Three‐dimensional thermorheological behavior of isotactic polypropylene across glass transition temperature

The aim of this work was to determine the three‐dimensional thermorheological behavior of isotactic polypropylene (i‐PP) in the region of its glass transition temperature (T_g) by a master curve. The i‐PP is a widespread polymer with a T_g ～ 0°C. Dynamic mechanical analysis (DMA) at varying frequencies and temperatures and bulk tests at varying temperatures and times are carried out to obtain the relaxation spectra. Traditionally, the combination of time and temperature is done for thermorheological simple material by the creation of a master curve based on the Arrhenius or William–Landel–Ferry (WLF) equation. This investigation shows that these equations do not fit the behavior across the glass transition of i‐PP. Instead, a new arc tangent function is derived. Additionally, it can be shown that the shifting factors differ from shear to bulk load. Therefore, the mode of mechanical stress seems to have an influence on the thermorheological behavior. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 877–880, 2004     

Application of a fractional model for simulation of the viscoelastic functions of polymers

In the present work the dynamic behavior of two representative polymeric materials, experimentally studied in previous works, has been analyzed by a fractional derivative model. It is shown that the well‐known fractional derivative Zener model, in its simplest form as a four‐parameter model is capable of capturing the main features of the dynamic moduli of the polymeric structures examined. Furthermore, the time dependent viscoelastic functions, namely the compliance and the relaxation modulus could be simulated with the same model parameter values, indicating this way that the fractional model can provide a method of interconversion between viscoelastic material functions. The model's inadequacy of describing the loss modulus peak asymmetry, exhibited by the materials, has been encountered by the five‐parameter version of the fractional Zener model. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43505.     

The glass transition of amorphous polymers: About a continuous equation of state and its derivatives

Describing the pressure-volume-temperature (PVT) behavior of polymers is often hindered due to limitations of models and theories. In this work, we propose the logistic function to derive a phenomenological equation of state (EOS) that overcomes these limitations. Without dividing the temperature domain into several intervals, this continuous EOS describes the PVT behavior of amorphous polymers in the equilibrium state, the vitreous state and at glass transition. Discontinuities at glass transition are inherently eliminated. The EOS is continuously differentiable with respect to temperature and pressure. The thermal expansion coefficient and compression modulus thus can be determined at any valid reference state. The EOS linearly depends on temperature both in the equilibrium state and vitreous state. Furthermore, a parameter of the EOS is interpreted as the pressure-dependent glass transition temperature. Using PVT data of polyethersulfone (PES), measured in the temperature range of 20 − 360 °C and pressure range of 10 − 200 MPa in both the isobaric and standard isothermal mode, the validity of the EOS is discussed. Polymer processing simulation and solid mechanics benefit from the EOS and its derivatives, respectively. In addition, the EOS can be used to determine the glass transition temperature from PVT data.     

Deuteron n.m.r. in relation to the glass transition in polymers

²H n.m.r. is introduced as a tool for investigating slow molecular motion in the glass transition region of amorphous polymers. In particular, we compare ²H spin alignment echo spectra of chain deuterated polystyrene with models for restricted rotational Brownian motion. Molecular motion in the polystyrene-toluene system has been investigated by analysing ²H n.m.r. of partially deuterated polystyrene and toluene, respectively. The diluent mobility in the mixed glass has been decomposed into ‘solid’ and ‘liquid’ components where the respective average correlation times differ by more than 5 decades.     

