Intrinsic viscosity defined

Brenner (1974) has presented numerical results for the suspension stresses in various flows. Figure 6-14 plots the intrinsic viscosity [defined in Eq. (6-6)] for oblate and prolate spheroids of various aspect ratios as functions of the Peclet number. Note that as the aspect ratio of the spheroid increases, the zero-shear viscosity increases, and the suspension shows more shear thinning. The suspension also becomes more elastic when the aspect ratio p for prolate or 1/ for oblate spheroids) is large see Fig. 6-15, which plots Ni N2 versus Pe for prolate spheroids of various aspect ratios p. Typically, N2 is roughly an order of magnitude less than Ni, so this plot of Nj, mainly reflects the behavior of V,. 

Viscosities are often expressed relative to the viscosity of the pure solvent by introducing the terms relative viscosity ( /r), specific viscosity (//sp) and intrinsic viscosity ([> ]), defined as follows ... 

If it is recalled that the so-called intrinsic viscosity, defined as... 

Particles dispersed in an aqueous medium invariably carry an electric charge. Thus they are surrounded by an electrical double-layer whose thickness k depends on the ionic strength of the solution. Flow causes a distortion of the local ionic atmosphere from spherical symmetry, but the Maxwell stress generated from the asymmetric electric field tends to restore the equilibrium symmetry of the double-layer. This leads to enhanced energy dissipation and hence an increased viscosity. This phenomenon was first described by Smoluchowski, and is now known as the primary electroviscous effect. For a dispersion of charged hard spheres of radius a at a concentration low enough for double-layers not to overlap (d> 8a ic ), the intrinsic viscosity defined by eqn. (5.2) increases... 

In the case of nonspherical axisynunetric particles, Equation 11.35 is no longer valid and the intrinsic viscosity, defined as the low volume fraction limit of the reduced viscosity, is no longer 2.5 due to the energy dissipation increase. The intrinsic viscosity has been calculated under specific conditions for a given aspect ratio r. Limiting values are shown in Table 11.3. For more details, read references [7] and [24],... 

Anotlier simple way to obtain the molecular weight consists of measuring tire viscosity of a dilute polymer solution. The intrinsic viscosity [q] is defined as tire excess viscosity of tire solution compared to tliat of tire pure solvent at tire vanishing weight concentration of tire polymer [40] ... 

Hven fractionated polymer samples are generally polydisperse, which means that the molecular weight determined from intrinsic viscosity experiments is an average value. The average obtained is the viscosity average as defined by Eqs. (1.20) and (2.40) as seen by the following argument ... 

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 intrinsic viscosity usually changes rapidly with temperature in the vicinity of the -point hence it may be necessary to define this temperature experimentally with some accuracy—preferably within a degree or two. The -point may be deduced from accurate osmotic or... 

In their seminal work in 1949, Zimm and Stockmayer [69] defined the ratio of the mean square radii of gyration of a branched and a linear polymer of equal molecular weight as the parameter g and is related to the parameter g, which is the ratio of the intrinsic viscosities of a branched and a linear polymer [65-69]. 

In a polymer solution the specific viscosity is defined as tjsp — (tj — ri0)/t]0 with the solution and solvent viscosity i] and i]lt, respectively. The intrinsic viscosity (Staudinger index) of a polymer is defined as... 

Intrinsically conducting polymers, 13 540 Intrinsic bioremediation, 3 767 defined, 3 759t Intrinsic detectors, 22 180 Intrinsic fiber-optic sensors, 11 148 Intrinsic magnetic properties, of M-type ferrites, 11 67-68 Intrinsic photoconductors, 19 138 Intrinsic rate expressions, 21 341 Intrinsic semiconductors, 22 235-236 energy gap at room temperature, 5 596t Intrinsic strength, of vitreous silica, 22 428 Intrinsic-type detectors, cooling, 19 136 Intrinsic viscosity (TV), of thermoplastics, 10 178... 

Intrinsic-viscosity measurement leads to the viscosity-average Molecular weight, which may be defined as under ... 

The most widely accepted parameter defining the elution volume V in SEC is the hydrodynamic volume, (13) which for flexible coils of finite dilution is proportional to the product of the molecular weight M and the intrinsic viscosity [n] ( =... 

As specific viscosities are additive in the limit of infinite dilution, the weight average intrinsic viscosity is obtained for a polydisperse polymer and My is defined as... 

Benoit and co-workers [18] proposed that the hydrodynamic volume, Vr which is proportional to the product of [17] and M, where [17] is the intrinsic viscosity of the polymer in the SEC eluent, may be used as the universal calibration parameter (Fig. 18.3). For linear polymers, interpretation in terms of molecular weight is straightforward. If the Mark-Houwink-Sakurada constants K and a are known, log [t7]M can be written log M1+ + log K, and VT can be directly related to M. The size-average molecular weight, Mz, is defined by this process ... 

Much the most usual method of estimating branching is from the intrinsic viscosity ratio g1, defined in Eq. (4.2). In addition to the intrinsic viscosity of the sample, its (viscosity-average) MW must also be known, so that the denominator of the fraction (4.2) can be found. It is usual to use the light scattering technique for this, assuming that Afw = or if any information on the MWD is available, a correction may be applied to M . Recently it has become common to combine GPC measurements with those of viscosity see Subsection 9.2.4. 

The length L and diameter d of a rigid rod are related to the major axis a and minor axis b of the equivalent ellipsoid of revolution by a=L and b=(3/2)ll2d. It should be noted that, for actual molecules in solution, the quantity d can be defined only vaguely. With these relations, Simha s equation (64) for the intrinsic viscosity of an elongated ellipsoid of revolution can be rewritten for a thin rod (L/d> 1)... 

Other dimensionless groups that compare the thickness of the adsorbed polymer layer to the radius of the particle or the radius of gyration of the polymer to the particle radius in polymer/colloid mixtures can also be easily defined. We are mostly concerned with the volume fraction and the Peclet number Pe in our discussions in this chapter. However, the other dimensionless groups may appear in the equations for intrinsic viscosity of dispersions when the dominant effects are electroviscous or sterically induced. 

If intrinsic viscosity is used to evaluate the molecular weight of a polydisperse sample, the molecular weight so obtained is an average value. Equation (1.20) defined the viscosity average, which is the kind of average obtained. We are now in a better position to see how this comes about. 

To this end, branching has been determined conventionally in dilute solution by the ratio of intrinsic viscosities of branched and linear polymers having the same molecular weight, defined by (3) ... 

Tn GPC the product [77] M has been widely accepted as a universal calibration parameter, where [77] is the intrinsic viscosity and M is the molecular weight. This product is defined by the Einstein-Simha viscosity expression (I) as... 

MARK.-HOUW1NK EQUATION. Defines the relationship between the intrinsic viscosity and molecular weight for homogeneous linear polymers. 

Calculation of the Endocellulase Activity from the Intrinsic Viscosity Values. The enzymic degradation of polymeric substrates can occur at different bonds in the same substrate molecule, and the enzymic activity has to be defined here as the initial number of moles of glyco-sidic bonds split per second (53). This definition corresponds to the definition of the katal, symbolyzed kat. This unit is defined as the catalytic amount of any catalyst (including any enzyme) that catalyzes a reaction rate of one mole per second in an assay system (54), and it is recommended by the International Union of Pure and Applied Chemistry (55) for the quantitative evaluation of catalytic activities. 

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