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1. Effects of Chain Ends on Thermal and Mechanical Properties and Recyclability of Poly( γ ‐butyrolactone)

   https://doi.org/10.1002/pola.29180  

   Tang, Jing ; Chen, Eugene Y. ‐X. ( September 2018 , Journal of Polymer Science Part A: Polymer Chemistry)

   This work investigates effects of poly(γ‐butyrolactone) (PγBL) with different initiation and termination chain ends on five types of materials properties, including thermal stability, thermal transitions, thermal recyclability, hydrolytic degradation, and dynamic mechanical behavior. Four different chain‐end‐capped polymers with similar molecular weights, BnO‐[C(=O)(CH₂)₃O]_n‐R, R = C(=O)Me, C(=O)CH=CH₂, C(=O)Ph, and SiMe₂CMe₃, along with a series of uncapped polymers R′O‐[C(=O)(CH₂)₃O]_n‐H (R′ = Bn, Ph₂CHCH₂) withM_nranging from low (4.95 kg mol⁻¹) to high (83.2 kg mol⁻¹), have been synthesized. The termination chain end R showed a large effect on polymer decomposition temperature and hydrolytic degradation, relative to H. Overall, for those properties sensitive to the chain ends, chain‐end capping renders R‐protected linear PγBL behaving much like cyclic PγBL. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem.2018,56, 2271–2279

    

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2. Morphological/nanostructural control toward intrinsically stretchable organic electronics

   https://doi.org/10.1039/C8CS00834E  

   Ma, Rujun ; Chou, Shu-Yu ; Xie, Yu ; Pei, Qibing ( March 2019 , Chemical Society Reviews)

   The development of intrinsically stretchable electronics poses great challenges in synthesizing elastomeric conductors, semiconductors and dielectric materials. While a wide range of approaches, from special macrostructural engineering to molecular synthesis, have been employed to afford stretchable devices, this review surveys recent advancements in employing various morphological and nanostructural control methods to impart mechanical flexibility and/or to enhance electrical properties. The focus will be on (1) embedding percolation networks of one-dimensional conductive materials such as metallic nanowires and carbon nanotubes in an elastomer matrix to accommodate large external deformation without imposing a large strain along the one-dimensional materials, (2) design strategies to achieve intrinsically stretchable semiconductor materials that include direct blending of semiconductors with elastomers and synthesizing semiconductor polymers with appropriate side chains, backbones, cross-linking networks, and flexible blocks, and (3) employing interpenetrating polymer networks, bottlebrush structures and introducing inclusions in stretchable polymeric dielectric materials to improve electrical performance. Moreover, intrinsically stretchable electronic devices based on these materials, such as stretchable sensors, heaters, artificial muscles, optoelectronic devices, transistors and soft humanoid robots, will also be described. Limitations of these approaches and measures to overcome them will also be discussed. 

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3. Hermite Rational Function Interpolation with Error Correction

   https://doi.org/10.1007/978-3-030-60026-6_19  

   Kaltofen, Erich L. ; Pernet, Clement ; Yang, Zhi-Hong ( September 2020 , Proc. Computer Algebra in Scientific Computing (CASC) 2020)

   We generalize Hermite interpolation with error correction, which is the methodology for multiplicity algebraic error correction codes, to Hermite interpolation of a rational function over a field K from function and function derivative values. We present an interpolation algorithm that can locate and correct <= E errors at distinct arguments y in K where at least one of the values or values of a derivative is incorrect. The upper bound E for the number of such y is input. Our algorithm sufficiently oversamples the rational function to guarantee a unique interpolant. We sample (f/g)^(j)(y[i]) for 0 <= j <= L[i], 1 <= i <= n, y[i] distinct, where (f/g)^(j) is the j-th derivative of the rational function f/g, f, g in K[x], GCD(f,g)=1, g <= 0, and where N = (L[1]+1)+...+(L[n]+1) >= C + D + 1 + 2(L[1]+1) + ... + 2(L[E]+1) where C is an upper bound for deg(f) and D an upper bound for deg(g), which are input to our algorithm. The arguments y[i] can be poles, which is truly or falsely indicated by a function value infinity with the corresponding L[i]=0. Our results remain valid for fields K of characteristic >= 1 + max L[i]. Our algorithm has the same asymptotic arithmetic complexity as that for classical Hermite interpolation, namely soft-O(N). For polynomials, that is, g=1, and a uniform derivative profile L[1] = ... = L[n], our algorithm specializes to the univariate multiplicity code decoder that is based on the 1986 Welch-Berlekamp algorithm. 

