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Abstract
First, the minimum energy (geometry
optimization DFT-DMol3) is obtained among C48 optimized ring carbon-system, and
one non-optimized chitosan copolymer unit. Second, C24 and C9 optimized rings,
each one interacting with an optimized chitosan copolymer unit (Ch). With the
aim to investigate structural properties, the first case is optimized by
applying smearing; and the second without smearing. Two parallel hypothetical
carbon chains of 12 carbon atoms, symmetrically arranged are optimized in C24
carbyne ring; and one hypothetical 5 carbon-chain parallel to another 4
carbon-chain end optimized in a cumulene C9-ring. These carbon-ring structures
here defined as activated carbons (AC), correspond to big pore size diameter
obtained without chemical agent acting on them. Single point calculations are
to build potential energy surfaces with GGA-PW91 functional to deal with exchange
correlation energies for unrestricted spin, all-electron with dnd basis set.
Only in the first case, orbital occupation is optimized with diverse smearing
values. To determine structure stability, the minimum energy criterion is
applied on AC+Ch nanocomposite. To generate fractional occupation, virtual
orbitals are formed in this occupation space, whether homo-lumo gap is small
and there is certain density near Fermi level. This fractional occupation
pattern depends on the temperature. It must be noticed that when AC and Ch are
solids, there is no adsorption; however, by applying smearing it was possible
to find potential energy surfaces with a high equilibrium energy indicating
glass phase transition in Chitosan due to the chemisorption given at the minimum
of energy. AC+Ch molecular complex nanocomposite is expected to be applied not
only in medicine but also in high technology.
Introduction
With the aim to figure out a
molecular complex formed through the interaction between a system of 48 carbons
arranged in planar way and a copolymer unit of chitosan, potential energy
surfaces were built [1,2] using single point step by step calculations. The
problem is studied considering that a molecular complex is obtained by changing
smearing value according to the energy value convergence. Considering that
electrons occupy orbitals with the lowest energies and with an integral
occupation number in calculations of density functionals, a smearing change
indicates a fractional occupation in virtual orbitals within this space of
occupation. The smearing calculations correspond to the explicit inclusion of
the fractional occupation numbers of the DFT calculations, requiring an
additional term to achieve a functional energy from variation theory [35]. The
contribution of this term to the density functional force exactly cancels the
correction term as a function of the change in the occupation number. For
occupation numbers satisfying a Fermi distribution, the variation total-energy
functional is identical in form to the grand potential [3-6]. From the grand
canonical distribution or Gibbs distribution, the normalized probability
distribution of finding the system in a state with n particles and energy 𝐸𝑛𝑟 [7], the Z grand partition function of the system, and the
number of particles remains according to the Fermi energy ℰf =μ(T,V,n). When T
= 0 the fermion gas is in the state of minimum energy in which the particles
occupy the n states of 𝜓𝑖 of lower energy, since the exclusion principle of Pauli
does not allow more than one particle in each state. Therefore, the Fermi
function 𝑓(ℰ) gives the probability that certain states of available
electron energy are occupied at a given temperature.
Other options for the shape of the
occupancy numbers result from the different associated functional with finite
temperature to DFT but without physical meaning, such as the temperature or the
entropy associated with this term [3]. These terms, although numerically small
must be included in the practical calculations that allow numbers of fractional
occupation [3,8]. To consider the scope of smearing, it is known that electrons
occupy orbitals with the lowest energies, and occupancy numbers are integers;
nonetheless, there is a need for a fractional occupation in virtual orbitals within
this space of occupation. We apply this when the HOMO-LUMO gap is small and
there is especially a significant density near of Fermi level [9], thus in
order to obtain the fractional occupation a kT term is implemented. This
fractional occupation pattern depends on the temperature. The systems C48
carbinoid, C24 carbyne-ring, and C9 cumulene-ring (almost-planar) are
arrangements obtained through DFT geometry optimization of two hypothetical
parallel zigzag linear carbon chains. We consider these systems as carbon
physically activated, due to the pore size diameter, and since no activating
chemical agent has been applied. Carbyne is known as linear carbons alternating
single and triple bonds (-C≡C-) n or with double bonds (=C=C=)n (cumulene)
[10]. Polyyne is known as a allotrope carbon having H(-C≡C-) nH chemical
structure repeating chain, with alternating single and triple bonds [11] and
hydrogen at every extremity, corresponding to hydrogenated linear carbon chain
as any member of the polyyne family HC2nH [12] with sp hybridization atoms. It
is known that polyyne, carbyne and carbinoid have been actually synthesized as
documented by Cataldo [13]. Bond length alternation (BLA) of carbyne pattern is
retained in the rings having an even number of atoms [10]. Additional care must
be taken with carbyne rings since the Jahn-Teller distortion (the counterpart
of Peierls instability in non-linear molecules) is different in the C4N and
C4N+2 families of rings [14-16]. There is a great variety of applications of
activated carbon as an adsorbent material, and it has been used in areas
related to the energy, and the environment, generating materials with a
high-energy storage capacity [17].
