Fully computable a posteriori error bounds for stabilised FEM approximations of convection–reaction–diffusion problems in three dimensions

Fully computable upper bounds are developed for the discretisation error measured in the natural (energy) norm for convection–reaction–diffusion problems in three dimensions. The upper bounds are genuine upper bounds in the sense that the numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem. All constants appearing in the bounds are fully specified. Examples show the estimator to be reliable and accurate even in the case of complicated three‐dimensional problems. Copyright © 2013 John Wiley & Sons, Ltd.     

The Covalent Functionalization of Graphene on Substrates

The utilization of grown or deposited graphene on solid substrates offers key benefits for functionalization processes, but especially to attain structures with a high level of control for electronics and “smart” materials. In this review, we will initially focus on the nature and properties of graphene on substrates, based on the method of preparation. We will then analyze the most relevant literature on the functionalization of graphene on substrates. In particular, we will comparatively discuss radical reactions, cycloadditions, halogenations, hydrogenations, and oxidations. We will especially address the question of how the reactivity of graphene is affected by its morphology (i.e., number of layers, defects, substrate, curvature, etc.).     

Nucleation,Crystallization, and Thermal Fractionation of Poly (ε‐Caprolactone)‐Grafted‐Lignin: Effects of Grafted Chains Length and Lignin Content

Poly(ε‐caprolactone)‐grafted‐lignin (PCL‐g‐lignin) copolymers with 2 to 37 wt % lignin are employed to study the effect of lignin on the morphology, nucleation, and crystallization kinetics of PCL. Lignin displays a nucleating action on PCL chains originating an intersecting lamellar morphology. Lignin is an excellent nucleating agent for PCL at low contents (2–5 wt %) with nucleation efficiency values that are close to or >100%. This nucleating effect increases the crystallization and melting temperature of PCL under nonisothermal conditions and accelerates the overall isothermal crystallization rate of PCL. At lignin contents >18 wt %, antinucleation effects appear, that decrease crystallization and melting temperatures, reduce crystallinity degree, hinder annealing during thermal fractionation and significantly retard isothermal crystallization kinetics. The results can be explained by a competition between nucleating effects and intermolecular interactions caused by hydrogen bonding between PCL and lignin building blocks. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1736–1750     

The influence of short‐chain branching on the morphology and structure of polyethylene single crystals

The influence of short‐chain branching on the formation of single crystals at constant supercooling is systematically studied in a series of metallocene catalyzed high‐molecular‐weight polyethylene samples. A strong effect of short‐chain branching on the morphology and structure of single crystals is reported. An increase of the axial ratio with short‐chain branching content, together with a characteristic curvature of the (110) crystal faces are observed. To the best of our knowledge, this is the first time that this observation is reported in high‐molecular‐weight polyethylene. The curvature can be explained by a continuous increase in the step initiation—step propagation rates ratio with short‐chain branching, that is, nucleation events are favored against stem propagation by the presence of chain defects. Micro‐diffraction and WAXS results clearly indicate that all samples crystallize in the orthorhombic form. An increase of the unit cell parameter a₀ is detected, an effect that is more pronounced than in the case of single crystals with ethyl and propyl branches. The changes observed are compatible with an expanded lattice due to the presence of branches at the surface folding. A decrease in crystal thickness with branching content is observed as determined from shadow measurements by TEM. The results are in agreement with additional SAXS results performed in single crystal mats and with indirect calorimetry measurements. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1751–1762