Density functional theory study on the thermodynamics and mechanism of carbon dioxide capture by CaO and CaO regeneration

Abstract

Reducing CO₂ emission is one of the most important events to solve the global climate problem. The carbonation reaction of CaO and the reverse reaction are potential methods for CO₂ capture and concentration from dilute flue gases at high temperature. In this paper, the thermodynamics and mechanisms of CO₂ capture by CaO and CaO regeneration from CaCO₃ were studied and identified in the framework of density functional theory (DFT). In the calculation, the exchange-correlation term was approximated by Perdew–Wang (PW91), a function within the generalized gradient approximation (GGA) family. The reaction energies of carbonation reaction and calcination reaction were calculated to be −147.64 kJ mol⁻¹ and 180.60 kJ mol⁻¹, respectively. To study the reaction between CO₂ and CaO, the transition states of carbonation and calcination were also analyzed. The results showed that the carbonation of CaO was rather fast, and the activation energy of carbonation reaction was 0 kJ mol⁻¹, which indicated that the reaction process was not the rate-determining step during the process of CO₂ capture. The regeneration of CaO by CaCO₃ calcination occurred at higher temperature, with the activation energy of 166.85 kJ mol⁻¹, and the rate of calcination was controlled by the chemical reaction.

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1. Introduction

Anthropogenic carbon dioxide (CO₂) emission is a major contributor to the greenhouse effect that causes global warming, which is now recognized to be a major risk to mankind.¹ Power generation combustion systems are responsible for one-third of anthropogenic CO₂ emission, and coal is known to release larger amounts of CO₂ per unit power generation than oil or natural gas. Reduction of anthropogenic CO₂ emission, especially from fossil combustion, is urgently required to solve climate problems. Many researchers have found unique approaches to deal with CO₂, i.e. activation of CO₂, chemical transformation of CO₂,² adsorption of CO₂,³ etc., where CO₂ can be used efficiently, such as synthesizing hydrocarbons from CO₂ and water,⁴ reacting CO₂ in a simulated Martian atmosphere with H₂ into a rocket propellant,⁵ or electrochemically splitting the CO₂ molecules from Mars' atmosphere into O₂ and CO for exploration of Mars,⁶ and so on. A favorable approach for reducing such CO₂ emission is to capture CO₂ from dilute gas mixtures (flue gas), then produce a concentrated stream. After the CO₂ has been purified and compressed, it can be transported and stored in deep rocks or possibly in deep oceans.⁷

CO₂ separation from dilute gas is the first and most energy intensive step, and many efforts have been devoted to developing new methods for CO₂ capture and separation. Current CO₂ capture technologies mainly include solid sorbent absorption, liquid solvent absorption, membrane separation, distillation of a liquefied gas stream and refrigerated separation.^8,9 Processes utilizing simple sorbents, e.g., limestone or dolomite, have significant advantages given the relatively low cost, abundance, and availability of these materials. Ca-based sorbents can be used for CO₂ capture,¹⁰ whose application in fluidized bed conversion systems has received increasing attention recently.^11–14

CO₂ can be separated through a multicycle process via the carbonation reaction of CaO with the CO₂ from flue gas and then the regeneration of the sorbent CaO through CaCO₃ calcination reaction in a fluidized bed, as illustrated in Fig. 1.¹⁴ The background of this method dates back to 1967, when DuMotay and Marechal first patented the use of lime to aid the gasification of carbon by steam.¹⁵ This process consists of two fluidized bed reactors, carbonator and calciner, which are connected by solid transport pipes. After reaction, CO₂-clean flue gas exiting in the carbonator is released to the atmosphere, while the product CaCO₃ is transported to the calciner to regenerate CaO and produce pure CO₂ stream. The regenerated CaO is then transported back to the carbonator for cycle use, while the CO₂ released from the regenerator is concentrated enough to be purified, compressed, and stored.

Fig. 1 CaO carbonation–calcination cycle to capture CO₂.

The process proposed above happens at high temperature, and the reversible chemical reactions^16,17 are expressed as eqn (1) and (2).

