Contribution of crazing to the toughness of amorphous and semicrystalline polymers

Crazes or craze-like deformation bands occur in many different polymers. Mechanisms of initiation and growth of the crazes have been studied using different techniques of electron microscopy. Examples of modifying amorphous and semi-crystalline polymers are given to demonstrate to which extent the macroscopic toughness of the polymers is affected by changes in the microscopic structure and by the amount of crazes.     

Enthalpy recovery in semicrystalline polymers

Constitutive equations are derived for enthalpy recovery in glassy polymers after thermal jumps. The model is based on the theory of cooperative relaxation in a version of the trapping concept. It is demonstrated that a critical temperature T_cr and a critical degree of crystallinity f_cr exist in a semicrystalline polymer above which structural relaxation vanishes.     

The rigid amorphous fraction in semicrystalline macromolecules

The first experimental evidence of the existence of the rigid amorphous fraction (RAF) was reported by Menczel and Wunderlich for several semicrystalline polymers. It was observed that the hysteresis peak at the glass transition was absent when these polymers were heated much faster than they had previously been cooled. In the glass transition behavior of poly(ethylene terephthalate) (PET), the hysteresis peak gradually disappeared as the crystallinity increased. At the same time, it was noted that the ΔC _p of higher crystallinity PET samples was much smaller than could be expected on the basis of the crystallinity calculated from the heat of fusion. It was also observed that this behavior was not unique to PET only, but is characteristic of most semicrystalline polymers: the sum of the crystallinity calculated from the heat of fusion and the amorphous content calculated from the ΔC _p at the glass transition is much less than 100% (a typical difference is ~20–30%). This 20–30% difference was attributed to the existence of the “RAF”. The presence of the RAF also affected the unfreezing behavior of the “mobile (or traditional) amorphous fraction.” As a consequence, the phenomenon of the enthalpy relaxation diminished with increasing rigid amorphous content. It was suggested that the disappearance of the enthalpy relaxation was caused by the disappearance or drastic decrease of the time dependence of the glass transition. To check the validity of this suggestion, the glass transition had to be also measured on cooling in order to overlay it on the DSC curves measured on heating. However, before this overlaying work could be accomplished, the exact temperatures on cooling had to be determined since the temperature of the DSC instruments that time could not be calibrated on cooling using the usual low molecular weight standards due to the common phenomenon of supercooling. Therefore, a temperature calibration method needed to be developed for cooling DSC experiments utilizing high purity liquid crystals using the isotropic → nematic, the isotropic → cholesteric, and other liquid crystal → liquid crystal transitions. After the cooling calibration was accomplished, the cooling glass transition experiments indicated that the glass transition in semicrystalline polymers is not completely time independent, because its width depends on the ramp rate. However, it was shown that the time dependence is drastically reduced, and the midpoint of the glass transition seems to be constant which can explain the absence of the enthalpy relaxation. The work presented here has led to a number of studies showing the universality of the rigid amorphous phase for semicrystalline polymers as well as an ASTM standard for DSC cooling calibration.     

Radiation modification of semicrystalline polymers

Three problems of the radiation modification of polymers are dealt with. Different methods of grafting are compared with respect of the formation of true graft copolymer and homopolymer in the polyethylene-styrene system; the prevention of the penetration of monomer by grafting polytetrafluoroethylene is shown; the mechanical properties of crosslinked ethylene polymers below and above the melting point are discussed.     

Thermal density fluctuations in amorphous polymers as revealed by small angle X-ray diffraction

Summary Thermal density fluctuations in amorphous polymethyl methacrylate, polycarbonate and polyethylene terephthalate were studied by means of small angle X-ray scattering. The measurements were performed in a temperature range from 20 °C up to about 50 °C above the glass transition temperatureT _g of the individual sample.AboveT _g the experimental values of the fluctuations are proportional to the isothermal compressibility and the temperature of the sample as predicted by the fluctuation theory for a system in thermodynamic equilibrium.At temperatures belowT _g this relation is no longer correct. The experimentally determined fluctuations are now proportional to the compressibility of the sample in the equilibrium state atT _g and to the actual temperature of the glassy sample. By considering a statistical ensemble with exchange of energy, particles and order between the systems of the ensemble an equation can be derived for the fluctuations of the number of particles per given volume which predicts the observed behaviour. The order parameter takes into account the fact that the properties of the glassy state depend on the way by which the state was produced.

