Elasticity restoration

The expansion of the coil domain produces an elastic restoring force which opposes the expansion by tending to restore the molecule to its most probable conformation. 

Elastomer Impression Materials. Dentistry requires impression materials that are easily handled and accurately register or reproduce the dimensions, surface details, and interrelationship of hard and soft oral tissues. Elexible, elastomeric materials are especially needed to register intraoral tooth stmctures that have undercuts. The flexibility of these elastomers allows their facile removal from undercut areas while their elasticity restores them to their original shape and size. 

When an elastic polymer network is stretched, the polymer chains are deformed. The verification of the theory has been largely based on measurements of the elastic restoring forces... 

FERROELECTRIC EFFECT. The phenomenon whereby certain crystals may exhibit a spontaneous dipole moment twhich is called ferroelectric by analogy with ferromagnetic—exhibiting a permanent magnetic moment). The effect in the most typical case, barium manate. seems to he due to a polarization catastrophe, in which the local electric fields due lo the polarizuiion itself increase faster than die elastic restoring forces on the ions in Ihe crystal, thereby leading to an asymmetrical shift in ionic positions, and hence lo a permanent dipole moment. Ferroelectric crystals... 

In extensional flow, droplets or high-viscosity particles are drawn out into filaments that ultimately break up into smaller droplets. For the droplets to break up, the load must be maintained for a certain period of time. It can also be beneficial to deform the droplet, allow it to relax briefly and then apply the load again. This enables elastic restoring forces in high-viscosity droplets to be overcome. 

It is easy to understand that these solutions must exhibit viscoelastic properties. Under shear flow the vesicles have to pass each other and, hence, they have to be deformed. On deformation, the distance of the lamellae is changed against the electrostatic forces between them and the lamellae leave their natural curvature. The macroscopic consequence is an elastic restoring force. If a small shear stress below the yield stress ery is applied, the vesicles cannot pass each other at all. The solution is only deformed elastically and behaves like Bingham s solid. This rheological behaviour is shown in Figure 3.35. which clearly reveals the yield stress value, beyond which the sample shows a quite low viscosity. 

At equilibrium the electrical force causing compression is balanced by the elastic restoring force, as expressed by the equation ... 

Following the Pincus picture [42], an elastic restoring force develops,... 

The elastic term takes into account the elastic restoring force, tending to establish a spatially uniform LC ordering. It is expressed as... 

In equation (6-53) / is the total elastic restoring force exerted by the sample. For many purposes it is more convenient to deal with expressions relating the stress to the deformation rather than the total force as in equation (6-53). For this purpose we define a stress cross-sectional area of the undeformed sample. We further define N0 = NIVq as the number of network chains per unit volume of the undeformed sample, where V0 = LqA0. 

The swelling and bending behaviour of hydrogels results from the equilibrium of different forces osmotic pressure forces, electrostatic forces, visco-elastic restoring forces, etc. To describe the different phenomena occurring in the gels and between the gel and solution phase adequately, the modelling can be performed on different scales (Fig. 3) ... 

Suppose that there are in a molecule positive and negative charges susceptible of relative displacement under the influence of a field. The polarization that occurs may be formally represented as the movement of a charge e through a distance x. If there were no field, the displacement would be reversed, so that an elastic restoring force may be formally postulated. The potential energy increase attending the elastic displacement is... 

The maximum amount of energy that can be converted using a given amount of film depends on the material properties. Several different material properties come into play including the maximum strain that can be imposed before mechanical failure, the maximum electric field that can be supported before electrical breakdown, and the need to maintain elastic restoring forces. 

The elasticity of rubbers is very different from that of materials such as metals or even glassy or semicrystalline polymers. Young s moduli for metals are typically of the order of 10 MPa (see table 6.1) and the maximum elastic extension is usually of order 1% for higher extensions fracture or permanent deformation occurs. The elastic restoring force in the metal is due to interatomic forces, which fall off extremely rapidly with distance, so that even moderate extension results in fracture or in the slipping of layers of atoms past each other, leading to non-elastic, i.e. non-recoverable, deformation. 

D. Bhaumik, K. Bhaumik, B. Dutta-Roy, and M. Engineer, Polar Modes with Elastic Restoring Forces, Bose Condensation, and the Possibility of a Metastable Ferroelectric State, Phys. Lett. 62A, 197-200 (1977). 

Any spatial distortion of n leads to elastic restoring torques, which are determined in the standard continuum description of nematics (exclusively used in this review) by three elastic constants Ki (splay), K2 (twist) and Ks (bend). In addition, the electric field E gives rise to an electric torque on the director. The balance of these torques, reflected in the resulting equilibrium director configuration, corresponds to the minimum of the orientational free energy J- n). For positive dielectric anisotropy (ca = — x) the dielectric torque (oc is destabihzing in the pla-... 

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