Power law relationship between yield stress and shear modulus for glassy polymers

The published data on the yielding of glassy polymers under a variety of testing conditions reveal that the yield stress increases with the elastic modulus. However, fundamental understanding of the interrelation has not yet been established. In this paper, a power law relation between the shear yield stress τ_y and the shear modulus G is presented: T₀τ_y/Tτ_y0 = (T₀G/TG₀)ⁿ, where T is the absolute temperature, T₀. is reference temperature, and τ_y0 and G₀ are, respectively, the shear yield stress and the shear modules at T₀. The exponent n takes a value 1.63 for amorphous polymers without exception, whereas it is about 0.8–0.9 for crystalline polymers. The exponent 1.63 for amorphous polymers is in good agreement with the value derived from the approximation of the Bowden–Raha dislocation analog. This law may enable us to investigate a model for the yielding of glassy polymers.     

Short‐time elasticity of polymer melts: Tobolsky conjecture and heterogeneous local stiffness

An extended molecular‐dynamics study of the short‐time “glassy” elasticity exhibited by a polymer melt of linear fully‐flexible chains above the glass transition is presented. The focus is on the infinite‐frequency shear modulus G_∞ manifested in the picosecond time scale and the relaxed plateau G_p reached at later times and terminated by the structural relaxation. The local stiffness of the interactions with the first neighbors of each monomer exhibits marked distribution with average value given by G_∞. In particular, the neighborhood of the end monomers of each chain are softer than the one of the inner monomers, so that G_∞ increases with the chain length. G_p is not affected by the chain length and is largely set by the nonbonding interactions, thus confirming for polymer melts the conjecture formulated by Tobolsky for glassy polymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1401–1407     

Dynamic birefringence of oligostyrene: A symptom of “polymeric” mode

The dynamic birefringence and the dynamic viscoelasticity of an oligostyrene, A1000, whose molecular weight (M_w = 1050) was comparable to the Kuhn segment size, M_K, were examined near and above the glass‐transition temperature in order to characterize polymeric features of very short chains with M ∼ M_K. 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, G_G*(ω), resulting in the positive birefringence. G_G*(ω) for A1000 agreed with that for high M polystyrenes when compared at a comparable reduced frequency scale. The polymeric component, G_R*(ω), giving rise to the negative birefringence was lower than G_G*(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 G_R* 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     

Plastic deformation of glassy polystyrene: A unified model of yield and the role of chain length

A study was made of yield and plastic flow in glassy polystyrene. A range of 12 linear atactic polystyrenes was studied: monodisperse, bimodal blends, and a polydisperse commercial sample. M_n varied between 66,000 and 490,000 g/mol. These were given standardized thermal treatments and then subjected to uniaxial compression tests in the glassy state over the temperature range 40 to 95 °C and nominal strain-rates 10⁻⁴ to 10⁻³ s⁻¹. Their constitutive responses were interpreted in terms of the physically based three-dimensional constitutive model for small or large deformations in amorphous polymers proposed earlier (Polymer 1995, 36, 3301–3312), including plastic strain-induced structural rejuvenation. In multimode form, the model captured closely both linear viscoelastic response and yield and plastic flow. When the reduction of Vogel temperature caused by chain ends was incorporated in the model, it predicted a fall in yield stress with reducing molecular length. This was also observed in experimental data, with the rate of fall approximately in agreement. The results provide further support for the model as a unifying framework for describing the physical properties of polymer glasses. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2027–2040, 2004     

Effect of chain structure on the glass transition temperature and viscoelastic property of cis‐1,4‐polybutadiene via molecular simulation

In this work, by adopting the united atom model of cis‐1,4‐poly(butadiene) (PB), we systemically investigate the effect of the chain structure on the glass transition temperature (T_g) and the viscoelastic property of PB system. First, we analyze the atom translational mobility, bond reorientation dynamics, torsional dynamics, conformational transition rate, and dynamic heterogeneity of the PB chains with different chain structures in detail by determining the corresponding T_g. In addition, our results clearly indicate that with the decrease of the amount of the free end atoms of PB via the end‐linking method, the mobility of the PB chains quickly decreases. As a result, the T_g of the PB chains gradually increases. Depending on the chain structure and the calculation method, the T_g of the PB chains varies from 154 to 240 K. In addition, the temperature dependence of the dynamic properties has different Arrhenius behaviors above and below T_g. The calculated activation energy varies from 7.37 to 16.37 KJ/mol for different chain structures above T_g, which can be compared with those for other polymers. In addition, through the end‐linking approach the strong interaction between the PB chains improves the storage modulus G′ and the loss modulus . Meanwhile, the immobility of the free end atoms effectively reduces the friction loss of the chains under the shear field, which is reflected by the low loss factor . In summary, this work can further help to understand the effect of the chain structure on the dynamic properties of the PB chains. Meanwhile, it provides an effective approach to reduce the energy loss during the dynamic periodic deformation, which can cut the fuel consumption via the end‐linking method. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1005–1016     

