Energetic elasticity

Here./g is called the energetic elasticity, and/ is called the entropic elasticity. For instance, the spring exhibits a high elasticity mainly contributed by the energetic elasticity due to the metallic bonds for the strong interactions of iron atoms, while the rubber exhibits a high elasticity mainly contributed by the entropic elasticity due to the chain conformations for the large deformations of polymers. 

The first term fe = dU/dL)pj gives the part of the tension due to the internal energy, and the second term fs = T df/dT)p L gives the part due to entropy. Thus, the tension is separated into two parts with different origin. These are called energetic elasticity and entropic elasticity. 

In rubbers, however, the modulus increases in proportion to the temperature due to the reduction of the entropy by the constraint brought by deformation. Thus, entropic elasticity and energetic elasticity have opposite tendencies as a function of the temperature. 

One particularly successful example of a Tersoff potential is the reactive empirical bond-order (REBO) potential developed by Brenner (26-29) to describe the covalent bonding interactions in carbon and hydrocarbon systems. Originally developed for use in simulating the chemical vapor deposition of diamond (26), the REBO potential has recently been extended to provide more accurate treatment of the energetic, elastic, and vibrational properties of solid carbon and small hydrocarbons (29). 

One of the most characteristic properties of gel is the rubber elasticity. Rubber elasticity has attracted attention since fire early era of polymer science research and has been developed through statistical mechanics [35, 36]. The basis of rubber elasticity is the micro-Brownian motion of the polymer chains [37]. Specifically, the rubber elasticity originates fixrm entropy and is mechanistically different from the energetic elasticity of fire crystalline solid. The ideal relationship between stress and strain is given by... 

The competition between the polar and steric dipoles of molecules may also lead to internal frustration. In this case, the local energetically ideal configuration cannot be extended to the whole space, but tends to be accomodated by the appearance of a periodic array of defects. For example, the presence of the strong steric dipole at the head of a molecule forming bilayers will induce local curvature. As the size of the curved areas increases, an increase in the corresponding elastic energy makes energetically preferable the... 

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

In uniaxial deformation, the energetic contribution to the total elastic force [4,5,16,80-82] is given by the thermodynamically exact relation... 

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