Viscoelasticity polymeric systems

Contrary to the phase separation curve, the sol/gel transition is very sensitive to the temperature more cations are required to get a gel phase when the temperature increases and thus the extension of the gel phase decreases [8]. The sol/gel transition as determined above is well reproducible but overestimates the real amount of cation at the transition. Gelation is a transition from liquid to solid during which the polymeric systems suffers dramatic modifications on their macroscopic viscoelastic behavior. The whole phenomenon can be thus followed by the evolution of the mechanical properties through dynamic experiments. The behaviour of the complex shear modulus G (o)) reflects the distribution of the relaxation time of the growing clusters. At the gel point the broad distribution of... 

The space-time resolution of these techniques reveals the molecular motions leading to the viscoelastic and mechanical properties of polymeric systems. This knowledge is of great importance for scientific reasons and is also a basis for the design of tailor-made materials. 

The purpose of this chapter is to remind the reader of the basis of the theory of elasticity, to outline some of its principal results and to discuss to what extent the classical theory can be applied to polymeric systems. We shall begin by reviewing the definitions of stress and strain and the compliance and stiffness matrices for linear elastic bodies at small strains. We shall then state several important exact solutions of these equations under idealised loading conditions and briefly discuss the changes introduced if realistic loading conditions are considered. We shall then move on to a discussion of viscoelasticity and its application to real materials. 

Summary In this chapter, a discussion of the viscoelastic properties of selected polymeric materials is performed. The basic concepts of viscoelasticity, dealing with the fact that polymers above glass-transition temperature exhibit high entropic elasticity, are described at beginner level. The analysis of stress-strain for some polymeric materials is shortly described. Dielectric and dynamic mechanical behavior of aliphatic, cyclic saturated and aromatic substituted poly(methacrylate)s is well explained. An interesting approach of the relaxational processes is presented under the experience of the authors in these polymeric systems. The viscoelastic behavior of poly(itaconate)s with mono- and disubstitutions and the effect of the substituents and the functional groups is extensively discussed. The behavior of viscoelastic behavior of different poly(thiocarbonate)s is also analyzed. 

Mechanical and dielectric behavior of poly(methacrylate)s with cyclohexyl groups in the side chain have been reported as it was described above and the viscoelastic information obtained from these polymeric systems is very broad and give confidence about the molecular origin of the fast relaxation processes that take... 

Polymers differ from other substances by the size of their molecules which, appropriately enough, are referred to as macromolecules, since they consist of thousands or tens of thousands of atoms (molecular weight up to 106 or more) and have a macroscopic rectilinear length (up to 10 4 cm). The atoms of a macromolecule are firmly held together by valence bonds, forming a single entity. In polymeric substances, the weaker van der Waals forces have an effect on the components of the macromolecules which form the system. The structure of polymeric systems is more complicated than that of low-molecular solids or liquids, but there are some common features the atoms within a given macromolecule are ordered, but the centres of mass of the individual macromolecules and parts of them are distributed randomly. Remarkably, the mechanical response of polymeric systems combines the elasticity of a solid with the fluidity of a liquid. Indeed, their behaviour is described as viscoelastic, which is closely connected with slow (relaxation time to 1 sec or more) relaxation processes in systems. 

In practice, there are few materials employed in the formulation of pharmaceutical and biomedical systems that conform to either Hooke s law or Newtonian theory (16,18). Most polymeric systems exhibit behavior in which the applied stress is proportional to both the resultant strain and the rate of strain, i.e., exhibit varying degrees of both elastic and viscous behavior simultaneously. Such materials are known as viscoelastic (the term elastoviscous is sometimes used when referring to materials that exhibit predominantly viscous behavior). 

Elasticity often stems from the resistance of the bonds in a material to extension or bending. Deformation will thus increase bond energy (see Figure 3.1). Another cause is that the conformational entropy of a material will decrease upon deformation this occurs especially in polymeric systems and it is further discussed in Chapter 6. In either case, the material will return to its original state upon release of stress—i.e., behave in a purely elastic manner—provided that no bonds have been broken. In a viscoelastic material, part of the bonds break upon deformation. (A purely viscous material has no permanent bonds between the structural elements.)... 

In a dynamic experiment, a small-amplitude oscillatory shear is imposed to a molten polymer confined in the rheometer. The shear stress response of the polymeric system can be expressed as in Equation 22.14. In this equation, G and G" are dynamic moduli related to the elastic storage energy and dissipated energy of the system, respectively. For a viscoelastic fluid, two independent normal stress differences, namely, first and second normal stress differences can be defined. These quantities are calculated in terms of the differences of the components of the stress tensor, as indicated in Equation 22.15a and 22.15b, and can be obtained, for instance, from the radial pressure distribution in a cone-and-plate rheometer [5]. Some other experiments used in the determination of the normal stress differences can be found elsewhere [9, 22] ... 

As can be seen, the Maxwell-Weichert model possesses many relaxation times. For real materials we postulate the existence of a continuous spectrum of relaxation times (A,). A spectrum-skewed toward lower times would be characteristic of a viscoelastic fluid, whereas a spectrum skewed toward longer times would be characteristic of a viscoelastic solid. For a real system containing crosslinks the spectrum would be skewed heavily toward very long or infinite relaxation times. In generalizing, A may thus he allowed to range from zero to infinity. The concept that a continuous distribution of relaxation times should be required to represent the behavior of real systems would seem to follow naturally from the fact that real polymeric systems also exhibit distrihutions in conformational size, molecular weight, and distance between crosslinks. 

Nano-sized objects may be different in physical nature, e.g. perfectly elastic inorganic nanoparticles, viscoelastic polymeric nanoparticles, viscous micelles however, all injectable nano-systems share a common macroscopic property under the conditions employed during the application, they flow, i.e. they are... 

As has been pointed out, viscoelastic behavior is frequently associated with flowing polymeric systems. Usually, such behavior is especially pronounced in molten or thermally softened polymers. Elastic effects should be contrasted with the viscous effects (i.e., viscous heating). In the latter case, the energy necessary to move the fluid is dissipated as heat. In the former instance, however, energy put into an elastic system can be recovered. This suggests the possibility of a form of energy storage in a viscoelastic system. 

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