Crystallization of alkanes under quiescent and shearing conditions

We report molecular dynamics simulation of crystallization of model alkane systems conducted under constant pressure conditions. We have studied crystallization of n-eicosane (C₂₀H₄₂) and n-hexacontane (C₆₀ H₁₂₂) under quiescent and shearing conditions. We find preshearing before subjecting the melt to quiescent crystallization enhances the crystallization of higher molecular weight hexacontane, whereas, for low molecular weight eicosane, no significant change can be detected. For both alkanes applying steady planar shear significantly speeds up the crystallization. The crystal growth rate increases with the shear rate. However, we find that the critical shear rate above which the crystallization is enhanced, is inversely proportional to the size of the chains. In all cases the Weissenberg numbers of the sheared systems are moderate. We estimate them to be in the range of 0.01–10. Our quiescent simulations for eicosane predict crystallization temperature and lattice parameters of the crystalline phase in good agreement with experimental measurements. We have compared an order parameter used in the simulations against one analogous to that used in dilatometry experiments. Using this order parameter as a measure of crystallinity we predict the crystal growth rate of n-eicosane to be a maximum at ∼300 K in good agreement with experiments. Fitting crystallization growth data to Avrami's model we have calculated Avrami growth functions and exponents for many cases. For quiescent crystallization of n-eicosane we found the Avrami exponent calculated using our order parameter for defining degree of crystallinity, agrees well with that obtained in the experiments. For C60 the crystallization process is very slow at quiescent conditions; however preshearing enhances the crystal growth.     

Extensional-flow-induced crystallization of isotactic polypropylene

A filament stretching extensional rheometer with a custom-built oven was used to investigate the effect of uniaxial flow on the crystallization of polypropylene. Prior to stretching, samples were heated to a temperature well above the melt temperature to erase their thermal and mechanical histories and the Janeschitz-Kriegl protocol was applied. The samples were stretched at extension rates in the range of 0.01 s^-1 ￡ [(e)\dot] ￡ 0.75 s^-10.01\,\mbox{s}^{-1}\le \dot{{\varepsilon }}\le 0.75\,{\rm s}^{-1} to a final strain of ε = 3.0. After stretching, the samples were allowed to crystallize isothermally. Differential scanning calorimetry was applied to the crystallized samples to measure the degree of crystallinity. The results showed that a minimum extension rate is required for an increase in percent crystallization to occur and that there is an extension rate for which percent crystallization is maximized. No increase in crystallization was observed for extension rates below a critical extension rate corresponding to a Weissenberg number of approximately Wi = 1. Below this Weissenberg number, the flow is not strong enough to align the contour path of the polymer chains within the melt and as a result there is no change in the final percent crystallization from the quiescent state. Beyond this critical extension rate, the percent crystallization was observed to increase to a maximum, which was 18% greater than the quiescent case, before decaying again at higher extension rates. The increase in crystallinity is likely due to flow-induced orientation and alignment of contour path of the polymer chains in the flow direction. Polarized light microscopy verified an increase in number of spherulites and a decrease in spherulite size with increasing extension rate. In addition, small angle X-ray scattering showed a 7% decrease in inter-lamellar spacing at the transition to flow-induced crystallization. Although an increase in strain resulted in a slight increase in percent crystallization, no significant trends were observed. Crystallization kinetics were examined as a function of extension rate by observing the time required for molten samples to crystallize under uniaxial flow. The crystallization time was defined as the time at which a sudden increase in the transient force measurement was observed. The crystallization time was found to decrease as one over the extension rate, even for extension rates where no increase in percent crystallization was observed. As a result, the onset of extensional-flow-induced crystallization was found to occur at a constant value of strain equal to ε _c  = 5.8.     

