Experiment 7 Viscosity

To investigate the rheological properties of some Newtonian and non Newtonian fluids. 

Corn flour or custard powder Plastic funnel and stand to hold it Beaker 

A weight, such as a large nut (the metal sort, not the edible one ), AA 

You will find that the weight takes longer the second time. This is because tomato ketchup is a shear-thinning fluid, i.e. its viscosity decreases when it has been sheared. When it is left to stand, the 

This mixture is shear-thickening. At low shear rates, for example when gently poured or stirred, it flows easily and your fingers can move freely through it. However, at high shear rates it behaves like a solid. When you try to stir it quickly the spoon gets stuck and cracks appear. 

---

The authors of [40] used L. L. Blyler s and T. K. Kwei s formula to process experimental data [41, 8] and obtained good correlation between theory and experiment. In all the processed experiments viscosity was established in accordance with pressure at channel input. To describe data presented by C. J. Ma and C. D. Han [2-5], who1 studied freon-containing polymer melts, the same paper supposed that the entire volume of gas is expended in part on the increase of the free volume of the composition, and that the occupied volume also changes in its presence. This consideration made it possible for the authors of [40] to attain fair correlation between theory and practice. This makes, in our opinion, the ideas expressed in [39, 40] worthy of the most serious attention, however critical the following evaluation of these works may appear to the reader. 

Before discussing details of their model and others, it is useful to review the two main techniques used to infer the characteristics of chain conformation in unordered polypeptides. One line of evidence came from hydrodynamic experiments—viscosity and sedimentation—from which a statistical end-to-end distance could be estimated and compared with values derived from calculations on polymer chain models (Flory, 1969). The second is based on spectroscopic experiments, in particular CD spectroscopy, from which information is obtained about the local chain conformation rather than global properties such as those derived from hydrodynamics. It is entirely possible for a polypeptide chain to adopt some particular local structure while retaining characteristics of random coils derived from hydrodynamic measurements this was pointed out by Krimm and Tiffany (1974). In support of their proposal, Tiffany and Krimm noted the following points ... 

In order to eliminate the complications of mass transfer and changing droplet size in the coalescence experiments, the solutions were allowed to equilibrate for at least one month at 25.0 C 0.5°C. Interfacial tension was determined on the spinning drop apparatus in the course of the coalescence experiments. Viscosities were determined using Canon-Fenske viscometers. Density measurements were made on an analytical balance by measuring the buoyancy of a solid plummet immersed in the fluid. 

In the context of the structural perturbations at fluid-solid interfaces, it is interesting to investigate the viscosity of thin liquid films. Eaily work on thin-film viscosity by Deijaguin and co-workers used a blow off technique to cause a liquid film to thin. This work showed elevated viscosities for some materials [98] and thin film viscosities lower than the bulk for others [99, 100]. Some controversial issues were raised particularly regarding surface roughness and contact angles in the experiments [101-103]. Entirely different types of data on clays caused Low [104] to conclude that the viscosity of interlayer water in clays is greater than that of bulk water. 

From stochastic molecnlar dynamics calcnlations on the same system, in the viscosity regime covered by the experiment, it appears that intra- and intennolecnlar energy flow occur on comparable time scales, which leads to the conclnsion that cyclohexane isomerization in liquid CS2 is an activated process [99]. Classical molecnlar dynamics calcnlations [104] also reprodnce the observed non-monotonic viscosity dependence of ic. Furthennore, they also yield a solvent contribntion to the free energy of activation for tlie isomerization reaction which in liquid CS, increases by abont 0.4 kJ moC when the solvent density is increased from 1.3 to 1.5 g cm T Tims the molecnlar dynamics calcnlations support the conclnsion that the high-pressure limit of this unimolecular reaction is not attained in liquid solntion at ambient pressure. It has to be remembered, though, that the analysis of the measnred isomerization rates depends critically on the estimated valne of... 

Small molecules in low viscosity solutions have, typically, rotational correlation times of a few tens of picoseconds, which means that the extreme narrowing conditions usually prevail. As a consequence, the interpretation of certain relaxation parameters, such as carbon-13 and NOE for proton-bearing carbons, is very simple. Basically, tlie DCC for a directly bonded CH pair can be assumed to be known and the experiments yield a value of the correlation time, t. One interesting application of the measurement of is to follow its variation with the site in the molecule (motional anisotropy), with temperature (the correlation... 

