Viscosity semi-dilute

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-... 

In semi-dilute solutions, the Rouse theory fails to predict the relaxation time behaviour of the polymeric fluids. This fact is shown in Fig. 11 where the reduced viscosity is plotted against the product (y-AR). For correctly calculated values of A0 a satisfactory standardisation should be obtained independently of the molar mass and concentration of the sample. 

For concentrated solutions of polystyrene in n-butylbenzene, Graessley [40] has shown that the reduced viscosity r red Cnred=(r ( y)- rls)/(rlo rls)) can be represented on a master curve if it is plotted versus the reduced shear rate (3 ((3= y/ ycnt= y-A0). For semi-dilute solutions a perfect master curve is obtained if (3 is plotted versus a slope corrected for reduced viscosity, T corp as shown in Fig. 16. 

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. 

Attempts to measure the depletion force in nonadsorbing polymer medium with an SEA have failed essentially because measurements are hindered by the slow exclusion of the polymer from the narrow gap due to the large viscosity of the polymer solutions. However, depletion forces have been measured in solutions of living polymers in a semi-dilute regime by Kdkicheff et al. [50]. The... 

For convenience, this chapter has been divided into three sections in which the viscosity of dilute solutions and dispersions, non-Newtonian flow, and the viscoelastic properties of semi-solid systems are discussed. 

We close this section by examining the status of applications of these methods to polymer monolayers. Initially, ISR was used to probe the 2D nematic state of phthalocyaninatopolysiloxane, descriptively called a hairy rod , dispersed in eicosanol [ 149], and subsequently applied to a set of poly(f-butyl methacrylate) in the semi-dilute regime and beyond [150]. In the semi-dilute regime, the surface viscosity is found to scale linearly with molecular weight, which is in good accord with the results of Sacchetti et al. [134]... 

Theory (Odijk et al., 1977/79, Mandel et al., 1983/86) predicts that in the dilute state (c < c ) most of the parameters of the solution (intrinsic viscosity, diffusivity, relaxation times) will be functions of the molar mass, but not of the polymer concentration. In the so-called semi-diluted solution state the influence of the polymer concentration (and that of the dissolved salts) becomes very important, whereas that of the molar mass is nearly absent. Experiments have confirmed this prediction. 

In order to overcome this difficulty, Rudin and Strathdee (1974) developed a semi empirical method for predicting the viscosity of dilute polymer solutions. The method is based on an empirical equation proposed by Ford (1960) for the viscosity of a suspension of solid spheres ... 

Rheology is a powerful method for the characterization of HA properties. In particular, rotational rheometers are particularly suitable in studying the rheological properties of HA. In such rheometers, different geometries (cone/plate, plate/plate, and concentric cylinders) are applied to concentrated, semi-diluted, and diluted solutions. A typical rheometric test performed on a HA solution is the so-called "flow curve". In such a test, the dynamic viscosity (q) is measured as a function of the shear rate (7) at constant strain (shear rate or stress sweep). From the flow curve, the Newtonian dynamic viscosity (qo), first plateau, and the critical shear rate ( 7 c), onset of non-Newtonian flow, could be determined. 

The relationship between observed viscosity and intrinsic viscosity depends on the volume occupied by the polymer chains (dependent on the first power of their concentration) and the interactions between polymer chains (in the dilute and semi-dilute regions, dependent on the second power of their concentration). The resulting equation, eqn. (4.17), is known as the Huggins equation, with kii being the (dimensionless) Huggins coefficient, which measures chain-chain interaction ... 

It is important to note that the typical application of xanthan uses a semi-dilute, not dilute solution. Interactions between the chains, which are not considered in this study, play an important role in the viscosity of these solutions. 

Adam, M., and Delsanti, M., Viscosity of semi-dilute polymer solutions, J. Phys. (Paris), 43, 549-557 (1982). 

Heo, Y., and Larson, R. G., The scaling of zero-shear viscosities of semi-dilute polymer solutions with concentration, J. RheoL, 49, 1117-1128 (2(X)5). 

Jamieson, A. M., and Telford, D., Newtonian viscosity of semi-dilute solutions of polystyrene in tetrahydrofuran, Mocroma/eca/es, 15, 1329-1332 (1982). 

Jamieson, A. M., Simha, R., Newtonian viscosity of dilute, semi-dilute and concentrated polymer solutions. Chapter 1, in Polymer Physics From Suspensions to Nanocomposites and Beyond, Utracki L. A. and Jamieson A. M., Editors, J. Wiley Sons, New York (2010). 

This relationship can help us to learn about the viscosity of a polymer solution. In particular, we can use it to figure out how the viscosity depends on the number of monomer units At in a chain (in the limit N 1). Presumably, we need to know first how E and t depend on N. So we should venture a little investigation. Let s consider E and r separately, and concentrate on the case of a pol3Tner melt, to make it easier. In principle, the same sort of logic should apply to concentrated and semi-dilute solutions. 

Physico-chemical behaviour in aqueous solution was studied by viscosity measurements. Expected associative behaviour has been evidenced in pure water, while in salt media, the associative behaviour strongly depends on PCL chains length. For shorter PCL chains, intramolecular hydrophobic interactions are predominant, even in the semi-dilute regime. This non-classical behaviour for an associative polyelectrolyte opens the way to the conception of amphiphilic matrices with hydrophobic clusters for controlled release applications. 

At describing the viscosity properties of diluted solution one usually proceeds from the linear dependence of an increment in viscosity on the polymer solution concentration. However, in the case of polar polymers to which CHT belongs there is a possibility of the occurrence of reversible agglomeration process which can take place not only in the area of semi-diluted solutions but even in the area of diluted ones. In this case the contribution to viscosity is made not by separate particles with V volume but by their aggregates whose volume V(n) depends not only on the number of particles constituting it, but also on their density characterized by fraction dimensions D [3] ... 

For the brushes, the degree of interpenetration is small. Within this interpenetration zone the concentration can be viewed as semi-dilute, and the effective viscosity is that of chains which have the dimensions of the correlation length (i). As a result the additional shear force over that of the pure... 

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