The expression for the anisotropy decay contains a numerator and a denominator.

The numerator is the difference in parallel-polarized and perpendicular-polarized components of the emission. The expression for this is essentially a product of a term which depends on the rotational correlation time and a term which depends on lifetime.

The denominator is essentially the total intensity decay of the emission which only depends on the lifetime.

When the numerator is divided-by the denominator the terms containing the lifetime (total intensity decay) cancel leaving only the terms containing the rotational correlation time.

Note that this is only true when the rotational motion and intensity decays are independent and unassociated. For associative decay the situation is more complex. 

I am happy to write this out for you but it is difficult to do in text mode.

The steady-state anisotropy involves the integrated parallel and integrated perpendicular intensities. You need to solve the integrals and insert them into the expression for the anisotropy.

Again happy to show you but hard to write it out in text mode.

Hope this helps.

Best Wishes,

Andrew

The expression for the anisotropy decay contains a numerator and a denominator.

The numerator is the difference in parallel-polarized and perpendicular-polarized components of the emission. The expression for this is essentially a product of a term which depends on the rotational correlation time and a term which depends on lifetime.

The denominator is essentially the total intensity decay of the emission which only depends on the lifetime.

When the numerator is divided-by the denominator the terms containing the lifetime (total intensity decay) cancel leaving only the terms containing the rotational correlation time.

Note that this is only true when the rotational motion and intensity decays are independent and unassociated. For associative decay the situation is more complex. 

I am happy to write this out for you but it is difficult to do in text mode.

The steady-state anisotropy involves the integrated parallel and integrated perpendicular intensities. You need to solve the integrals and insert them into the expression for the anisotropy.

Again happy to show you but hard to write it out in text mode.

Hope this helps.

Best Wishes,

Andrew

Dear Andrew,

Thank you so much for this bright answer.

Oh, math! you are right! I think the paradox has been solved ,

I have fallowed  associative model, that was amazing too. I learned a lot.

Hi Andrew  Great answer and very informative.  Why not write out the further description in longhand, scan in the document with your lucid handwriting on it, and then attach to this answer? I think we'll all learn a little more with this (relatively easy to accomplish) further addition.  Anisotropy is a fascinating aspect from all angles - bad pun intended -  first started to grasp some of the nuances in liquid crystal work with birefringence and tendency to form ordered phases.

Andrew gave you a very good answer.

Please launch google scholar and insert the part of your question:

here the link:

https://scholar.google.de/scholar?hl=de&q=What+is+the+relationship+between+fluorescence+lifetime+and+anisotropy%3F&btnG=&lr=

you´ll earn a lot of hits.

Good luck

JRG

Dear Hamid,

by the way, it is worth noting that the steady-state fluorescence anisotropy depends on the fluorescence decay time. Thus, in the simplest case:  r=r(0)/(1+T/Q). This is a transposed form of the so called Perrin equation for spherical rotors.

Regards,

Aleksander

I have concluded this discussion in this Pdf file.

You can find the matematical proof of each model

Hamid