Chitin is, after cellulose, the most
abundant biopolymer in nature. When the degree of deacetylation of chitin
reaches about 50% (depending on the origin of the polymer), it becomes soluble
in aqueous acidic media and is called chitosan [18]. Chitosan is applied to
remediation of heavy metals in drinking water and other contaminants by
adsorption. The affinity of chitosan with heavy metals makes the bisorption
process stable and advantageous, being only by the alginates present in brown
algae matched [19]. The glass transition temperature of chitosan is 203°C
(476.15 K) according to Sakurai et al. [20], 225°C (498.15 K) according to
Kadokawa [21], and 280°C (553.15 K) according to Cardona-Trujillo [22]. One can
differentiate specific reactions involving the -NH2 group at nonspecific
reactions of -OH groups. This is important to difference between chitosan and
cellulose, where three -OH groups of nearly equal reactivity are available
[23,24]. In industrial applications, several solids having pores close to
molecular dimensions (micropores < 20 Å) are used as selective adsorbents
because of the physicochemical specificity they display towards certain
molecules in contrast to the mesoporous substrates (20-500 Å) and macropores
(> 500 Å). Adsorbents with these selective properties include activated
carbon among others [25]. Chitosan-based highly activated carbons have also
application for hydrogen storage [26]. In principle, electronic structure of
diatomic molecules has been built through the overlapping knowledge of the
interacting atomic orbitals [27]. In this case, the orbitals correspond to
bonding (σg, πg) and antibonding (σu, πu) orbitals of hydrogen, carbon,
nitrogen and oxygen diatomic molecules, whose H2, C2, N2, and O2 groundstate
electronic configurations are 
and 
with 2, 8, 10 and 12 valence
electrons, respectively. Actually, the reactivity sites in a molecule
correspond to the highest occupied molecular orbitals (HOMO) and lowest
unoccupied molecular orbitals (LUMO). HOMO as base (donor), and LUMO as acid
(acceptor) are particularly important MOs to predict reactivity in many types
of reaction [28,29]. Activated carbon and chitosan have been independently
applied as sorption materials to increase environmental quality standards.
Then, we expect AC-Ch nanocomposite to have a powerful handleable adsorption
property of pollutants that can be applied not only in wastewater treatment,
but also in medicine against intoxication, in batteries to increase storage
capacity, in electrodes of fuel cells, and in more possible applications,
according to the pore size distribution to be generated on this new material.
Methodology
The interaction between an activated
carbon molecule (AC) and a unit of the chitosan copolymer (Ch) is studied by
means of DFTDMol3 [30-32]. The AC system is a hypothetical model of two
parallel linear chains of 24 carbons each one geometrically optimized using
DFT, converging into a plane molecular carbon system. In this system six nodes
were formed allowing 7 interconnected rings of different bond lengths and
sizes: 2 of 6 carbons, 4 of 8 carbons and one of 16 carbons. By summing these
quantities gives 54 carbons since the carbons are in the nodes double counted.
When subtracted they are the 48 carbons of the AC system. This system has a
length of 28.4Å comparable to that of the chitosan copolymer unit (Ch). The
reactants are AC + Ch corresponding to C48 + C14H24N2O9.
