A strip resonance technique for measuring the ultrasonic viscoelastic parameters of polymeric sheets with application to cellulose

An acoustic strip resonance apparatus that measures the viscoelastic response of polymeric sheets over the temperature range of 100–400°K and at frequencies from 20 to 100 kHz is described. This is a computer-controlled instrument which uses the resonant frequency and the quality factor of standing waves in strips to calculate the ratio of complex Young's modulus to density. Results are presented for cellophane and paper samples. These are consistent with measurements reported by others at lower frequencies. That is, (1) a single predominant secondary relaxation process which corresponds to the γ relaxation occurring at 200°K and 1 Hz is found in dry samples at 260°K and 60 kHz; (2) as moisture is added, the γ relaxation weakens and a higher temperature, β, relaxation appears; and (3) at low temperature, moisture addition initially increases the mass specific Young's modulus. The effects of methanol on the viscoelastic parameters of cellulose were also measured and found to be similar to those of water.     

Rheo-optical studies of high polymers. XVIII. Significance of the vertical shift in the time-temperature superposition of rheo-optical and viscoelastic properties

To determine the true reason for the increase in birefringence and the decrease in relaxation modulus for high-density polyethylene with rising temperature, changes in crystalline structure as well as in thermal, viscoelastic, and rheo-optical properties with temperature were measured, by several techniques, including DSC, DLI, infrared dichroism, x-ray diffraction, and NMR. The values for degree of crystallinity obtained from the DSC fusion curve, density, and infrared absorbances coincide very well and show almost no divergence till about 80°C. The optical vertical shift factor pT can be related to the ratio of the orientation function for the crystal c axis at an arbitrary temperature to that at the references temperature, f_ε/f_ε0. The mechanical vertical shift factor b_T, on the other hand, is associated with the temperature dependence of the mobile fraction, as determined by NMR measurements, but not with variations in degree of crystallinity.     

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.     

Elevated temperature nanoindentation characterization of poly(para-phenylene vinylene) conjugated polymer films

Temperature dependent mechanical properties of poly(p-phenylene vinylene) (PPV) were investigated using quasi-static (QS) and dynamic nanoindentation (NI) at temperatures over the range of 25 to 100 °C. The reduced modulus decreased from about 4.40 GPa to 3.64 GPa over this temperature range. The plasticity indices at all measurement temperatures were lower than the critical value of 0.875, characterizing material “sink-in”, rather than “pile-up” during measurements. The plasticity index showed a non-monotonic trend, with a minimum value at around 70 °C. Analysis of indentation stress relaxation data, obtained at different temperatures, was also performed using generalized Maxwell viscoelastic models. From these analyses, a relaxation mode, with a characteristic relaxation time of approximately 0.5 s, was evident. The characteristic time remained relatively unchanged over the temperature range of 25 to 100 °C. However, the relaxation modulus associated with this mode showed the expected decrease with increase in temperature.     

Rubber networks containing unattached macromolecules. III. Nonlinear stress relaxation in the system ethylene–propylene terpolymer with ethylene–propylene copolymer and behavior of extracted networks

Further stress relaxation experiments, mostly at 50°C, are reported on mixtures of crosslinkable ethylene–propylene terpolymer with saturated ethylene–propylene copolymer (molecular weights 3.6 and 45 × 10⁴) containing up to 50% by weight of copolymer, crosslinked by sulfur to leave the saturated copolymer unattached and free to reptate in the copolymer network. Stress relaxation was measured in small simple elongations (stretch ratio about 1.15) on samples which had been extracted to remove a large part of the unattached copolymer and dried. The relative increase in modulus at long times (10⁴ sec) increased with the proportion extracted; at short times (1 sec), extraction of the lower molecular weight copolymer increased the modulus to about the same extent but extraction of the higher molecular weight copolymer affected it very little. The relaxation modulus of the copolymer extracted from sample 50H (50% copolymer of high molecular weight), obtained by difference, agreed with that for the total copolymer except for a small difference probably attributable to molecular weight selectivity in the extraction. Stress relaxation was measured on sample 50H at six higher elongations up to a stretch ratio of 3. The dependence of stress on time and strain was consistent with an analysis based on the following assumptions: (a) linear additivity of the network and unattached copolymer contributions, (b) strain–time factorization of the stress contributions from the individual components, (c) a strain dependence for the unattached component corresponding to the presence of a Mooney–Rivlin C₂ term only, (d) a strain dependence for the network component which does not follow the Mooney–Rivlin equation but is dominated by a simple neo-Hookean term.     

