Elastic force energetic component

Force-temperature ("thermoelastic") relations lead to a quantitative assessment of the relative amounts of entropic and energetic components of the elasticity of the network. 

Starting from Eq. (79), Kilian9,501 obtained the following expressions for the entropic and energetic components of the elastic force f in simple extension... 

By combining equation (6-26) with equation (6-10), the energetic component of the elastic force fe becomes... 

The energetic and entropic components of the elastic force, fe and fs, respectively, are obtained from thermoelastic experiments using the following equations ... 

Figure 3.8 Energetic dE/dL)p j and entropic T df/dT)p i components of the elastic force.

Thermodynamic analysis of rubber elasticity enables one to resolve the elastic force into entropic and energetic components, thereby elucidating the origin of rubberlike elasticity in general. It also indicates that intermolecular interactions do not affect the force and must be independent of the extent of the deformation and thus of the spatial configurations of the chains. Since the spatial configurations are independent of intermolecular interactions, the amorphous chains must be in random unordered configurations, the dimensions of which should be the unperturbed values. ... 

Elastic interaction occurs when the displacement fields from steps substantially superpose. Atoms located in the vicinity of steps tend to relax stronger compared to those farther away. The resulting displacements or lattice distortions decay with increasing distance perpendicular to the steps. Atoms situated in between two steps experience two opposite forces and cannot fully relax to an energetically more favorable position as would be the case with quasiisolated steps. The line dipoles at steps are due to Smoluchowski smoothing [160] and interact electronically. Only dipole components perpendicular to the vicinal surface lead to repulsion whereas parallel components would lead to attractive interaction. The dipole-dipole interaction seems to be weaker than the elastic one. For instance, steps on vicinal Ag(lll) have weak dipoles as was shown in a theoretical study [161]. Entropic interaction is due to the condition that steps may not cross and leads to an effective repulsive potential, the weakest interaction type. This contribution is always present and results from the assumption that cavities under the surface are unstable. Experiments and theory investigating steps on surfaces were recently reviewed [162]. 

The solid friction is calculated by an energetic approach which is described in [1] and in more depth by Bartel [10]. The components of the solid friction are deformation and adhesion. The first one can be calculated from the elastic-, plastic deformations of the macro and micro geometry. To calculate the adhesion force, some assumptions have to be taken into account at the moment Adhesive bonding can only occur if plastic deformation of the material takes place and secondly if local temperatures exceed a critical value which lead to a desorption of the fluid film. Since the simulation program is not able to determine local temperatures yet, the second assumption cannot be tested. But it seems reasonable that the plastically deformed micro asperity also experience local temperature peaks. Since it is quite sophisticated to get reliable values for the shear strength in adhesive bonding, in this work one sixth of the universal hardness or plastic pressure limit of 100Cr6 (SAE 52100), respectively, is used ... 

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