the curing process were chosen. These treatments were: 2 h at 50 °C, 30 min at l l 0 °C and 30 min at 180 °C.

The curing times were selected through isothermal measurements in order to obtain a complete crosslinking of the resin. The amounts of surface modifier (epoxy prepolymer + curing agent) added to mica flakes varied from 0.5 to 3%. The wettability index variations are plotted in Fig. 2 and show that the hydrophobicity of the mica surface increased as both the curing temperature and the amount of coating increased.

For this study, two amounts of surface modifier added to particles were chosen: 1 % corresponding to a partial encapsulation and 3% corre..<; ponding to a total encapsulation. Below the value of 1 %, the su1face treatment did not seem to be effective. Moreover, the highest curing temperature was selected, i.e. 30 min at 180 °C.

4.1.2. Mechanical properties. According to previous results, the composites presented in Table 2 were studied.

Moreover, blends of PP /PE copolymer and epoxy resin were also elaborated through the same extrusion-injection process in the case of the TETA curing agent The amount of epoxy resin was about I and 3%. Table 3 shows all the blends used for this study.

For all composites and blends presented respectively in Table 2 and in Table 3, the impact direction was perpendicular to the thickness of the sample. Charpy impact resilience was measured on notched samples for blends.

As shown on Fig. 3, the following results can be listed: (i) the presence of an epoxy resin did not significantly modify the Young's modulus, either for composites or for blends; (ii) the presence of an epoxy treatJnent on mica flakes seems to increase the yield stress but this increase is independent of the amount of coating ; (iii) in the presence of an epoxy resin used either in composites or in blends, the impact strength wa<; drastically decreased and this decrease in impact st1• ength was proportional to the amount of coating; and (iv) no significant variations in HOT values were observed. Therefore, if an epoxy coating did not significantly modify tensile properties, it led to a fall in impact properties. Finally, it appeared more interesting to have a partial encapsulation of mica flakes (coating amount of I%) for better mechanical performance. The curing profiles of the epoxy prepolymer by the three curing agents were optimised through DSC measurements using the experimental procedure described above. The onset temperature as well as the temperature con飞sponding to the maximum of the curing peak and the curing enthalpy are given in Table 4.

From these results. the curing reaction induced by the TETA curing agent occurred at a lower temperature and involved a more energetic reaction than that from the two other curing agents (PEA2 and PEA3). According to the thermograms shown in Fig. 4, two curing profiles were chosen: 2 h at 80 °C and 30 min at 210 °C. The curing times were selected through isothermal measurements. As shown in Fig. 5, the following results can be listed: (i) for both TETA and PEA3 curing agents, no significant variations in the Young's modulus, the yield stress, the impact strength or the HDT values according to the curing temperature were obtained and (ii) in the ca5e of the PEA2 curing agent, a high curing temperature seemed to decrease the composite strength (Young's modulus and HDT) whereas the impact strength increased. Finally, according to these results, it was a low temperature of 80 °C which was preferred.

According to these results, the composites de-

Influence叫the epoxy resin/ curing agent ratio

The influence of the epoxy resin/ curing agent ratio was studied in the case of the PEA2 and the PEA3 curing agents and for two epoxy resin/curing agent ratios: 9/ I

J K L M
and 9.5/0.5. The mechanical prope1ties of the corresponding composites listed in Table 6 were compared. As shown in Fig. 6, no significant variations in the Young's modulus, the yield stress or the impact strength, nor in the HOT values were observed. Moreover, 血s behaviour was independent of the nature of the polyetheramine used as curing agent. This result seems to justify the previous choice of a ratio of 9 / I to optimize the amount of coating and the curing temperature.

lr ifiuence of the coating process and叫the nature of the su,和ce modifier

All composites used for the study of the influence of both the coating process and the nature of the surface modifier are given in Table 7. epoxy systems; (iv) the Young's modulus of the epoxy-coated mica flakes reinforced composites did not vary when the wet deposition process was used; (v) the PEA2cured epoxy treatment gave the highest Young's modulus compared to the PEA3cured epoxy treatment when the dry coating process was used; (vi) moreover, the Young's moduli of composites D, F and H which were wet-coated were between the Young's moduli of the composites J (PEA2) and L (PEA3) which were both dry-coated.

For the impact results, data show that: (i) composites reinforced by silane coated filler、 have the highest impact strength; (ii) except for PEA3-cured epoxy treated mica reinforced composites (dry process), the impact strength of composites reinforced by epoxy-coated mica flakes is similar to those of composites reinforced by untreated fillers; (iii) the PEA2 curing agent leads to lower impact properties than the PEA3 curing agent f or the dry coating process.

