Amorphous Glassy Research Articles

非結晶性高分子材料ＰＣおよびＰＶＣの降伏過程

Despite of much research on the effects of factors such as temperature and strain rate on yield stress in amorphous glassy polymers, the yield phenomenon, including stress drop starting just after yielding, has not been understood qualitatively. Furthermore, the importance of this constitutive law can improve the processes of forming and injection molding. In order to investigate yielding and formation process of shear bands followed by slip lines in amorphous glassy polymers, simple shear tests were executed under constant speed and creep at room temperature using quenched and annealed specimens of polycarbonate and polyvinyl chloride. The deformation process was observed through a polarizing microscope during the test. It is shown that for as-received and annealed materials, yielding occurs after the initiation of slip lines, and the formation and extension of shear bands, while for quenched materials, yielding begins at the formation of shear bands without slip lines. These results may be able to predict whether there are two types of the plastic deformation in amorphous glassy polymers.

Cracks and crazes: on calculating the macroscopic fracture energy of glassy polymers from molecular simulations.

We combine molecular dynamics simulations of deformation at the submicron scale with a simple continuum fracture mechanics model for the onset of crack propagation to calculate the macroscopic fracture energy of amorphous glassy polymers. Key ingredients in this multiscale approach are the elastic properties of polymer crazes and the stress at which craze fibrils fail through chain pullout or scission. Our results are in quantitative agreement with dimensionless ratios that describe experimental polymers and their variation with temperature, polymer length, and polymer rigidity.

Effects of Conditioning, Aging, and Copolymer Content on the Diffusion of Propane and Pentane in Amorphous Glassy Perfluorodioxole by Pulse Field Gradient NMR

The diffusion of pentane and propane in TFE/PDD copolymer was studied using pulse field gradient NMR as a function of time after sample preparation. Pentane and propane display tortuous diffusion behavior in TFE/PDD copolymer (65% PDD) which means the apparent diffusion constant of these molecules slows as a function of the time, milliseconds to seconds, over which diffusion is observed in the pulse field gradient NMR experiment. High-permeability polymers are known to have changes in permeability as a result of aging and conditioning. These changes occur over a period of hours, days, and weeks so the determination of apparent diffusion constants was repeated on the same sample over this time scale. Pentane or propane was added to a freshly cast film of the copolymer and then sealed in an NMR tube. The first measurement of apparent diffusion constants was made within 24 h and then repeated a few weeks later and then a year later. Diffusion became more rapid after a few weeks which was ascribed to conditioning by the penetrant. More rapid diffusion at short times or small length scales indicates the introduction of high free volume regions, and the more rapid diffusion at longer lengths scales indicates improved connectivity between these regions. After a year, diffusion at short time scales corresponding to short length scales slowed. This was interpreted as resulting from the densification of smaller high free volume regions. Over longer length scales diffusion remained relatively constant which was interpreted as little change in the connectivity of high free volume regions. Diffusion as seen in the pulse field gradient experiment was compared for two copolymer compositions: 65% PDD and 87% PDD. Diffusion in 87% PDD copolymer is faster and no evidence of tortuosity is observed, both of which are consistent with a larger proportion of high free volume regions.

単純せん断におけるポリカーボネイト材のせん断帯挙動

In order to investigate a constitutive law associated with shear band in amorphous glassy polymers, polycarbonate specimens were tested under forward and backward loadings in simple shear at room temperature. It was shown that (1) the shape of shear stress-strain curve was decided by the formation, lengthening and widening of the shear band at both loading paths, (2) the stress drop at yielding was very sensitive to the lengthening of shear band and (3) once the shear band formed, the yield drop did not occur at backward loading.

