Z Oumekloul
email: z.oumekloul@edu.umi.ac.ma

S Lahlali

A Mir

A Akjouj

Evolution of LSPR of gold nanowire chain embedded in dielectric multilayers

The objective of this paper is to improve the sensitivity and the performance of nano-sensors by using the simulation, which was done by finite element method in 2D plasmonic nanostructures. Meanwhile, the effects of geometric parameters of a hexagonal gold nanostructure, and the influence of two dielectrics Si 3 N 4 and SiO x were treated. In order to have better sensitivity, the nature and the thickness of a deposed dielectric were controlled. Whenever we change the geometric parameters of the metallic nanostructure, we see changes in nanoparticle's plasmonic response. Adjusting the theoretical curve to experimental LSPR curve allowed the geometry of the plasmonic interface to be fixed and evaluation of the change in the wavelength at resonance (λ R ) as a function of the SiO x overlayers thickness. The theoretical data were compared with experimental results obtained on glass/Au nanowires/SiO x and glass/Au Nanowires/Si 3 N 4 interfaces.

Introduction

The terms "nanomaterial" and "nanostructured material" appeared in the early 90s, but the study and use of nanomaterials are older. The colloids are the first community of this functionalized state of matter. However, a colloidal system was rarely perceived as a material, but rather as a fluid with special properties. Michael Faraday already studied the manufacture of nanoparticles by colloidal chemistry in the 19th century in the 1850s [START_REF] Faraday | Experimental relations of gold (and other metals) to light[END_REF]. Faraday was well aware that colloidal gold behave very differently from macroscopic grain size vis-a-vis the visible light.

Currently there is strong demand for bio-sensing devices based on surface plasmon resonance (SPR) of noble metal nanoparticles in specific silver and gold deposited on functionalized surfaces [2][3][4][START_REF] Maier | Plasmonics -a route to nanoscale optical devices[END_REF][6][7][8][9][10][11][12][13][14][15][16][17]. Optical properties of metallic nanomaterials are determined by a set of parameters such as the chemical composition of the substrate in which the metal is deposited, the size particles and form, as well as the environment surrounding these metal nanomaterials. The LSPR are very sensitive to modifications in the medium close the surfaces. The effects of the refractive index of the surrounding medium on the plasmonic band LSPR (Localized Surface Plasmon Resonance) have been studied for many years [17][18][19][START_REF] Homola | Surface Plasmon Resonance Based Sensors[END_REF]. Schultz studied the influence of the refractive index of the surrounding single silver nanoparticles in various oils [21].

After adding oil, the color of silver nanoparticles is changed from blue to green, indicating a shift to red color. The color of the modified nanoparticles turns blue when removing the oil. In the same year, Van Duyne uses silver nanoparticles as probes for detecting the formation of a monolayer on the surface of the nanoparticles [22].

The nanosensors based on LSPR have several advantages for bio sensing since it presents high sensitivity by detecting changes in the refractive index with no label and is flexible for the detection of biomolecular interactions of nanoparticles [19,[START_REF] Homola | Surface Plasmon Resonance Based Sensors[END_REF][23][24][25][26]. On top of that, the detection is in real time and allows the use of micro fluidic systems, low cost and ease for the instrumental configuration. These benefits show that these nanosensors can be applied in a wide range of areas, such as the medical field [START_REF] Homola | Surface Plasmon Resonance Based Sensors[END_REF][27][28][29][30], that of food security [31,32], or the one on the monitoring of the environment [19].

In this work, we will numerically simulate the optical response of metal nanoparticles by changing the peak LSPR wavelength, for a hexagonal geometry based on the Drude-Lorentz-model for gold deposited on a glass substrate. On one hand, our study is carried out according to different geometric parameters of this hexagonal structure, and on the other hand, it depends on the thickness of the dielectric layers of SiO x and Si N 3 4 deposited above the gold nanoparticles. Calculations are performed using the finite element method (FEM), which solves Maxwell's equations. The aim of our work is not only to improve the performance and sensitivity of future nanosensors, but also to control them by changing the settings of the geometry, and the nature and thickness of the dielectric deposited on the structure for better quality detection.

This paper is organized as follows: In section 2 we present the technique of the formation of gold nanowires on glass and covered by Si 3 N 4 or SiO x . Section 3 briefly the Lorentz -Drude model. Section 4 present the optical characterization of the structure and simulation. Sections 5, 6 and 7 study the effects of the geometrical parameters of the Au nanowires and dielectric layers on the plasmonic responses, respectively. The conclusion is presented in section 8.

Experimental section

Formation of gold nanostructures on glass

Glass slides (n = 1.51) were cleaned in isopropanol and acetone in an ultrasound bath at room temperature, rinsed copiously with Milli-Q water, and dried under a stream of nitrogen. The clean substrates were transferred into an evaporation chamber. Gold nanostructures deposition was carried out by thermal evaporation of 4 nm thick gold films using MEB 550 S. Postdeposition annealing of the Au-covered slides was carried out at 500 °C for 1 min under nitrogen atmosphere, using a rapid thermal annealer (Jipelec Jet First 100). The reproducibility of the Au evaporation was evaluated by measuring the LSPR signals of a batch of 8 samples. The standard deviation in the wavelength (λ R ) and maximum absorption (I max ) is typically 2 nm and 0.02 abs units, respectively.

Deposition of dielectric overlayers 2.2.1. SiO x

SiO x overlayers were deposited on glass coated with Au nanostructures (glass/Au NWs) by plasma-enhanced chemical vapor deposition in a Plasmalab 800 Plus at a pressure of 0.005 Torr for 1 h. The growth conditions used were as follows: substrate temperature, 300 °C; gas mixture, SiH 4 (5% in N 2 ) and N 2 O (the gas flow was 150 and 700 sccm for SiH4 and N2O, respectively); total pressure in the reactor, 1 Torr; and power, 20 Watt at 13.56 MHz. Under these experimental conditions, the deposition rate was 68.1 nm/min and the silica films display a refractive index n = 1.45. A total thickness of 300 nm was deposited and the thinner films were obtained by etching the SiO x layer.

Si 3 N 4

Si 3 N 4 overlayers were deposited on glass coated with Au nanostructures by plasma-enhanced chemical vapor deposition in a Plasmalab 800Plus. The growth conditions used were as follows: substrate temperature, 200 °C; gas mixture of SiH 4 (5% in N 2 ) at 360 sccm gas flow, NH 3 at 20 sccm; total pressure in the reactor 1 Torr; power: 10 W at 13.56 MHz. Under these experimental conditions, the deposition rate is 7.2 nm/min and the films display a refractive index of n = 2.01. A total thickness of 300 nm was deposited and the thinner films were formed by etching of the Si 3 N 4 layer.

Etching of the Si 3 N 4 and SiO x layers

The Si 3 N 4 and SiO x films are etched by a reactive ion etching (RIE) process using a gas mixture plasma in a RIE etching Plasmalab 80plus equipped with a laser interferometer (Jobin Yvon) at 670 nm. The etching rate was calibrated using two separate techniques. First, the etching rate was estimated within the plasma chamber by an interferometer on a Si 3 N 4 and SiO x layer on plane silicon. Then, the etching rate was estimated by ellipsometry measurements. The etching rate is 48 nm/min for Si 3 N 4 using the following etching parameters: gas mixture SF 6 and Ar at 20 and 10 sccm gas flow, respectively, 50 W forwarded power, and 10 mTorr chamber pressure. The etching rate is 27.2 nm/min for SiO x using the following etching parameters: gas mixture CHF 3 and CF 4 at 20 sccm gas flow each, 180 W forwarded power, and 50 mTorr chamber pressure.

Instrumentation

UV-vis spectrometer

Absorption spectra were recorded with a Perkin-Elmer Lambda UV/ vis 950 spectrophotometer in cuvettes of 10 mm dimension. The wavelength range was 400-800 nm.

Scanning electron microscopy (SEM)

SEM images were obtained with an electron microscope ULTRA 55 (Zeiss) equipped with a thermal field emission emitter and a high-efficiency In-lens SE detector.

