Computer Simulation of Creep and Fracture of Highly Drawn Polymers

Abstract

A computer kinetic model was proposed describing creep and fracture of the microfibrilla in the drawn semicrystalline polymer and allowing for the concurrent and interrelated processes of slippage of polymer chains, redistribution of the polymer units between the amorphous regions and chains scissions. A self-consistent system of non-linear kinetic equations for tie chains length distribution function was written and its numerical analysis was made with a computer. As a result, a stress-strain curve for a single microfibrilla and an averaged curve for a high drawn polymer fiber were obtained. Also a portion of tie chains scissions and the concentration of defects in crystallites as a function of fiber deformation were obtained.     

Molecular dynamics simulation of hydroxyapatite–polyacrylic acid interfaces

Polymer–hydroxyapatite (HAP) composites are widely studied as potential bone replacement materials. The HAP–polymer interfacial molecular interactions have significant role on the mechanical response of composite systems. We have used molecular dynamics (MD) simulations to evaluate the nature of these interfaces in polyacrylic acid–hydroxyapatite composites. We have obtained the parameters for monoclinic hydroxyapatite in CVFF (consistent valence force field) from the known potential energy function of apatites. Our simulations indicate that potential sites for chelation and hydrogen bond formation between HAP and polyacrylic acid (PAAc) exist. Earlier, we have synthesized in situ HAP–polymer composites wherein intimate interaction between HAP and polymer is enabled through participation of polymer during HAP mineralization. Our simulations indicate that for in situ HAP, the most favorable orientation of PAAc for attachment with HAP is along the c-axis of HAP aligned parallel to polymer chains. Also, binding energy for ex situ HAP composites is found to be lower as compared to that of in situ HAP.     

Influence of Mechanical Vitrification on Flexible-Chain Polymer Drawing Process

Abstract

Factors, responsible for orientation interruption and polymer fracture under drawing are discussed in terms of molecular mobility. Mechanical vitrification, i.e. inhibition of micro-Brownian motion of chains during deformation and especially under tensile stress is considered to be the main physical factor limiting orientation processes. Broad-line NMR was used to study molecular motion in stretched polymers at different temperatures. Stretching results in the growth of virtual glass transition temperature and thereby in a dramatic deterioration in draw conditions. A simple theoretical model was used to describe the molecular dynamic processes in polymer under load. In this model nonvitrified regions of polymer were considered as the Newton liquid whose weight fraction was equal to the mobile fraction measured by NMR. The equation to describe the dynamics of the orientation process was proposed and specifically solved for nylon-6. The obtained diagrams enable one to choose optimal conditions for drawing. Instances when the draw process should be carried out in two or more steps are discussed.     

Role of entanglements and bond scission in high strain-rate deformation of polymer gels

A key factor that limits the practical implementation of polymer gels is low gel toughness. Here, we present coarse-grained molecular dynamics simulations of the effects of solvent molecular weight on the toughness of entangled and non-entangled polymer gels in the ballistic impact regime. Our results demonstrate that higher molecular weight solvents enhance gel toughness, and that mechanical properties including strength and toughness can be influenced by bond scission. Further, we find a remarkable two-step gel fracture mechanism on the molecular level: network chains undergo scission first (and well before fracture), followed by scission of solvent chains. For strain rates greater than inverse relaxation time of the solvent, long, highly entangled solvent chains provide fracture resistance even after the network chains break by effectively increasing the number of chains that must be broken as a crack propagates.     

平均吸引势模型状态方程用于固体在超临界流体中溶解度的计算

基于膨胀液体概念，把超临界流体看作是被气体膨胀了的液体，并假设体系的分子吸引势为范德华气体和凝聚液体吸引势的体积平均值、导出了一个平均吸引势模型状态方程。该方程较好地关联了纯溶剂蒸汽压及超临界二氧化碳的Ｐ－Ｖ－Ｔ关系；并关联了１４种固体溶质在超临界二氧化碳中的溶解度数据，结果优于ＲＫ、ＳＲＫ及ＰＲ方程。     

Damage of unfilled crosslinked rubbers as the scission of polymer chains: Modeling and tensile experiments

This article develops a damage model for unfilled crosslinked rubbers based on the concept of scission of polymer chains. The model is built up on the well‐known Gent elastic potential complemented by a kinetic equation describing effects of polymer chain scission. The macroscopic parameters in the damage model are evaluated through the parameters for undamaged elastomer. Qualitative analysis of changing molecular parameters of rubbers under scission of polymer chains resulted in easy scaling modeling the dependences of these parameters on the damage factor. It makes possible to predict the rubber failure in molecular terms as mechanical devulcanization. The model was tested in tensile quasistatic experiments with both the monotonous loading and repeated loading–unloading. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Molecular dynamics simulation of a flexible polymer network in a liquid crystalline solvent; dynamical properties

