*Article* **Molecular Dynamics Simulation of Nanoscale Elastic Properties of Hydrated Na-, Cs-, and Ca-Montmorillonite**

**Lianfei Kuang 1, Qiyin Zhu 1,\*, Xiangyu Shang <sup>2</sup> and Xiaodong Zhao <sup>1</sup>**


**Abstract:** The knowledge of nanoscale mechanical properties of montmorillonite (MMT) with various compensation cations upon hydration is essential for many environmental engineering-related applications. This paper uses a Molecular Dynamics (MD) method to simulate nanoscale elastic properties of hydrated Na-, Cs-, and Ca-MMT with unconstrained system atoms. The variation of basal spacing of MMT shows step characteristics in the initial crystalline swelling stage followed by an approximately linear change in the subsequent osmotic swelling stage as the increasing of interlayer water content. The water content of MMT in the thermodynamic stable-state conditions during hydration is determined by comparing the immersion energy and hydration energy. Under this stable hydration state, the nanoscale elastic properties are further simulated by the constant strain method. Since the non-bonding strength between MMT lamellae is much lower than the boning strength within the mineral structure, the in-plane and out-of-plane strength of MMT has strong anisotropy. Simulated results including the stiffness tensor and linear elastic constants based on the assumption of orthotropic symmetry are all in good agreement with results from the literature. Furthermore, the out-of-plane stiffness tensor components of C33, C44, and C55 all fluctuate with the increase of interlayer water content, which is related to the formation of interlayer H-bonds and atom-free volume ratio. The in-plane stiffness tensor components C11, C22, and C12 decrease nonlinearly with the increase of water content, and these components are mainly controlled by the bonding strength of mineral atoms and the geometry of the hydrated MMT system. Young's modulus in all three directions exhibits a nonlinear decrease with increasing water content.

**Keywords:** molecular dynamics; mechanical properties; montmorillonite; basal spacing