Ellipsometry

Spectroscopic ellipsometry data in the visible range were obtained with a UVISEL Jobin Yvon Horiba Spectroscopic Ellipsometer equipped with DeltaPsi 2 data analysis software. The system acquired a spectrum ranging from 2 to 4.5 eV with 0.05 eV intervals. Data were obtained using an angle of incidence of 70°with the compensator set at 45°and fitted by regression analysis to a film-on-substrate model as described by their thickness and their complex refractive indices.

Theoretical model

Calculations are performed using the finite element method (FEM), which solves Maxwell's equations by discretizing space. Our calculation is performed in a two-dimensional (2-D) box (along x and y axes) with a propagation along the y axis. Perfect matching layer (PML) conditions are applied at the boundaries y of the box, to avoid reflections of outgoing waves. Along the x direction, the unit cell is repeated periodically (see Fig. 1) and the structure is supposed to be infinite along the z direction. Space is discretized in both x and y directions using a triangular mesh.

The input electromagnetic field, having TM polarization, is generated at the left part of the unit cell by a current source parallel to the x axis and having a planar profile along the x direction. The transmitted signal, probed at the end of the right part of the unit cell, is recorded as a function of frequency. All the transmission spectra are normalized with respect to the one corresponding to a structure without the array of metallic nanoparticles.

The plasmonic nanostructure studied in this word is constructed by the gold nanowires deposited on a dielectric substrate and the latter are covered by air (see Fig. 1). The metal of dielectric constant is described by the Lorentz-Drude model for described the frequency-dependent complex permittivity of metal (gold) the formula is given by Ref. [33]:

∑ =+ -+ ∞ = εω ε fω ωωi ω Γ () m M m p m m 0 2 2 2 (1)
where ∞ ε is the relative permittivity at infinite frequency, ω p is the plasma frequency, ω m , f m , and Γ m are, respectively, the resonance fre- quency, the strength, and the damping frequency of the mth oscillator. The Lorentz-Drude model uses M = 5 damped harmonic oscillators to describe the small resonances observed in the metal's frequency response. The values of the constants in Eq. ( 1) are given in Table 1. This model allows us to fit experimental data for the frequency-dependent dielectric constant of metals such as gold [33] including both the real and imaginary parts, with good agreement in the visible wavelength range (400 < λ < 800 nm). The hexagonal gold nanowire (NW) used in this nanostructure is characterized by its height H, the two diameters L and l, as well as the period p (see Fig. 1). During the study, we take into account a normal incidence of the incident electromagnetic field on the type of excitation, and we vary the wavelength in the visible range in order to detect the LSPR at the metal structure by modifying one of the previously defined geometrical parameters. Käll et al. [34], studied the LSPR frequency variation in function of the thickness of layers of tricosenoic acid 22 (a dielectric with a refractive index n = 1.53). In this study, the thickness of the acid tricosenoic-22 deposited on the considered nanostructures varies from 0.0 to 340 nm [34]. The layers of dielectric are deposited on a SiO 2 substrate, upon which two types of nanostructures have been studied experimentally. A random network of metallic gold nano-discs then a random network of air nano-holes perforated in a gold film with a thickness of 20 nm, deposited on SiO 2 . A similar study was carried out with gold nanostructures deposited on SiO 2 substrate. The layers of dielectric deposited on the metallic nanoparticles were SiO x material [35], and their thicknesses ranged from 0.0 to 300 nm. The displacement of the observed properties of LSPR peaks in this study showed a red shift which was used for a study of the hybridization of the DNA molecule. These results showed the simultaneous influence of the dielectric refractive index deposited on the nanoparticles and its thickness on the behavior of the optical response at the interface LSPR. Galopin et al. have recently made the same comparison by using rectangular nanorods 2D [13]. Based on their experience, one can note a rather random particle shape, which requires them to determine statistical uncertainty with the dimensions of the nanoparticles in the overall structure. Akjouj et al. found that the most probable values for l and a respectively ± nm 25 8 in diameter and 16 to 8 nm inter-particle distance. For the third dimension which is the height H of the values obtained is ± nm 13.6 3 [36]. However, to keep the shape of our hexagonal structure, requires that the parameter L is larger than l, we took in this case L = l + 5 nm. The parameters selected for our structure resulting from these statistical results and the values chosen are: l =28nm, L = 33 nm, p = 80 nm, H = 15 nm.

Optical characterization of the structure and simulation

In Fig. 2, we compare the case where the thickness of the dielectric SiO x deposited upon the metallic gold structures, whose thickness is d = 140 nm, as well as in the case where the gold metallic structure are in direct contact with air (no dielectric SiO x ) whose thickness is d = 0 nm. We note a strong absorption around = λ nm 545 R for both experimental and theoretical peaks, this value corresponds to the wavelength resonance that is to say, the plasmons excitation mode. Furthermore, one can grant the slight shift in magnitude to the sensitivity of the structure due to better sensitivity of hexagonal structure. However, we can decrease or increase the theoretical amplitude by adjusting it in function of the structure parameters, allowing to the experimental and theoretical results to be very close. In the second case we note a strong absorption in the vicinity of the wavelength resonance ≃ λ nm 568 R for both theoretical and experimental peaks, this value shows a shift towards the higher wavelengths of the absorption peak (almost a displacement of 23 nm in the visible band for a thickness of 140 nm) compared to case where d = 0 nm. This shows sensitivity of the structure to the displacements of the absorption peak for dielectric environment. The results obtained show a good agreement in terms of wavelength resonance. However there is a small difference in amplitude and the width of the peaks, which is due to a number of considerations including the comparison of a real system consisting of particles with

Table 1

The gold parameter values for Drude -Lorentz model [23].

Influence of the geometrical parameters on plasmons response

The modification of the geometric parameters of the metal structure (hexagonal) causes a change in the optical response of these nanoparticles. In this paragraph, we will focus on the changes caused by these geometric parameters. We admit the following values: l = 30 nm, L = 40 nm, p = 80 nm, H = 15 nm, and each time, a parameter is varied, we keep the values of the others constant.

The influence of the parameter H

Fig. 3-a shows the variation of the transmission coefficient for H = 5, 10, 15 and 18 nm with a thickness of SiOx d = 140 nm deposited on the gold hexagon. Calculations Data: L = 40 nm, l = 30 nm, p = 80 nm, the substrate index n = 1.51, (constant thickness equal to 140 nm).

We noticed a displacement to toward lower wavelengths with increasing H, accompanied by a decrease in the amplitude which shows high sensitivity for low heights especially for H = 5 nm (almost -7 dB). The minimum of the transmission coefficient corresponds to the resonance wavelength at which the incident wave is coupled to free electrons of metal particles, creating plasmons at the interface SiO 2 /Au/ SiO x .

Fig. 3(b) shows changing the plasmons resonant wavelength of the particles according H. A strong quasi-hyperbolic decay is observed in the resonance wavelength from 780 nm to 560 nm when the height of particles vary from 5 nm to 20 nm, and it continues to be smaller but significant for a variation of the wavelength from 560 nm to 525 nm when H ranges from 20 nm to 40 nm.

The influence of the parameter p

In this section, we will study the influence of the frequency p over plasmonic resonance by calculating the transmission coefficient for TM polarization. The period of structure is a very important parameter as it depends on the resonance related to the excitation of surface plasmons and describes the dipolar interactions in between particles at nanometre's level.

The calculation data are: L = 40 nm, l = 30 nm, H = 15 nm for p = 45, 50, 60, 70, 80 and 90 nm. It is therefore possible to see the influence of the geometry of the structure, by varying p, one can easily see the effect on the transmission spectrum for a TM polarization. Fig. 4(a) presents the transmission spectrum versus the wavelength. Gradually, as the particles approach each other, the optical behavior of structure becomes increasingly sensitive; when the particles approach, p = 45 nm, it shows a strong absorption of incident energy (-15 dB). This indicates that each dipole (metal structure) is subjected to an electric field resulting from the sum of the incident field and local fields produced by each of the neighboring dipole, and when the inter-particle distance is small, the mutual influence of particles has a strong coupling which makes the area more sensitive, for a better detection. The symmetric and homogenous charge distributions on both the left and right borders of the nanoparticle (see below Fig. 4 (a)) represent a quite evident consequence of the mode excitation for p = 45 nm induced by the TM wave.

