Application of the variational-moment approach to problems of the theory of elasticity of shells

We consider a method of obtaining an approximate system of equations of elasticity theory for shells, based on representing the components of the stress tensor and the displacement vector as a sum of products of moment characteristics depending on the coordinates of the base surface of the shell and functions of the normal coordinate to the base surface.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 56–59.     

Highly Recyclable and Tough Elastic Vitrimers from a Defined Polydimethylsiloxane Network

Despite intensive research on sustainable elastomers, achieving elastic vitrimers with significantly improved mechanical properties and recyclability remains a scientific challenge. Herein, inspired by the classical elasticity theory, we present a design principle for ultra-tough and highly recyclable elastic vitrimers with a defined network constructed by chemically crosslinking the pre-synthesized disulfide-containing polydimethylsiloxane (PDMS) chains with tetra-arm polyethylene glycol (PEG). The defined network is achieved by the reduced dangling short chains and the relatively uniform molecular weight of network strands. Such elastic vitrimers with the defined network, i.e., PDMS-disulfide-D, exhibit significantly improved mechanical performance than random analogous, previously reported PDMS vitrimers, and even commercial silicone-based thermosets. Moreover, unlike the vitrimers with random network that show obvious loss in mechanical properties after recycling, those with the defined network enable excellent thermal recyclability. The PDMS-disulfide-D also deliver comparable electrochemical signals if utilized as substrates for electromyography sensors after the recycling. The multiple relaxation processes are revealed via a unique physical approach. Multiple techniques are also applied to unravel the microscopic mechanism of the excellent mechanical performance and recyclability of such defined network.     

Chemical interaction of CdTe and Cd1? x Zn x single crystals with aqueous H2O2 + HBr + Citric acid solutions

The chemical etching of single crystals of CdTe and Cd_1−x Zn _x Te solid solutions in bromine-evolving aqueous H₂O₂ + HBr + citric acid solutions is considered. Simplex design of experiments is used to construct the projections of etching rate isosurfaces and to map the polishing and nonpolishing composition regions. Dissolution in the polishing etchants is diffusion-controlled. As the zinc content of Cd_1−x Zn _x Te is raised, the etching rate increases; the boundaries of the polishing region do not change to any significant extent. The polish composition and the dynamic chemical polishing conditions are optimized for the semiconductors examined. Original Russian Text ? Z.F. Tomashik, I.I. Gnativ, V.N. Tomashik, I.B. Stratiichuk, 2007, published in Zhurnal Neorganicheskoi Khimii, 2007, Vol. 52, No. 7, pp. 1234–1238.     

Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations

The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with f=4 arms in a Θ -solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with N=300 , 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries.     

Chemical etching of CdxHg1-x Te single crystals in bromine-releasing aqueous H2O2-HBr-solvent solutions

The nature and mechanism of dissolution of single crystals of a Cd_0.21Hg_0.79Te solid solution in H₂O₂-HBr-solvent bromine-releasing aqueous solutions were determined, with water, ethylene glycol, and tartaric, citric, and lactic acids used as solvents. Projections of the surfaces of equal etching rates were constructed and the concentration limits were found for solutions that can be used for chemical-dynamical polishing of the surface of Cd_0.21Hg_0.79Te single crystals.     

Generalized three-point difference schemes of high-order accuracy for systems of second-order nonlinear ordinary differential equations

For systems of second-order nonlinear ordinary differential equations with the Dirichlet boundary conditions, we develop generalized three-point difference schemes of high-order accuracy on a nonuniform grid. The construction of the suggested schemes requires solving four auxiliary Cauchy problems (two problems for systems of nonlinear ordinary differential equations and two problems for matrix linear ordinary differential equations) on the intervals [x _j−1, x _j ] (forward) and [x _j , x _j+1] (backward) at each grid point; this is done at each step by any single-step method of accuracy order $ \bar m $ \bar m = 2[(m+1)/2]. (Here m is a given positive integer, and [·] is the integer part of a number.) We prove that such three-point difference schemes have the accuracy order $ \bar m $ \bar m for the approximation to both the solution u of the boundary value problem and the flux K(x)d u/dx at the grid points.     

Generalized three-point difference schemes of high order of accuracy for nonlinear ordinary differential equations of the second order

For nonlinear ordinary differential equations of the second order with a derivative on the right-hand side and boundary conditions of the first kind, we construct and justify generalized three-point difference schemes of high order of accuracy on a nonuniform mesh. The existence and uniqueness of their solutions are proved, and an a priori estimate of the accuracy is obtained.     

Cooligomerization of dominant monomers of C9 fraction of liquid pyrolysis products: comparison of heterogeneous catalytic approach with common methods

Cooligomerization of liquid products of the C9 fraction of diesel fuel pyrolysis to produce cooligomers of wide application is suggested to be carried out with silica-alumina catalysts, among which the activated bentonite clay seems to be optimal. Cooligomerization of the mixture simulating the C₉ fraction composition was studied to compare the suggested heterogeneous catalytic method with other methods of cooligomers production. Different methods have been compared in terms of yield of cooligomers and their properties, namely molecular weight and its distribution, density, unsaturation and colour. The ratio of monomer units in cooligomer has been determined and the monomers conversion degrees have been calculated for different cooligomerization methods. Reasons of structure and composition differences of cooligomers obtained by different methods are suggested.      

The stressed state of a cylindrical shell with a circular neck loaded by internal pressure

We study the stressed state of a thin cylindrical shell with a circular neck loaded by a constant internal pressure. We start from the equations obtained using Reissner's variational principle applying expansions of the components of the stress tensor and the displacement vector with respect to the coordinates along the normal to the base surface of the shell. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Effect of Fatty Acid Polyunsaturation on Synthesis and Properties of Emulsion Polymers Based on Plant Oil-Based Acrylic Monomers

This study demonstrated that polymerization behavior of plant oil-based acrylic monomers (POBMs) synthesized in one-step transesterification reaction from naturally rich in oleic acid olive, canola, and high-oleic soybean oils is associated with a varying mass fraction of polyunsaturated fatty acid fragments (linoleic (C18:2) and linolenic (C18:3) acid esters) in plant oil. Using miniemulsion polymerization, a range of stable copolymer latexes was synthesized from 60 wt.% of each POBM and styrene to determine the impact of POBM chemical composition (polyunsaturation) on thermal and mechanical properties of the resulted polymeric materials. The unique composition of each plant oil serves as an experimental tool to determine the effect of polyunsaturated fatty acid fragments on POBM polymerization behavior and thermomechanical properties of crosslinked films made from POBM-based latexes. The obtained results show that increasing polyunsaturation in the copolymers results in an enhanced crosslink density of the latex polymer network which essentially impacts the mechanical properties of the films (both Young’s modulus and toughness). Maximum toughness was observed for crosslinked latex films made from 50 wt.% of each POBM in the monomer feed.