Nanoscale Tensile, Shear, and Failure Properties of Layered Silicates as a Function of Cation Density and Stress

Abstract

Mechanical properties of layered silicates on the nanometer scale have been associated with large uncertainty. We attempt to clarify the linear elastic properties including tensile moduli, shear moduli, and potential failure mechanisms for the minerals pyrophyllite, montmorillonite, and mica in the order of increasing cation exchange capacity (CEC) under a broad range of stress using electronic structure calculations, semiempirical classical molecular dynamics simulation, and the comparison to available macroscopic experimental data. In-plane tensile moduli (xx and yy) are ∼160 GPa independent of CEC and stress, whereas perpendicular tensile moduli (zz) range from 5 to 60 GPa as a function of CEC at low stress (0.01 to 1 GPa) and approach in-plane values at high stress. In-plane shear moduli (xy) are ∼70 GPa independent of CEC and the shear strength increases from ∼1 to ∼3 GPa with increasing cation density. Shear moduli parallel to the layers (xz and yz) are between 2 and 20 GPa as a function of CEC, with a shear strength of 0.2 to 1 GPa beyond which the layers exhibit lateral shear flow. Tensile zz moduli, shear moduli, and shear strength in the xz and yz direction reach a local minimum at a cation density of 0.3 relative to mica. The simulation suggests sliding of the layers, in-plane kinks, and cation intrusion into the layers as potential failure mechanisms equal to amorphization on the macroscale. The anisotropy and stress-dependence of the mechanical properties is determined by the presence of rigid layers and flexible interlayer spaces of variable cation density. Current classical simulation models tend to overestimate in-plane moduli (xx, yy, xy) in a systematic way relative to electronic structure (DFT) and experimental results.

Bending of Layered Silicates on the Nanometer Scale: Mechanism, Stored Energy, and Curvature Limits

“…In contrast, the perpendicular modulus is significantly lower and depends on cation density and stress. 48 The data are supported by macroscale measurements 23,25,26,29 and multiscale computation 48 however, some previous studies also reported overestimates of the in-plane modulus between 230 and 400 GPa along with an underestimated thickness of single layers of 0.67 nm. 34,39,41,43À45,47 The true layer thickness in the absence of Received: August 30, 2011 ABSTRACT: Bending and failure of aluminosilicate layers are common in polymer matrices although mechanical properties of curved layers and curvature limits are hardly known.…”

“…We equilibrated the aluminosilicate layer by molecular dynamics simulation initially in planar conformation, followed by a decrement in bending radius of the templates, repeated equilibration, and so forth, until small bending radii were achieved. 48 Each carbon wrap contained between 1330 and 1425 carbon atoms, and the arithmetic average of the radii of curvature of the outer and inner wrap matched the target radius of curvature of the mineral (Figure 2a). Wrap atoms carried no charge, solely providing van der Waals confinement for the layered silicates similar to a biological or a synthetic polymer matrix.…”

“…As a result, the chosen distance between the outer and the inner carbon wraps was 1.70 nm for mica (layer thickness Figure 1. Structural models of mica-type aluminosilicates in all-atomic resolution, including mica (5 Â 3 Â 1 supercell), montmorillonites, and pyrophyllite (5 Â 3 Â 2 supercells, ref 48). The change in area density of alkali ions between the aluminosilicate layers can be seen.…”

“…Computed in-plane moduli of aluminosilicates can be often higher than true values according to measurements and DFT calculations on smaller models. 48 The deviation is caused by approximations in the energy expression such as the assumption of numerous covalent bonds and associated quadratic bond stretching and angle bending terms in the octahedral and tetrahedral sheets. Another shortcoming is the disallowance of bond breakage.…”

“…48 Also, the underlying approximation of layered silicates as ideal (smooth) plates is debatable because of the presence of rough surfaces with cations ( Figure 1). The bending stiffness D 1 is subject to a sensitive third-power dependence on the layer thickness h and varies between (1.1 and 3.2) Â 10 À17 J for pyrophyllite, montmorillonite, and mica.…”