Assessing the derivation of time parameters from branched polymer coarse-grain model.

The parameterization of rheological models for polymers is often obtained from experiments via the top-down approach. This procedure allows us to determine good fitting parameters for homogeneous materials but is less effective for polymer mixtures. From a molecular simulation point of view, the timescales needed to derive those parameters are often accessed through the use of coarse-grain potentials. However, these potentials are often derived from linear model systems and the transferability to a more complex structure is not straightforward. Here, we verify the transferability of a potential computed from linear polymer simulations to more complex molecular shapes and present a type of analysis, which was recently formulated in the framework of a tube theory, to a coarse-grain molecular approach in order to derive the input parameters for a rheological model. We describe the different behaviors arising from the local topological structure of molecular sub-units. Coarse-grain models and mean-field based tube theory for polymers form a powerful combination with potentially important applications.

Strain induced crystallization of polymers at and above the crystallization temperature by coarse-grained simulations.

We examine the behavior of short and long polymers by means of coarse-grained computer simulations of a by-polyvinyl alcohol inspired model. In particular, we focus on the structural changes in the monomer and polymer scales during cooling and the application of uni-axial true strain. The straining of long polymers results in the formation of a semi-crystalline system at temperatures well above the crystallization temperature, which allows for the study of strain induced crystallization.

Backbone oriented anisotropic coarse grains for efficient simulations of polymers.

Despite the fact that anisotropic particles have been introduced to describe molecular interactions for decades, they have been poorly used for polymers because of their computing time overhead and the absence of a relevant proof of their impact in this field. We first report a method using anisotropic beads for polymers, which solves the computing time issue by considering that beads keep their principal orientation alongside the mean local backbone vector of the polymer chain, avoiding the computation of torques during the dynamics. Applying this method to a polymer bulk, we study the effect of anisotropic interactions vs isotropic ones for various properties such as density, pressure, topology of the chain network, local structure, and orientational order. We show that for different classes of potentials traditionally used in molecular simulations, those backbone oriented anisotropic beads can solve numerous issues usually encountered with isotropic interactions. We conclude that the use of backbone oriented anisotropic beads is a promising approach for the development of realistic coarse-grained potentials for polymers.

Quenching of fully symmetric mixtures of oppositely charged microgels: the role of soft stiffness.

Using molecular dynamics simulations, we investigate the self-assembly of a coarse-grained binary system of oppositely charged microgels, symmetric in size and concentration. The microgel pair interactions are described by an effective pair potential which implicitly accounts for the averaged ionic contributions, in addition to a short-range elastic repulsion that accounts for the overlapping of the polymer chains, the latter being described by the Hertzian interaction. Particular emphasis is placed on the role played by the strength of the soft repulsive interaction on the resulting particle aggregation. It is found that the possibility of particle inter-penetration in oppositely charged soft particles results in a much wider variety of cluster morphologies in comparison with their hard-spheres counterparts. Specifically, the softness of the steric interactions enhances the competition between repulsive and attractive electrostatic interactions, leading to the formation of aggregates that are comprised of strongly bounded charged particles displaying a low degree of charge ordering.

Self-assembly of magnetically functionalized star-polymer nano-colloids.

We explore the potential of star-polymers that carry super-paramagnetic nano-particles as end-groups with respect to the single-molecule self-assembly process. With the aid of molecular dynamics simulation, the configurations of these macromolecules are analyzed as a function of functionality, magnetic interaction strength, and the length of the polymeric arms. By means of an external magnetic field the nano-particles can be controlled to form static or dynamic dipolar chains, resulting in conformations of isolated stars that can be characterized by the average number of chains and length. The single-molecule conformation diagram in the plane of magnetic interaction strength vs. the star-functionality is obtained. Further, the molecules are characterized by means of various shape and size order parameters.

Concentration-induced planar-to-homeotropic anchoring transition of stiff ring polymers on hard walls.

