Visualization of deformation-induced structural rearrangements in amorphous polymers

A technique is proposed for decorating amorphous polymers: Before the deformation (shrinkage) of an amorphous polymer, its surface is decorated with a thin metal coating. The subsequent deformation is accompanied by surface structure formation, which makes the processes that occur in the polymer visible. The proposed technique makes it possible to visualize and describe the mechanism of transfer of the polymer from the surface into the bulk and vice versa and to obtain direct information about the direction of the actual local stress. The technique makes it possible to obtain information about the topological heterogeneity of rubber networks, to reveal the features of structural rearrangements that occur during the cold rolling of amorphous polymers, and to describe the phenomenon of self-elongation during annealing of the oriented PET. These microscopic data explain the following features of the structural and mechanical behavior of glassy polymers from a unified viewpoint: stress relaxation in a polymer in the elastic (Hookean) region of the stress-strain curve, an increase in stress in a deformed glassy polymer during its isometric annealing below T _g, the low-temperature shrinkage of a deformed polymer glass in the strain range below its yield point, the storage of internal energy in a deformed glassy polymer in the strain range below the yield point, some anomalies of thermophysical properties, and some other features.     

Thermodynamics of the deformation of segmented polyurethanes with various percentages of hard block I. The initial deformation

The thermodynamic analysis of the uniaxial stretching of the polybutadiene polyurethanes of various compositions and mechanical history was carried out using deformation calorimetry. The initial small strain deformation was found to result from the volume elasticity of the hard phase. Samples containing up to 50% of the hard block behave like typical thermoelastoplastics, which are characterized by the plastic-to-rubber transition and large reversible deformations. More rigid samples behave similar to typical solid crystalline polymers aboveT _g.It is great pleasure for us to dedicate this paper to Prof. Dr. H.-G. Kilian on the occasion of his 60th birthday.     

Plasticity of Semicrystalline Polymers

Semi-crystalline polymers can be deformed up to a very high strain. The deformation process involves frequently a complete molecular rearrangement of the chain-folded lamellar morphology into a more or less chain-unfolded fibrillar microstructure. This transformation is likely to occur through an intermediate state of high molecular disorder at a local scale. It led to the formulation of a concept of strain-induced melting-recrystallization process as a main mechanism of the structure transformation. In contrast, several structural features occurring at moderate plastic strains are relevant to strictly crystallographic processes. The plastic deformation process of semicrystalline polymers and the micromechanisms involved are discussed. A critical discussion of experimental findings is made to point out the strength or the deficiency of the various argumentations. It is demonstrated that the crystallographic slip mechanisms, including slips: transverse and along the chains are the basic deformation mechanisms in the deformation sequence, active at all strain levels. Direct microscopic evidence of chain slip activity even at well advanced stages of the deformation process is presented. In contrary, the melting-recrystallization seems to be restricted to the high-strain stage accompanied by chain unfolding and perhaps limited to only a small fraction of the crystalline phase. In addition the experimental results demonstrates clearly that the cavitation, necessary in the Peterlin's model, is really unessential in producing high deformation and appearance of the final highly oriented structure. This can be effectively accomplished with only crystallographic mechanisms employed. A very important role in the deformation sequence is played by the partially reversible shear deformation of amorphous interlamellar layers, producing not only high orientation of amorphous component but also influencing deeply the deformation of crystalline phase, since both phases are strongly connected and must deform simultaneously and consistently.     

Tilted lamellae in an affinely deformed 3D macrolattice and elliptical features in small‐angle scattering

Lamellar reflections in small‐angle X‐ray and neutron scattering patterns of uniaxially drawn semicrystalline polymers appear to fall on elliptical or hyperbolic arcs. We attribute this to a 3D lattice of tilted lamellae, a macrolattice. Affine deformation of this lattice, such as during uniaxial draw, moves and spreads the reflections along elliptical arcs, and nonaffine deformation, such as during rolling, moves and spreads the reflections along an arc that deviates from an ellipse. Discrete reflections are the product of two functions: the elliptical trace that is the Fourier transform of the affinely deformed lattice and the radial streak that is the Fourier transform of the individual lamella in the reciprocal space. Four‐point patterns are obtained if the lamellar‐surface normal is tilted away from the fiber‐axis, and two‐point patterns if it is not. This model is used to discuss the transformation between four‐ and two‐point patterns and other changes in lamellar morphology that occur during drawing and annealing of oriented semicrystalline polymers. The deformation of the macrolattice of crystalline lamellae, need not be correlated to the tilt of the lamellae. The tilt of the lamellae is shown to be important. It reflects the cross‐sectional area mismatch at the lamellar surface between crystalline stems and amorphous chains segments, and this indicates the internal strain in the interfibrillar amorphous regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1277–1286, 2006     