T between 650 °C and 850 °C, depending on pressure, ΔH⁰_{1023 K} = −168.5 kJ mol⁻¹, ΔH⁰_{298 K} = −178 kJ mol⁻¹T > 900 °C, depending on pressure, ΔH⁰_{298 K} = 178 kJ mol⁻¹.

The CO₂ capture efficiency could achieve 95% for this method.¹⁶ The carbonation reaction is exothermic, while the reverse one is endothermic, so the energy can be efficiently used in a steam cycle.¹⁸

The carbonation reaction is a typical gas–solid reaction with the formation of a solid product. The reaction involves two quite different stages: a fast one taking minutes at first, kinetically controlled, and a slow stage, controlled by diffusion through the layer formed, which lasts hours to days.¹⁹ Based on the nature of the reaction, it seems that a pure chemical reaction controlling regime is very short and can be neglected without much error in the mathematical modeling.²⁰

For calcination reaction, three possible rate-limiting processes have been proposed: (1) heat transfer through the particle to the reaction interface; (2) mass transfer of the CO₂ released from the reaction surface through the porous system, and (3) chemical reaction. However, mass transfer or chemical reaction has been considered as the rate-limiting process by most authors.²¹

To improve the design of carbonation–calcination fluidized bed and to increase CO₂ capture efficiency, it is imperative to make clear of the rate-controlling steps for both reactions. To reveal which roles the chemical reactions play in the carbonation/calcination processes, this work mainly focuses on the thermodynamics and mechanisms of CaO carbonation process and CaO regeneration process through density functional theory (DFT). It is difficult to model reaction mechanisms by experiments, however, theoretical calculation can do it efficiently on molecular or atomic level. The mechanisms of reductive decompositions of CaSO₄ by CO and CH₄ have been proposed through computer simulation, and the calculated activation energies were in good agreement with experimental values, which confirmed the validity of computer simulation and density functional theory (DFT).^22,23 DFT calculations can also provide a satisfied estimation of the relative stability of different surfaces and surface reactions,²⁴ especially with modern functions.²⁵ Here, the micro-processes, activation energies and reaction energies of the two reactions were analyzed through DFT calculation, to support the development of CO₂ capture concepts and to improve the design of the fluidized bed as outlined in Fig. 1.

2. Calculation

All the DFT calculations were carried out in Dmol³ module of Materials Studio 5.0. Nonlocal generalized gradient approximation (GGA)²⁶ function and Perdew–Wang²⁷ exchange-correlation function were selected. A basis set of numeric atomic functions which can provide precise solutions to the Kohn–Sham equations for the atoms were used in Dmol³. To obtain accurate results of stable structure, transition state (TS) and vibration frequency, ‘Fine’ precision with double numerical plus polarization (DNP) function basis sets were adopted for calculations in this paper. The threshold values for energy, gradient, displacement convergence and self-consistent-field (SCF) density convergence were 1 × 10⁻⁶ Ha, 0.002 Ha/Å, 0.005 Å and 1 × 10⁻⁶ Ha. To improve the SCF convergence efficiency during optimization, a small electron thermal smearing value of 0.005 Ha was employed.

The surface energy of CaO and CaCO₃ were calculated to select the reaction surface, the calculation process would be described in detail in section 3. As a result, the (100) and (110) surfaces were determined for CaO and CaCO₃, respectively. Here, (100) surface refers to the crystal face which is parallel to the yz plane and (110) refers to the crystal face parallel to the z crystal axis. To avoid the interactions between periodic images with the surface, a vacuum region of 15 Å was added above the surface. All the structures were first relaxed thoroughly before reaction calculations.

To search the transition state (TS), linear synchronous transit/quadratic synchronous transit (LST/QST) algorithm was used. First, the LST optimization was performed, doing an LST maximization, which followed by an energy minimization in directions conjugate to the reaction pathway, to yield a structure lower in energy and closer to the true TS, namely approximated TS. Secondly, QST maximization was performed on the approximated TS, with another conjugate gradient minimization performed. The cycle was repeated until a stationary point was located. Then the calculation of the activation energies for carbonation of CaO and calcination of CaCO₃ could be completed. All the optimized structures were considered to be stable with the only one imaginary frequency for TS structures.

