Development of a Meshless Kernel-Based Scheme for Particle-Field Brownian Dynamics Simulations.

We develop a meshless discretization scheme for particle-field Brownian dynamics simulations. The density is assigned on the particle level using a weighting kernel with finite support. The system's free energy density is derived from an equation of state (EoS) and includes a square gradient term. The numerical stability of the scheme is evaluated in terms of reproducing the thermodynamics (equilibrium density and compressibility) and dynamics (diffusion coefficient) of homogeneous samples. Using a reduced description to simplify our analysis, we find that numerical stability depends strictly on reduced reference compressibility, kernel range, time step in relation to the friction factor, and reduced external pressure, the latter being relevant under isobaric conditions. Appropriate parametrization yields precise thermodynamics, further improved through a simple renormalization protocol. The dynamics can be restored exactly through a trivial manipulation of the time step and friction coefficient. A semiempirical formula for the upper bound on the time step is derived, which takes into account variations in compressibility, friction factor, and kernel range. We test the scheme on realistic mesoscopic models of fluids, involving both simple (Helfand) and more sophisticated (Sanchez-Lacombe) equations of state.

Buckling kinetics of graphene membranes under uniaxial compression.

Despite past investigations of the buckling instability, the kinetics of the buckling process is not well understood. We develop a generic framework for determining the buckling kinetics of membranes under compressive stress (σ_{b}) via molecular dynamics simulations. The buckling time (t_{b}) is modeled by an extended Boltzmann-Arrhenius-Zhurkov equation accounting for temperature (T) and scale-dependent bending rigidity. We discern three regimes: (I) t_{b} decreases with T; (II) t_{b} increases with T; (III) t_{b} is T independent. Regime II coheres with the predictions of the theory of fluctuating sheets (TFS). Regime I is seen at small scales due to fluctuations about equilibrium and is not predicted by the TFS.

Solvation Free Energy of Dilute Grafted (Nano)Particles in Polymer Melts via the Self-Consistent Field Theory.

Predicting the distribution of a chemical species across multiple phases is of critical importance to environmental protection, pharmaceuticals, and high added-value chemicals. Computationally, this problem is addressed by determining the free energy of solvation of the species in the different phases using a well-established thermodynamic formulation. Following recent developments in sterically stabilized colloids and nanocomposite materials, the solvation of polymer-grafted nanoparticles in different solvents or polymer melts has become relevant. We develop a Self-Consistent Field theoretical framework to determine the solvation free energy of grafted particles inside a molten polymer matrix phase at low concentrations. The solvation free energy is calculated based on the notion of a pseudochemical potential introduced by Ben-Naim. Grafted and matrix chains are taken to be of the same chemical constitution, but their lengths are varied systematically, as are the particle radius and the areal density of grafted chains. In addition, different affinities between the nanoparticle core and the polymer (contact angles) are considered. At very low or very high amounts of grafted material, solvation depends on the adhesion tension between the bare particle and the matrix or on the surface tension of the grafted polymer, respectively. The dependence of the solvation free energy on molecular characteristics is more complicated at intermediate grafting densities and high curvatures, where the contribution of the entropy of grafted chains becomes significant. In general, solvation is less favored in cases where the matrix chains are much shorter than the grafted ones. The former tend to penetrate and swell the brush, thus generating conformational and translational entropy penalties. This effect becomes more pronounced when considering large particles since the grafted chains have less available space and extend more. For extremely low amounts of grafted material, we observe the opposite trend, albeit weak. Based on our calculations, we propose a generic model for estimating the solvation free energies of grafted nanoparticles in polymer melts from their molecular characteristics. The model and associated SCF formulation, illustrated here for chemically identical grafted and matrix chains, can be extended to obtain partition coefficients of grafted nanoparticles between different polymer melts.

Multiscale simulations of polyzwitterions in aqueous bulk solutions and brush array configurations.

Zwitterionic polymers are very promising candidates for antifouling materials that exhibit high chemical stability as compared to polyethylene glycol-based systems. A number of simulation and experimental studies have emerged over recent years for the investigation of sulfobetaine-based zwitterionic polymers. Investigating the structural and thermodynamic properties of such polymers requires access to broad time and length regimes, thus necessitating the development of multiscale simulation strategies. The present article advocates a mesoscopic dissipative particle dynamics (DPD) model capable of addressing a wide range of time and length scales. The mesoscopic force field was developed hand-in-hand with atomistic simulations based on the OPLS force field through a bottom-up parameterization procedure that matches the atomistically calculated strand-length, strand-angle and pair distribution functions. The DPD model is validated against atomistic simulations conducted in this work, and against relevant atomistic simulation studies, theoretical predictions and experimental correlations from the literature. Properties examined include the conformations of SPE polymers in dilute bulk aqueous solution, the density profile and thickness of brush arrays as functions of the grafting density and chain length. In addition, we compute the potential of mean force of an approaching hydrophilic or hydrophobic foulant via umbrella sampling as a function of its position relative to the poly-zwitterion-covered surface. The aforementioned observables lead to important insights regarding the conformational tendencies of grafted polyzwitterions and their antifouling properties.