The effect of benzenesulfonamide plasticizers on the glass transition temperature of an amorphous aliphatic polyamide

The plasticizing effect of benzenesulfonamides (BSAs) on an amorphous aliphatic polyamide (AAPA) has been studied using dynamic mechanical analysis of copper‐supported spin‐coated mixtures. It follows that N‐(n‐butyl)BSA (BBSA), an amorphous liquid hydrogen bonding BSA, is fully miscible with AAPA because their mixtures are characterized by a single glass transition (T_g) throughout the compositional range. The T_g–composition dependence, however, is not linear because experimental results suggest a 20 K fall in T_g occurring around 0.65 BBSA units per amide unit, which coincides with the system shifting from a polymer‐like to a liquid‐like glass‐forming material. When considering a crystallizable hydrogen‐bonding plasticizer such as ethylBSA (EBSA), AAPA/EBSA mixtures become fully crystalline at a 1.3 EBSA unit per amide group. Nevertheless, melting point depression together with the single T_g observed throughout the compositional range on quenched (and therefore amorphous) samples confirms the miscibility of AAPA chains with the plasticizer. N,N‐DialkylBSAs, which lack the sulfonamide proton and therefore the possibility of hydrogen bonding with amide groups, quickly phase separate from AAPA, the glass transition of the latter staying mainly unaffected apart from a small (9 K) decrease at 10–15 mol% plasticizer. © 2001 Society of Chemical Industry     

Attempt to correlate the yield processes above and below the glass transition in glassy polymers

This paper is concerned with a model which attempts to describe quantitatively, by the same elementary process, the yield behaviour above and below T_g, as well as the effect of annealing on the yield stress. This model links together theories we have previously proposed and relies on the following main assumptions: the deformation processes imply the cooperation of n activated segments and that the free energy increase of an activated segment depends on the structural state of the polymer. A satisfactory agreement is found with yield stress data on polycarbonate (PC), over a very large range of temperatures and strain rates. The correlation between the yield stress and the annealing treatment is also reasonable.     

A comparative study of the effect of some paraffinic oils on rheological and dynamic properties and behavior at low temperature in EPDM rubber compounds

The influence of some paraffinic oils on rheological properties, dynamic properties, and behavior at low temperature of various ethylene–propylene–diene monomer rubber (EPDM) compounds was studied. Three different types of EPDM, Dutral TER 4049, Dutral Ter 4038, and Nordel IP 4770 R, and five different paraffinic oils were used. The properties of the compounds were evaluated with reference to the oil characteristics: viscosity, composition, glass transition temperature, and solubility parameter. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1825–1834, 2005     

Dielectric properties of polyarylate (PAr) around the glass transition

Dielectric characterization of the α-relaxation in polyarylate (PAr) has been carried out by means of a dielectric spectroscopy technique in a frequency range of 10–30 kHz. Complementary thermally stimulated depolarization currents (TSDC) and differential scanning calorimetry d.s.c.) measurements have also been performed. The results are interpreted in terms of the standard Cole-Cole plot and Havriliak-Negami distribution for the dielectric relaxation times. Information about the temperature and frequency dependence of a.c. conductivity is also obtained from the experimental curves. However, the behaviour of the main dielectric relaxation time is deduced from the experimental data in a wide range of temperature around the glass transition. This behaviour results in close agreement with the theoretical predictions of a free-volume approach for the dielectric α-relaxation recently proposed by the authors.     

Melt rheological behavior of intimately mixed short sisal–glass hybrid fiber‐reinforced low‐density polyethylene composites. I. Untreated fibers

The melt rheological behavior of intimately mixed short sisal–glass hybrid fiber‐reinforced low‐density polyethylene composites was studied with an Instron capillary rheometer. The variation of melt viscosity with shear rate and shear stress at different temperatures was studied. The effect of relative composition of component fibers on the overall rheological behavior also was examined. A temperature range of 130 to 150°C and shear rate of 16.4 to 5470 s^?1 were chosen for the analysis. The melt viscosity of the hybrid composite increased with increase in the volume fraction of glass fibers and reached a maximum for the composite containing glass fiber alone. Also, experimental viscosity values of hybrid composites were in good agreement with the theoretical values calculated using the additive rule of hybrid mixtures, except at low volume fractions of glass fibers. Master curves were plotted by superpositioning shear stress and temperature results. The breakage of fibers during the extrusion process, estimated by optical microscopy, was higher for glass fiber than sisal fiber. The surface morphology of the extrudates was analyzed by optical and scanning electron microscopy. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 432–442, 2003     

