Well‐defined non‐linear polyethylene‐based macromolecular architectures

Polyethylene (PE)‐based 3‐ and 4‐miktoarm star [PE(PCL)₂, PE(PCL)₃] and H‐type [(PCL)₂PE(PCL)₂] block copolymers [polycaprolactone (PCL)] were synthesized by a combination of polyhomologation, chlorosilane chemistry, and ring opening polymerization (ROP). The following steps were used for the synthesis of the miktoarm stars: (a) reaction of a hydroxy‐terminated polyethylene (PE‐OH), prepared by polyhomologation of dimethylsulfoxonium methylide with a monofunctional boron initiator followed by oxidation/hydrolysis, with chloromethyl(methyl)dimethoxysilane or chloromethyltrimethoxysilane; (b) hydrolysis of the produced ω‐di(tri)methoxysilyl‐polyethylenes to afford ω‐dihydroxy‐polyethylene (difunctional initiator) and ω‐trihydroxy‐polyethylene (trifunctional initiator); and (c) ROP of ɛ‐caprolactone with the difunctional (3‐miktoarm star) or trifunctional macroinitiator (4‐miktoarm star), in the presence of 1‐tert‐butyl‐2,2,4,4,4‐pentakis(dimethylamino)‐2λ⁵,4λ⁵‐catenadi(phosphazene) (t‐BuP₂). The H‐type block copolymers were synthesized using the same strategy, but with a difunctional polyhomologation initiator. All intermediates and final products were characterized by HT‐GPC, ¹H NMR and FTIR analyses. Thermal properties of the PE precursors and all final products were investigated by DSC and TGA. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2129–2136     

Arm‐first synthesis of star polymers with polywedge arms using ring‐opening metathesis polymerization and bifunctional crosslinkers

This work presents a two‐step, one‐pot process to make star polymers with polywedge arms. In a one‐pot reaction, after the polywedge arms are synthesized, crosslinker species are added to the reaction, rapidly forming star polymers. Crosslinker species with different degrees of conformational freedom were designed and synthesized and their capacity to generate star polymers was evaluated. Mass conversions up to 92% and stars with up to 17 arms were synthesized with the most rigid crosslinker. The effects of arm molecular weight and molar ratio of crosslinker to arm on mass conversion and arms per star were explored further. Finally, the size‐molecular weight scaling relationship for polywedges with linear and star architectures was compared, corroborating theoretical results regarding star polymers with arms much larger than their core. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 732–740     

Three‐arm star block copolymers of aromatic polyether and polystyrene from chain‐growth condensation polymerization,atom transfer radical polymerization,and click reaction

Well‐defined (AB)₃ type star block copolymer consisting of aromatic polyether arms as the A segment and polystyrene (PSt) arms as the B segment was prepared using atom transfer radical polymerization (ATRP), chain‐growth condensation polymerization (CGCP), and click reaction. ATRP of styrene was carried out in the presence of 2,4,6‐tris(bromomethyl)mesitylene as a trifunctional initiator, and then the terminal bromines of the polymer were transformed to azide groups with NaN₃. The azide groups were converted to 4‐fluorobenzophenone moieties as CGCP initiator units by click reaction. However, when CGCP was attempted, a small amount of unreacted initiator units remained. Therefore, the azide‐terminated PSt was then used for click reaction with alkyne‐terminated aromatic polyether, obtained by CGCP with an initiator bearing an acetylene unit. Excess alkyne‐terminated aromatic polyether was removed from the crude product by means of preparative high performance liquid chromatography (HPLC) to yield the (AB)₃ type star block copolymer (M_n = 9910, M_w/M_n = 1.10). This star block copolymer, which contains aromatic polyether segments with low solubility in the shell unit, exhibited lower solubility than A₂B or AB₂ type miktoarm star copolymers. In addition, the obtained star block copolymer self‐assembled to form spherical aggregates in solution and plate‐like structures in film. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis,purification, and characterization of “perfect” star polymers via “Click” coupling

