Revealing the Role of Chain Conformations on the Origin of the Mechanical Reinforcement in Glassy Polymer Nanocomposites.

Understanding the mechanism of mechanical reinforcement in glassy polymer nanocomposites is of paramount importance for their tailored design. Here, we present a detailed investigation, via atomistic simulation, of the coupling between density, structure, and conformations of polymer chains with respect to their role in mechanical reinforcement. Probing the properties at the molecular level reveals that the effective mass density as well as the rigidity of the matrix region changes with filler volume fraction, while that of the interphase remains constant. The origin of the mechanical reinforcement is attributed to the heterogeneous chain conformations in the vicinity of the nanoparticles, involving a 2-fold mechanism. In the low-loading regime, the reinforcement comes mainly from a thin, single-molecule, 2D-like layer of adsorbed polymer segments on the nanoparticle, whereas in the high-loading regime, the reinforcement is dominated by the coupling between train and bridge conformations; the latter involves segments connecting neighboring nanoparticles.

A methodology for determining the local mechanical properties of model atomistic glassy polymeric nanostructured materials.

We propose a methodology for calculating the distribution of the mechanical properties in model atomistic polymer-based nanostructured systems. The use of atomistic simulations is key in unravelling the fundamental mechanical behavior of composite materials. Most simulations involving the mechanical properties of polymer nanocomposites (PNCs) concern their global (average) properties, which are typically extracted by applying macroscopic strain on the boundaries of the simulation box and calculating the total (global) stress by invoking the Virial formalism over all atoms within the simulation box; thus, extracting the pertinent mechanical properties from the corresponding stress-strain relation. However, in order to probe the distribution of mechanical properties within heterogeneous multi-component polymer-based systems, a detailed computation of stress and strain fields within specific sub-domains is necessary. For example, it is well known for multi-component nanostructured systems, such as PNCs, that the mechanical behavior of the polymer/nanofiller interphases, or interfaces, is crucial for determining the global mechanical properties of the composite materials. Here we propose a new methodology to probe the distribution of mechanical properties by directly computing the (local) stress and strain at the atomic level, and averaging over user-defined subdomains. The workflow of our computational method possesses the following features:•Calculating the stress and strain per atom (or per particle) for nanostructured microscopic (here atomistic) model configurations, under an imposed applied deformation.•Averaging the local, per-atom defined, stress and strain on user-defined subdomains within the nanostructured model system.•Predicting the mechanical properties within the specific subdomains, focusing on polymer/solid interphases.

Modeling the evolution of COVID-19 via compartmental and particle-based approaches: Application to the Cyprus case.

We present two different approaches for modeling the spread of the COVID-19 pandemic. Both approaches are based on the population classes susceptible, exposed, infectious, quarantined, and recovered and allow for an arbitrary number of subgroups with different infection rates and different levels of testing. The first model is derived from a set of ordinary differential equations that incorporates the rates at which population transitions take place among classes. The other is a particle model, which is a specific case of crowd simulation model, in which the disease is transmitted through particle collisions and infection rates are varied by adjusting the particle velocities. The parameters of these two models are tuned using information on COVID-19 from the literature and country-specific data, including the effect of restrictions as they were imposed and lifted. We demonstrate the applicability of both models using data from Cyprus, for which we find that both models yield very similar results, giving confidence in the predictions.

Wetting of prototypical one- and two-dimensional systems: thermodynamics and density functional theory.

Consider a two-dimensional capped capillary pore formed by capping two parallel planar walls with a third wall orthogonal to the two planar walls. This system reduces to a slit pore sufficiently far from the capping wall and to a single planar wall when the side walls are far apart. Not surprisingly, wetting of capped capillaries is related to wetting of slit pores and planar walls. For example, the wetting temperature of the capped capillary provides the boundary between first-order and continuous transitions to condensation. We present a numerical investigation of adsorption in capped capillaries of mesoscopic widths based on density functional theory. The fluid-fluid and fluid-substrate interactions are given by the pairwise Lennard-Jones potential. We also perform a parametric study of wetting in capped capillaries by a liquid phase by varying the applied chemical potential, temperature, and pore width. This allows us to construct surface phase diagrams and investigate the complicated interplay of wetting mechanisms specific to each system, in particular, the dependence of capillary wetting temperature on the pore width.

