Antony Memboeuf

László Drahos

György Lendvay
email: lendvay@chemres.hu

K Vekey
email: vekey@chemres.hu

Károly Vékey
email: karolyvékey@chemres.hu

oligomers»

Dear Sir, There are various difficulties studying macromolecular systems. One on these is that the applicable theoretical and experimental methodologies often have significant limitations. A common solution is to use smaller "model" compounds; study them in detail; and extrapolate these results to the larger system. Although very useful, this raises the question, how accurate is the extrapolation? In the present Letter we want to give an example related to activation energies, which have large importance describing fragmentation processes. There are diverse methods determining activation energies in mass spectrometry; many values obtained this way can be found in the literature [START_REF] Levsen | Fundamental Aspects of Organic Mass Spectrometry[END_REF][START_REF] Armentrout | The Encyclopedia of Mass Spectrometry -Volume 1: Theory and Ion Chemistry[END_REF][START_REF] Bowers | Gas Phase Ion Chemistry[END_REF]. However, most of these relate to small molecules. Available methods for studying compounds over ca. 200 Da size are less accurate; and there are few reliable values [START_REF] Busman | Activation-Energies for Gas-Phase Dissociations of Multiply Charged Ions from Electrospray Ionization Mass-Spectrometry[END_REF][START_REF] Freitas | Gas Phase Activation Energy for Unimolecular Dissociation of Biomolecular Ions Determined by Focused RAdiation for Gaseous Multiphoton ENergy Transfer (FRAGMENT)[END_REF][START_REF] Laskin | Fragmentation energetics of small peptides from multiple-collision activation and surface-induced dissociation in FT-ICR MS[END_REF][START_REF] Schafer | Determination of the activation energy for unimolecular dissociation of a non-covalent gas-phase peptide: Substrate complex by infrared multiphoton dissociation Fourier transform ion cyclotron resonance mass spectrometry[END_REF][START_REF] Vékey | Average Activation Energies of Low-energy Fragmentation Processes of Protonated Peptides Determined by a New Approach[END_REF][START_REF] Wainhaus | Determination of activation energies for ion fragmentation by surface-induced dissociation[END_REF][START_REF] Wong | Activation of protonated peptides and molecular ions of small molecules using heated filaments in fourier-transform ion cyclotron resonance mass spectrometry[END_REF][START_REF] Sztáray | Leucine Enkephaline -a mass spectrometry standard[END_REF]. "Common wisdom" suggests that, for the same reaction type, increasing the molecular size should decrease the barrier height (i.e. the critical energy, but not the internal energy needed for fragmentation!): Increasing size typically stabilizes the product ion (and product radical, if any) with respect to the parent compound. With the advance of experimental techniques to study macromolecules, it may become useful to be able to estimate, how molecular size influences the activation energy.

To understand the factors influencing the size dependence of fragmentation energetics, reliable information would be desirable. Theoretical methods achieved the level of accuracy that makes them an accepted source of reliable data. We intend to provide this kind of information using a well-defined model system. Poly(ethylene glycols) -PEG-oligomers have been selected to study the influence of molecular size on fragmentation energetics. Studying homopolymers (like PEGs) has the advantage that structural features do not change with increasing size. This simplifies studying size effects and makes results easier to interpret [START_REF] Memboeuf | Size Effect on Fragmentation in Tandem Mass Spectrometry[END_REF]. In the case of peptides, which are in the forefront of interest, the presence of various amino acid residues modifies chemical behaviour, which can mask the size effect completely [START_REF] Dongre | Influence of peptide composition, gas-phase basicity, and chemical modification on fragmentation efficiency: Evidence for the mobile proton model[END_REF].

Quantum chemistry, in particular, density functional theory was used to determine the mechanism of fragmentation. Calculations have been carried out using two different functionals: the popular B3LYP [START_REF] Becke | Density-functional exchange-energy approximation with correct asymptoticbehavior[END_REF][START_REF] Becke | Density-functional thermochemistry 2. The effect of the Perdew-Wang generalized-gradient correlation correction[END_REF][START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF] and the more recently developed M05-2X [START_REF] Zhao | Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions[END_REF]. The former has been generally used in the study of reactions of polyatomic molecules. The latter generally gives a more accurate description of loose-type interactions (e.g. H-bonds), and in particular, barrier heights for reaction; in this respect, this functional generally provides barrier heights and fragmentation energies within 0.2 eV with respect to the highest-level ab initio methods [START_REF] Kosztyu | Testing the performance of density functionals for the calculation of energetic properties of complex-forming radical-molecule reactions[END_REF]. Optimization of the geometry of the structures were performed using the 6-31G(d) basis set, followed by single point energy calculation using the larger 6-311++G(2d,2p). The character of the stationary points was identified using normal mode frequency analysis. Each minimum is genuine (there are no imaginary frequencies), each potential barrier is a first-order saddle point (there is one imaginary-frequency mode).

PEG oligomers are most often studied in mass spectrometry as even electron, positively charged lithium adducts ([M+Li] + ). [START_REF] Lattimer | Tandem Mass-Spectrometry of Lithium-Attachment Ions from Polyglycols[END_REF] Occasionally protonated, sodiated or other cationized species are also observed, although their fragmentation is not so characteristic. More precisely, in the case of protonated species (much weaker signal than with other adducts), mainly low mass daughter ions are observed limiting the structural information available [START_REF] Lattimer | Tandem Mass-Spectrometry of Poly(Ethylene Glycol) Proton-Attachment and Deuteron-Attachment Ions[END_REF]. On contrary, for sodiated, similarly for potassiated species, loss of the cation is almost the only fragment observed [START_REF] Lattimer | Tandem Mass-Spectrometry of Lithium-Attachment Ions from Polyglycols[END_REF]. Concerning lithium cationized PEGs, the main fragmentation process is the loss of one or several monomer units (the latter may be formed either in a one step process or in sequential reactions) [START_REF] Lattimer | Tandem Mass-Spectrometry of Lithium-Attachment Ions from Polyglycols[END_REF][START_REF] Girod | Tandem mass spectrometry of doubly charged poly(ethylene oxide) oligomers produced by electrospray ionization[END_REF][START_REF] Selby | Dissociation Characteristics of M+X (+) Ions (X=H, Li, K) from Linear and Cyclic Polyglycols[END_REF]. The lowest energy process of lithiated PEG is the loss of a monomer unit (C 2 H 4 O) from the end of the chain. We have studied the mechanism of this process in detail. There are several alternative reaction channels leading to C 2 H 4 O loss, the lowest energy channel among these leads to the loss of acetaldehyde, as shown for the trimer in Scheme 1.

