1. Introduction

Our aim in here is to get an improvement of chitosan as adsorbent of pollutant agents as CO₂ by modifying porosity in its structure, which can be changed to a nanocomposite by adding some form of carbon ring. This is important due to air pollution is a mixture of solid particles and gases in the air. Car emissions, chemicals from factories, dust, pollen, and mold spores suspended as particles, contribute to air pollution. We have previously been working using chitosan to clean water [¹-¹⁰]. At this time our searching is for taking profit of chitosan and carbon rings as new nanocomposite to be applied for cleaning of air pollutant gas as carbon dioxide (CO₂). The capture of atmospheric carbon dioxide has increased due to a global increase in temperature. Atmospheric CO₂ levels have contributed to distinguish the need for ambient air cleaning. In this case a new material is proposed for pollutant gas capture. There are poisonous air pollutants as ozone gas, which is a major part of air pollution in cities. Ozone is a combination between pollution, heat, and sunlight, which is called smog. Among the effects of the air pollution in the environment are the following problems: global warming, climate change, acid rain, smog effect, deterioration of fields, extinction of animal species, respiratory health problems, deterioration in building materials.

Atmospheric carbon dioxide (CO₂) capture research has been increased due to a global rise in temperature. Levels of atmospheric CO₂ have contributed to distinguish need for capture processes. To reduce CO₂ emissions is a worldwide research matter, from emission sources as power plants burning fossil fuels, carbon capture and storage have been widely proposed [¹¹]. The CO₂ capture has been achieved through chemical absorption (using aqueous amine solutions) for removing it from natural gas since long time ago [¹²]. Then, it is considered that already exists a technology readiness level (TRL) of 9. This technology use to be utilized in two post-combustion capture facilities in coal-fired power plants [¹³,¹⁴,¹⁵,¹⁶]. Advances in polymeric membranes have allowed technology to successfully reach demonstration scale (TRL 7). According to this, with our nanocomposite, new polymeric membranes might be constructed. Lithium ortho-silicate is solid sorbent for capturing CO₂. Characteristics of the absorption reaction studied by thermogravimetric and volumetric methods exhibit influence of heat and mass transfer limitations in packed bed. This method measures absorption reaction characteristics in experiments. The CO₂ absorption rate depends on the CO₂ pressure and reactor temperature. The maximum absorption rate observed is at 670°C when the conversion fraction is 0.3 [¹⁷].

Nanoparticles (NP) prepared with chitosan and chitosan derivatives possess a positive surface charge and mucoadhesive properties such that can adhere to mucus membranes and release the drug payload in a sustained release manner. Chitosan-based NP have various applications i14n non-parenteral drug delivery for the treatment of cancer, gastrointestinal diseases, pulmonary diseases, drug delivery to the brain and ocular infections according to the review [¹⁸]. Chitosan is a cationic biopolymer with potential applications in the food industry because of its unique nutritional and physiochemical properties. These properties depend on its ability to interact with anionic surface-active molecules, such as phospholipids, surfactants, and bile acids. [¹⁹]

Chitosan characteristics as adsorbent have been shown in literature. Monomer chitosan (C₆H₁₃O₅N) interacting with hBN nanosheet (B₄₈N₄₈H₂₄) in the armchair geometry with mono-hydrogenated ends yield chemisorption. The monomer is adsorbed parallel to the nanosheet inducing torsion in the nanosheet. The system at hand exhibits high polarity (3.076 D) like the interaction of chitosan and BN nanotube, and the amine group and hBN nanosheet as reported in literature [²⁰]. The aflatoxins interaction with chitosan is computationally investigated by DFT-B3LYP functional with 6-31g(d) basis set. Through a total energy calculation, the most negative charge is on oxygen atoms of aflatoxins, being the preferred site to interact with chitosan. Aflatoxins are physisorbed and confirmed by the simulated IR spectra [²¹]. To represent the graphene or boron nitride nanosheet as a CnHm-like cluster to study the adsorption of the monomer of chitosan, represented by the monomeric unit (C₆H₁₃O₅N), on the graphene surface (G + MCh). As another case, the adsorption of MCh on the G nanosheet functionalized with boron (G + B) has been explored [²⁰,²²-²⁵].

