Phase behavior of pseudo-IPN's of polycarbonate-urethane and polystyrene

The pseudo-IPN's of PCU/PS with different M_n and narrow MWD of the linear PS have been synthesized and characterized. The effect of M_n and composition on the phase morphology of the pseudo-IPN's of PCU/PS has been studied by DSC and SEM. The pseudo-IPN's with ultra-high M_n of the linear PS appeared to possess a single T_g and no SEM-resolvable domains at 35 wt % PS and below. This metastable state may reflect the result of a high extent of entanglement of the linear PS chains with the PCU network and the limited molecular mobility of the linear PS chains with high M_n. © 1993 John Wiley & Sons, Inc.     

New upper bounds on Zagreb indices

The first Zagreb index M ₁(G) is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index M ₂(G) is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph G. In this paper we obtain an upper bound on the first Zagreb index M ₁(G) of G in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ₁), second maximum vertex degree (Δ₂) and minimum vertex degree (δ). Using this result we find an upper bound on M ₂(G). Moreover, we present upper bounds on and in terms of n,  m, Δ₁, Δ₂, δ, where denotes the complement of G.     

The effect of network chain-length distribution,specifically bimodality,on strain-induced crystallization

Polyurethane elastomers were prepared from a series of poly(ethylene oxide) samples by end-linking the chains into “model” trifunctional networks. The molecular weight M_c between crosslinks in such networks is simply the number-average molecular weight M_n of the precursor polymer. End-linking samples separately gave networks with unimodal distributions of network chain lengths, whereas end-linking mixtures of two samples having very different values of M_n gave bimodal distributions with average values of M_c equal to the average value of M_n for the two samples. Stress-strain isotherms in elongation were obtained for these networks, both unswollen and swollen to various extents. Strain-induced crystallization was manifested in elastic properties that changed significantly with changes in temperature. Swelling has more complicated effects, since it causes deformation of the network chains as well as melting of some of the crystallites. Comparisons among stress-strain isotherms at constant M_c indicate that bimodality facilitates strain-induced crystallization.     

3J(HH)?Pμ,ν correlation for planar 7-membered cyclic π-systems—structural effects on 3J(HH)

It is shown that sterically unperturbed vicinal HH coupling constants in planar 7-membered π-systems correlate linearly with the HMO π-bond order: ³J(HH) = 20.91P_μ,_ν–3.85 (r.m.s. error 0.26 Hz, correlation coefficient =0.988). Systematic deviations from this relationship which most probably originate from valence angle changes are found for fused π-systems containing rings of different size. Model calculations using the CNDO/2 method as well as finite perturbation theory and INDO wave functions support the experimental findings. An improvement of existing ³J(HH)? P_μ,_ν correlations for planar 6-membered rings is possible if CNDO/2 π-bond orders are used instead of HMO or PPP-SCF data.     

Grafting onto carbon black by the reaction of reactive carbon black having epoxide groups with several polymers

The grafting of functional polymers onto carbon black surface by the reaction of epoxide groups introduced onto the surface was investigated. The introduction of epoxide groups was achieved by the reaction of the phenolic hydroxyl and carboxyl groups on carbon black with chloromethyloxirane in the presence of sodium hydroxide. The amount of epoxide groups introduced onto the channel black Neospectra II was equal to 0.40 meq/g. The epoxide groups were reacted with polypropylene glycol, silicone diol (SDO), silicone diamine (SDA), and polyethyleneimine to give polymer-grafted carbon blacks. For example, the percentage of grafting of SDO (M_n = 1.0 × 10³) and SDA (M_n = 3.9 × 10³) reached to 23.6 and 67.2%, respectively. The percentage of grafting increased with the molecular weight (M_n) of the polymers, while the number of grafted chain (G_n) decreased. In the case of SDO, the relationship between M_n and G_n was found to be G_n = 4.68 × 10^?2 M. The carbon black obtained from the reaction gave stable colloidal dispersions in tetrahydrofuran and the stability of dispersion increased with an increase in the percentage of grafting.     

