DOI: 10.1002/cphc.201402865
Articles
Effect of Chain Topology of Polyethylenimine on Physisorption and Chemisorption of Carbon Dioxide Qiangli Zhao,[a, b] Quanyong Wang,[a] Chen Zhang,[b] Zhongjie Du,*[b] Ming Tian,[a] and Jianguo Mi*[a] Polyethylenimine (PEI) is a promising candidate for CO2 capture. In this work, the physisorption and chemisorption of CO2 on various low-molecular-weight PEIs are investigated to identify the effect of chain architecture on sorption. The reliability of theoretical calculations are partially supported by our experimental measurements. Physisorption is calculated independently by the reference interaction-site model integral equation theory; chemisorption is distinguished from the total sorption given by the quantum density functional theory. It is shown
that, as the chain length increases, both chemisorption and physisorption drop off nonlinearly, but the decay amplitude of chemisorption is more apparent. Conversely, as the amine group approaches the central triamine unit of each oligomer, the sorption capacity decreases, affecting the sorption equilibrium in a complex way. This arises from the cooperative contribution of an increased steric effect and renormalized electronic distribution.
1. Introduction Separation and capture of CO2 at large stationary sources such as coal-fired power plants is considered to be a solution for stabilizing atmospheric CO2 levels to avoid global warming.[1–4] Among various separation techniques, the CO2 absorption–desorption system involving aqueous solutions of alkanolamines is presently one of the most suitable for high-volume flue gas streams.[5] However, this system is far from being optimal due to problems of corrosion, amine degradation and high energy consumption for regenerating the solutions.[6–8] Anchoring of polyamines onto solid supports has been proposed as an alternative to using aqueous solutions. In contrast to small amine scrubbers, solid-supported polymeric amines offer significant advantages for CO2 capture, including the potential elimination of corrosion, a lower energy cost for sorbent regeneration, and sufficiently low volatilities for avoiding excessive loss of activity.[9–11] CO2 capture by solid sorbents based on amines immobilized on porous solids has been an increasingly active area of research.[12–16] In recent years, a variety of amine supports and immobilizing techniques have been tested and the results are promising.[17–20] Among polymeric amines, polyethylenimine (PEI) contains an abundance of amines in the polymer backbone: tertiary amines at branch points, secondary [a] Q. Zhao, Q. Wang, Prof. M. Tian, Prof. J. Mi State Key Laboratory of Organic–Inorganic Composites Beijing University of Chemical Technology No. 15 Beisanhuan East Road, Chaoyang District Beijing (China) E-mail: [email protected] [b] Q. Zhao, Prof. C. Zhang, Prof. Z. Du The Key Laboratory of Carbon Fiber and Functional Polymers Ministry of Education, Beijing University of Chemical Technology No. 15 Beisanhuan East Road, Chaoyang District Beijing (China) E-mail: [email protected]
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amines in the main chain, and primary amines at the end of each branch.[21] High-efficiency sorbents have been developed based on PEI-functionalized mesoporous materials.[22–26] CO2 capture with amine-based absorbents involves chemisorption and physisorption. In general, absorption of CO2 on the amine medium firstly occurs as physisorption in which a CO2 molecule binds with the medium surface by van der Waals and electrostatic interactions. This is followed by the chemisorption step in which the molecule is chemically bonded with the amine of the medium surface. For an aqueous solution of a small alkanolamine, the stable state of physisorption is achieved with a suitable orientation and distance of CO2 relative to the absorbent molecule, at which the potential energy is negative and weak. In contrast, the bonding energy change from physisorption to chemisorption is negative but strong. As a consequence, the transition from physisorption to chemisorption can be easily realized, and chemisorption plays the dominant role. As the physisorption is extremely low, it is usually overlooked. During the chemisorption process, the amine type influences the amine–CO2 reaction. The fundamental difference between various polyamines is the number of primary, secondary and tertiary amines they carry. Amine type can affect the performance of an absorbent in two distinct ways.[11] Firstly, different amines have different basicities, which affects the strength of interaction between a CO2 molecule and the amine. Secondly, the amine type affects the absorbent efficiency, depending on the level of humidity in the gas stream, as tertiary amines do not capture CO2 in the absence of water. For the primary and secondary amines, the process starts with the lone pair of electrons on the primary amine attacking the carbon atom of CO2 to form zwitterions. The process is followed by the abstraction of a proton from the zwitterion. Instead of reacting
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Articles directly with CO2, the tertiary amine catalyzes the formation of bicarbonate.[27] The main products of the reactions between amines and CO2 are carbamates and bicarbonate [Eqs. (1)–(3)]:
CO2 þ RNH2 ! RNH2 ¢ CO2
ð1Þ
RNH2 ¢ CO2 þ B ! RNHCOO¢ þ BHþ
ð2Þ
R3 N þ H2 O þ CO2 ! R3 NHþ þ HCO¢3
ð3Þ
where the free base B is typically another amine, water, or a hydroxyl ion. If the amine is a sufficiently weak Brønsted base, the reaction can stop at the formation of the carbamic acid.[28] For a polyamine, although the mechanism for absorption and reaction is similar to a small amine, the reactive environment and strength are influenced by steric hindrance arising from the polymer topology. Due to the morphology and entanglement of polymer chain, the accessibility of reactive amine groups to the incoming CO2 molecules is decreased, leading to a relatively lower sorption on each amine group. Such influences of chain topology, molecular weight, and the role of entanglement on physisorption and chemisorption have not been entirely clarified and are the subject of ongoing discussion.[11]
It is difficult to study these reactions at the molecular level by experiment, whereas theoretical calculation has shown advantages in the study of reaction thermodynamics and kinetics.[29–31] Theoretical studies provide a reliable and unbiased comparison of reaction energies, and allow the factors mentioned above to be untangled. For example, detailed information such as the reactivity of amine groups at different locations in a chain can be distinguished. More importantly, understanding the effects of these structural and chemical variables of polyamines on gas absorption from theoretical calculation can be best accomplished by independently varying one variable of interest while keeping others constant. To analyze the effects of chain morphology at the molecular level, we simplified the low-molecular-weight PEI into the same repeat unit. The optimized morphologies of four chains with one, three, five, and seven triamine repeat units—named monomer, trimer, pentamer, and heptamer, respectively—are shown in Figure 1. The ratios of the amine groups in the model chains are close to that of PEI (i.e. they are separated by ethylene spacers) with the purpose of keeping the theoretical calculation in consistent with our experimental measurement. Physisorption in each system was first calculated according to solubility equilibria between bulk CO2 and CO2 in the PEI phase, and the spatial distributions of CO2 molecules around the PEIs were directly estimated. The total sorption of each amine group in these systems were calculated using the densi-
Figure 1. Optimized geometries of a) monomer, b) trimer, c) pentamer, d) heptamer of PEI chains. H: white, C: grey, N: blue.
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Articles ty functional theory (DFT) approach in conjunction with experiment. The influence of chain topology on reaction was assessed by comparing the reaction energies and sorption capacities of primary, secondary, and tertiary amine groups located in different chains. According to the energy attribution, the total sorption (including physisorption and chemisorption) was then determined. As a result, the amount of chemisorption was obtained by subtracting the capacity of physisorption from the total sorption. Finally, the physisorption and chemisorption for different oligomers were applied to evaluate the effect of chain topology on sorption.