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Zusammenfassung Es wurden thermische Dichtefluktuationen in amorphem Polymethylmethacrylat, Polycarbonat und Polyäthylenterephthalat mit Hilfe der Röntgenkleinwinkelstreuung untersucht. Die Messungen erstrecken sich über einen Temperaturbereich von 20 °C bis zu etwa 50 °C oberhalb der GlastemperaturT _g der jeweiligen Probe.In Übereinstimmung mit den Ergebnissen der Fluktuationstheorie sind die Fluktuationen oberhalb vonT _g proportional zur isothermen Kompressibilität und zur Temperatur der Probe.Unterhalb der Glastemperatur ist diese Beziehung nicht mehr erfüllt. Hier ist die Fluktuation proportional zur Kompressibilität der Probe im Gleichgewichtszustand beiT _g und zur Temperatur. Auf der Basis einer statistischen Gesamtheit mit der Austauschmöglichkeit von Energie, Partikel und Ordnung zwischen den Systemen der Gesamtheit kann eine Beziehung für die Dichtefluktuation abgeleitet werden, die mit den experimentellen Ergebnissen übereinstimmt. Der zusätzliche Ordnungsparameter berücksichtigt die Tatsache, daß die Eigenschaften im Glaszustand wegabhängig sind.

     

Chain dimensions in plastically deformed semicrystalline polymers

The effect of plastic deformation on the chain dimensions of polymers in the semicrystalline state was investigated using linear hydrogenated polybutadiene (HPB), a model ethylene/butene-1 copolymer having about 40% crystallinity at room temperature. Dilute blends of deuterium-labeled chains with various molecular weights (20,000 ≤ M ≤ 214,000) in the same unlabeled matrix (M = 95,000) were uniaxially stretched at 25°C to extension ratios of α = 2.4 and 4.4. Radius of gyration normal to the stretch direction R_⊥ was measured for the labeled chains by small-angle neutron scattering. The molecular extension ratio inferred from these data α_m = R/R was significantly smaller than α for short chains (M < 50,000) but increased to the affine range α_m = α for M > 100,000. This variation in α_m/α closely parallels the molecular weight dependence of mechanical strength and ductility in HPB over the same range.     

Mapping of chemically accessible regions in semicrystalline polymers

Important chemical and mechanical properties in semicrystalline polymers are determined by the noncrystalline or nonordered regions. Hence, characterizing these regions is important in developing a morphological model to better define and predict the chemical and mechanical behavior of polymeric materials. With this objective, preferential tagging was accomplished by covalent linking of a heavy element to poly(ethylene terephthalate) (PET). In scanning transmission electron microscopy (STEM), contrast was obtained using a low concentration of thallium (0.4%), the tagging element, thus providing a map of the more accessible regions within the semicrystalline structure. Differential scanning calorimetry (DSC) and wide-angle x-ray scattering (WAXS) were used to characterize the PET film. Elemental analysis using energy dispersive x-ray analysis (EDAX) was used to confirm the presence of the heavy element in the tagged regions. The STEM imaging results were then compared with the characterization results from the DSC and WAXS measurements to gain an understanding of the domains and their size ranges in the semicrystalline microstructure of PET. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1443–1450, 1998     

