Viscosity characteristic

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

Because of the rotation of the N—N bond, X-500 is considerably more flexible than the polyamides discussed above. A higher polymer volume fraction is required for an anisotropic phase to appear. In solution, the X-500 polymer is not anisotropic at rest but becomes so when sheared. The characteristic viscosity anomaly which occurs at the onset of Hquid crystal formation appears only at higher shear rates for X-500. The critical volume fraction ( ) shifts to lower polymer concentrations under conditions of greater shear (32). The mechanical orientation that is necessary for Hquid crystal formation must occur during the spinning process which enhances the alignment of the macromolecules. 

The direct application of this expression in order to estimate the degree of thermomechanic destruction in connection with polymer processing is hindered because the process rate constant depends on the temperature and intensity of thermo-mechanical impact on a material. Consequently, of significant interest is the issue of selecting an attribute for characterizing the degree of destruction. Most researchers consider it worthwhile to simply use viscosity variable (r a) or characteristic viscosity variable. 

In extrusion problems, the rate of deformation is directly proportional to the rotational speed of the screw. Hence, a characteristic viscosity can be defined as... 

Assuming a characteristic viscosity of fj = me aTlA/n, where the characteristic rate of deformation is taken as 7 = u/b, where t f is the fill time and u = i 2/t / the characteristic velocity, we can write the viscosity in dimensionless form as... 

The exponents in the above expressions can be estimated beforehand from the dependence of the limiting values of the characteristic viscosity at low and high frequencies on the length of the macromolecule. 

The real and imaginary components of characteristic viscosity have been calculated according to equations (6.20) for zv = 2, (pi = 0.5, 0 = 0.5. The dashed curves depicts the alternation of the dependencies in the case when an internal relaxation process is taking into account, whereas equations (6.28) are used at r/2n = 10-5. 

The limit of the characteristic viscosity at low frequencies, according to (6.20), is defined as... 

For a non-draining coil, the characteristic viscosity defined by equation (6.23) can be expressed in the form... 

The initial characteristic viscosity defined by equation (6.23) is seen to be independent of the characteristics of intramolecular friction, but this is a consequence of the simplifying assumptions. It has been shown for a dumbbell (Altukhov 1986) that, when account of the internal viscosity and the anisotropy of the hydrodynamic interaction is taken simultaneously, the characteristics of these quantities enter into the expression for a viscosity of type (6.23). This result must be revealed also by the subchain model when account is taken of the anisotropy of the hydrodynamic interaction. 

The characteristic viscosity (6.22) is of special interest in the study of the influence of intramolecular friction on the dynamics of a macromolecule in a viscous liquid. At w —> oo, characteristic viscosity can be written as... 

Experimental studies indicate (Cooke and Matheson 1976, Noordermeer et al. 1975) that the limiting characteristic viscosity for a given polymer-homologous series is independent of the length of macromolecule and the type of solvent. Taking into account that t AT ", n AT-1 and yq M e, one can find the relation... 

The independence of the limiting characteristic viscosity on the type of solvent means that cpi is independent of the viscosity of the solvent, that is the dimensional characteristic of the internal friction of the macromolecule Cyi is proportional to the viscosity of the solvent and the internal friction is not solely internal. The conclusion that the solvent contributes significantly to the intramolecular viscosity was reported by Schrag (1991), and was dubbed as the solvent modification effect . 

The fact that the value of the characteristic viscosity at high frequencies is not zero indicates the existence of intramolecular (taking into account the solvent molecules) relaxation processes with relaxation times smaller than the reciprocal of the frequency of the measurement. The true limiting value is naturally zero and experiments sometimes reveal a step at a frequency uj which indicates the occurrence of a relaxation process with a relaxation time r a -1 which is compatible to the times of the deformation of a system. This phenomenon may be described by including the relaxing intramolecular viscosity, as it was done by Volkov and Pokrovskii (1978). 

It follows from equations (9.9) that the viscosity (or, what amounts to the same thing, the characteristic viscosity) is independent of the velocity gradient for flexible chains (p = 0). For chains with an internal viscosity, the viscosity... 

The polymers were fractioned into 8-14 components by coacervate extraction from the benzene - methanol system. For fractions and nonfractioned polymers, characteristic viscosities [t ], were me-asured. Because that was the first example of studying conformations of macromolecules of this ty-pe in diluted solutions, authors of the work [56] paid much attention to selection of an equation, which would adequately describe hydrodynamic behavior of polymeric chains. Figure 10 shows de-pendencies of [q] on molecular mass (MM), represented in double logarithmic coordinates. Parame-ters of the Mark-Kuhn-Hauvink equation for toluene medium at 25°C were determined from the slo-pe and disposition of the straight lines. 

In the first case, characteristic viscosity of the fraction, r ], with the known molecular mass in ideal -solvent was measured. This method is based on the known Flory-Fox relation [38], The second method represents measurements of the fraction [r ] in good thermodynamic solvents and extrapolation of experimental data in accordance with the known techniques [39 - 41], Because in the cur-rent work [36] all measurements were performed in good thermodynamic solvent, unperturbed di-mensions of macromolecules, , were determined by graphical extrapolation in accordance with the Shtockmayer-Fixman, suggested by the authors for flexible macromolecules, in [t ] M1/2-M12 coordinates (Figure 6). 

Table 5. Molecular masses and characteristic viscosities of copolymer 3 fractions (Table 1, structure I) at different temperatures...

Liquid polymers are useful as tackifiers for rubbers, 72) and acrylic coatings. The most interesting are hydroxytelechelic polybutadienes, especially liquid butadiene-acrylonitrile (85/15) copolymers (trademark CN-15, ARCO). This product, known since 1971 as a tackifier, has the following characteristics viscosity 493 poises at 30 °C, tv[n = 4400, hydroxyl number/chain = 2.5. The incorporation of 5% of CN-15 in ethylene-propylene rubber (EPT Nordel 1070) increases its tack considerably 173) close to that of natural rubber or butyl rubbers (Table 4.1). 

In Eqs. (10-20), the six Leslie viscosities are given in terms of the characteristic viscosities 1 and ao (described below), the tumbling parameter k, the second and fourth moments... 

The bend and especially the compressive moduli of lamellar block copolymers are therefore typically lower, or at least no higher, than those of small-molecule smectic-A liquid crystals, while the viscosities of the former are usually much larger than the latter. By analogy with nematics, for layered materials one can define characteristic Ericksen numbers as Erj = r]yh /K and Er = where is a characteristic viscosity and... 

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