The activation energy and reaction energy are defined as eqn (3) and (4) respectively:

E_a = E_TS − E_R (3)

E = E_P − E_R (4)

where E_R, E_TS and E_P are the energies of reactants, transition states and products, respectively. E_a is the activation energy of the reaction, while E is the reaction energy.

3. Results and discussion

Selection of function

In this situation, the DFT calculations were carried out with PW91 exchange-correlation function, which was proved to be able to obtain accurate results which are in good agreements with the experimental values.²²

Crystal parameters and surfaces

To test the adequacy of the basis set further, a series of calculations had been performed on crystal structures of CaO, CaCO₃ and CO₂ molecule with GGA/PW91/DNP. The calculated cell parameters of CaO were a = b = c = 4.8105 Å, and the error was 0.002%, compared with the experimental data 4.8106 Å.²⁸ The most commonly existence form of CaCO₃ in naturally-occurring minerals and industrial products is calcite.²⁹ The reaction of CaO and CO₂, as shown in eqn (1), always results in the formation CaCO₃ of calcite structure.³⁰ So the calcite structure for CaCO₃ was adopted in this calculation. The calculated cell parameters for CaCO₃ were a = b = 4.990 Å, c = 17.061 Å, while the experimental ones²⁸ were 4.989 Å and 17.062 Å respectively.

The optimization of isolated CO₂ molecule was performed in a large cubic box of 10 × 10 × 10 Å. The calculated bond length was 1.175 Å, while the experimental data was 1.162 Å.³¹ The calculated values of the bending frequency, symmetric stretching frequency, and asymmetric stretching frequency of CO₂ were 641 cm⁻¹, 1332 cm⁻¹, 2372 cm⁻¹ and the experimental values were 667 cm⁻¹, 1333 cm⁻¹, 2349 cm⁻¹, respectively. The good agreements between calculated results and the experimental data confirmed the validity of the present DFT calculations.

The CaO carbonation reaction and CaCO₃ calcination reaction can be described by the unreacted-core model, which is also known as the shrinking-core model, where the reactions occur on heterogeneous surface.^32,33 Hence, stable crystal surface which would be considered as reaction surface should be determined primarily. To compare the stability of various surfaces, the surface energy would be calculated first. For CaO and CaCO₃, E_surf is calculated through eqn (5):

E_surf = [E_slab − E_bulk]/2A (5)

E_slab refers to the total energy of the slab. The subscript slab refers to a two-dimensional structure created from the bulk, which is thick enough and has two surfaces. E_bulk is the energy for bulk CaO or CaCO₃ that has the same number of atoms with the slab, and A is the surface area.

The energy values of (100), (110), and (111) surfaces of CaO crystal were calculated. The results were 0.795 J m⁻², 1.419 J m⁻², and 1.659 J m⁻², respectively, so (100) surface was more stable and more easily obtained when CaO crystals were cleaved or in nature, being consistent with experimental data²⁸ and ab initio calculated results.³⁴ Meanwhile, the (110) surface of calcite crystal was calculated to be the most stable surface³⁵ by DFT calculation. Therefore, next calculations would be performed on the (100) surface for CaO and (110) surface for CaCO₃, respectively.

Carbonation of CaO with CO₂

In order to determine the initial site of CO₂ on the (100) surface of CaO crystal, the electron density of CaO, the frontier orbitals (including the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO)) of CO₂ and CaO were calculated, as shown in Fig. 2. The HOMO and LUMO of CO₂ were mainly reflected in O atom and C atom respectively, and the HOMO and LUMO of CaO were reflected in O and Ca. The gap of HOMO (CO₂)–LUMO (CaO) was 6.79 eV, and the gap of HOMO (CaO)–LUMO (CO₂) was 2.828 eV. It is more likely that CaO (HOMO) donates electrons to CO₂ (LUMO) rather than CO₂ (HOMO) to CaO (LUMO), resulting in the breaking of old Ca–O bond and the formation of new C–O bond. In other words, CO₂ will react with surface oxygen of CaO, as revealed by experimental methods.³⁶

Fig. 2 Total electron density and frontier orbitals of CaO and CO₂ (red ball: O atom, grey ball: C atom and green ball: Ca atom): (a) CO₂(LUMO) (b) CO₂(HOMO) (c) electron density (CaO) (d) CaO(LUMO) (e) CaO(HOMO).