Two-dimensional numerical analysis of non-isothermal melt spinning with and without phase transition

A model and simulation method are developed for two-dimensional non-isothermal melt spinning of a visco elastic melt. The visco elastic stress is evaluated from a non-isothermal Giesekus constitutive equation developed by application of the pseudo-time method to the isothermal form of the model [J. Non-Newt. Fluid Mech. (2001)]. The crystallization kinetics is described with the model proposed by Nakamura et al. [J. Appl. Polym. Sci. 17 (1973) 1031], whereas the crystallization rate, which is a function of both temperature and molecular orientation, is evaluated according to the equation proposed by Ziabicki [Fundamentals of Fiber Formation, Wiley, New York, 1976]. The set of non-linear governing equations is solved by using the DEVSS-G/SUPG finite element method. Melt spinning is simulated for two different polymers: amorphous polystyrene and fast-crystallizing Nylon-6,6. The analysis demonstrates that although the kinematics in the thread-line are approximately one-dimensional, the radially non-uniform thermal history, caused by the leading order variation of the temperature gradient ∂T/∂r, gives rise to radially non-uniform visco elastic stresses. This stress gradient results in radially non-uniform molecular orientation and a strong radial variation in crystallinity for Nylon-6,6. The radially non-uniform stress profiles obtained from the simulations are in good agreement with experimental results for melt spinning of polystyrene. Simulations of Nylon-6,6 show that the thermally-induced crystallization depends strongly on the choice of the Avrami index n, and a sharp increase in crystallinity due to stress-induced crystallization is predicted only when the molecules are highly oriented in the drawing direction at high drawing speeds. The significant influences of visco elasticity, air drag, and operating conditions on non-isothermal melt spinning dynamics also are predicted.     

Process validation of the normalized rheological function behavior during polymer crystallization

The film casting process of an isotactic polypropylene was adopted as the source of data to evaluate the behavior of a crystallizing polymer. The increase in viscosity due to the crystallization was quantified, and a model was proposed to estimate the normalized rheological function (NRF) during the process. The estimation was based also on the availability of rich sets of data, i.e., the polymer temperature and crystallinity, the film velocity and width distribution along the draw direction, gathered during the process. The quasi-experimental NRF evolutions were compared with just two of the very numerous hardening models proposed in literature, and the main result is that the process is coherent with the choice of an NRF model which predicts the increase in viscosity only for substantial crystallinity amount.     

Modeling the film casting process using a continuum model for crystallization in polymers

In this paper, the film casting process has been simulated using a new model developed recently using the framework of multiple natural configurations to study crystallization in polymers (see Rao and Rajagopal Z. Angew. Math. Phys. 53 (2002) 265; Polym. Eng. Sci. 44(1) (2004) 123; Simulation of the film blowing process for semicrystalline polymers, in press, 2004). In the film casting process, the material starts out as a viscoelastic melt and undergoes deformation and cooling, resulting in a semi-crystalline solid. In order to model the complex changes taking place in the material and predict the behavior of the final solid it is important to use models that are capable of describing these changes. The model used here has been formulated within a general thermodynamic framework that is capable of describing dissipative processes. In addition it handles in a direct manner the change of symmetry in the material; it thus provides a good basis for studying the crystallization process in polymers. The polymer melt is modeled as a rate type viscoelastic fluid and the crystalline solid polymer is modeled as an anisotropic elastic solid. The initiation criterion, marking the onset of crystallization and equations governing the crystallization kinetics arise naturally in this setting in terms of the appropriate thermodynamic functions. The mixture region, wherein the material transitions from a melt to a semi-crystalline solid, is modeled as a mixture of a viscoelastic fluid and an elastic solid. This is in marked contrast to earlier approaches where in the simulation has been done assuming that the material was a viscous fluid and the transition to a solid like behavior is achieved by increasing the viscosity to a large value resulting in a highly viscous fluid and not an elastic solid. The results of our simulations compare well against experimental data available in literature. In addition to these quantitative comparisons have carried out parametric study to study the influence of the different parameters on the film casting process.     

