Logarithmic viscosity

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. 

The viscosity ratio or relative viscosity, Tj p is the ratio of the viscosity of the polymer solution to the viscosity of the pure solvent. In capillary viscometer measurements, the relative viscosity (dimensionless) is the ratio of the flow time for the solution t to the flow time for the solvent /q (Table 2). The specific (sp) viscosity (dimensionless) is also defined in Table 2, as is the viscosity number or reduced (red) viscosity, which has the units of cubic meters per kilogram (m /kg) or deciUters per gram (dL/g). The logarithmic viscosity number or inherent (inh) viscosity likewise has the units m /kg or dL/g. For Tj g and Tj p, the concentration of polymer, is expressed in convenient units, traditionally g/100 cm but kg/m in SI units. The viscosity number and logarithmic viscosity number vary with concentration, but each can be extrapolated (Fig. 9) to zero concentration to give the limiting viscosity number (intrinsic viscosity) (Table 2). 

Fig. 9. Plots of viscosity number (/c) and the logarithmic viscosity number (/c) vs concentration. Extrapolations to 2ero concentration...

Zafarani-Moattar, M.T. and Shekaari, H. Volumetric and speed of sound of ionic liquid, l-butyl-3-methylimidazolium hexafluorophosphate with acetonitrile and methanol at T = (298.15 to 318.15) K, /. Chem., Eng. Data, 50,1694,2005. Wang, J. et al.. Excess molar volumes and excess logarithm viscosities for binary mixtures of the ionic liquid l-butyl-3-methylimidazolium hexafluorophosphate with some organic solvents, /. Solution Chem., 34, 585, 2005. 

Figure 11. A plot of the rate of increase of logarithmic viscosity vs. the feed composition in mole fractions of DCP at 140° C...

Figure 12. A double-logarithmic plot of the rate of increase of logarithmic viscosity vs. the feed composition in mole fractions of DCP (----------------------) at 140°C and (---) at 155°C...

Asphaltene content bears directly on the physical properties of the liquid product. Viscosity is of particular interest because of the importance of this parameter to operation of liquefaction plants and as a measure of the extent of liquefaction. The correlation between asphaltene content and the viscosity of the liquid has been a subject of a number of investigations (23-27). The logarithm of the viscosity ratio, In 7j/rj0 (where i and y0 are the viscosities of the solution and solvent, respectively) was found to be a linear function of concentration when asphaltene was redissolved in the pentane-soluble oil isolated from a coal-derived liquid (24). The slopes of these lines, termed the logarithmic viscosity numbers, are a measure of the contribution to the viscosity of a solution attributable to asphaltene. By comparison of logarithmic viscosity numbers of asphaltenes and their acidic and basic subfractions, it was determined that intermolecular association, which is especially strong between the acid and base subfractions, is responsible for a significant portion of the viscosity of these solutions. 

Comparison of extrapolations obtained by this equation provides some insight into the relative importance of phenol content and molecular weight to viscosity. For example, a typical asphaltene from a noncatalytic process might have a phenol content of 2 meq/g and a molecular weight of 700. The calculated logarithmic viscosity number is 5.7 mL/g. By extrapolation in the... 

Inherent viscosity Logarithmic viscosity number Vrel 1 itth... 

Figure 2.18 Variation of logarithmic viscosity as a function of inverse temperature for a simple glass forming liquid (schematic), r] is in Poises.

Inherent Viscosity (r jnh) In solutions and colloidal dispersions, the natural logarithm of the relative viscosity (rj/rjQ), all divided by the solute or dispersed-phase concentration (C). r/jnh = C l In(ri/ri0). In the limit of vanishing concentration, it reduces to the intrinsic viscosity. Also termed the logarithmic viscosity number. 

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