3.1 Quantum chemical computation
3.1.1 Orbital energies of epoxy coating molecule
The reaction of DGEBA epoxy resin and the curing agent, BDA gives an epoxy coating (DGEBA-BDA) with geometry optimized molecular structure given in Fig. 1(i). The frontier molecule orbital electron distributions, namely, HOMO and LUMO orbitals as well as electrostatic potential (ESP) of the epoxy coating are also given in Fig. 1(ii), (iii) and (iv), respectively. A critical look at Fig. 1(ii) shows that HOMO is located at one of the benzenediamine moiety, which indicates that this molecular group in the DGEBA-BDA epoxy coating molecule is associated with high electron density, and therefore represents the site through which electrons are donated to the metal during coating-metal interactions. Figure 1(iii) shows that LUMO is located at the Bisphenol A moiety of the epoxy coating molecule. This represents the site where electrons are accepted during metal-coating interactions. The ESP map offers valuable information about molecular interactions by indicating reactive electrophilic and nucleophilic sites. Thus, the ESP electron density of the epoxy coating molecule shown in Fig. 1(iv) gives a structure delineated by red and blue colours. The area given in red colour indicates negative potential and electron-deficient region that is most likely to undergo nucleophilic reactions. The blue region of the structure refers to area of positive potential, and it is associated to electron-rich areas. This implies that electrophilic reactions are most probable there.
(i) (ii)
The energy values of the frontier molecular orbitals (EHOMO and ELUMO) for the DGEBA-BDA epoxy coating were obtained from the geometry-optimized structure, and the rest of DFT quantum chemical parameters were calculated using the equations (1) to (12). The values obtained are given in Table 3.
Table 3
Quantum chemical parameters of DGEBA-BDA epoxy
EHOMO | ELUMO | \(\varDelta\)E | I | A | χ | µ | η | Ϭ | Ѡ | ε | \(\varDelta\)N | \(\varDelta\)E1 | \(\varDelta\)E2 |
− 4.706 | -1.018 | 3.688 | 4.706 | 1.018 | 2.862 | -2.862 | 1.844 | 0.542 | 2.221 | 0.450 | 0.534 | 4.062 | 2.958 |
A high value of EHOMO (highly negative value) and low value of ELUMO (less negative value) are responsible for strong metal-coating interactions. Hence, the high value of EHOMO and low value of ELUMO for DGEBA-BDA epoxy coating molecule indicate that the coating molecule has high propensity to react with and/or adsorb on the metal surface by donating electrons to as well as accepting electrons from the metal surface. The high reactivity and effectiveness of the coating molecule is corroborated by a low value of energy gap, ΔE (ELUMO – EHOMO). Thus, the relatively small value of ΔE for DGEBA-BDA epoxy coating molecule indicates that it was highly reactive and can readily adsorb on the metal surface.
3.1.2 Fukui indices results of epoxy coating molecule
The analysis of the active sites (atoms) in the coating molecule is conducted via condensed Fukui functions, which often provides supplemental information that confirms the reactivity and inhibitive capability of potential protective molecules which EHOMO and ELUMO provide. Thus, Fig. 2 shows the Fukui electrophilic and nucleophilic maps, optimized structure of the epoxy coating showing numbering of atom, and graphical representation of the highest as well as lowest values of the dual descriptor (F2(r)).
(i) (ii)
The sites for nucleophilic (F+(r)) and electrophilic (F−(r) reactions could be evaluated in terms of the electronic populations described elsewhere [8, 9, 12]. The value of dual descriptor (F2(r)) which is estimated using Eq. (14) is used to give direction to chemical reaction.
$${F}^{2}\left(r\right) \approx {F}^{+}\left(r\right)- {F}^{-}\left(r\right)$$
14
The calculated Fukui indices (F+(r) and F−(r)), and the dual descriptor (F2(r)) for the epoxy coating molecule under investigation are given in Table 4. The atoms with the high values of F+(r) form the chemical species of the aromatic benzene amine ring which are located at each end of the molecule. These sites are considered as charge acceptors (C15, C16, C19, C25, C27, C28) during epoxy coating – mild steel interactions, if F2(r) > 0. In contrast, atoms with high values of F−(r) represent sites for electron donation. In general, atoms with the highest electron-donating regions are C1, C3, N7, N8, N33, C36, and N41, which are indicated by F2(r) < 0. These observations are well depicted in Fig. 2(iv). Interestingly, these results are quite in agreement with the electron distribution over the HOMO and LUMO surfaces.
