SINGLE AND DOUBLE EDGE INTERFACE CRACK SOLUTIONS FOR ARBITRARY FORMS OF MATERIAL COMBINATION

In this paper interfacial edge crack problems are considered by the application of the finite element method. The stress intensity factors are accurately determined from the ratio of crack-tip-stress value between the target given unknown and reference problems. The reference problem is chosen to produce the singular stress fields proportional to those of the given unknown problem. Here the original proportional method is improved through utilizing very refined meshes and post-processing technique of linear extrapolation. The results for a double-edge interface crack in a bonded strip are newly obtained and compared with those of a single-edge interface crack for different forms of combination of material. It is found that the stress intensity factors should be compared in the three different zones of relative crack lengths. Different from the case of a cracked homogeneous strip, the results for the double edge interface cracks are found to possibly be bigger than those for a single edge interface crack under the same relative crack length.     

A hybrid level set method for modelling detonation and combustion problems in complex geometries

We present an accurate and fast wave tracking method that uses parametric representations of tracked fronts, combined with modifications of level set methods that use narrow bands. Our strategy generates accurate computations of the front curvature and other geometric properties of the front. We introduce data structures that can store discrete representations of the location of the moving fronts and boundaries, as well as the corresponding level set fields, that are designed to reduce computational overhead and memory storage. We present an algorithm we call stack sweeping to efficiently sort and store data that is used to represent orientable fronts. Our implementation features two reciprocal procedures, a forward ‘front parameterization’ that constructs a parameterization of a front given a level set field and a backward ‘field construction’ that constructs an approximation of the signed normal distance to the front, given a parameterized representation of the front. These reciprocal procedures are used to achieve and maintain high spatial accuracy. Close to the front, precise computation of the normal distance is carried out by requiring that displacement vectors from grid points to the front be along a normal direction. For front curves in two dimensions, a cubic interpolation scheme is used, and G ¹ surface parameterization based on triangular patches is used for the three-dimensional implementation to compute the distances from grid points near the front. To demonstrate this new, high accuracy method we present validations and show examples of combustion-like applications that include detonation shock dynamics, material interface motions in a compressible multi-material simulation and the Stephan problem associated with dendrite solidification.     

Metal‐ and solvent‐free,clickable synthesis and postpolymerization functionalization of poly(triazole)s

In this study, a series of linear poly(triazole)s (PTAs) were successfully synthesized by the metal‐ and solvent‐free, thermal click polymerization of diazide and dialkyne (A₂ + B₂) monomers. All click polymerizations proceeded smoothly at 80 °C in an open atmosphere without protection from oxygen and moisture. After being polymerized for 36 h, the crude polymer was further fractionated into three fractions using a multistep precipitation method. By selectively choosing precipitating agents, this process produced poly(triazole) fractions with low polydispersity index (<1.30). The resulting PTAs are soluble in common organic solvents and stable at a temperature up to 320 °C. Furthermore, the methyl benzoate moieties in the main chain can serve as useful building blocks for further postpolymerization functionalization, yielding 1,2,4‐triazole derivatives. This functionalization strategy offers potential for the development of novel triazole‐based materials. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Segmented block copolyesters using click chemistry

Copper(I) catalyzed azide‐alkyne 1,3‐Huisgen cycloaddition reaction afforded the synthesis of triazole‐containing polyesters and segmented block copolyesters at moderate temperatures. Triazole‐containing homopolyesters exhibited significantly increased (～40 °C) glass transition temperatures (T_g) relative to high temperature, melt synthesis of polyesters with analogous structures. Quantitative synthesis of azido‐terminated poly(propylene glycol) (PPG) allowed for the preparation of segmented polyesters, which exhibited increased solubility and mechanical ductility relative to triazole‐containing homopolyesters. Differential scanning calorimetry demonstrated a soft segment (SS) T_g near ?60 °C for the segmented polyesters, consistent with microphase separation. Tensile testing revealed Young's moduli ranging from 7 to 133 MPa as a function of hard segment (HS) content, and stress at break values approached 10 MPa for 50 wt % HS segmented click polyesters. Dynamic mechanical analysis demonstrated an increased rubbery plateau modulus with increased HS content, and the T_g's of both the SS and HS did not vary with composition, confirming microphase separation. Atomic force microscopy also indicated microphase separated and semicrystalline morphologies for the segmented click polyesters. This is the first report detailing the preparation of segmented copolyesters using click chemistry for the formation of ductile membranes with excellent thermomechanical response. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

