Glasses-shaped triblock copolymer prepared by combination of atom transfer radical polymerization and ring opening polymerization

A glasses-shaped triblock copolymer of poly(ε-caprolactone)-b-polystyrene-b-poly(ε-caprolactone) (PCL-b-PS-b-PCL) is prepared by combining atom transfer radical polymerization (ATRP) and ring opening polymerization (ROP). Polystyrene (PS) star polymers are prepared via ATRP using a tetra-functional initiator, followed by azidation to yield azide end-functionalized star polymers. An alkyne-functionalized coupling agent, 2,2-bis[(2-propyn-1-yloxy)methyl]-1-propanol is employed to produce hydroxy 8-shaped PS via copper(I)-catalyzed alkyne-azide cycloaddition. Herein, hydroxy 8-shaped PS with high purity is obtained through preparative size exclusion chromatography (Prep SEC) and high-performance liquid chromatography, followed by the characterizations using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS), size exclusion chromatography (SEC), infrared, and proton nuclear magnetic resonance (¹H NMR) spectroscopy. The hydroxy groups of the 8-shaped PS are utilized as initiators for the ROP of ε-caprolactone to obtain linear chains attached to the 8-shaped architecture. After SEC fractionation, the glasses-shaped triblock copolymer is characterized using ¹H NMR and SEC. This unprecedented topology possesses two free chain-ends and two cycles; thus, both the properties of linear and cyclic polymers may be expected to be observed.     

An efficient three-dimensional adaptive quasicontinuum method using variable-node elements

A new quasicontinuum (QC) implementation using the so-called “variable-node finite elements” is reported in this work. Tetrahedral elements, which have been exclusively utilized for the conventional QC are replaced by hexahedral elements in conjunction with the so-called variable-node elements. This enables an effective adaptive mesh refinement in QC, leading to fast and efficient simulations compared with the conventional QC. To confirm the solution accuracy, comparison is made for a nanoindentation problem with a molecular dynamics simulation as well as a molecular mechanics solution. Further examples of nanoindentation are shown and discussed to demonstrate the effectiveness of the present scheme.     

Derivation of a Darcy’s Law for a Porous Medium Composed of Two Solid Phases Saturated by a Single- Phase Fluid: A Homogenization Approach

The objective of this article is to derive a macroscopic Darcy’s law for a fluid-saturated moving porous medium whose matrix is composed of two solid phases which are not in direct contact with each other (weakly coupled solid phases). An example of this composite medium is the case of a solid matrix, unfrozen water, and an ice matrix within the pore space. The macroscopic equations for this type of saturated porous material are obtained using two-space homogenization techniques from microscopic periodic structures. The pore size is assumed to be small compared to the macroscopic scale under consideration. At the microscopic scale the two weakly coupled solids are described by the linear elastic equations, and the fluid by the linearized Navier–Stokes equations with appropriate boundary conditions at the solid–fluid interfaces. The derived Darcy’s law contains three permeability tensors whose properties are analyzed. Also, a formal relation with a previous macroscopic fluid flow equation obtained using a phenomenological approach is given. Moreover, a constructive proof of the existence of the three permeability tensors allows for their explicit computation employing finite elements or analogous numerical procedures.     

A cell boundary element method for elliptic problems

An elementary analysis on the cell boundary element (CBEM) was given by Jeon and Sheen. In this article we improve the previous results in various aspects. First of all, stability and convergence analysis on the rectangular grids are established. Moreover, error estimates are improved. Our improved analysis was possible by recasting of the CBEM in a Petrov‐Galerkin setting. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

A new quadratic nonconforming finite element on rectangles

A new quadratic nonconforming finite element on rectangles (or parallelograms) is introduced. The nonconforming element consists of P₂ ⊕ Span{x²y,xy²} on a rectangle and eight degrees of freedom. Our element is essentially of seven degrees of freedom since the degree of freedom associated with the integration on rectangle is essentially of bubble‐function nature. Global basis functions are constructed for both Dirichlet and Neumann type of problems; accordingly the corresponding dimensions are counted. The local and global interpolation operators are defined. Error estimates of optimal order are derived in both broken energy and L²(Ω) norms for second‐order of elliptic problems. Brief numerical results are also shown to confirm the optimality of the presented quadratic nonconforming element. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Microporous manganese formate: a simple metal-organic porous material with high framework stability and highly selective gas sorption properties

Novel microporous metal-organic framework material composed of Mn(II) and formate ions displays permanent porosity, high thermal stability, and size-selective gas sorption behavior. The framework is stable enough to maintain single crystallinity after the complete guest removal at 150 degrees C under a reduced pressure. Most importantly, it selectively adsorbs H2 and CO2 but not N2 and other gases with larger kinetic diameters, which appears to be due to the small aperture of the channels. Despite a moderate H2 storage capacity, which is however still higher than that of any zeolite, its H2 surface coverage is one of the highest among the known microporous materials. Thus this new zeolite-like material made of a simple organic building block may find useful applications in gas separation and sensor.