Wear and friction in glassy polymers: Microscratch on blends of polystyrene and poly (2,6-dimethyl-1,4-phenylene oxide)

The microscopic process of abrasive wear and friction in glassy polymers was studied by using a special microscratch technique. A miscible blend of polystyrene (PS) and poly(phenylene oxide) (PPO) was used. It was found that as the composition varies there seems to exist two wear regimes in the blends controlled by different breakdown mechanisms corresponding to the brittle—ductile transition. Detailed study of the contact loads and SEM micrographs indicate that abrasive wear in the glassy polymers is controlled by microcracking under the asperity contacts. The critical load τ_c for initiating microscopic cracks can be linked to the macroscopic wear via a statistical Weibull model where τ_c is taken to be the mean of a strength distribution function. On the other hand, the friction coefficient was found to be independent of the composition but to vary strongly with the contact load. It approaches zero at the extrapolated zero load, but increases rapidly and eventually levels off with contact load. This behavior can be understood by a simple frictional adhesion model in which the polymer deformation during a frictional contact is analyzed by considering the compressive plastic ploughing and shearing yielding around the asperity contact. The shear strength S_o of the polymer/asperity contacts was found to vary with the normal load. The vertical scratch hardness H_v, which characterizes the spontaneous indentation yielding on the polymer surface, was found to be independent of scratch length and depth, and indeed can be regarded as a material constant. Although both S_o and H_v can accurately describe the frictional behavior of the glassy polymers, they bear no correlation to abrasive wear in the same materials. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1295–1309, 1997     

Unimodal molecular weight distribution of commercial polymers from viscoelastic data

This article presents a method that provides the molecular weight distribution (MWD) of polymeric material from rheological data. The technique has been developed to deal with linear polymers with a log‐normal molecular weight distribution. The rheological data must include the shear storage modulus, G′(ω), and the shear loss modulus, G″ (ω), ranging from the terminal zone to the rubberlike zone. It was not necessary to achieve the relaxation spectrums via the extremely unstable problem of inverting integral equations. The method has been tested with different polymers (polydimethylsiloxane, polyisoprene, random copolymer of ethylene and propylene, and polystyrene) and the calculated MWDs were in good agreement with experimental data. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1539–1546, 2000     

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

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

Photoviscoelastic behavior of amorphous polymers during transition from the glassy to rubbery state

Tensile stress‐relaxation experiments with simultaneous measurements of Young's relaxation modulus, E, and the strain‐optical coefficient, C_?, were performed on two amorphous polymers—polystyrene (PS) and polycarbonate (PC)—over a wide range of temperatures and times. Master curves of these material functions were obtained via the time‐temperature superposition principle. The value of C_? of PS is positive in the glassy state at low temperature and time; then it relaxes and becomes negative and passes through a minimum in the transition zone from the glassy to rubbery state at an intermediate temperature and time and then monotonically increases with time, approaching zero at a large time. The stress‐optical coefficient of PS is calculated from the value of C_?. It is positive at low temperature and time, decreases, passes through zero, becomes negative with increasing temperature and time in the transition zone from the glassy to rubbery state, and finally reaches a constant large negative value in the rubbery state. In contrast, the value of C_? of PC is always positive being a constant in the glassy state and continuously relaxes to zero at high temperature and time. The value of C_σ of PC is also positive being a constant in the glassy state and increases to a constant value in the rubbery state. The obtained information on the photoelastic behavior of PS and PC is useful for calculating the residual birefringence and stresses in plastic products. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2252–2262, 2001     

Two negative minima of the first normal stress difference in a cellulose‐based cholesteric liquid crystal: Helix uncoiling

The shear rate dependence of material functions such as shear viscosity (η) and the first normal stress difference (N₁) were given and interpreted earlier by Kiss and Porter. Their widely accepted work revealed the possibility of having a negative minimum of N₁ for polymeric liquid crystals. In this work, we disclose for the first time the evidence of two negative N₁ minima on a sheared cellulosic lyotropic system. The lower shear rate minimum is ascribed to the uncoiling of the cholesteric helix, as theoretically predicted earlier. Our findings contribute also to the understanding of the other minimum already reported in the literature and attributed to the nematic director tumbling mode. Moreover, the elastic change that the LC‐HPC sample undergoes during the helix unwinding of the cholesteric structure is also by means of oscillatory measurements. This study is a contribution for the understanding of the structure‐properties relationship linked with the complex rheological behavior of chiral nematic cellulose‐based systems and may help to improve their further processing. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 821–830     

