Debye considered in 1912 the behavior of polar molecules placed between the condenser plates. We can see fig (A) in the absence of an electric field or a thermal motion; the molecules are randomly oriented and have no net dipole moment.
As shown in fig (B), if an electric field is applied across the plates of the condenser, it molecules the combined electric field and thermal motion.
Absence of electric field
Presence of electric field
Debye calculated the average component permanent dipole moment μ that molecule in the direction of an electric field in function temperature. In the absence of an electric field, a randomly oriented dipole, all orientations are equally probable.
It means the number of dipole moments directed within solid angle dw is adw,
A = constant it depends on the number of molecules under observation
U is the potential energy of a polar molecule with μ molecular dipole moment. Angle Q = electric field of strength E is,
For Boltzmann distribution, the number of molecules oriented within solid angle dw is,
The average value of diploe moment in the direction of the field is,
Now, integrals take over all the possible orientations,
Therefore equation (4) takes from the,
Standard integrals,
and
Here, L(x) = Langevin function
Here, a graph plotted Langevin function L(x) against x.
At room temperature x<<1, expanding L(x) as power series, only first term giving L(x) = x/3
See in graph μind decreases with increasing temperature, also μind α to E.
However, proportionality between μind and E cannot be maintained; if E is large, then saturation occurs.
If all molecules were completely oriented, E would not increase
αμdepends upon permanent dipole moment and temperature (T). It is declining with increasing temperatures.
At higher temperatures, thermal motion deduced the dipole orientation in the field.
But Clausius – mossotti equation, the αμ term was ignored, and Debye took into both αd and αμ
SI Units,
The above equation (13) and (14) is known as the Debye equation.