The copper (I)‐catalyzed azide‐alkyne cycloaddition “click” reaction was successfully applied to prepare well‐defined 3, 6, and 12‐arms polystyrene and polyethylene glycol stars. This study focused particularly on making “perfect” star polymers with an exact number of arms, as well as developing techniques for their purification. Various methods of characterization confirmed the star polymers high purity, and the structural uniformity of the generated star polymers. In particular, matrix‐assisted laser desorption ionization‐time‐of‐flight mass spectrometry revealed the quantitative transformation of the end groups on the linear polymer precursors and confirmed their quantitative coupling to the dendritic cores to yield star polymers with an exact number of arms. In addition to preparing well‐defined polystyrene and poly(ethylene glycol)homopolymer stars, this technique was also successfully applied to amphiphilic, PCL‐b‐PEG star polymers. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis of fluorine‐containing star‐shaped poly(vinyl ether)s via arm‐linking reactions in living cationic polymerization

Various types of fluorine‐containing star‐shaped poly(vinyl ether)s were successfully synthesized by crosslinking reactions of living polymers based on living cationic polymerization. Star polymers with fluorinated arm chains were prepared by the reaction between a divinyl ether and living poly(vinyl ether)s with fluorine groups (C₄F₉, C₆F₁₃, and C₈F₁₇) at the side chain using cationogen/Et_1.5AlCl_1.5 in a fluorinated solvent (dichloropentafluoropropanes), giving star‐shaped fluorinated polymers in high yields with a relatively narrow molecular weight distribution. The concentration of living polymers for the crosslinking reaction and the molar feed ratio of a bifunctional vinyl ether to living polymers affected the yield and molecular weight of the star polymers. Star polymers with block arms were prepared by a linking reaction of living block copolymers of a fluorinated segment and a nonfluorinated segment. Heteroarm star‐shaped polymers containing two‐ or three‐arm species were synthesized using a mixture of different living polymer species for the reaction with a bifunctional vinyl ether. The obtained polymers underwent temperature‐induced solubility transitions in various organic solvents, and their concentrated solutions underwent sol–gel transitions, based on the solubility transition of a thermoresponsive fluorinated segment. Furthermore, a slight amount of fluorine groups were shown to be effective for physical gelation when those were located at the arm ends of a star polymer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Solvent replacement to thermo‐responsive nanoparticles from long‐subchain hyperbranched PSt grafted with PNIPAM for encapsulation

Long‐subchain hyperbranched polystyrene (lsc‐hp PSt) with uniform subchain length was obtained through copper‐catalyzed azide‐alkyne cycloaddition click chemistry from seesaw macromonomer of PSt having one alkynyl group anchored at the chain centre and two azido group attached to both chain ends [alkynyl‐(PSt‐N₃)₂]. After precipitation fraction, different portions of lsc‐hp PSt having narrow overall molecular weight distribution were obtained for further grafting with alkynyl‐capped poly(N‐isopropylacrylamide) (alkynyl‐PNIPAM), which was obtained via single‐electron transfer living radical polymerization of NIPAM with propargyl 2‐bromoisobutyrate as the initiator and grafted onto the peripheral azido groups of lsc‐hp PSt via click chemistry. Thus, amphiphilic lsc‐hp PSt grafted with PNIPAM chains (lsc‐hp PSt‐g‐PNIPAM) was obtained and would have star‐like conformation in tetrahydrofuran (THF). By replacing THF with water, lsc‐hp PSt‐g‐PNIPAM was dissolved at molecular level in aqueous solution due to the hydrophilicity of PNIPAM and exhibited thermal induced shrinkage of PNIPAM arms. The water‐insoluble lsc‐hp PSt would collapse densely and could be served as a reservoir to absorb hydrophobic chemicals in aqueous solution. The influence of overall molecular weight of lsc‐hp PSt on the absorption of pyrene was studied. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

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.