Rudina Bleta
email: bleta@chimie.ups-tlse.fr

Pierre Alphonse

Lise Lorenzato

Nanoparticle Route for the Preparation in Aqueous Medium of Mesoporous TiO 2 with Controlled Porosity and Crystalline Framework

Mesoporous TiO 2 with tunable pore size and mono-, bi-, and tricrystalline frameworks was prepared from titania nanoparticles synthesized by a sol-gel method. The synthesis was performed by using an amphiphilic triblock copolymer, Pluronic F127, as a structure-directing agent and titanium isopropoxide as a precursor. The structure-directing agent was added in a presynthesized colloidal suspension composed of bicrystalline titania nanoparticles dispersed in an aqueous medium. By varying the ratio between the number of ethoxy units and the number of titanium atoms (EO/Ti), mesoporous TiO 2 materials with controlled pore size were synthesized. Materials were characterized by TG/DTA, XRD, SEM, TEM, and N 2 adsorption-desorption analysis. In the absence of copolymer, the porosity was low, indicating efficiently packed TiO 2 nanoparticles. As the EO/Ti ratio was increased, the average pore size and the specific surface area became larger, whereas the crystallite size of anatase and brookite became smaller. The addition of copolymer induced the enrichment of the brookite polymorph, prevented particle growth, and delayed the formation of rutile. Bimodal (mesoporous-macroporous) N-doped titania with a pure anatase framework was obtained by using diethanolamine (DEA) as the source of nitrogen.

Introduction

Mesoporous materials comprising nanoparticles distributed through mesopores of tunable pore size and high specific surface area have been the subject of considerable interest during the past decade. 1 Among the different transition-metal-based nanoparticles, titanium dioxide has received particular attention because of its excellent photoactivity, chemical stability, and nontoxicity. [2][3][4][5] The common polymorphic forms of TiO 2 are anatase (tetragonal), brookite (orthorhombic), and rutile (tetragonal). The polymorph content is reported to be strongly dependent on the thermal treatment temperature 6 during which particles coarsen, but also on the sol-gel conditions of the synthesis reaction (hydrolysis ratio, pH, type of catalyst). 7 Mesoporous TiO 2 materials with tailored pore size, high specific surface area, and well-defined crystalline frameworks have potential applications in different fields such as solar energy conversion, 8 photocatalysis, 9,10 catalytic production of gases, 11 and Li-ion batteries. 12 The pore size and specific surface area greatly impact the physical properties of a mesoporous material and can play a relevant role in its activity. 2 For instance, in catalytic applications, a tunable pore size can optimize the diffusion rate of reactants toward the adsorption sites, whereas a high surface area can maximize the interface between the reactant flow and the catalyst surface. Pore size can be tuned by addition of a structure-directing agent 13 of different hydrophobic chain length or by addition of a swelling agent (e.g., mesytilene). 14 These additives are removed at the end of synthesis either by calcination in air or by extraction with a solvent. 15 The specific surface area is affected mostly by the hydrolysis ratio. 16 In general, a high water/alkoxide ratio ensures a more complete hydrolysis of the alkoxide, favoring nucleation versus particle growth and leading to small particles and high specific surface areas. 17 The evaporation-induced self-assembly (EISA) process 18 has proven to be well adapted for the design of ordered mesoporous TiO 2 materials. In this approach, metal chlorides or metal alkoxides are used as inorganic precursors in ethanol 19 (or water-ethanol 20,21 ) medium, and block copolymers are employed as structure-directing agents. These precursors are introduced simultaneously in the reaction medium, yielding an inorganic network by co-condensation of the hydrophilic clusters (oxo-metal oligomers) around the voids of the liquid-crystalline phase formed by the copolymer during solvent removal. 21,22 A novel method, termed the "nanoparticle route", 23,24 has given highly reproducible results for the synthesis of stable mesostructured titania sols. In comparison with the classical EISA process, where condensation of the metal ions and selfassembly of the block copolymer templates occur simultaneously, in the nanoparticle route, copolymer is added in the presynthesized titania nanoparticulate sol, and only the selfassembly process between copolymer and nanoparticles is allowed to take place. This method has led to the successful preparation of mesoporous nanocrystalline anatase films with organized symmetry and high photocatalytic activity. 24 By using presynthesized TiO 2 nanoparticles from TiCl 4 precursor in ethanol medium, Kwon et al. 23 obtained ordered mesoporous materials with pseudocubic symmetry or 2D-hexagonal structure when employing C 16 EO 20 or C 16 EO 10 , respectively, as the structure-directing agent. However, nanoparticles in the sol were not crystalline, and the evolution of the pore size was not examined. Teoh 25 reported recently a decrease of the pore size (from 7.4 to 4.8 nm) and an increase of the specific surface area (from 113 to 285 m 2 g -1 ) with the block copolymer content, using TiCl 4 as the inorganic precursor. Replacing the commonly used TiCl 4 precursor with tetrabutyl titanate (TBT), Liu et al. 26 reported the synthesis of large-pore mesoporous titania in the presence of PEO 20 PPO 70 PEO 20 [PEO ) poly(ethylene oxide), PPO ) poly(propylene oxide)] used as a structure-directing agent in ethanolic medium. The expansion of the pore size from 10 to 14 nm with the alkoxide content was associated with butanol formed during the hydrolysis of TBT, which might be located at the hydrophilic-hydrophobic interface between PEO and PPO blocks 27 and might act as a swelling agent by modulating the interfacial curvature of the micellar system.

In this work, we report an easy and reproducible synthesis method for producing mesoporous titania with a mono-, bi-, or tricrystalline framework and tunable pore size. The first step is the preparation of nanoparticles using titanium isopropoxide [Ti(iOPr) 4 ] as a precursor and a large excess of water (hydrolysis ratio ) [H 2 O]/[Ti] ) 84) in a sol-gel synthesis. Under these conditions, hydrolysis is very fast, and nucleation and growth are completed within a few seconds, producing ultrafine primary particles whose size ranges from 2 to 8 nm. 28 These particles agglomerate very rapidly, producing large precipitates of macroscopic dimensions. 29 Peptization through the action of an inorganic acid (HNO 3 ) is used to break up the aggregates into small aggregates and primary particles. The final result is a clear suspension containing primary bicrystalline (anatase and brookite) titania particles or agglomerated structures dispersed in water and whose size ranges from 15 to 100 nm. 29 Copolymer is then added, and self-assembly occurs between copolymer and preformed crystalline nanoparticles. This method provides, in addition, a facile route to obtain very stable sols for several months, 30 which would be of interest for the large-scale production of titania coatings. The purpose of the present work was to investigate the impact of the copolymer amount on the structural and textural characteristics of the resulting mesoporous titania. Block copolymers are expected to adsorb onto TiO 2 particles, providing steric stabilization. 31 This could have a marked effect on the crystallite growth upon calcination, as well as on the degree of packing. 30 Therefore, knowledge of this influence is necessary in order to produce materials with controlled porosity and high specific surface areas. To the best of our knowledge, this is the first systematic investigation of the pore size and crystallinity as functions of the copolymer content in mesoporous titania prepared by the nanoparticle route.

Experimental Methods

2.1. Synthesis of Titania Sols. Titanium dioxide nanoparticles were synthesized by a modified sol-gel method adapted from the literature. 32 In a 250 mL flask, 30 mL (0.1 mol) of titanium isopropoxyde [Ti(iOPr) 4 , Acros Organics] was dissolved in 27 mL (0.35 mol) of isopropanol (Acros Organics). Then, 160 mL of hot distilled water was added rapidly at 85 °C under vigorous stirring at a hydrolysis ratio of h ) [H 2 O]/ [Ti] ) 84. After 15 min, 1.3 mL of nitric acid (HNO 3 68%, Fluka) ([HNO 3 ]/[Ti] ) 0.2) was added dropwise to peptize the hydroxide precipitate. The mixture was maintained under reflux at 85 °C for 16 h. The final product was a stable translucent suspension of titanium dioxide nanoparticles. Pluronic F127 (Sigma), PEO 106 PPO 70 PEO 106 , was then added to the nanoparticulate sol, and the mixture was maintained under stirring for 3 h at room temperature. The ratio between the number of ethoxy units and the number of titanium atoms (EO/Ti) was varied from 0.6 to 2.6. In some experiments, diethanolamine (DEA, Fisher Biotech) dissolved in isopropanol was introduced prior to the peptization step. 33 Xerogels were obtained after drying 10-mL samples by evaporation at 35-80 °C for 48 h in Teflon plates, after which time they were calcined in a furnace either at 400 °C for 6 h or at 500 °C for 4 h using a heating ramp of 2 °C min -1 . The powders were ground before characterization. Samples are identified according to this notation: F(EO/Ti)_(DEA/Ti)_calcination temperature. For example, F0.6_T400 indicates an EO/Ti ratio of 0.6, no DEA, and a calcination temperature of 400 °C, whereas F1.2_DEA 0.9_T400 indicates an EO/Ti ratio of 0.6, a DEA/Ti ratio of 1.2, and a calcination temperature of 400 °C.