The nanocomposite is built joining one carbon double ring to one unit of copolymer chitosan. It is well known that geometry optimization of two parallel linear carbon chains of same size provide one polygonal carbon ring after interaction of these two chains [²⁶]. A carbon double ring molecule appears in this case, for two parallel C 8 linear carbon chains interacting due to the initial chirality. According to the chirality and the size of carbon chains, more number of rings might appear, and only one when these stay parallel at 1.54 Å of separation.

2. Methodology

VAMP software in BIOVIA Materials Studio is a semiempirical method for calculating the heat of formation at 298°K, in contrast to ab initio methods, which compute electronic energy. The heat of formation is determined from a combination of computed and parameterized data as discussed by Stewart [²⁷], and it is obtained using VAMP for a molecular configuration geometry which depends on computational parameters. After building a structure, it needs refining for getting a stable geometry [²⁷-²⁹].

Geometry optimization is applied using gradient norm of 0.4 kcal/mol/Å, partial general Hessian, Hamiltonian NDDO-AM1, spin restricted Hartree Fock, and CISD configuration interaction type. Using this methodology, and according to single point calculations shown in Fig. 1, the calculated energy for breaking one oxygen from CO₂ molecule is 147.28 kcal/mol while the experimental value of the dissociation energy (O-CO) of the CO₂ molecule is 125.749 kcal/mol [³⁰]. The difference corresponds to 14.6 %. On the other hand, frequency calculation for geometry optimization accomplished on a CO₂ molecule gives four vibrational normal modes:

Figure 1 a) Potential energy curve for OELUMO-CO breaking, showing the size of the well of potential. b) OCO after geometry optimization. Oxygen atoms in red color, and carbon atom in gray color. 

The heat of formation 79.82 kcal/mol obtained using frequency calculations does not near of the experimental value with 36.52 % of error; however, frequency values converted from cm -1 to kcal/mol (532.48=1.52, 1480.17=4.23 and 2565.81=7.34) stay in the physisorption region.

Along with the previous frequency calculation, frontier orbitals HOMO and LUMO are obtained as another option in the properties of this VAMP methodology. HOMO LUMO orbitals have been used in here to propose reaction sites for facilitating the corresponding chemical reactions. Gap HOMO-LUMO energy (14.04 eV) in one CO 2 molecule indicates a stable system and little reactive (see Fig. 2).

Figure 2 Energy of HOMO-LUMO on a CO₂ molecule. a) CO₂ molecule of size 2.379 Å. b)EHOMO=-13.211 eV c) ELUMO=0.853 eV d) Gap (ELUMO-EHOMO)=14.04 eV. 

Calculations are carried out using cero global charge. However, as an example a comparison between Coulson and Mulliken atomic charges for the C  16 carbon double ring obtained after geometry optimization of two carbon chains as input (see Fig. 3) are shown in Tables I and II.

Figure 3 Input and output of the geometry optimization on two C₈ carbon chains. Two C₈-carbon chains separated at distance of one C-C bond length 1.54 Å. 

By symmetry in the C₁₆ carbon double ring, we see that atoms 1 and 9, 2 and 10, and so on, have very similar charges, both for the Coulson and Mulliken atomic charge. In both cases the largest charge corresponds to atoms 3 and 11, while the smallest charge corresponds to charges 8 and 16 in the Coulson case, and 1 and 9 in the Mulliken case. Connectivity calculations according to Estrada inferences [³¹] on no bonding to s- and f -shell scheme, bond type, and converting representation to Kekulé are accomplished for bond length tolerances from 0.6 to 1.15 Å.

