Thermophysical behaviour of solid polymers in simple elongation: A structural and molecular interpretation

Thermodynamic aspects of reversible simple extension of solid polymers have been considered in terms of the conventional equation of state and equations have been obtained for the thermodynamic functions. It is shown that simple deformation of solids is accompanied by inversion of internal energy which is controlled by coefficient of thermal expansion. Work, heat and internal energy as functions of strain have been determined by deformation calorimetry for the typical glass-like and crystalline polymers and it has been found that in uniaxially oriented crystalline polymers at aboveT _g the internal energy undergoes inversion due to the negative coefficient of thermal expansion. It has been demonstrated that the thermoelastic behaviour of two-phase crystalline polymers is controlled by the volume (irrotational) elasticity of amorphous regions rather than by shape elasticity typical of rubber elasticity. From this position, a thermophysical analysis of the deformation of the basic models of oriented crystalline polymers and combined investigation of the thermal phenomena and structural changes in oriented PE and PP have been carried out. It has been shown that the Peterlin-Prevorsek model which implies existence of both intra- and interfibrillar amorphous regions quite adequately account for the thermophysical and structural effect observed in tension of the oriented specimens in the original and annealed state. Thermoelastic properties of super-oriented crystalline polymers have also been discussed in brief.Dedicated to Professor Dr. F. H. Müller     

Micromechanical modeling of the elastic properties of semicrystalline polymers: A three‐phase approach

The mechanical performance of semicrystalline polymers is strongly dependent on their underlying microstructure, consisting of crystallographic lamellae and amorphous layers. In line with that, semicrystalline polymers have previously been modeled as two and three‐phase composites, consisting of a crystalline and an amorphous phase and, in case of the three‐phase composite, a rigid‐amorphous phase between the other two, having a somewhat ordered structure and a constant thickness. In this work, the ability of two‐phase and three‐phase composite models to predict the elastic modulus of semicrystalline polymers is investigated. The three‐phase model incorporates an internal length scale through crystalline lamellar and interphase thicknesses, whereas no length scales are included in the two‐phase model. Using linear elastic behavior for the constituent phases, a closed form solution for the average stiffness of the inclusion is obtained. A hybrid inclusion interaction model has been used to compute the effective elastic properties of polyethylene. The model results are compared with experimental data to assess the capabilities of the two‐ or three‐phase composite inclusion model. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Infrared dichroism of polyethylene crystallized by orientation and pressure in a capillary viscometer

Polarized infrared absorption spectra have been obtained by Fourier-transform spectroscopy for several crystalline and noncrystalline absorption bands of polyethylene crystallized by orientation and pressure in capillary viscometer. An analysis of data obtained at room temperature yielded degrees of crystallinity which are in good accord with values obtained from calorimetry and density measurements. The dichroism of the infrared absorption bands for the crystalline region revealed an extreme degree of orientation consistent with previous x-ray studies and also demonstrated that the degree of orientation is a good or better than that obtained from drawn polyethylene films with extension ratios of 20. Dichroism of bands from the amorphous phases revealed that the noncrystalline chain segments are in a comparatively relaxed state compared with results for drawn films having extension ratios of about 2 to 7. This is 1/10 to 1/3 the extension ratio of drawn polyethylene which shows maximum crystalline orientation. The results also indicated that the ratio of the GTG′ to GG segment conformations in the amorphous regions is larger than that of amorphous portions in unoriented polyethylene. The vinyl endgroups were shown to be highly oriented, while the main bulk of the amorphous polymer was fairly relaxed, i.e., of low orientation. It is concluded that the amorphous polyethylene state is strongly dependent on the nature of the crystalline–amorphous interface.     

Micromechanical modeling of anisotropic behavior of oriented semicrystalline polymers

Some manufacturing processes of polymeric materials, such as injection molding or film blowing, cause the final product to be highly anisotropic. In this study, the mechanical behavior of drawn polyethylene (PE) tapes is investigated via micromechanical modeling. An elasto‐viscoplastic micromechanical model, developed within the framework of the so‐called composite inclusion model, is presented to capture the anisotropic behavior of oriented semicrystalline PE. Two different phases, namely amorphous and crystalline (both described by elasto‐viscoplastic constitutive models), are considered at the microstructural level. The initial oriented crystallographic structure of the drawn tapes is taken into account. It was previously shown by Sedighiamiri et al. (Comp. Mater. Sci. 2014, 82, 415) that by only considering the oriented crystallographic structure, it is not possible to capture the macroscopic anisotropic behavior of drawn tapes. The main contribution of this study is the development of an anisotropic model for the amorphous phase within the micromechanical framework. An Eindhoven glassy polymer (EGP)‐based model including different sources of anisotropy, namely anisotropic elasticity, internal stress in the elastic network and anisotropic viscoplasticity, is developed for the amorphous phase and incorporated into the micromechanical model. Comparisons against experimental results reveal remarkable improvements of the model predictions (compared to micromechanical model predictions including isotropic amorphous domains) and thus the significance of the amorphous phase anisotropy on the overall behavior of drawn PE tapes. © 2019 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 378–391     

