Crystallization kinetics of syndiotactic polypropylene

Melting-point and spherulite growth rate measurements for a sample of syndiotactic polypropylene (S = 0.716 and η = 0.356) were analyzed for the parameters characterizing crystal formation and growth: T_m = 159 ± 2°C, σ_e = 47 erg cm ^?2, σ = 4.4 erg cm^?2, and q = 5.6 kcal per mole of folds. The q and σ_e values place syndiotactic polypropylene in the group of “unhindered” polymers. Failure of the isotactic-polypropylene spherulite growth rate data to follow current theories of crystal growth precluded a comparison of crystal parameters of the two stereoisomers. At comparable degrees of supercooling, the absolute growth rates for the two forms are of the same order of magnitude and exhibit one or more crossover(s) in relative position.     

Kinetics of growth of developing spherulites

A model containing two rate constants is presented for the development of spherulites from sheaves. One, G_R, is a radial spherulite growth constant while the other, G_S, describes the rate of increase of apex angle of the sheaf. On the basis of this model, Avrami kinetics are developed which predict a change in the Avrami constant n from 5 to 3 as the sheaf develops into a spherulite. H_V light-scattering patterns are calculated according to this model and are found to compare favorably with those found during the early stages of the crystallization of poly(ethylene terephthalate).     

Mutual influence of LDPE and PP in their blends during crystallization

An indication for the mutual influence of LDPE and PP was the change of the morphology parameters of PE and PP at different ratios of the polymers in blends. That influence depends on the blend composition and is different for PE and PP. It is especially interesting in the blend PE75/PP25 where the influence between PE and PP shows dependence also on the sample geometry. Melting parameters, non-isothermal crystallization parameters - crystallization peak temperature T_c, crystallization begin temperature T_onset, half-width w_1/2 of the crystallization peak, degree of crystallinity α and crystallization rate coefficient CRC, as well as the isothermal kinetics parameters showed dependence on the blend composition. It was established that PE is more stable then PP concerning the mutual influence of both polymers on their crystallization. It was established that PE affects the crystal nucleation of PP and causes a decreasing of PP spherulite size.     

Thermal decomposition kinetics of multiwalled carbon nanotube/polypropylene nanocomposites

In this study, non-isothermal crystallization of neat high density polyethylene (HDPE) and HDPE/titanium dioxide (TiO₂) composite was studied using differential scanning calorimetry. Non-isothermal kinetic parameters were determined by Jeziorny approach and Mo’s method. Polarized optical microscopy and wide angle X-ray diffraction were applied to observe the crystal morphology and investigate the crystal structure, respectively. It was found TiO₂ particles could act as nucleating agent during the crystallization process and accelerate the crystallization rate. The Avrami index indicated nucleating type and growth of spherulite of HDPE was relatively simple. The result of activation energy indicated it was more and more difficult for the polymer chains to crystallize into the crystal lattice as the crystallization progressed. HDPE/TiO₂ composites exhibited lower ΔE values, suggesting TiO₂ particle could make the crystallization of HDPE easier. HDPE/TiO₂ composites had much smaller spherulite size than that of neat HDPE. HDPE formed more perfect crystal when TiO₂ particles were added into its matrix without changing the original crystal structure of HDPE.     

Influence of crystallization temperature,molecular weight,and additives on the crystallization kinetics of poly(ethylene terephthalate)

The spherulite growth rate, the maximum spherulite radius, and the overall rate of crystallization of poly(ethylene terephthalate) (PETP) were measured by means of scattering and transmission of depolarized light. The influence of crystallization temperature, molecular weight, and additives on the above-mentioned quantities was investigated. An expression has been derived for the spherulite growth rate of PETP as a function of crystallization temperature and the number-average molecular weight for M?_n in the range of 19,000 to 39,000.     

A growing 2D spherulite and calculus of variations Part I: A 2D spherulite in a linear field of growth rate

We propose to take the calculus of variations in order to compute the shape of a growing 2D spherulite in an uniaxial field of growth rate. We are concerned with the growth line (a path that is traveled in the shortest possible time from nucleus to a point (x₁, y₁), where a molecule just crystallizes) and the growth front (the times between spherulite and supercooled material). The Euler differential equation—a result of the calculus of variations—is derived for all uniaxial growth ratesv (x). Here we especially investigatev(x)=px+q.     

