Dielectric studies of poly(vinyl chloride)

Measurements of the dielectric constant and loss factor of polyvinyl chloride (PVC) have been made over a wide range of temperature and frequency. Maxima in dielectric loss were observed at a temperature corresponding to the α or glass transition temperature and secondary β transition temperature. The sensitivity of these maxima to both frequency and thermal pretreatment was investigated. It was found that the position of the β peak on the temperature axis changed markedly with frequency, while the glass transition or α peak showed only small variations. Neither the α nor the β peak were very sensitive to thermal pretreatment, but interesting changes in the minimum between these peaks were observed. In quenched samples a distinct shoulder peak at T_β < T_s < T_α was observed; it was possible to eliminate it by a slow cooling of the samples. The effect of plasticizer content was also studied.     

Morphology and physical properties of poly(butylene terephthalate)

Liquid nitrogen-quenched PBT samples produce much larger spherulites of an optic axis orientation different from the of the air-cooled samples. Optical and scanning electron microscopy show that glass fibers in the glass-reinforced PBT sample nucleate the growth of well-defined spherulites along the glass fiber axis. Fracture studies at temperatures below and above the T_g indicate, respectively, brittle and ductile interspherulite boundary fracture. From dynamic mechanical studies, three transitions designated by α (flow transition), β (T_g), and γ (secondary relaxation) are observed. The magnitudes of the β and γ transitions are larger for the more amorphous quenched sample than the air-cooled sample, suggesting their amorphous phase origin. Addition of glass fibers raises the dynamic modulus and flow temperature, but suppresses the γ transition without significantly affecting the melting and glass transition temperatures.     

Modelling of the Hydrolysis of Benzylpenicillin to 6-Aminopenicillanic Acid and Phenyl Acetic Acid by an Immobilised Penicillin Amidase in a Small Pilot Plant Batch Recirculated Reactor

This paper deals with the modelling of the hydrolysis of benzylpenicillin to 6-aminopenicillanic acid (6-APA) and phenyl acetic acid (PAA) in a small pilot plant batch recirculated reactor by an immobilised penicillin amidase preparation. By using the following linearised form for an integrated Michaelis-Menten equation Et/V₀X=α+β| In (1-X)/X| where α and β are reaction kinetic parameters, good correlations are obtained of α and β with linear velocity across the reactor, substrate concentration and temperature of operation. A process to determine α and β from initial velocity measurements is outlined. The applicability of the above equation to published data is also analysed.     

Fracture and yielding behaviors of polystyrene/ethylene‐propylene rubber blends: Effects of interfacial agents

The aim of this work is to investigate the effects of two triblock copolymers, used as coupling agents, on fracture and yielding behaviors of a blend of 80 volume % of polystyrene (PS) and 20 volume %of ethylene‐propylene rubber (EPR), over a large range of loading rates and temperatures. For this purpose, blends containing different concentrations of two triiblock copolymers were studied at various test conditions. The focus was put on the time‐temperature dependence of fracture performance of the blends. Addition of triblock copolymer makes the PS/EPR blend more ductile. The time‐temperature dependence of the brittle‐ductile transition in fracture performance of the blend is controlled by an energy activation process. The interfacial agent lowers the temperature at brittle‐ductile transition and reduces the energy barrier controlling the fracture process. This effect, however, is much more pronounced for the lower molecular weight interfacial agent. The correlation between temperature, loading rate and yield stress of the blends seems to be controlled by a molecular relaxation process according to the Ree‐Eyring theory. This model, based on the assumption of two relaxation processes (α and β) acting in parallel, allows prediction of yield stress at various loading rates and temperatures. Addition of the interfacial agents results in a reduction of the activation energy and an increase in the activation volume V* for both the α and β processes. Furthermore, the similarity of the value of the activation energy ΔH_β in the β yielding process and the energy barrier ΔH controlling the brittle‐ductile transition in fracture seems to suggest that a similar secondary relaxation mechanism controls the yielding and the fracture behavior of the blend.     

Viscoelastic relaxations in polyepoxide joints related to the strength of bonded structures at impact rate shear loading

The aim of this paper is to show the excellent impact behavior of a modified epoxy joint on consideration of the viscoelastic relaxation processes of an adhesive. The investigation of the epoxy joint properties, over a range of strain rates ($ \mathop \gamma \limits^ \cdot $ = 10 ^?2 to 10⁴ S^?1) and temperatures (?30, 24, 60, 80°C), shows that there is a good correlation between high impact resistance and the presence of a secondary transition. We successfully applied the Bauwens approach to explain the strain rate sensitivity of the yield stress in terms of a difference in relaxation times at low and high strain rates (α and β). Our purpose is to confirm these results by applying the Escaig model, which reviews thermoset behavior in terms of a thermally activated dislocation propagation mechanism. The Bauwens approach and the Escaig model lead to the same conclusion: They indicate that there is a critical strain rate $ \mathop \gamma \limits^ \cdot $_β (T), correlated to a critical temperature T_β ($ \mathop \gamma \limits^ \cdot $), that corresponds to the limits between the two modes of deformation required to free the different kind of molecular motions implied in the deformation process, the α mode to the α + β mode. But at low temperature (?30°C), these models are no longer valid, which means that there is a heterogeneous deformation process, characterized by local molecular motions, which involve a decrease of the polymer entropy and a permanent evolution of molecular structure.     