The reaction proceeds through a quite complex, concerted mechanism. The sequence of intramolecular events was followed by calculating the Intrinsic Reaction Coordinate (IRC) and viewing the geometry changes along the path. First, a strong hydrogen bond is formed between the terminal hydroxyl group and an ether oxygen. This is an intermediate structure (i.e. local minimum). Subsequently this hydrogen shifts to bind more strongly to the mid-chain ether oxygen, forming a new terminal OH group; while at the same time the terminal oxygen starts to form a carbonyl bond. This initiates (in a concerted fashion) a 1-2 hydrogen shift between two carbon atoms; and this leads to the highest-energy point along the path (transition state, TS, Scheme 1). The height of the barrier for the trimer is 2.54 eV at the B3LYP/6-311++G(2d,2p) level of theory. (Here and elsewhere in the text we quote values determined at this level; the Table shows results using M05-2X as well.) On the downhill side of the potential barrier, the newly formed bonds strengthen which leads to the formation of a loosely bound ion-molecule complex between a lithiated PEG dimer and acetaldehyde. This complex breaks with only a small energy requirement (and no energy barrier) into the products. Regarding the mechanism described, we would like to make a few further comments. (1) The critical energy of fragmentation of PEG trimer is 2.54 eV. Compared to most organics it is very high; about two times higher, than that observed for most peptides [START_REF] Laskin | Fragmentation energetics of small peptides from multiple-collision activation and surface-induced dissociation in FT-ICR MS[END_REF][START_REF] Vékey | Average Activation Energies of Low-energy Fragmentation Processes of Protonated Peptides Determined by a New Approach[END_REF][START_REF] Wainhaus | Determination of activation energies for ion fragmentation by surface-induced dissociation[END_REF][START_REF] Memboeuf | Size Effect on Fragmentation in Tandem Mass Spectrometry[END_REF]. This does explain, why do PEG oligomers require far larger collision energy for fragmentation than most other protonated compounds [START_REF] Memboeuf | Size Effect on Fragmentation in Tandem Mass Spectrometry[END_REF] of similar mass. (2) It is somewhat surprising that the TS is quite loose, the activation entropy is estimated to be only 7.9 J/mol/K based on frequency analysis and the rigid-rotor harmonic oscillator approximation. This corresponds to an Arrhenius type preexponential factor of 2.3 10 13 s -1 . (3) The reaction is facilitated by the presence of the Li + cation. In the absence of Li + the barrier is 0.3 eV higher. This suggests a charge-induced process. (4) The type of cation does not have a significant effect on the reaction mechanism: In the case of a sodium adduct the barrier height is similar (higher by ~0.2 eV). ( 5) The early suggestion [START_REF] Lattimer | Tandem Mass-Spectrometry of Lithium-Attachment Ions from Polyglycols[END_REF], that the reaction proceeds through the transfer of the alcoholic H only was also studied. This reaction channel leads to ethylene oxide and requires 0.6 eV higher critical energy (this difference is well beyond the "error bar" of the method), so it can not compete efficiently with the low energy process leading to acetaldehyde.

Probably the most significant finding in the present communication is the size dependence of the critical energy. First of all, it has been established, that the reaction proceeds through the same low energy channel for other oligomers as well (from the dimer to the hexamer). Increasing the size of the PEG does not change the main characteristics of the process. Independently of molecular size, monomer loss remains the lowest energy channel (both experimentally [START_REF] Memboeuf | Structure and energetics of polyethylene-glycol cationized by Li+, Na+, K+ and Cs+: a first-principles study[END_REF] and according to the calculations: other channels were found to require more energy). The activation energies for various PEG oligomers are shown in Table 1. This shows that the critical energies decrease somewhat with molecular size, but the change is relatively minor (7-16% depending on the level of calculations, see Table 1 To increase confidence in the results, we have repeated the calculations using a different dft functional, M05-2X as well, which has been found to describe loose bonds (like hydrogen bonds) better and yield more reliable barrier heights than the more conventional B3LYP method. The results are given in Table 1. These show qualitatively the same trend; although the activation energies are a little higher (by ca. 0.35 eV); and the change with molecular size is smaller. Results using both functionals show that the limiting value for the critical energy is reached around the tetramer or pentamer.

Activation energies can be compared to the binding energy of the lithium cation (lithium affinities) (Table 1; while values for the 10-, 14-and 18-mer are 5.68, 5.65 and 5.70 eV, respectively using the M05-2X functional). It can be seen that the lithium affinity increases very strongly with oligomer size, and the limiting value is reached only around the 10-or 12-mer. This is a far larger change than that of the activation energy. Note that lithium affinity is larger (or much larger) than the critical energy of fragmentation (monomer loss). This explains why, in contrast to Na + or Cs + , the Li + cation is not "lost" in a fragmentation; resulting in a structurally useful MS/MS fragmentation. As Na + or Cs + affinities are significantly smaller; in these cases loss of Na + or Cs + instead of a monomer EG unit may become dominant, resulting in MS/MS spectra that, for structure elucidation, are nearly useless.

Results presented in this communication indicate that PEGs (and likely other polyethers) require high (ca. 2.5-3 eV) critical energy for fragmentation. This explains the experimental observation that their MS/MS fragmentation requires far larger collision energies than needed for peptides and most other organics of similar size. In general, larger oligomers require somewhat lower activation energies for fragmentation. However, this is only a minor effect; critical energies among various oligomers decrease by only about 10%. We believe this is the first systematic study to determine how much the activation energy for decomposition depends on molecular size in even-electron ions. As we lack data for other systems it is difficult to generalize; but seems most likely that the size dependence of critical energies has a minor influence on mass spectrometric fragmentation behaviour.

Scheme 1 :

 1 Scheme 1: Mechanism of fragmentation of the PEG trimer, as calculated at the B3LYP/6-311++G(2d,2p)//B3LYP/6-31G(d) level of theory.

Table 1 .

 1 for details). Critical energies of fragmentation and Li + binding energy in eV as a function of the number of monomers and

		B3LYP (in eV)	M05-2X (in eV)
	No. of
	monomers	Barrier	Li	+ binding	Barrier	Li	+ binding
		height		energy	height		energy
	2	2.70		3.35	2.98		3.71
	3	2.54		3.90	2.90		4.12
	4	2.42		4.15	2.80		4.28
	5	2.25		4.53	2.78		4.68
	6	2.28		4.69	2.77		4.89
	at two different levels of theory: B3LYP/6-311++G(2d,2p)//B3LYP/6-31G(d) (abbreviated as B3LYP) and M05-2X/6-
	311++G(2d,2p)//M05-2X/6-31G(d) (abbreviated as M05-2X) where A//B means an energy calculation at level A at the
	geometry optimized at level B.

Acknowledgements

This work has been supported by the Hungarian Scientific Research fund (grant No. OTKA K77938, GL). We gratefully acknowledge financial support of the Sixth Framework Program of the European Community for funding the POLY-MS project (MEST-CT-2005-021029).


