Supramolecular inclusion complexation of polyhedral oligomeric silsesquioxane capped poly(ε‐caprolactone) with α‐cyclodextrin

Supramolecular inclusion complexes (ICs) involving polyhedral oligomeric silsesquioxane (POSS) capped poly(?‐caprolactone) (PCL) and α‐cyclodextrin (α‐CD) were investigated. POSS‐terminated PCLs with various molecular weights were prepared via the ring‐opening polymerization of ?‐caprolactone (CL) with 3‐hydroxypropylheptaphenyl POSS as an initiator. Because of the presence of the bulky silsesquioxane terminal group, the inclusion complexation between α‐CD and the POSS‐capped PCL was carried out only with a single end of a PCL chain threading inside the cavity of α‐CD, which allowed the evaluation of the effect of the POSS terminal groups on the efficiency of the inclusion complexation. The X‐ray diffraction results indicated that the organic–inorganic ICs had a channel‐type crystalline structure. The stoichiometry of the organic–inorganic ICs was quite dependent on the molecular weights of the POSS‐capped PCLs. With moderate molecular weights of the POSS‐capped PCLs (e.g., M_n =3860 or 9880), the stoichiometry was 1:1 mol/mol (CL unit/α‐CD), which was close to the literature value based on the inclusion complexation of α‐CD with normal linear PCL chains with comparable molecular weights. When the PCL chains were shorter (e.g., for the POSS‐capped PCL of M_n = 1720 or 2490), the efficiency of the inclusion complexation decreased. The decreased efficiency of the inclusion complexation could be attributed to the lower mobility of the bulky POSS group, which restricted the motion of the PCL chain attached to the silsesquioxane cage. This effect was pronounced with the decreasing length of the PCL chains. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1247–1259, 2007     

A rapidly convergent five-point algorithm for univariate minimization

This paper presents an algorithm for minimizing a function of one variable which uses function, but not derivative, values at five-points to generate each iterate. It employs quadratic and polyhedral approximations together with a safeguard. The basic method without the safeguard exhibits a type of better than linear convergence for certain piecewise twice continuously differentiable functions. The safeguard guarantees convergence to a stationary point for very general functions and preserves the better than linear convergence of the basic method.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.Research sponsored by the Institut National de Recherche en Informatique et Automatique, Rocquencourt, France, and by the Air Force Office of Scientific Research, Air Force System Command, USAF, under Grant Number AFOSR-83-0210.Research sponsored, in part, by the Institut National de Recherche en Informatique et Automatique, Rocquencourt, France.     

Polymeric nanocomposites containing polyhedral oligomeric silsesquioxanes prepared via frontal polymerization

Frontal polymerization (FP) has been successfully applied, for the first time, to obtain polymeric nanocomposites containing polyhedral oligomeric silsesquioxanes (POSS) in an amine‐cured epoxy matrix. Variations of maximum temperature (T_max) and front velocity (V_f) have been studied. A comparison of these products with the corresponding materials, obtained by the classical batch polymerization technique, demonstrated that FP allows a higher degree of conversion than batch polymerization. The products have been characterized in terms of their thermal behavior with DSC analysis. SEM and X‐ray analyses revealed the morphology and the structures of the nanocomposites. The nanocomposites obtained by FP have the same characteristics of those synthesized, in much longer times, by batch polymerization. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4514–4521, 2007     

Lp-based combinatorial problem solving

A tutorial outline of the polyhedral theory that underlies linear programming (LP)-based combinatorial problem solving is given. Design aspects of a combinatorial problem solver are discussed in general terms. Three computational studies in combinatorial problem solving using the polyhedral theory developed in the past fifteen years are surveyed: one addresses the symmetric traveling salesman problem, another the optimal triangulation of input/output matrices, and the third the optimization of large-scale zero-one linear programming problems.     

A Nanocage for Nanomedicine: Polyhedral Oligomeric Silsesquioxane (POSS)

Ground‐breaking advances in nanomedicine (defined as the application of nanotechnology in medicine) have proposed novel therapeutics and diagnostics, which can potentially revolutionize current medical practice. Polyhedral oligomeric silsesquioxane (POSS) with a distinctive nanocage structure consisting of an inner inorganic framework of silicon and oxygen atoms, and an outer shell of organic functional groups is one of the most promising nanomaterials for medical applications. Enhanced biocompatibility and physicochemical (material bulk and surface) properties have resulted in the development of a wide range of nanocomposite POSS copolymers for biomedical applications, such as the development of biomedical devices, tissue engineering scaffolds, drug delivery systems, dental applications, and biological sensors. The application of POSS nanocomposites in combination with other nanostructures has also been investigated including silver nanoparticles and quantum dot nanocrystals. Chemical functionalization confers antimicrobial efficacy to POSS, and the use of polymer nanocomposites provides a biocompatible surface coating for quantum dot nanocrystals to enhance the efficacy of the materials for different biomedical and biotechnological applications. Interestingly, a family of POSS‐containing nanocomposite materials can be engineered either as completely non‐biodegradable materials or as biodegradable materials with tuneable degradation rates required for tissue engineering applications. These highly versatile POSS derivatives have created new horizons for the field of biomaterials research and beyond. Currently, the application of POSS‐containing polymers in various fields of nanomedicine is under intensive investigation with expectedly encouraging outcomes.

     

Volume fluctuations in potassium silicate glass studied by molecular dynamics

Potassium-silicate glass, 0.05K₂O·0.95SiO₂, was prepared by molecular dynamics under three different regimes (cooling rates, simulating box sizes) to study their influence to temperature regimes of volume fluctuations. Partial volume fluctuations (VF) were introduced with the help of Voronoi polyhedra tessellation. Dynamic and static fluctuations were suggested as a measure for time- and space-related fluctuations. Separation of the dynamic and static VFs anticipates glass transition. The glass transition was related with the change of the temperature course of the static VFs. The dynamic VFs changed their temperature regimes well below the glass transition and the transition temperature was related with the change of the transport regime. Glass transition cages the atoms but Voronoi polyhedra are definitely shaped well below the glass transition temperature.     

On the complete set packing and set partitioning polytopes: Properties and rank 1 facets

This paper studies two polytopes: the complete set packing and set partitioning polytopes, which are both associated with a binary $n$-row matrix having all possible columns. Cuts of rank 1 for the latter polytope play a central role in recent exact algorithms for many combinatorial problems, such as vehicle routing. We show the precise relation between the two polytopes studied, characterize the multipliers that induce rank 1 clique facets and give several families of multipliers that yield other facets.     

Grünbaum colorings of even triangulations on surfaces

A Grünbaum coloring of a triangulation G is a map c : such that for each face f of G, the three edges of the boundary walk of f are colored by three distinct colors. By Four Color Theorem, it is known that every triangulation on the sphere has a Grünbaum coloring. So, in this article, we investigate the question whether each even (i.e., Eulerian) triangulation on a surface with representativity at least r has a Grünbaum coloring. We prove that, regardless of the representativity, every even triangulation on a surface has a Grünbaum coloring as long as is the projective plane, the torus, or the Klein bottle, and we observe that the same holds for any surface with sufficiently large representativity. On the other hand, we construct even triangulations with no Grünbaum coloring and representativity , and 3 for all but finitely many surfaces. In dual terms, our results imply that no snark admits an even map on the projective plane, the torus, or the Klein bottle, and that all but finitely many surfaces admit an even map of a snark with representativity at least 3.