The Mechanism of CO2 Adsorption under Dry and Humid

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The Mechanism of CO Adsorption under Dry and Humid Conditions in Mesoporous Silica-supported Amine Sorbents Kuijun Li, Joel D. Kress, and David Spencer Mebane J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b08808 • Publication Date (Web): 14 Sep 2016 Downloaded from http://pubs.acs.org on September 20, 2016

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The Journal of Physical Chemistry

The Mechanism of CO2 Adsorption under Dry and Humid Conditions in Mesoporous Silica-supported Amine Sorbents Kuijun Li,† Joel D. Kress,‡ and David S. Mebane∗,† Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV, USA, and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA E-mail: [email protected]

∗

To whom correspondence should be addressed Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV, USA ‡ Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA †

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Abstract The anomalous behavior of CO2 adsorption in anhydrous and humid conditions in silica-supported, polyethylenimine (PEI)-impregnated sorbents has been elucidated in a new chemical model. New quantum chemical calculations show that the zwitterion, whose existence was called into question by earlier theoretical and spectroscopic studies, can be stabilized by water as well as amines, to an extent that zwitterions can serve as diffusive intermediates for CO2 transport through PEI. Water-stabilized zwitterions are more numerous and have a lower activation energy for deprotonation leading to the formation of carbamate compared with amine-stabilized zwitterions. Calculations also show that bicarbonate is disfavored in the system compared with hydronium carbamate, in accord with spectroscopic evidence. A reaction-diffusion model based on this new chemistry and quantitatively linked to quantum calculations reproduces the anomolous experimentally observed macroscopic behavior of the sorbents in a quantitative fashion.

Introduction Silica-supported amine (SSA) sorbents for CO2 capture have been the subject of intense research in recent years because of the potential of the technology for capture from point sources 1–6 or directly from the atmosphere. 7–13 SSA sorbents consist of a substrate with ordered porosity (such as SBA-15) or disordered porosity (silica xerogel), loaded with amine groups either covalently tethered to the substrate through the reaction between aminosilane and silanol groups on the silica surface 14–19 or through the direct impregnation of polymer amines into the silica mesopores to form an ionic bond at the silanol sites. 20–28 An aminosilane layer can be formed within the interior pores of the silica support when amines are covalently bonded with silanol groups by grafting or ionic bonded with silanol groups by impregnation. The active groups within the impregnated sorbents are typically ethylamines whereas the tethered groups are propyl amines; although steric hinderances and substrate interactions can block active sites for both types of sorbent, chemically speaking both behave similarly 2


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to the better-studied aqueous alkanolamines with respect to adsorption of CO2 and H2 O, with a few important exceptions. The earliest mechanism proposed for the formation of carbamate in aqueous alkanolamines is a two-step zwitterion mechanism: 29–32

+ − − ⇀ R2 NH + CO2 (g) − ↽ − − R2 NH CO2

(1)

− + −− ⇀ R2 NH + R2 NH+ CO− − − R2 NCO2 : R2 NH2 2 ↽

(2)

The zwitterion forms as a short-lived intermediate before its deprotonation by a free base (which can be another amine) to form a carbamate. There is no direct evidence of the existence of the zwitterion even in aqueous solution. 33 A possible explanation is that the energetics of zwitterion formation are disfavorable, such that the concentration of zwitterions falls below the detection limit of spectroscopic techniques. A previous quantum chemistry study suggested the latter possibility, concluding that ethylamine zwitterions may be barely stable even in an aqueous environment. 28 Alternatively, Crooks and Donnellan proposed a single-step, termolecular reaction mechanism for the formation of carbamate: 34,35

− + − ⇀ R2 NH···B + CO2 (g) − ↽ − − R2 NCO2 : BH

(3)

where B represents a base molecule that can be amine or water. An amine that is hydrogen bonded with a free base reacts with CO2 to form carbamate while simultaneously losing its proton to the base. da Silva and Svendsen suggested that this single-step, third order reaction mechanism is consistent with both ab initio calculations and experimental observations. 36 However, the experimentally established diffusion of CO2 through PEI or highly loaded functionalized sorbents requires a mobile intermediate, which the termolecular mechanism does not provide. Several anomalies observed in SSA sorbents have thus far defied a full mechanistic ex3



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planation. It has been frequently reported that the capacity of SSA sorbents with high amine loadings is a function of the internal surface area in addition to the temperature and amine loading of the sorbent. 23,26,37,38 When starting from a low temperature and the purge state, thermogravimetry (TGA) experiments show that capacity first increases with increasing temperature in dry CO2 before passing through a maximum and finally decreasing again as thermodynamically expected. 20,22,23,27,39 These facts point to the existence of a diffusive limitation in highly loaded sorbents, leading to meta-stable states; this hypothesis has been confirmed by attenuated total reflectance spectroscopy experiments. 40 The addition of water to the system causes the metastable behavior to vanish and dramatically increases the capacity of SSA sorbents for the adsorption of CO2 . 41–43 Cooperating with an amine group and CO2 , water can act as a free base for deprotonation of zwitterions and can enable the formation of products such as carbonic acid and bicarbonate. 21,44–48 Bicarbonate is formed through

+ − −− ⇀ R2 NH + CO2 (g) + H2 O(g) ↽ − − R2 NH : HCO3

(4)

