Reduced specific viscosity, measurements

Table I illustrates the structures of the modified polyarylethers, their glass-transition temperatures, and their reduced specific viscosities (RV) measured in chloroform at 25°C at a concentration of 0.2 g/100 mL.

The reduced specific viscosities of GDH in solution with 10" M GTP and 10 M NADH have been measured, and a value of intrinsic viscosity of [17] = 3.2 ml/g obtained by extrapolation to zero protein concentration (107). The transverse and axial rotary frictional coefficients of macroscopic models, similar to the physical model depicted in Fig. 2, were measured, and the viscosity calculated from these coefficients agrees with the measured value however, it is not possible to define whether the subunits adopt a staggered or eclipsed conformation, as viewed down the threefold axis, and other models may give the same result. 

Polymer solutions are never ideal since dissolved macromolecules influence each other even at very low concentration. On the other hand, a reliable correlation of solution viscosity and molecular weight is only possible if the dissolved macromolecules are not affected by mutual interactions they must be actually independent of each other. Therefore, the viscosity of polymer solutions should be determined at infinite dilution. However, such measurements are impossible in practice. So one works at an as low as possible polymer concentration and extrapolates the obtained values to zero concentration. To do so, the elution time measurements are not only carried out for one single polymer concentration but for varying polymer concentrations (e.g., 10, 5, 2.5, 1.25 g/1). For each solution, the value of the reduced specific viscosity is figured out (the data will make evident that this quantity is clearly concentration-dependent even at the lowest possible polymer... 

Viscosimetric determinations. The Newtonian intrinsic viscosity of the xanthan molecule was determined by measuring the viscosities of several dilute polymer solutions with a Contraves Low-Shear viscometer. Extrapolation at zero polymer concentration of the reduced specific viscosity gave the value of the intrinsic viscosity, and the Huggins constant was calculated from the slope of the curve. 

The specific viscosity measures the sole contribution of the solute to the viscosity enhancement with respect to the solvent and is given by = (v ho)/ho- However, to compare different solutes, it is more convenient to consider the reduced viscosity which takes into account the solute concentration = (jl — o)/(C o)- Finally,... 

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). 

Experimental considerations For the measurement typically several concentrations are prepared and the specific viscosity t]sp or reduced viscosity f)red — r jr 0 are extrapolated to zero concentration. In the literature three different approaches are used to obtain the intrinsic viscosity and, with known [f)]-M relation, the molar mass. 

Intrinsic Viscosity. The intrinsic viscosities, [rf], of some of the crosslinked polymers (copolymer 2.2 mole % HEM A) were measured by successive dilution on the reacted solutions. Figure 12 shows that the change in [ry] at 25 °C. was, within the experimental error, related directly to the change in specific viscosity at 80°C. As Figure 13 shows, cross-linking reduced the intrinsic viscosity of the polymer solution and also altered the slopes of the lines for both rj/c and log (1 -f- rj)/c against c. 

Viscosity measurements of the polymer solutions are carried out with an Ubbelodhe viscometer. The viscosities are measured in dilute aqueous solution in neutral pH. The time of flow for solutions is measured at four different concentrations (i.e. 0.1%, 0.05%, 0.025% and 0.0125%). From the time of flow of polymer solutions (t) and that of the solvent (t, for distilled water), relative viscosity(Ti, ), specific viscosity (tj p), reduced viscosity (t ) and inherent viscosity(Tij jj) are obtained by the following relations ... 

At low concentrations, the specific viscosity /]sp of a polymer solution increases linearly with the concentration c. The Huggins Eq. (4.9) was developed to eliminate this concentration dependence. Dividing the specific viscosity by the concentration c gives the reduced viscosity /]red> hich should be independent of the concentration. The observed linear relation between the reduced viscosity is caused by intermolecular interactions. The Huggins constant is a measure for these intermolecular interactions (see Chap. 5). The linear relationship between the reduced viscosity q ed the concentration c is only valid at low concentrations. As soon as the concentration is so high that interactions between several polymer coils become important, q ed increases superproportional with the concentration. This behavior can clearly be seen in Fig. 5.1. 

In viscosimetric measurements the product KnX[q] is a measure for the solvent quality that describes these additional interactions and the expansion of the coil by the solvent molecules (similar to the exponent a of the [/j]-M-relationship see The influence of the solvent quality on the [/j)-M-relationship in Chap. 6). Solely at theta-conditions the Huggins constant is zero and therefore the product KhX[/jP. At theta-conditions, the long-range interactions between polymer segments are compensated by the solvent even at higher concentrations (see Chap. 8). In this case, the specific viscosity /jgp of a dilute solution increases linearly with the concentration and the reduced viscosity is independent of the concentration and is equivalent to the intrinsic viscosity. 

Relative viscosity and specific viscosity are dimensionless, but reduced viscosity has units of the reciprocal of concentration, or dl/ g. The value of reduced viscosity varies with polymer concentration. Measurements can be made at several concentrations (usually four) and then presented graphically (see Figure 3.3). 

The specific viscosities are measured for a series of polymer solutions of varied polymer concentrations, which can easily be done by dUuting the initial polymer solution. The obtained specific viscosities are then divided by the respective concentration, to give the reduced viscosity ( /red)- As can be seen from (6.7), the intrinsic viscosity (//iv) of the polymer solution is... 

This test method is used to determine dilute solution viscosity for all polymers that dissolve completely without chemical reaction or degradation to form solutions that are stable with time at a temperature between ambient and approximately 150°C. The results of the tests are expressed as relative, inherent, or intrinsic viscosity. Reduced and specific viscosity can also be calculated. Table 7-4 shows recommended test conditions for dilute solution viscosity measurements. 

Viscosity measurements of diluted HPMC solutions were performed by Ubbelhode capillary viscometer (flow time for bidistilled water was 195.6 s at 30 °C), immersed in a water thermostat at 30 °C. Proper volumes of 3.0 g/lOOcm SDS solution were added to 15 cm of HPMC solution in order to obtain desired SDS concentration. For each solution, 3-5 viscosity measurements were taken and average values were calculated. The results were expressed as specific, reduced and intrinsic viscosity. 

Specific viscosity (risp) of FAXMB and FAXN solutions were measured with an AVS 400 capillary viscosimeter (Schott Cerate, Hofheim, Germany), equipped with an Oswald capillary tube (flow water time 75.15 s). The risp was related to the FAXMB or FAXN concentration (risp/C) to obtain their reduced viscosity tired (mL/g) according to Rao (1993). The intrinsic viscosity [tj] was determined by the Mead, Kraemer and Fouss method (Kraemer, 1938 Mead and Fouss, 1942). 

---