Some fundamental aspects of the kinetics of flow-induced crystallization of polymers

Some indispensable fundamental aspects of the kinetics of polymer crystallization are summed up. Those aspects are of particular interest in the development of crystalline structures during polymer processing. In this connection also a monograph (Janeschitz-Kriegl 2009) must be mentioned, which has been written last year by the first author of this article. The present paper contains a selection of particularly interesting subjects. It turns out that many of these subjects have eluded a mathematical treatment. The pertinent list is given in the introduction. And those people, who feel pressed to produce computer programs, are exhorted to mind the content of the present article and also of the mentioned monograph in avoiding arbitrary assumptions.     

Coupling between kinetics and rheological parameters in the flow-induced crystallization of thermoplastic polymers

Flow Induced Crystallization (FIC) is the common term to indicate the acceleration in polymer crystallization kinetics due to the action of flow. FIC is expected to be the result of the coupling between the intrinsic (quiescent) crystallization kinetics and the rheological response of the polymer. The choice of a suitable rheological model, therefore, is a crucial requirement for a successful FIC model. Recent work of our group^[1] has demonstrated that the Doi-Edwards rheological model (DE), based on the concept of chain reptation, can be easily incorporated into classical crystallization models to successful predict the enhancement in nucleation rate under the action of a steady shear flow. In this paper, the interaction between the rheological parameters of the DE model and the crystallization kinetics parameters is investigated in more details. In particular, the effect of the crystallization temperature, which acts on both the polymer relaxation time and the free energy jump between liquid and solid phase, is determined and discussed.     

Bulk and solution crystallization kinetics of isotactic polybutene-1

The crystallization kinetics of an unfractionated sample of isotactic polybutene-1 have been studied from the melt and from dilute solutions in amyl acetate by the dilatometric method. The kinetics of bulk crystallization followed the Avrami equation for most of the transformation with a deviation towards the end of the crystallization process. The Avrami exponent is found to be temperature dependent with the value of n ≈ 3 at high undercooling (indicating a homogeneous nucleation process) and n ≈ 4 at lower undercooling (indicating a heterogeneous nucleation process). The temperature coefficients of the rate constants indicate a nucleation controlled process of crystallization.     

Extensional flow-induced crystallization of a polyethylene melt

Measurements of flow-induced orientation and crystallization have been made on a high-density polyethylene melt (HDPE) undergoing a planar extensional flow in a four-roll mill. The HDPE was suspended as a cylindrical droplet at the flow stagnation point in a linear low density polyethylene (LLDPE) carrier phase. Deformation and crystallization of the HDPE droplet phase were monitored using video imaging in conjunction with measurement of the birefringence and dichroism to quantify the in-situ transformation kinetics. Planar deformation rates along the symmetry axis of the molten HDPE phase were on the order of 0.03 s^?1. Measurements of the initial transformation rate following flow cessation at 131.5°C and 133.2°C show a dependence on initial amorphous phase orientation and the total Hencky strain achieved during flow. The flow-induced crystallization rate is enhanced over the quiescent transformation rate by orders of magnitude, however, the dependence on temperature is less dramatic than expected for a nucleation-controlled growth mechanism. Analysis demonstrates that the melting point elevation model cannot account either qualitatively or quantitatively for the phenomena observed, suggesting that alternative explanations for the strong orientation dependence of the transformation rate are needed.     

A simple model of flow-induced crystallization memory

Flow induced crystallization of polymer systems exhibits strong memory effects. Crystalline structures gradually change when the flow is switched off and the polymer is relaxed prior to crystallization. A simple model based on the multidimensional theory of crystal nucleation^[1] is proposed. Steady, potential flow applied to a polymer fluid above melting temperature (T_p > T_m) results in molecular orientation of crystallizing units. The flow controls formation of molecular clusters which convert into athermal nuclei when the system is cooled down to crystallization temperature, T_c < T_m. Orientation effects gradually disappear when the melt is relaxed above T_m in the absence of flow or stress.     

