Exact Solution of a(2+1)-Dimensional Anisotropic Star in Finch and Skea Spacetime

We provide a new class of interior solution of a(2+1)-dimensional anisotropic star in Finch and Skea spacetime corresponding to the BTZ black hole. We develop the model by considering the MIT bag model EOS and a particular ansatz for the metric function grrproposed by Finch and Skea [M.R. Finch and J.E.F. Skea, Class. Quantum.Grav. 6(1989) 467]. Our model is free from central singularity and satisfies all the physical requirements for the acceptability of the model.     

Directional Self‐Assembly of Fluorinated Star Block Polymer Thin Films Using Mixed Solvent Vapor Annealing

We demonstrate the directional alignment of perpendicular‐lamellae domains in fluorinated three‐armed star block polymer (BP) thin films using solvent vapor annealing with shear stress. The control of orientation and alignment was accomplished without any substrate surface modification. Additionally, three‐armed star poly(methyl methacrylate‐block‐styrene) [PMMA‐PS] and poly(octafluoropentyl methacrylate‐block‐styrene) were compared to their linear analogues to examine the impact of fluorine content and star architecture on self‐assembled BP feature sizes and interdomain density profiles. X‐ray reflectometry results indicated that the star BP molecular architecture increased the effective polymer segregation strength and could possibly facilitate reduced polymer domain spacings, which are useful in next‐generation nanolithographic applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1663–1672     

List star edge coloring of k-degenerate graphs

A star edge coloring of a graph is a proper edge coloring such that every connected 2-colored subgraph is a path with at most 3 edges. Deng et al. and Bezegová et al. independently show that the star chromatic index of a tree with maximum degree $\Delta$ is at most $?\frac{3\Delta }{2}?$, which is tight. In this paper, we study the list star edge coloring of $k$-degenerate graphs. Let $c{h}_{st}^{\prime }\left(G\right)$ be the list star chromatic index of $G$: the minimum $s$ such that for every $s$-list assignment $L$ for the edges, $G$ has a star edge coloring from $L$. By introducing a stronger coloring, we show with a very concise proof that the upper bound on the star chromatic index of trees also holds for list star chromatic index of trees, i.e. $c{h}_{st}^{\prime }\left(T\right)\le ?\frac{3\Delta }{2}?$ for any tree $T$ with maximum degree $\Delta$. And then by applying some orientation technique we present two upper bounds for list star chromatic index of $k$-degenerate graphs.     

Brush‐First ROMP of poly(ethylene oxide) macromonomers of varied length: impact of polymer architecture on thermal behavior and Li+ conductivity

The properties of polymeric materials are dictated not only by their composition but also by their molecular architecture. Here, by employing brush‐first ring‐opening metathesis polymerization (ROMP), norbornene‐terminated poly(ethylene oxide) (PEO) macromonomers ( MM‐n , linear architecture), bottlebrush polymers ( Brush‐n , comb architecture), and brush‐arm star polymers ( BASP‐n , star architecture), where n indicates the average degree of polymerization (DP) of PEO, are synthesized. The impact of architecture on the thermal properties and Li⁺ conductivities for this series of PEO architectures is investigated. Notably, in polymers bearing PEO with the highest degree of polymerization, irrespective of differences in architecture and molecular weight (~100‐fold differences), electrolytes with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) as an Li⁺ source exhibit normalized ionic conductivities (σ_n) within only 4.9 times difference (σ_n = 29.8 × 10^?5 S cm^?1 for MM‐45 and σ_n = 6.07 × 10^?5 S cm^?1 for BASP‐45 ) at a concentration of Li⁺ r = [Li⁺]/[EO] = 1/12 at 50 °C. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 448–455     

A New Approach for the Synthesis of Miktoarm Star Polymers Through a Combination of Thiol–Epoxy “Click” Chemistry and ATRP/Ring‐Opening Polymerization Techniques

A new approach was developed for synthesis of certain A₃B₃‐type of double hydrophilic or amphiphilic miktoarm star polymers using a combination of “grafting onto” and “grafting from” methods. To achieve the synthesis of desired miktoarm star polymers, acetyl protected poly(ethylene glycol) (PEG) thiols (M_n = 550 and 2000 g mol^?1) were utilized to generate A₃‐type of homoarm star polymers through an in situ protective group removal and a subsequent thiol–epoxy “click” reaction with a tris‐epoxide core viz. 1,1,1‐tris(4‐hydroxyphenyl)ethane triglycidyl ether. The secondary hydroxyl groups generated adjacent to the core upon the thiol–epoxy reaction were esterified with α‐bromoisobutyryl bromide to install atom transfer radical polymerization (ATRP) initiating sites. ATRP of N‐isopropylacrylamide (NIPAM) using the three‐arm star PEG polymer fitted with ATRP initiating sites adjacent to the core afforded A₃B₃‐type of double hydrophilic (PEG)₃[poly(N‐isopropylacrylamide)] (PNIPAM)₃ miktoarm star polymers. Furthermore, the generated hydroxyl groups were directly used as initiator for ring‐opening polymerization of ε‐caprolactone to prepare A₃B₃‐type of amphiphilic (PEG)₃[poly(ε‐caprolactone)]₃ miktoarm star polymers. The double hydrophilic (PEG)₃(PNIPAM)₃ miktoarm star polymers showed lower critical solution temperature around 34 °C. The preliminary transmission electron microscopy analysis indicated formation of self‐assembly of (PEG)₃(PNIPAM)₃ miktoarm star polymer in aqueous solution. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 146–156     

Amphiphilic dendritic copolymers of tert‐butyl‐glycidylether and glycidol as a nanocontainer for an anticancer ruthenium complex

