i shall think

If you want to determine fluorescence quantum yield, you should check "Correction of fluorescence spectra and measurement of fluorecence quantum efficiency" by Parker & Rees (Analyst 1960, 85, 587-600); You can also check on the internet for a document from Jobin Yvon "A Guide to Recording Fluorescence Quantum Yields"

The following are just a suggestions but one of them may work for your situation.  

The difficulty that you seem to have is that it takes quite a bit of time to measure a quantum yield (speaking from experience) and your systems quantum yield is changing with time making it impossible to measure accurately. Therefore is suggest measuring the Quantum Yield indirectly by one of the two following methods.

Method 1:

Given that the Quantum Yield (QY) is equal to the rate of fluorescence (kF) times the lifetime (t ).  (ie QY=kFt ).

If you measure the quantum yield of the the compound BEFORE adding the catalysts and also measure its excited state lifetime you will be able to extract a value for kF.   The value of kF is intrinsic to the molecule and should not change even after the addition of the catalyst.

Once you have kF and provided that you have the means of measure lifetime rapidly (ie. TCSPC)  you could then simple measure the lifetime at given time intervals and apply the equation above to obtain the quantum yield as a function of time.  

Method 2:

You may be able to use fluorescence spectroscopy to obtain the QY as a function of time.  To do this I would measure the emission spectrum at several time intervals and plot the intensity vs. time.  this should give you a negative slope that can then be used to extract a rate constant (see any phys chem text book to remind you how to get first and second order rate constants from such a graph).  I believe that the rate will most likely be first order.

If it is first order you can then simply apply the equation:

QY(t) = QYoe-kt   where k is the first order rate constant that you obtained from the graph above and QYo is the initial quantum yield BEFORE adding the catalyst.   Using this equation will then allow you to calculate the QY at any given time.  

Of course these methods will only work if you catalyst is relativity  slow acting (ie.  you are able to make the measurements before before there is any kind of significant change)     

I hope this helps. 

Thank you very much for the advice.

There are two common ways to measure Fluorescence Quantum Yield(FQY), the first is absolute and the second is relative method. It is very obvious that both these two methods have their own advantages and disadvantages. The direct method is difficult and needs special instruments, however the relative method is simple and widespread. This method was introduced by Parker and Rees in 1960 as was also mentioned in above comments by Adam Langlois.

In relative method, an unknown FQY sample is measured by using another sample with known FGY in the same physical conditions.

For example, I measured FQY of DCM dye with relative method. In the experiments FQY of DCM was considered as unknown FQY and CVP dye was also considered as standard sample with known FQY. With the same excitation source (Frequency doubled Nd:YAG laser) the fluorescence spectra of both these dyes collected. In addition, absorbance of these dyes were measured in the same condition.

Finally with using the formula mentioned in this article (Fluorescence Quantum Yields of a Series of Red and Near-Infrared Dyes Emitting at 600- 1000 nm, Analytical chemistry, 2011) FQY of DCM dye was achieved.