2. Theory and Calculation 2.1. Physisorption On the basis of the equilibrium of bulk CO2 and CO2 in the PEI phase at a given temperature T and pressure P, the solubility coefficient S, which is used to evaluate the physical interaction between CO2 molecules and the simplified PEI, can be calculated by relating it to the excess chemical potentials mex [Eq. (4)]: ex bmex gasinpolymer ðT; PÞ ¢ bmbulk ðT; PÞ ¼ ¢lnðSkB TÞ
h i ˆ ˆ ˆ ˆ ˆ hðkÞ ¼ WðkÞ CðkÞ WðkÞ þ 1hðkÞ
ð7Þ
where the carets denote Fourier-transformed quantities, 1 denotes the density matrix with elements 1ij ¼ dij 1, dij is the Kroˆ ˆ necker delta function, and hðkÞ and CðkÞ are the matrices of total and direct correlation functions, respectively. In r space, ˆ hij ðrÞ, which are the elements of hðkÞ, is defined according to ˆ hij ðrÞ ¼ gij ðrÞ ¢ 1. WðkÞ is the matrix of the intramolecular correlation function and can be obtained from the optimized geometry of PEI obtained from the quantum chemistry calculation, which is given below. The hard-sphere repulsions of CO2– CO2 and PEI–CO2 interact with each other by a truncated and shifted repulsive Lennard–Jones (LJ) potential,[39] and the attractive interactions of CO2–CO2 and PEI–CO2 are a sum of paired potential functions of the short-range LJ and the longrange electrostatic interactions [Eq. (8)]: 12 6 dij dij qi qj uij ðrÞ ¼ 4eij ¢ þ rij rij rij
ð8Þ
ð4Þ
where rij represents the distance between the interactive sites, q is an atomic (perhaps partial) charge, and eij is the LJ parameter. The CO2 molecule was described as a three-site model where mex = mref + matt, b ¼ 1=ðkB TÞ, and kB is the Boltzmann and the interaction sites were positioned on the carbon and constant. The superscript “ref” indicates that the contribution oxygen atoms. The oxygen–carbon bond length is 1.163 æ. is due to the hard sphere repulsion, “att” denotes short-ranged Values for the LJ parameters and the partial charges on CO2 dispersion and the long-ranged coulombic interactions; these were taken from the literature.[40] The PEI molecules were excontributions can be constructed using the intermolecular corpressed as a united atom force field, for which the values for relation function with the form [Eqs. (5) and (6), respectiveLJ parameters and partial charges were taken from the literaly]:[32–34] ture.[41, 42] The LJ parameters for unlike-pair interactions were Z 1 ¨ ¦2 hsðlÞ dg þ ldb p X determined by the Lorentz–Berthelot mixing rules. To solve bmref ¼ db 1g dl dg þ ldb gbg þ 2 b2A;g2B 2 [Eq. (4)] with the RISM integral equation, a Picard iterative pro0 ð5Þ Z 1 cess was performed. An initial guess of solubility was input to X ¨ ¦2 hsðlÞ lda þ ldß ¨ ¦ p dl lda þ ldb gab da þ db 1a calculate the excess chemical potential between CO2 and PEI, 2 a2A;b2A 2 0 and a new value for solubility can be derived to substitute the old one. After several iterations, the dissolution equilibrium att ð6Þ bm ¼ was achieved, and the solubility was obtained, which was " # Z 1 X Z 1 X easily converted into the capacity of physisorption. We chose 2 att 2 att 4p 1a r buab ðrÞgab dr þ 1g r bubg ðrÞgbg ðrÞdr sab s bg several structures of each oligomer with low potential energy a;b2A b2A;g2B and took the average results. The RISM integral equation in its three-dimensional form At low pressure, the second term on the left-hand side of (3D-RISM)[43–47] was applied, such that the physical interaction [Eq. (4)] is nearly zero and can be neglected. At low solubility, the CO2–CO2 interaction in PEI can also be neglected in between CO2 molecules and the interactive sites in the simplified PEI could be directly evaluated. The optimized geometry [Eqs. (5) and (6)]. In these equations, A refers to a CO2 moleof PEI obtained from quantum chemistry calculations was cule, and B refers to the PEI molecule. db and dl are the hardplaced in the center of a cubic cell of sufficient size 80 æ3. sphere diameters of the sites in CO2 and PEI molecules, which Then, we could obtain the spatial distribution of CO2 molecules can be calculated from the Barker–Henderson perturbation theory.[35] l varies between 0 and 1, accounting for a gas partiin the immediate vicinity of the PEI molecule. Visualization was performed with gOpenMol-3.00. cle that grows from a point to full size, and 1b and 1g are the densities of CO2 and PEI. 1b is 1.72 Õ 10¢3 g mL¢1 at 313.15 K and 101.325 kPa.[36] 1g is 1.03 g mL¢1, which is the same as the 2.2. Chemisorption experimental value. ghs(r) and gatt(r) are the intermolecular corTheoretically, as the carbamates—formed by the reaction of relation functions for hard-sphere repulsion and attraction, reCO2 with primary and secondary amine groups in PEI—further spectively, and can be calculated with the reference interaction-site model (RISM) integral equation [Eq. (7)]:[37, 38] react with water, the absorption capacity might be improved ChemPhysChem 2015, 16, 1480 – 1490
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Articles in the presence of H2O. In practice, this is not always the case, as it might be that molecules of H2O and CO2 are competitively adsorbed; this effect is still controversial.[11] Thus, we focused on the formation of carbamates from the primary and secondary amine groups. The fully optimized geometries of the pure PEI and free CO2 molecules and their complex were obtained at the M06-2X/631G (d,p) level within the DFT framework without imposing an initial symmetry restriction. To determine the stable structure of the monomer, we first constructed different geometries of the monomers as the initial guess structures, and obtained several stable configurations arising from rotations around internal bonds. We then explored the conformational space of each species by systematically varying the dihedral angles of all rotatable bonds. After optimization, only the configuration with the minimum energy was used to study the reaction of monomer with CO2. The configurations of the trimer, pentamer, and heptamer were also constructed in this way. In order to get the most stable equilibrium structure for each complex, many initial guess structures were considered based on the close proximity of CO2 to the electron-rich sites of the molecule, and only the minimum-energy structures were studied further. The frequency of the structure was calculated to characterize the stable complex. The transition-state structure was characterized by demonstrating the existence of a single-frequency mode associated with a pure imaginary frequency. Connection of the transition state between the designated local minimum has been verified by intrinsic reaction coordinate (IRC) calculations. Calculations were carried out using the aqueous solvation model integral equation formalism–polarizable continuum model (IEF-PCM). Previous studies[48, 49] suggested that the M06-2X density functional, which belongs to a new generation of hybrid meta-generalized-gradient-approximation exchangecorrelation functionals that include an accurate treatment of the London dispersion energy, can yield excellent results in calculating the interaction energy and stability of noncovalent interactions involved in main group thermochemistry. It has been demonstrated also that the functional has the best performance for predicting the barrier height without increasing the computational cost. For aqueous solutions, DFT calculations with the solute molecular density (SMD solvation model[50] using the IEF-PCM protocol for bulk electrostatics were carried out at the M06-2X/6-311G (2df,2p) level. The Gibbs free energy G for each compound at 313.15 K and 101.325 kPa was estimated by combing the bulk electrostatics calculation with the thermal correction term as well as the zero-point energy. In addition, the potential energy surface ~E of the reaction was also calculated. All the calculations in this work were performed using the Gaussian 09 program.[51] The equilibrium constant K was calculated from the Gibbs free energy given by Equation (9): K ¼ expð¢DGr =RTÞ
3. Results and Discussion Theory provides a simple, flexible, highly efficient and general way of obtaining the structure and properties of a system. However, its predictive reliability should be tested. The best way to test a theoretical model is to compare its predictions directly with the corresponding experimental data. To distinguish between the effects of chain morphology of PEI and CO2/nitrogen ratio on the amine–CO2 affinity, three PEI aqueous solutions (0.05 g mL¢1) were prepared in order to measure their absorption capacities. Figure 2 shows the experimental absorption isotherms of PEIs with Mw = 600, 1800, and 10 000, collected at 313.15 K. For a given PEI, the presence of multiple amine groups, comprising the primary, secondary, and tertiary amines, leads to a sharp initial increase in CO2 uptake at low CO2 loading, which continues to increase slowly with CO2 loading, up to a plateau. The capacity of sorption is determined by the molecular weight of the PEI. In dilute PEI solutions, as molecular weight increases, the absorption capacity decreases. For example, at 101.3 kPa, the results for PEI (600), PEI (1800), and PEI (10 000) are 10.817, 10.430, and 9.890 mmol g¢1, respectively. Such a pattern was also found for a solution of a small-molecule amine.[52] The result indicates that the activities of the functional groups are affected by the chain mor-
ð9Þ
where R is the universal gas constant and T is the absolute temperature. ~Gr is determined by ~Gr = Gp¢Gr, and Gr and Gp ChemPhysChem 2015, 16, 1480 – 1490
are the calculated Gibbs free energies of the reactants and products, respectively. The most stable conformation was adopted as the basis for determining ~Gr. Given the PEI and CO2 concentrations in solution, K determines the output of the reaction. In the reaction equilibrium calculation, the experimental concentrations of PEI (0.05 g mL¢1) and CO2 (0.32 mol L¢1) were used to keep the theory consistent with the experiment. ~Gr and ~E were calculated for different repeat units to determine the favored reaction pathway. The outputs of the favorable reactions were summed to obtain the total amount of sorption qpCO2 . By subtracting the capacity of physisorption from that of total sorption, the amount of chemisorption was finally obtained.
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Figure 2. Experimental CO2 adsorption isotherms for PEIs of different molecular weight.