Graphical properties of polyhexes: Perfect matching vector and forcing

From the viewpoint of graph theory and its applications, subgraphs of the tiling of the plane with unit squares have long been studied in statistical mechanics, In organic chemistry, a much more relevant case concerns subgraphs of the tiling with unit hexagons. Our purpose here is to take a mathematical view of such polyhex graphsG and study two novel concepts concerning perfect matchingsM. First, the forcing number ofM is the smallest number of edges ofM which are not contained in any other perfect matching ofG. Second, the perfect matching vector ofM is written (n ₃,n ₂,n ₁,n ₀), wheren _k is the number of hexagons with exactlyk edges inM. We establish some initial results involving these two concepts and pose some questions.     

Studies of self-diffusion of poly(dimethylsiloxane) chains in PDMS model networks by pulsed field gradient NMR

We have measured the diffusion of poly(dimethylsiloxane) (PDMS) chains in PDMS model networks by using a pulsed field gradient NMR technique. The model networks have been prepared by tetrafunctional endliking of linear PDMS chains having molecular weights M_n of 3,700 and 7,400 g mol^?1. The diffusants have been incorporated in the networks by immersing pieces of them in PDMS linear chains with molecular weights M_n between 3,000 and 12,000 g mol^?1 and molecular weight distributions M_w/M_n between 1.1 and 1.7. Although spin-echo attenuation results were fitted to a model which takes into account polydispersity of the diffusant, these results did not exhibit any dependency upon the molecular weight distribution. The self-diffusion coefficients of PDMS chains in the PDMS model networks were found to be smaller than in the melt, and the exponents for the diffusion coefficient dependence on M_n in the networks were found to be about-1.3. Free diffusion will give an exponent equal to-1, whereas free volume contributions or behavior intermediate between free and entangled diffusion will increase the magnitude of the exponent.     

Sharp Bounds for the Second Zagreb Index of Unicyclic Graphs

The second Zagreb index M ₂(G) of a (molecule) graph G is the sum of the weights d(u)d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we give sharp upper and lower bounds on the second Zagreb index of unicyclic graphs with n vertices and k pendant vertices. From which, and C _n have the maximum and minimum the second Zagreb index among all unicyclic graphs with n vertices, respectively.     

Construction of ZnII‐based rac‐Helical Chains Containing Semi‐rigid Dipolar Ligand 1,4‐Bis(benzimidazol‐1‐ylmethyl)benzene

A Zn^II compound based on the semi‐rigid dipolar ligand 1,4‐bis(benzimidazol‐1‐ylmethyl)benzene (L), {[Zn( L )₂Cl₂]·2DMF}_n ( 1 ) has been synthesized successfully under solvothermal conditions. X‐ray single crystal diffraction shows that the complex contains P‐helical and M‐helical chains with 2₁ screw axis but crystallizes as a racemate. Through π···π stacking interactions between two well‐overlapping benzimidazoleyl rings from two adjacent chains, the 3D racemic supramolecular network is assembled. Furthermore, the IR, TGA and luminescent properties are also investigated in this work.     

Synthesis of well‐defined polyacrylonitrile by ICAR ATRP with low concentrations of catalyst

