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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.

The determination of the energy of activation (barrier height) of elementary events involved in relaxation (fluctuation) transitions in polymers from the temperature dependence of the specific heat is discussed. The dependence is derived by the method of differential scanning calorimetry. It is emphasized that the correct determination of the energy of activation must include the temperature variation of the barrier. The deviation of the preexponential in the Arrhenius temperature dependence from the value predicted theoretically demonstrates that the barrier does depend on temperature. Experimental data from which the realistic energy of activation of the α relaxation in polymers can be found are given.

The experimental temperature dependences of the thermal expansion coefficient and the mean-square amplitude of atomic vibrations in the longitudinal direction (along the axes of chain molecules) in poly(ethylene) crystals of different sizes are measured using x-ray diffraction in the temperature range 5–350 K. Theoretical calculations of the temperature dependences of the thermal expansion coefficient and the mean-square amplitude of atomic vibrations in poly(ethylene) crystals are carried out. It is shown that the results of calculations are in good agreement with experimental data. The temperature ranges in which the quantum character of lattice dynamics affects the thermal expansion coefficient and the mean-square amplitude of vibrations are determined. It is revealed that the shear longitudinal modes play an important role in the lattice dynamics of crystals with a chain structure.

A set of ceramic samples based on silicon carbide with substantially varying integral porosity (from 1 to 10 %) was studied. The pore size distribution was examined by optical microscopy (for pores ranging from 10 mm to hundreds of microns in size), scanning electron microscopy (0.5 - 10 mm), and small-angle X-ray scattering (0.04 - 0.20 mm). The obtained pore size distribution function was used to estimate the integral porosity of ceramics, which was compared with the estimates of porosity obtained by the dilatometric technique. Relative contributions of large, small, and fine pores into the integral porosity of ceramics were found. The average pore sizes and average distances between them were estimated for each range of pore sizes.

Reversible thermal deformation coefficients (TDCs) of oriented samples of a flexible-chain polymer (polyethylene) and of a number of rigid-chain polymers were measured in the longitudinal and transverse directions near room temperature. The same samples were used to measure the TDCs of crystallites by x-ray diffraction. The magnitudes of the TDCs of macroscopic oriented samples and of constituting crystallites and the characteristics of the thermal deformation of flexible-chain and rigid-chain polymers are compared. A conclusion is made that the mechanisms that determine thermal deformation in the longitudinal and transverse directions for the flexible-chain and rigid-chain polymers are different.

The possibility of predicting the lifetime of loaded materials at variable (increasing) temperature is demonstrated on the basis of a kinetic approach to the problem of the failure of such materials.

True deregulation of the utility industry can not happen without the creation of vibrant energy trading markets that allow buyers and sellers of energy to freely engage in trading activities over a wide range of energy sources, products, and geographies. The creation of such markets is being impeded by the absence of adequate trading tools. Unfortunately, the trading facilities from other industries (such as the stock and commodity trading) can not be easily applied to power markets, due to peculiar technical characteristics of energy trading. Development of sophisticated energy trading tools is of paramount importance to the electric power industry. This article features an energy trading system (Open Access Same-Time Information Systems) developed by Open Access Technology, International, Inc. (OATI) and deployed in the Mid-Continent Area Power Pool (MAPP) region in January 1997.

The paper describes the principles, theoretical calculation procedure, and apparatus used for the realization of the temperature wave technique. The efficiency of the technique for the studies of relaxation transitions in polymers when the thermophysical characteristics are in the complex form has been demonstrated. The temperature dependences of the moduli and arguments of thermophysical characteristics for different frequencies of temperature oscillations have been obtained for polyvinylacetate. The vibrational and configurational components of the heat capacity have been found. The effect of polymer plasticization and also of changes in the chemical composition of molecules on complex thermophysical characteristics has been shown using styrene-butylacrylate as an example.

The dependence of the energy characteristics on an adiabatically slowly increasing external force is determined analytically for an anharmonic oscillator. The analytical results are confirmed by a numerical calculation. The nature of the force dependences of the energy characteristics are determined and discussed.

