Glassy Zone Research Articles

Time–temperature correlations of amorphous thermoplastics at large strains based on molecular dynamics simulations

In this paper, we investigate the time–temperature correlation of amorphous thermoplastics at large strains based on coarse-grained molecular dynamics simulations. This correlation behavior is characterized by the strain hardening modulus in uniaxial tension simulations at different strain rates across the glass transition region. The temperature regime is divided into a melt zone, a glassy zone, and a transition zone between them, according to the storage modulus calculated from dynamic mechanical analysis (DMA) at small strains. In the melt zone, the existence of time–temperature superposition (TTS) at large strains is verified by constructing a master curve of the hardening modulus. The obtained shift factors are then compared to those from DMA at small strains, showing that the TTS behavior is transferable between small and large strains. In the glassy zone, the effects of time and temperature are not superposable at large strains but still can be correlated. To demonstrate this correlation behavior, we introduce a level set of the hardening modulus with a variable pair of strain rate and temperature. Pairs lying in the same level result in coincident stress–strain curves at large strains. The transferability of the correlation behavior between large and small strains is validated by comparing these stress–strain curves at small strains in the pre-yield region. In the transition zone, the correlation behavior is studied with both aforementioned methods, showing that TTS is applicable to large strains but not transferable to small strains. Finally, we propose a phenomenological constitutive model for uniaxial tension to demonstrate the time–temperature correlation at large strains, considering different constant strain rates and temperatures.

Understanding the spatio-temporal evolution of fractures in pillow basalt

We investigated the origin and spatio-temporal evolution of cooling fractures in pillow basalt which undergo thermal contraction after their eruption in an aqueous environment. Through a computer-based simulation using Fourier transformation, the thermo elastic stress displacement profiles within individual pillow units are determined. The scaled model (pillow diameter - 1 meter) generated radial, linear fractures perpendicular to pillow margin and irregular discrete flaws in the pillow interior like the ones observed in natural examples. Radial linear fractures of 3–5 centimetre in length have been measured in pillows of average one-metre diameter from the Maradihalli region, in the Chitradurga Schist Belt, India. An estimated time of 94–118 minutes was required to get radial fractures of similar length in the simulation. Our model efficiently replicated the generation and distribution of thermal fractures and allowed an estimation of cooling time for the peripheral glassy zone but has limitations in deciphering the formation of fracture networks in progressively crystalline inner zone of pillows.

Thermo-mechanical properties and blend behaviour of cellulose acetate/lactates and acid systems: Natural-based plasticizers

This work brings together thermo-mechanical and structural information for plasticized cellulose acetate (CA) by lactates and octanoic acid. CA are processed with plasticizer due to their high Tg and their strong H-bonding network. We prepared CA / plasticizer blends by corotative twin screw extruder and by solvent casting methods. The study of the different relaxations and of the glassy zone modulus was performed by dynamic mechanical analysis (DMA). The miscibility range of cellulose acetate blends were identified by the analysis of the tan δ. Depending on the composition of the system, one or two transitions are noted, this last result indicates the presence of a phase rich in CA and another in plasticizer. To connect this information to crystallinity and molecular organization, X-ray diffraction analyses were carried out. The disappearance of crystallinity allows the plasticization of previously inaccessible zones, causing a glassy modulus drop of more than 1000 MPa.

A Mathematical Model for Amorphous Polymers Based on Concepts of Reptation Theory

Mechanical behaviors of amorphous polymers have been investigated in all aspects from macroscopic thermodynamics to molecular dynamics in past five decades. Most models either have too complex mathematics or can only explain mechanical behaviors of specific materials under certain defined conditions. In this article, a mathematical model is proposed to understand mechanical behaviors of amorphous polymers with aid of the concepts of reptation theory. This new model is capable to match most experimental results of different amorphous polymers for a wide range of time and temperature effect from rubber zone to glassy zone. Above glass transitional temperature, the model shows hyperelastic behavior. Below glass transitional temperature, elastic–viscoplastic properties can be obtained. In the proposed model, no yielding surface is assumed. Hyperelasticity and Mullin's effect are illustrated in a different way without assuming strain energy function in advance. Yielding stress is controlled by Young's moduli, defect density, and defect velocity of molecular chains. Anisotropic plasticity is simply controlled by anisotropic Young's moduli. Therefore, no additional anisotropic parameters are needed to define anisotropic yielding surface. Strain rate, temperature, and hydrostatic pressure effects on yielding stress are through their effect on Young's moduli. Linear elastic, hyperelastic, viscoelastic, and viscoplastic models are put into one single equation, which makes the mathematical structure very easy to understand and easy to use. This model is validated by comparing with five existed experimental data. Proposed model also shares some features similar to the old well‐known large deformation models for amorphous polymers. POLYM. ENG. SCI., 59:2335–2346, 2019. © 2019 Society of Plastics Engineers