Molecular dynamics simulation was performed for the systems consisting of a flexible regular tetrafunctional polymer network and a low molecular liquid crystal (LC) solvent. The LC solvent comprises of anisotropic rod-like semiflexible linear molecules composed of beads bonded by a FENE potential. Rigidity was induced by a bending potential, proportional to the cosine of the angle between neighbouring valence bonds. All interactions between non-bonded beads are described by the repulsive part of the Lennard–Jones potential. For comparison the simulations of the system of flexible polymer chains in a low molecular LC solvent and a system of pure low molecular LC solvent were also carried out. The influence of the network and linear chain polymer on the translational and rotational mobility of low molecular LC solvent was studied. The influence of the LC solvent ordering on the local translational mobility of the polymer chains was also observed.     

Effect of ultrasound on the viscoelasticity and rheology of polystyrene extruded through a slit die

The rheological and processing behavior (melt fracture performance) of polystyrene extruded through a slit die is studied as a function of the ultrasound vibration intensity. The apparent viscosity reduces 29% and die pressure reduces 22% compared with that without ultrasound vibration. The viscosity of the melt decreases exponentially as ultrasound intensity increases and an Arrhenius equation fits the data well. Ultrasound vibration also leads to a decrease of the die swell ratio and a postponement of melts fracture. Characteristic relaxation times at the onset of melt fracture are calculated according to the hypothesis that the melt fracture behavior of a polymer is affected by a balance between its viscous (viscosity) and elastic properties (recoverable shear). Ultrasound vibration shortens the relaxation time of polystyrene molecular chains. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2907–2911, 2006     

A lattice‐fluid,group‐contribution treatment of the glass transition of homopolymers,copolymers, and polymer solutions

The glass transition temperature of polymers and polymer solutions was approached through a combination of the group‐contribution, lattice‐fluid equation of state and the Gibbs–DiMarzio criterion. The model assumes zero entropy at the glass transition temperature and treats molecules as semiflexible chains. This stiffness is associated with a flex energy obtained from the glass transition temperature at atmospheric pressure. Whereas the application of the model is straightforward for homopolymers and polymer solutions, a new formalism using the dyad concept was developed for copolymers. It takes into account the copolymer composition as well as the sequencing of the monomers. The results obtained are consistent with experimental data. For polymer solutions, the model predictions are semiquantitative depending on the system. The interaction parameter required for binary systems was found to have little effect on the glass transition temperature predictions. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 697–705, 2003     

Polymer chains in semidilute solutions confined to a square channel: mean-field Gaussian chain theory and comparison with simulation results

We extend the mean-field Gaussian chain theory, originally developed for non-dilute solutions of athermal polymer chains in a slit, to solutions in a channel with a square cross section. The formulation allows one to calculate the monomer density profile, the chemical potential of the confined polymer chain, and therefore the partition coefficient. For the mean-field potential, we used the first-order approximation that neglects local monomer density fluctuations and the second-order approximation that takes into account the fluctuations. The results of the density profile and the partition coefficient were compared with those obtained in the lattice Monte Carlo simulations. The theoretical results obtained with the first-order approximation agreed well with the simulation results for chains of 100 beads below the average monomer density of ca. 0.2. At higher concentrations, the second-order results gave a better agreement. This cross over indicates a change in the interactions between polymer chains from those in one-dimension to those in three-dimensions as the correlation length in the confined solution becomes sufficiently shorter than the channel width.     

The mechanism of cavitation-induced polymer scission; experimental and computational verification

In this paper we describe qualitatively and quantitatively the non-random scission of polymers by ultrasound. Scission experiments have been performed using monodisperse polymethyl methacrylate dissolved in methyl methacrylate, showing that fracture occurs close to the center of the polymer chain. A mechanism is proposed for this non-random fracture, from which it can be concluded that complete stretching of the polymer chains is required before breakage can occur. The developed model, which is a combination of strain rate and drag force calculations, predicts a limiting molecular weight, which has experimentally been confirmed. The scission rate depends almost quadratically on the molecular weight, which is derived by modeling the experimental time-dependent molecular weight distributions. This dependence supports the requirement of complete stretching of the polymer chain before breakage. The developed degradation model is also capable to describe the effects of various process variables on cavitation-induced polymer scission.     