We study the structure and interfacial ordering of stiff ring polymers close to repulsive walls. For this purpose, we employ an anisotropic effective model in which the rings are pictured as soft, penetrable discs [P. Poier, C. N. Likos, A. J. Moreno and R. Blaak, Macromolecules, 2015, 48, 4983]. We have studied this model in the bulk and in the presence of a wall, employing Density Functional Theory and computer simulations. While the Ornstein-Zernike equation in combination with the Hypernetted Chain Approximation gives results that are in quantitative agreement with computer simulations, a simple Mean Field approximation strongly overestimates the interaction between the effective particles in the bulk. We discover that by increasing density one can induce a reorientation of the effective rings in the vicinity of a wall, which prefer to orient themselves parallel to the surface (face-on or planar) for low densities ρ and reorient orthogonal to the wall (edge-on or homeotropic) for higher values of ρ. This transition in the surface-structure can be observed in both computer simulations, as well as in an appropriate density functional theory. We trace its physical origin in the penetrable character of the rings, which allows for a reduction of the surface tension contribution due to ring-ring interactions upon the emergence of homeotropic ordering on the wall and increasing the density of the system.

Anisotropic effective interactions and stack formation in mixtures of semiflexible ring polymers.

By means of extensive computer simulations, we investigate the formation of columnar structures (stacks) in concentrated solutions of semiflexible ring polymers. To characterize the stacks we employ an algorithm that identifies tube-like structures in the simulation cell. Stacks are found both in the real system and in the fluid of soft disks interacting through the effective anisotropic pair potential derived for the rings [P. Poier et al., Macromolecules, 2015, 48, 4983-4997]. Furthermore, we investigate binary mixtures of cluster-forming and non-cluster-forming rings. We find that monodispersity is not a requirement for stack formation. The latter is found for a broad range of mixture compositions, though the columns in the mixtures exhibit important differences to those observed in the monodisperse case. We extend the anisotropic effective model to mixtures. We show that it correctly predicts stack formation and constitutes a significant improvement with respect to the usual isotropic effective description based only on macromolecular centers-of-mass.

Thermodynamic stability and structural properties of cluster crystals formed by amphiphilic dendrimers.

We pursue the goal of finding real-world examples of macromolecular aggregates that form cluster crystals, which have been predicted on the basis of coarse-grained, ultrasoft pair potentials belonging to a particular mathematical class [B. M. Mladek et al., Phys. Rev. Lett. 46, 045701 (2006)]. For this purpose, we examine in detail the phase behavior and structural properties of model amphiphilic dendrimers of the second generation by means of monomer-resolved computer simulations. On augmenting the density of these systems, a fluid comprised of clusters that contain several overlapping and penetrating macromolecules is spontaneously formed. Upon further compression of the system, a transition to multi-occupancy crystals takes place, the thermodynamic stability of which is demonstrated by means of free-energy calculations, and where the FCC is preferred over the BCC-phase. Contrary to predictions for coarse-grained theoretical models in which the particles interact exclusively by effective pair potentials, the internal degrees of freedom of these molecules cause the lattice constant to be density-dependent. Furthermore, the mechanical stability of monodisperse BCC and FCC cluster crystals is restricted to a bounded region in the plane of cluster occupation number versus density. The structural properties of the dendrimers in the dense crystals, including their overall sizes and the distribution of monomers are also thoroughly analyzed.

Microscopically resolved simulations prove the existence of soft cluster crystals.

We perform extensive monomer-resolved computer simulations of suitably designed amphiphilic dendritic macromolecules over a broad range of densities, proving the existence and stability of cluster crystals formed in these systems, as predicted previously on the basis of effective pair potentials [B. M. Mladek et al., Phys. Rev. Lett. 96, 045701 (2006)]. Key properties of these crystals, such as the adjustment of their site occupancy with density and the possibility to heal defects by dendrimer migration, are confirmed on the monomer-resolved picture. At the same time, important differences from the predictions of the pair potential picture, stemming from steric crowding, arise as well, and they place an upper limit in the density for which such crystals can exist.

Telechelic star polymers as self-assembling units from the molecular to the macroscopic scale.

