Transport, Zwitterions, and the Role of Water for CO2 Adsorption inMesoporous Silica-Supported Amine SorbentsDavid S. Mebane,*,†,‡ Joel D. Kress,§ Curtis B. Storlie,§ Daniel J. Fauth,† McMahan L. Gray,†

and Kuijun Li‡

†National Energy Technology Laboratory, Morgantown, West Virginia 26507, and Pittsburgh, Pennsylvania 15236, United States‡Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, West Virginia 26506, United States§Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States

ABSTRACT: The uptake of CO2 in highly loaded, silica-supported, polyethylenimine(PEI)-impregnated sorbents was investigated in a reaction-diffusion model of the CO2adsorption process. The model successfully replicated the pseudoequilibrium behaviorexperimentally observed in thermogravimetry (TGA) experiments. A parametric study andsensitivity analysis of the model revealed that the stability and mobility of diffusiveintermediatesassumed in the model to be zwitterionseffectively control the observablecapacity of the sorbent. A subsequent quantum chemical study called into question thestability of zwitterions in PEI but suggested that physically bonded moieties involving water,amines, and CO2 may be better candidates for diffusive intermediates. The implications are astrong dependence of the observable CO2 capacity of the sorbent on the presence of waterin the gas stream, which was found to be consistent with TGA results.

■ INTRODUCTION

Given the enormous role of fossil fuels in global powergeneration and the slow pace of the scale-up of renewableresources, carbon capture and storage (CCS) is increasinglyrecognized as a key strategy in the fight against global climatechange, but CCS faces its own challenges. One of the principalchallenges is that the current state-of-the-art postcombustionseparation technologyaqueous amine scrubbingreducesthe thermal efficiency of the generation process to which it isattached by approximately 30%, with a corresponding increasein the cost of electricity in the neighborhood of $0.07/kWh.1

New separation technologiessuch as solid sorbents or ionicliquidscould decrease these numbers, but they remainunproven at industrial scales. The Department of Energy’sCarbon Capture Simulation Initiative (CCSI) is a project aimedat reducing the typical 20−30 year timeline for developmentand deployment of new technologies in the power generationsector through the use of science-based simulation. Solidsorbents have been the technology of primary focus in the firsttwo years of the project; this article contains results on thephysicochemical modeling and theoretical study of a particularclass of sorbentsmesoporous silica-supported amine (SSA)sorbentsobtained during the course of the project’s first twoyears.A review of the development history for SSA sorbents can be

found in a broad review of carbon capture technology writtenby Choi et al.2 Generally amine groups are loaded onto amesoporous silica substrate with either ordered porosity (suchas SBA-15) or disordered porosity (silica xerogel). The aminesmay be covalently tethered to the substrate through thereaction of an aminosilane with silanol groups on the silica

surface3−8 or through the direct impregnation of amines intothe silica support.9−16

It has long been clear that transport of CO2 through theamine bulk is the key limiting factor for the reaction rate (andthereby the working capacity for uptake of CO2) for SSAsorbents with a relatively high amine loading. Evidence comesin the form of the frequently reported maximum in capacity as afunction of temperature,9,11,12,16 as well as the observeddependence of capacity on the internal surface area of thesorbent.12,15 However, previously reported kinetic models forSSA sorbents17−20 have utilized semiempirical kinetic ap-proaches which are not suitable for describing these effects.The uptake of CO2 in aqueous alkanolamines (which is the

most intensively studied amine−CO2 interaction) has mostoften been described as the formation of alkylammoniumcarbamates through a zwitterion mechanism.21−24 Thezwitterion mechanism does not enjoy universal support,however, and an alternative termolecular mechanismcommonly represented as a reaction between gaseous CO2and an amine that is already in a hydrogen-bonded relationshipwith a free basehas been proposed.25,26 The distinction is asubtle one. The zwitterion mechanism is written

+ ⇌ + −R NH CO (g) R NH CO2 2 2 2 (1)

+ ⇌ ++ − − +R NH R NH CO R NCO R NH2 2 2 2 2 2 2 (2)

whereas the termolecular mechanism reads

Received: July 31, 2013Revised: November 25, 2013Published: November 26, 2013

Article

pubs.acs.org/JPCC

© 2013 American Chemical Society 26617 dx.doi.org/10.1021/jp4076417 | J. Phys. Chem. C 2013, 117, 26617−26627

+ ··· ⇌ +− +CO (g) R NH NHR R NCO R NH2 2 2 2 2 2 2 (3)

The termolecular mechanism would suggest a reaction order of2 relative to the amine in nonaqueous solutions, while fractionalorders between 1 and 2 are experimentally observed.23