粘弹性流体非等温本构方程

本文将Giesekus提出的单模式平均构型分子模型推广到非等温情形,然后利用人们熟知的粘温关系式来计及温度和热历史对应力张量的影响,得到一个描述聚合物浓溶液和熔体非等温流变性质的本构方程,不必在分子模型中引入人为的假定来考虑非等温效应.对于非等温应力发展的计算表明,这一本构方程能避免以前研究者提出的本构方程的缺点,合理地描述聚台物流体的非等温流变性质.     

Advances in molecular design and synthesis of regioregular polythiophenes

Regioregular poly(3-alkylthiophene)s (rrP3ATs) are an important class of pi-conjugated polymers that can be used in plastic electronic devices such as solar cells and field-effect transistors. rrP3ATs can be ordered in three dimensions: conformational ordering along the backbone, pi-stacking of flat polymer chains, and lamellar stacking between chains. All of these features lead to the excellent electrical properties of these materials. Creative molecular design and advanced synthesis are critical in controlling the properties of the materials as well as their device performance. This Account reports the advances in molecular design of new functional polythiophenes as well as the associated polymerization methods. Many functionalized regioregular polythiophenes have been designed and synthesized and show fascinating properties such as high conductivity, mobility, chemosensitivity, liquid crystallinity, or chirality. The methods for the synthesis of rrP3ATs are also applicable to other functional side chains. Di- and triblock copolymers consisting of rrP3AT and polyacrylate or polystyrene have also been successfully synthesized, which can facilitate the assembly of the polythiophene segments. The synthesis of rrP3ATs has evolved into a simple and economical system in which the synthesis can be carried out quickly at room temperature and is thus suitable for large-scale manufacturing. Intensive study has revealed that the regioregular polymerization of 3-alkylthiophenes proceeds by a chain-growth mechanism and can be made into a living system. This feature enables precise control of the molecular weight and facile end-group functionalization of the polymer chains, leading to tailor-made regioregular polythiophenes for specific applications. In addition, researchers have recently designed and synthesized regiosymmetric polythiophenesthese are regioregular but not coupled in a head-to-tail fashionby various methods. These reports indicate that these regiosymmetric polymers show very high mobilities when used in field-effect transistors due to their highly ordered structure. The remarkable performance of regioregular polythiophenes in recent years has allowed for the rapid development in printable electronics and seems destined to lead to further advances in this field.     

A molecular dynamics study of the effect of ethyl branches on the orthorhombic structure of polyethylene

Molecular dynamics computer simulations are presented for polyethylene crystals containing ethyl branches. The crystals are simulated using an all-atom (explicit hydrogen) molecular mechanics force field. The effect of the branches in expanding the crystalline unit cell is demonstrated for a range of branch densities. We compare the behaviour of two types of model, each consisting of arrays of 48 chains. In the first, the polyethylene chains are effectively infinite in length, by virtue of the periodic boundary conditions, which link the polymer chains across the faces of the simulation box. In the second model, we simulate long n-alkanes. Two different chain lengths are considered, containing 24 or 48 carbon atoms. By examining the individual torsional angles and the setting angles of each segment of each chain, it is possible to demonstrate that branches are incorporated into the unit cell without the introduction of gauche defects in the polymer backbones. The effect of large numbers of branches is to expand the cell to such an extent that a mobile rotator phase is induced i.e. the system forms a dynamic rotationally disordered crystal in which chain sliding occurs readily. Although such high branch densities in the crystalline phase are not accessible experimentally, the prediction of a mesophase is interesting, because it may have implications for crystallisation. For example, the mesophase could occur transiently during crystallisation, as has been suggested for linear chains, and it would fulfil the dual role of allowing the growing crystals to thicken, and providing the branches with the opportunity to diffuse out of the crystal.     

‘Nano-tree’—type spherical polymer brush particles as templates for metallic nanoparticles

We present a new type of spherical polymer brush particles that consist of a solid poly(styrene) core (diameter: ca. 100 nm) onto which chains of a bottlebrush polymer have been densely grafted. These systems were prepared in aqueous dispersion by photo emulsion-polymerization using the macromonomer poly(ethylene glycol) methacrylate (PEGMA). In opposite to conventional spherical polyelectrolyte brushes carrying linear polymer chains, the system prepared here has a shell consisting of regularly branched chains (‘nano-tree’-type morphology). The branches consist of oligo(ethylene glycol) chains (n=13) terminated by a hydroxyl group. We demonstrate that these particles can be used as nanoreactors for the generation and immobilization of well-defined silver nanoparticles. Cryo-TEM and FESEM images show that Ag nanoparticles with diameter of ∼7.5±2 nm are homogeneously embedded into the PS-PEGMA brushes. Moreover, the composite particles exhibit an excellent colloidal stability. The catalytic activity is investigated by monitoring the reduction of 4-nitrophenol by NaBH₄ in presence of these silver nano-composite particles. The rate constant k_app was found to be strictly proportional to the total surface of the nanoparticles in the system. The study of the temperature dependence shows that the rate constants k_app obtained at different temperatures leads to an activation energy of 62 kJ/mol.     

