Certifying convergence of Lasserre’s hierarchy via flat truncation

Consider the optimization problem of minimizing a polynomial function subject to polynomial constraints. A typical approach for solving it globally is applying Lasserre’s hierarchy of semidefinite relaxations, based on either Putinar’s or Schmüdgen’s Positivstellensatz. A practical question in applications is: how to certify its convergence and get minimizers? In this paper, we propose flat truncation as a certificate for this purpose. Assume the set of global minimizers is nonempty and finite. Our main results are: (1) Putinar type Lasserre’s hierarchy has finite convergence if and only if flat truncation holds, under some generic assumptions; the same conclusion holds for the Schmüdgen type one under weaker assumptions. (2) Flat truncation is asymptotically satisfied for Putinar type Lasserre’s hierarchy if the archimedean condition holds; the same conclusion holds for the Schmüdgen type one if the feasible set is compact. (3) We show that flat truncation can be used as a certificate to check exactness of standard SOS relaxations and Jacobian SDP relaxations.     

Fluorinated polymerizable phosphonium salts from PH3: Surface properties of photopolymerized films

An array of highly fluorinated polymerizable phosphonium salts (HFPPS) were synthesized from PH₃ and utilized in UV‐curable formulations. Inclusion of these salts at very low loading (0.1–1 wt %) into hexanediol diacrylate (HDDA) resulted in hydrophobic surfaces. The water repellency was achieved with short C₄F₉ fluorocarbon appendages in the monomer as opposed to the bioaccumulative C₈F₁₇ appended polymers. The physical properties of these new monomers were also characterized. The molecular architecture of the monomers had a pronounced effect on both their physical properties along with the degree of hydrophobicity imparted in the polymer. Salts utilizing the bis(trifluoromethylsulfonyl)imide anion displayed excellent compatibility with HDDA, while the chloride salts were insoluble. Time‐of‐flight secondary ion mass spectrometry (TOF‐SIMS) confirmed the presence of the HFPPS at the surface of the polymer coating. For the first time this demonstrates how these salts may be used to functionalize the surface of a UV‐cured film with ionic species. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2782–2792     

Poly(aryl ether ketone) composite membrane as a high‐performance lithium‐ion batteries separator

We described the design and synthesis of a modified poly(aryl ether ketone) bearing phenolphthalein and allyl groups (P‐PAEK) via nucleophilic polycondensation. A new kind of composite separator, crosslinked P‐PAEK/polyvinylidene fluoride (c‐P‐PAEK/PVDF) membrane was successfully prepared using phase separation, phase inversion method, and UV crosslinking technique. As a separator of lithium‐ion battery, c‐P‐PAEK/PVDF membrane demonstrates high porosity and uniform distribution of pores with interconnected pathways. Low thermal shrinkage, distinct shut‐down effect, high liquid electrolyte uptake capacity, and exciting liquid electrolyte wettability of the prepared c‐P‐PAEK/PVDF membrane have been revealed through comprehensive study. Moreover, the c‐P‐PAEK/PVDF membrane was applied to assemble a conventional Li/LiFePO₄ coin cell, which exhibited hopeful cell performance. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2714–2721     

Synthesis and characteristics of photopolymerized benzophenone

Photopolymerization is extensively used in today's industrial field due to its advantages of rapid reaction, environmental friendly, energy saving and economical. Benzophenone is a most common photoinitiator (PI) using in photopolymerization because of its superior ability to initiate acrylate monomers. However, the intrinsic nature of initiator molecules is that they migrate out of polymer network, which limits its application, especially in the domain of food packaging materials. A polymerizable PI 4‐methylbenzophenone acrylate (MBPAc) was synthesized by a facile procedure and characterized by ¹H NMR, ¹³C NMR, and MS analyses. A systematic study of the photopolymerization kinetics of MBPAc was explored by the Real‐Time Fourier Transform Infrared Spectrometer. The results show that the final conversion and photopolymerization rate of acrylate monomers are closely related to the factors of their chemical structure, viscosity, functionality and light intensity, which means MBPAc is an efficient PI. Ultraviolet‐visible Spectrophotometer and vitro cytotoxicity measurement results indicate that the noncytotoxic MBPAc shows significantly lower migration than its analogue. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 313–320     

Computational insight into asymmetric uranyl‐salophen coordinated with α, β‐unsaturated aldehydes and ketones

The study of the catalytic activity and activation mechanism of asymmetric uranyl‐salophens with α, β‐unsaturated aldehydes or α, β‐unsaturated ketones, is a research hotspot. In this paper, the complexes of the uranyl–salophen(U‐S) modified by unilateral benzene, coordinated with cyclohexenone, cyclopentenone and acrolein, were investigated using density functional theory calculations at the level of B3LYP/6‐311G(d, p) basis set. The results showed that the uranyl‐salophen(U‐S) weakened the large π bond between C = C and C = O of the α, β‐unsaturated aldehydes and ketones, making the unsaturated aldehydes and ketones activated. In addition, the molecular‐recognition selectivity of the asymmetrical uranyl‐salophen for cyclohexenone and cyclopentenone were much higher than for acrolein.