Glass formation by severe plastic deformation of crystalline Cu|Zr nano-layers

We use molecular dynamics simulation to study the formation of glasses during severe plastic deformation of crystalline Cu|Zr nano-layers in a simple shear geometry. The early stage of plasticity is governed by dislocation plasticity. Dislocation-interface interaction induces interface roughening and slow atomic-level intermixing around interfaces. A solid-state crystal-to-amorphous transition starts near the interfaces. At high strain, the interfaces are refined to merge, leading to the formation of an intermixed glassy zone that eventually spans our simulation cell. Dislocation emission is then suppressed and strain is fully accommodated by this glassy phase. We characterize the crystal-to-amorphous transition using local structural measures, such as the pair distribution function and Voronoi analysis. The onset of glass formation occurs at a critical shear strain that increases with layer thickness. Our simulations indicate that the parameter controlling this onset is the theoretical affine interface distance, i.e. the amorphization occurs at a critical value of around 3–4 nm that increases slightly with the increase of layer thickness. Our work provides insights on mechanically driven glass formation in multicomponent systems, as e.g. realized in ball-mills or high-pressure torsion experiments.

Dynamical rigidity of cellulose derivatives in melts

Dynamic birefringence and viscoelasticity for cellulose acetate butyrate, CAB, were measured simultaneously at various temperatures covering a wide frequency region from the rubbery plateau to the glassy zone in order to discuss the viscoelastic segment size of cellulose. The segment sizes for cellulose derivatives are larger than vinyl polymers, reflecting the stiff chain structure of β-linked D-glucose units (about 10 glucose units per segment).

Dynamic Segment Size of the Cellulose Chain in an Ionic Liquid

Viscoelasticity and strain-induced birefringence under oscillatory shear flow of cellulose/1-buthyl-3-methylimidazolium chloride (BmimCl) solutions were measured at various temperatures covering a wide frequency zone from the terminal flow to the glassy zone for dilute (2 wt %) and semiconcentrated solution (10 wt %) to clarify the dynamical segment size of the cellulose chain. The estimated dynamical segment size, MS, obtained from viscoelasticity is much smaller than that from flow birefringence. MS estimated from dynamic birefringence was 2300 corresponding to 14 repeating glucose residues from 2–10 wt %, showing weak concentration dependence. This value is comparable to the reported value of Kuhn segment size, MK. This relationship, MS ≈ MK, holding even at dilute solution, is in contrast with the large difference (MS ≈ 5MK) for polystyrene in dilute solution, indicating that the chain rigidity affects the relationship between MS and MK.

Temperature and strain rate dependence of syntactic foam under tensile and shear loads

The behaviour of syntactic foam is strongly dependent on temperature and strain rate. This research focuses on the behaviour of syntactic foam made of epoxy and glass microballoons in the glassy, transition and rubbery regions. Both epoxy and epoxy foam are investigated separately under tension and shear loadings in order to study the strain rate and temperature effects. The results indicate that the strength and strain to failure data can be collapsed onto master curves depending on temperature reduced strain rate. The highest strain to failure occurs in the transition zone. The presence of glass microballoons reduces the strain to failure over the entire range considered, an effect that is particularly significant under tensile loading. However, as the microballoons increase the elastic modulus significantly in the rubbery zone but reduce it somewhat in the glassy zone, the effect on the strength is more complicated. Different failure mechanisms are identified over the temperature-frequency range considered. As the temperature reduced strain rate is decreased, the failure mechanism changes from microballoon fracture to matrix fracture and debonding between the matrix and microballoons.

Origin of crystal-poor, differentiated magmas: insights from thermal gradient experiments

