Polymer solutions dilute viscosity

The opportunity to measure the dilute polymer solution viscosity in GPC came with the continuous capillary-type viscometers (single capillary or differential multicapillary detectors) coupled to the traditional chromatographic system before or after a concentration detector in series (see the entry Viscometric Detection in GPC-SEC). Because liquid continuously flows through the capillary tube, the detected pressure drop across the capillary provides the measure for the fluid viscosity according to the Poiseuille s equation for laminar flow of incompressible liquids [1], Most commercial on-line viscometers provide either relative or specific viscosities measured continuously across the entire polymer peak. These measurements produce a viscometry elution profile (chromatogram). Combined with a concentration-detector chromatogram (the concentration versus retention volume elution curve), this profile allows one to calculate the instantaneous intrinsic viscosity [17] of a polymer solution at each data point i (time slice) of a polymer distribution. Thus, if the differential refractometer is used as a concentration detector, then for each sample slice i. 

Anotlier simple way to obtain the molecular weight consists of measuring tire viscosity of a dilute polymer solution. The intrinsic viscosity [q] is defined as tire excess viscosity of tire solution compared to tliat of tire pure solvent at tire vanishing weight concentration of tire polymer [40] ... 

Dilute Polymer Solutions. The measurement of dilute solution viscosities of polymers is widely used for polymer characterization. Very low concentrations reduce intermolecular interactions and allow measurement of polymer—solvent interactions. These measurements ate usually made in capillary viscometers, some of which have provisions for direct dilution of the polymer solution. The key viscosity parameter for polymer characterization is the limiting viscosity number or intrinsic viscosity, [Tj]. It is calculated by extrapolation of the viscosity number (reduced viscosity) or the logarithmic viscosity number (inherent viscosity) to zero concentration. 

Capillary viscometers are useful for measuring precise viscosities of a large number of fluids, ranging from dilute polymer solutions to polymer melts. Shear rates vary widely and depend on the instmments and the Hquid being studied. The shear rate at the capillary wall for a Newtonian fluid may be calculated from equation 18, where Q is the volumetric flow rate and r the radius of the capillary the shear stress at the wall is = r Ap/2L. 

The number average molecular weight is required. This is obtained directly from measurements of a colligative property, such as the osmotic pressure, of dilute polymer solutions (see Chap. VII). It is often more convenient to establish an empirical correlation between the osmotic molecular weight and the dilute solution viscosity, i.e., the so-called intrinsic viscosity, and then to estimate molecular weights from measurements of the latter quantity on the products of polymerization. 

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. 

The empirical dependence that is established for a polymer of a specified chemical structure is only valid for a given solvent and temperature. Viscosity of polymer solutions are generally higher as compared to those of pure solvent. A number of viscosity designation have been defined for dilute polymer solutions. For the sake of consistency, the more common usage is adopted in present discussion. 

Equation describing the dependence of the reduced viscosity, t] Ic, on the mass concentration of the polymer, c, for dilute polymer solutions of the form... 

Viscosity is a measure of the resistance to flow of a material, mixture, or solution. Here we will consider the viscosity of solutions containing small, generally 1 g/100 cc (called 1% solutions) and less, amounts of polymer. The study of such dilute polymer solutions allows a determination of a relative molecular weight. The molecular weight is referred to as relative since... 

FIGURE 3.20 Reduced and inherent viscosity-concentration lines for a dilute polymer solution. 

Viscosity measurements of dilute polymer solutions are carried out using a viscometer, such as any of those pictured in Figure 3.21. The viscometer is placed in a constant temperature bath and the time taken to flow through a space is measured. 

PVAc may be produced by the polymerization of vinyl acetate (Equation 6.47). The viscosity of the solution continues to increase until the reaction is complete. Dilute polymer solutions are used to prevent the onset of autoacceleration because of the gel effect. 

Attempts have been made to identify primitive motions from measurements of mechanical and dielectric relaxation (89) and to model the short time end of the relaxation spectrum (90). Methods have been developed recently for calculating the complete dynamical behavior of chains with idealized local structure (91,92). An apparent internal chain viscosity has been observed at high frequencies in dilute polymer solutions which is proportional to solvent viscosity (93) and which presumably appears when the external driving frequency is comparable to the frequency of the primitive rotations (94,95). The beginnings of an analysis of dynamics in the rotational isomeric model have been made (96). However, no general solution applicable for all frequency ranges has been found for chains with realistic local structure. 

Bueche,F. Influence of rate of shear on the apparent viscosity of a -dilute polymer solutions and b-bulk polymers. J. Chem. Phys. 22,1570-1576 (1954)... 

Viscosity Measurements. Although in typical polymer-plasticizer systems, the polymer is the major component, it is possible to use the viscosity of dilute polymer solutions as a measure of the solvent power of the liquid for the polymer. Thus, liquids with high solvent power for the polymer cause a stretching out of the chain molecules, whereas a liquid of poor solvent power causes the chains to coil up. This is because, in the liquid with poor solvent power, the segments of the polymer chain (the monomer units) prefer to stay close to each other, while in a good solvent, interaction between polymer segments and solvent molecules is preferred. 

The DTO model ignores the overall translations and rotations of the molecule as a whole and refers only to internal vibrational modes. It is therefore incapable of explaining on its own the viscosity of dilute polymer solutions. The enhanced viscosity of dilute polymer solutions is undoubtedly due to a hydrodynamic damping of the polymer as a whole as it translates and rotates in the shear field. This was very well described by Debye (21). We should point out that the Debye viscosity is alternatively derivable from the RB theory. 

Gundert F, Wolf BA (1986) Viscosity of dilute polymer solutions molecular weight dependence of the Huggins coefficient Makromol Chem 187 2969... 

Peyser P, Little RC (1971) The drag reduction of dilute polymer solutions as a function of solvent power, viscosity and temperature J Appl Polym Sci 15 2623... 

The dependence of viscosity r of dilute polymer solutions on concentration c can be described by a polynomial in the form [31,38],... 

G. G. Fuller and L. G. Leal, The effects of conformation-dependent friction and internal viscosity on the dynamics of the nonlinear dumbbell model for a dilute polymer solution, J. Non-Newt. Fluid Mech. 8, 271 (1981). 

Shape effect of PFPE molecules or magnetic particles in suspension, including agglomeration phenomena at low concentration, interaction among these particles, and effects of floes can be examined via solution viscosity (r ) measurement. For a very dilute polymer solution [108], there is no interaction among polymer molecules, and the solution viscosity results from the contribution of the solvent plus the contribution of the individual polymer molecules. The intrinsic viscosity, therefore, is a measure of the hydrodynamic volume of a polymer molecule as well as the particle aspect ratio. Figure 1.24 shows the determination of the intrinsic viscosity for Zdol4000 in three different solvents. 

Comparison with experimental data demonstrates that the bead-spring model allows one to describe correctly linear viscoelastic behaviour of dilute polymer solutions in wide range of frequencies (see Section 6.2.2), if the effects of excluded volume, hydrodynamic interaction, and internal viscosity are taken into account. The validity of the theory for non-linear region is restricted by the terms of the second power with respect to velocity gradient for non-steady-state flow and by the terms of the third order for steady-state flow due to approximations taken in Chapter 2, when relaxation modes of macromolecule were being determined. 

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