Effect of poly(butylene succinate) crystals on spherulitic growth of poly(ethylene oxide) in binary blends of the two substances

The effects of the lamellar growth direction, extinction rings, and spherulitic boundaries of poly(butylene succinate) (PBSU) on the spherulitic growth of poly(ethylene oxide) (PEO) were investigated in miscible blends of the two crystalline polymers. In the crystallization process from a homogeneous melt, PBSU first developed volume‐filling spherulites, and then PEO spherulites nucleated and grew inside the PBSU spherulites. The lamellar growth direction of PEO was identical with that of PBSU even when the PBSU content was about 5 wt %. PEO, which intrinsically does not exhibit banded spherulites, showed apparent extinction rings inside the banded spherulites of PBSU. The growth rate of a PEO spherulite, G_PEO, was influenced not only by the blend composition and the crystallization temperature of PEO, but also by the growth direction with respect to PBSU lamellae, the boundaries of PBSU spherulites, and the crystallization temperature of PBSU, T_PBSU. The value of G_PEO first increased with decreasing T_PBSU when a PEO spherulite grew inside a single PBSU spherulite. Then, G_PEO decreased when T_PBSU was further decreased and a PEO spherulite grew through many tiny PBSU spherulites. This behavior was discussed based on the aforementioned factors affecting G_PEO. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 539–547, 2009     

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.     

Spherulite growth rates of in situ prepared poly(propylene terephthalate)/SiO2 nanocomposites

The spherulite growth rates of in situ prepared PPT/SiO₂ nanocomposites containing 2–5 wt% nano-silica were studied. Measurements of the spherulite growth rates were carried out by applying non-isothermal experiments using polarized light microscopy (PLM). Comparison with results from isothermal PLM tests showed good agreement. Isothermal crystallizations after self-nucleation were also performed using differential scanning calorimetry (DSC) and the inverse crystallization half-times were estimated. The Lauritzen–Hoffman analysis was applied by using data from both isothermal and non-isothermal PLM experiments and the DSC results. Regimes II–III transition were observed at critical breakpoint close to 195 °C. The regimes I–II transition was not so clear, because of the semi-rigid macromolecular chains of the polymers. Results using DSC data were in satisfactory agreement to those using PLM spherulite growth data.     

Thermokinetic parameters and thermal hazard evaluation for three organic peroxides by DSC and TAM III

The thermokinetic parameters were investigated for cumene hydroperoxide (CHP), di-tert-butyl peroxide (DTBP), and tert-butyl peroxybenzoate (TBPB) by non-isothermal kinetic model and isothermal kinetic model by differential scanning calorimetry (DSC) and thermal activity monitor III (TAM III), respectively. The objective was to investigate the activation energy (E _a) of CHP, DTBP, and TBPB applied non-isothermal well-known kinetic equation to evaluate the thermokinetic parameters by DSC. We employed TAM III to assess the thermokinetic parameters of three liquid organic peroxides, obtained thermal runaway data, and then used the Arrhenius plot to obtain the E _a of liquid organic peroxides at various isothermal temperatures. In contrast, the results of non-isothermal kinetic algorithm and isothermal kinetic algorithm were acquired from a highly accurate procedure for receiving information on thermal decomposition characteristics and reaction hazard.     

Self‐decelerated crystallization in poly(butylene terephthalate)/poly(ε‐caprolactone) blends

Isothermal crystallization of poly(butylene terephthalate) (PBT) blended with oligomeric poly(ε‐caprolactone) (PCL) is investigated by polarized optical microscopy and differential scanning calorimetry at various temperatures (T_c). The growth rate of PBT spherulites is found to depend on time (t), as the spherulite radius (r) linearly increases with t at the early stages of crystallization (r ∝ t), then, with the progress of phase transition, the spherulite radius becomes dependent on the square root of the time (r ∝ t^1/2) until termination of crystal growth. The nonlinear advance of the crystal growth front is caused by a varied composition of the melt phase in contact with the growing crystals, due to diffusion of mobile PCL chains away from the spherulite surface. The melt phase becomes spatially inhomogeneous, causing self‐deceleration of PBT crystallization until a limit composition that prevents further crystallization is reached in the melt. The maximum crystallinity achievable during isothermal crystallization decreases with T_c. The lowering of the temperature after termination of the isothermal crystallization allows to complete the crystal growth, but the final developed crystallinity still depends on T_c, being lower at higher T_cs. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3148–3155, 2007     

Small-angle light scattering by random assemblies of incomplete spherulites. I. Sheaflike textures

The calculation of the scattering from a sheaflike sector of a two-dimensional spherulite has been carried out as a function of the apex angle of the sector. It is found that while for a complete spherulite the H_v scattered intensity is zero at zero scattering angle, there is an increasing intensity of scattering at 0° as the sector angle narrows. For very small values of the sector angle, the scattering becomes similar to that of a rod, with the exception that a scattering maximum is still seen at an angle close to that at which the spherulite scattering maximum occurs. The predictions of the model compare favorably with the scattering patterns observed for polymers in early stages of spherulitic growth.     