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Articles phology and, hence, they show different adsorption efficiencies. In the theoretical part of our study, the capacities of physisorption were first calculated. The results were 0.282, 0.264, 0.253, 0.248, and 0.245 mmol g¢1 for the monomer, trimer, pentamer, heptamer, and nonamer, respectively. In order to relate the effect of chain length to physisorption, the spatial distribution functions of CO2 around the central triamine repeat moieties of low-molecular-weight (up to heptamer) PEI molecules were calculated with the same threshold function g(r) > 2.0 (Figure 3). In these images, the location of the CO2 molecule is
Figure 4. The typical global spatial density distribution function of CO2 around the pentamer with the thresholds g(r) > 2.8 (cyan), g(r) > 2.2 (red), and g(r) > 2.0 (yellow). The tertiary amines of each repeat unit are labeled A– E. The hydrogen atoms are not shown and atoms are coded C: green and N: red.
Figure 3. The typical spatial density distribution functions of CO2 around the central repeat unit in a) monomer, b) trimer, c) pentamer, and d) heptamer, with the threshold g(r) > 2.0. The hydrogen atoms are not shown and atoms are coded C: green and N: red.
represented by its carbon atom occupation. In general, the adsorbed CO2 molecules are well structured around the adsorbents due to van der Waals and electrostatic interactions. In Figure 3 a, the central molecule is the monomer and the surrounding CO2 molecules occupy a near circle around it. The distribution reveals that CO2 molecules prefer to interact with the amine groups. CO2 adsorption by a PEI molecule depends mainly on the amine groups, due to the strong van der Waals forces and electron density. In addition, a short chain can provide space for CO2 occupation. In Figure 3 b–d, the densities close to amine groups are shown to be well defined also, but they display the collar-shaped density, and the occupation region narrows with increasing chain length. The amine groups, especially those located near the center of the chain, are caged by the neighboring groups. This stabilizes the polymer and also reduces the accessibility of nitrogen for attracting CO2. Thus, the distribution scope and strength are apparently reduced. Similar patterns were found for other geometries. ChemPhysChem 2015, 16, 1480 – 1490
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A global map of CO2 density distribution in the vicinity of the pentamer is shown in Figure 4. The five repeat units are labeled A–E along the chain, indicated at the tertiary amine group of each unit. The yellow regions, for which the isovalues are 2.0, show relatively broad CO2-adsorption areas. Both the amine groups and the alkyl groups contribute to the distribution. The higher-density regions (red), are located mainly around the amine groups. The cyan regions, for which the isovalues are 2.8, are mostly located in the immediate vicinity of primary and secondary amine groups, especially those in units A and E, whereas for the middle repeat unit (C), the density distribution is sparse. These areas become smaller from the end to middle, meaning that the adsorption strength is reduced. The end units of A and E, which have much space to interact with CO2 molecules, show stronger adsorption capacities. The units B, C and D (especially C) are constrained by the surrounding groups; the interactions between the groups and CO2 molecules are thereby dampened, leading to the reduced adsorption. By inspection of Figures 3 and 4, the contributions of different groups to the physisorption are clearly seen. The total sorptions were then calculated for the monomer, trimer, pentamer, and heptamer. The DFT-calculated potential energy profiles for the reactions of CO2 with amine groups in the monomer are summarized in Figure 5. In Figure 5 a, the initial potential energy of R-M1, acting as the reference, is the sum of the energy of free monomer and pure CO2. ComplexM1 is an intermediate formed prior to bond formation between carbon in CO2 and nitrogen in the primary amine; the complex state corresponds to physisorption. The energy of complex, representing the physisorption energy, is 7.68 Kcal mol¢1 lower than that of the reactants. It is likely that the O¢ C¢O angle starts to bend with respect to the collinear structure by electron flow from amine to the CO2 p* orbital. After passing through TS-M1, the intermediate zwitterion-M is produced. The proton-transfer step proceeds from the zwitterion, and from here two possible paths were considered. The first path is the intramolecular proton transfer from the nitrogen atom to the oxygen of CO2 to form carbamic acid P-M1 (Fig-
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Figure 5. Potential energy surfaces for the reaction between the monomer and CO2 a) to form carbamic acid through an intramolecular proton transfer from the nitrogen atom to the oxygen of CO2 and b) to form a carbamate anion through the reaction of the zwitterion and secondary amine group. c) Bicarbonate formation by reaction of the tertiary amine with CO2 and a water molecule. The terms R-Mm, complex-Mm, zwitterion-M, TS-Mm, and P-Mm represent the reactants, complexes, intermediate, transition states, and products, respectively, and “m” donates different species.
ure 5 a). According to studies on small-molecule amines, the carbamic acid formed in this way is stable.[53, 54] In the second path (Figure 5 b), a secondary amine group acts as a base to produce carbamate P-M2. It is apparent that the process is free of a reaction energy barrier. It is shown that both of the two paths are accessible. Due to the much lower activation energy, the P-M2 reaction channel is more favorable than the formation of P-M1. The distance between the carbon atom and the interacting nitrogen atom is shortened from 2.65 to 2.25 æ as TS-M1 is formed from complex-M1, and the length of the newly formed C¢N bond is 1.59 æ. Figure 5 c shows a representation of the energy surfaces of a tertiary amine reacting with CO2. The energy for the reference state (R-M2) is the sum of the energies of the monomer, water, and CO2. The tertiary amine lacks the free proton and it can only catalyze the formation of bicarbonate. The physisorption region over which complex-M2 is formed is located approximately 3.98 æ from the nitrogen (to the carbon atom of CO2), and the chemisorption region around 3.28 æ. As the tertiary amine is located at the branch point, which is strongly hindered by the surrounding groups, it is difficult for CO2 and H2O to get close. Figure 6 shows the potential energy surface for the reaction of trimer with CO2. According to our calculation, the carbaChemPhysChem 2015, 16, 1480 – 1490
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mate-formation path is more favorable for the primary and secondary amine groups, thus we present the energy surfaces of this channel and the calculations were based on this reaction channel. The trimer has three repeat units and the relative energies for the two ends are extremely close. As such, we analyzed only one end (indicated as A in Figure 6) and the middle unit (B), both of which have the same groups and connections. Figure 6 a shows the primary and secondary amine groups reacting with CO2. The reference energy of R-T1 is the sum of the free trimer and pure CO2. The relative energies of P-TA1 and P-TB1 are negative for the two reactions. Due to the surrounding alkyl groups and solvation effects, P-TA1 is more stable than P-TB1, which stabilizes the final product. Formation of complex-TA1 is more exothermic than for complex-TB1, thereby CO2 is much more accessible to the primary amine of the tail unit. This is also apparent from the distance between the carbon atom of CO2 and the interacting nitrogen atom. For the reaction at the tail unit, ths distance is shortened from 2.69 to 2.23 æ, and the newly formed bond is 1.57 æ in length. For the central repeat unit, the distance is shortened from 2.71 to 2.25 æ, and the newly formed bond is 1.58 æ in length. The tail unit of the trimer is more active than the center, according to a comparison of the energy surface. From the optimized struc-
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Figure 6. Comparison of the reactions between CO2 and amine groups at the end (bottom line) and central (top line) units of the trimer. a) The reaction occurs between the primary and secondary amines and CO2. b) The reaction occurs between the tertiary amine, CO2, and water. The symbols R-Tm, complexTXm, zwitterion-TX, TS-TXm, and P-TXm stand for reactants, complexes, intermediates, transition states, and products, respectively, and “m” indicates different species.
