Example calculations intrinsic viscosity

Finally, we note that both solvation and ellipticity can occur together. The contours shown in Figure 4.13a illustrate how various combinations of solvation and ellipticity are compatible with an experimental intrinsic viscosity. The particle considered in Example 4.4 has an intrinsic viscosity of 4.50 and was calculated to be hydrated to the extent of 0.60 g HzO per gram of protein. The same value of [17] is also compatible with nonsolvated ellipsoids of... 

EXAMPLE 13.5 Determination of the Thickness of Adsorbed Polymer Layer from the Intrinsic Viscosity of the Dispersion. An adsorbed layer of thickness 8RS on the surface of spherical particles of radius R increases the volume fraction occupied by the spheres and therefore makes the intrinsic viscosity of the dispersion greater than predicted by the Einstein theory. Derive an expression that allows the thickness of the adsorbed layer to be calculated from experimental values of intrinsic viscosity. 

The enzymic activity was proportional to the change of the inverse of the numerical average molecular weight per time unit. The linear relationship between Mv and Mn allowed a simple calculation of the activity from the knowledge of the intrinsic viscosity at zero shear rate as a function of the reaction time. A practical example is given. 

An example illustrating the application of Eq. (2.4) for calculating Mn is shown in Fig. 2.2. The position of the line at 45° reflects the exact equality of the Mn values calculated from the concentration of active centers and those determined by measurement of intrinsic viscosity, [r ]. Bearing in mind possible experimental errors and the accuracy of the equation relating [tj] and Mn, we can conclude that the correspondence between the two series of Mn values is satisfactory. 

If the particles are strongly anisotropic then, as illustrated in Figure 8.9(a), their rotational motion in the shear field is greatly enhanced. Additional energy is dissipated in maintaining this motion and the viscosity is increased. Since only single particles are concerned in this process, it will increase the intrinsic viscosity above the value of 2.5 for spherical particles. For example, it is calculated that for rods having an axial ratio of 15 the intrinsic viscosity rises to 4.0. 

The parameter ji defined in Eq 2.81 is a measure of the polymer-polymer miscibility — negative values indicate immiscibility, positive the miscibility. Three series of blends were examined (1) PVC/PMMA, (2) PiBMA/PMMA, and (3) PiBMA/PVC. In agreement with the calculated values of the parameter the first of these three blends was found miscible, whereas the two other immiscible in the full range of composition. However, the method is, at best, qualitative. For example, the effect of solvent on the parameter was not investigated, but fundamentals of intermolecular interactions make it dubious that non-polar and strongly polar solvents will lead to the same value of the parameter The author observed that the method breaks down for polymer pairs that form molecular associations. Intrinsic viscosity measurements were also used to evaluate intermolecular interactions in blends of cellulose diacetate with polyvinylpyrrolidone [Jinghua et al, 1997]. 

Because of the attraction and repulsion forces, the conventionally determined intrinsic viscosity of mixtures of different polymers may appear higher or lower than that calculated from Equation (9-125) from the mass contributions w, and intrinsic viscosities [17], of the components. Examples of this are the values for mixtures of poly(styrene) and poly(methyl methacrylate) (Table 9-5). 

One way to overcome such problems is to consider solvent(l)/polymer(2)/ polymer(3) ternary systems any method that determines either AG or its derivatives should make it possible to calculate Xi3- Thus, for example, osmotic pressure measurements were used to characterize PS/PVME blends dissolved in either toluene or ethylbenzene (Shiomi et al. 1985). The Xi3 was found to depend on the blends composition. Elimination of the solvent effects gave X23/E1 = —10 (7.41 — 11.0103). Thus, the system was expected to remain miscible up to a PVME volume fraction of 03 = 0.67. Osmotic pressure has also been used to determine X23 = 0.070 for PS with poly(p-chloro styrene) in toluene, 2-butanone, and cumene (Ogawa et al. 1986). For the same system, X23 = 0.087 was calculated from intrinsic viscosity measurements. Thus, the system is thermodynamically immiscible. More recently, osmotic pressure measurements in cyclohexanone of a ternary system resulted in X23ipoly(vinylchloride-co-vinylacetate) blends with a series of acrylic copolymers (Sato et al. 1997). 

