Shear viscosity-concentration

Figure 14.8 shows the shear viscosity-concentration dependencies for EDA... 

Figure 20 Linear polymers and microgels (a) qualitative representation of solution conformations (b) qualitative zero-shear viscosity-concentration behaviors. (Reprinted with permission from Ref. 46.)...

Polymer solutions are often characterized by their high viscosities compared to solutions of nonpolymeric solutes at similar mass concentrations. This is due to the mechanical entanglements formed between polymer chains. In fact, where entanglements dominate flow, the (zero-shear) viscosity of polymer melts and solutions varies with the 3.4 power of weight-average molecular weight. 

Controlled stress viscometers are useful for determining the presence and the value of a yield stress. The stmcture can be estabUshed from creep measurements, and the elasticity from the amount of recovery after creep. The viscosity can be determined at very low shear rates, often ia a Newtonian region. This 2ero-shear viscosity, T q, is related directly to the molecular weight of polymer melts and concentrated polymer solutions. 

Both high bulk and surface shear viscosity delay film thinning and stretching deformations that precede bubble bursting. The development of ordered stmctures in the surface region can also have a stabilizing effect. Liquid crystalline phases in foam films enhance stabiUty (18). In water-surfactant-fatty alcohol systems the alcohol components may serve as a foam stabilizer or a foam breaker depending on concentration (18). 

In this apparatus the polymer melt is sheared between concentric cylinders. The torque required to rotate the inner cylinder over a range of speeds is recorded so that viscosity and strain rates may be calculated. 

The reactive extrusion of polypropylene-natural rubber blends in the presence of a peroxide (1,3-bis(/-butyl per-oxy benzene) and a coagent (trimethylol propane triacrylate) was reported by Yoon et al. [64]. The effect of the concentration of the peroxide and the coagent was evaiuated in terms of thermal, morphological, melt, and mechanical properties. The low shear viscosity of the blends increased with the increase in peroxide content initially, and beyond 0.02 phr the viscosity decreased with peroxide content (Fig. 9). The melt viscosity increased with coagent concentration at a fixed peroxide content. The morphology of the samples indicated a decrease in domain size of the dispersed NR phase with a lower content of the peroxide, while at a higher content the domain size increases. The reduction in domain size... 

The rheological behavior of storage XGs was characterized by steady and dynamic shear rheometry [104,266]. Tamarind seed XG [266] showed a marked dependence of zero-shear viscosity on concentration in the semi-dilute region, which was similar to that of other stiff neutral polysaccharides, and ascribed to hyper-entanglements. In a later paper [292], the flow properties of XGs from different plant species, namely, suspension-cultured tobacco cells, apple pomace, and tamarind seed, were compared. The three XGs differed in composition and structural features (as mentioned in the former section) and... 

FIGURE 3.21 Plots of shear viscosity versus time for (a) acrylic rubber (ACM)-silica and (b) epoxidized natural mbber (ENR)-silica hybrid nanocomposites in solution at different tetraethoxysilane (TEOS) concentrations, continuously for five days. The numbers in the legends indicate wt% TEOS concentration. (From Bandyopadhyay, A., De Sarkar, M., and Bhowmick, A.K., J. Polym. Sci., Part B Polym. Phys., 43, 2399, 2005. Courtesy of Wiley InterScience.)... 

Taking into account the relevance of the range of semi-dilute solutions (in which intermolecular interactions and entanglements are of increasing importance) for industrial applications, a more detailed picture of the interrelationships between the solution structure and the rheological properties of these solutions was needed. The nature of entanglements at concentrations above the critical value c leads to the viscoelastic properties observable in shear flow experiments. The viscous part of the flow behaviour of a polymer in solution is usually represented by the zero-shear viscosity, rj0, which depends on the con-... 

On the basis of a relationship between T Sp and the dimensionless product c [rj], simple three-term equations can be developed to correlate the zero-shear viscosity with the concentration and molar mass. 

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

The experimental zero-shear viscosities obtained for polystyrene (PS) of different molar masses (with a very narrow molar mass distribution Mw/Mn=1.06-1.30) and different concentrations in toluene and fra s-decalin are plotted as log r sp vs. log (c- [r ]) in Fig. 6. 

The influence of the molar mass and concentration above the zero-shear viscosity has been described. In the following sections the influence of these parameters in the region of Newtonian and non-Newtonian regimes will be discussed. 

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

Below a critical concentration, c, in a thermodynamically good solvent, r 0 can be standardised against the overlap parameter c [r)]. However, for c>c, and in the case of a 0-solvent for parameter c-[r ]>0.7, r 0 is a function of the Bueche parameter, cMw The critical concentration c is found to be Mw and solvent independent, as predicted by Graessley. In the case of semi-dilute polymer solutions the relaxation time and slope in the linear region of the flow are found to be strongly influenced by the nature of polymer-solvent interactions. Taking this into account, it is possible to predict the shear viscosity and the critical shear rate at which shear-induced degradation occurs as a function of Mw c and the solvent power. 

The zero-shear viscosity and the dynamic viscosity (at low frequencies) diverge at high concentration, while they are constant at low concentration [99,100,102-105],... 

The rheological properties of a fluid interface may be characterized by four parameters surface shear viscosity and elasticity, and surface dilational viscosity and elasticity. When polymer monolayers are present at such interfaces, viscoelastic behavior has been observed (1,2), but theoretical progress has been slow. The adsorption of amphiphilic polymers at the interface in liquid emulsions stabilizes the particles mainly through osmotic pressure developed upon close approach. This has become known as steric stabilization (3,4.5). In this paper, the dynamic behavior of amphiphilic, hydrophobically modified hydroxyethyl celluloses (HM-HEC), was studied. In previous studies HM-HEC s were found to greatly reduce liquid/liquid interfacial tensions even at very low polymer concentrations, and were extremely effective emulsifiers for organic liquids in water (6). 

Figure 5.17 The low shear viscosity as a function of concentration for a latex particle with an electrolyte concentration of 10 4M and radius of 38 nm. This is compared with the modified Eyring23 model and the hydrodynamic contribution to the flow...

Zero shear viscosities have been determined in solution over a wide range of concentrations with a cone-plate Rheometrics Stress Rheometer. For linear macromolecules, the viscosity is proportional to c below the so called "entanglement concentration", c above c, is proportional to c. However, the viscosity will rise steeply at some concentration below c in the case where particular interconnections are formed at the concentration at which the molecules come into contact with one another. Ideally this will be the overlap threshold c. Below c, the molecules may associate partially but cannot form a network continuous over the entire sample space. Above c, plastic flow will require separation and... 

Figure 11 Logarithmic plot of the zero shear viscosities of PS-(S03Li)2 against the concentration in cumene, samples as given in Table II.

The limiting low shear or zero-shear viscosity r 0 of the molten polymer can be related to its weight-average molecular weight, M 9 by the same relations noted for concentrated solutions rj0 = KMW for low molecular weight and rj0 = Kfor high molecular weight. 

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