Localisation phenomena in glassy polymers: influence of thermal and mechanical history

The macroscopic deformation behaviour of amorphous polymers is dominated by localisation phenomena like necking and crazing. Finite element simulations show that the details of the intrinsic post-yield behaviour, strain softening and strain hardening, determine the severity of strain localisations. In order to perform these numerical simulations an accurate constitutive model is required. The compressible Leonov model is, for this purpose, extended to include temperature effects. Experimentally it is demonstrated that by a small increase in strain softening (by annealing of polycarbonate) or substantial decrease (by mechanical rejuvenation of polystyrene), transitions from ductile to brittle and, respectively, brittle to ductile can be realised. An analytical stability analysis is performed that predicts stable or unstable neck growth dependent on the ratio between yield stress and hardening modulus. The extensive simulations and experimental results lead to the conclusion that in order to macroscopically delocalise strain, and thus improve toughness, one has to reduce strain softening or enhance strain hardening, either by improving the intrinsic behaviour of polymers, or by creating an optimised micro-structure.     

RHEOLOGICAL BEHAVIOR OF POLYMER MELTS (Ⅰ)UNIFIED MOLECULAR THEORY OF NON-LINEAR ISCOELASTICITY WITH CONSTRAINTS OF GAUSSIAN CHAIN ENTANGLEMENT FOR POLYMER MELTS

An approach with statistical mechanics and a unified molecular theory of non-linearviscoelasticity with constraints of Gaussian chain entanglement for polymer melts were proposed.Amultimode model structure for a single polymer chain with tail segments and N reversibleentanglement sites on the test polymer chain was developed.The probability distribution function ofthe end-to-end vector for a single polymer chain at entangled state and the viscoelastic free energyof deformation for polymer melts were calculated.Four types of stress-strain relationship and mem-ory function were derived from this theory.The above theoretical relationships were verified by experi-mental data of PS(polystyrene)and LDPE(low density polyethylene)melts.     

Entanglement Loss in Fast-Flowing Entangled Polymer: Numerical Simulation of The Short-Chain Behavior and Interpretation of Phenomenology

Although some of the important consequences of flow-induced entanglement loss in entangled polymer rheology have recently been recognized, this specific molecular mechanism has rarely been investigated quantitatively based on experiments or molecular theories. For the first time, the amount of entanglement loss of a short entangled linear polymer (i.e., seven entanglements per chain at equilibrium) during fast-flow deformation is directly tracked in the stochastic simulation of an existing reptation model. The primary finding is that significant entanglement loss is observed in both fast elongation and fast shearing, and, contrary to some earlier conjectures, is particularly pronounced in elongational flow when polymer chain stretching formally commences. Furthermore, according to the current simulation in which three different CCR (Convective Constraint Release) schemes are considered, entanglement loss appears to have very prominent effects on the elongational rheology of an entangled linear polymer – an observation that had rarely been recognized or considered before. On the other hand, the currently explored features of flow-induced entanglement loss are tentatively linked to a wide variety of peculiar empirical properties of temporarily entangled polymer liquids. In particular, we are thus able to provide a consistent molecular explanation of the fairly well-known phenomenological effects of polydispersity and long-chain branching leading to a pronounced strain-hardening phenomenon, in view of two newly proposed effects of heterogeneous relaxations in preventing, directly or indirectly, fast entanglement loss during flows.     

Strain-induced crystallization of cis-1,4-polybutadiene containing dispersed 1,2-polybutadiene crystalline particles

Some grades of cis-1,4-polybutadiene contain dispersed crystalline particles made up of a block copolymer having amorphous cis-1,4- and crystalline 1,2 blocks. The particles are known to enhance the strain-induced crystallization of cis-1,4 matrix rubber. The deformational behavior was examined by dynamic shear measurements at small deformation and tensile stress–strain measurements at large deformation. In the shear measurements (linear behavior), the temperature dependence of the shift factor in the time-temperature superposition has been evaluated. The higher temperature dependence was observed for the lower crystalline particle content and higher degree of branching of the matrix rubber. The presence of the crystalline particles resulted in the viscosity enhancement like that expected from the dispersed particles. In the tensile measurements (non-linear behavior), the rubbers showed strain softening. The higher degree of strain softening was observed for the higher amount of the crystalline particles and lower degree of branching. The strain softening is a result of the crystalline particles facilitating the elongation. Because these particles posses the branches which are cis-1,4 chains of the block copolymer, the branches are lubricating the system during the stretching. The length of the branches must be short enough so as to produce no significant entanglement constraint. This observation is in accord with the previous one that a relatively long branch gives strain hardening, whereas a relatively short branch gives strain softening. The strain softening was found to enhance the strain-induced crystallization. This conclusion is opposite to what one might expect from the entanglement constraints by the long branches, forcing the orientation of the chains, and thus enhancing the strain-induced crystallization. © 1996 John Wiley & Sons, Inc.     

