Algebraic expressions of Clebsch–Gordon coefficients for the group chain O† ⊃ C

Using the algebraic expressions of the projection operators for the group chain O ? C, concise algebraic expressions of the Clebsch–Gordon (CG) coefficients are derived in the group chain O ? C for both single‐valued and double‐valued representations. The simplicity of the expressions is that they are merely functions of the quantum numbers of the group chain O ? C. The symmetry of the CG coefficients is also derived. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Algebraic solutions for point groups: The octahedral group for the group chain O⊃T⊃C3

Using the right‐induced technique and the eigenfunction method, concise algebraic expressions of the projection operators for both single‐valued and double‐valued representations are found for the group chain O?T?C₃ in terms of the projection operators of T?C₃. Extremely simple relations are discovered between the symmetry adapted functions (SAFs) of the groups T and O; namely the SAFs of the subgroup T which have proper symmetry are the SAFs of the group O. The projection operators and SAFs are functions of only the quantum numbers of the group chain [the analogy of ( j,m) for the group chain SO₃?SO₂], without involving any irreducible matrix elements. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 259–270, 2001     

Algebraic solutions for point groups: Cubic groups G in the group chain G⊃T⊃D2⊃C2

Concise algebraic expressions of the symmetry‐adapted functions (SAFs) for both single‐valued and double‐valued representations are derived for the group chain O⊃T⊃D₂⊃C₂ and O⊃D₄⊃D₂⊃C₂, which are functions of only the quantum numbers of the respective group chain without involving any irreducible matrix elements. It is shown that the SAFs of the cubic groups G=O,T_d,T_h,O_h can be expressed in a simple way in terms of the SAFs of the group T. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 585–599, 2000     

Unique Euler angles and self‐consistent multiplication tables for double point groups

The standard Euler angle parameterization of rotations is not unique. This is a particular problem when considering spinor representations. We enlarge the domain of the Euler angles from an SO₃ covering to an SU₂ covering, 0≤α<2π, 0≤β≤π, 0≤γ<4π. With this modification we can find unique Euler angles for operations of the double groups and thus construct self‐consistent group tables for those groups. Factor systems can then be described for the projective representations. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 1–9, 1999     

Analytical irreducible representation bases of the single and double icosahedral groups and their applications

An equivalent basis of icosahedral molecules is introduced in which the basis functions can be transformed under the operations in the icosahedral group (I_h). In this equivalent basis, the irreducible representation basis (IRB) of I_h, including the double‐valued IRB of I, is deduced analytically based on the method introduced in the literature [J. Comput. Chem. 17 , 851 (1996)]. Therefore the concepts of symmetry‐matrix and symmetry‐supermatrix can be used in the single‐ and multiconfiguration self‐consistent field methods (including relativistic effects) to reduce the storage of two‐electron integrals and calculations of Fock matrix during iterations by a factor of ca. 10,000. In addition, the equivalent basis of I_h can also be used to reduce the calculations of atoms and representations of rank ≥ 2 tensors. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 615–624, 2000     

Pendant side‐chain sterics against electrostatic forces: Influencing short‐range ordering in random polyelectrolytes

The length of pendant side chains in charged, random, comb‐shaped polymers dictates the nature of their short‐range ordering. Random copolymers, and terpolymer, of 4‐vinylpyridine (4VP), styrene, and isoprene were synthesized and subsequently fully quaternized with 1‐alkylbromides having varying number of carbons on the alkyl group ranging from 2 to 8. Evaluation by wide angle X‐ray scattering revealed that dipole–dipole attraction facilitates the formation of ionomer cluster morphology in samples with two carbons on the pendant side chain, whereas for samples with four or more carbons on the pendant side chains, side‐chain sterics was dominant resulting in periodic backbone spacing. Copolymers with isoprene, having flexible backbones, favor the formation of ionomer cluster morphology while styrene copolymers having rigid backbones disfavor the formation of ionomer clusters. An “in‐line” dipole model was developed to predict the separation distance at which both ionomer cluster and backbone–backbone morphologies could coexist. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1325–1336     

Influence of the catalyst and polymerization conditions on the long‐chain branching of metallocene‐catalyzed polyethenes