Comparative rheological study of ionic semi-IPN composite hydrogels based on polyacrylamide and dextran sulphate and of polyacrylamide hydrogels

Ionic semi-interpenetrating polymer networks composite hydrogels were synthesized by free-radical polymerization using dextran sulphate (DxS), acrylamide as monomer and N,N′-methylene(bis)acrylamide as cross-linking agent. The viscoelastic properties of these composite hydrogels were investigated by oscillatory shear measurements under small deformation conditions comparative with those of polyacrylamide gels. Changes of the rheological properties of composite hydrogels have been studied in terms of polymerization temperature, cross-linker ratio, initial monomer concentration and molar mass of DxS. The results showed that the stability of the composite hydrogels obtained at room temperature (22?°C) was relatively low because the storage modulus (G′) was only eight times higher than the loss modulus (G″), while for those obtained by cryopolymerization (?18?°C), the stability was improved, the G′ values being about 30 times higher than those of G″. This behaviour indicated that, by conducting the synthesis of hydrogels below the freezing point of the reaction solutions, an enhancement of the hydrogels elasticity was achieved. The network parameters, i.e. the average molecular weight between two cross-links and the cross-link density of the composite hydrogels prepared at ?18?°C, were estimated from rheological data.     

Morphology and modulus–temperature behavior of semicrystalline poly(ethylene terephthalate) (PET)

The influence of the thermal history on the morphology and mechanical behavior of PET was studied. The degree of crystallinity (density measurements) and the morphological structure (electron microscopy and small-angle x-ray diffraction) depend on the crystallization temperature. The viscoelastic parameters obtained from the modulus–temperature curves are mainly determined by the morphology of the samples. The glass-transition temperature, T_i, is a function of the crystallinity and the crystallization temperature. It is maximum for a crystallinity between 0.34 and 0.39 for a sample crystallized isothermally between 120 and 150°C. This dependence on crystallization conditions is ascribed to the conformation of the amorphous chain segments between the crystalline lamellae as well as the concentration and the molecular weight of the polymer material rejected during isothermal crystallization. Both factors are supposed to be temperature-dependent. The value of the rubbery modulus is a function of both the volume concentration of the crystalline lamellae and the structure of the interlamellar amorphous regions (chain folds, tie molecules, chain ends, and segregated low molecular weight material). Annealing above the crystallization temperature of isothermally crystallized samples has a marked influence on their morphology and mechanical behavior. The morphological structure and the viscoelastic properties of annealed PET samples are completely different from those obtained with samples isothermally crystallized at the same temperature.     

Parameters of the temperature dependence of the rate of magnetic relaxation of protons in water and its solutions including seawater

The results of measurements of the temperature dependence of the relaxation rate (1/T ₁) of protons in seawater with 35‰ salinity and salt solutions with different concentrations at temperatures from ?22°C to +120°C are presented. The possibility of approximating the temperature dependence of the magnetic relaxation rate by different functions in pure water, seawater, and solutions of the salts of the latter was studied. The parameters of this dependence and their variation under the influence of salt components are given. The least mean square deviation was obtained, and the best convergence was determined according to the statistical criteria for aqueous electrolytes of moderate concentrations for the function in the form of the sum of exponentials, in which the number of terms depended on the solution concentration. It is shown that the parameters of the thermal dependence of the relaxation rate represented by different functions can be used in combination for studying the dynamic properties of the solutions of low and moderate concentrations.     

