Computer simulation of rearrangements in chains of glassy polymethylene subjected at low temperature inelastic deformation

Molecular dynamics simulation of glassy polymethylene (PM) plastic deformation is performed up to ? = 30% in uniaxial compression regime at a temperature of 50 K, which is ～140 K below T _g of the polymer. All atoms of PM chains are represented explisitly (all-atom model). Calculations were performed for two series of samples with different molecular mass distribution of chains: Samples have average degree of polymerization DP ≈ 212 with Mn ≈ 3000 and Mw ≈ 9500 (the first series) and DP ≈ 350, Mn ≈ 5000 and Mw ≈ 9500 (the second series). Each sample contains 12288 -CH₂- monomeric units per computational sell. Nonaffine displacements of carbon atoms and conformational rearrangements in chains during deformation are visualized and analyzed. The transformation of relatively fragments of chains up to 16–20 monomer units length are basic structural units, non-conformational displacements of which controls plastic process. Relatively large nonaffine displacements are observed even in the range of low strains, which are usually interpreted as Hookean strains. In the range of yield tooth and steady plastic flow, the number of these displacements increases along with their amplitude. Conformational set of PM chains does not show a serious change during deformation. Analysis had shown that the number of conformational rearrangements of trans-gauche type in PM chains during deformation is small and such rearrangements do not play decisive role in the considered range of PM plasticity, even at ? > 15%, at the stage of the developed plastic flow.     

Mechanisms of anelastic deformation in solid polymers: Solidlike and liquidlike processes

Several aspects of anelastic deformation of glassy polymers that cannot be explained in terms of existing theories are considered. Resemblance in the stress-strain response for solids of various natures and structures, including semicrystalline and glassy polymers, organic and inorganic solids, and low-molecular-mass and high-molecular-mass compounds, is analyzed. It was pointed out that the phenomena of the yield peak, strain softening, strain concentration (localization) in narrow shear bands, and transient effects are characteristic of the plastic deformation of any solid. The same is true for differences in the kinetics and mechanism of deformation at low (T _def < 0.7T _g) and high deformation temperatures (T _def > 0.7T _g). The mechanism of plastic deformation is discussed in detail for glassy polymers; at microscopic and nanoscale levels, plastic deformation proceeds via two stages: initial nucleation of small-scale shear transformations and their further coalescence. This coalescence leads to the advance of the shear front in the sample and to the nucleation and displacement of classical shear bands. The heat of plastic deformation is released out at the coalescence of shear transformations. It was assumed that shear transformations are responsible for the development and evolution of the yield peak in glassy polymers, strain softening, and other phenomena. The proposed mechanism of deformation in glasses fully agrees with the results of thermodynamic measurements and other experimental data reported in the literature. Computer simulation makes it possible to visualize the scenario of nucleation and evolution of shear transformations at the atomic level.     

Structure and plastic deformation of aromatic main-chain mesomorphic copolyesters

