Zero shear viscosity polymer concentration

G. Zero-shear viscosity of concentrated polymer solutions... 

The average molecular weight, polydispersity, temperature, hydrostatic pressure, and shear rate dependences of polymer melt viscosity will be discussed in Chapter 13, resulting in a set of correlations which can be used to obtain a rough estimate of melt viscosity as a function of all of these variables. A new correlation will be presented for the molar viscosity-temperature function. The dependences of the zero-shear viscosity of concentrated polymer solutions on the average molecular weight and on the temperature will also be discussed. Finally, a new model that was developed to predict the shear viscosities of dispersions of particles in both polymeric fluids and ordinary molecular fluids will be presented. 

The zero-shear viscosity of a concentrated polymer solution can be treated by a modified version of the method used to calculate the zero-shear viscosity of a polymer melt. The modifications take the two effects of the solvent (plasticization and true dilution of the polymer) into account. Approximations are involved, however, in determining the appropriate mixing rules for the plasticization effect and the magnitude of the true dilution effect. The zero-shear viscosity of concentrated polymer solutions will be discussed briefly in Section 13.G. 

G. Zero-Shear Viscosity of Concentrated Polymer Solutions... 

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. 

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-... 

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. 

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 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. 

Controlled stress viscometers are useful for determining the presence and the value of a yield stress. The structure can be established from creep measurements, and the elasticity from the amount of recovery after creep. The viscosity can be determined at very low shear rates, often in a Newtonian region. This zero-shear viscosity, T 0, is related direcdy to the molecular weight of polymer melts and concentrated polymer solutions. 

The zero-shear viscosity r 0 has been measured for isotropic solutions of various liquid-crystalline polymers over wide ranges of polymer concentration and molecular weight [70,128,132-139]. This quantity is convenient for studying the stiff-chain dynamics in concentrated solution, because its measurement is relatively easy and it is less sensitive to the molecular weight distribution (see below). Here we deal with four stiff-chain polymers well characterized molecu-larly schizophyllan (a triple-helical polysaccharide), xanthan (double-helical ionic polysaccharide), PBLG, and poly (p-phenylene terephthalamide) (PPTA Kevlar). The wormlike chain parameters of these polymers are listed in Tables... 

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]... 

This was in contrast to a glycerine solution having the same zero-shear-viscosity which was dispersed after a few pipe diameters at a relatively low Reynolds number. For injection concentrations of 0.25% and 0.3%, the polymer thread did not remain... 

For concentrated solutions of amorphous polymers, Bueche s mathematical model shows the ratio of zero shear viscosities of branched and linear polymer above the critical molecular weight in the entanglement region to be (28) ... 

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-... 

Intrinsic viscosity is very useful as a measure of the hydrodynamic volume of food polymers and has been used for studying the role of polymer concentration on zero-shear viscosity of several food polymers (Chapter 4). 

Unlike biopolymer dispersions where the intrinsic viscosity is known and the polymer concentration can be chosen a priori, often for fluid foods the concentration of soluble (e.g., pectins in fruit juices) and insoluble solids can be determined only posteriori, and the determination of their zero-shear viscosities is also difficult due to instrument limitation and due to the existence of yield stress. However, in many foods, it may be possible to identify the components, called key components, that play an important role in the rheological properties. 

In earlier studies on solutions of synthetic polymers (Ferry, 1980), the zero-shear viscosity was found to be related to the molecular weight of the polymers. Plots of log r] versus log M often resulted in two straight lines with the lower M section having a slope of about one and the upper M section having a slope of about 3.4. Because the apparent viscosity also increases with concentration of a specific polymer, the roles of both molecular size and concentration of polymer need to be understood. In polymer dispersions of moderate concentration, the viscosity is controlled primarily by the extent to which the polymer chains interpenetrate that is characterized by the coil overlap parameter c[r] (Graessley, 1980). Determination of intrinsic viscosity [r]] and its relation to molecular weight were discussed in Chapter 1. The product c[jj] is dimensionless and indicates the volume occupied by the polymer molecule in the solution. 

Launay et al. (1986) suggested that there could be two transitions, instead of one transition shown in Figure 4-6, before the onset of high concentration-viscosity behavior. The critical concentration at the boundary between the semidilute and concentrated regimes is denoted as c. Such behavior was also found for citrus pectin samples with different values of DE at pH 7 and 0.1 M NaCl (Axelos et al., 1989 Lopes da Silva and Rao, 2006). Because the intrinsic viscosity of a biopolymer can be determined with relative ease. Figure 4-6 can be used to estimate the zero-shear viscosity of that biopolymer at a specific polymer concentration at 25°C. 

A similar, and even more dramatic, viscosity enhancement was observed by Buscall et al. (1993) for dispersions of 157-nm acrylate particles in white spirit (a mixture of high-boiling hydrocarbons). These particles were stabilized by an adsorbed polymer layer, and then they were depletion-flocculated by addition of a nonadsorbing polyisobutylene polymer. Figure 7-9 shows curves of the relative viscosity versus shear stress for several concentrations of polymer at a particle volume fraction of 0 = 0.40. Note that a polymer concentration of 0.1 % by weight is too low to produce flocculation, and the viscosity is only modestly elevated from that of the solvent. For weight percentages of 0.4-1.0%, however, there is a 3-6 decade increase in the zero-shear viscosity ... 

A major goal in the physics of polymer melts and concentrated solutions is to relate measurable viscoelastic constants, such as the zero shear viscosity, to molecular parameters, such as the dimensions of the polymer coil and the intermolecular friction constant. The results of investigations to this end on the viscosity were reviewed in 1955 (5). This review wiU be principaUy concerned with advances made since in both empirical correlation (Section 2) and theory of melt flow (Section 3). We shall avoid data confined to shear rates so high that the zero shear viscosity cannot be reliably obtained. The shear dq endent behavior would require an extensive review in itself. 

The zero-shear viscoelastic properties of concentrated polymer solutions or polymer melts are typically defined by two parameters the zero-shear viscosity (f]o) and the zero-shear recovery compliance (/ ). The former is a measure of the dissipation of energy, while the latter is a measure of energy storage. For model polymers, the infiuence of branching is best established for the zero-shear viscosity. When the branch length is short or the concentration of polymer is low (i.e., for solution rheology), it is found that the zero-shear viscosity of the branched polymer is lower than that of the linear. This has been attributed to the smaller mean-square radius of the branched chains and has led to the following relation... 

The effect of polymer concentration on the zero-shear viscosity of a concentrated solution can often be estimated by starting from the viscosity of the polymer melt and assuming that the effect of adding the solvent can be deconvoluted into two different types of perturbations [7] ... 

In summary, the following procedure can be used to predict, at a very approximate level of accuracy, the zero-shear viscosity riss(Mw,T,d>p) for concentrated polymer solutions ... 

Figure 13.11. Comparison of observed [7] and predicted zero-shear viscosities (N-sec/m2) of concentrated solutions of polystyrene with Mw=3.7-105 in xylene, as functions of the polymer concentration (g/cc), at two different temperatures (T=287K and T=318K).

Step 22. Calculate the viscosity of a polymer melt and/or the zero-shear viscosity of a concentrated polymer solution. The molecular weight dependence of the zero-shear viscosity is given by equations 13.2 and 13.3, where the critical molecular weight Mcr (Equation 13.6) is... 

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