A model for the viscoelastic and viscoplastic responses of glassy polymers

Abstract A constitutive model is derived for the viscoelastic and viscoplastic behavior of amorphous glassy polymers at isothermal loading with small strains. It is assumed that an amorphous polymer is strongly heterogeneous at the micro-scale. It is treated as an ensemble of cooperatively rearranging regions (CRR) which relax at random times as they are thermally agitated. CRRs are bridged by links (long chains which form less cohesive space between relaxing domains and transform the macro-strain in a specimen to rearranging regions). With the growth of strain, some links break (which reflects partial disentanglement of chains and scission of bonds in the less cohesive domains). This results in nucleation and aggregation of quasi-point defects (QPD) which provide some freedom for CRRs to displace with respect to each other. At the micro-level, the viscoelastic response of a polymer is reflected by rearrangement of CRRs, whereas the viscoplastic behavior is associated with coalescence of QPDs and creation of isolated islands of CRRs. Stress–strain relations for uniaxial loading are developed using the laws of thermodynamics. The constitutive equations are verified by comparison with experimental data for polycarbonate and poly(methyl methacrylate) at ambient temperature. Fair agreement is demonstrated between results of numerical simulation and observations in relaxation tests and in tests with constant strain rates.

Modeling the viscoelastoplastic behavior of amorphous glassy polymers

AbstractConstitutive equations are derived for the viscoelastic and viscoplastic responses of amorphous glassy polymers at isothermal loading with small strains. A polymer is modeled as an ensemble of cooperatively relaxing regions (CRR) that are rearranged at random times as they are thermally agitated. At relatively low stresses, CRRs are bridged by links that ensure that the macro‐strain in a specimen coincides with micro‐strains in relaxing regions. When the average stress exceeds a threshold strength for the links, some of them break, and relaxing domains begin to slide with respect to one another. Rearrangement of CRRs reflects the viscoelastic behavior, whereas sliding of micro‐domains is associated with the viscoplastic response of glassy polymers. Kinetic equations are proposed for the evolution of viscoplastic strains and the strength of an ensemble of links. These equations are verified by comparison with experimental data in tensile relaxation tests and in tensile and compressive tests with constant strain rates. Fair agreement is demonstrated between results of numerical simulation and observations for a polyurethane resin and poly(methyl methacrylate).

The effect of temperature on physical aging of glassy polymers

AbstractConstitutive equations are derived for the linear viscoelastic response of amorphous glassy polymers subjected to physical aging. Stress–strain relations are applied to fit experimental data for poly(methyl methacrylate), poly(styrene‐co‐acronitrile), and poly(vinyl acetate) in tensile relaxation tests and in torsional dynamic tests at various temperatures. Fair agreement is demonstrated between observations and results of numerical simulation. It is revealed that an increase in the annealing temperature results in an increase in the rate of relaxation and a decrease in the apparent rate of structural recovery. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 3309–3320, 2001

The Nonlinear Viscoelastic Response of Glassy Polymers Subjected to Physical Aging

Constitutive equations are developed for the nonlinear viscoelastic behavior of amorphous glassy polymers in the sub-yield region. A polymeric glass is treated as an ensemble of cooperatively rearranging regions bridged by links. Stress-strain relations are derived and verified by comparison with experimental data in static mechanical tests on polycarbonate and poly(methyl methacrylate). We analyze the effects of the straining state (tension, compression and torsion), strain intensity, temperature and time of annealing on stress relaxation. Fair agreement is demonstrated between observations and results of numerical simulation.

Physical aging and nonlinear viscoelasticity of amorphous glassy polymers

Constitutive equations are developed for the nonlinear viscoelastic response of polymeric glasses subjected to physical aging. An amorphous polymer is treated as an ensemble of cooperatively rearranged regions (CRRs) connected by links. A CRR is modeled as a point trapped in its potential well on the energy landscape. At random times, CRRs hop to higher energy levels as they are thermally agitated. In the stress-free state, all CRRs are located at the bottom levels of their potential wells. Under loading, they ascend to higher energy levels, the ascent energy being proportional to the mechanical energy of the relaxing region. In the sub-yield region, some links between CRRs break, providing additional degrees of freedom for relaxing regions (which results in an increase in the rate of rearrangement). Stress–strain relations are derived and verified by comparison with experimental data in relaxation tests for polycarbonate and poly(methyl methacrylate) [PMMA]. Fair agreement is demonstrated between observations and results of numerical simulation. The effect of annealing temperature, waiting time and the strain level on adjustable parameters in the constitutive equations is studied in detail. It is demonstrated that the time–aging time superposition principle is not necessary for the description of physical aging. Analysis of experimental data in the framework of the coarsening concept reveals that mechanical loading does not induce rejuvenation of glassy polymers, but results in an increase in the relaxation rate in accordance with the theory of thermomechanically activated processes.