G Montes-Hernandez
email: german.montes-hernandez@ujf-grenoble.fr

R Chiriac

F Toche

F Renard

Gas-solid carbonation of Ca(OH) 2 and CaO particles under non-isothermal and isothermal conditions by using a thermogravimetric analyzer: Implications for CO 2 capture

Keywords: Gas-solid carbonation, nanosized Ca(OH) 2 particles, non-isothermal, isothermal, CO 2 capture

the mineralization of adsorbed CO 2 on CaO particles implies a solid state transformation, i.e., CaCO 3 formation from CaO-CO 2 interactions. This could be explained by an atomic excitation than at high temperature allows the local migration of one oxygen atom from the solid towards the adsorbed CO 2 leading to its mineralization into carbonate (porous or non-porous layer) around the reacting particles; chemically the mineralization of CO 2 also implies the breaking of one covalent bond in the CO 2 molecule.

Abstract

The gas-solid carbonation of alkaline sorbents has been actively investigated as an alternative method to CO 2 capture from industrial combustion sources and CO 2 contained in the air. This study has a two-fold objective: firstly, quantify the gas-solid carbonation extent and the carbonation kinetics of Ca(OH) 2 and CaO; and secondly, propose a reaction mechanism of gassolid carbonation for CaO under dry conditions (relative humidity close to 0), i.e., when the action of water is negligible. The main results of our study have revealed that a high proportion of Ca(OH) 2 nanoparticles were transformed into CaCO 3 particles by gas-solid carbonation (carbonation extent, ξ>0.94) under non-isothermal conditions. Moreover, this gas-solid reaction requires low activation energy (E a 16kJ/mol) at a constant heating rate of 5 or 10K/min. A similar carbonation extent was determined for gas-solid carbonation of in-situ synthesized CaO under non-isothermal conditions. However, the gas-solid carbonation of CaO takes place in a broader temperature range, implying a more complex thermokinetic behavior (overlapping of carbonation regimes or steps). Concerning the gas-solid carbonation of Ca(OH) 2 and CaO under isothermal conditions, a high carbonation extent (>0.9) was determined for CaO at 600 (873K) and 800°C (1073K). Conversely, the gas-solid carbonation of Ca(OH) 2 particles was relatively low (<0.56) at 400°C (673K) after 6h of reaction. This case is in agreement with the formation of a dense non-porous layer of carbonate mineral around the core of the reacting Ca(OH) 2 particles, thereby limiting the transfer of CO 2 .

Finally, an alternative reaction mechanism is proposed for the gas-solid carbonation of CaO, when the relative humidity is close to 0. This macroscopic control at high temperature avoids CO 2 dissociation with molecular water at the CaO-CO 2 interface. For these specific conditions,

Introduction

Gas-solid reactions are ubiquitous in many natural and artificial environments (e.g., instantaneous or slow reactions of volcanic ash, dust and aerosols with natural and/or anthropogenic atmospheric gases). In basic or applied research, gas-solid reactions have been widely used to investigate the oxidation, reduction, chemical vapor deposition, dehydroxylation, carbonation (or mineralization of CO 2 ), decarbonation and other non-limited chemical processes. In particular, there has been growing interest in gas-solid carbonation processes using alkaline sorbents because of their potential to capture CO 2 via non-catalytic exothermic reactions, allowing the selective mineralization of CO 2 from a complex mixture of several gases (e.g., from industrial combustion processes). Once carbonated, the resulting crystals are then decarbonated at high temperature (with the actual temperature value depending on the nature of the carbonate produced [START_REF] Prigiobbe | Gas-solid carbonation kinetics of air pollution control residues for CO 2 storage[END_REF][START_REF] Stendardo | Carbon dioxide capture with dolomite: A model for gas-solid reaction within the grains of a particulate sorbent[END_REF][START_REF] Zevenhoven | Heat optimisation of staged gas-solid mineral carbonation process for long-term CO 2 storage[END_REF][START_REF] Sun | A discrete-pore-size-distribution-based gas-solid model and its application to the CaO + CO 2 reaction[END_REF][START_REF] Shtepenko | Characterization and preliminary assessment of a sorbent produced by accelerated mineral carbonation[END_REF], releasing pure CO 2 by a calcination (or decarbonation) process.

