Synthesis of nonsymmetric chain end functionalized polyisobutylenes

We present the synthesis of nonsymmetric α‐ω‐functionalized polyisobutylenes (PIBs) bearing different functional moieties on their chain ends. Thus, on one chain end either, a short tri‐ethylene oxide chain (TEO) or a phosphine oxide ligand is attached, whereas the other chain end is substituted by hydrogen bonding moieties (thymine/2,6‐diaminotriazine). The nonsymmetric PIBs were synthesized via living cationic polymerization using methyl‐styrene epoxide as initiator, followed by quenching reaction with 3‐bromopropyl‐benzene. Subsequent bromide/azide exchange and the use of the azide/alkyne click reaction allowed the synthesis of (a) (α)‐TEO‐(ω)‐thymine‐telechelic PIB ( 7a ), (b) (α)‐triethyleneoxide‐(ω)‐triazine telechelic PIB ( 7b ), and (c) (α)‐phosphinoxide‐(ω)‐thymine‐telechelic PIB ( 13 ) with molecular weights M_n ～ 4000 g mol^?1 and low polydispersities (M_w/M_n = 1.3). The chemical identity of the final structures was proven by extensive ¹H NMR investigations and matrix‐assisted laser desorption/ionization‐mass spectroscopy (MALDI). The presented method for the first time offers a simple and highly versatile approach toward supramolecular nonsymmetric α‐ω‐functionalized PIB. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

On duality for a generalized Monge-Kantorovich problem

The existence of a minimizer for a special version of the Monge-Kantorovich problem is solved using classical tools of functional analysis, and it is shown that the minimizer is not unique. Our variational problem has a connection to the Michell problem in optimal design.     

Operational logics and the Hahn-Jordan property

The main result established in this paper is the following: If the base normed spaceV of completely additive weights is a norm-determining subspace of the space of finitely additive weights V acting on the order unit space spanning the operational logic, thenV has the -Jordan-Hahn property iff V has the approximate Jordan-Hahn property. Several examples illustrating the theory are given.Dedicated to the memory of Professor Charles H. Randall.     

The Predual of an Order-Unit Banach Space

We give a shortened and simplified proof of theknown theorem that a Banach space which is a predual ofan order-unit Banach space is a base-normedspace.     

The Hausdorff chirality measure and a proposed Hausdorff structure measure

The Hausdorff chirality measure quantifies the chirality of a geometric representation of an object by measuring the degree of coincidence of the object with its mirror image. It can also allow comparison between a chiral dopant and host molecules which may illuminate mechanisms for chirality transfer. It has been applied to real molecules very infrequently in comparison to application of chiral indices as it is complex and time consuming to calculate. In this paper we introduce and verify a simulated annealing algorithm for the Hausdorff chirality measure that has proven rapid, robust and relatively simple to apply. We verify the method, finding good agreement between its results and those of Mislow and co-workers. We introduce a Hausdorff structure measure that does not permit overlap and allows a structure to be built one molecule at a time. We present results for a simple model and real biphenyl molecules and discuss promising building blocks of crystal and incommensurate structures formed in relation to experimental results.