Time Viscosity curves

Pectins in aqueous solutions show pseudoplastic non-thixotropic behaviour, independent of their degree of methoxylation. Figure 1 shows the viscosity curve of a 2,5 % pectin solution, sheared the preselected shear rate-time function. The viscosity curves for the increasing and decreasing shear rate are superimposed. The pseudoplasticity of pectin solutions decreases with decreasing concentration. 

ARe>s is the Reynolds number based on the solvent properties, /zs is the solvent viscosity, D is the pipe diameter, F is the velocity in the pipe, and A is the fluid time constant (from the Carreau model fit of the viscosity curve). 

Fig. 3.14. The data is for a very broad range of times and temperatures. The superposition principle is based on the observation that time (rate of change of strain, or strain rate) is inversely proportional to the temperature effect in most polymers. That is, an equivalent viscoelastic response occurs at a high temperature and normal measurement times and at a lower temperature and longer times. The individual responses can be shifted using the WLF equation to produce a modulus-time master curve at a specified temperature, as shown in Fig. 3.15. The WLF equation is as shown by Eq. 3.31 for shifting the viscosity. The method works for semicrystalline polymers. It works for amorphous polymers at temperatures (T) greater than Tg + 100 °C. Shifting the stress relaxation modulus using the shift factor a, works in a similar manner.

The rate of decrease in viscosity, and the value of the lower limit at which the viscosity becomes stable depends on the type of nitrocellulose and on the solvent used. The higher the initial viscosity, the faster viscosity falls. However, the viscosity curves as a function of time never cross one another. 

Work done by Brauer (10) pointed out that the waves arising in a falling film at low viscosity are about 2.6 times higher than the mean film thickness defined by Equation 1. In Figure 2, the mean thickness of the film according to Equation 1 is expressed as a function of the peripheral load for different product viscosities (curve 1 water 1 CST, curve 2, 3 higher viscosities. 

Falling off of the log viscosity-time cure curve can also occur due to dewetting, or wall slip, at the cone-sample interface. This occurs rarely, in our experience, and probably more with highly filled samples as gelation is approached. A kinetic order greater than unity could also produce a curvature similar to C, but evidence of such kinetic orders for condensation polymerization reactions has not been reported from chemorheological studies, to our knowledge. (Certain types of addition polymerization reactions may show non-first-order viscosity kinetics.)(13)... 

Kinetic plots have been obtained for the polymerization of several monomers. Time vs. conversion and conversion vs. reduced viscosity curves of p-PDA Et at various temperatures are shown in Figs. 4 and 5. 

Attempts are also known to relate the type of time dependence of viscosity in the curing process to the kinetics of the reaction. Thus, upon curing of diglycidyl ester of Bisphenol A by triethanolamine, the viscosity curve Tj (t) was approximated by two linear segments [40]. The appearance of an inflection point is explained by the authors on the basis of the formation of a meshing network an the linearity of the tj (t) dependence in the first party by the fact that a curing reaction is of a zeroth order. 

As an example. Fig. 34 gives the temperature — time diagram for different stages of the process of obtaining glass-reinforced thermoset [130, 131]. Regions I-IV in this diagram actually correspond to different parts of the viscosity curve... 

The impact of the halogens chlorine, bromine and iodine on the viscosity of liquid sulfur has been studied most extensively. They all lower the viscosity dramatically, even in low concentrations, and the effectiveness in this respect decreases from chlorine to iodine. At the same time the maximum of the viscosity curve is shifted to higher temperatures. For example, the addition of 0.02% of I2 gives a viscosity maximum of 5.7 Pa s at 225 °C while... 

In contrast, Figure 95 shows a plot of the response to shear stress of polymers made at a high temperature in the solution process [407,521]. Once again, the reaction time was varied to produce polymers in different yields. The reaction temperature was also varied to produce polymers of varying MW. Under these conditions, the catalyst exhibited full activity immediately. The response to shear stress is in essence an approximation of the slope of the melt viscosity curve. A high response to shear stress indicates rheological breadth, which can derive from breadth in the MW distribution, or from LCB. In this case, the MW distribution was quite ordinary and did not vary with time. Therefore, the response to shear stress can serve as a surrogate for the level of LCB. 

High-pressure viscosity measurements can also be of considerable practical importance. For example, in the field of lubrication it has been recognized for some time that the fluid in a lubricated contact can experience several giga-pascals of pressure. Theory predicts that the derivative of viscosity with respect to pressure is a critical parameter in determining the metal-metal contact and thus the wear in such a system. However, this derivative is itself a strong function of pressure, and a more accurate estimate of viscosity effects is gained by experimentally determining the entire pressure-viscosity curve up to the actual pressures of operation. 

The several processing techniques described in this chapter represent the current methods for effecting the liquification of the formulation, the timely flow into the cavity, and the required heat and pressure to enable the chemical reaction to proceed to completion as rapidly as practical in order to achieve an acceptably short production cycle with full densification of the plastic. (See the time-temperature-viscosity curves in Fig. 6.1.)... 

The magnetic viscosity S(H) can be determined from the slope of the Af(t)-ln(f) curve and is foimd to vary with tiie field, generally going through a m udmum in the vicinity of the coercivity. The activation volume v is also determined experimentally because both S(H) and Xm(H) can be obtained from the time decay curves and remanence curves, respectively. O Grady et al. (1994) used the above analysis to study the magnetization reversal in (14.3 ATb/85 AFe) as a fimction of the number of bilayers. The time decay curves for a sample with 32 bilayers is shown in fig. 45 and the activation volumes as a function of bilayer number in fig. 46. 

An alternative method of analysing the data is to treat the monolayer as a mechanical entity. The interfadal stress, i.e. n versus time decay curve may be Fourier-transformed to obtain the dilatational elasticity, e, and viscosity, k, of the film as a function of frequency (m) of deformation. For a step change in area, AA, which... 

Keywords peroxide, molar weight distribution (MWD), rheology, crystallization, extrusion, melt flow index (MFI), controlled rheology (CR), peroxide-degradation, residence time distribution (RTD), halflifetime of peroxides, melt elasticity, die swell, viscosity curve, shear rate, elongational viscosity, melt fracture, heterophasic PR... 

At this point, the melt timer is started and the instrument holds the sample to allow it to come to temperature. Once the allotted time is over, the piston begins to move and the first data point is begun. Figure 12 shows a typical pressure trace from a nine-point viscosity curve for polyethylene. 

The viscosity of polymeric materials is a very strong function of temperature. A temperature difference of 10°C can make a 30-50% difference in the viscosity of many polyolefins, and as much as 200% for some engineering polymers such as polyvinyl chloride (PVC). Time-temperature superposition determines the effect of temperature by shifting viscosity curves measured at different temperatures onto a single, temperature-independent master curve. The shift factor is... 

Aside from viscosity curves, the capillary rheometer can be used to determine other material properties. The effects of time and temperature on processability and chemical stability can be studied, and other properties such as the melt density can be measured. Elastic data can be collected with accessories such as a die swell measurement system, and extensibility measurements can be performed with a melt tensile tester. The capillary rheometer is the instrument of choice for any practically oriented polymer laboratory. 

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