The kinetics of polyarylate hydrolytic embrittlement

The hydrolysis of polyarylate in water between 55 and 98°C was found to be a zero-order process with an activation energy of 19.2 kcal/mol, determined by changes in molecular weight. The equation for the effect of temperature on the rate of hydrolysis is ln k = 34.1 ? 10⁴/T, where k is in day^?1. The decrease in molecular weight is accompanied by a loss in ductility. The transition from a ductile to brittle failure in tension occurs at M?_w of about 35,000 and M?_n of 12,700. At 27°C (80°F) and high humidity environment this would occur after 21 years. But during injection molding, the material, if not properly dried, would embrittle in a matter of seconds.     

Physical properties and supermolecular structure of perfluorinated ion-containing (nafion) polymers

The supermolecular structure and viscoelastic and diffusion properties of a perfluorinated polymer containing sulfonic acid (Nafion) were investigated. The breakdown of time–temperature super-position for the dry salt and and acid in the presence of 0.5 H₂O/SO₃H as well as the results of small-angle x-ray scattering suggest that the ions in this material are clustered. Above 180°C, the reestablishment of the time–temperature superposition in the salt suggests that ions in the clusters become mobile. Dynamic mechanical studies were performed over a temperature range from ?190°C to above the glass transition temperatures T_g of the materials. The T_g of the salts is found at ca. 220°C, while in the acid it occurs at 110°C. A β peak in the acid is found at ca. 20°C, while in the salts it occurs between 140°C and 160°C. The β peak shifts to a lower temperature with the addition of water in both the acid and the salts, while the α and γ peaks are unaffected. The latter is located at ca. ?110°C at 1 Hz. Dielectric behavior has also been studied as a function of water content for the acid sample and the potassium salt at frequencies of 100 Hz to 10 kHz. Two relaxations with different activation energies were observed. The position of both peaks shifts to a lower temperature as the water content increases. Finally, the diffusion of water in Nafion in the acid form has been determined. The diffusion coefficient can be represented by the equation      

Process analysis of phase transformation of α to β-form crystal of syndiotactic polystyrene investigated in supercritical CO2

Mechanism of solid phase transformation of α to β form crystal of syndiotactic polystyrene (sPS) was investigated in supercritical CO₂. The phase transformation occurred in the original pure α and mixed (α+β) form sPS in supercritical CO₂ was traced as a function of temperature and pressure by means of wide angle X-ray diffraction (WAXD), differential scanning calorimetry (DSC). At appropriate temperature and pressure, sPS underwent solid phase transitions from α to β form. Higher temperature or higher pressure favored this transformation. Compared to the original pure α form sample, the original β form crystal in the mixed (α+β) form sample acted as the nucleus of β form crystal, so that reduced the transition temperature and pressure.     

Effect of filler particle size on dynamic mechanical properties of poly(methyl methacrylate)

Dynamic mechanical properties of poly(methyl methacrylate) (PMMA) filled with mica flakes (M) or glass beads (G) were investigated as functions of particle size and filler concentration. With increasing particle size, dynamic modulus E′ slightly decreases for system G, while it increases rapidly at first and then approaches the limiting value for system M. Primary dispersion temperature T_α increases with increasing filler concentration. With increasing particle size, T_α decreases for system G but increases for system M. For the mica-filled system, the effect of particle size on the modulus can be explained in terms of orientation of the filler by comparing the experimental data with Wu's and Padawer and Beecher's predictions of the modulus. In order to explain the dependence of T_α on particle size and concentration, an equation for T_α has been proposed: where K_f is a constant and S is the specific surface area of filler per gram of polymer. For system G, T_α can be expressed by the above equation, irrespective of particle size and filler concentration. In the case of system M, it is suggested that T_α is affected also by orientation in addition to the surface area of the filler.     

