Zero shear viscosity, concentration

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. 

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-... 

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. 

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],... 

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. 

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... 

Fig. 19. Zero-shear viscosity of aqueous xanthan solutions at different sodium chloride concentration C, [140]...

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]... 

Another often used representation of the viscoelastic flow behavior utilizes normal stress coefficients P/ = Ni/y. Figure 10 depicts flow curves of a family of PAA/water solutions differing in concentrations and therefore in their viscosities. Normalized by the zero-shear viscosity fiQ and by a constant shear rate /q shear stress value of to= 1 N/m they produce master curves for viscosity and the normal stress coefficient. The preparation... 

The usefulness of c tf as an approximate reducing parameter for the zero shear viscosity at moderate concentrations is very well established. Master equations of the form... 

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) ... 

Figure 12 Plot of the symmetric CH stretching frequency in C14AO/SDS mixed micelles at 20°C. a) the total surfactant concentration is 10 wt.% and all samples are from the Lt phase. Also plotted are the zero shear viscosities, q0. b) die total surfactant concentration is 18 wt.% and the surfactant structure varies dramatically with composition (Reproduced with permission from ref. 49. Copyright 1990 Steinkopff Verlag).

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-... 

The low shear rheology measurements also show a rapid increase in the viscoelastic properties (modulus and zero shear viscosity) with increase of bentonite concentration above the gel point (> 30 g dm bentonite). Several models have been proposed to account for the elastic properties of concentrated dispersions, of which that originally proposed by van den Tempel (25) and later developed by Papenhuizen (26) seems to be the most appropriate for the present system. According to this model, if the interaction energy minimum between adjacent particles is sufficiently negative, a three-dimensional network structure may ensue, giving an elastic component. Various models can be used to represent the three dimensional structure, the simplest of which would be either an ideal network where all particles are... 

The increase in gel strength with increase in bentonite concentration above the gel point is consistent with the increase in yield value and modulus. On the other hand, the limited creep measurements carried out on the present suspension showed a high residual viscosity Oq of the order of 9000 Nm s when the bentonite concentration was 45g dm. As recently pointed out by Buscall et al (27) the settling rate in concentrated suspensions depends on 0. With a model system of polystyrene latex (of radius 1.55 vim and density 1.05 g cm ) which was thickened with ethyl hydroxy ethyl cellulose, a zero shear viscosity of lONm was considered to be sufficient to reduce settling of the suspension with = 0.05. The present pesticide system thickened with bentonite gave values that are fairly high and therefore no settling was observed. 

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