Crystallization kinetics in shearing-induced oriented and stretched poly(ethylene oxide)

Isothermal crystallization kinetics in the melting of poly(ethylene oxide) (PEO) were investigated as a function of the shear rate and crystallization temperature by optical microscopy. The radial growth rates of the spherulites are described by a kinetics equation including shearing and relaxation combined effects and the free energy for the formation of a secondary crystal nucleus. The free-energy difference between the liquid and crystalline phases increased slightly with rising shearing rates. The experimental findings showed that the influence of the relaxation of PEO, which is related to the shear-induced orientation and stretch in a PEO melt, on the rate of crystallization predominated over the influence of the shearing. This indicated that the relaxation of PEO should be more important so that the growth rates increase with shearing, but it was nearly independent of the shear rate within the measured experimental range.

Miscibility and crystallization behavior of PBT/epoxy blends

The miscibility and the isothermal crystallization kinetics for PBT/Epoxy blends have been studied by using differential scanning calorimetry, and several kinetic analyses have been used to describe the crystallization process. The Avrami exponents n were obtained for PBT/Epoxy blends. An addition of small amount of epoxy resin (3%) leads to an increase in the number of effective nuclei, thus resulting in an increase in crystallization rate and a stronger trend of instantaneous three-dimensional growth. For isothermal crystallization, crystallization parameter analysis showed that epoxy particles could act as effective nucleating agents, accelerating the crystallization of PBT component in the PBT/Epoxy blends. The Lauritzen-Hoffman equation for DSC isothermal crystallization data revealed that PBT/Epoxy 97/3 had lower nucleation constant K, than 100/0, 93/7, and 90/10 PBT/Epoxy blends. Analysis of the crystallization data of PBT/Epoxy blends showed that crystallization occurs in regime II. The fold surface free energy, sigma(e) = 101.7-58.0 x 10(-3) J/m(2), and work of chain folding, q = 5.79-3.30 kcal/mol, were determined. The equilibrium melting point depressions of PBT/Epoxy blends were observed and the Flory-Huggins interaction parameters were obtained.

Isothermal crystallization of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

Isothermal crystallization behavior of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) was investigated by means of differential scanning calorimetry and polarized optical microscopy (POM). The Avrami analysis can be used successfully to describe the isothermal crystallization kinetics of PHBV, which indicates that the Avrami exponent n = 3 is good for all the temperatures investigated. The spherulitic growth rate, G, was determined by POM. The result shows that the G has a maximum value at about 353 K. Using the equilibrium melting temperature (448 K) determined by the Flory equation for melting point depression together with U-* = 1500 cal mol(-1), T-infinity = 30 K and T-g = 278 K, the nucleation parameter K-g was determined, which was found to be 3.14+/-0.07 x 10(5) (K-2), lower than that for pure PHB. The surface-free energy sigma = 2.55 x 10(-2) J m(-2) and sigma(e) = 2.70+/-0.06 x 10-2 J m(-2) were estimated and the work of chain-folding (q = 12.5+/-0.2 kJ mol(-1)) was derived from sigma(e), and found to be lower than that for PHB. This implies that the chains of PHBV are more flexible than that of PHB.

Miscibility, crystallization kinetics, and morphology of poly(beta-hydroxybutyrate) and poly(methyl acrylate) blends

The miscibility, spherulite growth kinetics, and morphology of binary blends of poly(beta-hydroxybutyrate) (PHB) and poly(methyl acrylate) (PMA) were studied with differential scanning calorimetry, optical microscopy, and small-angle X-ray scattering (SAXS). As the PMA content increases in the blends, the glass-transition temperature and cold-crystallization temperature increase, but the melting point decreases. The interaction parameter between PHB and PMA, obtained from an analysis of the equilibrium-melting-point depression, is -0.074. The presence of an amorphous PMA component results in a reduction in the rate of spherulite growth of PRE. The radial growth rates of spherulites were analyzed with the Lauritzen-Hoffman model. The spherulites of PHB were volume-filled, indicating the inclusion of PMA within the spherulites. The long period obtained from SAXS increases with increased PMA content, implying that the amorphous PMA is entrapped in the interlamellar region of PHB during the crystallization process of PHB. All the results presented show that PHB and PMA are miscible in the melt. (C) 2000 John Wiley & Sons, Inc.