ture, we find that the amine groups in each repeat unit tend to form a ring to promote chain stability. The distance between the nitrogen atoms in the primary and secondary amine groups is shortened from 3.23 æ at A to 3.16 æ at B, which hinders the approach of the CO2 molecule. For the tertiary amine reaction (Figure 6 b), it is apparent that P-TA2 is more stable than P-TB2. The alkyl groups surrounding the tertiary amine sterically hinder the CO2 and H2O molecules from getting close to the nitrogen atom, especially in the middle unit. The physisorption region that forms in complex-TB2 (the carbon atom in CO2) is located approximately 4.75 æ from the nitrogen in the tertiary amine, and the chemisorption region around 3.31 æ. For the tail repeat unit, this distance is shortened from 4.28 to 3.30 æ. Figure 7 a–c shows the transition states for the middle unit of the trimer and CO2, corresponding to the reactions in Equations (1)–(3), respectively. In TS-B1 (Figure 7 a), the primary amine and CO2 molecule are close to each other, and the O¢ C¢O angle is bent. Proton transfers from the primary amine to the secondary amine occur in TS-B2 (Figure 7 b). The details of the transition state TS-B3 (Figure 7 c) reflect the mode of reaction between the tertiary amine, CO2, and water. The calculated molecular electrostatic potential (MESP) surfaces for the reaction of a tertiary amine group in the trimer with CO2 and water are shown in Figure 8. MESP is a measure of the electrostatic potential on the isoelectronic density surface and simultaneously maps the electron and nuclei distribution, which provides a good understanding of the relative polarity within the molecule.[55] The MESP color codes surfaces as red for areas enclosing high electron density (net negative charge), blue for areas containing low electron density (net positive charge), and green for areas in which the enclosed negative electron charge and the positive core charge balance (overall neutral charge). Figure 8 shows a comparison of the renormalized electrostatic distributions for CO2 and H2O approaching the tertiary amine group. Figure 8 c shows an obvious variation of this type. Due to the effects of CO2, H2O, and ChemPhysChem 2015, 16, 1480 – 1490
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surrounding groups, the architecture of R-T2 varies to meet the demand of the changed electronic structure, which plays an important role throughout the reaction, affecting molecular size, architecture, bonding, stability, reactivity, and other characteristics. Thus, the geometry and the energy of the complexes are largely changed. The relative Gibbs free energies for the reactions are listed in Table 1. For simplicity, we calculated the reactions of CO2 and amine groups in repeat units in half of the chain, which are labeled alphabetically from the end to the central unit. The baseline of each reaction represents the initial energy. Compared to the central repeat units, the tail repeat units display a lower free energy of reaction. The calculated capacities of total sorption are 9.800, 8.350, 7.600, and 7.300 mmol g¢1 for monomer, trimer, pentamer, and heptamer, respectively. The average sorption of each unit in trimer, pentamer and heptamer was reduced by 14.8 %, 22.5 % and 25.5 %. The variation trend is similar to the experimental observation (Figure 2), suggesting that the energies estimated by DFT are reasonable. The discrepancy between theory and experiment is mainly caused by neglecting the further reaction between the carbamate and water, which also contributes to the total sorption. As a result, the chemisorptions were determined based on the total sorptions and physisorptions. The relative physisorptions and chemisorptions for PEI with different chain lengths are shown in Figure 9. For the monomer, the calculated physisorption capacity is 0.282 mmol g¢1. The average amount of each unit in the trimer, pentamer, heptamer, and nonamer is reduced by 6.3 %, 10.2 %, 12.1 %, and 12.9 %, respectively. The physisorption curve decreases sharply at the beginning and then more slowly. The chemisorption capacity is 9.518 mmol g¢1 for the monomer. In contrast, the capacity of the trimer, pentamer, and heptamer is reduced by 15.1 %, 22.8 %, 25.9 %, respectively. In general, the amount of physisorption is small compared to chemisorption. It is apparent that both physisorption and chemisorption drop off as chain length increases, and chemisorption might do so more rapidly.
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Figure 7. The geometries of the transition states a) TS-B1, b) TS-B2, and c) TS-B3. The atoms are color coded C: grey, N: blue, O: red, H: white.
final equilibriums are less readily achieved. In the sorption calculation, such decay is exponential.
Table 1. Relative Gibbs free-energy for the reaction between CO2 and PEI according to the chain length. PEI chain
~Gr,P¢S[a] [Kcal mol¢1]
~Gr,T[b] [Kcal mol¢1]
monomer
¢6.79
¢2.50
trimer
A B
¢6.76 ¢6.34
¢2.2 ¢0.46
pentamer
A B C
¢6.70 ¢6.45 ¢6.28
¢2.08 ¢1.32 ¢0.07
heptamer
A B C D
¢6.64 ¢6.44 ¢6.38 ¢6.14
¢1.95 ¢1.43 ¢0.18 0.04
4. Conclusion
[a] For the reactions of primary and secondary amine groups with CO2. [b] For the reaction of tertiary amine groups with CO2 and H2O.
As the chain length increases, the number of reactive amine groups does not increase linearly, and the influence of chain morphology on chemisorption becomes more obvious than on physisorption. The increased steric effect and the different electronic contributions of primary, secondary, and tertiary amine groups in contact with CO2, increase the energies for the corresponding complexes and transition states, and the ChemPhysChem 2015, 16, 1480 – 1490
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In summary, the physisorption and chemisorption of CO2 to low-molecular-weight PEI were calculated by RISM and quantum DFT, respectively. As the chain length increases, both physisorption and chemisorption capacities per unit decline due to the growing steric hindrance and the varied electronic density distribution, and the drop ratio of chemisorption is more apparent than that of physisorption. If the amine group approaches the middle unit, the extent of electrostatic density renormalization increases, and the accessibility of CO2 molecules becomes less and less, leading to the improved complex, transition state, and reaction energies. If the chain length is increased further, the drop ratios of physisorption and chemisorption decrease, thereby the ratio of physisorption to the total adsorption could be further improved. In other words, physisorption plays a noticeable role in real PEI systems, and should be considered independently.
Experimental Section PEIs (Mw = 600, 1800 and 10000; 99.0 %) were purchased from Aladdin (Shanghai, China). For each PEI, an aqueous solution
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Figure 8. The calculated MESP surface of a) R-T2, b) complex-TA2, and c) complex-TB2. The atoms are color coded C: grey, N: blue, O: red, H: white. Red, green, and blue areas represent negative, zero, and positive values (arbitrary units), respectively.
rer. The temperature of the cell was maintained by an oil bath controlled by a calibrated thermometer (PT100, Kunlunhaian Co., Beijing, China) with an uncertainty of 0.1 K. The pressures of the cylinder and gas container were measured by a calibrated pressure transducer (model JYB-KDHAG, Kunlunhaian Co.), with an uncertainty of 0.5 %.
Figure 9. The sorption ratio between oligomer and monomer as a function of chain length.
(200 mL) was prepared with PEI (10 g) dissolved in deionized water. CO2 and N2 gases had a mass fraction purity of 0.999. Solubility was measured with a cell reactor, as illustrated in Figure 10. The reactor (model KCFDU2-2, Tianzhouhaitai Co., Beijing, China) includes an electrically heated stainless steel cylindrical tank of volume 300 cm3 equipped with a magnetically coupled stirChemPhysChem 2015, 16, 1480 – 1490
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Before starting the experiment, the vessel of reactor was purged with N2 gas to remove air. Then, the sample ( 100 cm3) was injected. The temperature of the solution was adjusted to 313.15 K and maintained at 313.15 0.3 K. Absorption was allowed to occur for 10 h, with stirring at a rate of 100 rpm, during which time it was assumed that the vapor–liquid equilibrium had been achieved. The initial equilibrium pressure of the vessel at each time was Pv(n), whereas Pv(1) was the pressure without CO2 at the beginning of the experiment. The CO2 gas was introduced into the reactor from a gas container with a known volume Vgc, at the given initial temperature Tgc1 and pressure Pgc1. The subsequent temperature and pressure were Tgc2 and Pgc2, respectively. The quantity added into the reactor nCO2 was calculated using the Peng–Robinson cubic equation.[56] After achieving the equilibrium at each time point, the pressure of the vessel was Pt. The amount of CO2, ngCO2 , remaining in the gas phase was obtained using the relationship with partial pressure, PCO2 , which was determined by assuming that the phase obeyed Dalton’s law,[57] and can be written as PCO2 ¼ Pt ¢ Pvð1Þ .
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Figure 10. Diagram of the experimental equipment: 1) N2 inlet valve, 2) CO2 inlet valve, 3) liquid outlet valve, A) magnetic stirrer, B) oil bath, C) heating jacket, D) gas thermal detector, E) liquid thermal detector, F) gas outlet valve, and G) liquid inlet valve.
By subtracting the number of moles of CO2 in the vapor phase from the total number of moles of CO2 fed to the vessel, the amount of CO2 in the PEI solution was obtained using n1CO2 ¼ nCO2 ¢ ngCO2 . By performing a blank experiment to measure CO2 solubility in deionized water with nwCO2 , we calculated the number of moles of CO2 adsorbed by PEI as npCO2 ¼ n1CO2 ¢ nwCO2 . As such, the amount of CO2 loading in PEI was defined as qpCO2 ¼ npCO2 =mP [mmol CO2 per g PEI], in which mP is the mass of PEI injected into the vessel. The uncertainty of qpCO2 was determined from the uncertainty in temperature, pressure, and volume, which were 0.1 %, 0.5 %, and 0.5 %, respectively, to give an estimated uncertainty in qpCO2 of 8.0 %; the estimated pressure uncertainty was 2.0 %.[58]
Acknowledgements This work was supported by the National Natural Science Foundation of China (Nos. 21276010 and 51373019), and by Chemcloudcomputing of Beijing University of Chemical Technology. Keywords: density functional theory · electronic renormalization · reference interaction-site model · sorption efficiency · steric effects [1] P. Mohanty, L. D. Kull, K. Landskron, Nat. Commun. 2011, 2, 401. [2] D. M. D’Alessandro, B. Smit, J. R. Long, Angew. Chem. Int. Ed. 2010, 49, 6058 – 6082; Angew. Chem. 2010, 122, 6194 – 6219. [3] M. Z. Jacobson, Energy Environ. Sci. 2009, 2, 148 – 173. [4] P. Markewitz, W. Kuckshinrichs, W. Leitner, J. Linssen, P. Zapp, R. Bongartz, A. Schreibera, T. E. Mìller, Energy Environ. Sci. 2012, 5, 7281 – 7305. [5] A. L. Kohl, R. Nielsen, Gas Purification, 5th ed., chapter 2, Gulf Professional Publishing, Houston, 1997. [6] A. Sayari, Y. Belmabkhout, E. Da’na, Langmuir 2012, 28, 4241 – 4247. [7] F. Porcheron, A. Gibert, P. Mougin, A. Wender, Environ. Sci. Technol. 2011, 45, 2486 – 2492. [8] G. T. Rochelle, Science 2009, 325, 1652 – 1654. [9] P. Bollini, S. A. Didas, C. W. Jones, J. Mater. Chem. 2011, 21, 15100 – 15120.