However, the lack of definitive evidence for the zwitterion inmono- and diethanolamine solutions has led to continueddebate, including recent kinetic and computational studiesarguing for27,28 and against29−32 the presence of zwitterions inaqueous alkanolamines.However, for SSAs, there is a cogent argument in favor of a

reactive intermediate due to the role such a species can play inexplaining the ability of CO2 to diffuse through an immobilizedamine bulk phase. It appears from the above-referenced studieson highly loaded SSAs5,6,8−16 that CO2 diffuses through theamine bulk in nominally anhydrous conditions. There are twoplausible mechanisms for this diffusion: transfer of CO2between amine sites and long-range translational motion ofthe amine sites themselves. The latter is clearly not possible inthe grafted amine sorbents, and unlikely in directly impregnatedsorbents, since an IR study by Wang et al. offers strongevidence that amines become anchored to the substratethrough proton exchange with surface silanols, which leads toionic association.33 In the absence of water, this leaves thezwitterion as the most logical candidate for a diffusiveintermediate.In the following, a model of CO2 uptake in a highly loaded

SSA sorbent is presented. It consists of a multiscalemicrostructural model, which enables the separation of gas-phase and amine bulk-phase transport of CO2. The latter isassumed to take place through a zwitterion-mediatedmechanism. A detailed analysis of the model behavior, whichincludes a parametric and sensitivity study, reveals twoimportant findings. One is that the model qualitatively capturesthe transport-limited behavior seen in experiments. The secondis that the stability and mobility of the reactive intermediateplay a dominant role, controlling not only the kinetics but alsothe experimentally observable CO2 capacity of the sorbent.Subsequent to this analysis, a quantum chemical study of the

energetics of zwitterion formation for ethylamines in both dryand humidified environments was performed. It was found thatzwitterions are only stableat least for certain chemistriesina polar environment similar to that of water. Additionally, a pairof gas-phase stable physically bonded conformations involvingwater, amine, and CO2 were discovered, either of which couldserve as a reactive intermediate. This finding, combined withthe importance of diffusive intermediates in determiningsorbent capacity, suggests that in fact highly loaded SSAs willhave very limited capacity for the uptake of CO2 in trulyanhydrous conditions. As a result, measurements of CO2capacity in nominally dry conditions may significantly under-estimate the true capacity of these sorbents for the formation ofcarbamate.

■ THERMODYNAMIC AND KINETIC THEORYMicrostructural Model. Nitrogen adsorption analyses for

silica xerogels typically reveal significant pore volumes in themesopore range, while SEM images and mercury porosimetryexperiments reveal a macroporous structure.34−36 This impliesa bimodal pore size distribution that manifests itself in ahierarchical pore structure. Gas moves freely through themacropores but is limited by Knudsen diffusion as it enters themesoporous regions. Within the mesoporous regions, CO2 may

diffuse in the gas phase or adsorb at the amine surface, diffusingthrough the bulk to reach amine sites not in contact with thegas.It is therefore necessary to split the microstructure into three

length scales. The largest length scale is that of the macroscaleparticle (generally on the order of millimeters), at which CO2moves via gas-phase bulk diffusion, a process that we willassume is very fast compared to kinetic limitations at the lowerlength scales. The intermediate length scale is that of themesoporous regions of the support, on the order of 100 nm to10 μm.36 The smallest length scale will be that of the smallerregions within the mesoporous areas that are completely filledwith PEI and silicathese regions can be viewed as areas ofoxide and immobilized polymer found between the openmesopores. The length scale of these regions depends on thedegree of mesoporosity remaining after polymer impregna-tionit will approach that of the intermediate scale in the limitof zero remaining mesoporosity.At each of the two smaller length scales, gas-phase CO2 (in

the case of the intermediate scale) or adsorbed CO2 (for thesmallest scale) diffuses in from multiple directions. SEM imagessuggest that the shape of the region at the intermediate scale isquasi-spherical,35,36 whereas it is probably reasonable to expectthat the typical shape of the amine−silica composite at thesmallest scales is not spherical. (Indeed, for ordered substratessuch as MCM-41, a cylindrical model may be appropriate forthis length scale. However, spheres can be utilized in principlewithout loss of generality.) The use of spheres can be thoughtof as a general method for modeling chemical penetration intoa closed region of any arbitrary shape; empirical microstructuralparameters can properly account for the difference between thespherical and actual cases if such parameters depend on thestate of infiltration.The spheres will not have fixed locations with respect to one

another as in a conventional grain model because this presumesa certain structure for the spaces between grains. Rather, thereis a certain “sphere density” at the large and intermediate lengthscales. These densities, the sphere radii, and the porosities andinternal surface areas at each length scale are interrelated

ε ρ π− = R1431 2 2

3

(4)

ρ ε π= −a R(1 )41 2 2 22

(5)

and

ε ρ π− = R1432 3 3

3

(6)

ρ π=a R42 3 32

(7)

where ε is the porosity; ρ is the number density of spheres; R isthe sphere radius; and a is the internal surface area; and thesubscripts 1, 2, and 3 denote the large, intermediate, and smalllength scales, respectively. Figure 1 illustrates the relationshipsbetween the different modeling scales.Under the assumption of the fast gas-phase diffusion of CO2

at the large scale and the assumption of spherical symmetry atthe intermediate and small scales, the problem then becomesone of reaction and diffusion in two dimensions.

