Effect of the molecular structure of the polymer and nucleation on the optical properties of polypropylene homo- and copolymers.

Two soluble nucleating agents were used to modify the optical properties of nine PP homo- and random copolymers. The ethylene content of the polymers changed between 0 and 5.3 wt%. Chain regularity was characterized by the stepwise isothermal segregation technique (SIST), while optical properties by the measurement of the haze of injection molded samples. Crystallization and melting characteristics were determined by differential scanning calorimetry (DSC). The analysis of the results proved that lamella thickness and change in crystallinity influence haze only slightly. A model was introduced which describes quantitatively the dependence of nucleation efficiency and haze on the concentration of the nucleating agent. The model assumes that the same factors influence the peak temperature of crystallization and optical properties. The analysis of the results proved that the assumption is valid under the same crystallization conditions. The parameters of the model depend on the molecular architecture of the polymer. Chain regularity determines supermolecular structure and thus the dependence of optical properties on nucleation

Moment-sos and spectral hierarchies for polynomial optimization on the sphere and quantum de Finetti theorems

We revisit the convergence analysis of two approximation hierarchies for polynomial optimization on the unit sphere. The first one is based on the moment-sos approach and gives semidefinite bounds for which Fang and Fawzi (2021) showed an analysis in O(1/r2) for the r-th level bound, using the polynomial kernel method. The second hierarchy was recently proposed by Lovitz and Johnston (2023) and gives spectral bounds for which they show a convergence rate in O(1/r), using a quantum de Finetti theorem of Christandl et al. (2007) that applies to complex Hermitian matrices with a "double" symmetry. We investigate links between these approaches, in particular, via duality of moments and sums of squares. We also propose another proof for the analysis of the spectral bounds, via a "banded" real de Finetti theorem, and show that the spectral bounds cannot have a convergence rate better than O(1/r2). In addition, we show how to use the polynomial kernel method to obtain a de Finetti type result for real maximally symmetric matrices, improving an earlier result of Doherty and Wehner (2012)

Identifiability for mixtures of centered Gaussians and sums of powers of quadratics

We consider the inverse problem for the polynomial \nmap that sends an -tuple of quadratic forms in \nvariables to the sum of their th powers. This map cap- \ntures the moment problem for mixtures of centered \n-variate Gaussians. In the first nontrivial case = 3, \nwe show that for any \xe2\x88\x88 \xe2\x84\x95, this map is generically one- \nto-one (up to permutations of 1 , \xe2\x80\xa6 , and third roots \nof unity) in two ranges: \xe2\xa9\xbd ( \n2 \n) + 1 for < 16 and \xe2\xa9\xbd \n(+5 \n6 \n)\xe2\x88\x95(+1 \n2 \n) \xe2\x88\x92 (+1 \n2 \n) \xe2\x88\x92 1 for \xe2\xa9\xbe 16, thus proving generic \nidentifiability for mixtures of centered Gaussians from \ntheir (exact) moments of degree at most 6. The first \nresult is obtained by the explicit geometry of the tan- \ngential contact locus of the variety of sums of cubes of \nquadratic forms, as described by Chiantini and Ottaviani \n[SIAM J. Matrix Anal. Appl. 33 (2012), no. 3, 1018\xe2\x80\x93 \n1037], while the second result is accomplished using the \nlink between secant nondefectivity with identifiability, \nproved by Casarotti and Mella [J. Eur. Math. Soc. (JEMS) \n(2022)]. The latter approach also generalizes to sums of \nth powers of -forms for \xe2\xa9\xbe 3 and \xe2\xa9\xbe 2

Ion energy thresholds and stability of cubic boron nitride

Boron nitride (BN) film growth of mass selected B and N ion deposition has been investigated in a wide range of ion energies. We observed an ion energy window for the cubic BN (c-BN) growth between 75 eV and at least 15/20 keV. The observed low energy threshold for the growth of c-BN is lower than the c-BN nucleation threshold and fits well to the cylindrical spike model. On the high-energy side, c-BN growth was achieved using 15 keV nitrogen and 20 keV boron ions. Additionally, we studied the stability of c-BN under ion irradiation. These studies showed that cubic boron nitride is extremely stable under ion irradiation. It remains stable under nitrogen and argon ion irradiation with energies between 10 and 30 keV up to fluences approximately 10(17) cm(-2). However, if the c-BN/t-BN interface is irradiated, a complete transition to sp(2)-bonded BN already occurs at a low ion fluence of 10(16) cm(-2). (C) 2003 Elsevier Science B.V. All rights reserved

Structural Aspects of 1,3,5-Benzenetrisamides−A New Family of Nucleating Agents

Structural studies of substituted 1,3,5-benzenetrisamides, a new family of highly versatile and efficient nucleating and clarifying agents for polymeric materials, are reported. Subtle details of the molecular structure of these species are shown to have a major influence on their solid-state order, morphology, and ability to nucleate specific polymorphs of isotactic polypropylene and induce a broad spectrum of useful mechanical and optical properties in the latter material

Structural aspects of 1,3,5-benzenetrisamides−A new family of nucleating agents

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