Table 4
Fukui electrophilic F+(r), nucleophilic F−(r) & dual Fukui descriptor F2(r) for epoxy
Atoms | F+(r) | F−(r) | F2(r) | Atoms | F+(r) | F−(r) | F2(r) |
C1 C2 C3 C4 C5 C6 N7 N8 C9 C10 C11 O12 O13 C14 C15 C16 C17 C18 C19 C20 C21 | 0.007 0.009 0.001 0.001 0.008 0.004 0.007 -0.001 -0.004 -0.003 -0.018 0.018 0.005 0.016 0.036 0.037 -0.003 0.029 0.038 -0.012 -0.014 | 0.041 0.005 0.045 0.011 0.017 0.010 0.053 0.031 -0.017 -0.006 -0.003 -0.010 0.015 -0.002 0.001 0.002 0.003 0.002 0.001 -0.002 -0.002 | -0.034 0.004 -0.044 -0.010 -0.009 -0.006 -0.046 -0.032 0.013 0.003 -0.015 0.028 -0.010 0.018 0.035 0.035 -0.006 0.027 0.037 -0.010 -0.012 | C22 C23 C24 C25 C26 C27 C28 O29 C30 C31 C32 N33 O34 C35 C36 C37 C38 C39 C40 N41 | -0.014 -0.004 0.027 0.047 0.023 0.032 0.043 0.019 -0.016 -0.002 -0.004 -0.001 -0.006 0.002 0.003 0.012 0.007 0.005 0.009 0.006 | 0.001 0.000 0.001 0.000 -0.002 0.001 0.000 0.002 0.001 -0.002 -0.015 0.033 0.009 0.009 0.039 0.004 0.036 0.009 0.014 0.044 | -0.015 -0.004 0.026 0.047 0.025 0.031 0.043 0.017 -0.017 0.000 0.011 -0.034 -0.015 -0.007 -0.036 0.008 -0.029 -0.004 -0.005 -0.038 |
3.1.3 Orbital energies of chitosan and silane-modified chitosan molecules
The optimized structure and frontier molecular orbital density distributions (i.e., HOMO and LUMO orbitals) of the chitosan are shown in Fig. 3. Figure 3(i) shows the optimized structure of chitosan, and Fig. 3(ii) and Fig. 3(iii) depict plots of HOMO and LUMO orbitals, respectively. Good observation of Fig. 3(ii) shows that HOMO is mainly located on the nitrogen atom associated to – NH2 moiety of the chitosan molecule. On the other hand, LUMO is distributed on the nitrogen atom linked to – NHCOCH3 group of the chitosan molecule.
Further, the chitosan was modified with silane additives (tetraethoxysilane and (3-Aminopropyl) ethoxy silane) with the aim to enhance the hydrophobicity of the chitosan. The HOMO and LUMO orbital distributions of the silane-modified chitosan were equally modified (See Fig. 4 and Fig. 5). Thus, the HOMO and LUMO of TEOS-modified chitosan (Fig. 4(ii) and Fig. 4(iii), respectively) were noticed on the – Si atom of the silane additive. Further, HOMO and LUMO were also seen on the – Si atom on the AMPTES-modified chitosan (Fig. 5(ii) and Fig. 5(iii), respectively). The orbital energies obtained are as given in Table 5. The energy gap `(ΔE) also changed tremendously following the trend, chitosan > TEOS-modified chitosan > AMPTES-modified chitosan. This implies that AMPTES-modified chitosan nanocluster displayed the lowest energy gap, and therefore possessed the highest potential for corrosion inhibition.
