While crystallization behavior of isotactic polypropylene homopolymers had been subject to a wide range of experimental and modeling studies, this is not the case for propylene-ethylene random copolymers (PPR). This class of polymers offers up to now significant challenges, both from an experimental as well as a modeling perspective. The ethylene incorporation in the propylene chains, as well as the distribution of this comonomer, has a marked effect on the crystallization kinetics. Moreover, the presence of these defects causes a clear separation between primary crystallization (i.e. space filling) and subsequent secondary crystallization (increase of crystallinity in filled space) within the spherulitic skeletons, particularly subsequent at high primary crystallization temperatures. In this work, the underlying mechanism is first quantified by means of a combination of in-situ WAXD and SAXS experiments, as well as ex-situ WAXD experiments and calorimetric measurements. Based on these experiments an extended model framework is presented, capable of predicting multiphase non-isothermal crystallization kinetics as well as the final crystallinity as a function of the applied thermal conditions relevant for processing. The chemical composition distribution (CCD) of the ethylene comonomer serves as critical input to parameterize the model. Optical microscopy- and DSC experiments are used for parameterization of the primary crystallization model. The model developed in this study is, in principle, applicable to all polypropylenes, ranging from homo-polymers to random copolymers with variable comonomer content and/or CCD but, so far, only applied and validated on one PPR. To validate the model and the parameters for a given PPR, several non-isothermal and isothermal experiments (the latter followed by subsequent cooling) are conducted over a wide range of crystallization temperatures and cooling rates. The good match between experiments and model predictions demonstrates the power of the newly developed framework. The final crystallinity, the amount of α- and γ-phase, and the ratio between primary and secondary crystallization can be predicted as a function of the time-temperature history. To the best knowledge of the authors, it is the first time that such a direct connection with the CCD is incorporated in a crystallization model. Consequently, the model offers a new tool to bridge the gap between chemical structure and resulting product properties, which now has come one step closer for PPR systems.

This paper provides a model of the crystallization kinetics of polyamide 6 (PA6), including primary and secondary crystallization, lamellar thickness distribution, and the evolution of the mobile and rigid fractions of the amorphous phase. The kinetics includes the two-phase structure, the monoclinic a-phase and the pseudo-hexagonal gamma-meso phase, of which the fractions depend on the thermal history during solidification. The model is parameterized with experimental results from the literature. The thickness of the rigid amorphous layer was the only parameter to be estimated. The obtained results indicate that the fraction of the amorphous rigid fraction depends not only on the thermal history but also on the crystalline phase and if the rigid amorphous layer was formed in combination with the alpha- or gamma-meso phases. These results provide the bases for predicting and controlling mechanical properties, which can strongly depend on processing conditions as, for example, experienced during injection molding.

The extrusion of highly filled elastomers is widely used in the automotive industry. In this paper, we numerically study the effect of thixotropy on 2D planar extrudate swell for constant and fluctuating flow rates, as well as the effect of thixotropy on the swell behavior of a 3D rectangular extrudate for a constant flowrate. To this end, we used the Finite Element Method. The state of the network structure in the material is described using a kinetic equation for a structure parameter. Rate and stress-controlled models for this kinetic equation are compared. The effect of thixotropy on extrudate swell is studied by varying the damage and recovery parameters in these models. It was found that thixotropy in general decreases extrudate swell. The stress-controlled approach always predicts a larger swell ratio compared to the rate-controlled approach for the Weissenberg numbers studied in this work. When the damage parameter in the models is increased, a less viscous fluid layer appears near the die wall, which decreases the swell ratio to a value lower than the Newtonian swell ratio. Upon further increasing the damage parameter, the high viscosity core layer becomes very small, leading to an increase in the swell ratio compared to smaller damage parameters, approaching the Newtonian value. The existence of a low-viscosity outer layer and a high-viscosity core in the die have a pronounced effect on the swell ratio for thixotropic fluids.

In this paper, an experimental strategy is presented to characterize the rheological behavior of filled, uncured rubber compounds. Oscillatory shear experiments on a regular plate-plate rheometer are combined with a phenomenological thixotropy model to obtain model parameters that can be used to describe the steady shear behavior. We compare rate- and stress-controlled kinetic equations for a structure parameter that determines the deformation history-dependent spectrum and, thus, the dynamic thixotropic behavior of the material. We keep the models as simple as possible and the characterization straightforward to maximize applicability. The model can be implemented in a finite element framework as a tool to simulate realistic rubber processing. This will be the topic of another work, currently under preparation. In shaping processes, such as rubber- and polymer extrusion, with realistic processing conditions, the range of shear rates is far outside the range obtained during rheological characterization. Based on some motivated choices, we will present an approach to extend this range.