结晶聚合物的单轴拉伸和取向态结构：Ⅱ.取向结晶聚合物的结构模型和塑性形变

概述了有关取向结晶聚合物结构及塑性形变的各种模型和实验证据，共包括参考文献４２篇。     

Depolarization thermocurrents in amorphous polymers

The depolarization thermocurrent (DTC) method gives the dependence of the dielectric relaxation time on temperature. It has been used for investigations of relaxations obeying an Arrhenius-like law in crystalline polymers. The analysis of this method shows it is possible to study mechanisms described by the Williams-Landel-Ferry (WLF) equation. The critical temperature appearing in the free-volume theory of Cohen and Turnbull and also in the statistical thermodynamic theory of Adam and Gibbs can then be measured with good accuracy. The thermal coefficient of expansion of the free-volume and the WLF coefficient for any reference temperature can also be obtained. Since analysis of the experimental DTC spectrum is particularly simple, this method seems to be a very useful tool for examination of relaxation transitions in amorphous polymers. As an example, results obtained for poly(methyl methacrylate) are presented; they are consistent with published data.     

A three-phase microstructural model to explain the mechanical relaxations of branched polyethylene: a DSC,WAXD and DMTA combined study

The thermal transitions of well-characterised single-site catalysed polyethylenes having various degrees of short chain branching have been studied by differential scanning calorimetry, X-ray diffraction and dynamic mechanical thermal analysis. A critical discussion based on the results obtained by means of the different techniques is presented. The results suggest that the γ transition is independent of the branching content and degree of crystallinity, pointing towards a sub-glass local relaxation mechanism related to both amorphous and crystalline fractions. The temperature of the β transition, T _β from dynamic mechanical measurements, is in agreement with the glass transition temperature obtained by calorimetry, T _g. Moreover, T _γ, and also T _β are directly related to a change in the thermal expansion coefficient of the amorphous phase observed by X-ray scattering. It is found that the corresponding scattering distance of the amorphous halo depends on crystallinity. In addition, the calorimetric heat capacity values at T _β do not account for the total amorphous fraction determined for each material. The relaxation motions assigned to the amorphous phase glass transition seems to parallel the subsequent melting of the crystalline structure, suggesting a hierarchical motion of different structures as temperature increases. Dynamic mechanical thermal analysis supports these observations, showing a broad transition in the phase angle involving first the relaxation of amorphous phase, then the (presumable) more rigid intermediate phase, and finally the crystalline phase, as the temperature increases.     

A unified modeling approach for amorphous shape memory polymers and shape memory polymer based syntactic foam

Shape memory polymers (SMPs) and shape memory polymer composites have drawn considerable attention in recent years for their shape memory effects. A unified modeling approach is proposed to describe thermomechanical behaviors and shape memory effects of thermally activated amorphous SMPs and SMP‐based syntactic foam by using the generalized finite deformation multiple relaxation viscoelastic theory coupled with time–temperature superposition property. In this paper, the thermoviscoelastic parameters are determined from a single dynamic mechanical analysis temperature sweep at a constant frequency. The relaxation time strongly depends on the temperature and the variation follows the time–temperature superposition principle. The horizontal shift factor can be obtained by the Williams–Landel–Ferry equation at temperatures above or close to the reference temperature (T_r), and by the Arrhenius equation at temperatures below T_r. As the Arruda–Boyce eight‐chain model captures the hyperelastic behavior of the material up to large deformation, it is used here to describe partial material behaviors. The thermal expansion coefficient of the material is regarded as temperature dependent. Comparisons between the model results and the thermomechanical experiments presented in the literature show an acceptable agreement. Copyright © 2016 John Wiley & Sons, Ltd.     

Effects of thermal treatment of biaxially oriented poly(ethylene terephthalate)

Two distinguishable effects of thermal exposure of biaxially oriented poly(ethylene terephthalate) (PET) have been observed in the temperature range from room temperature to 140°C. Upon heating above the glass transition temperature T_g of the film an irreversible shrinkage of a few percent occurred with a concomitant decrease in the rate of creep. Some loss of orientation in the noncrystalline phase with an attendant slight increase in density is believed to be responsible. Since the film was anisotropic in its plane, different amounts and rates of shrinkage were observed along with differing thermal expansion coefficients in various directions relative to the primary optic axis. Upon cooling the 50% crystalline PET from above T_g to lower temperatures, reversible “physical aging” was observed. Creep rates were found to decrease with the residence time below T_g. As with purely amorphous polymers, the effects of the aging are removed by heating the specimen above T_g where the density of the amorphous phase achieves equilibrium values.     