Chemistry. Assuming a homogeneous environment ofamine sites that are active for the adsorption of CO2, thezwitterion mechanism for the anhydrous formation ofcarbamate is given by eqs 1 and 2. Assuming that eq 1 remains

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in equilibrium and that the entire system follows idealthermodynamics (neither of these assumptions have anyparticular justification, other than that they exclude from theanalysis some factors not related to transport, which is the focusof this study), the surface site fraction of zwitterions is

κκ

=−

+z

p xp

(1 2 )1

z

zs

s

(8)

where p = p(CO2); x = [R2NCO2−]; kz is the equilibrium

constant; and the subscript s denotes the value at the gas−amine interface.Further assuming ideal kinetics, the rate of the proton

transfer step given by eq 2 is

κκ

∂∂

= − − −⎡⎣⎢

⎤⎦⎥

xt

k x z zx

(1 2 )xz

2

(9)

where κ is the equilibrium constant for the overall reaction 1, 2.Gas Diffusion. The mass balance for diffusion at the

intermediate length scale is

ε∂∂

= −∇ · +c

tN q

( )22 g 2 (10)

where c is the concentration of CO2 in the gas; Ng is themicrostructure-averaged gas flux; and q2 is the source term. Thesource term q2 has both chemical and transport aspects, as CO2is removed from the gas both through the progress of thechemical reactions 1 and 2 at the gas−amine interface andthrough the transport of CO2 away from the interface throughdiffusion into the amine bulk. A zwitterion balance for the layerof amine sites at the interface with the gas is

∂∂

= − −∂∂

−n azt

q n axt

q ts 2s

2 s 2s

2, (11)

where ns is the area density of amine sites at the interface, andq2,t is the rate of transfer of zwitterions away from the surfacelayer and into the amine bulk. Differentiating eq 8 with respectto time leads to

κκ κ

κ κκ

∂∂

=−

+∂∂

+−

+∂∂

−+

∂∂

zt

xp

pt

p xp t

pp

xt

(1 2 )(1 )

(1 2 )(1 )

21

z

z z

z z

z

s s2

s2

s

(12)

Combining eqs 11 and 12 leads to an expression for q2

κκ κ

κ

κκ

= −−

+∂∂

+−

+∂∂

+−+

∂∂

−

⎡⎣⎢

⎤⎦⎥

q n ax

ppt

p xp t

pp

xt

q

(1 2 )(1 )

(1 2 )(1 )

11

z

z z

z

z

zt

2 s 2s2

s2

s2,

(13)

Since the pores at the intermediate length scale are less than50 nm in diameter, Knudsen diffusion will dominate for gastransport

ετ

= − ∇N D cg2

2K 2

(14)

where τ2 is the tortuosity. The Knudsen diffusivity is37

π= ⎜ ⎟⎛

⎝⎞⎠D K

RTM

43

8K o

1/2

(15)

where M is the molar weight of CO2 and CO2 and Ko is theKnudsen flow parameter (in units of length), which depends onthe structure of the porosity.

Diffusion in the Amine Bulk. Further extending theassumption of ideality to the bulk transport model, thezwitterion mechanism for transport of CO2 in an immobilizedamine bulk phase leads to the following expression for themobility of zwitterions

ζ= − −−Δ⎛

⎝⎜⎞⎠⎟u x z

GRT

(1 2 )expb bb

(16)

= − − *x z u(1 2 ) b (17)

where ζb is a factor depending on the average geometrysurrounding the diffusing species and the frequency ofcollisions with other amine sites, and ΔGb is the free energybarrier for the hopping of a CO2 group from one amine site tothe next. The form of the preexponential term (with nodependence on temperature) reflects the assumption that thesites in the amine, while spatially constrained, are nonethelessable to move translationally over short distances. Themicrostructure-modified diffusive flux of CO2 is then

ετ

μ = − − − *∇N n z x z u(1 2 ) zb3

3v b 3

(18)

where ε3 is the volume fraction of amine at the smallest lengthscale; τ3 is the amine tortuosity;38 nv is the number of aminesites (that are available for CO2 adsorption) per unit volume inthe amine; and μz is the chemical potential of zwitterions