Thermally and flow induced crystallization of polymers at low shear rate

In semi-crystalline thermoplastic products, final properties are strongly dependent on the thermo-mechanical history experienced by the polymer melt during processing. More precisely, structural heterogeneities such as rigidity gradients and shrinkage anisotropy are directly related to the crystalline microstructure. Therefore, accurate prediction of part properties by a processing computer simulation code requires the implementation of an appropriate crystallization kinetics model, including both the effects of thermally and flow induced structure development. One issue is the necessity to improve the modeling of shear/extensional experimental data by relating the crystallization accelerating factors to an easily accessible material related variable. Several authors modeled the effect of the flow on the crystallization kinetics by using the isokinetic approach of Nakamura. Often, the resulting kinetic equations of these models account only for the evolution of the crystallinity fraction α leaving the influence of crystalline morphology aside. We may quote the work of Guo and Narh [1], which connects the flow influence on the crystallization rate to the increase in the thermodynamic melting temperature in the Nakamura model. In 2005, R.I. Tanner presented a comparison of some models describing the polymer crystallization at low shear deformation rates under isothermal conditions. Based on Tanner's study, we developed a model of crystallization at low shearing, applied to non-isothermal flows, using only macroscopic measurable parameters. The key features of the concentrated suspension theory were used to characterize the effect of crystallization on the viscosity. In addition, we assumed that the flow generates additional crystallization nuclei via a parameter which combines the deformation and the deformation rate. The concept of germination-growth is introduced using the fundamentals of the Avrami–Kolmogorov theory, coupled with a modified Schneider's approach. The model is applied to a polypropylene, in a cooled Couette flow configuration. The results show the enhancement of the crystallization kinetics due to the shearing. The definition of global parameters simplifies the type and the number of experiments needed for the model parameter identification. The use of Schneider's approach leads to a new way of discriminating the relative roles of the flow and the temperature on the crystallization phenomenon. The competition between the two driving causes is presented and discussed: at low cooling rate or at high temperature, the shearing effect predominates. Other interesting results show the size distribution of the spherulites as well as the volume proportion for each crystalline size in the polymer.     

聚合物注射成型流动残余应力的数值分析

建立了可压缩黏弹性聚合物熔体在薄壁型腔中充模/保压过程中非等温、非稳态流动 的数学模型,用数值方法实现了注射成型过程中流动应力和取向建立及松弛过程的模拟,研 究了熔体温度、模具温度和注射速率等工艺条件对分子冻结取向的影响,取得了与实验相符 的结果.     

高分子材料注塑固化阶段的残余应力分析

在结晶性高分子材料注塑过程的固化阶段，温度分布、材料细观结构和应力应变之间相互耦合，因而其变化规律非常复杂．本文在井上等人考虑材料细观结构变化的金属热加工工艺应力分析［３～６］的基础上，发展了一套用于高分子注塑固化阶段残余应力分析的本构描述和有限元分析方法．在本构模型中，同时考虑了温度变化、结晶和“冻结取向”对变形的贡献．     

Towards a rheological classification of flow induced crystallization experiments of polymer melts

Departing from molecular based rheology and rubber theory, four different flow regimes are identified associated to (1) the equilibrium configuration of the chains, (2) orientation of the contour path, (3) stretching of the contour path, and (4) rotational isomerization and a deviation from the Gaussian configuration of the polymer chain under strong stretching conditions. The influence of the ordering of the polymer chains on the enhanced point nucleation, from which spherulites grow, and on fibrous nucleation, from which the shish-kebab structure develops, is discussed in terms of kinetic and thermodynamic processes. The transitions between the different flow regimes, and the associated physical processes governing the flow induced crystallization process, are defined by Deborah numbers based on the reptation and stretching time of the chain, respectively, as well as a critical chain stretch. An evaluation of flow induced crystallization experiments reported in the literature performed in shear, uniaxial and planar elongational flows quantitatively illustrates that the transition from an enhanced nucleation rate of spherulites towards the development of the shish-kebab structure correlates with the transition from the orientation of the chain segments to the rotational isomerization of the high molecular weight chains in the melt. For one particular case this correlation is quantified by coupling the wide angle X-ray diffraction and birefringence measurements of the crystallization process to numerical simulations of the chain stretch of the high molecular weight chains using the extended Pom-Pom model in a cross-slot flow.     

