Viscosity, critical yield curves

Constant stress (creep) measurements A constant is stress is applied to the system and the strain y or compliance J (y/a) is followed as a function of time. By measuring creep curves at increasing stress values, it is possible to obtain the residual (zero-shear) viscosity ri 6) and the critical stress that is, the stress above which the structure starts to break down. <7 is sometimes referred to as the true yield value. 

Basically, a constant stress cr is applied on the system and the compliance J(Pa ) is plotted as a function of time (see Chapter 20). These experiments are repeated several times, increasing the stress in small increments from the smallest possible value that can be applied by the instrament). A set of creep curves is produced at various applied stresses, and from the slope of the linear portion of the creep curve (when the system has reached steady state) the viscosity at each applied stress, //, can be calculated. A plot of versus cr allows the limiting (or zero shear) viscosity /(o) and the critical stress cr (which may be identified with the true yield stress of the system) to be obtained (see also Chapter 4). The values of //(o) and <7 may be used to assess the flocculation of the dispersion on storage. 

A closer look at the trends of the straight lines in Section 4.3.1 reveals a deviation that is common to all the curves. To illustrate this, let us take two curves that display this behaviour particularly clearly and that are suitable from the point of view of shear rate. When considering the shear rates plotted here, it must be remembered that at. Vy = 1000 s " the flow is in the critical range for the transition to turbulent flow, and also that low shear rates result in very low volumetric flow rates during measurement and are therefore subject to sizeable variations. For this reason Sy = 500 s was chosen as a suitable shear rate. The specimens chosen were Pebax with Loxiol and PS N 2000, in each case with Printex XE-2. The specimens with Printex XE-2 are especially suitable because even small differences in concentration lead to measurable changes in viscosity and the readings therefore yield a particularly clear picture. 

The rheology of filled polymers has been reviewed extensively [44,45], In general, viscosity curves of highly filled polymers show a yielding behavior at low shear rates followed by a power-law behavior at high shear rates [44], For most of the filled thermoplastics with small particles such as glass beads, calcium carbonate, talc, and carbon black, etc., the viscosity increases with the filler concentration. For some filled systems, however, the viscosity increases with the filler content up to the critical concentration, then decreases [46] or becomes little dependent on the filler concentration [47], This is particularly true for glass fiber-filled polymers. 

From the slope of the linear portion of the creep curve (after the system reaches a steady state), the viscosity at each applied stress, is calculated. A plot of % versus (T (Figure 7.40) allows one to obtain the limiting (or zero shear) viscosity and the critical stress eta (which may be identified with the true yield stress of the system). 

Thus, one measures creep curves as a function of the applied stress (starting from a very small stress of the order of 0.01 Pa). This is illustrated in Fig. 3.45. The viscosity Pu (which is equal to the reciprocal of the slope of the straight portion of the creep curve) is plotted as a function of the applied stress. This is schematically shown in Fig. 3.46. Below a critical stress the viscosity reaches a limiting value, p(o) namely the residual (or zero shear) viscosity. Above a , p decreases rapidly with a further increase in the shear stress (the shear thinning regime). It reaches another Newtonian value Poo, which is the high shear limiting viscosity. 0, may be identified as the critical stress above which the structure of the suspension is broken down . Ucr is denoted as the true yield stress of the suspension. 

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