2.2. Characterization Methods. Thermogravimetry (TG) and differential thermal analysis (DTA) were carried out on 20 mg of xerogel using a Setaram TG-DTA 92 microbalance and platinum crucibles. The experiments were performed under air using a heating ramp of 5 °C min -1 , from room temperature to 800 °C. In some experiments, the evolved gas composition was monitored by a quadrupole mass spectrometer (Leybold Inficon Transpector H200M). Powder X-ray diffraction (XRD) data were collected on a Bruker D4 Endeavor X-ray diffractometer in a Bragg-Brentano configuration with a Cu KR radiation source at 40 kV and 40 mA. Scans were run over the angular domain 20°< 2θ < 80°with a step size of 0.016°. Crystalline phases were identified by comparing the experimental diffraction patterns to Joint Committee on Powder Diffraction Standards (JCPDS) powder diffraction files for anatase, brookite, and rutile. The refinement of the diffractograms was performed using the FullProf software [START_REF] Rodriguez-Carvajal | FULLPROF: A Program for Rietveld Refinement and Pattern Matching Analysis[END_REF] and its graphical interface WinPlotr. [START_REF] Roisnel | A Windows Tool for Powder Diffraction Pattern Analysis[END_REF] Because of the numerous brookite reflections and the strong overlap of the diffraction lines, we failed to find an acceptable solution by directly applying the Rietveld method. Profile matching refinement was used instead to determine unit cell parameters, background, peak shape, and zero shift. The quality of the fit was determined visually by inspection of the difference plot and statistically by the goodness of fit (χ 2 ), defined by where w i is the weight assigned to each observation; y io and y ic are the observed and calculated intensities, respectively, at the ith step; N is the number of points used in the refinement; and P is the number of least-squares parameters refined. The refinement was considered satisfactory when χ 2 was less than 4. The average crystallite size D was calculated from the Scherrer formula, 36 D ) Kλ/(β cos θ), where K is the shape factor (a value of 0.9 was used in this study, considering that the particles are spherical), λ is the X-ray radiation wavelength (1.54056 Å for Cu KR), β is the full width at half-maximum (fwhm), and θ is the Bragg angle. In addition, Rietveld refinements 37 over a shorter 2θ range of 20-35°were performed to determine the content of each polymorph. In this mode of refinement, only the scale factor was allowed to vary. The relative errors associated with the crystallite sizes and polymorph contents were computed from FullProf files.

Nitrogen adsorption-desorption isotherms were collected at 77 K using a Micromeritics ASAP 2010M instrument. Prior to analyses, 200-400-mg samples were outgased at 300 °C overnight (approximately 15 h) to remove the species adsorbed on the surface. Specific surface areas were determined by the BET method. 38 Pore size distribution was calculated from the N 2 isotherm at 77 K based on the NLDFT (nonlocal density functional theory) 39 model assuming a cylindrical pore structure. The software used was Autosorb 1 from Quantachrome Instruments. The quality of the agreement between experimental and calculated isotherms was evaluated by the profile factor R p , defined as

χ 2 ) ∑ w i (y io -y ic ) 2 /(N -P) R p ) 100 ∑ |y io -y ic |/ ∑ y io
where y io and y ic are the observed and calculated volumes, respectively, at the ith step.

Classical methods, based on the Kelvin equation, such as the BJH (Barrett-Joyner-Halenda) approach, are not applicable for micropores and narrow mesopores. NLDFT describes the sorption and phase behavior of fluids in narrow pores on a molecular level and provides a much more accurate approach for pore size analysis. This method has largely been applied to the characterization of micro-and mesoporous carbons, [40][41][42] silicas, and zeolites. 40,43,44 The relative errors associated with adsorption-desorption analysis were estimated to be the following: S BET , 5%; adsorbed volume (av), 5%; S cum (DFT), 5%; pore volume (pv) (DFT), 5%; pore size (ps) (DFT), 20%. Fieldemission gun scanning electron microscopy (FEG-SEM) observations were performed at 5 kV with a JEOL-JSM-6700F field-emission microscope. Transmission electron microscopy (TEM) observations were performed with a JEOL-JEM-1011 microscope operating at 100 kV at medium magnification. Rheology measurements on the sols were done with an Anton Paar Physica MCR rheometer fitted with a cone-and-plate device. The dimensions corresponding to the geometry were 50 mm for the diameter and 1°for the angle. The minimum distance between the plate and truncated cone was 0.05 mm. Rheograms were recorded at 20 °C, with shear rate being increased and decreased stepwise over the range of 1 to 1000 s -1 , with a total time period of 300 s for both the increasingand decreasing-shear-rate sweeps.

Results and Discussion

3.1. Thermal Analyses. The temperature at which the complete decomposition of organics occurs can be determined by TG/DTA. Figure 1 shows the thermograms recorded for xerogels prepared without and with F127 (EO/Ti ) 0.6), dried at 35 and 80 °C, respectively. A higher drying temperature was required for the samples prepared with F127 because of the tendency of the copolymer to retain water, giving a sticky paste. The TG curve of the F127-free sample reveals two peaks. The first one, corresponding to a mass loss of about 14%, has a maximum at 90 °C. It is endothermic and can be attributed to the removal of physically adsorbed water. The second mass loss, representing 9-10%, gives a very broad endothermic peak with a maximum toward 310 °C. Mass spectrometry analysis of the evolved gases during the thermal process revealed that this peak is associated with the detection of masses 30 and 46, corresponding to NO and NO 2 , respectively. Thus, this peak can be attributed to the decomposition of nitrate groups. Although the concentration profile of NO + NO 2 roughly matches the shape of the TG peak, a low amount of NO and NO 2 is already detected at temperatures as low as 140 °C. Hence, part of mass loss corresponding to the first TG peak (14%) actually comes from nitrate decomposition. Indeed, thermal analysis performed on a sample that had not been peptized (without addition of HNO 3 ) gave a total mass loss of about 10%. On the other hand, for the HNO 3 /Ti concentration ratio used in our experiments (∼0.2), the mass loss produced by nitrate decomposition would be 14.5%. The large temperature range observed for nitrate decomposition (140-380 °C) reveals the wide range of interactions of these groups with the TiO 2 surface. Only a small amount of carbon species (mass 12) was detected by the mass spectrometry analysis. This shows that (i) the alkoxides are fully hydrolyzed (very few -OR groups remain) and (ii) the isopropanol is almost completely removed during the synthesis. The DTG curve shows that, from 380 °C, the decomposition is achieved. However, a slow drift of the TG curve was still observed. No species other than water were detected in the evolved gases. Thus, a slow dehydroxylation occurs, ending at 530 °C. This is just the onset temperature for a small exothermic peak in the DTA curve that corresponds to the crystallization to rutile. Hence, as soon as the oxide becomes completely dehydrated, it crystallizes into rutile. The mass loss observed between 380 and 530 °C is 0.25-0.30%. This low dehydroxylation rate can be explained by a diffusion-limited process due to the fact that most of the remaining hydroxyl groups are probably trapped inside the crystallites. These defects delay the crystal growth and the transformation into rutile.

The addition of F127 (Figure 1b) has a marked effect on the thermal decomposition process. After the mass loss of about 7% recorded below 150 °C, which can be attributed to the loss of physically adsorbed water, the main feature of the TG and DTA profiles is a strong and narrow exothermic peak at 270 °C. This peak corresponds to the combustion of the copolymer. This reaction is accelerated by the decomposition of nitrate groups, producing NO and NO 2 , which are strong oxidants. From 250 °C, there is a sharp change in the kinetics regime, probably because all nitrate groups have been decomposed, the oxidation rate becomes limited by the diffusion of oxygen. The combustion process ends at 420 °C. It is followed, as for the F127-free sample, by a weak mass loss (about 0.3%) observed up to 530 °C. In that case, the dehydroxylation kinetics is faster. This can be attributed to a smaller particle size. No evidence related to phase crystallization into rutile was detected from the DTA curve.

3.2. Effect of Addition of the Structure-Directing Agent.

Samples Prepared without Copolymer: Effect of the Calcination Temperature.

