2.1. Adsorption of Acid Molecules
Figure 1 shows the adsorption process of the five acid molecules. As shown in the
Figure 1a–e, all five acid molecules were quickly adsorbed onto the crystal with an increase in simulation time. However, the instances where the three low molecular acids were adsorbed completely onto the surfaces and stably remained on the surface went through about 50 ps, whereas the two high molecular acids went through nearly 100 ps. This shows that the three low molecular acids can easily be adsorbed onto the cellulose surface because of their smaller momentum, whereas the two high molecular acids had great difficulty in reaching the surface. Considering the oil environment in a transformer, the two high molecular acids exerted a stronger steric effect than the three low molecular acids. This made it more difficult for the two high molecular acids to reach the cellulose surface.
Figure 2 shows the dynamic diagram of the adsorption process of five acid molecules at different times. It can be seen from the
Figure 1 that all three low molecular acids were adsorbed by cellulose at 50 ps, while the two high molecular acids were not well adsorbed by cellulose.
There is one carboxyl group in each of the five acids, which is a typical polar group. Because cellulose is polar as well, the adsorption potential of the carboxylic group with cellulose is definitely higher than those of other non-polar groups with cellulose. Moreover, the active group for all the five organic acids is the carboxyl group; hence, the sites where the carboxyl groups were adsorbed are very significant.
Figure 3 shows the respective distances of the centroids of the five acid molecules (
Dmole) and the centroids of the carboxyl groups (
Dcarb) from the surface change with the simulation time in the final 100 ps of the MD. As shown by the graphs, the splits between the curves of the two centroids become increasingly obvious with an increase in molecular weight of the acid.
Table 1 shows the respective distances of the two centroids from the surface when the acid molecules were interacting stably with cellulose. If the carboxyl groups and other parts of the acid molecules have the same adsorption interaction with cellulose, the two centroids should coincide. However, as shown in the table, the distances of the two centroids from the surface are not equal to each other. Both the carboxyl group and cellulose are polar, whereas other parts (namely the alkyl chain except for levulinic acid) are non-polar. Therefore, the interaction between the carboxyl group and cellulose is much stronger than that between other parts and cellulose, making the carboxyl group much closer to the cellulose surface than other parts. Meanwhile, the data in the table clearly show that
Dmole increased with an increase in its molecular weight, as well as the difference between the distances of the two centroids (
Ddiff =
Dmole −
Dcarb). This indicates that the carboxyl group is the stable adsorbed point, whereas other parts of the acid molecule were adsorbed unstably. The greater the molecular weight of the organic acid, the looser its adsorption onto cellulose.
Levulinic acid has an additional carbonyl group aside from the carboxyl group compared with the four other organic acids, as shown in
Figure 4. The carbonyl oxygen atom can form hydrogen bonds with cellulose, which would increase adhesion to the cellulose surface; however, its carboxyl group can also form hydrogen bonds with cellulose, causing spatial competition between the carboxyl group and the carbonyl group.
Figure 4 shows that the distances of the centroids of both the levulinic acid molecule and the carbonyl oxygen atom from the surface vary with the simulation time in the last 100 ps of MD. The changes in the dihedral angle defined in
Figure 4 with the simulation time are given simultaneously.
As shown in
Figure 5a, the distance of the carbonyl oxygen atom from the surface (
Dcarbonyl) is smaller than that between the centroid of the levulinic acid molecule from the surface (
Dmole) most of the time. From
Figure 5b, before the levulinic acid molecule was adsorbed onto the surface of cellulose, the dihedral angle was about 180°, indicating that the carbonyl group and the carboxyl group lay in opposite directions. When the levulinic acid molecule was stably absorbed onto the surface, the dihedral angle decreased to about 120°. This is mainly because the levulinic acid molecule underwent self-adjustment of the spatial structure under the influence of cellulose, and consequently, both the carbonyl and carboxyl groups got closer to the surface of cellulose and formed stronger interactions with it. However, the adjustment of the spatial structure will inevitably increase the potential energy. Whether the newly generated spatial structure can exist stably depends mainly on the competition between the deformation energy of the levulinic acid molecule and the adsorption energy of cellulose.
Figure 5c shows the molecular structure of the levulinic acid molecule before it was adsorbed on the cellulose surface, the dihedral angle before the adsorption is marked. Analogously,
Figure 5d shows the molecular structure of the levulinic acid molecule after it has been adsorbed on the cellulose surface, the dihedral angle after the adsorption is also marked.
2.3. Solubility Parameter
The solubility parameter, proposed by Hildebrand et al. [
15] in the mid-20th century, is defined as the square root of the cohesive energy density:
where
CED represents cohesive energy density, which refers to the energy needed by 1 mol condensate per unit volume to overcome the gasification of intermolecular forces, and
V represents molar volume.
The solubility parameter has been widely applied in polymer engineering and related fields as an important parameter for measuring the compatibility of the insulation materials.
According to the theory of similarity and intermiscibility, a solute can only be dissolved or swollen in a solvent that is of similar solubility to the solute.
Table 5 shows the calculated and experimental solubility parameters of the five organic acids. The calculating details are as follows. Firstly, five amorphous cells were constructed. Each cell contained 200 molecules of the same acid. Other parameter settings, such as the force field, are the same as those mentioned above. Then, a 200 ps NPT dynamic run in which the temperature is maintained at 298 K was used. Other parameter settings are the same as the above molecular dynamic settings, namely, temperature was maintained using the Andersen algorithm. For the non-bonded interactions, the atom-based method [
16,
17] and the Ewald summation method [
18,
19] were employed to evaluate the electrostatic and van der Waals interactions, respectively. This is followed by an energy minimization.
As shown in the table, the calculated solubility parameters deviate from their experimental values in the low molecular acids, whereas they agree roughly with the experimental values in the high molecular acids. The solubility parameters of the three low molecular acids are approximate to the solubility parameter of cellulose in contrast to those of the two high molecular acids, which are more similar to that of oil. The result explains the experimental phenomenon that the low molecular acids are to a large degree absorbed by cellulose, contrary to the high molecular acids that tend to dissolve in the oil. For the Coulomb component of the solubility parameter, either its absolute value or proportion decreases with an increase in the molecular weight. Contrarily for the van der Waals component, although its absolute value decreases with an increase in the molecular weight, its occupied proportion indeed increases. The proportion of the polar group in the acid molecule again determines this change.