By means of multiscale molecular simulations, we show that telechelic-star polymers are a simple, robust, and tunable system, which hierarchically self-assembles into soft-patchy particles and mechanically stabilizes selected, open crystalline structures. The self-aggregating patchy behavior can be fully controlled by the number of arms per star and by the fraction of attractive monomeric units at the free ends of the arms. Such self-assembled soft-patchy particles while forming, upon augmenting density, gel-like percolating networks, preserve properties as particle size, number, and arrangement of patches per particle. In particular, we demonstrate that the flexibility inherent in the soft-patchy particles brings forward a novel mechanism that leads to the mechanical stability of diamond and simple cubic crystals over a wide range of densities, and for molecular sizes ranging from about 10 nm up to the micrometer scale.

Patchy colloids: state of the art and perspectives.

Recently, an increasing experimental effort has been devoted to the synthesis of complex colloidal particles with chemically or physically patterned surfaces and possible specific shapes that are far from spherical. These new colloidal particles with anisotropic interactions are commonly named patchy particles. In this Perspective article, we focus on patchy systems characterized by spherical neutral particles with patchy surfaces. We summarize most of the patchy particle models that have been developed so far and describe how their basic features are connected to the physical systems they are meant to investigate. Patchy models consider particles as hard or soft spheres carrying a finite and small number of attractive sites arranged in precise geometries on the particle's surface. The anisotropy of the interaction and the limited valence in bonding are the salient features determining the collective behavior of such systems. By tuning the number, the interaction parameters and the local arrangements of the patches, it is possible to investigate a wide range of physical phenomena, from different self-assembly processes of proteins, polymers and patchy colloids to the dynamical arrest of gel-like structures. We also draw attention to charged patchy systems: colloidal patchy particles as well as proteins are likely charged, hence the description of the presence of heterogeneously distributed charges on the particle surface is a promising perspective for future investigations.

Heterogeneity Effects in Highly Cross-Linked Polymer Networks.

Despite their level of refinement, micro-mechanical, stretch-based and invariant-based models, still fail to capture and describe all aspects of the mechanical properties of polymer networks for which they were developed. This is for an important part caused by the way the microscopic inhomogeneities are treated. The Elastic Network Model (ENM) approach of reintroducing the spatial resolution by considering the network at the level of its topological constraints, is able to predict the macroscopic properties of polymer networks up to the point of failure. We here demonstrate the ability of ENM to highlight the effects of topology and structure on the mechanical properties of polymer networks for which the heterogeneity is characterised by spatial and topological order parameters. We quantify the macro- and microscopic effects on forces and stress caused by introducing and increasing the heterogeneity of the network. We find that significant differences in the mechanical responses arise between networks with a similar topology but different spatial structure at the time of the reticulation, whereas the dispersion of the cross-link valency has a negligible impact.

Rheological properties of polymer chains at a copper oxide surface: Impact of the chain length, surface coverage, and grafted polymer shape.

We employ a recently derived semirealistic set of coarse-grained interactions to simulate polymer brushes of cis-1,4-polybutadiene grafted on a cuprous-oxide surface within the framework of dissipative particle dynamics. We consider two types of brushes, I and Y, that differ in the way they are connected to the surface. Our model explores the impact of free polymer chain length, grafting density of the brush, and imposed shear rate on the structural and dynamic properties of complex metal oxide polymer interfaces.

Dynamical arrest in low density dipolar colloidal gels.

We report the results of extensive molecular dynamics simulations of a simple, but experimentally achievable model of dipolar colloids. It is shown that a modest elongation of the particles and dipoles to make dipolar dumbbells favors branching of the dipolar strings that are routinely observed for point dipolar spheres (e.g., ferrofluids). This branching triggers the formation of a percolating transient network when the effective temperature is lowered along low packing fraction isochores (phi<0.1). Well below the percolation temperature the evolution of various dynamical correlation functions becomes arrested over a rapidly increasing period of time, indicating that a gel has formed. The onset of arrest is closely linked to ongoing structural and topological changes, which we monitor using a variety of diagnostics, including the Euler characteristic. The present system, dominated by long-range interactions between particles, shows similarities to, but also some significant differences from the behavior of previously studied model systems involving short-range attractive interactions between colloids. In particular, we discuss the relation of gel formation to fluid-fluid phase separation and spinodal decomposition in the light of current knowledge of dipolar fluid phase diagrams.