The other quantum chemical parameters derived from the orbital energies are also summarized in Table 5. Table 5 shows the AMPTES-modified chitosan molecule is associated with higher value of EHOMO, lower value of ELUMO, lower value of ΔE, high softness (Ϭ), lower hardness (η), and high chemical potential (µ) which are related to high corrosion protective capability [16, 13]. Additionally, lower values of electronegativity (χ) and electron affinity (A) also indicate that AMPTES-modified chitosan molecule is highly reactive and can transfer as well as accept electrons during metal/coating interactions. A good look at ε and Ѡ values in Table 5 shows that AMPTES-modified chitosan nanocluster (AMCN) is more nucleophilic and less electrophilic than other molecules. This implies that the AMPTES-modified chitosan molecule is rich in electrons and therefore most probable to adsorb onto the mild steel surface.
However, the unmodified chitosan molecule showed highest ionization potential. With addition of silane additives, the ionization potential of silane-modified chitosan molecule decreased in value. Lowest ionization potential was observed with TEOS-modified chitosan nanocluster, which ought not to be. This could be due to effect of hydrophobicity of the silane on the chitosan molecule.
Table 5
Quantum chemical parameters of Chitosan (CN), TEOS-modified chitosan nanocluster (TMCN) and AMPTES-modified chitosan nanocluster (AMCN).
ID | EHOMO | ELUMO | \(\varDelta\)E | I | A | χ | µ | η | Ϭ | Ѡ | ε |
CN | -322.710 | -286.828 | 35.828 | 322.710 | 286.828 | 304.769 | -304.769 | 17.941 | 0.0557 | 2588.600 | 0.000386 |
TMCN | -262.530 | -229.425 | 33.105 | 262.530 | 229.425 | 245.977 | -245.977 | 16.555 | 0.0604 | 1827.384 | 0.000547 |
AMCN | -264.864 | -232.438 | 32.426 | 264.864 | 232.438 | 248.651 | -248.651 | 16.213 | 0.0616 | 1906.721 | 0.000524 |
3.1.4 Fukui indices results of chitosan molecule and silane-modified Chitosan molecules
The calculated Fukui indices for chitosan, TEOS-modified chitosan and AMPTES-modified chitosan molecules are given in Table 6. As indicated earlier, atoms with F2(r) > 0 suggest sites for electron acceptance and atoms with F2(r) < 0 indicate sites where electron donation takes place. Considering the molecules in Table 6, for chitosan, N(221) is the electron acceptor region, whereas C(45), O(120), O(147) and N(192) are electron donor regions. As for the TEOS-modified chitosan, the electron acceptor regions are located at C(6), C(63), C(109), C(120) and O(161), whereas the electron donor regions are Si(21), Si(35), Si(42), O(43), C(88), O(150) and C(225). In the AMPTES-modified chitosan, the electron acceptor regions are C(21), N(33) and C(76), while O(19), N(26), Si(75), Si(92) and C(276) are the electron donor regions. Comparing the obtained results with those of the quantum chemical computations, it could be concluded that the highest inhibitive potential of the AMPTES-modified chitosan could be attributed to presence of nitrogen atoms which participated in the electron donor – acceptor interactions.
Table 6
Fukui functions for chitosan, TEOS and AMPTES silane-modified chitosan molecules
Chitosan | TEOS-modified chitosan | AMPTES-modified chitosan |
Atoms | F+(k) | F−(k) | F2(r) | Atoms | F+(k) | F−(k) | F2(r) | Atoms | F+(k) | F−(k) | F2(r) |
N(221) | 0.003 | 0.002 | 0.001 | C(6) | 0.003 | 0.002 | 0.001 | O(19) | 0.004 | 0.006 | -0.002 |
C(45) | 0.009 | 0.010 | -0.001 | Si(21) | 0.014 | 0.015 | -0.001 | C(21) | 0.005 | 0.004 | 0.001 |
O(120) | 0.001 | 0.002 | -0.001 | Si(35) | 0.013 | 0.014 | -0.001 | N(26) | 0.006 | 0.007 | -0.001 |
O(147) | 0.003 | 0.004 | -0.001 | Si(42) | 0.008 | 0.009 | -0.001 | N(33) | 0.005 | 0.004 | 0.001 |
N(192) | 0.001 | 0.002 | -0.001 | O(43) | 0.011 | 0.012 | -0.001 | Si(75) | 0.004 | 0.006 | -0.002 |
| | | | C(63) | 0.006 | 0.005 | 0.001 | C(76) | 0.003 | 0.002 | 0.001 |
| | | | C(88) | 0.005 | 0.006 | -0.001 | Si(92) | 0.007 | 0.008 | -0.001 |
| | | | C(109) | 0.005 | 0.004 | 0.001 | C(276) | 0.001 | 0.002 | -0.001 |
| | | | C(120) | 0.010 | 0.009 | 0.001 | | | | |
| | | | O(150) | 0.004 | 0.005 | -0.001 | | | | |
| | | | O(161) | 0.002 | 0.001 | 0.001 | | | | |
| | | | C(225) | 0.006 | 0.007 | -0.001 | | | | |
3.2 Molecular Dynamics (MD) Simulation
To gain insights into the nature of adsorption of DGEBA-BDA epoxy coating and chitosan molecules on mild steel surface, a computational study based on MD simulation was conducted. The simulation was done by firstly, immersing the modeled mild steel in simulated seawater (96.5 wt.% H2O, 3.5 wt.% Cl−) as illustrated in Fig. 6.
