Viscoelastic behavior frequency dependence

Some information concerning the intramolecular relaxation of the hyperbranched polymers can be obtained from an analysis of the viscoelastic characteristics within the range between the segmental and the terminal relaxation times. In contrast to the behavior of melts with linear chains, in the case of hyperbranched polymers, the range between the distinguished local and terminal relaxations can be characterized by the values of G and G" changing nearly in parallel and by the viscosity variation having a frequency with a considerably different exponent 0. This can be considered as an indication of the extremely broad spectrum of internal relaxations in these macromolecules. To illustrate this effect, the frequency dependences of the complex viscosities for both linear... 

A particular question of interest is whether the DNA torsional motions observed on the nanosecond time scale are overdamped, as predicted by simple Langevin theory, and as observed for Brownian motions on longer time scales, or instead are underdamped, so that damped oscillations appear in the observed correlation functions. A related question is whether the solvent water around the DNA exhibits a normal constant viscosity on the nanosecond time scale, or instead begins to exhibit viscoelastic behavior with a time-, or frequency-, dependent complex viscosity. In brief, are the predictions for... 

Dynamic mechanical analysis (DMA) or dynamic mechanical thermal analysis (DMTA) provides a method for determining elastic and loss moduli of polymers as a function of temperature, frequency or time, or both [1-13]. Viscoelasticity describes the time-dependent mechanical properties of polymers, which in limiting cases can behave as either elastic solids or viscous liquids (Fig. 23.2). Knowledge of the viscoelastic behavior of polymers and its relation to molecular structure is essential in the understanding of both processing and end-use properties. 

The behavior near the gel point can be disturbed by viscoelastic effects and, more precisely, by the proximity of the vitrification phenomenon. This is defined by a frequency-dependent peak on G"(t) or tan 8 (t) curves. 

This is an important parameter to analyze the viscoelastic behavior of different materials mainly in the case of polymeric materials where the dependence of tan 8 with the chemical structure of the polymeric materials give important information about the relaxation processess that take place is these systems. tan8 is commonly used as a first experimental approach to obtain information about the viscoelastic behavior of polymers as function of the frequency, where it is possible to reach experimental information about the effect of the side chain structure of the polymers on conformational and relaxational responses. 

In this book, we review the most basic distinctions and similarities among the rheological (or flow) properties of various complex fluids. We focus especially on their linear viscoelastic behavior, as measured by the frequency-dependent storage and loss moduli G and G" (see Section 1.3.1.4), and on the flow curve— that is, the relationship between the "shear viscosity q and the shear rate y. The storage and loss moduli reveal the mechanical properties of the material at rest, while the flow curve shows how the material changes in response to continuous deformation. A measurement of G and G" is often the most useful way of mechanically characterizing a complex material, while the flow curve q(y ) shows how readily the material can be processed, or shaped into a useful product. The... 

Fig. 23 (a) Frequency-dependent linear viscoelastic moduli (G closed symbols, G" open symbols) of a colloidal star with nominal values f = 12Sarms and = SOkgmol at a concentration 5 wt% in -tetradecane and different temperatures (circles 40°C, squares. 5O C. triangles 55°C). A liquid-lo-solid transition is marked between 50 and 55°C. Lines with slopes 1 and 2 indicate terminal behavior of G" and G, respectively. Inset The temperature dependence of the hydrodynamic radius /fh of the same star, indicating swelling, (b) Respective moduli for the same system at 4() C in two different solvents, n-decane (circles, solid-like behavior) and n-tetracane (triangles, Uquid-Uke behavior) [26]... 

The values of G, G", and tan 8 all tend to depend on co. The most common situation is that G and G" increase in magnitude with increasing frequency, though at different rates. Viscoelastic behavior depends on the time scale of deformation, but the relations vary widely among materials. This will be further discussed below. 

In accordance with the results of the adntittance measurements, the dependence of the change in the resonant frequency corresponding to the reduced state of the polymer on the charge injected during the electropolymerization is linear, except for very thick films (Fig. 3.15). Usually such a deviation indicates a transformation from elastic to viscoelastic behavior however, in this case it was assigned to the poor adherence of the deposited polymer, since the energy loss measured was small even for thick films [157]. 

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