Single point potential energy curves
were constructed [1,2] by using smearing. The following conditions to find
AC+Ch (Activated Carbon+Chitosan) interaction energy are: functional GGA-PW91
[31,33-36], unrestricted spin, dnd bases, and orbital occupation with various
smearing values. Considering that we obtained a solution for the energy value
convergence, the interaction by changing the smearing value was studied. Since
electrons occupy orbitals with lower energies and integral occupation numbers
in calculations of density functional, a smearing change indicates fractional
occupation and virtual orbital within this occupation space [19]. When
generating a fractional occupation, virtual orbitals are in this occupation
space generated, if the HOMO-LUMO gap is small, and there is certain density
near the Fermi level [1], then it is implemented the fractional occupation term
kT. This pattern of fractional occupation depends on temperature. Covalent
connectivity calculations [37] according to DMol3 on no-bonding to s- and
f-shell scheme, bond type, and converting representation to Kekulé, for bond
length tolerances from 0.6 to 1.15 Ǻ were accomplished in this molecular
complex mostly composed of carbon. Area calculations have been carried out by
inserting triangles in each amorphous carbon ring and using the
Heron formula:
where P=(a+b+c)/2 is the
perimeter of a triangle of a, b, c sides; while the pore size diameter (PSD) is
calculated as an approximation to the circle area. Periodic systems can be
constructed using amorphous builder of BIOVIA Materials Studio, these are
useful to calculate Radial Distribution Functions and the area under the curve
on a significant interval.
Results
Chitosan
Optimized by Applying Smearing
The default smearing value of
0.005Ha corresponds to T=1578.87 K and P=224.806 atm. We now exhibit electron
smearing behavior using the known Fermi-Dirac statistic [38]. Facing two
hydrogen atoms and using geometry optimization calculations, we built energy as
a function of smearing value. Figure 1 shows the total energy variation when
the system is optimized with respect to smearing value [39] (Figure 1). The
fractional occupational pattern depends on the temperature, and this is derived
from the energy change of Fermi distribution [6] as: 𝛿𝐸 = 𝑇𝑘; where k is Boltzmann constant. Considering a model in
which the electrons are free and given that clouds of electrons are being a
Fermi gas considered. The pressure is: 2/3 δE/δV [38]. From the latter two
previous equations, temperature and pressure change is observed in Table 1
given the 𝛿𝐸 smearing energy. The planar molecular hypothetical system
of 48 carbons is built by applying geometry optimization at two linear chains
of 24 carbons as shown in Figure 2a, and the chitosan copolymer molecular
system is built without applying geometry optimization, as observed in Figure
2b. Approaching enough these two molecular systems we studied a new molecular
complex at different smearing values. The molecular model of carbon is
symmetrically arranged in planar geometry, and it is physically activated
through geometry optimization. We called activated carbon (AC) to the resulting
planar carbon system. The length of this planar system is comparable to that
one of chitosan (Ch). Each six-carbon ring has an area 4.34 Å2, each
eight-carbon ring along with this has an area 8.74 Å2, each eight-carbon ring
along with the sixteen-carbon ring has an area 8.55 Å2, and the sixteencarbon
ring has an area 27.32 Å2. Considering each one of this area as circle areas
the pore size diameter distribution is from 2.35 Å to 5.9 Å, which correspond
to micropore size distribution of this carbon system. When considering the
whole area of this system for calculating the pore size diameter 9.48 Å
[40,41]. Chitosan is very well known to be macropore size [42].
Searching for a new molecular
complex, Figure 3 exhibits the potential energy curve of the interaction
between AC and Ch having equilibrium at (1.6Å, -1089Kcal/mol). In this case
chitosan was not geometrically optimized in order to build the potential energy
curve observed in Figures 3b & 3c. It was really easy to build this curve
using smearing energy 0.05 Ha for every single point calculated, and hard to
build it at 0.03 Ha. We also tried lower values than this, and we obtained poor
or none results (Figure 3). After applying geometry optimization at smearing
0.05 Ha, and subsequently at 0.03 Ha. The smearing at 0.02 Ha is shown in
Figure 4a. Then, we built the potential energy curve as shown in Figure 4b in
step by step single point calculations for AC + Ch face to face interaction,
when 2.264 Å is the separation between their corresponding centers of mass. The
latter has a potential well depth of 165 Kcal/ mol at a distance of 2.2 Å, meaning
formation of a new molecular complex at an adsorption energy greater than 20
kcal/mol in the chemisorption range [43] (Figure 4). Covalent connectivity [37]
to the resulting system in Figure 4a was applied under the conditions
previously mentioned in methodology, and the molecular complex observed in
Figure 5 is obtained. In this complex the reactants and products are C48 +
C14H24N2O9 and C49H3O3 + CH2 + C4H6O2 + CH3NO + C2H2O + CH2O + C2H2 + CHNO +
CH3, respectively. Carbon bonds are single, double, and triple, as an example
the C12 ring has eight double bonds, one triple bond, and three single bonds,
where all the carbon valence electrons are shared. Furthermore, C8 and C16
rings have double bonds in one side of the ring, and single and triple bonds in
the other side; and C6 ring has four double bonds and two single bonds. This
whole carbon system has been activated by chitosan, and double bonds, and
single and triple bonds are the representative characteristics of carbine-type
molecules (Figure 5).