Crystal-poor, differentiated magmas are commonly erupted from shallow, thermally zoned magma chambers. In order to constrain the origin of these magmas, we have experimentally investigated crystallization, differentiation and crystal-melt separation in presence of a thermal gradient. Experiments have been designed taking advantage of the innate temperature gradient of the piston cylinder apparatus and carried out on a phonolitic system at 0.3 GPa and temperature ranging from 1,050 to 800°C. Crystallization degree and melt composition in experimental products vary as a function of the temperature gradient. In particular, melt composition differentiates from tephri-phonolite (starting material) to phonolite moving from the hotter, glassy zone (T ≤ 1,050°C) towards the cooler, heterogeneously crystallized zone (T ≤ 900°C) of the charge. The heterogeneously crystallized zone is made up of: (1) a crystal-rich, mushy region (crystallinity >30 vol%), (2) a rigid crystal framework (crystallinity ≤80 vol%) and (3) glassy belts of phonolitic glass at the top. Thermal gradient experiments picture crystallization, differentiation and crystal-melt separation processes occurring in a thermally zoned environment and reveal that relatively large volumes of crystal-poor melt (glassy belts) can originate as a consequence of the instability and collapse of the rigid crystal framework. Analogously, in thermally zoned magma chambers, the development and collapse of a solidification front may represent the controlling mechanism originating large volumes of crystal-poor, differentiated magmas.

On the Viscoelastic Segment Size of Cellulose

Dynamic birefringence and viscoelasticity of cellulose acetate propionate were measured at various temperatures covering a wide frequency region from the rubbery plateau to the glassy zone in order to determine the viscoelastic segment size of cellulose. The complex Young's modulus was separated into two components, R and G components. From the limiting modulus at high frequencies of the R component, molecular weight of viscoelastic segment was determined as 3100. This value is the largest one among amorphous polymers previously determined. Larger dynamic segment size reflects the rigid chain structure of β linked D-glucose units (about 10 glucose units per segment). Number of segments per entanglement strand was also estimated to be 4. Reflecting the small segment number per entanglement strand, most of reorientation of segment (relaxation of stress) was found to be delayed until the terminal flow zone.

Hot macro-hardness of Zr52.5Al10Ni10Cu15Be12.5 bulk metallic glass

The hot hardness behavior of Zr52.5Al10Ni10Cu15Be12.5 bulk metallic glass is studied from ambient temperature to the temperature over Tx (the onset crystallization temperature) using a hot macro-hardness tester and scanning electron microscopy (SEM). The results show that the hot hardness behavior of Zr52.5Al10Ni10Cu15Be12.5 bulk metallic glass can be classified into 4 zones: the glassy zone in which the hardness almost linearly decreases with the increase of temperature, the viscoelastic zone in which the hardness is nearly unchanged, the viscous flow zone in which the hardness quickly tends towards near zero with temperature, and the crystallization zone in which the hardness sharply increases. The high temperature deformation behavior and the easy processable deformation region for bulk metallic glasses are also discussed on the basis of the hot marco-hardness.

Characterization of low temperature dielectric processes in Poly(dicyclohexyl-itaconate)

Thermally stimulated depolarization current experiments (TSDC) have been carried out on poly(dicyclohexyl itaconate) (PDCHI) in the glassy state. The polymer exhibits three relaxation zones in the interval of temperature studied: a δ-relaxation at ∼130 K, a complex γ-process, in the temperature interval of 140 K to 200 K, and the β-process in the range of 210–270 K. The loss factor of PDCHI in the glassy zone has been reproduced from the partial depolarization data by using the elementary relaxation times and activation energies. The results show the existence of at least two relaxation processes in γ- and β-zones. A tentative explanation of the molecular origin of the observed secondary relaxations has been done by means of molecular mechanics (MM). At this respect, we perform a comparison of the relaxational data of PDCHI and those corresponding to PCHMA. This comparison allows us to confirm the relevant role played by the cyclohexyl ring in the δ- and γ-relaxations.

‘Column on column’ structures as indicators of lava/ice interaction, Ruapehu andesite volcano, New Zealand

Lava flows of the Mangawhero Formation (ca. 15–60 ka) on Ruapehu volcano erupted during the last glaciation. In a distal flow lobe at Tukino, on the east side of the mountain, small secondary columns (10–20 cm thick) have formed on the sides of large, rectangular, primary (0.5–3 m thick) cooling columns. Thick (10 m+) zones of such small columns form a lateral and basal outer rind of the lobe. As they do not mark glassy zones of quenching, these secondary columns are interpreted as being formed by a second cooling event at temperatures below the boundary between the low creep and elastic regimes (∼ 600 °C) by rapid influx of copious amounts of water. Temperature drops deduced from extensional strains of the two sets of columns were used to gauge the viability of such a two-stage process. Absence of reliable data on andesite contraction coefficients was overcome by using a sliding scale to assess a large range of values. The estimates indicate that two-stage chilling is feasible. After flowing across relatively ice-poor terrain, the lava flow must have interacted with a valley glacier that provided water for further chilling the already formed primary columns and formation of the outer rind small columns. Given this evidence for lava/ice interaction, it is likely that prominent, thick flows elsewhere in the Mangawhero Formation may have been constrained to their ridge-top locations by ice conditions similar to those described by Lescinsky and Sisson [Lescinsky, D.T., Sisson, T.W., 1998. Ridge-forming, ice-bounded lava flows at Mount Rainier, Washington. Geology, 26, 351–354].