There is a drop in the resonant wavelength from 720 nm to 582 nm (138 nm decrease), when p vary from 45 nm to 80 nm [see Fig. 4(b)]. Then there is a low decrease, from 582 nm to 580 nm, where p ranges from 80 nm to 90 nm. For low coupling between the metallic nanostructures, p variation has almost no effect on the response of the particles. So, compared to other structures considered as the gold ribbon a better result can still be seen. This structure concentrates and absorbs the field in a very sub-wavelength volume, which represents a crucial interest for detection. Fig. 4(c) represents the electric field distribution at the incident wavelengths (of the dips) λ R = 718 nm. At these wavelengths, the field is trapped in the nanoparticle cavity and does not

The influence of the parameter L

The effect of parameter L will be observed in the transmission spectrum for TM polarization while keeping these constant parameters: H = 15 nm, L = 35 nm p = 80 nm for L = 40, 45, 50, 55, 60 and 65 nm.

From the transmission spectrum (Fig. 5-a) an increase in the resonant wavelength was observed towards higher wavelengths (toward red) when increasing L. The movement takes place from 600 nm to 759 nm for a progressive increase of L = 40 nm-65 nm. This means an increase in variation of 150 nm for an increase of L = 25 nm. We also note a strong absorption, more specifically for L = 65 nm (almost -14 dB), that can be connected to the energy containment in the presence of a large exchange surface on the dielectric/metal interface. Starting from 60 nm, we observe the appearance of another peak around 600 nm. The latter appeared due to the change of the charging orientation of the dipolar mode.

Fig. 5-b shows the evolution of the resonance wavelength depending on L, which links it directly to the behavior of the resonance wavelength of the plasmons. Indeed, it is noticed, between 40 nm and 50 nm, that the plasmon resonance wavelength is growing a non-linear manner with L. Between 50 nm and 60 nm, of the plasmon resonance is growing almost linearly with L, which shows a reasonable agreement with the result obtained for the parameter p, since by increasing L, nanostructures approach and coupling remain increasingly strong, leading on the one hand to a high sensitivity. On the other hand to a movement toward the infrared, which presents an advantage to the biosensor in the infrared range.

The influence of the parameter l

Likewise, it is possible to study the influence of the transmission curve (Fig. 6) for TM polarization. Thus, the choice of the other parameters is given by: L = 60 nm, H = 15 nm, p = 80 nm for the values L = 30, 35, 40, 45, 50 and 55 nm.

Fig. 6(a) shows that parameter l has great influence on the peaks amplitude, because the displacement does not matter between the values. There is a displacement of 23 nm for l =30nm-35 nm, 14.5 nm for l =35nm-40 nm, 0 nm for l =40nm-45 nm, 7.5 nm for l =45nm-50 nm and 22 nm l = 50 nm-55 nm. For l = 30 nm and 55 nm, we have almost the same resonance wavelength (725 nm and 717 nm respectively), but the second value is better in terms of amplitude. Fig. 6(b) shows the evolution of l on the resonance wavelength of each peak as a function of l.

Based on Fig. 6(b) an almost linear decrease is observed between l = 30 nm to 40 nm, for this interval, the peaks move to the short lengths wave and remain constant between 40 nm and 45 nm then grow to larger wavelengths from 45 nm to 55 nm. As for the amplitude, there is a gradual improvement due to the width of l which is in direct contact with the dielectric making better sensitivity for this hexagonal structure.

According to the observation of the various figures, we see that the resonance shape peaks and the value of the resonant frequency evolve according to the geometric parameters choice of the hexagonal structure. This give better results for the sensitivity of biosensors.

Effect of dielectric layers on the plasmons response

In sections 6.1 and 6.2 of this part, we will focus on the effect of the refractive index and the thickness of dielectric medium deposited on top of the metal structure. The two dielectrics studied are silicon oxide SiO x whose refractive index is n SiOx = 1.45 and the silicon nitride Si N 3 4 whose refractive index is n Si N 34 = 2.01. They are widely used experimentally for their poor absorption and can protect nanoparticles from morphological changes when applied to aqueous solutions or organic solvents. The choice of these two dielectric is not arbitrary that is why we will study them:

✓ The refractive index of the substrate is higher than that of the dielectric layer

> nn () SiO SiOx 2 .
✓ The substrate refractive index is lower than that of the dielectric layer filed < nn () SiO Si N 23 4 .

We used the following silicon oxide alloys and silicon nitride, deposited on metallic gold nanostructures immobilized to the glass, to study the behavior of the plasmons response and choose the best dielectric and the thickness to enhance the sensitivity of detection of the biosensor.

The effect of SiO x

The effect of the thickness of SiO x deposited on the hexagonal structure of gold is carried out when used in giving the thickness of the SiO x layer the values d = 20 nm, 80 nm, 120 nm, 160 nm, 280 nm, while preserving the following parameters: L = 40 nm, l = 30 nm, p = 80 nm. Fig. 7 shows the curve of the transmission coefficient of an interface SiO x -Air for TM polarization.

There is an oscillation in the resonance wavelength for a range of value of the thickness of the dielectric with a quite good sensitivity. These oscillations observed in the spectrum are due to coupling between the plasmons mode and the modes of a Fabry-Perot cavity connected to the presence of the oxide layer silicon SiO x presented above the gold nanowire chain: Light incoming perform multiple round-trip within the cavity defined by SiO x and SiO 2 , and partially spring at each reflection.

The effect of the SiN 3 4 dielectric overlayer thickness

When changing the SiO x dielectric by the chemical compound of formula Si N 3 4 , the plasmons response of gold nanoparticles changes. Silicon nitride is a hard ceramic whose physical properties are maintained over a wide temperature range. Fig. 8 (a) shows the evolution of the transmission spectra versus wavelength of an interface Si N 3 4 /Air, depending on the thickness of the Si N 3 4 dielectric layers for values d = 20 nm, 80 nm, 120 nm, 160 nm and 280 nm, for TM polarization. The hexagonal gold nanowires have the following calculation parameters: L = 40 nm, l = 30 nm, p = 80 nm, with the index of the substrate = n 1, 51

SiO2 . An increase in the amplitude is deduced, so a strong absorption which improves the sensibility in an extraordinary way, which is doubled when compared to the SiO x case, and also to the sensitivity of the structure studied in Fig. 8. ) and ∆n the change in the refractive index induced by the absorbate. Van Duyne and co-workers explored experimentally the long-range distance dependence of LSPR nanosensors using self-assembled monolayers (SAMs) of 11-mercaptoundecanoic acid and Cu 2+ ions absorbed on surface-confined noble metals nanoparticles [27]. It was found that the shift of λ R with increasing adsorbate thickness is nonlinear and has a sensing range that is dependent on the composition, shape, width, and height of the nanoparticles. The use of atomic layer deposition of Al 2 O 3 enabled, in addition, the study of both the long-and short-range distance dependence of the LSPR nanosensors [37,38]. At short distances from the nanoparticles surface, the LSPR λ R shift follows a steep linear slope, but as the distance from the nanoparticles increases, the curve bends over and eventually levels off once a saturation point is reached. This is clearly not observed for the interfaces under study. (see Fig. 8(b))]. The oscillation is anharmonic and the plasmon shift is faster in the blue-shifting regions (e.g., 90 nm, 255 nm, etc.) than in the redshifting regions (e.g., 20 nm, 185 nm, etc.). The results in Fig. 8(b) indicate that refractive index sensitivity increases with increasing distance (i.e., the particle are infinitely and increasingly more sensitive to layer thicknesses). Finally, let us notice that the dielectric deposited on the metallic gold nanostructure having a wide index relative to that of the substrate, leads to better results thanks to the sensitivity of the plasmonic response function of the thickness d. This structure absorbs the concentrated field in a volume with sub-wavelength, which represents a crucial interest for detection.