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Effect of Chain Topology of Polyethylenimine on Physisorption and Chemisorption of Carbon Dioxide Qiangli Zhao,[a, b] Quanyong Wang,[a] Chen Zhang,[b] Zhongjie Du,*[b] Ming Tian,[a] and Jianguo Mi*[a] Polyethylenimine (PEI) is a promising candidate for CO2 capture. In this work, the physisorption and chemisorption of CO2 on various low-molecular-weight PEIs are investigated to identify the effect of chain architecture on sorption. The reliability of theoretical calculations are partially supported by our experimental measurements. Physisorption is calculated independently by the reference interaction-site model integral equation theory; chemisorption is distinguished from the total sorption given by the quantum density functional theory. It is shown
that, as the chain length increases, both chemisorption and physisorption drop off nonlinearly, but the decay amplitude of chemisorption is more apparent. Conversely, as the amine group approaches the central triamine unit of each oligomer, the sorption capacity decreases, affecting the sorption equilibrium in a complex way. This arises from the cooperative contribution of an increased steric effect and renormalized electronic distribution.
1. Introduction Separation and capture of CO2 at large stationary sources such as coal-fired power plants is considered to be a solution for stabilizing atmospheric CO2 levels to avoid global warming.[1–4] Among various separation techniques, the CO2 absorption–desorption system involving aqueous solutions of alkanolamines is presently one of the most suitable for high-volume flue gas streams.[5] However, this system is far from being optimal due to problems of corrosion, amine degradation and high energy consumption for regenerating the solutions.[6–8] Anchoring of polyamines onto solid supports has been proposed as an alternative to using aqueous solutions. In contrast to small amine scrubbers, solid-supported polymeric amines offer significant advantages for CO2 capture, including the potential elimination of corrosion, a lower energy cost for sorbent regeneration, and sufficiently low volatilities for avoiding excessive loss of activity.[9–11] CO2 capture by solid sorbents based on amines immobilized on porous solids has been an increasingly active area of research.[12–16] In recent years, a variety of amine supports and immobilizing techniques have been tested and the results are promising.[17–20] Among polymeric amines, polyethylenimine (PEI) contains an abundance of amines in the polymer backbone: tertiary amines at branch points, secondary [a] Q. Zhao, Q. Wang, Prof. M. Tian, Prof. J. Mi State Key Laboratory of Organic–Inorganic Composites Beijing University of Chemical Technology No. 15 Beisanhuan East Road, Chaoyang District Beijing (China) E-mail: [email protected] [b] Q. Zhao, Prof. C. Zhang, Prof. Z. Du The Key Laboratory of Carbon Fiber and Functional Polymers Ministry of Education, Beijing University of Chemical Technology No. 15 Beisanhuan East Road, Chaoyang District Beijing (China) E-mail: [email protected]
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amines in the main chain, and primary amines at the end of each branch.[21] High-efficiency sorbents have been developed based on PEI-functionalized mesoporous materials.[22–26] CO2 capture with amine-based absorbents involves chemisorption and physisorption. In general, absorption of CO2 on the amine medium firstly occurs as physisorption in which a CO2 molecule binds with the medium surface by van der Waals and electrostatic interactions. This is followed by the chemisorption step in which the molecule is chemically bonded with the amine of the medium surface. For an aqueous solution of a small alkanolamine, the stable state of physisorption is achieved with a suitable orientation and distance of CO2 relative to the absorbent molecule, at which the potential energy is negative and weak. In contrast, the bonding energy change from physisorption to chemisorption is negative but strong. As a consequence, the transition from physisorption to chemisorption can be easily realized, and chemisorption plays the dominant role. As the physisorption is extremely low, it is usually overlooked. During the chemisorption process, the amine type influences the amine–CO2 reaction. The fundamental difference between various polyamines is the number of primary, secondary and tertiary amines they carry. Amine type can affect the performance of an absorbent in two distinct ways.[11] Firstly, different amines have different basicities, which affects the strength of interaction between a CO2 molecule and the amine. Secondly, the amine type affects the absorbent efficiency, depending on the level of humidity in the gas stream, as tertiary amines do not capture CO2 in the absence of water. For the primary and secondary amines, the process starts with the lone pair of electrons on the primary amine attacking the carbon atom of CO2 to form zwitterions. The process is followed by the abstraction of a proton from the zwitterion. Instead of reacting
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Articles directly with CO2, the tertiary amine catalyzes the formation of bicarbonate.[27] The main products of the reactions between amines and CO2 are carbamates and bicarbonate [Eqs. (1)–(3)]:
CO2 þ RNH2 ! RNH2 ¢ CO2
ð1Þ
RNH2 ¢ CO2 þ B ! RNHCOO¢ þ BHþ
ð2Þ
R3 N þ H2 O þ CO2 ! R3 NHþ þ HCO¢3
ð3Þ
where the free base B is typically another amine, water, or a hydroxyl ion. If the amine is a sufficiently weak Brønsted base, the reaction can stop at the formation of the carbamic acid.[28] For a polyamine, although the mechanism for absorption and reaction is similar to a small amine, the reactive environment and strength are influenced by steric hindrance arising from the polymer topology. Due to the morphology and entanglement of polymer chain, the accessibility of reactive amine groups to the incoming CO2 molecules is decreased, leading to a relatively lower sorption on each amine group. Such influences of chain topology, molecular weight, and the role of entanglement on physisorption and chemisorption have not been entirely clarified and are the subject of ongoing discussion.[11]
It is difficult to study these reactions at the molecular level by experiment, whereas theoretical calculation has shown advantages in the study of reaction thermodynamics and kinetics.[29–31] Theoretical studies provide a reliable and unbiased comparison of reaction energies, and allow the factors mentioned above to be untangled. For example, detailed information such as the reactivity of amine groups at different locations in a chain can be distinguished. More importantly, understanding the effects of these structural and chemical variables of polyamines on gas absorption from theoretical calculation can be best accomplished by independently varying one variable of interest while keeping others constant. To analyze the effects of chain morphology at the molecular level, we simplified the low-molecular-weight PEI into the same repeat unit. The optimized morphologies of four chains with one, three, five, and seven triamine repeat units—named monomer, trimer, pentamer, and heptamer, respectively—are shown in Figure 1. The ratios of the amine groups in the model chains are close to that of PEI (i.e. they are separated by ethylene spacers) with the purpose of keeping the theoretical calculation in consistent with our experimental measurement. Physisorption in each system was first calculated according to solubility equilibria between bulk CO2 and CO2 in the PEI phase, and the spatial distributions of CO2 molecules around the PEIs were directly estimated. The total sorption of each amine group in these systems were calculated using the densi-
Figure 1. Optimized geometries of a) monomer, b) trimer, c) pentamer, d) heptamer of PEI chains. H: white, C: grey, N: blue.
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Articles ty functional theory (DFT) approach in conjunction with experiment. The influence of chain topology on reaction was assessed by comparing the reaction energies and sorption capacities of primary, secondary, and tertiary amine groups located in different chains. According to the energy attribution, the total sorption (including physisorption and chemisorption) was then determined. As a result, the amount of chemisorption was obtained by subtracting the capacity of physisorption from the total sorption. Finally, the physisorption and chemisorption for different oligomers were applied to evaluate the effect of chain topology on sorption.
