A global investigation of phase equilibria using the Perturbed-Chain Statistical-Associating-Fluid-Theory (PC-SAFT) approach

The recently developed Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) is investigated for a wide range of model parameters including the parameter m representing the chain length and the thermodynamic temperature T and pressure p. This approach is based upon the first-order thermodynamic perturbation theory for chain molecules developed by Wertheim and Chapman et al. and includes dispersion interactions via the second-order perturbation theory of Barker and Henderson. We systematically study a hierarchy of models which are based on the PC-SAFT approach using analytical model calculations and Monte Carlo simulations. For one-component systems we find that the analytical model in contrast to the simulation results exhibits two phase-separation regions in addition to the common gas-liquid coexistence region: One phase separation occurs at high density and low temperature. The second demixing takes place at low density and high temperature where usually the ideal gas phase is expected in the phase diagram. These phenomena, which are referred to as "liquid-liquid" and "gas-gas" equilibria, give rise to multiple critical points in one-component systems, as well as to critical end points (CEP) and equilibria of three fluid phases, which can usually be found in multicomponent mixtures only. Furthermore, it is shown that the "liquid-liquid" demixing in this model is not a consequence of a "softened" repulsive interaction as assumed in the theoretical derivation of the model. Experimental data for the melt density of polybutadiene with molecular mass Mw=45000g/mol are correlated here using the PC-SAFT equation. It is shown that the discrepancies in modeling the polymer density at ambient temperature and high pressure can be traced back to ...Comment: 33 pages, 14 figure

Spherically averaged versus angle-dependent interactions in quadrupolar fluids

Employing simplified models in computer simulation is on the one hand often enforced by computer time limitations but on the other hand it offers insights into the molecular properties determining a given physical phenomenon. We employ this strategy to the determination of the phase behaviour of quadrupolar fluids, where we study the influence of omitting angular degrees of freedom of molecules via an effective spherically symmetric potential obtained from a perturbative expansion. Comparing the liquid-vapor coexistence curve, vapor pressure at coexistence, interfacial tension between the coexisting phases, etc., as obtained from both the models with the full quadrupolar interactions and the (approximate) isotropic interactions, we find discrepancies in the critical region to be typically (such as in the case of carbon dioxide) of the order of 4%. However, when the Lennard-Jones parameters are rescaled such that critical temperatures and critical densities of both models coincide with the experimental results, almost perfect agreement between the above-mentioned properties of both models is obtained. This result justifies the use of isotropic quadrupolar potentials. We present also a detailed comparison of our simulations with a combined integral equation/density functional approach and show that the latter provides an accurate description except for the vicinity of the critical point.Comment: Phys. Rev. E, accepte

Nonanalytical equation of state of the hard sphere fluid

An equation of state of the hard sphere fluid which is not analytical at the freezing density is proposed and tested. The nonanalytical term is based on the the classical nucleation theory and is able to capture the observed ``anomalous increase'' of pressure at high densities. It is combined with the virial expansion at low densities.Comment: 5 pages, 3 figure

Hierarchical simulations of hybrid polymer-solid materials

Complex polymer-solid materials have gained a lot of attention during the last 2-3 decades due to the fundamental physical problems and the broad spectrum of technological applications in which they are involved. Therefore, significant progress concerning the simulations of such hybrid soft-hard nanostructured systems has been made in the last few years. Simulation techniques vary from quantum to microscopic (atomistic) up to mesoscopic (coarse-grained) level. Here we give a short overview of simulation approaches on model polymer-solid interfacial systems for all different levels of description. In addition, we also present a brief outlook concerning the open questions in this field, from the point of view of both physical problems and computational methodologies

A multi-scale method for complex flows of non-Newtonian fluids

We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. Compared to previous proposals, our approach takes into account the fact that the material response can depend strongly on the local flow type and we show that this is a necessary feature to correctly capture the macroscopic dynamics. In particular, we highlight the importance of extensional rheology in simulating generic flows of polymeric fluids.Comment: 18 pages, 9 figure

Reduced-order hybrid multiscale method combining the molecular dynamics and the discontinuous-galerkin method

We present a new reduced-order hybrid multiscale method to simulate com- plex fluids. continuum and molecular descriptions. We follow the framework of the heterogeneous multi-scale method (HMM) that makes use of the scale separation into macro- and micro-levels. On the macro-level, the governing equations of the incompressible flow are the continuity and momentum equations. The equations are solved using a high-order accurate discontinuous Galerkin Finite Element Method (dG) and implemented in the BoSSS code. The missing information on the macro-level is represented by the unknown stress tensor evaluated by means of the molecular dynam- ics (MD) simulations on the micro-level. We shear the microscopic system by applying Lees-Edwards boundary conditions and either an isokinetic or Lowe-Andersen thermostat. The data obtained from the MD simulations underlie large stochastic errors that can be controlled by means of the least-square approximation. In order to reduce a large number of computationally expensive MD runs, we apply the reduced order approach. Nume al experiments confirm the robustness of our newly developed hybrid MD-dG method