A possible mechanism for cross-tie fibril generation in crazing of amorphous polymers

A possible mechanism for cross-tie fibril generation in crazes of amorphous polymers is proposed. Detailed finite element calculations are performed on an axisymmetric model of a single fibril inside the craze. These calculations suggest that the hydrostatic stress inside the fibril is large enough to cause cavitation and subsequent growth of initial imperfections inside the fibril. The calculations demonstrate that these cavities will then grow by local plastic flow around them, leading to a continuous network of main fibrils interconnected by cross-tie fibrils.     

Strength and deformation of rigid polymers: structure and topology in amorphous polymers

Glassy polymer is formed because the irregular chain architecture prevents crystallisation. Computer simulations allow Voronoi tessellation of atomic groups (for example monomers) to be carried out and measured along the molecular chain, which reveals significant density fluctuations. A Voronoi polyhedron is constructed for each particle according to a unique mathematical procedure [J Reiner Angew Math 134 (1908) 198]. When measured in terms of Voronoi polyhedra, amorphous structures show wide variations in packing density on the atomic/monomer scale, with a characteristic skewed distribution. The Voronoi method can be applied to all polymers; however, in this paper only uncrosslinked amorphous polymers are considered. Constriction points around a chain segment are defined as a locally specific configuration and arrangement of adjacent chains such that the local density within a sphere of radius approximately equal to two monomer diameters comes close to or below the hypothetical crystalline density. The topological theory of molecular structure developed by Bader defines the concepts of atoms and bonds in terms of the topological properties of the observable charge distribution [Rep Prog Phys 44 (1981) 893]. In polymers the high density regions become an even stronger topological feature, and are referred to as the constriction points.     

A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures

The mechanical response of solid amorphous polymers is strongly dependent on the temperature and strain rate. More specifically, the yield stress increases dramatically for the low temperatures as well as for the high strain rates. To describe this behavior, we propose a new formulation of the cooperative model of Fotheringham and Cherry where the final mathematical form of the model is derived according to the strain rate/temperature superposition principle of the yield stress. According to our development, the yield behavior can be correlated to the secondary relaxation and we propose an extension of the model to temperatures above the glass transition temperature. For a wide range of temperatures and strain rates (including the impact strain rates), the predicted compressive yield stresses obtained for the polycarbonate (PC) and the polymethylmethacrylate (PMMA) are in excellent agreement with the experimental data found in the literature.     

Two-step micro cellular foaming of amorphous polymers in supercritical CO2

Microcellular foaming of amorphous rigid polymers, polymethylmethacrylate (PMMA) and polystyrene (PS) was studied in supercritical CO₂ (ScCO₂) in the presence of several types of additives, such as triblock (styrene-co-butadiene-co-methylmethacrylate, SBM and methylmethacrylate-co-butylacrylate-co-methylmethacrylate, MAM) terpolymers. This work is focused in the two-step foaming process, in which the sample is previously saturated under ScCO₂ being expanded in a second step out of the CO₂ vessel (e.g. in a hot oil bath) where foaming is initiated by the change of temperature near or above the glass transition temperature of the glass/polymer glassy system. Samples were saturated under high pressures of CO₂ (300 bar), at room temperature, for 16 h, followed by a quenching at a high depressurization rate (150 bar/min). In the last step, foaming was carried out at different temperatures (from 80 °C to 140 °C) and different foaming times (from 10 s to 120 s). It was found that cellular structures were controlled selecting either the additive type or the foaming conditions. Cell sizes are ranging from 0.3 μm to 300 μm, and densities from 0.50 g/cm³ to 1 g/cm³ depending on the polymers considered.     

Micromechanics of the growth of a craze fibril in glassy polymers

The primary objective of this work is to model the growth and eventual failure of a craze fibril in a glassy polymer, starting from a primitive fibril. Experimental investigations have shown that properties like the entanglement density of a polymer play a pivotal role in determining whether macroscopic failure of a polymer occurs through crazing or shear yielding. Failure is seen to be related to the formation of a soft ‘active zone’ at the craze-bulk interface, through disentanglement. The present work aims at explaining some of the experimental findings about fibril growth and failure in glassy polymers on the basis of a continuum model of a craze with a constitutive model that accounts for yield, network hardening and disentanglement. The results show that this approach is capable of providing explanations for experimentally observed facts such as the propensity to crazing in polymers with low entanglement density and the linearity between the stretch in a fibril and the maximum stretch of a molecular strand in the fibril.     