Thermodynamic characteristics of inelastic deformation (work W _def, heat Q _def, and stored energy ΔU _def) are studied for aromatic main-chain copolyesters (CPEs) based on p-hydroxybenzoic acid and poly(ethylene terephthalate) (Rodrun and SKB-1), p-hydroxybenzoic acid, naphthalene carboxylic acid, and terephthalic acid with hydroquinone and dioxyphenyl (HX-6000 and HX-7000). The samples are deformed under an active uniaxial compression by ?_def ≈ 50% at room temperature. All CPEs are semicrystalline polymers; their degree of crystallinity is (depending on their prehistory) 5–30%, and the melting temperature of crystallites is 275–350°C. Seemingly, the glassy component of CPEs includes two interpenetrating glassy structures, S-1 and S-2, with different glass-transition temperatures Tg: 90–120 and 250–270°C, respectively. During loading, all coexisting crystalline and glassy structures of CPEs store residual strain ?_res. The kinetics of the temperature-stimulated strain recovery of ?_res is measured. In component S-1, strain recovery occurs in the temperature interval ranging from T _room to 120°C. In the crystalline phase, this process occurs in the melting-temperature interval. In component S-2, strain recovery ?_res commences at T > 120°C. In CPEs, all structural components are involved in deformation at different ?_def. At small strains only component S-1 is deformed; then, at ?_def ≈ 10–15%, component S-2 is involved in the deformation. Crystallites join this process at ?_def > 20–25% (? _y = 8–10%). In CPE, two modes of deformation arise: reversible elastic (retarded elastic) and true plastic irreversible deformation. True plastic permanent strain always exists in the deformed CPEs. Deformation of all CPEs proceeds easier than that of all “common” glassy polymers (polystyrene, poly(methyl methacrylate), etc.). In CPEs, the yield stress and compressive modulus appear to be ≈40–50% lower than in “common” glassy polymers. It seems that the mesomorphic structure of LC CPEs enhances the elementary plastic processes in them. Thermodynamic characteristics of the S-1 phase plasticity are compared with the behavior of “common” glassy polymers. At the early stages of loading, nearly all mechanical work of deformation W _def spent is stored in phase S-1 in the form of δU _def, as in all “common” glassy polymers. This fact implies that the inelastic deformation of LC glasses commences with the nucleation of small-scale and localized intermolecular transformations of the nonconformational type. In both mesomorphic and “common” glassy polymers, the stage of nucleation of such transformations controls the overall kinetics of the inelastic and plastic deformation. Nucleation does not depend on chain rigidity, a circumstance that conflicts with the model of forced elasticity. It seems that crystallites in CPE are deformed according to crystallographic mechanisms. Currently, neither the structure nor the deformation mechanism of component S-2 is known.     

Residual strain recovery,molecular mobility,and plasticity of solid aromatic copolyesters of <Emphasis Type="Italic">p</Emphasis>-hydroxybenzoic acid with poly(ethylene terephthalate)

The processes of thermally stimulated recovery of internal energy stored by a specimen during deformation and of residual strain ?_res in weakly oriented liquid-crystalline 80: 20 and 60: 40 (by mole) copolyesters of p-hydroxybenzoic acid with PET, as well as in nonoriented (amorphous and crystalline) PET, were studied. All the materials were deformed via uniaxial compression at room temperature. It was shown that ?_res is built up in all phases that coexist in the materials: the glassy, crystalline, and intermediate phases, of which the last presumably contains imperfect crystals of a small size. Excess energy of strain is stored in the glassy phase with a built-in LC order and, probably, in copolyester crystallites. The main deformation processes in the glassy component of the materials are the nucleation and development of small-scale shear transformations in exactly the same manner as in the earlier studied glassy polymers that do not form an LC structure. Consequently, enhanced rigidity of the polyesters chains and their LC order have no qualitative effect on the mechanism of plastic deformation of the copolyester glasses. However, the LC structure leads to a decrease in the yield stress σ_y and the compression and shear moduli of the copolyesters in comparison with those of conventional glassy polymers i.e., reduces the resistance of the materials toward plastic deformation. With an increase in strain, various forms of Brownian motion of chains, beginning from the rotation of p-hydroxybenzoic acid fragments, become successively involved in the process of their deformation at room temperature. Correspondingly, the thermally stimulated recovery of ?_res exhibits peaks of small-scale motions of aromatic chain fragments in the glassy phase of copolyesters, a phenomenon that is not observed in PET and other aliphatic polymer glasses. The intensity of these peaks depends on the value of ?_res built up by the specimen. Even small strains (≈5?40%) in the specimens irreversibly destroy the initial orientation of chains in copolyesters. To explain this effect, the concept of domain disorientation of their structure is proposed.     

