Characterizing the kinetics of volume recovery in glasses by instantaneous temperature-jump experiments

This article proposes a temperature-jump (T-jump) approach for characterizing the kinetics of volume recovery in glassy materials. The kinetic characterization is based on the Kovacs-Aklonis model. This incorporates a retardation-time spectrum which shifts according to both the temperature and the instantaneous volume. The proposed experiments involve measuring the change in recovery rate caused by an abrupt temperature jump. Although an analogous procedure has been used to determine the activation energy for linear viscoelastic creep, the analysis for volume recovery is complicated by its inherent nonlinearity. Nevertheless, accounting for the nonlinearity by a reduction of the time scale permits the T-jump results to be analyzed. In particular, the T-jump approach can be used to: (i) test a particular functional form for the shift factor and (ii) determine the previously unmeasurable parameter x, which defines the relative importance of the temperature dependence and the volume dependence in this function. In addition, numerical simulations indicate that the proposed method can be implemented in the laboratory.     

Viscoelastic characterization of polymers using instrumented indentation. I. Quasi‐static testing*

The use of instrumented indentation to characterize the mechanical response of polymeric materials was studied. A model based on contact between a rigid probe and a linear viscoelastic material was used to calculate values for the creep compliance and stress relaxation modulus for two glassy polymeric materials, epoxy and poly(methyl methacrylate), and two poly(dimethyl siloxane) (PDMS) elastomers. Results from bulk rheometry studies were used for comparison with the indentation stress relaxation results. For the two glassy polymers, the use of sharp pyramidal tips produced responses that were considerably more compliant (less stiff) than the rheometry values. Additional study of the deformation remaining in epoxy after indentation creep testing as a function of the creep hold time revealed that a large portion of the creep displacement measured was due to postyield flow. Indentation creep measurements of the epoxy with a rounded conical tip also produced nonlinear responses, but the creep compliance values appeared to approach linear viscoelastic values with decreasing creep force. Responses measured for the unfilled PDMS were mainly linear elastic, with the filled PDMS exhibiting some time‐dependent and slight nonlinear responses in both rheometry and indentation measurements. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1794–1811, 2005     

An investigation of the yield and postyield behavior and corresponding structure of poly(methyl methacrylate)

The mechanical behavior of glassy polymers is time and temperature dependent as evidenced by their viscoelastic and viscoplastic response to loading. The behavior is also known to depend strongly on the prior history of the material, changing with time and temperature without chemical intervention. In this investigation, we examine the effects of this process of physical aging on the yield and postyield behavior and corresponding evolution in the structural state of glassy polymers. This has been achieved through a systematic program of uniaxial, isothermal, constant strain–rate tests on poly(methyl methacrylate) (PMMA) specimens of different thermal histories and by performing positron annihilation lifetime spectroscopy (PALS) measurements prior to and after mechanical deformation. PALS is an indicator of the free volume content, probing size and density of free volume sites and can be considered to be a measurement of structural state. The results of the mechanical tests show that aging acts to increase both the initial yield stress and the amount of strain softening which occurs subsequent to yield. Moreover, the amount of strain softening was found to be independent of strain rate indicating that softening is related to an evolution in structure as opposed to deformation kinetics. Furthermore, after sufficient inelastic straining, the initial thermal history is completely erased as evidenced by identical values of flow stress following strain softening, for both annealed and quenched polymer. Strong confirmation of the structural state or free volume related nature of the strain softening process is obtained by our companion PALS measurements. PALS detects an increase in the size of free volume sites following inelastic deformation and finds the initially annealed and quenched specimens to posses the same post-deformation distribution. The size of sites is found to evolve steadily with inelastic strain until it attains a steady-state value. This evolution of free volume with strain follows the observed softening of the flow stress to a steady-state value. These results provide experimental evidence that an increase in free volume with inelastic straining accompanies the strain softening phenomenon in glassy polymers and that strain softening is indeed a de-aging process. Based on our experimental results a mechanistically based constitutive model has been formulated to describe the effects of thermal history on the yield and postyield deformation behavior of glassy polymers up to moderate strains. The model is found to successfully capture the effects of physical aging, strain softening, strain rate, and temperature on the inelastic behavior of glassy polymers when compared with experimental results. © 1993 John Wiley & Sons, Inc.     