Filament stretching rheometry is a prominent experimental method to determine rheological properties in extensional flow whereby the separating plates determine the extension rate. In literature, several correction factors that can compensate for the errors introduced by the shear contribution near the plates have been introduced and validated in the linear viscoelastic regime. In this work, a systematic analysis is conducted to determine if a material-independent correction factor can be found for non-linear viscoelastic polymers. To this end, a finite element model is presented to describe the flow and resulting stresses in the filament stretching rheometer. The model incorporates non-linear viscoelasticity and a radius-based controller for the plate speed is added to mimic the typical extensional flow in filament stretching rheometry. The model is validated by comparing force simulations with analytical solutions. The effects of the end-plates on the extensional flow and resulting force measurements are investigated, and a modification of the shear correction factor is proposed for the non-linear viscoelastic flow regime. This shows good agreement with simulations performed at multiple initial aspect ratios and strain rates and is shown to be valid for a range of polymers with non-linear rheological behaviour.

A finite element model is presented to describe the flow, resulting stresses and crystallization in a filament stretching extensional rheometer (FiSER). This model incorporates nonlinear viscoelasticity, nonisothermal processes due to heat release originating from crystallization and viscous dissipation as well as the effect of crystallization on the rheological behavior. To apply a uniaxial extension with constant extension rate, the FiSER plate speed is continuously adjusted via a radius-based controller. The onset of crystallization during filament stretching is investigated in detail. Even before crystallization starts, the rheology of the material can change due to the effects of flow-induced nucleation on the relaxation times. Both nucleation and structure formation are found to be strongly dependent on temperature, strain rate and sample aspect ratio. The latter dependence is caused by a clear distribution of crystallinity over the radius of the filament, which is a result of the nonhomogeneous flow history in the FiSER. Therefore, this numerical model opens the possibility to a priori determine sample geometries resulting in a homogeneous crystallinity or to account for the nonhomogeneity.

Viscosity controls an important issue in polymer processing. This paper reports on the terminal viscosity behavior of a polymer melt containing grafted nanosilica particles. The melt viscosity behavior of the nanocomposites was found to depend on the interaction between the polymer matrix and the nanoparticle surface. In the case of polycarbonate (PC) nanocomposites, the viscosity decreases by approximately 25% at concentrations below 0.7 vol% of nanosilica, followed by an increase at higher concentrations. Chemical analysis shows that the decrease in viscosity can be attributed to in situ grafting of PC on the nanosilica surface, leading to a lower entanglement density around the nanoparticle. The thickness of the graft layer was found to be of the order of the tube diameter, with the disentangled zone being approximately equal to the radius of gyration (Rg) polymer chain. Furthermore, it is shown that the grafting has an effect on the motion of the PC chains at all timescales. Finally, the viscosity behavior in the PC nanocomposites was found to be independent of the molar mass of PC. The PC data are compared with polystyrene nanocomposites, for which the interaction between the polymer and nanoparticles is absent. The results outlined in this paper can be utilized for applications with low shear processing conditions, e.g., rotomolding, 3D printing, and multilayer co-extrusion.

The effect of shear flow on the crystallization of homopolymers has been widely studied, however more complex systems such as nanocomposites or polymer blends nanocomposites (PBNANOs) have received less attention. In this work, the effect of pressure and shear flow on the crystallization process of polypropylene-based nanocomposites and polypropylene/polyethylene terephthalate PBNANOs have been studied employing dilatometry (PVT), X-ray, rheology, and DSC. The material systems used allow studying the effect of shear in the presence of nanoparticles that do not have a nucleating effect, as well as the combined effect of shear and nucleating nanoparticles. Nucleating nanoparticles increase the crystallization temperature more significantly because of the combined effect of nucleation and flow. For carbon nanotubes, nucleation is more pronounced due to stronger interactions with PP chains, as demonstrated by rheological measurements. For PBNANOs the effect of shear on crystallization is more significant due to the higher amount of available surfaces.