Dynamic birefringence of cyclic olefin copolymers

Dynamic birefringence and viscoelasticity of amorphous polymers containing cyclic olefins were simultaneously measured over a wide frequency region from the rubbery to the glassy zone. The obtained results are discussed in terms of optical anisotropy and main chain flexibility. For copolymers of ethyelene and cyclododecene, the stress optical coefficient in the rubbery region, C R, decreased with increasing of cyclododecene contents. This could be attributed to the reduction in the nematic interaction and flexible main chain structure of cyclic olefin unit. On the other hand,in copolymers of ethylene and norbornene, systematic trend of composition dependence of C R was unclear, suggesting differences in the sequence distribution of monomers in the main chain, probably due to usage of different catalyses. Main chain flexibility decreased with increasing of cyclic olefin units when its content exceeds the 50 mol%. On the other hand, polymers produced by ring-opening polymerization of cyclic olefin showed larger C R values among the studied polymers, which can be attributed to large optical anisotropy of resulting cyclic olefin units and less-flexible main chain structure.

Viscoelastic properties of polystyrene using dynamic rheometry

Dynamic mechanical thermal analysis (DMTA) of polystyrene samples of different molecular weights has been investigated using a shear-sandwich unit. Information on the viscoelastic properties of such materials at melt temperatures is of interest as this can lead to an improved understanding of polymer behaviour in processing and fabrication technologies. Samples were subjected to a strain which varied in a sinusoidal manner with time and the resultant response of the sample in terms of storage shear modulus ( G′) and loss shear modulus ( G″) was investigated (at a number of different temperatures) with increasing frequency of the applied strain. Results were assessed using the time–temperature superposition principal. Master curves show four characteristic features: a terminal zone at low frequencies, a fluid–elastic transition zone, a rubbery zone and a glassy zone at high frequencies. These features are indicative of different stress relaxation processes. The average molecular weight between entanglements ( M e) was determined from the storage modulus associated with the rubbery zone. This was found to be approximately half the value of M c (the critical average molecular weight for entanglement). The effects of molecular weight were clearly seen in the terminal zone where the polymer behaves analogous to a Newtonian fluid. The non-Newtonian behaviour of the material was reflected by a sharp increase in G′ and a decrease in the dynamic viscosity ( Y′) with frequency. Acceleration factors derived from time–temperature superposition showed good adherence to the Arrhenius relationship with an activation energy for viscous flow found to be essentially independent of polymer molecular weight suggesting the unit of flow is a collection of chain segments rather than the whole chain itself.

The Significance of the Rouse Segment: Its Concentration Dependence

Dynamic birefringence and dynamic viscoelasticity of polystyrene/tricresyl phosphate solutions were measured over a wide reduced frequency region from the rubbery to the glassy zone for concentrations ranging from 0.20 g cm-3 to bulk. The rubbery (polymeric) component of the modulus whose molecular origin is attributed to the segment orientation was separated from solvent contribution with aid of the modified stress−optical rule. The size of the Rouse segment was calculated from the limiting modulus of the rubbery component at high frequencies. The stress−optical coefficient, which is a measure of size of the optical segment, was found to be insensitive to polymer concentration. This result indicates that the main chain orientation created by the unit stress is insensitive to polymer concentration, implying that statistical nature of polymer chain is not affected by the presence of solvent. This result is in accord with a conformational study, which indicates that the radius of gyration of PS chains is almost constant at any concentration. On the other hand, with decreasing concentration, the estimated molecular weight of the Rouse segment increased from 900 for bulk to the reported value of 5000 for dilute solutions. It is shown that the Rouse segment can be related to the instantaneous main chain orientation induced by unit deformation. The larger value of the Rouse segment size in dilute solution indicates that the strain-induced main chain orientation (orientation of backbone) in solution is reduced compared with that in bulk. The molecular origin of the present results may be attributed to the difference of the rigidity between the solvent and the polymer chain in the glassy region, which would cause inhomogeneous strain distribution in local scale and suppress the main chain orientation.

