On the theory of biaxial orientation of amorphous polymers

The macromolecule orientation distribution function for biaxial orientation is calculated on the basis of a network model of a linear amorphous polymer. The dependence of the distribution function on the biaxial stretch ratio, orientation temperature, and certain other factors is investigated. A relation is established between the distribution function and the experimentally observed birefringence. The birefringence of biaxially oriented polymethyl methacrylate is measured in relation to the degree of deformation. The experimental data are compared with theory.Moscow Lenin State Pedagogical Institute, Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, No. 5, pp. 771–779, September–October, 1970.     

Biaxial orientation of amorphous linear polymers

The mechanical properties of biaxially oriented polymethyl methacrylate, obtained on a broad range of stretch ratios and under a variety of orientation conditions, have been investigated. There is a fundamental difference between the variation of the forced elastic limit with increase in stretch ratio, which is monotone increasing, and the variation of such properties as the brittle strength, brittle temperature, true strength and elongation at break, which have an optimum at a certain stretch ratio. It is shown that the presence of an optimum is associated with the transformation of the supermolecular structures in the process of biaxial high-elastic deformation. A relation is established between the mechanical properties of biaxially oriented polymethyl methacrylate (orientation hardening) and the density of the molecular network.For communication 1 see [3].Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 586–593, July–August, 1971.     

Biaxial orientation of amorphous linear polymers

The dependence of the birefringence and orientation stress on the biaxial stretch ratio and orientation conditions has been experimentally investigated. The temperature dependence of these characteristics is explained in terms of the network structure of amorphous polymers. It is shown that the transformations of the supermolecular structures in the process of biaxial orientation depend on the orientation temperature — at higher temperatures better organized structures are formed. There is a formal relationship between the effect of orientation temperature on supermolecular structure formation and on the relaxation process responsible for the formation of a more thermally stable molecular network.Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 17–23, January–February, 1971.     

The theory of orientational drawing of linear amorphous polymers

On the basis of modern ideas on the structure of linear, amorphous polymers a model of a molecular, three-dimensional network with temporary cross-links and van der Waals interaction between the chains is presented. Using this model as a starting point, a differential equation for the deformation of a linear, amorphous polymer in the viscoelastic state is derived. The differential equation for the orientation of a linear, amorphous polymer, which describes the evolution of distribution functions for statistical segments, is obtained. Previously obtained results follow from this theory as special cases.V. I. Lenin State Pedagogic Institute, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1021–1028, November–December, 1974.     

On the theory of infrared dichroism of oriented amorphous polymers

A network model of a linear amorphous polymer is used as a basis for calculating the infrared dichroism of uniaxially and biaxially oriented material. The dependence of the dichroism on the uniaxial and biaxial stretch ratios, orientation temperature, and certain other factors is investigated. Previously published experimental data are discussed.Moscow Lenin State Pedagogical Institute, Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, No. 6, pp. 979–984, November–December, 1970.     

Reversibility of the orientation effect in linear polymers

It is established that the orientation effect in polymethylmethacrylate, assessed from the alteration in its properties, does not completely vanish after stabilization of the volume of the polymer during heating. A comparative evaluation of the physicomechanical properties in the unoriented, oriented, and oriented-and-restored states of the polymer indicates that some traces of orientation are retained.Lenin Kom somol Riga Institute of Civil-Aviation Engineers. Translated from Mekhanika Polimerov, No. 5, pp. 830–834, September–October, 1973.     

Thermomechanical method for determining the molecular weights of amorphous linear polymers

A thermomechanical investigation of polyisobutylene specimens under various time and stress conditions enabled us to extend the applicability of this method of determining the molecular weight of an undissolved polymer. The previously proposed mechanical model of a polymer, which is the basis of the relationship between the molecular weight of the polymer and the difference between the yield and glass-transition temperatures, must be refined to make allowance for the supramolecular structure.Mekhanika Polimerov, Vol. 3, No. 4, pp. 586–590, 1967     

Strength properties of oriented amorphous linear polymers in relation to their structure

Tensile tests have been conducted at room temperature on uniaxially oriented films of a number of amorphous linear polymers. It has been shown that the mechanical properties of the oriented polymers in the glassy state are chiefly determined by two parameters of the structure—the degree of orientation of the macromolecule segments and the concentration of stressed chains per unit volume, irrespective of the molecular weight of the polymer and the orientational stretching conditions.Mekhanika Polimerov, Vol. 3, No. 3, pp. 455–460, 1967     

Effect of physicalstate on tearing of filled systems based on linear amorphous polymers