Mechanical relaxation spectroscopy of three triepoxide-based polymers

Three network structure polymers formed by the chemical reactions of a triepoxide with aniline, 3-chloroaniline,and 4-chloroaniline were prepared and their shear modulus relaxation spectra studied over the 10⁻³- to 1-Hz range and temperatures up to their rubber modulus region. The decrease in the unrelaxed modulus with increase in temperature is found to be a reflection of both an increase in volume, and a decrease in the relaxed modulus of the sub-T_g relaxations process. It is quantitatively shown that the increase in the rubber modulus with increase in temperature above T_g is predominantly due to an increase in the entropy and not to a decrease in the number of cross-links density on thermal expansion. The unrelaxed modulus remained unaffected by the change in the overall size of the phenyl groups of the amines and of the steric hindrance to their rotations caused by the proximity of the chlorine atom to the cross-linking N-atom in the network structure, but the rubber modulus was effected. The shear modulus spectra could be fitted to a stretched exponential decay function with a temperature-independent stretch parameter of 0.25 for two polymers and 0.22 for one. The time–temperature superposition of the spectra did not yield a master curve, and a vertical displacement of the data also failed to produce it. This was more clearly demonstrated by the spectra of the mechanical loss tangent. After considering the various contributions to the shear modulus, it was concluded that deviations from the time–temperature superposition of the spectra are intrinsic to these polymers and arise from the change in the viscoelastic functions for segmental dynamics on change in the temperature such that the overall distribution of relaxation times remains unaffected. The mechanical loss tangent of the three polymers is found to be higher than that of polycarbonate at ambient temperature, implying a higher loss of mechanical energy before these polymers may fracture. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3071–3083, 1999     

Hardness Equation for Ormosils

Hardness of ormosils coating on various kinds of substrates is important, and by considering recent progresses in understanding the hardness of ionic crystals or covalent crystals, new hardness equations for calculating the hardness of glasses or ormosils from chemical compositions were derived. When we applied an indenter to the surface of glass or sol-gel coatings, the surface of indenter is a declined one to the flat surface of glass or coating, thus the applied force should be analyzed by using the shear modulus, S, and Young's modulus, E. This is now well accepted for the analysis of hardness of ionic or covalent bonding inorganic materials. For example, by considering the binding energy and plastic deformation, Gilman showed that Hv of NaCl crystal can be calculated by an equation including elastic stiffness which indicated a good agreement between calculated and observed value. For covalent crystals he reported that the strength of chemical bonds could be correlated with the glide (shear) activation energy for covalent crystals quantitatively. These explanations are basically applied to the hardness of silicate glasses and ormosils. By considering both shear modulus and Young's modulus we have derived equations for calculating the hardness of glasses or ormosils from chemical composition, which includes packing density of atoms and bond energy per unit volume has been taken account. The agreements between calculated and observed hardness values for ormosils were comparatively good.     

Plasticity Mechanism for Glassy Polymers: Computer Simulation Picture

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

Thermal transitions in and structures of dried polyelectrolytes and polyelectrolyte complexes

Dynamic mechanical analysis (DMA) was used to explore the thermomechanical properties of dried polyelectrolytes and polyelectrolyte complexes (PECs) with different thermal and humidity histories. Although differences in the amount of water remaining in polyelectrolytes and PECs were small for ambient versus dessicator storage, the properties of polyelectrolyte‐based materials were drastically different for different humidity histories. Glass transition temperatures (T_gs) of poly(diallyldimethylammonium chloride) (PDADMAC) were shown to vary by 100 °C, depending on humidity and thermal histories. These parameters also change glassy storage modulus values by 100%. Furthermore, we observe that dried PDADMAC is highly lossy. DMA of dried poly(styrene sulfonate) (PSS) was more complex and did not exhibit a glass transition in the tested range. DMA of a PEC of PDADMAC and PSS revealed a humidity history‐dependent water melt in the first heating cycle, as well as storage modulus values of dried and annealed PECs that only varied by 17–26% over a 275 °C temperature range. Based on these results, we report for the first time humidity history as controlling structure and properties of polyelectrolyte‐based materials. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 684–691     

由碳酸钠诱导形成的油酸钠蠕虫状胶束的流变学性质

当Na₂CO₃浓度逐渐增加时, 用流变学的方法研究了阴离子表面活性剂油酸钠(NaOA)在溶液中从胶束转变成蠕虫状胶束的过程. 首先测量体系剪切粘度(η)和剪切速率的关系得到零剪切粘度(η₀). 然后由动态振荡实验得到复合粘度(|η^*|)、动态模量(储能模量G'、损耗模量G"和结构松弛时间τ_s)等物理量. 应用Cox-Merz规则和Cole-Cole图, 证明NaOA (0.040～0.080 mol/L)/Na₂CO₃ (0.25～0.50 mol/L)体系形成蠕虫状胶束, 且蠕虫状胶束的动态粘弹性在NaOA (0.050～0.080 mol/L)/Na₂CO₃ (0.35～0.45 mol/L)范围是符合Maxwell模型的线性粘弹性流体.     