Extensional flow-induced crystallization in polyethylene melt spinning

Polyethylene was spun into a heated chamber, with the spin-line temperature controlled in the range of 90–120°C. Within narrow limits, the stretch rate of the fiber was also controlled. Spin-line and crystallization onset conditions were characterized. Characteristics of fibers as-spun were measured via wide-angle x-ray scattering (WAXS), density, scanning electron microscopy, and differential scanning calorimetry. Spin-line data indicate that elongational flow enhances crystallization rate and that time under spin-line conditions is an important parameter. Analysis of WAXS data shows a typical “b-axis radial” orientation, the details of which change with spin-line parameters. This orientation is consistent with growth of lamellar crystals on extended-chain fibrils (shishkebab model). Other physical data are also consistent with this microstructure. Microcamera x-ray patterns show a similarity of microstructure generation in spinning and drawing.     

The kinetics of Al-Si spinel phase crystallization from calcined kaolin

The crystallization of Al-Si spinel from medium ordered kaolin with high content of kaolinite was investigated using the differential thermal analysis (DTA). The apparent activation energy of the process was evaluated from the dependence of exothermic peak of crystallization on heating rate. Within the applied interval of heating rate (1-40 K min⁻¹) the temperature of peak maximum increases from initial value of 1220.5 K in about 54.2 K. The apparent activation energy of the process 856±2 kJ mol⁻¹was calculated using the Kissinger equation. The growth morphology of Al-Si spinel crystal was evaluated from the Avrami parameter. The average value of morphology parameter determined within the observed interval of heating rate is 3.08±0.03. This value indicates that crystallization mechanism of Al-Si spinel phase proceeds by bulk nucleation of the new phase with constant number of nuclei and that the three-dimensional growth of crystals is controlled by the reaction rate on the phases interface.     

The influence of flow-induced crystallization on the impact toughness of high-density polyethylene

The relation between the impact toughness and flow-induced crystalline orientation of high-density polyethylene (HDPE) was investigated. Flow-induced crystalline orientation was created in the samples via injection moulding and the amount of orientation was controlled through variation of processing conditions (injection temperature) and sample thickness. The impact toughness behaviour was found to be strongly dependent on the amount of crystalline orientation, whereas the loading direction also had a strong influence, e.g. giving highest impact properties in flow direction. Subsequently, injection moulded samples of HDPE modified with calcium carbonate filler particles were tested. In this case a similar relation between crystalline orientation and loading direction was found, whereas the total amount of flow-induced crystallization was observed to be strongly influenced by the presence of the filler particles.     

The crystallization kinetics of polyamide-12

The crystallization kinetics of polyamide-12 has been investigated using a combination of differential scanning calorimetry (DSC) and hot-stage optical microscopy. The DSC data for isothermal crystallization were consistent with a simple two-parameter Avrami model for isothermal crystallization and optical measurements of the spherulite growth rates and nucleation density. On the basis of semiempirical expressions for these quantities, it is shown that with small adjustments the model can also account for DSC data for nonisothermal crystallization, provided that corrections are made for the dynamic heat balance between the sample and the DSC oven. Received: 9 March 2000 Accepted: 28 September 2000     

A continuum model for the dynamics of flow-induced crystallization

A model for flow-induced crystallization is developed which is based on ideas from the theory of strain-induced crystallization, coupled with an irreversible thermodynamic formalism based on the continuum Hamiltonian Poisson Brackets. The latter allows accounting for the changing energetics during simultaneous flow deformation and extended-chain crystallization. Input parameters to the model include the molecular relaxation time, a crystallization parameter, and the molecular weight. Calculations of the crystallization rate, chain elongation, stress, and birefringence are presented for a variety of flow kinematics and flow histories, including transient processes following cessation of flow. Induction times based on a reasonable choice for the induction crystallinity follow experimentally observed trends reported in the literature. © 1996 John Wiley & Sons, Inc.     

