Correlation of the elastic characteristics of Arimid PM with the elasticity modulus of its crystal lattice

Studies were made of the elastic characteristics (longitudinal elasticity modulus, elastic recovery) of Arimid PM fibers and of the longitudinal elasticity modulus of the crystal lattice of these samples. The elasticity modulus of the crystallites was determined by x-ray diffraction studies of loaded fibers. It is shown that the studied samples practically instanteneously recover their starting length after removing the load; the sample and its crystal lattice have comparatively low elasticity moduli with nearly identical values. Based on this data, reasons are discussed for the high elastic recovery of Arimid fibers and for the low elasticity modulus of its crystal lattice.Leningrad Branch, All-Union Scientific-Research Institute of Synthetic Fibers. Translated from Mekhanika Polimerov, No. 5, pp. 771–773, September–October, 1972.     

Elasticity of the crystal lattice of polyethylene terephthalate

The elasticity of the crystal lattice of polyethylene terephthalate was studied along and across the axes of the polymer molecules. The elastic modulus across the chains depended on the degree of crystallinity and the interplane distances in the directions of thea and b parameters of the unit cell. The nature of the elastic deformation in the crystal lattice was analyzed, and its elastic modulus along and across the axes of the chains was calculated. On loading biaxially oriented amorphous-crystalline polymers with a tensile stress applied in the direction of one of the orientation axes of the polymer, the stresses in the crystallites oriented along and across the external applied force and the amorphous regions in series with them were equal to the stress in the sample averaged over the cross section.Deceased.Translated from Mekhanika Polimerov, No. 6, pp. 982–986, November–December, 1972.     

Terminal defects in crystalline polyethylene

Conclusions 1. It was shown that the terminal defect in polyethylene contains a set of partial twist disclinations with different Frank vectors for different chains.2. It was found that the structure of the terminal defect changes during elongation of the chain and outward from the crystallite. It was also found that the volume of the void formed by the presence of the chain and remains constant; the elongation process is accompanied by a conservative motion of the disclination loops along the chains, which causes creep of the screw dislocations.3. The conformational changes were calculated for a segment moving in the crystal field of neighboring chains in regular and high-pressure PE; the values of the energy of activation of the chain and motion were obtained (10.3·10^–16 and 3.6·10^–16 erg/monomer for the regular and high-pressure PE, respectively), indicating a higher rate of annealing of PE in the high-pressure phase.For communication II, see [2].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 793–798, September–October, 1978.     

The Coordinate of the Singular Point of Generating Functions of Clusters in the High-Temperature Dynamics of Spin Lattice Systems with Axially Symmetric Interaction

We investigate generating functions for equipped trees composed of double bonds of two sorts on a hypercubic lattice of dimension d with built-in fragments. Rules for constructing these clusters are chosen to ensure the estimate for coefficients of power series in time for the longitudinal and transverse autocorrelation functions of the spin system with axially symmetric interaction. We derive a system of two equations for the tree-generating functions and an equation for the generating functions of chains leading from the root to a fragment in a tree using the Bethe approximation and under the condition that mainly bonds of one sort are taken into account. For the face-centered hypercubic lattice, we find the first terms of the 1/d expansion for the coordinate of the singular point of the generating function in both the anisotropic and the isotropic cases taking fragments in the forms of a triangle from four bonds and a four-fold bound pair into account. The obtained result is written in terms of ratios of lattice sums and is generalized to nuclear spin systems with dipole–dipole interaction. The theoretical value of the singular-point coordinate agrees well with the experimental value calculated from the tail of the absorption spectrum of the nuclear magnetic resonance in a barium fluoride monocrystal.     

Plastic deformation of models of a crystalline polymer with increased lattice defectivity

Conclusions 1. On the basis of two-dimensional models, the structure of a polymeric crystal containing more than one lattice defect has been determined on an electronic computer. The types of defects are: a) double vacancy, model I; b) two isolated vacancies, model II; c) a combination of isolated vacancies and double vacancies, model III. Plastic deformation curves have been calculated for all three models.2. It has been observed that increase in the degree of defectivity in a crystalline polymer significantly reduces the elastic limit and reduces the strength limit of the structure very little. The elastic limit falls particularly strongly with increase of the defectivity in a state of hydrostatic stress.3. Increase in the density of crystallographic defects causes significant mutual rearrangement of the coordination polygons of the crystal lattice, which occurs as the result of plastic deformation.Report presented at the Third All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1976.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 397–402, May–June, 1977.     