Considerations of the “freezing-in” of flow-induced orientation in polymer melts by vitrification with application to processing

We develop the implications of the experimentally tested hypothesis that (i) birefringence developed during flow is quantitatively frozen-in during vitrification of glass-forming polymer melts and (ii) that the rheo-optical law may be combined with a knowledge of the stress field existing immediately prior to vitrification to yield birefringence distributions. This hypothesis is applied to various problems including multiaxial stretching of sheets, melt spinning, tubular film extrusion and injection molding. Special problems concerned with internal temperature distributions are discussed. We examine difficulties which may arise in application of the hypothesis due to residual thermal stresses. Comparisons are made to other methods of representing orientation development during flow.     

Crystallization of an ethylene-based butene plastomer: the effect of uniaxial extension

In this paper, the effect of uniaxial extension on the crystallization of an ethylene-based butane plastomer is examined by using rheometry coupled with differential scanning calorimetry (DSC). Uniaxial extension experiments were performed at temperatures below and above the peak melting point of the polyethylene in order to characterize its flow-induced crystallization behavior at extensional rates relevant to processing. The degree of crystallinity of the stretched samples was quantified by DSC, i.e., by analyzing the thermal behavior of samples after stretching. Analysis of the tensile strain-hardening behavior very near the peak melt temperature revealed that crystallization depends on temperature, strain, and strain rate. In addition, it was revealed that a very small window of temperatures spanning just 1–2°C can have a dramatic effect on polymer crystallization. Finally, flow-induced crystallization experiments at temperatures close to the peak melting point have shown the recrystallization of multiple crystalline structures within a polymer matrix, witnessed by double peaks within a narrow window of 89–93°C in the DSC thermographs, with the most demonstrable double peak behavior occurring at a temperature of 91°C, a temperature that is just 1°C cooler than the peak melt temperature of the polymer.     

Quiescent and shear-induced crystallization of polyprophylenes

In this paper, the effect of shear on the flow-induced crystallization (FIC) of several polypropylenes of various macrostructures was studied using rheometry combined with polarized microscopy. Generally, an increase in strain and strain rate or decrease of temperature is found to decrease the thermodynamic barrier for crystal formation and thus enhancing crystallization kinetics at temperatures between the melting and crystallization points. Secondly, popular models based on suspension theory which are used to relate the degree of crystallinity to normalized rheological functions (such as viscosity) are validated experimentally. For this purpose, the space filling of crystals in the polarized micrographs determined from image processing was plotted as a function of normalized viscosity under various shear rates. It is found that the constant(s) of various suspension models should be dependent on the flow parameters in order for the suspension models to describe the effect of shear on FIC, particularly at higher shear rates.     

A rheological study of shear induced crystallization

The isothermal crystallization of three isotactic polypropylene (iPP) types, with different molar mass (distributions), was studied after a well defined shear treatment of the melt at an elevated temperature and a subsequent quench to the crystallization temperature. For these experiments a standard rheometer of the cone and plate configuration was used. The development of the crystallization was monitored by dynamic oscillatory measurements. Shearing in the melt was shown to enhance subsequent crystallization at lower temperatures. Not only the total shear at constant rate is of importance, but also the chosen combination of rate and shearing time. Moreover, a pronounced influence of molar mass was detected. The exploration of the melting temperatures and times which are necessary for an erasion of the memory effects showed that the effect of shearing could not completely be erased, possibly as a consequence of mechanical degradation.     