2. Theory and Calculation 2.1. Physisorption On the basis of the equilibrium of bulk CO2 and CO2 in the PEI phase at a given temperature T and pressure P, the solubility coefficient S, which is used to evaluate the physical interaction between CO2 molecules and the simplified PEI, can be calculated by relating it to the excess chemical potentials mex [Eq. (4)]: ex bmex gasinpolymer ðT; PÞ ¢ bmbulk ðT; PÞ ¼ ¢lnðSkB TÞ
h i ˆ ˆ ˆ ˆ ˆ hðkÞ ¼ WðkÞ CðkÞ WðkÞ þ 1hðkÞ
ð7Þ
where the carets denote Fourier-transformed quantities, 1 denotes the density matrix with elements 1ij ¼ dij 1, dij is the Kroˆ ˆ necker delta function, and hðkÞ and CðkÞ are the matrices of total and direct correlation functions, respectively. In r space, ˆ hij ðrÞ, which are the elements of hðkÞ, is defined according to ˆ hij ðrÞ ¼ gij ðrÞ ¢ 1. WðkÞ is the matrix of the intramolecular correlation function and can be obtained from the optimized geometry of PEI obtained from the quantum chemistry calculation, which is given below. The hard-sphere repulsions of CO2– CO2 and PEI–CO2 interact with each other by a truncated and shifted repulsive Lennard–Jones (LJ) potential,[39] and the attractive interactions of CO2–CO2 and PEI–CO2 are a sum of paired potential functions of the short-range LJ and the longrange electrostatic interactions [Eq. (8)]: 12 6 dij dij qi qj uij ðrÞ ¼ 4eij ¢ þ rij rij rij
ð8Þ
ð4Þ
where rij represents the distance between the interactive sites, q is an atomic (perhaps partial) charge, and eij is the LJ parameter. The CO2 molecule was described as a three-site model where mex = mref + matt, b ¼ 1=ðkB TÞ, and kB is the Boltzmann and the interaction sites were positioned on the carbon and constant. The superscript “ref” indicates that the contribution oxygen atoms. The oxygen–carbon bond length is 1.163 æ. is due to the hard sphere repulsion, “att” denotes short-ranged Values for the LJ parameters and the partial charges on CO2 dispersion and the long-ranged coulombic interactions; these were taken from the literature.[40] The PEI molecules were excontributions can be constructed using the intermolecular corpressed as a united atom force field, for which the values for relation function with the form [Eqs. (5) and (6), respectiveLJ parameters and partial charges were taken from the literaly]:[32–34] ture.[41, 42] The LJ parameters for unlike-pair interactions were Z 1 ¨ ¦2 hsðlÞ dg þ ldb p X determined by the Lorentz–Berthelot mixing rules. To solve bmref ¼ db 1g dl dg þ ldb gbg þ 2 b2A;g2B 2 [Eq. (4)] with the RISM integral equation, a Picard iterative pro0 ð5Þ Z 1 cess was performed. An initial guess of solubility was input to X ¨ ¦2 hsðlÞ lda þ ldß ¨ ¦ p dl lda þ ldb gab da þ db 1a calculate the excess chemical potential between CO2 and PEI, 2 a2A;b2A 2 0 and a new value for solubility can be derived to substitute the old one. After several iterations, the dissolution equilibrium att ð6Þ bm ¼ was achieved, and the solubility was obtained, which was " # Z 1 X Z 1 X easily converted into the capacity of physisorption. We chose 2 att 2 att 4p 1a r buab ðrÞgab dr þ 1g r bubg ðrÞgbg ðrÞdr sab s bg several structures of each oligomer with low potential energy a;b2A b2A;g2B and took the average results. The RISM integral equation in its three-dimensional form At low pressure, the second term on the left-hand side of (3D-RISM)[43–47] was applied, such that the physical interaction [Eq. (4)] is nearly zero and can be neglected. At low solubility, the CO2–CO2 interaction in PEI can also be neglected in between CO2 molecules and the interactive sites in the simplified PEI could be directly evaluated. The optimized geometry [Eqs. (5) and (6)]. In these equations, A refers to a CO2 moleof PEI obtained from quantum chemistry calculations was cule, and B refers to the PEI molecule. db and dl are the hardplaced in the center of a cubic cell of sufficient size 80 æ3. sphere diameters of the sites in CO2 and PEI molecules, which Then, we could obtain the spatial distribution of CO2 molecules can be calculated from the Barker–Henderson perturbation theory.[35] l varies between 0 and 1, accounting for a gas partiin the immediate vicinity of the PEI molecule. Visualization was performed with gOpenMol-3.00. cle that grows from a point to full size, and 1b and 1g are the densities of CO2 and PEI. 1b is 1.72 Õ 10¢3 g mL¢1 at 313.15 K and 101.325 kPa.[36] 1g is 1.03 g mL¢1, which is the same as the 2.2. Chemisorption experimental value. ghs(r) and gatt(r) are the intermolecular corTheoretically, as the carbamates—formed by the reaction of relation functions for hard-sphere repulsion and attraction, reCO2 with primary and secondary amine groups in PEI—further spectively, and can be calculated with the reference interaction-site model (RISM) integral equation [Eq. (7)]:[37, 38] react with water, the absorption capacity might be improved ChemPhysChem 2015, 16, 1480 – 1490
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Articles in the presence of H2O. In practice, this is not always the case, as it might be that molecules of H2O and CO2 are competitively adsorbed; this effect is still controversial.[11] Thus, we focused on the formation of carbamates from the primary and secondary amine groups. The fully optimized geometries of the pure PEI and free CO2 molecules and their complex were obtained at the M06-2X/631G (d,p) level within the DFT framework without imposing an initial symmetry restriction. To determine the stable structure of the monomer, we first constructed different geometries of the monomers as the initial guess structures, and obtained several stable configurations arising from rotations around internal bonds. We then explored the conformational space of each species by systematically varying the dihedral angles of all rotatable bonds. After optimization, only the configuration with the minimum energy was used to study the reaction of monomer with CO2. The configurations of the trimer, pentamer, and heptamer were also constructed in this way. In order to get the most stable equilibrium structure for each complex, many initial guess structures were considered based on the close proximity of CO2 to the electron-rich sites of the molecule, and only the minimum-energy structures were studied further. The frequency of the structure was calculated to characterize the stable complex. The transition-state structure was characterized by demonstrating the existence of a single-frequency mode associated with a pure imaginary frequency. Connection of the transition state between the designated local minimum has been verified by intrinsic reaction coordinate (IRC) calculations. Calculations were carried out using the aqueous solvation model integral equation formalism–polarizable continuum model (IEF-PCM). Previous studies[48, 49] suggested that the M06-2X density functional, which belongs to a new generation of hybrid meta-generalized-gradient-approximation exchangecorrelation functionals that include an accurate treatment of the London dispersion energy, can yield excellent results in calculating the interaction energy and stability of noncovalent interactions involved in main group thermochemistry. It has been demonstrated also that the functional has the best performance for predicting the barrier height without increasing the computational cost. For aqueous solutions, DFT calculations with the solute molecular density (SMD solvation model[50] using the IEF-PCM protocol for bulk electrostatics were carried out at the M06-2X/6-311G (2df,2p) level. The Gibbs free energy G for each compound at 313.15 K and 101.325 kPa was estimated by combing the bulk electrostatics calculation with the thermal correction term as well as the zero-point energy. In addition, the potential energy surface ~E of the reaction was also calculated. All the calculations in this work were performed using the Gaussian 09 program.[51] The equilibrium constant K was calculated from the Gibbs free energy given by Equation (9): K ¼ expð¢DGr =RTÞ
3. Results and Discussion Theory provides a simple, flexible, highly efficient and general way of obtaining the structure and properties of a system. However, its predictive reliability should be tested. The best way to test a theoretical model is to compare its predictions directly with the corresponding experimental data. To distinguish between the effects of chain morphology of PEI and CO2/nitrogen ratio on the amine–CO2 affinity, three PEI aqueous solutions (0.05 g mL¢1) were prepared in order to measure their absorption capacities. Figure 2 shows the experimental absorption isotherms of PEIs with Mw = 600, 1800, and 10 000, collected at 313.15 K. For a given PEI, the presence of multiple amine groups, comprising the primary, secondary, and tertiary amines, leads to a sharp initial increase in CO2 uptake at low CO2 loading, which continues to increase slowly with CO2 loading, up to a plateau. The capacity of sorption is determined by the molecular weight of the PEI. In dilute PEI solutions, as molecular weight increases, the absorption capacity decreases. For example, at 101.3 kPa, the results for PEI (600), PEI (1800), and PEI (10 000) are 10.817, 10.430, and 9.890 mmol g¢1, respectively. Such a pattern was also found for a solution of a small-molecule amine.[52] The result indicates that the activities of the functional groups are affected by the chain mor-
ð9Þ
where R is the universal gas constant and T is the absolute temperature. ~Gr is determined by ~Gr = Gp¢Gr, and Gr and Gp ChemPhysChem 2015, 16, 1480 – 1490
are the calculated Gibbs free energies of the reactants and products, respectively. The most stable conformation was adopted as the basis for determining ~Gr. Given the PEI and CO2 concentrations in solution, K determines the output of the reaction. In the reaction equilibrium calculation, the experimental concentrations of PEI (0.05 g mL¢1) and CO2 (0.32 mol L¢1) were used to keep the theory consistent with the experiment. ~Gr and ~E were calculated for different repeat units to determine the favored reaction pathway. The outputs of the favorable reactions were summed to obtain the total amount of sorption qpCO2 . By subtracting the capacity of physisorption from that of total sorption, the amount of chemisorption was finally obtained.