A study has been made of the temperature dependence of the service behavior, deformation, and tear rate of filled systems based on SKS-85. It is established that the introduction of fillers which enhance the strength of systems in the high-elastic state effect a loss of strength in the vitreous state. The observed reversal of the strengthening effect from positive to negative is explained by weakening of the adhesive strength of the bond between polymer and filler particles caused by the increase and concentration of shrinkage stresses during cooling of the specimens. This effect is called temperature inversion of the reinforcing action of fillers.Mekhanika Polimerov, Vol. 1, No. 6, pp. 98–102, 1965     

Determination of the parameters of the reticulate structure of amorphous linear polymers subjected to orientational stretching

As a result of interlacing the macromolecules in linear block polymers form a sort of molecular network. The structure of this network affects the strength characteristics of oriented amorphous linear polymers in the brittle state. An important characteristic of the reticulate structure is the number of network chains per unit volume. The literature describes a method of determining this quantity based on the degree of stretching and the stress developed during stretching of the softened polymer. This method is not sufficiently accurate, since it disregards the presence in linear pclymers of network nodes of different stability. The proposed method of calculating this quantity is based on an analysis of the "equilibrium contraction" curves and takes into account the relaxation processes in the polymers. It is more accurate than that previously employed.Mekhanika Polimerov, Vol. 2, No. 2, pp. 163–169, 1966     

On the excursion theory for linear diffusions

We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting the parameter of the exponential time tend to zero it is seen that these results connect to the corresponding results for excursions of stationary diffusions (in stationary state). We characterize also the laws of the diffusion prior and posterior to the last zero before the exponential time. It is proved using Krein’s representations that, e.g. the law of the length of the excursion straddling an exponential time is infinitely divisible. As an illustration of the results we discuss the Ornstein–Uhlenbeck processes.     

On the frame invariance of linear elasticity theory

It is widely believed that classical linear elasticity theory does not conform to the Galilean frame invariance of general (non-relativistic) field theories. This view is traced here to an interpretation of the relationship between the deformation gradient and the displacement gradient which does not reflect the tensor character of the variables involved. Frame invariance is shown to follow if tensor character is imposed on this relationship at the outset.     

On the frame invariance of linear elasticity theory

It is widely believed that classical linear elasticity theory does not conform to the Galilean frame invariance of general (non-relativistic) field theories. This view is traced here to an interpretation of the relationship between the deformation gradient and the displacement gradient which does not reflect the tensor character of the variables involved. Frame invariance is shown to follow if tensor character is imposed on this relationship at the outset.     

Thermal conductivity of amorphous polymers

The dependence of the thermal conductivity and thermal diffusivity of amorphous polymers on pressure and temperature has been experimentally determined.     

On the oscillation theory of periodic linear differential equations

For equations in a broad class of linear differential equations of arbitrary order having periodic coefficients, we set forth a procedure for determining large regions in the plane in which no solution f(z) ? 0 can have infinitely many zeros. This permits us to determine locations in the plane where the zeros of a solution must be concentrated. Our results apply to higher-order analogues of the well-known Mathieu equation. The class of equations we treat has been investigated in several recent papers (e.g. [6, 7, 8, 9]) from the point of view of determining the frequency of zeros of the solutions     

Strength of rigid oriented amorphous polymers

A method is proposed for obtaining uniaxially oriented specimens of amorphous unfractionated polymer with a particular oriented chain length. The length of the oriented chains and their molecular weight M_c depend importantly on the conditions under which the polymer is stretched. It is shown that the strength of specimens obtained by stretching at constant M_c increases linearly with the relative fraction of oriented phase. The slope of this linear relation increases with the length of the oriented molecular chains. The ratio of the maximum strength of fully oriented polystyrene to the strength of the unoriented material is found to be 78 instead of the value of 6 given in [6].Mekhanika Polimerov, Vol. 3, No. 6, pp. 1048–1053, 1967     

On the theory of linear systems of ordinary differential equations

Author's abstract of dissertation for the attainment of the scientific degree of Doctor of the Physical and Mathematical Sciences. Dissertation defended May 24, 1968 at the sitting of the Council of the Mechanical and Mathematical Faculty of the M. V. Lomonosov State University.Official opponents: Doctor of the Physical and Mathematical Sciences D. V. Anosov, Doctor of the Physical and Mathematical Sciences Professor R. é Vinograd, and Doctor of the Physical and Mathematical Sciences Professor Ya. G. Sinai.Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 483–490, October, 1968.