Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_{e} which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for N_{e} from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.

ABSTRACT:The strain hardening behavior of model polymer glasses is studied with simulations over a wide range of entanglement densities, temperatures, strain rates, and chain lengths. Entangled polymers deform affinely at scales larger than the entanglement length as assumed in entropic network models of strain hardening. The dependence of strain hardening on strain and entanglement density is also consistent with these models, but the temperature dependence has the opposite trend. The dependence on temperature, rate, and interaction strength can instead be understood as reflecting changes in the flow stress. Microscopic analysis of local rearrangements and the primitive paths between entanglements is used to test models of strain hardening.

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results. There is a substantial energetic contribution to the stress that rises rapidly as segments between entanglements are pulled taut. The thermal component of stress is less sensitive to entanglements, mostly irreversible, and directly related to the rate of local plastic arrangements. Entangled and unentangled chains show the same strain hardening when plotted against the microscopic chain orientation rather than the macroscopic strain.The stress needed to deform a polymer glass increases as the strain rises. This strain hardening plays a critical role in stabilizing polymers against strain localization and fracture, and reduces wear [1]. While models have had some success in fitting experimental data, fundamental inconsistencies in fit parameters and trends imply that our understanding of the microscopic origins of strain hardening is far from complete.Most theories of strain hardening [2,3] are based on rubber elasticity theory [4]. These entropic network models assume that polymer glasses behave like crosslinked rubber, with the number of monomers between crosslinks equal to the entanglement length N e . The increase in the stress σ due to deformation by a stretch tensorλ is attributed to the decrease in entropy as polymers are stretched between affinely displaced entanglements. One finds [3]where σ 0 is the yield or plastic flow stress, G R is the strain hardening modulus, L −1 is the inverse Langevin function, g(λ) describes the entropy reduction for Gaussian chains, and L −1 (h)/3h corrects for the finite length of segments between entanglements. The value of N e enters in h, which is the ratio of the Euclidean distance between entanglements to the contour length.Stress-stretch curves for a wide variety of glassy polymers can be fit to Eq. 1, but the fit parameters are not consistent with the microscopic picture underlying entropic network models [5]. For example, values of N e from fitting h may be several times smaller than those obtained from the plateau modulus G 0 N [3]. Entropic network models predict G R ≈ G 0 N near T g , but measured G R are about 100 times larger [6]. G R also rises as T decreases [6,7], while any entropic stress must drop to zero as T → 0 [5]. Recent work [7,8] shows that changes in G R correlate with those in the plastic flow stress. Indeed entire stress-stretch curves collapse when normalized by σ 0 [7]. This is not expected from entropic models, where σ 0 is treated as an independent parameter arising from local plasticity. A more conceptual difficulty in entropic models is that, unlike rubber, glasses are not able to dynamically sample chain conformations.In this Letter we use simulations to examine the microscopic origins of strain hardening. While our results for the total stress can be fit to Eq. 1, network models are not consistent with ...

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only observed in shape recovery of deformed samples when heated above the glass transition. While short chains do not form an entangled network, they exhibit partial shape recovery, orientation, and strain hardening. Stresses for all chain lengths collapse when plotted against a microscopic measure of chain stretching rather than the macroscopic stretch. The thermal contribution to the stress is directly proportional to the rate of plasticity as measured by breaking and reforming of interchain bonds. These observations suggest that the correct microscopic theory of strain hardening should be based on glassy state physics rather than rubber elasticity.

Hybrid molecular dynamics/Monte Carlo simulations are used to study melts of unentangled, thermoreversibly associating supramolecular polymers. In this first of a series of papers, we describe and validate a model that is effective in separating the effects of thermodynamics and chemical kinetics on the dynamics and mechanics of these systems, and is extensible to arbitrarily nonequilibrium situations and nonlinear mechanical properties. We examine the model's quiescent (and heterogeneous) dynamics, nonequilibrium chemical dynamics, and mechanical properties. Many of our results may be understood in terms of the crossover from diffusion-limited to kinetically-limited sticky bond recombination, which both influences and is influenced by polymer physics, i. e. the connectivity of the parent chains.

It has recently been proposed that the miscibility of nanoparticles with a polymer matrix can be controlled by grafting polymer chains to the nanoparticle surface. As a first step to study this situation, we have used molecular dynamics simulations on a single nanoparticle of radius R (4σ ≤R≤ 16σ , where σ is the diameter of a polymer monomer) grafted with chains of length 500 in a polymer melt of chains of length 1000. The grafting density Σ was varied between 0.04-0.32 chains/σ 2 . To facilitate equilibration a Monte Carlo doublebridging algorithm is applied -new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. For the long brush chains studied here, the structure of the brush assumes its large particle limit even for R as small as 8σ , which is 1 consistent with recent experimental findings. We study autophobic dewetting of the melt from the brush as a function of increasing Σ. Even these long brush and matrix chains of length 6 and 12 N e , respectively, (the entanglement length is N e ∼ 85) give somewhat ambiguous results for the interfacial width, showing that studies of two or more nanoparticles are necessary to properly understand these miscibility issues. Entanglement between the brush and melt chains were identified using the primitive path analysis. We find that the number of entanglements between the brush and melt chains scale simply with the product of the local monomer densities of brush and melt chains.

We analyze the entanglement of polymer brushes embedded in long-chain melts and in good and ϑ solvents. Individual entanglements are identified using a modified version of primitive path analysis. Due to entropic collapse, the brushes embedded in the melt are more self-entangled than those in the implicit solvents. The self-entanglement of the brushes in the good and ϑ solvents as a function of coverage follows a simple scaling argument. We observe a depletion of entanglements near the systems' confining walls and offer several possible explanations. In the melt-embedded systems, the brushes entangle predominantly with the melt at low coverage and with themselves at high coverage. The peak of the brush−melt entanglement density is highest at an intermediate coverage, but the integrated areal brush−melt entanglement density continues to increase with coverage for the studied systems. This areal density correlates well with earlier measurements of the work of adhesion.

Polymer cold-drawing is a process in which tensile stress reduces the diameter of a drawn fibre (or thickness of a drawn film) and orients the polymeric chains. Cold-drawing has long been used in industrial applications, including the production of flexible fibres with high tensile strength such as polyester and nylon. However, cold-drawing of a composite structure has been less studied. Here we show that in a multimaterial fibre composed of a brittle core embedded in a ductile polymer cladding, cold-drawing results in a surprising phenomenon: controllable and sequential fragmentation of the core to produce uniformly sized rods along metres of fibre, rather than the expected random or chaotic fragmentation. These embedded structures arise from mechanical-geometric instabilities associated with 'neck' propagation. Embedded, structured multimaterial threads with complex transverse geometry are thus fragmented into a periodic train of rods held stationary in the polymer cladding. These rods can then be easily extracted via selective dissolution of the cladding, or can self-heal by thermal restoration to re-form the brittle thread. Our method is also applicable to composites with flat rather than cylindrical geometries, in which case cold-drawing leads to the break-up of an embedded or coated brittle film into narrow parallel strips that are aligned normally to the drawing axis. A range of materials was explored to establish the universality of this effect, including silicon, germanium, gold, glasses, silk, polystyrene, biodegradable polymers and ice. We observe, and verify through nonlinear finite-element simulations, a linear relationship between the smallest transverse scale and the longitudinal break-up period. These results may lead to the development of dynamical and thermoreversible camouflaging via a nanoscale Venetian-blind effect, and the fabrication of large-area structured surfaces that facilitate high-sensitivity bio-detection.