(i) (ii)
Secondly, the modeled DGEBA-BDA epoxy coating molecule was adsorbed onto the framework containing the mild steel and seawater. Figure 6(iii) shows the side view of equilibrium adsorption configuration of DGEBA-BDA epoxy coating molecule. A good look at the Fig. 6(iii) shows that the DGEBA-BDA epoxy coating molecule adsorbed on the mild steel surface to form polymeric film blanket on the mild steel surface. The chitosan molecules were also seen adsorbed onto the mild steel surface alongside the epoxy coating molecule (Fig. 6(iv)). The orientation of the coating molecules clearly shows that the oxygen and nitrogen atoms from both epoxy and chitosan molecules were favourably positioned for adequate adsorption.
Despite the remarkable anticorrosion properties of epoxy coating and chitosan-modified epoxy coating already reported in the literature [17, 18], recent experiments [3, 19, 20] aimed at improving the surface properties of epoxy coatings suggest that silanization of epoxy coatings holds great prospects for robust anticorrosion performance. Thus, each of tetraethoxysilane (TEOS)-modified chitosan nanocluster and (3-aminopropyl ethoxy) silane (AMPTES)-modified chitosan nanocluster was added to epoxy coating to enhance the surface properties of epoxy coating for better anticorrosion performance. Figure 7 shows the adsorption of the silane-modified epoxy coatings on mild steel surface after Forcite quench simulation in 3.5 wt. % NaCl solution. The side view of the diagrams shows that orientation of the coating molecules favours spontaneous adsorption on the mild steel surface. To determine the effect of silane additives on the adsorption performance of the epoxy coating, adsorption energies were computed and analysed.
3.2.1 Adsorption Energies
The adsorption energy is another important parameter that is used to determine the adsorption strength of (DGEBA-BDA) epoxy-mild steel interaction. This parameter gives an insight into the bonding strength of the coating molecule with mild steel and can be used to predict the anticorrosion performance of the coating molecule. Studies have shown that molecules with higher negative value of adsorption energy on mild steel is expected to form stronger bonds with the mild steel surface and consequently provides a better anticorrosion performance for the mild steel substrate [8, 21].
Hence, the MD simulation was used to determine the adsorption energy of the unmodified epoxy coating, chitosan-modified epoxy coating and silane-modified chitosan/epoxy coatings molecules on the mild steel surface. This involved, firstly, calculation of single point energy of individual component and systems of the adsorbate and adsorbent, which are energies of mild steel surface in salt solution (Esurf.+sol.), coating molecules in salt solution (Ecoat+sol.) and salt solution. The results of the single point energy calculations are given in Table SI 1. Secondly, the overall adsorption energies (Eads) were determined using Eq. (13) which has already been established as described elsewhere [8, 9, 13]. Hence, Table 7 shows the adsorption energies for the different coating formulations estimated using Eq. (13). As can be seen in Table 7, the Eads values for the adsorption of the coating molecules on mild steel surface in 3.5 wt.% salt solution follows the trend; unmodified epoxy coating < chitosan-modified epoxy coating < TEOS-modified chitosan/epoxy coating < AMPTES-modified chitosan/epoxy coating.
Table 7
Adsorption energies (Eads) and estimated potential protection efficiency for the different coating formulations on mild steel surface.
