Self-healing polymeric materials with branched architectures and reversible cross-linking functionalities at the periphery of branches were synthesized by atom transfer radical polymerization (ATRP). Poly(n-butyl acrylate) grafted star polymers were prepared by chain extension ATRP from cross-linked cores comprised of poly(ethylene glycol diacrylate). These polymers were further used as macroinitiators for the consecutive chain extension ATRP of bis(2-methacryloyloxyethyl disulfide) (DSDMA), in which way disulfide reversible cross-links (SS) were introduced at the branch peripheries. The SS cross-linked polymers were then cleaved under reducing conditions to form thiol (SH)-functionalized soluble star polymers. The SH-functionalized star polymer solutions were deposited on silicon wafer substrates and converted to insoluble SS re-cross-linked films via oxidation. The self-healing of prepared polymer films was studied by continuous atomic force microscopy (AFM) imaging of cuts micromachined with the AFM tip and by optical microscopy. The re-cross-linked star polymer (X3) showed a rapid spontaneous self-healing behavior, with the extent of healing dependent on the initial film thickness and the width of the cut. The self-healing behavior observed for this sample was attributed to the regeneration of SS bonds via thiol–disulfide exchange reactions. This study demonstrated the suitability of grafted multiarm polymer architectures as building blocks of self-healing polymeric materials and pointed to the importance of low intrinsic viscosity of material and high accessibility of functional groups responsible for healing.

The kinetics of copper-mediated controlled/ living radical polymerization (CRP) of methyl acrylate (MA) in the presence of Cu 0 and two different ligands that form active catalyst complexes with copperTPMA (tris(2-pyridylmethyl)amine) and Me 6 TREN (tris(2-(dimethylamino)ethyl)amine) are compared. The critical difference between the ligands is that TPMA forms a Cu I complex that undergoes essentially no disproportionation in a mixture of MA and dimethyl sulfoxide (DMSO), DMSO/MA (v/v = 1/2), while the complex with Me 6 TREN undergoes disproportionation to a limited extent. Parameters such as the surface area of Cu 0 wire, the concentration of added Cu II X 2 /L, and ligand concentration were examined. Both the Me 6 TREN-and TPMA-based catalysts efficiently controlled the polymerization of MA. The TPMA-based system showed a power law order of 0.47 for the apparent propagation rate constant with the Cu 0 surface area, very similar to the reported value for the Me 6 TREN-based system, which showed a power law of 0.44. These results demonstrate that the polymerization of MA in DMSO in the presence of metallic copper can be explained by a core atom-transfer radical polymerization (ATRP) process in which the Cu 0 acts as a supplemental activator and reducing agent, rather than through the proposed single-electron-transfer living radical polymerization (SET-LRP) mechanism, which requires additional assumptions, such as complete and instantaneous disproportionation of Cu I /L species.

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A quartz crystal microbalance (QCM) consists of a resonator, which measures the resonance frequency of the quartz slab. When coupled with a network analyzer or coupled with impulse excitation technology, QCM gives additional impedance or dissipation information, respectively. This report provides a set of equations that bring the QCM community a convergence of the dissipation and impedance analysis. Equations derived from the complex frequency shift were applied to quantitatively analyze the dissipation data of polymer brushes obtained from QCM-D. The obtained viscoelastic properties of polymer brushes were then compared with those obtained by the Voigt model method. We believe that these equations will be useful in quantitative studies of interfacial phenomena accompanied with mass or viscoelasticity changes.

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Applying Bogoliubov transformations and Bargmann-Hilbert spaces, we obtain analytic representations of solutions to the 2-photon and two-mode quantum Rabi models. In each case, a transcendental function is analytically derived whose zeros give the energy spectrum of the model. The zeros can be numerically found by standard root-search techniques. We also present analytic solution to the driven Rabi model with broken Z 2 symmetry.

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