On the Representation of the Stored Energy for Elastic Materials with Full Transverse Response-Symmetry

We solve the representation problem for the stored energy of both transversely-isotropic and transversely-hemitropic elastic materials. Our method is based on giving the problem a form allowing application of a modified version of the classical representation theorem by Cauchy for scalar-valued mappings over the Nth power of a vector space. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effect of blend composition on diffusivity and solubility of small molecules in polystyrene/poly(vinyl methyl ether) blends

The capillary column inverse gas chromatography technique was used to determine diffusivity and solubility data for several solvents in polymer blends composed of polystyrene and poly(vinyl methyl ether) (PVME). Diffusivity behaved as expected, increasing as the concentration of PVME increased in the blend. Knowing only the free‐volume parameters for the pure polymers, the free‐volume theory was successfully applied to predict the dependence of the diffusion coefficients on the blend composition. Transport in blends above the glass transition temperature is controlled by free volume, and the effect of concentration fluctuations is minimal at the temperatures studied. Experimental data show an increase in the partition coefficient of some solvents in the blends with respect to the pure polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2071–2082, 2007     

On vector-valued curves that allow a C 1,α parametrization

Let X be a Banach space and α ∈ (0, 1]. We find equivalent conditions for a function f: [0,1] → X to admit an equivalent parametrization, which is C ^1,α (i.e., has α-Hölder derivative). For X = ?, a characterization is well-known. However, even in the case X = ?² several new ideas are needed.     

A qualitative approach to adsorption mechanism identification on microporous carbonaceous surfaces

The paper presents results of research on identification of localized and other adsorption mechanisms, on geometrically heterogeneous graphite-like carbonaceous surfaces. It attempts to get an insight into properties of individual adsorptive molecule movement near attractive adsorption sites, arising from adsorbent surface geometrical heterogeneities. In particular, a shape and volume of space occupied by the continuously moving molecule mass center are investigated. To this aim, kinematic equilibrium of the particle moving near a hypothetical microporous carbonaceous adsorbent wall is considered, and then compared with thermodynamic equilibrium. The proposed approach enables to examine effects of certain surface geometry on the shape and volume of space occupied by adsorbed particles, and so to outline temperature conditions for the localized adsorption mechanism predomination. Thus, it provides a cognitive basis to answer the question, what particular mechanism (localized or other—e.g. mobile) should be assumed for a class of adsorption systems in order to select the most appropriate mathematical adsorption model. Hence, it makes it possible for more reliable examination of real porous structures, based on adsorption measurements.     

Cationic copolymerization of racemic‐β‐butyrolactone with L,L‐lactide: One‐pot synthesis of block copolymers

Cationic copolymerization of racemic‐β‐butyrolactone (β‐BL) with l,l ‐lactide (LA) initiated by alcohol and catalyzed by trifluoromethanesulfonic acid proceeding by activated monomer (AM) mechanism was investigated. Although both comonomers were present from the beginning in the reaction mixture, polymerization proceeded in sequential manner, with poly‐BL formed at the first stage acting as a macroinitiator for the subsequent polymerization of LA. Such course of copolymerization was confirmed by following the consumption of both comonomers throughout the process as well as by observing the changes of growing chain‐end structure using ¹H NMR. ¹³C NMR analysis and thermogravimetry revealed the block structure of resulting copolymers. The proposed mechanism of copolymerization was confirmed by the studies of changes of ¹H NMR chemical shift of acidic proton in the course of copolymerization, providing an indication that indeed protonated species and hydroxyl groups are present throughout the process, as required for AM mechanism. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4873–4884     

Curves with finite turn

In this paper we study the notions of finite turn of a curve and finite turn of tangents of a curve. We generalize the theory (previously developed by Alexandrov, Pogorelov, and Reshetnyak) of angular turn in Euclidean spaces to curves with values in arbitrary Banach spaces. In particular, we manage to prove the equality of angular turn and angular turn of tangents in Hilbert spaces. One of the implications was only proved in the finite dimensional context previously, and equivalence of finiteness of turn with finiteness of turn of tangents in arbitrary Banach spaces. We also develop an auxiliary theory of one-sidedly smooth curves with values in Banach spaces. We use analytic language and methods to provide analogues of angular theorems. In some cases our approach yields stronger results (for example Corollary 5.12 concerning the permanent properties of curves with finite turn) than those that were proved previously with geometric methods in Euclidean spaces. The author was partially supported by the grant GAČR 201/03/0931 and by the NSF grant DMS-0244515.     

On the new procedure for the determination of surface conditions in thin films with internal layer inhomogeneity

A method for determining the surface conditions on both surfaces of the film, based in the thickness dependence of localized states is proposed.     

Ordering of hexagonal layers in phase β- and β′-Mg2Al3

Two phases, β and β′, in Mg₂Al₃ have been compared. Structural rod-like domains composed of sets of hexagonal layers have been described. The main set containing 11 layers does not change during β′–β transformation. The short sequences of layers on the β′ phase transform into clusters in the β-phase. The centres of the domains form a superstructure with a modulation vector equal to 3/22.