For HOT results, data show that: (i) the HOT values increased in the presence of a surface treatment; (ii) for epoxy systems, HDT values are higher when the wet process is used and these values are similar to those of silane-coated composites.

Some difficulties can exist in attempting to get insight into the filler/ matrix interaction by the determination of the Young's modulus. Nevertheless, the values of the yield stress depend on this interaction amongst others. Data show similar yield stress values for composites reinforced by epoxy-coated fillers. whatever the deposition process, and for composites reinforced by untreated ones. Therefore, this could be due to a poor interaction between the epoxy-treated filler and the polymer matrix. Equally, the increase in the yield stress for the silane-coated mica reinforced composites gives evidence of a good adhesion.

The epoxy-coated mica/polyolefine composites have a greater Young's modulus than the untreated mica/polyolefine composites. This result could be due to a good dispersion of mica ffakes in the polymer matrix and/or the presence of a stiff interphase arising from the epoxy resin crosslinking. Indeed. wettab血y tests showed that the epoxy-treated mica surf 、 ace becomes hydrophobic, compared to the raw mica surface which is hydrophilic. Therefore, the presence of an epoxy treatment seems to improve the dispersion of mica particles compared to untreated particles.

Furthermore, when the dry coating process is used, the PEA2-cured epoxy coated and the silane-coated mica reinforced composites have a similar Young's modulus. But this is higher than the Young's modulus of PEA3-cured epoxy-treated mica reinforced composites. On the one hand, wettability results show that the hydrophobicity of the PEA2-cured epoxy-coated mica surface is higher than that of the PEA3-cured epoxy-coated mica surface. Therefore, the PEA2-cured epoxy treated mica flakes should be better dispersed in the polymer matrix than the PEA3cured epoxy-treated ones. Bur, on the other hand. the curing agent PEA3 has been supplied to be more flexible than the curing agent PEA2. It should involve a 、ofter interphase. This last assumption 、eems to be in good agreement with the impact 邸ts.

When the wet coating deposition is used, these previous differences in Young's modulus are smoothed because this wet process is expected to induce a more homogeneous encapsulation of the mica flakes by the epoxy resin. Moreover, quite a good dispersion of mica flakes in the polymer matrix might exist regarding to the HOT tests.

CONCLUSIONS

This study deals with the use of an epoxy resin as surface modifier of mica flakes before their incorporation in a polyolefine. The results show that the curing temperature of the epoxy resin, as well as the epoxy resin/curing agent ratio have no significant influence on the mechanical properties. Thus, a curing temperature of 80 °C and an epoxy resin/curing agent ratio of 9/1 were chosen. Nevertheless, an increase in the amount of coating added to particles resulted in a considerable decrease in impact strength. Therefore, an amount of coating of l % corresponding to a partial encapsulation of mica flakes was chosen. Moreover, the nature of the curing agent and the deposition process have a great influence on the mechanical characteristics. The epoxy treatments presented in this paper appear to create a stiff 、 and brittle interphase leading to a slight increase in ten叫e propetties but to a drastic fall in impact properties.

Research will be carried out in order to use other curing agents which are much more flexible in order to obtain a less brittle interphase. Nevertheless. this soft curing agent should be combined with a commonly used one (for example, a tetraethylenetetramine curing agent) in order to improve impact properties without modification of tensile properties. Concerning the deposition process, the re.c;ults appear to advocate the wet process. But the high value of the Young's modulus obtained for the PEA2-cured epoxy-coated mica reinforced compo 、ites when these fillers are dry-treated should lead u、 to keep this last process under consideration.

Figure 1 .Figure 2 .

 12 Figure 1. DSC plot of the crosslinking of the epoxy prepolymer (Epikote 828) by the curing agent TETA for an epoxy prepolymer/ curing agent ratio of 9 / I (heating rate: I 0 °C/ min) 80

Figure 3 .

 3 Figure 3. lntluence of the amount of surface modifier (Epikote 828 + TETA) added to the mica flakes on the mechanical characteristics of (0) composites (prtl<.'ess: wet -(.,uring: I 80 °C -epoxy resin/curing agent ratio: 9/ I) and of�) blends.

Figure 4 .

 4 Figure 4. DSC plots of the crosslinking of the epoxy prepolymer (Epikote 828) by the three curing agents for an epoxy prepolymer/ curing agent ratio of 9 / I (heating rate: J0 °C/min).