The calculated LSPR curves are corroborated by the experimental LSPR curves recorded on glass/Au nanowire coated with SiO x of increasing thicknesses. Fig. 9 shows the obtained shift in λ R together with the ones predicted through modeling. The square dots represent the theoretical results whereas the triangle-shaped dots corresponds to the experimental ones. For all the Si 3 N 4 overlayer, the theoretical results agree with the experimental one.

Study of the sensitivity

The plasmonics LSPR nano-sensors works by variation of the resonance wavelength. It is clear that the plasmonic response of metallic nanoparticles is strongly depend on their size and shape. In addition, this dependence affects the importance of the spectral shift of the resonance, following the change in the refractive index of the medium located near the metal nanowires. We showed a high sensitivity of the metal nanoparticle plasmon response with different geometrical parameters of Au nanoparticles and/or refractive index of the dielectric deposited on the top of the Au nanoparticles. Fig. 1 show the proposed sensing structure, where the layer dielectric is on the top of Au nanowire. To qualify the performance of the proposed sensor, we compute a sensing S. The expression used to calculate the sensitivity is given by:

= S ∆λ ∆n , R
where ∆n is the variation of the refractive index between the dielectric (SiO x ) and one of the other substance used and ∆λ R the variation of the resonance wavelength.

In the first part, we investigate theoretically the influence of the refractive index of the overcoating relative to the underlying substrate, supporting the metal nanostructures, on the sensitivity of the multilayered interface for sensing. This is indeed a highly important parameter for the development of a sensitive LSPR interface. The structure studied here consists of gold nanowires of height H = 15 nm and the diameters L = 40 nm and l = 30 nm deposited on a SiO 2 substrate and coated with dielectric film with d = 20 nm (see Fig. 1). The lattice parameter p = 80 nm. Three different cases can thus be distinguished: (i) the refractive index of the substrate is higher than that of the deposited dielectric layer; (ii) the refractive index of the substrate is the same as that of the deposited dielectric layer; and (iii) the refractive index of the substrate is lower than that of the deposited dielectric layer. The interface is furthermore covered by a air. To obtained theses three case, we use the following dielectrics: HO ₂ , CH 6 6 , ITO and Si N ₃ ₄ and air as reference.

Table 2 presents a comparison of sensitivity between different dielectrics deposited on the Au nanowires. The thickness of the dielectric layer is d = 20 nm in all case studied here. We noticed that benzene has a very high sensitivity; it can be explained by the fact that the benzene has the same refractive index as the substrate (glass). In other words, because of the fact that the refractive index are the same, there is an absence of the interface between the substrate and the dielectric. In this case, the Fabry-Perot cavity mode disappears which is not the case for where the refractive index of the dielectric is different from the substrate refractive index [cases (i) and (iii)]. In the last case, when the refractive index of the over-layer is higher than substrate refractive index, the sensitivity is relatively good. In this situation, the oscillations cavity mode increases and coupled with plasmonic monde, however the existence of the interface between the substrate and the dielectric affects the sensibility because they reduce the confinement of the electric field supported by Au nanowires. From this model it emerged that the sensitivity exclusively depends on the LSPR band location and the refractive index of the dielectric. We conclude that the optimal sensitivity is obtained when the index of the overlayer is of the same nature as that the refractive index of the substrate.

In the second part, we compare the evolution of the sensitivity between different geometrical gold nanowires but with the same basic area (1500 nm 2 ). The sensitivity of the structures considered has been determined by identifying the position of the main resonance mode on their transmission spectra when the middle of the detection is air and Si 3 N 4 . The structure studied here consists of gold nanowires of height H = 25 nm and the diameters L = 80 nm and l = 40 nm deposited on a SiO 2 substrate and coated by dielectric film with thickness d =3 0n m . In this study, we have used Si 3 N 4 as a dielectric because the sensitivity of nanoparticles situated in a homogeneous host matrix (i.e. this situation correspond to the case where the refractive index of the substrate and the dielectric is the same) is independent of their shape [38]. The sensibility was also approximated in this study by ∆λ ∆n /

LSPR

.W e observe that the nanowire with the base in hexagonal form present a greater sensitivity than the other geometric shapes of the nanowire. The results are summarized in Table 3.

The origin of the high sensitivity of the infrared plasmon band is due to the high electrical field confinement between the Au nanostructures and due to the shape of the nanostructures itself. The hexagonal structure supports a strong localization of the electric field in the corners of the gold NPs that are numerous in our structure compared to others (we may well see it in the mapping of the field), In fact, the sensitivity of a plasmonic structure is also dependent on the location of the field around the nanoparticles at the resonance. The hexagonal geometry has 6 hot spots, two of which are in contact with the substrate, which generally has losses in terms of localized field intensity. We can draw the following conclusion; the exaltation of the electric field in the neighborhood NPs improves the sensitivity of the device. Additionally, the choice of the covering layer, which is accompanied by an index contrast with the substrate, amplifies the confinement of the electrical field due to interference created by the Fabry-Perot cavity.

The theoretical results obtained show that hexagonal nanowires is two time more sensitive than a triangular nanowire, three time more than a circular nanowire and 2.3 more sensitive than rectangular nanowire (see Table 3). These results will improve the performance of future nano-biosensors.

Conclusion

We have developed a theoretical study of optical properties of hexagonal gold metal nanoparticles, deposited on a glass substrate, SiO 2 , upon one of the dielectric, SiO x or Si N 3 4 by exploiting the resonance localized surface plasmons (LSPR) capable of detecting molecules at a nano-scale. In fact, the hexagonal structure is 2.3 times better than the rectangular because the sensitivity of the hexagonal is 621 nm/ RIU, and thus way greater than the other structures. We have seen that the plasmons response of the hexagonal structure based on geometrical parameters showed better sensitivity than gold ribbon. This has improved the sensitivity of the interface, which allows us to have nanosensors very sensitive in order to be more adequate to the biological and chemical detection. It was also seen that the resonance wavelength of the plasmons response manifest an oscillatory variation in function of the thickness of dielectric layers deposited on the particles. This phenomenon is interpreted in terms of the coupling of mode surface plasmons particles with those of the optical cavity, which consists of SiO x , bounded on both sides of the detection medium and SiO 2 substrate. The same result was shown with Si N 3 4 , which has a contrast index greater with SiO 2 but slightly shifted towards longer wavelengths and with a better sensitivity. Significant efforts have been made experimentally in the last years to increase the sensitivity of the refractive index of the interface LSPR, but it seems necessary to wait a few years to see technical improvement, particularly with the new generation of detectors.

Fig. 1 .

 1 Fig. 1. (a) Schematic representation of the structure studied in this work. The gold nanowire is characterized by the height H and the diameters L and l. The inter-nanowire distance "p" is defined as the distance between two nearest neighboring gold nanowires. The input source is placed in the glass substrate and the detector in air. (b) 3D model of the plasmonic nanostructure. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 1

 1 Fig.1displays the schematic illustration of the sensor configuration used for the theoretical studies. A layer of gold nanoparticles of diameters L and l, height h, and interparticle distance p are deposited on a transparent glass substrate (n O Si 2 =1.51), coated with dielectric films of either SiO x (n SiOx =1.45) or Si 3 N 4 (n Si N 34 =2.01) and covered with a nonabsorbing medium such as air with n air =1.The hexagonal gold nanowire (NW) used in this nanostructure is characterized by its height H, the two diameters L and l, as well as the period p (see Fig.1). During the study, we take into account a normal incidence of the incident electromagnetic field on the type of excitation, and we vary the wavelength in the visible range in order to detect the LSPR at the metal structure by modifying one of the previously defined geometrical parameters. Käll et al.[34], studied the LSPR frequency variation in function of the thickness of layers of tricosenoic acid 22 (a dielectric with a refractive index n = 1.53). In this study, the thickness of the acid tricosenoic-22 deposited on the considered nanostructures varies from 0.0 to 340 nm[34]. The layers of dielectric are deposited on a SiO 2 substrate, upon which two types of nanostructures have been studied experimentally. A random network of metallic gold nano-discs then a random network of air nano-holes perforated in a gold film with a thickness of 20 nm, deposited on SiO 2 . A similar study was carried out with gold nanostructures deposited on SiO 2 substrate. The layers of dielectric deposited on the metallic nanoparticles were SiO x material

Fig. 2 .

