Brownian dynamics simulations of nanosheet solutions under shear

Abstract

The flow-induced conformation dynamics of nanosheets are simulated using a Brownian Dynamics (BD) formulation applied to a bead-rod sheetlike molecular model. This is the first-ever use of BD to simulate flow-induced dynamics of two-dimensional structures. Using this framework, we simulate dilute suspensions of coarse-grained nanosheets and compute conformation dynamics for simple shear flow. The data show power law scaling relationships between nanosheet parameters (such as bending moduli and molecular weight) and the resulting intrinsic viscosity and conformation. For nonzero bending moduli, an effective dimension of 2.77 at equilibrium is calculated from the scaling relationship between radius of gyration and molecular weight. We also find that intrinsic viscosity varies with molecular weight with an exponent of 2.12 ± 0.23; this dependence is significantly larger than those found for linear polymers. Weak shear thinning is observed at high Weissenberg number (Wi). This simulation method provides a computational basis for developing manufacturing processes for nanosheet-derived materials by relating flow forces and nanosheet parameters to the resulting material morphology.

Buckling, crumpling, and tumbling of semiflexible sheets in simple shear flow

“…Relatively less work, though, has focused on the behavior of 2D semiflexible sheets in low-Reynoldsnumber flows, despite the increasing relevance of transition metal dichalogenides, graphene 22 , graphene oxide 23,24 , and 2D polymers 25,26 in advanced technologies. Xu and Green 27,28 looked at sheets under shear and biaxial extensional flow, and Babu and Stark 29 have studied tethered sheets in fluids, confirming predicted scaling laws of Frey and Nelson 30 regarding thermal fluctuations in the presence of hydrodynamic interactions. Additionally, Dutta and Graham 31 have studied Miura-patterned sheets and observed various interesting dynamical regimes involving periodic tumbling, unfolding, and quasiperiodic limit cycles.…”

Brownian dynamics simulation of two‐dimensional nanosheets under biaxial extensional flow

“…As mentioned in our prior study, we describe the extended conformation of the nanosheet by computing an ellipsoid which has the same moment of inertia tensor as the nanosheet; the lengths of the principal axes are computed as . We utilize the semiaxial lengths of this ellipsoid as our measure of nanosheet shape and extension . For example, a perfectly flat nanosheet would have and .…”

“…The methodology of the simulation is based on our prior work on the morphology dynamics of nanosheets under shear flow, and we follow that same formulation here. We represent a nanosheet using a two‐dimensional lattice with beads and bonds.…”

“…We compute intrinsic biaxial extensional viscosity for biaxial extensional flow as: where and are the and components of the stress tensor. We calculate our stress tensor in the same way as shown in the previous paper . The stress tensor per number density is calculated using Kramer's formula, which is written as: where is the total force on bead …”

“…We recently developed a technique for Brownian dynamics (BD) simulations of 2‐D macromolecules (such as nanosheets) in flow . This was the first exploration of how applied flow fields affect nanosheet morphology.…”