Quantum Entanglement and Electron Correlation in Molecular Systems

We study the relation between quantum entanglement and electron correlation in quantum chemistry calculations. We prove that the Hartree–Fock (HF) wave function does not violate Bell's inequality, and thus is not entangled, whereas the configuration interaction (CI) wave function is entangled since it violates Bell's inequality. Entanglement is related to electron correlation and might be used as an alternative measure of the electron correlation in quantum chemistry calculations. As an example we show the calculations of entanglement for the H₂ molecule and how it correlates with the traditional electron correlation, which is the difference between the exact and the HF energies.     

一维关联无序系统中电子态的研究

本文讨论了长程幂率关联对一维无序系统本征波函数,本征能量及并发纠缠的影响,并观察其是否能体现系统局域性的变化。结果表明只用并发纠缠这个测度足以反映空间关联的特性。还将DNA分子链作为关联安德森模型的例子,研究其准周期模型与无序模型的并发纠缠,并证明了并发纠缠与关联有类似性质,足以通过并发纠缠这个测度来反映关联的特性。     

Effect of chain entanglement on the melt-crystallization behavior of poly(<Emphasis Type="SmallCaps">l</Emphasis>-lactide) acid

Chain entanglements and the entanglement degree determine many processes and behaviors of polymers. In this work, poly(l-lactide) acid (PLLA) samples with markedly decreased entanglements were obtained via a freeze extraction method and the kinetics of entanglement recovery process of freeze-extracted samples was monitored by dynamic rheology approach. The crystallization kinetics of freeze-extracted PLLA samples was further studied by polarized optical microscope, which revealed that the entanglement degree greatly influences the crystallization of PLLA and lower degree of entanglement or disentanglement was conducive to the melt-crystallization of PLLA. The spherulites grew faster in partially disentangled melt than in well entangled melt.     

RHEOLOGICAL BEHAVIOR OF POLYMER MELTS (I) UNIFIED MOLECULAR THEORY OF NON-LINEAR ISCOELASTICITY WITH CONSTRAINTS OF GAUSSIAN CHAIN ENTANGLEMENT FOR POLYMER MELTS

An approach with statistical mechanics and a unified molecular theory of non-linearviscoelasticity with constraints of Gaussian chain entanglement for polymer melts were proposed.Amultimode model structure for a single polymer chain with tail segments and N reversibleentanglement sites on the test polymer chain was developed.The probability distribution function ofthe end-to-end vector for a single polymer chain at entangled state and the viscoelastic free energyof deformation for polymer melts were calculated.Four types of stress-strain relationship and mem-ory function were derived from this theory.The above theoretical relationships were verified by experi-mental data of PS(polystyrene)and LDPE(low density polyethylene)melts.     

PDA型PUR弹性体的制备与性能

以聚己二酸二乙二醇酯二醇(PDA)为软段,4,4′–二苯基甲烷二异氰酸酯(MDI)和1,4–丁二醇(BDO)为硬段,采用预聚体法制备一系列PDA型PUR弹性体。采用力学性能测试、广角X射线衍射(WAXD)、傅立叶变换红外光谱(FTIR)、差示扫描量热(DSC)、热重(TG)分析和维卡软化点温度测定等研究手段,研究硬段含量对其力学性能、微观形态和热性能的影响。结果表明,随着硬段含量的增加,PDA型PUR弹性体的硬度、拉伸强度、300%定伸应力、拉伸永久变形和撕裂强度都增大,当硬段含量为40.1%时,弹性体的综合力学性能最佳,硬度(邵A)为88,拉伸强度为33.9 MPa,300%定伸应力为12.5 MPa,拉伸永久变形为31%,撕裂强度为90.3 k N/m;WAXD分析表明,弹性体为无定型结构;FTIR分析表明,硬段含量的增加使弹性体总的氢键化程度增加,微相分离程度改善;DSC测试表明,硬段含量的增加使弹性体的微相分离程度提高;TG和维卡软化点温度测试表明,弹性体的热性能随着硬段含量的增加而提高,当硬段含量为40.1%时,弹性体的初始分解温度(失重5%的温度)和维卡软化点温度分别达到324.5℃和144.1℃,具有较好的热性能。     

Dynamics of solutions of entangled polymers

A simple network model for the relaxation dynamics of entangled polymer fluids is presented. It has been assumed that entanglement friction is the principal dissipative mechanism for all but the longest wavelength modes in the entanglement region, and this gives rise to a peak in the relaxation spectrum. This model is shown to predict viscoelastic response functions whose qualitative features agree well with those observed experimentally, and in particular the well-known, ‘C²’ effect of entanglement coupling is derived in a natural manner.     