 2 Fig. 2. Experimental and theoretical absorption spectra recorded on a glass/Au NWs interface without (red and black lines) and with a 140 nm thick SiO x layer coating (blue and green). Parameters used for model: l = 28 nm, L = 33 nm, p = 80 nm and H = 15 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3 .

 3 Fig. 3. (a) The transmission coefficient for a thickness d = 140 nm of SiOx deposited on the gold hexagonal structure (dielectric constant calculated by the Drude-Lorentz model) equal for TM polarization. (b) Evolution of LSPR λ R peak versus the heig H. (c) The field map show the distribution of the complex electric field amplitude for the resonance appearing in the spectrum for H = 15 nm ( = λ nm 584.07 R ). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 4 .

 4 Fig. 4. (a) Transmission coefficient for a thickness d = 140 nm SiO x deposited on hexagonal gold structure (dielectric constant calculated by the Drude-Lorentz model) equal for TM polarization with surface charge of dipolar mode at resonance frequency = λn m ( 717.9 ) R . (b) Evolution of the resonance wavelength as a function of p. (c) Presents the electric field map at p = 45 nm = λn m ( 717.9 ) R . (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 6 .

 6 Fig. 6. (a) The transmission evolution of wavelength when l taking the values 30, 35, 40, 45, 50 and 55 nm. (b) Evolution of the resonance wavelength as a function of l.

Fig. 8 (

 8 b) shows the change in λ R as a func- tion of Si N 3 4 thickness. It was predicted that the LSPR shift should saturate at ≈≈ ∆λ m∆n nm 46 R [27,28,37], where m is the refractive index sensitivity for the glass/Au NWs interface ( == mn m 90 δλ δn R

Fig. 8 ( 34 .

 834 b) shows that the presence of a Si N 3 4 overlayer causes theoretically first a red shift until saturation at ≈ λ R is observed, followed by a red shift until ≈ The resonances (corresponding to the maximum of the amplitude of the oscillations) and the anti-resonances (corresponding to the minimum of the amplitude of the oscillations) are similar to the classical Fabry-Perot cavity. Moreover, the periodicity of the oscillation can be calculated by the equation = d λn /2 pR , where n is the refractive index of the dielectric layer [ ≈= ×

Fig. 7 .

 7 Fig. 7. Spectral shape and position of the LSPR peak of transmission depending on the thickness of SiO x layer.

Fig. 8 .

 8 Fig. 8. (a) Evolution of the transmission spectrum vs the wavelength corresponding to the structure of Fig. 1 for different values of the thickness of SiN 34 ; d = 20 nm, 80 nm, 120 nm, 160 nm, 280 nm. (b) Oscillation of resonance wavelength.

Fig. 9 .

 9 Fig. 9. Evolution of λ R with the thickness of the Si 3 N 4 overlayer; comparison of experimental (triangle-shaped dots) and theoretical (square dots) data.

Table 2

 2 Comparison table in sensitivity between different substances for hexagonal gold nanoparticles.

	Dielectric	Refractive index	Sensitivity (nm/RIU)
	Water	1.33	249.5
	Benzene	1.50	607
	ITO	2.00	406.5
	SiN 3 4	2.01	415.7

Table 3

 3 Comparison table in sensitivity between circular, rectangular, hexagonal and triangular gold nanowires (the basic area of the nanowire = 1500 nm 2 ).

	Geometry	Sensitivity
	Circular	202.0 nm/RIU
	Rectangular	270.3 nm/RIU
	Triangular	307.0 nm/RIU
	Hexagonal	620.8 nm/RIU

Acknowledgments Z.O. and S.L. gratefully acknowledge the hospitality of the Institute of Electronics, Microelectronics and Nanotechnologies (IEMN), UMR CNRS 8520 and Department of Physics, University of Lille.


M Courtial

M.-N De Noirfontaine

F Dunstetter

M Signes-Frehel

P Mounanga

K Cherkaoui

A Khelidj

Effect of polycarboxylate and crushed quartz in UHPC: Microstructural investigation

The context of this study was to find an extrudable formulation of Ultra High Performance Concretes usable in an aggressive environment. In the five mixtures of this study, the only variable parameters are the polycarboxylate (PCE) dosage and the crushed quartz to micro silica ratio. This paper is devoted to a systematic microstructural study using Scanning Electronic Microscopy (SEM), with the idea to link the microstructure with the macroscopic results. Through this study, the effect of the polycarboxylate on the hydration of the type of cement used here is pointed out. From 1.8% to 2% polycarboxylate content, we observe a change in the hydration time for the two calcium silicates, the major phases of anhydrous cement. In the presence of microsilica and with 2 wt.% PCE, we observe a higher consumption of dicalcium silicate, which should not have reacted with such a low water content (Water/Cement = 0.16).

Introduction

Ultra High Performance Concretes (UHPC) introduced by Richard and Cheyrezy [START_REF] Richard | Reactive powder concretes with high ductility and 200-800 MPa compressive strength[END_REF] in the nineties are defined as concretes with a compressive strength higher than 150 MPa [START_REF] Setra | Bétons Fibrés à Ultra-Hautes Performances[END_REF]. UHPC can be used to build differently, in situations where no other concrete can fulfil the technical or architectural requests. Using the self-placing character of UHPC, one can create thin, light manufactured pieces with various shapes, which reduces the execution time and weight structure. More and more applications can be found throughout the world, especially bridges or net facades or net roofs appreciated by architects at the present time. From the sustainability point of view, a UHPC contains three times more cement per m 3 than ordinary concrete, thus using three times more energy and producing three times more CO 2 . However, as long as the required quantity is divided at least by a factor three, the balance sheet remains favourable. One can even expect a better ratio taking into account its exceptional durability, thus supposing lower maintenance cost for the service life time of the structure. Moreover, one can also expect to be able to use the demolished materials as high quality recycled granulates for new concrete.

The progress of water reducers makes it possible to keep a good workability at low water to cement ratio (W/C). In a UHPC, W/C typically lies in the 0.15-0.21 range and polycarboxylates were found to be the most effective superplasticizers for this kind of concrete.

Excellent performance of UHPC in terms of strength and durability are based on the search for a minimal porosity. Two distinct approaches are combined:

-The size of aggregates. Summarizing the parameters of numerous types of concrete, Richard and Cheyrezy [START_REF] Richard | Composition of reactive powder concretes[END_REF] found that the crack size is proportional to the maximum aggregate size. In this way, one can consider that a first principle for the design of UHPC is to divide the size of the largest aggregate by a factor 100, with a grain size below 650 lm.

-Maximizing the density of the granular packing [START_REF] De Larrard | Optimization of ultra-high-performance concrete by the use of a packing model[END_REF]. Instead of the three grain sizes -gravel, sand and cement -found in ordinary concrete, UHPC exhibit four grain sizes: sand, cement, crushed quartz and silica fume (microsilica). Silica fume is added in order to fill the space between the smallest grains. Since 2002, an additional millimetric grain size can also be added to UHPC.