Although Didas, et al. proposed that bicarbonate was observed based on the comparison of IR spectrum during adsorption for very low amine loadings and long timescales, 49 earlier FTIR studies concluded that there is no bicarbonate in the system. 42,42,50–54 Whether or not water leads to the formation of additional adsorbed states for CO2 , the vanishing metastability implies that water must have an effect on the diffusion of CO2 . Bacsik et al. detected additional free amine groups in the presence of water vapor using FTIR. 42 (Gebald et al. drew similar conclusions. 55 ) Water is known to change the semi-crystalline structure of aminopolymers, substituting amine-amine hydrogen bonds with amine-water bonds, thus significantly opening up the structure. However, water is also likely to affect the diffusion mechanism for CO2 . Although it has been observed that H2 O adsorption is unaffected by the presence of

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ultradiluted CO2 , 55 competitive adsorption between water and CO2 has also been observed under high CO2 concentration, with higher concentrations of CO2 leading to a decrease in the overall adsorbed capacity of CO2 . 56 Electronic structure calculations as applied to the formation of carbamic acid in alkanoland ethyleneamines were reviewed in a recent study on the uptake of CO2 in supported amine sorbents. 57 This included an assessment of the accuracy of quantum chemical methods based on recent benchmarking studies. 58,59 In conjunction with an accurate basis set (6311++G** ), it was concluded that the wavefunction-based approach of Møller-Plesset 2nd order perturbation theory (MP2) along with the hybrid DFT approach of PBE0 60 were best supported by experiment. Ref. 57 considered amine molecules of varying sizes, up to the 5-site chain of tetraethylenepentamine (TEPA). The results showed a weak dependence of the adsorption enthalpy on both the alkyl chain length (methyl vs ethyl) and primary vs. secondary amines. It was thus concluded that the results of the small-molecule study were transferrable to the PEI polymer chain. Such observations enable a focus on smaller molecules in place of more arduous computations using macromolecules. The molecules considered in the present study were monomethylamine (MMA), dimethyleneamine (DMA), and diethylenetriamine (DETA). Using quantum chemical calculations as a theoretical basis, this work proposes a number of new mechanistic developments that serve to address these questions. The proposals are supported by qualitative and quantitative comparison with the available experimental evidence, primarily through a reaction-diffusion model utilizing the quantum chemical results. The first proposal pertains to the formation of zwitterions: it is found that amines and H2 O stabilize zwitterions under anhydrous conditions and humid conditions, respectively. Concentrations of the water- and amine-stabilized zwitterions under normal conditions are very low, but nonetheless numerous enough to provide a pathway for diffusion of CO2 through PEI. The second proposal pertains to a primary state of adsorbed CO2 in the presence of water: hydronium carbamate. Calculations show that this species exists in much higher con-

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centrations than bicarbonate, and that it can play a significant role in the CO2 adsorption reaction in humidified conditions. A reaction-diffusion model based on these proposals shows that they are sufficient to explain the metastable behavior in dry CO2 and its alleviation on the addition of water, as well as the competitive adsorption behavior.

Quantum Chemistry Study Methods Electronic structure calculations were performed with Gaussian 09 61 using a 6-311+G** basis set and the PBE0 hybrid DFT. Again the PCM was employed to introduce the effects of a slightly polar environment provided by anhydrous PEI, with εr = 2.9. From the analytical Hessian, vibrational frequencies and zero-point energies (ZPEs) were calculated. Enthalpies of reaction were calculated as ∆H = ∆E + P ∆V , where ∆E = electronic energy + ∆ZP E + ∆Etrans + ∆Erot . The translational ∆Etrans and rotational ∆Erot are calculated for the CO2 gas phase molecule only. The non-ZPE contribution to ∆Evib is negligible relative to the ZPE contribution for gas-phase molecules. For the work term, ideal behavior was assumed, yielding P ∆V = ∆nRT = −RT . This strategy assumes that ∆Etrans and ∆Erot and the non-ZPE contribution to the vibrational ∆Evib are equivalent for reactants and products in the adsorption reactions considered. (This is a good approximation in the limit that each entity is a piece of a long-chain polymer.) The same strategy is also assumed for the contributions to the changes in entropy ∆S. Therefore, ∆S was estimated using only the contributions from the gas phase molecules (either H2 O or CO2 ). Note that Svib is negligible relative to Strans and Srot for gas phase molecules. The Synchronous Transit-Guided Quasi-Newton method 62,63 (Gaussian keywords QST2 and QST3) was employed for the transition state searches. An initial guess for the transition state structure, required for the QST3 procedure, was constructed from a linear combination of the Cartesian coordinates of the reactants (zwitterion) and products (carbamate) 6


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structures. The structure of this initial guess was visualized so to ensure there were no issues with steric hindrance and/or overlapping moieties between molecules. Many times this initial guess failed to yield a suitable transition state. Upon failure, then the coordinates of the initial guess were modified by changing slightly the bond distances involved in the proton transfer (especially those bonds involved in the ring structures). Upon success, the frequency spectrum of each transition state was calculated and the structure of the normal mode motion of the imaginary frequency corresponding to the transition state was visualized to ensure that the motion did indeed correspond to the reaction path that was desired. For example, many times the imaginary frequency normal mode corresponded to the torsional barrier of the rotation of one of the methyl groups. In this case this “transition state” was discarded and another QST calculation was started using a slightly different initial guess for the QST search.