Extensional flow induced crystallization from solution

Summary An experimental apparatus and technique were developed for studying the crystallization of polyethylene from solutions undergoing an oscillatory, constant stretch rate, extensional flow. Investigation of the resulting fiber morphology, obtained at various temperatures and stretch rates, shows that the fibers exhibit a bead and stringlike appearance. Study of the melting, acid etching, and selective dissolution behavior of the fibers leads to the conclusion that fiber growth occurs in a fashion which directly results in the bead and string morphology and that the morphology is not a result of secondary, epitaxial crystal growth as previously believed. A model for the growth process, as suggested by the data, is presented.Evidence is also presented to suggest that at certain temperatures and stretch rates, a triclinic phase transformation occurs during the flow process. The effect is to produce two separate melting entities which appear to be stretch rate sensitive, in line with previously published studies on the effects of stretching on the behavior of bulk polymer.

---

Zusammenfassung Eine experimentelle Apparatur sowie ein Verfahren wurden entwickelt zur Untersuchung der Kristallisation von Polyäthylen aus Lösungen, welche oszillatorischen Dehnströmungen mit konstanten Dehngeschwindigkeiten unterworfen waren. Untersuchungen der resultierenden Fasermorphologie, die aus Versuchen mit unterschiedlichen Temperaturen und Dehngeschwindigkeiten resultierten, ergeben ein perlen- und kettenförmiges Erscheinungsbild der Faser. Prüfung des Schmelzverhaltens, der Säure-Ätzbarkeit und der selektiven Löslichkeit der Faser erlauben den Schluß, daß das Faserwachstum in einer Art und Weise vonstatten geht, die sofort zur perlen- und kettenförmigen Morphologie führt, und daß diese Morphologie nicht durch sekundäres, epitaxiales Kristallwachstum entsteht, wie man bisher annahm. Auf der Grundlage der experimentellen Ergebnisse wurde ein Modell für den Wachstumsprozeß vorgeschlagen.Fernerhin wird der Beweis erbracht, daß in gewissen Temperatur- und Deformationsgeschwindigkeits-Bereichen eine trikline Phasentransformation während des Fließprozesses vonstatten geht. Zwei unterschiedliche Schmelzeinheiten werden erzeugt, welche von der Dehngeschwindigkeit abhängig sind, ein Ergebnis, das in Einvernehmen mit früher veröffentlichten Untersuchungen über den Einfluß von Dehnbeanspruchungen auf das Verhalten von festen Polymeren ist.

     

Hydrodynamically induced crystallization of polymers from solution

Summary This paper primarily describes an investigation into the origin of persistent lamellar overgrowth of fibrillar crystals with a Shish-kebab morphology. Fibers grown from stirred p-xylene solutions of high molecular weight polyethylene at 108 °C exhibited an average spacing of 1 x 10³ Å between the lamellae when cooled down to room temperature in a normal way. Fibers quenched in liquid nitrogen displaved smaller lamellae with a periodicity of 0.4 x 10³ Å.It was found that the lamellae could be dissolved at 108 °C and recrystallized isothermally on the backbones at temperatures up to 94.6 °C. The spacing between the lamellae increased strongly with temperature in the range between 90.0 °C and 94.6 °C.The temperature dependence of this periodicity could be accounted for by the theory of secondary nucleation in polymer crystallization. The Poisson distribution of the numbers of lamellae along the backbones also suggests that lamellar growth is essentially controlled by the crystallization kinetics.The fibrillar polyethylene crystals grown at elevated temperatures from flowing solutions may be visualized as backbones constituted by partially crystallized polymer molecules and dangling ends extending from the backbones into the surrounding solution resembling centipedes.