It must be noticed that geometry
optimization of this whole system provides a lowest unoccupied molecular
orbital (LUMO - electron acceptor) receiving an electron pair from the highest
occupied molecular orbital (HOMO - electron donor). The donor HOMO from the
base and the acceptor LUMO from the acid, combine with a molecular orbital
bonding, which in our case corresponds to the orbitals 242-HOMO for E=-0.18317
Ha and 243-LUMO for E=- 0.17786, for a Fermi energy of -3136.28 Ha with A as irreducible
representation of symmetry C1. The total orbitals number is 274. The orbital
occupation is 202 A (2) plus 78 electrons in 65 orbitals, for a total number of
482 active electrons and binding energy of -22.997 Ha, at 2 steps. However, in
order to get HOMO and LUMO drawn in this model, we run an energy calculation.
Then, this molecular complex as seen in Figures 6a & 6b has HOMO-484 with
E=-0.16398 Ha, LUMO-485 E=-0.16196 Ha, and Fermi energy Ef = -3161.44 Ha, for
the reactivity sites with 482 active electrons. The total number of valence
orbitals is 1070. The orbital occupation is 206 A (1) alpha and 206 A (1) beta,
and 35.00 alpha electrons in 62 orbitals plus 35 beta electrons in 62 orbitals.
HOMO as base-donor, and LUMO as acid-acceptor are the MOs locating possible
reactivity in this reaction. An acid-acceptor can receive an electron pair in
its lowest unoccupied molecular orbital from the base-donor highest occupied
molecular orbital. That is to say, the HOMO from the base and the LUMO from the
acid combine with a bonding molecular orbital in the ground state see Figure
6c.
After applying covalent connectivity
[37] to the resulting system in Figure 6, we again applied geometry
optimization for smearing 0.02Ha, and we obtain different molecular orbitals in
the results, as shown in Figure 7. This molecular complex as seen in Figure 7
has HOMO-482 with E=-0.17650 Ha, LUMO-483 E=0.16060 Ha, and Fermi energy Ef =
-3162.004 Ha, for the reactivity sites with 482 active electrons. The orbital
occupation is 204 A (1) alpha and 204 A (1) beta, and 37.00 alpha electrons in
62 orbitals plus 37 beta electrons in 62 orbitals. The molecular complex
observed in Figure 7 has the same products previously mentioned. It must be
noticed that the lowest unoccupied molecular orbitals (LUMO-acceptor) only draw
orbitals in the CH3 product, the rest of the molecular orbitals correspond to
the highest occupied molecular orbitals (HOMOdonor) complex. Then, this is a
very stable molecular system only allowing reactivity through the methyl
radical CH3 (Figure 7) The potential energy curve in Figure 3b is very near to
physisorption; however, smearing energy in this case corresponds with a very high
temperature, which actually occurrs little inside sun surface. In this work, we
gradually get down smearing energy searching until reaching the glass
transition temperature of chitosan. The smearing energy value 0.02 Ha
corresponds with temperature 6315.49 K according to Table 1, and it is still
too high; however, is this way we have been achieving geometry optimization to
reach right smearing values according to experimental measurements. After
successful convergence in geometry optimizations at 0.01, 0.007, 0.005, 0.003,
and 0.002 smearing energies, the convergence at smearing energy 0.0017 Ha has
been unsuccessful after more than 10000 SCF iterations for an oscillating
energy with an energy tolerance of 0.00002 Ha. After these calculations, we
continued rising the smearing energy until 0.00175, and after more than 5000
SCF, convergence is successfully accomplished. The temperature 552.6 K reached
for smearing at 0.00175 agrees with glass transition temperature range
[498.15K, 553.15K] of chitosan, according to experimental measurements [20-22].
Figure 8 illustrates the final stage
of the molecular complex formed. We can observe that while C48 has been
deformed mainly in its planarity, the chitosan ended broken in the two initial
groups of each polymer, also apparently divided in several smaller molecules.