Calcination is a postsynthesis step that results in a more crystalline product. 45 Generally, calcination causes particles to form hard agglomerates that have an increased degree of packing, which facilitates the phase transformation. [45][46][47] Figure 2 presents XRD patterns of TiO 2 prepared without copolymer as a function of calcination temperature. The TGA measurement obtained from the sample with EO/Ti ) 0.6 dried at 80 °C showed that the organic template F127 was eliminated in the temperature range 250-420 °C. A temperature of 400 °C was chosen as the first calcination temperature because it is the best compromise between a small crystallite size, a high specific surface area, and the complete removal of the organic template. The sample dried at room temperature (RT) was added for comparison. At room temperature and at 400 °C, XRD peaks were identified at values of 2θ that present a good match with library pattern of anatase (A; JCPDS, PDF card no. 00-021-1272) and brookite (B; JCPDS, PDF card n°01-076-1934). All peaks are broad, which is indicative of the formation of small crystallites as the consequence of the high hydrolysis ratio (h ) 84) used in our sol-gel synthesis. When the calcination temperature was increased to 500 °C, in addition to anatase and brookite, a low-intensity peak arising from rutile (R; JCPDS, PDF card no. 00-034-0180) was observed. XRD peaks became sharper, indicating the formation of well-crystallized phases. This matches well with TG/DTA results in Figure 1, where the onset temperature at which the transformation to rutile starts is about 530 °C (a little higher than 500 °C because the heating rate used shifted the transformation to higher temperatures). When the samples were heated at 600 °C, intense sharp peaks of majority rutile with a low-intensity peak arising from the remaining anatase were obtained. Brookite peaks were no longer present at this temperature.

It has been shown that the transformation sequence among the three titania polymorphs is size-dependent. Rutile is the thermodynamically stable bulk phase; however, both calorimetry measurements and theoretical calculations (DFT) have shown that rutile has the highest surface enthalpy, followed by brookite, and then anatase. 48 The surface enthalpies of the three polymorphs are sufficiently different that the thermodynamic phase stability of nanoparticles is actually governed by their size. 49,50 Roughly, the most stable polymorph for surface areas larger than 40 m 2 g -1 is anatase. Then, in the range of 40-6 m 2 g -1 , brookite becomes the most stable phase, and finally, below 6 m 2 g -1 , rutile is the stable polymorph. 48 Table 1 shows the crystallite sizes and the phase contents in our samples. In the sample dried at room temperature, the crystallite sizes of anatase (A) and brookite (B) were about 6 and 5 nm, respectively, 30 and anatase was the predominant polymorph (73%). When the temperature was increased to 400 °C, crystallites increased in size to about 9 nm (A) and 7 nm (B) by coarsening. [45][46][47] On the other hand, the anatase and brookite contents seemed to remain unchanged considering the errors associated with the percentages of the various polymorphs.

The growth kinetics of anatase and brookite are similar at 400 °C. This is no longer the case at 500 °C, where the anatase crystal size increased by a factor of 3 whereas the brookite size increased by a factor of only 2. Moreover, both the anatase and brookite contents decreased to form rutile (8%). Although anatase and brookite should be the stable phases in this size domain, the sizes of all of the particles were not uniform, and particles whose surface areas are lower than 6 m 2 g -1 could transform into rutile. 6 When the temperature was increased to 600 °C, crystallites grew to the point that anatase and brookite were metastable (surface area < 6 m 2 g -1 ). Rutile became the predominant phase (85%), with little anatase (15%) and no brookite. The rutile crystallites coarsened very rapidly, up to 81 nm.

Influence of EO/Ti

Molar Ratio. a. Crystalline Microstructure. Figure 3 shows XRD patterns of samples prepared with different EO/Ti molar ratios varying from 0 to 2.6 for given calcination temperatures of 400 and 500 °C. For all values of EO/Ti, samples calcined at 400 °C for 6 h presented similar structural features: anatase and brookite coexisting and peaks becoming broader with increasing EO/Ti ratio, which is consistent with a decrease of the crystallite size. More pronounced structural changes were observed from the XRD patterns of samples calcined at 500 °C for 4 h (Figure 3 F127-free TiO 2 (F0_T500) showed intense sharp peaks of anatase, brookite, and rutile, as previously indicated in Figure 2. After addition of copolymer, as the EO/Ti molar ratio was increased, the three polymorphs were found to coexist, but the rutile reflections decreased significantly in intensity. Indeed, at EO/Ti ) 2.6, the rutile percent content (0.5%) became negligible with respect to the contents of anatase and brookite. Table 2 lists the particle sizes calculated by the Scherrer formula. It can be noticed that increasing the copolymer content resulted in smaller crystallites. Both the anatase and brookite particle size decreased, from 9 to 7 nm for anatase and from 7.5 to 6.5 nm for brookite at 400 °C when EO/Ti was increased from 0 to 2.6. The anatase content decreased from 73% to 53%, whereas the brookite content increased from 27% to 47%. This transformation of anatase into brookite is surprising because, in this size range (surface area . 40 m 2 g -1 ), the reverse conversion is expected, due to the lower surface energy of anatase, as reported by Banfield et al.. 50 The extent of this conversion was found to increase with the amount of copolymer. The thermo- grams (Figure 1b) show that the combustion of the copolymer was very fast. As the copolymer is adsorbed at the surface of oxide particles, the local pressure produced by this fast combustion can, perhaps, induce a crystal transformation toward the more dense structure of brookite. Another possibility, which is the effect of steam produced by the combustion, is less probable because it has been shown that the hydrothermal aging of TiO 2 sols does not result in significant changes in brookite content. 7 At 500 °C, the anatase and brookite particle sizes decreased from 27 to 9 nm (A) and from 16 to 7 nm (B), whereas the rutile particle size decreased from 33 to 6 nm. This can be understood from the fact that copolymer itself will adsorb on the surface of the TiO 2 nanoparticles, inducing a steric stabilization. 51 Indeed, as copolymer was added to the preformed nanoparticulate sol, hydrolysis of titanium isopropoxyde [Ti(iOPr) 4 ] is achieved before the self-assembly process between copolymer and nanoparticles occurs. When the copolymer is removed during the calcination step, it leaves voids between the particles, reducing the coordination number and delaying the sintering. 52 b. Textural Properties. The evolution of adsorption-desorption isotherms with copolymer content is shown in Figure 4a. All isotherms could be identified as type IV, characteristic of mesoporous materials, with a type H1 hysteresis loop according to the IUPAC classification. 53 Pore volumes, corresponding to the volume adsorbed at P/P 0 ) 0.995, and specific surface areas, calculated in the relative pressure range 0.1-0.25, are reported in Table 3. Pore size distributions (PSDs) computed by NLDFT are shown in Figure 4b. In most cases of H1 hysteresis, the desorption branch is correlated with the equilibrium phase transition; therefore, PSDs were calculated from the desorption branches of the isotherms. Cumulative surface areas and pore volumes resulting from DFT calculations are also reported in Table 3 for comparison purposes.

Without F127, the PSD was narrow, giving only one peak centered at about 5 nm. Comparison of this size with the crystallite size of anatase (9 nm; see Table 1) indicates that this kind of porosity corresponds to holes in rather close-packed spherical crystallites. For the lower EO/Ti ratio (0.6), the addition of copolymer produced only a small increase of surface area and porous volume, but the PSD was already significantly affected. It became broader, and the maximum shifted slightly, by about 0.4 nm, toward larger pores. Increasing the EO/Ti ratio to 0.9 produced a very strong effect. The surface area almost doubled, and the pore volume tripled. Most of the pores smaller than 6 nm were removed. The PSD, centered at about 8 nm, was rather narrow. As the crystallite size for this copolymer amount was about 7 nm (Table 2), this porosity was no longer due to the holes in packed crystallites but rather to a selfassembly of colloidal TiO 2 particles around the micelles formed by the PEO-PPO-PEO copolymer. Increasing the EO/Ti ratio to 1.2 still increased the surface area and the pore volume, but to a smaller extent than for 0.9. It also produced a broader PSD, which had a maximum shifted to about 10 nm with a shoulder at 12 nm. Moreover, the isotherm showed that some N 2 adsorption had occurred for relative pressure larger than 0.9, which indicates the presence of macropores.

A TEM image (Figure 5) of the sample with EO/Ti ) 1.2 heated at 150 °C shows that the addition of copolymer produced materials not with organized porosity but rather with a wormlike structure, as revealed by the fact that the clear background can still be seen through the thicker zones. SEM images provide a better idea of the porosity generated by the copolymer templating (Figure 6a,b). The aggregation of the spherical crystallites, whose diameters ranged between 6 and 10 nm, created a network of interconnected pores.

A detrimental effect on surface area and porous volume was observed upon further increasing the EO/Ti ratio to 2.6, but this did not significantly alter the PSD. Actually, the amount of copolymer was larger than the quantity required for obtaining a full covering of TiO 2 crystallites. The increasing concentration of F127 in the colloidal sol might lead to a reduced intermicellar separation, 22 which might, in turn, lead to some shrinkage of the pore structure during calcination.