μ μ= +− −

⎜ ⎟⎛⎝

⎞⎠RT

zx z

log1 2z z

0

(19)

the form of which accounts for site limitations. This leads to

ετ

= − * − ∇ + ∇N RTn u x z z x[(1 2 ) 2 ]b3

3v b 3 3

(20)

The final mass-balance equation at the smallest length scalethen becomes

εετ

∂∂

= *∇ · − ∇ + ∇ − ∂∂

nzt

RTn u x z z x nxt

[(1 2 ) 2 ]v 33

3v b 3 3 3 v

(21)

Assembly of the Model. Now that the equations for eachlength scale have been derived, it remains to assemble theminto an integrated model. This begins with the observation thateach length scale corresponds to a separate three-dimensionaldomain. The functions x and z are field variables over all threesets of coordinates, while p is a field variable over the largesttwo length scales. In general, this means that x and z arefunctions over nine spatial dimensions plus time and that p is afunction over six spatial variables plus time. However, the

Figure 1. Illustration of the three length scales of the microstructuralmodel: (1) macroporosity, (2) mesoporous particles, and (3) silica−PEI composite.

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approximations that gas diffusion is fast at the largest lengthscale, combined with spherical symmetry at the lower twolength scales, will reduce the number of spatial dimensions totwo for x and z and one for p. The indices for these coordinatesystems are labeled r2 and r3, such that

=x x r r t( , , )2 3

=z z r r t( , , )2 3

=p p r t( , )2

Distinct mass balances are written in each dimension, withthe balance at the intermediate length scale restricted to the axisat r3 = 0. It is coupled to the mass balance at the smallest lengthscale through its source term. Combining eq 10 and eqs 13−15(along with the observation that k2,t = RTub*(nvNa)

2/3, with NaAvogadro’s number) and eq 20 leads to

εκ

κετ π

κκ κ

κ

+−

+∂∂

=

∇ −−+

∂∂

+−

+∂∂

−

⎜ ⎟⎡⎣⎢

⎤⎦⎥

⎛⎝

⎞⎠

⎡⎣⎢

⎤⎦⎥

RTn ax

ppt

KRTM

p RTa npp

xt

p xp t

RTq

(1 2 )(1 )

43

8

11

(1 2 )(1 )

z

z

z

z z

zt

2 s 2s2

2

2o

1/2

22

2 ss s

2 2,

(22)

where

= * − −

− − −

q RTn a u n N z x z

z x z

( ) [ (1 2 )

(1 2 )]

t2, s 2 b v a2/3

s 1 1

1 s s (23)

and

∇ = ∂∂

∂∂

⎛⎝⎜

⎞⎠⎟r r

rr

122

22

222

2

The mass balance in the solid phase is written

εετ

∂∂

= *∇ · − ∇ + ∇ − ∂∂

zt

RTu x z z xxt

[(1 2 ) 2 ]33

3b 3 3 3

(24)

where

∇ · = ∂∂

∂∂

⎛⎝⎜

⎞⎠⎟r r r

r1

332

3 232

∇ = ∂∂r3

3

When combined with eq 9, eqs 22−24 form a closed set ofpartial differential equations for the reaction−diffusion system.The boundary conditions are zero flux at r3 = 0 and r2 = 0, aDirichlet boundary condition for the pressure (given by thecomposition of the bulk gas) at r2 = R2. The flux 23 links thedomains 2 and 3 at r3 = R3.Solution and Implementation. The model was solved

numerically using a line-by-line iterative approach. Details ofthe numerical solution and implementation appear in a priorpublication.39

Simulated TGA curves are derived from the model solutionusing the formula

ρ= + w Mn x z( )/v (25)

where w is the weight fraction appearing in the normalizedTGA output; M is the molecular weight of CO2; ρ is the

density of the sorbent; and x and y are the average site fractionsof carbamic acid and zwitterions in the sorbent, respectively.

■ STATISTICAL METHODS FOR SENSITIVITYANALYSIS

Dispensation of Model Parameters. MicrostructuralParameters. The parameters ε2 and a2 are amenable to directmeasurement from N2 adsorption analyses. These parametersenable a calculation of ρ3 and R3 from eqs 6 and 7. The solidfraction ε3 can similarly be estimated from residual porositymeasurements (wherein the porosity of the impregnatedsorbent is compared to that of the blank substrate). R2 canbe based on an analysis of grain size such as that availablethrough SEM metallographic sections. Because these parame-ters are amenable to direct measurment and are in any eventsecondary to the main goals of this work, they were fixed atwhat could be considered a set of typical values: R2 = 10 μm, a2= 107 m2/m3, ε2 = 0.01, and ε3 = 0.5. These last two parametersreflect a fully loaded sorbent substrate.The remaining influence of the microstructure on transport

comes from the empirical parameters Ko, τ2, and τ3, referring toKnudsen diffusion, gas-phase tortuosity, and polymer-phasetortuosity, respectively. The Knudsen flow parameter, Ko, is aconstant which depends only on the mesoporous structure. Theparameters τ, on the other hand, characterize not only therelevant microstructure as it affects the respective transportprocess but also the difference in transport modes between thatof a sphere and the actual microstructure-averaged geometry.They are strictly functionals of the spatial coordinates of theappropriate field variables