A novel polymerization approach via thiol‐yne addition

The ability of thiyl radicals to add to terminal unsaturations in an efficient way made them considered being one of the click reactions. Recently, thiol‐yne addition reactions have been used extensively for the synthesis of crosslinked networks and dendrimers and postpolymerization functionalization protocols. Herein, we report a novel step‐growth type reaction for highly functional linear polymers using a monoalkyne and dithiol compound. First, we investigated the model reaction between 1‐octyne and 1‐octanethiol as well as 1,4‐butanedithiol compounds, which were initiated via self‐, thermal‐, and UV‐initiation; the UV‐initiation was found to be the most efficient method and completed within 2‐h reaction time. The same conditions were applied for the polymerization of four different functional alkynes bearing different functional groups with two dithiol compounds. All polymerizations resulted in highly functional linear polymers with number averaged molecular weights ranging from 5 to 30 kDa, except for propargylic acid and its methyl ester, where only oligomers formed. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Perfluorocyclohexenyl aryl ether polymers via polycondensation of decafluorocyclohexene with bisphenols

A novel class of semifluorinated perfluorocyclohexenyl (PFCH) aryl ether homo/copolymers was successfully synthesized with high yield through the step‐growth polymerization of commercially available bisphenols and decafluorocyclohexene in the presence of a triethylamine base. The synthesized polymers exhibit variable thermal properties depending on the functional spacer group (R). PFCH aryl ether copolymers with random and alternating architectures were also prepared from versatile bis‐perfluorocyclohexenyl aryl ether monomers. The PFCH polymers show high thermal stabilities with a 5% decomposition temperature ranging from 359 to 444 °C in air and nitrogen atmosphere. These semifluorinated PFCH aromatic ether polymers contain intact enchained PFCH olefin moieties, making further reactions such as crosslinking and application specific functionalization possible. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 232–238     

Mechanistic aspects on molecular structure formation of polymeric networks from diisocyanates with amidine compounds

Polymeric networks are produced by step‐growth polyaddition and co‐polyaddition reactions of 1‐ethylimidazoline in combination with various diisocyanates. Five aromatic, two aliphatic diisocyanates and a polyurethane prepolymer are used as particular reactant in N,N‐dimethylformamide as solvent at room temperature. Obviously, 1‐ethylimidazoline can serve as trifunctional monomer, which enables a crosslinking reaction with diisocyanates. Molecular structure elements of the polymeric networks were studied by solid state 13C‐NMR spectroscopy revealing that detailed molecular structure formations are determined whether aromatic or aliphatic diisocyanates are used. Quantum chemical calculations were used as supporting method to elucidate the complex reaction cascades. Hence, it can be shown that beside 3:1 stoichiometric structures 2:1 based structures are formed as well. These structures are observed as kinetically controlled products only when aromatic diisocyanate monomers are used. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 977–985     

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.     

Synthesis of oligo(spiroketal)s by polycondensation of silyl ethers derived from naturally occurring myo‐inositol with 1,4‐cyclohexanedione

Oligo(spiroketal)s (OSKs) were synthesized from myo‐inositol, a naturally occurring cyclic compound bearing six hydroxyl groups. The successful synthesis of OSKs was achieved using silyl ethers 2 derived from 1,4‐di‐O‐alkylated myo‐inositol 1 as monomers, which underwent polycondensation with 1,4‐cyclohexanedione (CHD) at 0 °C in the presence of trimethylsilyl triflate as a catalyst. Because of the irreversible nature of the condensation reaction of silyl ethers with ketones, the resulting OSKs 7 had higher molecular weights than previously reported OSKs that were obtained by polycondensation of tetraols 1 with CHD, where backward hydrolysis of the ketal functions occurred. In addition, another series of OSKs, 8, were synthesized using silyl ethers 3 derived from 2,5‐di‐O‐alkylated myo‐inositol 6 , which are more symmetric monomers than silyl ethers 2 . Silyl ethers 3 underwent efficient polycondensation with CHD, whereas tetraol 6 did not, demonstrating that the derivation of such tetraols into the corresponding silyl ethers is a powerful strategy to access OSKs. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2407–2414