A MONTE CARLO STUDY OF THE GLASS TRANSITION OF POLYMETHYLENE*

By this Monte Carlo simulation we studied the glass transition of polymethylene using themodified bond-fluctuation model combined with considering the rotational-isomeric state model. Theconfigurational properties in the polymethylene (PM) melts, such as the mean length, the mean energy perbond and the mean square radius of gyration were monitored. We found that the chains cannot be in theequilibrium states after a very long time when the temperature of the dense PM chains decreases to 120 K. Asthe melt vitrifies, these quantities gradually become independent of temperature in a narrow range. The glasstransition temperature T_g depends upon the chain length of PM chains, and extrapolation to (CH_2)_∞givesT_g~∞=212 K. The dynamics in the PM melts was also studied. It was found that the diffusion coefficients canbe described by the Vogel-Fulcher law and the Vogel-Fulcher temperature T_0 is 124 K. This method may beused to investigate the glass transition of other real polymer chains.     

A molecular study on the reinforcement of polymethylene elastomers

Monte Carlo simulations are carried out on filled networks of polymethylene (PM), which are modeled as composites of PM chains and three-dimensional cubic lattices of filler particles. Calculations are carried out for PM chains with various chain lengths n and various cubic unit dimensions a. The elastic behavior is investigated by using a realistic rotational-isomeric-state (RIS) model and enumeration calculation method. The average conformations, such as a priori probability P_η and the segmental orientation function 〈P₂(cosζ)〉 of PM chains are also calculated. In the process of tensile deformation, the a priori probability P_t increases with elongation ratio λ, however, it decreases with increasing cubic unit dimensions a. The segmental orientation distribution function 〈P₂(cosζ)〉 of deformed PM chains decreases with increasing cubic unit dimensions a, especially in the region of large deformation. Average Helmholtz free energy per bond becomes small when increasing cubic unit dimensions a, and average energy per bond becomes large when increasing cubic unit dimensions a. We find that the elastic force increases with elongation ratio for small λ, and abruptly for large λ. In the meantime, the energy contribution to elastic force is negative and significant. It is also shown that the elastic force and the energy contribution to elastic force is almost the same with various cubic unit dimensions a. The ratio f_u/f ranges from −0.4 to −0.6 at T=425 K. The reinforcement effects on the Helmholtz free energy 〈A〉 and energy 〈U〉 are important; however, the effect on the elastic force is insignificant. Our calculation may provide some insight into the macroscopic phenomena of rubber elasticity.     

Inelastic deformation of glassy polyaryleneetherketone: Energy accumulation and deformation mechanism

The plastic deformation of glassy non-annealed polyaryleneetherketone (PAEK) was investigated via deformation calorimetry and thermally stimulated recovery of residual strain. Polymer samples were deformed at room temperature under uniaxial compression up to ε_def =–(40?50)% at a rate of 0.04 min^?1. It was found that PAEK behaves in the deformation process similarly to many other glassy polymers: It stores internal energy excess at loading and contains two types of different inelastic strain carriers, namely the delayed elastic (ε_de) and plastic (ε_pl) strain carriers. The maximum level of the accumulated energy in PAEK reaches ≈ 8.3 J/g, which is close to those for glassy polystyrene and polycarbonate. Nearly all the deformation energy stored in PAEK is carried by the delayed-elastic strain. The carriers of plastic strain carry no extra energy or a very small amount of it. The inelastic deformation of glassy PAEK proceeds in two stages. The carriers of ε_de are nucleated at the first stage of the deformation process, and the carriers of ε_pl are nucleated at the second stage. It was shown that, during glassy-polymer loading, the molecular level structures carrying ε_pl never appear by themselves, but appear only as a result of spontaneous reorganization of ε_de. In other words, the plastic deformation appears in PAEK owing to the two-step process. This situation is typical for all glassy polymers.     

