Crystallization kinetics, assessment

The crystallization kinetics was assessed using several models, such as Ozawa theory and Jeziomy model [75]. 

This work, with the aim of assessing the influence produced by these fillers on the polypropylene microstructure, and hence determining their effect on the physical properties of the resulting composites, reports on a study designed to analyze, by means of an individualized approach, the effect produced by sepiolite, talc and the elastomeric copolymer on the isothermal crystallization kinetics and on the glass transition temperature of the polypropylene. This study permits to correlate more adequately the changes produced in the microstructure of the composites and their physical properties. 

A related problem of interest is when a polymer is not crystalline as prepared, but is potentially crystallizable. This situation is commonly encountered in crys-tallizable copolymers, and is also found in homopolymers. Some typical examples of this phenomenon are found in poly(styrene) synthesized by means of alfin type catalysts,(50) poly(methyl methacrylate), prepared by either free-radical or ionic methods,(39,51,52) and poly(carhonate).(53) Treatment with particular solvents or diluent at elevated temperatures can induce crystallinity in these polymers. The reason for the problem is kinetic restraints to the crystallization process. Treatment with appropriate diluents alleviates the problem. The principles involved, and the diluent requirements will he enunciated in the discussion of crystallization kinetics. For present purposes it should be recognized that the crystallizability of a polymer, particularly a copolymer, cannot be categorically denied unless the optimum conditions for crystallization have been investigated. Thus, in light of the previous discussion regarding the minimum concentration of chain units required for crystallization, and the need to have favorable kinetic conditions, the lack of crystallization in any given situation needs to be carefully assessed. 

Similarly, several authors have presented MSMPR methods for kinetics determination from continuous crystallizer operation (Chapter 3), which have become widely adopted. In an early study, Bransom etal. (1949) anticipated Randolph and Larson (1962) and derived a crystal population balance to analyse the CSD from the steady state continuous MSMPR crystallizer for growth and nucleation kinetics. Han (1968) proposed a method of kinetics determination from the moments of the CSD from a cascade of continuous crystallizers and assessed the effect of sample position. Timm and Larson (1968) suggested the use of the extra information present in transient response data to determine kinetics, followed by Sowul and Epstein (1981), Daudey and de Jong (1984) and Jager etal. (1991). Tavare (1986) applied the j-plane analysis to the precipitation of calcium oxalate, again assuming nucleation and growth only. 

Poly(cyclohexyl acrylate) was shown to be miscible with PS with ucst behavior [720]. Random copolymers of cyclohexyl acrylate with n-butyl acrylate showed miscibility with PS above 50% cyclohexyl acrylate[721]. Poly(cyclohexyl methacrylate)/isotactic PS blends showed miscibility based on calorimetry and NMR studies [722]. The NMR results showed homogeneous behavior at a scale of 2.5-3.5 nm. Poly(4-trimethylsilyl styrene) miscibility with polyisoprene was observed with a lest behavior (critical temperature = 172 ° C at degree of polymerization of 370) [723]. The interaction parameter, showed the following relationship = 0.027—9.5/T. Isotactic and syndiotactic polystyrene both exhibit crystallinity, whereas atactic polystyrene is amorphous. Atactic PS/isotactic PS blends exhibited crystallization kinetics, which decreased linearly with atactic PS addition indicating miscibility [724]. The TgS of aPS and iPS are identical, thus Tg methods could not be employed to assess miscibility. Atactic PS/syndiotactic PS blends were also noted to be miscible with rejection of atactic PS in the interfibrillar region between the lamellar stacks of sPS [725]. 

Figure 7.3 Scheme of the conical zone in space and time drawn for 2D crystallization. From two spherulites nucleated at time r, only one, with a center at point P, that is, at distance r(r,t) from A can reach A at time t. Modified from Piorkowska, E., et al. Critical assessment of overall crystallization kinetics theories and predictions. Prog. Polym. ScL 2006,57,549-575. Copyright 2006, with kind permission from Elsevier. 

The literature concerning the experimental results of the overall crystallization kinetics of homopolymers is quite vast. It encompasses virtually all types of repeating units of crystallizable polymers. From this abundance, a representative set of examples has been chosen that illustrates the basic experimental results. These data allow for a quantitative assessment of the theoretical developments that have been presented so far. 

In Figure 4 the half-time (xi/2 ) for Pebax 7033 composites crystalhzation at different crystallization temperatures is shown as derived from the crystallization kinetics for the composite materials presented in Table 2. Plotting half-time crystallization as a function of crystalhzation temperatiu e is a method for assessing the time required for crystal growth conversion. It is seen that the PPTA AS fiber composites had a decrease in the half-time for the crystallization from that of the virgin Pebax. This trend is attributed to a nucleating effect of the aramid fibers on the Pebax 7033 crystallization. It was found from the optical microscopy transcrystahization studies, that the largest amoimt of transcrystalhzation occmred for the succinyl chloride treated PPTA Pebax 7033 composites. The half time of... 

ABSTRACT The kinetics and mechanisms of the phase transformation of 2-line ferrihydrite to goethite and hematite are being assessed as a function of pH, temperature and Fe/As, Fe/Se, Fe/Mo molar ratios using batch experiments, BET analyses, XRD, and XANES. Initial results from XRD analyses show that ferrihydrite is stable at high pH ( 10) for up to seven days at 25°C, but considerable crystallization occurs at elevated temperatures. Specifically, XRD data show that ferrihydrite is transformed to a mixture of hematite and goethite at 50°C (-85% hematite and -15% goethite) and 75°C (-95% hematite and -5% goethite) after 24 hours and these ratios remain constant to the end of the experiments (seven days). 

Several investigators have offered various techniques for estimating crystallization growth and nucleation parameters. Parameters such as kg, 6, and ki are the ones usually estimated. Often different results are presented for identical systems. These discrepancies are discussed by several authors (13,14). One weakness of most of these schemes is that the validity of the parameter estimates, i.e., the confidence in the estimates, is not assessed. This section discusses two of the more popular routines to evaluate kinetic parameters and introduces a method that attempts to improve the parameter inference and provide a measure of the reliability of the estimates. 

It is often said that all authors are responsible for the entire content of a manuscript. This is a meritorious ideal, but unrealistic. Most manuscripts have multiple authors, and very often, a single author is responsible for only a portion of the work being presented. For example, the manuscript may contain a crystal structure, determined by an expert crystallographer spectral data, determined by an expert spectroscopist kinetic data, determined by an expert kineticist etc. In cases such as this, a single author cannot be held responsible for all of the results presented. A more realistic assessment of what authorship implies is that each author should have read the manuscript carefully and understood the findings, but the technical responsibility is only for the area in which a given author... 

Thus, the proposed method for analyzing the kinetics of defect formation, based on the quasi-epitaxy model, clearly demonstrates the role of the surface in the ADC equilibrium and allows one to assess the effects of temperature and Jb of the equilibration of defect concentrations. Computer simulations of defect formation kinetics in II-VI crystal non-equilibrium chalcogen vapor systems indicate that steady state defect concentrations in the surface layer are reached very rapidly and, accordingly, are not... 

From viewpoint of the process of deposition or growth, it would be of interest to make an assessment of the step roughness as defined by the density of kink atoms per unit step length, because it would give an important kinetic parameter of growth. The step roughness can be given as the reciprocal of a normalized mean distance parameter Aink /do,Me, where ink is the mean distance between kink atoms and do,Me is the atomic diameter. For the most dense step [110] on a cubic (100) face of a fee crystal, the mean distance parameter is [2.1, 2.15]... 

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