Ab initio simulations of bond breaking in sulfur crosslinked isoprene oligomer units.

Sulfur crosslinked polyisoprene (rubber) is used in important material components for a number of technical tasks (e.g., in tires and sealings). If mechanical stress, like tension or shear, is applied on these material components, the sulfur crosslinks suffer from homolytic bond breaking. In this work, we have simulated the bond breaking mechanism of sulfur crosslinks between polyisoprene chains using Car-Parrinello molecular dynamic simulations and investigated the maximum forces which can be resisted by the crosslinks. Small model systems with crosslinks formed by chains of N = 1 to N = 6 sulfur atoms have been simulated with the slow growth-technique, known from the literature. The maximum force can be thereby determined from the calculated energies as a function of strain (elongation). The stability of the crosslink under strain is quantified in terms of the maximum force that can be resisted by the system before the crosslink breaks. As shown by our simulations, this maximum force decreases with the sulfur crosslink length N in a step like manner. Our findings indicate that in bridges with N = 1, 2, and 3 sulfur atoms predominantly, carbon-sulfur bonds break, while in crosslinks with N > 3, the breaking of a sulfur-sulfur bond is the dominant failure mechanism. The results are explained within a simple chemical bond model, which describes how the delocalization of the electrons in the generated radicals can lower their electronic energy and decrease the activation barriers. It is described which of the double bonds in the isoprene units are involved in the mechanochemistry of crosslinked rubber.

Framework for a High-Throughput Screening Method to Assess Polymer/Plasticizer Miscibility: The Case of Hydrocarbons in Polyolefins.

Polymer composite materials require softening to reduce their glass transition temperature and improve processability. To this end, plasticizers (PLs), which are small organic molecules, are added to the polymer matrix. The miscibility of these PLs has a large impact on their effectiveness and, therefore, their interactions with the polymer matrix must be carefully considered. Many PL characteristics, including their size, topology, and flexibility, can impact their miscibility and, because of the exponentially large number of PLs, the current trial-and-error approach is very ineffective. In this work, we show that using coarse-grained molecular simulations of a small dataset of 48 PLs, it is possible to identify topological and thermodynamic descriptors that are proxy for their miscibility. Using ad-hoc molecular dynamics simulation setups that are relatively computationally inexpensive, we establish correlations between the PLs' topology, internal flexibility, thermodynamics of aggregation, and degree of miscibility, and use these descriptors to classify the molecules as miscible or immiscible. With all available data, we also construct a decision tree model, which achieves a F1 score of 0.86 ± 0.01 with repeated, stratified 5-fold cross-validation, indicating that this machine learning method can be a promising route to fully automate the screening. By evaluating the individual performance of the descriptors, we show this procedure enables a 10-fold reduction of the test space and provides the basis for the development of workflows that can efficiently screen PLs with a variety of topological features. The approach is used here to screen for apolar PLs in polyisoprene melts, but similar proxies would be valid for other polyolefins, while, in cases where polar interactions drive the miscibility, other descriptors are likely to be needed.

Sorption and diffusion of carbon dioxide and nitrogen in poly(methyl methacrylate).

Molecular dynamics simulations are performed to determine the solubility and diffusion coefficient of carbon dioxide and nitrogen in poly(methyl methacrylate) (PMMA). The solubilities of CO2 in the polymer are calculated employing our grand canonical ensemble simulation method, fixing the target excess chemical potential of CO2 in the polymer and varying the number of CO2 molecules in the polymer matrix till establishing equilibrium. It is shown that the calculated sorption isotherms of CO2 in PMMA, employing this method well agrees with experiment. Our results on the diffusion coefficients of CO2 and N2 in PMMA are shown to obey a common hopping mechanism. It is shown that the higher solubility of CO2 than that of N2 is a consequence of more attractive interactions between the carbonyl group of polymer and the sorbent. While the residence time of CO2 beside the carbonyl group of polymer is about three times higher than that of N2, the diffusion coefficient of CO2 in PMMA is higher than that of N2. The higher diffusion coefficient of CO2, compared to N2, in PMMA is shown to be due to the higher (≈3 times) swelling of polymer upon CO2 uptake.

Coarse-grained modeling for macromolecular chemistry.

The physical phenomena and properties of macromolecules such as polymers or biological materials cover a wide range of length and time scales: from Ångströms and subpicoseconds to millimeters and minutes. Multiscale simulation methods link different computer simulation approaches, which cover these scales and the respective levels of resolution. Different simulation methods that bridge the atomistic description of the system to a coarser level have been developed in order to reach the mesoscopic time and length scales important for many material properties. Here, we give a short introduction to multiscale simulation approaches in macromolecular chemistry. Then, we review the coarse-grained simulation models developed to drive a simple model from a more detailed one. Some different methodological aspects such as time scale and dynamics in coarse-grained simulations and several typical problems are briefly addressed, finishing with a look at future challenges.