τ τ= p[ ]2 2

τ τ= |r z( ) [ ]r3 2 3 2

The form of these functionals is not general. If themicrostructure-averaged shape is spherical, however, then τ isa constant; this will be the assumption used at both lengthscales. The microstructural parameters (Ko/τ2 and τ3) thereforebelong to the studied set.

Chemical Equilibrium and Kinetic Parameters. Theequilibrium parameters are the enthalpies ΔH, ΔH2 andentropies ΔS1, ΔS2 associated with reactions 1 and 2. Thekinetic parameters are the activation enthalpy ΔH2

⧧ andpreexponential factor ζ (a parameter which includes theactivation entropy) of the forward reaction rate constant k.

Transport and Site Density. There are two transportparameters associated with the mobility of CO2 in bulk PEI:the preexponential factor and activation energy, ζb* and ΔHb

⧧,respectively, for the mobility ub*. The volumetric density nv ofadsorption sites in PEI is included in the study due to theuncertainty about the density of immobilized PEI as well as theextent of association between amine sites and the substrate.Finally, the number of sites per unit area of the gas−PEIinterface is ns = f(nv)

2/3/Na1/3, where f is an estimated parameter

and Na is Avogadro’s number.Variance Decomposition. The principal sensitivity anal-

ysis was performed using variance decomposition. The vectorof model parameters is denoted for the model described aboveas Θ = [θ1, ..., θ12]. Of particular interest is the total varianceindex j, j = 1, ..., 12; this measure is reviewed in detail in refs40−43. The total variance index j for a model parameter j at aparticular state point ξ = {p, T, t} is calculated as

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ξξ

ξξ

ξ

=Θ |Θ

Θ

= −Θ |Θ

Θ

−

−

w

ww

w

( )E[Var( ( ; ) )]

Var( ( ; ))

1Var(E[ ( ; ) ])

Var( ( ; ))

jj

j

(26)

where E(Y) and Var(Y) are expected value and variance,respectively, of a random variable Y, E(Y|Z) is the conditionalexpectation of a random variable Y given Z, and Θ−j = {θ1, θ2,..., θj−1, θj+1, ..., θn}. The functional j can be interpreted as theproportion of the total variance of the model output (at ξ) thatis due to parameter θj, including the effects of its interactionswith other parameters. Evaluating the integrals involved withthe calculation of the j requires numerical methods ofquadrature, the most convenient being Monte Carlo integra-tion.Model Emulator. The Monte Carlo process needed to

calculate the j typically requires many thousands ofevaluations of the sorbent model. As this is not computationallyfeasible, a model emulator can be used to provide estimates forsj and j.

43−47 That is, first collect a modest number of modelruns from the computer model, fit a response surface (i.e., theemulator), then use the emulator to perform the computation-ally intensive calculations.The emulator used to produce the SA results below is the

Adaptive COmponent Selection and Shrinkage Operator(ACOSSO).48 It belongs the Smoothing Spline (SS) ANOVAclass of nonparametric regression methods. The SS-ANOVAapproach is to estimate the functional components of thefunctional ANOVA decomposition

∑ ∑ ∑θ θ θΘ = + + + ···

+ Θ

= = = +f b f f

f

( ) ( ) ( , )

( )

j

p

j jj

p

k j

p

j k j k

p

01 1 1

,

1,..., (27)

where f j are the main effect functions; f j,k are the two-wayinteraction functions; and p is the dimension of Θ. In general,the expansion in eq 27 extends up through p-way interactions.However, it is rarely the case in practice that interactionsbeyond orders of two or three are very important. Therefore,the model is usually truncated after the two-way interactions,and three-way can be added if any lack of fit is present. Thetwo-way interaction model was used to produce the resultsbelow. The functional components ( f j, f j,k) are estimated byadding a roughness penalty to a least-squares optimization overa rich class of smooth functions, just as in the simple univariatesmoothing spline problem (see ref 49 for example). TheACOSSO approach uses an L1 type penalty (like that used inthe LASSO50) to simultaneously achieve smooth estimates ofthe functional components and sparse solutions (i.e., variableselection). See ref 48 for the full details of the ACOSSOemulation method.

