Computer simulation of crystallization kinetics and morphology in fiber-reinforced thermoplastic composites. I. Two-dimensional case

A body of experimental evidence suggests that reinforcing fibers influence both the crystallization kinetics and morphology of those composite materials that are based on crystallizable thermoplastics. The absence of an analytical model to predict the effect of fibers on crystallization has hindered data analysis. A new approach, using computer simulation of polymer crystallization, makes it possible to study the influence that reinforcing fibers have on the crystallization kinetics and morphology of semicrystalline polymers. Fibers depress the crystallization rate relative to an unreinforced polymer since they constrain spherulitic growth by an impingement mechanism. On the other hand, reinforcing fibers can also enhance crystallization rate by providing added surface nucleation sites. This work describes a two-dimensional simplification of the crystallization process that occurs in bulk materials. It is demonstrated that the relative bulk and fiber nucleation densities, in addition to the fiber fraction, fiber diameter, and spherulitic growth rate control the crystallization kinetics and also the spherulitic and transcrystalline morphologies that develop in reinforced thermoplastic composites. © 1993 John Wiley & Sons, Inc.     

Computer simulation of crystallization kinetics and morphology in fiber-reinforced thermoplastic composites. II. Three-dimensional case

A three-dimensional computer simulation has been used to predict crystallization kinetics and crystalline morphology in composite materials that are based on crystallizable thermoplastics. Reinforcing fibers in three-dimensional simulations show similar behavior to those in two-dimensional simulations; fibers suppress crystallization relative to an unreinforced polymer since they constrain spherulitic growth by an impingement mechanism, and also enhance crystallization by providing added surface nucleation sites. The effects of varying controlling parameters on crystallization kinetics and morphology are qualitatively the same as those observed in the two-dimensional case. The relative bulk and fiber nucleation denisities, in addition to the fiber volume fraction, fiber diameter, and spherulitic growth rate control the crystallization kinetics and crystalline morphology that develop in reinforced thermoplastic composites. It is more difficult to achieve the transcrystalline morphology in slices of three-dimensional composites than it is in two-dimensional composites because nuclei in 3-D systems are not constrained to positions in or near a 2-D plane. © 1993 John Wiley & Sons, Inc.     

Computer simulation of crystallization kinetics and morphology in fiber-reinforced thermoplastic composites. III. Thermal nucleation

A computer simulation has been used to predict crystallization kinetics and crystalline morphology in composite materials based on thermally nucleated crystallizable matrices. As demonstrated for athermally nucleated composites, the presence of reinforcing fibers increases the complexity of the system. Fibers are shown to have a dual effect on the spherulitic crystallization process. The influence that fibers have depends on the interplay between the enhancing effects that fibers have on nucleation and the depressing effects that fibers have on spherulitic growth. Fibers that do not provide additional nuclei to the system depress the rate of crystallization relative to an unreinforced polymer, while fibers that add nuclei to the system increase the rate of crystallization. The transcrystalline morphologies that develop in thermally nucleated fiber-reinforced polymers are controlled primarily by the relative numbers of bulk and fiber nuclei. The extent of transcrystalline regions can be suppressed either by increasing the rate of bulk nucleation, or by decreasing the rate of fiber nucleation. Finally, the qualitative appearance of the morphology in the transcrystalline region was found to be indicative of the mode of fiber nucleation. © 1995 John Wiley & Sons, Inc.     

Static and shear induced crystallization of glass fiber reinforced poly(m‐xylylene adipamide) with nucleating additives

Static and shear induced crystallization studies were carried out on a glass fiber reinforced poly(m‐xylylene adipamide) with various fiber contents. The crystallization experiments were performed using calorimetry and a shearing hot stage coupled with an optical microscope. The crystallization times were measured as a function of the temperature, the shear rate, and the fiber content. In static conditions, no nucleating ability of the fibers was highlighted. However, the shear treatment led to a substantial decrease of the crystallization times for all materials. Moreover, the shear effect is largely influenced by the fiber content, because the shear really undergone by the matrix between the fibers is locally higher than the nominal shear. A previously proposed crystallization kinetics model based on both Avrami and Hoffman–Lauritzen equations and taking into account the nucleating effect of the shear is improved. Hence, the fibers effect is included taking into account the higher local shear between the fibers. The nucleation rate due to the shear is described by a power law of the shear rate, where the prefactor is linked to the fibers amount. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2982–2992, 2007     

Effect of stereosequence length on crystallization kinetics of propylene oxide polymers