Results In Ref.28, quantum chemistry calculations called into question the stability of zwitterion diffusive intermediates in PEI, but suggested that physically bonded moieties involving water, amines and CO2 may be better candidates for diffusive intermediates. Electronic structure calculations were performed with Gaussian 09 61 using a 6-311+G** basis set and the PCM solvation model (where appropriate). The zwitterion was found unstable for all chemistries investigated (MMA and DMA) at both MP2 and PBE0 levels of theory in both the gas phase and in a slightly polar environment (εr = 2.9) similar to that of anhydrous PEI. For solvation in water (εr = 78), PBE0 yielded a stable zwitterion for both MMA and DMA. When explicit water molecules were considered, CO2 binds to either 1) H2 O bound directly to an amine (linear structure) or 2) in a ring structure consisting of CO2 and H2 O and an amine. The energy of formation in the gas phase were found to be -28 and -47 kJ/mol, respectively, for the linear and ring topologies, using the B3LYP hybrid DFT. 64,65 However, the kinetic study showed that the corresponding activation energy barriers for carbamate 7



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formation are as high as 300 kJ/mol, which is not consistent with experimental results. This led to a search for alternative intermediates and the major finding that stabilized zwitterion species are better candidates. Under anhydrous conditions, the zwitterion can be stabilized by another amine and forms ammonium carbamate as follows:

+ − − ⇀ R2 NH···NHR2 + CO2 (g) − ↽ − − R2 NH CO2 −R2 NH − + −− ⇀ R2 NH+ CO− − − R2 NCO2 + R2 NH2 2 −R2 NH ↽

(5) (6)

Two amine molecules react with one CO2 molecule to form a zwitterion at the gas-amine interface. Deprotonation by another amine forms ammonium carbamate both at the surface and after diffusion into the amine bulk. The reactions and molecular structures during this process are in Figure 1(a). As shown in the figure, the formation of energy of the zwitterion is slightly positive 5 kJ/mol (metastable relative to reactants). The barrier to deprotonation is high since the transition state consists of a four-membered ring where the proton is intermediate between the amine nitrogen and the carbamate oxygen. The second amine does not participate in the transfer except to provide hydrogen bonding stabilization. Under humid conditions, the zwitterion can be stabilized by water:

− ⇀ R2 NH + H2 O(g) − ↽ − − R2 NH−H2 O

(7)

+ − − ⇀ R2 NH−H2 O + CO2 (g) − ↽ − − R2 NH CO2 −H2 O

(8)

Hydronium-carbamate is formed as following:

− + −− ⇀ R2 NH+ CO− − − R2 NCOO : H3 O 2 −H2 O ↽

(9)

The formation reactions and molecular structures for hydronium carbamate through water stabilized zwitterions are shown in Figure 1(b). In contrast to the anhydrous zwitterions, 8


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Reaction (5) is zwitterion formation under anhydrous conditions. The zwitterion forms the ammonium carbamate pair as showed in reaction (6) at the surface or after diffusing into the amine bulk. When water is present in the gas, it reacts with free amine sites at the surface to form bonded amine-water species (physically bonded), which can diffuse into the bulk. At the interface, this amine-water species will react with gas-phase CO2 to form the new zwitterion stabilized by water as showed in reaction (8). This zwitterion forms hydronium carbamate at the surface or after diffusing into the bulk according to reaction (9). Reactions (5), (7) and (8) only occur at the amine-gas interface and quickly equilibrate. Reactions (6) and (9) occur at the surface and in the bulk.

Microstructural Model A hierarchical pore structure with bimodal pore size distribution has been observed in the silica xerogels through nitrogen adsorption analyses, SEM images and porosimetry experiments. 66–69 The present model is similar to a two layer model proposed by Wang and Song, 70 in which separate PEI domains – corresponding to an exposed PEI layer and an inner bulky PEI layer – were responsible for access to the gas and diffusion. 70 A microstructural model that split the sorbent into three length scales was developed by Mebane and colleagues. 71 In this model, the largest pores are macroscopic; transport is by gas-phase diffusion and is thus relatively fast. The intermediate length scale is the mesoporous regions of the support in which gas movement is limited by Knudsen diffusion. The third length scale is the region inside the mesopores that are filled with PEI and silica. Although Knudsen diffusion is a slower process than gas-phase diffusion, previous studies revealed that it is still faster than the rate-limiting solid-state diffusion processes. The current model thus reduces to a single dimension consisting of the amine bulk, with exposure to the gas at one boundary and radial symmetry reflecting a grain model. The average grain size (which is related to the total adsorption area) can be obtained from N2 adsorption analysis, knowledge of the weight fraction of active material and simple microstructure-average calculations. More details about the 11



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microstructural model can be found in 28 and 71.

Reaction and Diffusion Assuming ideal thermodynamics and assuming that reactions (5), (7) and (8) remain in equilibrium, the surface site fractions of the three diffusive intermediates are

z1s = κ5 PCO2 Ss2

(10)

z 2 s = κ 7 PH 2 O S s

(11)

z3s = κ8 PCO2 z2s

(12)

with z1 , z2 and z3 the site fractions of amine-stabilized zwitterions, physically adsorbed water and water-stabilized zwitterion, respectively; PCO2 and PH2 O are the partial pressures of CO2 and H2 O in the gas; κ5 , κ7 , κ8 are equilibrium constants; and S is the free amine site fraction. The subscript s denotes the gas-amine interface. Assuming ideal kinetics, the formation rates of ammonium carbamate and hydronium carbamate are: ∂x = k6 z1 − k−6 x2 ∂t ∂y = k9 z3 − k−9 y ∂t

(13) (14)

Where x and y represent the site fractions of ammonium carbamate and hydronium carbamate, respectively. k6 , k9 , k−6 , k−9 are the forward and backward reaction rates of (6) and (9) and κ = kf /kr . The diffusion mechanism is a hopping model: the CO2 and H2 O groups in z1 and z2 move from one free amine to the next and the CO2 group in z3 hops from one z2 to the next. The