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4. Understanding interfacial segregation in polymer blend films with random and mixed side chain bottlebrush copolymer additives

   https://doi.org/10.1039/D1SM01146D  

   Mei, Hao ; Mahalik, Jyoti P. ; Lee, Dongjoo ; Laws, Travis S. ; Terlier, Tanguy ; Stein, Gila E. ; Kumar, Rajeev ; Verduzco, Rafael ( October 2021 , Soft Matter)

   Bottlebrush polymers are complex macromolecules with tunable physical properties dependent on the chemistry and architecture of both the side chains and the backbone. Prior work has demonstrated that bottlebrush polymer additives can be used to control the interfacial properties of blends with linear polymers but has not specifically addressed the effects of bottlebrush side chain microstructures. Here, using a combination of experiments and self-consistent field theory (SCFT) simulations, we investigated the effects of side chain microstructures by comparing the segregation of bottlebrush additives having random copolymer side chains with bottlebrush additives having a mixture of two different homopolymer side chain chemistries. Specifically, we synthesized bottlebrush polymers with either poly(styrene- ran -methyl methacrylate) side chains or with a mixture of polystyrene (PS) and poly(methyl methacrylate) (PMMA) side chains. The bottlebrush additives were matched in terms of PS and PMMA compositions, and they were blended with linear PS or PMMA chains that ranged in length from shorter to longer than the bottlebrush side chains. Experiments revealed similar behaviors of the two types of bottlebrushes, with a slight preference for mixed side-chain bottlebrushes at the film surface. SCFT simulations were qualitatively consistent with experimental observations, predicting only slight differences in the segregation of bottlebrush additives driven by side chain microstructures. Specifically, these slight differences were driven by the chemistries of the bottlebrush polymer joints and side chain end-groups, which were entropically repelled and attracted to interfaces, respectively. Using SCFT, we also demonstrated that the interfacial behaviors were dominated by entropic effects with high molecular weight linear polymers, leading to enrichment of bottlebrush near interfaces. Surprisingly, the SCFT simulations showed that the chemistry of the joints connecting the bottlebrush backbones and side chains played a more significant role compared with the side chain end groups in affecting differences in surface excess of bottlebrushes with random and mixed side chains. This work provides new insights into the effects of side chain microstructure on segregation of bottlebrush polymer additives. 

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5. Green function estimates on complements of low-dimensional uniformly rectifiable sets

   https://doi.org/10.1007/s00208-022-02379-8  

   David, Guy ; Feneuil, Joseph ; Mayboroda, Svitlana ( March 2022 , Mathematische Annalen)

   It has been recently established in David and Mayboroda (Approximation of green functions and domains with uniformly rectifiable boundaries of all dimensions.arXiv:2010.09793) that on uniformly rectifiable sets the Green function is almost affine in the weak sense, and moreover, in some scenarios such Green function estimates are equivalent to the uniform rectifiability of a set. The present paper tackles a strong analogue of these results, starting with the “flagship degenerate operators on sets with lower dimensional boundaries. We consider the elliptic operators$$L_{\beta ,\gamma } =- {\text {div}}D^{d+1+\gamma -n} \nabla $$$L_{\beta ,\gamma }=-\text{div}{D}^{d+1+\gamma -n}\nabla$associated to a domain$$\Omega \subset {\mathbb {R}}^n$$$\Omega \subset R^n$with a uniformly rectifiable boundary$$\Gamma $$$\Gamma$of dimension$$d < n-1$$$d<n-1$, the now usual distance to the boundary$$D = D_\beta $$$D=D_{\beta }$given by$$D_\beta (X)^{-\beta } = \int _{\Gamma } |X-y|^{-d-\beta } d\sigma (y)$$$D_{\beta }{\left(X\right)}^{-\beta }={\int }_{\Gamma }{|X-y|}^{-d-\beta }d\sigma \left(y\right)$for$$X \in \Omega $$$X\in \Omega$, where$$\beta >0$$$\beta >0$and$$\gamma \in (-1,1)$$$\gamma \in (-1,1)$. In this paper we show that the Green functionGfor$$L_{\beta ,\gamma }$$$L_{\beta ,\gamma }$, with pole at infinity, is well approximated by multiples of$$D^{1-\gamma }$$$D^{1-\gamma }$, in the sense that the function$$\big | D\nabla \big (\ln \big ( \frac{G}{D^{1-\gamma }} \big )\big )\big |^2$$$|D\nabla (ln(\frac{G}{D^{1-\gamma }})){|}^2$satisfies a Carleson measure estimate on$$\Omega $$$\Omega$. We underline that the strong and the weak results are different in nature and, of course, at the level of the proofs: the latter extensively used compactness arguments, while the present paper relies on some intricate integration by parts and the properties of the “magical distance function from David et al. (Duke Math J, to appear).

    

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