Swelling clay modeling from the molecular scale
Laurent Brochard
Laboratoire Navier (UMR 8205), École des Ponts ParisTech, Univ. Gustave Eiffel, CNRS,
6-8 avenue Blaise Pascal, 77455 Marne-la-Vallée, France
Clays are geo-materials containing extremely fine mineral grains with peculiar hydro-mechanical behaviors, the most well-known of which being the drying shrinkage. This behavior originates from the adsorption of water in the inter-layer space between nanometric minerals, which induces large deformations. It has been evidenced since the 1950s by X-Ray Diffraction (XRD) [1] that the swelling of clay is ‘crystalline’ at the nanometer scale, i.e., it occurs by sudden changes in the basal spacing. Much progress in the fundamental understanding of clays has been made in the last 30 years, thanks to the development of realistic molecular simulations techniques. The swelling upon humidification remains however specifically hard to evaluate, because the usual grand canonical algorithm is too inefficient. In this work, we set up and implement (LAMMPS) a biased Monte Carlo algorithm inspired by a previous algorithm of Hensen et al. [2], which was adapted to the more recent force field considered here (ClayFF). The hydro-mechanical behavior is obtained by simulations at fixed basal distances, combined with a thermodynamic analysis of the (meta)stability of the various hydration states [3]. This allows establishing at the same time the swelling and the hysteresis under arbitrary external loading. If the first works [3] were limited to 5 different relative humidities and two hydration states (1W et 2W), the present work establishes the most complete stability diagram so far, in the case of a reference (Wyoming) sodium montmorillonite [4]. It covers all the humidity range (from 0.001% to 100%) and all the hydration states (0W, 1W, 2W, 3W, capillary). A major result, easily derived from this diagram, is the accurate prediction of the free crystalline swelling, as it is measured by XRD.
While molecular approaches now provide a quantitative understanding of the mineral layer scale, up-scaling to the clay matrix remains a challenge, in particular because the meso-scale (nm to m) is hardly accessible to experimental observation, and the microstructure at this scale can only be inferred indirectly (e.g., from small angle scattering). As an alternative to experiments, granular ’meso-scale’ simulations have emerged which aim at taking advantage of the fine understanding obtained at the molecular scale to propose ’coarse-grained’ models at larger scales. The meso-scale physics involves phenomena that are little explored at the molecular scale, in particular the flexibility of the mineral layer and the mechanics of stacks of layers [5]. We propose a meso-scale model for sodium Wyoming montmorillonite, designed specifically to capture the hydration transitions at the layer scale and address the peculiar thermo-hydro-mechanical couplings at conditions representative of geomechanical applications[6]. This meso-scale model is used to investigate in detail the mesostructure and its evolution during mechanical and osmotic loadings.
[1] Mooney et al. (1952) Journal of the American Chemical Society, 74 (6), 1371–1374
[2] Hensen et al. (2001). The Journal of Chemical Physics, 115(7), 3322–3329.
[3] Tambach et al. (2004). The Journal of Physical Chemistry B, 108(23), 7586–7596.
[4] Brochard, L. (2021). The Journal of Physical Chemistry C, 125(28), 15527–15543.
[5] Honorio et al. (2018) Soft Matter, 14 (36), 7354–7367.
[6] Asadi et al. (2022) Soft Matter, 18 (41), 7931–7948.