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diffusive fluxes are as follows: ¯b = − ǫ3 nv z1 (1 − 2x1 − y − z1 − z2 − z3 )u∗b ∇3 µz1 N 1 1 τ3 ¯b = − ǫ3 nv z2 (1 − 2x1 − y − z1 − z2 − z3 )u∗b ∇3 µz2 N 2 2 τ3 ¯ b = − ǫ 3 n v z 3 z 2 u ∗ ∇ 3 µz3 N b3 3 τ3

(15) (16) (17)

where ǫ3 is the volume fraction of amine in the sorbent; τ3 is the tortuosity in the amine bulk, nv is the number of amine sites available for adsorption per unit volume in the amine; u∗b = b ζb exp −∆G is a mobility with ζb a factor depending on the average geometry surrounding RT

the diffusing species and the frequency of collisions with other amine sites; and ∆Gb is the free energy barrier for the hopping of a CO2 group from one amine site to the next. µz1 , µz2 , µz3 are the chemical potentials of diffusive intermediates:

z1 + RT log µz1 = 1 − 2x − y − z1 − z2 − z3 z2 0 µz2 = µz2 + RT log 1 − 2x − y − z1 − z2 − z3 z3 0 µz3 = µz3 + RT log 1 − 2x − y − z1 − z2 − z3 µ0z1

(18) (19) (20)

This leads to the final mass balance equations: h ∂z1 ǫ3 ∗ n v ǫ3 = RT nv ub1 ∇3 · (1 − 2x − y − z2 − z3 )∇3 z1 ∂t τ3 i ∂x + z1 ∇3 (2x + y + z2 + z3 ) − nv ∂t h ∂z2 ǫ3 n v ǫ3 = RT nv u∗b2 ∇3 · (1 − 2x − y − z1 − z3 )∇3 z2 ∂t τ3 i + z2 ∇3 (2x + y + z1 + z3 ) h ǫ3 ∂z3 = RT nv u∗b3 ∇3 · (1 − 2x − y − z1 − z2 )∇3 z3 n v ǫ3 ∂t τ3 i ∂y + z3 ∇3 (2x + y + z1 + z2 ) − nv ∂t 13


(21)

(22)

(23)


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Solution and Implementation The model was solved numerically using finite volume in space and Crank-Nicolson in time. Details about the solution and discretization can be found in previous papers. 28,71 Simulated TGA curves follow from the model solution using the formula

wCO2 = MCO2 nv (¯ x + y¯ + z¯1 + z¯3 )/ρ

(24)

wH2 O = MH2 O nv (¯ y + z¯2 )/ρ

(25)

where w is the weight fraction appearing in the normalized TGA output; MCO2 and MH2 O are the molecular weights of CO2 and H2 O, respectively; ρ is the density of the sorbent, and a bar denotes an average site fraction.

Model Parameters The parameters related to the adsorption process include microstructural parameters, material loading, chemical equilibrium parameters, kinetic parameters and transport parameters. The solid fraction ǫ3 can be calculated from residual porosity measurements. Here we use ǫ3 = 0.5 which is based on a typical organics loading in the sorbent. f is an estimated parameter in the calculation of the number of sites per unit area of the gas-PEI interface. The equilibrium parameters are the enthalpies ∆H5 , ∆H6 , ∆H7 , ∆H8 , ∆H9 and entropies ∆S5 , ∆S6 , ∆S7 , ∆S8 , ∆S9 associated with reactions (5), (6), (7), (8), (9), respectively. The kinetic parameters are the activation enthalpy ∆H6‡ , ∆H9‡ , and preexponential factor γ6 , γ9 (a parameter which includes the activation entropy) of the backward reaction rate constants k−6 and k−9 . There are two transport parameters associated with the mobility of CO2 and H2 O for each intermediate in bulk PEI: the preexponential factor and activation energy, ζb∗1 and ∆Hb‡1 , for the mobility u∗b1 ; ζb∗2 and ∆Hb‡2 , for the mobility u∗b2 ; ζb∗3 and ∆Hb‡3 , for the mobility u∗b3 , respectively. nv is the the volumetric density of adsorption sites in PEI. Finally, 1/3

the number of sites per unit area of gas-PEI interface is ns = f (nv )2/3 /Na , where f is an 14


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estimated parameter and Na Avogadro’s number. Guided by quantum chemistry and previous experience, the parameter values were selected and inserted into the model implementation to fit against the TGA data. The parameter values used in the simulation and corresponding values calculated by quantum chemistry are listed in Table 1. Since reactions 6 and 9 are unimolecular, the “quantum chemistry” preexponential factor in Table 1 is estimated from a rule of thumb 72 and set equal to a typical bond frequency = 1013 /sec. The parameter values used in the model are comparable with the calculations from quantum chemistry; however, quantities appearing in continuum models are average quantities not directly comparable with the results of quantum calculations. Differences between the calculated value and the quantities used in the model reflect this fact: starting from the quantum result, modest changes were made in order to achieve better correspondence between theory and experiment. Parameters related to transport were not calculated because of the difficulty in obtaining accurate results for transport in a polymer.