ID | Coating formulation | Eads (kcal/mol) | % Pc | % Pch |
(i) | Epoxy coating | − 1,189.33 | - | - |
(ii) | Chitosan-modified epoxy coating | − 2,305.77 | 48.42 | - |
(iii) | TEOS-modified chitosan/epoxy coating | − 2,630.00 | 54.78 | 12.33 |
(iv) | AMPTES-modified chitosan/epoxy coating | − 3,094.65 | 61.58 | 25.49 |
This implies that AMPTES-modified chitosan/epoxy coating with adsorption energy, − 3,094.65 kcal/mol was highest, whereas unmodified epoxy coating with Eads − 1,189.33 kcal/mol was the lowest. Thus, it is imperative to note as reported elsewhere [22, 23] that high negative value of Eads indicates that the coating molecules interacted and adsorbed strongly on the mild steel surface. In this case, the strong interaction of the coating molecules with the mild steel surface could be attributed to the presence of polar functional groups such as –OH (hydroxyl), –NH2 (amino) and pi – electrons of the several aromatic rings in the epoxy coating; –CH2OH, –NH2 and –NHCOCH3 of the chitosan molecules; –OCH2CH3, –OCH3, –NH2, of the silanes. Also, the negative sign of Eads suggests spontaneous adsorption/interaction between the coating molecules and mild steel surface.
3.2.3 Radial distribution function
The radial distribution function which helps to determine the bond length of interacting molecules can be calculated using MD simulation. This parameter gives an insight into the type of interaction between two molecules. The interaction between two or more molecules can be a chemical adsorption (chemisorption) or a physical adsorption (physisorption). Chemical adsorption is associated with shorter bond length between 1.0 and 3.5A, and gives high bond strength, while physical adsorption is marked by bond length greater than 3.5A and correspondingly indicates lower bond strength [8, 9]. Thus, if the interaction between a coating molecule and metal substrate is a chemical interaction, a high bond strength is expected and consequently the molecule is expected to perform as a good corrosion inhibitor. However, if it is a physical interaction, the bond length is lower in strength and the molecule might not perform well in corrosion protection of the metal.
Thus, the bond length of the atoms of DGEBA-BDA epoxy coating with respect to mild steel were analyzed using the radial distribution function (see Figure SI 1 – Figure SI 4). The values of the bond lengths determined by the RDF analysis are given in Table 8. Based on the correlation of bond length of interacting atoms to chemical and physical adsorptions, it could be seen that atoms of the AMPTES-modified chitosan were more chemically adsorbed on the steel surface than TEOS-modified chitosan, unmodified chitosan and epoxy molecules. These results are quite in agreement with the obtained adsorption energies.
Table 8
Bond length analysis for the interactions of atoms of epoxy, chitosan, TEOS-modified chitosan and AMPTES-modified chitosan nanocluster with mild steel surface.
Epoxy | Chitosan | TEOS-modified chitosan | AMPTES-modified chitosan |
Interaction | Bond length, A | Interaction | Bond length, A | Interaction | Bond length, A | Interaction | Bond length, A |
Steel - O | 3.27 | Steel-O | 2.61 | Steel-O | 3.23 | Steel-O | 2.59 |
Steel - N | 3.25 | Steel-N | 3.79 | Steel-N | 3.15 | Steel-N | 3.03 |
Steel - C | 3.55 | Steel-C | 3.03 | Steel-C | 2.85 | Steel-C | 2.31 |
| | | | Steel-Si | 3.09 | Steel-Si | 3.01 |
3.2.4 Molecular surface area
Surface area of the adsorbed molecules were determined to be able to understand the coverage on the metal surface. It relates to molecular orientation on the substrates surface. This is important because it gives idea on the protective efficiency of the adsorbed coating molecules. Hence, Table 9 presents surface areas per molecule for epoxy, chitosan, TEOS-modified chitosan and AMPTES-modified chitosan nanocluster. From the Table 9, epoxy molecule has the lowest surface area whereas AMPTES-modified chitosan shows the highest value. Thus, AMPTES-modified chitosan exhibits the highest protective potential.