We present a rheometer that combines the possibility to perform in situ X-ray experiments with a precise and locally controlled uniaxial extensional flow. It thus allows us to study the crystallization kinetics and morphology evolution combined with the rheological response to the applied flow field. A constant uniaxial deformation rate is ensured, thanks to a fast control scheme that drives the simultaneous movement of the top and bottom plates during a pulling experiment. A laser micrometer measures the time evolution of the smallest diameter, where the highest stress is concentrated. The rheometer has a copper temperature-controlled oven with the ability to reach 250 °C and a N2 connection to create an inert atmosphere during the experiments. The innovation of our rheometer is the fixed location of the midfilament position, which is possible because of the simultaneous controlled movement of the two end plates. The copper oven has been constructed with four ad hoc windows: two glass windows for laser access and two Kapton windows for X-ray access. The key feature is the ability to perfectly align the midfilament of the sample to the laser micrometer and to the incoming X-ray beam in a synchrotron radiation facility, making it possible to investigate the structure and morphologies developed during extensional flow. The rheological response measured with our rheometer for low-density polyethylene (LDPE) is in agreement with the linear viscoelastic envelope and with the results obtained from the existing extensional rheometers. To demonstrate the capability of the instrument, we have performed in situ-resolved X-ray experiments on LDPE samples exhibiting extensional flow-induced crystallization.

ABSTRACTThe influence of stress, temperature, and relative humidity on plasticity‐controlled failure of molded and laser‐sintered polyamide 12 (PA12) has been investigated. Ree–Eyring's flow theory is employed and modified to take into account the effect of relative humidity on the deformation kinetics. By introducing the concept of critical strain, time to failure in plasticity‐controlled regime is predicted starting from the yield kinetics. Creep test is performed to estimate the critical strain and to validate model predictions. The model predictions are in good agreement with the experimental results, showing that the model is a suitable and reliable tool to evaluate mechanical response as function of temperature and relative humidity. We demonstrate that, while, at high applied strain rates, a significant difference is found, the mechanical response under constant strain rate as well as the failure kinetics in plasticity‐controlled regime of the sintered PA12 are comparable with those of the molded material. © 2019 The Authors. Journal of Applied Polymer Science published by Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48525.

We report on the role of temperature and shear on the melt behavior of iPP in the presence of the organic compound N1,N1'-(propane-1,3-diyl)bis(N2-hexyloxalamide) (OXA3,6). It is demonstrated that OXA3,6 facilitates a viscosity suppression when it resides in the molten state. The viscosity suppression is attributed to the interaction of iPP chains/subchains with molten OXA3,6 nanoclusters. The exact molecular mechanism has not been identified; nevertheless, a tentative explanation is proposed. The observed viscosity suppression appears similar to that encountered in polymer melts filled with solid nanoparticles, with the difference that the OXA3,6 compound reported in this study facilitates the viscosity suppression in the molten state. Upon cooling, as crystal growth of OXA3,6 progresses, the decrease in viscosity is suppressed. Retrospectively, segmental absorption of iPP chains on the surface of micrometer-sized OXA3,6 crystallites favors the formation of dangling arms, yielding OXA3,6 crystallites decorated with partially absorbed iPP chains. In other words, the resulting OXA3,6 particle morphology resembles that of a hairy particle or a starlike polymer chain. Such hairy particles effectively facilitate a viscosity enhancement, similar to branched polymer chains. This hypothesis and its implications for the shear behavior of iPP are discussed and supported using plate-plate rheometry and slit-flow experiments combined with small-angle X-ray scattering analysis.

ABSTRACTThe objective of this work is to investigate the effect of the molecular mobility and resin formulation of UV‐curable acrylate systems on conversion and ultimate mechanical properties. Thin single‐layer films are produced from a series of nine mixtures of bisphenol A ethoxylate diacrylate, having different molecular weights (BisDAn = 2, BisDAn = 4, and a 50/50 mixture), with different amounts of tetraethylene glycol diacrylate (TEGDA) (0, 10, and 30 wt %). Fourier transform infrared analysis, tensile, and dynamic mechanical tests are carried out on UV post‐cured resins, and the results are correlated with the amount of TEGDA. A higher content of TEGDA gives rise to an increase in conversion and glass‐transition temperature. Tests on pure BisDAn = 2 and mixtures of BisDAn = 2 and BisDAn = 4 (BisDAn = 2 + 4) show that with increasing TEGDA content, the crosslink density increases. An increase in molecular weight of the acrylate monomer changes the final mechanical properties of UV‐cured products. A material having a rubber behavior is the result of this change. Next to UV post‐curing, the effect of thermal post‐curing is studied. The results show that thermal treatments affect the mechanical properties mainly if the polymer has a low crosslink density. Formulations highly loaded with TEGDA lead to polymers with high crosslink density, low network mobility, and consequently low mechanical properties if thermally treated. Correlations between, on the one hand, resin formulation and process conditions and, on the other hand, the final mechanical properties of UV‐cured systems are established allowing to optimize the structure–mechanical properties relationship in acrylate networks. © 2019 The Authors. Journal of Applied Polymer Science published by Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48498.