Analyzing polymer crazing as quasifracture

This paper deals with a viscoelastic boundary element method for analyzing a polymer quasifracture usually called a craze in polymers. A time-dependent boundary stiffness is considered on the quasifracture envelope surface. The viscoelastic property of the glassy polymer is represented by a generalized Kelvin model with multiple retardation times. According to the linear viscoelastic correspondence principle, the associated elasticity solution can be solved by applying the general integral boundary element method. Then the viscoelastic solution in the time domain can be obtained by applying a collocation Laplace inversion transformation. Using these methods, the quasifracture problem composed of an isolated craze opening with time-dependent stiffness traction in a stressed rectangular plate is analyzed. The displacement profile and the stress distribution around the craze envelope surface are computed.     

Sharp fronts due to diffusion and stress at the glass transition in polymers

We derive and analyze a model for sharp fronts in glassy polymers. We take the major effect of a diffusing penetrant on the polymer entanglement network to be the inducement of a differential viscoelastic stress. This couples diffusive and mechanical processes through a viscoelastic response where the strain depends upon the amount of penetrant present. Analytically, the major effect is to produce explicit delay terms, via a relaxation parameter, to account for the fundamental difference between a polymer in its rubbery state and the polymer in its glassy state, namely the finite relaxation time in the glassy state owing to slow response to changing conditions. We produce concentration profiles in good agreement with observations on sharp front formation. In addition the model can account for the phenomenon of sorption overshoot.     

Study of the segmental dynamics in semi-crystalline poly(lactic acid) using mechanical spectroscopies

The glass transition of poly(L-lactic acid) (PLLA) occurs not far above typical service temperatures (room or body temperatures) which has consequences on the material properties during its use, such as damping or the occurrence of structural relaxation. This work aims at characterising the glass transition dynamics of a semi-crystalline PLLA using both dynamic mechanical analysis (DMA) and thermally stimulated recovery (TSR). The main viscoelastic parameters have been characterised at 1 Hz using DMA and the master curve obtained after isothermal experiments at different temperatures provided a full picture of the solid-state rheological behaviour throughout a wide frequency range. The activation energies calculated from the shift factors agree with the TSR ones, exhibiting a maximum near the T(g). Above the T(g), the results can be described with the WLF model. In the glassy state, the activation energy decreases with decreasing temperatures being always higher than the prediction of the Adam and Gibbs theory, at least down to temperatures 30 degrees C below the T(g). This suggests the existence of non-arrested degrees of freedom in the glassy state, being consistent with the existence of a significant degree of cooperativity in the TSR results.     

Nonlinear stress relaxation of a styrene–butadiene random copolymer

The isothermal uniaxial stress relaxation response in the vicinity of the glass-to-rubber transition has been measured for a lightly crosslinked poly(styrene–butadiene) random copolymer, 85% styrene by weight. The volume change during stress relaxation was determined by measuring the time-dependent lateral contraction of the specimen with a Hall-effect proximity detector. The specimen exhibited an instantaneous dilation upon application of the strain and a subsequent time-dependent volume decrease. The stress relaxation behavior and the associated volume relaxation were determined for a variety of strains and temperatures in both the linear and nonlinear viscoelastic regime. As the applied strain was increased the isothermal tensile modulus decreased and the shape of the log(modulus) vs. log(time) curve was altered. At equal levels of strain the tensile modulus exhibited increasing deviations from the linear viscoelastic response as the temperature was decreased. The maximum difference between the nonlinear tensile modulus and the linear viscoelastic response was observed at short times. Subsequently, the nonlinear tensile modulus began to approach the linear viscoelastic modulus with increasing time. Both the instantaneous dilation and the magnitude of the time-dependent part of the volume change increased as the level of applied strain was increased and/or as the temperature was decreased. The observed nonlinearity in the tensile stress relaxation response has been quantitively related to the experimentally measured volume relaxation with a free-volume model.     

Free volume quantities and viscoelasticity of polymer glasses

We have investigated, in terms of the Cohen-Turnbull theory, a relationship for polycarbonate (PC) glasses between average stress relaxation times, <to, and average free volume sizes, 〈v_f〉, obtained from positron annihilation lifetime spectroscopy. This examination suggests that the minimum free volume required for stress relaxation, v*, decreases with decreasing temperature and that, near the glass transition temperature, only a subset of extremely large free volume elements contributes to the stress relaxation of PC glasses. This suggestion is consistent with the idea that near the glass transition temperature, the viscoelastic response is dominated by large-scale, main-chain motion, whereas at lower temperature it is controlled by local motion. Moreover, comparison with the v* value estimated from gas diffusivity through various PC species at room temperature shows that the required free volume size for stress relaxation in the glass transition region is much larger than that for gas diffusion. Previously we showed that the Doolittle equation fails to correlate viscoelastic relaxation times of polymer glasses with changing temperature; determining the free volume fraction, h, from theoretical analysis of volume recovery data and theory, the Doolittle equation is shown to be valid in PC above 135°C (T_g - 14°C) irrespective of temperature and physical aging times. This result supports the idea suggested in the previous article that, as glassy polymers approach the transition region, viscoelastic properties increasingly tend to be controlled by free volume. © 1996 John Wiley & Sons, Inc.     

