Polymers nonlinear properties

Pyshnograi GV (1994) The effect of the anisotropy of macromolecular tangles on the nonlinear properties of polymer fluids stretched along a single axis. J Appl Mech Techn Phys... 

Polymers show interesting properties and can be used in optics and optoelectronics3.4.5. Specially oriented polymers can exhibit optical nonlinear properties and can be used for optical processing purposes. For quadratic NLO polymers the potential applications are mainly fi uency doubling leading to a blue source for optical recording and an electrooptical modulator for optical communications. 

In the last chapter we discussed the relation between stress and strain (or instead rate-of-strain) in one dimension by treating the viscoelastic quantities as scalars. When the applied strain or rate-of-strain is large, the nonlinear response of the polymeric liquid involves more than one dimension. In addition, a rheological process always involves a three-dimensional deformation. In this chapter, we discuss how to express stress and strain in three-dimensional space. This is not only important in the study of polymer rheological properties in terms of continuum mechanics " but is also essential in the polymer viscoelastic theories and simulations studied in the later chapters, into which the chain dynamic models are incorporated. 

Based on these three criteria, more than two hundred polymers were chosen for inclusion in this work. The properties presented for each polymer include some of great current interest, such as surface and interfacial properties, pyrolyzability, electrical conductivity, nonlinear optical properties, and electroluminescence. Not aU the properties are available for all the polymers included, and some properties may not even be relevant for certain polymer classes. Some polymers exhibit properties shown by few others—such as electrolununescence—and those have been presented as "Properties of Special Interest."... 

Moreover, organic functionalization of a polymer chain can lead to improvement in the physical properties, such as thermal stability and mechanical strength of the resulting siloxanes (Figure 3.1). Appropriate substitution on the polysiloxane backbone can lead to diverse materials such as liquid crystals," crosslinking agents, conductive and electroluminescent polymers, nonlinear optical materials,and bactericides. ... 

The relation between the EA response and the macroscopic nonlinear properties of the material has been drawn by a classical approach. In Section 19.3.3, the mechanism behind the field-induced variation will be explored by a quantum mechanical approach. In molecular solids and in conjugated polymers, where the states are localized to a high degree, the change in a with the electric field is in general ascribed to a Stark shift of the molecular energy levels. 

Bubek, C., Relationship between structure and third-order nonlinear optical properties of conjugated polymers. Nonlinear Opt., 10, 13-22 (1995). 

Because of the versatility of the polyurethane system it is possible to introduce comonomers which can affect the physical properties of the derived polymers. For example, photo cross-linkable polyurethanes are formulated using 2,5-dimethoxy-2,4 -diisocyanato stilbene as a monomer (76). Comonomers, having an azoaromatic chromophore, are used in optical bleaching applications (77), or in the formation of photorefractive polymers (78). The latter random poljnners have second-order nonlinear optical (NLO) properties. Linear poljnners are also obtained from HDI/PTMG and diacetylenic diols. These polymers can be cross-linked through the acetylenic linkages producing a network polymer with properties similar to poly(diacetylenes) (79). 

However such benefits are obtained at expenses of some additional fabrication procedures. After deposition, organic materials are centrosymmetric on a macroscopic scale and they can not be endowed of second order nonlinear properties. Poling, i.e. the orientation of the microscopic molecular dipoles, is required in order to break this symmetry. One of the major challenges concerns the effective translation of high molecular nonlinearities (/ry3), where /r is the chromophore dipole moment and p is the first molecular hyperpolarizability, into large macroscopic EO activities rss) in poled polymers with high alignment temporal stability [15,16]. 

TABLE 3. Effect of a Nonlinear Structural Unit on Polymer Physical Properties... 

Properties of alloys are dependent on the nature of the polymers, interfacial attraction between the phases and the morphology. Properties can be additive (linear behavior) and based on the linear contribution from each polymer fraction. Properties can exhibit a synergistic combination of properties (positive nonlinear behavior) where the properties are better than those predicted by linear behavior. 

Utilization of the second-order nonlinearity of a material requires that the nonlinear molecules or side-groups be arranged in a non-centro-symmetric configuration. In the previous section it was pointed out that the more commonly used polymer deposition techniques resulted in an isotropic, amorphous film, and would thus show no second-order nonlinear properties. However, controlled deposition and/or subsequent processing can be employed to create a degree of molecular alignment. 

Chapter 14 sketches nonlinear properties of polymer solutions, some classical and some quite modem. Strange behaviors can arise in polymer solutions because the normal stress differences are nonzero, i.e., the diagonal components of the pressure tensor can be unequal. Memory effect properties, such as stress and strain relaxations, and responses to imposing multiple strains, are noted. Finally we consider very recent developments in the study of nonlinear effects, such as shear banding and nonquiescent relaxation following imposition of a sudden strain. 

Bulk tensile testing has shown that adhesives generally exhibit plasticity and, hence, nonlinear material properties are required to model their behavior over the fiill load range. Nonlinear properties may also be required for adherends. Thus, a combination of elasto-plastic material models may be used to predict the behavior of adhesive joints under load. The definition of the yield surface is important when using elasto-plastic material models. Von Mises yield surface is commonly used for the analysis of metals, which assumes that the yield behavior is independent of hydrostatic stress. As a result, the yield surface is identical in tension and compression. However, the yield behavior of polymers has been shown to exhibit hydrostatic stress dependence (Ward and Sweeney 2004) as the yielding starts earlier in tension than in compression. Thus, a yield criterion which includes hydrostatic stress effects should be used to determine the yield surface. Various yield criteria with hydrostatic stress dependence such as Drucker-Prager, Mohr-Columb, and modified Drucker-Prager/cap plasticity model have been implemented in commercially available finite element software. 

In Chapter 4 it was explained that the linear elastic behavior of molten polymers has a strong and detailed dependency on molecular structure. In this chapter, we will review what is known about how molecular structure affects linear viscoelastic properties such as the zero-shear viscosity, the steady-state compliance, and the storage and loss moduli. For linear polymers, linear properties are a rich source of information about molecular structure, rivaling more elaborate techniques such as GPC and NMR. Experiments in the linear regime can also provide information about long-chain branching but are insufficient by themselves and must be supplemented by nonlinear properties, particularly those describing the response to an extensional flow. The experimental techniques and material functions of nonlinear viscoelasticity are described in Chapter 10. 

As shown in Chapter 6, theories containing appropriate forms for all these mechanisms have often proved to be accurate in predicting the linear viscoelastic properties of linear polymers. (In Chapter 11 we will show that even the nonlinear properties of linear polymers can be predicted accurately in some cases.) In fact, theories for the linear viscoelasticity of polydisperse linear polymers are now well enough developed that one can (at least in principle) invert them to infer the molecular weight distribution from linear viscoelastic data see Chapter 8. 

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