Time-temperature superposition and dynamic mechanical behavior of atactic polystyrene

The dynamic mechanical behavior of monodisperse atactic polystyrene (mol. wt. 98,000) has been measured in the frequency range, 10⁻⁵ to 10 Hz and temperature range 359–374K. The time-temperature superposition of the entire data in the frequency range of overlap seems less satisfactory in both the real and imaginary components of the complex shear modulus, G′ and G″, respectively. The lack of adequate superposition becomes pronounced in the tan ϕ (G″/G′) plots. The tan ϕ plots provide a more discerning criteria for the superposition than the G′ or G″ spectra. An analysis based on an earlier model for anelastic deformation shows that of the several changes that may occur in the dynamic mechanical behavior on heating of polystyrene, the predominant ones are both an increase in the size of the microshear domains and the correlations of movement of segments near entanglements. These decrease the contribution to the modulus on heating near T_g so that the time-temperature superposition is vitiated.     

A New Molecular Theory of Non‐Linear Viscoelasticity for Vitrifiable (or Crystallizable) Thermoplastic Polyurethane Elastomers

The molecular theory of non‐linear viscoelasticity for vitrifiable thermoplastic polyurethane elastomers (VTPUE) is a refinement and extension of viscoelastic theory of thermoplastic elastomers and polyurethanes to glassy transition, a structural model and a mechanism of vitrification for glassy polymers were proposed. Five kinds of constituent chains with Nagai chain constraint consisting of soft‐domains, hard‐domains, and entanglements are used as the elementary structural and statistical ensemble units for the correlation of molecular and phase‐domain structures to the static and dynamic mechanical behaviors. So the influences of non‐Gaussian in character, the phase separation of domain, the network topology of structure, the affined deformation of constituent chains, and the thermal history are all taken into account in the constituent chains of the theory. Free energies of deformation for the VTPUE segment copolymer were calculated by the statistical mechanics with the probability distribution functions of the sizes for the five kinds of constituent chains. Then the static constitutive equations and modulus of four types of deformation and the dynamic shear viscosity, modulus and loss tangent of VTPUE are derived from the proposed theory. The theory is successful in relating the molecular chain parameters C₁₀₀, C₀₂₀, and C₂₀₀ to the constitutive equations and modulus under large deformations and the micro‐domain structure to the complex shear viscosity and modulus and the loss tangent. The dynamic shear modulus and loss tangent of VTPUE are related to the domain structures through the fraction of hard segments (W_h), the molecular weight of soft segment (M_ns), and the growth dimensional parameters of hard and soft domains (β). Two series of linear VTPUE copolymers (ES and ET) with different fractions(W_h) of hard segments and molecular weight (M_ns) of soft segments were prepared. Their static and dynamic mechanical properties were studied by uni‐axial extension and dynamic analysis tests. Then the constitutive equation at uni‐axial extension and the expressions of shear modulus and loss tangent are verified by these experimental data, and excellent agreement between the theory and experiments is achieved. It is shown, that the proposed theory can predict the viscoelastic behavior of vitrifiable thermoplastic polyurethanes.     

Viscoelasticity of oriented poly(ethylene terephthalate)

Time–temperature superposition can be successfully applied to both the stress relaxation and dynamic mechanical properties of oriented PET fibers. Two curves result; one is the time dependence of the modulus at constant temperature, while the other is the shift, log aT, of this curve along the time scale as a function of temperature. This temperature dependence is less than that for both unoriented PET and typical amorphous polymers above T_g. It is about the same as that for oriented nylon 66 and unoriented glassy poly(methyl methacrylate). The isothermal modulus has the same time dependence as that of the unoriented PET; however, it is a factor of 3.3 larger. The modulus curve is almost identical in both shape and magnitude with that of oriented nylon 66. However, a temperature of 82°C. is required to place the viscoelastic dispersion region of PET at the same time scale as nylon 66 at 25°C. This temperature increase is the major difference in viscoelasticity between these two oriented polymers.     

