The Interplay of Modulus,Strength, and Ductility in Adhesive Design Using Biomimetic Polymer Chemistry

High‐performance adhesives require mechanical properties tuned to demands of the surroundings. A mismatch in stiffness between substrate and adhesive leads to stress concentrations and fracture when the bonding is subjected to mechanical load. Balancing material strength versus ductility, as well as considering the relationship between adhesive modulus and substrate modulus, creates stronger joints. However, a detailed understanding of how these properties interplay is lacking. Here, a biomimetic terpolymer is altered systematically to identify regions of optimal bonding. Mechanical properties of these terpolymers are tailored by controlling the amount of a methyl methacrylate stiff monomer versus a similar monomer containing flexible poly(ethylene glycol) chains. Dopamine methacrylamide, the cross‐linking monomer, is a catechol moiety analogous to 3,4‐dihydroxyphenylalanine, a key component in the adhesive proteins of marine mussels. Bulk adhesion of this family of terpolymers is tested on metal and plastic substrates. Incorporating higher amounts of poly(ethylene glycol) into the terpolymer introduces flexibility and ductility. By taking a systematic approach to polymer design, the region in which material strength and ductility are balanced in relation to the substrate modulus is found, thereby yielding the most robust joints.     

T1Effects in Sequential Dynamic Susceptibility Contrast Experiments

Residual effects of an initial bolus of gadolinium contrast agent have been previously demonstrated in sequential dynamic susceptibility contrast MR experiments. While these residual effects quickly reach a saturation steady state, their etiology is uncertain, and they can lead to spurious estimates of hemodynamic parameters in activation experiments. The possible influence ofT₁effects is now investigated with experiments in whichT₁weighting is varied as well as with serial regionalT₁measurements. Little evidence for significant residualT₁effects is found, suggesting instead that susceptibility effects underlie these observations. An initial saturation dose of contrast agent minimizes this effect.     

Anionic iron(II) alkoxides as initiators for the controlled ring‐opening polymerization of lactide

Hetero‐bimetallic Fe(II) alkoxide/aryloxides were evaluated as initiators for the ring‐opening polymerization of rac‐lactide. [(THF)NaFe(O^tBu)₃]₂ ( 1 ) and [(THF)₄Na₂Fe(2,6‐diisopropylphenolate)₄] ( 2 ) (THF = tetrahydrofuran) both polymerized lactide efficiently at room temperature, with complex 1 affording better control over the molecular weight parameters of the resultant polymer. At conversions below 70%, a linear increase in molecular weight with conversion was observed, indicative of a well‐controlled polymerization process. Complex 2 is the first example of a dianionic Fe(II) alkoxide and has been structurally characterized to reveal a distorted square planar FeO₄ array in which both Na counterions bridge two aryloxide ligands and are further complexed by two THF ligands. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3798–3803, 2003     

The Geometry of the Newton Method on Non-Compact Lie Groups

An important class of optimization problems involve minimizing a cost function on a Lie group. In the case where the Lie group is non-compact there is no natural choice of a Riemannian metric and it is not possible to apply recent results on the optimization of functions on Riemannian manifolds. In this paper the invariant structure of a Lie group is exploited to provide a strong interpretation of a Newton iteration on a general Lie group. The paper unifies several previous algorithms proposed in the literature in a single theoretical framework. Local asymptotic quadratic convergence is proved for the algorithms considered.     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

Proximality and Chebyshev sets

This paper is a companion to a lecture given at the Prague Spring School in Analysis in April 2006. It highlights four distinct variational methods of proving that a finite dimensional Chebyshev set is convex and hopes to inspire renewed work on the open question of whether every Chebyshev set in Hilbert space is convex.     

Kinetic and thermodynamic considerations of the bracketing method: Entropy-driven proton-transfer reactions in a Fourier transform mass spectrometer

Several reports of experimentally derived proton affinity values and gas-phase basicity values for amino acids and peptides have recently appeared in the literature. Here, we show that the thermodynamic quantity that is measured by the Fourier transform mass spectrometry proton transfer bracketing of amino acids and peptides is gas-phase basicity and not proton affinity. Both experimental and theoretical evidence supports this conclusion. The difference between the values determined by proton transfer bracketing measurements for lysine versus leucine is consistent with a difference in gas-phase basicity rather than proton affinity. The rate of proton transfer from protonated lysine to a series of reference compounds have been measured. Entropy-driven, endothermic proton transfer is found to occur at the collision rate. Recent ab initio and semi-empirical calculations of the proton affinity of lysine are found to agree with the value that is derived from bracketing studies when one assumes that gas-phase basicity is measured. While entropy-driven reactions have been observed previously in high-pressure mass spectrometers, this is the first evidence for such reactions at low pressure in a Fourier transform mass spectrometer.     

A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291