How good are coarse-grained polymer models? A comparison for atactic polystyrene.

This review provides an overview of the various coarse-grained models that have been developed in the past few years for amorphous polystyrene. Different techniques to develop the force fields and different mapping schemes lead to models that perform differently depending on the properties investigated. This review collects and compares the models to guide the reader in the choice of the best model for the application of interest. It is expected that the central features of the various coarse-graining procedures will also apply to systems other than polystyrene and that some of the conclusions about different coarse-graining strategies are general.

IBIsCO: a molecular dynamics simulation package for coarse-grained simulation.

IBIsCO is a parallel molecular dynamics simulation package developed specially for coarse-grained simulations with numerical potentials derived by the iterative Boltzmann inversion (IBI) method (Reith et al., J Comput Chem 2003, 24, 1624). In addition to common features of molecular dynamics programs, the techniques of dissipative particle dynamics (Groot and Warren, J Chem Phys 1997, 107, 4423) and Lowe-Andersen dynamics (Lowe, Europhys Lett 1999, 47, 145) are implemented, which can be used both as thermostats and as sources of friction to compensate the loss of degrees of freedom by coarse-graining. The reverse nonequilibrium molecular dynamics simulation method (Müller-Plathe, Phys Rev E 1999, 59, 4894) for the calculation of viscosities is also implemented. Details of the algorithms, functionalities, implementation, user interfaces, and file formats are described. The code is parallelized using PE_MPI on PowerPC architecture. The execution time scales satisfactorily with the number of processors.

Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain.

A scheme is described for performing molecular dynamics simulations on polymers under nonperiodic, stochastic boundary conditions. It has been designed to allow later the embedding of a particle domain treated by molecular dynamics into a continuum environment treated by finite elements. It combines, in the boundary region, harmonically restrained particles to confine the system with dissipative particle dynamics to dissipate energy and to thermostat the simulation. The equilibrium position of the tethered particles, the so-called anchor points, are well suited for transmitting deformations, forces and force derivatives between the particle and continuum domains. In the present work the particle scheme is tested by comparing results for coarse-grained polystyrene melts under nonperiodic and regular periodic boundary conditions. Excellent agreement is found for thermodynamic, structural, and dynamic properties.

Studying long-time dynamics of imidazolium-based ionic liquids with a systematically coarse-grained model.

A coarse-grained ionic liquid model has been developed to investigate the structure and dynamic properties of 1-n-alkyl-3-methylimidazolium hexafluorophosphate [C(n)mim][PF(6)] ionic liquids with alkyl chains up to ten carbon atoms. Two mapping schemes are compared, showing that different ways of grouping the atoms into coarse-grained beads affect differently the structure and dynamics of the liquid. The simulations predict that upon increasing the length of the alkyl tail the diffusion coefficients of the cations expectedly decrease while the anion diffusion becomes slightly faster. Moreover, the reduced dynamic heterogeneity of the liquids at low temperature is due to a decrease in the number of the slow particles only. At the timescale where the models show their highest dynamic heterogeneity, the cross-over displacement, after which part of the anions show fast dynamics, is consistently higher in C(10) than in C(4) and it is higher than the one found for the cations. This suggests that the cages in which the anions are trapped (at this time scale) are larger in [C(10)mim][PF(6)] than in [C(4)mim][PF(6)]. For the cations, the cross-over displacement has almost the same value for [C(4)mim][PF(6)] and [C(10)mim][PF(6)].

Author Correction: A nano-mechanical instability as primary contribution to rolling resistance.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Large-scale state-dependent membrane remodeling by a transporter protein.

That channels and transporters can influence the membrane morphology is increasingly recognized. Less appreciated is that the extent and free-energy cost of these deformations likely varies among different functional states of a protein, and thus, that they might contribute significantly to defining its mechanism. We consider the trimeric Na+-aspartate symporter GltPh, a homolog of an important class of neurotransmitter transporters, whose mechanism entails one of the most drastic structural changes known. Molecular simulations indicate that when the protomers become inward-facing, they cause deep, long-ranged, and yet mutually-independent membrane deformations. Using a novel simulation methodology, we estimate that the free-energy cost of this membrane perturbation is in the order of 6-7 kcal/mol per protomer. Compensating free-energy contributions within the protein or its environment must thus stabilize this inward-facing conformation for the transporter to function. We discuss these striking results in the context of existing experimental observations for this and other transporters.

Fast dynamics in coarse-grained polymer models: the effect of the hydrogen bonds.

