Carbon Capture: Theoretical Guidelines for Activated Carbon-Based CO2 Adsorption Material Evaluation

Activated carbon (AC)-based materials have shown promising performance in carbon capture, offering low cost and sustainable sourcing from abundant natural resources. Despite ACs growing as a new class of materials, theoretical guidelines for evaluating their viability in carbon capture are a crucial research gap. We address this gap by developing a hierarchical guideline, based on fundamental gas–solid interaction strength, that underpins the success and scalability of AC-based materials. The most critical performance indicator is the CO2 adsorption energy, where an optimal range (−0.41 eV) ensures efficiency between adsorption and desorption. Additionally, we consider thermal stability and defect sensitivity to ensure consistent performance under varying conditions. Further, selectivity and capacity play significant roles due to external variables such as partial pressure of CO2 and other ambient air gases (N2, H2O, O2), bridging the gap between theory and reality. We provide actionable examples by narrowing our options to methylamine- and pyridine-grafted graphene.

JPCL Editorial Comments and Our Responses 1. Please add postal codes to all author affiliations.Thank you for bringing this to our attention.We included the postal codes in both the main paper and the SI on pages 1 and S1, respectively.
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JPCL Reviewer Comments and Our Responses
1. What does FM stand for in the manuscript?
Thank you for pointing this out, this should not have slipped past us.FM stands for Functional Molecule.We have indicated this at its first occurrence, on page 4 of the main paper.
"Next, for a lower EN difference (>0.9 √) 26 with CO2, we moved to O-containing functional molecules (FMs) adsorbing in the basal plane on PG." 2. In Figure 2, the full name of FM, PG, DG, FG should be inserted.
Thank you for pointing this out.Functional Molecule (FM), Pristine Graphene (PG), Doped Graphene (DG), and Functionalized Graphene (FG) are the terms.To be consistent, we have indicated all of these in the captions of figures 2, 3, and 4.
"Figure 2. Dopants and functional molecules (FMs) screened in order from least to most stable CO2 Eads (a) and their corresponding CO2 Eads (b).The most stable CO2 configurations on pristine graphene (PG), doped graphene (DG), and functionalized graphene (FG) are either top (T) or hollow (H) sites and T or inserted (I) sites, respectively.Eads of the most stable sites are reported here whereas the comprehensive results of all sites can be found in Tables S1 and S3 and Figures S3-S8 3. How can the authors distinguish physisorption from chemisorption? Thank you for pointing this out and giving us the opportunity to explain further.We included a new section titled "Physisorption-Chemisorption Boundary on Graphene Materials" in the SI paper for more clarification on this topic (page S6).
"From a physical chemistry perspective, physisorption typically corresponds to nonbonding interactions like van der Waals whereas chemisorption often involves a significant charge transfer accompanied with formation of chemical bonds.More practically, the boundary between physisorption and chemisorption is commonly accepted to be in the range of -0.41 to -0.51 eV, 14 and we found it to be apt for our system.For instance, the CO2 adsorption energy of methylamine functionalized graphene is right below the physisorption-chemisorption boundary (-0.367eV), and we found that there was no N-C bond formed with a distance of 2.893 Å (see Table S3).In addition, CO2 exhibited no Bader charge transfer with methylamine (see Table S13).On the other hand, imidazole functionalized graphene adsorbed CO2 with an energy just above the physisorption-chemisorption boundary (-0.574eV) and formed a N-C bond with a distance of 1.611 Å (see Table S3).Furthermore, CO2 and imidazole showed Bader charge transfer with N (of C3N2H4), C (of CO2), O1 (of CO2), and O2 (of CO2) gaining -0.45, 0.21, 0.11, and 0.07 e, respectively.A similar CO2 adsorption energy range (-0.41 to -0.78 eV) is commonly accepted for direct air capture applications. 15,16" 4. In graphene, authors considered the N and O dopants to control electronegativity.How about B and P dopant?What is the reason why the authors did not consider this dopant?This is a great point and thank you for giving us the opportunity to explain why B and P were not considered as a dopant.They were not considered as a dopant due to the smaller differences in electronegativity with graphene and ultimately CO2, in comparison to N and O. Additionally, it is very easy to include N and O as these elements are naturally more abundant than B and P. We included a sentence on page 4 for clarification.