3. Results and discussion

Two parallel C₈ single-bond carbon chains at a separation distance of 1.54 Å (the experimental value of C-C bond is 1.535 Å) have been set in the input for geometry optimization, as observed in Fig. 3 with certain chirality. After interaction of these carbon chains through geometry optimization (four times using the methodology mentioned previously), the output exhibits a carbon double ring, one C₆ ring and one non-circular C₁₂ ring sharing one C-C single bond, on which after applying connectivity and bond type for no bonding to s- and f -shell, the biggest ring is double bond, and the smallest ring has two triple and four single bonds (see Fig. 4).

Figure 4 Conectivity applied on the output of Fig. 3. C₁₆ carbon double ring (C₆ and C₁₂) sharing one bond length after geometry optimization. Gray color for carbon atoms. 

Carbon rings alternating single and triple bonds (-C≡C-) _n are known as carbyne or acetylenic structures, however, when only double bonds are present (=C=C=) _n [³²,³³] cumulenic structures are formed. In this case, this carbon double ring alternates carbyne and cumulene rings.

The heat of formation of the C₁₆ carbon double ring is 669.41468 kcal/mol. The output is also calculated to show the HOMO-LUMO for bonding (blue orbitals) and antibonding (yellow orbitals), thus, as it can be seen in Fig. 5, blue bonds between atoms in the molecule are the places for insertion of other atoms of another molecule according to the electron sharing between them.

Figure 5 HOMO-LUMO of this C₁₆ carbon double ring, two joined (C₆-C₁₂) carbon rings. 

To continuation a sketch of one unit of copolymer chitosan (C₁₄H₂₄N₂O₉) has been built to be taken as Input for geometry optimization, on which cleaning has been applied as first approximation to bond lengths and angles, as shown in Fig. 6.

Figure 6 Input: Building a copolymer chitosan structure plus a rough cleaning. Gray, white, red, and blue color for carbon, hydrogen, oxygen, and nitrogen atoms, respectively. 

After this, the Output of geometry optimization using VAMP is accomplished. This result exhibits HOMO-LUMO for the corresponding bonding and antibonding places, as shown in Fig. 7. Such molecular structure has: Chemical Formula = C₁₄H₂₄N₂O₉, NetMass = 364.351, NumAtoms = 49, NetCharge = 0.00000 e, EHOMO=-6.723 eV (orbital 72), ELUMO=-3.893 eV (orbital 73). Considering EGAP=ELUMO-EHOMO, EGAP=2.83 eV. Then, we proceeded to use software ‘Modify’ from BIOVIA Materials Studio for applying ‘Charges’ with Initial charge = Formal, and Parameter set = Qeq-charged1.1. After applying ‘calculate’ NetCharge = -6.0000 e, and the EGAP calculation is still the same. This EGAP corresponds to singlet of multiplicity due to Spin Down [³⁴,³⁵] for even electron number.

Figure 7 Output: HOMO-LUMO of the bonding and antibonding places. 

Then, to get a chitosan-carbon nanocomposite, these were put together in the input with a configuration on which one carbon atom of the non-circular carbon ring is close to a C-N bond length. A new configuration is obtained in the output, where the non-circular carbon ring is perpendicular to one unit of copolymer chitosan and one oxygen atom was captured by the non-circular carbon ring, and this whole system has been inserted into chitosan forming a nanocomposite with C₃₀H₂₄N₂O₉ chemical formula. We see in the output of the geometry optimization (Fig. 8) the insertion of the C₁₆ double carbon atom in the C₁₄H₂₄N₂O₉ copolymer molecule of chitosan which has been rotated 90° approximately. Chitosan has been modified because one of its oxygen atoms stays now adsorbed in the smallest ring of C₁₆ carbon double ring. Then, the C₃₀H24N₂O₉ configuration of the chemical structure is the new product, which is one nanocomposite unit.

Figure 8 Input-Output about geometry optimization on interaction between chitosan and carbon double ring, with the C₆ carbon ring bonded to chitosan at the end. 