Viscoelasticity of low molecular weight polystyrene. Separation of rubbery and glassy components

The complex shear modulus was measured for four low molecular‐weight polystyrenes (M_w = 10,500, 5970, 2630, and 1050) near and above the glass transition temperature. For the lowest molecular weight sample, the method of reduced variables, the time–temperature superposition principle, was applicable, while it was not applicable for the higher M samples. For these higher M samples, it was assumed that the complex modulus is composed of two components (R and G components). The R component was estimated by subtracting the G component, which was assumed to be the same as the modulus of the lowest molecular weight sample. The time–temperature superposition principle was applicable to each of the R and G components, and the shift factors were different from each other. The contribution of the R component to the total complex modulus decreased with decreasing M. Anomalous temperature dependence of the steady‐state compliance for low M polymers as Plazek reported could be attributed to difference in temperature dependence of the two components. The estimated complex modulus for the R component was in accord with that calculated by spring‐bead model theory. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 389–397, 1999     

Relation between the network structure and dynamic mechanical properties of a typical amine-cured epoxy polymer

The dynamic mechanical properties of a series of epoxy polymers of known network structure have been investigated. It was shown that the distance between crosslinks could be predicted from either the shift in the glass transition temperature T_g or by use of the dynamic modulus above T_g. The front factor in the equation of state for rubber elasticity was near unity for stoichiometric equivalence of epoxy and amine and increased slowly with excess of either component.     

Viscoelastic properties of 1,2-polybutadiene—comparison with natural rubber and other elastomers

Viscoelastic properties of uncrosslinked 1,2-polybutadiene (91.5% vinyl, 7.0% cis, 1.5% trans, number-average molecular weight 99,000) were studied by dynamic shear measurements between 0.15 and 600 cps (torsion pendulum and Fitzgerald transducer) and shear creep measurements over time periods up to 3.7 × 10⁴ sec., in the temperature rang from 5 to 50°C. More limited dynamic measurements were made on a sample of unvulcanized natural rubber with number-average molecular weight 350,000 at frequencies from 0.4 to 400 cps and temperatures from 13 to 48°C. All data were reduced to 25°C. by shift factors calculated from equations of the WLF form with the following coefficients: 1,2-polybutadiene, c₁ = 6.23, c₂ = 72.5; natural rubber, c₁ = 5.94, c₂ = 151.6. In the transition zone, the relative positions of the loss tangent curves on the logarithmic frequency scale for these and other rubbers (1,4-polybutadiene with 50% trans configuration; styrene–butadiene rubber with 23.5% styrene content; and polyisobutylene) provided relative measures of local segment mobility. At 25°C., these ranged over a factor of 3700 with 1,2-polybutadiene and polyisobutylene the lowest and 1,4-polybutadiene the highest. When the frequency scale of each rubber was reduced to a temperature 100°C. above its glass transition temperature, however, the loss tangent curves for all except polyisobutylene were nearly coincident; the latter still showed a lower mobility by a factor of about 1/800. The terminal relaxation time and steady-state compliance for the 1,2-polybutadiene calculated from the Rouse theory were larger than those observed experimentally. The level of compliance corresponding to the entanglement network of 1,2-polybutadiene, J_eN, was calculated by integration over the loss compliance, J″, to be 1.62 × 10^?7 cm.²/dyne; integration over G″ to obtain the corresponding modulus gave reasonable agreement. From such J_eN, values, the average number of chain atoms between entanglement points, jZ_e, was estimated as follows: 1,2-polybutadiene, 132; natural rubber, 360; 1,4-polybutadiene, 110; styrene–butadiene rubber, 186; polyisobutylene, 320. Values of jZ_e were also estimated from the minimum in the loss tangent and compared with those reported from the molecular weight dependence of viscosity. The three sources were in generally good agreement.     

The effect of fiber orientation and stacking sequence on carbon/E-glass/epoxy intraply hybrid composites under dynamic loading conditions

This study investigated the dynamic mechanical properties of hybrid intraply carbon/E-glass epoxy composites with different orientations and stacking sequences under different loading conditions with increasing temperature. A neat epoxy and five various hybrid composites such as Carbon (0°)/E-glass (90°), Carbon (45°)/E-glass (135°), Carbon (90°)/E-glass (0°), Carbon/E-glass (alternating layer), and Carbon/E-glass (alternating layer 45°) were manufactured. Three-point bending test and dynamic mechanical test were conducted to understand the flexural modulus and viscoelastic behavior (storage modulus, loss modulus, and loss tangent) of the composites. Dynamic mechanical test was performed with the dual cantilever method, at four different frequencies (1, 5, 10, and 20 Hz) and temperatures ranging from 30 to 150°C. The experimental results of storage modulus, loss modulus, and loss tangents were compared with the theoretical findings of neat epoxy and various hybrid composites. The glass transition temperature (T_g) increased with the increase in frequency. A linear fit of the natural log of frequency to the inverse of absolute temperature was plotted in the activation energy estimation. The interphase damping (tanδ_i) between plies and the strength indicator (S_i) of the hybrid composites were estimated. It was observed that the neat epoxy had more insufficient storage and loss modulus and a high loss tangent at all the frequencies whereas hybrid composites had high storage and loss modulus and a low loss tangent for all the frequencies. Compared with other hybrid composites, Carbon (90°)/E-glass (0°) had higher strength and activation energy. The result of reinforcement of hybrid fiber in neat epoxy significantly increases the material's strength and stability at higher temperatures whereas decreasing free molecular movement.     