To provide knowledge to improve the mechanical performance of Polyamide 12 (PA12) sintered products, we have studied experimentally the mechanical response and structure development under constant strain rate of compression moulded and laser sintered PA12 by means of in situ small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD) experiments. It is found that at low temperatures, i.e., below the glass transition temperature, the brittle failure of laser sintered samples is determined by the fast formation of voids that originate at the beginning of the macroscopic plastic deformation. This effect appears to be faster at temperatures below room temperature and it is less effective at higher temperatures. When tested at 120 ∘ C, sintered PA12 shows a better mechanical response in terms of yield stress and a comparable strain at break with respect to moulded PA12. This can be explained by considering that sintered samples have slightly thicker crystals that can sustain higher stress at high temperature. However, this also leads to the formation of a larger number of voids at low testing temperatures. This work does not attempt to quantify the micromechanics behind crystals deformation and disruption, but it provides a deeper insight in the difference between the mechanical response of moulded and sintered PA12.

The effect of prolonged storage at elevated temperatures on the isothermal crystallization kinetics of Polyamide 12 (PA12), the most used polymer in selective laser sintering (SLS), has been studied by means of Flash DSC experiments. The experimental results are described and modelled with a full multi phase crystallization model which allowed us to estimate the growth and nucleation kinetics for every PA12 crystal phase. Virgin PA12 powder has been annealed at different temperatures for different times to quantify the molecular weight evolution due to post condensation. To check the effect of thermal treatments on the final viscosity, rheology measurements have been carried out. We show that thermal annealing results in a significant increase in molecular weight and viscosity which lead to a reduction of the crystallization rate in a limited temperature range. At very low temperature the crystallization kinetics, expressed in terms of peak-time of crystallization, appears to be independent on the annealing treatment while in the temperature range between 100∘C and 150∘C a significant rate reduction is observed. We demonstrate that the crystallization kinetics in this temperature range is governed by the crystal growth process, i.e. the increase in molecular weight due to post-condensation causes a reduction of the growth rate of the main crystalline phases of PA12, namely α' and γ-phase. Similar to the low temperature crystallization, at temperature higher than 150∘C the annealing does not noticeably affect the growth rates and the crystallization kinetics of virgin and annealed PA12 overlap. These results can provide a better insight of the effect of reusing PA12 powder in the SLS process.

Being able to properly model the material structure formation during processing is a fundamental step to predict final product properties, especially for semicrystalline polymers, like isotactic PolyPropylene (iPP), which can develop a multiplicity of different crystalline phases and morphologies. For this reason, in the present work a complete model is presented which can predict the complex structure formation of iPP in conditions comparable to injection moulding. The model includes a full coupling between the non-isothermal flow of a non-linear viscoelastic fluid and its crystallization process, properly capturing the mutual interaction between the two and is implemented in a finite element framework and as such applicable for general processing applications. The model is the result of many years of numerical and experimental research in our group and finally provides a complete simulation tool able to reproduce the complex iPP crystallization behaviour in conditions equivalent to processing. The model can predict not only the local crystalline composition, distinguishing between the multiple phases and morphologies that can develop inside iPP, but also the effect of the structure formation on the rheology. Comparisons with the unique in-situ data of Troisi et al. [1] demonstrate the good performance of the model and encourage further research to adapt the model to simulate other relevant processes and processing conditions. The results presented here are input for future work on structure related mechanical properties, see for example Caelers et al. [2,3]. Notice that the approach as presented here is not specific for iPP. A similar methodology, sometimes with additional modelling, is used for other polymers.