The adsorption when non-circular C₁₂ carbon ring is the nearest one to chitosan copolymer, according to the output after geometry optimization remains as observed in Fig. 9 in two perspectives. This Figure clearly exhibits the facilities given by HOMO-LUMO for providing reaction sites in this interaction, which in this case corresponds to attractive forces. Furthermore, this nanocomposite has: Chemical Formula = C₃₀H₂₄N₂O₉, NetMass = 556.527, NumAtoms = 65, NetCharge = 0.00000 e, EHOMO=-6.952 eV (orbital 104), ELUMO=-4.296 eV (orbital 105), EGAP=ELUMO-EHOMO=2.656 eV corresponding to Spin Down and singlet of multiplicity due to the absence of electrons. By applying ‘Charges’ with Initial charge = Formal, and Parameter set = Qeq_charged1.1., it results NetCharge = -5.0000 e, and EGAP=ELUMO-EHOMO=-4.258 eV - (-6.96eV) = 2.702 eV. This EGAP corresponds to Spin Up [34,35] due to odd number of electrons, and doublet of multiplicity.

Figure 9 Two perspectives of geometry optimization on interaction between chitosan and carbon double ring, with the greatest ring bonded to chitosan in one side. 

To confirm that non-circular carbon ring is responsible of this chemical adsorption, we extract one of its interaction sites, which is the C-C carbon molecule in Fig. 10a). According to C-C bond length of Fig. 5, it has antibonding orbitals. The other part of Fig. 10a) has been extracted from Chitosan molecule. The whole Fig. 10a) has been extracted from the Input of Fig. 8, and it is now the Input on which a geometry optimization is applied, obtaining a new conformation shown in Fig. 10b). In the latter, we observe C-C bond as head on perpendicular to C-H bond length greater than the initial one C-C bond side on perpendicular to C-H, meaning that in Fig. 10b) one carbon atom of C-C is inserting in the bond of the C-H. Applying connectivity from BIOVIA MS Modeling, chemical adsorption is clearly observed in Fig. 10c).

Figure 10 Interaction between reaction sites and of C₁₆ carbon double ring and C₁₄H₂₄N₂O₉ copolymer chitosan, respectively. This notation implies that C₂ is part of the C₁₆ carbon ring, and HC is part of the C₁₄H₂₄N₂O₉ chitosan molecule. 

Antibonding orbitals carry at to repulsive effects, then in Fig. 11, which exhibits orbitals of Fig. 10a), it is observed that bonding is located between C-H carbon atom and the bond length of C-C, as expected.

Figure 11 HOMO-LUMO of Fig. 10a) in two perspectives. 

One CO₂ molecule can be independently captured by either C₁₆ non-circular ring or C₁₄H₂₄N₂O₉ chitosan copolymer. An example of the former is shown in three steps of Fig. 12 (input, output, and connectivity); however, in Fig. 12b), it is observed a potential energy curve of the conformation shown in Fig. 12a). This interaction between linear CO₂ with heat of formation of -99.029128 kcal/mol and planar C₁₆ carbon double ring (having a heat of formation of 611.621 kcal/mol) considers rigid molecules and it exhibits a well of potential with a small size of energy around 2 kcal/mol as in Fig. 12b). The output in Fig. 12c) exhibits a conformation where the CO₂ is non-linear, given that it considers the same input of Fig. 12a), now with relaxed molecules, and Fig. 12d) exhibits the connectivity between the molecules in Fig. 12c), which is the insertion of CO₂ in the C₁₆ carbon double ring. now with carbyne oxide C₁₇O₂ (with heat of formation of 535.445 kcal/mol) structure, due to the alternating single and triple bonds. The adsorption energy of Fig. 12a) is calculated as:

Figure 12 CO₂ attacking C₁₆ carbon double ring. a) Input, for geometry optimization, b) Interaction for the previous configuration, c) Output, of the geometry optimization, d) Connectivity. 

