Assessment of an anisotropic coarse-grained model for cis-1,4-polybutadiene: a bottom-up approach.

The spherical representation usually utilized for the coarse-grained particles of soft matter systems is an assumption and pertinent studies have shown that both structural and dynamical properties can depend on anisotropic effects. On these grounds, we develop coarse-grained equations of motion which take into account explicitly the anisotropy of the beads. As a first step, this model incorporates only conservative terms. Inclusion of the dissipative and random terms is in principle possible but is beyond the scope of this study. The translational dynamics of the beads is tracked using the position and momentum of their center of mass, while their rotational dynamics is modeled by representing their orientation through the use of quaternions, similarly to the case of rigid bodies. The associated force and torque controlling the motion are derived from atomistic molecular dynamics (MD) simulations via a bottom-up approach and define a coarse-grained potential. The assumptions of the model are clearly stated and checked for a reference system of a cis-1,4-polybutadiene melt. In particular, the choice of the angular velocity as a slow variable is justified by comparing its dynamics to atomic vibrations. The accuracy of this approach to reproduce static structural features of the polymer melt is assessed.

ROSE bitumen: Mesoscopic model of bitumen and bituminous mixtures.

We present a mesoscopic model for bitumen and bituminous mixtures. The model, which is based on dissipative particle dynamics, consists of different dynamical entities that represent the different characteristic time scales. Through the stress relaxation function, the mechanical properties of the model are investigated. For pure bitumen, the viscosity features super-Arrhenius behavior in the low-temperature regime in agreement with experimental data. The frequency-dependent viscoelastic properties show purely viscous behavior at low frequencies with increasing elasticity and hardening at higher frequencies, as expected. The model dynamics are analyzed in the framework of longitudinal hydrodynamics. The thermal process is two orders of magnitude slower than the attenuation of the density-wave propagation; hence the dynamic structure factor is dominated by a sharp Rayleigh peak and a relatively broad Brillouin peak. The model is applied to study triblock-copolymer-modified bitumen mixtures. Effects of the polymer concentration and end-block interactions with the bitumen are investigated. While the polymer concentration has an effect on the mechanical properties, the effect of increasing repulsive interactions between the bitumen and the polymer end-blocks is much more dramatic; it increases the viscosity of the mixture and shifts the onset of the elastic behavior to lower frequencies. For increased repulsion, the polymer end-blocks form small clusters that can be connected by a dynamic polymer backbone network. A simple Flory-Huggins analysis reveals the onset of segregation of the end-blocks in the bitumen mixture in agreement with the simulation data. Hence the changed mechanical properties are due to the emergence of large-scale structures as the repulsion is increased, which conforms to known mechanisms of microphase separation in polymer-modified bitumens.

Coarse-grained simulations of cis- and trans-polybutadiene: A bottom-up approach.

We apply the dissipative particle dynamics strategy proposed by Hijón et al. [Faraday Discuss. 144, 301-322 (2010)] and based on an exact derivation of the generalized Langevin equation to cis- and trans-1,4-polybutadiene. We prove that it is able to reproduce not only the structural but also the dynamical properties of these polymers without any fitting parameter. A systematic study of the effect of the level of coarse-graining is done on cis-1,4-polybutadiene. We show that as the level of coarse-graining increases, the dynamical properties are better and better reproduced while the structural properties deviate more and more from those calculated in molecular dynamics (MD) simulations. We suggest two reasons for this behavior: the Markovian approximation is better satisfied as the level of coarse-graining increases, while the pair-wise approximation neglects important contributions due to the relative orientation of the beads at large levels of coarse-graining. Finally, we highlight a possible limit of the Markovian approximation: the fact that in constrained simulations, in which the centers-of-mass of the beads are kept constant, the bead rotational dynamics become extremely slow.

Non-Newtonian behavior and molecular structure of Cooee bitumen under shear flow: A non-equilibrium molecular dynamics study.

The rheology and molecular structure of a model bitumen (Cooee bitumen) under shear are investigated in the non-Newtonian regime using non-equilibrium molecular dynamics simulations. The shear viscosity, normal stress differences, and pressure of the bitumen mixture are computed at different shear rates and different temperatures. The model bitumen is shown to be a shear-thinning fluid at all temperatures. In addition, the Cooee model is able to reproduce experimental results showing the formation of nanoaggregates composed of stacks of flat aromatic molecules in bitumen. These nanoaggregates are immersed in a solvent of saturated hydrocarbon molecules. At a fixed temperature, the shear-shinning behavior is related not only to the inter- and intramolecular alignments of the solvent molecules but also to the decrease of the average size of the nanoaggregates at high shear rates. The variation of the viscosity with temperature at different shear rates is also related to the size and relative composition of the nanoaggregates. The slight anisotropy of the whole sample due to the nanoaggregates is considered and quantified. Finally, the position of bitumen mixtures in the broad literature of complex systems such as colloidal suspensions, polymer solutions, and associating polymer networks is discussed.

Cooee bitumen. II. Stability of linear asphaltene nanoaggregates.

