Elastic force entropic component

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

Figure 5.7. Thermoelasticity experiments to estimate the entropic component of elastic force in pure water (curves B) and in the solvent mixture of 30% ethylene glycol 70% water (curves A). On increasing ethylene to 30%, the heat of the transition approaches zero, which means that the solvent entropy change approaches zero. The purpose of the experiment is to see if solvent entropy change contributes to the force developed on raising the temperature. Interestingly, the 90% entropic elastic force...

From Equation (1) the entropic component of the elastic force, /s, is proportional to -AS, that is, an increase in entropic elastic force results from a decrease in entropy. Also the formation of hydrophobic hydration from bulk water constitutes an inherently negative AS, and, of course, the loss of hydrophobic hydration constitutes a positive change in entropy. This change in solvent entropy due to formation of hydrophobic hydration has been credited as an important contribution to entropic elastic force (Weis-Fogh and Anderson, 1970 Wasserman and Salemme, 1990 Alonso et al., 2001). Therefore, the immediate question becomes whether experimental results support or eliminate a decrease in solvent entropy as a source of entropic elastic force. 

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. ... 

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

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]. 

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