Crystallization kinetics in mixtures of poly(epsilon-caprolactone) and poly(styrene-co-acrylonitrile)

Isothermal crystallization kinetics in the miscible mixtures of poly(epsilon-caprolactone) (PCL) and poly(styrene-co-acrylonitrile) (SAN) have been investigated as a function of the composition and the crystallization temperature by optical microscopy. The radial growth rates of the spherulites have been described by a kinetic equation including the interaction parameter and the free energy for the formation of secondary crystal nuclei. Fold surface free energies decrease slightly with the increase of SAN content. The experimental findings show that the influence of the glass transition temperature of the mixture, which is related to the chain mobility, on the rate of crystallization predominates over the influence of the surface free energies. This indicates that the glass transition temperature of the mixture should be of more importance, so that the growth rates decrease when the content of the noncrystallizable component increases. In addition, the Flory-Huggins interaction parameter obtained by fitting the kinetic equation with experimental data is questionable.

Molecular dynamics studies of the effects of branching characteristics on the crystalline structure of polyethylene

Molecular dynamics simulations were carried out on single chain models of linear low-density polyethylene in vacuum to study the effects of branch length, branch content, and branch distribution on the polymer’s crystalline structure at 300 K. The trans/gauche (t/g) ratios of the backbones of the modeled molecules were calculated and utilized to characterize their degree of crystallinity. The results show that the t/g ratio decreases with increasing branch content regardless of branch length and branch distribution, indicating that branch content is the key molecular parameter that controls the degree of crystallinity. Although t/g ratios of the models with the same branch content vary, they are of secondary importance. However, our data suggests that branch distribution (regular or random) has a significant effect on the degree of crystallinity for models containing 10 hexyl branches/1,000 backbone carbons. The fractions of branches that resided in the equilibrium crystalline structures of the models were also calculated. On average, 9.8% and 2.5% of the branches were found in the crystallites of the molecules with ethyl and hexyl branches while C13 NMR experiments showed that the respective probabilities of branch inclusion for ethyl and hexyl branches are 10% and 6% [Hosoda et al., Polymer 1990, 31, 1999–2005]. However, the degree of branch inclusion seems to be insensitive to the branch content and branch distribution.

Novel morphology of polyethylene crystals created upon melt crystallization of spin-coated film

We demonstrate a strikingly novel morphology of high-density polyethylene (HDPE) crystal obtained upon melt crystallization of spin-coated thin film. This crystal gives windmill-like morphology which contains a number of petals. A detailed inspection on this morphology reveals that each petal is actually composed of terrace-stacked PE lamellae, in which the polymer chains within crystallographic a-c planes adopt similar to 45 degrees tilting around b-axis. The surrounding domains associated with a petal of the windmill composed of twisted lamellar overgrowths with an identical orientation of their long axis, which is the crystallographic b-axis shared by the petal and its corresponding twisted lamellar overgrowths.

Insight into growth details and characteristics of windmill-like polyethylene crystals

The crystallization detail of polyethylene (PE) has been scarcely studied via in-situ approach since it is an extremely fast process. In this work, optical microscopy is used to investigate crystallization details and characteristics of windmill-like polyethylene crystals. It has been shown that the straight edges of the petals appear firstly and grow in pairs from their central junctions, which subsequently induce the surrounding domains in between each pairs of petals to nucleate and crystallize into twisted lamellar overgrowths. The remaining terrace-stacked lamellae which form curved edges of the petals start to develop only after the straight edges of the petals together with the twisted lamellar overgrowths have completed their growth. It is confirmed that the preferential growth direction of these petals are along crystallographic [113] axis, which has an angle of 65, with the typical direction along b-axis adopted also by the twisted lamellar overgrowths.

Crystallization kinetics of narrow molecular weight distribution metallocene short-chain-branched polyethylene

Isothermal and non-isothermal crystallization kinetics of three metallocene-catalysed short-chain-branched polyethylene (SCBPE) fractions with different degree of branching were investigated by using differential scanning calorimetry (DSC). Narrow molecular weight fractions (M-w = 20,000 and M-w/M-n < 1.15) are used and the degree of branching (CH3 per 1000C) are 1.6, 10.4, 40 respectively. The regime I - II transition temperature are 119.8C, 115.9 degreesC, 113.3 degreesC with the decreasing of degree of branching. Increasing the branch content decreases the rate of secondary nucleation, i,relative to the rate of surface spreading and so increases the range of supercooling over which regime I exists. The rate of bulk crystallization for both isothermal and non-isothermal crystallization decreases with the increasing of degree of branching. Both Ozawa Equation and Kissinger Equation are invalid for non-isothermal crystallization kinetics of SCBPE fractions,that means the effects of the branched chain on crystallization process are more complex than expected.