Asphaltene and smaller aromatic molecules tend to form linear nanoaggregates in bitumen. Over the years bitumen undergoes chemical aging and during this process, the size of the nanoaggregate increases. This increase is associated with an increase in viscosity and brittleness of the bitumen, eventually leading to road deterioration. This paper focuses on understanding the mechanisms behind nanoaggregate size and stability. We used molecular dynamics simulations to quantify the probability of having a nanoaggregate of a given size in the stationary regime. To model this complicated behavior, we chose first to consider the simple case where only asphaltene molecules are counted in a nanoaggregate. We used a master equation approach and a related statistical mechanics model. The linear asphaltene nanoaggregates behave as a rigid linear chain. The most complicated case where all aromatic molecules are counted in a nanoaggregate is then discussed. The linear aggregates where all aromatic molecules are counted seem to behave as a flexible linear chain.

Cooee bitumen: chemical aging.

We study chemical aging in "Cooee bitumen" using molecular dynamic simulations. This model bitumen is composed of four realistic molecule types: saturated hydrocarbon, resinous oil, resin, and asphaltene. The aging reaction is modelled by the chemical reaction: "2 resins → 1 asphaltene." Molecular dynamic simulations of four bitumen compositions, obtained by a repeated application of the aging reaction, are performed. The stress autocorrelation function, the fluid structure, the rotational dynamics of the plane aromatic molecules, and the diffusivity of each molecule are determined for the four different compositions. The aging reaction causes a significant dynamics slowdown, which is correlated to the aggregation of asphaltene molecules in larger and dynamically slower nanoaggregates. Finally, a detailed description of the role of each molecule types in the aggregation and aging processes is given.

Four-component united-atom model of bitumen.

We propose a four-component united-atom molecular model of bitumen. The model includes realistic chemical constituents and introduces a coarse graining level that suppresses the highest frequency modes. Molecular dynamics simulations of the model are carried out using graphic-processor-units based software in time spans in order of microseconds, which enables the study of slow relaxation processes characterizing bitumen. This paper also presents results of the model dynamics as expressed through the mean-square displacement, the stress autocorrelation function, and rotational relaxation. The diffusivity of the individual molecules changes little as a function of temperature and reveals distinct dynamical time scales. Different time scales are also observed for the rotational relaxation. The stress autocorrelation function features a slow non-exponential decay for all temperatures studied. From the stress autocorrelation function, the shear viscosity and shear modulus are evaluated, showing a viscous response at frequencies below 100 MHz. The model predictions of viscosity and diffusivities are compared to experimental data, giving reasonable agreement. The model shows that the asphaltene, resin, and resinous oil tend to form nano-aggregates. The characteristic dynamical relaxation time of these aggregates is larger than that of the homogeneously distributed parts of the system, leading to strong dynamical heterogeneity.

Dynamics and Structure of Bitumen-Water Mixtures.

Systems of Cooee bitumen and water up to 4% mass are studied by molecular dynamics simulations. The cohesive energy density of the system is shown to decrease with an increasing water content. This decrease is due mainly to an increase in the interaction energy which is not high enough to counterbalance the increase in volume due to the addition of water. It is not due to a decrease of interaction energy between the slightly polar asphaltene molecules. The water molecules tend to form a droplet in bitumen. The size and the distribution of sizes of the droplets are quantified, with multiple droplets being more stable at the highest temperature simulated. The droplet is mainly located close to the saturates molecules in bitumen. Finally, it is shown that the water dynamics is much slower in bitumen than in pure water because it is governed by the diffusion of the droplet and not of the single molecules.

Finite-size effects in a model for plasticity of amorphous composites.

We discuss the plastic behavior of an amorphous matrix reinforced by hard particles. A mesoscopic depinning-like model accounting for Eshelby elastic interactions is implemented. Only the effect of a plastic disorder is considered. Numerical results show a complex size dependence of the effective flow stress of the amorphous composite. In particular, the departure from the mixing law shows opposite trends associated to the competing effects of the matrix and the reinforcing particles, respectively. The reinforcing mechanisms and their effects on localization are discussed. Plastic strain is shown to gradually concentrate on the weakest band of the system. This correlation of the plastic behavior with the material structure is used to design a simple analytical model. The latter nicely captures reinforcement size effects in (logN/N)(1/2), where N is the linear size of the system, observed numerically. Predictions of the effective flow stress accounting for further logarithmic corrections show a very good agreement with numerical results.

Simple Statistical Model for Branched Aggregates: Application to Cooee Bitumen.

We propose a statistical model that can reproduce the size distribution of any branched aggregate, including amylopectin, dendrimers, molecular clusters of monoalcohols, and asphaltene nanoaggregates. It is based on the conditional probability for one molecule to form a new bond with a molecule, given that it already has bonds with others. The model is applied here to asphaltene nanoaggregates observed in molecular dynamics simulations of Cooee bitumen. The variation with temperature of the probabilities deduced from this model is discussed in terms of statistical mechanics arguments. The relevance of the statistical model in the case of asphaltene nanoaggregates is checked by comparing the predicted value of the probability for one molecule to have exactly i bonds with the same probability directly measured in the molecular dynamics simulations. The agreement is satisfactory.