---

Zusammenfassung Dieser Bericht befaßt sich mit einer Untersuchung des Ursprungs von persistenter lamellarer Überwachsung von Faser-Kristallen mit Schaschlik-Morphologie.Faser-Kristalle, gewachsen aus geruhrten Xylol-Lösungen von hochmolekularem Polyäthylen bei 108 °C, zeigen ein mittleres Intervall zwischen den Lamellen von 1 x 10³ Å, wenn auf normae Weise abgekühlt zur Zimmertemperatur. Fasern, abgeschreckt im flüssigen Stickstoff, zeigen kleinere Lamellen mit einem Zwischenraum von etwa 0.4 x 10³ Å. Es wurde festgestellt, daß die Lamellen bei 108 °C gelöst werden können und von neuem auf den Faserkernen bis zu 94.7 °C kristallisieren. Die Temperaturabhangigkeit dieser Periodizität kann erklärt werden auf Grund der Theorie der sekundären Keimbildung bei polymerer Kristallisation. Wie sich zeigt, gruppiert sich die lamellare Überwachsung um den Kern entsprechend einer Poisson-Verteilung, was darauf hinweist, daß die lamellare Überwachsung wesentlich durch die Kristallisationskinetik bedingt wird.Die faserigen Polyathylenkristalle, bei erhöhter Temperatur hergestellt aus gerührten Lösungen, kann man sich als teilweise kristallisierte Moleküle, im Faserkerne aufgenommen, vorstellen mit langen Kettenenden im umgebenden Lösungsmittel, so ziemlich als einen Tausendfüßler.

---

---

With 12 figures     

A kinetics study of crystallization from discotic mesophases

The polymorphism of hexa- n -octanoate of rufigallol (RHO) was used to investigate the crystallization kinetics when starting from two different discotic mesophases, namely, a hightemperature enantiotropic mesophase and a low-temperature monotropic mesophase. In all cases, an Avrami exponent of n 3 was obtained, suggesting two-dimensional sporadic nucleation and growth. Although the same overall mechanism was predicted to operate for all crystallization temperatures investigated, the Avrami constant b has a temperaturedependence which is different for different starting columnar phases, indicating a strong influence on the rates of nucleation and of growth of the different molecular arrangements of the starting mesophases. Differential scanning calorimetry was used for the studies, supplemented by direct observations through optical polarizing microscopy.     

Hydrodynamically induced crystallization of polymers from solution

Summary This paper primarily describes the large diversity in morphology of fibrillar polyethylene crystals precipitated from stirred solutions at elevated temperatures. Shish-kebabs crystallized at 112°C from stirred xylene solutions of linear polyethylene exhibit lamellar overgrowths having thicknesses of the order of 150 Å from which it was concluded i. a. that at crystallization temperatures above 100°C only backbones are formed and that the surrounding polymer molecules deposit epitaxially on the substrate at lower temperatures. The variation in the appearance of the overgrowth and the inhomogeneity of the samples can be traced back to irregular stacking and to differences in washability of the fibrillar crystals, these differences being largely due to the non-uniform flow pattern along the various stirrer parts. Unusual lamellar shapes, interconnections, sheets between lamellae, the veil on the Shish-kebab noted byKeller andMachin, may well be explained byKeith, Padden andVadimskys mechanism of crystallization-induced orientation of macromolecules between the lamellae and the consequent formation of extendedchain crystals. The lamellar overgrowth appears to be arranged along the backbone according to a logarithmic normal distribution, and the average diameter of the lamellar crystals increases with the average spacing, both being approximately equal in size. The fibrillar crystals end in smooth tapered tails having lengths varying between 5 and 8 .These observed fibre ends agree best with the unroll model proposed for fibrillar crystal growth in flow fields if on the average each molecule introduces one chain fold and the chain ends are randomly assimilated by the crystal lattice. Linear polyethylene below molecular weight of 50×10³ and low density polyethylene did not crystallize in fibrillar habit. whereas copolymers of ethylene and slight amounts of propylene and butylene proved capable of forming fibrillar crystals and isotactic polypropylene yielded smooth and overgrown fibres.