To simulate the reaction, an unit cell of CaO with a vacuum region of 15 Å was first used as the reactant. Different reaction sites were tested for CO₂ on CaO (100) surface. Comparing the distances between C atom and three O atoms around it in the resulted structures with the central value of 1.29 Å of bulk carbonates,³⁷ it was concluded that only a carbonate-like structure was formed and the carbonation reaction would not occur no matter how long the initial distance of C_(CO2)–O_(CaO) (R₃) was. When R₃ was larger than 5.0 Å, no structural change would happen during geometry optimization. When R₃ was too short, a structure with a large imaginary frequency formed, in which R₃ was prolonged to 1.307 Å, and the bond lengths of CO₂ changed to 1.277 Å and 1.314 Å, respectively. Although the values were close to those of bulk carbonates, the atoms in the structure were disorder, as shown in Fig. 3(a), and the energy of the structure was too high. The conclusion was that a collapse of structure rather than a chemical reaction occurred. When R₃ was larger than 1.0 Å, the CO₂ molecule will be rejected or drown to keep R₃ about 1.49 Å, which was almost equal to the sum of covalent radius of C and O, as shown in Fig. 3(b). In addition, the C–O lengths of CO₂ molecule were about 1.24 Å, and the C–O–C angle of absorbed CO₂ was 134.87°. The long C_(CO2)–O_(CaO) separation and relatively small increase in C–O bond lengths over the calculated gas-phase value of 1.175 Å indicated that the CO₂ molecule physisorbed on the CaO (100) surface,³⁸ and the adsorption energy was calculated to be only −48.10 kJ mol⁻¹, which also confirmed the speculation. The electrons transfers were also calculated for comparison through Mulliken Population analysis, as shown in Fig. 4. The negative charge of O(CO₂) was increased from −0.280 to −0.534, and for O(CaO) it decreased from −1.322 to −1.076. The electrons were found to transfer from O atom in CaO to C atom in CO₂, and then to O atoms in CO₂, the total electrons transferred to the adsorbed CO₂ was −0.51. To compensate the charge transfer, tiny electrons transfer also occurred in other atoms.

Fig. 3 Adsorption of CO₂ on original unit cell CaO (100) surface (red ball: O atom, grey ball: C atom and green ball: Ca atom): (a) R₃ = 0.8 Å (b) R₃ = 1.2 Å.

Fig. 4 Mulliken Population analysis of atoms in single CO₂ (upper left), CaO (100) (lower left) and adsorption structure (right) (red ball: O atom, grey ball: C atom and green ball: Ca atom).

The surface chemistry of the cubic alkaline earth oxides (MgO, CaO, SrO, and BaO) is dominated by the Lewis basicity of surface oxide anions.³⁹ This basicity increases along with the alkaline earth family as the metal ions become larger and more electropositive, and then become increasingly available for reaction.⁴⁰ CO₂ has been proved to physisorb on weak base MgO (100) surface, while the adsorption style of CO₂ on CaO (100) surface is controversial. The results of the geometry of CO₂ adsorption on CaO surface are discrepant. Schneider³⁸ found that CO₂ physisorbed on the weak base MgO surface and chemisorbed on the progressively more basic CaO through BaO surfaces, judged from the geometric parameters, i.e. r(O_s–C) = 1.475 Å, r(C–O) = 1.250 Å, α(O–C–O) = 134.2° for MgO system and r(O_s–C) = 1.384 Å, r(C–O) = 1.270 Å, α(O–C–O) = 129.1° for CaO system, and so on. Pacchioni⁴⁰ calculated the geometries of CO₂ on CaO (100) surface to be r(O_s–C) = 1.376 Å, r(C–O) = 1.262 Å, α(O–C–O) = 130° and concluded that the CO₂ reacted with CaO to form carbonate. Karlsen⁴¹ reported that CO₂ was considerably distorted on CaO surface with the adsorption geometry of r(O_s–C) = 1.49 Å, r(C–O) = 1.23 Å, α(O–C–O) = 134°. Kadossov⁴² obtained the bond length between the C atom in CO₂ and O sites as 1.40–1.55 Å and the O–C–O angle of adsorbed CO₂ as 130° and inferred the formation of carbonates. The above results in this work are not very satisfactory, so further work is needed to reveal the adsorption mode. The surface structure we used above might be too small to eliminate the interactions between CO₂ and the periodic images of itself through destabilizing lateral steric repulsions, so thorough charge transfer during the absorption process would be suppressed. Then the surface structure was replaced by a 2 × 2 × 1 supercell of CaO (100) to eliminate the disturbance of the periodic images for further investigation, as shown in Fig. 5(a).

