In this section, we present the atomic configurations, electronic band structures and density of states, and optical absorption spectra of DNT/cellulose, DNT/epoxy, and C-S-H/BNNT composites.
3.1. DNT/Cellulose and DNT/Epoxy Nanocomposites
The optimized atomic configurations of the sp
3 tube (3,0) DNT, cellulose chain, and epoxy are illustrated in
Figure 1. The DNT shown in
Figure 1a consists of 96 total atoms which can be viewed as stacked benzene rings forming a one-dimensional thread. The C – H bond length is measured to be 1.10 Å. The C – C bond length between the carbon atoms in a benzene ring is 1.54 Å, while those between the adjacent benzene rings are 1.58 Å. These measured C – C bond lengths of the DNT are in good agreement with the computed values (1.54 Å – 1.57 Å) from the previous report [
29]. The modeled cellulose chain has 45 total atoms, as presented in
Figure 1b. Its C – C, C – H, and C – O bond lengths range from 1.52 Å – 1.54 Å, 1.10 Å – 1.11 Å, and 1.40 Å – 1.43 Å, respectively, while O – H bond has a length of ~ 0.97 Å. In
Figure 1c, the selected epoxy model is illustrated and consists of 55 total atoms. The C – C, C – H, C – O, and O – H bond lengths range from 1.39 Å – 1.54 Å, 1.10 Å – 1.11 Å, 1.37 Å – 1.43 Å, and 0.96 Å – 0.97 Å, respectively.
The optimized structures of DNT/cellulose nanocomposites are displayed in
Figure 2. The minimum interaction distances
between DNT and cellulose, calculated binding energies
, and the results of Bader charge transfer analyses
are obtained and summarized in
Table 1. The first configuration illustrated in
Fig. 2a, where the backbone of the cellulose lies parallel to the nanothread, yields the strongest interaction relative to the interaction energies of the DNT/cellulose complex systems. This is attributed to the orientation of cellulose on DNT, which leads to a more expansive interface. The shortest distance between the non-hydrogen atoms of the nanothread and cellulose is 3.67 Å (C – O), and the calculated binding energy is –0.797 eV. In
Fig. 2b, the cellulose is oriented perpendicular to the tube, and the minimum distance between their non-hydrogen atoms is measured to be 3.42 Å (C – O), and the binding energy is –0.730 eV. In
Fig. 2c, the minimum distance and binding energy are calculated to be 3.48 Å (C – O) and –0.726 eV, respectively. In all structures, negative values of the binding energies indicate an exothermic process. The non-bonded interaction between the DNT and cellulose and the obtained values of
suggests a physical type of adsorption dominated by vdW forces.
To further examine the interaction of the DNT and cellulose composites, the CDD and ELF are obtained for all structures. The CDD is calculated by taking the difference between the charge density of the composites and the charge densities of the isolated constituents. The CDD isosurfaces presented in
Figure 3 (a, d, g) show that the charges are mainly distributed along the nanothread interface. The yellow and cyan isosurface implies gain and loss of charge, respectively. To inspect charge transfer, a Bader charge transfer analysis is performed. A 0.008 e (DNT/cellulose – 1) and 0.006 e (DNT/cellulose – 3) charge transfer from the cellulose to the DNT are acquired. In contrast, a 0.004 e charge transfer from the DNT to cellulose is obtained for DNT/cellulose – 2 composite. The ELF isosurface and 2D ELF contour are displayed in
Fig. 3 (b, e, h) and
Fig. 3 (c, f, i). ELF [
87] is a measurement of electron localization in atomic and molecular systems and is represented on a scale from 0 to 1. When ELF values exceed 0.7, electrons are considered localized, indicating the presence of core or bonding regions or lone pairs. Meanwhile, when ELF values fall between 0.7 and 0.2, electron localization resembles that of an electron gas and is typical of metallic bonds [
88]. The ELF isosurface illustrated in
Fig. 3 (b, e, h) shows a relatively uniform electron density across the composites. The 2D ELF contour displayed in
Fig. 3 (c, f, i) further confirms the non-bonding interactions between cellulose and DNT. No overlapping of ELF is observed, as evident in the distinct blue region between the cellulose and nanothreads.
