Studies of the temperature dependence of spherulitic growth rates, in the context of the Lauritzen−Hoffman secondary nucleation theory, and investigations of the crystallization time and temperature dependence of the melting behavior, in the context of the nonlinear Hoffman−Weeks (HW) extrapolation, are reported for isotactic polypropylene prepared with Ziegler−Natta catalysts. The quantitative agreement between estimations of the equilibrium melting temperature, Tm, through an analysis of spherulitic growth rate data and use of the nonlinear HW approach provides strong support for the latter method. The results of these studies indicate specifically that Tm (it-PP, α-phase) is in the vicinity of 212−215 °C, some 30 °C above the most commonly quoted value. This new value of the equilibrium melting temperature of it-PP leads to predictions of the crystallization temperature dependence of the initial lamellar thickness and of the correlation between the lamellar thickness and observed melting temperature, w...

Equilibrium Melting Temperature and Undercooling Dependence of the Spherulitic Growth Rate of Isotactic Polypropylene

A new method to determine the correct Gibbs−Thomson plot and equilibrium melting temperature (Tm0) of polymers was proposed. The Gibbs−Thomson plot method is reliable, because the Gibbs−Thomson equation is directly derived from thermodynamical relations. In this method, the heating rate dependence of melting temperature (Tm) was omitted by applying the theory of the “melting kinetics”, and the effect of lamellar thickening on Tm was also omitted by observing thick lamellae. A differential scanning calorimeter (DSC) was used for observation of Tm as a conventional method. Transmission electron microscope (TEM) was used to observe a distribution of lamellar thickness (l). It was shown theoretically that peak temperature of melting endotherm (Tm(DSC)) corresponded to averaged reciprocal l (〈l-1〉) for the case of sharp distributions of Tm and l-1. The Gibbs−Thomson plot, Tm (DSC) vs 〈l-1〉, was carried out. A reliable Gibbs−Thomson plot and Tm0 = 186.2 °C were obtained for a fraction of isotactic polypropylene...

Equilibrium Melting Temperature of Isotactic Polypropylene with High Tacticity: 1. Determination by Differential Scanning Calorimetry

Crystallization and melting behaviour of photodegraded polypropylene — II. Re-crystallization of degraded molecules

Membrane formation via thermally induced phase separation (TIPS) : Model development and validation

In part 1 of this series, we proposed a new method to determine the correct equilibrium melting temperature (Tm0) Effects of the “melting kinetics” and lamellar thickening were omitted from Tm The correct Tm0 of isotactic polypropylene (iPP) ([mmmm] = 996%, Mn = 64 × 103, and Mw/Mn = 24) was observed to be 1861 °C In this paper, the rigorous Gibbs−Thomson plot was obtained by using the direct correspondence between maximum melting temperature (Tm,max) and maximum lamellar thickness (lmax) Tm,max and lmax were observed by means of optical microscope and transmission electron microscope (TEM), respectively The validity of the Gibbs−Thomson plot obtained by means of a differential scanning calorimeter (DSC) (part 1 of this series) was confirmed by comparing it with the rigorous Gibbs−Thomson plot in this paper The Hoffman−Weeks plot is widely used as one of the methods to obtain Tm0 It was shown that the Hoffman−Weeks plot is correct only when l ∝ 1/ΔT, where ΔT is the degree of supercooling, is sa

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Equilibrium Melting Temperature of Isotactic Polypropylene with High Tacticity. 2. Determination by Optical Microscopy

Isothermal crystallization of isotactic polypropylene in dotriacontane. IV: Effect of dilution and crystallization temperature on overall crystallization kinetics

Isothermal crystallization of isotactic polypropylene in dotriacontane. III: Effect of dilution and crystallization temperature on growth rate

Spherulitic crystallization presents an inverse Stefan problem, which is solved by numerical methods using the DuFort-Frankel scheme and Lagrangian coordinate systems. The numerical solution shows excellent agreement with the analytical solution in the Cartesian coordinate system. A systematic error in the numerical solution for the spherical and cylindrical coordinate systems is examined by a material balance for the system. The systematic error was found to decrease rapidly as the dimensionless time increased and the grid spacing decreased.

Yu F. Wang

Papers

Isothermal crystallization of isotactic polypropylene in dotriacontane. IV: Effect of dilution and crystallization temperature on overall crystallization kinetics

Isothermal crystallization of isotactic polypropylene in dotriacontane. III: Effect of dilution and crystallization temperature on growth rate

Spherulitic crystallization: An analysis of inverse stefan problems in cartesian, cylindrical, and spherical coordinate systems