For UHPC, with compressive strength in the range 150-200 MPa, i.e. without any subsequent treatment, the direct result of hydration on porosity is as follows: due to the low W/C, the capillary porosity disappears and the Interface Transition Zone (ITZ) is filled up with C-S-H hydrates produced by the pozzolanic reaction of silica fume. In order to improve the performance of UHPC and attain this performance more rapidly [START_REF] Cheyrezy | Des matériaux innovants pour des ouvrages économiques[END_REF], a thermal treatment can be performed. Above 90 °C, a pozzolanic reaction of crushed quartz occurs; above 200 °C, one observes a decreasing of the C-S-H inter-layer spacing, together with an increasing of the C-S-H crystallinity. A last treatment consists in a compressive treatment performed either before or during the setting, in order to eliminate the air bubbles introduced by the concrete placing and the first cracks arising from the chemical shrinkage during setting.

Another key point is the high value of the Young's modulus (50-60 GPa) observed on UHPC, which is a result of (i) the choice of the mineralogy of sand and mainly and (ii) the large amount of remaining clinker which acts as an ideal aggregate, owing to its high own Young's modulus. However the consequence is a high fragility. Introducing microfibers allows achievement of a high ductile concrete at the macroscopic scale (flexural strength: 30-55 MPa) together with high compressive strength [START_REF] Acker | Ductal Ò technology: a large spectrum of properties, a wide range of applications[END_REF].

Finally, let us mention an important property of UHPC: its selfhealing capability. The residual clinker is able to react with external water flowing through cracks appearing later during the life of the material [7].

The aim of this study is to investigate extrudable UHPC for the manufacture of concrete pipes for use in aggressive environments. We started from the granular composition optimized by Richard and Cheyrezy [START_REF] Richard | Composition of reactive powder concretes[END_REF]: cement: 1, sand: 1.1, silica fume: 0.25 (cement mass ratio). Instead of a polyacrylate superplasticizer, Morin et al. [START_REF] Morin | Superplasticizer effects on setting and structuration mechanisms of ultrahigh-performance concrete[END_REF] and Feylessoufi et al. [START_REF] Feylessoufi | Early ages shrinkage mechanisms of ultra-high-performance cement-based materials[END_REF] used a new generation of superplasticizer, a polycarboxylate (PCE) with variable mass proportions, i.e., 0.5%, 1% and 1.5% for W/C = 0.2, and 1.8% for W/C = 0.16.

We selected five compositions based on these studies at W/C = 0.16 referred to as UHPC1 to UHPC5 [START_REF] Cherkaoui | Early-age volume changes of extrudable reactive powder concrete[END_REF]. For the UHPC1, UHPC2 and UHPC3 formulations, the only varying parameter is the PCE content, in the range 0.5-1.8%. In the two UHPC4 and UHPC5 formulations, a fixed portion (1/4) of silica fume is replaced by crushed quartz, whereas the PCE content is modified from 1.8% (UHPC4) to 2% (UHPC5).

Using these five selected formulations, two series of investigations have been performed:

-A study of several properties of these materials: extrudability, microcalorimetry, shrinkage, mechanical properties (strength and Young's modulus) and durability (gas and water permeability). This study is detailed elsewhere [START_REF] Mounanga | Extrudable reactive powder concretes: hydration, shrinkage and transfer properties[END_REF]. It is shown that replacing silica fume by crushed quartz enhances all the properties, with the best results for the UHPC4 formulation. The UHPC3 formulation is not extrudable unlike the four others.

-A systematic study of their microstructure has been carried out using Scanning Electron Microscopy (SEM) together with X-ray Powder Diffraction (XRD). The SEM results are presented here. The aim of this paper is to link the microstructure and the effect of the superplasticizer content and the crushed quartz substitution on the performance. The effect of the polycarboxylate content on the hydration of the type of cement used here is also pointed out.

Many SEM studies can be found in the open literature about UHPC, most of them being devoted to (i) the paste-fiber binding [START_REF] Reda | Microstructural investigation of innovative UHPC[END_REF][START_REF] Garas | Creep of UHPC in tension and compression: effect of thermal treatment[END_REF][START_REF] Orgass | Fibre reinforced ultra-high strength concretes[END_REF], (ii) the effect of substitution or addition of the raw materials (first recommended by Richard and Cheyrezy [START_REF] Richard | Composition of reactive powder concretes[END_REF]) by sustainable materials [START_REF] Vellmer | Seeing at the nanoscale: hydration of pozzolanic and cementitious materials[END_REF][START_REF] Nikolic | Mix design and engineering properties of ultra high performance self-compacting concrete[END_REF][START_REF] Wang | Preparation of Ultra-High Performance Concrete with common technology and materials[END_REF][START_REF] Klobes | Investigation on the microstructure of ultra high performance concrete[END_REF][START_REF] Korpa | Phase development in normal and ultra high performance cementitious systems by quantitative X-ray analysis and thermoanalytical methods[END_REF][START_REF] Nguyen | Rice husk ash as a mineral admixture for ultra high performance concrete[END_REF] and (iii) going with thermal or pressure treatments. Matte et al. [START_REF] Matte | Durability of reactive powder composites: influence of silica fume on the leaching properties of very low water/binder pastes[END_REF][START_REF] Matte | Simulated microstructure and transport properties of ultra-high performance cementbased materials[END_REF] investigated the lixiviation effects. Müller et al. [START_REF] Müller | Micro texture and mechanical properties of heat and autoclaved ultra high performance concrete (UHPC)[END_REF] studied heat-treated and autoclaved UHPC samples. Using an Environmental SEM, Möser et al. [START_REF] Möser | Durability and microstructural development during hydration in ultra-high performance concrete[END_REF] investigated the stages of hydration. Sorelli et al. [25] described the industrial materials they used to measure the Young's modulus by nanoindentation.

This study is devoted to UHPC samples cured at room temperature for at least 3 months.

Materials and methods

Materials and mixtures

The UHPC samples studied were prepared using Portland cement CEM I 52.5 N CE PM-ES-CP2 NF (produced by Lafarge in the Le Havre plant), amorphous white silica fume (Condensil), crystalline crushed quartz powder (C500, Sibelco), siliceous sand (CV32, Sibelco), polycarboxylate superplasticizer (PCE), and water (W/C = 0.16). The superplasticizer is the Cimfluid 2002 of Axim-Italcementi, in liquid form (dry matter 35%). The fineness (S), the density (q) and the particle size of the solid compounds are given in Table 1 and Fig. 1. To use a low W/C such as 0.16 in UHPC, particularly slightly milled cement is required.

The chemical and mineralogical analysis of the cement is given in Table 2. Silica fume (white colored) contains 93.50% of amorphous SiO 2 and 6.10% of minor oxides. The two calcium silicates C 3 S (alite) and C 2 S (belite) and the two calcium aluminates C 3 A and C 4 AF are written in the cement notations (C = CaO, S = SiO 2 , A=Al 2 O 3 ,F=F e 2 O 3 ). The cement has a very low C 3 A content to decrease both the hydration heat and the ettringite formation. The low alcali and sulphate contents Table 1 Specific area (S) and density (q) of the solid compounds of UHPC provided by the producers.

Materials

S (cm 2 /g) q (g/cm promote the cubic symmetry of C 3 A, which is less reactive than the orthorhombic form, and decrease the ettringite production. Moreover, the cement contains a low limestone filler content to active the hydration kinetic.

The composition of the five UHPC mixtures investigated is given in Table 3. The batch mixing procedure is described elsewhere [START_REF] Mounanga | Extrudable reactive powder concretes: hydration, shrinkage and transfer properties[END_REF].

Methods

The microstructure of the UHPC samples was observed on polished sections and fractures. The material is embedded in ultra-low viscosity epoxy resin by vacuum impregnation. Once the resin has hardened, a sequence of fine particle size diamond polishing pastes is used in order to get the required flat surface. Finally, the samples are sputtered with gold in order to lower the charging effect under the electron beam.

The SEM examinations were performed using a Field Emission Scanning Electron Microscope (FESEM, Model Hitachi S-4800), with either secondary electron (SE) (topological contrast) or backscattered scanning electron (BSE) imaging (chemical contrast). X-ray microanalysis (EDX) is also performed. The accelerating voltage is 10 kV for imaging and 15 kV for EDX. The photographs presented here are representative images of the microstructure, since we prepared large polished sections (1,2-in. diameter) and we collected more than 100 images per sample.