Study of the multilayered nanostructure and thermal stability of PMMA/PS amorphous films

The nanolayered structure of a forced-assembly of two immiscible amorphous polymers, prepared by layer-multiplying coextrusion, is analyzed for the first time by means of USAXS. The experimental long spacings for the series of PMMA/PS films studied show a good correlation with the nominal periodicity values of the stacks. In addition, the long spacings, derived from a localized area in AFM, are also in good agreement with the USAXS values averaged over much larger areas. The structural variation, after thermal treatment, of two samples with nominal periodicities of 174 and 215 nm is reported. In the range RT-140 °C, the nanolayered structure is mostly well preserved as evidenced by AFM. However, the absence of USAXS maxima after annealing at temperatures included in the above range has been tentatively explained by interfacial coarsening and spinodal dewetting occurring between the forced-assembled polymer layers. Above 140 °C, the interfacially driven break-up of the layers ends up with the final disappearance of the multilayered structure.     

Relaxation of amorphous multichain polymer systems using inverse kinematics

Atomic scale simulations of polymer materials is a topic of interest since it permits to reduce costly experiments to determine their physicochemical properties. In this context, modeling heterogeneously ordered multichain systems such as amorphous polymers, remains a challenging problem. A recently proposed two-step method consists of iteratively generating the structures using a simplified energy model, and subsequently relaxing the system, considering a more accurate model, in order to reduce its potential energy. This work proposes an improvement of this method by integrating a novel relaxation technique, which applies analytical rebridging moves inspired by robotics. A comparative analysis using models of amorphous polyethylene with different sizes and densities shows that the rebridging scheme described here is very effective for the simulation of long alkanes.     

High‐resolution 13C–nuclear magnetic resonance study of heterogeneous amorphous polymers

The combination of solid‐state nuclear magnetic resonance (NMR) techniques is very helpful for examining the behavior of heterogeneous amorphous polymers. With the magic‐angle spinning (MAS) technique, employing special conditions, only the mobile fraction of the molecule can be assigned. Cross‐polarization magic‐angle spinning (CPMAS) permits the evaluation of changes in the NMR line shapes and chemical shifts. The employment of proton spin‐lattice relaxation times (T₁ and T₁ρ) gives useful information on the molecular dynamic in heterogeneous polymers. From these parameters the response of the molecular mobility behavior of the polymer chains can be obtained. The results of the present work are discussed in this article in terms of molecular mobility and domain formations of heterogeneous amorphous polymers in order to understand the relations in the structure–mobility property. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 473–476, 2003     

Thermodynamically stable amorphous drug dispersions in amorphous hydrophilic polymers engineered by hot melt extrusion

In this study thermodynamically stable dispersions of amorphous quinine, a model BCS class 2 therapeutic agent, within an amorphous polymeric platform (HPC), termed a solid-in-solid dispersion, were produced using hot melt extrusion. Characterisation of the pre-extrudates and extrudates was performed using hyper-differential scanning calorimetry (DSC), powder X-ray diffraction (PXRD) and Raman spectroscopy. Water uptake by the raw materials was determined using dynamic vapour sorption (DVS) analysis. Furthermore, the presence or absence of crystalline drug following storage at 25 °C/60% relative humidity and 40 °C/75% relative humidity in a sealed glass jar, and at 40 °C/75% relative humidity in an open glass jar for 3 months was determined using PXRD. Amorphous quinine was generated in situ during extrusion from both quinine base (5%, 10%, 20% w/w drug loading) and from quinine hydrochloride (5%, 10% w/w drug loading) and remained thermodynamically stable as a solid-in-solid dispersion within the HPC extrudates. When processed with HPC, quinine hydrochloride (20% w/w) was converted to amorphous quinine hydrochloride. Whilst stable for up to 3 months when stored under sealed conditions, this amorphous form was unstable, resulting in recrystallisation of the hydrochloride salt following storage for 1 month at 40 °C/75% relative humidity in an open glass jar. The behaviour of the amorphous quinine hydrochloride (20% w/w) HPC extrudate was related, at least in part, to the lower stability and the hygroscopic properties of this amorphous form.     

