Eley–Rideal model of heterogeneous catalytic carbamate formation based on CO2–MEA absorptions with CaCO3, MgCO3 and BaCO3

The mechanism was proposed of heterogeneous catalytic CO2 absorptions with primary/secondary amines involving ‘catalytic carbamate formation’. Compared with the non-catalytic ‘Zwitterion mechanism’, this Eley–Rideal model was proposed for CO2 + RR′NH with MCO3 (M = Ca, Mg, and Ba) with four elementary reaction steps: (B1) amine adsorption, (B2) Zwitterion formation, (B3) carbamate formation, and (B4) carbamate desorption. The rate law if determining step of each elementary step was generated based on ‘steady-state approximation’. Furthermore, the solid chemicals were characterized by SEM and BET, and this rate model was verified with 39 sets of experimental datasets of catalytic CO2–MEA absorptions with the existence of 0–25 g CaCO3, MgCO3 and BaCO3. The results indicated that the rate-determining step was B1 as amine adsorption onto solid surface, which was pseudo-first-order for MEA. This was the first time that the Eley–Rideal model had been adopted onto the reactions of CO2 + primary/secondary amines over alkaline earth metal carbonate (MCO3).

equations with the non-catalytic one and estimate the enhancement of solid chemicals. This Eley-Rideal model was suitable for describing catalytic CO 2 absorption with primary/secondary amines, which was quite useful for the kinetic studies of heterogeneous catalysis in the field. The main reactions are listed below of CO 2 reaction with primary/secondary amines in aqueous solutions, firstly [2,6]. Blauwhoff et al. [6] have already generated the main equations after conducting the kinetics of CO 2 -amine in aqueous solutions.
For heterogeneous catalysts, solid alkaline significantly enhances the catalysis over trace [OH 2 ]. There are three advantages of solid alkaline over [OH 2 ] ions in liquid. Firstly, the homogeneous catalysis is relatively weak because the concentration of [OH 2 ] is negligible and constrained by the vapourliquid equilibrium of amine-CO 2 -H 2 O system [3]. The solid catalysts are abundant and vary with different masses. Secondly, the [OH 2 ] is detrimental to the CO 2 desorption process, which can hardly be separated out of the solution, but the insoluble solid alkaline chemicals could be separated out of the liquid phase. Thirdly, different types and masses of solid catalysts can be placed into the layers between structured packing materials in a packing column of CO 2 absorber [22], which is highly tunable. From experimental procedures [22,23], CO 2 absorption with bubbling was quite effective when solid chemicals were suspended at gas -liquid interface, indicating that the heterogeneous catalytic CO 2 absorption was more likely to occur on the surface.