Table 9
Molecular area for epoxy, chitosan nanocluster and silane modified nanocluster
Monomer/nanocluster | Molecular area |
Epoxy | 641.004 |
Chitosan nanocluster | 1129.179 |
TEOS-modified chitosan | 1502.724 |
AMPTES-modified chitosan | 1923.005 |
3.2.2 Anticorrosion potential of silane-modified chitosan/epoxy coating
Based on the quantum chemical computations and molecular dynamics simulations results, it is now established that TEOS- and AMPTES-modified chitosan possessed lower energy gap than the unmodified chitosan, and therefore possessed higher tendency to impart coating – metal interaction, which is a precursor for better corrosion inhibition. Additionally, TEOS- and AMPTES-modified chitosan possessed more nucleophiles than the unmodified chitosan, which implies that the molecules are richer in electrons and therefore more probable to adsorb onto the mild steel surface than the unmodified chitosan.
Further, silane-modified chitosan exhibited lower values of electronegativity (χ), electron affinity (A) and hardness (η) with higher softness (Ϭ) and higher chemical potential (µ), which are related to high corrosion protective capability. The adsorption energies (Eads) of the silane-modified chitosan/epoxy coating were observed to be higher (more negative) than the unsilanized chitosan/epoxy and plain epoxy coatings (less negative). Interestingly, it is an established knowledge that molecules that display higher negative value of adsorption energy is expected to form stronger bonds with metal surface, and consequently provides a better anticorrosion performance for the metal substrate.
Thus, to quantify the effect of silane modification of chitosan on the anticorrosion performance of the epoxy coating, the anticorrosion potential protection efficiencies of the coatings (% Pc) were estimated via adsorption energy (Eads) values using Eq. (15):
$$\%{P}_{c}=\left(\frac{{E}_{ads}^{Mepoxy}-{E}_{ads}^{Uepoxy}}{{E}_{ads}^{Mepoxy}}\right)X100$$
15
where \({E}_{ads}^{Mepoxy}\) is the adsorption energy of the modified epoxy coating and \({E}_{ads}^{Uepoxy}\) is for the unmodified epoxy coating. From the Table 7, it was observed that when epoxy coating was modified with chitosan, the increase in potential protection efficiency over the unmodified epoxy was observed to be 48.42 %. When the chitosa was modified with TEOS and AMPTES, and then introduced into the epoxy coating, the potential protection efficiency over the unmodified epoxy coating increased to 54.78 % and 61.58 %, respctively. Onthe other hand, the performance of silane-modified chitosan/epoxy coating over unsilanized chitosan/epoxy coating was appraised. The protection efficiency (% Pch) of 12.33 % and 25.49 % were stimated fo TEOS and AMPTES, respectively. This implies that silane modification of chitosan greatly enhanced the anticorrosion performance of epoxy coating. Thus, silane-modified chitosan/epoxy coating is potentially more corrosion-resistant than the unsilanized chitosan/epoxy and plain epoxy coatings.
Conclusions
The effect of silane modification of chitosan on anticorrosion performance of epoxy coating has been investigated using quantum chemical computations and molecular dynamics simulation techniques. Quantum chemical computations indicate that silane-modified chitosan possessed lower energy gaps, electronegativity (χ), electron affinity (A) and hardness (η) with higher softness (Ϭ) and higher chemical potential (µ) than the unmodified chitosan. These observed parameters are indicators of high corrosion protective capability, and therefore suggest that silane-modified chitosan possessed higher tendency for corrosion inhibition performance than the unmodified chitosan. This could be attributed to presence of hydrophobic moieties which possess water-resistant characteristics. The MD simulation results showed that adsorption energies (Eads) of the silane-modified chitosan/epoxy coating were higher (more negative) than the unsilanized chitosan/epoxy and plain epoxy coatings (less negative), and consequently suggests better anticorrosion performance. The observed effect is most pronounced with (3- aminopropyl) trimethoxy silane (AMPTES)-modified chitosan, possibly due to presence of – OH, – N, – Si atoms of the silane additive. The Fukui functions, radial distribution function (RDF) and molecular surface area values confirmed that AMPTES-modified chitosan possess the highest potential for corrosion protection. Based on the obtained adsorption energies and potential protection efficiencies, it could be inferred that silane-modified chitosan/epoxy coating is potentially more corrosion-resistant than the unsilanized chitosan/epoxy and plain epoxy coatings, and therefore holds promise for durable service in seawater environment.