A study was made on the effects of polymerization conditions on the long‐chain branching, molecular weight, and end‐group types of polyethene produced with the metallocene‐catalyst systems Et[Ind]₂ZrCl₂/MAO, Et[IndH₄]₂ZrCl₂/MAO, and (n‐BuCp)₂ZrCl₂/MAO. Long‐chain branching in the polyethenes, as measured by dynamic rheometry, depended heavily on the catalyst and polymerization conditions. In a semibatch flow reactor, the level of branching in the polyethenes produced with Et[Ind]₂ZrCl₂/MAO increased as the ethene concentration decreased or the polymerization time increased. The introduction of hydrogen or comonomer suppressed branching. Under similar polymerization conditions, the two other catalyst systems, (n‐BuCp)₂ZrCl₂/MAO and Et[IndH₄]₂ZrCl₂/MAO, produced linear or only slightly branched polyethene. On the basis of an end‐group analysis by FTIR and molecular weight analysis by GPC, we concluded that a chain transfer to ethene was the prevailing termination mechanism with Et[Ind]₂ZrCl₂/MAO at 80 °C in toluene. For the other catalyst systems, β‐H elimination dominated at low ethene concentrations. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 376–388, 2000     

Well‐defined pH‐sensitive block glycopolymers via reversible addition–fragmentation chain transfer radical polymerization: Synthesis,characterization, and recognition with lectin

pH‐Sensitive block glycopolymers of poly(2‐(diethylamino)ethyl methacrylate) (PDEAEMA) and poly(3‐O‐methacryloy‐α,β‐D ‐glucopyranose) (PMAGlc) were synthesized via reversible addition–fragmentation chain transfer (RAFT) radical polymerization based on protected glycomonomer 3‐O‐methacryloyl‐1,2:5,6‐di‐O‐isopropylidene‐D ‐glucofuranose (MAIpGlc). It was found that RAFT homopolymerization of MAIpGlc proceeded in a controlled fashion with 4‐cyanopentanoic acid dithiobenzoate as chain transfer agent. Using the dithioester‐capped PDEAEMA as macro‐RAFT agent, block copolymerization of MAIpGlc was in good control as indicated by the linear pseudo first‐order kinetic plot, the linear increment of number‐average molecular weights as well as narrow and symmetrical gel permeation chromatography peaks, and low polydispersities. Well‐defined diblock copolymers of DEAEMA and MAIpGlc were prepared successfully through the chain extension of PDEAEMA. The deprotection of MAIpGlc units in trifluoroacetic acid/H₂O solution afforded PDEAEMA‐b‐PMAGlc block glycopolymer. The self‐assembly behavior of PDEAEMA‐b‐PMAGlc in aqueous solution was investigated by using ¹H NMR, UV‐vis spectroscopy, dynamic light scattering, and transmission electron microscopy. The results demonstrated that spherical micelles with PDEAEMA as the hydrophobic cores and PMAGlc as the hydrophilic shells were formed in alkaline aqueous solution. These glucose‐installed micelles had specific recognition with Concanavalin A. The combination of pH‐sensitivity of PDEAEMA and biomolecular recognition of PMAGlc in one micellar system may create a multifunctional platform for targeted delivery, biomimetics, and biodection. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3350–3361, 2010     

Effects of substituted side‐chain position on donor–acceptor conjugated copolymers

