Temperature dependence of the mechanical properties of polymers of different chemical structure in the temperature range from 4.2 to 300°K

Conclusions 1. The temperature dependences obtained for the ultimate alongation, tensile strength, and elastic modulus of various polymers showed that the relationship between the mechanical properties and chemical structure of macromolecules found in our earlier work at 4.2°K is retained at 78°K and, possibly, up to 90°K.2. It was shown that the passage of the tensile strength through a maximum upon warming from 4.2°K results from a corresponding increase in deformability, which is accompanied by a decrease in the elastic modulus and deviation of the polymer bodies from Hooke's law progressively with increasing temperature.3. It was shown that the amorphization of crystallizing polymers, for example, by quenching, gives a marked change in the deformability, tensile strength, and elasticity of the polymer body over the entire range from 300 down to 4.2°K.4. Study of the mechanical properties of polymers at 78°K in a helium medium and liquid nitrogen showed a marked effect of contact of the polymer with liquid nitrogen on these properties. This effect is different for polymers of varying chemical structure as well as for the same polymer in different physical states.Report presented at the Third All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1976.L. Ya. Karpov Scientific-Research Institute of Physical Chemistry, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 387–391, May–June, 1977.     

Effect of electron irradiation on the mechanical and thermal properties of some polymer materials

The effect of electron irradiation on the mechanical properties (deformability) of polyethylene terephthalate (PET), polytetrafluoroethylene (PTFE), polyimide (PI), and Fenilon (Fe) films, as well as the thermal properties (heat conductivity and capacity) of PTFE is studied experimentally. The thickness of the films was 40–50 m. Mechanical tests showed that polyimide films were more resistant to radiation than the other films. The investigation of the changes in the thermal properties of PTFE due to electron irradiation revealed that the phase transitions observed at temperatures of 293 and 303 K in unirradiated PTFE were shifted to lower temperature regions.Abai Alma-Ata State University, Kazakhstan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 683–689, 1998.     

Groups with a class of Frobenius-Abelian elements

Let G be a group, a G ^#, and let F_a be the set of all Frobenius subgroups with noninvariant factor a in G. In Theorems 1–3, we show that if a ² 1and G has sufficiently many subgroups a, a ^g F _a. then a^G F _a.An element a is called (almost) Frobenius if, for (almost) all elements a ^g,the subgroup a, a ^g either belongs to F _a or is Abelian. In Theorems 4–5, we investigate the structure of a ^G in G for the case where a is an (almost) Frobenius-Abelian element of order 2.In Theorem 6, we prove that a binary factorable group is locally completely factorable. Translated fromAlgebra i Logika, Vol. 34, No. 5, pp. 531–549, September-October, 1995.     

The hyperbolic n-space as a graph in Euclidean (6n−6)-space

We construct for each n2 an isometric C-imbedding HⁿE^6n–6 of the n-dim. hyperbolic space into the Euclidean space E^6n–6 whose image is the graph of a C-map RⁿR^5n–6. This generalizes a well known result of D. Blanusa 1955 (the case n=2).     

Mechanical behavior of a number of polymers at helium temperatures

An experimental investigation of the mechanical behavior of a number of polymers in the range 4.2–240°K has been made. It has been shown that at helium temperature the Poisson ratio is governed by the free volume. It has been established that the dynamic Young's modulus and shear modulus of these polymers at 4.2°K depend on the chemical structure: their values are determined by the mean distance between neighboring macromolecule chains.     

Viscoelastic parameters of certain polymers in the temperature interval 4.2–240°K

The principal elastic constants of Nylon 6, Nylon 7, Nylon 6.10, Nylon 11, Nylon 12, PVC, PMMA, polystyrene, and polyvinylfluoride have been calculated from data on the velocity of ultrasonic longitudinal and shear waves measured at a frequency of 5 MHz on the temperature interval 4.2–240°K. It is shown that at cryogenic temperatures the dynamic moduli of elasticity are, to a considerable extent, determined by the characteristics of the chemical structure of the polymers. It is suggested that the Poisson's ratios of the polymers depend on their free volume.Scientific-Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 604–609, July–August, 1973.     