Proposed mechanism of heterogeneous catalysis: Eley-Rideal model
As mentioned, both Eley-Rideal model and Langmuir-Hinshelwood model mechanisms were applicable in the field of heterogeneous catalytic reactions on gas -solid interface [26]. After detailed investigation and analysis, Eley-Rideal model could be more suitable for carbamate formation reaction because of the acid-base nature of CO 2 and RNH 2 . CaCO 3 , MgCO 3 and BaCO 3 contained abundant basic active sites on the surface, and they were pre-absorbed with MEA molecules from experimental procedures. From figure 1, the CO 2 molecules reacted with MEA that was instantaneously adsorbed on the solid surface when approaching the surface. CO 2 was unlikely to be directly adsorbed onto the solid surface. If CO 2 was adsorbed onto the solid surface without collision of any amine molecules, the carbamate formation reaction did not occur at all. In the Eley -Rideal mechanism, a gas-phase reagent such as CO 2 directly reacted with an adsorbed species (adspecies) RR 0 NH, and the product carbamate either desorbed or remained adsorbed on the surface depending on the exothermic reaction [24]. Mostly, the product desorbed the surface due to the heat release [24].
The heterogeneous catalytic carbamate formation is proposed in figure 1. The molecular interaction of CO 2 , MEA and active sites '*' were similar to the proposed mechanism of catalytic CO 2 þ MeOH over ZrO 2 -MgO catalyst via the ER model [25]. Figure 1 illustrates the molecular interactions on the solid surface. A large number of MEA molecules had been pre-attached to the active sites on the solid surface according to experimental procedures. When the gas bubbles (containing pure CO 2 ) hit the catalyst surface, CO 2 molecule was transferred onto the amine adsorbed on active sites, where the heterogeneous catalytic reactions took place. The solid surface area was much larger than the gasliquid interface, and it facilitated CO 2 absorptions via enhanced mass transfer. In short, figure 1 is the Eley -Rideal model of catalytic CO 2 þ MEA with gas-solid interaction, except that the solid surface was covered by amine solvents with MEA and H 2 O molecules.
The apparent rate law was developed [26] with four elementary reaction steps: (B1-B4) in table 2, where 'B' represents 'base'. Amine adsorption was the start-up (B1). CO 2 reacted with MEA to generate Zwitterion (B2). Another water/base accepted the protons transferred from the Zwitterion, and carbamate was formed with heat release (B3). The carbamate desorption with completed reaction (B4). In short, B1 was amine chemisorption, and B2 was CO 2 aminolysis/Zwitterion formation. B3 was proton detachment/carbamate formation, and B4 was carbamate desorption. The amine adsorption (B1) involved the mass transfer of MEA from bulk of liquid onto solid surface. According to literature, Zwitterion formation without solid catalysts required activation energy Ea of 9.6-10.2 kcal mol 21 (40.2 -42.7 kJ mol 21 ) under non-catalytic reaction with simulation [28] and about 40 kJ mol 21 with experiments [19]. The exact activation energy of B2 was not tested, but it could be calculated with simulation or tested with further kinetic analysis with the equation of lnk ¼ Ea/RT. The carbamate formation (B3) is exothermic [2]. The product, carbamate, does not fit to the increased surface temperature. It desorbs with high translational and internal energy via B4 [26], depending on the exothermic reaction of B3.
These elementary steps were suitable for both primary and secondary amines (MEA, DEA, DIPA, MMEA etc., with unified form of RR 0 NH) with 'carbamate (RR 0 N-COO 2 )' as product. However, they were unsuitable for tertiary amines (R 3 N). The CO 2 -R 3 N reactions involved different reaction schemes, mechanisms and products of bicarbonate (HCO À 3 ) for CO 2 reaction with tertiary amines (R 1 R 2 R 3 N) so that B1-B4 were unsuitable for it. However, different primary and secondary amines have different values of k 21 . K and k 2 in equation (2.7) [4], so that each amine had its own rate-determining step (RDS) among B1-B4. The development of apparent rate law derivations based on these elementary steps was similar to the electronic supplementary material of catalytic CO 2 with MeOH for the synthesis of DMC [26]. Compared with non-catalytic Zwitterion mechanism, both mechanisms contained the elementary reaction steps of carbamate formation and Zwitterion de-protonation under different phases. The Eley-Rideal model contained adsorption (B1) and desorption of amine (B4) on the solid surface.