The optical properties and electrical properties of a series of low‐band‐gap conjugated copolymers, in which alkyl side chains were substituted at various positions, were investigated using donor–acceptor conjugated copolymers consisting of a cyclopentadithiophene derivative and dithienyl‐benzothiadiazole. With substituted side chains, the intrinsic properties of the copolymers were significantly altered by perturbations of the intramolecular charge transfer. The absorption of poly[2, 6‐(4,4‐bis(2‐octyl)‐4H‐cyclopenta‐[2,1‐b:3,4‐b′]dithiophene)‐alt‐4, 7‐bis(4‐octyl‐thiophene‐2‐yl)benzo‐2,1,3‐thiadiazole] [ PCPDT‐ttOTBTOT ( P2 )], which assumed a tail–tail configuration, tended to blue shift relative to the absorption of poly[2,6‐(4,4‐bis(2‐octyl)‐4H‐cyclopenta‐[2,1‐b:3,4‐b′]dithiophene)‐alt‐4,7‐bis (thiophene‐2‐yl)benzo‐2,1,3‐thiadiazole] [ PCPDT‐TBTT ( P1 )]. The absorption of poly[2,6‐(4,4‐bis(2‐octyl)‐4H‐cyclopenta‐[2,1‐b:3, 4‐b′]dithiophene)‐alt‐4,7‐bis(3‐octyl‐thiophene‐2‐yl)benzo‐2,1,3‐thiadiazole] [ PCPDT‐hhOTBTOT ( P3 )], which assumed a head–head configuration, was blue shifted relative to that of P2 . The electrical transport properties of field‐effect transistors were sensitive to the side chain position. The field‐effect mobility in P2 (μ₂ = 1.8 × 10^?3 cm²/V s) was slightly lower than that in P1 (μ₁ = 4.9 × 10^?3 cm²/V s). However, the mobility of P3 was very low (μ₃ = 3.8 × 10^?6 cm²/V s). Photoexcitation spectroscopy showed that the charge generation efficiency (shown in transient absorption spectra) and polaron pair mobility in P1 and P2 were higher than in P3 , yielding P1 and P2 device performances that were better than the performance of devices based on P3 . © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

The relationship between end‐group concentrations and stability of spin‐coated thin polymer films investigated by ToF‐SIMS depth profiling

Stable and unstable spin‐coated polymer films were prepared using various solvents and substrates. The relationship between polymer end‐group concentrations and stability of spin‐coated polymer films was revealed by time‐of‐flight secondary ion mass spectrometry depth profiling. A high concentration of bromine end groups at the interface between the polymer and the substrate helped to prevent the dewetting of films. In contrast, the bromine end groups were found to be more evenly distributed in unstable thin films. The extent to which the bromine end groups segregate to the interface depended on the competitive interactions between the polymer, the solvent and the substrate. Stronger polymer–solvent and solvent–substrate interactions prevented the segregation of the bromine end groups to the interface, resulting in unstable polymer films. Copyright © 2013 John Wiley & Sons, Ltd.     

Effect of side‐chain end groups on the optical,electrochemical, and photovoltaic properties of side‐chain conjugated polythiophenes

Three new side‐chain conjugated polythiophene derivatives, poly{3‐[2‐(3‐methoxy‐4‐octyloxy‐phenyl)‐vinyl]‐thiophene} (P3MOPVT), poly{3‐[2‐(3,5‐dimethoxy‐4‐octyloxy‐phenyl)‐vinyl]‐thiophene} (P3DMOPVT), and poly{3‐[2‐(3,4‐dioctyloxy‐phenyl)‐vinyl]‐thiophene} (P3DOPVT), were synthesized by Wittig‐Hornor reaction and GRIM method and compared with poly{3‐[2‐(4‐octyloxy‐phenyl)‐vinyl]‐thiophene} (P3OPVT) for investigating the effect of the end groups of the conjugated side‐chain on the properties of the polymers. Owing to the electron‐donating ability of methoxy groups, the visible absorption peaks of P3MOPVT and P3DMOPVT solutions and films become stronger and red‐shifted compared with P3OPVT. The electrochemical bandgaps of the four polymers are 2.15 eV for P3OPVT, 1.99 eV for P3MOPVT, 1.85 eV for P3DMOPVT, and 2.36 eV for P3DOPVT, respectively, which indicate that the electron‐donating ability of the methoxy end group on the conjugated side chain of P3MOPVT and P3DMOPVT and the large steric hindrance of the two octyloxy end groups on the conjugated side chain of P3DOPVT have obvious influence on the electrochemical properties of the side‐chain conjugated polythiophenes. Polymer solar cells were fabricated with a structure of ITO/PEDOT:PSS/Polymer:PCBM/LiF/Al. The best device, based on P3DMOPVT, shows a power conversion efficiency of 1.63% under the illumination of AM1.5, 80 mW/cm². © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4916–4922, 2006     

Naked and Self‐Clickable Propargylic‐Decorated Single‐Chain Nanoparticle Precursors via Redox‐Initiated RAFT Polymerization