End defects in crystalline polyethylene. 1. Statement of the problem and modeling of the steric structure of end defects

Conclusions 1. Changes in the conformations of polyethylene molecules around the end of a neighboring chain and around the ends of two neighboring chains have been determined on an electronic calculator for various directions of end bending.2. It has been ascertained that a column of bivacancies disappears with simultaneous formation of spiral dislocations at smaller distances from the chain end to the crystallite surface than in the case of a single-vacancy column.3. Energies of formation of end defects and the bonding energy of defects upon aggregation have been calculated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 400–407, May–June, 1978.     

Limit distribution function of inhomogeneities in regions with random boundary. II

A system of charged particles and inhomogeneities randomly distributed in accordance with the same law in the neighborhoods of corresponding sites of a planar crystal lattice is investigated. The limit distribution function of the inhomogeneities is determined.Institute of Nuclear Physics, Uzbek Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 84–97, January, 1993.     

Mechanics of a polymer chain stretched in an amorphous region of an amorphous-crystalline polymer. Effect of external crystal boundaries

The tensile load on a polymer chain extending across an amorphous region of an amorphous-crystalline polymer, from one crystal to another, has been calculated theoretically. The analysis is carried out for the case of large extensions of the amorphous region, when it is necessary to take into account the conditions of anchorage of the chain at the external boundaries of the crystals. A rigorous criterion has been established for the applicability of an earlier theory [1] in which the external boundaries were not taken into consideration. It is concluded that the critical load on the chains cannot be reached in that model in the range of deformations of the amorphous region studied. It is noted that the expression for the displacement of the chain segments is a solution of the Frenkel-Kontorov model of a point dislocation in a crystal with a boundary.Mekhanika Polimerov, Vol. 2, No. 5, pp. 664–670, 1966     

Structural changes in a cotton fiber under load

Mechanical tests and x-ray studies have shown that a shift of the meridional reflection towards smaller angles signifies the stretching of the crystallite lattice in the meridional direction. The shift has been used to determine the modulus of elasticity of the crystal lattice of cotton. The microdeformation (of the crystal lattice) and the macrodeformation (extension of the specimen as a whole) are compared. The modulus of elasticity of the crystal lattice is an order greater than that of the fiber itself.V. I. Lenin Tadzhik State University, Dushanbe. Translated from Mekhanika Polimerov, No. 4, pp. 594–598, July–August, 1973.     

Surface forces in model hexagonal and cubic planar structures

Conclusions 1. Perturbation in the structure of the surface layer of hexagonal and cubic crystal structures produces attraction between the surface particles.2. The surface tension of a fiber depends qualitatively on the surface interaction forces. The nature of these forces is determined by the peculiarities of the microstructures, surface expansion of the lattice, microdefects, and perturbations on the surface.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 799–801, September–October, 1978.     

Lattice transformation in a polymer crystal model with defect

With the help of a computer, the transformation curves of the lattice force, i.e., the degree of stretching, have been calculated at different values of compressive forces for the hexagonal model of a polymer crystal having a vacancy at the center. The configurations of the system of particles of this model in the positions of stable and unstable equilibrium have been determined.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 992–997, November–December, 1974.     

Incomparability and Intersection Properties of Boolean Interval Lattices and Chain Posets

In a canonical way, we establish an AZ-identity (see [2]) and its consequences, the LYM-inequality and the Sperner property, for the Boolean interval lattice. Furthermore, the Bollobas inequality for the Boolean interval lattice turns out to be just the LYM-inequality for the Boolean lattice. We also present an Intersection Theorem for this lattice.Perhaps more surprising is that by our approach the conjecture of P. L. Erdöset al.[7] and Z. Füredi concerning an Erdös–Ko–Rado-type intersection property for the poset of Boolean chains could also be established. In fact, we give two seemingly elegant proofs.     