Acrylonitrile (AN) was polymerized by initiators for continuous activator regeneration (ICAR) atom transfer radical polymerization (ATRP). The effect of the ligand, tris(2‐pyridylmethyl)amine (TPMA) and N,N,N',N'‐tetrakis(2‐pyridylmethyl)ethylenediamine (TPEN), in the Cu‐based catalyst, the amount of catalyst, several alkyl halide initiators, targeted degree of polymerization, and amount of azobisisobutyronitrile (AIBN) added were studied. It was determined that the best conditions utilized 50 ppm of CuBr₂/TPMA as the catalyst and 2‐bromopropionitrile (BPN) as the initiator. This combination resulted in 46% conversion in 10 h and polyacrylonitrile (PAN) with the narrowest molecular weight distribution (M_w/M_n = 1.11–1.21). Excellent control was maintained after lowering the catalyst loading to 10 ppm, with 56% conversion in 10 h, experimental molecular weight closely matching the theoretical value, and low dispersity (M_w/M_n < 1.30). Catalyst loadings as low as 1 ppm still provided well‐controlled polymerizations of AN by ICAR ATRP, with 65% conversion in 10 h and PAN with relatively low dispersity (M_w/M_n = 1.41). High chain end functionality (CEF) was confirmed via ¹H NMR analysis, for short PAN chains, and via clean chain extensions with n‐butyl acrylate (BA). © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1961–1968     

Characterization of a single sample of an unknown polymer by size exclusion chromatography

The relationship between viscosity constants, k', a and K_η from the equations of Huggins and Mark-Kuhn-Houwink has been considered. It is shown, theoretically, that the sum of k' and a must be constant for all flexible-chain macromolecules irrespective of the solvent used. On this basis, a combination of chromatography and viscometry measurements can be used to characterize a new species. The method has been applied to the new polymer, poly[methyl(pyridin-3-yl) siloxane] ( 1 ) where no suitable calibration standards are available. The value of a, k', and K_η for 1 has been calculated. The calculated constants enabled an estimation of different average molecular weights (M_nM_wM_z) and polydispersity (M_w/M_n) from a minimum of experimental data. The new method is general and can be applied to any homogeneous linear flexible-chain nondraining macromolecule.     

Fracture of model polyurethane elastomeric networks

Fracture properties of model elastomeric networks of polyurethane have been investigated with a double‐edge notch geometry. The networks were synthesized from monodisperse end‐functionalized polypropylene glycol precursors and a trifunctional isocyanate. All reagents were carefully purified and nearly defect‐free ideal networks were prepared at a stoichiometry very close to the theoretical one. Three networks were prepared: an unentangled network of short chains (M_n = 4 kg mol^?1), an entangled network of longer chains (M_n = 8 kg mol^?1) and a bimodal network with 8 kg mol^?1 and 1 kg mol^?1 chains. The presence of entanglements was found to increase significantly the toughness of the rubber, in particular at room temperature, relative to the bimodal networks and to the short chains network. Fracture experiments were carried out at different strain rates and temperatures and showed for all three networks a marked decrease in fracture toughness with increasing temperature and decreasing strain rate which mirrored reasonably well the rate and temperature dependence of tan δ, the dissipative factor. However the proportionality factor between tan δ, and G_IC was very material dependent and the shift factors obtained for the master curves of the viscoelastic properties could not be used to build fracture energy master curves. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Study of phase transitions in 4-n-alkoxybenzilidene-4′-n-alkylanilines by one and two dimensional 13C NMR

Abstract

The phase transition of a series of homologous liquid-crystalline compounds, nO.m (4-n-alkoxybenzilidene-4′-n-alkylanilines), from the nematic phase to the smectic A phase has been studied by ¹³C NMR. The order parameters, determined by a two dimensional technique called separated local field spectroscopy combined with off-magic angle spinning, of different molecular segments of these compounds are related linearly to the ¹³C chemical shifts. Changes in the order parameters of the phenyl rings as well as those of the chains during the S_A–N transition depend on the nature of the phase transition. These changes are quantitatively related to the McMillan ratio, which is defined as the ratio between the S_A–N transition temperature (T _SAN) and the nematic to isotropic transition temperature (T _NI), i.e. M = T _SAN/T _NI. The S_A–N transition is first order for M > M _TCP, and second order for M < M _TCP, where TCP is the tricritical point. The value of M _TCP was found to be 0·958 ± 0·004, in excellent agreement with that obtained from spin probe studies (0·959 ± 0·005) reported by Freed and co-workers [1].     