Thermally induced low-temperature relaxation of plastic deformation in glassy organic polymers and silicate glasses

A deep analogy between the processes of low-temperature thermally induced relaxation of plastic deformation in amorphous polymers and inorganic glasses is observed. The results of the calculation of the activation energy and activation volume of this relaxation process in terms of the excited state model satisfactorily agree with the experimental data obtained for both epoxy polymer systems and sheet silicate glasses. This evidence allows us to conclude that the initial stage of macroscopic plastic deformation in glassy systems involves small critical displacements of excited atoms (groups of atoms) that are provided by local rearrangements of neighboring particles (entropy fluctuations). In the vicinity of the yield point, the number of excited atoms per unit volume induced by the action of mechanical stresses appears to be quite sufficient (10²⁶–10²⁷ m^?3) for promotion of a marked plastic deformation of glasses and preservation of appreciable amounts of internal energy.     

Plastic deformation of glassy polymethylene: Computer-aided molecular-dynamic simulation

Molecular-dynamic simulation of low-temperature plastic deformation (T _def = 50 K, T _def/T _g ≤ 0.3) is studied for glassy polymethylene under the regime of active uniaxial compression and tension for a cell composed of 64 chains containing 100 -CH₂ groups in each (as united atoms) and with periodic boundary conditions. Thirty-two such cells are created, and, in each cell, polymethylene chains in the statistical coil conformation are independently constructed. The cells are subjected to isothermal uniaxial compression at T _def = 50 K by ɛ = 30% and by ɛ = 70% under uniaxial tension. In the course of loading, a σ-ɛ diagram is recorded, while the mechanical work spent on deformation, the changes in the overall potential energy of the system, and the contributions from various potential interactions (noncovalent van der Waals bonds, chemical links, valence and torsional angles) are estimated. The results are averaged over all 32 cells. The relaxation of stored potential energy and residual strain after complete unloading of the deformed sample is studied. The relaxation of stored energy and residual strain is shown to be incomplete. Most of this energy and strain is stored in the sample at the deformation temperature for long period. The conformational composition of chains and the average density of polymer glass during loading are analyzed. Simulation results show that inelastic deformations commence not with the conformational unfolding of coils but with the nucleation of strain-bearing defects of a nonconformational nature. The main contribution to the energy of these defects is provided by van der Waals interactions. Strain-bearing defects are nucleated in a polymer glass during tension and compression primarily as short-scale positive volume fluctuations in the sample. During tension, the average density of the glass decreases; during compression, this parameter slightly increases to ɛ ≈ 8% and then decreases. An initial increase in the density indicates that, during compression and at ɛ < 8%, coils undergo compactization via an increase in chain packing. During compression, the concentration of trans conformers remains unchanged below ɛ ≈ 8% and then decreases. During compression, it means that in a glass, coils do not increase their sizes at strains below ɛ ≈ 8%. During tensile drawing, coils remain unfolded below ɛ ≈ 35%; at higher strains, coils become enriched with trans conformers or unfold. At this stage, the concentration of trans conformers linearly increases. The development of a strain-induced excess volume (strain-bearing defects) entails an increase in the potential energy of the sample. Under the given conditions of deformation, nucleation of strain-bearing defects and an increase in their concentration are found to be the only processes occurring at the initial stage of loading of glassy polymethylene. The results of computer-aided simulation are compared with the experimental data reported in the literature.     

Elastic behavior of non-Gaussian polymethylene chains

In this paper, elastic behaviors of non-Gaussian polymethylene (PM) chains with chain length N=100 are investigated by rotational isomeric state model. Here the tetrahedral lattice of PM chain and the non-local interaction of Sutherland potential are adopted. In the metropolis movement of PM chain, a four-bond movement model is used. The average energy and average Helmholtz free energy with various elongation ratios λ are calculated by Monte Carlo simulation method. The average energy increases with elongation ratio λ and the average Helmholtz free energy decreases with elongation ratio λ. The elastic force f and the energy contribution to elastic force f_u can be obtained from f=∂〈A〉/∂r and f=∂〈U〉/∂r. We find that the elastic force f increases with elongation ratio λ and the energy contribution f_u decreases with elongation ratio λ, and f_u is less than zero. The ratio f_u/f is close to −0.21 for λ?1.25, and −0.04 to −0.35 for λ>1.25 at T=364 K. In our calculation, the rubber elasticity may be discussed in terms of the chemical structure of polymer chains.     