Crystallization kinetics of crystalline fractions of propylene oxide polymers made with different catalysts have been studied by isothermal dilatometric and microscopical measurements. Isothermal microscopical measurements indicate that spherulite growth in these polymers proceeds from predetermined nuclei. The half time for spherulitic appearance is less than, but of the same order as, the half time for complete crystallization. Only by taking this factor into account can the dilatometric data be represented by the Avrami equation. The deviation of the crystallization isotherm from that predicted from the microscopical data using the Avrami theory is attributed to a secondary crystallization process taking place within the spherulite. Crystallization continues long after spherulites completely occupy the available volume in the polymer. By assuming that the secondary crystallization proceeds as a first-order process in the uncrystallized, but crystallizable, portions of the melt, it is shown that the crystallization isotherms can be completely described in terms of four parameters. These are: (1) the time constant for the primary crystallization process; (2) the time constant for nucleation; (3) the time constant for the secondary crystallization process, and (4) the extent of secondary crystallization. The important conclusions of these studies are: the rates of nucleation and of spherulitic growth are far more dependent on temperature than on stereoregularity; the ratio of the rate of the secondary crystallization process to that of the primary crystallization process is almost independent of temperature, but increases with increasing stereoregularity of the polymer.     

Estimation of the nucleation and crystal growth contributions to the overall crystallization energy barrier

Classical kinetic theories of polymer crystallization were applied to isothermal crystallization kinetics data obtained by polarized optical microscopy (PLOM) and differential scanning calorimetry (DSC). The fitted parameters that were proportional to the energy barriers obtained allow us to quantitatively estimate the nucleation and crystal growth contributions to the overall energy barrier associated to the crystallization process. It was shown that the spherulitic growth rate energy barrier found by fitting PLOM data is almost identical to that obtained by fitting the isothermal DSC crystallization data of previously self‐nucleated samples. Therefore, we demonstrated that by self‐nucleating the material at the ideal self‐nucleation (SN) temperature, the primary nucleation step can be entirely completed and the data obtained after subsequent isothermal crystallization by DSC contains only contributions from crystal growth or secondary nucleation. In this way, by employing SN followed by isothermal crystallization, we propose a simple method to obtain separate contributions of energy barriers for primary nucleation and for crystal growth, even in the case of polymers where PLOM data are very difficult to obtain (because they exhibit very small spherulites). Comparing the results obtained with poly(p‐dioxanone), poly(ε‐caprolactone), and a high 1,4 model hydrogenated polybutadiene, we have interpreted the differences in primary nucleation energy barriers as arising from differences in nuclei density. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1478–1487, 2008     

橫晶与纤维界面的形态观察

在纤维表面的异相成核密度达到足够高的程度时,晶粒的生长由径向转变为沿垂直于纤维表面的方向生长,即横晶生长(transcrystalline growth)。在许多纤维增强的高聚物复合材料中都可以得到横晶结构。横晶的结构和球晶是完全相同的。横晶是球晶的一种特殊情况,即取向球晶。虽然横晶中片晶的生长方向是相同的,但是在横晶与纤维之间,即在纤维表面区域却是非取向的。利用刻蚀剂或离子对材料进行刻蚀处理,控制刻蚀程度,可以使纤维和取向的横晶之间的非取向区首先被刻蚀液或离子刻蚀破坏掉。而取向的横晶结构区域则被保留下来。用扫描电子显微镜就可以观察到这两种结构区。     

Correlation between crystallization kinetics and microdomain morphology in block copolymer blends exhibiting confined crystallization

The crystallization kinetics of poly(ethylene oxide) (PEO) blocks in poly(ethylene oxide)‐block‐poly(1,4‐butadiene) (PEO‐b‐PB)/poly(1,4‐butadiene) (PB) blends were previously found to display a one‐to‐one correlation with the microdomain morphology. The distinct correlation was postulated to stem from the homogeneous nucleation‐controlled crystallization in the cylindrical and spherical PEO microdomains, where there existed a direct proportionality between the nucleation rate and the individual domain volume. This criterion was valid for confined crystallization in which the crystallization was spatially restricted within the individual domains. However, it was possibly not applicable to PEO‐b‐PB/PB, in that the melt mesophase was strongly perturbed upon crystallization. Therefore, it may be speculated that the crystal growth front developed in a given microdomain could intrude into the nearby noncrystalline domains, yielding the condition of cooperative crystallization. To establish an unambiguous model system for verifying the existence of microdomain‐tailored kinetics in confined crystallization, we crosslinked amorphous PB blocks in PEO‐b‐PB/PB with a photoinitiated crosslinking reaction to effectively suppress the cooperative crystallization. Small‐angle X‐ray scattering revealed that, in contrast to the noncrosslinked systems, the pre‐existing domain morphology in the melt was retained upon crystallization. The crystallization kinetics in the crosslinked system also exhibited a parallel transition with the morphological transformation, thereby verifying the existence of microdomain‐tailored kinetics in the confined crystallization of block copolymers. Homogeneous nucleation‐controlled crystallizations in cylindrical and spherical morphologies were demonstrated in an isothermal crystallization study in which the corresponding crystallinity developments followed a simple exponential rule not prescribed by conventional spherulitic crystallization. Despite the effective confinement imposed by the crosslinked PB phase, crystallization in the lamellar phase still proceeded through a mechanism analogous to the spherulitic crystallization of homopolymers. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 519–529, 2002; DOI 10.1002/polb.10121     