The rate equations of four elementary steps and the suitable RDS of MEA solvents
The rate law if rate determining of elementary reaction steps B1-B4 was developed with details in Support Information A in the electronic supplementary material. This methodology was the same as Figure 1. the 'derivation of apparent rate laws' based on elementary steps þ rate-limiting steps of the 'CO 2 þ MeOH reactions' via Eley -Rideal model [25], which was introduced in the electronic supplementary material [26]. It was originated from the steady-state approximation, a classical method in the kinetics of reaction rates [25 -27]. The steady-state approximation involved setting the rate of change of a reaction intermediate in a reaction mechanism equal to zero, and then kinetic equations could be simplified. For instance, if B1 was assumed to be the rate-determining step, the other three steps were regarded as steady-state, and the rate of the formation of the intermediate equalled the rate of its destruction, so that the overall apparent rates r 2 to r 4 were set to 0 [26]. Therefore, r 1 was generated with exact equation. The same works were developed on r 2 , r 3 and r 4 , where B2, B3, and B4 were assumed to be rate limiting. This overall rate law if rate determining was developed in table 2 with full and simplified formats. The simplification was conducted based on chemical reactions and liquid conditions. Within basic amine solution, [H þ ] was negligible ([H þ ] , 10 28 % 0). The P CO2 was 1 atm. Finally, we started to evaluate the exact rate-determining step for MEA as the special case. Although B1 -B4 were equally possible to be RDS for various primary and secondary amines, the instantaneous reaction kinetics of CO 2 -MEA should exclude B3 and B4. Neither of them was likely to be the rate-determining (slowest) step. For B3 ( proton transfer), the surrounding was basic with massive MEA. Zwitterion deprotonation is instantaneous k 21 . K ( k 2 for MEA (much easier to lose proton than N-C bond cleavage) [4]. Moreover, carbamate formation was completed under B4 (desorption). Herein, the possible rate-determining step could be either B1 or B2 for MEA, indicating that the heterogeneous catalytic carbamate formation was either amine adsorption controlled (B1) or reaction controlled (B2). The step of B1 took time, and B2 had an energy barrier (Ea) of N-C bond formation.
rate law if rate determining, with full and simplified formats B1  (2) experimental data of (a, t) with calculated dataset of (X A , t), and (3) integrated method, representing F(X A ) versus time under different cases and sub-cases.

Catalyst characterization and catalytic CO 2 absorption with MEA
The characterization of solid CaCO 3 , MgCO 3 and BaCO 3 was conducted with the scanning electron microscope (SEM) (FEI XL-30). CaCO 3 and MgCO 3 were tested by Brunauer -Emmett-Teller (BET) in surface area, pore size and surface area of solids. The SEM was operated at an acceleration voltage of 25 kV. The BET was measured at 77 K on a BeiShiDe 3H-2000PS4 apparatus. Since they were solid chemicals that were commercially available, there was no need to conduct XRD or XPS analyses. The BET of BaCO 3 were conducted [29] with a BET ASAP 2020 from Micromeritics (Georgia, USA). It was degassed at 1508C for 5 h. Barrett -Joyner -Halenda (BJH) method was employed to calculate surface area, pore volume and pore size from absorption/desorption isotherms [29]. The CO 2 absorption process was similar to that of other works [23]. A set of stirred-cell reactor was built with the suspension of pelletized chemicals for the experiments, and the internal diameter of the reactor was 8.4 cm, with a constant interfacial area of 55.4 cm 2 . The solids were wrapped into two balls and suspended onto the gas -liquid interface. The intersection area of two solid balls was about 9.8 cm 2 (2.5 cm in diameter for each). The amine solvents were pre-filled into the reactor, with part of the MEA solvents pre-adsorbed onto the solid surface. The reactor was placed in a cool water bath with a magnetic stirrer. The CO 2 flow rate was in the range of 1.0-1.5 l min 21 . A thermometer was placed inside the reactor to detect the temperature. Pure CO 2 was introduced to a water-scrubbing process and then flowed into the batch reactor containing amine solvents with bubbles.
After being introduced into amine solvents, the CO 2 reacted with MEA solvent via both non-catalytic and catalytic reaction pathways. For the non-catalytic pathway, the CO 2 directly reacted with MEA solvent, and the kinetics had been intensively studied [2]. For the catalytic pathway, the CO 2 reacted with the MEA molecules pre-adsorbed onto the solid surface, which was the focus of this study.

3.2
The data of X A versus time, for CO 2 -MEA at a range of X A , 0.80 Afterwards, full sets of CO 2 -MEA absorption experiments were conducted with CaCO 3 , MgCO 3 and BaCO 3 to provide database of (X A , t) from the experimental data of (a, t). The mass of chemicals was selected as 5, 10, 15 and 20 g (25 g for BaCO 3 ). Amine concentrations were 1, 3 and 5 mol l 21 , respectively. The absorption profiles of CO 2 loading (a) versus time had been completed elsewhere. The CO 2 loading (a) of the amine solutions was tested with Chittick apparatus, and the AAD% of the experimental tests was 2.5% [23]. The conversion of amines X A was calculated from CO 2 loading (a) with equations below.