A thermodynamic theory on the nonlinear viscoelasticity of glassy polymers, 1. Constitutive equation

We have developed a nonlinear viscoelastic constitutive equation, which can predict the yield behavior of polymers. This constitutive equation results from the viewpoints that the plastic flow of glassy polymers can be described by a soliton, which is expected to unify the existing concepts for viscoelasticity and yield of glassy polymers, such as dislocation, disclination and free volume. Although our approach is based on molecular concepts and irreversible thermodynamics, it is phenomenological.     

Comparison of optical and mechanical limits of linear relaxation behavior in glassy polycarbonate

The decay in birefringence of glassy polycarbonate held at constant extension has been studied at 23°C, in the time-scale range 10–10³ sec, up to about 6% strain. The results show that, under these conditions, the birefringence can be validly expressed as a linear hereditary integral of the strain history up to a relatively high strain level which is about 3.4% for an experimental time-scale of 100 sec. Comparison with previously obtained data on the stress relaxation behavior of the same polymer shows that, other factors remaining constant, mechanical relaxation is linear only up to about 1.1% strain. The earlier onset of mechanical nonlinearity is discussed and it is suggested that the mechanical relaxation spectrum is richer than the optical spectrum in relatively long relaxation times, corresponding to relatively slow molecular motions. It is further suggested that these slow molecular motions are accelerated first as the polymer is extended beyond the limit of linear viscoelastic behavior. The observed nonidentity between strain limits for linear mechanical and linear optical behavior is discussed in the light of current practices in photomechanical stress analysis.     

单向应力条件下松弛时间率相关的非线性粘弹性本构模型

基于单向拉伸实验研究和内变量理论 ,提出了一种新的简单的一维非线性粘弹性本构关系 .对两种粘弹性材料 ,即高密度聚乙烯和聚丙烯进行了不同加载速率作用下的拉伸实验研究 ,实验结果表明 ,两种材料的应力应变关系与加载速率相关 ;对材料的应力应变实验数据进行拟合发现 ,材料的松弛时间具有很强的应变率相关性 ,当应变率发生数量级变化时 ,材料的松弛时间也发生数量级的变化 .采用内变量理论 ,导出了在单轴应力条件下松弛时间率相关的非线性粘弹性本构关系的迭代形式 ,并给出其收敛条件 .当采取一次迭代形式时 ,本构关系退化为松弛时间率相关的Maxwell模型 .数值拟合的结果表明 ,一次迭代形式的本构关系就可以很好地拟合和预测实验结果 .     

Solid-phase rheology of an anisotropic polymer (vectra A)

The solid-phase rheology of a thermotropic polyester which is liquid crystalline in the melt (Vectra A) was studied for one-dimensional finite-amplitude deformations, including step-strain and recovery, step-stress and recovery, and step-strain followed by small-amplitude oscillations. The rheology is complex, and cannot be described by existing models. Below a critical strain, which is history-dependent, Vectra A deforms as a linear viscoelastic solid. Above the critical strain the deformation is both viscoplastic and viscoelastic. There appears to be a maximum recoverable strain of about 0.03, beyond which all deformation is nonrecoverable. A large number of relaxation modes is required to describe the stress, and one time scale is inadequate to describe the time-dependence of yielding and plastic flow.     

Surface rheology and foaming properties of sodium oleate and C12(EO)6 aqueous solutions

The dynamic surface tension (DST) and the surface viscoelastic modulus of sodium oleate aqueous solutions at different concentrations were measured using an image analysis tensiometer based on the oscillating bubble technique. The diffusion coefficient of oleate moieties was calculated from DST measurements and the surface viscoelastic modulus using the Langmuir-Szyszkowski and the diffusion-controlled adsorption models. The viscoelastic moduli obtained from model calculations were compared with the corresponding experimental values. The diffusion coefficient of C(12)(EO)(6) in water and the parameters of the Langmuir-Szyszkowski adsorption isotherm were taken from the literature and used to calculate the surface viscoelastic modulus of its aqueous solutions at different concentrations. The foaming properties of both C(12)(EO)(6) and sodium oleate solutions, viz., the foam conductance and the water volume fraction in the foam, were measured using a commercial Foamscan device. Foaming experiments with C(12)(EO)(6) and sodium oleate solutions were carried out either under static conditions; i.e., the foam conductance and the water volume fraction were measured as a function of time after the generation of a fixed volume of foam, or under dynamic conditions; i.e., the foam conductance and the water volume fraction were measured during foam formation. The variations in the foam permeability as a function of surfactant concentration were related to the viscoelastic properties of the air/water interface and to the presence of micelles in the foam films. With foams in which the water volume fraction was higher than 0.05, the foam electrical conduction could be described using a simple parallel resistor model and their conductance measurements were related to the foam water volume fraction. The results related to water drainage under static conditions were used to interpret water drainage under dynamic conditions. Preliminary conjectures on the influence of foam permeability and water volume fraction on the yield of the flotation deinking process were drawn from these results.     

