Shear viscosity-concentration dependencies

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

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. 

It should be noted that the Doi and Ohta theory predicts oifly an enhancement of viscosity, the so called emulsion-hke behavior that results in positive deviation from the log-additivity rule, PDB. However, the theory does not have a mechanism that may generate an opposite behavior that may result in a negative deviation from the log-additivity rule, NDB. The latter deviation has been reported for the viscosity vs. concentration dependencies of PET/PA-66 blends [Utracki et ah, 1982]. The NDB deviation was introduced into the viscosity-concentration dependence of immiscible polymer blends in the form of interlayer slip caused by steady-state shearing at large strains that modify the morphology [Utracki, 1991]. 

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). 

At least, in absolute majority of cases, where the concentration dependence of viscosity is discussed, the case at hand is a shear flow. At the same time, it is by no means obvious (to be more exact the reverse is valid) that the values of the viscosity of dispersions determined during shear, will correlate with the values of the viscosity measured at other types of stressed state, for example at extension. Then a concept on the viscosity of suspensions (except ultimately diluted) loses its unambiguousness, and correspondingly the coefficients cn cease to be characteristics of the system, because they become dependent on the type of flow. 

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... 

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-... 

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. 

The measurement of viscosity is important for many food products as the flow properties of the material relate directly to how the product will perform or be perceived by the consumer. Measurements of fluid viscosity were based on a correlation between relaxation times and fluid viscosity. The dependence of relaxation times on fluid viscosity was predicted and demonstrated in the late 1940 s [29]. This type of correlation has been found to hold for a large number of simple fluid foods including molten hard candies, concentrated coffee and concentrated milk. Shown in Figure 4.7.6 are the relaxation times measured at 10 MHz for solutions of rehydrated instant coffee compared with measured Newtonian viscosities of the solution. The correlations and the measurement provide an accurate estimate of viscosity at a specific shear rate. 

Viscosity Measurements. A Zimm-Couette type low shear viscometer was used. The intrinsic viscosities were estimated from single concentration viscosity measurements using the equations for the concentration dependence of the specific viscosity (5,6). The Mark-Houwink equation was used to determine My (5,6). 

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]. 

In Sect. 6.3, we have neglected the intermolecular hydrodynamic interaction in formulating the diffusion coefficients of stiff-chain polymers. Here we use the same approximation by neglecting the concentration dependence of qoV), and apply Eq. (73) even at finite concentrations. Then, the total zero-shear viscosity t 0 is represented by [19]... 

The effects of interaction on viscoelastic properties at low concentrations depend on the Simha parameter. For example, Ferry has pointed out the importance of c[jj] for the transition from Zimm-like to Rouse-like behavior in the dynamic properties and in the observed values of J (15). The shear rate dependence of viscosity undergoes a corresponding transition as a function of... 

Williams has derived the molecular weight and concentration dependence of a viscoelastic time constant t0 (actually the characteristic time governing the onset of shear rate dependence in the viscosity) from his theory (217-219). Employing a dimensional argument, he equates the parameters which control the shear rate dependence of chain configuration and the intermolecular correlation function. The result agrees with the observed form of characteristic relaxation time in concentrated systems [Eq.(6.62)] ... 

However, as soon as a finite contribution of the form effect is contained in the value of Maxwell constant, the said conditions are no longer superfluous. In fact, the form effect is highly concentration dependent in the range of low concentrations (138, 63), and has a shear rate dependence different from that of intrinsic birefringence and viscosity. In other words, due to the presence of the form effect, the ratio of Maxwell constant and intrinsic viscosity can no longer be interpreted as twice the stress-optical coefficient in the sense of Chapter 2. 

Figure 3. Concentration dependence of viscosity for benzene solutions of some block copolymers and one polybutadiene (P 5) at 25°C. Viscometers with long capillaries were used and viscosities were extrapolated to zero shear gradient (34).

Figure 11.3. (a) Viscosity of PDMS melts swollen with carbon dioxide measured as a function of shear rate and carbon dioxide content at 50 °C. (b) Master viscosity curve produced by applying concentration-dependent scaling factors (see text). A Pure PDMS, 4.84 wt % C02, O 9.03 wt % C02, 14.4 wt % C02 A 20.7 wt % C02. Data denoted by are Newtonian viscosity measurement for pure PDMS. Data from Gerhardt (1994). 

The motion of polymers in concentrated solution and bulk is of major theoretical and practical concern. For example, the strong dependence of zero-shear viscosity on molecular weight (approximately the 3.4 power) and the marked decrease of viscosity 1) with shear rate y not only bespeak some of the unusual properties of long-chain molecules but also are of essential importance in virtually every processing operation. Yet the reasons for these unusual behaviors have become clear only recently. The reptation con-... 

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