Crystal-amorphous interphases in binary semicrystalline/amorphous polymer blends

Crystal-amorphous interphases in binary polymer blends that are miscible in the melts but phase separate due to crystallization of one polymer have been investigated theoretically by employing lattice models and experimentally by dielectric spectroscopy measurements. Theory predicts the extent of tight adjacent re-entry to depend strongly on the energy E_q disfavoring the tight-fold conformations and to increase slightly with favorable interaction energy - χ_AB in the blends. The interfacial region of varying composition is predicted to depend strongly on χ_AB, with the interfacial thickness varying with the reciprocal of |χ_AB|^1/2. Therefore, in the limit χ_AB → 0 the amorphous polymer, which is miscible in the melt, is predicted to be completely excluded from the interlamellar region, in agreement with experimental results. Dielectric relaxation experiments on semicrystalline blends of poly(vinylidene fluoride) (PVDF) with poly(methyl methacrylate) (PMMA) or poly(vinyl pyrrolidone) (PVP) show the existence of nearly pure PVDF interphase which is not penetrated by PMMA or PVP, despite their strongly favorable interactions with PVDF. These experimental results are discussed and compared with theoretical predictions.     

Plastic flow and multiple fracture of semicrystalline polymers

The mechanism of plastic flow of isotactic polypropylene is considered in terms of Eyring's equation. It is demonstrated that to explain the dependence of the yield point on temperature a dependence of activation volume on overcooling (T_m-T) must be admitted. The effects of drawing rate and temperature on the ultimate elongation of polypropylene are discussed in the case of two-step drawing. The critical conditions of extrusion in solid state are considered. Criteria of transformation of a steady flow into unsteady state are suggested. Multiple fracture of semicrystalline polymers under critical conditions of plastic is described.     

The dielectric constant of lamellar semicrystalline polymers

The problem of representing the dielectric constant of semicrystalline polymers in terms of the dielectric constants and volume fractions of the constitutent crystalline and amorphous phases is considered. For locally lamellar morphology, bounds based on uniform electric and displacement fields are derived. The equations also include the degree of crystal orientation as a parameter. For unoriented polymers the bounds are considerably tighter than the Hashin–Shtrikman bounds, the latter being the best possible without knowledge of phase geometries. The bounds presented here are sufficiently tight to represent the dielectric constant with practical accuracy for a number of examples of semicrystalline polymers. A treatment is also given of the dielectric constant where the lamellar morphology is further specified as being organized into spherulite-like structures. These bounds are somewhat tighter than the lamellar bounds.     

The mechanical moduli of lamellar semicrystalline polymers

Bounds on the elastic constants are derived for semicrystalline polymers whose local morphology is lamellar. Local response matrices (stiffness and compliance) are formulated in three dimensions that simultaneously incorporate uniform in-plane strain and additive forces from layer to layer of crystalline and amorphous phases and uniform stress and additive displacements normal to the lamellar surfaces. Spatial averaging of the stiffness and compliance matrices under the assumption of axially symmetric orientation gives the upper and lower bounds on the longitudinal and transverse tensile moduli and the axial and transverse shear moduli as functions of the separate phase elastic constants, the volume percent crystallinity, and the moments of the orientation 〈cos²θ〉 and 〈cos⁴θ〉. The bounds are much tighter than the Voight upper and Reuss lower bounds that do not recognize phase geometry. Using the known crystal elastic constants of polyethylene, sample calculations on isotropic unoriented materials show that the divergence of bounds at high crystallinity necessitated by the extreme crystal anisotropy shows up only at very high crystallinity. At low temperature the bounds are tight enough to specify G₁, the amorphous modulus, from the measured G and the known crystal elastic constants. At higher temperatures and lower G, the bounds are not tight enough for this purpose but the shear modulus versus crystallinity and temperature data are well fitted by the lamellar lower bound using a temperature-dependent, crystallinity-independent G₁.     

Processing of semicrystalline polymers by high-stress extrusion

A study has been conducted on the solid-state extrusion of three semicrystalline polymers:poly-propylene (PP), poly(vinylidene fluoride) (PVDF), and high-density polyethylene (HDPE). HDPE has been extruded in continuous lengths with area reductions up to 25× at temperatures substantially below the melting region. Such extrusion has been identified as a solid-state process, since measurements of the temperature of the polymer during extrusion indicate the absence of significant heating due to deformation. In contrast, continuous lengths of PP and PVDF could not be obtained substantially below their melting temperatures, indicating that crystallization during extrusion is an important process for these polymers. Under severe extrusion conditions (low temperatures, high area reductions. etc.), all three polymers failed within the tapered region of the extrusion die. Two modes of failure have been identified, brittle fracture and, surprisingly, necking. Grid-line distortion patterns and a highly simplified upper-bound plasticity analysis both indicate that shear deformations are a major factor during high-stress extrusion.     