Linear viscoelastic behavior of poly(ethylene terephtalate) above Tg amorphous viscoelastic properties Vs crystallinity: Experimental and micromechanical modeling

Linear viscoelastic behavior of amorphous and semicrystalline poly(ethylene terephtalate), (PET), was experimentally investigated. PET’s samples with different crystallinities (Xc) were prepared and viscoelastically characterized. Based on our experimental results (properties of the amorphous PET and semicrystalline polymers), micromechanical model was used to, first predict the viscoelastic properties of the semicrystalline polymers and second predict the changes on the viscoelastic properties of the amorphous phase when the crystallinity increases. For the micromechanical modeling of semicrystalline material’s viscoelastic properties, difficulties lie on the used numerical methods (Laplace-Carson transformation) and also on the actual physical and mechanical properties of the amorphous phase. In this paper we tried to simplify the Laplace-Carson-based method by using a pseudo-elastic one that avoids the numerical difficulties encountered before. The time-dependant problem is so replaced by a frequency-dependant set of elastic equations. Good agreement with low crystallinity fraction was found however large discrepancies appear for medium and high crystallinity. The poor agreement raises the issue of which amorphous mechanical properties should be taken as input in the micromechanical model? According to the dynamic mechanical analysis (DMA) experimental data, multiple amorphous phases with different glass transition temperatures were observed for each tested semicrystalline sample. For each sample, new glass transition temperature related to an equivalent amorphous phase was determined. DMA tests done at 1 Hz help estimating the mechanical properties of the new amorphous phase based on its new glass transition temperature. Using the new micromechanical approach developed in this paper, the changes occurring on the viscoelastic behavior of the amorphous phase upon crystallization were estimated. Good agreement was found after comparing the micromechanically estimated amorphous behavior with the experimentally estimated one leading to believe that the physical and mechanical properties of the amorphous phase change upon crystallization and taking on account this phenomenon is a key to a good prediction of the semicrystalline behavior using micromechanical models.     

Performance prediction of weldline structure in amorphous polymers

The presence of a weldline generally reduces the mechanical strength of injection molded parts. A typical remedy to eliminate the problem of weak weldline structure has been to increase the melt temperature. This, however, is not an acceptable solution in some situations. A general solution to the weak weldline problem requires an in-depth understanding of the thermomechanical history of the injection molding process. A theoretical model for the strength of weldlines is presented that provides a comprehensive physical insight of the bonding process at the weldline interface. The model is based on the self-diffusion of molecular chains across the polymer-polymer interface and the frozen-in orientation that remains parallel to the interface. Both factors are analyzed separately and then superimposed to predict the strength of weldlines from known processing conditions and geometry. Experimental results show good correlation with predictions.     

Hollow Co2SiO4 microcube with amorphous structure as anode material for construction of high performance lithium ion battery

To solve the problem of large volume expansion of cobalt silicate electrode during cyclic process and low electric conductivity, Co₂SiO₄ with amorphous, porous and hollow structure is firstly designed to act as high performance lithium ion battery (LIB) anode. Compared with crystalline materials, the amorphous Co₂SiO₄ microcube could facilitate Li⁺ diffusion to enhance their performance of LIBs because of isotropic characteristics. Here, the amorphous Co₂SiO₄ hollow microcube (named as a-Co₂SiO₄ HC) was prepared by mild hydrothermal method with use of MnCO₃ microcube as hard-template. Benefitting from the advantages of such structure, Li⁺ diffusion rate was greatly accelerated and the volume expansion can be alleviated. The as-prepared amorphous Co₂SiO₄ hollow microcube as anode material of LIBs exhibited significantly improved electrochemical performance of 610 mAh g⁻¹ even after 380 cycles at 500 mAh g⁻¹ than their crystalline counterpart (only 280 mAh g⁻¹ retained after 380 cycles). This work is a good try to employ amorphous metal silicate in LIBs and simultaneously motivate the exploration of other amorphous materials for high performance LIBs, SIBs, catalysts, etc.     