Structural arrangement of crystalline/amorphous phases of polyethylene‐block‐polystyrene copolymer as induced by orientation techniques

A polyethylene‐block‐polystyrene copolymer film having a bicontinuous crystalline/amorphous phases was tensile‐drawn under various conditions for the structural arrangement of these phases. The prepared film could be drawn below the melting temperature of the polyethylene component, with the highest drawability obtained at 60°C. However, the initial bicontinuous structure was gradually destroyed with increasing strain because the drawing temperature was lower than the glass‐transition temperature of the polystyrene component. Correspondingly, a necking phenomenon was clearly recognizable when samples were drawn. In contrast, drawing near the melting temperature of the polyethylene component produced less orientation of both the crystalline and amorphous phases, resulting in homogeneous deformation with lower drawing stress. These results indicated that the modification of the lower ductility of the polystyrene component was key to the effective structural arrangement of both phases by tensile drawing. Here, a solvent‐swelling technique was applied to improve polystyrene deformability even below its glass‐transition temperature. Tensile drawing after such a treatment successfully induced the orientation of both the crystalline and amorphous phases while retaining their initial continuities. A change in the deformation type from necking to homogeneous deformation was also confirmed for the stress–strain behavior. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1731–1737, 2006     

An x-ray pole figure analysis on biaxially deformed polyethylene film

The orientational states induced upon two-step biaxially stretching low-density polyethylene at 25°C have been investigated. A pole figure analysis of the (200), (020), and (002) crystalline planes has been employed to elucidate the evolution of the molecular crystalline orientation as a function of biaxial stretching. The initial uniaxial-like orientation induced along the extrusion direction of the films was gradually lost upon transverse stretching and, consequently, replaced by a biaxial orientation as suggested by the orientation functions. In these cases, the a crystallographic axis was observed to be strongly oriented along the film normal, thus confining the c and b axes to the film plane. The pole figures clearly indicate that the c and b axes are preferentially aligned 45° with respect to the stretching directions. This unique orientational state of the orthorhombic unit cell of polyethylene has been termed a biaxial-double orientation. Birefringence measurements on the biaxial samples indicated that the amorphous and crystalline regions are simultaneously biaxially oriented. The evolution of the crystalline orientation as a function of stretching was conveniently followed on a White/Spruiell orientation triangle. Quantification was hindered, however, by the presence of different crystal populations in the biaxially stretched samples. © 1994 John Wiley & Sons, Inc.     

Orientation of uniaxially stretched poly(ethylene naphthalene 2,6‐dicarboxylate) films by polarized infrared spectroscopy

Poly(ethylene naphthalene‐2,6‐dicarboxylate) has been uniaxially stretched at different draw ratios and at two different temperatures below and above its glass transition (T_g ～ 120 °C) respectively, at 100 and 160 °C. Crystallinity has been evaluated from calorimetric analyses and compared to the values deduced by FTIR spectroscopic data. As expected, the obtained results are quite similar and show that films stretched at lower temperature (100 °C) are more crystalline than those stretched at 160 °C. Optical anisotropy associated with orientation has been evaluated by birefringence and show that films stretched at 100 °C are more birefringent than those stretched at 160 °C as a result of a higher chain relaxation above T_g. Polarized FTIR was also performed to evaluate the individual orientation of amorphous and crystalline phases by calculating dichroic ratios R and orientation functions 〈P₂(cos θ)〉 and also show that amorphous and crystalline phases are more oriented in the case of films stretched below T_g. Nevertheless, the orientation of the amorphous phase is always weaker than that of the crystalline phase. Films stretched at 100 °C show a rapid increase in orientation (and crystallinity) with draw ratio and 〈P₂(cos θ)〉 reaches a limit value when draw ratio becomes higher than 3.5. Films drawn at 160 °C are less oriented and their orientation is increasing progressively with draw ratio without showing a plateau. A careful measurement of the IR absorbance was necessary to evaluate the structural angles of the transition moments to the molecular chain axis. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1950–1958, 2007     

