Shear viscosity filled polymers

The existence of yield stress Y at shear strains seems to be the most typical feature of rheological properties of highly filled polymers. A formal meaing of this term is quite obvious. It means that at stresses lower than Y the material behaves like a solid, i.e. it deforms only elastically, while at stresses higher than Y, like a liquid, i.e. it can flow. At a first approximation it may be assumed that the material is not deformed at all, if stresses are lower than Y. In this sense, filled polymers behave as visco-plastic media with a low-molecular and low-viscosity dispersion medium. This analogy is not random as will be stressed below when the values of the yield stress are compared for the systems with different dispersion media. The existence of yield stress in its physical meaning must be correlated with the strength of a structure formed by the interaction between the particles of a filler. 

The fact that the appearance of a wall slip at sufficiently high shear rates is a property inwardly inherent in filled polymers or an external manifestation of these properties may be discussed, but obviously, the role of this effect during the flow of compositions with a disperse filler is great. The wall slip, beginning in the region of high shear rates, was marked many times as the effect that must be taken into account in the analysis of rheological properties of filled polymer melts [24, 25], and the appearance of a slip is initiated in the entry (transitional) zone of the channel [26]. It is quite possible that in reality not a true wall slip takes place, but the formation of a low-viscosity wall layer depleted of a filler. This is most characteristic for the systems with low-viscosity binders. From the point of view of hydrodynamics, an exact mechanism of motion of a material near the wall is immaterial, since in any case it appears as a wall slip. 

Rheological properties of filled polymers can be characterised by the same parameters as any fluid medium, including shear viscosity and its interdependence with applied shear stress and shear rate elongational viscosity under conditions of uniaxial extension and real and imaginary components of a complex dynamic modulus which depend on applied frequency [1]. The presence of fillers in viscoelastic polymers is generally considered to reduce melt elasticity and hence influence dependent phenomena such as die swell [2]. 

Yield stress values can depend strongly on filler concentration, the size and shape of the particles and the nature of the polymer medium. However, in filled polymer melts yield stress is generally considered to be independent of temperature and polymer molecular mass [1]. The method of determining yield stress from flow curves, for example from dynamic characterization undertaken at low frequency, or extrapolation of shear viscosity measurements to zero shear rate, may lead to differences in the magnitude of yield stress determined [35]. 

The relationship between steady-shear viscosity and dynamic-shear viscosity is also a common fundamental rheological relationship to be examined. The Cox-Merz empirical rule (Cox, 1958) showed for most materials that the steady-shear-viscosity-shear-rate relationship was numerically identical to the dynamic-viscosity-frequency profile, or r] y ) = r] m). Subsequently, modified Cox-Merz rules have been developed for more complex systems (Gleissle and Hochstein, 2003, Doraiswamy et al., 1991). For example Doriswamy et al. (1991) have shown that a modified Cox-Merz relationship holds for filled polymer systems for which r](y ) = t] (yco), where y is the strain amplitude in dynamic shear. 

The complex viscosity can be related to the steady-shear viscosity rf) via the empirical Cox-Merz rule, which notes the equivalence of steady-shear and dynamic-shear viscosities at given shearing rates ri y) = rj (co). The Cox-Merz rule has been confirmed to apply at low rates by Sundstrom and Burkett (1981) for a diallyl phthalate resin and by Pahl and Hesekamp (1993) for a filled epoxy resin. Malkin and Kulichikin (1991) state that for highly filled polymer systems the validity of the Cox-Merz rule is doubtful due to the strain dependence at very low strains and that the material may partially fracture. However, Doraiswamy et al. (1991) discussed a modified Cox-Merz rule for suspensions and yield-stress fluids that equates the steady viscosity with the complex viscosity at a modified shear rate dependent on the strain, ri(y) = rj yrap3), where y i is the maximum strain. This equation has been utilised by Nguyen (1993) and Peters et al. (1993) for the chemorheology of highly filled epoxy-resin systems. 