Exercises and several practical examples of calculations of the molar mass or the intrinsic viscosity from [/2]-M-relationships and vice versa are given in [49]. 

Therefore the critical concentration is proportional to the reciprocal intrinsic viscosity. The factor of 2.5 assumes that the polymer coils behave like hard spheres in solution. Viscosimetric measurements for the determination of the intrinsic viscosity have to be performed in dilute solutions at concentrations clearly below c for an exact linear extrapolation according to the Huggins equation (Eq. 4.9). This condition is fulfilled for example in Fig. 4.2, where it is shown that the data points for the viscosimetric determination are below the critical concentration calculated from Eq. (7.7). 

The shape of the particles also has an effect on the viscosity. Most advanced ceramics are fabricated using nearly equiaxial particles, but the effect of shape would be important, for example, in the colloidal processing of ceramic composites reinforced with whiskers (short single crystal fibers) or platelets. Figure 4.43 shows the results of theoretical calculations for the intrinsic viscosity [i)] as a function of the axial ratio for particles with the shape of prolate ellipsoids. For an axial ratio of 15-20, which may be relevant to the use of whiskers or platelets in ceramic composites, the results show that [t ] has a value of —4.5 compared to 2.5 for spherical particles. 

As an example of the different results which are obtainable by the two procedures, we shall consider data on urea-denatured horse serum albumin. These data were obtained from parallel diffusion and viscosity measurements in solvents containing various amounts of urea (Neurath and Saum, 1939). The intrinsic viscosity increased and the diffusion coefficient decreased with increasing urea concentration. The value of w (and, therefore, 7,) was arbitrarily fixed. This then permitted a calculation of p to be made from a single hydrodynamic measurement since the value of 7 was assumed known at each concentration of urea. Thus, p was computed from V, determined from an equation equivalent to Eq. (1-3), using the viscosity data. An independent value of p was computed from 1/f, determined from Eqs. (I-IO) and (I-ll), using the diffusion data. The values of the dimensions computed from the viscosity and from the diffusion data are shown in Table IV. 

At a fixed DP the intrinsic viscosities of the maltodextrins are less than those of the cellodextrins. If it is assumed that the partial molar volume accurately describes the volume occupied by the "solute particle then it is possible to obtain information on particle shape through calculation of the value of v. Alternatively a spherical shape may be assumed and a volume calculated which represents the effective hydrodynamic volume of the malto-oligomer and "associated" water molecules (table III). For example, the extrapolated intrinsic viscosity of maltohexaose in water at 25 C is... 

Saito, et al.,[ prepared solutions of 0.1 g, 0.2 g, and 0.3 g of the vinylidene fluoride polymers in 50 ml of dimethylformamide (DMF) and measured the specific viscosity of these solutions at 30°C using a Ubbellohde viscometer. A plot of the ratio of specific viscosity to the corresponding solution concentration was made as a function of polymer concentration. The line of best fit to the data was extrapolated to zero concentration the intercept gave the value of the intrinsic viscosity for the polymer. Equation 5.13 could then be used to calculate the molecular weight of the polymer. A value of 300,000 was determined for the resin product of the copolymerization example previously described. This resin had excellent film forming properties as demonstrated by pressing 1 g of the poly-... 

Polyvinyl fluoride characterization as a resin has not been published. DuPont produces films (Tedlar ) which are specified by typical film properties (described in Ch. 13). One characteristic that has been described in a number of early patents is intrinsic or inherent viscosity to compare different grades of In an example, polyvinyl fluoride was dissolved by stirring at the reflux temperature in hot cyclohexanone and the relative viscosity R V) was measured in a bath at 144°C after 75 minutes. Time of efflux of PVF solution (Ti) and solvent (Tq) through a viscometer such as Canon-Fenske was measured and relative viscosity was calculated according to Eq. (5.17). The ratio of the natural logarithm of relative viscosity to the concentration of polyvinyl solution (C, g/dl) is called the intrinsic or inherent viscosity (in Eq. 5.18, dl/g). 

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