Viscosity of a polymer solution

The viscosity of a polymer solution is one of its most distinctive properties. Only a minimum amount of research is needed to establish the fact that [77] increases with M for those polymers which interact with the solvent to form a random coil in solution. In the next section we shall consider the theoretical foundations for the molecular weight dependence of [77], but for now we approach this topic from a purely empirical point of view. 

For practical purposes, it is convenient to define the relaxation time in terms of macroscopic quantities which can be readily determined. Within the validity limit of Hookean connectors (Eq. 13), the low-shear viscosity of a polymer solution is given by the relation ... 

Recently, we explored the effect of molecular weight on the pattern and employed post-dewetting processes to alter the shape of the dewetted polymer droplets. Since the viscosity of a polymer solution is nonlinear with respect to concentration and also strongly dependent on polymer weight, we expected a drastic effect. Figure 11.4... 

The ratio of the viscosity of a polymer solution to that of the solvent is called the relative viscosity (17 ). This value minus 1 is called the specific viscosity and the reduced viscosity or viscosity number is obtained by dividing by the polymer concentration c (rj /c). The intrinsic viscosity, or LVN, is obtained by extrapolating r) p/c to zero polymer concentration. These relationships are given in Table 3.6, and a typical plot of r) /c and InrjJc is shown in Figure 3.20. 

Explain why the viscosity of a polymer solution decreases as the temperature increases. 

The viscosity of a polymer solution is one of its most distinctive properties. The spatial extension of the molecules is great enough so that the solute particles cut across velocity gradients and increase the viscosity in the manner suggested by Figure 4.8. In this regard they are no different from the rigid spheres of the Einstein model. What is different for these molecules is the internal structure of the dispersed units, which are flexible and swollen with solvent. The viscosity of a polymer solution depends, therefore, on the polymer-solvent interactions, as well as on the properties of the polymer itself. 

How does the viscosity of a polymer solution differ from the viscosity of dispersions What factors are important in the case of the former ... 

Another term, reduced viscosity, is used to describe the ability of the polymer to increase the viscosity of the solvent (rired = risp / c, where c is the concentration of the polymer in the solution). The reduced viscosity of a polymer solution directly results from the intermolecular interactions (polymer and solvent molecules). These effects are then eliminated by extrapolating to an infinite dilution. The dependence of the reduced viscosity on the concentration of the polymer solution is given as ... 

When the intrinsic viscosity of a polymer solution is reduced by changing the solvent or by introducing crosslinks during polymerization,... 

It is to be expected that the influence of temperature on the viscosity of a polymer solution lies somewhere between that of the pure solvent and that of a polymer melt. 

In reality the interactions between polymer and solvent molecules, which determine the solution viscosity, are very complicated and dependent on a great number of parameters. The literature mentions the solubility parameters of polymer and solvent, polymer chain stiffness, free volume of the solution, etc. In principle, all these factors should be taken into account in predicting the viscosity of a polymer solution. However, the available experimental data are insufficient for this purpose. 

Another very useful approach to molar mass information of complex polymers is the coupling of SEC to a viscosity detector [55-60]. The viscosity of a polymer solution is closely related to the molar mass (and architecture) of the polymer molecules. The product of polymer intrinsic viscosity [r ] times molar mass is proportional to the size of the polymer molecule (the hydrodynamic volume). Viscosity measurements in SEC can be performed by measuring the pressure drop AP across a capillary, which is proportional to the viscosity r of the flowing liquid (the viscosity of the pure mobile phase is denoted as r 0). The relevant parameter [r ] is defined as the limiting value of the ratio of specific viscosity (qsp= (n-noVflo) and concentration c for c—> 0 ... 

The viscosity of a polymer solution as compared to the viscosity of the pure solvent is measured by the pressure drop AP across an analytical capillary-transducer system. The specific viscosity is obtained from AP/P, where P is the inlet pressure of the system. As the concentrations in SEC are usually very low, [q] can be approximated by qsp/c. 

Chemically, gelation is a process of crosslinking after the completion of esterification (see Figure 4). Physically, it is a process of continuously increasing the viscosity of a polymer solution with time, depending on the nature of the polymer solvent system and on the temperature. The... 

The introduction of macromolecules into the fluid disturbs the streamlines, thus causing an additional energy dissipation, the amount of which depends upon the size and shape of the particles. As a result the viscosity of a polymer solution is always greater than that of the pure solvent. 

The viscosity of a polymer solution is highly dependent on concentration, temperature, and MW, as discussed below. 

As Eq. (6) shows, the viscosity of a polymer solution is highly dependent on temperature. The sample zone of a high-MW polymer is pressed much closer to the cold wall in ThFFF. Its viscosity is more enhanced than with a low-MW polymer. The concentration effect, therefore, is more serious for high-MW polymers in ThFFF. 

Measure the bulk viscosity of a polymer solution at different shear rates. Then we have J, versus y. Obtain K and n by fitting the data into the power-law equation ... 

The dominate factor which controls the solution properties of mobility control polymers is the configuration (and hence size) that the molecule assumes in a given environment. Although the viscosity of a polymer solution is related to the hydrodynamic size of the polymer molecules, it is difficult to determine the unique relationship between viscosity and size. However, exten-... 

In the Newtonian range the viscosity of a polymer solution can be measured by passing the solution through a capillary and measuring the efflux time at a given temperature. At higher concentrations the parallel plate or cone/plate designs are used. 

Figure 2.15 Viscosity of a polymer solution as a function of concentration...

The viscous flow of a polymer solution involves a shearing action in which different layers of the solution move with differing velocities. As we observed earlier, there is a pronounced increase in the viscosity of a polymer solution relative to that of the pure solvent even at low concentrations of the polymer. In this respect, the polymer solute behaves as a coUoidal dispersion, which is known to retard the flow of adjacent layers of a liquid under shearing force. For spherical colloidal particles, the viscosity of the solution, Tj, relative to that of the pure solvent, Tio, is referred to as the relative viscosity, given by... 

Hory and Fox suggested that as the viscosity of a polymer solution will depend on the volume occupied by the polymer chain, it should be feasible to relate coil size and [rj]. They assumed that if the unperturbed polymer is approximated by a hydrodynamic sphere, then [Tjjg, the limiting viscosity number in a theta solvent, could be related to the square root of the molar mass by... 

Another parameter that can be related to molecular weight is the relative viscosity, defined as the ratio of the viscosity of a polymer solution rj to the viscosity of the solvent rjo (see Table 3.3). Reliable for molecular weights >10 g/mol, the viscosities can be determined by measuring flow times through capillary tubes (diameters 1 mm), usually with gravity as the driving force for the flow. Automated instrumentation is widely available. Rotational and oscillatory type viscometers are used where a uniform, well-defined, or low shear rate is required. The ratio of the two viscosities, is called the relative... 

---