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.     

Characterization of Rubber Epoxy Blends by Thermal Analysis

Differential scanning calorimetry (DSC), thermogravimetric analysis (TG) and dynamic mechanical analysis (DMA) of the blends ofepoxy cresol novolac (ECN) resin toughened with liquid carboxy terminated butadiene-co-acrylonitrile (CTBN) rubber have been carried out. Exothermal heat of reaction (ΔH) due to crosslinking of the resin in presence of diaminodiphenyl methane(DDM, as amine hardener) showed a decreasing trend with increasing rubber concentration. Enhancements of thermal stability as well as lower percentage mass loss of the epoxy-rubber blends with increasing rubber concentration have been observed in TG. Dynamic mechanical properties reflected a monotonic decrease in the storage modulus (E′) with increasing rubber content in the blends. The loss modulus (E″) and the loss tangent(tanδ) values, however, showed an increasing trend with rise of the temperature up to a maximum (peak) followed by a gradual fall in both cases. Addition of 10 mass% of CTBN resulted maximum E″ and tanδ. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electric,dielectric, and dynamic mechanical behavior of carbon black/styrene‐butadiene‐styrene composites

The conductivity of styrene‐butadiene‐styrene block copolymers containing different amounts of extraconductive carbon black (CB) was investigated as a function of the mold temperature. The composites exhibited reduced percolation thresholds (between 1.0 and 2.0 vol % CB). The dynamic mechanical analysis characterization revealed that the glass‐rubber‐transition temperatures of both segments were not affected by the CB addition, although the damping of the polybutadiene phase displayed a progressive drop with an increase in the CB concentration. The normalized curves of tan δ/tan δ_max (where tan δ represents the value of the loss tangent at any measurement temperature and tan δ_max represents the loss tangent peak value at the corresponding temperature T_max) versus T/T_max (where T is the temperature and T_max is the maximum temperature), corresponding to both polystyrene and polybutadiene phases as well as the activation energy related to the glass‐rubber‐transition process, did not present any significant change with the addition of CB. The dielectric analysis revealed the presence of two relaxation peaks in the composite containing 1.5 vol % CB, the magnitude of which was strongly influenced by the frequency, being attributed to interfacial Maxwell‐Wagner‐Sillars relaxations caused by the presence of different interfaces in the composite. The mechanical properties were not affected by the presence of CB at concentrations of up to 2.5 vol %. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2983–2997, 2003     

Measurement of high frequency linear viscoelastic functions of a nitrile‐butadiene rubber compound by ultrasound spectroscopy

The storage and loss components of the complex wave modulus, M*(ω), measured on a nitrile‐butadiene rubber compound (NBR‐DIN 53538) by ultrasound spectroscopy at a temperature of 293.2 K, were combined with the components of the complex shear modulus, G*(ω), measured on the same sample in a commercial Rheometric Scientific ARES instrument with torsion geometry at different frequencies and temperatures, and superposed in a master plot using the time–temperature superposition principle. From the combined measurements the components of the complex bulk modulus, K*(ω), were obtained by means of the exact formula M*(ω) = K*(ω) + (4/3)G*(ω). Some of the features of the complex bulk modulus reported in the literature for polymeric materials are confirmed for the NBR‐DIN mixture. The maxima in G″(ω) and K″(ω) are separated by more than one order of magnitude in the frequency scale and furthermore, the shapes of the peaks are different. The simple idea, that, for many polymers, the mechanisms for relaxation in shear and in bulk are of the same basic nature appears not to be supported by the present data. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 91–102, 2007     