A molecular model of creep and stress relaxation in crystalline polymers

A possible model of defect formation in a polymer crystal lattice is considered. The results of an investigation of creep and stress relaxation in crystalline polymers are interpreted on the basis of the model proposed.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 6, pp. 969–975, November–December, 1971.     

Crown-free Lattices and Their Related Graphs

This paper investigates links between some classes of graphs and some classes of lattices. We show that a co-atomic lattice is crown-free (i.e. dismantlable) if and only if it is a maximal clique lattice of a strongly chordal graph. We also prove that each crown-free lattice that is not a chain contains at least two incomparable doubly-irreducible elements x ₁ and x ₂ such that ↑ x ₁ and ↑ x ₂ are chains.     

Evidence for a Phase Transition in Three-Dimensional Lattice Models

It was recently discovered that an eigenvector structure of commutative families of layer-to-layer matrices in three-dimensional lattice models is described by a two-dimensional spin lattice generalizing the notion of one-dimensional spin chains. We conjecture the relations between the two-dimensional spin lattice in the thermodynamic limit and the phase structure of three-dimensional lattice models. We consider two simplest cases: the homogeneous spin lattice related to the Zamolodchikov–Bazhanov–Baxter model and a chess spin lattice related to the Stroganov–Mangazeev elliptic solution of the modified tetrahedron equation. Evidence for the phase transition is obtained in the second case.     

Effect of uv irradiation on the mobility of the molecular chains in polyethylene

Conclusions 1. A decrease in the mobility of molecular chains in polyethylene after UV irradiation was discovered by the spin probe method. This decrease is proportional to the time of irradiation.2. A discontinuity lacking in unirradiated polyethylene was found on the curve for the logarithm of the rotational correlation time of the spin probe in polyethylene as a function of the inverse temperature. It was shown that the nature of the discontinuity is related to a "thawing out" of the rotational motion of the chains in the crystalline phase.Institute of the Mechanics of Metal-Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel. Translated from Mekhanika Polimerov, No. 4, pp. 603–608, July–August, 1976.     

Semimodular compact groups

A study of compact groups in which the lattice of all closed subgroups satisfies one of the following requirements: the Jordan-Dedekind condition for chains; semimodularity below; the same plus the existence of complements; the same plus the existence of relative complements —is presented.Translated from Matematicheskie Zametki, Vol. 3, No. 5, pp. 503–510, May, 1968.     

Effect of certain factors on the vibrations of polymers

The authors' work on the effect of various factors on the vibrations of the polymer chain is reviewed. A method of calculating chain vibrations is briefly described, an expression is given for the strain energy of a polymer molecule in the nonlinear approximation, the frequency shift of the vibrations of a molecule under load is calculated and discussed, the effect of intermolecular interaction in the polymer crystal and the disorder of the chain on the vibration spectrum is taken into account, and the change in the intensity of the normal vibrations when the chain is loaded and the effect of anharmonicity on the band width are investigated. In conclusion, the stress distribution over the interatomic bonds is estimated.A. F. Ioffe Physico-Technical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 33–46, January–February, 1975.     

Master symmetries for Volterra equation, Belov–Chaltikian and Blaszak–Marciniak lattice equations

It is shown how to derive master symmetries for nonlinear lattice equations systematically using the basic principles but without using either their zero curvature equations or the bi-Hamiltonian structure. This has been illustrated for Volterra equation, two coupled Belov–Chaltikian (BC), and three coupled Blaszak–Marciniak (BM) lattice equations. The existence of a sequence of master symmetries is one of the characteristics of completely integrable nonlinear partial differential and differential–difference equations admitting Hamiltonian structure.     

Computer approximation of families of curves of physically nonlinear creep of polymer materials

The determination of confidence intervals of deformations was studied for an individual measurement and arithmetical mean common for all points of an experimental family of curves. From the experimental data on the creep of polyamide resin and five different analytical equations of physically nonlinear creep, the problems of the computer approximation of families of creep curves and the determination of the material parameters are discussed. A method is proposed for a quantitative evaluation of the degree of correspondence of the initial data to the similarity of isochronous creep curves and the similarity of the creep curves.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 220–229, March–April, 1976.