Multilevel character of deformation of polymers

The inhomogeneity in the creep rate of polymers on different scales of deformation has been studied by laser interferometry. The main results have been obtained for the amorphous-crystalline polymer polytetrafluoroethylene. The deformation characteristics are the oscillation periods of the rate (jumps of deformation), oscillation amplitudes of the rate, and the scatter of these quantities. Application of computer methods for processing of the results has made it possible to determine the difference and similarity between jumpwise deformations on different structural levels, including the nanolevel. For a more distinct separation of deformation levels, the measurements have been made in a magnetic field and outside the magnetic field. Deformation jumps have been found on five levels: from 4 nm to more than 10 μm. Introduction of a sample into a magnetic field changes the characteristics of jumps; in this case, the scatter in the values of jumps always increases, whereas their average value varies differently on different scale levels. The measurement of the parameters of deformation jumps on different scales allows one to study the laws of the development of the deformation process and the evolution of structural inhomogeneities.     

Nanoscale deformation irregularities of γ-irradiated poly(methyl methacrylate)

Development of deformation jumps in the creep of poly(methyl methacrylate) (PMMA) has been studied. The structural levels of deformation have been determined from the creep rate oscillation periods (deformation jumps) measured by the interferometric method. Special attention is given to a new method of data processing, which enables one to reveal previously undetectable nanoscale deformation jumps. By the example of PMMA specimens preliminarily exposed to γ radiation with doses D=55–330 kGy and unexposed specimens, the presence of nanoscale deformation jumps with the values dependent on the dose D and time of creep has been shown. The obtained results confirm the existence of 10–20-nm domains in amorphous polymers and make it possible to study the multilevel organization of the deformation process, starting from the nanoscale.     

Jumplike deformation of polymer materials on the micrometer and submicrometer structural levels

Jumplike creep is considered as a reflection of the structural heterogeneity of amorphous polymers on the mesoscopic and nanoscopic levels. The D-450 epoxy resin, poly(vinyl chloride), poly(vinyl butyral), and a composite consisting of the D-450 epoxy resin and diabase microparticles are studied at a temperature of 290 K. The creep rate of the specimens under compression is measured with a laser interferometer in submicrometer-scale deformation increments. Periodic variations of the creep rate with time or under deformation correspond to a jumplike (stepwise) behavior of the creep. It is shown that diabase particles (5–10 μm in size) are responsible for the appearance of micrometer-scale jumps in the creep of the composite and that the deformation jumps on the nanometer level are comparable to the sizes of the globules. The role of the resolution of the method employed in the evaluation of the scale of deformation jumps and structural units is considered.     

Discontinuous deformation and morphology of polymers

The morphological nature of discontinuous (jumplike) deformation is studied. Recording creep behavior of materials using a laser interferometer permits one to determine the parameters of deformation jumps on a micron scale. The objects of investigation were poly(dimethylsiloxane) (PDMS) and a composite material consisting of PDMS and quartz (SiO₂). It is shown that the height and sharpness of jumps depend on the composition of the material and the stage of deformation. An analysis of differential scanning calorimetry (DSC) curves of the materials in the deformed and initial states suggests that deformation results in ordered domains in rubberlike polymers. This confirms the assumption that deformation jumps reflect the presence and the evolution of structural inhomogeneities in amorphous polymers.     

Structural heterogeneity and jumplike deformation of polymers on the mesoscopic level

This paper reports on the results of research into the jumplike deformation of two polymers based on poly(oxymethylene) (POM) with structural aggregates (spherulites) of different micrometer-scale sizes at a temperature of 290 K, as well as of polyimide (PI) and a PI + graphite composite at temperatures of 290 and 690 K. The creep rate under compression is measured with a laser interferometer in 0.3-μm deformation increments. It is found that, in the course of deformation on the micrometer scale, the creep rate varies nonmonotonically. Periodic variations of the creep rate correspond to a jumplike (stepwise) behavior of the creep. It is shown that the mean jumps in the microdeformation correspond to the mean sizes of poly(oxymethylene) grains and graphite particles in polyimide. The results obtained are in agreement with previously drawn conclusions: the deformation jumps are determined by the scale of ordered microaggregates typical of the structure under investigation.     

