Viscoelastic measurements

As for the glassy polymers discussed in Chapter 15, there have been far more studies of viscoelastic properties of crystalline polymers as a function of temperature at constant or nearly constant frequency. 

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Viscoelastic Measurement. A number of methods measure the various quantities that describe viscoelastic behavior. Some requite expensive commercial rheometers, others depend on custom-made research instmments, and a few requite only simple devices. Even quaHtative observations can be useful in the case of polymer melts, paints, and resins, where elasticity may indicate an inferior batch or unusable formulation. Eor example, the extmsion sweU of a material from a syringe can be observed with a microscope. The Weissenberg effect is seen in the separation of a cone and plate during viscosity measurements or the climbing of a resin up the stirrer shaft during polymerization or mixing. 

Viscoelastic fluids that are more concentrated are characteri2ed with devices that are similar to the rotational viscometers described previously. However, instead of constant rotational motion in one direction, a sinusoidal oscillatory motion is provided. Some instmments allow both viscosity and viscoelastic measurements. 

PMMA-b-PBA shows improved izod impact strength compared to PMMA homopolymer (41). Polyisobutylene (PIB) or its hydrogenated one (PIB-H) also acts as an impact modifier [31]. PSt-b-PIB, PSt-b-PIB-H, and PMMA-b-PIB-H derived from MAI have high- and wide-range molecuiar weight and show high flexibiiity and flow property [42]. The improved flexibiiity of PMMA-b-PEG synthesized as an elastomer, was confirmed by dynamic viscoelastic measurement [43]. 

However, it yields dynamic modulus. Some other techniques were also used to characterize hydrogels, for example, viscoelastic measurements [28, 30, 31] and swelling equilibrium [20]. 

The specimen was prepared by the following method. After mixing HAF carbon black (50 phr) with natural rubber (NR) in a laboratory mixer, carbon gel was extracted from unvulcanized mixture as an insoluble material for toluene for 48 h at room temperamre and dried in a vacuum oven for 24 h at 70°C. We made the specimen as a thin sheet of the carbon gel (including carbon black) by pressing the extracted carbon gel at 90°C. The cured specimen was given by adding sulfur (1.5 phr) to the unvulcanized mixture and vulcanized for 30 min at 145°C. The dynamic viscoelastic measurement was performed with Rheometer under the condition of 0.1% strain and 15 Hz over temperatures. 

All the viscoelastic measurements were carried out in the Rheometrics Dynamic Spectrometer RDS-770 at a frequency of 1Hz, a strain of 0.1%, and a temperature range of -140° to 140°C incremented every 2 degrees. The Texas Instrument Terminal Silent 700 was tapped to provide a hookup to an IBM 308X main frame computer located some miles away. The output of the Rheometrics unit was converted to a data file to be used in conjuc-tion with SAS (1). All statistical manipulations, software developments, and the necessary graphics that are reported here were carried out with the aid of SAS. 

The three polymers that were chosen for study, e.g. PMMA (2), BPDN (3), and Hytrel (4), were selected because they represent a wide range of viscoelastic materials. These materials were processed into plaques. The plaques were annealed at 12S°C between highly polished chrome plated flat plates and cooled slowly to minimize the effects of residual stresses. Viscoelastic measurements were made under conditions cited above on two test specimens that were cut from... 

The spectrum method. Since we are dealing with linear viscoelastic measurements, the following equation might provide a very general approach for an estimate of G (o) ... 

Fig. 4 Dynamic viscoelasticity measurements after equal mixing of 5 wt%...

Whilst obtaining this is the ultimate goal for many rheologists, in practice it is not possible to develop such an expression. However, our mechanical analogues do allow us to develop linear constitutive equations which allow us to relate the phenomena of linear viscoelastic measurements. For a spring the relationship is straightforward. When any form of shear strain is placed on the sample the shear stress responds instantly and is proportional to the strain. The constant of proportionality is the shear modulus... 

These two mathematical Equations (4.59) and (4.60) illustrate an important feature about linear viscoelastic measurements, i.e. the central role played by the relaxation function and the compliance. These terms can be used to describe the response of a material to any deformation history. If these can be modelled in terms of the chemistry of the system the complete linear rheological response of our material can be obtained. 

