Dynamic frequency sweep experiments

Plots of log G versus log prepared using numerieal data of dynamic frequency sweep experiments provided by J. Roovers. 

An Advanced Rheometric Expansion System (ARES, TA Instruments) was used in oscillatory shear mode with parallel plate geometry. Strain amplitude was fixed at 2% and dynamic frequency sweep experiments with angular frequency ( ) from 0.1 to 100 s were performed at 280°C. PET and all blends were tested under nitrogen atmosphere, while pure LCP, which was found not to degrade, was tested under air. The complex viscosity ( 7 ), dynamic storage (GO and loss (G") moduli were obtained. All rheological measurements are an average of four runs. 

Effects of instrument compliance can induce large errors on shear measurements of elastic and viscoelastic properties of materials [1,2]. These effects are caused not only by the transducer but also the machine itself (load frame), and the rheometer fixtures. We present examples of rheometer compliance effects on the measurement of the material properties of small molecule glass formers and a commercially available polydimethysiloxane (PDMS) rubber. A TA Instruments ARES Rheometer was used with a strain gage transducer (Honeywell-Sensotec). Stress relaxation, aging experiments, and dynamic frequency sweep experiments were performed. We also propose a procedure to correct for comphance effects in stress relaxation experiments and dynamic frequency sweep experiments. Suggestions are made for both instrument and experimental design to avoid and/or reduce compliance effects. 

Figure 4. PDMS dynamic frequency sweep experiment performed at 25 °C. h is the sample thickness for (he samples. There is an apparent effect of instrument compliance for the 50 mm diameter experiment. The sohd symbols are imcorrected data. The hollow S5onbols are corrected data.

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

Figure 8.9 Temperature dependence of G for a highly asymmetric SIS triblock copolymer specimen having a 0.18 weight fraction of PS block (Vector 4111, Dexco Polymers Company), which was annealed at 140 °C for 2 days prior to the isochronal dynamic temperature sweep experiments at an angular frequency of 0.01 rad/s in the heating process. (Reprinted from Sakamoto et al., Macromolecules 30 1621. Copyright 1997, with permission from the American Chemical Society.)...

Figure 12.52 describes the temperature dependence of dynamic storage modulus G during the isochronal dynamic temperature sweep experiment at an angular frequency (ty) of 0.1 rad/s for PS, PS-t-COONa, (PS-t-COONa)/Cloisite 20A nanocomoposite, and (PS-t-COONa)/Cloisite 30B nanocomposite. The following observations are worth noting in Figure 12.52. Not only is the magnitude of G for PS-t-COONa much larger than that for neat PS, but also the values of G for PS-t-COONa decrease slowly, as compared with the values of G for neat PS, with increasing temperature. We attribute this observation to the formation of ionic clusters in PS-t-COONa. It has been reported...

A torsion dynamic rheometer, Rheometric SCIENTIFIC RDA-II, was employed with a plate-plate fixture (i.e., 25 mm in diameter). Frequency sweep experiments were performed in the range 0.1 to 100 rad/s at 190°C in the linear viscoelastic range of the MDPE s. The tests were performed to obtained indirect evidences of the differences in molecular weights and molecular weight distribution of the samples. 

Dynamic melt viscosity studies on the star blocks and a similar triblock were carried out using a Rheometric Mechanical Spectrometer (RMS) (Rheometrics 800). Circular molded samples with -1.5 mm thickness and 2 cm diameter were subjected to forced sinusoidal oscillations (2% strain) between two parallel plates. The experiment was set in the frequency sweep mode. Data were collected at 180 and 210 °C. 

Experiments on recovery of dynamic functions after the application of large strain amplitude perturbation were performed to understand the modulus recovery kinetics. To determine the recovery kinetics, samples underwent the following test sequences (a) frequency sweep, (b) strain sweep, (c) relaxation time of 2 min, (d) frequency sweep, (e) strain sweep, (f) relaxation time of 2 min, (g) frequency sweep, and (h) strain sweep [50]. Figure 7 shows the comparative subsequent strain sweep results performed immediately after a relaxation time of... 

