Andrei A. Gusev

Bridging the gap between atomistic and coarse-grained models of polymers : Status and perspectives

Recent developments that increase the time and distance scales accessible in the simulations of specific polymers are reviewed. Several different techniques are similar in that they replace a model expressed in fully atomistic detail with a coarse-grained model of the same polymer, atomistic → coarse-grained (and beyond!), thereby increasing the time and distance scales accessible within the expenditure of reasonable computational resources. The bridge represented by the right-pointing arrow can be constructed via different procedures, which are reviewed here. The review also considers the status of methods which reverse this arrow, atomistic ← coarse-grained. This “reverse-mapping” recovers a model expressed in fully atomistic detail from an arbitrarily chosen replica generated during the simulation of the coarse-grained system. Taken in conjunction with the efficiency of the simulation when the system is in its coarse-grained representation, the overall process Open image in new window permits a much more complete equilibration of the system (larger effective size of Δt) when that equilibration is performed with the coarse-grained replicas (II → III) than if it were attempted with the fully atomistic replicas (I → IV).

Dynamics of small molecules in dense polymers subject to thermal motion

A new transition‐state theory model has been proposed that is based on the concept that the dynamics of small molecules dissolved in dense polymers is coupled to the elastic thermal motion of dense polymers but can be treated separately from their structural relaxation. The model has been used to study the dynamics of light gases dissolved in atomistic microstructures of poly(isobutylene) and bisphenol‐A‐polycarbonate. Short‐time scale MD runs have been used to characterize the elastic thermal motion of the host matrix. This information on mobility is then used for a stochastic simulation of solute dynamics up to approximately 10 μs. Three time regimes have been observed: a short‐time, high‐mobility domain, a time domain of anomalous diffusion, and a diffusive regime at long times. From the long‐time data diffusion coefficients for He, H2, Ar, O2, and N2 have been estimated. Comparison with experimental data has resulted in satisfactory agreement indicating that the mechanisms of the motion of small gases...

Fiber packing and elastic properties of a transversely random unidirectional glass/epoxy composite

Image analysis was used to characterize the microstructure of a unidirectional glass/epoxy composite which was found to be transversely randomly packed. Starting from a measured distribution of fiber diameter, a Monte Carlo procedure was employed to generate periodic computer models with unit cells comprising of random dispersion of a hundred non-overlapping parallel fibers of different diameter. The morphology generated in this way showed excellent agreement with that of the actual composite studied. An ultrasonic velocity method was used to measure a complete set of composite elastic constants and those of the epoxy matrix. On the basis of periodic three-dimensional meshes, the composite elastic constants of the Monte Carlo models were calculated numerically. Numerical and measured elastic constants were in good agreement. It was shown numerically that the randomness of the composite microstructure had a significant influence on the transverse composite elastic constants while the effect of fiber diameter distribution was small and unimportant. The predictive potential of the Halpin-Tsai and some other models commonly employed for predicting the elastic behavior of unidirectional composites was also assessed.

Numerical simulation of the effects of volume fraction, aspect ratio and fibre length distribution on the elastic and thermoelastic properties of short fibre composites

In this paper a new numerical procedure by Gusev, for predicting the elastic and thermoelastic properties of short fibre reinforced composites, is described. Computer models, comprising 100 non-overlapping aligned spherocylinders, were generated using a Monte Carlo procedure to produce a random morphology. Periodic boundary conditions were used for all the generated structures. Where necessary, the generated microstructures were based on measurements of real materials: for example a measured fibre length distribution was used to seed the Monte Carlo generator to produce a computer model with an equivalent fibre length distribution (FLD). The generated morphologies were meshed using an intelligent 3 dimensional meshing technique, allowing the elastic and thermo-elastic properties of the microstructures to be calculated. The numerical predictions were compared with those from three commonly used micromechanical models, namely those attributed to Halpin/Tsai, Tandon/Weng and Cox (shear lag). Firstly, the effect of volume fraction and aspect ratio were investigated, and the numerical results were compared and contrasted with those of the chosen models. Secondly, the numerical approach was used to investigate what effect a distribution of fibre lengths, as seen in real materials, would have on the predicted mechanical properties. The results were compared with simulations carried out using a monodispersed fibre length, to ascertain if the distribution of lengths could be replaced with a single length, and whether this length corresponded to a particular characteristic of the distribution, for example the first moment or average length.