The most surprising result is that such simple non-linear relaxation behaviour can give rise to such complex behaviour of the stress with time. In Figure 6.3(b) there is a peak termed a stress overshoot . This illustrates that materials following very simple rules can show very complex behaviour. The sample modelled here, it could be argued, can show both thixotropic and anti-thixotropic behaviour. One of the most frequently made non-linear viscoelastic measurements is the thixotropic loop. This involves increasing the shear rate linearly with time to a given... 

Evidence for the formation of gels from aPS systems is obtained from simple mechanical, (1.4.5) viscoelastic, (7.8) thermodynamic (1.6) and spectroscopic ( ) techniques. Simple tube tilting, falling ball methods and differential scanning calorimetry have been used to determine the phase diagrams for a number of systems. Viscoelastic measurements on the aPS-carbon disulfide system show that the low frequency response indicative of a... 

The static modulus and dynamic storage modulus were investigated for some open-celled PE foams by static compression tests and dynamic viscoelastic measurements in compression mode. Experimental data were compared with theoretical predictions. 8 refs. 

The dynamic storage modulus of closed-cell PE foams was investigated by dynamic viscoelastic measurement in the compression mode. It was found that dynamic modulus correlated with compression hardness and that the resistance against pressure inside the cells had no effect upon static modulus or dynamic storage modulus. 8 refs. 

Schrag,J.L., Johnson,R.M. Application of the Birnboim multiple lumped resonator principle to viscoelastic measurements of dilute macromolecular solutions. Rev. Sci. Inst. 42, 224-232 (1971). 

Under viscoelastic measurements poly(cycloalkyl methacrylates) show a loss maximum (designated y), located in the very low temperature range (T <-60 °C), as illustrated in Fig. 6 in the case of poly(cyclohexyl methacrylate). Such a series of polymers has been extensively studied by Heijboer in his Ph.D. thesis [5], by performing viscoelastic studies at 1 Hz (sometimes 180 kHz) as a function of temperature and exploring quite a large number of cycloalkyls, either substituted or not. In cyclopentyl, cyclohexyl, cyclohep-tyl derivatives, the y transition was shown to occur at ca. - 185 °C (180 Hz), - 80 °C (1 Hz), - 180 °C (1 Hz), respectively. The associated activation energies, a> are 13, 47, 26kJmol 1 for the cyclopentyl, cyclohexyl, cycloheptyl derivatives, respectively. 

In any circumstance where the whole displacement of a polymer chain is involved, it is important to characterise friction arising from the surroundings. This is achieved through the monomeric friction coefficient, , which can be determined from melt viscoelasticity measurement of the Newtonian viscosity, corresponding to the low frequency plateau in rj (co). f is calculated... 

Linear viscoelastic measurements using infrared dichroism on the compatible blend polyethylene oxide) and poly(methyl methacrylate) were reported by Zawada et al. [139]. Unlike Monnerie and coworkers [127], who reported seeing only orientation in the PMMA component, and none in the PEO, Zawada et al. observed alignment in the PEO. However, since the PEO was of lower molecular weight (as was the case for Monnerie and coworkers), its relaxation timescales were substantially faster than the PMMA. This may explain the lack of any measurable orientation by Monnerie and coworkers, who studied quenched samples, since their preparation may have allowed the PEO to relax prior to testing. 

On the other hand, water uptake is a continuous problem for polyimides and particularly for polynadimides [133]. Dynamic mechanical spectrometry (viscoelastic measurements) have been used to investigate the network degradations due to hydrolytic process [134]. It was shown on a special PMR resin (AFR 700 B) that network reformations are possible through post-curing. In addition, for fluorinated systems, 19F NMR can be used to follow the hydrolysis of the im-ide groups [135]. 

Static and dynamic linear viscoelastic measurements are used to gain insights into the relationships between cheese structure and rheological behavior. Non-linear viscoelastic measurements have been used to a relatively small degree to measure the response of cheese to large deformations. 

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