Figure 5 .

 5 Figure 5. Influence of the curing prof ile of epoxy-coated mica flakes (0) 2 h at 80 °C �) 30 min at 210 °C on 1he mech anic al charac1eristics of compo、ites (proce、s: wet -coating amount: I%epoxy resin/curing agent ratio: 9/ I)

Figure 6 .

 6 Figure 6. Influence of the epoxy resin/curing agent ra1io (□) 9/1(团)9.5/0.5 on the mechanical characteris1ics of composi1es (process: dry-coating amount: I% -curing: 80 °C)

Figure 7 Figure 7 .

 77 Figure 7 compares the mechanical properties depending on (i) the nature of the curing agent for all composites and (ii) the coating process for composites reinforced by epoxy coated mica flakes when PEA2 and PEA3 curing agent are used.Concerning the tensile properties, data show that: (i) the Young's modulus and the yield stress increased in the presence of a surface treatment; (ii) the Young's modulus and the yield stress were better with the silane treatment compared to epoxy treatments; (iii) no significant variations in the yield stress were obtained for

Table I . Parameters which influence. the performance of the epoxy based surface treatments Parameter number Description Parameters

 I

	l 2 3 4	coating process epoxy resin/curing agent ratio coating amount curing 1empera1ure	dry or wet 9/1 or 9.5/05 I or 3% 80or2l0 °C

Table 2 .

 2 Composites used to study the influence of the amount of epoxy coating added to particles

	Curing agent Coating Coating Epoxy resin/ Curing profile process amount curing agent	Composites
				ratio
	TETA TETA	wet wet	0% 1% 3%	9/1 9/1	A I 80 °C (30 min) B I 80 °C (30 min) C
	Table 3.
	Blends used to study the influence of the amount of epoxy coating added to particles
	Curing agent Coating amount	Epoxy resin/ Curing profile	Blends
				cunng agent
				ratio
	TETA TETA	3% 1%		9/1 9/1	l80

°C (30 min) TETA-1% 180 °C (30 min) TETA-3%

Table 4 .

 4

	Curing agent	Tonsc1 ( °C)	兀11ax ( °C)	En1halpy(.J/g)
	TETA	70	104	369
	PEA2	76	124	106
	PEA3	80	126	101
	4.2. Jnf tuence of the(. . uring remperarure
	4.2.J. Calorimetry measurements.

Onset temperature、 (T on 、et), temperatures corre、ponding to the maximum of the curing peak (T max) and enthalpies of the curing reaction between Epikote 828 and each curing agent

Table 5 .

 5 Composites used to study the influence of the curing profile of each curing agent

	Curing agent CoaunO c	Coatin2 乙	Epoxy resin/	Curing pro什le	Composites
		proces�	amount	curing agent
				ratio
	TETA TETA PEA2 PEA2 PEA3 PEA3	wet wet wet wet wet wet	彶 % % 勿 赁 赞	9 9 9 9 9 9	/ I I I / I	80 °C (2 h) 210 °C (30 min) 80 °C (2 h) 210 °C (30 min) 80 °C (2 h) 210 °C (30min)	D E F G H _
	4.2.2. Mechanical properties.
	scribed in Table 5 were studied.

Table 6 .

 6 Composites u、ed 10 study 1he inf luence of thee肛)xy resin/ curing agent ratio

	Curing	Coatinu 二	Coating	Epox y resin/	Curing pr的le Composites
	agent	process	amou nt	curing agent
				ratio
	PEA2 PEA2 PEA3 PEA3	dr y dr y dry dr y	l 吭 1% I o/c I o/c	9/1 9.5/0.5 9/1 9.5/0.5	80 °C (2 h) 80 °C (2 h) 80 °C (2 h) 80 °C(2 h)

Table 7 .

 7 Composites used w study the intluence of both the coa1ing process and the of the surface modifier

	Curing	Coating	Coating	Epoxy resin/ Curing profile Composites
	agent	process	amoum	curing agent
				ratio
			0%			A
	TETA	we1	1%	9/1	80 °C (2 h)	D
	PEA2	wet	1%	9/1	80 °C (2 h)	F
	PEA2	dr y	1%	9/1	80 °C (2 h)	J
	PEA3	wel	1%	9/1	80 °C (2 h)	H
	PEA3	dr y	1%	9/1	80 °C (2 h)	L
	silane	dr y	1.5%			N

Acknowledgement

The authors are very indebted to the following students of the Ecole des Mines d'Al七s: Mr. N. Besson, Ms. S. Gandouin, Ms. A. Gard七s, Ms. M. L. Richard and Mr. B. Veirun for their helpful contribution in both the elaboration of the composite materials and their mechanical characterization.


