Tensile strength of rubber described via the formation and rupture of load-bearing polymer chains.

A theoretical picture describing the tensile strength σ_{T} of elastomers is developed. σ_{T} is composed of three factors: (1) the tensile strength of individual polymer load-bearing chains (LBCs) according to Eyring's theory, (2) an occupation number of LBC states using Fermi statistics, and (3) an excluded volume factor reducing the number of possible LBCs due to the presence of filler particles or crosslinks between polymers. This description is compared to experimental tensile strengths of carbon black (N339)-filled EPDM (Keltan 4450) as well as to other experiments in the literature studying the effects of temperature, filler concentration, and particle size as well as crosslink density.

Scaling theory of rubber sliding friction.

Current theoretical descriptions of rubber or elastomer friction are complex-usually due to extensive mathematical detail describing the topography of the solid surface. In addition, the viscoelastic properties of the elastomer material itself, in particular if the rubber is highly filled, further increase the complexity. On the other hand, experimental coefficients of sliding friction plotted versus sliding speed, temperature or other parameters do not contain much structure, which suggests that a less detailed approach is possible. Here we investigate the coefficient of sliding friction on dry surfaces via scaling and dimensional analysis. We propose that adhesion promotes viscoelastic dissipation by increasing the deformation amplitude at relevant length scales. Finally, a comparatively simple expression for the coefficient of friction is obtained, which allows an intuitive understanding of the underlying physics and fits experimental data for various speeds, temperatures, and pressures.

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.

Specific heat capacity enhancement studied in silica doped potassium nitrate via molecular dynamics simulation.

Molten salts serve an important purpose for short term heat energy storage and as heat transfer fluids in solar power plants. Different experimental groups have shown that certain mixtures containing salts doped with small amounts of nanoparticles exhibit much greater specific heat capacities compared to the same base salts without nanoparticles. This effect is technically interesting and economically important. Thus far, however, it is not understood. Our aim is the theoretical investigation of the specific heat capacity in the aforementioned nanofluids on the molecular level using simulations. Here we present results for liquid potassium nitrate doped with silica nanoparticles. We discuss the observed increase of the specific heat in terms of the particle induced hydrodynamic reinforcement and liquid structure. The theoretical background of this discussion is a ω-space resolved phonon theory of liquids in conjunction with differential spectral densities, computed for the different systems with and without nanoparticles.

Modelling Filler Dispersion in Elastomers: Relating Filler Morphology to Interface Free Energies via SAXS and TEM Simulation Studies.

The properties of rubber are strongly influenced by the distribution of filler within the polymer matrix. Here, we introduce a Monte Carlo-based morphology generator. The basic elements of our model are cubic cells, which, in the current version, can be either silica filler particles or rubber volume elements in adjustable proportion. The model allows the assignment of surface free energies to the particles according to whether a surface represents, for instance, 'naked' silica or silanised silica. The amount of silanisation is variable. We use a nearest-neighbour site-exchange Monte Carlo algorithm to generate filler morphologies, mimicking flocculation. Transmission electron micrographs (TEM) as well as small angle scattering (SAS) intensities can be calculated along the Monte Carlo trajectory. In this work, we demonstrate the application of our morphology generator in terms of selected examples. We illustrate its potential as a tool for screening studies, relating interface tensions between the components to filler network structure as characterised by TEM and SAS.

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.

On the specific heat capacity enhancement in nanofluids.

Molten salts are used as heat transfer fluids and for short-term heat energy storage in solar power plants. Experiments show that the specific heat capacity of the base salt may be significantly enhanced by adding small amounts of certain nanoparticles. This effect, which is technically interesting and economically important, is not yet understood. This paper presents a critical discussion of the existing attendant experimental literature and the phenomenological models put forward thus far. A common assumption, the existence of nanolayers surrounding the nanoparticles, which are thought to be the source of, in some cases, the large increase of a nanofluid's specific heat capacity is criticized and a different model is proposed. The model assumes that the influence of the nanoparticles in the surrounding liquid is of long range. The attendant long-range interfacial layers may interact with each other upon increase of nanoparticle concentration. This can explain the specific heat maximum observed by different groups, for which no other theoretical explanation appears to exist.

Phase coexistence for charged soft dumbbell and ionic soft sphere systems via molecular dynamics simulation.

