Poroelastic model for adsorption-induced deformation of biopolymers obtained from molecular simulations

Molecular simulation of adsorption of water molecules in nanoporous amorphous biopolymers, e.g., cellulose, reveals nonlinear swelling and nonlinear mechanical response with the increase in fluid content. These nonlinearities result from hydrogen bond breakage by water molecules. Classical poroelastic models, employing porosity and pore pressure as basic variables for describing the “pore fluid,” are not adequate for the description of these systems. There is neither a static geometric structure to which porosity can sensibly be assigned nor arrangements of water molecules that are adequately described by giving them a pressure. We employ molar concentration of water and chemical potential to describe the state of the “pore fluid” and stress-strain as mechanical variables. A thermodynamic description is developed using a model energy function having mechanical, fluid, and fluid-mechanical coupling contributions. The parameters in this model energy are fixed by the output of the initial simulation and validated with the results of further simulation. The poroelastic properties, e.g., swelling and mechanical response, are found to be functions both of the molar concentration of water and the stress. The basic fluid-mechanical coupling coefficient, the swelling coefficient, depends on the molar concentration of water and stress and is interpreted in terms of porosity change and solid matrix deformation. The difference between drained and undrained bulk stiffness is explained as is the dependence of these moduli on concentration and stress.

Figure 1

(a) Representation of the repetitive chain fragment of amorphous cellulose. The oxygen atoms forming hydrogen bonds with water, O2, O3, and O6, are labeled next to their positions. (b) Illustration of hydrogen bonds in disordered structure. Adsorbed water molecules break hydrogen bonds and push the chains apart, increasing pore space.

Figure 2

MD results (dots) and poroelastic model results (blue line). (a) Chemical potential difference |Δµ| as a function of the concentration at zero stress condition with reference experiment represented as empty squares [35]. (b) Adsorption isotherm: water concentration versus relative humidity. (c) Volumetric strain versus concentration during free swelling. (d) Undrained bulk modulus as a function of concentration. (e) Hydrogen bonds within the polymer per unit volume as a function of concentration. Breaking of the hydrogen bonds is the main mechanism of the material mechanical weakening. (f) Validation of the poroelastic model. Comparison of the poroelastic prediction of the swelling at a volumetric tensile stress of 100 MPa with the MD results.

Figure 3

Prediction of the mechanosorptive behavior with poroelastic model: (a) influence of the volumetric tensile stress on chemical potential difference (–Δµ) curves. (b) Influence of volumetric tensile stress on adsorption isotherms.

Figure 4

(a) Swelling coefficient $B$ as a function of the volumetric tensile stress. (b) Undrained and drained bulk modulus as function of the concentration for two volumetric tensile stresses.