Skin mechanics is of importance in various fields of research when accurate predictions of the mechanical response of skin is essential. This study aims to develop a new constitutive model for human skin that is capable of describing the heterogeneous, nonlinear viscoelastic mechanical response of human skin under shear deformation. This complex mechanical response was determined by performing large amplitude oscillatory shear (LAOS) experiments on ex vivo human skin samples. It was combined with digital image correlation (DIC) on the cross-sectional area to assess heterogeneity. The skin is modeled as a one-dimensional layered structure, with every sublayer behaving as a nonlinear viscoelastic material. Heterogeneity is implemented by varying the stiffness with skin depth. Using an iterative parameter estimation method all model parameters were optimized simultaneously. The model accurately captures strain stiffening, shear thinning, softening effect and nonlinear viscous dissipation, as experimentally observed in the mechanical response to LAOS. The heterogeneous properties described by the model were in good agreement with the experimental DIC results. The presented mathematical description forms the basis for a future constitutive model definition that, by implementation in a finite element method, has the capability of describing the full 3D mechanical behavior of human skin.

Cross-nucleation is defined as the nucleation of one polymorph on the surface of another polymorph of the same substance. Although the description of this particular form of heterogeneous nucleation is mainly phenomenological, recently dedicated quantitative studies are performed on several systems. In this work we propose a model framework that captures the phenomenon of cross-nucleation for a spherulitic seed-surface geometry, as well as the kinetic competition between the seed growth and the cross-nucleus formation, by the introduction of a tangential growth rate of the daughter polymorph. Regardless of the growth rate of the parent spherulite, this model describes the experimental data up to and including the final amount of cross-nuclei on its periphery, solely based on one parameter, the cross-nucleation rate. Furthermore, a strong temperature dependency of the kinetic competition between concomitantly growing α- and β-phase isotactic polypropylene is observed and related to the previously reported anomalous behavior of this cross-nucleating system.

Flow-induced crystallization of α- and γ-phases was studied for a propylene/ethylene random copolymer with 3.4 mol % ethylene at two high temperatures of 132 and 142 °C by combining a pressure-driven slit flow device with real-time synchrotron wide-angle X-ray diffraction. At 132 °C, it was found that both α- and γ-phases were generated at shear stresses ranging from 0.091 to 0.110 MPa and that the γ-phase always appeared later than the α-phase. However, for 142 °C and the same stresses, only the α-phase formed. Only upon cooling the partially crystallized copolymer did the γ-phase emerge. The lack of γ-crystals obtained at 142 °C is opposite to the behavior reported for quiescent crystallization under pressure, for which increasing temperature results in more and even pure γ-crystals. In the current study, the absence of γ-phase at 142 °C is tentatively associated with lack of epitaxial nucleation on α-lamellae and to relatively low growth rate of γ-crystals.

The effect of processing conditions during injection on the structure formation and mechanical properties of injection molded polyamide 6 samples was investigated in detail. A large effect of the mold temperature on the crystallographic properties was observed. Also the the effect of pressure and shear flow was taken in to consideration and analysed. The yield and failure kinetics, including time-to-failure, were studied by performing tensile and creep tests at several test temperatures and relative humidities. As far as mechanical properties are concerned, a strong influence of temperature and relative humidity on the yield stress and time-to-failure was found. A semi-empirical model, able to describe yield and failure kinetics, was applied to the experimental results and related to the crystalline phase present in the sample. In agreement with findings in the literature it is observed that for high mold temperatures the sample morphology is more stable with respect to humidity and temperature than in case of low mold temperatures and this effects could be successfully captured by the model. The samples molded at low temperatures showed, during mechanical testing, a strong evolution of the crystallographic properties when exposed to high testing temperature and high relative humidity, i.e., an increase of crystallinity or a crystal phase transition. This makes a full description of the mechanical behavior rather complicated.

The crystallization of Polyamide 12 (PA12) has been investigated using a new experimental setup which allows in-situ synchrotron Wide Angle X-ray Diffraction (WAXD) during Flash-DSC measurements. The experimental results are used to parameterize and validate a new numerical model to quantify the quiescent crystallization kinetics, under isothermal conditions, of the three important crystal structures of PA12, i.e. the, γ−, α′− and mesomorphic phase. The experimental approach is based on nucleation and growth after quenching the material from the melt to an isothermal temperature, described by the Schneider rate equations and the Kolmogorov-Avrami expression for the space filling. The experimental overall crystallization rate, expressed in terms of the crystallization half-time, as well as the phase composition, are well captured by the model over a wide range of temperatures, i.e. between the glass transition and the melting temperature. It is shown that at temperature below and above 100°C different nucleation mechanisms are dominant causing the bimodal dependence of the crystallization rate. This work forms the basis for a full model for non-isothermal conditions for which transitions between different phase have to be taken into account.