Dynamics of light gases in rigid matrices of dense polymers

Transition‐state theory was employed to study the dynamics of light gases dissolved in rigid microstructures of glassy polycarbonate and rubbery polyisobutylene modeled in atomistic detail. The gaseous molecules migrated through the polymer structures in a sequence of ‘‘hops’’ between local minima of the potential energy. The solute dynamics was characterized by three time domains: at short times, <10−12 s, the mobility was very high and the molecules traveled on a scale of 5 A; this was followed by a domain of anomalous diffusion; at long times the tiniest molecules (He and H2) followed the Einstein diffusion law. Larger molecules (Ar, O2, and N2) did not reach the diffusive regime at the time scale of simulation (up to ca. 10−3 s) but were trapped instead in the vicinity of their initial sites without any progress in translational motion. It was concluded that the rigid‐matrix approach is inadequate for studying the dynamics of light gases in dense polymers, except for He.

Direct numerical predictions for the elastic and thermoelastic properties of short fibre composites

Abstract In this paper we compare the predictions of the thermoelastic properties of misaligned short glass fibre reinforced composites, calculated using the finite-element-based numerical approach of Gusev, with experimental measurements. Characterisation of the microstructure of the two injection moulded materials chosen for examination, in particular the fibre length and fibre orientation distributions, were used to ensure that the computer models were built with the same microstructure as the ‘real’ materials. Agreement between the measurements, in particular for the longitudinal Youngs modulus E 11 and the longitudinal and transverse thermal expansion coefficients, α 1 and α 2 , and the numerical predictions was found to be excellent. A comparison was also made with the most commonly used micromechanical models available from the literature. The approaches of Tandon and Weng, Takao and Taya and McCullough [Polym Comp 5 (1984) 327; J Comp Mater 21 (1987) 140] were found to give good agreement with both the numerical and measured values, although only the numerical approach showed the same relationship between α 1 and the degree of orientation as shown by the real materials.

Finite element predictions for the thermoelastic properties of nanotube reinforced polymers

The overall effective thermoelastic properties of nanotube reinforced polymers (NRP) were estimated numerically by using a finite element based procedure. Three-dimensional multi-inclusion periodic computer models were built for three different nanotube orientation states, namely, fully aligned, two-dimensional random in-plane and three-dimensional random states. The enhancement of the Youngs modulus as well as the decrease of the thermal expansion coefficient were calculated numerically, assuming technologically relevant combinations of the nanotube aspect ratio and volume fraction. Maximal changes of the thermoelastic properties can be achieved in the longitudinal direction of NRPs with fully aligned carbon nanotubes whereas two-dimensional random in-plane and three-dimensional random composite morphologies exhibit more moderate enhancements but in more than one direction. Numerical predictions for the enhancements of the thermoelastic properties confirmed that carbon nanotubes can be considerably more effective for the reinforcement of polymers than conventional glass or carbon fibres.

The influence of platelet disorientation on the barrier properties of composites: a numerical study

Direct finite element calculations are carried out to study the relationship between the platelet orientational distribution and the overall effective barrier properties (gas permeability) of mineral filled composites. We consider multi-inclusion computer models with microstructures representative of the dilute, semi-dilute and concentration regimes. In the dilute regime, our numerical predictions validate the results of multiple scattering expansion theory. For the semi-dilute and concentration regimes representative of most real composites, we present numerical estimates quantifying the difference between the barrier properties of composites with fully aligned and randomly oriented platelets. Our numerical results can also be used to quantify the effect of the geometric factor on the gas barrier properties of polymer–mineral hybrid nanocomposites.

A model for transport of diatomic molecules through elastic solids

SummaryThe distribution function ϱ of diatomic molecules, dissolved in a solid matrix subject to thermal elastic motion, was evaluated in closed form, assuming separability between the translational and rotational degrees of freedom of the solute molecules. The approach was applied to studying the transport of oxygen molecules through atomistic microstructures of atactic poly(vinylchloride) of ca. 40 Å at 318 K. The solubility coefficient was determined from the normalization constant of ϱ. The diffusion coefficient was evaluated from the long-term random walks of O2 molecules on the network of local maxima of ϱ. Comparison with experimental data resulted in satisfactory agreement, indicating the viability of the approach.

Effect of Particle Agglomeration on the Elastic Properties of Filled Polymers

We conducted a numerical finite-element-based study on the reinforcing effect of particle agglomeration on the stiffness of sphere-filled polymers. Two different types of agglomerates were considered. The first type was made up of 10 nonoverlapping identical spheres, whereas the second type were 10 slightly fused spheres. Numerical results reveal that by using agglomerates with fused spheres, one can significantly increase the composite stiffness, whereas the use of nonfused agglomerates does not allow one to achieve any additional stiffness increase compared to a composite with evenly dispersed nonagglomerating spheres.