Cooperative relaxations in amorphous polymers studied by thermally stimulated current depolarization

Thermally stimulated current depolarization (t.s.c.) was used to study the relaxations in amorphous polymers including poly (ethyl methacrylate) (PEMA), poly (methyl methacrylate) (PMMA), polystyrene (PS), polycarbonate (PC) and polyarylate (PAR) over temperature ranges covering the β and (glass transition) regions. A.c. dielectric was used to obtain activation energies (E_a) for PS and PC to verify the accuracy of those values determined by the t.s.c. thermal sampling method. At temperatures below the glass transition (T_g) the values of E_a were found to agree with those predicted using an activated states equation with a zero activation entropy. This is evidence of the localized, non-cooperative nature of the low temperature secondary β relaxations which are found to be characterized by a continuous variation of activation energies as a function of temperature. The measured values of E_a depart from the zero activation entropy curve and exhibit a prominent maximum at T_g. This behaviour is known to be due to an enhanced degree of cooperativity of segmental relaxations near T_g. The results indicate that the main advantage of the thermal sampling method is the high sensitivity and high temperature resolution for cooperative relaxations. For the polymers studied here, only PEMA and PMMA show a substantial population of cooperative relaxations more than 60°C below T_g. This is tentatively explained in terms of structural heterogeneity due to variable tacticity in the methacrylates. Compensation of the t.s.c. relaxation spectra plotted in Arrhenius or Eyring plots was found for all polymers to differing degrees. Some discussion of compensation is made in terms of independently measured values of the coefficient of thermal expansion.     

Effect of organoclay structure on morphology and properties of nanocomposites based on an amorphous polyamide

An amorphous polyamide (a-PA) and three organoclays, M₃(HT)₁, M₂(HT)₂ and (HE)₂M₁T₁, were melt processed to explore the effect of the organoclay structure on the extent of exfoliation and properties of these nanocomposites. Wide angle X-ray scattering, transmission electron microscopy, and stress-strain behavior were used to determine the degree of exfoliation of the nanocomposites. For quantitative assessment of the structure of the nanocomposites, a detailed particle analysis was made to provide various averages of the clay dimensions and aspect ratio. The results evaluated from different methods were generally consistent with each other. Nanocomposites based on the organoclays with one alkyl tail and hydroxyl ethyl groups gave well-exfoliated structures and high matrix reinforcement while nanocomposites from two-tailed organoclay contain a considerable concentration of intercalated stacks. Nanocomposites from the organoclays with one alkyl tail showed slightly better exfoliation and matrix reinforcement than those from the organoclays with hydroxyl ethyl groups. The organoclay structure trends for a-PA are analogous to what has been observed for nylon 6; this suggests that a-PA, like nylon 6, has good affinity for the pristine silicate surface of the clay leading to better exfoliation and enhanced mechanical properties with one-tailed organoclay than multiple-tailed organoclay. Furthermore, heat distortion temperatures were predicted from the dynamic mechanical properties of nanocomposites.     

Effect of yielding on the viscoelastic response of amorphous glassy polymers

Constitutive equations are derived for the nonlinear viscoelastic behavior of amorphous glassy polymers. The model is based on the theory of cooperative relaxation in a version of the trapping concept. Stress–strain relations are applied to fit experimental data for polycarbonate in the sub‐yield and post‐yield regions. Fair agreement is demonstrated between observations and results of numerical simulation. It is revealed that yielding causes substantial changes in the energy landscape of amorphous polymers. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 2383–2393, 2001     

Structure and properties of biaxial‐oriented crystalline polymers by solid‐state crossrolling