Inhomogeneity of deformation of solids at the nanometer level

A new method for processing interferometrically recorded deformation data has been implemented for studying an inhomogeneity in the rate and parameters of deformation jumps at the nanostructure level, which provides detection of deformation jumps of less than 300 nm. It is shown that the lower limit for deformation jumps lies in the range 10–30 nm for aluminum and is 130 nm for amorphous polymer (poly(methyl methacrylate)). It is assumed that the sizes of jumps correspond to scales of ordered structures, as was previously established for higher level structures. The results obtained make it possible to investigate more thoroughly the multilevel character of deformation and to evaluate the sizes of the nanostructural units, their evolution during deformation and under the effect of external fields, as well as their relation to the microscopic and macroscopic inhomogeneities of deformation.     

Jumplike deformation of γ-irradiated polymethyl methacrylate

Nonuniformity of the microdeformation rate and the parameters of microdeformation jumps were studied in the creep regime for a polymethyl methacrylate irradiated by various dozes of the Co-60 γ radiation. The creep rate during compression of the polymethyl methacrylate was measured by an interferogram on 300-nm deformation increments. It is shown that the periods L of rate oscillations (jumps of deformation) on three scale levels are dependent on the irradiation doze and are also changed after prolonged exposure of samples in air. In the doze range 0 to 330 kGy, both a decrease and an increase in L are observed, which corresponds to the unstable kinetics of radiation chemical processes. The deformation jumps permit estimates of the radiation effect on various structural levels. It is concluded that the effect of radiation on coarser microstructural formations is the largest.

     

Activation parameters of stepped deformation of polymers

Creep rates on short deformation base lines before and after a change in temperature and stresses were measured by interferometry to determine the activation energies and activation volumes of the process. It is shown that the activation parameters of polymer creep vary not only at a macroscopic level but also within the micron-size deformation steps. The largest potential barrier corresponds to the lowest rate in a step and plays the role of a “physical node.” The results confirm the supposition that micron-size jumps (steps) of polymer deformation are caused by the nonmonotonic nature of intermolecular interactions in microvolumes of this level. Fiz. Tverd. Tela (St. Petersburg) 40, 1635–1638 (September 1998)     

Serrated creep of zinc single crystals under compression in a magnetic field

The compressive creep rate of zinc single crystals was measured for sample deformation increments of 150 nm, which permits the measurement of deformation jumps larger than 300 nm. A weak magnetic field B = 0.2 T is shown to increase the average creep rate and decrease the height and sharpness of submicron-sized deformation jumps. Preliminary holding of a sample in a magnetic field also influences the creep rate and the characteristics of deformation jumps. The data are explained in terms of a model relating the effect of a magnetic field to the destruction of barriers to dislocation motion.     

Effect of carbonization temperature on the microplasticity of wood-derived biocarbon

The uniaxial compression strength under stepped loading and the 325-nm-stepped deformation rate of biocarbon samples obtained by carbonization of beech wood at different temperatures in the 600–1600°C range have been measured using high-precision interferometry. It has been shown that the strength depends on the content of nanocrystalline phase in biocarbon. The magnitude of deformation jumps at micro- and nanometer levels and their variation with a change in the structure of the material and loading time have been determined. For micro- and nanometer-scale jumps, standard deviations of the differences between the experimentally measured deformation rate at loading steps and its magnitude at the smoothed fitting curve have been calculated, and the correlation of the error with the deformation prior to destruction has been shown. The results obtained have been compared with the previously published data on measurements of the elastic properties and internal friction of these materials.     

Jumpwise deformation of polymethyl methacrylate in the microplasticity region

The deformation rate with a step of 325 nm has been measured under uniaxial compression at the initial stage of creep and shape recovery of a polymethyl methacrylate (PMMA) sample after unloading. The effect of low γ-ray doses and magnetic fields on the deformation has been studied. It has been shown that a weak pre-exposure of the PMMA sample structure to radiation and magnetic fields can cause a slight hardening in the microplasticity region. The deformation jump sizes have been determined on micro- and nanoscales. The effect of irradiation and magnetic fields manifests itself as redistributed contributions of various jumps to the deformation.     