Rigid amorphous fraction in poly(ethylene terephthalate) determined by dilatometry

Volumetric thermal analysis of semicrystalline poly(ethylene terephthalate), PET, with different content of crystalline phase was carried out using mercury-in-glass dilatometry. The effect of crystals on the thermal properties of amorphous phase (glass transition temperature, T _g, thermal expansion coefficients, α) were determined. At cold-crystallization (106°C, up to 4 h), crystalline content of 2.4–25.3 vol.% was achieved. Increasing content of crystalline phase broadens the glass transition region and increases T _g. The change of thermal expansion coefficient during glass transition is lower than that predicted by the two-phase model, which indicates the presence of a third fraction — rigid amorphous fraction (RAF), whose content steadily increases during crystallization. However, its relative portion (specific RAF) is significantly reduced. Further significant decrease in specific RAF appears after annealing at a higher temperature.     

Plastic deformation kinetics for glassy polymers and blends

Measurements of the plastic deformation kinetics for several glassy (PS, PC, PI-polyimide, PET, epoxy-amine network), semi crystalline polymers (PBT, PET) and blends (ABS, PC:ABS, PC: PBT) were performed for the unidirectional compression loading conditions by using constant temperature deformation calorimetry. The experiments have permitted us to follow the changes of the mechanical work (A), the heat of deformation (Q) and differences between these quantities, i.e., internal energy (U) stored in samples during their loading and unloading. Experiments have shown that the large portion (45–85%) of the mechanical work of deformation (A) is converted to heat (Q). The rest ofA is converted to internal energy (U) stored in deformed samples. U is quite high as compared with metals [1,2]. After complete unloading of plastically deformed samples, i.e., samples carrying irreversible atT _def plastic deformation ( _irr ), some amount (U) of stored energy disappeared. The amount of (U and (U) are different for different polymers. All data are analyzed in the framework of the model proposed in [3,4]. The experiments support the deformation model where the plasticity of glassy polymers is the process of nucleation and development of so-called PDs-plastic local shear defects of nonconformational and nondilatational nature.Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday     

Relationship between fracture toughness and intrinsic deformation parameters in isotropic and flow‐oriented linear low‐density polyethylene

The fracture toughness of isotropic and flow‐oriented linear low‐density polyethylene (LLDPE) is evaluated by the Essential Work of Fracture (EWF) concept, with a special setup of CCD camera to monitor the process of deformation. Allowing for the molecular orientation, flow‐oriented sample, prepared via melt extrusion drawing, is stretched parallel (oriented‐0°) and perpendicular (oriented‐90°) to its original melt extrusion drawing direction, respectively. The obtained values of specific EFW w_e are 34.6, 10.2, and 4.2 N/mm for the oriented‐0°, isotropic and oriented‐90° sample, respectively. With knowledge of intrinsic deformation parameters deduced from uniaxial tensile tests, moreover, a relationship between specific EFW w_e the ratio of true yield stress to strain hardening modulus σ_ty/G is well established. It means that the fracture toughness of polyethylene is determined by both crystalline and amorphous parts, rather than by one of them. Moreover, the true yield stress seems to be nondecisive factors determining the fracture toughness of polyethylene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2880–2887, 2006     

Piezoelectric properties and molecular motion of poly(β-hydroxybutyrate) films

Piezoelectric, elastic, and dielectric properties of films of poly(β-hydroxybutyrate) (PHB), an optically active natural polymer, were measured as functions of frequency and temperature. In mechanical properties, three relaxation processes were observed at 10 Hz: the α dispersion at 130°C, the β dispersion at room temperature, and the γ dispersion at ?120°C. It was concluded from x-ray diffraction and the thermal expansion coefficient that the α dispersion can be ascribed to thermal molecular motions in the crystalline phase, that the β dispersion is the primary dispersion due to the glass transition, and that the γ dispersion is related to local molecular motion of the main chains in the amorphous phase. Piezoelectric relaxations were also observed in these relaxation regions. It is proposed that the high-temperature process is due to ionic dc conduction. The piezoelectric relaxation at room temperature is ascribed to the increase of piezoelectric activity in the oriented noncrystalline phase, in which the sign of the piezoelectric modulus is opposite to that in the oriented crystalline phase.     

Negative thermal expansion in oriented crystalline polymers

Measurements on the thermal expansivity α_∥ and α_? (along and normal to the draw direction, respectively) have been carried out for a series of oriented polymers with widely different crystallinities (0.36–0.81) and draw ratios (1–20) and over large temperature ranges covering the major amorphous transitions in each case. While α_? increases with temperature, α_∥ tends to decrease sharply above the transition temperature. For highly crystalline polymers, α_∥ decreases to values typical of polymer crystals (?1 × 10^?5 K^?1) and this can be attributed to the constraining effect of the crystalline bridges connecting the crystalline blocks. However, for polymers of lower crystallinity, α_∥ may become an order of magnitude more negative and this remarkable phenomenon is attributed to the rubber–elastic contraction of taut tie-moleucles. Since taut tie-molecules and bridges have drastically different effects on α_∥ at high temperatures, this allows a rough determination of their relative fractions.     