Non-isothermal crystallization behavior of polypropylene with nucleating agents and nano-calcium carbonate

The non-isothermal crystallization kinetics of isotactic polypropylene (iPP) and nucleated iPP was investigated by DSC. The crystalline morphology of iPP was observed by polarized light microscopy. It was found that the crystallization rate increased with the addition of nanometer-scale calcium carbonate (nm-CaCO₃) particles. The addition of dibenzylidene sorbitol (DBS) could greatly reduce the spherulite size of iPP. The crystallization temperature for the iPP with DBS was higher than for non-nucleated iPP. DBS was an effective nucleating agent for iPP. The results of measurements suggested that there was a coordinated action to the crystallization of iPP when the organic nucleating agents (DBS) and nm-CaCO₃ were added to iPP together. Comparison to the modified Avrami equation and Ozawa equation, another method—Mo’s method can describe the non-isothermal crystallization behavior of iPP and nucleated iPP more satisfactorily.     

Exclusion effect of carbon dioxide on the crystallization of polypropylene

We investigated the crystallization growth of isotactic polypropylene under carbon dioxide (CO₂) at various CO₂ pressures and temperatures by in situ observation with a digital high‐fidelity microscope and a specially designed high‐pressure visualized cell. The fibrils within the spherulite were distorted and branched by crystallization under CO₂ at pressures higher than 2 MPa, and this suggested the exclusion of CO₂ from the growth front of the fibrils. The spherulite growth rate (G) at 140 °C increased with the CO₂ pressure, attained a maximum value around 0.3 MPa, and then decreased. Above 6 MPa, it became slower than that under air at the ambient pressure. An analysis of the crystallization kinetics by the Hoffman–Lauritzen theory revealed that the pressure dependence of G could be ascribed to the change in the transportation rate of crystallizable molecules (β_g) with pressure; that is, β_g increased and then decreased with pressure. The increase in β_g at a low pressure was caused by the plasticizing effect of CO₂, whereas the decrease in β_g at a high pressure was due to the exclusion of CO₂ from the crystal growth front. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1565–1572, 2004     

Measurement of spherulite growth rates using tailored temperature programs

A method recently proposed for measuring spherulite growth rates (G) using temperature programs, tailored for each polymer, is reviewed. This method, compared to the conventional isothermal procedure, permits to expand the temperature range where spherulite growth rates can be measured. Examples of application of this method are reported, in particular, the spherulite growth rates of isotactic polypropylene (iPP) and poly(l-lactic acid) (PLLA) are analyzed. For iPP, growth rates were obtained from 112 to 148 °C using different cooling rates and a self-nucleation procedure. For PLLA, measurements in both isothermal and non-isothermal conditions allowed to overcome the difficulties due to the very high nucleation density that prevent determination of growth rates at low crystallization temperatures. For this polymer the entire curve of G vs. T was obtained.     

Synthesis,characterization, and investigation of the thermal behavior of Cu(II) pyrazolyl complexes

In the present contribution, a procedure to estimate parameters using non-isothermal data was applied. The estimation procedure is based on the use of an energy balance in DSC furnace. The approach found all kinetic parameters of autocatalytic model (E ₁, E ₂, A ₁, A ₂, m, n) besides the ultimate reaction heat and their confidence regions by using deterministic and heuristic algorithms. The application of this approach to isothermal data was done in a previous work and similar results were obtained. The results show that the use of an energy balance is a good methodology to estimate cure kinetic parameters of non-isothermal experiments.     