Evidence from the viscosities, densities, refractive indices and measurements of the vapour pressure of these mixtures also supports the above conclusions. Acetyl nitrate has been prepared from a mixture of acetic anhydride and dinitrogen pentoxide, and characterised, showing that the equilibria discussed do lead to the formation of that compound. The initial reaction between nitric acid and acetic anhydride is rapid at room temperature nitric acid (0-05 mol 1 ) is reported to be converted into acetyl nitrate with a half-life of about i minute. This observation is consistent with the results of some preparative experiments, in which it was found that nitric acid could be precipitated quantitatively with urea from solutions of it in acetic anhydride at —10 °C, whereas similar solutions prepared at room temperature and cooled rapidly to — 10 °C yielded only a part of their nitric acid ( 5.3.2). The following equilibrium has been investigated in detail ... 

Before we are in a position to discuss the viscosity of polymer melts, we must first give a quantitative definition of what is meant by viscosity and then say something about how this property is measured. This will not be our only exposure to experimental viscosity in this volume—other methods for determining bulk viscosity will be taken up in the next chapter and the viscosity of solutions will be discussed in Chap. 9—so the discussion of viscometry will only be introductory. Throughout we shall be concerned with constant temperature experiments conducted under nonturbulent flow conditions. 

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 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... 

We shall follow the same approach as the last section, starting with an examination of the predicted behavior of a Voigt model in a creep experiment. We should not be surprised to discover that the model oversimplifies the behavior of actual polymeric materials. We shall continue to use a shear experiment as the basis for discussion, although a creep experiment could be carried out in either a tension or shear mode. Again we begin by assuming that the Hookean spring in the model is characterized by a modulus G, and the Newtonian dash-pot by a viscosity 77. ... 

The Maxwell and Voigt models of the last two sections have been investigated in all sorts of combinations. For our purposes, it is sufficient that they provide us with a way of thinking about relaxation and creep experiments. Probably one of the reasons that the various combinations of springs and dash-pots have been so popular as a way of representing viscoelastic phenomena is the fact that simple and direct comparison is possible between mechanical and electrical networks, as shown in Table 3.3. In this parallel, the compliance of a spring is equivalent to the capacitance of a condenser and the viscosity of a dashpot is equivalent to the resistance of a resistor. The analogy is complete... 

Although the Rouse theory is the source of numerous additional relationships, Eq. (3.98) is a highpoint for us, because it demonstrates that the viscosity we are dealing with in the Rouse theory for viscoelasticity is the same quantity that we would obtain in a flow experiment. Several aspects of this statement deserve amplification ... 

It is a frustrating aspect of Eq. (9.20) that the observed intrinsic viscosities contain the effects of ellipticity and solvation such that the two cannot be resolved by viscosity experiments alone. That is, for any value of [77], there is a whole array of solvation-ellipticity values which are consistent with the observed intrinsic viscosity. 

Experiments based on the Poiseuille equation make intrinsic viscosity an easily measured parameter to characterize a polymer. In the next section we consider how this property can be related to the molecular weight of a polymer. 

Table 9.3 lists the intrinsic viscosity for a number of poly(caprolactam) samples of different molecular weight. The M values listed are number average figures based on both end group analysis and osmotic pressure experiments. Tlie values of [r ] were measured in w-cresol at 25°C. In the following example we consider the evaluation of the Mark-Houwink coefficients from these data. 

Since viscometer drainage times are typically on the order of a few hundred seconds, intrinsic viscosity experiments provide a rapid method for evaluating the molecular weight of a polymer. A limitation of the method is that the Mark-Houwink coefficients must be established for the particular system under consideration by calibration with samples of known molecular weight. The speed with which intrinsic viscosity determinations can be made offsets the need for prior calibration, especially when a particular polymer is going to be characterized routinely by this method. 

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 ... 

Protein molecules extracted from Escherichia coli ribosomes were examined by viscosity, sedimentation, and diffusion experiments for characterization with respect to molecular weight, hydration, and ellipticity. These dataf are examined in this and the following problem. Use Fig. 9.4a to estimate the axial ratio of the molecules, assuming a solvation of 0.26 g water (g protein)"V At 20°C, [r ] = 27.7 cm g" and P2 = 1.36 for aqueous solutions of this polymer. 

---