Simulation Results and Discussion The model and parameter values presented in the previous section were used to predict macroscopic experimental behavior in dry and humidified CO2 . The results were qualitatively and quantitatively compared with experimental data obtained from the literature. Some of these experiments were produced in conjunction with an earlier study involving the authors of this work. These experiments involved an hyperbranched PEI-impregnated sorbent with a loading of 22.5 wt.%. Full details of sorbent synthesis and related experimental procedures have been described in detail in previous publications. 56,71

Diffusion-Limited Metastability Figure 4(a) shows simulated curves of CO2 adsorption after exposure to a purged sorbent under different temperatures moving from low to high (322K, 338K, 358K, 365K and 381K)

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Table 1: Model parameter values used in simulation and calculated from quantum chemistry. Subscripts refer to reaction numbers appearing in the text; H and S are enthalpy and entropy, respectively; H ‡ denotes an activation enthalpy and γ a reaction rate constant preexponential factor; ζ a diffusion coefficient preexponential factor

parameter τ3 f nv (mol/m3 ) ∆H5 (kJ/mol) ∆S5 (J/mol-K) ∆H6 (kJ/mol) ∆S6 (J/mol-K) ∆H6‡ (kJ/mol) log10 (γ6 ) ∆H7 (kJ/mol) ∆S7 (J/mol-K) ∆H8 (kJ/mol) ∆S8 (J/mol-K) ∆H9 (kJ/mol) ∆S9 (J/mol-K) ∆H9‡ (kJ/mol) log10 (γ9 ) ∆Hb‡1 (kJ/mol) log10 (ζb1 ) ∆Hb‡2 (kJ/mol) log10 (ζb2 ) ∆Hb‡3 (kJ/mol) log10 (ζb3 )

model value quantum chemistry 4.0 1.5 10500 -5.3 -180 -69 -25 102 13.1 -67 -190 -19.5 -185 -54 -25 92 13 30 -7.0 30 -3.5 55 -2.5

– – – 5 -190 -75 -10 120 13 -35 -195 -16 -200 -42 -10 62 13 – – – – – –

and from 0 to 1 bar CO2 concentration in anhydrous conditions. The maximum adsorption occurs at 358K. Figure 4(b) shows the carbamate site fraction in the surface and bulk under different temperatures corresponding to pseudoequilibrium: surface carbamate site fractions remain in equilibrium with the gas, while the rapid decrease of carbamate site fractions moving into the bulk indicates a diffusion limitation. The system regains equilibrium when the temperature rises above 358K. Both the maximum adsorption at 358K and non-equilibrium adsorption at low temperature indicate the existence of limitation for intermediates diffusing into the bulk. As shown in Figure 4(c), the addition of water to the system likewise

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returns the system to the equilibrium behavior. The curve at 322K displays the competitive adsorption effects also seen in experiment: displaced at the surface by CO2 , water has less opportunity to stabilize zwitterions when the CO2 concentration is high.

Dry CO2 Adsorption Simulation results under anhydrous conditions are compared with experiment in Figure 5. The experimental data points (drawn from TGA data reported in Ref. 28) reflect a sequence of temperatures moving from high temperature to low. Solid symbols are the experimental data; open symbols are simulation results. Figure 5 shows the experimental data and simulation results as the CO2 concentration increases from 0 to 100%. The model captures the correct trends and quantitative correspondence is good: the maximum deviation is 17.8% at T=330 K and CO2 =4%, with considerably closer agreement at most other points.

Humid CO2 Adsorption The simulation results for adsorption under humid conditions also match experiment both qualitatively and quantitatively as shown in Figure 6. The adsorbed weight fraction under humid CO2 containing 9% H2 O is twice that under anhydrous conditions in the same CO2 concentration and operating temperature. As CO2 concentration increases, the weight fractions continue to increase at high temperatures, but slightly decrease at lower temperatures after an initial increase, in the simulation as well as in the experiment. The maximum deviation is 38.2% at T=381 K and CO2 =4% – this is the experimental result with the lowest absolute value of the adsorbed weight fraction – but the correspondence between model and experiment is generally much closer than this. Quantitative agreement at T= 322 K is particularly good.

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Figure 4: (a) Simulated TGA weight fraction as a function of partial pressure and (b) carbamate site fraction as a function of distance from the gas-PEI interface in 1 atm CO2 (c) simulated TGA for CO2 adsorption under humidified conditions 18


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Conclusions That zwitterions in ethylamines can be stabilized by other amines under anhydrous or by water molecules under humid conditions is the central proposal of a new mechanism for CO2 adsorption in highly loaded supported amine sorbents. A second proposal is that bicarbonate is unlikely to form in large concentrations, but that hydronium carbamate will play a major role in the adsorption of CO2 in humid conditions. Water stabilization of diffusive intermediates combined with the advent of the hydronium-linked adsorption pathway can explain the differences between anhydrous and humid CO2 adsorption. A reaction-diffusion model based on this new chemistry and quantitatively linked to quantum calculations reproduces the experimentally observed behavior in a quantitative fashion.

Acknowledgement Help and support from David C. Miller is gratefully acknowledged. Los Alamos National Laboratory is operated by LANS, LLC for the NNSA of the U.S. DOE under Contract No. DE-AC52-06NA25396. Funding for this work was provided by the Department of Energy through the Carbon Capture Simulation Initiative.