When the calcination temperature was increased to 500 °C, without copolymer, the surface area was reduced by one-half, and the pore volume shrank by 40% (see Table 3). With copolymer, the pore structure was stabilized, and for example, the pore volume decreased by less than 10% for EO/Ti ) 0.9. The comparison between experimental and calculated data in Table 3 indicates that surface areas and pore volumes are underestimated by the DFT method. About the surface area discrepancy, a possible explanation is that these oxides contain a small amount of micropores that is not considered by DFT because no experimental data were recorded in the low-pressure range. On the other hand, DFT computations do not take into account the macroporosity present in our samples, which could explain the underestimation of the pore volume.

A scheme for the self-assembly of TiO 2 colloidal particles is shown in Figure 7. According to this scheme, titania colloids initially form aggregates whose size, determined by photon correlation spectroscopy and TEM in another study, 30 is in the range 80-90 nm. After peptization with HNO 3 , aggregates are broken up into small particles, forming a stable sol (Figure 7a). At low concentrations of F127 (Figure 7b), nanoparticles are sterically stabilized by the copolymer-colloid interactions. It is generally assumed 54,55 that these block copolymers adsorb from aqueous solutions onto hydrophobic surfaces such as polystyrene latex blocks through their PPO blocks, whereas the solvated PEO blocks extend out into the solution as tails and loops. In the case of titania, the presence of hydroxyl groups on the surface of the nanoparticles makes these colloids hydrophilic; therefore, the adsorption mechanism between PEO blocks and TiO 2 nanoparticles should be hydrogen bonding. In our system, such an adsorption was accompanied by a change in the sol viscosity that decreased through a minimum at EO/ Ti ) 0.15 (η ≈ 2 mPa s) and remained still lower than that of TiO 2 (η ≈ 6 mPa s) for EO/Ti < 0.9, reflecting the stabilizing effect of copolymer on titania colloids (Figure 8). This minimum of the sol viscosity is explained by assuming that F127 adsorbs on the surface of TiO 2 particles, producing a stabilization effect on the colloidal sol. This effect has also been observed with poly(ethylene glycol) (PEG 2000) and was interpreted, in our previous work, 30 as a progressive reorganization of the aggregates toward a more compact packing. The viscosity measured beyond EO/Ti ) 0.9 strongly increased from 9 mPa s (EO/Ti ) 1.2) to 100 mPa s (EO/Ti ) 2.6). Addition of copolymer beyond EO/Ti ) 0.9 provided a saturation of TiO 2 colloids, and this probably led to the formation of micelles. In that case, the self-assembly of the cross-linked crystallized nanoparticles around the micelles, in an organic-inorganic network (Figure 7b), could explain the expansion of the pore size up to 8-12 nm. Studies are underway to determine the adsorbed copolymer amount beyond which micelles form and the layer thickness on TiO 2 colloids, and this will be the subject of another article. However, an EO/Ti ratio of 1.2 seems to be close to the optimum for a stable porous structure. Addition of a large amount of copolymer with respect to TiO 2 colloid is detrimental for a high porosity because the intermicellar space can be reduced, which leads to shrinkage of the pore size upon calcination.

Effect of the Addition of Diethanolamine (DEA).

Several attempts have been made in recent years to shift the TiO 2 absorption onset from the ultraviolet to the visible region. A great interest has been devoted to the synthesis of N-doped titania because this "new family" of materials has shown the ability to absorb in the visible range and can therefore be used as a visible-light catalyst. 56 The first work on the synthesis of N-doped titania was reported in 2001 by Asahi et al., 57 who prepared TiO 2-x N x films by sputtering TiO 2 targets for several hours in a N 2 /Ar gas mixture. Thereafter, there have been several reports of the synthesis of N-doped titania by introducing N into TiO 2 by means of dc magnetron sputtering in N 2 -containing plasma; 58 by metal-organic chemical vapor deposition (MOCVD) using Ti(i-PrO) 4 and N 2 O at 420 °C; 59 by hydrolysis of Ti(SO 4 ) 2 with NH 3 in dry air at 400 °C; 60 by hydrolysis of TiCl 4 with a N-containing base [aqueous NH 3 , (NH 4 ) 2 CO 3 , or NH 4 HCO], followed by calcination at 400 °C; 61 or by a solvothermal process using TiCl 3 -hexamethylenetetramine (HMT)-alcohol solution. 62 In a different way, Gole et al. 63 recently reported a new method to produce TiO 2-x N x samples by using direct nitridation of TiO 2 with alkylammonium salts. This method consists of first preparing a nanoparticle colloidal solution by controlled hydrolysis of Ti[OCH(CH 3 ) 2 ] 4 in aquous/isopropanol media (pH 2, HNO 3 ). The colloidal solution is then mixed with an excess of triethylamine to form nitrited TiO 2-x N x nanocolloids. The samples were yellow crystallites, and they absorbed well into the visible and near-infrared regions. XRD and high-resolution TEM revealed that the crystal structure of the nitrited samples was the anatase form. These results demonstrated that, by forming and adjusting an initial TiO 2 nanoparticle size distribution and mode of nanoparticle treatment, it is possible to extend and tune the absorption of a doped TiO 2-x N x nanoparticle sample into the visible region. 63 In the present study, we used diethanolamine (DEA) as a source of nitrogen at a DEA/Ti molar ratio of 0.9 and two different EO/Ti ratios (EO/Ti ) 1.2 and 2.0). The samples recovered after calcination at 400 °C for 6 h were colored dark yellow. In contrast to the samples prepared without DEA, presented previously, in which the anatase and brookite polymorph coexisted, the XRD patterns of the samples prepared with DEA indicated only the presence of the anatase polymorph (Figure 9a). Comparison with Figure 3a (sample heated at 400 °C) reveals that diffraction peaks were sharper (because there was no longer any brookite), and the Scherrer formula gave a crystallite size of about 10 nm for DEA/Ti ) 0.9 compared to 7 nm without DEA. Thus, introducing N into titania colloids suppresses the formation of the brookite polymorph but with the side effect of increasing the crystallite size. The promotion of anatase with respect to a mixture of anatase and brookite and the increase of the crystallite size have already been reported as an effect produced by N-doping. [56][57][58][59][60][61][62][63] However, when the EO/Ti ratio was increased to 2, the crystallite size decreased to 8 nm, in agreement with the results obtained previously in the system without DEA. It is evident that a systematic study must be done by varying the EO/Ti ratio and the DEA concentration before drawing general results. The present result, however, suggests that employing copolymer in association with DEA can be used as an alternative to inhibit brookite formation and to prevent crystallite growth in N-doped titania.

For relative pressures larger than 0.7, the adsorption isotherm (Figure 9b) is quite different from the isotherm recorded in undoped titania. In the PSD, the main pore family centered at 10 nm, attributed to the self-assembly of the nanoparticles around the micelles, is missing. The main peak, at 5 nm, corresponds to pores generated by the packing of primary spherical particles. Moreover, the amount of N 2 adsorbed above P/P 0 ) 0.9 is twice as large, which indicates a larger proportion of macroporosity. The pore structure, which can be seen in the TEM image (Figure 10), shows that some self-organization of the colloidal particles still occurs under these conditions (domains surrounded by white circles). When the EO/Ti ratio was increased from 1.2 to 2.0, the pore volume and the surface area increased (Table 4). Although the pore size distribution remained centered at 5 nm, a new family of small pores centered at about 3 nm was also noticed.

Conclusions

Stable bicrystalline titania nanoparticles dispersed in an aqueous medium were synthesized by a sol-gel method using Ti(iOPr) 4 as the precursor. Addition of triblock copolymer, as a structure-directing agent, to the presynthesized bicrystalline titania nanoparticles, led to the formation of highly porous mesoporous TiO 2 . By varying the ratio between the number of ethoxy units and the number of titanium atoms (EO/Ti), mesoporous titania with tunable pore sizes (from 5 to 10 nm) and high specific surface areas (from 120 to 240 m 2 g -1 ) was successfully prepared. The addition of copolymer delayed the formation of the rutile polymorph and prevented particle growth upon calcination. When diethanolamine (DEA) was used as a source of nitrogen, bimodal (mesoporous-macroporous) titania with a pure anatase framework was obtained. All titania sols obtained by this method, except those containing DEA, were stable for several months, and they can therefore be used for the large-scale production of coatings.

Figure 1 .

 1 Figure 1. TGA and DTA curves of (a) TiO 2 and (b) F0.6_TiO 2 xerogels dried under air.

  b).

Figure 2 .

 2 Figure 2. XRD patterns of titania nanoparticles heated at increasing temperatures: room temperature (RT), 400, 500, and 600 °C. Anatase (A; PDF 00-021-1272), brookite (B; PDF 01-076-1934), and rutile (R; PDF 00-034-0180).

Figure 4 .

 4 Figure 4. Evolution of (a) adsorption-desorption isotherms and (b) pore size distribution as the function of EO/Ti molar ratio for samples calcined at 400 °C.