On the use of pressure‐volume‐temperature data of polyethylene liquids for the determination of their solubility and interaction parameters

Specific volumes of high‐density and low‐density polyethylene liquids at several elevated temperatures and pressures were measured. The measured specific volumes were then used to estimate the thermal expansion coefficients $\left( {{\rm \alpha = }\frac{{\rm 1}}{v}\left( {\frac{{\partial v}}{{\partial T}}} \right)_P } \right)$ and isothermal compressibility $\left( {{\rm \beta = } - \frac{{\rm 1}}{v}\left( {\frac{{\partial v}}{{\partial P}}} \right)_T } \right)$ of the polymers. Two different approaches were used in which one was simply to fit the raw data by second order polynomials to obtain (?v/?T)_P and (?v/?P)_T, while the other by the Sanchez‐Lacombe (S‐L) equation of state. It was found that the resultant α and β obtained from the above methods differ significantly, indicating that the S‐L equation of state may not be suitable for determining α and β at elevated temperatures. When these two sets of α and β were used to calculate the corresponding solubility parameters and then the Flory‐Huggins interaction parameters (χ) of the polymers, the results also differ considerably. Nonetheless, χ obtained from the first method agrees well with the results obtained from small angle neutron scattering measurements while the S‐L equation of state method does not. The current results suggest that solubility and interaction parameters obtained from pressure‐volume‐temperature experiments depend critically on the manner by which the data analysis is performed. Polym. Eng. Sci. 44:853–860, 2004. © 2004 Society of Plastics Engineers.     

The experimental results and simulation of temperature dependence of brittle‐ductile transition in PVC/CPE blends and PVC/CPE/nano‐CaCO3 composites

The effect of chlorinated polyethylene (CPE) content and test temperature on the notched Izod impact strength and brittle‐ductile transition behaviors for polyvinylchloride (PVC)/CPE blends and PVC/CPE/nano‐CaCO₃ ternary composites is studied. The CPE content and the test temperature regions are from 0–50 phr and 243–363 K, respectively. It is found that the optimum nano‐CaCO₃ content is 15 phr for PVC/CPE/nano‐CaCO₃ ternary composites. For both PVC/CPE blends and PVC/CPE/nano‐CaCO₃ ternary composites, the impact strength is improved remarkably when the CPE content or test temperature is higher than the critical value, that is, brittle‐ductile transition content (C_BD) or brittle‐ductile transition temperature (T_BD). The T_BD is closely related to the CPE content, the higher the CPE content, the lower the T_BD. The temperature dependence of impact strength for PVC/CPE blends and PVC/CPE/nano‐CaCO₃ ternary composites can be well simulated with a logistic fitting model, and the simulation results can be illustrated with the percolation model proposed by Wu and Jiang. DMA results reveal that both PVC and CPE can affect the T_BD of PVC/CPE blends and PVC/CPE/nano‐CaCO₃ composites. When the CPE content is enough (20 phr), the CPE is more important than PVC for determining the T_BD of PVC/CPE blends and PVC/CPE/nano‐CaCO₃ composites. Scanning electron microscopy (SEM) observations reveal that the impact fractured mechanism can change from brittle to ductile with increasing test temperature for these PVC systems. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Temperature‐Dependent Scaling Behavior of Dynamic Hysteresis in Pb(Zr,Ti)O3 Ceramics

The dynamic hysteresis scaling behaviors of Nb‐doped Pb(Zr_0.52Ti_0.48)O₃ ceramics have been investigated as a function of electric field amplitude (E₀) and frequency (f) at different temperatures (T). The loop area <A> of saturated loops is found to follow various power laws as <A> ∝ E₀^0.3065 at fixed f and <A> ∝ f ^0.0120 at fixed E₀. Furthermore, the linear scaling relation <A> = k₃ f^αE₀^β + b₃ is estimated under various temperatures. The exponents α (=0.01) and β (=0.10) are T‐independent, whereas the slopes k₃ and y‐intercepts b₃ are T‐dependent because the increasing temperature in the same phase range only decreases the threshold field of the reversal rather than change the dynamic reversal process.     

Effect of physical aging on tensile stress relaxation and tensile creep of cured EPON 828/epoxy adhesives in the linear viscoelastic region

The effect of physical aging on viscoelastic properties was studied for several cross-linked epoxies in the glassy state. Tensile creep and tensile stress relaxation were measured during isothermal physical aging, following rapid quenching of samples annealed above the glass-transition temperature (T^g). The momentary creep curves measured at 21°C, 45°C, and 61°C below T^g for different epoxies could be fitted to an empirical equation for the creep compliance D(t): Values for β and t_o were obtained, and the dependence of t_o on the aging time was determined. Shift factors were calculated to investigate changes in molecular mobility during physical aging. The momentary stress relaxation was measured on the same epoxy materials as used for the creep studies. The stress relaxation curves were fitted to the following equation for the tensile modulus E(t): Values for α and t_o were obtained. The influence of physical aging on-t_o was again studied by calculating shift factors as a function of the aging time. The results are compared with the results of the creep tests and discussed in the context of current molecular theories of physical aging of glassy polymers.     

