Dependence of viscosity

In amoriDhous poiymers, tiiis reiation is vaiid for processes tiiat extend over very different iengtii scaies. Modes which invoived a few monomer units as weii as tenninai reiaxation processes, in which tire chains move as a whoie, obey tire superjDosition reiaxation. On tire basis of tiiis finding an empiricai expression for tire temperature dependence of viscosity at a zero shear rate and tiiat of tire mean reiaxation time of a. modes were derived ... 

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. 

The Molecular Weight Dependence of Viscosity Experimental Aspects... 

A basic theme throughout this book is that the long-chain character of polymers is what makes them different from their low molecular weight counterparts. Although this notion was implied in several aspects of the discussion of the shear dependence of viscosity, it never emerged explicitly as a variable to be investi-tated. It makes sense to us intuitively that longer chains should experience higher resistance to flow. Our next task is to examine this expectation quantitatively, first from an empirical viewpoint and then in terms of a model for molecular motion. 

To account for a first-power dependence of viscosity on molecular weight for lower molecular weights. 

For the same polymer this parameter has values of 4.47 X 10" and 5.01 X 10 " kg sec" at 298 and 398 K, respectively. Since density is far less sensitive to temperature, these results show that the primary temperature dependence of viscosity is described by the temperature dependence of f. 

To the extent that the segmental friction factor f is independent of M, then Eq. (2.56) predicts a first-power dependence of viscosity on the molecular weight of the polymer in agreement with experiment. A more detailed analysis of f shows that segmental motion is easier in the neighborhood of a chain end because the wagging chain end tends to open up the structure of the melt and... 

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... 

In connection with a discussion of the Eyring theory, we remarked that Newtonian viscosity is proportional to the relaxation time [Eqs. (2.29) and (2.31)]. What is needed, therefore, is an examination of the nature of the proportionality between the two. At least the molecular weight dependence of that proportionality must be examined to reach a conclusion as to the prediction of the reptation model of the molecular weight dependence of viscosity. 

Temperature dependence of viscosity of the gas over a wide range of temperatures is given by equation 1 where Tis in Kelvin and T q is the value of Ti at 273 K. 

The dependence of viscosity on temperature is critical to the handling of molten polymers in mol ding, extmsion, and other manufacturing processes. In fact, the drop in viscosity with increasing temperature makes these operations possible. Therefore, viscosity—temperature relationships are... 

The temperature dependence of viscosity of resin solutions can be expressed by the WLE equation (eq. 3) where the reference temperature T is taken as the lowest temperature for which data ate avaUable (92,93). 

Non-Newtonian fluids vary significantly in their properties that control flow and pressure loss during flow from the properties of Newtonian fluids. The key factors influencing non-Newtonian fluids are their shear thinning or thickening characteristics and time dependency of viscosity on the stress in the fluid. 

Kandyrin, L. B. and Kuleznev, V. N. The Dependence of Viscosity on the Composition of Concentrated Dispersions and the Free Volume Concept of Disperse Systems. Vol. 103, pp. 103-148. 

The majority of investigators consider it permissible and convenient to use, when calculating the boundary layer thickness, the relationships describing the concentration dependence of viscosity in the high and medium concentration range (basically Mooney s equation) [67 — 71]. 

At least, in absolute majority of cases, where the concentration dependence of viscosity is discussed, the case at hand is a shear flow. At the same time, it is by no means obvious (to be more exact the reverse is valid) that the values of the viscosity of dispersions determined during shear, will correlate with the values of the viscosity measured at other types of stressed state, for example at extension. Then a concept on the viscosity of suspensions (except ultimately diluted) loses its unambiguousness, and correspondingly the coefficients cn cease to be characteristics of the system, because they become dependent on the type of flow. 

The simple result is attained when dependence of viscosity on shear rateq(Yapp)can be ignored in the interval of apparent shear rates realized along channel axis. Then,... 

While mathematically attractive, this force law is of limited interest physically it represents only the interaction between permanent quadrupoles, and even this with neglect of angles of orientation. However, although the details of the dependence of viscosity upon temperature are affected by the force law used, the general form of the hydrodynamic equation in the Navier-Stokes approximation is not affected. 

Example 8.9 Find the temperature distribution in a laminar flow, tubular heat exchanger having a uniform inlet temperature and constant wall temperature Twall- Ignore the temperature dependence of viscosity so that the velocity profile is parabolic everywhere in the reactor. Use art/P = 0.4 and report your results in terms of the dimensionless temperature... 

Monkos, Karol 1997. Concentration and temperature dependence of viscosity in lysozyme aqueous solutions. Biochimica et Biophysica Acta 1339, 304-310. 

Figure 8.7 Temperature dependences of viscosity for several solvents measured with conventional Ostwald viscometers. Markers exhibit experimental results. Data points were interpolated by polynomial function the calculated curves are drawn with lines.

Modify the dependence of viscosity on shear rate, producing low viscosity at high rates, and vice versa. 

Zhu D, Haidekker MA, Lee J-S, Won Y-Y, Lee JC (2007) Application of molecular rotors to the determination of the molecular weight dependence of viscosity in polymer melts. Macromolecules 40 7730-7732... 

Fig. 33. Dependence of viscosity on the shear rate of microgel solutions in C2H5OC2 H4OCOCCH3. EUP(MA+HD), c/t 70/30, EUP/S and EUP/EDMA(D), AIBN, P.-S. polystyrene [136].

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