Fracture in glassy polymers: a molecular modeling perspective

Unexpected Ductility in Semiflexible Polymer Glasses with Entanglement Length Equal to Their Kuhn Length

Semiflexible polymer glasses (SPGs), including those formed by the recently synthesized semiflexible conjugated polymers, are expected to be brittle because classical formulas for their craze extension ratio λ_{craze} and fracture stretch λ_{frac} predict that systems with N_{e}=C_{∞} have λ_{craze}=λ_{frac}=1 and hence cannot be deformed to large strains. Using molecular dynamics simulations, we show that in fact such glasses can form stable crazes with λ_{craze}≃N_{e}^{1/4}≃C_{∞}^{1/4}, and that they fracture at λ_{frac}=(3N_{e}^{1/2}-2)^{1/2}≃(3C_{∞}^{1/2}-2)^{1/2}. We argue that the classical formulas for λ_{craze} and λ_{frac} fail to describe SPGs' mechanical response because they do not account for Kuhn segments' ability to stretch during deformation.

Fracture in Silica/Butadiene Rubber: A Molecular Dynamics View of Design-Property Relationships

Despite intense investigation, the mechanisms governing the mechanical reinforcement of polymers by dispersed nanoparticles have only been partially clarified. This is especially true for the ultimate properties of the nanocomposites, which depend on their resistance to fracture at large deformations. In this work, we adopt molecular dynamics simulations to investigate the mechanical properties of silica/polybutadiene rubber, using a quasi-atomistic model that allows a meaningful description of bond breaking and fracture over relatively large length scales. The behavior of large nanocomposite models is explored systematically by tuning the cross-linking, grafting densities, and nanoparticle concentration. The simulated stress-strain curves are interpreted by monitoring the breaking of chemical bonds and the formation of voids, up to complete rupture of the systems. We find that some chemical bonds, and particularly the S-S linkages at the rubber-nanoparticle interface, start breaking well before the appearance of macroscopic features of fracture and yield.

Uniaxial Deformation and Crazing in Glassy Polymer-Grafted Nanoparticle Ultrathin Films

The deformation behavior of neat, glassy polymer-grafted nanoparticle (PGN) monolayer films is studied using coarse-grained molecular dynamics simulations and experiments on polystyrene-grafted silica. In both the simulations and experiments, apparent crazing behavior is observed during deformation. The PGN systems show a relatively more uniform, perforated sheet craze structure and significantly higher strain at break than reference homopolymers of the same length. Short chain, unentangled PGN monolayers are also simulated for comparison; these are brittle and break apart without crazing. The entangled PGN simulations are analyzed in detail for systems at both high and moderate graft density. Stress-strain curves show three distinct regions: yielding and strain localization, craze widening, and strain hardening preceding catastrophic failure. The PGN stress-strain behavior appears more similar to that of longer chain, highly entangled homopolymer films than to the reference homopolymer films of the same length as the graft chains, suggesting that the particles effectively add additional entanglement points. The moderate graft density particles have higher strain-to-failure and maximum stress than the high graft density particles. We suggest this increased robustness for lower graft density systems is due to their increased interpenetration of graft chains between neighboring particles, which leads to increased interparticle entanglements per chain.

Entanglement Density-Dependent Energy Absorption of Polycarbonate Films via Supersonic Fracture

The fracture behavior of glassy polymers is strongly coupled to molecular parameters such as entanglement density as well as extrinsic parameters such as strain rate and test temperature. Here we use laser-induced projectile impact testing (LIPIT) to study the extreme strain rate (≈107 s-1) puncture behavior of free-standing polycarbonate (PC) thin films. We demonstrate that changes to the PC molecular mass and the degree of plasticization can lead to substantial changes in the specific puncture energy. We relate these changes to the alteration of the entanglement density of the polymer that determines the underlying failure mechanism as well as the size of the deformation zone.

Crystallization of finite-extensible nonlinear elastic Lennard-Jones coarse-grained polymers

The ability of a simple coarse-grained finite-extensible nonlinear elastic (FENE) Lennard-Jones (LJ) polymer model to be crystallized is investigated by molecular dynamics simulations. The optimal FENE Lennard-Jones parameter combinations (ratio between FENE and LJ equilibrium distances) and the optimal lattice parameters are calculated for five different perfect crystallite structures: simple tetragonal, body-centered tetragonal, body-centered orthorhombic, hexagonal primitive, and hexagonal close packed. It was found that the most energetically favorable structure is the body-centered orthorhombic. Starting with an equilibrated polymer liquid and with the optimal parameters found for the body-centered orthorhombic, an isothermal treatment led to the formation of large lamellar crystallites with a typical chain topology: folded, loop, and tie chains, and with a crystallinity of about 60%-70%, similar to real semicrystalline polymers. This simple coarse-grained Lennard-Jones model provides a qualitative tool to study semicrystalline microstructures for polymers.