The integral method of analysis with F(X A ) ¼ kt for RDS (B1, B2)
There was few precedent researches of rate model verification of the developed equations of B1-B4 in table 2 and the parameters of K 1 -Kx were hard to calculate, so that the rate equations needed to be verified from the definition of reaction rates r A ¼ À ((dC A )=(dt)) as the fundamental of reaction kinetics [27]. With database of (X A , t) in electronic supplementary material, table SA.1-SA.3, 'integral method of analysis' was adopted for rate equation validation [7], which was a fundamental methodology of chemical reaction engineering [27].
The goal was to establish the direct correlation of 'r ¼ C A0 ((dX A )=(dt)) (3.4)' with its integrated format of 'F(X A ) ¼ Kt'. We developed several proper integrated equations of F(X A ) 5 Kt with the combination of the definition of reaction rate of equation (3.4) and the specific format of reaction rate (r) of equations (3.5)-(3.7) in order to verify B1 or B2 as the rate-determining step. The [CO 2 ] was not included, for it had already been verified as the first order for absorption [2].
The rate equation of CO 2 absorption was equation (3.4) by amine concentration (C A ) or conversion (X A ) at the right side, For the left side, r A ¼ f (X A ) was adopted by either B1 or B2 in table 2. The integrated rate equations were carried out with equations (3.5)-(3.7) under different sub-cases with brief analyses in Appendices. There was only one set of dataset of (X A , t) obtained from experiments. However, there were several different formats of F(X A ) equations (3.5)-(3.7) based on different rate equations (r) in table 2. Consequently, there was one accurate model fitting data (X A , t) among equations (3.5)-(3.7), different sub-cases included k a ¼ 1/2 K 1 K 4 ¼ 0.05, 0.005, and 0 for sub-cases.
For equation (3.7), k a reflected the ratio of u carbamate =n sites . To verify the rate models of RDS ¼ B2, k a was selected as 0.05, 0.025 and 0.005, representing that 10%, 5% and 1% of the total active sites were covered with carbamate. The extreme condition was also tested, where k a ¼ 0 (similar to 0th order). Each sub-case of equations (3.5)-(3.7) was verified by 39 sets of experimental data of (X A , t). Each set of (X A , t) with its specific parameter (concentration, catalyst, mass, i.e. 1.0 mol l 21 , CaCO 3 , 5 g) generated different sets of (F(X A ), t) based on different RDS of equations (3.5)-(3.7). Different curves of (F(X A ), t) reflected different rate equations (r). For each set of data (F(X A ), t), there were five points with different conversion of X A ¼ 0.0, 0.4, 0.5, 0.6, 0.7 and 0.8. These curves of (F(X A ), t) could be either linear or curvy.
These integrated rate equations (3.5) -(3.7) were developed with a general format of 'F(X A ) ¼ Kt', which was a linear equation of 'Y ¼ kX'. If the curves of (F(X A ), t) were linear and straight, it meant (F(X A ), t) was quite fitting for 'F(X A ) ¼ Kt' of equations (3.5) -(3.7), and its related specific rate equation (r) was fitting for the mechanism of B1 or B2. The higher R 2 of the lines of 'F(X A ) ¼ Kt' of equations (3.5)-(3.7) indicated the better fitting of the dataset of 'r ¼ C A0 ((dX A )=(dt))' responded to experimental dataset (X A , t). Therefore, we selected the highest standard R 2 . 0.99 as the criteria. After repeated verifications of 39 sets of experimental data (X A , t) with linear regressions, the set containing most lines of R 2 . 0.99 of equations (3.5)-(3.7) was verified as the highly accurate rate model.  3 . From BET, the surface areas were 0.428 m 2 g 21 for CaCO 3 and 9.498 m 2 g 21 for MgCO 3 from this work. BaCO 3 is reported by others as 4.66 m 2 g 21 for surface area, pore volume of 0.008 cm 3 g 21 and pore size of 6.46 nm [29]. These surface areas were much larger than gas -liquid interfacial area (55.4 cm 2 ) of the reactor [23]. The pore diameters were 31.3 nm (CaCO 3 ), 4.31 nm (MgCO 3 ) from this study and 6.46 nm (BaCO 3 ) from other work [29], which facilitated the external mass transfer of MEA molecules onto solid surface.  The overall CO 2 absorption process with the existence of solid alkaline was briefly explained from B1 to B4 in table 2. The amine adsorbed onto the surface from liquid phase firstly, with relatively slow rate (B1). Then CO 2 reacted with MEA (RNH 2 ) with N-C bond formation (B2). The rate was instantaneous and enhanced with heterogeneous catalysis. The Zwitterion released proton to H 2 O or other base to generate carbamate (RNH-COO 2 ) and the exothermic reaction released heat (B3). The released heat facilitated diffusion and drove desorption of carbamate back to the aqueous phase (B4). The carbamate finally desorbed the surface due to the exothermic reaction [24]. Mostly, the product desorbed the solid surface due to the heat release, and there was little carbamate remaining.    can be directly extracted from graphical method from experimental data [2], but the power law model is a straightforward but over-simplified method lacking detailed intrinsic reaction mechanism and elementary steps [2].  The derivation of apparent rate law [26] was hard and time-consuming, but it accurately verified the mechanism and elementary steps.