Field strength effect on elastoplastic behavior of aluminoborosilicate glass: I. Elastic moduli and indentation size effect

The modifier field strength (FS) is believed to play an important role in determining the elastic–plastic responses of aluminoborosilicate (ABS) glasses, but its effect is not well understood. Three novel alkali and three alkaline earth (AE) ABS compositions were created for this study which is the first part of two studies that explored the elastoplastic responses of these glasses. Six compositions were designed using different network modifiers (NWMs) to cover a range of cation FS. The glasses were also designed such that the concentrations of NWM and Al₂O₃ were similar, which maximized the three-coordinated boron fraction in the network. It is well known that modifier FS can affect the coordination number (CN) of Al and B in an ABS glass structure, for example, a higher FS modifier can promote B³ → B⁴ and higher [Al^5,6], but the degree of this depends on network former (NWF) ratios. Previous work used solid-state NMR spectroscopic analysis on the current glasses to find that there was variation between [B⁴] and [Al⁴] between the two glass series (alkali vs. AE) but that was attributed to synthesis factors and no trend with FS was associated with the varying NWF CN. Further, ²⁹Si ssNMR showed no evidence of NBOs which made sense based on composition. The conclusion, therefore, was that there was a far greater correlation with modifier FS for the increased mechanical and physical properties rather than the CN of Al and B. Part I of the current work focused on the elastic moduli, Poisson's ratio, the indentation size effect (ISE), and the bow-in parameter. This part laid out the foundation to investigate the intersection of these elastoplastic properties with hardness and crack resistance as a function of NWM FS. Results showed that: (i) the Young's, bulk, and shear moduli increased with modifier FS, whereas Poisson's ratio did not trend with FS; (ii) the alkali glasses had a significantly higher magnitudes of ISE compared to the AE glasses; and (iii) the bow-in parameter was load dependent and decreased with modifier FS at the highest indentation load.     

Kinetic modeling of the peroxide cross-linking of polymers: From a theoretical model framework to its application for a complex polymer system

Peroxides react with polymers in a variety of ways. The fundamental comprehension and prediction of pertinent kinetics of reactions is consequently indispensable. Based on the mechanisms of reactions of cross-linking process, a new theoretical kinetic model framework was developed. The kinetic model was then applied to the reactions of cross-linking process of various peroxides and a chosen complex polymer compound, namely partially hydrogenated poly(acrylonitrile-co-1,3-butadiene). Whereas the initial macromolecular backbone structure was determined utilizing attached proton test carbon nuclear magnetic resonance, the evolution of overall concentration of cross-links was monitored through viscoelastic characteristics of the system. The model demonstrated good agreement with experimentally measured data and, moreover; the evolution of concentrations of various crucial species inherent to the cross-linking process were predicted. The most significant advantage of the developed kinetic model is that it may be readily applied to an assortment of polymer/peroxide systems.     

The effect of confinement in nanoporous polymers on the glass transition temperature

The glass transition temperature (T_g) of nanoporous polyetherimide (PEI) and PEI thin films was investigated. The T_g decreased from its bulk value in both of these confined systems. Monte Carlo simulations were performed to calculate the nearest neighbor pore-to-pore distances in the nanoporous PEI. A quantitative analogy between the nanoporous PEI and PEI thin films is proposed through an equivalence of nearest neighbor pore-to-pore distances and thin film thickness. The effect of confinement is believed to be due to the interface regions, which possess higher chain mobility than the bulk. When these high mobility interface regions are sufficiently close together, the excess mobility at the interface region affects the dynamics of the system by restraining percolation of the slow domains resulting in the observed decrease in T_g.     