Effect of nematic ordering on the elasticity and yielding in disordered polymeric solids

The relation between elasticity and yielding is investigated in a model polymer solid by Molecular‐Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers — both with bond disorder — as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio τ_Y/G between the shear yield strength τ_Y and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the shear modulus and the decrease of the shear yield strength, as observed in experiments on nematic thermosets. A tentative explanation of the subsequent reduction of the ratio τ_Y/G in terms of the distributions of the per‐monomer stress is offered. © 2017 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2017 , 55, 1760–1769     

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     

The proper glass transition temperature of amorphous polymers on dynamic mechanical spectra

Glass transition is crucial to the thermal and dynamical properties of polymers. Thus, it is important to detect glass transition temperature (T _g) with a sensitive and proper method. Dynamic mechanical analysis (DMA) is one of the most frequently used methods to determine T _g due to its advantage of high sensibility. However, there is controversy in the past literatures to determine the proper glass transition temperature among three transition temperatures, i.e., T _g1, T _g2 and T _g3 in the dynamic mechanical spectra, which correspond to the temperature abscissa of intersect value of two tangent lines on storage modulus (E′), the peak of the loss modulus (E″) and the peak of the loss tangent (tan δ). In this work, these three transition temperatures were compared with the glass transition temperature determined by DSC (T _gDSC). Based on the discussion of different modes of molecular motion around the glass transition region, it is demonstrated that T _g1 and T _g2 have the same molecular mechanism as T _gDSC, i.e., local segmental motion which is enthalpic in nature and determines the proper glass transition temperature, while T _g3 is assigned to the transition temperature of entropic Rouse modes, thus cannot be used as the proper glass transition temperature.     

The ageing phenomenon of polyethersulphone hollow fibre membranes for gas separation and their characteristics

We have studied the ageing behaviour of PES/NMP (polyethersulphone/N-methyl pyrrolidone) hollow fibres for gas separation that were prepared from 35% and 37% dope. The effect of ageing on hollow fibres spun from low and high shear rate (103 vs. 862 s⁻¹) has also been investigated, in terms of their transport properties (permeation flux and separation performance), thermal, mechanical and tensile properties. Hollow fibres in this study were aged for around four months in ambient air at room temperature prior to testing.In general, the gas permeation flux drops steeply during the 40 days following fabrication and levels off thereafter. The O₂/N₂ selectivity decreases slightly over time. Hollow fibres spun with high shear rate seem to age faster than those spun with low shear rate. The gas fluxes of both membranes were found to follow a log–log relationship with ageing time. For almost all the gases used in this study, the gas flux decay rate, calculated from the slope of the log–log plot of gas flux vs. ageing, is higher for membranes spun with high shear rate. The effect of shear rate on ageing is less significant for smaller gas molecules that travel faster such as He and H₂. No significant effect of ageing on gas selectivity was observed. Experimental results also indicate that the storage modulus and loss modulus of the hollow fibres increase with ageing. Hollow fibres spun with high shear rates give a slightly higher increase in these moduli than those spun at low shear rates. Surprisingly, tangent δ (energy dissipation) and glass transitional temperature are not sensitive to ageing. We also found that the tensile yield strength and Young's modulus of the hollow fibres increase slightly with ageing. The hollow fibre membranes spun at high shear rates also show a higher increment in tensile yield stress. However, the change in Young's modulus due to ageing was similar for fibres spun with high and low shear rates.     

Pressure relaxation of polystyrene and its comparison to the shear response

Isothermal pressure relaxation as a function of temperature in two pressure ranges has been measured for polystyrene using a self-built pressurizable dilatometer. A master curve for pressure relaxation in each pressure regime is obtained based on the time–temperature superposition principle, and time–pressure superposition of the two master curves is found to be applicable when the master curves are referenced to their pressure-dependent T_g. The pressure relaxation master curves, the shift factors, and retardation spectra obtained from these curves are compared with those obtained from shear creep compliance measurements for the same material. The shift factors for the bulk and shear responses have the same temperature dependence, and the retardation spectra overlap at short times. Our results suggest that the bulk and shear response have similar molecular origin, but that long-time chain mechanisms available to shear are lost in the bulk response. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3375–3385, 2007     