Plasticity Mechanism for Glassy Polymers: Computer Simulation Picture

This review summarizes the data published over the past two and a half decades on the mechanism of plastic deformation of bulk isotropic linear glassy polymers in uniaxial tension, compression, and shear at low deformation temperatures (Т_def < 0.6Т_g) and moderate loading rates. The main attention is focused on studies concerning the numerical computer simulations of plasticity of organic polymer glasses. The plastic behavior of glassy polymers at nano-, micro-, and macrolevels in the range of macroscopic strains up to ≈100% is discussed. Plasticity mechanisms are compared for organic, inorganic, metallic, polymer, and nonpolymer glasses with different chemical structures and types of interparticle interactions. The general common mechanism of plasticity of glassy compounds, the nucleation of plasticity carriers in them, and the structure of such carriers and their dynamics are covered. Within the framework of the common plasticity mechanism, the specific features of deformation in glassy polymers are analyzed. Specifically, the participation of conformational transformations in macromolecules in the deformation response of polymer glasses, change in intensity of the yield peak with the thermomechanical prehistory of the sample, and the role of van der Waals interactions in the accumulation of excess potential energy by the sample under loading are considered. The role of free volume and structural and dynamic heterogeneities in the plasticity of glasses is also discussed.     

Thermodynamics of inelastic deformation of amorphous and crystalline phases in linear polyethylene

Thermodynamic parameters (work W _def and heat Q _def) of inelastic deformation (uniaxial compression up to ɛ_def = 50%) are measured for six samples of high-molecular-mass linear PE at room temperature under the regime of active loading. Energy excess ΔU _def accumulated by the samples subjected to loading are calculated in terms of the first law of thermodynamics. All thermodynamic characteristics linearly increase with crystallinity χ of PE, thus making it possible to extrapolate their values to χ = 0 and 100% and to find the contributions of the amorphous and crystalline phases of the polymer to the overall thermodynamics of deformation. Both of the PE phases contribute to W _def and ΔU _def, while the crystalline phase alone contributes to heat Q _def. At ɛ ≥ 30%, the energy contribution from the amorphous phase exceeds that from the crystalline phase. A comparison between the plastic behavior of PE crystals and glassy polymers demonstrates that PE crystallites are easier deformed (requires less work W _def) than glassy polymers. At the same time, the amorphous phase of PE is harder to deform (requires more work W _def and stores more energy ΔU _def) than noncrystalline rubbers, apparently because of the deformation of tie chains. The thermodynamic characteristics of deformation are compared for three materials: crystalline metals, PE, and glassy polymers. The similarities and differences in their plastic behaviors are considered.     

Thermal jump measurement of the activation energy of trapped electrons in 3-methylpentane glass

When the temperature of a photoionized TMPD-3MP glassy solution is suddenly raised from 77 K to 77 K + ΔT (ΔT ～ 1 K), the recombination luminescence is enhanced, goes through a broad maximum and starts decaying. This is interpreted in terms of glass relaxation on warming. By means of a formally described model, the activation energy for electron detrapping is found to be 0.65 eV. In our opinion this large value indicates that electron detrapping is due to slow molecular rearrangements in the matrix.     

Peroxy radicals as motional probes at the end of isolated polystyrene chains and on the cellulose surfaces in vacuum

