Role of hydrogen bonding in hysteresis observed in sorption-induced swelling of soft nanoporous polymers

Hysteresis is observed in sorption-induced swelling in various soft nanoporous polymers. The associated coupling mechanism responsible for the observed sorption-induced swelling and associated hysteresis needs to be unraveled. Here we report a microscopic scenario for the molecular mechanism responsible for hysteresis in sorption-induced swelling in natural polymers such as cellulose using atom-scale simulation; moisture content and swelling exhibit hysteresis upon ad- and desorption but not swelling versus moisture content. Different hydrogen bond networks are examined; cellulose swells to form water–cellulose bonds upon adsorption but these bonds do not break upon desorption at the same chemical potential. These findings, which are supported by mechanical testing and cellulose textural assessment upon sorption, shed light on experimental observations for wood and other related materials.


Supplementary Method
As explained in our paper, state-of-the-art techniques such as Molecular Dynamics (MD) and Grand Canonical Monte Carlo (GCMC) do not allow describing coupled adsorption/swelling in porous materials. Indeed, while the former requires to work with a constant number of molecules, the latter only applies to systems having a constant volume.
Following previous works, including the work by Ghoufi  In practice, our hybrid molecular simulations were performed at T = 300 K using a Berendsen thermostat and an anisotropic external stress  = 0 Pa (with the following relaxation times: τT = 0.1 ps and τs = 1.0 ps). Water molecules are described using the SPC/E water model with the SHAKE algorithm to maintain its internal structure rigid. The MD trajectory was integrated using the velocity Verlet integrator with a timestep equal to 1 fs. Hybrid MD/GCMC molecular simulations consisted of performing a large number of blocks where one block corresponds to 2,000 GCMC insertion/deletion attempts followed by 200 MD timesteps. In total, 10 5 blocks were first performed to equilibrate the system followed by 2×10 4 additional blocks to accumulate statistics. In order to check the efficiency of the phase space sampling, we monitored the pressure and volume along the hybrid GCMC/NT simulations. Supplementary Figure 1  There is a non-negligible mismatch between the experimental saturating vapor pressure for water and its numerical counterpart when using the SPC/E water model. This raises the question whether adsorption isotherms should be compared when plotted as a function of reduced pressure P/P0 or absolute pressure P. Considering the fundamental definition of adsorption phenomena (in terms of Gibbs adsorption equation or Polanyi theory for instance), the thermodynamic parameter that governs the adsorbed amount is the chemical potential difference  =  -0 with respect to the chemical potential at saturation 0.
Indeed, at the saturation chemical potential i.e. at the bulk gas/liquid coexistence, adsorption from a relative humidity RH = 1 (P = P0) is maximum (any adsorption above 0 corresponds to intrusion and is therefore only relevant to hydrophobic materials). As a result, when comparing adsorption isotherms for different fluids, the natural choice is to use the chemical potential difference  =  -0. This is relevant when comparing different fluids but also different models for the same fluid when using molecular simulation (or as in the present paper when comparing experimental and simulation data). Considering that water vapor at room temperature behaves as an ideal gas, we used the following relationship RH = P/P0 = exp[/kBT].

Supplementary Discussion
PCFF is a force field parameterized against a broad range of experimental observables for organic compounds. It has been applied to modelling cellulose-based materials by many researchers who have found that it captures quantitatively or semi-quantitatively most physical properties. More in details, for instance, Chen et al. 2 built an amorphous cellulose model and showed that the final density obtained is consistent with its experimental counterpart (1.39 g cm -3 versus 1.48 g cm -3 ). Similarly, in the present work, we found that the final density of our models (ranging from 1.39 to 1.41 g cm -3 ) is consistent with typical experimental densities for cellulose (see Supplementary Table 1). As far as mechanical properties are concerned, Tanaka and Iwata 3 used molecular simulation with the same force field to assess Young's modulus of cellulose crystals; these authors found values in the range 124-155 GPa that are in good agreement with the experimental value (~138 GPa) 4 (no experimental mechanical data are available for amorphous cellulose). As for adsorption properties, in their molecular simulation of adsorption onto cellulose, Da Silva Perez et al. 5 found that the heat of adsorption for a large variety of aromatic compounds is consistent with their experimental counterpart (84% of the adsorbate-cellulose couples displayed differences < 20% between the measured and predicted heats of adsorption). Xu and Chen 6 also found that PCFF predicts formaldehyde diffusion in cellulose with a temperature dependence of the self-diffusion coefficient in good agreement with the experimental data.
Finally, in the context of the present work on water adsorption/desorption in cellulose, we emphasize that PCFF leads to cellulose/water hydrogen bonds with a typical energy (5.4 kcal mol -1 , see discussion in our manuscript) that is consistent with the conformational analysis made by Pizzi et al. 7,8 ; these authors estimated theoretically that the sorption energy is around 5.5 kcal mol -1 for cellulose I crystals and 6.5 kcal mol -1 for paracrystalline (amorphous) cellulose. Overall, the discussion above shows that the forcefield used in the present work provides a reasonable, at least semi-quantitative, description of cellulose (including its density, mechanical, and adsorption properties).