# Energy Transfer and rate equation

1. Aug 4, 2016

### HAYAO

What is the unit for energy transfer rate constant?

I am confused because of the order of reaction of energy transfer. Consider the case for following energy transfer A* + C → A + C*. The star represent excited state. Then the rate equation for A* would be as follows:
$\frac{d[A^{*}]}{dt} = \frac{d[C]}{dt} = k_{C^{*}\rightarrow A}[A][C^{*}] -k_{A^{*}\rightarrow C}[A^{*}][C]$
and you can see that energy transfer in this case is a second-order reaction.

If $[A^{*}]$ is in unit of concentration M (mol l-1), obviously the unit for $k_{A^{*}\rightarrow C}$ would be M-1 s-1. As so, units are different from typical photophysical process like fluorescence which is usually first order reaction. However, I have seen papers that treats energy transfer as first-order reaction (like this one), while I've seen ones that treats it as second-order reaction (like this one). Which one is right? I think that the latter is right, but then if you think about for example Forster transfer equation:
$k_{A^{*}\rightarrow C} = \frac{9000c^{4}ln10}{128\pi ^{5}n^{4}N_{A}\tau _{0}^{a}}\cdot \frac{\kappa ^{2}}{R^{6}}\int f_{a}(\upsilon )\varepsilon _{b}(\upsilon )\frac{d\upsilon }{\upsilon ^{4}}$
it is obvious that the unit is given as first-order reaction. Do you have to change the units into second-order reaction? If so, then how do you do that?

2. Aug 4, 2016

### Ygggdrasil

Like the rate constants for chemical reactions, the units for the rate constant depends on the exact mechanism of energy transfer. Collisional energy transfer is a different process than resonance energy transfer, so why would you necessarily expect the rate constants to be comparable?

3. Aug 4, 2016

### HAYAO

Because in the above two papers I have given as an example both considers the energy transfer to be in resonance mechanism. Despite so, both paper have different take on whether the transfer is first-order or second-order.

4. Aug 5, 2016

### Ygggdrasil

I think the equation for Förster resonance energy transfer assumes that the transfer occurs intramolecularly, especially because the equation requires defining the distance (R) between the transition dipoles as well as their relative orientation (κ2). Perhaps the difference between the two papers is whether they're considering intermolecular RET or intramolecular RET (again, the details of the exact mechanism are important).

5. Aug 5, 2016

### HAYAO

Yes, that is what I thought. But both papers consider intramolecular RET, hence the reason I am confused.