Fig. 5 (a) Relaxed CaO (100) supercell, illustrating the 2-layer, 32-atom (2 × 2 × 1) structure employed in following calculations; (b) general adsorption structure; (c) magnified style of the four related atoms (red ball: O atom, grey ball: C atom and green ball: Ca atom).

Different reaction sites were also tested for CaO (100) 2 × 2 × 1 structure. In all cases, the resulted bond length between the C atom in CO₂ and O atom in CaO was about 1.39–1.42 Å, the bond length of C–O in adsorbed CO₂ was prolonged to 1.26–1.27 Å, and the O–C–O angle of adsorbed CO₂ was about 129°, while the dihedral angle of the four atoms was about 180°, as shown in Fig. 5(b) and (c). The adsorption energy obtained here was calculated to be about −150 kJ mol⁻¹, being close to the experimental reaction heat of eqn (1), and the total electrons in the unit of CO₂–O(CaO) was 1.595–1.634, being close to 1.536 of CO₃²⁻ in calcite. All of these values indicated the occurrence of a chemical carbonation reaction.⁴²

In the case of the unit cell structure, the periodic imaginary molecules interacted with each other and competed for electrons, it seemed like that the CaO was too little to contribute enough electrons for chemical reaction with CO₂. In the carbonator, if CaO is not sufficient, a metastable carbonate-like state will form, which may decompose into CaO and CO₂ before transported to the calciner, thus decreasing the capture efficiency. So it should be paid more attention that the CaO sorbent must be excess to ensure chemical reaction rather than physical absorption in the fluidized bed.

CO₂ was found to be easily chemisorbed on CaO surface, resulting in the formation of carbonate. The carbonation reaction occurred as long as R₃ was shorter than 5 Å, which was far longer than the sum of the covalent radius of C and O. The strong reactivity of the CaO surface against CO₂ was in good agreement with experimental study.³⁶ The adsorption configuration of CO₂ was that the C atom adsorbed on O sites of CaO, and the O atoms in the adsorbed CO₂ were oriented upward away from the surface. CO₂ did not absorb either via the O atom or on Ca sites. A serial of reactions with different R₃ value were calculated for comparison and R₃ values were proved to have no influence on carbonation reaction. The reaction calculations were continued with R₃ = 2.0 Å. Two initial CO₂ orientations had been considered to further determine the favorable initial state of reaction, the linear CO₂ molecule being parallel with the edge of surface (M1) or parallel with the diagonal of the surface (M2), as shown in Fig. 6(a) and (b). The resulted structures had no significant difference, which were also illustrated in Fig. 6(c) and (d). A detailed comparison involving structural parameters and Mulliken population analysis had been made in Table 1. It was found that the initial CO₂ molecule orientation had no impaction on the carbonation reaction. So in the following TS searching calculations, there was no need to consider initial distance R₃ or initial CO₂ orientation, and an arbitrary initial state was adopted in the following calculations.

Fig. 6 Different initial orientations of linear CO₂ on CaO surface. (a) Parallel with the edge of surface; (b) parallel with the diagonal of surface; (c) and (d), the corresponding resulted structures of (a) and (b) (red ball: O atom, grey ball: C atom and green ball: Ca atom).