Protection of acetylenic monomers is a common practice to avoid parasitic side reactions during polymerization. Herein, we report that redox‐initiated RAFT polymerization allows the direct, room temperature synthesis of a variety of single‐chain nanoparticle precursors (displaying narrow molecular weight dispersity, / = 1.12 –1.37 up to = 100 kDa) containing well‐defined amounts of naked, unprotected acetylenic functional groups available for rapid and quantitative intrachain cross‐linking via metal‐catalyzed carbon–carbon coupling (i.e., C–C “click” chemistry). To illustrate the useful “self‐clickable” character of the new unprotected acetylenic precursors, single‐chain nanoparticles have been prepared for the first time in a facile and highly efficient manner by copper‐catalyzed alkyne homocoupling (i.e., Glaser–Hay coupling) at room temperature under normal air atmosphere.     

Chain length‐dependent termination in pulsed‐laser polymerization. VIII. The temperature dependence of the rate coefficient of bimolecular termination in the bulk polymerization of styrene

The photosensitized polymerization of styrene in bulk was investigated in the temperature range of 25–70°C with respect to the average rate coefficient of bimolecular chain termination k̄_t, especially its chain length dependence at low conversions, by means of pulsed laser polymerization (PLP). Three methods were applied: two of them were based on equations originally derived for chain length independent termination taking the quantity k_t contained therein as an average k̄_t, while the third one consisted in a nonlinear fit of the experimental chain length distribution (CLD) obtained at very low pulse frequencies (LF‐PLP) to a theoretical equation. The exponent b characterizing the extent of chain length dependence was unanimously found to decrease from about 0.17–0.20 at 25°C to 0.08–0.11 at 70°C, slightly depending on which of the three methods was chosen. This trend toward more “ideal” polymerization kinetics with rise of polymerization temperature is tentatively ascribed to a quite general type of polymer solution behavior that consists in a (slow) approach to a lower critical solution temperature (LCST), which is associated with a decrease of the solvent quality of the monomer toward the polymer, an effect that should be accompanied with a decrease of the parameter b. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 697–705, 2000     

Living free‐radical polymerization (reversible addition–fragmentation chain transfer) of 6‐[4‐(4′‐methoxyphenyl)phenoxy]hexyl methacrylate: A route to architectural control of side‐chain liquid‐crystalline polymers

Side‐chain liquid‐crystalline polymers of 6‐[4‐(4′‐methoxyphenyl)phenoxy]hexyl methacrylate with controlled molecular weights and narrow polydispersities were prepared via reversible addition–fragmentation chain transfer (RAFT) polymerization with 2‐(2‐cyanopropyl) dithiobenzoate as the RAFT agent. Differential scanning calorimetry studies showed that the polymers produced via the RAFT process had a narrower thermal stability range of the liquid‐crystalline mesophase than the polymers formed via conventional free‐radical polymerization. In addition, a chain length dependence of this stability range was found. The generated RAFT polymers displayed optical textures similar to those of polymers produced via conventional free‐radical polymerization. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2949–2963, 2003     

Single‐chain nanoparticles with well‐defined structure via intramolecular crosslinking of linear polymers with pendant benzoxazine groups

Controlled intramolecular collapse of linear polymer chains with crosslinkable groups is an efficient way to prepare single‐chain nanoparticles in the size range of 5–20 nm. However, the nature of the crosslinking group is critical. In present study, poly(styrene‐co‐chloromethyl styrene) [P(St‐co‐CMS)] was synthesized via reversible addition‐fragmentation chain transfer (RAFT) polymerization and then was converted into polystyrene azide (PS? N₃). Polystyrene containing benzoxazine side groups [P(St‐co‐BS)], which can be used as the precusor for the later intramolecular collapse, was obtained from PS? N₃ and 3‐(4‐(prop‐2‐ynyloxy)phenyl)‐3,4‐dihydro‐2H‐benzo[e][1,3]oxazine (P‐APPE) via the method of click chemistry. The sub‐20 nm polymeric nanoparticles with well‐defined structure via thermally intramolecular crosslinking of P(St‐co‐BS) were prepared. The structure change from the linear polymers to the single‐chain nanoparticles was confirmed by nuclear magnetic resonance (NMR), Fourier transform infrared (FTIR), and gel permeation chromatography (GPC). The morphology and the dimension of the nanoparticles were characterized by using transmission electron microscope (TEM), atomic force microscopy (AFM), as well as dynamic light scattering (DLS). The results reveal that the size of the nanoparticles can be regulated by changing the molecular weight of the precursors and the amount of pendant benzoxazine groups by the use of controlled polymerization techniques. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Unexpected end‐groups of poly(acrylic acid) prepared by RAFT polymerization