Viscoelastic properties of poly(methyl methacrylate) with high glass transition temperature by lithium salt addition

The effect of ion‐dipole interaction between lithium cations and oxygen atoms in poly(methyl methacrylate) (PMMA), which leads to the great enhancement of glass transition temperature (T_g), on the linear viscoelastic properties is studied using binary blends of PMMA and lithium trifluoromethanesulfonate (LiCF₃SO₃). The strong interaction at low temperature leads to the high modulus in the glassy region even near T_g. The interaction becomes weak as increasing the temperature. Consequently, the rheological terminal region is clearly detected without a marked enhancement of steady‐state compliance, although the zero‐shear viscosity increases by the LiCF₃SO₃ addition. The result indicates that the crosslinking due to the ion‐dipole interaction has a lifetime that decides the longest relaxation time. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2388–2394     

Deformation induced evolution of mobility in PMMA

The stress relaxation response in the glassy state just below T_g was measured for poly(methylmethacrylate) following application of constant strain rate uniaxial tensile deformation at various locations on the stress–strain curve, including the yield and post‐yield region. The macroscopic mobility was determined from analysis of the relaxation response. Up to a factor of 3 decrease in relaxation time was observed with the fastest relaxation occurring in the post‐yield softening region. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Rheology of (±)‐camphor‐10‐sulfonic acid doped polyaniline‐m‐cresol conducting gel nanocomposites

The rheological behavior of polyaniline‐(±champhor‐10‐sulfonic acid)_0.5‐m‐cresol [PANI‐CSA_0.5‐m‐cresol] gel nanocomposites (GNCs) with Na‐montmorillonite clay (intercalated tactoids) is studied. The shear viscosity exhibits Newtonian behavior for low shear rate (<2 × 10^?4 s^?1) and power law variation for higher shear rate. The zero shear viscosity (η₀) and the characteristic time (λ) increase but the power law index (n) decrease with increase in clay concentration. In the GNCs storage modulus (G′) and loss modulus (G″) are invariant with frequency in contrast to the pure gel. The G′ and G′ exhibit the gel behavior of the GNCs up to 105 °C in contrast to the melting for the pure gel at 75.7 °C. The percent increase of G′ of GNCs increases dramatically (619% in GNC‐5) with increasing clay concentration. The conductivity values are 10.5, 5.65, 5.51, and 4.75 S/cm for pure gel, GNC‐1, GNC‐3, and GNC‐5, respectively, promising their possible use in soft sensing devices. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 28–40, 2008     

Viscoelastic properties of decrosslinked irradiation‐crosslinked polyethylenes in supercritical methanol

The viscoelastic properties of decrosslinked irradiation‐crosslinked polyethylenes using a supercritical methanol were investigated via oscillatory dynamic shear measurements. Decrosslinked polymers at a low reaction temperature exhibited solid‐like rheological properties, as evidenced by a small slope at G′ and G″, a long relaxation time, slow stress relaxation behavior, and considerable yield stress. In contrast, decrosslinked polymers at a high temperature exhibited liquid‐like rheological properties that included a large slope in G′ and G″, a short relaxation time, fast stress relaxation behavior, and nonyield stress. The difference in the viscoelastic properties of the decrosslinked polyethylenes was attributed to the difference in the gel content with the reaction temperature. A higher gel content induced stronger solid‐like viscoelastic properties. Hence, the rheological measurements were useful for analyzing the molecular structure of decrosslinked polymers using a supercritical fluid. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1265–1270, 2010     

The linear rheological responses of wedge‐type polymers

The linear rheological responses of a series of specially designed wedge‐type polymers synthesized by the polymerization of large molecular weight monomers have been measured. These wedge polymers contained large side groups which contained three flexible branch chains per polymer chain unit. The master curves for these polymers were obtained by time temperature superposition of dynamic data at different temperatures from the terminal flow regime to well below the glass transition temperature, T_g. While these polymers maintained a behavior similar to that of linear polymers, the influence of the large side group structure lead to low entanglement densities and extremely low rubbery plateau modulus values, being near to 13 kPa. The viscosity molecular weight dependence was also somewhat higher than that normally observed for linear polymers, tending toward a power law near to 4.2 rather than the typical 3.4 found in entangled linear chains. The glassy modulus of these branched polymers is also found to be extremely low, being less than 100 MPa at T_g ?60 °C. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 899–906