Thanks to this overall carbonation-calcination route, pure CO 2 can be recovered prior to its injection underground and reuse, except for carbonates containing monovalent elements (e.g., Na, Li) which volatilize before the decarbonation process. Various alkaline sorbents have been proposed to capture and mineralize CO 2 via gas-solid carbonation such as binary oxides (e.g., CaO, MgO), hydroxides (e.g., Ca(OH) 2 , Mg(OH) 2 , NaOH), metastable powdered silicates (e.g., Li 2 SiO 3 , Na 2 SiO 3 , CaSiO 3 , MgSiO 3 ) and natural silicates (e.g., olivine, pyroxene, serpentine) [START_REF] Larachi | Role of steam, hydrogen and pretreatment in chrysotile gas-solid carboantion: opportunities for pre-combustion CO 2 capture[END_REF], Reddy et al., 2010;[START_REF] Stendardo | Carbon dioxide capture with dolomite: A model for gas-solid reaction within the grains of a particulate sorbent[END_REF][START_REF] Huntzinger | Carbon dioxide sequestration in cement kiln dust through mineral carbonation[END_REF][START_REF] Regnault | Experimental measurement of portlandite carbonation kinetics with supercritical CO 2[END_REF], 2009;[START_REF] Zevenhoven | Heat optimisation of staged gas-solid mineral carbonation process for long-term CO 2 storage[END_REF][START_REF] Wang | Carbonation of fly ash in oxy-fuel CFB combustion[END_REF][START_REF] Sun | A discrete-pore-size-distribution-based gas-solid model and its application to the CaO + CO 2 reaction[END_REF][START_REF] Gauer | Doped lithium orthosilicate for absorption of carbon dioxide[END_REF]Esski et al., 2005;[START_REF] Shtepenko | Characterization and preliminary assessment of a sorbent produced by accelerated mineral carbonation[END_REF][START_REF] Fernandez Bertos | A review of accelerated carbonation technology in the treatment of cement-based materials and sequestration[END_REF][START_REF] Lanas | Dolomitic limes: evolution of slaking process under different conditions[END_REF][START_REF] Purnell | Super-critical carbonation of glass-fibre reinforced cement. Part 2 : Microstructural observation[END_REF]. In all cases, the CO 2 -sorbent reaction takes place by the formation of a dense non-porous layer of carbonate minerals (or protective carbonate layer) around the reacting particles, to the extent that total carbonation efficiency cannot be achieved (<80%) (e.g. [START_REF] Prigiobbe | Gas-solid carbonation kinetics of air pollution control residues for CO 2 storage[END_REF][START_REF] Stendardo | Carbon dioxide capture with dolomite: A model for gas-solid reaction within the grains of a particulate sorbent[END_REF][START_REF] Huntzinger | Carbon dioxide sequestration in cement kiln dust through mineral carbonation[END_REF][START_REF] Sun | A discrete-pore-size-distribution-based gas-solid model and its application to the CaO + CO 2 reaction[END_REF][START_REF] Fernandez Bertos | A review of accelerated carbonation technology in the treatment of cement-based materials and sequestration[END_REF], except for cases of high relative humidity (HR>95%), small particle size (nanometric scale) and nature of sorbent [START_REF] Zeman | Effect of steam hydration on performance of lime sorbent for CO 2 capture[END_REF][START_REF] Seo | Effects of water vapour pretreatment time and reaction temperature on CO 2 capture characteristics of a sodium-based solid sorbent in a bubbling fluidized-bed reactor[END_REF][START_REF] Dheilly | Influence of storage conditions on the carbonation of powdered Ca(OH) 2[END_REF]. The formation of a protective carbonate layer leads to a physical increase in volume at the grain scale (expansion or swelling process) or a decrease in porosity (pore closure process) when porous materials are partially carbonated [START_REF] Sun | A discrete-pore-size-distribution-based gas-solid model and its application to the CaO + CO 2 reaction[END_REF][START_REF] Chen | Effects of porosity on carbonation and hydration resistance of CaO materials[END_REF][START_REF] Fernandez Bertos | A review of accelerated carbonation technology in the treatment of cement-based materials and sequestration[END_REF]. With respect to the reaction kinetics, gas-solid carbonation can be catalyzed by water activity (or relative humidity) at moderate temperature (<60 °C) and low CO 2 pressure (<2bar) [START_REF] Beruto | Liquid-like H 2 O adsorption layers to catalyse the Ca(OH) 2 /CO 2 solid-gas reaction and to form a non-protective solid product layer at 20°C[END_REF]; low water activity (<0.4) ultimately inhibits the reaction (Montes-Hernandez et al., 2010;[START_REF] Rao | Sonochemical treatment of FBC ash: A study of the reaction mechanism and performance of synthetic sorbents[END_REF]. From a mechanistic standpoint, this means that the molecular water adsorbed on hydrophilic and basic surface sites allows carbonate ion formation at the gas-solid interface followed by the formation of solid carbonate around reacting particles. Conversely, for dry gas-solid carbonation (i.e., in the absence of adsorbed water on reacting particles (water activity 1 0)), a high temperature (>120 °C) and a preferentially low CO 2 pressure (<1 bar) are required (Montes-Hernandez et al., 2010). In this case, the optimized reaction temperature depends directly on the textural properties (e.g., particle size, porosity) and chemical nature of absorbent [START_REF] Zevenhoven | Heat optimisation of staged gas-solid mineral carbonation process for long-term CO 2 storage[END_REF][START_REF] Wang | Carbonation of fly ash in oxy-fuel CFB combustion[END_REF][START_REF] Fernandez Bertos | A review of accelerated carbonation technology in the treatment of cement-based materials and sequestration[END_REF]. Note that the reaction mechanism for dry gas-solid carbonation;

i.e., when molecular water action is negligible (water activity 1 0), is still a debated question.

The gas-solid carbonation has generally been studied at the laboratory scale by using small reactors coupled with thermogravimetric and/or chromatographic measurements [START_REF] Blamey | Reactivation of CaO-based sorbents for CO 2 capture: Mechanism for the carbonation of Ca(OH) 2[END_REF][START_REF] Prigiobbe | Gas-solid carbonation kinetics of air pollution control residues for CO 2 storage[END_REF][START_REF] Regnault | Experimental measurement of portlandite carbonation kinetics with supercritical CO 2[END_REF]. Conversely, at pilot plant scale, fluidised bed reactors are usually proposed to perform solid-gas carbonation [START_REF] Reddy | Simultaneous capture and mineralization of coal combustion flue gas carbon dioxide (CO 2 )[END_REF][START_REF] Huntzinger | Carbon dioxide sequestration in cement kiln dust through mineral carbonation[END_REF]. As previously mentioned, solid-gas carbonation reactions are generally incomplete (<80%) for both cases due to the formation of a protective carbonate layer around the reacting particles. Concerning the gas-solid carbonation of Ca(OH) 2 particles, the high relative humidity, the CO 2 pressure and the high temperature (under non-isothermal conditions) can play a crucial role to enable solid-gas carbonation of Ca(OH) 2 particles to be completed. For example, [START_REF] Beruto | Liquid-like H 2 O adsorption layers to catalyse the Ca(OH) 2 /CO 2 solid-gas reaction and to form a non-protective solid product layer at 20°C[END_REF] clearly demonstrated that an increase in relative humidity catalyzes gas-solid carbonation and increases carbonation efficiency up to 85% at a constant low temperature (120°C) and low CO 2 pressure (16.5 mbar). These authors claim that the CO 2 pressure (<1bar) has a negligible effect on the carbonation process at any relative humidity (<90%). This assumption was later supported by [START_REF] Dheilly | Influence of storage conditions on the carbonation of powdered Ca(OH) 2[END_REF]. Their study showed that, under certain conditions (atmosphere with low level of CO 2 , high relative humidity (RH=100%) and low temperature (T=10°C)), the carbonation extent is approximately 93% after 10 days. It reaches 100% after 25 days with a wet hydroxide. Recently, it was demonstrated that Ca(OH) 2 nanoparticles can be completely transformed into nanosized calcite (<100 nm) via gas-solid carbonation under moderate CO 2 pressure (<40 bar) and low temperature (<60°C). For this case, the mineralization of CO 2 does not form the protective carbonate layer around the reacting particles of Ca(OH) 2 . As a result, the gas-solid carbonation of Ca(OH) 2 was more efficient in producing nanosized calcite with high potential for industrial applications (e.g., fillers in the papermaking industry and printing inks, antacid tablets, adsorbents, etc.) [START_REF] Montes-Hernandez | Linear Growth rate of nanosized calcite synthesized via gas-solid carbonation of Ca(OH) 2 particles in a static bed reactor[END_REF]Montes-Hernandez et al., 2010). The steam hydration of CaO is typically used to reactivate its performance as a sorbent in calcium looping applications. In this context, [START_REF] Materic | High temperature carbonation of Ca(OH) 2[END_REF] reported that the gas-solid carbonation extent was found to be higher when Ca(OH) 2 is directly carbonated at high temperature compared to gas-solid carbonation of CaO, i.e., after Ca(OH) 2 dehydration. This relevant insight has also been studied in more detail by [START_REF] Blamey | Reactivation of CaO-based sorbents for CO 2 capture: Mechanism for the carbonation of Ca(OH) 2[END_REF]. They investigated the gas-solid carbonation of powder and pellets of Ca(OH) 2 and hydrated calcined limestone and dolomite using a thermogravimetric analyzer coupled to a mass spectrometer performing online gas analysis of the off-gas.

