Viscosity behavior, linear

Tj max increases [19] linearly with M. An increase in the salt concentration moves Umax toward higher c so that c ax c, and it drastically lowers the value of Analogous to the viscosity behavior, the dynamic storage and loss moduli also show [22] a peak with c. The unusual behavior at low c where the reduced viscosity increases with dilution in the polyelectrolyte concentration range between and c, along with the occurrence of a peak in the reduced viscosity versus c, has remained as one of the most perplexing properties of polyelectrolytes over many decades. 

The viscosity of some polymers at constant temperature is essentially Newtonian over a wide shear rate range. At low enough shear rates all polymers approach a Newtonian response that is, the shear stress is essentially proportional to the shear rate, and the linear slope is the viscosity. Generally, the deviation of the viscosity response to a pseudoplastic is a function of molecular weight, molecular weight distribution, polymer structure, and temperature. A model was developed by Adams and Campbell [18] that predicts the non-Newtonian shear viscosity behavior for linear polymers using four parameters. The Adams-Campbell model is as follows ... 

While it can be expected that a number of physical properties of hyperbranched and dendritic macromolecules will be similar, it should not be assumed that all properties found for dendrimers will apply to hyperbranched macromolecules. This difference has clearly been observed in a number of different areas. As would be expected for a material intermediate between dendrimers and linear polymers, the reactivity of the chain ends is lower for hyperbranched macromolecules than for dendrimers [125]. Dendritic macromolecules would therefore possess a clear advantage in processes, which require maximum chain end reactivity such as novel catalysts. A dramatic difference is also observed when the intrinsic viscosity behavior of hyperbranched macromolecules is compared with regular dendrimers. While dendrimers are found to be the only materials that do not obey the Mark-Houwink-Sakurada relationship, hyperbranched macromolecules are found to follow this relationship, albeit with extremely low a values when compared to linear and branched polymers [126]. 

The suggested rod like structure of the pendant-type FVP-Co(III) complex is supported by the viscosity behavior of the polymer-complex solution (Fig. 3)2 The PVP-Co(III) complexes have higher viscosity than PVP this suggests that the polymer complex has a linear structure and that intra-polymer chelation does not occur. The dependence of the reduced viscosity on dilution and the effect of ionic strength further show that Co(en)2(PVP)Cl] Cl2 is a poly(electrolyte). The polymer complexes with higher x values have a rodlike structure due to electrostatic repulsion or the steric bulkiness of the Co(III) chelate. On the other hand, the solubility and solution behavior of the polymer complex with a lower x value is similar to that of the polymer ligand itself. 

The viscosity behavior of poly[(a-carboxymethyl)ethyl isocyanide] may be studied in neutral organic solvents. The concentration dependence of its reduced specific viscosity in 1,2-dichloroethane is shown in Fig. 11. A linear dependence indicates that the coefficients of higher concentration terms of the usual virial equations are negligibly small—a case which should be found with molecules, such as stiff rods, that give few intermolecular entanglements in dilute solution. 

Figure 6.2. Relations between shear stress, deformation rate, and viscosity of several classes of fluids, (a) Distribution of velocities of a fluid between two layers of areas A which are moving relatively to each other at a distance x wider influence of a force F. In the simplest case, F/A = fi(du/dx) with ju constant, (b) Linear plot of shear stress against deformation, (c) Logarithmic plot of shear stress against deformation rate, (d) Viscosity as a function of shear stress, (e) Time-dependent viscosity behavior of a rheopectic fluid (thixotropic behavior is shown by the dashed line). (1) Hysteresis loops of time-dependent fluids (arrows show the chronology of imposed shear stress).

Power law model fluid with temperature dependent viscosity m0 = e( a(-T Tm The rate of melting is strongly dependent on the shear thinning behavior and the temperature dependent viscosity of the polymer melt. However, we can simplify the problem significantly by assuming that the viscous dissipation is low enough that the temperature profile used to compute the viscosity is linear, i.e.,... 