Pressure and compressibility factor of bidisperse magnetic fluids.

In this work, we investigate the pressure and compressibility factors of bidisperse magnetic fluids with relatively weak dipolar interactions and different granulometric compositions. In order to study these properties, we employ the method of diagram expansion, taking into account two possible scenarios: (1) dipolar particles repel each other as hard spheres; (2) the polymer shell on the surface of the particles is modelled through a soft-sphere approximation. The theoretical predictions of the pressure and compressibility factors of bidisperse ferrofluids at different granulometric compositions are supported by data obtained by means of molecular dynamics computer simulations, which we also carried out for these systems. Both theory and simulations reveal that the pressure and compressibility factors decrease with growing dipolar correlations in the system, namely with an increasing fraction of large particles. We also demonstrate that even if dipolar interactions are too weak for any self-assembly to take place, the interparticle correlations lead to a qualitative change in the behaviour of the compressibility factors when compared to that of non-dipolar spheres, making the dependence monotonic.

An Anisotropic Effective Model for the Simulation of Semiflexible Ring Polymers.

We derive and introduce anisotropic effective pair potentials to coarse-grain solutions of semiflexible ring polymers of various lengths. The system has been recently investigated by means of full monomer-resolved computer simulations, revealing a host of unusual features and structure formation, which, however, cannot be captured by a rotationally averaged effective pair potential between the rings' centers of mass [Bernabei M.; Soft Matter2013, 9, 1287]. Our new coarse-graining strategy is to picture each ring as a soft, penetrable disk. We demonstrate that for the short- and intermediate-length rings the new model is quite capable of capturing the physics in a quantitative fashion, whereas for the largest rings, which resemble flexible ones, it fails at high densities. Our work opens the way for the physical justification of general, anisotropic penetrable interaction potentials.

Effective Interactions between Multilayered Ionic Microgels.

Using a one-component reduction formalism, we calculate the effective interactions and the counterion density profiles for microgels that feature a multilayered shell structure. We follow a strategy that involves second order perturbation theory and obtain analytical expressions for the effective interactions by modeling the layers of the particles as linear superpostion of homogeneously charged spheres. The general method is applied to the important case of core-shell microgels and compared with the well-known results for a microgel that can be approximated by a macroscopic, and homogeneously charged, spherical macroion.

Complexation and overcharging of polyelectrolyte stars and charged colloids.

We examine the complexation behavior of polyelectrolyte stars on oppositely charged colloidal particles with similar sizes by means of computer simulations employing the molecular dynamics approach. In particular the overcharging phenomenon is considered and its dependence on the charge and functionality of the stars. The complexes thus formed are a realization of inverse patchy particles (Bianchi et al 2011 Soft Matter 7 8313) for which both the number of patches and the total charge can be tuned.

Structural properties of dendrimer-colloid mixtures.

We consider binary mixtures of colloidal particles and amphiphilic dendrimers of the second generation by means of Monte Carlo simulations. By using the effective interactions between monomer-resolved dendrimers and colloids, we compare the results of simulations of mixtures stemming from a full monomer-resolved description with the effective two-component description at different densities, composition ratios, colloid diameters and interaction strengths. Additionally, we map the two-component system onto an effective one-component model for the colloids in the presence of the dendrimers. Simulations based on the resulting depletion potentials allow us to extend the comparison to yet another level of coarse graining and to examine under which conditions this two-step approach is valid. In addition, a preliminary outlook into the phase behavior of this system is given.

Monomer-resolved simulations of cluster-forming dendrimers.

We present results of monomer-resolved Monte Carlo simulations for a system of amphiphilic dendrimers of the second generation. Our investigations validate a coarse-grained level description based on the zero-density limit effective pair-interactions for low and intermediate densities, which predicted the formation of stable, finite aggregates in the fluid phase. Indeed, we find that these systems form a homogeneous fluid for low densities, which, on increasing the density, spontaneously transforms into a fluid of clusters of dendrimers. Although these clusters are roughly spherical in nature for intermediate densities, more complex structures are also detected for the highest densities considered.