Stefano Bernardi

Thermostating highly confined fluids

In this work we show how different use of thermostating devices and modeling of walls influence the mechanical and dynamical properties of confined nanofluids. We consider a two dimensional fluid undergoing Couette flow using nonequilibrium molecular dynamics simulations. Because the system is highly inhomogeneous, the density shows strong fluctuations across the channel. We compare the dynamics produced by applying a thermostating device directly to the fluid with that obtained when the wall is thermostated, considering also the effects of using rigid walls. This comparison involves an analysis of the chaoticity of the fluid and evaluation of mechanical properties across the channel. We look at two thermostating devices with either rigid or vibrating atomic walls and compare them with a system only thermostated by conduction through vibrating atomic walls. Sensitive changes are observed in the xy component of the pressure tensor, streaming velocity, and density across the pore and the Lyapunov localization of the fluid. We also find that the fluid slip can be significantly reduced by rigid walls. Our results suggest caution in interpreting the results of systems in which fluid atoms are thermostated and/or wall atoms are constrained to be rigid, such as, for example, water inside carbon nanotubes.

Transient-time correlation function applied to mixed shear and elongational flows

The transient-time correlation function (TTCF) method is used to calculate the nonlinear response of a homogeneous atomic fluid close to equilibrium. The TTCF response of the pressure tensor subjected to a time-independent planar mixed flow of shear and elongation is compared to directly averaged non-equilibrium molecular dynamics (NEMD) simulations. We discuss the consequence of noise in simulations with a small rate of deformation. The generalized viscosity for planar mixed flow is also calculated with TTCF. We find that for small rates of deformation, TTCF is far more efficient than direct averages of NEMD simulations. Therefore, TTCF can be applied to fluids with deformation rates which are much smaller than those commonly used in NEMD simulations. Ultimately, TTCF applied to molecular systems is amenable to direct comparison between NEMD simulations and experiments and so in principle can be used to study the rheology of polymer melts in industrial processes.

A new algorithm for extended nonequilibrium molecular dynamics simulations of mixed flow

In this work, we develop a new algorithm for nonequilibrium molecular dynamics of fluids under planar mixed flow, a linear combination of planar elongational flow and planar Couette flow. To date, the only way of simulating mixed flow using nonequilibrium molecular dynamics techniques was to impose onto the simulation box irreversible transformations. This would bring the simulation to an end as soon as the minimum lattice space requirements were violated. In practical terms, this meant repeating the short simulations to improve statistics and extending the box dimensions to increase the total simulation time. Our method, similar to what has already been done for pure elongational flow, allows a cuboid box to deform in time following the streamlines of the mixed flow and, after a period of time determined by the elongational field, to be mapped back and recover its initial shape. No discontinuity in physical properties is present during the mapping and the simulation can, in this way, be extended indefinitely. We also show that the most general form of mixed flow, in which the angle between the expanding (or contracting) direction and the velocity gradient axis varies, can be cast in a so-called canonical form, in which the angle assumes values that are multiples of π (when a mixed flow exists), by an appropriate choice of the field parameters.

Response theory for confined systems

In this work, we use the transient time correlation function (TTCF) method to evaluate the response of a fluid confined in a nanopore and subjected to shear. The shear is induced by the movement of the boundaries in opposite directions and is made of moving atoms. The viscous heat generated inside the pore is removed by a thermostat applied exclusively to the atomic walls, so as to leave the dynamics of the fluid purely Newtonian. To establish a link with nonlinear response theory and apply the TTCF formalism, dissipation has to be generated inside the system. This dissipation is then time correlated with a phase variable of interest (e.g., pressure) to obtain its response. Until recently, TTCF has been applied to homogeneous fluids whose equations of motion were coupled to a mechanical field and a thermostat. In our system dissipation is generated by a boundary condition rather than a mechanical field, and we show how to apply TTCF to these realistic confined systems, comparing the shear stress response so obtained with that of homogeneous systems at equivalent state points.

Local response in nanopores

In this work the transient time correlation function (TTCF) algorithm is applied to study highly confined molecular fluids. We focus on linear polymer chains of various lengths trapped in a slab pore which is a few nanometres thick and made of atomistic walls, and the behaviour and response of the polymer melt subject to shear flow are considered. The shearing is produced by shifting the walls in opposite directions, and the temperature inside the channel is controlled by a thermostat applied to the wall atoms alone, so as to mimic the dissipation of heat as it occurs in real devices. It is shown how the TTCF algorithm can be applied to extract the fluids dynamical and structural properties as they evolve from equilibrium and until a steady state has been established. We note that this procedure is applicable to fluids of any complexity and down to extremely low fields, comparable to those present in experimental devices. It is also shown that this technique can be used to probe local properties at specific locations across the channel. This feature is of particular significance because liquid properties inside nanoconfined geometries are mostly determined by the interactions at the interface and specifically by the structural reordering which affects the first few atomic/molecular layers close to the wall surface, e.g. slip.

Sieving of H2 and D2 Through End-to-End Nanotubes

We study the quantum molecular sieving of H2 and D2 through two nanotubes placed end-to-end. An analytic treatment, assuming that the particles have classical motion along the axis of the nanotube and are confined in a potential well in the radial direction, is considered. Using this idealistic model, and under certain conditions, it is found that this device can act as a complete sieve, allowing chemically pure deuterium to be isolated from an isotope mixture. We also consider a more realistic model of two carbon nanotubes and carry out molecular dynamics simulations using a Feynman-Hibbs potential to model the quantum effects on the dynamics of H2 and D2. Sieving is also observed in this case, but is caused by a different process.

Planar mixed flow and chaos: Lyapunov exponents and the conjugate-pairing rule

In this work we characterize the chaotic properties of atomic fluids subjected to planar mixed flow, which is a linear combination of planar shear and elongational flows, in a constant temperature thermodynamic ensemble. With the use of a recently developed nonequilibrium molecular dynamics algorithm, compatible and reproducible periodic boundary conditions are realized so that Lyapunov spectra analysis can be carried out for the first time. Previous studies on planar shear and elongational flows have shown that Lyapunov spectra organize in different ways, depending on the character of the defining equations of the system. Interestingly, planar mixed flow gives rise to chaotic spectra that, on one hand, contain elements common to those of shear and elongational flows but also show peculiar, unique traits. In particular, the influence of the constituent flows in regards to the conjugate-pairing rule (CPR) is analyzed. CPR is observed in homogeneously thermostated systems whose adiabatic (or unthermostated) equations of motion are symplectic. We show that the component associated with the shear tends to selectively excite some of those degrees, and is responsible for violations in the rule.