The rate-determining step verification of B1 and B2 based on F(X A ) ¼ Kt
If the definition of rate equation (3.4) was combined with equations (2.4) and (4.1), the overall rate equation was equation (4.2), along with the differential integrated rate equation listed as equations (4.3) and (4.4). The k[CO 2 ] were the slopes of figures 6 -8.        However, the experimental process was rather limited [23], and it was only adequate to verify the rate model as a start-up. This Eley-Rideal model still awaits much further analyses with updated experimental apparatus    such as GC-MS HPLC for the analysis of reaction products, molecular simulations and comprehensive mathematic simulations [2]. The molecular simulation needs to be calculated of catalytic CO 2 -MEA reactions with the existence of CaCO 3 with density function theory (DFT) to discover Ea of catalytic reactions. The kinetic analysis of another solid base 'KMgO/CNT (carbon nano-tubes)' with ER model will be future work, since this material was reported to be effective for CO 2 -MEA absorption recently [31].

Conclusion
The Eley-Rideal model was proposed for catalytic carbamate formation of CO 2 þ RR 0 NH with MCO 3 , based on the similar reactions of CO 2 þ MeOH over ZrO 2 -MgO catalyst [25]. For the case of MEA(RNH 2 ), the rate-determining step was B1 of amine adsorption. It was the pseudo-first-order for [MEA]. The heterogeneous catalysis enlarged the second rate constant (kz) of MEA to 20-100% higher. For DEA, the rate-determining step was among B1-B4, but it required intensive literature studies and experimental results based on highly accurate kinetic results to verify the equations properly. Solid surface contained much bigger gas-liquid interfacial area with abundant active sites, resulting in the enhancement and facilitation of molecule mass transfer and the reduction of activation energy Ea. The reduction of activation energy Ea was more important in accelerating reaction rates. The effect of mass transfer could be calculated from k Gav on the basis of experiments, and Ea could be calculated from either molecular simulation or Arrhenius equation based on experimental data of kinetics analyses.
Ethics. We received ethical approval from a 'lab safety and research ethics committee' of University of Shanghai for Science and Technology to carry out our study. This university provides consent in a research ethics and code of lab safety and ethics in scientific research and publication.
Data accessibility. The datasets supporting this article have been uploaded as part of the electronic supplementary material, A and B; including mechanism development (A) and experimental data (B).