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Figure 2. Experimental CO2 adsorption isotherms for PEIs of different molecular weight.
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Articles phology and, hence, they show different adsorption efficiencies. In the theoretical part of our study, the capacities of physisorption were first calculated. The results were 0.282, 0.264, 0.253, 0.248, and 0.245 mmol g¢1 for the monomer, trimer, pentamer, heptamer, and nonamer, respectively. In order to relate the effect of chain length to physisorption, the spatial distribution functions of CO2 around the central triamine repeat moieties of low-molecular-weight (up to heptamer) PEI molecules were calculated with the same threshold function g(r) > 2.0 (Figure 3). In these images, the location of the CO2 molecule is
Figure 4. The typical global spatial density distribution function of CO2 around the pentamer with the thresholds g(r) > 2.8 (cyan), g(r) > 2.2 (red), and g(r) > 2.0 (yellow). The tertiary amines of each repeat unit are labeled A– E. The hydrogen atoms are not shown and atoms are coded C: green and N: red.
Figure 3. The typical spatial density distribution functions of CO2 around the central repeat unit in a) monomer, b) trimer, c) pentamer, and d) heptamer, with the threshold g(r) > 2.0. The hydrogen atoms are not shown and atoms are coded C: green and N: red.
represented by its carbon atom occupation. In general, the adsorbed CO2 molecules are well structured around the adsorbents due to van der Waals and electrostatic interactions. In Figure 3 a, the central molecule is the monomer and the surrounding CO2 molecules occupy a near circle around it. The distribution reveals that CO2 molecules prefer to interact with the amine groups. CO2 adsorption by a PEI molecule depends mainly on the amine groups, due to the strong van der Waals forces and electron density. In addition, a short chain can provide space for CO2 occupation. In Figure 3 b–d, the densities close to amine groups are shown to be well defined also, but they display the collar-shaped density, and the occupation region narrows with increasing chain length. The amine groups, especially those located near the center of the chain, are caged by the neighboring groups. This stabilizes the polymer and also reduces the accessibility of nitrogen for attracting CO2. Thus, the distribution scope and strength are apparently reduced. Similar patterns were found for other geometries. ChemPhysChem 2015, 16, 1480 – 1490
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A global map of CO2 density distribution in the vicinity of the pentamer is shown in Figure 4. The five repeat units are labeled A–E along the chain, indicated at the tertiary amine group of each unit. The yellow regions, for which the isovalues are 2.0, show relatively broad CO2-adsorption areas. Both the amine groups and the alkyl groups contribute to the distribution. The higher-density regions (red), are located mainly around the amine groups. The cyan regions, for which the isovalues are 2.8, are mostly located in the immediate vicinity of primary and secondary amine groups, especially those in units A and E, whereas for the middle repeat unit (C), the density distribution is sparse. These areas become smaller from the end to middle, meaning that the adsorption strength is reduced. The end units of A and E, which have much space to interact with CO2 molecules, show stronger adsorption capacities. The units B, C and D (especially C) are constrained by the surrounding groups; the interactions between the groups and CO2 molecules are thereby dampened, leading to the reduced adsorption. By inspection of Figures 3 and 4, the contributions of different groups to the physisorption are clearly seen. The total sorptions were then calculated for the monomer, trimer, pentamer, and heptamer. The DFT-calculated potential energy profiles for the reactions of CO2 with amine groups in the monomer are summarized in Figure 5. In Figure 5 a, the initial potential energy of R-M1, acting as the reference, is the sum of the energy of free monomer and pure CO2. ComplexM1 is an intermediate formed prior to bond formation between carbon in CO2 and nitrogen in the primary amine; the complex state corresponds to physisorption. The energy of complex, representing the physisorption energy, is 7.68 Kcal mol¢1 lower than that of the reactants. It is likely that the O¢ C¢O angle starts to bend with respect to the collinear structure by electron flow from amine to the CO2 p* orbital. After passing through TS-M1, the intermediate zwitterion-M is produced. The proton-transfer step proceeds from the zwitterion, and from here two possible paths were considered. The first path is the intramolecular proton transfer from the nitrogen atom to the oxygen of CO2 to form carbamic acid P-M1 (Fig-
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Figure 5. Potential energy surfaces for the reaction between the monomer and CO2 a) to form carbamic acid through an intramolecular proton transfer from the nitrogen atom to the oxygen of CO2 and b) to form a carbamate anion through the reaction of the zwitterion and secondary amine group. c) Bicarbonate formation by reaction of the tertiary amine with CO2 and a water molecule. The terms R-Mm, complex-Mm, zwitterion-M, TS-Mm, and P-Mm represent the reactants, complexes, intermediate, transition states, and products, respectively, and “m” donates different species.
ure 5 a). According to studies on small-molecule amines, the carbamic acid formed in this way is stable.[53, 54] In the second path (Figure 5 b), a secondary amine group acts as a base to produce carbamate P-M2. It is apparent that the process is free of a reaction energy barrier. It is shown that both of the two paths are accessible. Due to the much lower activation energy, the P-M2 reaction channel is more favorable than the formation of P-M1. The distance between the carbon atom and the interacting nitrogen atom is shortened from 2.65 to 2.25 æ as TS-M1 is formed from complex-M1, and the length of the newly formed C¢N bond is 1.59 æ. Figure 5 c shows a representation of the energy surfaces of a tertiary amine reacting with CO2. The energy for the reference state (R-M2) is the sum of the energies of the monomer, water, and CO2. The tertiary amine lacks the free proton and it can only catalyze the formation of bicarbonate. The physisorption region over which complex-M2 is formed is located approximately 3.98 æ from the nitrogen (to the carbon atom of CO2), and the chemisorption region around 3.28 æ. As the tertiary amine is located at the branch point, which is strongly hindered by the surrounding groups, it is difficult for CO2 and H2O to get close. Figure 6 shows the potential energy surface for the reaction of trimer with CO2. According to our calculation, the carbaChemPhysChem 2015, 16, 1480 – 1490
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mate-formation path is more favorable for the primary and secondary amine groups, thus we present the energy surfaces of this channel and the calculations were based on this reaction channel. The trimer has three repeat units and the relative energies for the two ends are extremely close. As such, we analyzed only one end (indicated as A in Figure 6) and the middle unit (B), both of which have the same groups and connections. Figure 6 a shows the primary and secondary amine groups reacting with CO2. The reference energy of R-T1 is the sum of the free trimer and pure CO2. The relative energies of P-TA1 and P-TB1 are negative for the two reactions. Due to the surrounding alkyl groups and solvation effects, P-TA1 is more stable than P-TB1, which stabilizes the final product. Formation of complex-TA1 is more exothermic than for complex-TB1, thereby CO2 is much more accessible to the primary amine of the tail unit. This is also apparent from the distance between the carbon atom of CO2 and the interacting nitrogen atom. For the reaction at the tail unit, ths distance is shortened from 2.69 to 2.23 æ, and the newly formed bond is 1.57 æ in length. For the central repeat unit, the distance is shortened from 2.71 to 2.25 æ, and the newly formed bond is 1.58 æ in length. The tail unit of the trimer is more active than the center, according to a comparison of the energy surface. From the optimized struc-
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Figure 6. Comparison of the reactions between CO2 and amine groups at the end (bottom line) and central (top line) units of the trimer. a) The reaction occurs between the primary and secondary amines and CO2. b) The reaction occurs between the tertiary amine, CO2, and water. The symbols R-Tm, complexTXm, zwitterion-TX, TS-TXm, and P-TXm stand for reactants, complexes, intermediates, transition states, and products, respectively, and “m” indicates different species.