Gas-liquid critical parameters of charged soft dumbbells (CSDs) as function of the site-to-site separation on the dumbbells, d, obtained on the basis of molecular dynamics computer simulation are presented. A mean field theoretical description is developed, which explains the results at small and large d, respectively. We note that in the limit d→0 the CSD system exhibits gas-liquid phase separation solely driven by repulsion and dipole-dipole interaction. If the dumbbell bond is eliminated the CSD system becomes similar to the restricted primitive model of ionic fluids with hard core repulsion replaced by soft repulsion. We obtain the gas-liquid critical parameters for this model and discuss their relation to the CSD system.

Simulation study of structural, transport, and thermodynamic properties of TIP4P/2005 water in single-walled carbon nanotubes.

Because carbon nanotubes lack a strong interaction with water, its hydrogen bond network is altered mainly by the confining geometry alone, allowing one to study its influence on the structure of water. Here structural, transport, and thermodynamic properties are investigated for TIP4P/2005 water confined in single-walled carbon nanotubes, possessing diameters from 11 to 50 Å. Temperatures range from 220 to 600 K for the two pressures studied, 1 and 1000 atm. The results, based on grand canonical Monte Carlo techniques, include heats of adsorption, temperature and diameter dependent densities, density profiles, diffusion constants, and pressure tensor components. The main findings comprise the suppression of the density maximum in tubes with diameters below 50-25 Å, indicating that structures responsible for this anomaly are of comparable size. Furthermore the axial pressure can be described within the continuum limit with deviations only appearing for diameters below 20 Å. The diffusion constants are similar to that of bulk water, demonstrating that the agility of the hydrogen bond network is preserved in the confining geometries considered here.

Simulation study of the polarizable Stockmayer fluid in an external field.

Gas-liquid phase coexistence curves of the polarizable Stockmayer fluid in external electric fields are computed using molecular dynamics computer simulation. We study in particular the critical-point shift dependence on polarizability and external electric field distinguishing the cases of fixed charge density and fixed potential. The results are compared to a previously developed mean-field theory for the polarizable Stockmayer fluid in an external field. We also investigate the behavior of the isochoric heat capacity near gas-liquid criticality via finite-size scaling depending on polarizability and external field.

Monte Carlo simulation of osmotic equilibria.

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.

Predicting water sorption and volume swelling in dense polymer systems via computer simulation.

Atomistic model structures of amorphous polyamide 6 (PA-6) and of an adhesive system consisting of the diglycidyl ether of bisphenol A (DGEBA) as epoxy resin and isophorone diamine (IPD) as a curing agent are generated. For the adhesive, we use a new approach for the generation of the cross-linked polymer networks. It takes into account the chemical reaction kinetics of the curing reaction and, therefore, results in more realistic network structures. On the basis of the corresponding model structures, the equilibrium water content and the swelling ratio of amorphous PA-6 and of the DGEBA+IPD networks are calculated via computer simulation for different thermodynamic conditions. A hybrid method is used combining the molecular dynamics technique with an accelerated test particle insertion method. The results are in reasonable agreement with experiments and, in the case of the PA-6 system, with results obtained via other computer simulation methods.

Gas-liquid coexistence in a system of dipolar soft spheres.

The existence of gas-liquid coexistence in dipolar fluids with no other contribution to attractive interaction than dipole-dipole interaction is a basic and open question in the theory of fluids. Here we compute the gas-liquid critical point in a system of dipolar soft spheres subject to an external electric field using molecular dynamics computer simulation. Tracking the critical point as the field strength is approaching zero we find the following limiting values: T(c)=0.063 and ρ(c)=0.0033 (dipole moment µ=1). These values are confirmed by independent simulation at zero field strength.

Tracking gas-liquid coexistence in fluids of charged soft dumbbells.

The existence of gas-liquid coexistence in dipolar fluids with no other contribution to attractive interaction than dipole-dipole interaction is a basic and open question in the theory of fluids. Recent Monte Carlo work by Camp and co-workers indicates that a fluid of charged hard dumbbells does exhibit gas-liquid (g-l) coexistence. This system has the potential to answer the above fundamental question because the charge-to-charge separation, d , on the dumbbells may be reduced to, at least in principle, yield the dipolar fluid limit. Using the molecular-dynamics technique we present simulation results for the g-l critical point of charged soft dumbbells at fixed dipole moment as function of d . We do find a g-l critical point at finite temperature even at the smallest d value (10;{-4}) . Reversible aggregation appears to play less a role than in related model systems as d becomes small. Consequently attempts to interpret the simulation results using either an extension of Flory's lattice theory for polymer systems, which includes reversible assembly of monomers into chains, or the defect model for reversible networks proposed by Tlusty and Safran are not successful. The overall best qualitative interpretation of the critical parameters is obtained by considering the dumbbells as dipoles immersed in a continuum dielectric.