The effects of solvent type on the concentration dependence of the compression modulus of thermoreversible isotactic polystyrene gels

Solutions of isotactic polystyrene in either trans-decalin or 1-chlorodecane were transformed into gels by quenching from a high temperature (ca. 180°C) to ?20°C. The relaxation modulus in compression of these gels was measured over a range of concentrations of from 0.04 g/g to 0.40 g/g. At 22°C, the gels show a double logarithmic stress relaxation rate, m, which is higher than for PVC and gelatin gel systems. 120 s isochronal modulus concentration diagrams exhibit non-power law behavior, i.e., not only is the general trend such that the double logarithmic slope decreases with increasing concentration, but there are also regions in which abrupt changes in modulus occur over narrow ranges in concentrations. These features in the concentration dependence of the modulus are less pronounced than those found previously¹ in isotactic polystyrene/cis-decalin gels. The behavior is interpreted to be inconsistent with a fringed micelle picture of the gel structure. Preliminary results are reported indicating that polymer fraction and temperature of gel formation can significantly affect the modulus of the gels.     

Effect of the reference chain dimension on the viscoelastic and stress–strain behavior of poly(n-butyl methacrylate) networks

The linear viscoelastic and stress-strain behavior of poly(n-butyl methacrylate) networks at a content of crosslinking agent (ethyleneglycol dimethacrylate) of c? 0–1 × 10^?4 mole/cm³ was investigated in the main transition and rubberlike region in the temperature interval from 20 to 150°C. The dependence of the unperturbed chain dimensions on temperature was determined from thermoelastic measurements in the rubberlike region; this dependence was unaffected by the content of crosslinking agent. Application of time–temperature superposition to the linear viscoelastic behavior did not give a continuous superimposed curve in the proximity of the rubberlike region; superposition within the whole time region required introducing the change of the unperturbed chain dimensions with temperature. This correction was sufficient for a sample with a higher content of the crosslinking agent. However, for loose networks (c< 0.1 × 10^?4 mole/cm³) it was insufficient, because of another relaxation mechanism in the region of high temperatures. It was found that the intensity and temperature dependence of this relaxation mechanism, which is probably due to a change of the number of entanglements with temperature, are connected with the magnitude and the temperature dependence of the C₂ constant of the Mooney-Rivlin equation.     

Interaction of Formic Acid with the Silica Gel Network

Silica gels can be made by direct reaction of formic acid with tetraethyl orthosilicate. We have characterized wet gels of this type using a beam-bending technique that yields the elastic modulus, Poisson’s ratio, viscoelastic relaxation function, and permeability. When the experiment is performed in ethyl formate, the silica network behaves in an elastic fashion; the permeability is low (<1 nm²), indicating a pore radius of <4.3 nm. The capillary pressure generated in such small pores is estimated to be sufficient to cause collapse of the pores during drying, which would account for the observed ultramicropores in this type of gel. When the pore liquid contains formic acid, viscoelastic relaxation is relatively rapid. Studies of cyclosiloxane compounds indicate that formic acid can attack only the strained siloxane bonds of the network, which would account for the relaxation behavior. Aging in formic acid causes rapid initial shrinkage, because formic acid accelerates condensation of silanols, which drives syneresis; the modulus increases and the permeability decreases monotonically, so there is no indication of coarsening during aging in formic acid, even at 70°C.     

Viscoelastic phase diagram of fluorinated and grafted polymer films and proton‐exchange membranes for fuel cell applications

The influence of temperature and moisture activity on the viscoelastic behavior of fluorinated membranes for fuel cell applications was investigated. Uncrosslinked and crosslinked ethylene tetrafluoroethylene (ETFE)‐based proton‐conducting membranes were prepared by radiation grafting and subsequent sulfonation and their behavior was compared with ETFE base film and commercial Nafion^® NR212 membrane. Uniaxial tensile tests and stress relaxation tests at controlled temperature and relative humidity (RH) were carried out at 30 and 50 °C for 10% < RH < 90%. Grafted films were stiffer and exhibited stronger strain hardening when compared with ETFE. Similarly, both uncrosslinked and crosslinked membranes were stiffer and stronger than Nafion^®. Yield stress was found to decrease and moisture sensitivity to increase on sulfonation. The viscoelastic relaxation of the grafted films was found to obey a power‐law behavior with exponent equal to ?0.04 ± 0.01, a factor of almost 2 lower than ETFE, weakly influenced by moisture and temperature. Moreover, the grafted films presented a higher hygrothermal stability when compared with their membranes counterparts. In the case of membranes, a power‐law behavior at RH < 60% was also observed. However, a markedly different behavior was evident at RH > 60%, with an almost single relaxation time exponential. An exponential decrease of relaxation time with RH from 60 s to 10 s was obtained at RH ≥ 70% and 30 °C. The general behavior of grafted films observed at 30 °C was also obtained at 50 °C. However, an anomalous result was noticed for the membranes, with a higher modulus at 50 °C when compared with 30 °C. This behavior was explained by solvation of the sulfonic acid groups by water absorption creating hydrogen bonding within the clusters. A viscoelastic phase diagram was elaborated to map critical conditions (temperature and RH) for transitions in time‐dependent behavior, from power‐law scaling to exponential scaling. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1139–1148     