References (1) Rao, A. B.; Rubin, E. S. A technical, economic, and environmental assessment of aminebased CO2 capture technology for power plant greenhouse gas control. Environmental science & technology 2002, 36, 4467–4475. (2) Davison, J. Performance and costs of power plants with capture and storage of CO 2. Energy 2007, 32, 1163–1176. (3) Samanta, A.; Zhao, A.; Shimizu, G. K.; Sarkar, P.; Gupta, R. Post-combustion CO2 capture using solid sorbents: a review. Industrial & Engineering Chemistry Research 2011, 51, 1438–1463. 20


Page 20 of 29

Page 21 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(4) Bhown, A. S.; Freeman, B. C. Analysis and status of post-combustion carbon dioxide capture technologies. Environmental science & technology 2011, 45, 8624–8632. (5) Wang, M.; Lawal, A.; Stephenson, P.; Sidders, J.; Ramshaw, C. Post-combustion CO 2 capture with chemical absorption: a state-of-the-art review. Chemical Engineering Research and Design 2011, 89, 1609–1624. (6) Miller, D. C.; Litynski, J. T.; Brickett, L. A.; Morreale, B. D. Toward transformational carbon capture systems. AIChE Journal 2016, 62, 2–10. (7) Zeman, F. S.; Lackner, K. S. Capturing carbon dioxide directly from the atmosphere. World Resource Review 2004, 16, 157–172. (8) Yu, K. M. K.; Curcic, I.; Gabriel, J.; Tsang, S. C. E. Recent advances in CO2 capture and utilization. ChemSusChem 2008, 1, 893–899. (9) Keith, D. W. Why capture CO2 from the atmosphere? Science 2009, 325, 1654–1655. (10) Choi, S.; Drese, J. H.; Eisenberger, P. M.; Jones, C. W. Application of amine-tethered solid sorbents for direct CO2 capture from the ambient air. Environmental science & technology 2011, 45, 2420–2427. (11) Stuckert, N. R.; Yang, R. T. CO2 capture from the atmosphere and simultaneous concentration using zeolites and amine-grafted SBA-15. Environmental science & technology 2011, 45, 10257–10264. (12) Wang, Q.; Luo, J.; Zhong, Z.; Borgna, A. CO2 capture by solid adsorbents and their applications: current status and new trends. Energy & Environmental Science 2011, 4, 42–55. (13) Goeppert, A.; Czaun, M.; Prakash, G. S.; Olah, G. A. Air as the renewable carbon source of the future: an overview of CO 2 capture from the atmosphere. Energy & Environmental Science 2012, 5, 7833–7853. 21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(14) Leal, O.; Bolivar, C.; Ovalles, C.; Garcia, J. J.; Espidel, Y. Reversible adsorption of carbon dioxide on amine surface-bonded silica gel. Inorg. Chim. Acta 1995, 240, 183– 189. (15) Gray, M. L.; Soong, Y.; Champagne, K. J.; Pennline, H.; Baltrus, J. P.; Stevens, R. W.; Khatri, R.; Chuang, S. S. C.; Filburn, T. Improved immobilized carbon dioxide capture sorbents. Fuel Process. Technol. 2005, 86, 1449–1455. (16) Harlick, P. J. E.; Sayari, A. Applications of pore-expanded mesoporous silica. 5. Triamine grafted material with exceptional CO(2) dynamic and equilibrium adsorption performance. Ind. Eng. Chem. Res. 2007, 46, 446–458. (17) Hicks, J. C.; Drese, J. H.; Fauth, D. J.; Gray, M. L.; Qi, G. G.; Jones, C. W. Designing adsorbents for CO2 capture from flue gas-hyperbranched aminosilicas capable,of capturing CO2 reversibly. J. Am. Chem. Soc. 2008, 130, 2902–2903. (18) Zelenak, V.; Halamova, D.; Gaberova, L.; Bloch, E.; Llewellyn, P. Amine-modified SBA12 mesoporous silica for carbon dioxide capture: Effect of amine basicity on sorption properties. Microporous Mesoporous Mater. 2008, 116, 358–364. (19) Liang, Z.; Fadhel, B.; Schneider, C. J.; Chaffee, A. L. Stepwise growth of melaminebased dendrimers into mesopores and their CO2 adsorption properties. Microporous Mesoporous Mater. 2008, 111, 536–543. (20) Xu, X. C.; Song, C. S.; Andresen, J. M.; Miller, B. G.; Scaroni, A. W. Novel polyethylenimine-modified mesoporous molecular sieve of MCM-41 type as highcapacity adsorbent for CO2 capture. Energy Fuels 2002, 16, 1463–1469. (21) Franchi, R. S.; Harlick, P. J. E.; Sayari, A. Applications of pore-expanded mesoporous silica. 2. Development of a high-capacity, water-tolerant adsorbent for CO2. Ind. Eng. Chem. Res. 2005, 44, 8007–8013.