Experimental study of shear-induced crystallization of an impact polypropylene copolymer

The crystallization kinetics of polypropylene was observed during shear and after shear experiments under isothermal condition. The crystallizations were performed in a plate-plate and a fiber pull-out device. The nucleation density, the crystalline growth and the overall kinetics were measured and compared with data obtained in a similar way but during static experiments. The morphologies are spherulitic and formed from nuclei which seem to be randomly distributed. -phase spherulites are always observed but with a nucleation density and a growth rate which depend on shearrate. The nucleation density is strongly enhanced by shear and acts as the main factor on the overall kinetics. The overall kinetics can be analyzed with a two-step Avrami model, where an Avrami exponentn ₁ with a very high value is always observed first after shear and a more usual parametern ₂ for the subsequent crystallization period. This high value ofn ₁ seems to be related to the strong enhancement of nucleation density. The growth rate increases with the shear-rate, but the basic growth mechanisms do not seem to be modified. For crystallizations after shear the growth rate decreases with a long-time delay after shear but not down to the static value. The effect is characteristic of a partial relaxation of chain orientation after shear but with a very unusual time constant.     

Crystallization kinetics of poly(hexamethylene succinate)

Isothermal and nonisothermal crystallization kinetics of polyester 64 have been investigated by means of differential scanning calorimetry and optical microscopy. The Avrami analysis has been performed to obtain the kinetic parameters of primary crystallization. These indicate a three-dimensional spherulitic growth on heterogeneous nuclei for the isothermal crystallization, whereas an sporadic nucleation becomes dominant in the nonisothermal crystallization. The maximum crystallization rate of polyester 64 was deduced to take place at a temperature close to −3 °C. Polarizing light microscopy showed that spherulites with a negative birefringence are formed during isothermal crystallization, whereas transmission electron microscopy indicates that the b crystallographic axis is aligned parallel to the spherulitic radius.     

The effect of spherulitic truncation on small-angle light scattering

The effects of spherulitic truncation on the H_v small-angle light-scattering (SALS) patterns are determined by computer simulation of spherulite nucleation and growth. The simulation is carried out for simultaneous and sporadic nucleation of two-dimensional spherulites and simultaneous nucleation of three-dimensional spherulites. The scattered intensity differences between truncated spherulites and round spherulites are determined as functions of the type of growth and the volume (or area) fraction of spherulites. Methods for the determination of certain geometrical characteristics of spherulites systems by SALS are developed. These characteristics include the volume (or area). fraction of spherulites, the average spherulite radius, and the average spherulite volume (or area). The results of this study are essential in the quantitative analysis of H_v SALS from spherulitic systems. The simulation process is readily extendable to the examination of other morphological phenomena by SALS.     

Crystallization kinetics for low‐ether‐content polyether–polyester block copolymers with amide linkages

A series of low‐ether‐content polyether–polyester block copolymers with amide linkages were synthesized. Their crystallization kinetics and mechanisms were investigated. The crystallization kinetics were analyzed via Avrami treatment; an average value of 1.8 for the Avrami index was thus obtained. Athermal nucleation was evidenced by observations of a linear boundary between impinged spherulites under polarized light microscopy and transmission electron microscopy. The development of spherulitic morphology with a hedgehog texture was attributed to the mechanism of lamellar branching. On the basis of the morphological observations and Avrami analysis, a crystallization mechanism through a heterogeneous nucleation process with homogeneous lamellar branching was proposed. No regime transition was found for polyether–polyesters in the examined temperature ranges, and the crystallization was identified as regime I kinetics on the basis of a Lauritzen Z test. The copolymerization of poly(ether amide)s with polyesters led to a significant suppression of the crystallization rate of polyester crystals. The suppression was explained as the result of a dilution effect in nucleation combined with an increasing nucleation barrier. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2469–2480, 2001     

Crystalline Morphology and Crystallization Kinetics of Melt-miscible Crystalline/Crystalline Polymer Blends of Poly（vinylidene fluoride） and Poly（butylene succinate-co-24mol% hexamethylene succinate）