The role of network architecture on the glass transition temperature of epoxy resins

A series of epoxy networks were synthesized in which the molecular weight between crosslinks (M_c) and crosslink functionality were controlled independent of the network chain backbone composition. The glass transition temperature (T_g) of these networks was found to increase as M_c decreased. However, the rate at which T_g increased depended on crosslink functionality. The dependency of M_c on T_g is well described by two models, one based on the concept of network free volume while the other model is based on the principle of corresponding states. Initially, neither model could quantitatively predict the effect of crosslink functionality in our networks. However, our tests indicated that both the glass transition and the rubbery moduli of our networks were dependent on M_c and crosslink functionality, while the glassy state moduli were independent of these structural variables. The effect of crosslink functionality on the rubbery modulus of a network has been addressed by the front factor in rubber elasticity theory. Incorporation of this factor into the glass transition temperature models allowed for a quantitative prediction of T_g as a function of M_c and crosslink functionality. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 387–395, 1997     

Molecular dynamics study on the viscosity of glass-forming systems near and below the glass transition temperature

Temperature-dependent viscosity is critical to decipher two profound questions in condensed matter physics, namely the glass transition and the relaxation of amorphous solids. However, direct measurement of viscosity over a large temperature range is extremely difficult. Here, using classical molecular dynamics (MD) simulations, we report a novel method to calculate the equilibrium viscosity of supercooled liquid both above and below the glass transition temperature (T_g) and to estimate the nonequilibrium viscosity of glass down to room temperature. Based on the shoving model, we derived an analytical formula showing that the shear viscosity in logarithmic scale changes linearly with the shear-induced variation in shear modulus or potential energy of the glass-forming system. The shear viscosity as a function of steady-state potential energy of liquid under different shear strain rates can be directly calculated in MD simulations; together with its equilibrium potential energy, one can extrapolate the zero-strain-rate equilibrium viscosity. We verified the proposed model by reliably calculating equilibrium viscosity near T_g of four glass-forming systems (Kob–Andersen system, silica, Cu_45.5Zr_45.5Al₉, and silicon) with different fragilities. Furthermore, our model can estimate the nonequilibrium viscosity of glass below T_g; the upper-bound nonequilibrium viscosity of amorphous silica and silicon at room temperature are calculated to be ~10³² and 10²⁵ Pa·s, respectively.     

Interaction of epoxy resins with water: the depression of glass transition temperature

The depression of T_g in a number of epoxy-water systems has been investigated calorimetrically. Except where an unbalanced reaction stoichiometry was used, experimental results are in good agreement with theoretical predictions based on equations developed for the composition dependent T_g in polymer diluent-systems. Thermal analysis also demonstrates a complex thermal behaviour on rescanning of samples, attributed to diluent diffusing out of the sample. The importance of this behaviour in the context of solvent-induced physical ageing of epoxy resin composites is discussed.     

Reconstruction of histograms of the glass transition temperature of free radical copolymers from DSC thermograms

Most polymeric materials appear as complex mixtures of macromolecules characterized by distributions of specific properties that are essential to the quality of these products. Among such properties, the accurate determination of the glass transition temperature, and therefore, accurate representation of it, is a key issue. When analyzed using dynamic scanning calorimetry (DSC) techniques, many copolymers exhibit a wide range of temperature over which the glass transition takes place, and the width of the transition region is, therefore, not satisfactorily described by average T_g values, for example those computed from tangent curves drawn on thermograms. This article describes a method that allows us to characterize this spreading of the glass transition region by reconstructing weighted T_g distributions from DSC thermograms. As such an objective might appear as questionable from a strictly physical point of view, the significance of what is meant by “distribution” is specified in the text. A model is proposed that accounts for relaxation phenomena. The approach is validated by examining samples of BuA/Sty emulsion copolymers produced at different overall conversions and compositions, and examining the corresponding histograms of T_g were computed. The results show that accurate and consistent information on the glass transition behavior of the copolymer is obtained, and that the effective distribution is clearly connected with the composition drift in the polymer particles. The proposed algorithm allows one to obtain a maximum amount of information from DSC measurements, and provides a deeper insight into the “history” of complex polymer mixtures. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 357–367, 2000