The isolated polystyrene chains spin-labeled with peroxide radical at the free end (IPSOO) in which the chain roots were covalently bonded to the surface of microcrystalline cellulose (MCC) powder were produced by mechanochemical polymerization of styrene initiated by MCC mechanoradicals. The IPSOO was used as motional probes at the ends of isolated polystyrene chains tethered on the surface of MCC powder. Two modes for the molecular motion of IPSOO were observed. One was a tumbling motion of IPSOO on the MCC surface, defined as a train state, and another was a free rotational motion of IPSOO protruding out from the MCC surface, defined as a tail state. The temperature of tumbling motion (T _tum ) of IPSOO at the train state was at 90 K with anisotropic correlation times. T _tum (90 K) is extremely low compared to the glass transition temperature (T _g ^b ; 373 K) of polystyrene in the bulk. At temperatures above 219 K, the IPSOO was protruded out from the MCC surface, and freely rotated at the tail state. The train–tail transition temperature (T _train–tail ) was estimated to be 222 K. T _tum (90 K) and T _train–tail (222 K) are due to the extremely low chain segmental density of IPSOO on the MCC surface under vacuum. The interaction between IPSOO and the MCC surface is a minor contributing factor in the mobility of IPSOO on the surface under vacuum. It was found that peroxy radicals are useful probes to characterize the chain mobility reflecting their environmental conditions.     

Neutron powder diffraction and magnetic measurements on CsMnI3

Results of neutron powder diffraction and magnetic measurements on single crystals of CsMnI₃ are reported. Three-dimensional ordering takes place at T_c = 11.1(3) K. Above T_c very broad peaks occur in the neutron powder diffraction diagram, indicating one-dimensional correlations along the chain. Below T_c the Mn²⁺ ions are coupled antiferromagnetically along the chain. Interchain exchange leads to a 120° structure, slightly distorted due to anisotropy. One-third of the chains have their magnetic moment parallel to the c axis and the rest of the chains have magnetic moments making an angle of 50(2)° with the c axis. The magnetic moment as found from neutron diffraction extrapolated to 0 K is 3.7(1)μ_B, indicating a considerable zero-point spin reduction. The intrachain exchange $\text{J}\text{k}$ was found to be ?9.1(1)K, whereas the ratio of the inter- to intrachain interaction was determined as $\text{J′}\text{J}\text{= × 10}{}^{\mathrm{?3}}$. A spin flop occurs at H = 54 kOe on application of a magnetic field parallel to the c axis. When a field perpendicular to the c axis is applied a spin reorientation occurs at 1 kOe.     

A new method of deformation calorimetry applied to copper single crystals

A new method of deformation calorimetry is described by which the change of stored energy with deformation is measured. For the determination of the dynamic energy balance of plastic deformation, we deform metal single crystals by tension and measure the applied load K(t), the effective deformation rate E_exp and the temperature T(t) of our specimen with high accuracy during deformation. The load is determined by using a reference signal (load-fixpoint), the deformation rate by means of a tensionmeter which records the strain directly at the crystal. Measurement of specimen temperature is carried out with the aid of micro-thermistors of high temperature resolution, ΔT ? 2 · 10^?5 K, and time resolution Δt ? 0,1 s. An essential feature of our method is the procedure developed for evaluation of the T(t)-curves (which are severely influenced by unavoidable heat conduction) using the thermoelastic effect. It works by means of the response function of heat conduction which we record during elastic deformation of the specimen.Some results are given on the stored energy and its change of a copper single crystal deformed at room temperature.     

A Monte Carlo Study of the Elastic Behavior of Polymethylene Chains

The rubber elastic behaviors of long polymethylene (PM) chains are investigated using Monte Carlo simulations and considering the rotational‐isomeric‐state model. Through the Monte Carlo method we can generate many PM chains in the equilibrium states, and obtain the average Helmholtz free energy 〈A〉 and average energy 〈U〉. Chain dimensions and thermodynamic statistical properties of long PM chains under various elongation ratios λ are also calculated. We find that the elastic force f increases with elongation ratio λ, and that energy contribution f_u to the elastic force is negative and significant. The ratio f_u /f ranges from –0.37 to –0.32 at T = 300 K and from –0.53 to –0.40 at T = 413 K, and decreases with increasing temperature, which agrees with the experimental data. Our calculations may provide some insights into the macroscopic phenomena of rubber elasticity.     