Poly（vinylidene fluoride） （PVDF） and poly（butylene succinate-co-24 mol% hexamethylene succinate） （PBHS）, both crystalline polymers, formed melt-miscible crystalline/crystalline polymer blends. Both the characteristic diffraction peaks and nonisothermal melt crystallization peak of each component were found in the blends, indicating that PVDF and PBHS crystallized separately. The crystalline morphology and crystallization kinetics of each component were studied under different crystallization conditions for the PVDF/PBHS blends. Both the spherulitic growth rates and overall isothermal melt crystallization rates of blended PVDF decreased with increasing the PBHS composition and were lower than those of neat PVDF, when the crystallization temperature was above the melting point of PBHS component. The crystallization mechanism of neat and blended PVDF remained unchanged, despite changes of blend composition and crystallization temperature. The crystallization kinetics and crystalline morphology of neat and blended PBHS were further studied, when the crystallization temperature was below the melting point of PBHS component. Relative to neat PBHS, the overall crystallization rates of the blended PBHS first increased and then decreased with increasing the PVDF content in the blends, indicating that the preexisting PVDF crystals may show different effects on the nucleation and crystal growth of PBHS component in the crystalline/crystalline polymer blends.     

Crystallization kinetical and morphological peculiarities in binary crystalline/crystalline polymer blends

A survey is presented on the crystallization kinetics and the morphology of miscible crystalline/crystalline polymer blends. There are only few corresponding systems. In them, however, a number of strange kinetic and structural phenomena can be observed: (i) spherulitic crystallization of the components side‐by‐side, (ii) “interpenetrating crystallization,” (iii) “interlocking spherulitic crystallization,” and (iv) “interfilling crystallization.” Cocrystallization is forbidden for crystallographic reasons. The blend partners grow instead in their own lamellar stacks, and mixed lamellar stacks are a seldom and questionable exception. They crystallize also usually stepwise and not simultaneously. Upon step crystallization, the crystallization of the second component is determined by its redistribution with crystallization of the former. Those composition inhomogeneities are an independent issue that arises also with the development of the morphology in crystalline/amorphous blends, and a corresponding survey is yielded, too. The blend poly (vinylidene fluoride)/poly‐β‐hydroxybutyrate is a convenient model system as it can show all of these morphological and kinetic features after suitable thermal treatment. Some of them are demonstrated in the present publication. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1917–1931, 2007     

聚丙烯-g-聚氨酯共聚物的非等温结晶动力学研究

用DSC法研究了聚丙烯 (PP)和聚丙烯接枝聚氨酯的共聚物 (PP g PU)在不同冷却速率下的非等温结晶动力学 .用Avrami方程和莫志深改进法对DSC测定结果进行了处理 ,结果表明 ,PP g PU的动力学参数能很好的符合Avrami方程和莫志深改进方程 .PP接枝了聚氨酯支链后 ,结晶速率增大 ,球晶的生长和成核机制也相应发生改变 ,而其变化规律与接枝物的组成和结构密切相关     

碳纤维对聚丙烯结晶行为的影响

本文用偏光显微镜和示差扫描量热计(DSC)方法研究了碛纤维对聚丙烯结晶行为的影响。碳纤维表面对聚丙烯结晶过程具有明显的促进作用,纤维表面成核密度轻高,结晶生长成为横穿结晶,结晶特征温度随碳纤维加入而有不同程度的升高。结晶动力学表明:结晶生长本质仍是球晶机理,促进聚丙烯结晶的原因是碳纤维使结晶过程的表面自由能降低。     

Distribution kinetics of polymer crystallization and the Avrami equation

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates follow the classical surface-energy nucleation theory. Different mass dependences of growth and dissociation rate coefficients are proposed to investigate the fundamental features of nucleation and crystal growth. A comparison of moment solutions with numerical solutions examines the validity of the model. The proposed distribution kinetics model provides a different interpretation of the familiar Avrami equation.     

Effect of carbon nanotubes content on crystallization kinetics and morphology of polypropylene

Thermoplastic nanocomposites were prepared in a laboratory mixer using polypropylene (PP) and different amounts of single-walled carbon nanotubes (SWNT) in the range 0.25–2 wt%. The effect of SWNT content on the thermal and mechanical properties and also morphology of the PP/SWNT nanocomposites were studied. The results obtained from nonisothermal crystallization of PP and the nanocomposites, which were carried out using the differential scanning calorimetry technique, showed that not only the overall rate of crystallization of PP increased when SWNT was added to the polymer but also the rate of nucleation was higher and the crystallite size distribution was more uniform for the nanocomposites than for PP. From the optical microscopy studies, it was found that the PP spherulites decreased in size when SWNT was introduced into the polymer and also the mature spherical shaped crystals of PP changed in part to the immature kidney- or bean-shaped crystal forms in the nanocomposites. In addition, the crystallization kinetics was also studied by using isothermal spherulitic growth rate, and the values of nucleation constant, K_g, and end surface free energy, σ_e, were calculated for PP and the nanocomposites according to Lauritzen–Hoffman theory. The reductions of these two parameters were in agreement with the fact that the rate of crystallization of PP in nanocomposites was higher than that of the pristine polymer.