Strain hardening in polymer glasses: limitations of network models

Bond Orientation-Determined Enthalpic Stress in Polymer Glasses upon Deformation

The mechanical properties of polymer glass are determined by both intermolecular local packing structures and aligned intrachain configurations. These configurations involve multiple space scales, and the underlying mechanism is not well understood yet. By applying mechanical stimulation to cold-drawn polymer glasses, the present simulation work shows a one-to-one correspondence between arising retractive stress and the segment orientation parameter on the length scale of the intrachain connecting bond. Such retractive stress is a newly produced enthalpic stress when segment orientation on the length scale of bonds and particle mobility coexist. This reveals a potential mechanism of how the intrachain orientation on the length scale of bonds influences the mechanical behaviors of polymer glasses.

Computational indentation in highly cross-linked polymer networks

Indentation is a common experimental technique to study the mechanics of polymeric materials. The main advantage of using indentation is this provides a direct correlation between the microstructure and the small-scale mechanical response, which is otherwise difficult within the standard tensile testing. The majority of studies have investigated hydrogels, microgels, elastomers, and even soft biomaterials. However, a less investigated system is the indentation in highly cross-linked polymer (HCP) networks, where the complex network structure plays a key role in dictating their physical properties. In this work, we investigate the structure-property relationship in HCP networks using the computational indentation of a generic model. We establish a correlation between the local bond breaking, network rearrangement, and small-scale mechanics. The results are compared with the elastic-plastic deformation model. HCPs harden upon indentation.

Load-bearing entanglements in polymer glasses

Through a combined approach of experiment and simulation, this study quantifies the role of entanglements in determining the mechanical properties of glassy polymer blends. Uniaxial extension experiments on 100-nm films containing a bidisperse mixture of polystyrene enable quantitative comparison with molecular dynamics (MD) simulations of a coarse-grained model for polymer glasses, where the bidisperse blends allow us to systematically tune the entanglement density of both systems. In the MD simulations, we demonstrate that not all entanglements carry substantial load at large deformation, and our analysis allows the development of a model to describe the number of effective, load-bearing entanglements per chain as a function of blend ratio. The film strength measured experimentally and the simulated film toughness are quantitatively described by a model that only accounts for load-bearing entanglements.

Confinement effects on the mechanical heterogeneity of polymer fiber glasses

Both polymer fiber glasses and bulk polymer glasses exhibit nonlinear mechanical responses under uniaxial deformation. In polymer fibers, however, polymer chains are confined strongly and the surface area is relatively large compared to their volume. The confinement and the surface may lead to the spatially heterogeneous relaxation of chains in polymer fibers. In this work we perform molecular dynamics simulations and investigate the relation between the heterogeneous dynamics and the nonlinear mechanical responses at a molecular level. Our molecular simulations capture successfully not only the nonlinear mechanical response but also the dependence of mechanical properties on the strain rate of typical polymer glasses as in experiments. We find that the local elastic modulus and the nonaffine displacement are spatially heterogeneous in the pre-yield regime, which results in a lower elastic modulus for polymer fibers than bulk polymer glasses. In the post-yield regime, those mechanical properties become relatively homogeneous. Monomers with large nonaffine displacement are localized mainly at the interfacial region in the pre-yield regime while highly nonaffine monomers are distributed throughout the fibers in the post-yield regime. We show that the nonaffine displacement during deformation relates closely to the mechanical response of the polymer fibers. We also find that in the strain-hardening regime there is a significant difference in the energetic contribution to the stress between polymer fibers and bulk polymers, for which the modulus of the strain-hardening regime of the polymer fibers is smaller than that of bulk polymers.

Compression-induced anti-nematic order in glassy and semicrystalline polymers

We provide new insights into the molecular origin of the asymmetry between uniaxial tensile and compressive deformation of glassy and semicrystalline polymers using molecular dynamics simulations. The difference between the two responses strongly depends on the chain length and is the largest at intermediate chain lengths. Irrespective of chain length, the intra- and interchain organization of polymers under extension and compression are remarkably distinct. The chains align along the tensile axis leading to a global nematic order of the bonds and end-to-end vectors, whereas compression reorganizes polymers to lie in planes perpendicular to the compressive axis resulting in the emergence of an anti-nematic order and destruction of crystallinity. Regardless of the initial glassy or semicrystalline structure, the deformed state of polymers at large strains converge towards the same kind of structure that only depends on the deformation mode.

