Elasticity rheological measurements

In conclusions, we must reiterate that fat crystal networks demonstrate distinct structural hierarchies. A consideration of the microstructural level and constrac-tion of models based on elastic rheological measurements implicate all levels of structure in the determination of the macroscopic elastic moduli. Consideration of the fractal arrangement of the microstructural elements is integral to the construction of models that fit well with experimental data. Furthermore, it is seen that the fractal dimension and other network characteristics such as microstructural element size and microstructural size are indicators of macroscopic hardness, and that these factors can be manipulated by processing conditions to achieve tailored elastic characteristics of fat crystal networks. 

Polyolefin melts have a high degree of viscoelastic memory or elasticity. First normal stress differences of polyolefins, a rheological measure of melt elasticity, are shown in Figure 9 (30). At a fixed molecular weight and shear rate, the first normal stress difference increases as MJM increases. The high shear rate obtained in fine capillaries, typically on the order of 10 , coupled with the viscoelastic memory, causes the filament to swell (die swell or... 

The starting time for rheological measurements correspond to t = 120 min. Indeed, the rheological parameters were only recorded during the rennet-induced coagulation phase to avoid structural modifications during the acidification phase which may consequently influence the gelation process. Elastic and viscous properties of reconstituted milks... 

Dynamic rheological measurements have recently been used to accurately determine the gel point (79). Winter and Chambon (20) have determined that at the gel point, where a macromolecule spans the entire sample size, the elastic modulus (G ) and the viscous modulus (G") both exhibit the same power law dependence with respect to the frequency of oscillation. These expressions for the dynamic moduli at the gel point are as follows ... 

Figure 3.25 Storage modulus, elastic modulus, and loss angle for a cone and plate rheological measurement. The data are for a GPPS resin with an MFR of 1.5 dg/min (5 kg, 200°C) measured at 225°C...

When the helix amount increases the medium changes from a viscous liquid (sol) to an elastic solid (gel). The kinetics of gelation depends strongly on the quenching temperature. The rheological measurements that we performed are particularly focused on the sol-gel transition and on the definition of the "gel point". The greatest difficulty encountered is due to the weakness of the bonds which can easily be destroyed by the mechanical stress. 

The ODT can be located via a number of methods. From rheological measurements, the ODT is identified from a sharp decrease in the low frequency isochronal dynamic elastic moduli obtained during a heating ramp (Bates et al. 1990 Rosedale and Bates 1990) (Fig. 2.4(a)) however, this method does not generally provide a well-defined temperature for the ordered BCC-disordered phase... 

Figure 24. A comparison of the data obtained from a range of surface rheological measurements of samples of /3-lg as a function of Tween 20 concentration. ( ), The surface diffusion coefficient of FITC-jS-lg (0.2 mg/ml) at the interfaces of a/w thin films (X), the surface shear viscosity of /3-lg (0.01 mg/ml) at the o/w interface after 5 hours adsorption ( ), the surface dilational elasticity and (o) the dilational loss modulus of /3-lg (0.2 mg/ml).

The onset of formation of a 3-D elastically connected network of DDOA aggregates has been followed by rheological measurements [75], There is an abrupt increase of the storage modulus G at a characteristic time of the aggregation process that corresponds to the growth of the infinite network (Fig. 7). 

Gg (instantaneous modulus), Hg (residual viscosity) and G (shear modulus) all showed a rapid increase above 30g dm bentonite. This was attributed to the formation of a gel network structure in the continuous medium and the strength of such a gel increased with increase in bentonite concentration. The results could be qualitatively described in terms of the elastic floe model of Hunter and co-workers. Moreover, the settling characteristics of the structured suspensions were found to be consistent with the predictions from the rheological measurements. This demonstrates the value of rheological studies in predicting the longterm physical stability of suspension concentrates. 

The low shear rheology measurements also show a rapid increase in the viscoelastic properties (modulus and zero shear viscosity) with increase of bentonite concentration above the gel point (> 30 g dm bentonite). Several models have been proposed to account for the elastic properties of concentrated dispersions, of which that originally proposed by van den Tempel (25) and later developed by Papenhuizen (26) seems to be the most appropriate for the present system. According to this model, if the interaction energy minimum between adjacent particles is sufficiently negative, a three-dimensional network structure may ensue, giving an elastic component. Various models can be used to represent the three dimensional structure, the simplest of which would be either an ideal network where all particles are... 

Taimer, R. I. 1988. Recoverable elastic strain and swelling ratio, in Rheological Measurements, eds. A. A. Collyer and D. W. Clegg, pp. 93-118, Elsevier Applied Science, New York. 

Sometimes, this expectation is not met. At high flow rates, there can be hydrodynamic instabilities that lead to secondary flows which ruin the rheological measurement. Such instabilities occur in Newtonian fluids, due, for example, to inertial effects, such as those in Poiseuille flow at Reynolds numbers exceeding 2000 (Drazin and Reid 1981). For some complex fluids, even at low Reynolds number there are instabilities that are driven by elastic effects (Larson 1992). 

The mathematics of the elaboration of oscillatory rheological measurements is exactly Identical to that for dielectric spectroscopy, already described in sec. 11.4.8a. Since the modulus has two components it is advantageous to exploit the formalism of complex quantities. One of the components (the elastic component G ) is plotted on the real axis (x), the other (the viscous one, G") on the imaginary or y axis. Each point in the (x, y)-plane, also called the complex plane, represents the system rheologically in terms of G and G". Different frequencies yield different points. The overall modulus is now a complex quantity written as G. It is related to G and G". 

The addition of small amounts of alpha-omega dienes to the reactor, such as 1,9-decadiene, greatly increase LCB levels in polymers made with most catalysts, including Phillips catalysts. Even Ziegler catalysts, which are not known for producing LCB, produce large amounts when certain dienes are incorporated. Such polymers often exhibit some unusual properties, such as failure to dissolve in the normal solvents, probably because of the cross-linked gel-type matrix. Rheological measurements indicate extreme elasticity and memory. 

---