Dear Pratik.

If there is energy transfer from sensitizer to activator and if you are measuring the lifetime of sensitizer with and without activator, the lifetime will be faster in sensitizer activator pair. The change in the lifetime of sensitizer in presence of activator is mainly due to energy transfer between the ions.

In fact you can determine the yield of energy transfer by the simple relationship: yield= 1-(lifetime)/(lifetime without activator).

However since the electronic structure of upconversion systems is usually complex with several possible paths for energy migration, it is difficult to relate these data to a specific mechanism.

For an insight into energy transfer mechanism in UCNPs, you can have a look at this paper:

http://pubs.rsc.org/en/content/articlepdf/2015/cs/c4cs00188e

Dear Pratik,

You can see our recent paper which discuss energy transfer pathways by lifetime data.

Article Competing effects of sensitization and energy dissipation by...

Competing effects of sensitization and energy dissipation by Ni2+ incorporation in LaGaO3:Er,Ni upconverters

If T is total lifetime without activator, Ta be lifetime with M concentration of activator.

We get,

Ta proportional to T/M

hence Ta = kT/M, were k is proportionality constant

this proportionality constant is because of difference in conversion rate of different activators hence its value can vary with different samples but for a specific sample it should remain constant

Nonlinear spectral and lifetime management in upconversion nanoparticles by controlling energy distribution†

Yu Wang a, Renren Deng a, Xiaoji Xie b, Ling Huang *b and Xiaogang Liu *acd