Step Strain Experiments Research Articles

Relaxation Dynamics of Bidisperse Temporary Networks

Simultaneous measurement of IR dichroism and birefringence is used to examine the component relaxation in bidisperse, fully entangled melts of polybutadienes with 1% of the repeating units modified with 4-phenyl-1,2,4-trixoline-3,5-dione (urazole) groups. Since the urazole groups are capable of forming interchain hydrogen bonds, the rheological properties of these materials differ significantly from those of the analogous polybutadiene melts without polar stickers. Samples with 30, 50, and 70% long chains are examined by step strain and oscillatory shear experiments. In addition, the step strain experiments are carried out at two temperatures

Transient rheological behavior of a thermotropic liquid‐crystalline polymer. III. Step strain experiment and shear stress relaxation modulus

Shear stress relaxation modulus Gs(t,γ) was determined for a well‐characterized thermotropic liquid‐crystalline polymer, poly[(phenylsulfonyl)‐p‐phenylene 1,10‐decamethylene‐ bis(4‐oxybenzoate)] (PSHQ10) by conducting step strain experiments for a range of shear strains (γ). A fresh specimen was employed for each step strain experiment. We found that while time‐strain factorability [i.e., Gs(t,γ)=G(t)h(γ), where G(t) is the memory function and h(γ) is the damping function] was applicable to the isotropic region, it was not to the nematic region of PSHQ10. We further found that preshearing of a specimen decreased the magnitude of Gs(t,γ) considerably, suggesting that variations in the morphological state (i.e., domain texture) took place during shearing. The failure of time‐strain factorability for the PSHQ10 in the nematic region is believed to be attributable to variations in its morphology as affected by the level of applied shear strains.

On the use of stress growth data to determine strain-dependent material functions for factorable K-BKZ equations

The procedure of using experimental stress growth data to determine strain-dependent, or damping, functions for factorable K-BKZ constitutive equations is examined. Damping functions obtained using stress growth data from simple shear and planar extensional flows in conjunction with integrated forms of factored K-BKZ models are compared with the damping function obtained from shear step-strain experiments. Results for the low-density polyethylene (LDPE) known as IUPAC X are presented that demonstrate the difficulties encountered with this method, which can be quite serious for planar extensional flow. These results appear to be consistent with previous studies on several polymer melts where uniaxial extension stress growth data were used to determine damping functions. This body of evidence raises important questions about the use of this procedure and the strain-dependent and, apparently, test-dependent functions that are obtained. An explanation for these results is proposed which suggests that these observations may be due to an intrinsic shortcoming of K-BKZ theories.

Transient rheological behaviour of melts of liquid-crystalline polymers compared with that of flexible polymer melts

Transient rheological behaviour of melts of flexible polymers can be described qualitatively by factorable constitutive equations, the functions of which can be obtained by oscillatory and step strain experiments. In start-up experiments thermotropic LCP melts can exhibit very large overshoots of the stresses, followed by minima, after which steady states are reached through damped oscillations of the signals. It is also possible that the normal stress remains periodic for long times, with large amplitudes, as is shown for a nematic copolyester melt that has been squeezed during the gap setting process. These periodicities scale with the number of revolutions of the rotating plate. After cessation of flow the stresses relax quickly to values that may be unequal to zero and dependent on the position in the period of the stresses where flow is stopped. Dynamic experiments reveal that the melts are very elastic in that state.

Dynamics of polymeric liquids using polarization-modulated laser Raman scattering

A new experimental technique, ‘polarization-modulated laser Raman scattering’ (PMLRS), is presented for the study of the dynamics of polymeric materials subjected to transient flows. A detailed analysis of the experiment based on Jones-Mueller matrix calculus is presented. Jones and Mueller matrices that take into account the integrated effect of the deformed sample's birefringence are developed for a Raman scattering element, using either the 0° or 180° scattering geometries. To test the predictions of the theory a Raman scattering system, based on high-speed phase modulation (50 kHz) of the incident light coupled with phase-sensitive detection, has been developed. This system is also capable of simultaneously measuring birefringence. Single-step reversal extension and step strain experiments were conducted using a polyisobutylene melt. Experiments were done using the Raman scattered light associated with the v stretching vibration of C-H groups present in the specimen. The results obtained indicate that the Raman signal ratios all depend on the second- and fourth-order moments of the orientation distribution function of polymer segments and on the sample's birefringence.

Transient shear behavior of a thermotropic liquid crystalline polymer in the nematic state

Transient shear experiments show that a thermotropic liquid crystalline polymer (TLCP) in its nematic state behaves linear viscoelastically as long as the shear does not exceed a characteristic stress of 2×104 Pa or a characteristic strain of approximately γ=2, whichever is reached first. The relaxation modes, as determined in dynamic mechanical experiments, are sufficient for describing the linear viscoelastic behavior in step strain and start‐up at constant rate. Beyond this linear region, the behavior deviates drastically from that of conventional homopolymers: Negative first normal stress differences are measured during steady shear at rates below 0.5 s−1; long relaxation modes are more affected in a large step strain experiment than short relaxation modes [thus no factorization of G(t,γ) into separate time and strain functions]; no zero shear viscosity is detected in the accessible range; the normal stress relaxes faster than the shear stress; in a start‐up experiment at constant shear rate, the shear stress and the first normal stress difference both go through a maximum at approximately γ=2. The material, a random copolyester of 73 mol % 4‐hydroxybenzoic acid and 27 mol % 6‐hydroxy‐2‐naphthoic acid (Vectra A900 of Hoechst–Celanese), was shown to be stable at the experimental temperature of 290 °C for at least 1 h if first preheated to 320 °C.