Characterizing effects of fast melt deformation on entangled polymers in their glassy state

Fast deformation of entangled melts is known to cause chain stretching due to affinelike straining of the entanglement network. Since the chain deformation may also result in perturbations of covalent bond angles and bond length, there are always possible enthalpic effects. In this study, we first subject polystyrene and PMMA of different molecular weights to either uniaxial melt extension or planar extension and subsequently impose rapid thermal quenching to preserve the chain deformation. Then, such pre-melt-deformed samples are annealed at various temperatures below the glass transition temperature T_g. During annealing, these samples can undergo appreciable contraction on a time scale much shorter than the alpha relaxation time. Significant retractive stress is observed when such contracting samples are held fixed during the annealing. The stress level can be nearly as high as the Cauchy stress produced during melt stretching. These observations not only allowed us to investigate glassy chain dynamics as well as the molecular nature of mechanical stress but may also suggest that pre-melt-stretched polymers can cause segmental mobilization in the glassy state. The available evidence indicates that the retractive stress is enthalpic in origin, associated with the conformational distortion at the bond level produced by melt stretching.

Molecular mobility in driven monomeric and polymeric glasses

We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress σ while being deformed with strain rate ε[over ̇], the microscopic structural relaxation time τ_{str} is given by the universal relation σ/G_{∞}ε[over ̇] with G_{∞} a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxation time and τ_{str} is in fact further reduced even though σ rises during glassy strain hardening. We develop expressions to capture both effects and thus provide a framework for analyzing mobility measurements in glassy materials.

Mechanisms of reinforcement in polymer nanocomposites

Qualitatively different stress–strain responses of polymer nanocomposites are shown to result from the dynamical evolution of three principal molecular structural motifs in the polymer–filler network.

Assessing numerical methods for molecular and particle simulation

We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss the characteristics of different algorithms, including their essential conservation properties, the convergence of averages, and the accuracy of numerical discretizations. Formulations of the equations of motion which are suited to both equilibrium and nonequilibrium simulation include Langevin dynamics, dissipative particle dynamics (DPD), and the more recently proposed "pairwise adaptive Langevin" (PAdL) method, which, like DPD but unlike Langevin dynamics, conserves momentum and better matches the relaxation rate of orientational degrees of freedom. PAdL is easy to code and suitable for a variety of problems in nonequilibrium soft matter modeling; our simulations of polymer melts indicate that this method can also provide dramatic improvements in computational efficiency. Moreover we show that PAdL gives excellent control of the relaxation rate to equilibrium. In the nonequilibrium setting, we further demonstrate that while PAdL allows the recovery of accurate shear viscosities at higher shear rates than are possible using the DPD method at identical timestep, it also outperforms Langevin dynamics in terms of stability and accuracy at higher shear rates.

Ductile Glass of Polyrotaxane Toughened by Stretch-Induced Intramolecular Phase Separation

A new class of ductile glasses is created from a thermoplastic polyrotaxane. The hard glass, which has a Young's modulus of 1 GPa, shows crazing, necking, and strain hardening with a total elongation of 330%. Stress concentration is prevented through a unique stretch-induced intramolecular phase separation of the cyclic components and the exposed backbone. In situ synchrotron X-ray scattering studies indicate that the backbone polymer chains slip through the cyclic components in the regions where the stress is concentrated.

Role of the Intercrystalline Tie Chains Network in the Mechanical Response of Semicrystalline Polymers

We examine the microscopic origin of the tensile response in semicrystalline polymers by performing large-scale molecular dynamics simulations of various chain lengths. We investigate the microscopic rearrangements of the polymers during tensile deformation and show that the intercrystalline chain connections known as tie chains contribute significantly to the elastic and plastic response. These results suggest that the mechanical behavior of semicrystalline polymers is controlled by two interpenetrated networks of entanglements and tie chains.