Dimensional stability of regenerated cellulose film in relation to orientations of crystalline and noncrystalline phases

The dimensional stability of regenerated cellulose film on swelling with water is discussed in relation to the biaxial orientation of the two kinds of structural units, cellulose II crystallites and noncrystalline chain segments, and their anisotropic swelling (anisotropic absorption of water). Considerable dimensional stability in the plane of the film but enormous instability of thickness on swelling in water of some commercial cellophanes is qualitatively interpreted in terms of the planar orientation of crystal (101) planes along the film surface and the orientation of the noncrystalline chain segments parallel to the film surface. The dimensional changes on swelling from the completely dry state to 10% moisture regain were further interpreted quantitatively in terms of the degrees of biaxial orientation of the two kinds of structural units and their degrees of anisotropic swelling by modifying the Hermans monophase model for crystalline and noncrystalline biphase structures. The following degrees of anisotropic swelling of the structural units were thus obtained: q_{c, [101]} = 0.40%, q_{c, [101 ]} = ?0.33%, and q_a = 2.42%.     

Mechanical properties of oriented low‐density polyethylene with an oriented lamellar‐stack morphology

A quantitative study was undertaken of the anisotropy of low‐strain mechanical behavior for specially oriented polyethylene with controlled crystalline and lamellar orientation. The samples were prepared by the die drawing of injection‐molded rods of polyethylene and annealing. This produced a parallel lamellar structure for which a simple, three‐dimensional composite laminate model could be used to calculate the expected anisotropy. Experimental data, including X‐ray strain measurements of the lateral crystalline elastic constants, showed good quantitative agreement with the model prediction. The X‐ray strain measurements confirmed that the amorphous regions exert large constraints on the crystalline phase in the lateral directions, where an order of magnitude difference was found between the measured apparent lateral crystalline compliances in the lamellar‐stack sample and the expected values for a perfect crystal. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 755–764, 2000     

Polarized Raman studies of crystalline and amorphous orientation in polyethylene

Polarized Raman intensities have been obtained from thin films of oriented low-density polyethylene (PE) immersed in silicone oil to minimize surface scattering. Studies were made using the 1170 cm^?1 crystalline band and the 1081 cm^?1 amorphous band, and from these the orientation averages 〈cos² θ〉 and 〈cos⁴ θ〉 were calculated. These were found to compare favorably with the values of 〈cos² θ〉 for the polymer chain in the crystalline and amorphous phases obtained from measurements of infrared dichroism. Both orientation averages could be theoretically fitted by using reasonable parameters.     

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.     

Isobaric thermal expansivities of polyethylenes with various crystallinities over the pressure range from 0.1 to 300 MPa and over the temperature range from 303 to 393 K

A pressure-controlled scanning calorimeter (PCSC) has been applied for measuring the isobaric volume thermal expansivities (α_p) of crystalline polymers as a function of pressure up to 300 MPa at various temperatures. The measurements have been performed for several well-defined polyethylenes with various degrees of crystallinity at 302.6, 333.0, 362.6, and 393.0 K. The results are reported as values of coefficients in a correlation equation, which facilitates the use of reported data over large ranges of temperature and pressure. The general pressure-temperature behavior of α_p for all polyethylenes under study is such that α_p increases with temperature and decreases with pressure. The increase with temperature is smaller at high pressures and the isotherms of α_p have a tendency to converge at high pressures; α_p decreases linearly with the crystallinity of the polyethylene over the whole range of pressure and temperature under investigation. From the linear approximation of experimental data for polyethylenes with various crystallinities the estimated α_p for both crystal and amorphous phases of polyethylenes have been determined as a function of pressure up to 300 MPa at 302.6, 333.0, and 362.5 K. The obtained results have been compared with available literature crystallographic data and with the values derived from the Pastine theoretical equation of state for both crystalline and amorphous phases. © 1996 John Wiley & Sons, Inc.     

