On the connection of the superposition and homogeneous-solutions methods in wave propagation problems in a semi-infinite rigidly-clamped elastic layer

The process of harmonic wave propagation is investigated in a semi-infinite rigidly-clamped elastic layer. An analytic solution of the problem is obtained by the superposition method. The wave field expansion in the form of a normal mode series for a corresponding infinite waveguide is established. According to residue theory, the explicit form of the expansion coefficients is established with physical requirements of the radiation conditions taken into account.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 3–10, 1988.     

Solution behavior of polyimide‐graft‐polystyrene copolymers in selective solvents

A polyimide‐graft‐polystyrene (PI‐g‐PS) copolymer with a polyimide backbone and polystyrene side chains was synthesized by the “grafting from” method using styrene polymerization on a polyimide multicenter macroinitiator via ATRP mechanism. The side chain grafting density z = 0.86 of PI‐g‐PS is rather high for graft‐copolymers synthesized by the ATRP method. Molecular characteristics and solution behavior of PI‐g‐PS were studied in selective solvents using light scattering and viscometry methods. In all solvents, the backbone tends to avoid contact with a poor solvent. To describe the conformation and hydrodynamic properties of PI‐g‐PS macromolecules in thermodynamically good solvents for side chains and PI‐g‐PS, the wormlike spherocylinder model is used. Macromolecules of the studied graft‐copolymer are characterized by high equilibrium rigidities (Kuhn segment length >20 nm). In Θ‐conditions, PI‐g‐PS macromolecules may be modeled by a rigid prolate ellipsoid of revolution with a low asymmetry form and a collapsed backbone as the ellipsoid core. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1539–1546     

Interpolymer complexes of poly(N-vinylpyrrolidone) with copolyimide-grafted side chains of poly(methacrylic acid)

The process of formation and structural organization of interpolymer complexes formed by macromolecules of poly(N-vinylpyrrolidone) and poly(methacrylic acid) chains grafted onto polyimide in solution is investigated via the method of polarized luminescence. A luminescent label of anthracene structure is covalently bound to both polymers. Relaxation times characterizing intramolecular mobility of each of the components in their interpolymer complex are measured in relation to the composition of the system.     

Conformations of molecular brushes based on polyimide and poly(methyl methacrylate) in selective solvents: Experiment and computer simulation

The effect of solvent quality with respect to main and side chains on the conformations of molecular brushes is investigated by the methods of molecular hydrodynamics and optics as well as by computer simulation. Copolymers with a polyimide backbone and poly(methyl methacrylate) side chains are studied in solvents featuring strongly different thermodynamic qualities (chloroform, ethyl acetate, and 3-heptanone). The studied samples have close total molecular masses and backbone lengths but differ in grafting densities and lengths of side chains: a brush with densely grafted and relatively short side chains versus a brush with loosely grafted but very long side chains. For both types of brushes, similar changes in hydrodynamic behavior with improvement in the solvent quality are found experimentally. Computer simulation shows that these changes have different origins. In the former case, macromolecules are elongated, and their volumes grow simultaneously, while in the latter case, the shape of the macromolecules remains close to spherical and the changes in hydrodynamic parameters are mainly due to an increase in the volume of macromolecules.     

Synthesis and investigation of the solution behavior of graft block copolymers of polyimide and poly(methyl methacrylate)

Graft copolymers with a polyimide backbone and poly(methyl methacrylate) side chains are investigated in dilute chloroform and ethyl acetate solutions via the methods of molecular hydrodynamics and optics. Copolymer samples are prepared through the “grafting from” method via atom-transfer radical polymerization with a multicenter polyimide macroinitiator. In solutions of copolymers with low degrees of functionalization Z (40%), supermolecular structures are formed as a result of interactions between the polyimide backbones. In samples with Z → 100%, the backbone is well screened by side chains; therefore, molecular solutions are formed in both solvents. The hydrodynamic and conformational behavior of samples with high functionalization degrees changes after the transition from ethyl acetate to chloroform owing to the different thermodynamic qualities of the solvents with respect to the copolymer components. In both solvents, the backbone tends to avoid contact with a poor solvent. This effect is more pronounced in the case of ethyl acetate. Macromolecules of the studied graft copolymers are characterized by high equilibrium rigidities (>40 nm) that are 10 times higher than the corresponding characteristics of aromatic polyimides.     

Synthesis of multicentered polyimide initiators for the preparation of regular graft copolymers via controlled radical polymerization

Multicentered initiators for the controlled (pseudoliving) radical polymerization are synthesized via polymer analog transformation of hydroxyl-containing polyimides based on o-aminophenols. Conditions providing variations in the degree of functionalization of polyimides by initiating 2-bromoisobutyrate groups are determined, and optimum conditions for the preparation of macroinitators containing the above groups in each repeat polyimide unit are found. Via the method of controlled radical polymerization with the atom transfer on multicentered macroinitiators in the presence of complexes of univalent copper halides, graft copolymers of poly(methylmethacrylate) on polyimide backbone are obtained. Molecular-mass characteristics of graft copolymers are studied via multiple-detection size-exclusion liquid chromatography. Preparation of graft copolymers (polymer brushes) with a homogeneous grafting density and a homogeneous length of side chains necessitates grafting of the side chain on the polyimide initiator, which contains initiating groups in each repeat unit.