Figure 3 .

 3 Figure 3. XRD patterns of titania particles synthesized with various EO/Ti ratios. Samples were calcined for (a) 6 h at 400 °C and (b) 4 h at 500 °C.

a

  F ) [EO]/[Ti], T ) calcination temperature. b BET specific surface area determined in the relative pressure range 0.1-0.25. c Adsorbed volume at P/P 0 ) 0.995. d Cumulative surface area resulting from DFT calculations. e Pore volume resulting from DFT calculations. f Pore size resulting from DFT calculations.

Figure 5 .

 5 Figure 5. TEM image of mesoporous titania synthesized with EO/Ti ) 1.2 and heated at 150 °C.

Figure 6 .

 6 Figure 6. Morphology by FEG-SEM of mesoporous titania synthesized with EO/Ti ) (a) 0.6 and (b) 2.6. Samples were calcined for 6 h at 400 °C.

Figure 7 .

 7 Figure 7. Schematic illustration of the self-assembly process that takes place in colloidal TiO 2 sols. (a) In the absence of copolymer, the first agglomerates are broken up upon HNO 3 addition to form primary particles. (b) At low copolymer concentrations, nanoparticles are surrounded by a copolymer layer and are cross-linked in a network, whereas at high copolymer concentrations, self-assembly occurs around the micelles.

Figure 8 .

 8 Figure 8. Effect of addition of F127 on the viscosity of titania sols at [TiO 2 ] ) 1.2 M. Viscosity was measured at a shear rate of 100 s -1 . Rheometer temperature ) 20 °C. The dotted line is shown for visual aid.

Figure 9 .

 9 Figure 9. (a) XRD patterns and (b) evolution of adsorption-desorption isotherms and pore size distribution (inset) of titania particles synthesized with DEA/Ti ) 0.9 and EO/Ti molar ratios of 1.2 and 2.0. Samples were calcined at 400 °C for 6 h.

Figure 10 .

 10 Figure 10. TEM image of mesoporous titania synthesized with DEA/ Ti ) 0.9 and EO/Ti ) 1.2 and calcined at 400 °C for 6 h.

TABLE 1 : Effect of Calcination Temperature on the Characteristics of Titania Nanoparticles as Determined from XRD Patterns and N 2 Adsorption-Desorption Analysis

 1

		anatase	brookite	rutile
	sample a	cs b (nm)	ct c (%)	cs b (nm)	ct c (%)	cs b (nm)	ct c (%)	S BET d (m 2 g -1 )	p s e (nm)
	F0_RT	6.2 ( 0.5	70.3 ( 7.8	5.1 ( 0.4	29.7 ( 3.2	-	-	240.3 ( 12.0	4.5 ( 0.9
	F0_T400	9.1 ( 0.7	72.6 ( 7.4	7.4 ( 0.6	27.4 ( 2.8	-	-	118.7 ( 5.9	5.1 ( 1.0
	F0_T500	27.1 ( 2.2	67.8 ( 6.5	16.0 ( 1.3	23.8 ( 2.6	33.1 ( 2.6	8.4 ( 0.7	59.7 ( 3.0	5.5 ( 1.1
	F0_T600	42.2 ( 3.4	15.2 ( 1.9	-	-	80.9 ( 6.5	84.8 ( 8.7	5.3 ( 0.3	25.5 ( 2.5

a F ) [EO]/[Ti], T ) calcination temperature. b Crystallite size. c Polymorph content. d Specific surface area determined by BET method in the relative pressure range 0.1-0.25. e Pore size computed by NLDFT.

TABLE 2 : Structural Parameters of Mesoporous TiO 2 Synthesized with Different Amounts of Copolymer and Calcined at 400 and 500 °C, as Determined from XRD Data

 2

		anatase		brookite		rutile
	sample a	cs b (nm)	ct c (%)	cs b (nm)	ct c (%)	cs b (nm)	ct c (%)
	F0_T400	9.1 ( 0.7	72.6 ( 7.4	7.4 ( 0.6	27.4 ( 2.9
	F0.6_T400	7.6 ( 0.6	66.7 ( 6.9	7.1 ( 0.6	33.3 ( 3.5
	F0.9_T400	7.2 ( 0.6	62.0 ( 6.4	6.7 ( 0.5	38.0 ( 3.9	-
	F1.2_T400	7.0 ( 0.6	57.7 ( 5.9	6.7 ( 0.5	42.3 ( 4.4
	F2.6_T400	6.9 ( 0.6	53.2 ( 5.5	6.5 ( 0.5	46.8 ( 4.9
	F0_T500	27.1 ( 2.2	67.8 ( 6.9	16.0 ( 1.3	23.8 ( 2.6	33.1 ( 2.6	8.4 ( 0.8
	F0.9_T500	16.8 ( 1.4	60.2 ( 6.2	10.3 ( 0.8	36.7 ( 3.9	17.8 ( 1.4	3.1 ( 0.4
	F1.2_T500	14.2 ( 1.1	54.8 ( 5.7	9.2 ( 0.7	42.1 ( 4.3	14.3 ( 1.1	3.1 ( 0.4
	F2.6_T500	8.5 ( 0.7	50.1 ( 5.2	7.3 ( 0.6	49.4 ( 4.9	5.8 ( 0.5	0.5 ( 0.1

a F ) [EO]/[Ti], T ) calcination temperature. b Crystallite size. c Polymorph content.

TABLE 3 : Textural Characteristics of Samples Prepared with Different EO/Ti Molar Ratios and Calcined at 400 and 500 °C

 3

	DFT

TABLE 4 : Structural and Textural Characteristics of Samples Prepared with DEA and Copolymer F127

 4 ( 11.7 0.45 ( 0.02 218.9 ( 10.9 0.38 ( 0.02 3.2 ( 0.6 and 5.2 ( 1.0 0.34

	XRD

a (nm) ac b (%) S BET c (m 2 g -1 ) av d (cm 3 g -1 ) S cum e (m 2 g -1 ) pv f (cm 3 g -1 ) p s g (nm)

fit error (%) F1.2_DEA 0.9_T400 10.3 ( 0.8 100 202.5 ( 10.1 0.35 ( 0.02 174.5 ( 8.7 0.30 ( 0.02 3.2 ( 0.6 and 5.1 ( 1.

a Anatase crystallite size determined from XRD patterns. b Anatase content determined from XRD patterns. c Specific surface area determined by BET in the relative pressure range 0.1-0.25. d Adsorbed volume at P/P 0 ) 0.995. e Cumulative surface area resulting from DFT calculations. f Pore volume resulting from DFT calculations. g Pore size resulting from DFT calculations.

Acknowledgment. We acknowledge financial support from the Regional Councils of Aquitaine and Midi-Pyre ´ne ´es and the French Ministry of Industry (FCE/DGE) under the NAno COmposites MATerials (NACOMAT) project labeled by the Pole of Competitiveness "Ae ´ronautique, Espace et Syste `mes Embarque ´s" (2005-7123AESE/ID 2006-7123-06A-26). We are grateful to the laboratory instrumentation team for its fruitful help.


Adrien Gomez
email: adrien.gomez@ensiacet.fr

Catherine Azzaro-Pantel

Serge Domenech

Luc Pibouleau

Christian Latgé

David Haubensack

Patrick Dumaz

Exergy analysis for Generation IV nuclear plant optimization a

Keywords: exergy analysis, general formulation, thermodynamic simulator, CYCLOP, optimization criteria, generating cycles, genetic algorithm

. The exergy destruction is thus identified as a major criterion to minimize. For this purpose, a genetic algorithm embedded in the so-called MULTIGEN environment is used. Finally, the optimization criterion, based on exergy destruction minimization, is applied to electrical production by a Brayton-Rankine combined cycle connected to a nuclear reactor. Some typical results are presented. The perspectives of this work including the cogeneration of hydrogen and electricity are highlighted.

Introduction

Whatever the energy conversion system studied, the "delivered work" constitutes the "convertible" amount of the primary energy supplied to the system, referred as exergy. This approach, based on the simultaneous application of first and second law of thermodynamics, has received a renewed interest in analysis and design of electricity production and management [START_REF] Becerra-Lopez | Dynamic exergy analysis for capacity expansion of regional power-generation systems: Case study of far West Texas[END_REF][START_REF] Borelli | Exergy-based method for analyzing the composition of electricity cost generated in gas-fired combined cycle plants[END_REF], chemical processes (Rosen, 2008;Suphanit, 2007) and cogeneration plants [START_REF] Gomez | Optimisation of electricity / hydrogen cogeneration from Generation IV nuclear energy systems[END_REF]Ertesvag, 2007;[START_REF] Tsatsaronis | Exergoeconomic estimates for a novel zero-emission process generating hydrogen and electric power[END_REF]Kanoglu, 2009;[START_REF] Abusoglu | Exergetic and thermoeconomic analyses of diesel engine powered cogeneration: Part 1 -Formulations[END_REF][START_REF] Sayyaadi | Multi-objective approach in thermoenvironomic optimization of a benchmark cogeneration system[END_REF].