Ultrasonic velocity in epoxy resin at temperatures down to 4.2 K

Results are presented from measurements of the velocity of longitudinal and shear elastic waves (f=5 MHz) in ÉD-20 epoxy resin, at temperatures from 4.2 to 293 K. These data were used to calculate the moduli of elasticity E and G. Also, the moduli E (f=250 Hz) and G (f=2 Hz) of the ÉD-20 resin were measured directly. The calculated velocities of the low-frequency elastic waves c_t=(E/p)^1/2 and c_t=(G/p)^1/2 (where p is the density) were compared with the results from the ultrasonic measurements. The frequency dependence of elastic-wave velocity in the epoxy resin was evaluated. It was found that when the frequency was varied by four orders of magnitude, the dispersion of longitudinal-wave velocity was 18% at 4.2 K and 39% at 293 K. A quantitative criterion is proposed for estimation of the dispersion of sonic velocity from the results of measurements at any two frequencies. It was established that the sonic velocity at low temperatures varies linearly with the temperature, and in the case of longitudinal waves changes from c_l-3360 m/sec at 4.2 K to 2820 m/sec at 293 K. The shear-wave velocity changes from c_t=1630 m/sec at 5 K to 1340 m/sec at 293 K. The values of the dynamic Young's modulus E and shear modulus G at 4.2 K are 8.6 and 3.2 GPa, respectively. On a plot of c=f(T) for ED-20, a transition is observed at 180 K, due to reorientational rotation of methyl groups. The activation energy of the relaxation process is 3.6 kcal/mole. Large values are obtained for the dispersion of the dynamic modulus E:37.8% at 4.2 K and 93% at 293 K.Paper presented at 9th International Conference on the Mechanics of Composite Materials Riga, October, 1995.Moscow State Academy of Automotive Vehicle and Tractor Machinery Construction, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 460–466, July–August, 1996.     

Generalized concentration dependence of the viscosity of concentrated polymer solutions

The construction of a generalized concentration dependence of the viscosity of concentrated solutions is analyzed. It is shown that there should be a single dependence for different polymers in different solvents of the form: (/_o)^1–2k=1+(1–2k)c[], where k is the Huggins-Martin constant, and [] is the intrinsic viscosity. Deviations from this relation may be observed in the presence of structure formation in the solution or when the experimental temperature is close to the glass-transition temperature of the system."Plastpolimer" Okhtinsk Research-Production Association, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 172–175, January–February, 1976.     

Temperature dependence of E and tg δ for polymethylmethacrylate and polystyrene with different kaolin contents

The temperature dependence of the dynamic modulus of elasticity E and the loss tangent tg has been investigated for polymethylmethacrylate (PMMA) and polystyrene (PS) with different contents of kaolin filler (K), in the glassy state and in the region of incipient devitrification. It is concluded that supermolecular reinforcing structures appear in filled polymers in which the intermolecular forces are sufficiently strong.Mekhanika Polimerov, Vol. 3, No. 5, pp. 854–857, 1967     

Natural aging and dynamic mechanical properties of polymer matrices

The influence of natural six-month aging at 293 K of two kinds of epoxy resins with different network density on their dynamical properties was studied. All the samples were examined by forced resonance oscillations at a frequency of 200 Hz in the range of 120–520 K. The components of the complex Young's modulus E, E, tan , and low-frequency velocity of sound were measured. The basic temperature transitions including T_g and the network density were determined from the experimental data. It was established that after aging of epoxy resins cured by the cross-linking agent meta-phenylenediamine their network density decreased (cold degradation). By using the cross-linking agent 2,6-diaminopyridine, and T_g increased. An attempt is made to explain the nature of this phenomenon.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Moscow State Technical University, Russia. Translated from Mechanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 407–412, May–June, 1998.     

On Pal Type Weighted Lacunary (0 , 2 ; 0 )-Interpolation on Infinite Interval (?∞, +∞)

In this paper, we study the weighted (0, 2; 0)-interpolation on infinite interval, which means to determine a polynomial of degree 3n–1 when the function values are prescribed at two sets of points namely the zeros of H_n(x) and H_n(x) and the wieghted second derivative at the zeros of H_n(x).     

