Kinetics of a Diffusion Controlled Reaction as Measured by
Fluorescence Spectroscopy
Jonathan Smith
Adapted in part from Experimental Physical Chemistry, 2nd edition, Halpern 1997
We will study the kinetics of a reaction between an electronically excited anthracene molecule and a ground state quencher molecule (CBr4, Pyrene, or other appropriate molecule). The kinetics of this reaction can be followed by fluorescence spectroscopy because upon excitation, anthracene makes a transition to an excited electronic state (S0 -> S1). Anthracene decays from this state back to the ground electronic state by emitting a photon. This emission is called fluorescence emission and can easily be monitored within an instrument called a fluorimeter. The quencher molecule (quenchers) can collide with excited anthracene and quench the fluorescence emission through a bimolecular reaction. This quenching shows itself as diminished fluorescence emission as a function of quencher concentration. Before undertaking this investigation read McQuarrie and Simon section 15.1 through 15.3 on fluorescence and other radiative and non-radiative transitions. Prepare a diagram of the excitation and emission processes we will probe for anthracene. The background for this investigation is provided by Halpern2. An appropriate concentration for anthracene to observe fluorescence excitation and emission would be on the order of 1 x 10-4 M. All samples should be check by UV-Vis absorption spectroscopy to make sure the peak absorbance < 1 unit and to locate maxima for fluorescence excitation wavelength. An Ocean Optics spectrometer interfaced to a computer in the laboratory is the easiest way to carry this out. Include the absorption spectra with an arrow on spectra to indicate wavelength of excitation.
Important Transformations Involved in Fluorescence and Their Kinetics
A + hn ® A* photoexcitation (1)
fluorescence (2)
nonradiative decay (3)
quenching (4)
In the absence of quencher only the first three processes are important (1-3). As quencher concentration increases process 4 begins to compete with fluorescence leading to a diminished level of fluorescence. If we take I0 as the fluorescence emission intensity in the absence of quencher and I as the intensity in the presence of a given concentration of quencher, [Q], the following equation, known as the Stern-Volmer equation, becomes useful for determination of kq if we have a fluorescence lifetime, t0.
(5)
In order for quenching to compete with the radiative process quencher concentrations ranging from those of anthracene to 10-100 times the concentration may need to be explored. The fluorescence lifetime of anthracene was determined by Ware and Novros 3 to be t0= 5.52 x 10-9 sec. Determine if the kq is close to the diffusion controlled rate constant given by equation 35 in section 27.2 in Atkins1.
(6)
This equation arises from considering the rate at which reactants diffuse together:
(7)
where r* is the distance at which reaction occurs and D is the sum of diffusion coefficients for the reactants and NA is Avogadro’s number.
(8)
where
r1 is the radius of reactant 1.
If we assume r1 = r2 = r*/2 then we get
equation 6. For example, the diffusion
rate constant for a reaction at 298 K in hexane would be 2.0 x 1010
L mole-1 sec-1.
Table 1. Representative viscosities
|
Compound |
Viscosity, h [cP, 1 cP = 10-4 kg/m sec] at 298 K |
|
water |
0.891 |
|
methanol |
0.553 |
|
Benzene |
0.601 |
|
hexane |
0.326 |
|
CCl4 |
0.880 |
Steps:
· Outline a procedure for measuring the quenching rate constant, kq, by recording fluorescence emission spectra at multiple quencher concentrations, [Q]. You will first need to record the fluorescence excitation spectrum to determine the best wavelength to excite anthracene.
· Analyze data in SigmaPlot or Excel.
· Provide a rational for this form of the equation and determine if your quenching reaction is diffusion controlled. What would happen if we used a more viscous solvent? Higher temperature?
Useful Links
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to Kinetics and Thermodynamics Page
1.
Atkins, P. Physical Chemistry, 6
ed.; W. H. Freeman and Company:
2.
Halpern, A.
M. Experimental Physical Chemistry, second ed.; Prentice Hall:
3.
Ware, W. R.; Novros,
J. S. Journal of Physical Chemistry 1966, 70, 3246.
Created by Jonathan M. Smith
Updated September 27, 2006