Liquid-like behaviour

As noted in Chapter 1, viscoelastic fluids exhibit a combination of solid-like and liquid-like behaviour. Even a simple analysis of viscoelastic effects in process plant is beyond the scope of this book. This section is restricted to an outline of practical implications of elastic effects and a demonstration of the fact that viscoelastic liquids exhibit stronger elastic behaviour as the deformation rate is increased. 

The results given by Fig. 3.4-2 relative to measured viscosities are about 10%. Fig. 3.4-2 shows that the viscosity tends to a minimum at the critical state. Near the critical point, at constant pressure, there are two branches, one in which viscosity increases with increasing temperature (gas-like behaviour), and the other branch where the viscosity decreases with increasing temperature (liquid-like behaviour). 

In a rheomety experiment the two plates or cylinders are moved back and forth relative to one another in an oscillating fashion. The elastic storage modulus (G - The contribution of elastic, i.e. solid-like behaviour to the complex dynamic modulus) and elastic loss modulus (G" - The contribution of viscous, i.e. liquid-like behaviour to the complex modulus) which have units of Pascals are measured as a function of applied stress or oscillation frequency. For purely elastic materials the stress and strain are in phase and hence there is an immediate stress response to the applied strain. In contrast, for purely viscous materials, the strain follows stress by a 90 degree phase lag. For viscoelastic materials the behaviour is somewhere in between and the strain lag is not zero but less than 90 degrees. The complex dynamic modulus ( ) is used to describe the stress-strain relationship (equation 14.1 i is the imaginary number square root of-1). 

Note that this observation is in conflict with both a liquid-liquid-like behaviour of the hydrocarbo-naceous layer (in which case k is expected to increase linearly with rtc), and with adsorption of the solute on top of this layer (in which case k would be virtually independent of rtc). 

One possibility, used, e.g., by Rey and Gallego,49 is to use the eigenvalues of the matrix for the moments of inertia, Eq. (55). These quantities will first of all be able to catch transitions from a solid-like to a liquid-like behaviour, where the atoms change from being more or less confined at somewhat fixed positions... 

This is not simply because of the presence of rheology modifiers or other polymers a simple NaPA-stabilized GCC suspension will also show a plastic-like behaviour. Typically, this involves the suspension behaving like a solid at low shear rates and stresses, and only yielding to liquid-like behaviour above a certain yield stress [Pg.150]

The full range of adsorption isotherms under the lUPAC system is shown in Figure 7.46. Brunauer, Emmett and Teller were able to extend Langmuir s theory of monolayer adsorption to obtain an isotherm (the BET equation) which models Type II behaviour, for meso- and macroporous systems. Briefly, in the theory, molecules in one layer act as adsorption sites for molecules in the next layer, so that the adsorbed layer is not of uniform thickness, but rather is made up of a random stack of molecules. The theory has limitations, such as the assumption of liquid-like behaviour in all adsorbed layers but the first however, it has become a... 

However, by making use of this definition, one has to conclude that many systems which look like a gel are in fact not covered by this definition aqueous poly(vinyl alcohol)/borate systems, which are known to show liquid-like behaviour at low frequencies [7], solutions of phase separated atactic polystyrene at temperatures above the glass transition temperature of the swollen polystyrene crosslinks, solutions of ABA block copolymers above the glass transition temperature of the swollen A-blocks, and even gelatin, which also shows creep behaviour, as shown by Ross-Murphy et al. [8,9] and by Kramer et al. (private communication), and a relaxation mechanism at extremely low frequencies, as is shown in Fig. 7 of the Section on gelatin, and possibly ako poly(vinyl chloride) in plasticizers [10-13]. The advantage of the approach of Kramer et al. [3] is that these systems certainly are covered by their practical definition. 

In certain organic substances, composed of anisotropic molecules, the transition from the crystalline to the liquid state takes place in two or more distinct steps. In these materials between the solid and liquid states additional phases are formed which exhibit both liquid-like behaviour (fluidity) and crystalline-like features (macroscopic anisotropy). The substances showing this phenomenon are called liquid crystals the intermediate phases are termed liquid-crystal line phases or mesophases. By now thousands of liquid crystals are known and at least ten thermodynamically different mesophases are recognized. 

A typical dictionary definition of the verb to yield would be to give way under the action of force and this implies an abrupt and extreme change in behaviour to a less resistant state. The yield stress of a solid material, say a metal like copper, is the point at which, when the applied stress is increased, it first shows liquid-like behaviour in that it continues to deform for no further increase in stress. Similarly,... 

At very low frequencies, G" is much larger than G, and hence liquid-Kke behaviour predominates. However as the testing frequency is increased, G takes over and solid-like behaviour prevails. The determinant of which kind of behaviour is most significant is the value of the test frequency co relative to the relaxation time x. This is a simple way to define a Deborah number, De—the ratio of the relaxation time to the test time—and a measure of De in this case is cox. Hence, low Deborah numbers always indicate liquid-like behaviour, whereas high Deborah numbers means solid-like response. At the midpoint, where G" goes through a maximum G = G", and this takes place at a critical crossover frequency of co = 1/x. 

Figure 5.27 Experimental phase diagram of AB/ABA block copolymer blends dissolved in a B-selective solvent according to sol-gel and cloud-point measurements. A phase-separated regime is found to exist at low AB and total (AB + ABA) polymer concentrations. At higher AB or total polymer concentrations, the system forms a physical gel network. A further increase in AB content ultimately disrupts the ABA network and induces liquid-like behaviour. (Reprinted with permission from Vega, D. A., Sebastian, J. M., Loo, Y.-L. and Register, R. A. J. Polym. Sci. B Polym. Phys. 39, 2183, 2001. Copyright (2001) Wiley-Interscience.)...

Polymers may act as hosts for ions in much the same way that liquid solvents do. Suppose that a salt is introduced into a polymer when the solvation energy of the ions in the polymer host exceeds the ionisation energy of the salt, the individual ions separate and attach themselves to Lewis base sites on the polymer. Conductivity is possible above the glass transition temperature, where the polymer molecules are free to move. The free volume also provides room for the ions to move. The ionic conductivity possesses a diffuse liquid-like behaviour in addition to the hopping-type behaviour characteristic of an electron in a disordered solid. 

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