Steady state viscosity

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

It is known(J ) that when hydrophobe-modified W-SPs such as those in Figure 1 are formulated in water-borne latex coatings a significant time period 048 hours) is required to reach steady state viscosities this does not happen when either MC, HPMC, HEC... 

This expression can describe the viscosity change with time at a fixed rate and in the limit of long times provides the steady state viscosity at a of shear rate. The term fi(y) is an integral function of the strain. Approximate forms are available, for example ... 

The TA Instruments CSL2 rheometer can perform low frequency oscillatory measurements as well as steady-state viscosity determinations, even though it has a simple mechanical system. The sinusoidal wave form is generated mathematically in the computer rather than with an electromechanical drive system. The stress is controlled, and the resulting strain is determined and stored in memory. The computer analyzes the wave form and calculates the viscosity and elasticity of the specimen at the frequency of the test. As of this writing (1996), the oscillation software covers a frequency range of 10-4 -40 Hz. This range could be increased as faster software and computers become available. 

Fig. 8.1. Dynamic viscosity t] (a>) and steady state viscosity f](y) for undiluted narrow distribution polystyrenes. The data are plotted in reduced form to facilitate comparison. The dimensionless shear rate or frequency is t]0Mwy/gRT >r r/ M co/gRT. [See Eq.(8.3)]. The dynamic viscosities are for Mw = 215000 (O) and Mw = 581000 ( ) at 160° C (312). The steady shear viscosity is for Mw = 411000 (A) at 176° C (313). The shapes in the onset region are similar for the three curves, but the apparent limiting slope for the dynamic...

Fig. 8.2 Absolute complex viscosity / (

Fig. 8.3. Dynamic viscosity, absolute complex viscosity, and steady state viscosity for narrow distribution polystyrene. Data obtained at 25° C on a 0.071 gm/ml solution of polystyrene (Mw = 860000) in Aroclor (3/6)...

At higher shear rates the steady-state viscosity o(cc)/y begins to depend on y. If a constant shear rate in this range is imposed, the shear stress rises beyond its steady state value, passes through a maximum before eventually approaching the steady state, (t(oo) = rj(y)y. The stress at the maximum o-(tm) grows in relation to ff(oo) as y increases. The time to reach the maximum tm is found to be inversely proportional to shear rate ... 

The steady-state viscosity is a pragmatic way of predicting certain key properties of a sample. If the stresses used in the creep experiment are well chosen they will reflect the stresses applied to the sample by the action of gravity. Thus, the viscosity under these circumstances will help predict the ability of the material to resist sagging on a vertical surface (coatings). Other uses include prediction of sedimentation velocity or creaming velocity in two-phase dispersions. The ability of a paint to level out and therefore remove brush marks by... 

Many amorphous homopolymers and random copolymers show thermorheologically simple behavior within the usual experimental accuracy. Plazek (23,24), however, found that the steady-state viscosity and steady-state compliance of polystyrene cannot be described by the same WLF equation. The effect of temperature on entanglement couplings can also result in thermorheologically complex behavior. This has been shown on certain polymethacrylate polymers and their solutions (22, 23, 26, 31). The time-temperature superposition of thermorheologically simple materials is clearly not applicable to polymers with multiple transitions. The classical study in this area is that by Ferry and co-workers (5, 8) on polymethacrylates with relatively long side chains. In these the complex compliance is the sum of two contributions with different sets of relaxation mechanisms the compliance of the chain backbone and that of the side chains, respectively. 

Figure 7.10 shows a qualitative plot of the increase in the steady-state viscosity as a function of reaction time for the free-radical copolymerization of... 

Figure 7.10 Typical (steady-state) viscosity rise curve for the free-radical copolymerization of mono- and multiunsaturated monomers, correlated with the steps of the reaction mechanism.

Ctmcentrated stdutions of polypeptides sbow the Weisenbei effect 77). It is known that the extinction angle, of such solutitais can he calculated by substituting the trahies of the total normal stress,/, and of the steady-state viscosity, tj, of the solution with the equation in the form (75) ... 

Linear results or infinite value for steady state viscosity. 

Unbounded transient viscosity at high rates. Linear results or infinite value for steady state viscosity. 

Since the complex Auscosity is concentration-dependent just in the same manner as the steady-state viscosity, one can define a complex viscosity increment, v, and a complex intrinsic viscosity, [ ], similar to that for steady-state viscosity... 

Differences between solid-like and liquid-bke complex fluids show up in all three of the shearing measurements discussed thus far the shear start-up viscosity t), the steady-state viscosity rj(y), and the linear viscoelastic moduli G co) and G (o). The start-up stresses a = y/ +()>, t) of prototypical liquid-like and solid-like complex fluids are depicted in Fig. 1-6. For the liquid-like fluid the viscosity instantaneously reaches a steady-state value after inception of shear, while for the solid-like fluid the stress grows linearly with strain up to a critical shear strain, above which the material yields, or flows, at constant shear stress. 

Figure 5.20 Steady-state viscosity T] y) and dynamic complex viscosity rj u)) as functions of reduced shear rate (j>r) or frequency cox), for a 1.5% w/v solution of the associative thickener described in the caption to Fig. 5-18. (From Annable et al. 1993, with permission from the Journal of Rheology.)...

The viscous and elastic properties of orientable particles, especially of long, rod-like particles, are sensitive to particle orientation. Rods that are small enough to be Brownian are usually stiff molecules true particles or fibers are typically many microns long, and hence non-Brownian. The steady-state viscosity of a suspension of Brownian rods is very shear-rate- and concentration-dependent, much more so than non-Brownian fiber suspensions. The existence of significant normal stress differences in non-Brownian fiber suspensions is not yet well understood. 

Figure 11.8 The steady-state viscosity for solutions of poly(l,4-phenylene-2,6-benzobisthiazole) (PBZT) with viscosity-averaged molecular weight 37,400 (molecular length 170 nm), in methane sulfonic acid at concentrations of 1.5 ( ), 2.52(H), 3.0(A), 3.43(0), 6.11(0). 8.2(Q)% (by...

Doi and Edwards were able to develop an equation for the stress relaxation modulus G(t) of monodisperse entangled linear chain liquids in the terminal region without resorting to the independent alignment approximation From G(t), expressions can be obtained for the plateau modulus, the steady-state viscosity and steady-state recoverable compliance. The following dependences on chain length are obtained ... 

It can be shown that for most dilute solutions there exists a simple correlation between dynamic and steady state flow characteristics (16). For most detergent solutions the magnitude of the complex viscosity 1 n I at a certain angular frequency CO coincides with the steady state viscosity n, at the corresponding shear rate "f (12, 17). 

LLDPE similar to LLDPE-A polymer, the LPX-30. For PP a strain thinning effect may be suspected. In Fig. 22 the steady state viscosities for PP and BL ngCe) 3n(oi) were reported. For the other samples... 

Figure 5 Variations with temperature of the steady state viscosity q of gluten from Olympic x Gabo cross line -/17 4- 18/-) in water (filled symbols) and in deuterium dioxide (empty symbols), q was obtained from the recovery curves...

In these cases the relative velocity of the shearing plates is not constant but varies in a sinusoidal manner so that the shear strain and the rate of shear strain are both cyclic, and the shear stress is also sinusoidal. For non-Newtonian fluids, the stress is out of phase with the rate of strain. In this situation a measured complex viscosity (rf) contains both the shear viscosity, or dynamic viscosity (t] ), related to the ordinary steady-state viscosity that measures the rate of energy dissipation, and an elastic component (the imaginary viscosity ij" that measures an elasticity or stored energy) ... 

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