Potential of Mean Force between Bare or Grafted Silica/Polystyrene Surfaces from Self-Consistent Field Theory.

We investigate single and opposing silica plates, either bare of grafted, in contact with vacuum or melt phases, using self-consistent field theory. Solid-polymer and solid-solid nonbonded interactions are described by means of a Hamaker potential, in conjunction with a ramp potential. The cohesive nonbonded interactions are described by the Sanchez-Lacombe or the Helfand free energy densities. We first build our thermodynamic reference by examining single surfaces, either bare or grafted, under various wetting conditions in terms of the corresponding contact angles, the macroscopic wetting functions (i.e., the work of cohesion, adhesion, spreading and immersion), the interfacial free energies and brush thickness. Subsequently, we derive the potential of mean force (PMF) of two approaching bare plates with melt between them, each time varying the wetting conditions. We then determine the PMF between two grafted silica plates separated by a molten polystyrene film. Allowing the grafting density and the molecular weight of grafted chains to vary between the two plates, we test how asymmetries existing in a real system could affect steric stabilization induced by the grafted chains. Additionally, we derive the PMF between two grafted surfaces in vacuum and determine how the equilibrium distance between the two grafted plates is influenced by their grafting density and the molecular weight of grafted chains. Finally, we provide design rules for the steric stabilization of opposing grafted surfaces (or fine nanoparticles) by taking account of the grafting density, the chain length of the grafted and matrix chains, and the asymmetry among the opposing surfaces.

Structure and thermodynamics of grafted silica/polystyrene dilute nanocomposites investigated through self-consistent field theory.

Polymer/matrix nanocomposites (PNCs) are materials with exceptional properties. They offer a plethora of promising applications in key industrial sectors. In most cases, it is preferable to disperse the nanoparticles (NPs) homogeneously across the matrix phase. However, under certain conditions NPs might lump together and lead to a composite material with undesirable properties. A common strategy to stabilize the NPs is to graft on their surface polymer chains of the same chemical constitution as the matrix chains. There are several unresolved issues concerning the optimal molar mass and areal density of grafted chains that would ensure best dispersion, given the nanoparticles and the polymer matrix. We propose a model for the prediction of key structural and thermodynamic properties of PNC and apply it to a single spherical silica (SiO2) nanoparticle or planar surface grafted with polystyrene chains embedded at low concentration in a matrix phase of the same chemical constitution. Our model is based on self-consistent field theory, formulated in terms of the Edwards diffusion equation. The properties of the PNC are explored across a broad parameter space, spanning the mushroom regime (low grafting densities, small NPs and chain lengths), the dense brush regime, and the crowding regime (large grafting densities, NP diameters, and chain lengths). We extract several key quantities regarding the distributions and the configurations of the polymer chains, such as the radial density profiles and their decomposition into contributions of adsorbed and free chains, the chains/area profiles, and the tendency of end segments to segregate at the interfaces. Based on our predictions concerning the brush thickness, we revisit the scaling behaviors proposed in the literature and we compare our findings with experiment, relevant simulations, and analytic models, such as Alexander's model for incompressible brushes.

Efficient Mechanical Stress Transfer in Multilayer Graphene with a Ladder-like Architecture.

We report that few graphene flakes embedded into polymer matrices can be mechanically stretched to relatively large deformation (>1%) in an efficient way by adopting a particular ladder-like morphology consisting of consecutive mono-, bi-, tri-, and four-layer graphene units. In this type of flake architecture, all of the layers adhere to the surrounding polymer inducing similar deformation on the individual graphene layers, preventing interlayer sliding and optimizing the strain transfer efficiency. We have exploited Raman spectroscopy to quantify this effect from a mechanical standpoint. The finite element method and molecular dynamics simulations have been used to interpret the above experimental findings. The results suggest that a step pyramid-like architecture of a flake can be ideal for efficient loading of layered materials embedded into a polymer and that there are two prevailing mechanisms that govern axial stress transfer, namely, interfacial shear transfer and axial transmission through the ends. This concept can be easily applied to other two-dimensional materials and related van der Waals heterostructures fabricated either by mechanical exfoliation or chemical vapor deposition by appropriate patterning. This work opens new perspectives in numerous applications, including high volume fraction composites, flexible electronics, and straintronic devices.