Exergy, first called "useful energy" or "energy which can be mechanized" [START_REF] Scott | Exergy[END_REF] originated in the field of the steam engines (pistons, turbines). A major advantage of the exergy concept is that it integrates not only a quantitative but also a qualitative consideration of irreversibility sources in an energy conversion process. Irreversibility implies exergy destruction and, by extension, potential to harm the environment. Exergy is in fact the maximum fraction of the total energy that can be extracted to produce a work.

Nature has three principal modes for exergy storage [START_REF] Scott | Exergy[END_REF]: mechanical nonequilibrium (gravitational potential, kinetic and pressure differences); thermal non-equilibrium (temperature differences); chemical non-equilibrium (including electrochemistry) non-equilibrium. Electromagnetism can be viewed as another mode of storage, but is relatively marginal in terms of quantity, as compared with the others. The energy production system considered in this study involves a VHTR (Very High Temperature Reactor) concept, considered as the nearest-term reactor design. It can indeed be coupled on the one hand, with innovative electricity-generating cycles and, on the other hand, with massive H 2 production processes. Thus, due to a high exit core temperature (at least 950°C) reached by helium used for cooling, VHTR is dedicated to the cogeneration of electricity and hydrogen by Sulphur-Iodine (S-I) thermochemical cycle or by High Temperature Electrolysis of steam water. Globally, these processes require the simultaneous supply of electricity and heat at high temperature. The optimal design of these process configurations constitutes an important challenge and a general optimization criterion is needed.

In this paper, only the section devoted to electricity production is considered. For this purpose, a model based on exergy theory is developed for the studied energy conversion system, in order to evaluate the exergy destruction level of process components embedded in a thermodynamic simulator CYCLOP [START_REF] Haubensack | The COPERNIC/CYCLOP Computer Tool: Pre-Conceptual Design of Generation 4 Nuclear Systems[END_REF]: the main principles of this simulator are described briefly in Section 2. CYCLOP models several components (turbines, heat exchangers …) for which it is necessary to compute exergetic efficiency. The following part of this article deals with the exergetic balance for a general component, which represents the first step before exergy integration within CYCLOP simulator. Since each simulator has its own modelling language, with an associated formalism, it is necessary to adapt the rigorous exergy balance expression to its particular context: the adaptation in CYCLOP will be the core of Section 4, taking into account both exergy destruction on components and during exergy transfer between them. The result of this work leads to quantify the destruction of exergy, that will constitute in turn the adopted optimization criterion.

Finally, the optimization criterion, based on exergy destruction minimization, is applied to electrical production by the combined cycle connected to a nuclear reactor. The perspectives of this work including the cogeneration of hydrogen and electricity will be highlighted.

Principles of CYCLOP simulation tool

For the particular case of future Generation IV nuclear reactors, it is necessary to describe, study and optimize any power conversion cycle, and to compare several cycles based on the same core.

The so-called CYCLOP [START_REF] Haubensack | The COPERNIC/CYCLOP Computer Tool: Pre-Conceptual Design of Generation 4 Nuclear Systems[END_REF] simulator allows a user to model a power conversion system in its globality and to study the respective influence of any components characteristics or cycle thermodynamical points on the global net efficiency of the cycle (or any other global parameter that should be optimized).

CYCLOP (for CYCLe OPtimization) is a computer tool implementing an automatic resolution of mass and energy balances of any reactor (first law of thermodynamics). A reactor is designed as a set of fluid loops built out of energetic components connected together (figure 1) by thermodynamical points and exchanging energy through calorific, mechanical or electrical transfers. Several fluids are available: gas like helium and nitrogen, but also twophase fluids like water or carbon dioxide (from liquid to supercritical domains). Gas mixtures are also possible. Various components are available, like reactor cores, turbines, pumps, compressors, heat exchangers, alternators, steam generators, water condensers, dryers, etc... Each component is described by macroscopic parameters like isentropic efficiency, pressure loss, calorific loss, mechanical or energetic efficiency that implements the second principle of thermodynamics.

Figure 1 represents the Brayton cycle using CYCLOP formalism. The components are connected by energy flows: energy flows can present losses. Therefore, it is necessary to consider simultaneously exergy destruction on components and exergy loss during energy transfer. The objective of the following sections is to introduce the theory of the exergy, as a tool for effectiveness analysis, and as an optimization criterion for the systems modelled with CYCLOP.

Mechanical Transfer

Heat Transfer

Exergy balance for a system with no chemical reaction

The first step consists in carrying out an exergy balance for CYCLOP components in order to derive a general expression for an automatic computation within CYCLOP. The interest of any conversion system of energy is to exploit the maximal available amount of "useful" energy (heat at various temperatures, electrical energy, mechanics…). The concept of usable energy was initiated by Carnot but concretely described by George-Louis Gouy in 1889 [START_REF] Gouy | Sur l'énergie utilisable[END_REF]. The potentiality of a system, from the point of view of the production of work, can be expressed by a function traducing not only the internal energy of the system, but also the temperature and pressure of the external atmosphere (25°C, 1 atm) of the system.

If the first and second principles are applied to a simple system, as represented in Figure 2, it can be seen as an open system receiving heat from various hot sources, exchanging heat with the atmosphere and producing energy with various forms (heat with T s mean temperature, electricity, mechanical energy). By respecting the conventional signs of thermodynamic flows (positive value for received energy, negative for transferred energy or losses) and neglecting kinetic and potential energy of inlet and outlet flows, the enthalpy balance is expressed as:

0 1 1 1 . . 0 Q Q h m h m W W Q NHS i i th in NO k k k out NI j j j elec mech th                           (2)
The entropy balance can be written as follows:

gen in NI k k k out NO j j j S th NHS i i i th S s m s m T Q T Q T Q                           1 1 0 0 1 . . 0 (3)
Generally, the atmospheric energy contribution and its associated entropic flow are equal to zero, according to the principle of [START_REF] Gouy | Sur l'énergie utilisable[END_REF]. Eliminating Q 0 between Equations ( 2) and (3), we obtain:

    gen in NI k k k k out NO k j j j NHS i i i th elec mech S th S T s T h m s T h m T T Q W W T T Q  . . . . . 1 . 1 . 0 0 1 0 1 0 1 0 0                                               (4)
Equation ( 4) must be written from exergy production point of view, as:

0 Q th T 0 , P 0 T 1 T 2 T n T S = mean system temperature     gen out NO k j j j in NI k k k k NHS i i i th elec meca S th S T s T h m s T h m T T Q W h W T T Q  . . . . . 1 . 1 . 0 1 0 1 0 1 0 0                                             (5)
For the input and output mass flows, the associated exergy terms can be defined:

k k k s T h e . 0   (6)
This equation is generally identified [START_REF] Borel | Thermodynamique et Energétique, Presses Polytechniques romandes[END_REF][START_REF] Bejan | Advanced Engineering Thermodynamics[END_REF] as the exergetic balance expression for a given open system. Equation ( 5) is written here in the direction of energy production (thermal, mechanical and electrical) but the equation remains true whatever the case (system supplied with mechanical or electrical energy) since a formal limitation does not exist. Each term can be computed since the system is known.

From a thermodynamic point of view, the exergetic balance expression contains more information on the system, compared to an enthalpy assessment, and makes it possible to compare the various kinds of power with a common basis.

From the analysis of Equation ( 5), additional concepts can be pointed out:  Both mechanical and electrical energies are considered as pure exergy terms.  Thermal energy is considered as degraded by a Carnot factor, in its form of exergy, according to the associated temperature with the supplied power.  The mass flows can represent a source and a loss of energy for the studied system. The computation procedure of the average system temperature will be presented in section (4.4).  The entropy generation, that is equivalent to exergy destruction, must be minimized in order to maximize exergy production.

Equation ( 5) does not take into account the thermal losses towards the outside: this point will be investigated in section (4.3). This balance applies to any type of component, (exchanger, compressor,…) in a local way, but can also be used globally at the process limits: it is particularly the case of heat release to the outside (cooling towers for instance). This formulation must be yet adapted to CYCLOP formalism to deduce the expression of the final optimization criterion.

Formulation of exergy-based criteria

This section is devoted to the application of exergy and to the computation of exergy destruction implemented in CYCLOP simulator [START_REF] Haubensack | The COPERNIC/CYCLOP Computer Tool: Pre-Conceptual Design of Generation 4 Nuclear Systems[END_REF]. For all the following equations, we take into account a particular formalism that may differ from the classical thermodynamics convention. This formalism is justified by the implementation of exergy balance in CYCLOP source code. First, the rigorous exergetic balance must be adapted to calculate exergy destruction level, but the main objective of this part is to clarify several particular cases generated by CYCLOP formalism.

