Relative viscosity, dilute polymer solutions

The relative viscosities of polymer solutions are measured at different concentrations and a plot of the reduced viscosity versus concentration is made, in order to extrapolate to zero concentration. The concentration dependence of the viscosity of polymer solutions, in the dilute regime, may be expressed by several linear equations. For practical extrapolation to zero concentration, the most commonly employed are the Huggins equation ... 

Capillary viscometry is used for the determination of relative viscosity of polymer solutions in an appropriate solvent at diluted concentrations. Relative viscosity is dependent on concentration, so the concentration is specified for the solution. Relative viscosity is also dependent on the viscometer used therefore, the size of the tube used for the measurement... 

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... 

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. 

Two replicates from each of the experimental treatments were evaluated for changes in viscosity. Dilute solutions (0.10, 0.20, 0.30, 0.40 and 0.50 g/lOOml) of nylon 6,6 dissolved in 90% formic acid were made. Viscosities of the dilute polymer solutions were determined at 25 + O.l C using a size 75 Cannon-Fenske capillary viscometer. Flow time measurements were repeated for each solution and for the pure solvent until three consecutive readings within 0.2 seconds or 0.1% of the mean were obtained (24). The average of the three consecutive flow times was used to determine the relative viscosity for each solution. 

In addition, for the evaluation of the relative viscosity ri. (Eq. 2.9), only the determination of the running times of the pure solvent and the sample solution is necessary. The assumption is that the density of the dilute polymer solution Psoimion equals the density of the pure solvent Psoivent) because of the very small polymer concentration /jr ... 

The automatic relative viscometer is ideally suited for measuring dilute polymer viscosities. It provides faster analysis and greater precision than is obtainable with conventional glass tube viscometers (Ubbelohde or Cannon-Fenske), which it replaces. The principle of operation is based on measurement of pressure drops due to the continuous forced flow of solvent and sample through two stainless steel capillary tubes placed in series. The pressure drop across each capillary tube obeys Poiseuille s law. The pressme drop is measured by a differential pressure transducer. The sample solution is loaded into a sample loop via a syringe pump and then pushed into one of the two capillaries. A steady-state condition is reached when the sample solution completely fills capillary 2, solvent remaining in capillary 1 at all times. The relative viscosity of the sample solution is determined simply and directly by the ratio of the pressure drops. From the measured relative viscosity, all other solution viscosity measurements can be calculated. Solution viscosities are determined by the viscosity of the sample relative to the reference solvent. The relative viscometer measures the solvent and sample viscosity simultaneously, so errors due to temperatme fluctuation and solvent variations are avoided. The main advantages of this approach are ... 

I. To illustrate a dilute polymer solution, in which the viscoelasticity is a relatively minor perturbation of the Newtonian behavior of the solvent a solution of atactic polystyrene, 0.015 g/ml in Aroclor 1248, a chlorinated diphenyl with viscosity 2.57 poise at 25°C. The weight-average molecular weight was 860,000 with narrow molecular weight distribution. Dynamic shear data by Massa, Schrag, and Ferry are reduced to 25°C. 

Intrinsic viscosity (rj) is the viscosity of an infinitely diluted polymer solution. It is a measure of the hydrodynamic volume occupied by a macromolecule, which is closely related to the size and conformation of the chain, but is independent of concentration of macromolecule. In dilute solutions, by definition, the polymer chains are separated and there is negligible interaction between them. Therefore, the (rj) of polymer in solution depends only on the dimension and the molecular weight of polymer chain. Experimentally determined values of the relative and specific polymer viscosities were used to calculate it, according to Huggins [53] and Kraemer [64] equations given by... 

Viscosity—Concentration Relationship for Dilute Dispersions. The viscosities of dilute dispersions have received considerable theoretical and experimental treatment, partly because of the similarity between polymer solutions and small particle dispersions at low concentration. Nondeformable spherical particles are usually assumed in the cases of molecules and particles. The key viscosity quantity for dispersions is the relative viscosity or viscosity ratio,... 

The most interesting result of Refs. [58, 59] concerns the crossover regime between dilute and semidilute regions of polymer 0-solution. The author shows that in this crossover regime there exists the critical concentration c corresponding to the appearance of an infinite cluster of entangled with each other macromolecules. It is also shown that near this critical concentration the relative viscosity t r of the 0-solution has a scaling form ... 

Furthermore, if what we want to determine is the frictional forces between a single polymer molecule and the solvent, then we need to make the measurements in dilute solution, so that there is no contribution from poly-mer/polymer interactions. In fact, just as in osmometry and light scattering, we measure the relative viscosity over a range of dilute solution concentrations and extrapolate to zero concentration. 

The subscript 0 refers to the pure solvent) Because we are dealing with dilute solutions, we can make the additional assumption that the density of die solutions and solvent are (almost) the same and end up with the relative viscosity being equal to the ratio of ther time it takes the solution to pass between the marks relative to the time taken by the pure solvent If the relative viscosity depends in a simple way on the frictional forces between the polymer and solvent, then one might expect that a plot of versus c, the concentration, would be linear, as 77 should increase with how much polymer is present. Its slope, however, should be proportional to the size of the polymer molecule, in that you would expect r nl to increase at a faster rate with concentration for larger molecules... 

Many foods contain high-molecular weight polymers, such as proteins, pectins, and others. Often, they contribute significantly to the structure and viscosity of foods. In dilute solutions, the polymer chains are separate and the intrinsic viscosity, denoted as [ ], of a polymer in solution depends only on the dimensions of the polymer chain. Because [ ] indicates the hydrodynamic volume of the polymer molecule and is related to the molecular weight and to the radius of gyration, it reflects important molecular characteristics of a biopolymer. The concentrations of polymers used should be such that the relative viscosities of the dispersions are from about 1.2 to 2.0 to assure good accuracy and linearity of extrapolation to zero concentration (Morris and Ross-Murphy, 1981 da Silva and Rao, 1992). Intrinsic viscosity can be determined from dilute solution viscosity data as the zero concentration-limit of specific viscosity (ijsp) divided by concentration (c) ... 

As stated in Chapter 1, for the determination of intrinsic viscosity, [ ], of a polymer, viscosity values of several dilute solutions, when the relative viscosities ( / s) of the dispersions are from about 1.2 to 2.0, are determined. To facilitate such measurements, the so called Ubbelohde glass capillary viscometer is used that has a large reservoir to permit several successive dilutions of a polymer solution (Figure 3-19). Because intrinsic viscosity measurement is important, the test procedure for using the Ubbelohde viscometer is outlined here in brief (Cannon Instrument Co., 1982). 

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