Internal viscosity characteristic time

The excluded-volume parameter for PS was derived from viscosimetric data in good solvent collected by Nystrom and Roots for different molecular masses [113], The internal viscosity characteristic time Tq was obtained from best-fit data [12] of mechanical-dynamical results due to Massa, Schrag, Ferry, and Osaki [102,103] (see Figure 10). In analogy with what was previously found by other authors, notably Kirkwood and Riseman on the same polymer (PS) with different solvents [19], fitting the experimental data seems to require two different values of R ff = C/6to/s, one to obtain v q) through Eqn. (3.1.9) and a second one to evaluate to = I kg T, the latter... 

At low frequencies when power losses are low these values are also low but they increase when such frequencies are reached that the dipoles cannot keep in phase. After passing through a peak at some characteristic frequency they fall in value as the frequency further increases. This is because at such high frequencies there is no time for substantial dipole movement and so the power losses are reduced. Because of the dependence of the dipole movement on the internal viscosity, the power factor like the dielectric constant, is strongly dependent on temperature. 

In this case the theory, apart from the characteristic Rouse relaxation time r, contains three more parameters, namely the relaxation time r of the medium, the measure B of the increase in the resistance of the particle when it moves among the chains, and the measure of internal viscosity E associated with resistance to the deformation of the coil due to the present of ambient macromolecules. 

As far as the characteristic angle (10.28) is concerned, taking into account the dependence of the relaxation time and of the internal viscosity on the number of the mode (formulae (2.27) and (2.31)), one can write, with the aid of the zeta-function ()(x),... 

As a conclusion, if the viscosity ratio p between the internal and external phases lies between 0.01 and 2, the shear applied on a polydisperse emulsion made of large drops leads to a monodisperse one with a mean diameter governed by the stress. This fragmentation occurs through elongation of the drops and the development of a Rayleigh instability with a characteristic time of the order of one second. The obtained monodispersity probably results from the fact that the Rayleigh instability develops under shear for a critical diameter of the deformed drops. 

The theory of relaxation processes in macromolecules with internal rotation or torsional vibrations immersed in a viscous solvent with viscosity rj 0.01 P shows that, for local motions of a relaxation type with characteristic times t > 10 s, the so-called condition of high friction is satisfied in a vast majority of cases. Relaxation times are given by the equation... 

The preceding conclusions may be suitably checked upon comparison with PDMS. We send the interested reader to ref. 15 for the choice of the parameters. Unlike the case of PS, a molten polymer sample was also considered, in which case the hydrodynamic interaction was assumed to vanish [i.e., v(q) = 1] because of the hydrodynamic screening exerted by the polymer chains. In view of the apparently low energy barriers to the rotation around SUO chain bonds, we assumed the internal viscosity to be absent, that is. To = O Incidentally, we remark the difference from the case of polystyrene where, in addition to the intrinsic rotation barrier around C-C bonds adjoining tetrahedral-coordinated atoms ( 3 kcal/mol), the side phenyl rings contribute significantly to the rotational hindrance. In Figure 13 the characteristic times ti/2 [13/4 for the melts [115]] are plotted versus Q. 

Here, Ty is the so-called Vogel temperature, at which the viscosity diverges to infinity. The parameter Tq is the characteristic time related to molecular vibration and B is the activation temperature. Even in the case of the internal phase, the... 

Some information concerning the intramolecular relaxation of the hyperbranched polymers can be obtained from an analysis of the viscoelastic characteristics within the range between the segmental and the terminal relaxation times. In contrast to the behavior of melts with linear chains, in the case of hyperbranched polymers, the range between the distinguished local and terminal relaxations can be characterized by the values of G and G" changing nearly in parallel and by the viscosity variation having a frequency with a considerably different exponent 0. This can be considered as an indication of the extremely broad spectrum of internal relaxations in these macromolecules. To illustrate this effect, the frequency dependences of the complex viscosities for both linear... 

The fact that the velocity of a fluid changes from layer to layer is evidence of a kind of friction between these layers. The layers are mathematical constructs, but the velocity gradient is real and a characteristic of the fluid. The property of a fluid that describes the internal friction or resistance to flow is the viscosity of the material. Chapter 4 is devoted to a discussion of the measurement and interpretation of viscosity. For now, it is enough for us to recall that this property is quantified by the coefficient of viscosity 77 of a material. The coefficient of viscosity has dimensions of mass length-1 time-1, kg m-ls-1 in SI units. In actual practice, the cgs unit of viscosity, the poise (P), is widely used. Note that pure water at 20°C has a viscosity of about 0.01 P = 10-3kgm-ls-1... 

Before we come to further determinations of the unknown quantities, we shall estimate here the effect of the internal angular momentum on the motion of the liquid. Let a be the characteristic size of internal structural elements, then Sik pav, <7ik pv/a, where p is the viscosity coefficient. An estimate of the characteristic relaxation time of the balance of the internal and external rotation follows from equation (8.7)... 

Multi-Grout AV-202 (Avanti International) is a similar product, also of relatively high viscosities, described as water-soluble, hydrophillic polyurethane prepolymers. Gel time characteristics are shown in Fig. 11.46. 

The performance of an extruder is determined as much by the characteristics of the feedstock as it is by the machine. Feedstock properties that affect the extrusion process inciude buik properties, meit flow properties, and thermal properties. Important buik flow properties are the buik density, compressibility, particle size, particle shape, external and internal coefficient of friction, and agglomeration tendency. Important melt flow properties are the shear and eiongational viscosity as a function of strain rate and temperature. The commonly used melt indexer provides only limited information on the meit viscosity. Important thermal properties include the specific heat, the glass transition temperature, the crystalline melting point, the latent heat of fusion, the thermal conductivity, the density, the degradation temperature, and the induction time as a function of temperature. 

Many products in the chemical and agrochemical, cosmetic, pharmaceutical, and food industries are emulsion-based. Their internal structure is composed of one or more fluids, with one being flnely dispersed as droplets within the other one. The size distribution of the droplets mainly influences characteristic product properties as color, texture, flow- and spreadability, viscosity, mouth-feel, shelf-life stability, and release of active ingredients. It therefore has to be maintained for the life-time of a product. Due to the extremely high interfacial area in these systems, this microstructure is thermodynamically unstable. By applying emulsiflers and thickeners, emulsions are kinetically stabilized for a certain amount of time. Elowever, shelf-life stability always is a big chal-... 

Viscosity is the internal resistance to flow exhibited by a fluid and to suspended particles their size, volume content, etc. Low viscosity is one of the main characteristics required for monomers used in PIC, because it is essential to obtain the required depth of impregnation within a reasonable time of a few hours. 

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