Thermal conductivity and thermal expansivity of thermotropic liquid crystalline polymers

The thermal conductivity and thermal expansivity of a thermotropic liquid crystalline copolyesteramide with draw ratio λ from 1.3 to 15 have been measured parallel and perpendicular to the draw direction from 120 to 430 K. The sharp rise in the axial thermal conductivity K_par; and the drastic drop in the axial expansivity α_∥ at low λ, and the saturation of these two quantities at λ > 4 arise from the corresponding increase in the degree of chain orientation revealed by wide-angle x-ray diffraction. In the transverse direction, the thermal conductivity and expansivity exhibit the opposite trends but the changes are relatively small. The draw ratio dependences of the thermal conductivity and expansivity agree reasonably with the predictions of the aggregate model. At high orientation, K_par; of the copolyesteramide is slightly higher than that of polypropylene but one order of magnitude lower than that of polyethylene. In common with other highly oriented polymers such as the lyotropic liquid crystalline polymer, Kevlar 49, and flexible chain polymer, polyethylene, α_par; of the copolyesteramide is negative, with a room temperature value differing from those of Kevlar 49 and polyethylene by less than 50%. Both the axial and transverse expansivity show transitions at about 390 and 270 K, which are associated with large-scale segmental motions of the chains and local motions of the naphthalene units, respectively. ©1995 John Wiley & Sons, Inc.     

Orientation and mechanical properties of PBT and its blends with a liquid-crystalline copolyester

Blends of poly (butylene terephthalate) (PBT) and a liquid-crystalline copolyester (60 mol % poly(p-hydroxy benzoic acid)/40 mol % polyethylene terephthalate) (LCP) were prepared in the melt state. The investigation of mechanical properties indicated that, for the processing conditions used, neither the addition of up to 30 wt % LCP to PBT nor the cooling history affected significantly the tensile modulus E. For oriented specimens, a marked improvement of E was obtained for all the blends, and increased with the LCP content. This improvement was more marked for slowly cooled samples. X-ray diffraction was used to quantify the orientation of the crystalline PBT and liquid-crystalline LCP phases. It was shown that neither the thermal history nor the presence of up to 30 wt % LCP affected the orientation behavior of the PBT crystalline phase. For the LCP phase, measurements were not possible for concentrations lower than 10 wt %, and were more difficult and less precise than for PBT. Nevertheless, it was possible to show that a better orientation was obtained for the slowly cooled samples and for higher concentrations of LCP in the blends. This correlated with the enhancement of mechanical properties observed for the oriented samples.     

Liquid crystalline epoxy resin with improved thermal conductivity by intermolecular dipole–dipole interactions

To address tremendous needs for developing efficiently heat dissipating materials with lightweights, a series of liquid crystalline epoxy resins (LCEs) are designed and synthesized as thermally conductive matrix. All prepared LCEs possess epoxies at the molecular side positions and cyanobiphenyl mesogenic end groups. Based on several experimental results such as differential scanning calorimetry, polarized optical microscopy, and X‐ray diffraction, it is found that the LCEs exhibited liquid crystalline mesophases. When LCE is cured with a diamine crosslinker, the cured LCE maintains the oriented LC domain formed in the uncured state, ascribing to a presence of dipole–diploe and π–π interactions between cyanobiphenyl mesogenic end groups. Due to the anisotropic molecular orientation, the cured LCE exhibits a high thermal conductivity of 0.46 W m^?1 K^?1, which is higher than those of commercially available crystalline or amorphous epoxy resins. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 708–715     

Structural changes and chain radius of gyration in cold-drawn polyethylene after annealing: small- and wide-angle X-ray scattering and small-angle neutron scattering studies

Samples made from linear polyethylene were drawn at room temperature and subsequently annealed at high temperatures below the melting point. The structural changes of the crystalline lamellae and lamellar superstructures as well as the single chain radius of gyration were studied by means of combined small- and wide-angle X-ray scattering and small-angle neutron scattering (SANS). After drawing, the polymeric chain segments in the crystalline phase are preferentially oriented along the drawing direction with a high degree of orientation whereas the lamellae in the samples are found to be slightly sheared exhibiting oblique surfaces as evidenced by X-ray scattering. SANS indicates that the chains are highly elongated along the drawing direction. Annealing the deformed samples at temperatures where the mechanical alpha-process of polyethylene is active leads to a thickening of both crystalline lamellae and amorphous layers. The chains in the crystalline phase retain their high degree of orientation after annealing while the lamellae are sheared to a larger extent. In addition, there is also lateral growth of the crystalline lamellae during high-temperature annealing. Despite the structural changes of the crystalline and amorphous regions, there is no evidence for global chain relaxation. The global anisotropic shape of the chains is preserved even after prolonged annealing at high temperatures. The results indicate that the mobility of polyethylene chains-as seen, e.g., by 13C NMR-is a local phenomenon. The results also yield new insight into mechanical properties of drawn PE, especially regarding stress relaxation and creep mechanisms.     

