Poly(lactic acid) crystallization

Kinetic of crystallization from the melt and chain folding in polyethylene fractions revisited: theory and experiment

The kinetic theory of the rate of growth G and the initial lamellar thickness lg* of chain‐folded crystals is extended so that it is applicable at high undercoolings. Attention is centered on the details of how the first step element and the first fold are put down on the substrate. A parameter φ that varies between zero and unity, which apportions the free energy of attachment of the step element between the forward and backward reactions, is used to denote variations in this process. Expressions for G are derived from flux equations for two limiting cases: regime I, single surface nucleation act with rapid substrate completion and regime II, numerous surface nucleation acts with very slow substrate completion. Data from the literature on G for isotactic polystyrene (regime II) and polyethylene single crystals (regime I) are analyzed to obtain surface free energies, and these are used with the revised theory for lg* to predict the lamellar thickness of these polymers. Good agreement between lg* and publi...

Extension of theory of growth of chain‐folded polymer crystals to large undercoolings

The effect of molecular weight (MW) on the polymorphous crystallization and melting behavior of poly(l-lactide) (PLLA) were systemically studied by differential scanning calorimetry (DSC), polarized optical microscopy (POM), wide-angle X-ray diffraction (WAXD), and time-resolved Fourier transform infrared (FTIR) spectroscopy. It was found that the polymorphism of PLLA is not influenced much by MW, and the α‘- and α-form crystals are produced at low and high crystallization temperature (Tc), respectively, regardless of the MW. However, MW significantly affects the crystallization kinetics, and the crystallization rate reduces greatly with MW increasing. Moreover, the Tc- and MW-dependent melting behavior of PLLA was clarified with combining the DSC and FTIR results. It was found that the α‘- to α-crystalline phase transition occurs prior to the dominant melting in both the low- and high-MW PLLA crystallized at low Tc. Unlike the high-MW PLLA, in low-MW PLLA crystallized at low Tc, the α‘-form crystals only...

Polymorphous Crystallization and Multiple Melting Behavior of Poly(l-lactide): Molecular Weight Dependence

Under a variety of circumstances commonly encountered in practice linear macromolecules crystallize into the form of thin platelets whose large upper and lower surfaces consist of an array of molecular folds. We refer to these as “chain-folded crystals” or “chain-folded lamellae,” the latter term usually being reserved for folded structures in polymers crystallized from the melt. The theory of the rate of formation of these platelets will be outlined, and the prediction and origin of the thin dimension given. The thin dimension of the crystal platelets is determined by kinetic factors, and the elucidation of the kinetics of growth is therefore of importance in polymer morphology on both a molecular and a macroscopic scale.

The Rate of Crystallization of Linear Polymers with Chain Folding

A new method of estimating the equilibrium melting temperature, Tm, of a polymer is described, and applied to polychlorotrifluoroethylene (PCTFE). Experimentally determined values of the so-called observed melting point, !F^(obs), are plotted as a function of the isothermal crystallization temperature, Tx. When freed of secondary effects, such as recrystallization, the data fit a straight line of positive slope on a Ti (obs) versus Tx plot, Tx being the abscissa. This line is then extrapolated to its intersection with the line T^ (obs) = Tx. The temperature at this intersection is Tm. This intersection is at 224 °C for PCTFE, and Tm is quoted as 224± 1 °C. (The highest melting point actually attained for a specimen was 218.2 °C.) The value of Tm estimated using the extrapolation procedure is compared with that estimated using the customary method of slow stepwise warming. A theoretical justification is given for making the type of plot mentioned above. The most important assumption used in the theory is that one of the dimensions of the growing crystal retains a value rather close to that of the appropriate growth nucleus during an isothermal crystallization, the other two dimensions being large in comparison. Combination of this with the fact that the relevant dimension of the growth nucleus will vary as the reciprocal of the degree of supercooling leads to the prediction of melting points that increase linearly with crystallization temperature. The assumption that one of the dimensions of the crystal retains a value fairly close to that of a growth nucleus can readily be justified on the basis of polymer crystal growth with chain folds. Its justification in the case of the customary bundlelike mode of crystallization is less clear. It is demonstrated experimentally that even the largest detectible crystals in PCTFE are only about 70 percent thicker than a primary nucleus, when secondary effects are minimized. The application of the theory to systems other than PCTFE is discussed briefly, and some preliminary measurements on polyethylene mentioned. Some points relating to the shape of the melting curves of highly crystalline polymers are also brought out.