This study has a two-fold objective: firstly, quantify the gas-solid carbonation extent and carbonation kinetics of Ca(OH) 2 and CaO, and secondly, propose a reaction mechanism of gassolid carbonation for CaO under dry conditions (relative humidity close to 0), i.e., when the molecular water action is negligible. All carbonation experiments under non-isothermal or isothermal conditions were carried out in a thermogravimetric analyzer where high-purity CO 2 was injected (flow rate=50mL/minute). For non-isothermal conditions in particular, three heating rates (5, 10 and 20K/min) were investigated for Ca(OH) 2 and a single rate of 10K/min for CaO.

For classic thermogravimetric (TG) analyses and purging steps, 100% N 2 was used in the system.

Materials and methods

Starting reactants

Synthetic portlandite or powdered calcium hydroxide (Ca(OH) 2 ) Portlandite material or calcium hydroxide Ca(OH) 2 was provided by Sigma-Aldrich with 96% chemical purity, with about 3% of CaCO 3 and 1% of other impurities. The portlandite material is characterized by platy nanoparticles (sheet forms) forming micrometric aggregates with high porosity and/or high specific surface area (16 m 2 /g). The average particle size of 31nm was deduced from Rietveld refinement of XRD patterns (see Montes-Hernandez et al., 2010 and[START_REF] Montes-Hernandez | Linear Growth rate of nanosized calcite synthesized via gas-solid carbonation of Ca(OH) 2 particles in a static bed reactor[END_REF]. For the carbonation experiments, the portlandite was used without any physico-chemical treatment.

Carbon dioxide (CO 2 )

Carbon dioxide CO 2 was provided by Linde Gas S. A. with 99.995% chemical purity. This gas was directly injected at a rate of 50mL/min in the themogravimetric analyzer (small-reaction cell) without any treatment and/or purification.

Gas-solid carbonation experiments under non-isothermal conditions

All carbonation experiments under non-isothermal conditions were performed with a TGA/SDTA 851 e Mettler Toledo instrument under the following conditions: sample mass of about 10 mg, alumina crucible of 150 µl with a pinhole, heating rate of 10°C min -1 , temperature range from 30 (303K) to 1200°C (1473K) and 100% CO 2 atmosphere of 50 mL min -1 . Experiments with additional heating rates of 5 and 20°C/min were performed for carbonation of Ca(OH) 2 particles. Sample mass gain/loss and associated thermal effects were obtained by TGA/SDTA. In order to identify the different mass gain/loss steps, the TGA first derivative (mass gain/loss rate) was used. The TGA apparatus was calibrated in terms of mass and temperature. Calcium oxalate was used for the sample mass calibration. The melting points of three compounds (indium, aluminium and copper) obtained from the DTA signals were used for the sample temperature calibration.

A2

Note that the CaO particles were directly synthesized in the TG analyzer prior to the carbonation experiment as follows: (1) dehydration of Ca(OH) 2 particles from 30 to 900°C under 100% N 2 atmosphere, (2) cooling step from 900 to 30°C under 100% N 2 atmosphere and (3) carbonation experiment as explained above.

Gas-solid carbonation experiments under isothermal conditions

Experiments at six different temperatures (200, 300, 350, 400, 500, 600°C) were performed to carbonate the Ca(OH) 2 in the thermogravimetric analyzer. About 3 minutes were necessary to reach the reaction temperature and the flow of CO 2 was kept constant at 50 mL min -1 in all experiments. Note that 500 and 600°C are critical temperatures because the Ca(OH) 2 particles are dehydroxylated in this temperature range. The in-situ synthesized CaO was carbonated at 300, 600 and 800°C. The in-situ synthesis of CaO was carried out as follows: (1) dehydration of Ca(OH) 2 particles from 30 to 900°C under 100% N 2 atmosphere, (2) cooling step from 900 to investigated temperature under 100% N 2 atmosphere and (3) isothermal carbonation of CaO at investigated temperature (300, 600 and 800°C).

Results and discussion

The original results on dry gas-solid carbonation (relative humidity 1 0) of Ca(OH) 2 and CaO under non-isothermal and isothermal conditions are given below. Exclusively nanosized particles (<100 nm) of Ca(OH) 2 were used in the experiments. Moreover, an alternative reaction mechanism is proposed for gas-solid carbonation of Ca(OH) 2 at high temperature under dry conditions, i.e., when the relative humidity is close to zero (RH10). This reaction mechanism was supported by the dry gas-solid carbonation of CaO particles synthesized in-situ by complete 1B2 dehydration of Ca(OH) 2 from 30 to 900°C under N 2 atmosphere in the TG analyzer as described in Materials and Methods section.

3.1. Gas-solid carbonation of Ca(OH) 2 nanoparticles under non-isothermal conditions Figure 1 shows the gas-solid carbonation of Ca(OH) 2 nanoparticles under non-isothermal conditions at two different heating rates (5 and 10K/min). In both cases, a high carbonation extent (ξ=0.94) was obtained according to TG curves. Moreover, based on the 1 st derivative curves (DTG) for the three heating rates, it may be concluded that the level of carbonation detected from 300 to about 550K was insignificant. In this temperature range, the initial adsorbed water (slight amount 1-2%) was preferentially removed, indicating low or negative stability of molecular water on the Ca(OH) 2 surface when the temperature increased (drying process under 100% CO 2 ).

Concerning the carbonation process, a first step of slight carbonation was suspected in a reduced temperature range (from 550 to about 590K) followed by a second step of significant carbonation which takes place in a broad temperature range until an apparent equilibrium is reached (from 590 to about 900K) (see Fig. 1). This second carbonation step presents a sigmoidal thermokinetic behavior pattern as attested by a simple fitting of experimental curves. This gas-solid carbonation of Ca(OH) 2 nanoparticles can be expressed by the following general chemical reaction:

) ( 2 ) ( 3 ) ( 2 ) ( 2 ) ( g s g s O H CaCO CO OH Ca + → + (1)
Under dry conditions, i.e., when relative humidity (RH) is close to 0 in the system, it was assumed that the molecular water produced from reaction (1) was simultaneously expelled with respected to the formed carbonate from reaction 1. In other words, the molecular water produced during carbonation is not stable in the carbonate-hydroxide interfaces and/or pores. This assumption is valid for small Ca(OH) 2 particles (<30µm) as recently demonstrated by [START_REF] Blamey | Reactivation of CaO-based sorbents for CO 2 capture: Mechanism for the carbonation of Ca(OH) 2[END_REF]. However, another hypothesis was recently suggested by [START_REF] Materic | Ca(OH) 2 superheating as a low-attrition steam reactivation method for CaO in calcium looping applications[END_REF]2011), who claimed that Ca(OH) 2 particles present a higher thermal stability under a CO 2 -rich atmosphere (termed by authors "superheated dehydration"), which prevents significant conversion to CaCO 3 . Conversely, [START_REF] Blamey | Reactivation of CaO-based sorbents for CO 2 capture: Mechanism for the carbonation of Ca(OH) 2[END_REF] have clearly demonstrated that the socalled superheated dehydration is absent for fine Ca(OH) 2 ) particles (<30 µm).