■ QUANTUM CHEMICAL METHODSDensity functional theory (DFT) and wave function-basedmethods were performed using Gaussian 09.51 For DFT,B3LYP52 and PBE053,54 functionals were used. The wavefunction methods were second-order Møller−Plesset perturba-tion theory (MP2) along with a couple cluster approach withsingle and double substitutions (CCSD).55 The basis set usedfor all calculations was 6-31++G**. For calculations of species

in solution, the polarized continuum model (PCM) wasemployed.Electronic structure calculations as applied to the formation

of carbamic acid in alkanol- and ethyleneamines were reviewedin a recent study on the uptake of CO2 in supported aminesorbents.56 This included an assessment of the accuracy ofquantum chemical methods, based on recent benchmarkingstudies.57,58 In conjunction with an accurate basis set (like 6-311++G**), it was concluded that MP2 is expected to be themost accurate method, although the hybrid DFT approach ofPBE0 was also within “chemical accuracy” of 1 kcal/mol (4.2kJ/mol). In comparison to the calculated enthalpies for theadsorption of CO2 for a number of different ethylamines, asmall spread in binding energy was observed. This relativelysmall spread denotes a weak dependence on both the alkylchain length (methyl vs ethyl) and primary vs secondary amine.With this weak dependence, it was concluded that the resultswere transferrable to the PEI polymer chain. Such observationsenable a focus on smaller molecules in place of more arduouscomputations using macromolecules. The molecules consideredin the present study were monomethylamine (MMA),dimethyleneamine (DMA), and diethylenetriamine (DETA).

■ EXPERIMENTAL SECTION

Sorbent Synthesis. An SSA sorbent created at NETL wasinvestigated via thermogravimetric analysis (TGA), providing aset of results against which the model output can be evaluated.This sorbent, labeled NETL-196C, consists of linear PEI(molecular weight 423 g/mol) impregnated on a commerciallyavailable silica xerogel substrate (Fuji Silysia) with an as-received pore volume of 1.77 cm3/g and mean pore diameter of24.0 nm. Full details of the sorbent synthesis are available in aprior publication.39

Thermogravimetric Analysis. CO2 adsorption data forthe sorbent were experimentally obtained using a ThermoScientific ThermMax 300 thermogravimetric analyzer. In atypical experiment, a 50 mg sample was loaded within amicrobalance quartz sample bowl. Prior to adsorption measure-ments, the samples were heated to 105 °C in nitrogen (flowrate: 100 mL/min) at a heating rate of 5 °C/min and heldisothermally for 90 min to remove preadsorbed CO2 andmoisture. The temperature was then increased to the initialadsorption temperature (108 °C) before switching to a drymixture of 4%, 10%, and 18.5% CO2, balance nitrogen,maintaining a flow rate of 100 mL/min. Subsequent CO2adsorption steps were conducted at 100, 92, 65, 57, 49, and 41°C, followed by desorption steps at 65 and 108 °C. The holdtime was approximately 90 min for each step. For TGA runscontaining moisture, the purge gas stream was run through asparger imparting the requisite moisture content.

■ RESULTS AND DISCUSSION

TGA. The TGA results for dry CO2 atmospheres appear inFigure 2. While it is clear that equilibrium is not reached at 65,57, and 49 °C, the weight profile reaches a plateau at 41 °C.This is followed, however, by an increase of the temperature to65 °C, upon which the sorbent weight, after an initial sharpdrop, begins to rise again. This behavior shows that the plateauat 41 °C is not indicative of equilibrium. What is indicatedinstead is that after an initial adsorption at that temperature akinetic barrier is reached, effectively cutting off furtheradsorption. The clearest explanation for this effect is that

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CO2 is able to adsorb at the gas−amine interface at 41 °C butunable to move appreciably into the amine bulk.By contrast, the TGA curves collected with 9% H2O in the

gasseen in Figure 3show no such pseudoequilibria.Contrast of the weight gain at 10% CO2 between humid anddry conditions shows a considerable increase upon theintroduction of water. This increase is not fully explained bythe uptake of water by the sorbent, as the TGA trace for 9%H2O, balance N2 (red curve in Figure 3) shows. The anomalousdata at low temperatures seen in the CO2−H2O mixture arelikely due to low-temperature condensation of carbonic acid.Parametric Study. The parameter ranges used in the study

are found in Table 1. Model evaluations at several parametersettings, w(ξ; Θi), i = 1, ..., n, were collected. In this case, twosamples of 128 and 64 runs, respectively, for a total of 192model evaluations were obtained at the points [Θ1, ..., Θ192]. Ofthese 192 runs 61 of them failed, to leave a total of 131 validruns. The sample was obtained via a Latin Hypercube Sampling

