Chaotic and rheological properties of liquids under planar shear and elongational flows

The aim of this work is to present relevant rheological and chaotic properties of atomic liquid systems under steady planar shear (PSF) and elongational (PEF) flows, with the use of Nonequilibrium Molecular Dynamics (NEMD) techniques. These flows are widely employed in industrial applications, and, at a fundamental level, represent interesting models for the discussion of theoretical assumptions of statistical mechanics and dynamical systems theory. Whereas the use of the SLLOD algorithm of NEMD for PSF has been established for more than twenty years, the simulation of PEF for arbitrarily long times has recently been made possible through the combination of the SLLOD formulation with the so-called Kraynik-Reinelt (KR) periodic boundary conditions (pbcs) for the unit cell. Firstly, aspects regarding the chaotic behaviour of these types of flow are discussed, with an analysis of the spectra of Lyapunov exponents for systems of different sizes and at a number of different state points, under Gaussian isoenergetic and isokinetic constrained dynamics. The so-called conjugate-pairing rule (CPR), which, loosely speaking, pertains to systems with a homogeneous distribution of chaoticity among internal degrees of freedom, is established for PEF, whereas robust evidence for its violation under PSF is provided. Considerations about the link between Lyapunov exponents and viscosity, structural ordering at high values of external fields and phase space contractions are also put forward. Secondly, a novel algorithm for the implementation of the Nosé-Hoover mechanism for pressure conservation for PEF systems is illustrated and used in conjunction with a Gaussian isokinetic thermostat to achieve a so-called isokinetic-isobaric (or NpT) ensemble. Accurate results for the viscosity of a simple liquid in this ensemble are obtained, and a comparison with analogous findings for the isokinetic-isochoric (NVT) regime is provided. Furthermore, the analysis of the chaotic properties for PSF and PEF systems is extended to the case of NpT constrained dynamics with the use of the above method, showing that the degrees of freedom associated with the Nosé-Hoover (NH) barostat have no influence on chaoticity, regardless of whether the underlying algorithm describing the flow is symplectic. Then, a study that shows the independence of physical properties of homogeneous systems under steady PEF from KR pbcs is carried out. Using CPR and inspecting the Lyapunov exponents associated with the conserved degrees of freedom, the dynamics of phase-space trajectories and the values of transport coefficients are proven to be insensitive to any choice of initial parameters of periodic mappings on the unit cell. Finally, some concluding remarks and suggestions for future work complete the Thesis.