The evolution of the dynamic viscosity rp (co, x) or of the dynamic shear complex modulus G (co.x) as a function of conversion, x, can be followed by dynamic mechanical measurements using oscillatory shear deformation between two parallel plates at constant angular frequency, co = 2irf (f = frequency in Hz). In addition, the frequency sweep at certain time intervals during a slow reaction (x constant) allows determination of the frequency dependence of elastic quantities at the particular conversion. During such experiments, storage G (co), and loss G"(co) shear moduli and their ratio, the loss factor tan8(co), are obtained ... 

FT/ICR experiments have conventionally been carried out with pulsed or frequency-sweep excitation. Because the cyclotron experiment connects mass to frequency, one can construct ("tailor") any desired frequency-domain excitation pattern by computing its inverse Fourier transform for use as a time-domain waveform. Even better results are obtained when phase-modulation and time-domain apodization are used. Applications include dynamic range extension via multiple-ion ejection, high-resolution MS/MS, multiple-ion simultaneous monitoring, and flatter excitation power (for isotope-ratio measurements). 

Figure 3-40 Illustration of Estimation of Critical Stress from a Stress Sweep at a Fixed Frequency Dynamic Rheological Experiment. Alternatively, as described in the text, one may conduct a strain sweep experiment.

Rheology. The rheological properties of the blends and their components were determined on a Rheometrics Mechanical Spectrometer (RMS 800). Three kinds of dynamic oscillatory measurements (i.e. temperature, time, and frequency sweeps) were carried out. All experiments were done by using a parallel plate attachment with a radius of 12.5 mm and a gap setting from 1.2 to 1.8 mm. There was no significant dependence of the experimental results on the gap setting. 

Mechanical Properties. Dynamic mechanical properties were determined both in torsion and tension. For torsional modulus measurements, a rectangular sample with dimensions of 45 by 12.5 mm was cut from the extruded sheet. Then the sample was mounted on the Rheometrics Mechanical Spectrometer (RMS 800) using the solid fixtures. The frequency of oscillation was 10 rad/sec and the strain was 0.1% for most samples. The auto tension mode was used to keep a small amount of tension on the sample during heating. In the temperature sweep experiments the temperature was raised at a rate of 5°C to 8°C per minute until the modulus of a given sample dropped remarkably. The elastic component of the torsional modulus, G, of the samples was measured as a function of temperature. For the dynamic tensile modulus measurements a Rheometrics Solid Analyzer (RSA II) was used. The frequency used was 10 Hz and the strain was 0.5 % for all tests. 

Dynamic mechanical properties of all pure components and blends were measured as a function of percent strain and indicated a linear viscoelastic region up to approximately 30-35 percent. Therefore, all rheological experiments were conducted at a strain rate of 20 percent. In cases where thermal degradation occurred (as seen in time sweep), the heating chamber was continuously purged with liquid nitrogen. Frequency sweeps, and in some cases frequency-temperature sweeps, were performed on all pure components and blends. 

To increase the viscosity of polymer blends, additives [such as traditional fire retardants (mainly oxides) and, more recently, nanoclays] are added to polymer blend systems. The present authors recently conducted dynamic rheological measurements for the EVA/LDPE nanocomposite, as reported in [27]. Figure 8.3 (a) and (b) compare the complex viscosity of the EVA/LDPE blend with and without nanoclay as a function of frequency and temperature, respectively. Measurements were carried out on 1 mm-thick samples using a Rheometrics RDA n Dynamic Analyzer rheometer. The frequency-sweep tests were conducted from 0.1 to 100 rad/s with constant temperature (140 °C) and strain amplitude (1%). Eor the temperature-sweep measurements, samples were heated from 300 to 530 °C (15 °C/min) under nitrogen with constant frequency (10 rad/s) and strain amplitude (10%). In both experiments, there is a significant increase of viscosity above that for the neat... 

Using an Advanced Rheometric Expansion System (ARBS) with parallel plates of 2S mm diameter, we performed dynamic temperature sweep expo-iments under isochronal conditions with increasing temperature as well as decreasing temperature. The heating and cooling rate of these experiments was 0.5 °C/min. The strain amplitude (y,) and the angular frequency (ca) were low enough to satisfy a linear viscoelasticity. 

Fig. 27 (a) Effect of dynamic strain amplitude on storage modulus, (b) stress-strain behaviour of CR/EPDM blend in absence and in presence of nanoclay. For strain sweep experiment, tension mode was selected for the variation of the dynamic strain from 0.01 % to 40 % at 10 Hz frequency [106]... 

---