The effect of the addition of polypropylene grafted SiO2 nanoparticle on the crystallization behavior of isotactic polypropylene

The crystallization behavior of isotactic polypropylene (iPP)/silica particle (SiO₂, 26 nm) nanocomposite has been investigated. In addition to the non surface-modified SiO₂, iPP grafted SiO₂ was synthesized and adopted to this study with an aim to understand the role of grafted polymer chain on the crystallization process. The crystallization rate of non surface-modified iPP/SiO₂ composite stays constant up to 1 vol%. It suggests the very weak nucleation ability of nano-sized silica particle. While large acceleration effect was observed for iPP-grafted SiO₂/iPP composite. The spherulite density increased with increasing SiO₂ contents, and more interestingly, the spherulite growth rate also increased. This finding leads to the conclusion that the grafted iPP chain has a plasticizing effect that reduces the chain entanglements at the interface. Further increase in SiO₂ contents, the crystallization rate, the spherulite density, and the spherulite growth rate showed the steep decreases at higher SiO₂ content range regardless of the surface modifications of SiO₂. It was attributed to the confinement of matrix chain since the inter-particle distance of adjacent SiO₂ approaches to the end-to-end distance of matrix chain, which a large molecular motion is restricted. Moreover, the average size of SiO₂ aggregation in iPP matrix was successfully evaluated by analyzing the contents dependence of the growth rate, assuming that the inter-particle distance with zero growth rate coincided with end-to-end distance of matrix iPP chain.     

Simulation of isothermal cure of A powder coating

The curing of a thermosetting powder coating was studied by means of differential scanning calorimetry (DSC). The isothermal cure was simulated by non-isothermal experiments. The results of the simulation were compared with experimental isothermal data. From non-isothermal isoconversional procedures (free model), it was concluded that these permit simulation of the isothermal cure but do not enable us to determine the complete kinetic triplet (A preexponential factor, E activation energy, f(a) and/or g(a) function of conversion). Non-isothermal procedures based on a single heating rate or on master curves present difficulties for determination of all the kinetic parameters, due to the compensation effect between preexponential factor and activation energy. The kinetic triplet can be determined by a combination of various non-isothermal methods or by using experimental isothermal data in addition to non-isothermal data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crystal orientation in a semicrystalline polymer in relation to deformation of polymer spherulites. IV. Crystal orientation mechanism of nylon-6 under uniaxial stretching

A model relating crystal orientation to the deformation of nylon-6 spherulites under uniaxial stretching is discussed in terms of the orientation distribution functions of reciprocal lattice vectors of crystal planes, such as the (002) and (200) planes. The distribution functions calculated from the model are compared with those obtained from x-ray diffraction experiments. It is found that the crystal a axis and, consequently, the direction of hydrogen bonds within the crystal (α modification) orient parallel to the lamellar axis in the undeformed state, and that the crystal orientation behavior of nylon-6 is much different from that of low-density polyethylene, being characterized by much smaller values of the reorientation parameters of crystallites within orienting lamellae. Moreover, small-angle light scattering for H_v and V_v polarization is also calculated on the basis of the spherulite deformation model by taking the nylon-6 crystal as having orthogonal–biaxial symmetry in optical anisotropy. It is concluded that the H_v scattering can be realized in terms of the proposed model for spherulite deformation by taking into account a considerable contribution of hydrogen bonds to the molecular polarizability, so as to make the polarizability along the crystal a axis larger than that along the b axis. In other words, this conclusion suggests positively birefringent spherulites in the nylon-6 samples studied.     

Small-Angle light scattering from an anisotropic sphere: Anisotropy and size effects

The recently developed theory of light scattering from an anisotropic sphere (taken as a model for a spherulite) summarizes all information obtainable from such scattering system when the Rayleigh-Gans-Debye approximation is appropriate. The commonly used procedure of size determination from the maximum of the H_v intensity is tested for a number of models differing in radius size, inherent anisotropy δn and mean refractive index ¯n. It has been confirmed, that the parameter (¯n - 1)/δn plays the decisive role in the angular dependence of the H_v intensity and the influence of that parameter on the size determination and resulting accuracy is specified. The results differ for positive and negative spherulites and the stabilizing role of increasing spherulite size in accuracy of procedure is demonstrated. It has been shown that the RGD approximation is appropriate especially for the case of homogeneous spherulite texture (thus implying, that the refractive index of the surrounding is close to the average refractive index of a single spherulite). The results extrapolated outside of the RGD approximation display invariable U_max position for isotropic contribution with increasing sphere size in contrast to the oscillatory character of U_max predicted by the LM solution. It is proposed to construct the anisotropic solution under an approximation recently suggested for thin anisotropic shell. © 1994 John Wiley & Sons, Inc.