The Polychnitos ignimbrite of Lesvos island

Miocene volcanism on Lesvos was particularly explosive giving rise to two extensive pyroclastic formations, the Sigri pyroclastics to the west and the Polychnitos ignimbrite to the east of the island. The Polychnitos ignimbrite at 17.2±0.5 Ma (Borsi et al.1972) is part of the shoshonitic succession on Lesbos which ranges in composition from basalt to rhyolite and is both underlain and overlain by calcalkaline volcanic rocks (Pe-Piper and Piper 1993) resting on a late Paleozoic metamorphic basement which has acted as an impediment to the free flow of the ignimbrite. The Polychnitos ignimbrite consists of eight lithological units, six of which are presumed to be facies of the same ignimbrite sheet ("PK", "PU", "MGF I, II, III", "Z"). Ignimbrite deposition at elevated temperatures is advocated by its columnar jointing, eutaxitic texture, gas escape structures and glassy zones of intense welding. The typical mineral assemblage of all Polychnitos ignimbrite units consists of plagioclase, Kfeldspar and biotite. It displays phenocryst microtextures indicative of magma mixing. Magma mixing is corroborated of glasses of two discrete compositions. Lithic clast measurements indicate a northeasterly trending fissure vent passing from the northeastern corner of the Kalloni Gulf.

Dynamic birefringence of oligostyrene: A symptom of ?polymeric? mode

The dynamic birefringence and the dynamic viscoelasticity of an oligostyrene, A1000, whose molecular weight (Mw = 1050) was comparable to the Kuhn segment size, MK, were examined near and above the glass-transition temperature in order to characterize polymeric features of very short chains with M ∼ MK. The complex shear modulus, G*(ω), was similar to that for supercooled liquids: No polymeric modes such as the Rouse mode were detected at low frequencies of viscoelastic spectrum. On the other hand, the strain-optical coefficient was found to be negative in the terminal flow zone and positive in the glassy zone. Because the negative birefringence of polystyrene is originated by polymeric modes associated with chain orientation, the present results indicate that polymeric modes exist and become dominant for birefringence in the terminal flow. The data were analyzed using a modified stress-optical rule: The modulus and the strain-optical ratio were separated into polymeric (rubbery) and glassy components. The total modulus, G*(ω), was mostly due to the glassy component, GG*(ω), resulting in the positive birefringence. GG*(ω) for A1000 agreed with that for high M polystyrenes when compared at a comparable reduced frequency scale. The polymeric component, GR*(ω), giving rise to the negative birefringence was lower than GG*(ω) over the whole frequency range but its contribution to the birefringence exceeded that of the glassy component at low frequencies because of the larger optical anisotropy and longer characteristic relaxation time of the former. The limiting modulus of GR* at high frequencies was about 3 times lower than that for high M polystyrenes, indicating that the main-chain orientation of the oligostyrene on instantaneous deformation was reduced compared with that of high M polystyrenes. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 954–964, 2000

Viscoelasticity and Birefringence of Amorphous Polymers in the Glass Transition Zone.

Rheo-optical studies on viscoelasticity of amorphous polymers in the vicinity of the glass-to-rubber transition zone are reviewed. One of important progresses is a finding of the modified stress-optical rule, MSOR. The rule says that the stress has two molecular origins. One (R component) is due to the chain orientation like rubbery materials and the other (G component) is due to deformation of packing state of repeating units. The G component has common features for glass forming materials. The MSOR successfully explains many characteristic features of the viscoelasticity around the glass transition zone such as breakdown of time-temperature superposition principle. Another significance is that the MSOR provides a new method to analyze the viscoelasticity around the glass transition zone. The separation into the two origins gives better prospects on the relationship between viscoelasticity and the molecular structure. The method can be applied to other important issues including nonlinear viscoelasticity around the glass transition zone and sub-relaxations in the glassy zone.

Surface and Bulk Crystallization of Glass‐Ceramic in the Na2O‐CaO‐ZnO‐PbO‐Fe2O3‐Al2O3‐SiO2 System Derived from a Goethite Waste

A goethite waste from zinc hydrometallurgical processes has been used to produce a glass‐ceramic in the Na2O‐CaO‐ZnO‐PbO‐Fe2O3‐Al2O3‐SiO2system. The surface and bulk microstructure of this glass‐ceramic have been studied by using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The surface was comprised of crystalline and glassy areas. Two different types of crystalline growth and two morphologies were observed in the crystallized and glassy zones, respectively. The bulk microstructure was composed of a homogeneously distributed dendritic network comprised of small crystallites of magnetite. A glassy matrix was observed surrounding the magnetite network. Further heat treatment produced the precipitation of a nonstoichiometric zinc ferrite with magnetite crystals, being the nucleating agents of the secondary phase.