Elastic restoring force

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. 

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). 

In most systems, stable bubbles can only be formed in water or an aqueous solution if a surface active agent is present at the interface. When two bubbles are brought into contact, the resistance to coalescence will be determined by the nature of the surfactant film or monolayer. The result of coalescence is always a decrease of interfacial area. However, before coalescence can occur, the surface films around the bubbles are compressed. This gives an increase in O and provides an elastic restoring force tending to oppose the compression. 

Figure 9.3 Schematic illustration of the elastic restoring force for a polymer molecule after stretching. (MacRitchie, F. 1990. Chemistry at interfaces. San Diego, CA Academic Press.)...

When a polymer chain stretches, entropy tends to return the coil to its equilibrium configuration, leading to an elastic restoring force. Thus, elastic stresses are generated as the polymer chain stretches and relaxes in response to flow. A liquid exhibiting both elastic and viscous stresses is viscoelastic. We note that the ratio of a viscosity r/ to an elastic modulus G yields a characteristic relaxation time X rj/G characterizing the memory of a fluid of its past deformation history or the timescale for a stretched polymer chain to relax toward equilibrium. 

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