ture, we find that the amine groups in each repeat unit tend to form a ring to promote chain stability. The distance between the nitrogen atoms in the primary and secondary amine groups is shortened from 3.23 æ at A to 3.16 æ at B, which hinders the approach of the CO2 molecule. For the tertiary amine reaction (Figure 6 b), it is apparent that P-TA2 is more stable than P-TB2. The alkyl groups surrounding the tertiary amine sterically hinder the CO2 and H2O molecules from getting close to the nitrogen atom, especially in the middle unit. The physisorption region that forms in complex-TB2 (the carbon atom in CO2) is located approximately 4.75 æ from the nitrogen in the tertiary amine, and the chemisorption region around 3.31 æ. For the tail repeat unit, this distance is shortened from 4.28 to 3.30 æ. Figure 7 a–c shows the transition states for the middle unit of the trimer and CO2, corresponding to the reactions in Equations (1)–(3), respectively. In TS-B1 (Figure 7 a), the primary amine and CO2 molecule are close to each other, and the O¢ C¢O angle is bent. Proton transfers from the primary amine to the secondary amine occur in TS-B2 (Figure 7 b). The details of the transition state TS-B3 (Figure 7 c) reflect the mode of reaction between the tertiary amine, CO2, and water. The calculated molecular electrostatic potential (MESP) surfaces for the reaction of a tertiary amine group in the trimer with CO2 and water are shown in Figure 8. MESP is a measure of the electrostatic potential on the isoelectronic density surface and simultaneously maps the electron and nuclei distribution, which provides a good understanding of the relative polarity within the molecule.[55] The MESP color codes surfaces as red for areas enclosing high electron density (net negative charge), blue for areas containing low electron density (net positive charge), and green for areas in which the enclosed negative electron charge and the positive core charge balance (overall neutral charge). Figure 8 shows a comparison of the renormalized electrostatic distributions for CO2 and H2O approaching the tertiary amine group. Figure 8 c shows an obvious variation of this type. Due to the effects of CO2, H2O, and ChemPhysChem 2015, 16, 1480 – 1490
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surrounding groups, the architecture of R-T2 varies to meet the demand of the changed electronic structure, which plays an important role throughout the reaction, affecting molecular size, architecture, bonding, stability, reactivity, and other characteristics. Thus, the geometry and the energy of the complexes are largely changed. The relative Gibbs free energies for the reactions are listed in Table 1. For simplicity, we calculated the reactions of CO2 and amine groups in repeat units in half of the chain, which are labeled alphabetically from the end to the central unit. The baseline of each reaction represents the initial energy. Compared to the central repeat units, the tail repeat units display a lower free energy of reaction. The calculated capacities of total sorption are 9.800, 8.350, 7.600, and 7.300 mmol g¢1 for monomer, trimer, pentamer, and heptamer, respectively. The average sorption of each unit in trimer, pentamer and heptamer was reduced by 14.8 %, 22.5 % and 25.5 %. The variation trend is similar to the experimental observation (Figure 2), suggesting that the energies estimated by DFT are reasonable. The discrepancy between theory and experiment is mainly caused by neglecting the further reaction between the carbamate and water, which also contributes to the total sorption. As a result, the chemisorptions were determined based on the total sorptions and physisorptions. The relative physisorptions and chemisorptions for PEI with different chain lengths are shown in Figure 9. For the monomer, the calculated physisorption capacity is 0.282 mmol g¢1. The average amount of each unit in the trimer, pentamer, heptamer, and nonamer is reduced by 6.3 %, 10.2 %, 12.1 %, and 12.9 %, respectively. The physisorption curve decreases sharply at the beginning and then more slowly. The chemisorption capacity is 9.518 mmol g¢1 for the monomer. In contrast, the capacity of the trimer, pentamer, and heptamer is reduced by 15.1 %, 22.8 %, 25.9 %, respectively. In general, the amount of physisorption is small compared to chemisorption. It is apparent that both physisorption and chemisorption drop off as chain length increases, and chemisorption might do so more rapidly.
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Figure 7. The geometries of the transition states a) TS-B1, b) TS-B2, and c) TS-B3. The atoms are color coded C: grey, N: blue, O: red, H: white.
final equilibriums are less readily achieved. In the sorption calculation, such decay is exponential.
Table 1. Relative Gibbs free-energy for the reaction between CO2 and PEI according to the chain length. PEI chain
~Gr,P¢S[a] [Kcal mol¢1]
~Gr,T[b] [Kcal mol¢1]
monomer
¢6.79
¢2.50
trimer
A B
¢6.76 ¢6.34
¢2.2 ¢0.46
pentamer
A B C
¢6.70 ¢6.45 ¢6.28
¢2.08 ¢1.32 ¢0.07
heptamer
A B C D
¢6.64 ¢6.44 ¢6.38 ¢6.14
¢1.95 ¢1.43 ¢0.18 0.04
4. Conclusion
[a] For the reactions of primary and secondary amine groups with CO2. [b] For the reaction of tertiary amine groups with CO2 and H2O.
As the chain length increases, the number of reactive amine groups does not increase linearly, and the influence of chain morphology on chemisorption becomes more obvious than on physisorption. The increased steric effect and the different electronic contributions of primary, secondary, and tertiary amine groups in contact with CO2, increase the energies for the corresponding complexes and transition states, and the ChemPhysChem 2015, 16, 1480 – 1490
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In summary, the physisorption and chemisorption of CO2 to low-molecular-weight PEI were calculated by RISM and quantum DFT, respectively. As the chain length increases, both physisorption and chemisorption capacities per unit decline due to the growing steric hindrance and the varied electronic density distribution, and the drop ratio of chemisorption is more apparent than that of physisorption. If the amine group approaches the middle unit, the extent of electrostatic density renormalization increases, and the accessibility of CO2 molecules becomes less and less, leading to the improved complex, transition state, and reaction energies. If the chain length is increased further, the drop ratios of physisorption and chemisorption decrease, thereby the ratio of physisorption to the total adsorption could be further improved. In other words, physisorption plays a noticeable role in real PEI systems, and should be considered independently.
Experimental Section PEIs (Mw = 600, 1800 and 10000; 99.0 %) were purchased from Aladdin (Shanghai, China). For each PEI, an aqueous solution
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Figure 8. The calculated MESP surface of a) R-T2, b) complex-TA2, and c) complex-TB2. The atoms are color coded C: grey, N: blue, O: red, H: white. Red, green, and blue areas represent negative, zero, and positive values (arbitrary units), respectively.
rer. The temperature of the cell was maintained by an oil bath controlled by a calibrated thermometer (PT100, Kunlunhaian Co., Beijing, China) with an uncertainty of 0.1 K. The pressures of the cylinder and gas container were measured by a calibrated pressure transducer (model JYB-KDHAG, Kunlunhaian Co.), with an uncertainty of 0.5 %.
Figure 9. The sorption ratio between oligomer and monomer as a function of chain length.
(200 mL) was prepared with PEI (10 g) dissolved in deionized water. CO2 and N2 gases had a mass fraction purity of 0.999. Solubility was measured with a cell reactor, as illustrated in Figure 10. The reactor (model KCFDU2-2, Tianzhouhaitai Co., Beijing, China) includes an electrically heated stainless steel cylindrical tank of volume 300 cm3 equipped with a magnetically coupled stirChemPhysChem 2015, 16, 1480 – 1490
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Before starting the experiment, the vessel of reactor was purged with N2 gas to remove air. Then, the sample ( 100 cm3) was injected. The temperature of the solution was adjusted to 313.15 K and maintained at 313.15 0.3 K. Absorption was allowed to occur for 10 h, with stirring at a rate of 100 rpm, during which time it was assumed that the vapor–liquid equilibrium had been achieved. The initial equilibrium pressure of the vessel at each time was Pv(n), whereas Pv(1) was the pressure without CO2 at the beginning of the experiment. The CO2 gas was introduced into the reactor from a gas container with a known volume Vgc, at the given initial temperature Tgc1 and pressure Pgc1. The subsequent temperature and pressure were Tgc2 and Pgc2, respectively. The quantity added into the reactor nCO2 was calculated using the Peng–Robinson cubic equation.[56] After achieving the equilibrium at each time point, the pressure of the vessel was Pt. The amount of CO2, ngCO2 , remaining in the gas phase was obtained using the relationship with partial pressure, PCO2 , which was determined by assuming that the phase obeyed Dalton’s law,[57] and can be written as PCO2 ¼ Pt ¢ Pvð1Þ .
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Figure 10. Diagram of the experimental equipment: 1) N2 inlet valve, 2) CO2 inlet valve, 3) liquid outlet valve, A) magnetic stirrer, B) oil bath, C) heating jacket, D) gas thermal detector, E) liquid thermal detector, F) gas outlet valve, and G) liquid inlet valve.
By subtracting the number of moles of CO2 in the vapor phase from the total number of moles of CO2 fed to the vessel, the amount of CO2 in the PEI solution was obtained using n1CO2 ¼ nCO2 ¢ ngCO2 . By performing a blank experiment to measure CO2 solubility in deionized water with nwCO2 , we calculated the number of moles of CO2 adsorbed by PEI as npCO2 ¼ n1CO2 ¢ nwCO2 . As such, the amount of CO2 loading in PEI was defined as qpCO2 ¼ npCO2 =mP [mmol CO2 per g PEI], in which mP is the mass of PEI injected into the vessel. The uncertainty of qpCO2 was determined from the uncertainty in temperature, pressure, and volume, which were 0.1 %, 0.5 %, and 0.5 %, respectively, to give an estimated uncertainty in qpCO2 of 8.0 %; the estimated pressure uncertainty was 2.0 %.[58]
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