Thermodynamics of inelastic deformation of amorphous and crystalline phases in linear polyethylene

Thermodynamic parameters (work W _def and heat Q _def) of inelastic deformation (uniaxial compression up to ɛ_def = 50%) are measured for six samples of high-molecular-mass linear PE at room temperature under the regime of active loading. Energy excess ΔU _def accumulated by the samples subjected to loading are calculated in terms of the first law of thermodynamics. All thermodynamic characteristics linearly increase with crystallinity χ of PE, thus making it possible to extrapolate their values to χ = 0 and 100% and to find the contributions of the amorphous and crystalline phases of the polymer to the overall thermodynamics of deformation. Both of the PE phases contribute to W _def and ΔU _def, while the crystalline phase alone contributes to heat Q _def. At ɛ ≥ 30%, the energy contribution from the amorphous phase exceeds that from the crystalline phase. A comparison between the plastic behavior of PE crystals and glassy polymers demonstrates that PE crystallites are easier deformed (requires less work W _def) than glassy polymers. At the same time, the amorphous phase of PE is harder to deform (requires more work W _def and stores more energy ΔU _def) than noncrystalline rubbers, apparently because of the deformation of tie chains. The thermodynamic characteristics of deformation are compared for three materials: crystalline metals, PE, and glassy polymers. The similarities and differences in their plastic behaviors are considered.     

Theory of deformation and strain-induced crystallization of an elastomeric network polymer

A new theory of deformation and strain induced crystallization of network polymers has been developed. The effects of lattice vacancies, variation in distribution of trans and gauche bond conformations in stretched amorphous polymers, and the crystallite orientation in the partially crystalline stretched vulcanizate were considered in the evaluation of their partition functions. Stress-extension ratio relationships were evaluated for the amorphous and semicrystalline polymers. The rise in melting temperature due to strain induced crystallization is discussed. The new theory seems to be in closer agreement with the actual strain-induced crystallization process than earlier research.     

Thermodynamics of linear reversible deformation

The change in internal energy of a body on stretching can be determined by means of deformation calorimetry. Theoretically the changes in thermodynamic properties on stretching can be deduced from Hooke's law and the Thomson expression dQ = β₀TL df, which gives the amount of heat dQ absorbed when the force is changed from f to f+df; β₀ is the linear expansion coefficient of the isotropic specimen, T the absolute temperature, and L the length of the deformed specimen. This has been demonstrated here for the deformation of a metal, and of isotropic and oriented polyethylene.     

Mechano‐reversible physical aging of elastic oriented syndiotactic polypropylene

Syndiotactic polypropylene (sPP), obtained at 0 °C in the trans‐planar mesophase, was drawn at room temperature up to λ = 6, and left at room temperature for 1 year with fixed or relaxed ends. Data analysis allowed the clarification of the structure of the crystalline phases and their transformations during the aging. In both oriented samples similar structural changes were observed, although they were due to different aging mechanisms. The physical aging led to the crystallization in both samples of an oriented helical form, due to a partial transformation of the mesophase and of the amorphous phase. In the oriented sample aged with fixed ends, a small fraction of the crystalline trans‐planar form III became stable even by releasing the tension after 1 year. This last sample did not undergo the large shrinkage, always observed by unloaded sPP after drawing, and therefore was no more elastic. Also, the sample aged with free ends for 1 year showed a reduced elasticity in terms of both dissipated energy and permanent set. However, after a new deformation up to λ = 6, the fiber recovered its previous elasticity. Indeed a mechano‐reversibility was apparent for the oriented elastic sample of sPP aged at room temperature with free ends, leading to a renewed elasticity. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 599–606, 2008     

The influence of cavitation phenomenon on selected properties and mechanisms activated during tensile deformation of polypropylene

The cavitation phenomenon accompanies the tensile deformation of most semicrystalline polymers when negative pressure inside the amorphous phase is generated. Over the years, this phenomenon has been marginalized, due to the common belief that it does not have any significant influence on the properties or micromechanisms activated during plastic deformation of such materials. In this article, for the first time, the influence of the cavitation phenomenon on the value of yield stress/strain, the intensity of the lamellae fragmentation process, the reorientation dynamics of the crystalline and amorphous component, the degree of crystals orientation at selected stages of deformation, and the amount of heat generated as a result of activating characteristic micromechanisms of plastic deformation were systematically analyzed. The research has been conducted for cavitating/non‐cavitating polypropylene model systems with an identical structure of crystalline component during their tensile deformation. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1853–1868