The optimized atomic configurations of DNT/epoxy composites are displayed in
Figure 4. Calculated minimum interaction distance
, binding energy
, and charge transfer
are summarized in
Table 2. The first configuration illustrated in
Fig. 4a (DNT/epoxy – 1), where the epoxy wraps around the thread, has –0.224 eV binding energy and the minimum distance between the non-hydrogen atoms is measured to be 3.56 Å (C – O). In the second configuration (DNT/epoxy – 2), where the backbone of the epoxy is oriented slightly perpendicular to the thread, as displayed in
Fig. 4b, the closest distance between their atoms is 3.64 Å (C – O). Also, the binding energy is –0.236 eV, which is relatively higher than the interaction energy of DNT/epoxy – 1. In
Fig. 4c (DNT/epoxy – 3), the epoxy is aligned parallel to the DNT with a minimum distance of 3.60 Å (C – O) and a binding energy of –0.168 eV, which is the lowest among the three configurations of DNT/epoxy composites. Similar to the discussions above, all structures display noncovalent interactions, and the negative values of binding energies indicate an exothermic reaction. The non-bonded interactions between the DNT and epoxy as well as the measured minimum interaction distances, demonstrate physisorption mainly governed by weak vdW forces.
The CDD and ELF calculations are also performed for DNT/epoxy composites and are presented in
Figure 5. Our results yield similar behavior to those of DNT/cellulose composites. The CDD isosurface shows accumulation and depletion of charges mainly distributed along the nanothread interface. Bader charge transfer analysis reveals 0.003 e (DNT/epoxy – 1) and 0.019 e (DNT/epoxy – 2) charge transfer from the epoxy to the nanothread. A 0.002 e charge transfer from the DNT to epoxy is obtained for the DNT/epoxy – 3 composite. The DNT/epoxy complex systems' ELF isosurface shows uniform electron density across the composites. The 2D ELF plots confirm the non-bonded interactions with the visible blue region between the epoxy and nanothread. Owing to the hydrogenated surface of DNT, the vdW interactions between polymer and nanothread are weaker than those with similar systems. This behavior is consistent with previously reported interactions of diamond nanothreads with other polymers [
33,
34,
35,
36,
89,
90,
91].
Figure 6 illustrates the calculated electronic band structure of (3,0) tube DNT. According to GGA/PBE DFT calculations, benzene-derived diamond nanothreads are insulators with at least a 3.5 eV energy band gap, which is expected due to the intrinsic sp
3 bonding of carbon atoms just like diamond [
29,
30,
92,
93,
94,
95,
96]. Our result shows that pure sp
3 – (3,0) DNT has a direct band gap of 3.99 eV at the Γ point, which is close to the previously calculated value (3.98 eV) [
96]. The complex systems, meanwhile, show a slightly lower band gap. We observe a shift of bands at the higher energy level, resulting in DNT/cellulose – 1 and DNT/epoxy – 1 composites having a direct band gap of ~3.7 eV and ~3.6 eV, respectively. These minor modifications in the energy band gap are attributed to the weak interaction between the nanothread and polymers and the minimal charge transfer previously mentioned. This, in turn, leads to the realignment of the energy states. As discussed above, the interaction energies of DNT/cellulose – 1 and DNT/epoxy – 1 composites are 0.797 eV and 0.224 eV, respectively. The charge transfer from the cellulose to the nanothread is calculated to be 0.008 e while the charge transfer from the epoxy to DNT is 0.003 e. However, it is also noteworthy that GGA usually underestimates the band gap of materials.