Azetidine,pyrrolidine and hexamethyleneimine at 170 K

The crystal structures of the cyclic amines azetidine (C₃H₇N), pyrrolidine (C₄H₉N) and hexamethyleneimine (homopiperidine, C₆H₁₃N), of the series (CH₂)_nNH, with n = 3, 4 and 6, respectively, have been determined at 170 K, following in situ crystallization from the melt. These structures provide crystallographic data to complete the homologous series of cyclic amines (CH₂)_nNH, for n = 2–6. Azetidine and pyrrolidine contain chains propagating along 2₁ screw axes, in which the molecules are linked by co-operative N—H...N hydrogen bonds. Azetidine has two molecules in its asymmetric unit, while pyrrolidine has only one. Hexamethyleneimine contains tetrameric hydrogen-bonded rings formed about crystallographic inversion centres, with two molecules in its asymmetric unit. The observation of crystallographically distinct molecules in the hydrogen-bonded chains of azetidine and cyclic hydrogen-bonded motifs in hexamethyleneimine is consistent with expectations derived from comparison with monoalcohols forming chains or rings by co-operative O—H...O hydrogen bonds. The next member of the cyclic amine series, heptamethyleneimine, forms a cubic plastic phase on cooling from the melt.     

On Extremal Unicyclic Molecular Graphs with Prescribed Girth and Minimal Hosoya Index

Let G be an n-vertex unicyclic molecular graph and Z(G) be its Hosoya index, let F _n be the nth Fibonacci number. It is proved in this paper that if G has girth l then Z(G) ≥ F _l+1+(n−l)F _l +F _l-1, with the equality holding if and only if G is isomorphic to , the unicyclic graph obtained by pasting the unique non-1-valent vertex of the complete bipartite graph K _1,n-l to a vertex of an l-vertex cycle C _l . A direct consequence of this observation is that the minimum Hosoya index of n-vertex unicyclic graphs is 2n−2 and the unique extremal unicyclic graph is. The second minimal Hosoya index and the corresponding extremal unicyclic graphs are also determined.     

Synthesis of arborescent polystyrene by “click” grafting

A method was developed for the synthesis of arborescent polystyrene by “click” coupling. Acetylene functionalities were introduced on linear polystyrene (M_n = 5300 g/mol, M_w/M_n = 1.05) by acetylation and reaction with potassium hydroxide, 18‐crown‐6 and propargyl bromide in toluene. Polymerization of styrene with 6‐tert‐butyldimethylsiloxyhexyllithium yielded polystyrene (M_n = 5200 g/mol, M_w/M_n = 1.09) with a protected hydroxyl chain end. Deprotection, followed by conversions to tosyl and azide functionalities, provided the side chain material. Coupling with CuBr and N,N,N′,N″,N″‐pentamethyldiethylenetriamine proceeded in up to 94% yield. Repetition of the grafting cycles led to well‐defined (M_w/M_n ≤ 1.1) polymers of generations G1 and G2 in 84% and 60% yield, respectively, with M_n and branching functionalities reaching 2.8 × 10⁶ g/mol and 460, respectively, for the G2 polymer. Coupling longer (M_n = 45,000 g/mol) side chains with acetylene‐functionalized substrates was also examined. For a linear substrate, a G0 polymer with M_n = 4.6 × 10⁵ g/mol and M_w/M_n = 1.10 was obtained in 87% yield; coupling with the G0 (M_n = 52,000 g/mol) substrate produced a G1 polymer (M_n = 1.4×10⁶ g/mol, M_w/M_n = 1.38) in 28% yield. The complementary approach using azide‐functionalized substrates and acetylene‐terminated side chains was also investigated, but proceeded in lower yield. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1730–1740     

线性BC2nB (n＝1～12)的结构特征和电子光谱的理论研究

应用密度泛函理论, 在B3LYP/6-31G^*水平上优化得到了线性簇合物BC_2nB (n＝1～12, D_(h)的平衡几何构型, 并计算了它们的谐振动频率. 在优化平衡几何构型下, 通过TD-B3LYP/cc-pvDZ和TD-B3LYP/cc-pvTZ计算, 分别得到了n＝1～12和n＝1～7的电子跃迁的垂直激发能和对应的振子强度. 在B3LYP/6-311＋G^*水平上计算得到了簇合物BC_2nB (n＝1～12, D_(h)的电离能. 基于计算结果, 导出了BC_2nB体系电子跃迁能以及第一电离能与体系大小n的解析表达式.     