Relaxation dynamics of selected polymer chain segments and comparison with theoretical models

Simultaneous measurement of infrared dichroism and birefringence is used to study selected polymer segment dynamics in isotopically labeled block copolymers. Two different polymers were studied: polybutadiene and poly (ethylene propylene). The first type consisted of a triblock with a short middle block labeled and a diblock with a short end block labeled, while the second type consisted of a triblock with three equal blocks and the end blocks labeled. Results of step strain experiments at −10°C for polybutadiene and at room temperature for poly(ethylene propylene) indicated that segments located at chain ends relax faster than segments located at chain centers. These experimental data were compared to the predictions of two molecular models: the bead-spring model of Rouse and the tube model of Doi and Edwards, and it was found that both models correctly predict the qualitative features of segmental relaxation. However, the tube-model predictions were closer to the experimental results. In addition, when the effects of orientational coupling interactions between segments in the melt were incorporated into this model, its predictions quantitatively agreed with the experimental results. The orientational coupling coefficient for poly(ethylene propylene) was 0.45 as measured from previous work, and for polybutadiene it was found to be 0.4.

Transient flow of thermotropic liquid crystalline polymers in step strain experiments

The transient response of two thermotropic liquid crystalline polymers (a copolyester of 60 mol % p‐hydroxybenzoic acid, PHB, and 40 mol % poly(ethylene terephthalate), PET, and a copolyester of PHB and 2‐hydroxy‐6‐naphthoic acid, following step strains up to 20 strain units was measured. The relaxation curves typically show an initially rapid decay followed by a long relaxation tail. The lower the temperature, the more remarkable is the length of the long relaxation tail. This behavior makes the LCP uniquely different from most flexible chain polymers such as PET and polystyrene, which show a relaxation modulus which decreases continuously having no discontinuity in the slope. This behavior is probably due to unmelted solid phase which exists in the melt up to quite high temperatures. When the LCP’s are heated to temperatures well above their melting points as determined by DSC, then the long relaxation tails are eliminated. Furthermore, on cooling the sample rapidly down from a temperature well above the melting point the relaxation modulus resembles that at the higher temperature as a result of the supercooling effect. The relaxation modulus was also determined for samples subjected to lubricated squeezing flow. Whereas for polystyrene the relaxation modulus determined in lubricated squeezing flow was equal to that determined in step shear strain experiments, this was not the case for the LCP’s. It is not known whether the behavior reported here is common to nematic LCP’s or to the multiphase structure (crystallites, nematic phase, isotropic phase) which might be present.

Rheological properties of the liquid crystalline poly(γ‐benzyl α, L‐glutamate) gels in benzyl alcohol

AbstractWe have determined the degree of stiffness of a poly(γ‐benzyl α, L‐glutamate) (PBLG) chain in benzyl alcohol by measuring the intrinsic viscosities of dilute Solutions with differing molecular weights. Viscoelastic properties in oscillatory shear flow have been studied and the dependence of the loss and storage moduli on temperature, composition, and frequency are reported. We have also studied the transient shear stress relaxation behavior of the PBLG gel at different temperatures and concentrations. A comparison has been made between these gels and a classical poly(dimethyl siloxane) (PDMS) network, as well as, typical glassy polymers. Shear creep and recovery measurements have been made for this system. Some extensional step strain experiments using lubricated squeezing have been investigated. Tensile experiments have been made to determine stress‐strain relationship during elongation. Preliminary experiments using the impulse approach to viscoelasticity further indicate the high elastic contribution in the gel.

Comparison of the rheology of polymer melts in shear, and biaxial and uniaxial extensions

The experimental properties of different polymer melts, polystyrene, high density polyethylene and low density polyethylene are compared for the first time in three different deformations: step shear, step biaxial extension and steady uniaxial extension. Properties of three other melts are also studied in step biaxial and shear experiments. For our comparative purposes some data of Laun and Winter from the literature are used, as well as new data reported here. In all the step strain experiments, the stresses can be factored into a time dependent relaxation modulus and a strain dependent damping function. The data are interpreted using a differential constitutive equation of Larson which satisfies this time-strain separability and has a single parameter that describes the strain softening character of the material. Results show that differences in the properties of the melts are most pronounced in uniaxial extension and least in biaxial extension. All melts follow the Doi-Edwards prediction relatively closely in biaxial extension. In uniaxial extension, the branched material shows a strong strain hardening effect although its shear and biaxial properties are similar to the other melts. The constitutive model gives a reasonably good fit to the data in all three deformations for unbranched materials for the same value of the adjustable parameter; the model, however, fails for the branched low density polyethylene.

Relaxation of shear and normal stress components in step-strain experiments

The relaxation of torque and axial thrust following a rapidly imposed step in shear strain ( 0 < γ ⩽ 3.33) was measured for several undiluted polymers and polymer solutions using the cone-and-plate geometry in a Rheometrics mechanical spectrometer. Instrumental response times were favorable for calculating both the shear stress σ(γ, t) and the first normal stress difference N 1(γ, t) from torque and thrust data on two of the solutions. Those results confirm the relationship N 1(γ, t) = γσ(γ, t). Apparent departures from this relationship appear if σ(γ, t) and N 1(σ, t are calculated from torque and thrust data when the instrumental response criteria are not met.