Internal atomic–molecular vibrational dynamics of solids gives rise to short-lived localised states of atoms with a much higher energy or amplitude of vibrations, i.e., it gives rise to fluctuations. These fluctuations play the dominant role in a variety of physical processes, which include diffusion, evaporation, plastic deformation, highly elastic deformation of polymers, fracture, chemical reactions, electronic transi-tions, biological functions, and many others. The essentials of the fluctuation origin of these processes are given in the classical papers of Ya I Frenkel'. The microscopics of fluctuations of the energy of atoms has begun to develop successfully. The present paper provides a brief historical introduction, which is followed by the first results (obtained by computer simulation) that can account for the detailed characteristics of fluctuations: the lifetime of a fluctuation state of atoms, the size of a fluctuation region, and migration of fluctuations. Special attention is given to the mechanism of formation of energy fluctuations. Investigations of fluctuation dynamics in condensed media, regarded as a new and to some extent independent part of the physics of liquids and solids, have been given a decisive start by the fundamental work of Yakov Il'ich Frenkel'. He began his investigations back in the twenties and continued them with outstanding success throughout his life. The study reported below represents the attempt by the present authors to continue the development of the fruitful ideas of Yakov Il'ich.

X-ray scattering from a series of poly(ethylene terephthalate) (PET) fibers spun at differet speeds is analyzed to probe the morphology in the direction transverse to the fiber axis. Both the apparent crystal modulus, determined from the change in wide-angle X-ray scattering angle with fiber stretching, and the transverse degree of crystallinity indicate there is a substantial interfiberillar amorphous content. In the PET fiber spun at conventional speeds, only roughly one-quarter of the fiber cross-section is actually occupied by fibrils. The transverse crystallinity increases for fibers spun at speeds sufficient to cause crystallization in the spin line. The X-ray moduli and fibril diameters are correspondingly larger in these high speed spun fibers. © 1993 John Wiley & Sons, Inc.

The technique of temperature waves to measure the complex thermophysical characteristics of materials has been proposed. The relations for the moduli and arguments of these characteristics for the case of plane temperature waves have been calculated. The temperature dependences of the moduli and arguments of complex thermophysical characteristics of polyvinylacetate (PVAc) at different frequencies and also the temperature dependences of its vibrational and configurational heat capacities have been determined. It has been shown that the vibrational heat capacity of PVAc in the region of softening grows sharply and its configurational heat capacity goes through a peak. The segmental mobility has been found to affect the heat transfer in the polymer in an ambivalent way causing both a decrease and increase of thermal conductivity.

The time of expectation for breakdown (life-time, τ) was measured as a function of temperature (T) and tensile stress (σ) for a variety of polymers, including nylon-6, polyethylene, poly(ethylene terephthalate) and poly(tetrafluoroethylene). At moderate temperatures (above ∼200 K), the τ(1/T)σ dependences are exponential (of the Boltzmann-Frenkel type). The elementary acts of polymer fracture occur at these temperatures through the thermal-fluctuation above-barrier transitions. At low temperatures (below ∼200 K), τ is T-independent (an athermic plateau) and, therefore, the above-barrier mechanism is ruled out. It is concluded that the elementary acts of fracture proceed at low temperatures via the tunnel below-barrier mechanism. Possible types of tunnel processes (tunneling of atoms or electrons) are discussed.

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).

The dependence of the temperature on the external adiabatic deformation is determined for a one-dimensional model of a solid — chains of atoms with an anharmonic interaction. The resulting dependences of the average kinetic and potential components of the internal energy on this deformation are compared with a model of adiabatic loading of a single oscillator.

Experimental studies of the fracture kinetics of solids have shown that the process culminating in fracture of a stressed solid comprises a sequence of elementary events in which stressed atomic bonds are ruptured by local energy fluctuations. This recognition sparked investigations into elementary fracture events and into the fluctuations themselves that are responsible for bond rupture. Currently, only computer simulation of the dynamics of atoms offers the possibility of tracing, in considerable detail, the evolution of fluctuation events characterized by very short duration (∼10−13−10−12 s). An analysis is made of the results obtained in computer simulation experiments on the temporal and spatial localization of atomic-energy fluctuations and atomic-bond strains, fluctuation migration, the mechanism of fluctuation formation, the role of anharmonicity in atomic interactions, and the magnitude of the volume activated in an elementary fracture event.

