Construction of a new family of Bernstein‐Kantorovich operators

In the present paper, we construct a new sequence of Bernstein‐Kantorovich operators depending on a parameter α. The uniform convergence of the operators and rate of convergence in local and global sense in terms of first‐ and second‐order modulus of continuity are studied. Some graphs and numerical results presenting the advantages of our construction are obtained. The last section is devoted to bivariate generalization of Bernstein‐Kantorovich operators and their approximation behaviors.     

A class of similarity solutions for radial motions of compressible hyperelastic spheres and cylinders

A class of similarity solutions is obtained for radial motions of spherical and cylindrical bodies made of a certain type of compressible hyperelastic materials. The equations satisfied by the infinitesimal generators of the symmetry group of the unified governing first order field equations for spheres and cylinders are found. It is shown that these equations admit a special class of solutions which generate a five-parameter group of transformations. The form of the strain energy function corresponding to the resulting symmetry group is evaluated. The similarity variable is determined and ordinary differential equations satisfied by similarity solutions are obtained. Numerical solutions are given for a Ko material which falls into the class of admissible materials.     

Synthesis and stability of BODIPY‐based fluorescent polymer brushes at different pHs

We report a simple strategy for the grafting of poly(methacrylic acid) [poly(MAA)] brushes from silicon substrate by surface‐initiated RAFT polymerization and the subsequent coupling of BODIPY to these brushes to render them fluorescent. The poly(MAA) brushes were first generated by functionalization of hydrogen‐terminated silicon substrate with methyl‐10‐undecenoate which both leads to the formation of an organic layer covalently linked to the surface via Si? C bonds without detectable reaction of the carboxylate groups and couples to the polymerization initiator, followed by surface‐initiated RAFT polymerization of tert‐butyl methacrylate from these substrate‐bound initiator centers, and finally conversion of tert‐butyl groups to carboxylic acid groups. The poly(MAA) brushes were then made fluorescent by grafting a BODIPY derivative via an ester linkage. The stability of the BODIPY‐based fluorescent polymer brushes in buffer solutions at pH 6.0 to 12.0 with added salt was investigated by ellipsometry, fluorescence microscopy, grazing angle‐Fourier transform infrared spectroscopy, X‐ray photoelectron spectroscopy. The results of these measurements indicated that the organic molecule‐initiator bond (ester linkage) is unstable and can be hydrolyzed resulting in detaching of the immobilized polymer from the silicon substrate. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3586–3596     

Modeling and simulation of the coupled mechanical-electrical response of soft solids

Dielectric elastomer (DE) is one type of electro-active polymers (EAP) that responds to electrical stimulation with a significant shape and size change. As EAPs, dielectric elastomers are lightweight, inexpensive, pliable and can be fabricated into various shapes, all of which are attractive properties to justify the intense research in the field. This paper presents a nonlinear, electrical and mechanical coupled, large deformation finite element formulation for DEAs. Maxwell’s equations for the electroquasistatic fields were solved simultaneously with equation of linear momentum. The hyperelastic Ogden model and total Maxwell stress method were combined to describe the material. The formulation was based on the weak forms of Maxwell’s equation and linear momentum expressed in the reference configuration. The closed form consistent tangent moduli for dielectric elastomers were derived. The results of the simulation compared with the experiments have demonstrated the validity of the method from the computational aspect.     

High density cationic polymer brushes from combined “click chemistry” and RAFT‐mediated polymerization

A simple method for preparing cationic poly[(ar‐vinylbenzyl)trimethylammonium chloride)] [poly(VBTAC)] brushes was used by combined technology of “click chemistry” and reversible addition‐fragmentation chain transfer (RAFT) polymerization. Initially, silicon surfaces were modified with RAFT chain transfer agent by using a click reaction involving an azide‐modified silicon wafer and alkyne‐terminated 4‐cyanopentanoic acid dithiobenzoate (CPAD). A series of poly(VBTAC) brushes on silicon surface with different molecular weights, thicknesses, and grafting densities were then synthesized by RAFT‐mediated polymerization from the surface immobilized CPAD. The immobilization of CPAD on the silicon wafer and the subsequent polymer formation were characterized by X‐ray photoelectron spectroscopy, water contact angle measurements, grazing angle‐Fourier transform infrared spectroscopy, atomic force microscopy, and ellipsometry analysis. The addition of free CPAD was required for the formation of well‐defined polymer brushes, which subsequently resulted in the presence of free polymer chains in solution. The free polymer chains were isolated and used to estimate the molecular weights and polydispersity index of chains attached to the surface. In addition, by varying the polymerization time, we were able to obtain poly(VBTAC) brushes with grafting density up to 0.78 chains/nm² with homogeneous distributions of apparent needle‐like structures. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012