Mechanisms of Contact, Adhesion, and Failure of Metallic Nanoasperities in the Presence of Adsorbates: Toward Conductive Contact Design

The properties of contacting interfaces are strongly affected not only by the bulk and surface properties of contacting materials but also by the ubiquitous presence of adsorbed contaminants. Here, we focus on the properties of single asperity contacts in the presence of adsorbates within a molecular dynamics description of metallic asperity normal contact and a parametric description of adsorbate properties. A platinum-platinum asperity contact is modeled with adsorbed oligomers with variable properties. This system is particularly tailored to the context of nanoelectromechanical system (NEMS) contact switches, but the results are generally relevant to metal-metal asperity contacts in nonpristine conditions. Even though mechanical forces can displace adsorbate out of the contact region, increasing the adsorbate layer thickness and/or adsorbate/metal adhesion makes it more difficult for metal asperity/metal surface contact to occur, thereby lowering the electrical contact conductance. Contact separation is a competition between plastic necking in the asperity or decohesion at the asperity/substrate interface. The mechanism which operates at a lower tensile stress dominates. Necking dominates when the adsorbate/metal adhesion is strong and/or the adsorbate layer thickness is small. In broad terms, necking implies larger asperity deformation and mechanical work, as compared with decohesion. Optimal NEMS switch performance requires substantial contact conductance and minimal asperity deformation; these results indicate that these goals can be achieved by balancing the quantity of adsorbates and their adhesion to the metal surface.

Molecular dynamics simulations of uniaxial deformation of thermoplastic polyimides

The results of atomistic molecular-dynamics simulations of mechanical properties of heterocyclic polymer subjected to uniaxial deformation are reported. A new amorphous thermoplastic polyimide R-BAPO with a repeat unit consisting of dianhydride 1,3-bis-(3',4,-dicarboxyphenoxy)diphenyl (dianhydride R) and diamine 4,4'-bis-(4''-aminophenoxy)diphenyloxide (diamine BAPO) was chosen for the simulations. Our primary goal was to establish the impact of various factors (sample preparation method, molecular mass, and cooling and deformation rates) on the elasticity modulus. In particular, we found that the elasticity modulus was only slightly affected by the degree of equilibration, the molecular mass and the size of the simulation box. This is most likely due to the fact that the main contribution to the elasticity modulus is from processes on scales smaller than the entanglement length. Essentially, our simulations reproduce the logarithmic dependence of the elasticity modulus on cooling and deformation rates, which is normally observed in experiments. With the use of the temperature dependence analysis of the elasticity modulus we determined the flow temperature of R-BAPO to be 580 K in line with the experimental data available. Furthermore, we found that the application of high external pressure to the polymer sample during uniaxial deformation can improve the mechanical properties of the polyimide. Overall, the results of our simulations clearly demonstrate that atomistic molecular-dynamics simulations represent a powerful and accurate tool for studying the mechanical properties of heterocyclic polymers and can therefore be useful for the virtual design of new materials, thereby supporting cost-effective synthesis and experimental research.

The Influence of Crosslink Density on the Failure Behavior in Amorphous Polymers by Molecular Dynamics Simulations

The crosslink density plays a key role in the mechanical response of the amorphous polymers in previous experiments. However, the mechanism of the influence is still not clear. In this paper, the influence of crosslink density on the failure behavior under tension and shear in amorphous polymers is systematically studied using molecular dynamics simulations. The present results indicate that the ultimate stresses and the broken ratios (the broken bond number to all polymer chain number ratios) increase, as well as the ultimate strains decrease with increasing crosslink density. The strain concentration is clearer with the increase of crosslink density. In other words, a higher crosslink density leads to a higher strain concentration. Hence, the higher strain concentration further reduces the fracture strain. This study implies that the mechanical properties of amorphous polymers can be dominated for different applications by altering the molecular architecture.

Stress–strain behavior of block-copolymers and their nanocomposites filled with uniform or Janus nanoparticles under shear: a molecular dynamics simulation

We adopted molecular dynamics simulation to study the relation between the ordered structures and the resulting mechanical properties of block copolymers filled with uniform or Janus nanoparticles.

Polystyrene Glasses under Compression: Ductile and Brittle Responses

Polystyrene of different molecular weights and their binary mixtures are studied in terms of their various mechanical responses to uniaxial compression at different temperatures. PS of M_w = 25 kg/mol is completely brittle until it is above its glass transition temperature T_g. In contrast, upon incorporation of a high molecular weight component, PS mixtures turn from barely ductile a few degrees below its T_g to ductile over 40° below T_g. In the upper limit, a PS of M_w = 319 kg/mol yields and undergoes plastic flow, even at T = -70 °C. The observed dependence of mechanical responses on molecular weight and molecular weight distribution can be adequately rationalized by the idea that yielding and plastic compression are caused by chain networking.