Various calculations were performed in order to estimate the activation energy for this gas-solid carbonation process (sigmoidal thermokinetic process in Fig. 1) by using a simple relation, originally proposed by [START_REF] Augis | Calculations of the Avrami parameters for heterogeneous solid state reaction using a medication of the Kissinger[END_REF] in order to calculate conveniently the kinetic exponent m for the Johnson-Mehl-Avrami (JMA) model. In our study, the Augis and Bennett relation was used to calculate directly the activation energy (E a ) as follows:

) ( ) ( 5 . 2 2 max FWHM m T R E a = (2)
where T max is the maximum of the DTG peak related to sigmoidal thermokinetic behavior (see Fig. 1), FWHM is the full width at half maximum of the DTG peak, m is a kinetic exponent and R is the ideal gas constant (8.3144621J/molK). T max and FWHM parameters were determined by using a classic Gaussian model; m was determined from the ξ vs. t experimental curve using the JMA model. All parameters and calculated activation energies for non-isothermal gas-solid carbonation of Ca(OH) 2 nanoparticles at three different heating rates are summarized in Table 1.

A low activation energy (from 5.9 to 11.6 kJ/mol) is required to start the main carbonation step of Ca(OH) 2 particles at the three heating rates investigated. These estimated values are in agreement with the values reported by [START_REF] Nikulshina | Kinetic analysis of the carbonation reactions for capture of CO 2 from air via Ca(OH) 2 -CaCO 3 -CaO solar thermochemical cycle[END_REF]. In our study, a similar activation energy (about 6 kJ/mol) was determined in the experiments with 5 and 10 K/min heating rates.

Conversely, a higher activation energy (about 12 kJ/mol) was determined at the 20 K/min rate.

Based on these results, 10 K/min was considered as the optimized heating rate in our experiments.

As expected, the calcium carbonate (CaCO 3 ) formed in-situ from reaction (1) remains stable at higher temperature under a 100% CO 2 atmosphere compared with the pure calcium carbonate (calcite) decomposed under inert 100% N 2 atmosphere (see Fig. 2). This was probably due to a simultaneous decarbonation-carbonation process at high temperature before a classic and complete decarbonation reaction (

) ( 2 ) ( ) ( 3 g s s CO CaO CaCO + →
). In our study, the gas-solid carbonation of Ca(OH) 2 followed by the respective decarbonation of the carbonate formed (carbonation-calcination cycle under 100% CO 2 ) confirmed a complete carbonation process (ξ close to 1) through a simple mass balance. This means that the initial Ca(OH) 2 reactant was slightly carbonated (>3%); and the mineralization of CO 2 did not form a protective carbonate layer around the reacting particles of Ca(OH) 2 as typically described in the literature (e.g., [START_REF] Sun | A discrete-pore-size-distribution-based gas-solid model and its application to the CaO + CO 2 reaction[END_REF][START_REF] Chen | Effects of porosity on carbonation and hydration resistance of CaO materials[END_REF][START_REF] Fernandez Bertos | A review of accelerated carbonation technology in the treatment of cement-based materials and sequestration[END_REF]. For this reason, the gas-solid carbonation of Ca(OH) 2 in Fig. 2 was normalized to 100%.

Gas-solid carbonation of Ca(OH) 2 nanoparticles under isothermal conditions

Our results clearly show that complete gas-solid carbonation of Ca(OH) 2 nanoparticles is never achieved under isothermal conditions for any of the investigated temperatures (200, 300, 350, 400, 500 and 600°C) (see Fig. 3). It would appear that 400°C is the optimized temperature, but the carbonation extent (ξ iso ) at this temperature reaches an apparent equilibrium value of only about 0.57 (w/w) (see Table 2). No gas-solid carbonation of Ca(OH) 2 was detected at 200°C.

Only a small carbonation extent (ξ iso =0.10w/w) and a moderate extent (ξ iso =0.39w/w) were determined at 300 and 350°C, respectively. This is in agreement with the formation of a dense non-porous layer of carbonate mineral around the core of the reacting Ca(OH) 2 particles, leading to a passivation process as the intra-particle diffusion of CO 2 through the core of reacting particles is blocked, as explained in several studies (e.g., Montes-Hernandez et al., 2010;[START_REF] Stendardo | Carbon dioxide capture with dolomite: A model for gas-solid reaction within the grains of a particulate sorbent[END_REF][START_REF] Sun | A discrete-pore-size-distribution-based gas-solid model and its application to the CaO + CO 2 reaction[END_REF][START_REF] Fernandez Bertos | A review of accelerated carbonation technology in the treatment of cement-based materials and sequestration[END_REF]. Interpretation of the gas-solid carbonation at 500 and 600°C is more complex. For these cases, there may be competition between Ca(OH) 2 dehydroxylation and gas-solid carbonation of CaO and Ca(OH) 2 .

For the sake of simplicity, the values of carbonation extent at 500 and 600°C reported in Fig. 3 were normalized with the initial weight of Ca(OH) 2 .

The experimental curves shown in Fig. 3 were fitted using a kinetic pseudo-second-order model.

This model implies a fast carbonation step followed by a slow carbonation step. The latter was interpreted as a passivation step in our study. The integrated form of this kinetic model is given by the following hyperbolic equation:

t t t iso iso + = 2 / 1 max , ξ ξ (3)
where iso ξ is the carbonation extent as a function of time t under isothermal conditions, max , iso ξ is the maximum value of carbonation extent at apparent equilibrium and 2 / 1 t is the half-carbonation time, i.e., the time taken to achieve half the maximum value of carbonation extent. A non-linear regression by the least-squares method was performed to determine these kinetic parameters for each carbonation temperature. All values, including correlation factors and initial gas-solid carbonation rates (

2 / 1 max , 0 / t v iso ξ =
) are summarized in Table 2. Arrhenius law (linear form) is frequently used to determine the apparent activation energy and frequency factor for isothermal processes. In our study, the carbonation temperatures 300, 350 and 400°C revealed poor Arrhenius-type dependency (values not reported).