This fact is very well known experimentally, because one bonding solution
(epichlorhydrine, glutaraldehyde, or EGDE -ethylene glycol glycidyl ether-) is
commonly used to keep chitosan copolymer cross-linked for enhancing the
resistance of sorbent beads against acid, alkali, or chemicals [19]. The
products observed by applying covalent connectivity (under the bonding scheme
for no bonding to s- and f- shell, covalent connectivity and bond type, and
converting representation to Kekulé) are the following: C51H7NO4 + C4H6O2 +
C2H2O + C2H2 + CH3O + CHNO + CH3. As it can be seen part of each polymer remain
bonded to the AC system (Figure 8). Then, at smearing 0.00175 Ha we mostly
obtain highest occupied molecular orbitals for the molecular complex observed
in Figure 9. This output exhibits the orbitals a) HOMO-482 with an eigenvalue
of -0.17013 Ha, b) LUMO-483 with an eigenvalue of -0.16923 Ha, and c) HOMOLUMO.
The Fermi energy is Ef = 3162.0047053 Ha, for the reactivity sites with 482
active electrons. The orbital occupation is 238 A (1) alpha and 239 A (1) beta,
and 2.96 alpha electrons in 5 orbitals plus 2.04 beta electrons in 4 orbitals.
Chitosan
Optimized Without Smearing
First of all, the C24 carbyne-type
ring alternating single and triple bonds is obtained by applying connectivity
[37] and bond type to a C24 carbon ring which is the output of the input shown
in Figure 10a corresponding to the geometry optimization of two hypothetical
C12-carbon chains (Figure 10b). Then, Figure 10c exhibits an alternating single
and triple bonds C24-ring. Second, applying clean of BIOVIA Materials Studio on
chitosan copolymer molecule designed in Figure 2b, we obtain the input of a
chitosan copolymer molecule as in Figure10d, and the Output exhibiting geometry
optimization of the previous molecule is shown in Figure 10e. As we can
observe, in this case chitosan remained complete. We made this, after
suspecting that the initial bonds lengths and angles were not right in our
design of chitosan, because broken chitosan is not a satisfactory result. Then,
mixing the optimized C24 and Ch systems as shown in Figure 10f in the Input of
a C24-ring surrounding a chitosan copolymer molecule, and after applying
geometry optimization we obtain the Output of the previous CA-Ch nanocomposite
see Figure 10g. Finally, we applied bonding scheme criteria as in Figure
10h.The nanocomposite in Figure 10h is a good example of the possibility of modifying
the pore size distribution of chitosan when it is embedded into activated
carbon. Here we consider INPUT and OUTPUT for applying geometry optimization on
activated carbon and chitosan C14H24N2O9 system after each part has been
previously optimized, and we also applied bond criteria for connectivity, bond
type and kekulé representation. The C24-ring is carbyne type, and the chitosan
copolymer molecule has been optimized in three dimensions in this case. The
position of C24- ring surrounding a chitosan copolymer molecule has been only
proposed.
From the interaction through
geometry optimization of two linear carbon chains of four and five carbon atoms
as in Figure 11a, cumulene C9-ring shown in Figure 11b is obtained. This is a
clear evidence of Jahn-Teller effect, because we observe double bond lengths
alternating long/short with a difference among .02 and .03 Å, and the angles in
this non-planar (Figure 11b) cumulene molecule are also different. The expected
angles in a planar symmetrical molecule should be the same according to a
well-defined symmetry. We considered the interaction of chitosan with another
almost planar carbon ring of nine carbon atoms, now one in front to the other
as in Figure 11c. Then, in Figure 11d there is another example about building
pore size distribution among chitosan and activated carbon. In this case, we
consider INPUT and OUTPUT for geometry optimization of cumulene C9-ring and
chitosan C14H24N2O9, each one previously optimized by applying geometry
optimization to the whole system, and also considering the bond criteria for
connectivity, bond type and Kekulé representation as shown in Figure 11e. The
cumulene C9-ring and chitosan copolymer molecule have been optimized in three
dimensions, and we clearly observe the cumulene passing from face to face to
almost T-shape orientation taking three hydrogen atoms from chitosan. The input
position of cumulene C9 ring face to face with chitosan in that precise
location has been proposed, and the result has been excellent.
Discussion
We consider each carbon ring as
physically activated through geometry optimization, due to pore size diameter
remains in the average size compared against experimental measurements [41].
