On Stress-Strain Responses and Young's Moduli of Single Alkane Molecules, A Molecular Mechanics Study Using the Modified Embedded-Atom Method

In this work, molecular mechanics simulations were performed using a modified embedded-atom method (MEAM) potential to generate the stress-strain responses of a series of n-alkane molecules from ethane (C$_2$H$_6$) to undecane (n-C$_{11}$H$_{24}$) in tensile deformation up to the point of bond rupture. The results are further generalized to a single polyethylene (PE) chain. Force, true Cauchy stress, true virial stress, and Young's moduli were calculated as a function of true strain for all of the molecules. In calculating the stress of a single molecule, three methods (designated in this work as M1, M2, and M3) are suggested based on three different metrics to quantify both the instantaneous molecular cross-sectional area and volume during deformation. The predictions of these methods are compared to theoretical, first-principles, and experimental data. M1 gives true Cauchy and true virial stress results that are essentially equivalent, suggesting that it is a better method for calculating stress in alkane molecules and, hence, PE single chain. The MEAM predictions of the average elastic modulus for a single PE chain using M1, M2, and M3 are 401 GPa, 172 GPa, and 147 GPa, respectively. Though these results are disparate, M1 gives a modulus value that is strikingly close to the ab initio-calculated value of 405 GPa for the -CH$_2$CH$_2$- repeat unit of PE at 0 K. To further test the MEAM potential, the Young's modulus (C$_{33}$ elastic constant) of an orthorhombic PE crystal cell was calculated, but its value (184 GPa) underestimates the DFT-calculated value of 316 GPa by 42%.