22


Page 22 of 29

Page 23 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(22) Yue, M. B.; Chun, Y.; Cao, Y.; Dong, X.; Zhu, J. H. CO2 capture by as-prepared SBA-15 with an occluded organic template. Adv. Funct. Mater. 2006, 16, 1717–1722. (23) Son, W. J.; Choi, J. S.; Ahn, W. S. Adsorptive removal of carbon dioxide using polyethyleneimine-loaded mesoporous silica materials. Microporous Mesoporous Mater. 2008, 113, 31–40. (24) Drage, T. C.; Arenillas, A.; Smith, K. M.; Snape, C. E. Thermal stability of polyethylenimine based carbon dioxide adsorbents and its influence on selection of regeneration strategies. Microporous Mesoporous Mater. 2008, 116, 504–512. (25) Fadhel, B.; Hearn, M.; Chaffee, A. CO2 adsorption by PAMAM dendrimers: Significant effect of impregnation into SBA-15. Microporous Mesoporous Mater. 2009, 123, 140– 149. (26) Ma, X. L.; Wang, X. X.; Song, C. S. "Molecular Basket" Sorbents for Separation of CO2 and H2 S from Various Gas Streams. J. Am. Chem. Soc. 2009, 131, 5777–5783. (27) Sanz, R.; Calleja, G.; Arencibia, A.; Sanz-Perez, E. S. CO2 adsorption on branched polyethyleneimine-impregnated mesoporous silica SBA-15. Appl. Surf. Sci. 2010, 256, 5323–5328. (28) Mebane, D. S.; Kress, J. D.; Storlie, C. B.; Fauth, D. J.; Gray, M. L.; Li, K. Transport, zwitterions, and the role of water for CO2 adsorption in mesoporous silica-supported amine sorbents. The Journal of Physical Chemistry C 2013, 117, 26617–26627. (29) Caplow, M. Kinetics of Carbamate Formation and Breakdown. J. Am. Chem. Soc. 1968, 90, 6795–&. (30) Danckwerts, P. V. Reaction of CO2 with Ethanolamines. Chem. Eng. Sci. 1979, 34, 443–446.

23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(31) Versteeg, G. F.; Van Dijck, L. A. J.; Van Swaaij, W. P. M. On the kinetics between CO2 and alkanolamines both in aqueous and non-aqueous solutions. An overview. Chem. Eng. Commun. 1996, 144, 113–158. (32) Vaidya, P. D.; Kenig, E. Y. CO2 -alkanolamine reaction kinetics: A review of recent studies. Chem. Eng. Technol. 2007, 30, 1467–1474. (33) Xie, H. B.; Zhou, Y. Z.; Zhang, Y. K.; Johnson, J. K. Reaction Mechanism of Monoethanolamine with CO2 in Aqueous Solution from Molecular Modeling. J. Phys. Chem. A 2010, 114, 11844–11852. (34) Crooks, J. E.; Donnellan, J. P. Kinetics and Mechanism of the Reaction Between Carbon-dioxide and Amines In Aqueous-solution. J. Chem. Soc. Perkin Trans. 2 1989, 331–333. (35) Vaidya, P. D.; Kenig, E. Y. Termolecular Kinetic Model for CO(2)-Alkanolamine Reactions: An Overview. Chem. Eng. Technol. 2010, 33, 1577–1581. (36) da Silva, E. F.; Svendsen, H. F. Ab initio study of the reaction of carbamate formation from CO2 and alkanolamines. Ind. Eng. Chem. Res. 2004, 43, 3413–3418. (37) Fujiki, J.; Yamada, H.; Yogo, K. Enhanced adsorption of carbon dioxide on surfacemodified mesoporous silica-supported tetraethylenepentamine: Role of surface chemical structure. Microporous and Mesoporous Materials 2015, (38) Wang, X.; Ma, X.; Song, C.; Locke, D. R.; Siefert, S.; Winans, R. E.; Möllmer, J.; Lange, M.; Möller, A.; Gläser, R. Molecular basket sorbents polyethylenimine–SBA-15 for CO 2 capture from flue gas: Characterization and sorption properties. Microporous and Mesoporous Materials 2013, 169, 103–111. (39) Su, F.; Lu, C.; Kuo, S.-C.; Zeng, W. Adsorption of CO2 on amine-functionalized Y-type zeolites. Energy & Fuels 2010, 24, 1441–1448. 24


Page 24 of 29

Page 25 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(40) Wilfong, W. C.; Srikanth, C. S.; Chuang, S. S. In situ ATR and DRIFTS Studies of the Nature of Adsorbed CO2 on Tetraethylenepentamine Films. ACS applied materials & interfaces 2014, 6, 13617–13626. (41) Serna-Guerrero, R.; Da’na, E.; Sayari, A. New insights into the interactions of CO2 with amine-functionalized silica. Industrial & Engineering Chemistry Research 2008, 47, 9406–9412. (42) Bacsik, Z.; Ahlsten, N.; Ziadi, A.; Zhao, G. Y.; Garcia-Bennett, A. E.; MartinMatute, B.; Hedin, N. Mechanisms and Kinetics for Sorption of CO2 on Bicontinuous Mesoporous Silica Modified with n-Propylamine. Langmuir 2011, 27, 11118–11128. (43) Fan, Y.; Labreche, Y.; Lively, R. P.; Jones, C. W.; Koros, W. J. Dynamic CO2 adsorption performance of internally cooled silica-supported poly (ethylenimine) hollow fiber sorbents. AIChE Journal 2014, 60, 3878–3887. (44) Xu, X.; Song, C.; Miller, B. G.; Scaroni, A. W. Influence of moisture on CO2 separation from gas mixture by a nanoporous adsorbent based on polyethylenimine-modified molecular sieve MCM-41. Industrial & engineering chemistry research 2005, 44, 8113– 8119. (45) Xu, X.; Song, C.; Miller, B. G.; Scaroni, A. W. Adsorption separation of carbon dioxide from flue gas of natural gas-fired boiler by a novel nanoporous ?molecular basket? adsorbent. Fuel Processing Technology 2005, 86, 1457–1472. (46) Khatri, R. A.; Chuang, S. S.; Soong, Y.; Gray, M. Thermal and chemical stability of regenerable solid amine sorbent for CO2 capture. Energy & Fuels 2006, 20, 1514–1520. (47) Belmabkhout, Y.; Serna-Guerrero, R.; Sayari, A. Adsorption of CO2 from dry gases on MCM-41 silica at ambient temperature and high pressure. 1: Pure CO2 adsorption. Chem. Eng. Sci. 2009, 64, 3721–3728.