Effects of polydispersity on critical concentration of polymer solutions

A semiempirical equation is developed to compute the unperturbed parameter from the critical concentration of polymer solutions derived from the viscometric and kinetic data. This equation gives satisfactory results for various vinyl polymers including poly(vinyl chloride), polystyrene and poly(methyl methacrylate) among others that follow the Schulz molecular weight distribution function. It is found that the segments of a Gaussian polymer chain are associated with an equal number of foreign segments near its center of mass, when the polymer solution has attained a uniform segment density at the critical concentration. The effect of molecular weight distribution on the present studies is significantly large that it merits an empirical treatment. Defects of the model is also discussed.     

Steady-state behavior of star polymers in dilute flowing solutions via Brownian dynamics

A bead and spring model is considered for the Brownian dynamics simulation of the behavior of regular star polymer chains in a dilute solution under both shear flow and extensional (or elongational) flow. Finite extensibility, excluded volume, and hydrodynamic interaction are taken into account to make the polymer model as realistic as possible. The behavior of star-like chains in flow is similar to that of linear and ring polymers. Thus, dependence of a given property with the arm molecular weight is analogous to that found for linear polymers when using the total molecular weight. In shear flow, the deformation of the chain and the shear rate viscosity dependence (the flow curve), are studied. We find a slope for the shear-thinning region of the flow curve close to −2/3. In elongational flow the coil-stretch transition is characterized by giving the relationship between the critical elongational rate and the arm molecular weight, which turns out to be similar to the power law found in linear chains.     

Molecular dynamics simulation of a flexible polymer network in a liquid crystal solvent; structure and equilibrium properties

A flexible regular tetrafunctional polymer network containing a low molecular liquid crystal (LC) solvent was simulated with molecular dynamics. The LC solvent comprises of anisotropic rod-like semi-flexible linear molecules composed of beads bonded by a FENE potential. Flexibility was induced by a bending potential proportional to the cosine of the angle between neighbouring valence bonds. All interactions between non-bonded beads are described by the repulsive part of the Lennard-Jones potential. The average length of the network chain was chosen to be close to the length of a mesogen. The number of network cells was constant and the simulated systems differ from each other by the number of LC layers. The simulations of a system of flexible polymer chains in a low molecular LC solvent and a system of pure low molecular LC solvent were also carried out. Increasing the density of the composite system the LC solvent experiences the same phase transition as the pure LC: isotropic, nematic and smectic. The presence of the network shifts the isotropic-nematic transition to higher densities but does not significantly change the position of nematic-smectic transition. Transition of the LC solvent into the smectic state changes the morphology of the network. The periodicity of LC phase determines the number of network layers. The presence of linear chains in the LC solvent decreases the number of LC layers in the smectic phase.The LC order induces some stretching of the network chains along the direction of orientation and at the same time causes shrinkage in the perpendicular direction especially in the smectic phase.     

Optothermal properties of fibers. VIII. Structure orientation study of annealed Egyptian polyester fibers

A two-beam interferometric method is used to study the change of optical orientation functions and the molecular structure of annealed Egyptian poly(ethylene terephthalate) (PET) fibers. The acoustic method was used for measuring the density. The density results were used to calculate the degree of crystallinity of PET. It was found that annealing causes alignment to the fiber chains in the directions of the fiber axis. This alignment gives an increase in the optical orientation function and decrease in orientation angle. The value of Δα/3α₀, which depends upon the molecular structure of the polymer, remains constant. The obtained results of the optical and the density clarify that new reorientations occurred due to annealing at different conditions. The changes of the refractive index profile of annealed PET fibers are given. Microinterferograms and curves are given for illustration. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 2031–2050, 1997     

Effect of chain length and molecular architecture on the second virial coefficient of branched polymer molecules

The effects of chain length and molecular architecture on the second virial coefficient of branched polymer chains has been studied using a perturbation analysis. It is found that the deviation from the infinite chain length asymptote increases as the degree of branching increases for chains having less than about 100 statistical segments. A semi-empirical equation is proposed for higher values of the interaction parameter, z.