To further inspect the composites' electronic band structures, the total and partial density of states are provided in
Figure 7. The black solid line depicts the total DOS, while the DNT and cellulose/epoxy contributions are represented by blue solid and dotted lines, respectively. The DOS of carbon and hydrogen atoms of DNT are outlined by red and cyan solid lines, respectively. Also, the carbon, hydrogen, and oxygen atoms of the cellulose/epoxy are depicted by red, cyan, and magenta dotted lines, respectively. In
Figure 7a, the density of states of the DNT/cellulose composite shows that at the lower energy range [~ −2.3 eV, −6 eV], most contribution to the total DOS of the composite, comes from DNT, specifically from the carbon atoms of the nanothread. The cellulose shows a significant contribution at ~ −3.1 eV to −6 eV, with its oxygen atoms having the highest DOS relative to the total contribution of the cellulose.
Similarly, the DOS of DNT/epoxy nanocomposite presented in
Figure 7b shows that most contribution to the total DOS still comes from the DNT, specifically from its carbon atoms. The contributions of the epoxy in the valence band are observed at –2.5 eV to –3.0 eV, –3.5 eV to 4.5 eV, and –4.8 eV to –6.0 eV, mostly coming from its carbon and oxygen atoms. At around –3.5 eV to –4.5 eV, higher contributions of the atoms from epoxy are observed compared to those of DNT. Overall, it can be noticed that in both complex systems, the primary features of the pure (3,0) DNT are reproduced, suggesting that the electronic properties of the nanothread are preserved. Besides, we notice no strong hybridization between atoms of the nanothread and polymer. These observations further support our claim that DNT and cellulose/epoxy only interact weakly.
We have also explored the optical absorption spectra of the DNT/cellulose and DNT/epoxy composites. As illustrated in
Figure 8a, the adsorption of DNT onsets at ~4.4 eV and the cellulose at ~5.2 eV indicates insulating behavior (i.e., wide bandgap). The combined system produces the same characteristics as cellulose and DNT. On the other hand, the absorption spectra of DNT/epoxy presented in
Figure 8b reveal that the epoxy has absorption starting at ~3.6 eV while the DNT appears at ~4.4 eV, similar to the observation made in
Fig. 8a. These results further confirm the large energy band gaps of the composites illustrated on their electronic structures.
3.2. Calcium-Silicate-Hydrates and Boron Nitride Nanotube Nanocomposites
The optimized atomic structure of the C-S-H model, single layer C-S-H, BNNT(4,4), and the optimized configuration of the C-S-H/BNNT(4,4) composite are presented in
Figure 9. To simulate the interface of the C-S-H with the BNNT, a single layer of the C-S-H taken from the molecular dynamics results is utilized [
97]. The intralayer of prototype C-S-H has a 1:1 Ca to Si ratio, while two Ca ions and two water molecules are placed at the surfaces of the C-S-H. This model parallels the recent research showing that the surface of C-S-H is rich in Ca ions [
98]. Both the tendency of the Ca ions to diffuse in the system and the variability of the Ca:Si ratio are probable [
99]. These situations will not be covered in this work.
The prototype C-S-H here is adapted to our recent work that describes the interface of graphene-nanoribbon and SWCNT with the C-S-H[
81]. The isolated C-S-H has Ca–H
2O, Ca–O, and Si–O bonds ranging from 2.35-2.43 Å, 2.39-2.70 Å, and 1.62 –1.70 Å, respectively. The bond lengths are in agreement with experimental data[
98]. Turning to the isolated BNNT, the B-N bond in the tube direction is measured to be 1.44 Å, while in the circumferential direction, the B-N bond is 1.46 Å. These measured bond lengths here are close to the BNNT's report [
100]. The deviation is attributed to the fixed unit cell considered here and the overall method limitation.
The minimum interaction distance of C-S-H and BNNT is 2.68 Å (Ca–N). On the one hand, the interaction distance of the H2O – BNNT is 3.10 Å (O–B), and the Si-OH – BNNT distance is 2.40 Å and 3.21 Å for H-N and O-N, respectively. In the composite, minor changes to the Ca-O and Si-OH of the C-S-H at the interface are lower than 0.005 Å. The most observable change in the atomic structure of the C-S-H in the complex structure is the orientation of the confined H2O, in which the H points toward the O atoms, establishing a hydrogen bond. This minor structural change is mainly a signal of weakly bonded systems similar to the discussion in the preceding section.