Highly Transparent and Toughened Poly(methyl methacrylate) Nanocomposite Films Containing Networks of Cellulose Nanofibrils

Cellulose nanofibrils (CNFs) are a class of cellulosic nanomaterials with high aspect ratios that can be extracted from various natural sources. Their highly crystalline structures provide the nanofibrils with excellent mechanical and thermal properties. The main challenges of CNFs in nanocomposite applications are associated with their high hydrophilicity, which makes CNFs incompatible with hydrophobic polymers. In this study, highly transparent and toughened poly(methyl methacrylate) (PMMA) nanocomposite films were prepared using various percentages of CNFs covered with surface carboxylic acid groups (CNF-COOH). The surface groups make the CNFs interfacial interaction with PMMA favorable, which facilitate the homogeneous dispersion of the hydrophilic nanofibrils in the hydrophobic polymer and the formation of a percolated network of nanofibrils. The controlled dispersion results in high transparency of the nanocomposites. Mechanical analysis of the resulting films demonstrated that a low percentage loading of CNF-COOH worked as effective reinforcing agents, yielding more ductile and therefore tougher films than the neat PMMA film. Toughening mechanisms were investigated through coarse-grained simulations, where the results demonstrated that a favorable polymer-nanofibril interface together with percolation of the nanofibrils, both facilitated through hydrogen bonding interactions, contributed to the toughness improvement in these nanocomposites.

Age-dependent modes of extensional necking instability in soft glassy materials

We study the instability to necking of an initially cylindrical filament of soft glassy material subject to extensional stretching. By numerical simulation of the soft glassy rheology model and a simplified fluidity model, and by analytical predictions within a highly generic toy description, we show that the mode of instability is set by the age of the sample relative to the inverse of the applied extensional strain rate. Young samples neck gradually via a liquidlike mode, the onset of which is determined by both the elastic loading and plastic relaxation terms in the stress constitutive equation. Older samples fail at smaller draw ratios via a more rapid mode, the onset of which is determined only by the solidlike elastic loading terms (though plastic effects arise later, once appreciable necking develops). We show this solidlike mode to be the counterpart, for elastoplastic materials, of the Considère mode of necking in strain-rate-independent solids.

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.

Elastic yielding in cold drawn polymer glasses well below the glass transition temperature

This Letter reports elastic-driven internal yielding in strained ductile polymer glasses. After cold drawing of two different polymer glasses to neck at room temperature, we show that the samples display considerable retractive stress when warmed up above the storage temperature but still considerably below their glass transition temperatures. We conclude that the elastic yielding arises from the distortion of backbones leading to intra-segmental tension in the chain network.

Relaxation of non-equilibrium entanglement networks in thin polymer films

It is known that polymer films, prepared by spin coating, inherit non-equilibrium configurations which can affect macroscopic film properties. Here we present the results of crazing experiments that support this claim; our measurements indicate that the as-cast chain configurations are strongly stretched as compared to equilibrium Gaussian configurations. The results of our experiments also demonstrate that the entanglement network equilibrates on a time scale comparable to one reptation time. Having established that films can be prepared with an equilibrium entanglement network, we proceed by confining polymers to films in which the thickness is comparable to the molecular size. By stacking two such films, a bilayer is created with a buried entropic interface. Such an interface has no enthalpic cost, only an entropic penalty associated with the restricted configurations of molecules that cannot cross the mid-plane of the bilayer. In the melt, the entropic interface heals as chains from the two layers mix and entangle with one another; crazing measurements allow us to probe the dynamics of two films becoming one. Healing of the entropic interface is found to take less than one bulk reptation time.

Molecular dynamics simulation of rupture in glassy polymer bridges within filler aggregates

We present a series of nonequilibrium molecular dynamics simulations, investigating the rupture mechanisms in glassy polymer films confined between two solid surfaces. Such systems provide a useful model for the strong nonlinear reinforcement of rubber by colloidal filler particles. Depending on the degree of confinement three qualitatively different rupture modes have been found, which originate from the interplay of internal (polymer-polymer) and external (polymer-wall) interactions. In very thin films we observe the formation and stretching of many single-chain bridges between the confining surfaces. Progressing to thicker samples we observe fewer bridges, consisting of bundled polymer chains, and eventually just one large bridge in thick specimens. The yield stress and the elongational modulus of the polymer films have been calculated from the stress-strain curves at various temperatures and confinements and their behavior has been analyzed in terms of polymer-polymer and polymer-surface interaction energies. The thinnest films (5 monomer diameters) are always glassy in our simulations, while the others display a glass transition temperature around 0.50-0.55 (in units ε(0)/k(B) of the Lennard-Jones interaction energy), depending on their thickness. This range of values, which has been determined using both the nonequilibrium tensile simulations and equilibrium diffusion data, agrees with the transition temperature previously found by shear simulations [Baljon and Robbins, Science 271, 482 (1996)].