First‐principles enthalpy landscape analysis of structural recovery in glasses

The enthalpy landscape is used to derive from first principles the departure functions that quantify structural recovery and aging in glassy materials. The departure functions are identical in form to the phenomenological Kovacs–Aklonis–Hutchinson–Ramos model departure functions, but with the important difference is that the relaxation times do not depend on the instantaneous structure (e.g., volume). This first‐principles derivation elucidates a number of experimental observations in glassy materials, including the asymmetry of approach, the effective relaxation‐rate paradox, and the different time dependences for volume and enthalpy recovery. Example results that qualitatively display these phenomena are obtained with a simple enthalpy landscape. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2302–2306, 2003     

Fundamental relationship between the nonequilibrium glassy state and yield stress of amorphous polymers

This paper reports the theoretical prediction and experimental verification of the connection between the yield stress of amorphous polymers and the physical aging phenomenon. The analysis reveals the existence of a fundamental relationship between the nonequilibrium glassy state and the thermally activated process controlling viscoelastic and plastic deformation. The results show that the volume relaxation and deformation kinetics share the same relaxation times, and that the activation energy for deformation below T_g is much smaller than previously mentioned in the literature. This indicates that the phenomenon of physical aging plays a very important role in the deformation and processing of polymers at low temperatures. The effect of quenching and annealing on the yield stress is described in terms of the mean energy of hole formation, the departure of volume from its equilibrium state, the distribution of hole energies, and lattice volume. The same set of molecular parameters obtained from the molecular kinetic theory of the glass transition and volume relaxation predicts the yield stress as a function of cooling rate, annealing time, temperature, and strain rate.     

Aqueous suspensions of natural swelling clay minerals. 2. Rheological characterization

We report in this article a comprehensive investigation of the viscoelastic behavior of different natural colloidal clay minerals in aqueous solution. Rheological experiments were carried out under both dynamic and steady-state conditions, allowing us to derive the elasticity and yield stress. Both parameters can be renormalized for all sizes, ionic strength, and type of clay using in a first approach only the volume of the particles. However, applying such a treatment to various clays of similar shapes and sizes yields differences that can be linked to the repulsion strength and charge location in the swelling clays. The stronger the repulsive interactions, the better the orientation of clay particles in flows. In addition, a master linear relationship between the elasticity and yield stress whose value corresponds to a critical deformation of 0.1 was evidenced. Such a relationship may be general for any colloidal suspension of anisometric particles as revealed by the analysis of various experimental data obtained on either disk-shaped or lath- and rod-shaped particles. The particle size dependence of the sol-gel transition was also investigated in detail. To understand why suspensions of larger particles gel at a higher volume fraction, we propose a very simplified view based on the statistical hydrodynamic trapping of a particle by an another one in its neighborhood upon translation and during a short period of time. We show that the key parameter describing this hydrodynamic trapping varies as the cube of the average diameter and captures most features of the sol-gel transition. Finally, we pointed out that in the high shear limit the suspension viscosity is still closely related to electrostatic interactions and follows the same trends as the viscoelastic properties.     

Effect of physical aging on nucleation of amorphous indomethacin

Differential scanning calorimetry has been used to study glassy indomethacin aged at 0 and -10 degrees C for periods of time up to 109 and 210 days, respectively. The results demonstrate the emergence of a small melting peak of the alpha-polymorph after aging for 69 days at 0 degrees C and for 147 days at -10 degrees C (i.e., approximately 55 degrees C below the glass-transition temperature) that provides evidence of nucleation occurring in the temperature region of the beta-relaxation. The evolution of an endothermic recovery peak temperature features a plateau at longer annealing times that suggests that the glass has made significant progress toward reaching the supercooled liquid state. It has been found that the melting peaks become detectable after the recovery peak has reached the plateau. The results highlight the importance of studying physical aging in the temperature region of the beta-relaxation as a means of evaluating the physical stability of amorphous pharmaceutical materials.     

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.