Synthesis and characterization of poly(arylene ether imidazole)s

Poly(arylene ether imidazole)s were prepared by the aromatic nucleophilic displacement reaction of a bisphenol imidazole with activated aromatic dihalides. The polymers had glass transition temperatures ranging from 230 to 318°C and number-average molecular weights as high as 82,000 g/mol. Thermogravimetric analysis showed a 5% weight loss occurring ～ 400°C in air and ～ 500°C in nitrogen. Typical neat resin mechanical properties obtained at room temperature included tensile strength and tensile modulus of 14.2 and 407 ksi and fracture energy (G_lc) of 23 in. lb/in.² Titanium-to-titanium tensile shear strengths measured at 23 and 200°C were 4800 and 3000 psi, respectively. In addition, preliminary data were obtained on carbon fiber laminates. The chemistry, physical, and mechanical properties of these polymers are discussed.     

Tightening of gelatin chemically crosslinked networks assisted by physical gelation

Developing the use of polymers from renewable sources to build hydrogels with tailored mechanical properties has become an increasing focus of research. The impact of the thermo‐reversible physical networks of gelatin (arising from the formation of triple‐helices) on the structure formation of a chemical network, obtained by crosslinking with glutaraldehyde (a non‐catalytic crosslinker), was studied using optical rotation, oscillatory rheology, and large strain mechanical deformation. We observed a direct correlation between the storage shear modulus of the chemical network grown in the gel state (i.e., simultaneously with the physical network) and the amount of gelatin residues in the triple‐helix conformation (χ). Since χ is directly affected by temperature, the value of the storage modulus is also sensitive to changes in the temperature of gel formation. χ values as low as 12% lead to an increase of the shear storage modulus of the crosslinked gel by a factor of 2.7, when compared to a chemical network obtained in the sol state (i.e., in the absence of a physical network). Our results show that the physical network acts as a template, which leads to a greater density of the chemical crosslinks and a corresponding higher elastic modulus, beyond what is otherwise achieved in the absence of a physical network. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1850–1858     

Comparison of the transient stress–strain response of rubber to its linear dynamic behavior

Master curves of the small strain and dynamic shear modulus are compared with the transient mechanical response of rubbers stretched at ambient temperature over a seven‐decade range of strain rates (10^?4 to 10³ s^?1). The experiments were carried out on 1,4‐ and 1,2‐polybutadienes and a styrene–butadiene copolymer. These rubbers have respective glass transition temperatures, T_g, equal to ?93.0, 0.5, and 4.1 °C, so that the room temperature measurements probed the rubbery plateau, the glass transition zone, and the onset of the glassy state. For the 1,4‐polybutadiene, in accord with previous results, strain and strain rate effects were decoupled (additive). For the other two materials, encroachment of the segmental dynamics precluded separation of the effects of strain and rate. These results show that for rubbery polymers near T_g the use of linear dynamic data to predict stresses, strain energies, and other mechanical properties at higher strain rates entails large error. For example, the strain rate associated with an upturn in the modulus due to onset of the glass transition was three orders of magnitude higher for large tensile strains than for linear oscillatory shear strains. © 2011 Wiley Periodicals, Inc.* J Polym Sci Part B: Polym Phys, 2011     

Influence of carboxyl‐terminated (butadiene‐co‐acrylonitrile) loading on the mechanical and thermal properties of cured epoxy blends

A mixture of epoxy with liquid nitrile rubber, carboxyl‐terminated (butadiene‐co‐acrylonitrile) (CTBN) was cured under various temperatures. The cured resin was a two‐phase system, where spherical rubber domains were dispersed in the matrix of epoxy. The morphology development during cure was investigated by scanning electron microscope (SEM). There was slight reduction in the glass transition temperature of the epoxy matrix (T_g) on the addition of CTBN. It was observed that, for a particular CTBN content, T_g was found to be unaffected by the cure temperature. Bimodal distribution of particles was noted by SEM analysis. The increase in the size of rubber domains with CTBN content is due probably to the coalescence of the rubber particles. The mechanical properties of the cured resin were thoroughly investigated. Although there was a slight reduction in tensile strength and young's modulus, appreciable improvements in impact strength, fracture energy, and fracture toughness were observed. Addition of nitrile rubber above 20 parts per hundred parts of resin (phr) made the epoxy network more flexible. The volume fraction of dispersed rubbery phase and interfacial area were increased with the addition of more CTBN. A two‐phase morphology was further established by dynamic mechanical analysis (DMA). © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2531–2544, 2004