Rheooptical study of the early stages of flow enhanced crystallization in isotactic polypropylene

The effect of a shear flow on the early stages and the kinetics of isothermal crystallization of an isotactic polypropylene has been studied experimentally. In the shear rate region where crystallization proceeds through point-like precursors, the magnitude of the shear rate, the shearing time as well as the instant in time at which the deformation starts have all been varied, in combination with rheooptical measurements. These include depolarized light intensity and birefringence. In agreement with previous work, above a critical shear rate and a critical shearing time, the crystallization kinetics are enhanced. Somewhat surprisingly, below a characteristic time, t_0,max, the kinetics are not affected by the instant in time at which flow is applied or stops. As long as flow takes place before this critical dwell time, only the shearing time and primarily the magnitude of the shear rate seem to matter. When flow is started only after t_0,max, its effect to accelerate crystallization kinetics becomes less efficient. The range over which the different parameters have an effect have been compared to the rheological relaxation times and to the measurements of global chain extension. To investigate the effects of flow on the early stages in more detail, time resolved Small-Angle Light Scattering experiments were used to detect changes in the density and orientation fluctuations. Measurements explicitly compare the effect of temperature and shear flow on the kinetics and the intensity of the density fluctuations.Electronic supplementary material to this paper can be obtained by using the Springer Link server located at     

The mechanisms of ‘neck-like’ deformation in high-speed melt spinning. 2. Effects of polymer crystallization

As is shown in the first paper of the series, the main factor responsible for concentrated (‘neck-like’) deformation in high-speed melt spinning is the gradient of elongational viscosity along the spinline. In the present paper, stress-induced polymer crystallization is analyzed as a potential source of the rapid viscosity increase.A model of crystallization-controlled solidification is proposed, in which viscosity of the polymer increases with the degree of crystallinity, Θ, as

Full-size image (1K)

, reaching infinity (complete solidification) at Θ = Θ_cr. The critical crystallinity level has been interpreted as one required for ‘crosslinking’ of polymer chains present in the melt.In addition to viscosity increase, crystallization modifies the local temperature in the spinline and reduces viscosity.The analysis of stress effects shows that critical crystallization temperature, T_m, and crystallization rate, K, increase with the square of normal stress difference in the spinline, Δp = p_xx − p_rr. The onset of crystallization can be shifted by 20–40 K towards higher temperatures, and crystallization rate can increase by orders of magnitude when high take-up speeds increase the stress level.A simple model illustrating velocity profiles in crystallizing Newtonian jets is discussed.The analysis strongly supports the hypothesis that the high viscosity gradient resulting from rapid stress-induced crystallization provides the major mechanism of ‘neck-like’ deformation.     

Structure development during crystallization of polycaprolactone

In this paper, the quiescent crystallization of polycaprolactone (PCL) melts is studied by rheological measurements coupled to calorimetry and optical microscopy. Based on a comparison between the different techniques, we find that the increase in viscoelastic properties during crystallization starts only when a relatively high degree of crystallinity is reached, which corresponds to a much developed crystalline microstructure. Like other semicrystalline thermoplastic polymers, the crystallization of PCL can be seen as a gelation process. In this case, however, we find a peculiar critical gel behavior, as the liquid-to-solid transition takes place at a very high (~20%) relative crystallinity, and this value is independent of temperature. These facts, and the comparison with optical microscopy observations, suggest that the microstructure at the gel point is controlled by the interactions between the growing crystallites. The gel time (from rheometry) and the half-crystallization time [from differential scanning calorimetry (DSC)] both show an Arrhenius-like behavior and have the same pseudoactivation energy. A practical implication of this parallel behavior of t _gel and t _0.5 is that the rheological measurements can be used to extend to higher temperatures the study of crystallization kinetics where DSC is not sufficiently sensitive.This paper was presented at the second Annual European Rheology Conference (AERC) held in Grenoble, France, 21–23 April 2005.     