Dendritic copolymers comprising a hydrophobic core and hydrophilic shell with nearly equal numbers of hydroxyl groups in the shell and different densities in the core were prepared by a multi‐step process based on anionic ring‐opening polymerization. The diversity in the core density was obtained by using copolymer stars with poly(tert‐butyl‐glycidylether)‐block‐polyglycidol arms with nearly equal length of hydrophobic blocks and numbers of hydroxyl groups of polyglycidol but different numbers of arms as macroinitiators. The ability of the dendritic copolymers to serve as a nanocontainer for a ruthenium complex Ru(NH₃)₃Cl₃ with anticancer properties was studied. The possibility of improving the water solubility of this poorly soluble drug by loading it onto dendritic copolymers was investigated. The hydroxyl groups of the dendritic copolymers were used for complexation of the ruthenium compound to the shell. The loading efficiency was analyzed by UV–vis spectroscopy. The dendritic nanoparticles in their hydrated state were visualized using cryo‐TEM. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3488–3497     

Synthesis of well‐defined star‐shaped poly(ε‐caprolactone)/poly(ethylbene glycol) amphiphilic conetworks by combination of ring opening polymerization and “click” chemistry

Well‐defined star‐shaped hydrophobic poly(ε‐caprolactone) (PCL) and hydrophilic poly(ethylene glycol) (PEG) amphiphilic conetworks (APCNs) have been synthesized via the combination of ring opening polymerization (ROP) and click chemistry. Alkyne‐terminated six arm star‐shaped PCL (6‐s‐PCLx‐C?CH) and azido‐terminated PEG (N₃‐PEG‐N₃) are characterized by ¹H NMR and FT‐IR. The swelling degree of the APCNs is determined both in water and organic solvent. This unique property of the conetworks is dependent on the nanophase separation of hydrophilic and hydrophobic phases. The morphology and thermal behaviors of the APCNs are investigated by SEM and DSC respectively. The biocompatibility is determined by water soluble tetrazolium salt reagents (WST‐1) assay, which shows the new polymer networks had good biocompatibility. Through in vitro release of paclitaxel (PTX) and doxorubicin (DOX), the APCNs is confirmed to be promising drug depot materials for sustained hydrophobic and hydrophilic drugs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 407–417     

Preparation and Characterization of Linear and Miktoarm Star Side-Chain Liquid Crystalline block Copolymers with p-Methoxyazobenzene Moieties via a Combination of ATRP and ROP

One linear and two miktoarm star side-chain liquid crystalline (LC) block copolymers with p-methoxyazobenzene moieties were prepared by a combination of ring-opening polymerization (ROP) and atom transfer radical polymerization (ATRP) techniques. First, ROPs of ε -caprolactone (ε -CL) were carried out catalyzed by Sn(Oct)₂ using three multifunctional initiators, hydroxyethyl 2-bromoisobutyrate (AB type), 3-hydroxy-2-(hydroxymethyl)-2-methylpropyl 2-bromo-2-methylpropanoate (A₂B type) and 2,2-bis(hydroxymethyl)propane-1,3-diyl bis(2-bromo-2-methylpropanoate) (A₂B₂ type), at 110°C in toluene, respectively. Second, the previously obtained poly(ε -caprolactone)s (PCLs) with bromines functionalities were used as the macroinitiators to conduct ATRP of 6-(4-methoxy-4-oxy-azobenzene) hexyl methacrylate (MMAZO) with CuBr/PMDETA as the catalyst systems at 85°C in anisole to prepare the linear and miktoarm side-chain LC block copolymers (PCL-b-PMMAZO, (PCL)₂-(PMMAZO) and (PCL)₂-(PMMAZO)₂). The produced polymers were well-controlled with the controlled molecular weights and the relatively narrow molecular weight distributions (M _w/M _n ≤ 1.35). The structures of the obtained polymers were all characterized by NMR, FT-IR and GPC analysis. Furthermore, the LC properties of the linear and miktoarm star block copolymers were also investigated by differential scanning calorimetry (DSC) and thermal polarized optical microscopy (POM).     

Synthesis and Characterization of Four-Arm Star Poly(ϵ-caprolactone)-Block-Poly(cyclic-carbonate methacrylate) Copolymers by Combining Ring-Opening Polymerization With Atom Transfer Radical Polymerization

Well-defined four-arm star poly(?-caprolactone)-block-poly(cyclic carbonate methacrylate) (PCL-b-PCCMA) copolymers were synthesized by combining ring-opening polymerization (ROP) with atom transfer radical polymerization (ATRP). First, a four-arm poly(?-caprolactone) (PCL) macroinitiator [(PCL-Br)₄] was prepared by the ROP of ?-CL catalyzed by stannous octoate at 110°C in the presence of pentaerythritol as the tetrafunctional initiator followed by esterification with 2-bromoisobutyryl bromide. The sequential ATRP of CCMA monomer was carried out by using the (PCL-Br)₄ tetrafunctional macroinitiator (MI) and in the presence of CuBr/2, 2′-bipyridyl system in DMF at 80°C with [(MI)]:[CuBr]:[bipyridyl] = 1:1:3 to yield block polymers with controlled molecular weights (M_n (NMR) = 10700 to 27300 g/mol) by varying block lengths and with moderately narrow polydispersities (M_w/M_n = 1.2–1.4). Block copolymers with different PCL: PCCMA copolymer composition such as 50:50, 70:30 and 74:26 were prepared with good yields (48-74%). All these block copolymers were well characterized by NMR, FTIR and GPC and tested their thermal properties by DSC and TGA.