The effect of biaxial orientation by solid‐state crossrolling on the morphology of crystalline polymers including polypropylene (PP), high density polyethylene (HDPE) and Nylon 6/6 was investigated with polarized optical microscopy, atomic force microscopy, wide‐angle X‐ray scattering, and small‐angle X‐ray scattering techniques. It was found that crossrolling gradually changed the initial spherulitic structure into a biaxially oriented crystal texture with chain axis of crystals becoming parallel to the rolling direction for all three polymers. The effect of microstructure change on the macromechanical properties was studied in tension at both ambient temperature and ?40°C. In tension at room temperature, the localized necking deformation of HDPE and PP control changed upon orientation into homogeneous deformation for the entire sample length. This was attributed to that the oriented crystal morphology eliminated the stress concentration, which existed in the original spherulitic structure from lamellae orientation in the polar and equatorial regions. At ambient conditions, the elastic moduli of HDPE and PP were found to decrease slightly with orientation whereas the modulus of Nylon 6/6 increased with increasing orientation. This was due to the fact that the amorphous chains of HDPE and PP are in a rubbery state and orientation increased the shear relaxation in the orientation direction but the amorphous chains of Nylon 6/6 are in the glassy state inhibited the shear relaxation. Both the yield stress and strain hardening exponent increased with increasing orientation for all three polymers. In tension at ?40°C, orientation changed the failure mechanism of all three polymers from brittle fracture into ductile failure, as the original spherulitic structure was changed into an oriented structure with chain axis of crystals becoming parallel to the tension direction, which allowed chain slip deformation of crystals and resulted in oriented samples showing ductile failure. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Toward a viscoelastic modeling of anisotropic shrinkage in injection molding of amorphous polymers

A novel approach to predict anisotropic shrinkage of amorphous polymers in injection moldings was proposed using the PVT equation of state, frozen‐in molecular orientation, and elastic recovery that was not frozen during the process. The anisotropic thermal expansion and compressibility affected by frozen‐in molecular orientation were introduced to determine the anisotropy of the length and width shrinkages. Molecular orientation calculations were based on the frozen‐in birefringence determined from frozen‐in stresses by using the stress‐optical rule. To model frozen‐in stresses during the molding process, a nonlinear viscoelastic constitutive equation was used with the temperature‐ and pressure‐dependent relaxation time and viscosity. Contribution of elastic recovery that was not frozen during the molding process and calculated from the constitutive equation was used to determine anisotropic shrinkage. Anisotropic shrinkages in moldings were measured at various packing pressures, packing times, melt temperatures, and injection speeds. The experimental results of frozen‐in birefringence and anisotropic shrinkage were compared with the simulated data. Experimental and calculated results indicate that shrinkage is highest in the thickness direction, lowest in the width direction, and intermediate in the flow direction. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 2300–2313, 2005     

Effect of organoclay structure and mixing protocol on the toughening of amorphous polyamide/elastomer blends

An amorphous polyamide (a-PA) was blended with an ethylene-1-octene (EOR) elastomer with organoclays present to control the elastomer particle size. Four different organoclays, M₃(HT)₁, M₂(HT)₂, M₁H₁(HT)₂, and (HE)₂M₁T₁ and two different mixing protocols were used to investigate the effect of the organoclay structure and mixing protocol on the morphology and properties of the resulting blends. Wide angle X-ray scattering, transmission electron microscopy, and stress-strain behavior were used to evaluate the degree of exfoliation of the organoclays and the morphology of the elastomer particles for these blends. A detailed particle analysis was made to provide a quantitative assessment of elastomer particle size. The size and shape of the elastomer particles were dramatically affected by the amount of organoclay but the organoclay type and the mixing protocol led to slight differences. Broadly speaking, most of the MMT platelets are well exfoliated in the a-PA phase, but some locate at the interface and tend to envelop the EOR phase. The mechanical properties were not significantly affected by the organoclay type or the mixing protocol. While the organoclays reduced the EOR particles to size range where toughness might be expected, all blends proved to be brittle. A clear trade-off was observed between the Izod impact strength and tensile modulus for these blends containing organoclays.     

Atomistic molecular dynamics simulations of gas diffusion and solubility in rubbery amorphous hydrocarbon polymers

Diffusion coefficients D of H₂, He, O₂, N₂, and CO₂ in different rubbery amorphous polymeric matrices were estimated by atomistic molecular dynamics simulations at 298 K using the Einstein relationship, and compared with the relevant experimental values, where available. The simulated diffusion coefficients D of all the gases in all polymers considered almost regularly decreased with increasing molecular gas volumes and increasing polymer glass transition temperature. Further, solubility coefficients and heats of solution were obtained for all gases from Grand Canonical Monte Carlo simulations, which were also used to calculate sorption isotherms. In general, there is a good agreement between experimental and simulated values of diffusion and solubility coefficients for all gases considered.