The measurement of yield stress at low shear rates may be necessary for highly filled resins. Doraiswamy et al. (1991) developed the modified Cox-Merz rule and a viscosity model for concentrated suspensions and other materials that exhibit yield stresses. Barnes and Camali (1990) measured yield stress in a Carboxymethylcellulose (CMC) solution and a clay suspension via the use of a vane rheometer, which is treated as a cylindrical bob to monitor steady-shear stress as a function of shear rate. The effects of yield stresses on the rheology of filled polymer systems have been discussed in detail by Metzner (1985) and Malkin and Kulichikin (1991). The appearance of yield stresses in filled thermosets has not been studied extensively. A summary of yield-stress measurements is included in Table 4.6. 

Typically, WPC based on polypropylene and polyethylene show deviation from the Cox-Merz rule. This is due to the different nature of flow. Capillary flow is a pressure-driven flow, including entrance and exit effects, wall slip, friction in the barrel, and orientation effects. Parallel-plate flow is pure drag shear flow, in which particle-particle and matrix-particle interactions result in higher viscosities for filled polymers. In other words, a straightforward question is a 100-fold increase in shear rate and 100-fold increase in frequency result in the same effects the answer would be yes for neat polymers, and no for wood-filled composites. 

In filled polymer systems, it has been observed that the effect of filler content on viscosity decreases as shear rate increases [14, 49]. In the case of nanocomposite flllers, this effect has been explained in terms of a detachment/reattachment mechanism [49]. With respect to the dimensions of the flllers, it has been observed that as the surface area of the filler increases so does the viscosity of the filled polymer melt [18, 48]. For particles with similar shapes, an increase in the surface area means a reduction in particle size. In this sense, nanoflllers are expected to significantly increase the viscosity of polymer melts in relation to flllers with sizes in the range of micrometers. An analysis of filler shape and other relevant aspects of polymer flllers can be found in the work by Shenoy [50]. 

Fig. 13 (a) Viscosity versus shear rate and (b) frequency sweeps for 0.5 % (w/v) HM PAAm solution in 0.24 M CTAB-SDS solutions. The SDS amounts (in mol%) of CTAB-SDS mixtures are indicated. In (b), the elastic modulus G and viscous modulus G" are shown by filled and open symbols, respectively. Inset to (a) shows the specific viscosity, of polymer solutions plotted against their SDS content temperature = 35 °C. From [37] with permission from the Royal Society of Chemistry... 

This is to say a 10% change in volume. This volume decrease raises the shear viscosity, as described below. Note also that if a mould is filled at 1000 atmospheres it will contain 10% more polymer than if it were filled at 1 atmosphere this fact plays a central role in injection moulding. 

From about 1980, there have been extensive investigations of the shear viscosity of rubber-carbon black compounds and related filled polymer melts. Yield values in polystyrene-carbon black compounds in shear flow were found by Lobe and vhiite [L15] in 1979 and by Tanaka and White [Tl] in 1980 for polystyrene with calcium carbonate and titanium dioxide as well as carbon black. From 1982, White and coworkers found yield values in compounds containing butadiene-styrene copolymer [Ml, M37, S12, S18, T7, W29], polyiso-prene [M33, M37, S12, S18], polychloroprene [S18], and ethylene-propylene terpolymer [OlO, S18]. Typical shear viscosity-shear stress data for rubber-carbon black compounds are shown in Figs. 5(a) and (b). White et al. [S12, S18, W28] fit these data with both Eq. (56) and die expression... 

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. 

To understand and model the flow during the blending process, the bulk shear viscosity of a polymer blend must be understood. The rheology of multiphase systems has been investigated by many researchers (2, 71-73]. Figure 6.2 shows the schematics of both solid particle-filled Uquid (curve a) and polymer blends... 

Figure 6.2 Concentration dependence of shear viscosity for (a) a solid particle-filled liquid and (b)-(d) polymer blends.

The pressure required for shaping the product (sheet profile or pellets) depends upon the flow rate, the aperture geometry, and the viscosity of the filled polymer at the exit shear rate. In general, the viscosity of a polymer-filler mixture (pc) increases as the... 

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