Self‐emulsion polymerization of amphiphilic monomers—a green route to synthesis of polymeric nanoscaffolds

Self‐emulsion polymerization (SEP), a green route developed by us for the polymerization of amphiphilic monomers, does not require any emulsifier or an organic solvent except that the water‐soluble initiators such as 2,2′‐azobis[2‐(2‐imidazolin‐2‐yl)propane]dihydrochloride (VA‐044) and potassium persulfate (KPS) are only used. We report here the polymer nanoscaffolds from a number of amphiphilic monomers, which can be used for in situ encapsulation of a variety of nanoparticles. As a demonstration of the efficacy of these nanoscaffolds, the synthesis of a biocompatible hybrid nanoparticle (nanohybrid), prepared by encapsulating Fe₃O₄ magnetic nanoparticle (Fe₃O₄ MNPs) in poly(2‐hydroxyethyl methacrylate) in water, for MRI application is presented. The nanohybrid prepared following the SEP in the form of an emulsion does not involve the use of any stabilizing agent, crosslinker, polymeric emulsifier, or surfactant. This water‐soluble, spherical, and stable nanohybrid containing Fe₃O₄ MNPs of average size 10 ± 2 nm has a zeta potential value of ?41.89 mV under physiological conditions. Magnetic measurement confirmed that the nanohybrid shows typical magnetic behavior having a saturation magnetization (Ms) value of 32.3 emu/g and a transverse relaxivity (r2) value of 29.97 mM^?1 s^?1, which signifies that it can be used as a T2 contrast agent in MRI. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019     

Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

Lone-Pair Enhanced Birefringence in an Alkaline-Earth Metal Tin(II) Phosphate BaSn2(PO4)2

The first alkaline-earth metal tin(II) phosphate, BaSn₂(PO₄)₂, has been discovered, which consists of layered structures constructed from strictly alternating [SnO₃]⁴⁻ and [PO₄]³⁻ moieties. This compound is expected to have a large birefringence with Δn≈0.071 at 1064 nm, owing to the presence of stereochemically active lone pair metal cations.     

On the swelling behavior of poly(N-Isopropylacrylamide) hydrogels exposed to perfluoroalkyl acids

Per- and polyfluoroalkyl substances (PFAS) have rapidly accumulated in the environment due to their widespread use prior to commercial discussion in the early 21st century, and their slow degradation has magnified concerns of their potential toxicity. Monitoring their distribution is, therefore, necessary to evaluate and control their impact on the health of exposed populations. This investigation evaluates the capability of a simple polymeric detection scheme for PFAS based on crosslinked, thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) hydrogels. Surveying swelling perturbations induced by several hydrotropes and comparable hydrocarbon analogs, tetraethylammonium perfluorooctane sulfonate (TPFOS) showed a significantly higher swelling ratio on a mass basis (65.5 ± 8.8 at 15°C) than any of the other analytes tested. Combining swelling with the fluorimetric response of a solvachromatic dye, nile red, revealed the fluorosurfactant to initiate observable aggregation (i.e., its critical aggregation concentration) at 0.05 mM and reach saturation (i.e., its charge neutralization concentration) at 0.5 mM. The fluorosurfactant was found to homogeneously distribute throughout the polymer matrix with energy dispersive X-ray spectroscopy, marking the swelling response as a peculiar nexus of fluorinated interfacial positioning and delocalized electrostatic repulsion. Results from the current study hold promise for exploiting the physiochemical response of PNIPAM to assess TPFOS's concentration.     

Global strong solution of 3D tropical climate model with damping

We establish the global well-posedness of a strong solution to the 3D tropical climate model with damping. We prove that there exists the global and unique solution for α, β, γ satisfying one of the following three conditions: (1) \alpha ,\beta \ge \mathrm{4}; (2) ; (3) .     

Chase’s lemma and its context

Chase’s lemma provides a powerful tool for translating properties of (co)products in abelian categories into chain conditions. This note discusses the context in which the lemma is used, making explicit what is often neglected in the literature because of its technical nature.     

On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.     

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.