Comment on "Relationship between McQuarrie and Helfand equations for the determination of shear viscosity from equilibrium molecular dynamics"

Elastic moduli of a Brownian colloidal glass former

The static, dynamic and flow-dependent shear moduli of a binary mixture of Brownian hard disks are studied by an event-driven molecular dynamics simulation. Thereby, the emergence of rigidity close to the glass transition encoded in the static shear modulus [Formula: see text] is accessed by three methods. Results from shear stress auto-correlation functions, elastic dispersion relations, and the elastic response to strain deformations upon the start-up of shear flow are compared. This enables one to sample the time-dependent shear modulus [Formula: see text] consistently over several decades in time. By that a very precise specification of the glass transition point and of [Formula: see text] is feasible. Predictions by mode coupling theory of a finite shear modulus at the glass transition, of α-scaling in fluid states close to the transition, and of shear induced decay in yielding glass states are tested and broadly verified.

Shear-stress fluctuations and relaxation in polymer glasses

We investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasistatic and dynamical) shear-stress fluctuations as a function of temperature T and sampling time Δt. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time averaged for each shear plane) to the stress-fluctuation relation μ_{sf} for the shear modulus and the shear-stress relaxation modulus G(t). Using 100 independent configurations, we pay attention to the respective standard deviations. While the ensemble-averaged modulus μ_{sf}(T) decreases continuously with increasing T for all Δt sampled, its standard deviation δμ_{sf}(T) is nonmonotonic with a striking peak at the glass transition. The question of whether the shear modulus is continuous or has a jump singularity at the glass transition is thus ill posed. Confirming the effective time-translational invariance of our systems, the Δt dependence of μ_{sf} and related quantities can be understood using a weighted integral over G(t).

Transport and Helfand moments in the Lennard-Jones fluid. I. Shear viscosity

The authors propose a new method, the Helfand-moment method, to compute the shear viscosity by equilibrium molecular dynamics in periodic systems. In this method, the shear viscosity is written as an Einstein-type relation in terms of the variance of the so-called Helfand moment. This quantity is modified in order to satisfy systems with periodic boundary conditions usually considered in molecular dynamics. They calculate the shear viscosity in the Lennard-Jones fluid near the triple point thanks to this new technique. They show that the results of the Helfand-moment method are in excellent agreement with the results of the standard Green-Kubo method.