Phase transitions and relaxation processes in ethylene-vinyl acetate copolymers probed by fluorescence spectroscopy

The steady-state fluorescence of pyrene and anthracene are used to investigate the relaxation processes of several random ethylene-co-vinyl acetate copolymers, EVA, with defined comonomer compositions (EVA-9, EVA-18, EVA-25, EVA-33 and EVA-40). The temperature of the relaxation processes are compared with those of low-density polyethylene (LDPE) and poly(vinyl acetate) (PVAc). The polymer relaxation processes are assigned to T_g=300-310 K (glass transition temperature of the PVAc); T_α=270-300 K (relaxation processes of the ethylene units present in LDPE and EVA); T_g=220-250 K (glass transition of the LDPE and of the EVA); T_γ or T_β=160-190 K (relaxation processes of interfacial defects of methylenic chains of LDPE and rotation of the acetate group of the PVAc and the EVA); and T_γ=90-130 K (relaxation processes of small sequences of methylene units of LDPE and end groups of PVAc). An Arrhenius-type function was employed as an attempt to represent the experimental data of fluorescence intensity versus temperature above the γ-relaxation temperature. As obtained with other techniques, there is not a simple relationship between the polymer relaxation processes and the vinyl acetate content that can be explained by the morphology in these copolymers.     

Structural aspects of the metal-insulator transitions in V0.985Al0.015O2

The crystal structure of V_0.985Al_0.015O₂ has been refined from single-crystal X-ray data at four temperatures. At 373°K it has the tetragonal rutile structure. At 323°K, which is below the first metal-insulator transition, it has the monoclinic M₂ structure, where half of the vanadium atoms are paired with alternating short (2.540 Å) and long (3.261 Å) V-V separations. The other half of the vanadium atoms form equally spaced (2.935 Å) zigzag V chains. At 298°K, which is below the second electric and magnetic transition, V_0.985Al_0.015O₂ has the triclinic T structure where both vanadium chains contain V-V bonds, V(1)-V(1) = 2.547 Å and V(2)-V(2) = 2.819 Å. At 173°K the pairing of the V(1) chain remains constant: V(1)-V(1) = 2.545 Å, whereas that of the V(2) chain decreases: V(2)-V(2) = 2.747 Å. From the variation of the lattice parameters as a function of temperature it seems that these two short V-V distances will not become equal at lower temperatures. The effective charges as calculated from the bond strengths at 298 and 173°K show that a cation disproportionation has taken place between these two temperatures. About 20% of the V⁴⁺ cations of the V(1) chains have become V³⁺ and correspondingly 20% of the V⁴⁺ cations of the V(2) chains have become V⁵⁺. This disproportionation process would explain the difference between the two short V-V distances. Also it would explain why the T → M₁ transition does not take at lower temperatures.     

Plastic deformation of polypropylene. IV. Wide-angle x-ray scattering in the neck region

Wide-angle x-ray scattering (WAXS) patterns of two polypropylene samples, a quenched sample drawn at 21°C and an annealed sample drawn at 100°C, were investigated in a range of values of draw ratio λ very closely spaced through the neck region. In both cases, a range of small λ where deformation occurred by spherulite deformation was followed by one of higher λ where microfibrils were formed. The contribution to the WAXS pattern of microfibrils could be clearly distinguished from that of deformed spherulites because of the better orientation parallel to the draw direction of the former as compared to the latter. Additionally, for a drawing temperature of 21°C, microfibrils crystallize in the “smectic” phase as compared to the monoclinic phase for the initial sample and deformed spherulites. At this temperature, plastic deformation proceeds through the spherulite deformation mechanism up to λ = 1.4 accompanied by an increase in chain orientation with increasing λ. For λ > 1.4 plastic deformation appears to occur exclusively through microfibril formation. For drawing at 100°C, spherulite deformation is accompanied by very little change in chain orientation up to λ = 2, where microfibril formation begins. For λ > 2 (T_d = 100°C) plastic deformation is accompanied by both microfibril formation and some spherulite deformation as reflected by changes in both orientation and crystallite size. At this temperature the lateral crystallite size in the microfibrils is related to the long period according to the “equilibrium crystallite shape” previously found for annealed polypropylene.