Jumplike microdeformation of nanostructured metals

The parameters of microdeformation jumps for copper, aluminum, titanium, and Armco iron with the initial (annealed) structure and after equal-channel angular pressing are investigated in a creep mode under low compressive stresses. The strain rate is measured with a laser interferometer in 0.15-μm linear displacements. It is demonstrated that the values of the microstrain rate and the mean sizes of jumps for the annealed metals are larger than those for the metals subjected to severe deformation. It is revealed that there is a correlation between the jumps of microplastic deformation and the size of nanometal grains. The inference is made that, for nanostructured metals, as for other materials, the structural heterogeneity is one of the factors responsible for the jumplike deformation.     

Structural micromechanics of oriented polymers

To clarify whether the interfibrillar slippage occurs on plastic deformation of oriented polymers, flow creep of ultrahigh molecular weight polyethylene (UHMW PE) samples with various connectedness of microfibrils has been studied in a dead load mode at room temperature. The flow creep rate of melt-crystallized and gel-cast UHMW PE films drawn to various draw ratios, as well as of modified gel-crystallized samples (cross-linked/grafted or washed free of low molecular weight fraction) has been measured with the help of a unique laser interferometric technique (Doppler creep rate meter). The technique allows one to measure creep rates for deformation increments as small as 0.3 μ within an accuracy 1%. The interferometric technique enabled us to observe an extremely high variability of flow creep rate. It was recognized that the creep process accelerates or slows from time to time. A length of a loaded sample increased by multiple consecutive deformation jumps (or steps). The size distribution of the steps appeared to be controlled by the structure of interfibrillar regions. The influence of the latter on the variability of creep rate confirms a hypothesis that suggests a contribution of interfibrillar slippage to plastic deformation of oriented polymers. The observed phenomenon has been attributed to stick-slip motion of microfibrils and their aggregates sliding on each other under the action of applied stress. It was found that the creep rate decreases with increasing interfibrillar interaction.     

Regularities in the variation of the rate of stepped creep in polyethylene with different supermolecular structure

The study of stepped creep, previously discovered with micron-size deformation increments (ɛ) of polymers, in the form of a variation of the rate near the average value is continued. A scheme based on a laser interferometer was used to record the creep; this made it possible to perform precise measurements. Attention was focused on the degree of scatter of the rate h in the process of deformation of polyethylene fibers. It is shown that the creep rate of textured fibers is extremely nonuniform and pulsates continuously, forming beats of different periods, i.e., deformation jumps of different height. The ratio of h of the highest to the lowest rate for arbitrarily chosen small increments of the deformation has a maximum near the start of the “flow” stage and prior to fracture. The h-ɛ curve shifts along the deformation scale as the polymer structure changes, but the form of the curve and the overall level of h change very little. It is also established that the value of h for identical deformations is higher in more highly oriented polymers, and the value of h is higher in cross-linked structures than in unmodified structures. It is proposed that h reflects not only the deformation heterogeneity, but also influences crack formation during the creep process. Fiz. Tverd. Tela (St. Petersburg) 39, 580–585 (March 1997)     

Micro- and nanoscale instabilities of deformation in polymers

The rate and magnitude of the deformation in polymers under constant compressive stresses at room temperature have been measured. The use of laser interferometer has made it possible to perform measurements at small intervals of variations in the specimen length Δl = 0.325 μm, and the analysis of the form of beats has made it possible to estimate oscillations of the strain rate in nanoscale displacements. It has been shown that the average strain rate of polymers continuously varies and no creeping interval with a constant rate is observed. At all stages of smooth variations in the average rate, jumps of its current values corresponding to Δl from several nanometers to a hundred and more nanometers have been found. Changes in the structure with an increase in the deformation manifest themselves in an increase in the size of nanoscale jumps and in a complication of their shape.     

