## 3 Results and Discussion
To better understand the behaviors of PSSA, PIL, and cellulose in different solvents. The TI method was used to calculate the solvation free energies in [EMIM]Cl and aqueous solutions. Figure 4 shows the solvation free energy of each polymer chain per monomer unit in water and [EMIM]Cl. It can be seen clearly that the cellulose and PSSA chains, irrespective of their polymer chain length, had solvation free energies of between 10-30 kcal/mol, with the only exception of DP 10 ionized PSSA chain, which had 34 kcal/mol solvation free energy per monomer unit. For neutral and ionized PSSA chains, shorter chains had a slightly higher solvation free energy per monomer unit compared to that of the longer chains in both water and [EMIM]Cl. This was understandable, as shorter chains had overall more solvent molecules surrounding them. The differences in solvation free energies of the same polymer chain in water and the [EMIM]Cl solvents were small, with only a few kcal/mol per monomer unit for the neutral polymers. Both water and [EMIM]Cl are highly polar solvents. However, for ionized PSSA chains, solvation free energies were larger compared to the corresponding neutral PSSA chains. This was due to the fact that charged residues typically have stronger solvation free energies arising from the increased dipole-dipole interaction between the polymer and solvent. What was really surprising was the solvation free energies for the PIL chains in both water and [EMIM]Cl. The solvent free energies increased to about 80-90 kcal/mol per monomer unit in water, compared to the values of about 10-30 kcal/mol for PSSA and cellulose chains. This dramatic increase in solvation free energy was due to the polyelectrolyte nature of the PIL chains. The solvent free energies further increased to about 1000 kcal/mol for PIL chains in [EMIM]Cl solvent, a more than 10-fold increase than in water. This drastic increase in solvation free energy of the PIL chain was one of the main reasons that our catalyst was very effective in catalyzing the cellulose in [EMIM]Cl solvent, as well as in the mixed solvent of [EMIM]Cl/H\({}_{2}\)O [34; 35; 36]. Since both of our polymeric solid acid catalysts and cellulose substrates were in the solid state, solid-solid reactions are generally slow and ineffective due to the limited surface interactions. However, in the case of our PSSA/PIL catalyst,  
Figure 4: Solvation free energies (per DP) of polymeric catalysts and cellulose chains in [EMIM]Cl and aqueous solutions. the significantly larger solvation free energy of the PIL chain rendered the polymeric catalyst more solvable in [EMIM]Cl, and to some extent, in aqueous solutions as well. The solvated PIL chains open up the polymer catalyst and allows the cellulose chains to move in and to be hydrolyzed by the PSSA acid chains. The inclusion of the PIL chains was critically important for our designed polymeric solid acid catalyst. The reconstructed free energy surfaces (FES) can better demonstrate how PSSA or PIL interacts with cellulose in [EMIM]Cl and aqueous solutions. The FES were reconstructed for systems of different combinations of PSSA, PIL, and cellulose chains. The bias potentials were used to determine the FES after the hydrogen bonds started to form (CVs are larger than 0) for all the systems investigated. CV1 and CV2 describe the number of hydrogen bonds formed between the two polymer chains. The sampling of the free energy surfaces during the MD-MTD simulations was considered to be completed when the two CVs moved back and forth between different values randomly. Figure 5 is the reconstructed 2D free energy contour plot for the FES of system A (DP 10 neutral PSSA and cellulose in aqueous solution). Two regions of local minima were found, with an interaction of free energies at around \(-\)5.5 kcal/mol. The first region of the interaction minimum was located at CV1 = 0.2-3.8 and CV2 = 0.3-0.8, indicating the initial intermolecular interaction between the PSSA and cellulose chains.