The glassy state,ideal glass transition,and second‐order phase transition

According to Ehrenfest classification, the glass transition is a second‐order phase transition. Controversy, however, remains due to the discrepancy between experiment and the Ehrenfest relations and thereby their prediction of unity of the Prigogine‐Defay ratio in particular. In this article, we consider the case of ideal (equilibrium) glass and show that the glass transition may be described thermodynamically. At the transition, we obtain the following relations: and with Λ = (α_gβ_l − α_lβ_g)²/β_lβ_gΔα²; and The Prigogine‐Defay ratio is with Γ = TV(α_lβ_g − α_gβ_l)²/β_lβ_gΔβ, instead of unity as predicted by the Ehrenfest relations. Dependent on the relative value of ΔC_V and Γ, the ratio may take a number equal to, larger or smaller than unity. The incorrect assumption of perfect differentiability of entropy at the transition, leading to the second Ehrenfest relation, is rectified to resolve the long‐standing dilemma perplexing the nature of the glass transition. The relationships obtained in this work are in agreement with experimental findings. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 143–150, 1999     

Fine structures and fracture processes in plastic-rubber two-phase polymer systems IV. Temperature and strain rate dependences of tensile properties

Yield stress (σ_Y) and elongation to break (ε_b) were measured over a wide range of temperature under three different strain rates (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}) for a series of polyvinylchloride-rubber blends, ABS polymer and high-impact polystyrene. It was found that a temperature-strain rate reduction was possible for σ_Y and the composite curve obtained by the superposition was expressed by the following relation: where K₁ and K₂ are the material constants, and A_T is the shift factor. As for ε_b, a new maximum was found at around room temperature in addition to the known maximum at around the glass transition temperature of the matrix phase. The results are discussed in terms of the craze theory for rubber toughening of plastics.     

Study on conformational transition phenomena of poly(methyl methacrylate) in acetonitrile near theta conditions

The coil–globule transition for poly(methyl methacrylate) (PMMA) has been studied in a theta solvent, acetonitrile (Θ = 45 °C). The viscosity of PMMA was measured as a function of temperature in the range 26–55 °C. The contraction and expansion of the molecular chains are determined using the measured viscosity values. The temperature dependence of the intrinsic viscosity can be represented by a master curve in a versus |τ|M _w^1/2 (g^1/2 mol^−1/2) plot, where τ = |T − Θ|/T is the reduced temperature and M_w‐is the weight‐average molecular weight. A universal plot of reduced viscosity versus reduced blob parameter (N/N_c) shows the attainment of the collapsed state below the theta temperature. The dimensions of PMMA in acetonitrile (M_w = 3.15 × 10⁶ g mol⁻¹) decrease to 63 % at 26 °C of those in the unperturbed state. The results in this work are compared with those previously published. © 2000 Society of Chemical Industry     

Fracture characterization of recycled high density polyethylene/nanoclay composites using the essential work of fracture concept

The effect of nanoclay on the plane‐strain fracture behavior of pristine High density polyethylene (HDPE) and recycled HDPE blends was studied using the essential work of fracture (EWF) concept. The failure mode of EWF tested specimens was found to be associated with the specific non‐EWF (β_Bw_p,B). Adding 6‐wt% of nanoclay to pristine HDPE and 2‐wt% to recycle‐blends greatly decreased the β_Bw_p,B values and led to a transition from ductile to brittle failure mode. A fractographic study revealed that the difference in failure modes was caused by the changes in micro and macro morphologies, which could be related with the specific EWF (w_e,B). In the ductile failure, w_e,B is governed by the fibril size; adding nanoclay and recycled HDPE to pristine HDPE decreased the fibril size and subsequently lowered the w_e,B value. In the brittle failure, the w_e,B value was enhanced by creating a rough fracture surface. Adding nanoclay to pristine HDPE, a steadily decrease in w_e,B was measured until 4‐wt% after which the change was insignificant. Conversely, nanoclay content more than 2‐wt% in recycle‐blends greatly decreased the w_e,B value. A transition map was constructed to illustrate the potential failure mode and the associated fracture morphology based on the tested material compositions. POLYM. ENG. SCI., 56:222–232, 2016. © 2015 Society of Plastics Engineers     

Time–temperature dependent brittle fracture of viscoelastic solids

The Griffith formulation is used to study fracture behavior of poly(methyl methacrylate) (PMMA) as a function of strain rate and temperature over the range 4.4 × 10^?5 ≤ ε ≤ 4.4 × 10^?2 in./in./sec and 25°C ≤ T ≤ T_g, T_g being the glass transition temperature. It is found that the transition from brittle to ductile failure occurs abruptly at a temperature T_f which is dependent on strain rate and is approximately the same as the glass transition temperature of the material. The Griffith brittle fracture criterion is found to apply below T_f for all strain rates. The brittle fracture behavior is shown to obey the time–temperature equivalence principle in the same way as the material's other viscoelastic properties, having the same shift function.