Effect of the magnetic field on nanometer-scale deformation jumps in polymers

The effect of a constant magnetic field on the rate of jumplike creep under compression is investigated for vitreous polymers with a globular structure. The interferometric method used for recording the creep makes it possible to measure deformation jumps from 300 nm and larger. It is demonstrated that the sizes of deformation jumps in polyester and epoxy resins decrease in the magnetic field (B = 0.2 T). Taking into account that the deformation jump size corresponds to the size of structural inhomogeneities, it is assumed that macroglobules under the action of a constant magnetic field are separated into smaller structural units on the nanometer level.     

Interfaces between nanostructures and stepwise creep in highly oriented polymers

A comparative laser-interferometric study of steady creep in oriented ultrahigh-molecular-weight polyethylene films differing in the structure of interfaces between nanosized structural units has been carried out to gain a better understanding of the creep mechanism in oriented polymer materials. In contrast to conventional methods, laser interferometry permits measurement of creep rates from very small strain increments (0.3 μm) to within 1%. This technique made it possible to detect the stepwise nature of plastic deformation in creep. The data obtained suggest that the creep rate and its periodic changes are controlled by the structure of the interfaces, and that the plastic deformation itself occurs to a considerable extent through shear of nanosized structural units relative to one another by an “acceleration-deceleration” type. It is proposed that the “deceleration” phase is due to a glide resistance created by some “stoppers” having either physical or chemical nature, which become destroyed and reappear again in the course of creep. Fiz. Tverd. Tela (St. Petersburg) 41, 1788–1791 (October 1999)     

Strength and microplasticity of biocarbons prepared by carbonization in the presence of a catalyst

The microdeformation has been investigated under uniaxial compression of beech-derived biocarbons partially graphitized during carbonization in the presence of a Ni- or Fe-containing catalyst. The strength and ultimate fracture strain have been determined at different temperatures of carbonization of the samples in the absence or in the presence of a catalyst. It has been shown using high-precision interferometry that the deformation of biocarbon samples under uniaxial loading occurs through jumps (in magnitude and rate of deformation) with axial displacements in the nanometer and micrometer ranges. The use of a catalyst leads to a decrease in the size of nanometer-scale jumps and in the number of micrometer-scale jumps. The standard deviations of the strain rate on loading steps from the smooth average dependence of the strain rate on the displacement have been calculated for micrometer-scale jumps. A similar characteristic for nanometer- scale jumps has been determined from the distortion of the shape of beats in the primary interferogram. It has been shown that the variation in the standard deviation of the strain rate with a change in the carbonization temperature is similar to the corresponding dependence of the ultimate fracture strain.     

Double jumps and transition rates for two dipole-interacting atoms

Cooperative effects in the fluorescence of two dipole-interacting atoms, with macroscopic quantum jumps (light and dark periods), are investigated. The transition rates between different intensity periods are calculated in closed form and are used to determine the rates of double jumps between periods of double intensity and dark periods, the mean duration of the three intensity periods and the mean rate of their occurrence. We predict, to our knowledge for the first time, cooperative effects for double jumps, for atomic distances from one and to ten wave lengths of the strong transition. The double jump rate, as a function of the atomic distance, can show oscillations of up to 30% at distances of about a wave length, and oscillations are still noticeable at a distance of ten wave lengths. The cooperative effects of the quantities and their characteristic behavior turn out to be strongly dependent on the laser detuning. Received 19 March 2001 and Received in final form 13 June 2001     

Step deformation of solid amorphous polymers

The variation of step deformation kinetics in solids is studied as a function of morphological factors. Oscillations of creep rate at micrometer increments of the amount of deformation, which reflect the step nature of the process, are investigated from an interferogram. It is shown that the plasticization of polymethyl methacrylate by dibutyl phthalate blurs the steps, while their height varies insignificantly. The results are explained using the concept of the netlike structure of amorphous polymers. The data obtained confirm the universal nature of jumps as a mode of evolution of deformation in various solids. The jumps reflect the cooperative nature of motion of kinetic units, and the regular variation of the characteristics of the jumps lends support to the definition of creep as a process of structural self-organization.