Kinetics of ageing and re-embrittlement of mechanically rejuvenated polystyrene

Pre-deforming polystyrene by rolling results in elimination of strain softening and induces ductile deformation behaviour in a subsequent tensile test. However, both yield stress and strain softening recover in time as a result of ageing, resulting in renewed brittle failure behaviour. The kinetics of this process is addressed in this paper. Although the process of recovery of yield stress and strain softening shows no molecular weight dependence, the time-scale of renewed brittle fracture after rejuvenation does. Any localisation of strain can only be stabilised if the molecular network can transfer sufficient load. For relatively low molecular-weight polystyrene, the load bearing capacity is already exceeded at short ageing times, whereas for higher molecular-weight grades this takes longer. Since the creep compliance and shift-rate of mechanically rejuvenated polystyrene shows a pronounced increase as compared to thermally rejuvenated polystyrene, the segmental mobility in the mechanically rejuvenated samples has increased, despite a lower free volume. This indicates that a new explanation for ageing should be postulated, which is discussed.     

Effects of surface flaws on the wettability of solids

Wetting hysteresis, or the variability of contact angle, is recognized to be caused by several phenomena. In particular, we consider it to be due to heterogeneity of the solid surface in contact with the liquid. Results describing the deformation of an initially straight triple line in the proximity of an isolated, small, energetic inhomogeneity are summarized. The theory is extended to describe the behaviour of a wetting front near a circular, high-energy (i.e. corresponding to zero intrinsic contact angle) flaw of dimensions comparable to those of the triple line distortion. A simple model is proposed to explain the breakaway of the isthmus of liquid connecting the flaw to the bulk liquid. Separation time is found to be proportional to ^-5, where 0 is the intrinsic contact angle of the solid/ liquid system. The behaviour of a triple line on a solid possessing a randomly distributed population of identical, small, circular flaws is considered. Contact angle hysteresis can thus be explained, as can the noise often observed in a (dynamic) Wilhelmy plate experiment. A simple statistical model is proposed in which random force fluctuations related to a moving triple line are shown to correspond to the Poisson process of probability theory.     

The fine structure of pitch-based carbon fibres

Four types of pitch-based carbon figures have been characterised by the methods of high-angle X-ray diffraction and high-resolution electron microscopy. A 1000°C material from naptha pitch has a very poorly developed lattice structure which is much improved after treatment at 2000°C, although there is a gradation of lattice order: a few well-graphitized inclusions are also present in the 2000°C specimen. Fibres prepared from a crude-oil pitch and heat treated to 3000°C show an entangled network of well graphitized crystallites. After extension at 3000°C there is still a considerable degree of entanglement so that many crystallites lie approximately normal to the fibre axis. These may well be the cause of the low strength of the oriented material as compared with a similarly treated PAN-based carbon fibre.     

Exploring the entangled state and molecular weight of UHMWPE on the microstructure and mechanical properties of HDPE/UHMWPE blends

Three types of ultra-high molecular weight polyethylene (UHMWPE) with different entangled state and molecular weight were blended with high-density polyethylene (HDPE) matrix by melt blending. Rheology, 2D-SAXS, 2D-WAXD, DSC, and mechanical tests were used to study the evolution and difference of microstructure and mechanical properties of the blends. The addition of weakly entangled UHMWPE enhanced the chain diffusion and chain orientation ability under a specific flow field. Thus, the rheological properties and mechanical properties of the blends were improved with the mix of weakly entangled UHMWPE. The mechanical properties enhancement effect of HDPE/UHMWPE blends with weakly entangled UHMWPE was owing to the shish-kebab structure formed in the injection molding process. The molecular chains of UHMWPE with a low degree of entanglement and high molecular weight increased the lamella size and crystallinity of the blends during processing. This leads to the formation of more oriented shish structures and more kebab lamella. Besides, the molecular chains of weakly entangled UHMWPE were better interlocked and intertwined with other polyethylene chains in the amorphous region, acting as the tie molecules, significantly improving the impact resistance.     