The intrinsic viscosity (or limiting viscosity number) can be obtained by measuring the relative viscosity at different concentrations and then taking the limit of the specific viscosity when the concentration is extrapolated to zero (Fig. 17.7). The behavior of the intrinsic viscosity with concentration depends on the nature of both the specific polymer molecule and the solvent. Since the intrinsic viscosity of linear polymers is related to the MW, for linear macromolecules intrinsic viscosity measurements provide a simple method for the determination of MW when the relationship between viscosity and MW is known. 

The intrinsic viscosity behavior of polystyrene (PS) is very similar to that of linear PVAc. The following Mark-Houwink constants are often cited for PS in THF a = 0.706, K= 0.00016 (19,22). Therefore, PS and linear PVAc samples of the same molecular weight elute at nearly the same retention volume. Consequently, for certain PVAc products, the increased cost, complexity, and experimental uncertainty associated with analysis of SEC data by universal calibration may not be justified (26). 

Other macromolecular architectures, such as linear polymers, and any comparisons that have been made were performed with polydisperse samples of significantly different repeat unit structure. For example, the unique melt viscosity behavior of polyether dendrimers was compared with linear polystyrene and not with monodisperse linear analogs containing the same number of polyether repeat units based on 3,5-dihydroxybenzyl alcohol (2). Because of this, important issues, such as i) effect of the numerous chain end functional groups, ii) the effect of branching and, iii) the development of a well defined three-dimensional architecture cannot be addressed and the underlying reason for these inherent differences remains a mystery. 

The flow behavior of alkyl polyglycoside solutions is characterized by three different viscosity ranges. At low concentrations, the viscosity increases linearly with concentration. The results of measurements with an Ubbelohde... 

The early coordination polymeric materials were very difficult to characterize because of their insolubihty. It is worth noting that soluble, well-characterized systems have now been made. For example, linear cerium(IV) and zirconium(IV) Schifif base coordination polymers (13) have been synthesized and their MWs, solubilities and viscosity behavior have been investigated. ... 

The viscosity increases linearly with molecular weight. In a critical molecular weight region characteristic of the polymer, this behavior changes. The shear viscosity begins to increase rapidly with molecular weight and becomes dependent on shear rate (or shear stress) (37, 38,4oj ... 

Sen et al. [8] used molecular dynamics simulations to investigate why Mq is several times larger than M. They concluded that while the Rouse contribution to relaxation, which leads to the viscosity behavior described by Eq. 5.1, stops increasing with chain length N when N 40, the contribution of the largest relaxation times, which governs the zero-shear viscosity, increases linearly and only overtakes the Rouse contribution at about N 80, where it also begins to increase more rapidly with N. 

In Section 3.4 it was explained that polymers having very well defined structures can be prepared by means of anionic polymerization, and this technique has been widely used to prepare samples for rheological study. This has been a particularly fruitful approach to the study of the elfects of various types of long-chain branching structure on rheological behavior. Linear viscoelastic properties are very sensitive to branching. In this section we review what is known about the zero-shear viscosity, steady-state compliance, and storange and loss moduli of model branched polymers. 

The samples were also characterized in terms of their extensional viscosity behavior at 180°C. The linear viscoelastic envelope was determine from a start-up steady shear experiment to determine the zero-shear viscosity, which was then converted into zero-extensional viscosity using Trouton s rule tje = 3t o. 

For some materials the linear constitutive relation of Newtonian fluids is not accurate. Either stress depends on strain in a more complex way, or variables other than the instantaneous rate of strain must be taken into account. Such fluids are known collectively as non-Newtonian. Many different types of behavior have been observed, ranging from fluids for which the viscosity in the Navier-Stokes equation is a simple function of the shear rate to the so-called viscoelastic fluids, for which the constitutive equation is so different that the normal stresses can cause the fluid to flow in a manner opposite to that predicted for a Newtonian fluid. 

---