"In addition, this result ruled out B and P as dopants due to their smaller EN difference with C in graphene base material than dopants such as O and N. Therefore, we expect O and N to be better representatives of dopants for this system." 5. The authors said that the FM must bind with PG in the chemisorption range for the stable operation of CO2 adsorption process.What is the guideline for chemisorption range?This is based on calculation data or experimental data?The authors should discuss how the descriptor of thermal stability is chosen.Thank you for giving us the opportunity to expand on this discussion point.The idea is that the material should be unchanged throughout the CO2 desorption process, which in our case is heating the material to release CO2.If the material does not change during the heating process, then the material is thermally stable.Since our target CO2 adsorption energy is near the physisorption-chemisorption boundary, the material must be sufficiently above the chemisorption boundary and therefore well into the chemisorption range.If the functional molecule adsorbs on graphene in the chemisorption range (< -0.41 eV), then the material is thermally stable.All of our studies were computational and this is also a computational guideline.We included a definition of thermal stability on pages 7 and 8 for additional clarification.
"We define thermal stability as the ability of a material to stay unaltered during the CO2 desorption process."For thermal stability, the FM must bind with PG in the chemisorption range to eliminate their removal post CO2 desorption."While a general guideline is hard to propose, a higher Eads (in the chemisorption range) of the FM on PG compared to CO2 Eads on the corresponding FG is needed to ensure thermal stability."

In Fig 4(c)
, what is the meaning of CO2 adsorption energy?How is this related to defect sensitivity?More explanation is needed in the manuscript.Thank you for giving us the opportunity to explain this criterion further.The CO2 adsorption energy in Fig 4(c) corresponds to the adsorption energy of CO2 on a structure that includes a monovacancy defect.We meant defect sensitivity in the sense of how CO2 interacts or adsorbs on the material in the presence of defects in comparison to the case where no defects are included.We included a definition along with the reason we chose monovacancy defects in particular on page 8.
"We define a defect insensitive material as a desirable material whose CO2 Eads does not change when defects are introduced.In other words, the CO2 Eads of the pristine material and the material with defects are the same.Thus, to ensure the properties of the capture material are unaffected by the presence of defects, CO2 Eads must be invariant between PG and defect graphene.We considered monovacancy graphene (MG) defects as they alter CO2 Eads more than any other graphene defect (like the Stone-Wales defect) 19,27 due to the dangling C bonds interacting more strongly with CO2 (see Figure 4c, Table S5, and Figure S31)." 7. It has been known that monovacancy can greatly affect the adsorption energy of CO2 over the pristine case.Why did authors consider this as the guidelines for defect sensitivity?Theoretical background for this one should be presented in manuscript.
Thank you for allowing us to expand on this statement.We considered monovacancy graphene defects as they alter CO2 Eads more than any other graphene defect.We expanded on this statement on page 8.
"We considered monovacancy graphene (MG) defects as they alter CO2 Eads more than any other graphene defect (like the Stone-Wales defect) 19,27 due to the dangling C bonds interacting more strongly with CO2 (see Figure 4c, Table S5, and Figure S31)." We pointed the defect results in the SI tables and figures into the main paper on page 8.
"Methylamine adsorbs onto MG near the lower chemisorption threshold (see Table S4 and Figure S29) while adsorbing CO2 near our target CO2 Eads (see Figure 4c, Table S5, and Figure S32) and is therefore a defect insensitive material.However, pyridine forms two C-C bonds with MG and is much more stable than on PG (see Table S4 and Figure S30), but pyridine is near perpendicular to MG resulting in a less stable CO2 Eads when compared to pyridine FG (see Figure 4c, Table S5, and Figure S33)." 8. The authors should show the optimal range of descriptors for representing CO2 adsorption energy, thermal stability and material defects and selectivity and capacity in detail.In addition, the authors should show the origin of optimal descriptor range in detail.
Thank you for pointing this out and allowing us to expand on our criteria for carbon capture evaluation.We included the following to serve as a summary of the descriptors and their range in page 10-11.
"To ensure optimum performance, we opted for a target CO2 Eads of -0.41 eV.Moreover, a good candidate material must also be thermally stable during the CO2 desorption process.Only those FMs which adsorbed on graphene with a higher energy (< -0.41 eV) compared to the Eads of CO2 on graphene functionalized with that group passed this criterion of thermal stability.Since defects are unavoidable, it is imperative that the CO2 Eads remain unchanged in the presence of defects.Additionally, a good candidate material must also preferentially adsorb CO2 over other gases.In other words, the selectivity criterion requires the CO2 Eads to be higher than the rest.Finally, the CO2 Eads can also vary with the density or coverage of the FMs, and for optimum capacity, a FM that supports the target CO2 Eads with high coverage should be chosen." The origin of the target CO2 adsorption energy comes from choosing an adsorption energy that is between physisorption and chemisorption.This is because "Optimum performance necessitates an ideal range of Eads where CO2 is bound neither too strongly for ease in desorption nor too weakly for good selectivity" as stated in page 2 in the manuscript.We also included some discussion on the boundary of physisorption and chemisorption in the SI (page S6).
