Viscosity limiting number

Viscosity, T, can be expressed, in the region of low solute concentration c in the form  

Where r sp is the specific viscosity and r r(=ri/rio) is the viscosity ratio (or relative viscosity). 

The Mark-Houwink-Sakurada (MHS) equation (eqn (5.5)) offers a convenient means of determining the molecular weight of a polymer which is soluble in a solvent. It has been experimentally confirmed that the parameters Km and a in the MHS equation are constant over a wide range of molecular weights under the constraints of zero shear rate at given temperature for a 

The [T ] value of a branched polymer is smaller than that of the corresponding linear polymer. The MHS equation of a segmented polyurethane, synthesised from methylenebis (4-phenyl isocyanate), polycaprolactone and 2-aminoethanol in N, A -dimethylacetamide shows upward curvature at Mw 10 owing to an increase in the degree of branching per molecule in the region of 10 [41]. Therefore, it should be noted that of the branched polymer cannot be unconditionally determined by using the MHS equation established for the linear polymer. 

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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). 

The relative viscosity of a dilute dispersion of rigid spherical particles is given by = 1 + ft0, where a is equal to [Tj], the limiting viscosity number (intrinsic viscosity) in terms of volume concentration, and ( ) is the volume fraction. Einstein has shown that, provided that the particle concentration is low enough and certain other conditions are met, [77] = 2.5, and the viscosity equation is then = 1 + 2.50. This expression is usually called the Einstein equation. 

Viscosity, intrinsic Also called limiting viscosity number. For a plastic, it is the limiting value of an infinite dilution. It is the ratio of the specific viscosity of the plastic solution to its concentration in moles per liter. 

Having obtained the value of the limiting viscosity number, we can calculate relative molar mass using the semi-empirical equation ... 

In the following sections, synthesis of the anionic polymers, copolymer molecular weight, limiting viscosity number, electrolyte effects, solution shear thinning, screen factor, polymer radius of gyration, and solution aging will be discussed and data on the copolymers presented. 

Assays. Nitrogen assays to determine 1-amidoethylene unit content were done by Kjeldahl method. Limiting viscosity numbers were determined from 4 or more viscosity measurements made on a Cannon-Fenske capillary viscometer at 30°C. Data was extrapolated to 0 g/dL polymer concentration using the Huggins equation(44) for nonionic polymers and the Fuoss equation(45) for polyelectrolytes. Equipment. Viscosities were measured using Cannon-Fenske capillary viscometers and a Brookfield LV Microvis, cone and plate viscometer with a CP-40, 0.8° cone. Capillary viscometers received 10 mL of a sample for testing while the cone and plate viscometer received 0.50 mL. 

Limiting Viscosity Number. Limiting viscosity numbers for the polymers in distilled water are given in Table 3 Limiting viscosity number increases with increasing copolymer molecular weight. 

Further, after 12 to 14 percent hydrolysis, limiting viscosity number of the derived, partially-hydrolyzed copolymer is 3 to 10 times larger than that of its nonionic precursor. The ratio of [n] after... 

Limiting Viscosity Number Limiting Viscosity Number... 

Comparison of the limiting viscosity numbers determined in deionized water with those determined in 1 molar sodium nitrate shows a 20 per cent decrease in copolymer intrinsic viscosity in the saline solution. These results are consistent with previous studies using aqueous saline solutions as theta solvents for 2-propenamide polymers(47) Degree of hydrolysis controls the value of limiting viscosity number for the hydrolyzed copolymers in distilled water. 

Figure 14 gives limiting viscosity numbers for hydrolyzed copolymer 11 as a function of shear rate. Since limiting viscosity number is a function of molecular size, these data show that solution pseudoplasticity occurs because of compaction of the solvated polymer with increasing shear. 

Figure 14. Limiting viscosity numbers for hydrolyzed poly(starch g (2 propenamide)), sample 11.

Hydrolysis increases the terpolymer limiting viscosity number in water by a factor of up to 45. Other previously published data(66-68) show that these terpolymers are nonnewtonian viscosifiers, metal-ion complexing agents, and effective flocculators. These materials are still "small" molecules in aqueous solution, however, and do not function as effectively when used 1. as nonnewtonian viscosifiers or 2. drag reducing agents as do poly(l-amidoethylene-co-(sodium 1-carboxylatoethylene)) copolymers. 

Schoch and coworkers33 have examined the limiting viscosity number of... 

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