technique,59 but with a constraint on the entropy of reactionsfor 1 and 2, namely, that ΔS1 < ΔS2, reflecting the fact that thetransition from the gas to the adsorbed state should dominatethe total entropy change in the formation of carbamate fromgaseous CO2.For each successful run, a set of simulated TGA curves was

created, with a program of temperature changes at four setoxygen partial pressures adhering precisely to the programdescribed above. Those curves were qualitatively evaluated todetermine whether or not they captured the behavior indicativeof diffusion-limited pseudoequilibria seen in the experimentalsystem. This was in fact achieved for several cases; one of theclearest is shown in Figure 4. Inspection of the simulation datashows that, in fact, concentration gradients remain frozen inplace upon a decrease in temperature, indicating diffusivecontrol of not only the kinetic but also the apparent equilibriumbehavior of the system.The emulator was then fit to these data (at a particular state

point ξ) and then used to produce estimates of the sj(ξ) andj(ξ) via Monte Carlo integration. A separate emulator was fit

to the data w(ξ; Θi), i = 1, ..., n, for the four distinct pressures,each at 100 separate time points. The resulting estimated totalvariance indices are plotted across time for each of the fourpressure settings in Figure 5. The results show that three of thefour most sensitive parameters are those that control thestability and mobility of zwitterions, with the most sensitiveparameter the entropy of zwitterion formation (ΔS1). Similarly,

Figure 2. (a) TGA results for NETL-196C and (b) a close-up view ofthe same data highlighting the pseudoequilibrium at 41 °C. (Thelegend in part (a) pertains to both figures.) Time t = 0 in the plotscorresponds to the point at which CO2 was introduced into thechamber.

Figure 3. TGA results for NETL-196C in gas containing 9% H2O andeither 0% or 10% CO2, balance N2.

Table 1. Parameter Ranges Used in the Study

parameter low high

log10(Ko/τ2) −10.5 −8.0Δ3 1 10nv (mol/m3) 5000 25000f 0.1 5ΔH1 (kJ/mol) −57.9 −4.8ΔS1 (J/mol K) −200 −41.6ΔH2 (kJ/mol) −91.7 0ΔS2 (J/mol K) −200 −10ΔH2

⧧ (kJ/mol) 9.6 96.4log10(ζ) 1 8ΔHb

⧧ (kJ/mol) 19.2 125log10(ζb) −11 −2

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scatter plotsplots of the average weight gain of allparametrizations studied versus the value of a singleparametershown in Figure 6 confirm that the parameterscontrolling the number and mobility of diffusive intermediatesare the most influential on average.With any problem involving a complicated model it is

important to assess the robustness of the results. A simple, buteffective, approach to accomplish this in SA studies is to applyalternative emulators. Thus, we also applied the traditionalsquared exponential covariance Gaussian process model60 andthe Bayesian Smoothing Spline ANOVA model46 to producethe SA quantities. All approaches gave very similar results, soonly those for ACOSSO are shown. All of these emulationapproaches are reviewed in ref 47.

Quantum Chemistry. Given the results of the parametricstudy, which indicate the importance of the stability of diffusiveintermediates to the effective capacity of amine sorbents,zwitterion stability in ethylamines was considered in the contextof a quantum chemical study. Figure 7 depicts a zwitterionformed with dimethylamine (DMA). The energies of formationfor this species along with that of two other ethylaminezwitterion speciesmonomethylamine (MMA) and diethyltri-

Figure 4. Simulated TGA curve exhibiting transport control of theadsorption rate and capacity at low temperature, with behaviorqualitatively similar to the experimental data shown in Figure 2.

Figure 5. Total variance indices estimates via ACOSSO plotted across time for each of the four pressure settings: (a) 4%, (b) 10%, (c) 18.5%, and(d) 100% CO2, balance inert. Curves for the four most sensitive parameters are labeled explicitly, while the curves for the reamining parametersappear at the bottom.

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amine (DETA)in the gas phase and in solution werecalculated according to the methods detailed previously.The results appear in Table 2. All results appearing in the

table were calculated using the PCM solvation model (whereappropriate) and the 6-311++G** basis set. The zwitterion wasfound to be unstable for all chemistries investigated and alllevels of theory in the gas phase and in a polar environment (εr= 2.9) similar to that of anhydrous PEI. (Positive formationenergies are estimated using a stable zwitterion configuration

obtained in a much more highly polar medium.) For a dielectricmedium similar to that of water (εr = 78), results are mixed:PBE0 yields a stable zwitterion for both monoaminechemistries. MP2 yields a slightly downhill reaction for DMAbut an unstable zwitterion for MMA. The CCSD calculation forDMA also yields a stable zwitterion, with a slightly positiveformation energy. B3LYP predicts no stable zwitterions in H2O,although this is perhaps the least reliable of all the methodsused. The results for DETA are more uniformly uphill. Areasonable conclusion is that ethylamine zwitterions may be

Figure 6. Scatterplots of the integral over time of the CO2 loading curve for partial pressure of 10% versus the model parameters along with thecorresponding estimated main effect curves from ACOSSO (red line) for (a) enthalpy and (b) entropy of zwitterion formation and (c) enthalpy and(d) entropy of carbamate formation from the gas.