J M Julien

J-C Benezet

E Lafranche

J-C Quantin

A Bergeret

M F Lacrampe

P Krawczak

Development of Poly(Lactic Acid) Cellular Materials Physical and Morphological Characterization

Introduction

In this study the chemical foaming of two commercial PLA through extrusion process is investigated. Different processing conditions (extrusion flow rate, temperature and cooling system) as well as different contents of chemical foaming agent (CFA) were considered. The foaming aptitude of the PLA/CFA formulations is assessed on the basis of void content induced by extrusion in the final product. For each PLA, the experimental results allowed defining optimum set of extrusion conditions, leading to a maximal void content. Secondly, in the case of PLA-based foams extruded in optimal process conditions, the cells structure and mechanical properties were investigated as a function of chemical foaming agent content.  Cell density of PLA 7000D is higher than that of PLA 4032D (especially under 4 wt% CFA content).

Materials, Processing

Results, Analysis Conclusion

 The type of cooling has little effect on the morphology (except presence of macro-voids with air cooling).

Mechanical behaviour

 Samples are cut from extruded parts in a direction parallel to die axis.  Tensile tests are performed.

 CFA content has little effect on maximal and ultimate strains.  Increase in CFA content induces a reduction of yield stress and tensile strength of both PLA. This is correlated with increase in void fraction and thus reduction in effective sample cross-section.

 Optimized foaming extrusion leads to 45 % void fraction and homogeneous cellular structures with two PLA which differ at least by melt temperature.  Free and confined cooling cause similar morphologies except the presence of macro voids with free (air) cooling  Tensile strength is well correlated with CFA content and thus with void content  A better understanding of the foaming process is necessary to explain particular tends  Further achievements will be carried out: injection molding, alternative methods to quantify the morphology, …



  PLA 7000D, PLA 4032D (NatureWorks ® ) molecular weight -Ubbelohde capillary viscometer), T g (glass transition temperature -DSC), T m (melt temperature -DSC)  CFA Hydrocerol ® OMAN 698483 (Clariant Masterbatches) : sodium bicarbonate and citric acid encapsulated in PLA

  circularity index (I c ), cell density (N c ),cell size polydispersity (PDI),cell-wall thickness () and open-cell ratio (C o ) as function of CBA content -PLA 7000D temperature profile A and PLA 4032D temperature profile B; screw speed 30 rpm; die temperature 195 °Cfree cooling -( ) : standard deviation

  optimized at 30 rpm and 195 °C die temperature.  Competition between degradation and diffusion of CFA. Both PLA show the same behaviour with temperature profile B. The evolution is controlled by the amount of gas and thus the CFA content. Void fraction increases up to 45 % which is quite good for a CFA.  Cellular structure is rather homogeneous (PDI≈1) and low open-cell ratio (<26 %).  Both PLA are different on the open-cell evolution with CFA content.

Cooling system V f (%) d n (µm) d w (µm) PDI N c (cells/cm 3 )10 4  (µm)

	Free at air	44 (1.2) 98 (12.4)	99	0.98	92.93	47.64
	confined	46 (0.94) 98 (21.2)	101	0.97	92.50	46.58

Effect of the cooling system on the cellular structure. PLA 7000D (temperature profile A); screw speed 30 rpm; die temperature 195 °C; free cooling. ( ) = standard

deviation Polymer CFA (wt%) d n (µm) d w (µm) I c PDI N c (cells/cm 3 ) 10 4  (µm) C o (%) PLA7000D

		2	104 (31.2)	113	2.05 (0.7)	0.92	68.01	61.12	23.13 (0.5)
		3	100 (19.0)	102	1.50 (0.3)	0.98	81.17	53.58	13.86 (0.6)
		4	98 (12.4)	99	1.64 (0.3)	0.98	92.93	47.64	12 (0.4)
		2	137 (32.6)	145	1.7 (0.3)	0.94	22.51	111.94	19.12 (1.5)
	PLA4032D	3	133 (63.8)	157	1.7 (0.4)	0.85	30.09	85.03	24.49 (1.3)
		4	143 (28.1)	151	1.5 (0.3)	0.94	24.32	91.28	26.76 (1.1)
	Cell dimensions (