Rheology of lamellar liquid crystals in two and three dimensions: a simulation study

Abstract

We present large scale computer simulations of the nonlinear bulk rheology of lamellar phases (smectic liquid crystals) at moderate to large values of the shear rate (Peclet numbers 10 − 100), in both two and three dimensions. In two dimensions we find that modest shear rates align the system and stabilise an almost regular lamellar phase, but high shear rates induce the nucleation and proliferation of defects, which in steady state is balanced by the annihilation of defects of opposite sign. The shear rateγ c at onset of this second regime is controlled by thermodynamic and kinetic parameters; we offer a scaling analysis that relatesγ c to a critical "capillary number" involving those variables. Within the defect proliferation regime, the defects may be partially annealed by slowly decreasing the applied shear rate; this causes marked memory effects, and history-dependent rheology. Simulations in three dimensions show instead shear-induced ordering even at the highest shear rates studied here. This suggests thatγ c shifts markedly upward on increasing dimensionality. This may in part reflect the reduced constraints on defect motion, allowing them to find and annihilate each other more easily. Residual edge defects in the 3D aligned state mostly point along the flow velocity, an orientation impossible in two dimensions.

Structure formation of surfactant membranes under shear flow

“…Oriented lamellae have been obtained in simulations of a coarsegrained molecular model for lipids, [25][26][27] while defect dynamics has been investigated in simulations of a phasefield model of a smectic-A system. 28 Onion and intermediate states have large-scale structures of the order of micrometers, which are beyond typical length scales accessible to molecular dynamics (MD) simulations of coarse-grained surfactant molecules. In our study, we employ a meshless-membrane model, [29][30][31][32] where a membrane particle represents not a surfactant molecule but rather a patch of bilayer membranein order to capture the membrane dynamics on a mi-crometer length scale.…”

Dynamics of edge dislocations in a sheared lamellar mesophase

“…The apparent viscosity is found to be a linear function of the number of defects in the system in the late stages of coarsening. 16 In large systems, it is observed that in addition to ordering, there is also the creation of defects due to shear, suggesting that a minimum size is required for the creation of defects. Moreover, for a given system size, there is a minimum strain rate 16 which is required for the formation of defects.…”

“…16 In large systems, it is observed that in addition to ordering, there is also the creation of defects due to shear, suggesting that a minimum size is required for the creation of defects. Moreover, for a given system size, there is a minimum strain rate 16 which is required for the formation of defects. Two different defect creation mechanisms, the extensional and the compressional mechanism, have been identified 15,16 in simulations.…”

“…The lamellar modulation of the concentration field is modeled using a suitable free energy functional, and the dynamical equations for the coupled concentration field and the fluid momentum fields (equivalent to the model-H equations for a binary fluid 17 ) are solved. The relationship between the molecular properties and those in the mesoscale description have been established, 18,19 and the coarsening of an initially disordered lamellar phase has been studied as a function of the Reynolds number (ratio of inertia and viscosity) and the Schmidt number (ratio of kinematic viscosity and mass diffusivity), 15 or equivalently the Peclet number 16 which is the product of the Reynolds number and the Schmidt number.…”

“…A realistic sample of thickness 1 mm would typically contain about 10 4 −10 5 layers, whereas the largest system size in simulations is about 100 layers in two dimensions. These simulations [10][11][12][13][14][15][16] typically employ a mesoscale model, in which the concentration field is defined as the difference in the local concentrations of the hydrophilic and hydrophobic constituents of the lamellar phase. The lamellar modulation of the concentration field is modeled using a suitable free energy functional, and the dynamical equations for the coupled concentration field and the fluid momentum fields (equivalent to the model-H equations for a binary fluid 17 ) are solved.…”