The C48 optimized ring carbon-system and one non-optimized chitosan copolymer
unit has been studied considering the result after geometry optimization, as a
molecular complex obtained when smearing value changes for converging energy
values. Different elongation among single and triple carbon bonds in the carbyne-type
are due to Jahn-Teller effect [14]. Then, C24 carbynering when we optimize two
carbon chains at 3.074 Å of separation distance, is due to the Jahn-Teller
effect. The Jahn-Teller effect is also present in C48 carbinoid -ring for their
C8- and C4- carbinoid -rings. Carbon rings C4N (N<~8) exhibit a substantial
first-order Jahn-Teller distortion that leads to long/short (single/triple)
bond alternation decreasing with increasing N [14]. Whether we want to draw
HOMO-LUMO orbitals, it is necessary to ask for orbitals in the geometry
optimization as input data. At this work, for smearing energy 0.02 Ha we found
different HOMO LUMO orbital numbers among the initial system in Figure 5
without asking for orbitals in the geometry optimization calculation, and its
output asking for orbitals in a new energy calculation shown in Figure 6. Again
after practicing connectivity, bond type, and Kekulé representation at smearing
energy 0.02 Ha, we asked for orbitals, and we found in Figure 7 a small change
at the orbital numbers previously obtained, and the corresponding energies were
little different to the previous ones. We infer that bonding type change
produced the differences, and the correct values correspond to the correct
bonding type in the new molecular complex system formed.
The strongly dependence on smearing
means very closely spaced energy levels (high degeneracy) near Fermi level.
When there is a degenerate electron state, any symmetrical position of the
nuclei (except when they are collinear) is unstable. As a result of this
instability, the nuclei move in such a way that the symmetry of their
configuration is destroyed, the degeneracy of the term is being completely
removed [44,45]. High degeneracy indicates a high symmetry of the molecule,
then the system tends to be distorted, in such way that when moving, the
occupied levels are down and the unoccupied ones are up [46]. When levels are
very densely spaced, convergence is hard to reach, since very small changes
will occupy completely different states, and we get oscillations. These can be
damped by smearing out the occupancy over more states, so that we turn off the
binary occupancy of the states. We get down smearing width to glass transition
temperature by decreasing the smearing parameter in steps to gradually
stabilize our molecular complex system at the right temperature.
We initially observe distortion of
chitosan system, and then its possible breaking in some products. This is
partially in agreement with the results presented by Chigo et al. [46] in a study
of the interaction among graphene-chitosan for a relaxed system doped with
boron, in which they consider the interaction of pristine graphene with the
monomer of chitosan (G + MCh:C6H13O5N) in different configurations, whereas we
consider a chitosan copolymer molecule: C14H24N2O9 in only one orientation.
While Chigo et al. [46] found a perpendicular chitosan, molecule linked to a
carbon nanotube system, we obtained a cumulene carbon ring almost
perpendicularly linked to a chitosan copolymer molecule.
Conclusion
We found one mechanism to figure out
an optimized big molecular complex system by using DFT geometry optimization.
This mechanism is based on smearing calculations, and on decrements of smearing
energy in the molecular complex system until reaching the glass transition
temperature of one of the components, which in this case correspond to the
chitosan copolymer molecule. In order to get a molecular complex system AC +
Ch, it is needed a high temperature among them at least to the phase transition
temperature of either AC or Ch, because when they are solids there is only a
heterogeneous mixture at room temperature. The use of smearing allows to reach
high temperatures because according to Table 1 temperature increases as the
smearing energy increases. We observed that the use of smearing to optimize a
molecule as complex as the chitosan causes this to be fractionated,
nevertheless when putting it in a plate of coal we obtained the glass
transition temperature of the chitosan reported experimentally. The potential
well depth providing chemisorption indicates existence of phase transition in
one of our two molecular systems. This phase change is attributed to chitosan,
due to carbon is more stable, and because we reach glass transition temperature
of chitosan when dealing with the whole molecular complex system. In addition,
when applying covalent connectivity, the activated carbon is the most stable
molecular system keeping its molecular structure. According to HOMO and LUMO in
Figures 6 -9, the sites with the greatest reactivity correspond to double and
triple bonds. Besides, Figure 9 exhibits one amine functional group linked to
the carbon system now C51 carbon molecular complex formed with a particular
pore size distribution. Considering that after geometry optimization
physisorption provides bonding in two parts of the chitosan molecule, this is
an indication of a more environmental linking than that caused by cross-linking
solutions, because cross-linking solutions might be toxic in medicine applications.
The first chitosan molecule used, and optimized using smearing resulted to be
unstable, because finished broken in several products. The second chitosan
molecule used, and optimized without smearing, or with a very small smearing
value resulted to be very stable, on which we were able to add activated carbon
and to obtain good results. We have been able to optimize chitosan and add
activated carbon, and we have observed the change in pore size distribution,
even though we are missing its calculation, to assign the type of material
obtained (micropore, mesopore, or macropore). We are working on it.
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