Low‐molecular‐weight poly(acrylic acid) (PAA) was synthesized by reversible addition fragmentation chain transfer polymerization with a trithiocarbonate as chain‐transfer agent (CTA). With a combination of NMR spectroscopy and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry, the PAA end‐groups of the polymer were analyzed before and after neutralization by sodium hydroxide. The polymer prior to neutralization is made up of the expected trithiocarbonate chain‐ends and of the H‐terminated chains issued from a reaction of transfer to solvent. After neutralization, the trithiocarbonates are transformed into thiols, disulfides, thiolactones, and additional H‐terminated chains. By quantifying the different end‐groups, it was possible to demonstrate that fragmentation is the rate limiting step in the transfer reaction. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5439–5462, 2004     

UHMWPE with short‐chain branches synthesized by alkenyl substituted phenoxy–imine catalysts in ethylene polymerization

The alkenyl substituted phenoxy–imine complexes [2‐C₃H₅‐6‐(2, 3, 5, 6‐C₆F₄H‐N?CH)C₆H₃O]₂TiCl₂ (C₃H₅=? CH₂? CH?CH₂ or ? CH?CH? CH₃) are synthesized and characterized by ¹H NMR, ¹³C NMR, and elemental analysis. When activated by MAO, they show high activity for the polymerization of ethylene to UHMWPE under different conditions (temperatures and polymerization time). Most of the resulting polymers have high molecular weights (>1.0 × 10⁶ g·mol^?1) and high melting points as well as crystallinity. To clarify the effect of the alkenyl group on the catalytic performance and the resultant polymer microstructure, the corresponding saturated complexes of type [2‐C₃H₇?6‐(2, 3, 5, 6‐C₆F₄H‐N?CH)C₆H₃O]₂TiCl₂ where C₃H₇ = –CH₂? CH₂? CH₃ or ? CH(CH₃)₂ were synthesized and tested as catalysts in ethylene polymerization under the same reaction conditions. The microstructure and morphologies of these two species of PE samples were fully compared by the analysis of ¹³C NMR, GPC, DSC, and SEM. As a result, the allyl substituted complex show the highest activity to prepare the highest molecular weight polyethylene of all the catalysts. An interesting feature of the UHMWPE produced by these four catalysts is that they contain only a few short‐chain branches (mainly methyl, isobutyl and 2‐methylhexyl branches) in a low amount (<2.7 branches/1000 C). © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3808–3818     

Allyl sulfides and α‐substituted acrylates as addition–fragmentation chain transfer agents for methacrylate polymer networks

The rapid and uncontrolled nature of network formation from di(meth)acrylate monomers produces high shrinkage stress and results in polymers with oftentimes brittle mechanical properties. Methods for regulating polymerization and network formation are sought. One option is the use of addition–fragmentation chain transfer (AFCT) agents, which are well known to control molecular weight and molecular weight distribution of monofunctional (meth)acrylates. A series of novel and previously described AFCT reagents were synthesized and screened with laser flash photolysis to determine reactivity. Well‐performing AFCT reagents were then tested in polymerizations with monofunctional and difunctional methacrylates. With monofunctional monomers, the molecular weight and polydispersity of the resultant linear polymers tend to decrease with the addition of AFCT agent. In copolymerization with dimethacrylate monomers, the AFCT agents were found to substantially lower and sharpen the glass transition. Sharpness of the glass transition is here indicative of a more regular and homogenous network. After coupling of the instruments, photorheology was performed simultaneously with real‐time IR to show an increase in monomer conversion at the time of gelation, which appears to have a positive effect on reducing shrinkage stress. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 394–406