The Trapping Concept in Nonlinear Viscoelasticity of Amorphous Glassy Polymers

Nonlinear stress - strain relations are derived for the viscoelastic behavior of glassy polymers. An amorphous medium is treated as an ensemble of cooperatively rearranging regions (flow units). Any unit is thought of as a point in the phase space which hops (being thermally activated) to higher energy levels in its potential well on the energy landscape. The viscoelastic behavior of a polymer is modeled as a sequence of rearrangement events occurring at random times when relaxing regions reach (in hops) some liquid-like level. We assume that external loads affect the position of the liquid-like state with respect to the energy landscape, and the descent of the reference energy level is proportional to the average mechanical energy of a flow unit. This hypothesis is verified by comparison of observations for polycarbonate in tensile relaxation tests with results of numerical simulation. Fair agreement is demonstrated between experimental data and their predictions.

A model for structural relaxation in amorphous glassy polymers based on the aggregation–fragmentation theory

AbstractGoverning equations are derived for the kinetics of physical aging in polymeric glasses. An amorphous polymer is treated as an ensemble of cooperatively rearranged regions (CRRs). Any CRR is thought of as a string of elementary clusters (ECs). Fragmentation of the string occurs at random times at any border between ECs. Two strings aggregate at random instants to produce a new string. Aggregation and fragmentation are treated as thermally activated processes, and the rate of fragmentation is assumed to grow with temperature more rapidly than the rate of coalescence. A nonlinear differential equation is developed for the distribution of CRRs with various numbers of ECs. Adjustable parameters of the model are found by the fitting of experimental data for polycarbonate, poly(methyl methacrylate), polystyrene, and poly(vinyl acetate) (PVA). Fair agreement is established between observations and results of numerical simulation. For PVAc, the relaxation spectrum found by matching data in a calorimetric test is successfully employed to predict experimental data in a shear relaxation test. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1312–1325, 2001

Modelling nonlinear viscoelasticity and damage in amorphous glassy polymers

Constitutive equations are derived for the nonlinear viscoelastic behavior of amorphous glassy polymers in the subyield region. A polymer is thought of as an ensemble of cooperatively rearranged regions trapped in cages. In the phase space, a cage is modeled as a potential well, where a flow unit hops as it is thermally activated at random times. The viscoelastic response is treated as rearrangement of flow units. A rearrangement event occurs when a region reaches some liquid-like state in a hop. Damage of a polymer is modeled as breakage of van der Waals forces between monomeric units. It happens when the nominal strain in a relaxing region exceeds some threshold level. Stress-strain relations for a glassy polymer and a governing equation for the damage evolution are developed and verified by comparison with experimental data. Fair agreeement is demonstrated between results of numerical simulation and observations for polycarbonate.

A model of traps for yield in amorphous glassy polymers

Constitutive equations are derived for the viscoelastic and viscoplastic behavior of amorphous glassy polymers at isothermal loading with small strains. The model is based on the trapping concept: a disordered medium is treated as an ensemble of plastic flow units (with the characteristic size of micrometers), which, in turn, consist of a number of cooperative rearranging regions (with the characteristic length of nanometers). The viscoelastic response is described by rearrangement of relaxing regions, whereas the viscoplastic behavior is modeled as irreversible deformation of plastic units. Adjustable parameters are found by fitting observations for aromatic polyesters, nylon-66, polycarbonate block copolymers and an epoxy glass. Fair agreement is demonstrated between experimental data and results of numerical simulation.