Dynamic viscoelastic properties of unsintered polytetrafluoroethylene

The molecular motion of unsintered polytetrafluoroethylene (PTFE) was studied by dynamic viscoelastic measurements. From results for variously heat treated suspension polymerized (molding powder) PTFE, the following conclusions are drawn. Molding powder, as received, has a high degree of crystallinity according to calorimetric results and lower magnitude of the γ relaxation, but the behavior of the β relaxation suggests that the crystals are disordered more than those of the sintered PTFE. The β relaxation peak for an emulsion polymerized PTFE (fine powder) occurs at a higher temperature and is sharper than that for the molding powder, so that the crystals of the fine powder are better ordered than that for the molding powder. The behavior of the β relaxation for the radiation induced-polymerized PTFE is affected by polymerization conditions, particularly concentration of emulsifier. It is concluded from the results for the unsintered PTFE polymerized by various methods that the nature of crystalline state is decided during the course of simultaneous polymerization and crystallization. Molding powder as received has a relatively high magnitude of relaxation between 30°C to 180°C, but with little temperature dependence in this temperature range. This relaxation is diminished by gamma-ray irradiation. Since the molding powder has a complicated morphology, the relaxation in this temperature range is attributed to inter-particle friction rather than a relaxation associated with motion on the molecular level.     

Constitutive model calibration of the time and temperature-dependent behavior of high density polyethylene

HDPE is commonly used in pipelines and piping for industrial and societal infrastructure. Like most polymers, HDPE's mechanical properties are sensitive to temperature and show time dependent properties. The temperature effect on both the short and long term compressive and tensile behavior of HDPE, in a combined manner, have not been investigated thoroughly in the past. Especially the constitutive behavior of HDPE, incorporating temperature effects on its long and short term behavior, could be essential when designing such infrastructural components. Hence, the temperature effect on the short and long term response in tension and compression of HDPE is investigated in this study. The short term tensile and compressive stress-strain behavior at 23, 40, 60, and 80 °C were obtained through experiments at constant displacement rate and temperature. Tensile and compressive stress relaxation (e.g. long term) behavior at 23, 40, 50, 60, 70, and 80 °C were investigated through stress relaxation tests. The experimental results from the short term tests showed that both the tensile and compression moduli and yield strength of HDPE decrease linearly with the increase in temperature. It is also shown from the long term test that relaxation modulus in tension and compression are highly dependent on temperature. Based on the experimental results, the constitutive three network model (TNM) was calibrated and implemented in a FEA model, which was then validated through a three point bending (3 PB) relaxation test with a prescribed temperature profile. The FEA model and the calibrated model results agree markedly well with the experimental results, which indicates that the model can be used reliably to predict the temperature dependent short and long term behavior of HDPE in design and analysis of HDPE components.     