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Melting process and the equilibrium melting temperature of polychlorotrifluoroethylene

(I) The requirements for making a critical test of whether two‐ or three‐dimensional surface nucleation controls the radial growth of lamellar spherulites in bulk are discussed. Radial‐growth‐rate data were obtained on spherulites of polychlorotrifluroethylene (PCTFE) for a wide range of supercooling ΔT, and found to agree with a growth‐rate law based on coherent two‐dimensional surface nucleation, viz., G=G0 exp(—ΔF*/RT) exp[—Kg/T2(ΔT)]. Approximations for ΔF* are given. (II) Parameters related to the recently proposed ``kinetic'' viewpoint of homogeneous nucleation and growth of lamellar polymer crystals with chain folds are obtained. The nucleation constant Kg is analyzed to obtain σσe=184 erg2/cm4[σ is the lateral surface free energy, σe is the end (chain‐folded) surface free energy]. A similar value of σσe is obtained from bulk‐crystallization studies. The homogeneous nucleation process was identified at ΔTh=70°C, and a value of σ2σe=950 erg3/cm6 calculated from Kh in I=(NkT/h) exp(—ΔF*)exp[—Kh/T3(ΔT...

Rate of Spherulitic Crystallization with Chain Folds in Polychlorotrifluoroethylene

X‐Ray Study of Isothermal Thickening of Lamellae in Bulk Polyethylene at the Crystallization Temperature

The melting temperature of linear polyethylene has been obtained as a function of the time and temperature of crystallization. Recrystallization was minimized by a special melting procedure. By interpreting the melting points as characteristic of a given lamellar thickness, it was found that the thickness of crystals of appreciable age increased linearly with the logarithm of their time of existence. The lowest melting (i.e., thinnest) lamellae in a given specimen may be assumed to have either existed for only a short period of time, or to have been impeded in their growth in the chain direction, and they were found to have an estimated thickness close to that predicted by recent kinetic theories of polymer crystal growth with chain folding.

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Melting Temperature and Change of Lamellar Thickness with Time for Bulk Polyethylene.

The diffraction of x-rays by the crystalline n-paraffins, C36H74, C44H90, and C94H190, was examined at small angles - below seven degrees 2θ - as a function of temperature. The Bragg maxima (00l) that occur at these angles result from a lamellar repeat distance which depends on the molecular length. In general the intensity of these maxima was found to increase with increasing temperature in an approximately reversible manner. All the samples experienced solid-solid phase transitions in the temperature range of observation. Several possible mechanisms consistent with the temperature dependence of the intensity are considered.

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The Intensity as a Function of Temperature of the Low-Angle X-Ray Diffraction Maxima of the n-Paraffins: Hexatriacontane, Tetratetracontane, and Tetranonacontane.

James J. Weeks

Papers

Melting process and the equilibrium melting temperature of polychlorotrifluoroethylene

Rate of Spherulitic Crystallization with Chain Folds in Polychlorotrifluoroethylene

X‐Ray Study of Isothermal Thickening of Lamellae in Bulk Polyethylene at the Crystallization Temperature

Melting Temperature and Change of Lamellar Thickness with Time for Bulk Polyethylene.

The Intensity as a Function of Temperature of the Low-Angle X-Ray Diffraction Maxima of the n-Paraffins: Hexatriacontane, Tetratetracontane, and Tetranonacontane.