A condition for nonnegativity of an operator related to the Dirichlet operator

Let L₀ be a positive definite closed linear operator with domain of definition D(L₀) dense in the Hilbert space H; let(, ₁, ₂) be the positive boundary value space of the operator L₀ such that the restriction of L ₀ ^* to ker ₂ is the Friedrichs extension of the operator L₀. We establish a test for nonnegativity of an operator T of the form Ty=L ₀ ^* y+^*(₁–C)y, y D(T)= ker(₂+), where :H and C: are respectively a compact operator and a bounded nonnegative operator.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 32, 1990, pp. 30–33.     

The problem of calculation of change in density of rubber during temperature-frequency (time) reduction

A graphical method is proposed for determination of the coefficient of vertical displacement of curves of the frequency dependence of viscoelastic functions of polymers during temperature-frequency (time) reduction. With respect to temperature, the dependence of the quantity ₀/ (where ₀ and are the densities of the material at the reduction temperature T₀ and the initial temperature T, respectively) is allowed for by use of one constant, the volume coefficient of the rmal expansion .Scientific-Research Institute for the Plastics Industry, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1136–1137, November–December, 1972.     

Changes in the mechanical properties of polyimides induced by electron bombardment

The change in the tensile strength and relative elongation of PM polyimide with absorbed dose has been investigated. It is shown that after irradiation with very large doses (5 · 10¹⁰ rad) the mechanical properties are still satisfactory.Scientific Research Institute of Electrophysical Apparatus, Leningrad. Translated from Mekhanika Polimerov, No. 6, pp. 1111–1112, November–December, 1969.     

A new limit theorem for Gaussian stochastic processes possessing the Baxter property

Let(t) be a Gaussian stochastic process with zero mean and correlation functionR(t, s), and let . We obtain conditions for the weak convergence of the sequence of stochastic processes ,t [0, 1] and we find the form of the limiting distribution. As a corollary, in the stationary case we find the limiting distribution asn for .Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 90–97, 1987.     

The acoustic properties of polymers with an asymmetric potential barrier at liquid-helium temperatures

The pulse-phase compensation method has been used to measure the propagation velocities of longitudinal and shear waves in polyvinyl chloride, polyvinyl fluoride, and polystyrene at frequencies of 1 and 5 MHz on the temperature interval 2.1–240°K. It has been established that as the temperature falls to 2.1°K the speed of ultrasound in these polymers monotonically increases, the dispersion (frequency dependence) of the speed of sound being preserved over the entire temperature interval. Two possible causes of the viscoelastic relaxation observed in the investigated polymers in the region of helium temperatures are considered.Scientific-Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 749–751, July–August, 1973.     

Density-Dependent Incompressible Fluids with Non-Newtonian Viscosity

We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of p-coercivity and (p–1)-growth, for a given parameter p > 1. The existence of Dirichlet weak solutions was obtained in [2], in the cases p 12/5 if d = 3 or p 2 if d = 2, d being the dimension of the domain. In this paper, with help of some new estimates (which lead to point-wise convergence of the velocity gradient), we obtain the existence of space-periodic weak solutions for all p 2. In addition, we obtain regularity properties of weak solutions whenever p 20/9 (if d = 3) or p 2 (if d = 2). Further, some extensions of these results to more general stress tensors or to Dirichlet boundary conditions (with a Newtonian tensor large enough) are obtained.     

A problem suggested by R. Boas

A result is proved concerning the convergence of the improper integral of a function g(x), where xg(x) L (O, ) and the generalized sine coefficients of g are nonnegative.Translated from Matematicheskie Zametki, Vol. 5, No. 4, pp. 437–440, April, 1969.     

Calculation of the temperature of polymer or composite surfaces placed in an infrared laser field

We consider methods for calculating the surface temperature T_s of polymers upon exposure to infrared laser radiation during modification, pyrolysis, ablation, ignition, etc. We have shown that we need to calculate the values of T_s for polymers using different analytical expressions after estimating the value of the dimensionless parameter u = at_e, where is the absorption coefficient for the laser radiation, a is the thermal diffusivity, and t_e is the radiation exposure time. Under these conditions, we achieve the smallest calculation error and we can take into account volume absorption of radiation.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 540–546, July–August, 1995.     

Estimates of groups of deviations of Faber sums and strong summability of faber series on classes of ψ-integrals

We establish upper bounds for a group of *-deviations of Faber sums on the classes of -integrals in a complex plane introduced by Stepanets.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 451–461, April, 2004.