## 3 Results and Discussion
An energy barrier of 1.5 kcal/mol needed to be overcome to reach the second region of the minimum at CV1 = 1.0-4.4 and CV2 = 1.3-1.9. It appears that partial intermolecular interactions were more stable than the completely dehydrated interactions. An additional barrier of 5.5 kcal/mol was needed to be overcome, in order to form more hydrogen bonds between the PSSA and the cellulose chains. However, this stronger PSSA-cellulose interaction state appeared not to be favorable energetically, probably due to the decrease of entropy as a result of greater constraint on the polymer chains. Figure 6 shows the 2D free energy contour plot for the FES of the system B (DP 20 ionized PSSA, cellulose in aqueous solution). The FES appeared to be quite different, with the doubling of polymer chain length with the values of CVs at minima being almost twice that of system A. The longer PSSA  
Figure 5: The 2D free energy surface contour plot for system A, involving the interaction of DP 10 neutral PSSA and DP 10 cellulose in water. CV1 and CV2 represent the number of hydrogen bonds formed between them. and cellulose chains formed more hydrogen bonds. The global minima were found in the region at around CV1 = 3.8-6.1 and CV2 = 0.8-1.6. Conformational analysis at the global minima showed that a small fragment of PSSA was close to cellulose, to form a partially direct contact interaction. An energy barrier of about 5.5 kcal/mol had to be overcome in order to completely remove the water molecules and to form a direct contact interaction between the two chains, similar to the situation in system A. Figures 7 and 8 show the 2D free energy contour plots for the FES reconstructed from the system C (DP 20 neutral PSSA and 20 DP cellulose in [EMIM]Cl) and D (DP 20 neutral PSSA and 20 DP cellulose in [EMIM]Cl) respectively. Experimentally, the cellulose hydrolysis in [EMIM]Cl was much more efficient and selective [34; 35; 36]. In [EMIM]Cl, no desolvation barrier was observed, and the PSSA chain was seen to readily form direct contacts with the cellulose chain. The free energy minima in Figures 7 and 8 are for complexes when PSSA and the cellulose chains form partial direct contact. The lowest interaction free energies in the two systems are similar, at around \(\sim\)\(-\)11-12 kcal/mol. This significantly enhanced interaction free energy is largely due to the [EMIM]Cl solvent used. Water molecules form strong hydrogen bonds with both cellulose and PSSA, thereby reducing the strength of the interaction between the cellulose and PSSA chains. Figure 6: The 2D free energy surface contour plot for system B involving DP 20 ionized PSSA and DP 20 cellulose chain interactions in water. CV1 and CV2 represent the numbers of hydrogen bonds formed between the two polymer chains. Figures 9 and 10 show the 2-D free energy contour plots reconstructed from system E (DP 10 PIL and DP 10 cellulose chains in water) and F (DP 20 PIL and DP 20 cellulose chains in [EMIM]CI) respectively. The free energy landscape for the system in aqueous solution had one minimum at  
Figure 8: The 2-D free energy surface contour plot for system D involving DP 20 ionized PSSA and DP 20 cellulose chains in [EMIM]CI. CV1 and CV2 represent the numbers of hydrogen bonds formed between them. Figure 7: The 2D free energy surface contour plot for system C involving DP 20 neutral PSSA and DP 20 cellulose chains in [EMIM]CI. CV1 and CV2 represent the numbers of hydrogen bonds formed between them. CV1 = 0 and CV2 = 0 as seen from Figure 9. This indicates that PIL and cellulose chains are not likely to interact directly in water. In [EMIM]CI, there is a region at CV1 = 2.0-3.0 and CV2 = 1.1-1.9 that favors the partial direct cellulose and PIL interaction, as seen in Figure 4.0 The lowest interaction free energy was about \(-\)15 kcal/mol. Figure 4.1 The 2D free energy surface contour plot for system F involving DP 20 PIL and DP 20 cellulose chains in [EMIM]CI. CV1 and CV2 represent the numbers of hydrogen bonds formed between them.