Rheology shear rate

Accordingly, siloxy-substituted complexes have been found to give polymers with rheological behaviour indicative of long-chain branching [44, 60, 61, 83, 84], but the relations between molar mass, PD and the low shear-rate rheological behaviour are distinctive to each catalyst [83]. 

It is thus reasonable to conclude that, at this polymer concentration (1%), inter-polymer/polymer interaction plays the dominant role. The interaction involves the "tails" of bound SDS molecules on separate polymer molecules. Such alkyl group association is expected to be relatively weak and should be sensitive to shear. In fact, variable shear rate rheology measurements provide definitive information for selecting... 

Figure 8 shows low shear rate rheological results for an ethylene homopolymer and an ethylene/1-hexene copolymer with catalyst 15/MAO [81]. Ethylene homopolymers by this catalyst exhibit the rheological behavior of linear chain polymers. In contrast, the copolymer displays a higher molecular weight and broader MWD than the corresponding ethylene homopolymers and, as shown in Fig. 8, in the copolymer melt the elastic behavior dominates even at the lowest frequencies. Behavior like this suggests the presence of widely different relaxation times, as in a crosslinked network structure (but the polymer was completely... 

Low shear rate rheological characterization in comparison with the molecular weight and MWD from SEC is a sensitive, yet relatively simple and reliable way of detecting the LCB. In accordance with the in situ mechanism, the rheological behavior of conventional metallocene-catalyzed ethylene homopolymers heavily depends on polymerization conditions such as ethylene pressure, hydrogen concentration, and polymerization time. Therefore, the LCB is not only a function of the catalyst but also of the polymerization. Moreover, any deviation from the polymerization rate-controlled polymerization conditions (e.g., due to the presence of mass and heat transfer limitations) offers a pathway to broadening of polymer structure in terms of MWD, comonomer distribution, and also the LCB. 

Incorporation of viscosity variations in non-elastic generalized Newtonian flow models is based on using empirical rheological relationships such as the power law or Carreau equation, described in Chapter 1. In these relationships fluid viscosity is given as a function of shear rate and material parameters. Therefore in the application of finite element schemes to non-Newtonian flow, shear rate at the elemental level should be calculated and used to update the fluid viscosity. The shear rale is defined as the second invariant of the rate of deformation tensor as (Bird et at.., 1977)... 

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... 

C. Above this temperature, the shear stress at constant shear rate increases and the rheological exponent rises from 0.25 toward 0.5 at the final melting point (68). 

Solutions of rhamsan have high viscosity at low shear rates and low gum concentrations (90). The rheological properties and suspension capabiUty combined with excellent salt compatibihty, make it useful for several industrial apphcations including agricultural fertilizer suspensions, pigment suspensions, cleaners, and paints and coatings. 

Viscous Hquids are classified based on their rheological behavior characterized by the relationship of shear stress with shear rate. Eor Newtonian Hquids, the viscosity represented by the ratio of shear stress to shear rate is independent of shear rate, whereas non-Newtonian Hquid viscosity changes with shear rate. Non-Newtonian Hquids are further divided into three categories time-independent, time-dependent, and viscoelastic. A detailed discussion of these rheologically complex Hquids is given elsewhere (see Rheological measurements). 

Viscosity is equal to the slope of the flow curve, Tf = dr/dj. The quantity r/y is the viscosity Tj for a Newtonian Hquid and the apparent viscosity Tj for a non-Newtonian Hquid. The kinematic viscosity is the viscosity coefficient divided by the density, ly = tj/p. The fluidity is the reciprocal of the viscosity, (j) = 1/rj. The common units for viscosity, dyne seconds per square centimeter ((dyn-s)/cm ) or grams per centimeter second ((g/(cm-s)), called poise, which is usually expressed as centipoise (cP), have been replaced by the SI units of pascal seconds, ie, Pa-s and mPa-s, where 1 mPa-s = 1 cP. In the same manner the shear stress units of dynes per square centimeter, dyn/cmhave been replaced by Pascals, where 10 dyn/cm = 1 Pa, and newtons per square meter, where 1 N/m = 1 Pa. Shear rate is AH/AX, or length /time/length, so that values are given as per second (s ) in both systems. The SI units for kinematic viscosity are square centimeters per second, cm /s, ie, Stokes (St), and square millimeters per second, mm /s, ie, centistokes (cSt). Information is available for the official Society of Rheology nomenclature and units for a wide range of rheological parameters (11). 

Flow Models. Many flow models have been proposed (10,12), which are useful for the treatment of experimental data or for describing flow behavior (Table 1). However, it is likely that no given model fits the rheological behavior of a material over an extended shear rate range. Nevertheless, these models are useful for summarizing rheological data and are frequently encountered in the Hterature. 

The square root of viscosity is plotted against the reciprocal of the square root of shear rate (Fig. 3). The square of the slope is Tq, the yield stress the square of the intercept is, the viscosity at infinite shear rate. No material actually experiences an infinite shear rate, but is a good representation of the condition where all rheological stmcture has been broken down. The Casson yield stress Tq is somewhat different from the yield stress discussed earlier in that there may or may not be an intercept on the shear stress—shear rate curve for the material. If there is an intercept, then the Casson yield stress is quite close to that value. If there is no intercept, but the material is shear thinning, a Casson plot gives a value for Tq that is indicative of the degree of shear thinning. 

Additional complications can occur if the mode of deformation of the material in the process differs from that of the measurement method. Most fluid rheology measurements are made under shear. If the material is extended, broken into droplets, or drawn into filaments, the extensional viscosity may be a more appropriate quantity for correlation with performance. This is the case in the parting nip of a roUer in which filamenting paint can cause roUer spatter if the extensional viscosity exceeds certain limits (109). In a number of cases shear stress is the key factor rather than shear rate, and controlled stress measurements are necessary. 

Four modes of characterization are of interest chemical analyses, ie, quaUtative and quantitative analyses of all components mechanical characterization, ie, tensile and impact testing morphology of the mbber phase and rheology at a range of shear rates. Other properties measured are stress crack resistance, heat distortion temperatures, flammabiUty, creep, etc, depending on the particular appHcation (239). 

As substituent uniformity is increased, either by choosing appropriate reaction conditions or by reaction to high degrees of substitution, thixotropic behavior decreases. CMCs of DS >1.0 generally exhibit pseudoplastic rather than thixotropic rheology. Pseudoplastic solutions also decrease in viscosity under shear but recover instantaneously after the shear stress is removed. A plot of shear rate versus shear stress does not show a hysteresis loop. 

The rheological parameter variations with blend compositions are shown in Figs. 4,5 and 6. The variation of relaxation time (Fig. 4) seems to show an increasing pattern up to 40% of NBR, then there is a sharp decrease until 60% of NBR, and finally there is a further increase of relaxation time in the preblends. Preheating of blends, however, results in a longer relaxation time than in the preblends and a maximum at 50 50 ratio at all shear rates. 

The plot of the rheological parameters (relaxation time, shear modulus, and stored elastic energy) are shown in Figs. 22-24. The relaxation time increases as the ACM content is increased to attain a maximum at 60 40 = ACM XNBR blend ratio for the preblends. For lower shear rate the rise is sharp and after 60 40 blend ratio, // remains almost constant, whereas for the higher shear rate region the rise is not sharp and after 60 40 blend ratio ty decreases as ACM percent increased in the blend. In the case of the preheated blends the /y increases up to 50 50 blend ratio and then decreases with the addition of ACM in the blend. The preheating increases the ty in both shear rate regions. 

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