The experimental work on embryonic fracture cracks in polymers recently carried out in the A. F. Ioffe Physico-Technical Institute, Academy of Sciences of the USSR, is reviewed. The cracks have been studied by diffraction methods, chiefly by small-angle x-ray scattering. A principal result of this research is the possibility of formulating the general principle of a micromechanics of polymer fracture. The theory is based on data on the behavior of submicrocracks in polymers (size, concentration), the structural conditions and molecular mechanism of crack formation, the enlargement of submicrocracks, their influence on microcrack formation, and the growth of the macrocracks.

The study of very fine cracks formed in stressed solids was carried out using different types of solids, such as polymers, ionic crystals, and metals. Such methods as small-angle X-ray scattering, light scattering, and electron microscopy were used. Size, form, orientation and concentration of submicrocracks have been estimated. A study of the connection between submicrocracks and the structure of solids and of the kinetics of crack accumulation has been started. The development of the fracture process in solids on the basis of nucleation and successive coalescence of submicrocracks is discussed.

The dependence of the microhardness of PMMA and PS on indenter penetration time and temperature has been studied. It is shown that the microindentation process is a kinetic process. A relation is established between the kinetic characteristics of the microindentation process and the corresponding characteristics of the fracture process.

The electron-microscopic method was used to study the structure of unsaturated polyester films. The initial submicrocracks developing in the loaded films were studies by the low-angle x-ray diffraction method. It is shown that for these polymers a typical feature is the globular structure with a globule diameter of 103–3·103 A, and the transverse dimension of the submicrocracks developing under the action of a load practically coincides with the globule diameter.

Deformation of supermolecular structure elements of oriented crystalline polymers and nucleation of initial submicroscopic cracks induced by stress have been studied by the small-angle x-ray scattering technique. It is shown that the intrafibrillar amorphous interlayers have low strength and high deformability. The rupture of the weakest amorphous interlayers leads to nucleation of initial submicrocracks. The influence of submicrocracks on deformation around such cracks is revealed. The micromechanics of deformation and fracture of polymers is discussed.

The orientational drawing of polymers is known to be terminated because of sample rupture. The limiting draw ratio λlim 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(e-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 δL 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 λL 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 λlim, the relative standard deviation of the sizes of amorphous regions δA 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.

For many aliphatic and wholly aromatic polymer fibers, meridional small-angle x-ray reflections (SAXR's) are not observed. The morphological features which give rise to this effect have Received little attention in the literature. It is sometimes speculated that this is evidence of a morphological homogeneity along the fiber axis (no fluctuation of electron density–no long periods), ignoring other possible reasons (morphology is heterogeneous but very irregular or the maximum intensity of SAXR (Imax) is low and SAXR cannot be observed against the background of diffuse scattering.) Fibers with homogeneous crystalline morphology should have an elastic modulus Ef close to that of the crystallites Ecr along the polymer chains over a broad range of stresses. But, as was found in this work for the overwhelming majority of such nonreflection fibers (including Kevlar aramid fibers) there is a considerable difference between Ecr and Ef (for some nonreflection fibers the ratio Ecr/Ef is on the order of 10). This means that their morphology is heterogeneous along the fiber axis and contains “weaker” intercrystalline regions. This heterogeneity appeared to be regular enough to give rise to SAXR, as determined from the appearance of SAXR during elastic extension and after the beginning of pyrolysis in some nonreflection fibers. Thus, it was concluded that the lack of observable SAXR for these fibers is a result of the weakness of Imax relative to the diffuse scattering. Support for this statement is seen in the analysis of the decrease of Imax to zero with increasing draw ratio for poly(vinyl alcohol) fibers. The key factors influencing the decrease of Imax in this case were found to be the decrease of fibril diameter (fibril splitting), an increase of the dispersion of the long periods and some possible decrease in the density difference between crystalline and amorphous regions. The particular combinations of such factors can be different for each particular case of missing SAXR and are discussed in this paper.

