Other viscosity theories

A different approach was made by Dyre et al. (1996) to account for the experimental viscosity variations with temperature as an alternative to VTF and AG models. They considered the flow in viscous liquids to arise from sudden events involving motion and reorganization of several molecules. From the viewpoint of mechanism, the energy required for such flow is minimized if the surrounding liquid is shoved aside to create the necessary volume for rearrangement. This volume is fundamentally different from the volume of the free volume theory and is, in principle, an activation volume. The free energy involved may be written as 

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Deriving molecular dimensions in solution from viscosities depends on the model assumed for the conformations of the free molecules. Since any a- or - triple helical sections of our gelatins vrc>uld be melted at 30 C. we assume near randomness for the chains, and a lew ellipticity for the molecular envelopes. Further, the success of Flory s viscosity theory (17) has shown that the hydrodynamically effective volume of randomly coiled (and of many other) chain molecules is not very different from the volume encompassed by the meandering segments. Thus we treated our data as if they pertained to random coil molecules. The measured layer thicknesses then describe the level within the adsorbed interphase below v ich the segmental density is equal to, or larger, than the effective coil density of the free molecules. 

In this section, we present the molecular theory for the linear dynamic viscoelasticity of miscible polymer blends by Han and Kim (1989a, 1989b), which is based on the concept of the tube model presented in Chapter 4. Specifically, the reptation of two primitive chains of dissimilar chemical structures under an external potential will be considered, and the expressions for the linear viscoelastic properties of miscible polymer blends will be presented. We will first present the expressions for zero-shear viscosity ob. dynamic storage and loss moduli G co) and G " co), and steady-state compliance J° for binary miscible blends of monodisperse, entangled flexible homopolymers and then consider the effect of polydispersity. There are a few other molecular theories reported... 

VA viscosity in good solvents. The correction of excluded volume effect is made by using the Flory-Krigbaum-Orofino theory of the second virial coefficient A 2 or other analogous theories (12). 

So far we have introduced four Miesowicz viscosities. Two other viscosities can be proposed by considering the following. The director n in Fig. 4.1(a), if free to move, will rotate due to a viscous torque the viscosity coefficient 71 is introduced to describe this situation and characterises the torque associated with a rotation of n. For this reason 71 is often called the rotational viscosity or twist viscosity. The coefficient 71 generally determines the rate of relaxation of the director. Also, a rotation of n due to body forces will induce a flow. The viscosity coefficient 72 characterises the contribution to the torque due to a shear velocity gradient in the nematic and is sometimes referred to as the torsion coefficient in the velocity gradient it leads to a coupling between the orientation of the director and shear flow. The two viscosities 71 and 72 have no counterpart in isotropic fluids. We therefore have a total of six viscosities four Miesowicz viscosities plus 71 and 72. It turns out, as will be seen in the problems to be discussed in later Sections, that 7i and 72 are precisely the viscosities introduced in the constitutive theory at equations (4.78) and (4.79), namely. 

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. 

Equation (2.61) predicts a 3.5-power dependence of viscosity on molecular weight, amazingly close to the observed 3.4-power dependence. In this respect the model is a success. Unfortunately, there are other mechanical properties of highly entangled molecules in which the agreement between the Bueche theory and experiment are less satisfactory. Since we have not established the basis for these other criteria, we shall not go into specific details. It is informative to recognize that Eq. (2.61) contains many of the same factors as Eq. (2.56), the Debye expression for viscosity, which we symbolize t . If we factor the Bueche expression so as to separate the Debye terms, we obtain... 

AH these mechanisms except high bulk viscosity require a stabilizer in the surface layers of foam films. Accordingly, most theories of antifoaming are based on the replacement or modification of these surface-active stabilizers. This requires defoamers to be yet more surface active most antifoam oils have surface tensions in the 20 to 30 mN/m range whereas most organic surfactant solutions and other aqueous foaming media have surface tensions between 30 and 50 mN/m(= dyn/cm). This is illustrated in Table 3. 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

A shift in the velocity constant such as is observed in bulk esterification is the exception rather than the rule. A source of more general concern is the enormous increase in viscosity which accompanies polymerization. Both theory and experimental results indicate that this factor usually is of no importance except under the extreme conditions previously mentioned. Consequently, the velocity coefficient usually remains constant throughout the polymerization (or degradation) process. Barring certain abnormalities which enter when the velocity coefficient is sensitive to the environmental changes accompanying the polymerization process, application of the ordinary methods of chemical kinetics to polymerizations and other processes involving polymer molecules usually is permissible. 

Several assumptions were made in using the broad MWD standard approach for calibration. With some justification a two parameter equation was used for calibration however the method did not correct or necessarily account for peak speading and viscosity effects. Also, a uniform chain structure was assumed whereas in reality the polymer may be a mixture of branched and linear chains. To accurately evaluate the MWD the polymer chain structure should be defined and hydrolysis effects must be totally eliminated. Work is currently underway in our laboratory to fractionate a low conversion polydlchlorophosphazene to obtain linear polymer standards. The standards will be used in polymer solution and structure studies and for SEC calibration. Finally, the universal calibration theory will be tested and then applied to estimate the extent of branching in other polydlchlorophosphazenes. 

The rheological characteristics of AB cements are complex. Mostly, the unset cement paste behaves as a plastic or plastoelastic body, rather than as a Newtonian or viscoelastic substance. In other words, it does not flow unless the applied stress exceeds a certain value known as the yield point. Below the yield point a plastoelastic body behaves as an elastic solid and above the yield point it behaves as a viscoelastic one (Andrade, 1947). This makes a mathematical treatment complicated, and although the theories of viscoelasticity are well developed, as are those of an ideal plastic (Bingham body), plastoelasticity has received much less attention. In many AB cements, yield stress appears to be more important than viscosity in determining the stiffness of a paste. 

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