Advantage of the N‐Alkylation Strategy for Retaining the Molecular Planarity for Oligothiophene/Imidazole/1,10‐Phenanthroline‐Based Heterocyclic Semiconducting and Fluorescent Compounds

A family of planar oligothiophene/imidazole/1,10‐phenanthroline (OTIP)‐based heterocyclic, aromatic, semiconducting, and fluorescent compounds with N‐substituted alkyl chains (allyl, n‐butyl, n‐octyl, n‐dodecyl, and n‐cetyl) have been designed and synthesized. They all have specific N‐coordination sites, various donor–acceptor spacers, good molecular planarity, suitable solubility, and high thermal stability. In comparison with conventional double β‐alkylation of the thiophene ring, our results reveal that the single imidazole N‐alkylation strategy for OTIPs has the advantage of maintaining the planarity of the whole molecule, in addition to improving the solubility, which can be clearly verified by the small dihedral angles between adjacent thiophene/imidazole/1,10‐phenanthroline (TIP) rings in eight X‐ray single‐crystal structures. In particular, n‐dodecyl‐ and n‐cetyl‐substituted OTIPs ( 7 and 8 ) with the same molecular length of 2.37 nm (M_W=939 and 1052), show good molecular planarity with the aforementioned dihedral angles of 8.9(5) and 10.4(5)°. Furthermore, special attention has been paid to the physicochemical properties of seven symmetrical OTIPs ( 6 – 8 , 13 – 15 , and 19 ), including two to six thiophene rings in the middle of their molecular structures. To the best of our knowledge, this is the first synthetic, structural, and spectral investigation into the N‐alkylation of OTIP‐based compounds.     

Titanium complexes of dialkanolamine ligands as initiators for living ring‐opening polymerization of ε‐caprolactone

The titanium complexes with one ( 1a , 1b , 1c ) and two ( 2a , 2b ) dialkanolamine ligands were used as initiators in the ring‐opening polymerization (ROP) of ε‐caprolactone. Titanocanes 1a and 1b initiated living ROP of ε‐caprolactone affording polymers whose number‐average molecular weights (M_n) increased in direct proportion to monomer conversion (M_n ≤ 30,000 g mol^?1) in agreement with calculated values, and were inversely proportional to initiator concentration, while the molecular weight distribution stayed narrow throughout the polymerization (M_w/M_n ≤ 1.2 up to 80% monomer conversion). ¹H‐NMR and MALDI‐TOF‐MS studies of the obtained poly(ε‐caprolactone)s revealed the presence of an isopropoxy group originated from the initiator at the polymer termini, indicating that the polymerization takes place exclusively at the Ti–OⁱPr bond of the catalyst. The higher molecular weight polymers (M_n ≤ 70,000 g mol^?1) with reasonable MWD (M_w/M_n ≤ 1.6) were synthesized by living ROP of ε‐caprolactone using spirobititanocanes ( 2a , 2b ) and titanocane 1c as initiators. The latter catalysts, according MALDI‐TOF‐MS data, afford poly(ε‐caprolactone)s with almost equal content of α,ω‐dihydroxyl‐ and α‐hydroxyl‐ω(carboxylic acid)‐terminated chains arising due to monomer insertion into “Ti–O” bond of dialkanolamine ligand and from initiation via traces of water, respectively. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1230–1240, 2010