Based on a mesoscale model developed recently for polyamide-66, here we present a simple algorithm for reinserting the atomistic details neglected in the coarse-grained (CG) description. The resulting CG and detailed models are tested successfully against several structural properties including the number of hydrogen bonds (HBs). From a quantitative analysis of the HB dynamics and thermodynamics it turns out that the CG model is characterized by a weaker HB network than the corresponding atomic model. We show that the relaxation of the HB network and the diffusion of the polymer chains are coupled. Moreover, we find that the temperature-dependent scaling factor accounting for the fast dynamics of the CG model is strongly linked to the relaxation time of the HB at each temperature.

Phase Morphology of NR/SBR Blends: Effect of Curing Temperature and Curing Time.

The morphology of natural rubber/styrene⁻butadiene rubber blends (NR/SBR) was characterized by atomic force microscopy (AFM), with regard to curing temperature and curing time. The changes in blend morphology were directly visualized by AFM which confirmed the results of indirect experiments like differential scanning calorimetry (DSC). Comparing the phase morphologies at different curing temperatures indicated that the domain size of SBR increases with temperature at lower curing temperatures, but domain growing stops at the latest scorch time. This effect is explained by longer scorch times at low curing temperatures which facilitate phase separation, while the short scorch times at higher temperatures meant that the coalescence of SBR phases was hindered by cross-linking between polymer chains.

A nano-mechanical instability as primary contribution to rolling resistance.

Rolling resistance ranks among the top ten automobile megatrends, because it is directly linked to fuel efficiency and emissions reduction. The mechanisms controlling this phenomenon are hidden deeply inside the complexity of tire tread materials and do elude direct experimental observation. Here we use atomistic molecular modelling to identify a novel nano-mechanical mechanism for dissipative loss in silica filled elastomers when the latter are subjected to dynamic strain. The force-vs-particle separation curve of a single silica particle-to-silica particle contact, embedded inside a polyisoprene rubber matrix, is obtained, while the contact is opened and closed by a cyclic force. We confirm the occurrence of spontaneous relative displacements ('jolts') of the filler particles. These jolts give rise to energy dissipation in addition to the usual viscous loss in the polymer matrix. As the temperature is increased the new loss mechanism becomes dominant. This has important technical implications for the control and reduction of tire rolling resistance as well as for many other elastomer composite applications involving dynamic loading.

Validation of Force Fields of Rubber through Glass-Transition Temperature Calculation by Microsecond Atomic-Scale Molecular Dynamics Simulation.

Microsecond atomic-scale molecular dynamics simulation has been employed to calculate the glass-transition temperature (Tg) of cis- and trans-1,4-polybutadiene (PB) and 1,4-polyisoprene (PI). Both all-atomistic and united-atom models have been simulated using force fields, already available in literature. The accuracy of these decade old force fields has been tested by comparing calculated glass-transition temperatures to the corresponding experimental values. Tg depicts the phase transition in elastomers and substantially affects various physical properties of polymers, and hence the reproducibility of Tg becomes very crucial from a thermodynamic point of view. Such validation using Tg also evaluates the ability of these force fields to be used for advanced materials like rubber nanocomposites, where Tg is greatly affected by the presence of fillers. We have calculated Tg for a total of eight systems, featuring all-atom and united-atom models of cis- and trans-PI and -PB, which are the major constituents of natural and synthetic rubber. Tuning and refinement of the force fields has also been done using quantum-chemical calculations to obtain desirable density and Tg. Thus, a set of properly validated force fields, capable of reproducing various macroscopic properties of rubber, has been provided. A novel polymer equilibration protocol, involving potential energy convergence as the equilibration criterion, has been proposed. We demonstrate that not only macroscopic polymer properties like density, thermal expansion coefficient, and Tg but also local structural characteristics like end-to-end distance (R) and radius of gyration (Rg) and mechanical properties like bulk modulus have also been equilibrated using our strategy. Complete decay of end-to-end vector autocorrelation function with time also supports proper equilibration using our strategy.

Multiscale approach to equilibrating model polymer melts.

We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped Kremer-Grest model that allows chains to partially interpenetrate. Finally the Kremer-Grest force field is introduced to freeze the topological state and enforce correct monomer packing. We generate 15 melts of 500 chains of 10.000 beads for varying chain stiffness as well as a number of melts with 1.000 chains of 15.000 monomers. To validate the equilibration process we study the time evolution of bulk, collective, and single-chain observables at the monomeric, mesoscopic, and macroscopic length scales. Extension of the present method to longer, branched, or polydisperse chains, and/or larger system sizes is straightforward.

Fine-graining without coarse-graining: an easy and fast way to equilibrate dense polymer melts.

A technique to prepare well-equilibrated polymer melts is presented. The method, named fine-graining, consists of two steps: the generation of continuum random walks characterized by different Kuhn lengths and the insertion of the atomistic units on the "parent" random walk chains. The procedure ensures a good equilibration at long as well as short length-scales and it is very easy to implement. Melts of polyethylene, atactic polystyrene and polyamide-66 are equilibrated with this technique and their long and short range structural properties can be successfully compared with previous simulation and experimental data.