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

Shear yielding threshold and viscoelasticity in an amorphous glassy polymer: a study on a styrene–acrylonitrile copolymer

The framework of the present research is the study of the effects of viscoelasticity on the yield behaviour of amorphous glassy polymers. The research regards the shear yielding mechanism in an amorphous glassy polymer and the identification of a yield criterion, which takes into account the effect of mechanical history on the yield point (defined as the onset of plastic strain), is set as its final goal. To this end, constant strain-rate, creep and stress relaxation tests were carried out at room temperature under uniaxial compression conditions on a styrene–acrylonitrile copolymer. The results obtained emphasise that yield onset cannot be identified by a critical value of the applied stress or strain. Referring to models of the plastic deformation mechanism previously proposed in the literature, the anelastic strain, the anelastically stored energy and the viscoelastic energy were suggested to reach a threshold value at the yield point. All three parameters were evaluated at the yield threshold and showed fairly constant values irrespective of the mechanical history. Nevertheless, the data dispersion and the simplicity of the analogical model used to estimate these quantities did not allow to identify which of them actually controls the yield process.

Modeling of the competition between shear yielding and crazing in glassy polymers

Fracture in amorphous glassy polymers involves two mechanisms of localized deformations: shear yielding and crazing. We here investigate the competition between these two mechanisms and its consequence on the material's fracture toughness. The mechanical response of the homogeneous glassy polymer is described by a constitutive law that accounts for its characteristic softening upon yielding and the subsequent progressive orientational strain hardening. The small scale yielding, boundary layer approach is adopted to model the local finite-deformation process in front of a mode I crack. The concept of cohesive surfaces is used to represent crazes and the traction-separation law incorporates craze initiation, widening and breakdown leading to the creation of a microcrack. Depending on the craze initiation sensitivity of the material, crazing nucleates at the crack tip during the elastic regime or ahead of the crack. As the crazes extend, plasticity develops until an unstable crack propagation takes place when craze fibrils start to break down. Thus, the critical width of a craze appears to be a key feature in the toughness of glassy polymers. Moreover, the opening rate of the craze governs the competition between shear yielding and brittle failure by crazing.

Enthalpy relaxation in glassy polymers

Constitutive equations are derived for enthalpy recovery in amorphous glassy polymers. The model is based on the concept of cooperative relaxation which treats a polymer as an ensemble of flow units rearranging at random times. The rate of rearrangement is determined by the Eyring theory of thermally activated processes. Fair agreement is demonstrated between results of numerical simulation and experimental data for polycarbonate, poly(ether imide), poly(methyl methacrylate), polystyrene and a glycerol glass.

Dimension of the local-plasticity zone as a correlation length of the structure of polymers under inelastic deformation

The structural meaning of the dimension rpl of the zone of local plastic deformation in polymers is determined. In simulating the polymer structure as a percolation cluster, the quantity rpl is the correlation length of the structure of the polymer deformed until inelastic deformations appear. This rule holds for both amorphous glassy polymers and amorphous-crystalline polymers and for various types of the indicated zones (crazing or shear).

Solvent diffusion in amorphous glassy polymers

In this article, a mathematical model is proposed for predicting solvent self-diffusion coefficients in amorphous glassy polymers based on free volume theory. The basis of this new model involves consideration of the plasticization effects induced by small molecular solvents to correctly estimate the hole-free volume variation above and below the glass-transition temperature. Solvent mutual-diffusion coefficients are calculated using free volume parameters determined as in the original theory. Only one parameter, which can be predicted by thermodynamic theory, is introduced to express the plasticization effect. Thus, this model permits the prediction of diffusion coefficients without adjustable parameters. Comparison of the values calculated by this new model with the present experimental data, including benzene, toluene, ethyl benzene, methyl acetate, and methyl ethyl ketone (MEK) in polystyrene (PS) and poly(methyl methacrylate) (PMMA), has been performed, and the results show good agreement between the predicted and measured values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 846–856, 2000

Contact interactions between polymeric particles

The adhesion interaction between the particles of various amorphous glassy polymers and crystallizing poly(ethylene glycol) is investigated in the air and in the argon atmosphere. A strong effect of adsorption phenomena on the molecular attraction of polymers is disclosed.