"From a physical chemistry perspective, physisorption typically corresponds to nonbonding interactions like van der Waals whereas chemisorption often involves a significant charge transfer accompanied with formation of chemical bonds.More practically, the boundary between physisorption and chemisorption is commonly accepted to be in the range of -0.41 to -0.51 eV, 14 and we found it to be apt for our system.For instance, the CO2 adsorption energy of methylamine functionalized graphene is right below the physisorption-chemisorption boundary (-0.367eV), and we found that there was no N-C bond formed with a distance of 2.893 Å (see Table S3).In addition, CO2 exhibited no Bader charge transfer with methylamine (see Table S13).On the other hand, imidazole functionalized graphene adsorbed CO2 with an energy just above the physisorption-chemisorption boundary (-0.574eV) and formed a N-C bond with a distance of 1.611 Å (see Table S3).Furthermore, CO2 and imidazole showed Bader charge transfer with N (of C3N2H4), C (of CO2), O1 (of CO2), and O2 (of CO2) gaining -0.45, 0.21, 0.11, and 0.07 e, respectively.A similar CO2 adsorption energy range (-0.41 to -0.78 eV) is commonly accepted for direct air capture applications. 15,16" Other rationales for the choice of -0.41 eV as the target CO2 adsorption energy comes from parasitic energy studies in COFs and a DFT calculation on Mg-MOF-74, which is taken as a standard for CO2 adsorption.The following explanation in the manuscript can be found in page 4.
"The less stable boundary of this threshold range is consistent with our target CO2 Eads, which is motivated by the parasitic energy metric, 23 based on monoethanolamine, an industry standard, 24 used to screen covalent organic frameworks (COFs) for carbon capture in Deeg et al. 24 Parasitic energy contains the energy required to separate CO2 from flue gas (Qseparation), which should be minimized to reduce energy losses resulting in a CO2 heat of adsorption threshold of -0.46 eV. 24Further, the best COFs are comparable to Mg-MOF-74 (metal organic framework).A DFT calculation of CO2 Eads on Mg-MOF-74 is -0.41 eV (see Figure S2), which is assigned as our target CO2 Eads." 9. This study is related to the computational search scheme of graphene-based CO2 adsorbent.If other 2D materials is considered, the computational search scheme in this study can be applied?The authors need to discuss this point.Thank you for pointing this out to us and this is an excellent addition to our paper.We hypothesize that this theoretical guideline can be easily adapted for evaluating other 2D materials for CO2 capture.The list of criteria devised for CO2 capture that include optimum adsorption energy, thermal stability, defect insensitivity, high selectivity, and capacity is material agnostic.More specifically, the operational ranges for the secondary and ternary criteria are quantified relative to the primary CO2 adsorption energy, and thus those criteria remain unchanged.However, CO2 adsorption depends on the specifics of how CO2 interacts with the solid-sorber material, which in turn will influence the target adsorption energy.We included a statement touching on this in our conclusion on page 11.
"Furthermore, this theoretical guideline can be generalized to different carbon capture materials, like other 2D materials (MoS2, WSe2, CrO2, CrS2, VO2, VS2, h-BN, NbSe2, etc.), since the list of criteria devised for CO2 capture that include optimum Eads, thermal stability, defect insensitivity, high selectivity, and capacity is material agnostic.The CO2 Eads, the primary parameter that all the other criteria are dependent on, in turn relies on the knowledge of fundamental interactions between CO2 and the solid-sorber of interest.Such studies will play a critical role in the future designs of CO2 capture solutions." and S20-S28.""Figure 3. Charge density difference (CDD) plots, Bader charge difference (BCD), CO2 Eads, and the distances between N (of functional molecule (FM)) and C (of CO2) for graphene-derived materials (GDM) in top (T) and inserted (I) sites.BCD is reported for N (of FM), C (of CO2), and both O (of CO2) with top/left as O1 atom and right/bottom as O2 atom.""Figure 4. CO2 Eads (a) of most stable CO2 configurations on pristine graphene (PG) and functionalized graphene (FG), (b) thermal stability by functional molecule (FM) Eads on PG, (c) defect sensitivity by CO2 Eads on monovacancy graphene (MG), (d) selectivity by CO2, N2, O2, and H2O Eads, and (e) coverage effects by CO2 Eads (single point calculations without ionically relaxing PG) on G36 (36 C atoms), G60 (60 C atoms), and G96 (96 C atoms) PG sheets."