Geometry-induced phase transition in fluids: capillary prewetting.

We report a new first-order phase transition preceding capillary condensation and corresponding to the discontinuous formation of a curved liquid meniscus. Using a mean-field microscopic approach based on the density functional theory we compute the complete phase diagram of a prototypical two-dimensional system exhibiting capillary condensation, namely that of a fluid with long-ranged dispersion intermolecular forces which is spatially confined by a substrate forming a semi-infinite rectangular pore exerting long-ranged dispersion forces on the fluid. In the T-µ plane the phase line of the new transition is tangential to the capillary condensation line at the capillary wetting temperature T(cw). The surface phase behavior of the system maps to planar wetting with the phase line of the new transition, termed capillary prewetting, mapping to the planar prewetting line. If capillary condensation is approached isothermally with T>T(cw), the meniscus forms at the capping wall and unbinds continuously, making capillary condensation a second-order phenomenon. We compute the corresponding critical exponent for the divergence of adsorption.

On the moving contact line singularity: asymptotics of a diffuse-interface model.

The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the classical approach of a sharp liquid-gas interface and careful examination of the asymptotic behaviour as the contact line is approached is shown to resolve the stress and pressure singularities associated with the moving contact line problem. Various features of the model are scrutinised, alongside extensions to incorporate slip, finite-time relaxation of the chemical potential, or a precursor film at the wall.

General dynamical density functional theory for classical fluids.

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.

Spectral methods for the equations of classical density-functional theory: relaxation dynamics of microscopic films.

We propose a numerical scheme based on the Chebyshev pseudo-spectral collocation method for solving the integral and integro-differential equations of the density-functional theory and its dynamic extension. We demonstrate the exponential convergence of our scheme, which typically requires much fewer discretization points to achieve the same accuracy compared to conventional methods. This discretization scheme can also incorporate the asymptotic behavior of the density, which can be of interest in the investigation of open systems. Our scheme is complemented with a numerical continuation algorithm and an appropriate time stepping algorithm, thus constituting a complete tool for an efficient and accurate calculation of phase diagrams and dynamic phenomena. To illustrate the numerical methodology, we consider an argon-like fluid adsorbed on a Lennard-Jones planar wall. First, we obtain a set of phase diagrams corresponding to the equilibrium adsorption and compare our results obtained from different approximations to the hard sphere part of the free energy functional. Using principles from the theory of sub-critical dynamic phase field models, we formulate the time-dependent equations which describe the evolution of the adsorbed film. Through dynamic considerations we interpret the phase diagrams in terms of their stability. Simulations of various wetting and drying scenarios allow us to rationalize the dynamic behavior of the system and its relation to the equilibrium properties of wetting and drying.

Droplet spreading on chemically heterogeneous substrates.

Consider the spreading dynamics of a two-dimensional droplet over chemically heterogeneous substrates. Assuming small slopes and strong surface tension effects, a long-wave expansion of the Stokes equations yields a single evolution equation for the droplet thickness. The contact line singularity is removed by assuming slip at the liquid-solid interface. The chemical nature of the substrate is incorporated by local variations in the microscopic contact angle, which appear as boundary conditions in the governing equation. By asymptotically matching the flow in the bulk of the droplet with the flow in the vicinity of the contact lines, we obtain a set of coupled ordinary differential equations for the locations of the two droplet fronts. We verify the validity of our matching procedure by comparing the solutions of the ordinary differential equations with solutions of the full governing equation. The droplet dynamics is examined in detail via a phase-plane analysis. A number of interesting features that are not present in chemically homogeneous substrates are found, such as the existence of multiple equilibria, the pinning of the droplet fronts at localized chemical features, and the possibility for the droplet fronts to exhibit a stick-slip behavior.

Two-dimensional droplet spreading over random topographical substrates.

We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via statistical approaches, by representing substrate families as stationary random functions. The droplet shift variance at both early times and in the long-time limit is deduced and the droplet footprint is found to be a normal random variable at all times. It is shown that substrate roughness inhibits wetting, illustrating also the tendency of the droplet to slide without spreading as equilibrium is approached. Our theoretical predictions are verified by numerical experiments.