Systematic coarse‐graining of semicrystalline polyethylene

In an effort to accelerate simulations exploring deformation mechanisms in semicrystalline polymers, we have created structure‐based coarse‐grained (CG) models of polyethylene and evaluated the extent to which they can simultaneously represent its amorphous and crystalline phases. Two CG models were calibrated from target data sampled from atomistic simulations of supercooled oligomer melts that differ in how accurately they represent the distribution of bond lengths between CG sites. Both models yield semicrystalline morphology when simulations are performed at ambient conditions, and both accurately predict the glass transition and melt temperatures. A thorough evaluation of the models was then conducted to assess how well they represent various properties of the amorphous and crystalline phases. We found that the model that more faithfully reproduces the target bond length distribution poorly represents the crystalline phase, which results from its inability to reproduce correlations in the structural distributions. The second model, which utilizes a harmonic bond potential and thus reproduces the target bond length distribution less accurately, represents the structure and chain mobility within the crystalline phase more realistically. Furthermore, the latter model more faithfully reproduces the vastly different relaxation timescales of the phases, a critical feature for modeling deformation mechanisms in semicrystalline polymers. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 331–342     

Molecular deformation mechanisms of isotactic polypropylene in α‐ and β‐crystal forms by FTIR spectroscopy

The orientation behavior of isotactic polypropylene (iPP) in α‐ and β‐crystal form was investigated by rheo‐optical Fourier transformed infrared (FTIR) spectroscopy. This method enabled quantification of the degree of orientation as a feature of structural changes during uniaxial elongation in not only the crystalline phase but also the amorphous one. Molecular orientation mechanisms can be successfully derived from experimental results. Generally, three mechanisms were detected for iPP: (1) interlamellar separation in the amorphous phase, (2) interlamellar slip and lamellar twisting at small elongations, and (3) intralamellar slip at high elongations. The third mechanism was favored by α‐PP, whereas β‐PP favored the second mechanism, which, in fact, was responsible for the different mechanical properties of both materials at the macroscopic level. On the other hand, crystallization conditions may have significantly affected the amorphous orientation. Nevertheless, for both iPP types the chains in the amorphous phase always oriented less than did those in the crystalline phase. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4478–4488, 2004     

Modeling and simulation of morphology variation during the solidification of polymer melts with amorphous and semi‐crystalline phases

The solidification of polymer melts in practical processing such as extrusion, injection molding and blow molding can significantly influence the inner structure and performance of final products. The investigation of its mechanism has both scientific and industrial interests. In the study, the three‐dimensional mathematical model is developed for the simulation of morphology variation in the solidification of polymer melts with amorphous and semi‐crystalline phases. The amorphous phase is simulated as the finite extensible nonlinear elastic dumbbell with a peterlin closure approximation (FENE‐P) fluid and the semi‐crystalline phase is approximated as rigid rods that grow and oriented in the flow field. The model of amorphous phase and semi‐crystalline phase are coupled through the stress and momentum balance and the feedback of crystallinity to the system relaxation time. The evolution of crystallization kinetics process are described by using a set of Schneider equation that discriminating the relative roles of the thermal and the flow effect on the crystallization behavior. With the standard Galerkin formulation adopted as basic computational framework, the discrete elastic viscous stress splitting algorithm in cooperating with the streamline upwinding approach serves as a relatively robust numerical scheme by using penalty finite element–finite difference simulation with a decoupled solving algorithm. The proposed mathematical model and numerical method have been successfully applied to the investigation of solidification of polymer melts in the extrusion process. The variations of orientation and crystallization morphology during the solidification process are further discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Orientation of polymer molecules during melt spinning. II. Orientation of crystals in as-spun polyolefin fibers

Three different polyolefins, a linear polyethylene, an isotactic polypropylene, and an isotactic polybutene-1, were melt-spun into filaments. The degree of orientation of the filaments was measured by polarized-light microscopy, x-ray diffraction, and a retraction technique, and the results were then related to the melt-draw ratio. The increase in the elastic deformation ratio of polymer chains by spin-stretching, estimated by thermal retraction at a temperature above T_m, was monotonic with respect to the melt-draw ratio. On the other hand, as-spun filaments of polyethylene and polypropylene were characterized by a plateau in birefringence over the range of melt-draw ratios from 8 to 80. The change in orientation functions for crystals in these filaments was similar to the change of birefringence. On the other hand, the birefringence and the crystalline orientation functions for polybutene-1 increased smoothly with increasing melt-draw ratio. The most highly melt-drawn filaments of these polymers had a strongly oriented structure, corresponding to that in highly cold-drawn specimens.