## 3 Results and Discussion  
The MD-MTD simulations commenced when the two polymer chains were close to each other of about 5 A apart. The simulations were conducted for a total of between 100 to 200 ns. Although the initial intermolecular distances were relatively short, interactions between PSSA, PIL, and cellulose chains appeared to be different in [EMIM]Cl and aqueous solutions. In [EMIM]Cl, PSSA or PIL chains can quickly form hydrogen bonds with the cellulose chain soon after the simulations started. However, both PSSA and PIL chains moved apart from cellulose chain during the initial 20-30 ns simulations in aqueous solution. The different behaviors of polymeric catalysts and cellulose chains are critically affected by the solvent. [EMIM]Cl is an excellent solvent of cellulose, and has been widely applied to study cellulose hydrolysis catalyzed by different catalysts [61; 62; 63; 64]. On the contrary, cellulose is almost insoluble in aqueous solutions because water molecules hardly disrupt the intermolecular hydrogen bonds between the cellulose chains [65]. In MD-MTD simulations, the direct interactions between polymeric catalysts and cellulose chains are energetically favorable in [EMIM]Cl. In aqueous solution, the separated states are more favorable. The free energy for the direct interaction between the polymeric catalyst and cellulose chains were found to arise largely in aqueous solution, because water molecules form an extensive hydrogen bonding network and prevent PSSA, PIL, and cellulose chains from moving close to each other. Water molecules between the PSSA, PIL, and cellulose chains have to be removed so that the polymer chains can interact directly and form hydrogen bonds with each other. In MD-MTD simulations, biased potentials were continuously added into the system so that PSSA/PIL and cellulose chains can overcome different dehydration energy barriers to interact directly, as shown in Figure 3.  
A represents DP 20 ionized PSSA interacting with DP 20 cellulose in aqueous solution. B represents DP 10 neutral PSSA interacting with DP 10 cellulose in aqueous solution. C represents DP 20 PSSA and DP 20 PIL interacting system in water. D represents DP 10 PIL interacting with DP 10 cellulose in water. Figure 3 shows the barriers that need to be overcome in order for the two polymer chains to form any direct contact interaction. The dehydration energy barrier between the ionized PSSA and cellulose chains was about 21 kcal/mol. The neutral PSSA slightly increased the barrier to about 28 kcal/mol. This was surprising, as the ionized species typically had stronger solvation free energies, as shown in Figure 4. However, since the polymer chains in A were only half of those in B, polymer chain length also contributed to the energy barriers. Short chains had stronger solvation free energies per DP compared to the longer PSSA and ionized PSSA chains. More significantly, the entropic cost for an unattached short chain to bind was higher than that of a longer chain. As a result, the barrier in B was slightly higher than that of in A. The dehydration energy barrier for C between PIL and PSSA increased to about 40 kcal/mol. This was due to the much stronger solvation free energy of the PIL chains in water, as shown in Figure 4. The solvation free energies of the various polymer chains in water and ionic liquid will be discussed in more detail later. System D, involving interactions between PIL and cellulose, has the highest dehydration energy barrier, of about 123 kcal/mol. This is again due to the much stronger solvation free energy of the PIL chain, and the chains are much shorter. Figure 3: The free energy barrier before the formation of hydrogen bonds between the polymer chains for the four interacting systems (A: DP 20 ionized PSSA, DP 20 Cellulose; B: DP 10 PSSA, DP 10 Cellulose; C: DP 20 PSSA, DP 20 PIL; D: DP 10 PIL, DP 10 Cellulose) in aqueous solution. The affinity between solute and solvent molecules significantly affects the interactions between polymeric catalysts and cellulose chains.