Transient stress and interfacial area generated during breakup of a Newtonian thread immersed in a Newtonian medium

The transient stress and the transient average orientation generated by the breakup process of a long Newtonian filament imbedded in a quiescent Newtonian viscous liquid have been calculated. Rayleigh disturbances were used to describe the relaxation of the filament and the variation of interfacial area in the absence of flow during the course of disintegration process. The effect of viscosity ratio and initial radius of the filament were discussed. It was demonstrated that the predictions of the model in terms of the time-evolution of interfacial area can be used to select the best conditions for carrying out the breaking thread experiments. The predictions of the proposed model were compared to some experimental data on polyamide/polyethylene system.     

A microstructural flow-induced crystallization model for film blowing: validation with experimental data

The two-phase microstructural/constitutive model for film blowing of Doufas and McHugh (D-M) (J Rheol 45:1085–1104, 2001a) is validated against online film data of a linear low-density polyethylene (LLDPE) at a variety of processing conditions. The D-M model includes the effects of thermal and flow-induced (enhanced) crystallization (FIC) coupled with the rheological response of both the melt and semicrystalline phases under fabrication conditions. The model predictions of bubble radius, velocity, and crystallinity profiles are in quantitative agreement with available experimental data over a wide range of blow-up ratios (BUR), take-up ratios (TUR), and bubble cooling rates using the same set of material/model parameters. The model naturally predicts the location of the frost line as a consequence of system stiffening due to crystallization overcoming the pitfalls of traditional modeling approaches that impose it as an artificial boundary condition. For a wide range of processing conditions, it is found that key film mechanical properties including elongation to break, yield stress, tensile modulus, and tear strength correlate well with predicted locked-in extensional stresses and molecular orientation at the frost line enabling development of quantitative structure-process-properties relationships that are useful in product and process development. The D-M model for film blowing is physics-based including elements of molecular rheology (polymer kinetic theory), suspension, and nucleation theories as well as irreversible thermodynamics principles, yet being tractable for continuum-based numerical simulations with practical industrial applicability. The FIC enhancement factor of the model is shown to be proportional to $\exp \left (\lambda _{\text {eff},\textnormal {w}}^{2} -1\right )$ , where λ _eff,w is a molecular chain stretch ratio of the whole chain and proportional to exp (λ ² ? 1), where λ is the stretch ratio of the remaining (uncrystallized) amorphous chain, consistent with fundamental kinetic Monte Carlo simulations of flow-induced nucleation of Graham and Olmsted (Phys Rev Lett 103:115702-1–115702-4, 2009).     

Melt strengthening of poly (lactic acid) through reactive extrusion with epoxy-functionalized chains

Poly (lactic acid) is an industrially mature, bio-sourced and biodegradable polymer. However, current applications of this eco-friendly material are limited as a result of its brittleness and its poorly melt properties. One of the keys to extend its processing window is to melt strengthen the native material. This paper considers the chain extension as a valuable solution for reaching such an objective. An additive based on epoxy-functionalized PLA was employed during reactive extrusion. The reaction times as a function of chain extender ratios were determined by monitoring the melt pressure during recirculating micro-extrusions. Once residence times were optimized, reactive extrusion experiments were performed on a twin screw extruder. Size exclusion chromatography provided information about the molecular weight distributions (MWD) of the modified PLAs and revealed the creation of a high molecular weight shoulder. The rheological experiments highlighted the enhancement of the melt properties brought about by the chain extension. Shear rheology revealed some enlarged and bimodal relaxation time spectra for the extended materials which are in accordance with the MWD analysis. Such a modification directly amplified the shear sensitivity of modified PLAs. Regarding the rheological temperature sensitivity, it was found to be decreased when the chain extender content is raised as shown from the Arrhenius viscosity fit. The reduction of the polar interactions from neat to highly chain-extended PLAs is here proposed to explain this surprising result. Chain extension was also found to impact on the elongational melt properties where strain hardening occurred for modified PLAs. Investigation of the chain extension architecture was made from the rheological data and revealed a long-chain branched topology for the modified PLAs.