Polymer solutions viscosity measurements

The polymer solution viscosity measured before and after exposure to light may also be used in evaluating the quantum cleavage yield of the macromolecular chain, through Eq. (6) in which (MQo and (MQt are viscosity-averaged molecular weights of the initial and irradiated polymer ... 

PPS is well-recognized for its exceptional chemical resistance. There are no known solvents for PPS below 200°C. A comprehensive survey of solvents for PPS has been published (115). Extreme conditions are required to dissolve PPS in both common and exotic solvents. Solution viscosity measurements are made difficult by this high temperature requirement. Inherent viscosity measurements are performed in 1-chloronaphthalene at 206°C at a concentration of 0.4 g of polymer per deciliter of solution. The inherent viscosity of PPS solutions shows a usefiil response to increa sing molecular weight. Table 2 shows a correlation of inherent viscosity measurements with melt flow measurements. 

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. 

In principle all methods except viscosity measurement can be used to obtain absolute values of molar mass. Viscosity methods, by contrast, do not give absolute values, but rely on prior calibration using standards of known molar mass. The relationship between polymer solution viscosity and molar mass is merely empirical but the techniques are widely used because of their simplicity. All of the absolute methods are time-consuming and laborious and are not used on a routine basis. As well as the techniques already mentioned, there is the size-exclusion method of chromatography known as Gel-Permeation Chromatography (GPC). All of these methods are discussed in detail in the sections that follow. 

Solution viscosity measurements have sometimes been utilized as qioality control tests for this polymer. Chromatographs of three samples that showed Identical intrinsic viscosities (0.8 g/dl) in toluene are shown in Figure 9. These chromatographs indicate that the identical viscosities are the result of different combinations of high and low MW components. These three polymer samples probably have significantly different physical properties and if viscosity measurments alone are utilized for quality control purposes, they may be quite misleading. 

Fig Capillary viscometers commonly used for measurement of polymer solution viscosities (i) Ostwald-Fenske and (ii) Ubbelohde. 

Solution viscosity measurements for Mn are calibrated from the flow characteristics of linear molecules of the equilibrium molecular weight distribution. Branched polymers have a lower radius of gyration for their molar mass than the corresponding linear molecule. One, therefore, expects different flow properties as branching increases, hence causing the viscosity numbers to become less and less accurate and so should only be used for trends - not exact calculations. 

The experimental determination of polymer intrinsic viscosity is done through the measurement of polymer solution viscosity. The connotation of intrinsic viscosity [hi/ however, is very different from the usual sense of fluid viscosity. Intrinsic viscosity, or sometimes called the limiting viscosity number, carries a far more reaching significance of providing the size and MW information of the polymer molecule. Unlike the fluid viscosity, vdiich is commonly reported in the poise or centipoise units, the [h] value is reported in the dimension of inverse concentration xinits of dl/g, for exanple. The value of [hi for a linear polymer in a specific solvent is related to the polymer molecular weight (M) through the Mark-Houwink equation ... 

The dilute solution viscosity measurement is applicable to all polymers that dissolve to give stable solutions at temperatures close to the boiling point of the solvent. 

Viscometry. Viscosities of aqueous polymer solutions were measured using a Cannon-Fenske 50 viscometer immersed in a 20°C water bath. The limiting viscosity number was determined from 5 viscosity measurements using the Huggins equation (9). The limiting viscosity number of aged poly( 1-amidoethylene) in 0.01 M aqueous Na2SC>4 was 2.45 dL/g. 

Here kH is the Huggins coefficient. The intrinsic viscosity decreases and the Huggins coefficient increases, as micelles become smaller. On micellization, ijsp/c has been observed to increase for some systems but to decrease for others, and unfortunately there are no firm rules governing which case will prevail for a given block copolymer solution. The viscosities of polymer solutions are measured in capillary flow viscometers, which are described in detail by Macosko (1994). 

The concentrated solution viscosity measurement yields the weight-average degree of association of active chain ends rather than the more conventional number-average (mole fraction) value. However, the calculation of the equilibrium constant for association, K, can be accomplished if Mw and the heterogeneity index of the polymer sample are known. The latter parameter can be determined via postpolymerization characterization. 

A solution viscosity measurement is a hydrodynamic-thermodynamic technique, and the extent to which a polymer molecule increases the viscosity of a solvent depends on the nature of its interactions with that solvent (as well as on its own molecular weight). These interactions are characterized by the quantity a that appears in equation (3). The calibration of the method, using samples, of the same polymer having known molecular weights, in essence determines its value. The disadvantage of this calibration requirement is offset by the simplicity of the experimental measurements. 

Figure 2 shows the viscosities of the polymer solutions as measured at 25° 0.05 °C. in an Ubbelohde viscosimeter employing a concentration of 0.52 gram of polymer per 100 ml. of m-cresol. The viscosimeter had a flow time of more than 100 sec. for the pure solvent. 

My is derived from solution viscosity measurements through the Mark-Houwiiik equation [ii] = K My, where [n] is the limiting viscosity number and K and I are constants which depend on the polymer, solvent, and experimental conditions, but not on M (p. 96). 

The procedures outlined below do not remove the effects of polymer-solvent interactions, and so A/v of a particular polymer sample will depend to some extent on the solvent used in the solution viscosity measurements (Section 3.3.1). 

Solution viscosity measurements require very little investment in apparatus and can be carried out quite rapidly with certain shortcuts described in Section 3.3.4. As a result, this is the most widely used method for measuring a polymer molecular... 

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. 

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 ... 

This equation will be derived in Chapter 8. Dilute solution viscosity measurements are important characterization tools for polymers because... 

Tang et al. (1998) measured polymer solution/oil (P/0) relative permeability curves using the steady-state flow method. To calculate the polymer solution viscosity, they used... 

The dilute solution viscosity measurements were conducted using Ubbelohde viscometers generally conducted at 25 + 0.05°C in a thermo-stated bath. The reduced viscosity or viscosity number [defined as (t -ri0)/ri0c, where 0 is the viscosity of the polymer solution, 0o is the viscosity of the solvent (or mixed solvent), and c is the concentration of polymer in g/100 mL] was calculated for each solution measured. 

The so-called 0 (theta) conditions, in marginally weak solvents, are usually preferred in solution viscosity measurements. Polymer chains are believed to manifest their "unperturbed dimensions" under 0 conditions. This is a result of the nearly perfect balancing of the effects of "excluded volume" (a consequence of the self-avoidance of the random walk path of a polymer chain in a random coil configuration) by unfavorable interactions with the solvent molecules. 

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