Entropic force constant

II) a is an entropic force constant obtainable from the theory of rubber elasticity and equal to 3kTjo1. At 300° K, this quantity is about 50 dynes/cm. 

Figure 10.3 Carbide hardnesses vs. characteristic vibrational energy densities derived from average force constants (entropic specific heat). After Grimvall and Theissen (1986). The crystal structures are of the NaCi type. The hardness data are fromTeter (1998).

In essence, the ability to maximize entropy by sorting different-sized objects creates a kind of attractive force, called a depletion, or excluded-volume, force. These entropic forces operate for objects in the size range of approximately 10-8 to approximately 10 6 m. For entropy-induced ordering to occur, the particles must be constantly jostling each other and must be constantly agitated by solvent molecules, thus making gravity unimportant. 

As seen in Chapter 3, the force constant on the harmonic spring is of entropic origin. The spring forces on bead 1 and bead 2, denoted by Fi and F2, respectively, are given by... 

The entropic force inside each tube segment is linear with the spring constant k=3kBT/ Nj/). 

The result implies that a sequence behaves like a spring, showing a linear relation between force and extension. The force constant is proportional to the absolute temperature T, as is characteristic for forces of entropic origin. Note furthermore that 6r decreases on increasing the size of the sequence. 

This in an interesting result. It tells us that this entropic force increases linearly with the distance between the two end-groups, just as if they were connected by a mechanical spring. The stiffness constant, denoted 6, increases with temperature and decreases with an increasing size of the chain. 

Althongh van der Waals forces are present in every system, they dominate the disjoining pressnre in only a few simple cases, such as interactions of nonpolar and inert atoms and molecnles. It is common for surfaces to be charged, particularly when exposed to water or a liquid with a high dielectric constant, due to the dissociation of surface ionic groups or adsorption of ions from solution, hi these cases, repulsive double-layer forces originating from electrostatic and entropic interactions may dominate the disjoining pressure. These forces decay exponentially [5,6] ... 

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