Langevin-Debye formula

First, consider a very dilute gas of molecules [16]. The conventional theory of the static dielectric susceptibility % of such a gas invokes the notion of polarizable molecules with permanent dipole moments that are partially aligned by the external electric field . Standard techniques of statistical thermodynamics produce the Langevin-Debye formula for x Per molecule that reads... 

In other words, the conventional Langevin-Debye formula is recovered but with the expectation value of the square of the dipole moment operator in place of the square of the permanent dipole moment. 

If the dielectric consists of Nx molecules, having mutually non-interacting electric dipole moments p, (241) reduces to the well-known Langevin-Debye formula ... 

On resorting to the Oausius-Mosotti or the Langevin-Debye formula, we obtain ... 

The use of the Lorentz field for polar molecules with permanent momentsyU and polarizabilities a leads to the familiar Langevin-Debye formula... 

Clear cut simple relations between and have been established only for the primitive Lorentz and wtb store difficulty) Onsager local field models. Simple generalization of the Langevin-Debye formula (19) to relaxation gives a formula of the form (35) vith... 

The Debye-Langevin formula is applicable to polar dielectrics at definite restrictions. It achieves good fulfillment for gases and vapors at low pressure, and for highly dissolved solutions of polar liquids in nonpolar solvents. This formula is of great importance in the interpretation of molecular structures. 

---