A simple comparison between non-isothermal and isothermal gas-solid carbonation of Ca(OH) 2

shows clearly that non-isothermal carbonation is faster and the reaction is complete (2 close to 1) (see also Figure 4). In other words, for isothermal carbonation, a non-porous carbonate layer is assumed to form around the reacting particles as typically described in the literature (e.g., [START_REF] Sun | A discrete-pore-size-distribution-based gas-solid model and its application to the CaO + CO 2 reaction[END_REF][START_REF] Chen | Effects of porosity on carbonation and hydration resistance of CaO materials[END_REF][START_REF] Fernandez Bertos | A review of accelerated carbonation technology in the treatment of cement-based materials and sequestration[END_REF] while for non-isothermal carbonation, continuous Ca(OH) 2 -CaCO 3 transformation takes place until completion of the reaction as shown by the decarbonation curves in Fig. 2.

3.3. Gas-solid carbonation of CaO vs. gas-solid carbonation of Ca(OH) 2 : non-isothermal conditions As shown in Figure 5(a), the CaO particles were synthesized in-situ by dehydroxylation of Ca(OH) 2 from 30 to 900°C under 100% N 2 atmosphere followed by simple cooling of the CaO particles from 900 to 30°C also under 100% N 2 atmosphere. Finally, the dry gas-solid carbonation of CaO with pure CO 2 (100% CO 2 atmosphere of 50mL/min) was carried out using a heating rate of 10°C/min. The dry gas-solid carbonation of CaO particles takes place in a broad temperature range (from 100 to 900°C) and three main carbonation regimes or steps were qualitatively identified by plotting the first derivative curve (DTG) (see Fig. 5b). These carbonation steps were arbitrarily defined as slight, moderate and significant depending on the carbonation extent reached as a function of temperature. Unfortunately, the moderate and significant carbonation steps clearly overlapped, complicating the characterization of their peak values. For this reason, the relation ( 2) previously used to determine the activation energy of Ca(OH) 2 carbonation, was not directly applicable to CaO carbonation. On the other hand, a high carbonation extent was reached (ξ CaO =0.92) at the apparent equilibrium. Technically, this value was similar to the carbonation extent obtained for Ca(OH) 2 (ξ=0.94) (see Fig. 6). Conversely, the gas-solid carbonation of CaO takes place in a broader temperature range, implying more complex thermokinetic behavior (overlapping of carbonation regimes). Based on these results, it is assumed that the simultaneous expelling of produced molecular water during gas-solid carbonation of Ca(OH) 2 (reaction 1) could significantly enhance CO 2 transfer from the gas phase towards unreacted Ca(OH) 2 surfaces. In this way, micro-cracking produced by fast expelling of water vapor is suspected. Note that the fast and simultaneous expelling of produced molecular water during Ca(OH) 2 carbonation indicates that the CO 2 aqueous speciation at the CaCO 3 -Ca(OH) 2 interfaces will be zero and/or insignificant at high temperature (>300°C) and preferential for small Ca(OH) 2 particles (<30µm). This assumption is in agreement with recent results reported by [START_REF] Blamey | Reactivation of CaO-based sorbents for CO 2 capture: Mechanism for the carbonation of Ca(OH) 2[END_REF].

Dry gas-solid carbonation of CaO particles under isothermal conditions

The CaO particles were synthesized in-situ by dehydroxylation of Ca(OH) 2 from 30 to 900°C under 100% N 2 atmosphere followed by simple cooling of CaO particles from 900 to 800°C also under 100% N 2 atmosphere (similar to Fig. 5(a)). Finally, dry gas-solid carbonation of CaO with pure CO 2 (100% CO 2 atmosphere of 50mL/min) was carried out at constant temperature (300, 600 or 800°C). A very low carbonation extent was found at 300°C (<0.1) and similar highcarbonation extents were found at 600°C and 800°C. High temperature (>600°C) promotes a high-carbonation extent, probably due to the fact that this temperature is close to the decarbonation temperature of the actual carbonate formed (see Fig. 2). Concerning the gas-solid carbonation of CaO particles at 800°C, a small was found between two independent carbonation experiments after 4 to 6 hours of carbonation reaction. This small difference can only be related to the initial weight (not strictly controlled) (see Fig. 7). In this case, a high carbonation extent (ξ iso-CaO =0.91) was reached after 6 h of reaction, but the apparent equilibrium had still not been reached. A kinetic model can be used to predict the apparent equilibrium with respect to the maximum value of carbonation extent. A simple non-linear regression using eq. 3

(kinetic pseudo-second-order model) does not provide sufficient correlation with experimental kinetic data. For this reason, the kinetic experimental data were fitted using a kinetic doublepseudo-second-order model. This model assumes two kinetic regimes due to the presence of two types of reactive surface sites. Its integrated form is given by the following hyperbolic equation:

t t t t t t b b a a CaO iso CaO iso CaO iso + + + = - - - 2 / 1 max , 2 / 1 max , ) ( ) ( ξ ξ ξ (4)
where CaO iso-ξ is the carbonation extent as a function of time t under isothermal conditions,

=

).

As reported in Fig. 3, the highest gas-solid carbonation extent (about 0.57) was obtained for Ca(OH) 2 at 400°C. This value is significantly lower than the carbonation extent (0.91) obtained from gas-solid carbonation of synthesized CaO at 800°C, with a carbonation reaction duration of 6 h for both cases (see Fig. 8). The kinetic behavior was also found to differ for each case with a single kinetic pseudo-second-order model for the gas-solid carbonation of Ca(OH) 2 (one type of reactive surface site) and a double kinetic pseudo-second-order model for the gas-solid carbonation of CaO (two types of reactive surface site).

3.5. Reaction mechanism for dry gas-solid carbonation of Ca(OH) 2 and CaO

The reaction mechanism for carbonation of Ca(OH) 2 with a relative humidity (RH) > 0 has been successfully explained, assuming CO 2 dissociation in molecular water at the reacting interfaces (e.g., Montes-Hernandez et al., 2010;[START_REF] Beruto | Liquid-like H 2 O adsorption layers to catalyse the Ca(OH) 2 /CO 2 solid-gas reaction and to form a non-protective solid product layer at 20°C[END_REF]. However, the gas-solid carbonation reaction of Ca(OH) 2 at low temperature (30°C) and low CO 2 pressure (<2bar) was inhibited at RH10 (Montes-Hernandez et al., 2010). The dry gas-solid carbonation of Ca(OH) 2 can be reactivated at high temperature (>200°C). As mentioned above, the molecular water produced during the carbonation reaction of Ca(OH) 2 is not stable or is insignificantly stable on the reaction interfaces at high temperature, specially for small particles (<30µm). This implies fast and simultaneous expelling of the molecular water produced. Based on these arguments, an alternative reaction mechanism is proposed for the gas-solid carbonation of Ca(OH) 2 , when RH10. In this alternative, it is assumed that atomic excitation at high temperature allows the local migration of one oxygen atom from the solid towards the adsorbed CO 2 leading to its mineralization into carbonate (porous or non-porous layer) around the reacting particles;

chemically the mineralization of CO 2 also implies the breaking of one covalent bond in the CO 2 molecule. This simple reaction mechanism is also valid and clearly convincing for dry gas-solid carbonation (RH10) of CaO particles because it does not involve the production of molecular water during the carbonation process.