Molecular dynamics in crystallites of a number of polymers, such as polyethylene, nylon-6, poly-(vinyl alcohol), was studied at temperatures ranging from 4.2 to 400 K using the X-ray diffraction technique. Thermal expansion of the lattice was measured by the temperature-induced displacements of diffraction maxima. The thermal expansion coefficient was found to grow from 0 to ∼10−4 K−1, this fact being the evidence of the quantum statistics in the vibrational dynamics of straightened molecules over the whole temperature range. Characteristic temperatures of vibrations were estimated. The kinetics of fracture was studied using highly - oriented nylon-6 and KEVLAR-49 fibers. Tensile strength (σr) was measured as a function of loading rate σ and temperature (T) in the range from 4.2 to 400–600 K. The observed specific features of the σr(σ) and σr(T) curves at low temperatures correspond to tunnel scission of stressed chain molecules.

1. These results represent only a first step in the detailed study of nuclear cracks in crystals, but they are of considerable interest. These microcracks should be further examined to give more reliable scattering results. 2. Electron microscopy indicates that the size, shape, and orientation of the cracks are close to those obtained by light scattering; in fact it is found [20] that nuclear cracks arise mainly in slip planes, i.e., are oriented along [110]. The large dimension of a crack is a few μm, while the small one is in the 100 to 1000 A range. These results go with the dilatometry data mentioned above to indicate that light scattering is a reliable method of examining nuclear cracks.

Direct physical methods were used for studying molecular fracture in stressed polymers. The macromolecular ruptures were detected by electron paramagnetic resonance, infrared spectroscopy, and mass spectrometry. Nucleation of incipient submicrocracks was registered by small-angle X-ray scattering and light scattering. All methods were used to study fracture kinetics at different stresses and temperatures. The thermal fluctuation nature of microruptures is verified and the activation energy for the elementary events of polymeric fracture is estimated. This energy coincides with the activation energy for macrorupture evaluated in the study of the lifetime of polymers. Chain chemical reactions of stresses macromolecules disruption are proved to take part in formation of incipient cracks. The main features of the micromechanics of polymer fracture are listed.

The effect of reversible (elastic) extensions of oriented crystallizing polymers on long periods within them, recorded by small-angle x-ray diffraction, has been investigated. The reversible shift of the meridian maximum of diffraction intensity toward small angles (which means the increase of long periods) as well as the maximum diffraction intensity increase with polymer loading have been established. The agreement of relative increments of long periods and polymer-specimen dimensions is rather common, although some instances when the period deformation exceeded the specimen deformation have been observed (for highly annealed oriented polymers). The invariability of crystallites with polymer extension (according to large-angle x-ray diffraction) indicates that the deformation of long periods, which are formed by the alternation of crystalline and amorphous regions along the orientation axis, is caused by crystallites transference due to stretching the amorphous interlayers between them. The increase of small-angle diffraction intensity with the extension of oriented polymers is supposed to be due to two factors: (1) the reduction of crystallite share in long periods; and (2) the decrease of the density of extended amorphous interlayers which results in increasing the density difference of alternate crystallites and amorphous regions. The problem of more precise definition and checking of these conclusions is raised and attention is drawn to the great interest in investigating the amorphous-region properties in oriented crystallizing polymers, which determine the mechanical properties of polymers.

As a result of a study of the behavior under load of the elements of the supermolecular structure of oriented amorphous-crystalline polymers it is shown that the stresses on the crystallites and the amorphous zones in series with them in the direction of the chain axes are equal to the mean stress applied to the specimen along the orientation axis. The nature of the elasticity and deformability of the amorphous zones is analyzed. A relation is obtained between the strength properties of oriented polymers and the number of load-carrying chains in the amorphous zones.

The development of submicrocracks and the changes taking place in their concentration during loading and unloading cycles were studied by the low-angle x-ray scattering method in oriented amorphous-crystalline polymers (capron and polypropylene). The deformation (e) of the polymers was compared with the changes in submicrocrack concentration (Ncr).