Phase behavior of a reversibly assembling system in two dimensions: a Monte Carlo simulation study.

Using Monte Carlo simulation, we investigate the structural phase behavior of a continuum molecular model for self-assembling semiflexible equilibrium polymers in two dimensions. Particle-particle interaction is modeled via a Lennard-Jones potential with tunable anisotropic attraction. Depending on the strength of the anisotropy, we find the formation of reversible networks as well as stiff rodlike aggregates. The phase transition observed in the presence of the network structures is compared to predictions of the Tlusty-Safran defect model.

Dipolar particles in an external field: Molecular dynamics simulation and mean field theory.

Using molecular dynamics computer simulation we compute gas-liquid phase coexistence curves for the Stockmayer fluid in an external electric field. We observe a field-induced shift of the critical temperature DeltaTc. The sign of DeltaTc depends on whether the potential or the surface charge density is held constant assuming that the dielectric material fills the space between capacitor plates. Our own as well as previous literature data for DeltaTc are compared to and interpreted in terms of a simple mean field theory. Despite considerable errors in the simulation results, we find consistency between the simulation results obtained by different groups including our own and the mean field description. The latter ties the sign of DeltaTc to the outside constraints via the electric field dependence of the orientation part of the mean field free energy.

Effects due to molecular shape and flexibility on the permeability ratio of binary fluid mixtures in a model polymer network via computer simulation.

Sorption and diffusion of binary mixtures of small molecules in model polymer networks is studied via computer simulation. Three types of molecules identical in volume but different in shape and flexibility (compact, linear stiff, and linear flexible) are combined into binary mixtures (compact/linear stiff) and (linear stiff/linear flexible). The relative effects of shape and flexibility on separation factor and diffusion coefficient inside random polymer networks are studied using a molecular dynamics/Gibbs-ensemble Monte Carlo hybrid technique. In addition the effects of temperature, pressure, and network strand length are considered. We find that the compact molecules are preferentially absorbed into the network at all strand lengths and temperatures considered here. Flexibility only leads to minor preferential sorption under most conditions. Diffusion coefficients of the competing species inside the network are found to agree within the error bars.

From gas-liquid to liquid crystalline phase behavior via anisotropic attraction: a computer simulation study.

The partial phase behavior of a continuum molecular model for self-assembling semiflexible equilibrium polymers is studied via Monte Carlo and molecular dynamics simulation. We investigate the transfer from ordinary gas-liquid coexistence to the appearance of liquid crystallinity driven by excluded volume interaction between rodlike aggregates. The transfer between the two types of phase behavior is governed by a tunable anisotropic attractive interaction between monomer particles. The relation to dipolar fluid models, which are also known to form reversible chains, is discussed.

Phase behavior of the Stockmayer fluid via molecular dynamics simulation.

The gas-isotropic liquid-nematic liquid phase behavior of the Stockmayer fluid is studied using molecular dynamics simulation together with a mean field lattice model. We obtain coexistence curves of the Stockmayer fluid over a wide range of dipole strengths, temperatures, and densities, including the transition from the isotropic liquid to the ferroelectric liquid. In our simulations we do not observe the disappearance of the isotropic gas-isotropic liquid coexistence at high dipole strength contrary to earlier findings based on Monte Carlo techniques. Even though the formation of reversible dipole chains strongly affects the location of the critical point, it does not lead to its disappearance. These results are supported by a mean field lattice model which yields good qualitative, and in parts quantitative, agreement with our simulations. In addition, we also investigate the gas-isotropic liquid phase behavior for different polarizabilities.

Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid.

We develop a simple theory explaining the dependence of the gas-liquid critical point in the Stockmayer fluid on dipole strength. The theory is based on the Flory-Huggins lattice description for polymer systems in conjunction with a transfer matrix model for isolated chains of reversibly assembled dipolar particles. We find that the shift of the critical point as a function of dipole strength, which originally was found in computer simulation, strongly resembles the critical point shift as a function of chain length in ordinary linear polymer systems. In particular, the decrease of the critical density with increasing dipole strength is a consequence of the existence of reversible chains near criticality. In addition we report simulation results for gas-liquid critical points well above the limiting dipole strength found previously.