Figure 7. Zwitterion formed with dimethylamine.

Table 2. Formation Energies (kJ/mol) for ZwitterionSpecies According to Various Methods of Calculation andEthylamine Chemistries in Dielectric Media Representingthe Gas Phase, DPA (as a Proxy for PEI), and Water

εr = 1 εr = 2.9 εr = 78

method MMA DMA MMA DMA MMA DMA DETA

B3LYP 50.1 45.1 25.1 37.6 9.2 2.9 10.5PBE0 40.1 33.9 12.5 8.4 −8.4 −10.9 5.0MP2 60.2 42.6 15.9 −0.4 13.8CCSD 68.1 49.8 14.6 0.4

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barely stable in an aqueous environment, depending on thespecific chemistry, but are not stable in a polar environmentsimilar to that of anhydrous PEI.Explicit water molecules were also considered as a part of the

study. From these calculations, two different types of boundassociates involving amine, water, and CO2 emerged. These areshown in Figure 8(a) (linear topology) and (b) (ring

topology). Energies of formation in the gas phase were foundto be −28.0 and −47.2 kJ/mol for linear and ring topologies,respectively, using B3LYP.

■ DISCUSSIONThe salient conclusions of the study arise from the comparisonof the sensitivity results with the quantum chemical results. Theformer emphasize the importance of diffusive intermediates: itis the concentration of those intermediates that controls themeasured capacity of the sorbent because a diffusionmechanism is required to open up amine sites in the polymerbulk for the formation of carbamate. The quantum study raisesinteresting questions about the identity of those intermediates:the stability of zwitterions even in aqueous solution isquestionable; it seems therefore unlikely that the zwitterioncould serve as a diffusive intermediate in anhydrous PEI.However, quantum calculations have also shown that there areother candidates for the intermediate in humid CO2. To besure, the existence of the associates shown in Figure 8 is stillhypothetical, but it is at least not foreclosed by the quantumcalculations as is the case with the zwitterion. Additionally, ifthe concentration of diffusive intermediates controls capacity,then the TGA results of Figure 3 become strong evidence infavor of a role for water in the formation of diffusiveintermediates. Direct experimental evidence of the proposedintermediates could be available through IR spectroscopy, if thevibrational modes of water are affected appreciably by thephysical bonds formed with CO2 and the amine.There remains the question of adsorption in dry conditions,

which under the hypothesis presented would not involve accessto amine sites in the polymer bulk. It is possible that theobserved dry CO2 capacity reflects primarily surface or near-surface adsorption, as reflected in the dependence of thecapacity on the internal surface area of the sorbent. In addition,

trace amounts of water in the nominally dry experiment maylead to the formation of a small concentration of diffusiveintermediates, leading to limited transport of CO2 in thepolymer bulk.

■ CONCLUSIONSA combination of modeling, statistical analysis, quantumchemical calculations, and experimental results have led to anew hypothesis for CO2 capacity in highly loaded, PEI-impregnated SSA sorbents. This new hypothesis holds thatcapacity is primarily controlled by the availability of diffusiveintermediates for the transport of CO2 in bulk PEI. Theseintermediates are, in turn, dependent on the availability ofwater molecules. Specific chemistries for the intermediates havebeen proposed.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: david.mebane@mail.wvu.edu.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSHelp and support from David C. Miller and Leslie M. Moore isgratefully acknowledged. Partial support for David Mebane wasprovided by an ORISE postdoctoral fellowship. Funding forthis work was provided by the Department of Energy throughthe Carbon Capture Simulation Initiative.

This report was prepared as an account of work sponsoredby an agency of the United States Government. Neither theUnited States Government nor any agency thereof, nor any oftheir employees, makes any warranty, express or implied, orassumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information, apparatus,product, or process disclosed, or represents that its use wouldnot infringe privately owned rights. Reference herein to anyspecific commercial product, process, or service by trade name,trademark, manufacturer, or otherwise does not necessarilyconstitute or imply its endorsement, recommendation, orfavoring by the United States Government or any agencythereof. The views and opinions of authors expressed herein donot necessarily state or reflect those of the United StatesGovernment or any agency thereof.

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