All the samples have also been studied by X-ray Diffraction (XRD) using a Panalytical X'Pert Pro diffractometer equipped with a Co tube (Ka1, Ka2).

Results

The very low W/C rapidly limits the hydration reactions. The degree of hydration as calculated using the Powers model corrected by Jensen and [START_REF] Jensen | Water-entrained cement-based materials: I. Principles and theoretical background[END_REF] is low: a = 0.28 for the UHPC1, UHPC2 and UHCP3 compositions; a = 0.3 for the UHPC4 and UHPC5 compositions. Such an a value represents a 682-695 kg/m 3 amount of anhydrous cement at the end of hydration. The volume fractions of anhydrous cement, silica fume, hydrate, gel porosity, capillary porosity and chemical shrinkage are sketched in Fig. 2. The porosity of the five fresh compositions (respectively 3.3%, 3.95%, 5.15%, 4.65% and 4.97%) exhibit values between 3.3% and 5% in the same range as the range reported by Resplendino and Petitjean [START_REF] Resplendino | Ultra-high-performance concrete: first recommendations and examples of application[END_REF].

UHPC1 to UHPC3

In this series of compositions, the only modified parameter is the polycarboxylate (PCE) content, which increases from 0.5% to 1.8%. The extremely compact microstructure of a UHPC can be observed on the SEM examination of the samples of this series.

As an example, Fig. 3 shows back-scattered electron images of UHPC1 samples.

The (dark grey) sand grains are well dispersed in the paste. The paste between the sand grains exhibits a good homogeneity and contains:

-A lot of anhydrous cement (light grey).

-Hydrate compounds (medium grey).

-Silica fume well dispersed by the effect of the polycarboxylate superplasticizer. -ITZ well filled by hydrates arising from the pozzolanic reaction of silica fume. -Micro-cracks bypassing the anhydrous grains, arising from the sample preparation. These features are found in all the UHPC1 to UHPC3 samples, except for the occluded air, which is found in increasing proportion from the UHPC1 to the UHPC3 compositions, due to the increasing superplasticizer content.

As described by Scrivener and Kirkpatrick [START_REF] Scrivener | Innovation in use and research on cementitious material[END_REF] we observe the clinker grains either as polymineralic grains (3b) or as isolated monomineralic grains of alite, belite and aluminates. One clearly observes the characteristic polygonal shape of the alite crystals and the round-shaped belite crystals. Gypsum crystals are never found, which indicates that gypsum totally reacted with the aluminates.

Among the various hydrates, only C-S-H hydrates are well visible on polished sections. On fracture preparations (Fig. 4), the silica fume hydration is only superficial: we observe (Fig. 4a) silica fume spheres varying from 5 lm down to 50 nm, with only superficial C-S-H coverage. Silica fume is only slightly hydrated in spite of the high alkalinity on the paste. We observe only scarce portlandite crystals and only fine needles like ettringite crystals. Portlandite crystals are visible only in the largest pores, inside the entrapped air bubbles. A typical large crystal of alite, with little surface hydrates, is shown at Fig. 4b.

Powder X-ray diffraction analysis shows the M1 polymorph for alite, with the hMi Pc structure as described by de Noirfontaine et al. [START_REF] De Noirfontaine | Polymorphism of tricalcium silicate, the major compound of Portland cement clinker: 2. Modelling alite for Rietveld analysis, an industrial challenge[END_REF]. It clearly appears in the specific angular windows (Fig. 5) defined by Courtial et al. [START_REF] Courtial | Polymorphism of tricalcium silicate in Portland cement: a fast visual identification of structure and superstructure[END_REF], where the characteristic lines (referred to as E, F and I lines) of the M1 polymorph are found. Such a result is consistent with the chemical composition of the clinker [START_REF] Maki | Factors influencing the phase constitution of alite in Portland cement clinker[END_REF]: 1.56% SO 3 and 0.91% MgO (private communication).

UHPC4 and UHPC5

In this series, crushed quartz is partially substituted (25%, see Table 3) for silica fume. Here, the only modified parameter is the polycarboxylate (PCE) content: 1.8% and 2%. Concerning the microstructure observation, the main features are similar to what was found in the first series of samples (UHPC1 to UHPC3), except the presence of crushed quartz.

Between the two compositions of the series, UHPC4 and UHPC5, two major differences are observed concerning the microstructure (Fig. 6):

(i) The crushed quartz distribution is homogeneous throughout the UHPC4 paste (Fig. 6a), whereas it is very heterogeneous in the UHPC5 paste (Fig. 6b). In the latter, the crushed quartz is preferentially located at close contact with the sand grains, in the ITZ. The crushed quartz is easily recognizable on secondary electron micrographs due to its brilliant contrast related to charging effects. EDX analysis of quartz systematically exhibits a high Na content, the Na + ion being the counter-ion of the polycarboxylate ion. We systematically found a rod-like shape for the crushed quartz grains (Fig. 6c) in backscattered electrons mode. (ii) The cement hydration is different for the two compositions.

In UHPC5, only very few belite crystals remain, in polymineralic grains and also in monomineralic grains (Fig. 6c andd). This observation is confirmed by X-ray diffraction.

All the diffraction lines of belite considerably decrease in the diffraction pattern of UHPC5 samples.

UHPC3 0

One wonders if the promotion of belite hydration is related to the polycarboxylate content only or/and to the presence of crushed quartz. This is why we synthesized a supplementary mixture (named UHPC-3 0 ) similar to the UHPC3 mixture (i.e. without crushed quartz), but with a 2% polycarboxylate content instead of the 1.8% content used in the UHPC3 mixture. Once again we observe a decrease in the belite content by XRD.

Discussion

Effects of polycarboxylate and crushed quartz contents on short and long term performance of UHPC

This part discusses the link between the microstructure observed here and some of properties previously measured in Ref. [START_REF] Mounanga | Extrudable reactive powder concretes: hydration, shrinkage and transfer properties[END_REF] and summarized in Table 4: consistency versus extrudability, extrudability, compressive and flexural strengths and Young's modulus for UHPC [START_REF] Richard | Reactive powder concretes with high ductility and 200-800 MPa compressive strength[END_REF][START_REF] Setra | Bétons Fibrés à Ultra-Hautes Performances[END_REF][START_REF] Richard | Composition of reactive powder concretes[END_REF][START_REF] De Larrard | Optimization of ultra-high-performance concrete by the use of a packing model[END_REF][START_REF] Cheyrezy | Des matériaux innovants pour des ouvrages économiques[END_REF].

The first point is the effect of the polycarboxylate and crushed quartz contents on extrudability. A detailed account of the extrudability measurements is given in reference [START_REF] Mounanga | Extrudable reactive powder concretes: hydration, shrinkage and transfer properties[END_REF]. The difference of extrudability between UHPC3 and UHPC4 (1.8%SP) can be explained by a better viscosity of the UHPC4 paste when substituting 25% of the round shaped silica fume by rough crushed quartz. For a same content of crushed quartz, UHPC5 (2% SP) was found to be more easily extrudable than UHPC4 (1.8% SP) but the extruded UHPC5 is deformable. Our microstructural analysis brings a key for the understanding of this behaviour. The crushed quartz is found in the ITZ (Fig. 6b) for UHPC5 instead of in the paste (Fig. 5a) for UHPC4, with the result of increasing the flowability of the UHPC5 mixture and decreasing the pressure needed for its extrusion.

The second point concerns both mechanical strength and rigidity of the material [START_REF] Mounanga | Extrudable reactive powder concretes: hydration, shrinkage and transfer properties[END_REF]. The main consequence of the substitution of 25% of silica fume by crushed quartz in UHPC(4-5) is to increase the compressive and flexural strengths by a factor of about 20-25% versus UHPC(1-3) (Table 4). With crushed quartz, an additional grain size is found, intermediate between the grain sizes of cement and silica fume. The result is to increase the density of the initial packing and thereby the final density of UHPC. This phenomenon is more efficient when the crushed quartz is homogeneously distributed in the paste. This is probably why the mechanical strength is higher in UHPC4 than UHPC5.