Elasticity and plasticity in stiff and flexible oligomeric glasses

In this paper we focus on the mechanical properties of oligomeric glasses (waxes), employing a microscopic model that provides, via numerical simulations, information about the shear modulus of such materials, the failure mechanism via plastic instabilities, and the geometric responses of the oligomers themselves to a mechanical load. We present a microscopic theory that explains the numerically observed phenomena, including an exact theory of the shear modulus and of the plastic instabilities, both local and system spanning. In addition we present a model to explain the geometric changes in the oligomeric chains under increasing strains.

Strain Hardening During Uniaxial Compression of Polymer Glasses

The origin of high mechanical stresses in large deformation of polymer glasses has been elusive because both plasticity and elasticity take place. In this work on the nature of the mechanical responses, we carry out uniaxial compression experiments to make simultaneous mechanical and thermal measurements of polycarbonate. Our results confirm that two factors contribute to the growing mechanical stress in the post-yield regime, which is known as "strain hardening". Besides plastic deformation that is intersegmental in origin, chain tension as an intrasegmental component contributes considerably to the measured stress in post-yield. Such a conclusion modifies the previous consensus regarding the nature of strain hardening in mechanical deformation of polymer glasses.

Coarse-grained molecular dynamics simulations of the tensile behavior of a thermosetting polymer

Using a previously developed coarse-grained model, we conducted large-scale (∼ 85 × 85 × 85 nm(3)) molecular dynamics simulations of uniaxial-strain deformation to study the tensile behavior of an epoxy molding compound, epoxy phenol novolacs (EPN) bisphenol A (BPA). Under the uniaxial-strain deformation, the material is found to exhibit cavity nucleation and growth, followed by stretching of the ligaments separated by the cavities, until the ultimate failure through ligament scissions. The nucleation sites of cavities are rather random and the subsequent cavity growth accounts for much (87%) of the volumetric change during the uniaxial-strain deformation. Ultimate failure of the materials occurs when the cavity volume fraction reaches ∼ 60%. During the entire deformation process, polymer strands in the network are continuously extended to their linear states and broken in the postyielding strain hardening stage. When most of the strands are stretched to their taut configurations, rapid scission of a large number of strands occurs within a small strain increment, which eventually leads to fracture. Finally, through extensive numerical simulations of various loading conditions in addition to uniaxial strain, we find that yielding of the EPN-BPA can be described by the pressure-modified von Mises yield criterion.

Healing of polymer interfaces: Interfacial dynamics, entanglements, and strength

Self-healing of polymer films often takes place as the molecules diffuse across a damaged region, above their melting temperature. Using molecular dynamics simulations we probe the healing of polymer films and compare the results with those obtained for thermal welding of homopolymer slabs. These two processes differ from each other in their interfacial structure since damage leads to increased polydispersity and more short chains. A polymer sample was cut into two separate films that were then held together in the melt state. The recovery of the damaged film was followed as time elapsed and polymer molecules diffused across the interface. The mass uptake and formation of entanglements, as obtained from primitive path analysis, are extracted and correlated with the interfacial strength obtained from shear simulations. We find that the diffusion across the interface is significantly faster in the damaged film compared to welding because of the presence of short chains. Though interfacial entanglements increase more rapidly for the damaged films, a large fraction of these entanglements are near chain ends. As a result, the interfacial strength of the healing film increases more slowly than for welding. For both healing and welding, the interfacial strength saturates as the bulk entanglement density is recovered across the interface. However, the saturation strength of the damaged film is below the bulk strength for the polymer sample. At saturation, cut chains remain near the healing interface. They are less entangled and as a result they mechanically weaken the interface. Chain stiffness increases the density of entanglements, which increases the strength of the interface. Our results show that a few entanglements across the interface are sufficient to resist interfacial chain pullout and enhance the mechanical strength.

Structure and Strength at Immiscible Polymer Interfaces

Thermal welding of polymer-polymer interfaces is important for integrating polymeric elements into devices. When two different polymers are joined, the strength of the weld depends critically on the degree of immiscibility. We perform large-scale molecular dynamics simulations of the structure-strength relation at immiscible polymer interfaces. Our simulations show that immiscibility arrests interdiffusion and limits the equilibrium interfacial width. Even for weakly immiscible films, the narrow interface is unable to transfer stress upon deformation as effectively as the bulk material, and chain pullout at the interface becomes the dominant failure mechanism. This greatly reduces the interfacial strength. The weak response of immiscible interfaces is shown to arise from an insufficient density of entanglements across the interface. We demonstrate that there is a threshold interfacial width below which no significant entanglements can form between opposite sides to strengthen the interface.