Payne effect and shear elasticity of silica-filled polymers in concentrated solutions and in molten state

The viscoelastic properties of silica-filled copolymer in concentrated solutions and melts were investigated. A wide variety of rheological observations, such as Payne effect, percolation threshold and elastic effects, of non-porous silica dispersed in a ethylene vinyl acetate copolymer (EVA, 60 wt% of vinyl acetate) were studied in the molten state or diluted solutions in xylene. The concept of the filler network breakdown seems to be adequate in describing the strain-dependence of dynamic mechanical properties. Nevertheless, the degree of non-linearity was found to be the highest for the highest dilution. It appears for silica concentration lower than the percolation threshold of the filler suggesting another mechanism associated with trapped entanglement. On the other hand, we observe a silica content (Φ_c=(3.3±0.1)×10⁻²) for the onset of a gel-like behaviour in the terminal zone. This critical level, defined as the percolation threshold, appears to be independent of EVA dilution in xylene. Furthermore, this liquid-solid transition can be expressed in the same general relaxation patterns as chemical gelation systems with a self similar behaviour at the rheological gel point. However, the universal properties of percolation are not properly described and elastic effect are better depicted by the cluster-cluster aggregation model. On the other hand, the concentration-dependence of the equilibrium storage modulus of EVA at different dilutions in xylene yields evidence of a screened effect of copolymer chains in the entangled regime (?≥?_c) of elastic bending-twisting interaction between filler particles.     

Time-dependent rheological properties and transient structural states of entangled polymeric liquids—A kinetic network model

A kinetic network model has been developed to describe the nonlinear rheological behavior of entangled polymer solutions and melts in either steady-state or transient flows. This model is based on the concept of flow-induced structure variation, controlled by the simultaneous existence of entanglement loss and regeneration. When steady-state is attained, both processes occur at the same rate and the structural state (entanglement density) of the fluid remains constant with time. Under transient flow conditions, the fluid structure becomes time-dependent as a result of unequal rates of the two competing processes affecting entanglement density. The viscoelastic response of the fluid is, in turn, influenced by the varying structural state. This is incorporated into the model through the use of structure-dependent coefficients in the contravariant Maxwell constitutive equation for entanglement stress. Model predictions are generated for a number of transient flow programs, including the stress growth and relaxation, interrupted flow, sudden change in shear rate, and nonlinear creep experiments. Comparison with literature data supports not only the qualitative success but also the quantitative ability of this model.     

Primitive path analysis of linear polymer embedded in post array

We present an extensive set of simulation results for the relaxation processes of linear polymer chains embedded in post arrays using Monte Carlo algorithm. The data allow us to explore the crossover of chain dynamics from single-chain regime to entangled regime. Using primitive path analysis, the statistical information of the system, including the average value and the fluctuation of the length of primitive path, is also obtained. We have performed a clear test on Doi’s theory on contour length fluctuation and we find excellent agreement for Doi’s theory in entangled regime.     

Adhesive Failure and Deformation Behaviour of Polymers

An instrument has been developed to determine the adhesive fracture energy as a function of the most important parameters such as temperature, contact time etc. and to study the stress–strain behaviour during bond separation. Additionally, the deformation processes during debonding were observed by high speed photography. Investigations of two high molecular weight polymers, polyisobutylene (PIB) and polyethylhexylacrylate (PEHA), showed two different types of bond separation: “brittle” behaviour with low adhesive failure energy for PIB and the formation and deformation of fibrillar structures for PEHA leading to much higher strains at break and adhesive failure energies. It follows from mechanical measurements that both polymers differ mainly by their entanglement networks. The much longer entanglement spacing for PEHA leads to the formation of fibrillar structures which, in accordance with a theory of Good, seem to be the reason for strong adhesion.     

Effect of poly(ethylene oxide) with different molecular weights on the electrospinnability of sodium alginate

Although sodium alginate (SA) could not be electrospun from its aqueous solution, SA-based electrospun nanofibers can be fabricated with the help of polyethylene oxide (PEO). In this study, the influence of PEO on the electrospinnability of SA aqueous solution was investigated and the roles of chain entanglements and conformations of the blend system were emphasized. It was found that a little amount of PEO100 with high molecular weight could improve the electrospinnability of SA aqueous solution. However, a large amount of PEO2 with low molecular weight had no positive effect on the electrospinnability of SA aqueous solution. Dynamic laser light scattering (DLLS) results showed that only when the PEO molecular chains in aqueous solution were in an entangled state, PEO can enhance the electrospinnability of SA aqueous solution. The further study on rheological measurements showed that SA molecular chains could not form significant entanglements for the electrospinning even when the SA solution concentration approached concentrated regime. SA molecular chains are closely “overlapped” due to its rigid and extended conformation and cannot form effective chain entanglement. The main contribution of PEO100 to improve SA electrospinnability is offering entanglement sites and thereby enhancing the applicable entanglement degree of the blend system. Whereas, although the chain interaction between PEO2 and SA may improve slightly the flexibility of SA chains, the significant chain entanglements of the blend solution is not achieved. Three molecular models are proposed to depict visually the effect of PEO with different molecular weights on chain conformations and entanglements of SA.