) ( 3 ) ( 2 ) ( s g s CaCO CO CaO → + (5)
The formation of complex carbonate ions (e.g. unidentate or bidentate carbonate) via chemisorption process is not excluded during carbonation process at high temperature as early proposed by [START_REF] Busca | Infrared Spectroscopic identification of species arising from reactive adsorption of carbon oxides on metal oxide surfaces[END_REF] and [START_REF] Beruto | Thermodynamics and kinetics of carbon dioxide chemisorption on calcium oxide[END_REF].

Conclusion

In the present study, basic research was carried out to provide complementary insights into the gas-solid carbonation of Ca(OH) 2 and in-situ synthesized CaO under non-isothermal and isothermal conditions. All carbonation experiments were carried out in a thermogravimetric analyzer. The results revealed that Ca(OH) 2 -to-CaCO 3 and CaO-to-CaCO 3 solid state transformations are quasi-complete reactions under non-isothermal conditions when nanosized 1A2 reacting particles are used. This means that CO 2 mineralization does lead to the formation of a protective carbonate layer around the reacting particles of Ca(OH) 2 and CaO. However, the formation of a protective carbonate layer around the reacting particles explains the incomplete carbonation under isothermal conditions, particularly for Ca(OH) 2 .

Based on this experimental study, an alternative reaction mechanism is also proposed for the gas-solid carbonation of Ca(OH) 2 , when the relative humidity is close to 0. In this alternative, it is assumed that the molecular water produced during the carbonation reaction of Ca(OH) 2 is not stable or is insignificantly stable on the reacting interfaces at high temperature, especially for small particles (<30µm). This implies fast and simultaneous expelling of the molecular water produced. On the basis of these arguments it may be assumed that atomic excitation at high temperature allows the local migration of one oxygen atom from the solid towards the adsorbed CO 2 leading to its mineralization into carbonate (porous or non-porous layer) around the reacting particles. From a chemical standpoint, the mineralization of CO 2 also implies the breaking of one covalent bond in the CO 2 molecule. This simple reaction mechanism is also valid and clearly convincing for dry gas-solid carbonation (relative humidity10) of CaO particles because it does not involve the production of molecular water during the carbonation process. : gas-solid carbonation rate.

Figure 1. Gas-solid carbonation of Ca(OH) 2 nanoparticles under non-isothermal conditions at two different heating rates (5 and 10 °K/min). Carbonation extent (ξ) was determined from thermogravimetric (TG) curves and differential thermogravimetric (DTG) curves were used to identify the carbonation steps and determine the activation energy (see Eq. 2 and Table 1).

Figure 2. Calcite decomposition (decarbonation) under 100% N 2 atmosphere compared with decarbonation of calcium carbonate under 100% CO 2 atmosphere. The latter was formed in-situ from the gas-solid carbonation of Ca(OH) 2 . The gas-solid carbonation of Ca(OH) 2 (dashed curve)

was normalized to 100% in weight based on the decarbonation balance for the carbonate formed.

  -carbonation times, i.e., the time taken to achieve half of the maximum value of carbonation extent for each kinetic regime. A nonlinear regression by the least-squares method was performed to determine these kinetic parameters for each carbonation temperature. All values, including estimated errors are reached at apparent equilibrium is similar to the CaO carbonation extent obtained under non-isothermal conditions. Moreover, two kinetic regimes were clearly identified, the first kinetic regime takes only a couple of minutes (

3A2

Figure 3 .4B2Figure 4 .

 34 Figure 3. Gas-solid carbonation of Ca(OH) 2 under isothermal conditions for six different reaction

Figure 5 .

 5 Figure 5. (a) In-situ synthesis and dry gas-solid carbonation of CaO particles under nonisothermal conditions at constant heating rate (10°C/min). (b) Carbonation extent (ξ CaO ) was determined from thermogravimetric (TG) curve and differential thermogravimetric (DTG) curves were used for qualitative identification of the carbonation steps.

Figure 7 .

 7 Figure 7. Gas-solid carbonation of in-situ synthesized CaO under isothermal conditions (800°C)

Table 1 .

 1 Summary of thermokinetic parameters for non-isothermal gas-solid carbonation of Ca(OH) 2 nanoparticles at three different constant heating rates.

		Gaussian model		JMA model	Augis and Bennett
		1 st derivative vs. T		ξ ξ ξ ξ vs. t		relation
	H. rate	a intensity	σ	T max	FWHM	k A	m	E a =	( 5 . 2 FWHM ) ( max m T R	) 2
	°K/min	1/s	°K	°K	2.3548σ	1/s
	5	1.92x10 -4	51.98	703.33	122.40	1.1456x10 -4	14.2	5.9159 kJ/mol
	10	3.64x10 -4	54.16	712.66	127.53	2.2545x10 -4	13.9	5.955 kJ/mol
	20	7.00x10 -4	59.54	722.13	140.20	7.0912x10 -4	6.67	11.5912 kJ/mol

T: Temperature; 1 st derivative: first derivative on TG curve: ξ: fractional carbonation extent; t: time; JMA: Johnson-Mehl-Avrami; H.: heating; σ: standard deviation; a intensity : intensity of peak; T max : maximum value of peak; FWHM: full width at half maximum value of peak; k A : kinetic constant; m: kinetic exponent; E a : activation energy.

Table 2 .

 2 Summary of kinetic parameters for isothermal gas-solid carbonation of Ca(OH) 2 nanoparticles at six different temperatures.

		Kinetic pseudo-second-order model:
			ξ ξ ξ ξ iso vs. t
	T (°C)	ξ ξ ξ ξ iso,max	t 1/2 (s)							R	v 0 (1/s)
	200		Carbonation was not detected by TG
	300	0.1050±1x10 -4	3093±14							0.98	3.3947x10 -5
	350	0.3948±7x10 -4	7169±32							0.99	5.5070x10 -5
	400	0.5727±5x10 -4	2508±10							0.99	2.2834x10 -4
	500	0.0780±6.85x10 -5	115±3							0.80	6.7826x10 -4
	600	0.1318±5.13x10 -5	793±35							0.99	1.6620x10 -4
			ξ	iso	,	max	: maximum value of carbonation extent at
	apparent equilibrium; 2 / 1 t : the half-carbonation time;	0 v	=	ξ	iso	,	max	1 / t	/	2

iso ξ : carbonation extent as a function of time t ;

Acknowledgements

The authors are grateful to the French National Center for Scientific Research (CNRS) and the University Joseph Fourier in Grenoble for providing financial support.