Rheology relaxation methods

As mentioned above relaxation techniques are additional methods suitable to get insight into the mechanism of adsorption processes. Moreover, these methods represent the experimental tools to determine the dilational rheology of interfacial layers. The general principle of relaxation methods is the small disturbance of the interfacial layer, which has reached the equilibrium state beforehand. Particular methods are suitable to detect characteristic times of relaxations processes as they work each in a specific frequency range. This paragraph discusses briefly the most frequently used and very recently developed methods. 

We want to give only two examples of interfacial relaxation methods. The whole field of interfacial relaxations and rheology is so broad and of strong practical relevance that this topic deserves a whole book. At first, two examples, a harmonic and a transient experiment will be shown as example for slow relaxation experiments, while as second we will present results of experiments performed under ground and microgravity conditions, respectively, based on the principle of oscillating bubbles. 

The present chapter gives also detailed introduction to a large number of experimental methods, suitable for studying dynamic interfacial tensions. The methods are discussed in terms of the available time window. There are methods which complement each other such that a time interval from less than 100 microseconds up to hours and days of adsorption time can be covered (about ten orders of magnitude). The relaxation methods, also suitable for detecting the adsorption mechanism of surfactant s adsorption provide in addition the dilational rheology of interfacial layers. It is discussed that in particular these dilational rheological studies are most informative in respect to adsorption mechanisms, as the data interpretation includes the thermodynamic model as well as the adsorption dynamics. 

It appears that the quadrupole relaxation method is very well suited for the study of counterion binding in micellar solutions of different types as well as in liquid crystals. In contrast to some other methods, the NMR method is applicable irrespective of the macroscopic viscosity (or general rheological properties) of the sample. 

Most adsorbed surfactant and polymer coils at the oil-water (0/W) interface show non-Newtonian rheological behavior. The surface shear viscosity Pg depends on the applied shear rate, showing shear thinning at high shear rates. Some films also show Bingham plastic behavior with a measurable yield stress. Many adsorbed polymers and proteins show viscoelastic behavior and one can measure viscous and elastic components using sinusoidally oscillating surface dilation. For example the complex dilational modulus c obtained can be split into an in-phase (the elastic component e ) and an out-of-phase (the viscous component e") components. Creep and stress relaxation methods can be applied to study viscoelasticity. 

Rheological studies show some similarities with chemical relaxation studies. For instance, a rectangular shear rate is applied and the relaxation of the stress is monitored. This directly yields the stress relaxation time(s). One can also apply a sinusoidal deformation or strain of angular frequency 0). The response of the system is a two-component sinusoidal shear stress. The first component is in phase with the strain and corresponds to the elastic (storage) properties of the system. The second component is out of phase with the strain with a phase angle 5, and corresponds to the viscous loss in the system. These quantities give access to the storage (elastic) modulus G (co) and to the loss (viscous) modulus G"(o)), with G" ((o)/G (co) = tg5. As in the case of chemical relaxation methods with harmonic perturbation, the variations of G (w) and G" (co) with co yield the relaxation time(s) of the system. 

Our understanding of how the MWD of a linear polymer is reflected in its rheological behavior is now sufficiently advanced that it is possible to use rheological data to infer the MWD except when is it is very narrow or very broad. The earliest methods made use of the viscosity data and required no assumption regarding the shape of the distribution. More recent methods are based on the tube model. If reptation is the only relaxation method taken into account, use of the double-reptation scheme to account for constraint release makes it possible to infer the MWD from storage modulus data, but the omission of other relaxation mechanisms limits the applicability of this method. The most elaborate methods take into account all possible relaxation mechanisms, but their use requires the assumption of an equation to describe the distribution. For reliable results, the data must be very accurate and precise. 

Thus for undiluted polymers the relaxation behaviour can be examined over a wider range of apparent frequencies. Similar functions can be constructed for other regions of the phase diagram and other rheological experiments. The method of reduced variables has not been widely tested for aqueous crosslinked polymers. Typically these are polyelectrolytes crosslinked by ionic species. Some of these give rise to very simple relaxation behaviour. For example 98% hydrolysed poly(vinyl acetate) can be crosslinked by sodium tetraborate. The crosslink that forms is shown in Figure 5.31. 

Another possibility of determining the gel point with the help of rheological methods is dynamical mechanical spectroscopy. Analysis of change of dynamic mechanical properties of reactive systems shows that the gel point time may be reached when tan S or loss modulus G" pass a miximum [3,4,13], Some authors proposed to correlate the gel point with the intersection point of the curves of storage and loss moduli, i.e., with the moment at which tan 5 = 1 [14-16], However, theoretical calculations have shown that the intersection point of storage modulus and loss modulus meets the gelation conditions only for a certain law of relaxation behavior of the material and the coincidence erf the moment of equality G = G" with the gel point is a particular case [17]. The variation of the viscosity... 

While rheological measurements are wonderfully quantitative, they are usually poor qualitative probes of fluid structure. This is because in rheological experiments, the structural changes responsible for the measured relaxation behavior remain hidden. Thus, rheometry is often most useful when supplemented by other experimental methods that characterize fluid structure and flow-induced structural changes. Some of the most useful methods are microscopy, light, x-ray, and neutron scattering, and polarimetry. 

For the evaluation of the rheology of the silica dispersions, different test methods were applied (a) a shear rate-controlled relaxation experiment at = 0.5 s (conditioning), 500 s (shear thinning), and 0.5 s (relaxation) to evaluate the apparent viscosity, the relaxation behavior, and thixotropy (b) shear yield-stress measurements using a vane technique introduced by Nguyen and Boger [5] (c) low deformation dynamic tests at a constant frequency of 1.6 s in a stress range of ca. 0.5 - 100 Pa. All samples contained 3 wt% of fumed silica. 

B. J. Balcom, SPRITE imaging of short relaxation time nuclei, in Spatially Resolved Magnetic Resonance Methods, Materials, Medicine, Biology, Rheology, Geology, Ecology, Hardware (eds P. Bliimler, B. Blumich, R. Botto and E. Fukushima), Wilcy-VCH, Weinheim, 1998, Ch. 5, p. 75. 

The rheological consequences of the Maxwell model are apparent in stress relaxation phenomena. In an ideal solid, the stress required to maintain a constant deformation is constant and does not alter as a function of time. However, in a Maxwellian body, the stress required to maintain a constant deformation decreases (relaxes) as a function of time. The relaxation process is due to the mobility of the dashpot, which in turn releases the stress on the spring. Using dynamic oscillatory methods, the rheological behavior of many pharmaceutical and biological systems may be conveniently described by the Maxwell model (for example, Reference 7, Reference 17, References 20 to 22). In practice, the rheological behavior of materials of pharmaceutical and biomedical significance is more appropriately described by not one, but a finite or infinite number of Maxwell elements. Therefore, associated with these are either discrete or continuous spectra of relaxation times, respectively (15,18). 

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