Elastic properties, molecular basis

The fundamental driving force behind the remarkable elastic properties of the elastin polymer is believed to be entropic, where stretching decreases the entropy of the system and elastic recoil is driven by a spontaneous return to maximum entropy. The precise molecular basis for elasticity has not been fully elucidated and a number of models exist. Two main categories of structure-function models have been proposed those in which elastin is considered to be isotropic and devoid of structure, and those which consider elastin to be anisotropic with regions of order (Vrhovski and Weiss, 1998). 

Chandrasekhar, 1977). This cooperative behavior results in weak elastic properties. Then, the application of an electric field can easily change the molecular orientation, which is initially fixed by the mechanical boundary conditions. The concomitant changes in the optical properties form the basis of liquid crystal displays (LCD). 

Evidence for wall slip was suggested over thirty years ago [9,32,63]. One of the first attempts at a slip mechanism was the performance of a Mooney analysis by Blyler and Hart [32]. Working in the condition of constant pressure, they explicitly pointed out melt slip at or near the wall of the capillary as the cause of flow discontinuity. On the other hand, they continued to insist that bulk elastic properties of the polymer melt are responsible for the flow breakdown on the basis that the critical stress for the flow discontinuity transition was found to be quite insensitive to molecular weight. Lack of an explicit interfacial mechanism for slip prevented Blyler and Hart from generating a satisfactory explanation for the flow oscillation observed under a constant piston speed. 

The resultant adhesion of particles to a deformed surface is equal to the force of molecular interaction as determined by Eq. (11.70) or (11.71), weakened by the force of repulsion caused by the elastic properties of the contiguous bodies. The force of repulsion of surfaces that have been subjected to deformation can be taken into account on the basis of the Hertz law ... 

A considerable number of experimental studies, as well as theoretical developments, have been done on the equilibrium elastic properties of regular model silicone networks in absence of pendant chains. The goal of most of these studies has been to test quantitatively the molecular basis of the theory of rubber elasticity. One of the major concerns has been the influence of topological interactions between chains on elastic properties of the networks. However, despite the considerable amount of experimental work, there is still considerable debate concerning the validity and applicability of different models. 

Due to such densely packed molecularly interpenetrated structures, rubbers are incompressible under deformation. Each chain takes a Gaussian conformation following the Flory theorem for screened excluded-volume interaction. On the basis of these characteristics, we can derive the elastic properties of rubbers from a microscopic point of view. 

The need for a fully statistical mechanical theory of polymers in bulk is more than just a question of rigor or elegance. We mentioned earlier the questions cancerning the relation between average structural and elastic properties of polymer networks. More important, the present statistical theories of bulk polymer elasticity fail to account for interactions between different chains in the network. Therefore they cannot be expected to provide a proper molecular basis for an understanding of elasticity at large deformations, of crystallization upon stretching, etc. A description of these phenc mena requires a fully statistical mechanical description of the polymer network. In such a description, the observable properties of the system are formally presented in terms of the properties of the constituent polymers and their mutual interactions. Thus all macroscopic-properties are expressed in terms of the microscopic properties of the individual polymer chains. 

Once the existence of polymer chains as covalent structures became established a half century ago, the understanding of the molecular basis of the high elasticity characteristic of rubber-llke substances presented Itself as a foremost challenge. The first attempts to explain this remarkable property may be said to date from the beginning of molecular theory as applied to polymers. Although the subject today Is old. It Is of continuing Interest and one In which much remains to be done before an acceptable state of completion will have been attained. 

Elasticity is a macroscopic property of matter defined as the ratio of an applied static stress (force per unit area) to the strain or deformation produced in the material the dynamic response of a material to stress is determined by its viscosity. In this section we give a simplified formulation of the theory of torsional elasticity and how it applies to liquid crystals. The elastic properties of liquid crystals are perhaps their most characteristic feature, since the response to torsional stress is directly related to the orientational anisotropy of the material. An important aspect of elastic properties is that they depend on intermolecular interactions, and for liquid crystals the elastic constants depend on the two fundamental structural features of these mesophases anisotropy and orientational order. The dependence of torsional elastic constants on intermolecular interactions is explained, and some models which enable elastic constants to be related to molecular properties are described. The important area of field-induced elastic deformations is introduced, since these are the basis for most electro-optic liquid crystal display devices. 

Dynamic mechanical techniques are important in the characterization of the rheological properties of polymers. In dynamic mechanical analysis, a small-amplitude oscillatory strain is applied to a sample, and the resulting dynamic stress is measured as a function of time. The dynamic mechanical technique allows the simultaneous measurement of both the elastic and the viscous components of the stress response. Typically, the temperature and deformation frequencies are changed in order to determine the mechanical relaxation spectrum of the system. The molecular basis of changes in the dynamic mechanical properties can be investigated using dynamic IR dichroism. 

The various elastic and viscoelastic phenomena we discuss in this chapter will be developed in stages. We begin with the simplest the case of a sample that displays a purely elastic response when deformed by simple elongation. On the basis of Hooke s law, we expect that the force of deformation—the stress—and the distortion that results-the strain-will be directly proportional, at least for small deformations. In addition, the energy spent to produce the deformation is recoverable The material snaps back when the force is released. We are interested in the molecular origin of this property for polymeric materials but, before we can get to that, we need to define the variables more quantitatively. 

Some wild species have larger capacities for osmotic adjustment, a trait which may improve yield during drought (Table 3, Turner, 1986). Interesting examples of this are Dubautia species from Hawaii which differ in osmotic adjustment mainly as a result of differences in cell wall elasticity. Interspecific hybrids can be made which have intermediate properties (Robichaux, Holsinger Morse, 1986). Material such as this could make a basis for the molecular study of differences in cell wall elasticity. 

It is possible to classify polymers by their structure as linear, branched, cross-linked, and network polymers. In some polymers, called homopolymers, merely one monomer (a) is used for the formation of the chains, while in others two or more diverse monomers (a,p,y,...) can be combined to get different structures forming copolymers of linear, branched, cross-linked, and network polymeric molecular structures. Besides, on the basis of their properties, polymers are categorized as thermoplastics, elastomers, and thermosets. Thermoplastics are the majority of the polymers in use. They are linear or branched polymers characterized by the fact that they soften or melt, reversibly, when heated. Elastomers are cross-linked polymers that are highly elastic, that is, they can be lengthened or compressed to a considerable extent reversibly. Finally, thermosets are network polymers that are normally rigid and when heated do not soften or melt reversibly. 

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

The methods utilized to measure the viscoelastic functions are often close to the stress patterns occurring in certain conditions of use of polymeric materials. Consequently, information of technological importance can be obtained from knowledge of these functions. Even the so-called ultimate properties imply molecular mechanisms that are closely related to those involved in viscoelastic behavior. Chapters 16 and 17 deal with the stress-strain multiaxial problems in viscoelasticity. Application of the boundary problems for engineering apphcations is made on the basis of the integral and differential constitutive stress-strain relationships. Several problems of the classical theory of elasticity are revisited as viscoelastic problems. Two special cases that are of special interest from the experimental point of view are studied viscoelastic beams in flexion and viscoelastic rods in torsion. 

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