Energy Scaling Laws for Conically Constrained Thin Elastic Sheets

We investigate low-energy deformations of a thin elastic sheet subject to a displacement boundary condition consistent with a conical deformation. Under the assumption that the displacement near the sheet’s center is of order h|logh|, where h?1 is the thickness of the sheet, we establish matching upper and lower bounds of order h ²|logh| for the minimum elastic energy per unit thickness, with a prefactor determined by the geometry of the associated conical deformation. These results are established first for a 2D model problem and then extended to 3D elasticity.     

Evaluation of automated synthesis for chain and step‐growth polymerizations: Can robots replace the chemists?

This article explores current challenges in the use of automated parallel synthesizers in polymeric materials research. Four types of polymerizations were investigated: carbodiimide‐mediated polyesterification, diphenol phosgenation, free radical, and reversible addition‐fragmentation chain‐transfer (RAFT). Synthetic challenges of condensation polymerization, such as liquid and solid dispensing accuracy, dropwise addition, and toxic chemical handling, were successfully met using the automated synthesizer. Both solid and liquid dosing of the diphenol and diacid were successful for polyarylate synthesis. The high precision of liquid dispensing made it possible to achieve stoichiometric balance using reagent stock solutions. For all reactions, molecular weights and their reproducibility were comparable to those obtained with manual synthesis. For RAFT polymerizations, solvent and mol ratio of chain transfer reagent to initiator were successfully optimized on the automated synthesizer and a library of over 60 polymethacrylate copolymer compositions was generated. Considerable savings in time relative to manual methods were achieved when generating polymer libraries (e.g., 4.5× faster for 96 polymethacrylates and 20× faster for 45 for polycarbonates). © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 49–58, 2009     

Copolymerization of acrylonitrile. I. Copolymerization with styrene derivatives containing nitrile groups in the side chain

Acrylonitrile was copolymerized in bulk with cinnamonitrile (I), ethyl benzylidenecyanoacetate (II), and benzylidenemalononitrile (III) by radical initiation up to low conversions. The conventional scheme of copolymerization fitted all the three copolymer pairs.     

Analysis of a Compressed Thin Film Bonded to a Compliant Substrate: The Energy Scaling Law

We consider the deformation of a thin elastic film bonded to a thick compliant substrate, when the (compressive) misfit is far beyond critical. We take a variational viewpoint—focusing on the total elastic energy, i.e. the membrane and bending energy of the film plus the elastic energy of the substrate—viewing the buckling of the film as a problem of energy-driven pattern formation. We identify the scaling law of the minimum energy with respect to the physical parameters of the problem, and we prove that a herringbone pattern achieves the optimal scaling. These results complement previous numerical studies, which have shown that an optimized herringbone pattern has lower energy than a number of other patterns. Our results are different, because (i) we make the scaling law achieved by the herringbone pattern explicit, and (ii) we give an elementary, ansatz-free proof that no pattern can achieve a better law.