For heat transfer, the definition of temperatures associated with these flows depends on the operating conditions of each component. The thermal losses due to cooling loops must be taken into account since input flows and conditions are fixed. From a general point of view, exergy losses during energy transfer between components are modelled. Finally, a general procedure to check the automatic computation is proposed.

General exergy destruction model

Here, the assumptions and limitations of the energy criterion, based on exergy destruction, are presented.

Internal irreversibility of a component

At a component level, a thermodynamic machine is assumed to have:

 Several input/output mass flows;  Several input thermal sources;  Several input/output of electricity or mechanical energy.

The transformations within the component then induce losses of exergy (internal irreversibilities) which must be minimized. The exergetic balance can be presented in the form of three equations, taking into account the abovementioned input/output flows:

 A balance on mass flows,                  j j Out j Out j i i In i In i flow gen P T s T h m P T s T h m S T , , 0 0 0  (7)
 A balance on the electrical/mechanical outputs (pure exergy),

Loss l l Trans k k c mech elec gen W W W S T       Re / 0 (8)  A balance on thermal power,                                     S Loss l S l Trans k k k c Th gen T T W T T W T T W S T 0 0 0 Re 0 1 1 1 (9)
 The internal energy of the system is already calculated by CYCLOP and is expressed by:

          i i In i In i j j Out j Out j Int P T h m P T h m W , , (10)
The irreversibility balance for the system makes it possible to write Equation ( 11). The quantity "W" represents the exchanged power whatever the energy is. 11) quantifies only the overall internal irreversibilities. In the global balance, it is necessary to take into account simultaneously the internal irreversibilities and losses to atmosphere. These losses are included in equation ( 12):

                                                             S 0 S 0 k 0 Re Re Re 0 0 T at lost is power thermal if , 1 lost is power l /mechanica electrical if
  S Loss Loss Total i Destruct T W S T Ex gen      0 (12)
This formulation is simple in practice because it integrates all exergy destruction and losses of a component (both internal and external). Yet, it is always necessary to quantify output temperature and to know the input exergetic power: this problem is solved on paragraph 3.4.

Exergetic losses with mass flow and atmosphere

The components with inlet and outlet flows coming from the atmosphere are identified in an incomplete way by the Equation (11). Inlet and outlet exergy of these flows must be defined in addition to losses relative to components.

For losses induced by components, it is thus necessary to add the following term (Equation 13) to calculate the final criterion, which implicitly considers that energy that is rejected outside is not used to produce energy.

               NI j j j j NO i i i i flow Loss s T h m s T h m Ex 1 0 1 0  (13)

Evaluation of exergetic destruction and losses within CYCLOP

The total exergetic destruction and loss on a system, whatever its structure, is the sum of the exergetic destruction and losses (to the atmosphere) for each component to which exergy rejected to atmosphere via mass flows (Equations 12 and 13) is added. The total evaluation of destruction-losses should be minimized to maximize the energy production of the system (see Equation 14):

                 NI 1 0 NO 1 0 j j j j i i i i NCOMP i i Destruct Destruct s T h m s T h m x E x E    (14)
Under CYCLOP formalism, "transfer" objects represent an energy flow between two components. The transfer efficiency "r" represents the percentage of energy transmitted between two components. From a general point of view, the losses of exergy on an object "Transfer" are equal to:

  out l l th l j elec j i meca i in l l th l j elec j i meca i Destruct in l l th l j elec j i meca i Destruct T T W W W T T W W W Ex T T W W W r Ex                                                                           0 0 0 1 1 1 1 (15)
In this form, Equation ( 15) is a particular case of the general Equation ( 11) and thus does not require any modification of formulation. In the particular case of heat transfer, it can be considered that a source of heat supplies several exchangers. Equation ( 12) requires to specify the temperature associated with the received thermal power. Physically, the exchanger must be represented by an energy source, from the point of view of the fluid. The temperature T k (Equation 11) of the "received" power is the mean value between T in and T out . It is yet possible with CYCLOP that a "heat exchanger" component is not connected to another, via an object "Transfer". In this case, it directly supplies power, which is identified as a loss of exergy from system viewpoint.

The consideration of the thermal losses on the components must be studied because they induce a reduction in the capacity of work and transfer of the fluids used in the cycles of energy transformation: the same remark is valid for irreversibilities during chemical reactions.

The CYCLOP components that are directly concerned refer to those implied in an intrinsic heat transfer, that may be desired or not (case of heat loss). These losses can be modelled as an output:

 for CYCLOP components  for heat transfer between components ("transfer" object of CYCLOP)

Physically, the waste heat is considered in term of potential recoverable work for mass flows. This fact implies that only components CYCLOP that are crossed by mass have "the right to lose heat". This fact also implies that a priori the thermal losses will be associated with the level of temperature of the fluid undergoing them.

Let us illustrate the enthalpic and entropic balances on an example of thermal losses for a heat exchanger. For an elementary element of surface dA (figure 3) of a heat exchanger, a fluid undergoes a heat loss called ∂Q Loss , while crossing first the metal wall, then the insulating layer.

The principal assumptions involve:  a constant radial temperature of the fluid for a turbulent flow. The temperatures with the interface between the fluid and the metal wall are thus identical,  the materials of the metal wall and the insulating wall are homogeneous.

Entropy being a function of state, the change of the temperatures in the walls does not have any effect on the assessment of entropic flows.

The entropic balance on the metal wall is thus:

0       Metal gen M Loss F Loss S T Q T Q  (16)
The entropic balance on insulating wall takes the following expression:

0       Coat gen C Loss M Loss S T Q T Q  (17)
The enthalpic balance is simple because the ∂Q Loss quantity is preserved through the walls.

The exergetic balance between the transmitting fluid and the atmosphere gives the following relation:

                                                                          exchanger heat by lost Exergy S S T T T Q flows by lost Exergy T T Q coating on balance Exergy S T Q T Q T Q Q wall exchanger heat on balance Exergy S T Q T Q T Q Q Metal gen Coat gen C Loss F Loss Coat gen C Loss M Loss Loss Loss Metal gen M Loss F Loss Loss Loss                                                                                 0 0 0 0 0 1 1 0 (18)
Equation 18 shows that the thermal losses imply a loss of exergy which can be expressed according to the temperature of only the "transmitting" fluid. Without any other information than the lost power (calculated from component output by CYCLOP), exergy lost by the system is equal to exergy lost by the fluid, which implies that the flow of lost exergy is a function of the temperature of the transmitting fluid. For heat exchangers case, heat losses are modelled, with an exergy destruction during heat transfer between hot side and cold side, using Equation 15 and fixing the transfer efficiency value "r".

Heat supplying system modelling

General formulation and hypothesis

By assuming that no chemical reaction on the systems occurs, the problem of heat transfer is always the same: a hot system transfers heat towards a cold system (both being crossed by undergoing mass flows with temperature variations and pressure) through a material wall. Heat transfer, due to variations in temperature within the walls, makes it necessary to associate mean temperatures with the systems. For an exchange between two mass flows, the formulated assumptions are the following ones (see Figure 4):  There is no chemical reaction on hot or cold side  On a cross section of the fluid (cold and hot side), temperatures and pressures are homogeneous (no radial gradients during heat transfer). Thus, the hot side of the exchanger can be modelled as a sink of temperature emitting the required power Q, at a temperature T h : the calculation of this temperature takes into account the temperature change during the exchange. This temperature is commonly called "entropic temperature" and makes it possible to reduce the hot side of an exchanger in a heat source to T h constant.

Entropic temperature in ideal case: the Lorentz cycle

The Lorentz cycle [START_REF] Lior | Energy, Exergy, and the Second Law performance criteria[END_REF] (reversible) (figure 5) considers that the exchanges with both heat and cold sources are not isothermal, which is not the case with Carnot cycle. It consists of a compression of an isentropic ideal gas (1  2), followed by a heating phase (2  3) where temperature increases gradually until the maximum temperature of the cycle, T3, is reached. The ideal gas undergoes an isentropic relaxation the (3  4), then a cooling (4  1) with a gradual reduction in temperature. It is also considered that there are no pressure losses during both warming and cooling.

Figure 5 -(T,S) Diagram for Lorentz thermodynamic cycle

The exergetic balance relative to the so-called "half" hot exchanging gives:

0 1 0 0                 h h out h in h gen T T Q x E x E T S   (19)
Consequently, the value of the entropic temperature of the hot source is:

              h in h out h in h out T T T T h out h in h out h in h dT T Cp dT Cp T s T s T h T h T . . ( 20
)
This result, obtained by an exergetic balance, is the classical expression for the entropic temperature [START_REF] Lior | Energy, Exergy, and the Second Law performance criteria[END_REF]. This equation is admitted for a constant pressure.