Sorption and swelling of semicrystalline polymers in supercritical CO2

The equilibrium sorption and swelling behavior of four different polymers—poly(methyl methacrylate), poly(tetrafluoroethylene), poly(vinylidene fluoride), and the random copolymer tetrafluoroethylene–perfluoromethylvinylether–in supercritical CO₂—are studied at different temperatures (from 40 to 80 °C) and pressures (up to 200 bar). Swelling is measured by visualization, and sorption through a gravimetric technique. From these data, the behavior of amorphous and semicrystalline polymers can be compared, particularly in terms of partial molar volume of CO₂ in the polymer matrix. Both poly(methyl methacrylate) and the copolymer of tetrafluoroethylene exhibit a behavior typical of rubbery systems. On the contrary, polymers with a considerable degree of crystallinity, such as poly(tetrafluoroethylene) and poly (vinylidene fluoride), show larger values of partial molar volume. These can be related to the limited mobility of the polymer chains in a semicrystalline matrix, which causes the structure to “freeze” during the sorption process into a nonequilibrium state that can differ significantly from the actual thermodynamic equilibrium. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1531–1546, 2006     

Increased glass transition temperature in motionally constrained semicrystalline polymers

A large number of experimental results in the literature support and illuminate a model of behavior of chains and chain segments in the amorphous phase of semicrystalline polymers connecting the elevation of the glass transition temperature (T_g) above its normal value to several kinds of motional restrictions imposed on the chains and parts thereof. Accordingly, polymer chain, chain-segment and chain-fragment motions of all kinds comprise one or more torsions around main-chain bonds from one stable conformation to another, known as rotational isomerizations. When impediments are placed in front of thermal fluctuations and larger transversal and longitudinal motions of polymer chains, segments and shorter fragments in the amorphous phase, and the motions are thus restricted, the glass transition temperature is elevated relative to that of the same amorphous phase in the bulk under normal conditions. The obstructions may prevent either the onset of rotational isomerizations or of their completion once started. The completion of the torsional isomerizations and larger motions may be prevented by eliminating the free spaces necessary to accommodate the volumes of the interconverting chain fragments and segments even when they move in concert, or by preventing the creation of such free spaces. Another way to hinder the completion of such motions is by the introduction into the system of many rigid walls and other interfaces with strong attractive interactions with the polymer, that by geometrical constraints and attractive interactions suppress the rotational and larger motions and prevent their completion. Elimination of the necessary free volume is achievable by the application of compressive pressure, while the introduction of rigid attractive walls may be accomplished by the incorporation of crystallites, as in semicrystalline polymers, or by the addition of rigid finely comminuted foreign additives with very large surface areas or confining voids with high tortuosity. It is believed that motional restrictions imposed on the amorphous phase by the growth faces of polymer crystallites, especially in oriented semicrystalline polymers, are more effective than the restrictions imposed by the fold surfaces of these crystallites. The prevention of the onset of rotational isomerizations and larger motions may be achieved by stretching the polymer chains and chain segments in the amorphous phase and, by one means or another, pinning down the taut chains such that essentially all their rotational isomers are in the trans conformation: they cannot interconvert to the gauche conformation since it requires the chain’s end-to-end distance to decrease. Parallel alignment of relatively taut chain-segments may impose additional geometrical restrictions on both the onset and completion of rotational isomeric torsions and, of course, on longer-range motions. In all cases, the T_g of the motionally constrained parts of the amorphous phase, especially in semicrystalline polymers, is expected to rise. It is likely that the characteristic length associated with transversal motions and their suppression is R_c, the spatial distance between entanglements, which is of the same size scale, and may be the same as the tube diameter of the reptation model. Special emphasis was placed in this work on the semicrystalline polymers poly (ϵ-caprolactam) (nylon-6) and poly (ethylene terephthalate) (PET). © 1998 John Wiley & Sons, Ltd.