Structure deformations upon loading of oriented films of polycaproamide (Kapron) or polypropylene when submicroscopic cracks (dimensions of hundreds of Angstroms) have appeared in the samples in high concentration (up to 2 · 1015 cm−3) have been studied by x-ray diffraction methods at low and large angles. It has been established that the appearance of submicro-cracks causes relieving of the regions adjacent to them along the loading axis (extent about 1000 A) and an increase in stress in the lateral zone relative to the crack, which is manifested in an intensification of the stretching of these zones.

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.

Equipment has been developed for investigating small-angle X-ray diffraction in various phases of the loading period in cyclically extended polymers. The behavior of the large-period structure of oriented polycaprolactam (kapron) films in cyclic extension has been studied. The results are compared with the data on the behavior of the same structure in static tests.

1. In studying the temperature-stress dependence of life it is first of all necessary to relate the “pole shift” effect with structural instability of solids. 2. A method of approximate evaluation of the activation energy of the fracture process was considered for cases of the “pole shift” based on averaging of unstable structural characteristics.

Problems of the mechanical breakdown of polymer materials are discussed on the basis of kinetic considerations on such breakdown, viewed as a thermofluctuation-induced process of an accumulation of breaks in interatomic bonds (either break or damage). The present state of this problem is analyzed, both for static and for cyclic loads (fatigue). Some approaches for developing a theory of breakdown are reviewed. Theories related to the accumulation of damage in the volume of the sample receive particular attention. Recent studies on fatigue in polymer materials are listed.

Small-angle x-ray scattering has been used to estimate the longitudinal (L∥) and transverse (L⊥) dimensions of the submicrocracks formed in loaded polymers. The growth under load of macrocracks, initiated in the same polymers by a slit or a circular hole, has also been observed. The ratios L⊥/L∥ for the macro- and submicrocracks are found to coincide.

Small-angle x-ray scattering has been used to obtain a quantitative estimate of the concentration and size of the submicrocracks in Kapron and polypropylene equally extended at 1 and 1500 atm. Direct evidence of the retarding effect of pressure on fracture development has been obtained.

The development of submicroscopic cracking under load has been studied (by a small-angle X-ray scattering technique) in such oriented polymers as Kapron (Nylon 6), polypropylene, etc. The increase in crack density (Ncr) is compared with the variation of the tensile strain (e). The observed correlation between e and Ncr indicates that the processes of fracture and deformation of oriented polymers are closely connected. The presence of a similar correlation in loading-relaxation-repeat loading experiments establishes fracture as the primary process.

In the paper, the changes in axial and contour lengths of skeletal interatomic bonds in the chain molecules of polyethylene nanocrystals have been measured using X-ray diffractometry and Raman spectrometry. In the course of the measurements the samples were subjected to stretching and heating (mechanical and thermal actions). The measured force and temperature dependences were analyzed and the calculated description of the polymer nanocrystal strain was inferred from them. In so doing the original results were obtained for the thermal action. The potential energy components related to both the skeletal bond stretching and the chain molecule bending were determined for the strained polymer crystal. The sharp distinction between the ratios of these components for the object under mechanical and thermal actions was found.

An installation designed for measuring the relaxation component of thermal expansion, a typical feature of polymers due to the conformational mechanism of thermal expansion inherent in them, is described. The relaxation component manifests itself as a shift in the expansion variation phase relative to the temperature variations. The installation allows variations of the temperature-oscillation frequency and amplitude in the ranges of 10–3 to 10–1 Hz and 1–5 K, respectively. The expansion variation amplitudes were measured using a mechanotron with a sensitivity of at least 10–2 μm. The serviceability of the installation was demonstrated in studies of the thermal expansion of a polymer (polyvinylacetate, PVA). In these studies, a shift in the expansion–temperature phase in the polymer-vitrification region and its dependence on the temperature-oscillation frequency were recorded.

TABLE OF CONTENTS Introduction 45 1. Endurance of Solids under Load and the Fundamental Premises of the Kinetic Conception of Strength 46 2. Study of the Process of Failure of Materials by Direct Physical Methods 50 3. Cases of Complicated Failure 58 4. Some Problems in the Development of Kinetic Ideas on the Failure Process 59 5. Kinetic Theories of Failure 60 6. Conclusion 60 Bibliography 61