For a perfect gas and by considering C P as a constant on the interval of temperature:

  ) / ln( h out h in h out h in h T T T T T   (21)
In the case of the real exchangers, all the irreversible phenomena must be taken into account.

General expression of entropic temperature

The cycle of Lorentz does not take into account the pressure losses due to the heattransferring surfaces: consequently, there is generation of irreversibility. The exergetic balance on the so-called "half" hot exchanger is always identical, but the generated entropy is not null any more.

 h gen S     0 1 , , 0 0                 h h out h out h in h in h in h in h gen T T Q P T x E P T x E T S   (22)
The term of exergetic power must be expressed according to the temperature change during transfer, according to the following equation:

dQ T T T T Q outlet inlet h                    0 0 1 1 (23)
The entropic temperature h T is given by:

                              h out h out h in h in h out h out h in h in P T P T p P T P T p h dp T v T dT Cp dp T v T v dT Cp T , , , , . . . . . (24)
The obtained entropic temperature, under the assumptions of perfect gas and constant C P , is formally identical whereas their general expressions are different (Equations 20 and 21). By considering the pressure losses, the level of temperature of exit increases a little, which implies a reduction in the value of the entropic temperature h out T h T .

Exergetic efficiency

The exergetic balance highlights the concept of thermodynamical loss. It is thus possible to define an exergetic effciciency as follows:

   Sent Product ex Ex Ex  (25)
The exergetic power can represent a work, a mass or heat flow. According to the exergetic balance, it can be seen that the difference between the denominator and numerator of the exergetic efficiency  EX [START_REF] Bejan | Advanced Engineering Thermodynamics[END_REF] (Equation 25) is rigorously equal to the system exergetic losses.

Application of exergy theory to a combined He/He-N 2 /H 2 O cycle

The combined cycle is a more complex case for application of exergy theory. This example implements a cycle of Brayton (as in the preceding case) as well as a cycle of Rankine with phase shift: steam generation is a source of exergetic losses, as it will be noted thereafter. This generating cycle is modelled with CYCLOP and optimized with a monoobjective genetic algorithm [START_REF] Deb | A Fast and Elitist Multiobjective Genetic Algorithm: NSGA II[END_REF] implemented under the MULTIGEN environment [START_REF] Gomez | Teaching Mono and Multiobjective Genetic Algorithms in Process Systems Engineering : an illustration with the MULTIGEN environment[END_REF]. The principle of the optimization procedure will not be recalled here.

Cycle description and identification of the exergetic losses

The combined cycle (figure 6) is composed of three loops implying three different coolants:

 The primary loop, using helium, with a cooling by of the Intermediate Heat Exchanger (IHX) and a compensation of the pressure losses per insertion of a blower before return on the engine  The secondary loop, using a He-N 2 mixture (respectively 64% and 36% in mass), is a simple Brayton cycle: the IHX is the hot source whereas the steam generator is the cold well. This loop generates electricity.  The tertiary loop, using water with high pressure, is a cycle of Rankine with a relaxation with high pressure and another with low pressure. The thermal losses of the steam generator are treated by assimilation with the lost power with a temperature equal to the logarithmic mean temperature value of the hot side flow. These assumptions imply an artificial maximization of the exergetic losses on the level of the steam generator.

Losses on the level of the condenser also appear because no cold source was associated in this cycle model performed with CYCLOP. The temperature of condensation being fixed at 32°C, the association of this temperature to the lost power will have no impact on the optimization of the cycle: the only adjustment variable will be the lost power with the condenser. Consequently, the expression of the exergetic losses of the Steam Generator influences the optimization process.

The variables of optimization selected for this cycle are the following ones:

 The outlet temperature of the gas turbine (He-N 2 loop)  The outlet temperature of gas (secondary side He-N 2 ) of the Steam generator  The pressure ratio of the high pressure steam turbine The associated constraints are:

 The steam mass fraction at turbine exit must be higher than 85%, to avoid a damage of the turbine by a condensed water  The mean logarithmic pinching temperature curve of the exchanger of intermediate heat (IHX) is higher or equal to 30°C  The minimum pinch temperature of the steam generator is 10°C

The following stage consists in locating the exergetic losses on the system (see figure 6). The cycle analysis leads to identify:

 Flows and energy production: 600 MWth resulting from the nuclear reactor, electrical production on the generating engine of the secondary loop (He-N 2 ) and the high pressure steam loop.  Non used flows: latent heat at the condenser level.

Concerning condenser modelling, it must be pointed out that only the hot "half" exchanger (side condensation) is represented. The latent heat transmitted "to vacuum" is considered as lost by CYCLOP. Exergy destruction and losses are automatically calculated by CYCLOP simulator component by component, using equation 12, and final criteria is calculated with equation 14.

Optimization results

The optimization performed leads to a production of 288.8 MW for a total loss of exergy of 124,4 MW, which corresponds to an exergetic efficiency of 69.9%. Figure 7 displays the decomposition of the exergetic losses of the cycle components. Table 1 presents in detail the optimal operating conditions of the components. These values correspond to feasible orders of magnitude. The corresponding optimization variables take the following values:

 Temperature of exit of the gas turbine (He-N 2 ): 590.9°C  Temperature of exit gas (secondary side He-N 2 ) of the Steam generator: 164.8°C  Pressure ratio of relaxation of the high pressure steam turbine: 36.7.

The steam generator, with a loss of 38 MW exergy, contributes to 30.5% of the total losses of the cycle. This value is due to the combined effect of the following phenomena:  A temperature pinching of 30°C  Pressure losses of 20 bar (vaporization site) and 0.4 bar (gas side He-N 2 )  Thermal losses of 1.0 MW (exergetic)

The parameters of the genetic algorithm used in MULTIGEN environment [START_REF] Gomez | Teaching Mono and Multiobjective Genetic Algorithms in Process Systems Engineering : an illustration with the MULTIGEN environment[END_REF] This study illustrates that the performances of the steam generator must be improved to increase electrical production. The generator engine of the secondary loop He-N 2 (respectively the steam turbine) accounts for 18.8% of the losses (respectively 22.9 %) for a total of 51.9 MW (exergy) for the mechanical energy production. Let us recall that these losses reached 40,7 MW (exergy) for the direct cycle GT-MHR. The exergy destruction with the condenser is weaker, with 11.6 MW, but the half-exchanger side cold utility was not taken into account.

Due to the three loops, the impact analysis of the improvement of the equipment performances is complex, but a decrease in exergy destruction in the steam generator will lead to increase production. The steam cycle being limited in design, by the maximum pressure (150 bar) and by the temperature of the condenser, further work will now be devoted to the secondary loop and to the decrease in pinch temperature.

Conclusion

The application of the exergetic balance presents the advantage to compare, on the same basis, various forms of energy (thermal, electrical and mechanical) by a simultaneous consideration of first and second principles of thermodynamics. The major concept of the exergy theory is the concept of "useful energy" of an energy source. Mechanical, thermal or chemical non-equilibrium is at the origin of this exergetic potential.

The irreversibility created during transformations, or energy transfers, are taking into account by an entropic balance. Since such dissipated energy cannot be recovered, it is thus advisable to minimize them. By extension, the losses of recoverable energy (mainly due to thermal effects) will have to be also minimized and are considered as the irreversibility, since they are lost for energy transformation. The minimization of exergy destruction requires an increase in equipment efficiency either at the level of their operating conditions (flows, pressures and temperatures), or at technological level (intrinsic entropic losses of equipment, pressure losses in particular). This implies an increase in cost, independently of the operating conditions. The approach, proposed in this article, consists in minimizing the internal and external losses of a system for generating cycles and cogeneration systems. Exergy assessment will now be used and extended to the cogeneration of hydrogen and electricity which constitutes a natural perspective for VHTR reactors.

Nomenclature

Figure 1 -

 1 Figure 1 -Flowsheet of the Brayton cycle with CYCLOP

Figure 2 -

 2 Figure 2 -Exergetic model of a general thermodynamic machine.

Figure 3 -

 3 Figure 3 -Losses of energy through a metal and insulating wall of an exchanger

Figure 4 -

 4 Figure 4 -Heat exchanger modelling with exergy theory

Figure 6 -

 6 Figure 6 -Flowsheet of the pressured combined cycle He / He-N 2 / H 2 O

Figure 6 -

 6 Figure 6 -Identification of the exergetic losses on the cycle

Figure 7 -

 7 Figure 7 -Exergy destruction analisys for combined cycle He / He-N 2 / H 2 O

Table 1 -Optimal characteristics of components for minimum exergy destruction

 1

	are:
	 Number of individuals: 100  Number of generations: 200  Crossover probability: 90%  Mutation probability: 50%