In the latter result for a relaxed optimization, the heat of formation provides a chemisorption, while the rigid case provides a physisorption, according to the range handled by Atkins [³⁶] and others [³⁷-³⁹], around 5 kcal/ mol for physisorption and greater than 10 kcal / mol for chemisorption, approximately because it depends on the elements in the system. Then, through chemisorption CO₂ is captured by C₁₆ forming a new C₁₇O₂ molecule as observed in Fig. 12.

In case of more than one CO₂ molecules interacting with C₁₆ carbon double ring, in an input arrangement to the geometry optimization shown in Fig. 13a), we see in the output for the geometry optimization shown in Fig. 13b), that at least 50% of CO₂ gas are molecules adsorbed on this carbon ring, and the other 50% CO₂ molecules have been repulsed when 16 CO₂ molecules interact with C₁₆ carbon double ring as shown in Fig. 13c). The input exhibits a separation of 1.539Å between CO₂ molecules in a geometrical ordered arrangement. The electrostatic attractions and repulsions among these molecules provide around 50 % of CO₂ molecules tending to move away, and three carbon rings added to the C₁₆ carbon double ring. Then a new molecule of five rings has one carbon ring of ten atoms and another of six atoms, two new rings of six and one more new ring of four atoms. The latter has one oxygen and three carbon atoms, and in the two new rings of six atoms there are two oxygen atoms alternating with carbon atoms as shown in Fig. 13c). One carbon dioxide molecule is broken in an oxygen atom which stay bonded to the C₁₆ carbon double ring molecule, and a CO molecule moves away, consequently there is certain percentage of formation of carbon monoxide, while the carbon dioxide considerably decreases as pollutant.

Figure 13 C₁₆ carbon double ring is attacked by 16 CO₂ molecules. After minimum energy optimization around 50% of CO₂ molecules are adsorbed on C₁₆ carbon double ring. 

An example of interaction between one molecule of CO₂ and one molecule of copolymer chitosan is shown also in three steps in Fig. 14 (input, output, and connectivity): From these two cases using VAMP calculations, while CO₂ is captured by carbon double ring in the former, in the latter CO₂ is broken giving CO as new product. Then, among reactions between CO₂ and the nanocomposite C₃₀H₂₄N₂O₉, the CO₂ can be captured near to carbon atoms, and can be broken near to gas atoms.

Figure 14 Carbon dioxide CO₂ attacking C₁₄H₂₄N₂O₉ chitosan copolymer. a) Input, b) Output, c) Connectivity. 

4. Conclusions

The multiplicity of one unit of Chitosan-copolymer+C16 carbon double ring is singlet for NetCharge = 0.0000 e, while it is doublet when NetCharge = -5.0000. The latter corresponds to cationic character of chitosan. Considering EGAP↑ and EGAP↓ as gap energy of spin up and spin down, respectively, the difference between them is EGAP↑-EGAP↓=0.046 eV.

Carbon dioxide CO₂ molecules can be adsorbed by either nanocomposite or independently by C₁₆ double-carbon-ring or copolymer chitosan. The confidence of this semiempirical model in this case is about 15 % due to the comparison between experimental dissociation energy of CO₂ and the breaking of one oxygen atom from the CO₂ molecule.

The generated C₃₀H₂₄N₂O₉ nanocomposite has an improved superficial area with respect to the pristine either C₁₆ or C₁₄H₂₄N₂O₉, and for increasing CO₂ catching. In this case, the C₁₆ carbon molecule is that acting to degrade the oxygen atoms in molecules such as CO₂. Then, as much carbon molecules added to the copolymer the better is the adsorption of CO₂ in nanocomposite of this composition, given that porosity of chitosan has been changed to be adsorbent of pollutant agents.

We applied different methodologies with different results on the size of the carbon double ring. However, with the chosen Hamiltonians, it seems as if C₁₆ carbon double ring were activated in the insertion process on a chitosan unit, which promotes it to be in charge for catching CO₂, because the results for catching CO₂ on chitosan indicate that repulsion is easier than attraction.