25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(48) Aziz, B.; Zhao, G.; Hedin, N. Carbon Dioxide Sorbents with Propylamine GroupsSilica Functionalized with a Fractional Factorial Design Approach. Langmuir 2011, 27, 3822–3834. (49) Didas, S. A.; Sakwa-Novak, M. A.; Foo, G. S.; Sievers, C.; Jones, C. W. Effect of amine surface coverage on the co-adsorption of CO2 and water: spectral deconvolution of adsorbed species. The Journal of Physical Chemistry Letters 2014, 5, 4194–4200. (50) Knofel, C.; Martin, C.; Hornebecq, V.; Llewellyn, P. L. Study of Carbon Dioxide Adsorption on Mesoporous Aminopropylsilane-Functionalized Silica and Titania Combining Microcalorimetry and in situ Infrared Spectroscopy. J. Phys. Chem. C 2009, 113, 21726–21734. (51) Hiyoshi, N.; Yogo, K.; Yashima, T. Adsorption characteristics of carbon dioxide on organically functionalized SBA-15. Microporous Mesoporous Mater. 2005, 84, 357–365. (52) Bacsik, Z.; Atluri, R.; Garcia-Bennett, A. E.; Hedin, N. Temperature-Induced Uptake of CO2 and Formation of Carbamates in Mesocaged Silica Modified with n-Propylamines. Langmuir 2010, 26, 10013–10024. (53) Danon, A.; Stair, P. C.; Weitz, E. FTIR study of CO2 adsorption on amine-grafted SBA-15: elucidation of adsorbed species. The Journal of Physical Chemistry C 2011, 115, 11540–11549. (54) Fujiki, J.; Yogo, K. Carbon Dioxide Adsorption onto Polyethylenimine-Functionalized Porous Chitosan Beads. Energy & Fuels 2014, 28, 6467–6474. (55) Gebald, C.; Wurzbacher, J. A.; Borgschulte, A.; Zimmermann, T.; Steinfeld, A. Singlecomponent and binary CO2 and H2O adsorption of amine-functionalized cellulose. Environmental science & technology 2014, 48, 2497–2504.

26


Page 26 of 29

Page 27 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(56) Lee, A.; Mebane, D.; Fauth, D.; Miller, D. A model for the adsorption kinetics of CO2 on amine-impregnated mesoporous sorbents in the presence of water. 28th International Pittsburgh Coal Conference, Pittsburgh, PA. 2011. (57) Mebane, D. S.; Bhat, K. S.; Kress, J. D.; Fauth, D. J.; Gray, M. L.; Lee, A.; Miller, D. C. Bayesian calibration of thermodynamic models for the uptake of co 2 in supported amine sorbents using ab initio priors. Physical Chemistry Chemical Physics 2013, 15, 4355–4366. (58) Jurecka, P.; Sponer, J.; Cerny, J.; Hobza, P. Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. Phys. Chem. Chem. Phys. 2006, 8, 1985–1993. (59) Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 2008, 120, 215–241. (60) Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999, 110, 6158–6170. (61) Frisch, M.; Trucks, G.; Schlegel, H.; Scuseria, G.; Robb, M.; Cheeseman, J.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.; et al, gaussian 09, Gaussian. Inc., Wallingford, CT 2009, 4 . (62) Peng, C.; Bernhard Schlegel, H. Combining Synchronous Transit and Quasi-Newton Methods to Find Transition States. Israel Journal of Chemistry 1993, 33, 449–454. (63) Peng, C.; Ayala, P. Y.; Schlegel, H. B.; Frisch, M. J. Using redundant internal coordinates to optimize equilibrium geometries and transition states. Journal of Computational Chemistry 1996, 17, 49–56.

27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(64) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Physical review B 1988, 37, 785. (65) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. The Journal of chemical physics 1993, 98, 5648–5652. (66) Pirard, R.; Heinrichs, B.; Van Cantfort, O.; Pirard, J. P. Mercury porosimetry applied to low density xerogels; relation between structure and mechanical properties. J. SolGel Sci. Technol. 1998, 13, 335–339. (67) Frenzer, G.; Maier, W. F. Amorphous porous mixed oxides: Sol-gel ways to a highly versatile class of materials and catalysts. Annu. Rev. Mater. Res. 2006, 36, 281–331. (68) Kajihara, K.; Kuwatani, S.; Maehana, R.; Kanamura, K. Macroscopic Phase Separation in a Tetraethoxysilane-Water Binary Sol-Gel System. Bull. Chem. Soc. Jpn. 2009, 82, 1470–1476. (69) Le, Y.; Guo, D.; Cheng, B.; Yu, J. Amine-functionalized monodispersed porous silica microspheres with enhanced CO 2 adsorption performance and good cyclic stability. Journal of colloid and interface science 2013, 408, 173–180. (70) Wang, X.;

Song, C. Temperature-programmed desorption of CO 2 from

polyethylenimine-loaded SBA-15 as molecular basket sorbents. Catalysis today 2012, 194, 44–52. (71) Mebane, D. S.; Fauth, D. J.; Gray, M. L. A Rigorous Yet Scalable Kinetic Model for the Uptake of CO2 by Silica-Supported, PEI-Impregnated Sorbents. Proceedings of the 28th Annual International Pittsburgh Coal Conference. 2011. (72) Pearson, R. G.; Frost, A. A. Kinetics and mechanism; Wiley, 1961; p 73.

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The Mechanism of CO2 Adsorption under Dry and Humid

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