The interaction strength is quantified by calculating the binding energy per unit cell. The binding energy of the C-S-H/BNNT is -0.89 eV, which is lower in magnitude compared to the binding energy of the C-S-H/SWCNT (-5.0 eV) and C-S-H/graphene-nanoribbon (-3.24 eV) [
81]. Furthermore, the calculated binding energy here is much lower than the binding energy of graphene-based material with the monomer of C-S-H[
101].
The CDD and ELF are also provided to understand the interaction of BNNT and C-S-H composite. At the isosurface value of 0.02/Å
3, it is noticeable that Ca and N bonds overlapped, indicative of a shared electron type of interaction. We further confirm this result by calculating the CDD isosurface, showing an accumulation of electronic charge at the bond region. The overall charge transfer from C-S-H to the BNNT is 0.47 e. The total electron depletion of the Ca ions at the interface is 0.37 e. The total contribution of the Si-OH and H
2O is ~0.10 e, which is way lower owing to the size of the system considered. These results indicate that major charge transfer is attributed to the Ca ions at the interface, which drives the interaction of nanocomposites. This further confirms the findings in our recent work on the Ca ions at the interface, which drives the bonding between the C-S-H layer with the graphene-nanoribbon and SWCNT. The ELF isosurface and 2D contour are displayed in
Figure 10c and
Figure 10d, respectively. The result shows that the BNNT tends to interact with the lone pair of the Ca ions of the C-S-H. This is contrary to our previous work, where the Ca ion's lone pair vanishes upon adsorption of the graphene-nanoribbon and SWCNT.
The electronic band structures of the C-S-H, BNNT, and C-S-H/BNNT complexes are further calculated to reveal the composites' metallicity, as shown in
Figure 11. Our results show that the dispersive bands appear near the Fermi energy due to the lone pair of the Ca ions, as discussed here [
81]. On the one hand, the BNNT shows insulating properties having a bandgap of 3.77 eV located at the Γ point. This is in agreement with the reports presented in ref. [
102] with a bandgap of 3.87 eV and 4.11 eV calculated using PBE and BLYP functionals, respectively. The PBE functional is well-known for underestimating the bandgap of semiconductors and insulators. Moreover, the theoretical length of the BNNT (3.695Å) is used here to match the size of the unit cell of the C-S-H, while ref. [
102] allowing cell relaxation, giving 2.560 Å leads to minor disagreement with the bandgap of BNNT, aside from intrinsic error of the theory and approximations combined. The composite electronic band structure can be considered superimposed on the constituents, except for the minor shift of bands of the BNNT to lower energy due to charge accumulations. This is the usual result of weakly bonded systems, as demonstrated in the following references [
79,
80,
103,
104,
105]. We further provide the system's total and partial density of states shown in
Figure 12. The black dotted line depicts the total DOS, while the total contributions of the B, N, Ca, Si, H, and O atoms are depicted by purple, orange, green, yellow, cyan, and magenta dotted lines, respectively. The decomposed DOS of BNNT and C-S-H shows no strong hybridization indicative of weakly bonded systems, confirming our previous conclusions.
The absorption spectra are further calculated to provide reference to observables. Here, as can be observed in
Figure 13, the BNNT tends to have abrupt absorption at ~4.5 eV, indicative of insulating properties (i.e. wide bandgap nature). Meanwhile, the single C-S-H layer shows metallic characteristics having minor absorption at energy region < 3.0 eV. This is attributed to the dispersive bands at the vicinity of the Fermi level. In the complex structure, both the characteristics of BNNT and C-S-H absorption spectra are reproduced except for minor deviation owing to the realignment of bands. It should be noted that in a bulk system of C-S-H, the dispersive bands may vanish due to the presence of bulk H
2O in the interface.