Chemical Potential for an Internal Degree of Freedom

The notion of a chemical potential can also be extended to transformations in an internal degree of freedom of molecules, such as orientation of a polar molecule with respect to an external field (Fig 10.9), deformation of a macromolecule due to flow and similar phenomena [2]. This can be done by defining an internal coordinate 0 just as we define an external coordinate such as the position x. In this section we shall only consider the orientation of an electric dipole with 

Other quantities, such as concentration nt(0), entropy density (0), and the flow in 0-space can be defined as a function of 0, just as they were defined as functions of x. However, in spherical coordinates, since the volume element is equal to sinQdQd, we use the following definitions (Fig. 10.10) 

Jq sin0d0 = number of molecules whose orientation is changing from 0 to 0 -I- J0 per unit time 

For simplicity, we shall consider a unit volume and only one species, dropping the subscript k 

With these definitions it is clear that all the formalism developed in section 10.1 for the position x can be directly converted to 0 by formally replacing x 

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CHEMICAL POTENTIAL FOR AN INTERNAL DEGREE OF FREEDOM with 0. Accordingly, we are led to the equation... 

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