Thermal expansion of polymers subjected to low-amplitude temperature cycling

The temperature dependence of the thermal expansion of polymers subjected to small harmonic temperature oscillations about certain base temperatures near the glass transition range is considered. The conformational component of the expansion as a function of temperature is calculated in terms of the conformational transition kinetics. The temperature dependences of the expansion and the expansion vs. oscillation phase shift are analyzed with allowance for the vibrationally anharmonic component. The thermal expansion of polyvinylacetate at base temperatures of 295–320 K, oscillation frequencies of 0.3 and 0.1 Hz, and an oscillation amplitude of 0.8 K are studied experimentally. The measured and calculated data for the expansion and expansion vs. temperature phase shift are shown to be in good agreement.     

Determination of the activation energy for complicated relaxation processes

Different methods are considered for analyzing the temperature dependence of the relaxation rate in the Arrhenius form. It is emphasized that the possible changes in the barrier to elementary acts with variations in temperature should be taken into account in order to determine the relaxation activation energy correctly. Changes in the barrier to elementary acts are illustrated using experimental data on the temperature-frequency dependence of the dielectric relaxation in polymers. A theoretical approach offering realistic activation energies is proposed.     

Manifestation of quantum statistics in vibrational dynamics of poly(ethylene) crystals

The temperature dependences of the transverse expansion ?_⊥(T) and the longitudinal contraction ?_‖(T) (with respect to the axes of chain molecules) in large-sized poly(ethylene) (PE) crystal grains (100×60×60 nm) are measured using x-ray diffraction in the temperature range 5–380 K. The temperature dependence of the elongation of the molecular skeleton ?_C(T) is obtained by Raman spectroscopy. It is found that the dependences ?_⊥(T), ?_‖(T), and ?_C(T) exhibit a similar specific nonlinear behavior. Analysis of these dependences indicates that the nonlinearity is associated with the quantum statistics of transverse vibrations. The energies and amplitudes of zero-point (at T=0) transverse (torsional and bending) vibrations and the relevant zero-point components ?_‖(0) and ?_C(0) are estimated. It is revealed that the zero-point components make a considerable contribution to the dynamics of the PE crystal up to the melting temperature (～400 K).     

Polymer fibers drawn to the limit

The orientational drawing of polymers is known to be terminated because of sample rupture. The limiting draw ratio λ_lim reached may be different (either large or small) depending on the polymer and the actual drawing conditions. The purpose of the present work is to identify the change of supermolecular structure of polymer fibers which results in the termination of orientational drawing. Small-and wide-angle x-ray diffraction were used to study the variation of geometrical parameters of this structure with increasing draw ratio λ. The geometrical parameters discussed are the dispersions (fluctuation) of long periods and of longitudinal sizes of crystalline as well as amorphous regions. In this study we used fibers of poly(vinyl alcohol), poly(ε-caprolactam), polyoxymethylene, and poly(4,4′-diphenyloxide) pyromellitimide. It is found that the long period dispersion of these polymers, drawn under different conditions, increases to approximately the same value for different samples drawn to the limit, this relative standard deviation δ_L of long periods being 0.30-0.40. It is also found that the crystallite size dispersion does not increase with increasing λ; the increase of λ_L is due to increasing dispersion of the amorphous region lengths. For poly(vinyl alcohol) fibers drawn to the limit under different conditions and which have different λ_lim, the relative standard deviation of the sizes of amorphous regions δ_A turned out to be about the same (ca. 0.60). The latter evidence gives grounds to suggest that the rupture of polymers under drawing is associated with reaching a high degree of amorphous region size dispersion. In those regions which are considerably below the average size there probably will appear local overstress and molecular ruptures because the relative deformation of these regions is much larger than that of the adjacent regions in the cross section of the sample.     

Creep of polymers during tension under conditions of hydrostatic pressure

Hydrostatic pressure results in decrease in the creep rate of a polymer loaded by tensile stress. The decrease in the creep rate is associated with the increase in intermolecular interaction. The correlation found between the creep rate of material loaded by a constant tensile force and with change in the melting temperature of a polymer under pressure appears to be commensurate with change in intermolecular interaction.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 359–362, March–April, 1976.     

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.     

The strength properties of acicular single crystals of polyoxymethylene

The strength properties of acicular formations of polyoxymethylene, obtained by the directed polymerization of trioxane whiskers, have been studied. It has been found that the acicular single crystals obtained in this process exhibit a high strength.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 266–270, March–April, 1970.     

Possible manifestations of quantum effects in the boron microindentation kinetics

The kinetics of indentation of a solid (viz., the dependence of the indenter intrusion depth on the time, force, and temperature), is analyzed theoretically taking into account quantum effects in the atomic dynamics of solids. The experimental study of the temperature dependence of the boron microhardness reveals qualitative and quantitative agreement with calculated dependences. A possible manifestation of quantum (tunnel) effects in the boron microindentation kinetics is predicted.     

On an adiabatic invariant in the thermodynamics of solids

A thermodynamic invariant in the form of the ratio of a vibrational frequency in an anharmonic solid to the temperature in adiabatic processes is derived. The adiabatic invariance established is used to derive in a simple manner an expression for the temperature change due to elastic adiabatic loading of solids (Kelvin's equation). Fiz. Tverd. Tela (St. Petersburg) 41, 134–136 (January 1999)     

Energy of the frequency-elastic effect in solids

A decrease in the frequency of skeletal vibrations (frequency-elastic effect) has been measured using Raman spectroscopy, and the stretching of backbone interatomic bonds in polyethylene molecules under elastic tensile loading of oriented polyethylene fibers has been measured using X-ray diffraction. It has been found that there are differences in the sign and magnitude of the changes in the zero-point energy and the work of the external force. The energy of the frequency-elastic effect has been explained in terms of the influence exerted by the initial (before loading) anharmonic stretching of backbone bonds and the force of anharmonic pressure, with the separation of the anharmonic (potential) component of the zero-point energy of the solid. A change in the frequency of vibrations corresponds to a change in the harmonic component of the zero-point energy. The loading with an external force causes a redistribution of the zero-point energy components. An energy analysis of the loaded quantum anharmonic oscillator has confirmed the conclusion regarding the mechanism of energy transfer and revealed that, under loading, there is a redistribution of the average values of the kinetic and potential components of the internal energy of the oscillator.