Table 1 The structural parameters and Mulliken population analysis of relevant atoms involved in the interaction of CO₂ and CaO (distance unit: Å, energy unit: kJ mol⁻¹, angle unit: °)

	RC(CO2)–O(CaO)	RC–O	α(O–C–O)	ΔE	q(CO2)	q(CO3)
M1	1.412	1.264	128.50°	−147.03	−0.610	−1.606
M2	1.393	1.266	129.38°	−147.46	−0.634	−1.595

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To study the mechanism of the process of CO₂ capture, the transition states of carbonation reaction had been analyzed. The results showed that there was no transition state during the process, and the energy of the systems decreased gradually. The activation energy of carbonation reaction was 0 kJ mol⁻¹, being equal to experimental value.⁴³ The zero activation energy indicated that carbonation reaction was a fast process and during the CO₂ capture process, chemical reaction was not the rate determining step.

In the paper, the DFT methodology was applied to models of a “perfect” crystal of CaO. Then, the difference between calculated and experimental values might be due to the difference in the structures of calculated model and actual lime structure. In the process of CO₂ adsorption on CaO, different O(CaO) environment gives different adsorption energy.⁴⁴ It can be inferred reasonably that the experimental reaction heat value of −178 kJ mol⁻¹ is a comprehensive result of reactions in many different chemical environments, as the structures of matters in nature are more complex and uncontrolled. In addition, due to the limitation of calculation, what we calculated were under 0 K, while the experimental values were measured under 298 K, so difference between calculated and experimental values to some extent might exist reasonably.

Regeneration of CaO

CaO is regenerated by calcination of CaCO₃ through eqn (2). The calculated results showed that the energy was gradually increased in the calcination process. The TS structure with only one imaginary frequency had been determined by LST/QST method. The structural parameters and Mulliken population analysis of relevant atoms involved in the calcination of CaCO₃ were shown in Table 2. The values for CO₂ in the product were consistent with those in single CO₂ molecule calculated above, confirming the occurrence of calcination reaction. The reaction energy of CaCO₃ calcination was calculated to be 180.60 kJ mol⁻¹, which was in good agreement with the experimental value. The TS structure of calcination process shown in Fig. 7 was CO₂ physisorbing on the surface of CaCO₃. The activation energy was calculated to be 166.85 kJ mol⁻¹ (39.88 kcal mol⁻¹), being in agreement with those values reported in earlier research, 39 kcal mol⁻¹ or 40.6 kcal mol⁻¹.^45,46

Table 2 The structural parameters and Mulliken population analysis of relevant atoms involved in the calcination of CaCO₃ (distance unit: Å, energy unit: kJ mol⁻¹, angle unit: °)

	RC–O(1,2)		α(O1–C–O2)	Mulliken population analysis
				C	O1	O2	O3
Reactant	1.309	1.300	119.82	0.681	−0.765	−0.737	−0.715
TS	1.177	1.170	179.40	0.575	−0.304	−0.271	−1.325
Product	1.174	1.174	179.88	0.577	−0.289	−0.288	−1.320

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Fig. 7 Calcination process of CaCO₃ and structures of reactant (a), product (b), TS (c) (red ball: O atom, grey ball: C atom and green ball: Ca atom).

For CaCO₃ calcination, the reaction energy was larger than activation energy. So, in addition to break the C–O bond and optimize the structure of resulting CO₂, more energy was needed to remove CO₂ from CaCO₃ surface. One conclusion could be made that calcination reaction mainly involved two processes: (1) chemical reaction: formation of CO₂; (2) mass transfer: CO₂ escaping from surface, which could be described by the following equations:

CaCO₃ → CaO·CO₂ (6)

CaO·CO₂ → CaO + CO₂ (7)

For the two processes, chemical reaction was the rate-limiting step. So increasing reaction temperature can be used to fasten reaction rate, thus improving reaction efficiency. In actual applications of fluidized bed, as the calcination process going on, more and more intermediate states (CaO·CO₂) generate, so it should be ensured that the absorbed CO₂ can be desorbed and then removed in due course to minimize the effect of the reverse reaction.

Carbonation of CaO and calcination of CaCO₃ are reversible reactions, and the absolute reaction heat of them should be equal from theoretical point. But in this calculation, the difference between reaction heats of carbonation and calcination couldn't be ignored. A reasonable guess was made that the difference arises because of different chemical reaction environments, and different surface structures. Another set of calculations were done to confirm this guess. The reaction energies of single-molecule reactions were calculated, i.e., single CaO reacted with single CO₂ and single CaCO₃ decomposed, and the results were −268.40 kJ mol⁻¹ and 265.78 kJ mol⁻¹, respectively. The results suggested that chemical environments indeed played a role in the reactions. The CaCO₃ crystal structure can promote calcination reaction, while amorphous CaO structure may be in favor of carbonation process, which can be an instructor in the design of CO₂ capture fluidized bed.