Lateral habits of single crystals of metallocene-catalyzed low molecular weight short chain branched polyethylene from the melt

The lateral habits of low molecular weight short chain branched polyethylene single crystals from the melt were studied. Three crystallization temperatures (102, 104 and 106 degrees C) were selected for single crystal growth. It was found that the lateral habits of single crystals were asymmetric at all the crystallization temperatures selected. The electron diffraction patterns and tilting series experiments evidenced that there existed chain tilting in all the lamellae. It was the chain tilting that lead to the asymmetry of the growth rate and of lateral habits of the single crystals about the b-axis. The lateral habits substantially changed from the growth at 102 degrees C where the truncated lozenge single crystals formed with straight (110) faces to the growth at 104 degrees C where the lenticular single crystals appeared. This change occurred at 20 degrees C lower than that in a low molecular weight linear polyethylene with the same molecular weight. Furthermore, kinetics theory analysis evidenced that the change of lateral habits from truncated lozenge to lenticular shape resulted from the transition of growth regime. The results were the same as that of high molecular weight linear polyethylene but different to that of low molecular weight linear polyethylene. It may be attributed by the existence of short branched chains. (C) 2000 Elsevier Science Ltd. All rights reserved.

Study of ion solvation and ion association in polymer gel electrolyte with polyethylene oxide-co-polypropylene oxide as a plasticizer

Using a molal conductance method, ion solvation and ion association in polytriethylene glycol dimethacrylate (PTREGD)-LiClO4 gel electrolytes with amorphous ethylene oxide-co-propylene oxide (EO-co-PO, <(M)over bar (n)>, = 1750) as the plasticizer were investigated. It was found that the fraction of solute existing as single ions (alpha(i)) and ion pairs (alpha(p)) decreases, while that of triple ions (alpha(t)) increases linearly with increasing salt concentration. The dependence of these fractions on molecular weight of plasticizer was also examined. It was shown that alpha(i) and alpha(t) increase and alpha(p) decreases with increasing molecular weight. The result of temperature dependence of these fractions was very interesting: when the temperature is lower than 55 degrees C, alpha(i) increases while alpha(p) and alpha(t) decrease with increasing temperature; however, when the temperature is higher than 55 degrees C, the reverse is true.

Combination of nickel and titanium complexes containing nitrogen ligands as catalyst for polyethylene reactor blending

Ethylene was polymerized using a combination of Ni(diimine)Cl-2 (1) (diimine = 1,4-bis(2,6-di-isopropylphenyl)-acenaphthenediimine) and {Tp(Ms)*} TiCl3 (2) (Tp(Ms)* = hydridobis(3-mesitylpyrazol-1-yl)(5-mesityl-pyrazol-1-yl)) compounds in the presence of methyl-aluminoxane (MAO) at 30 degrees C. The productivity reaches a maximum at X-Ni = 0.75 (1400 kg of PE/mol[M] . h), and the produced polyethylene (PE) showed maximal melt flow index (0.13 g/10 min) and minimal intrinsic viscosity (2.24 dL/g) compared to polyethylenes obtained with different values of nickel loading fractions (X-Ni). Productivity intrinsic viscosity data, as well as melt flow index measurements markedly depend upon the content of the late transition metal, thus suggesting a synergic effect between nickel and titanium catalysts.

Polyethylene multiwalled carbon nanotube composites

Polyethylene (PE) multiwalled carbon nanotubes (MWCNTs) with weight fractions ranging from 0.1 to 10 wt% were prepared by melt blending using a mini-twin screw extruder. The morphology and degree of dispersion of the MWCNTs in the PE matrix at different length scales was investigated using scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM) and wide-angle X-ray diffraction (WAXD). Both individual and agglomerations of MWCNTs were evident. An up-shift of 17 cm(-1) for the G band and the evolution of a shoulder to this peak were obtained in the Raman spectra of the nanocomposites, probably due to compressive forces exerted on the MWCNTs by PE chains and indicating intercalation of PE into the MWCNT bundles. The electrical conductivity and linear viscoelastic behaviour of these nanocomposites were investigated. A percolation threshold of about 7.5 wt% was obtained and the electrical conductivity of PE was increased significantly, by 16 orders of magnitude, from 10(-20) to 10(-4) S/cm. The storage modulus (G') versus frequency curves approached a plateau above the percolation threshold with the formation of an interconnected nanotube structure, indicative of 'pseudo-solid-like' behaviour. The ultimate tensile strength and elongation at break of the nanocomposites decreased with addition of MWCNTs. The diminution of mechanical proper-ties of the nanocomposites, though concomitant with a significant increase in electrical conductivity, implies the mechanism for mechanical reinforcement for PE/MWCNT composites is filler-matrix interfacial interactions and not filler percolation. The temperature of crystallisation (T.) and fraction of PE that was crystalline (F-c) were modified by incorporating MWCNTs. The thermal decomposition temperature of PE was enhanced by 20 K on addition of 10 wt% MWCNT. (c) 2005 Elsevier Ltd. All rights reserved.

Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.