Kinetic concepts and local failure in the interfacial shear strength of epoxy-graphene nanocomposites.

Interfacial shear strength (IFSS) is a key property in the design of composites and nanocomposites. Many simulation studies quantify the interfacial characteristics of sandwichlike specimens in terms of the IFSS and pullout force; a common feature of these studies is that they employ finite model systems and are therefore subject to strong finite size effects. We propose an alternative approach which is applicable to both aperiodic and periodic computational specimens. The interfaces are subjected to multiple shear deformation simulations over a wide range of temperatures (T) and shear stresses (σ_{zx}). From these simulations we collect the failure times (t_{f}); by analyzing them in the framework of an extended Boltzmann-Arrhenius-Zhurkov kinetic equation we derive the IFSS, the limiting stress for barrierless transitions, the activation energy, the activation volume for failure, the sliding velocities, and a local elastic shear modulus for the interface. We test our methodology on epoxy diglycidyl ether bisphenol F-diethyl toluene diamine interfaces in contact with (i) pristine graphene, (ii) graphene with single-atom vacancies, and (iii) graphene with hydroxyl-ΟΗ groups. Differences in the mechanism of interfacial failure among these three systems are discussed.

Molecular dynamics simulations of EPON-862/DETDA epoxy networks: structure, topology, elastic constants, and local dynamics.

Structural, topological, mechanical and dynamical properties of EPON-862/DETDA epoxy networks are investigated with Molecular Dynamics (MD) simulations. The epoxy networks are composed of the resin Diglycidyl Ether Bisphenol F (DGEBF), also known as EPON-862, and the hardener Diethyl Toluene Diamine (DETDA). Systems with four different crosslinking degrees are examined; the effect of the degree of crosslinking on studied properties is thus determined. The computed quantities are retrieved by employing several simulation strategies and numerical methods of statistical mechanics in order to gain a rigorous and solid understanding of the aforementioned properties as well as to assess the accuracy and applicability of the methods employed. We quantify and analyze the local structure of the EPON-862/DETDA epoxy networks through the partial pair distribution functions, the Faber-Ziman partial structure factors and through simulated X-ray diffraction patterns, demonstrating good agreement with an experimental spectrum from a similar epoxy resin. The topology of the networks is examined with the aim of assessing percolation of connectivity, the properties of network fragments (subnetworks), and the distribution of functionalities of the crosslinks. The elastic constants of the systems are retrieved by employing two equilibrium (analysis of volume fluctuations, Parrinello-Rahman strain fluctuation relation) and one nonequilibrium (uniaxial tension/compression deformations at prescribed rate) method. Finally, the glass temperatures of the systems are estimated by calculating the density as a function of temperature and by analyzing the reorientational dynamics of bond vectors which describe relaxation processes at the segment level.

Slip Spring-Based Mesoscopic Simulations of Polymer Networks: Methodology and the Corresponding Computational Code.

In previous work by the authors, a new methodology was developed for Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of polymer melts. In this study, this methodology is extended for dynamical simulations of crosslinked polymer networks in a coarse-grained representation, wherein chains are modeled as sequences of beads, each bead encompassing a few Kuhn segments. In addition, the C++ code embodying these simulations, entitled Engine for Mesoscopic Simulations for Polymer Networks (EMSIPON) is described in detail. A crosslinked network of cis-1,4-polyisoprene is chosen as a test system. From the thermodynamic point of view, the system is fully described by a Helmholtz energy consisting of three explicit contributions: entropic springs, slip springs and non-bonded interactions. Entanglements between subchains in the network are represented by slip springs. The ends of the slip springs undergo thermally activated hops between adjacent beads along the chain backbones, which are tracked by kinetic Monte Carlo simulation. In addition, creation/destruction processes are included for the slip springs at dangling subchain ends. The Helmholtz energy of non-bonded interactions is derived from the Sanchez⁻Lacombe equation of state. The isothermal compressibility of the polymer network is predicted from equilibrium density fluctuations in very good agreement with the underlying equation of state and with experiment. Moreover, the methodology and the corresponding C++ code are applied to simulate elongational deformations of polymer rubbers. The shear stress relaxation modulus is predicted from equilibrium simulations of several microseconds of physical time in the undeformed state, as well as from stress-strain curves of the crosslinked polymer networks under deformation.