In the process of calcination, chemical reaction was the rate-determining step, however, mass transfer also played a role. It could be speculated that for the carbonation process, which was the reverse reaction of calcination reaction, chemical reaction was rapid, and CO₂ diffusion to CaO surface should be the critical stage. In practical cases, measurements to promote the contact between CO₂ and CaO, such as increasing the surface area of CaO through reducing the particle size of CaO or preparing micro-hole CaO, can efficiently improve CO₂ capture efficiency. Of course, enough CaO is also very important.

4. Conclusion

CaO and CaCO₃ have been widely used in CO₂ capture, through a cycle involving CaO carbonation to CaCO₃ and then regenerated from CaCO₃ by calcination. The mechanisms of the two reverse processes had been investigated via DFT calculations. The GGA/PW91 exchange-correlation function and DNP basis set was proved to be able to give reliable results through comparisons between the calculated basic structural parameters and the corresponding experimental values. Through primary calculations, the (100) surface of CaO crystal and (110) surface of CaCO₃ calcite respectively were proved to be more stable and more easily obtained when the crystals were cleaved or in nature, and the reaction calculations were done on the two surfaces with a vacuum of 15 Å above them.

CO₂ only showed physisorption on the unit cell of CaO (100) surface, due to competition for electrons transfer with its periodic imaginary molecules. Considering computation cost, a 2 × 2 × 1 supercell of CaO (100) surface was then employed, which was large enough to avoid the effect of periodic images. It was found that CO₂ molecule reacted with surface O atom through C atom to form carbonate, and no reaction via O atom or on Ca atom was found. In the reaction between CaO and CO₂, electrons transformed from surface O to C atom, and then to O atoms in CO₂. To compensate the charge transfer, tiny electrons transfer from other atoms in the surface structure also occurred. Along with the electron transfer, C–O bonds in CO₂ molecule were stretched to 1.26–1.27 Å and bent to a O–C–O angle of ∼129°, and the distance between C_(CO2) and O_(CaO) changed to 1.39–1.42 Å, leading to the formation of a new C–O bond. Through TS searching, the reaction energy and activation energy of carbonation process were calculated to be −147.64 kJ mol⁻¹ and 0 kJ mol⁻¹. The difference between calculated and experimental values might be due to the difference between model structure and actual CaO cleave surface structure, which needed further investigation. The zero activation energy indicated that chemical reaction was not the rate determining step during the CO₂ capture process.

CaO is regenerated by calcination of CaCO₃. The reaction energy of CaCO₃ calcination was calculated to be 180.60 kJ mol⁻¹, which was in good agreement with experimental values, 178 kJ mol⁻¹. The TS structure of calcination process was CO₂ physisorbing on CaCO₃ surface with the activation energy of 166.85 kJ mol⁻¹. The calcination reaction mainly involved chemical reaction process and mass transfer process, while the former one was the rate controlling step. In actual applications, it should be paid more attention to remove the product CO₂ away to promote the calcination reaction.

Nomenclature

Ea	Activation energy, kJ mol^−1
ETS	Energy of transition state structure, kJ mol^−1
ER	Energy of reactant structure, kJ mol^−1
E	Reaction energy, kJ mol^−1
EP	Energy of product structure, kJ mol^−1
Eslab	Total energy of slab, J m^−2
Esurf	Energy of surface, J m^−2
Ebulk	Energy of bulk CaO or CaCO3 that has the same number of atoms with slab, J m^−2
A	Surface area, m^−2

Acknowledgements

We acknowledge the financial support provided by the National Natural Science Foundation of China (Grant U1407126), Capacity Building of Qinghai Engineering Research Center for Integrated Utilization of Salt Lake (Grant 2015-GX-Q19A), and the Fundamental Research Funds for the Central Universities.

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