Synergies among the self-assembled β-nucleating agent and the sheared isotactic polypropylene matrix
Abstract The impacts of both shear temperature and shear rate on both the self-assembled β-nucleating agent (β-NA) in the hosting isotactic polypropylene (iPP) matrix and the subsequent crystallization of the hosting iPP matrix were investigated by polarized optical microscopy (POM) and wide-angle X-ray diffraction (WAXD), and small-angle X-ray scattering (SAXS) measurements, respectively. Under static condition, β-NA could self-assemble into snowflake-like aggregate. Once shear was applied, three kinds of self-assembled aggregates could be developed prior to the crystallization of matrix depending on the applied shear temperatures, that is, snowflake-like self-assembled aggregate at 200 °C, deformed snowflake-like one with smaller branches at 180 °C, tiny and dense needle-like one if shear temperature was further decreased to 160 °C. Since β-NA with various self-assembled aggregates can act as nucleating templates for the subsequent nucleation of iPP matrix, it is conceivable that the crystallization behavior of the iPP matrix can be altered. As expected, β-phase crystallinity, long period and lamellar thickness are steadily dependent on the shear temperature and shear rate. That is, when shear was applied at 200 °C, β-phase crystallinity, long period and lamellar thickness keeps almost constant regardless of the shear rate. If melt was sheared at 180 °C, β-phase crystallinity was decreased while long period and lamellar thickness remained unchanged with elevating shear rate. At lower shear temperature (i.e., 160 °C), β-phase crystallinity, long period and lamellar thickness were further decreased with increasing the shear rate. These results are of practical significance to understand the long-term ignored issue: apart from the loading of β-NA, different self-assembled aggregates formed in flow field are another crucial factor in determining the microstructure development of matrix.
A novel β‐nucleating agent for isotactic polypropylene
The nucleating ability of p-cyclohexylamide carboxybenzene (β-NA) towards isotactic polypropylene (iPP) was investigated by differential scanning calorimetry, X-ray diffraction, polarized optical microscopy and scanning electron microscopy. β-NA is identified to have dual nucleating ability for α-iPP and β-iPP under appropriate kinetic conditions. The formation of β-iPP is dependent on the content of β-NA. The content of β-phase can reach as high as 96.96% with the addition of only 0.05 wt% β-NA. Under non-isothermal crystallization the content of β-iPP increases with increasing cooling rate. The maximum β-crystal content is obtained at a cooling rate of 40 °C min–1. The supermolecular structure of the β-iPP is identified as a leaf-like transcrystalline structure with an ordered lamellae arrangement perpendicular to the special surface of β-NA. Under isothermal crystallization β-crystals can be formed in the temperature range 80–140 °C. The content of β-crystals reaches its maximum value at a crystallization temperature of 130 °C. © 2012 Society of Chemical Industry
Decidability of some intuitionistic predicate theories
Suppose T is a first order intuitionistic theory (more precisely, a theory of Heyting's predicate calculus, e.g., abelian groups, one unary function, dense linear order, etc.) presented to us by a set of axioms (denoted also by) T. Question. Is T decidable? One knows that if the classical counterpart of T (i.e., take the same axioms but with the classical predicate calculus as the underlying logic) is not decidable, then T cannot be decidable. The problem remains for theories whose classical counterpart is decidable. In [8], sufficient conditions for undecidability were given, and several intuitionistic theories such as abelian groups and unary functions (both with decidable equality) were shown to be undecidable. In this note we show decidability results (see Theorems 1 and 2 below), and compare these results with the undecidability results previously obtained. The method we use is the reduction-method, described fully in [12] and widely applied in [3], which is applied here roughly as follows: Let T be a given theory of Heyting's predicate calculus. We know that Heyting's predicate calculus is complete for the Kripke-model type of semantics. We choose a class M of Kripke models for which T is complete, i.e., all axioms of T are valid in any model of the class and whenever φ is not a theorem of T, φ is false in some model of M.