Pressure–volume–temperature behavior of two polycyanurate networks

The pressure–volume–temperature (PVT) behavior was studied for two polycyanurate networks having different crosslink densities using a pressurizable dilatometer. The samples were studied at temperatures ranging from 60 to 180 °C and at pressures up to 170 MPa to yield PVT data in both rubbery and glassy states. The Tait equation is found to well describe the isobaric temperature scan and isothermal pressure scan data. The thermal expansion coefficients, instantaneous bulk moduli, and thermal pressure coefficients are extracted from the data and their dependence on crosslink density is examined. The time‐dependent viscoelastic bulk modulus (K(t)) is also calculated in the vicinity of the α‐relaxation from previously published pressure relaxation experimental data, and the strength and shape of the dispersion are found to be independent of crosslink density. The limiting bulk moduli depend strongly on temperature with those of the more loosely crosslinked sample being lower at a given temperature and pressure, although at T_g(P), the limiting moduli of the more loosely crosslinked sample are slightly higher than those of the more highly crosslinked sample. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Rubber networks containing unattached macromolecules. I. Linear viscoelastic properties of the system butyl rubber–polyisobutylene

Mixtures of butyl rubber with polyisobutylene (molecular weights 0.055 and 2.3 × 10⁶) up to 50% by weight were crosslinked by sulfur, leaving the polyisobutylene molecules free to reptate in the butyl rubber network. Linear viscoelastic properties were measured in shear creep for periods up to 5 × 10⁵ sec at 25°C and oscillating shear deformations from 0.1 to 3 Hz, at temperatures from 2 to 63°C. Comparison with the properties of a butyl rubber crosslinked without polyisobutylene showed contributions to creep and mechanical loss attributable to the reptating species. Comparison with the properties of polyisobutylene (higher molecular weight) showed that the relaxation times associated with the reptating species in the upper part of the terminal zone are the same for different polyisobutylene contents (25% and 50%) and for 100% polyisobutylene in which no permanent network is present; their contributions to modulus appear to be proportional to the volume fraction of polyisobutylene to a power of about 2/3. The time required in stress relaxation for the portion of the modulus attributable to the reptating species to decay to half its plateau value is, based on the two molecular weights employed, proportional to the polyisobutylene molecular weight to the third power. The magnitude of the associated mechanical loss and its location on the frequency scale can thus be controlled independently.     

Segmental relaxation of water-aged ambient cured epoxy

The effects of long-term immersion on the viscoelastic characteristics of an ambient-temperature cured epoxy system, typical of systems used in infrastructure rehabilitation, are investigated using dynamic mechanical thermal analysis (DMTA). The study considers specimens aged at temperatures of immersion of 23, 37.8 and 60 °C. Time-temperature superposition principles were used to construct master curves of the storage modulus in the glass-rubber transition region for both wet and rejuvenated specimens. Viscoelastic parameters such as the relaxation time and the distribution parameters (β) were determined using KWW curve fits to the master curves. The free-volume content determined through curve fitting of the WLF is higher by about 0.4% for wet specimens than the rejuvenated specimens. Consequently, the fragility index and the activation energy of the relaxation around T_g are all reduced in the wet state. The viscoelastic properties of the aged epoxy specimens are strongly dependent on the temperatures of immersion although the level of water uptake in all cases is similar. Formation of multi-bound water molecules leads to the broadest glass-rubber relaxation in the wet state for specimens aged at 37.8 °C in deionized water, whereas the 60 °C aged specimens show the broadest relaxation in the rejuvenated state due to the formation of a heterogeneous network structure.     

The 4000 Å transition of crystal anthracene

New low temperature determinations of ?₂(ω) for crystal anthracene locate the 0-0 transition origin at 25096 ± 6 cm^?1 for the b-polarization. There is no Stokes shift of the fluorescence origin. The exciton bands which are optically accessible by probing the (ab) crystal face with normal incidence light polarized either parallel or perpendicular to the b-axis have a temperature dependent splitting. The Davydov splitting at 77°K is 267 ± 12 cm^?1. The temperature dependence of the k = 0 polariton splitting and the exciton bandwidths (b-polarization and a-polarization) are also given and together with the Davydov splitting provide a test of the adequacy of theories of exciton interactions. The polarization ratio measured as the ratio of the oscillator strengths of the two transitions (f_b/f_a) is quite temperature dependent for both the region of the (0-0) transition and over the total vibronic transition. At 77°K, the value of f_b/f_a is 8.0 for the origin region close to that expected of an oriented gas but is 4.5 over the total transition. Some spectral structure observed only in the b-polarized reflectance spectrum at temperatures less than 77°K is related to the existence of defects localized near the surface.