As can be seen in Fig. 3a, the microcracks bypass the anhydrous grains, since these grains are stiffer than the hydrates (E anh = 125-145 GPa versus E C-S-H = 47 GPa); they are stopped by the quartz sand grains (E SiO2 = 70 GPa > E C-S-H = 47 GPa). The Young's modulus values given here (Fig. 7) were measured by Velez et al. [START_REF] Velez | Determination by nanoindentation of elastic modulus and hardness of pure constituents of Portland cement clinker[END_REF] and Sorelli et al. [25] for the anhydrous compounds and by Vandamme et al. [33] for the hydrates. The path of the cracks can differ from one SEM study to another. It depends on the sample preparation of the fractures for SEM observations. If the applied strain is very high (the case of Moser et al. [START_REF] Möser | Durability and microstructural development during hydration in ultra-high performance concrete[END_REF]), the crack pass through both the hydrates (E = 47 GPa) and the sand grains (E = 70 GPa). If the strain is lower (our case), the cracks pass only trough the paste, running through the C-S-H and bypassing the anhydrous grains which have the highest Young's modulus (E = 125-145 GPa). We found [START_REF] Mounanga | Extrudable reactive powder concretes: hydration, shrinkage and transfer properties[END_REF] that the Young's modulus is higher with crushed quartz for UHPC [START_REF] De Larrard | Optimization of ultra-high-performance concrete by the use of a packing model[END_REF][START_REF] Cheyrezy | Des matériaux innovants pour des ouvrages économiques[END_REF] than without crushed quartz for UHPC(1-3). Concerning the higher value for UHPC4, two hypotheses can be proposed: (i) a reinforcement of the Young's modulus of the paste, more efficient when the crushed quartz is homogeneously distributed, (ii) a decreasing of the Young's modulus of the paste (UHPC5), related to the replacement of the high modulus of belite by the lower modulus of C-S-H. A lower endogenous shrinkage was mea- [START_REF] Mounanga | Extrudable reactive powder concretes: hydration, shrinkage and transfer properties[END_REF] for the UHPC4 samples. Such a result is consistent with a higher Young's modulus, which opposes the contraction of the pores at an early age, under the tensile forces effect due to the water desaturation of the porous network.

Table 4

Properties of the five selected UHPC. The first column provides a quality label for the consistency of the material relative to extrudability. The extrudability of each UHPC is given in column 2. The three others columns give the compressive and flexural strength (R c and R f ) and the dynamic Young's modulus (E dyn ).

UHPC

Effect of polycarboxylate on the hydration of silicates

The decrease in the belite content observed in the case of 2% of superplasticizer seems to be only due to an action of polycarboxylate in presence of the cement and silica fume used. Usually, belite hydration starts much later, after a 2 or 3-weeks (dormant period), compared to a few hours for alite. With the low water quantity used here, the hydration reaction of belite should not have occurred. Consequently, the detection of a decrease of the belite content in UHPC(5-3 0 ) can have two possible causes: either the activation of the hydration reaction of belite or an inhibition of the alite dissolution.

A polycarboxylate is made of a main chain of COO -groups -the backbone -with grafted side chains of polyethylene groups. The main chain, negatively charged, allows electrostatic adsorption on positively charged particles, ensuring electrostatic and/or steric repulsion forces between particles. The PCE mainly consumed by the ettringite, resulting from the hydration reaction of C 3 A and gypsum, has been widely considered in the literature.

But the cement used here, as is usual for UHPC, contains very low C 3 A percentages (2.7 wt.% compared to 8-12 wt.% in usual compositions) and C 4 AF seems to have slightly reacted. The polycarboxylate effect for low C 3 A content cement on the reactivity of silicates is less understood. Moreover, silica fume is present in our study. Microsilica is known to accelerate the silicate hydration process whereas the polycarboxylate superplasticizer is a strong retardant for silicate hydration. Using model pastes made of b-belite, colloidal nanosilica and PCE, Björnström and Panas [START_REF] Björnström | Antagonistic effect of superplasticizer and colloidal nano-silica in the hydration of Alite and Belite pastes[END_REF] clearly observed an acceleration of the hydration of belite. Using a real UHPC, with standard microsilica, standard cement and PCE, we confirm this result on standard materials.

Conclusion

This paper compares the microstructure of five UHPC formulations intended for extrudability, in order to highlight the macroscopic properties. The varying parameters were (i) the content in polycarboxylate superplasticizer and (ii) the substitution of silica fume (25%) by crushed quartz in UHPC with W/C of 0.16. The macroscopic variations in terms of rheology and extrusion, shrinkage, mechanical properties and durability-already published-have been highlighted here at the microscopic scale.

Whereas no visible change on the microstructure is observed without crushed quartz and within the range of compositions in polycarboxylate from 0.5% to 1.8%, an addition from 1.8% to 2% of polycarboxylate causes strong effects on the microstructure in presence of crushed quartz.

The first effect concerns the dispersion of quartz. Quartz is well dispersed in UHPC4 samples (1.8% PCE) whereas it is only located in the ITZ sand grains in UHPC5 samples (2% PCE).

The second very interesting effect concerns the reactivity of one of the two major constituents of the cement usually used in UHPC. The belite phase content strongly decreases when the addition of polycarboxylate content is modified from 1.8% to 2%. This effect is only due to the superplasticizer percentage and not to the crushed quartz. This result appears to be related to the simultaneous presence of several components of UHPC: slightly milled cement with low C 3 A percentage, silica fume and low W/C with PCE.

While solutions to accelerate the reactivity of belitic cements are hot topics today, this study provides an alternative solution to improve the short-term performance of this type of cement. Further investigations are in progress varying the cement and superplasticizer.

Fig. 1 .

 1 Fig. 1. Particle size distribution of the UHPC components, measured by laser granulometry.

Fig. 2 .

 2 Fig. 2. Volumetric phases distribution of a UHPC according to the Powers-Jensen model.

Fig. 3 .

 3 Fig. 3. Back-scattered electron images of UHPC1 sample (polished sections): (a) sand and paste with many anhydrous clinker grains. (b) Polymineralic grain of clinker containing alite, belite and C 4 AF (light grey), silica fume noted SF (middle grey), and C-S-H (dark grey).

Fig. 4 .

 4 Fig. 4. Secondary electron images in the UHPC3 paste (fractures): (a) silica fume and C-S-H hydrates and (b) crystal of alite, silica fume and hydrates.

Fig. 5 .

 5 Fig. 5. Powder X-ray diffraction of the cement investigated in this study. The angular windows (a) W3 and (b) W5, as defined by Courtial et al. [30], exhibit the characteristic lines (E, F and I) of the M1 polymorph of alite. The hkl indexes are related to the hMi Pc unit cell as described by de Noirfontaine et al. [29].

Fig. 6 .

 6 Fig. 6. Micrographs of UHPC4 and UHPC5 samples. (a and b) Secondary electron images: homogeneous versus heterogeneous crushed quartz repartition. In UHPC5, crushed quartz is preferentially fixed to the sand. (c and d) Back-scattered electron images: residual clinker. Belite is very visible in UHPC4 and difficult to find in UHPC5.

Table 2

 2 Chemical analysis and Bogue mineralogical composition (% in mass) of the cement.

	Oxydes	CaO	SiO 2	Al 2 O 3	Fe 2 O 3	MgO	K 2 OS O 3	Na 2 O
	Cement	64.58	21.39	3.66	4.25	0.96	0.28	2.63	0.10
	Phases	C 3 SC 2 SC 3 AC 4 AF	Gypse	CaCO 3
	Cement	67.5	10.7	2.64	12.8	3.3	1.5

Table 3

 3 Composition of the five selected UHPC

Acknowledgements

The authors would like to thank warmly Prof. Henri Van Damme for fruitful discussions and Dr. Travis Wade for his kind linguistic assistance.