Rotational diffusion was solved by Edwardes / Perrin / Langevin at their times. It is normally made for particles of Ellipsoid shape, since it is easier to solve analitycally. A long and thin ellipsoid is your rod. Try Google "ellipsoid brownian motion". The model is for macroscopic particles immersed in a viscous fluid, but should work also for long molecules in a gas.

Solution, thin ellipsoid of axis $a$ (roughly equivalent to $2a$ rod) and (small) radius $b$:

$D = \frac{kT}{C_r} $

Where $C_r$ is the friction for the ellipsoid rotating in the fluid; for our thin rod,

$ C_r \simeq \frac{16 \pi \eta}{3 P_r} $

Where again, the $P_r$ is an elliptic integral that represent the particle size, at the moment I don't manage to calculate:

$ P_r = \int ^{\infty} _0 \frac{dx}{(a^2 +x)^{\frac{3}{2}} (b^2 + x) } $

All this discussion work for orientation the mayor axis of a thin rod (rotation around the two perpendicular axes); if the particle has a stranger shape, I guess we must consider all components and tensors.

Here some paper where the model si discussed in english: Paper Wegener et al, A general ellipsoid cannot always .. Koening, Brownian motion of an ellipsoid And the book The Langevin equation by Coffey has a chapter. Wikipedia Perrin friction factors

Rotational diffusion was solved by Edwardes / Perrin / Langevin at their times. It is normally made for particles of Ellipsoid shape, since it is easier to solve analytically. A long and thin ellipsoid is your rod. Try Google "ellipsoid brownian motion". The model is for macroscopic particles immersed in a viscous fluid, but should work also for long molecules in a gas.

Solution, thin ellipsoid of axis $a$ (roughly equivalent to $2a$ rod) and (small) radius $b$:

$D = \frac{kT}{C_r} $

Where $C_r$ is the friction for the ellipsoid rotating in the fluid; for our thin rod,

$ C_r \simeq \frac{16 \pi \eta}{3 P_r} $

Where again, the $P_r$ is an elliptic integral that represent the particle size, at the moment I don't manage to calculate:

$ P_r = \int ^{\infty} _0 \frac{dx}{(a^2 +x)^{\frac{3}{2}} (b^2 + x) } $

All this discussion work for orientation the mayor axis of a thin rod (rotation around the two perpendicular axes); if the particle has a stranger shape, I guess we must consider all components and tensors.

Here some paper where the model is discussed in English: Paper Wegener et al, A general ellipsoid cannot always .. Koening, Brownian motion of an ellipsoid And the book The Langevin equation by Coffey has a chapter. Wikipedia Perrin friction factors

Rotational diffusion was solved by Edwardes / Perrin / Langevin at their times. It is normally made for particles of Ellipsoid shape, since it is easier to solve analitycally. A long and thin ellipsoid is your rod. Try Google "ellipsoid brownian motion". The model is for macroscopic particles immersed in a viscous fluid, but should work also for long molecules in a gas.

Solution, thin ellipsoid of axis $a$ (roughly equivalent to $2a$ rod) and (small) radius $b$:

$D = \frac{kT}{C_r} $

Where $C_r$ is the friction for the ellipsoid rotating in the fluid; for our thin rod,

$ C_r \simeq \frac{16 \pi \eta}{3 P_r} $

Where again, the $P_r$ is an elliptic integral that represent the particle size, at the moment I don't manage to calculate:

$ P_r = \int ^{\infty} _0 \frac{dx}{(a^2 +x)^{\frac{3}{2}} (b^2 + s) } $

All this discussion work for orientation the mayor axis of a thin rod (rotation around the two perpendicular axes); if the particle has a stranger shape, I guess we must consider all components and tensors.

Here some paper where the model si discussed in english: Paper Wegener et al, A general ellipsoid cannot always .. Koening, Brownian motion of an ellipsoid And the book The Langevin equation by Coffey has a chapter. Wikipedia Perrin friction factors

Rotational diffusion was solved by Edwardes / Perrin / Langevin at their times. It is normally made for particles of Ellipsoid shape, since it is easier to solve analitycally. A long and thin ellipsoid is your rod. Try Google "ellipsoid brownian motion". The model is for macroscopic particles immersed in a viscous fluid, but should work also for long molecules in a gas.

Solution, thin ellipsoid of axis $a$ (roughly equivalent to $2a$ rod) and (small) radius $b$:

$D = \frac{kT}{C_r} $

Where $C_r$ is the friction for the ellipsoid rotating in the fluid; for our thin rod,

$ C_r \simeq \frac{16 \pi \eta}{3 P_r} $

Where again, the $P_r$ is an elliptic integral that represent the particle size, at the moment I don't manage to calculate:

$ P_r = \int ^{\infty} _0 \frac{dx}{(a^2 +x)^{\frac{3}{2}} (b^2 + x) } $

All this discussion work for orientation the mayor axis of a thin rod (rotation around the two perpendicular axes); if the particle has a stranger shape, I guess we must consider all components and tensors.

Here some paper where the model si discussed in english: Paper Wegener et al, A general ellipsoid cannot always .. Koening, Brownian motion of an ellipsoid And the book The Langevin equation by Coffey has a chapter. Wikipedia Perrin friction factors