---

Zusammenfassung Der Bericht befaßt sich zuerst mit der großen morphologischen Mannigfaltigkeit faseriger, bei erhöhter Temperatur aus gerührten Lösungen gefällter Polyäthylenkristalle. Bei 112°C aus gerührten Xylollösungen von linearem Polyäthylen herauskristallisierte Schaschlik-Strukturen zeigen eine lamellare Überwachsung mit einer Dicke von etwa 150 Å, woraus u. a. geschlossen wird, daß sich bei Kristallisations-temperaturen über 100°C nur Faserkerne bilden und daß die umringenden polymeren Moleküle sich bei niedrigeren Temperaturen epitaxial auf dem Substrat ablagern. Die Verschiedenheit in der Form der Überwachsung und die Inhomogenität der Proben lassen sich erklären durch eine unregelmäßige Ablagerung auf dem Rührer und durch Unterschiede in der Auswaschbarkeit der faserigen Kristalle, welche Unterschiede weitgehend auf das nicht einheitliche Strömungsbild längs der verschiedenen Rührerteile zurückzuführen sind. Ungewöhnliche lamellenartige Formen, interlamellare Verbindungen, Häutchen zwischen den Lamellen und die vonKeller undMachin festgestellte Verschleierung der Schaschlikgebilde lassen sich sehr gut durch denKeith-, Padden- undVadimsky-Mechanismus einer durch die Kristallisation verursachten Orientierung von Makromolekülen zwischen den Lamellen und durch die anschließende Bildung von extended-chain Kristallen erklären. Wie sich zeigt, gruppiert sich die lamellare Überwachsung um den Kern entsprechend einer logarithmischen Normalverteilung; der mittlere Durchmesser der lamellaren Kristalle nimmt zu mit der mittleren Größe der Zwischenabstände, wobei beide ungefähr gleich groß sind. Die faserigen Kristalle enden in allmählich spitz auslaufenden Gebilden mit Längen von etwa 5 bis 8 . Diese Faserenden stimmen gut überein mit dem für das Wachsen faseriger Kristalle in Strömungsgebieten vorgeschlagenen unroll-Modell, falls im Durchschnitt jedes Molekül eine Kettenfaltung einleitet und die Kettenenden willkürlich in das Kristallgitter aufgenommen werden. Lineares Polyäthylen mit einem Molekulargewicht unter 50×10³ und Hochdruckpolyäthylen kristallisieren nicht in der faserigen Form, während —wie sich zeigt—Copolymere von Äthylen und geringen Propylen- und Butylenmengen in der Lage sind, faserige Kristalle zu bilden und isotaktisches Propylen schöne und überwachsene Fibrillen ergibt.

---

---

With 25 figures in 28 details     

Poiseuille/squeeze flow-induced crystallization in microinjection-compression molded isotactic polypropylene

Microinjection-compression molding was used to fabricate isotactic polypropylene part with microscale thickness. The combined effect of shear (up to the order of 10⁵ s⁻¹) and elongational deformations imposed by the Poiseuille (injection stage) and squeeze (compression stage) flow resulted in pronounced flow-induced crystallization under rapid quenching. Hierarchical crystalline morphology, characterized by two oriented layers, a transitional layer in between, and an isotropic core layer, was detected through the thickness in the upstream region initially filled in injection stage, whereas skin-core morphology appeared in the downstream region filled in subsequent compression stage. Under the molding conditions imposing sufficient strain rates, predominant shish-kebabs developed in the oriented layer. Furthermore, the oriented layer thicknesses, crystallinity, β-form content, and melting behavior of molded parts, all of which were closely correlated with the calculated strain rates, as well as the location of inner oriented layer could be manipulated via varying the compression-related parameters. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

An analysis of local flow effects in flow-induced orientation and crystallization

An analysis is presented of the effects of external flow kinematics on the so-called local flow in seeded, flow-induced crystallization and orientation. The flow field around a growing crystal or nucleation seed is modelled by the Stokes flow equations past a prolate ellipsoid of high aspect ratio. Exact solutions for various flow kinematics, worked out elsewhere by the singularity method, are applied here to the analysis of local gradients. The results show that along the symmetry axis of the spheroid, the extensional gradients which result for various free-stream velocity fields are primarily the result of the constant-velocity free-stream component. However, free-stream, extensional flow can significantly enhance the region of such high gradients. Along the symmetry plane of the spheroid, primarily shearing gradients result, with small extensional gradients occurring when the free-stream flow has extensional components. Results of chain extension and birefringence calculations are also presented and discussed.