Stern–Volmer relationship

The Stern-Volmer equation describes in physical chemistry, the dependence of the quantum yield and the intensity of the fluorescence of a fluorescent dye of the concentration of substances that quench the fluorescence (so-called quencher). With the Stern-Volmer equation can be described by the concentration of the quencher in certain circumstances, the dependency of the lifetime of the excited state of a fluorescent dye.

The equation comes from a collaboration between the physical chemist Otto Stern and Max Volmer on physico-chemical Institute of the Berlin University in Walther Nernst. The Stern-Volmer equation was described by Stern and Volmer, 1919 in the article "On the decay time of the fluorescence " which was published in the scientific journal Physical Journal, for the first time.

The equation is in its classical form:

The fluorescence intensity of the fluorescent dye is ( the fluorophore ) in the absence of the quencher, the fluorescence intensity thereof in the presence of the quencher, the concentration of the quencher and the Stern-Volmer constant.

Frequently the following notation of the Stern-Volmer equation is preferred:

If the term plotted against the concentration, the result is a simple linear relationship. The slope of the line is then the Stern-Volmer constant.

An important prerequisite for the validity of the Stern-Volmer equation, the same access to all the molecules of the fluorophore by the quencher is: for all molecules of the fluorophore must apply the same Stern-Volmer constant. If a portion of the molecules of the fluorophore to the quencher better or less accessible - and thus their fluorescence better or worse deleted - as the Stern-Volmer equation in the above form is not applicable. It must then be modified.

Another important requirement is the Stern-Volmer equation, the quencher may quench the fluorescence in only one way. Deletes the quencher, the fluorescence in various ways, the Stern-Volmer equation in the above form is not applicable. It must then be modified.

• 2.1 derivation

The Stern- Volmer constant for dynamic quenching

Also referred to as dynamic quenching or dynamic quenching - - With dynamic fluorescence quenching, the quencher collide with the fluorophore. The fluorophore is in the collision in its excited state, the fluorophore in the excited state returns to the ground state without emitting photons. Therefore, the dynamic fluorescence quenching is also referred to as collisional quenching. The dynamic fluorescence quenching is therefore based on the energy of the excited fluorophore is released radiationless.

The Stern- Volmer constant is for the dynamic fluorescence quenching:

It is the bimolecular Quenchingkonstante and the lifetime of the excited state of the fluorophore in the absence of the quencher.

The bimolecular Quenchingkonstante can be calculated directly from the lifetime of the unperturbed fluorophore (= 0), and the lifetime of the fluorophore to the quencher concentration:

The bimolecular Quenchingkonstante is also displayed as:

Here, the bimolecular rate coefficient for collisions is: this coefficient indicates the probability with which the Fluorophormolekül and the quencher collide. The bimolecular rate coefficient can be calculated using the Smoluchowski equation. Said parameter is the Quencheffizienz and indicates the probability that the excited fluorophore, the quencher clears in a collision. The Quencheffizienz can take values ​​between zero and one: Is equal to zero, the excited fluorophore is never deleted by the quencher, no matter how often it hits the fluorophore. The quencher is in the sense of dynamic Fluoroeszenzlöschung then no quencher. If the Quencheffizienz equal to one, so the quencher deletes the excited fluorophore at each ereignendem to shock.

For dynamic quenching the reduction of the lifetime of the excited state in the presence of the quencher is characteristic. Each is the long-lived excited state, the more likely will be a collision between the quencher and the fluorophore excited, and thus the deletion. Therefore, the following relationship applies for the dynamic fluorescence quenching:

For the same concentration of the quencher is in the dynamic fluorescence quenching when the temperature rises, the value of which in principle is greater, that is, the quencher erases faster than at a lower temperature at a higher temperature: the diffusion rate of the quencher - and thus also the bimolecular rate coefficient - taking with increasing temperature to reducing the number of collisions with the fluorophore, and thus the number of erase operations, also increases. This is an important distinction between dynamic and static fluorescence quenching, since it basically behaves in the static fluorescence quenching other way around.

The former was for a homogeneous Fluorophorpopulation. If more than one Fluorophorpopulation ago - so when multiple fluorophores are present or if the members of a fluorophore species reside in different chemical environments and thereby significantly in their fluorescence behavior, ie measurable differ - then is the Stern-Volmer equation for dynamic quenching for a heterogeneous Fluorophorpopulation:

It is the Stern-Volmer constant for the dynamic quenching of the ith Fluorophorpopulation and the proportion of the total of the ith Fluorophorpopulation intensity of fluorescence:

It is the fluorescence intensity of the ith Fluorophorpopulation.

Derivation

The fluorophore F passes through the absorption of a photon - symbolized by the expression - R * in an excited state through:

Here, the absorption rate constant, with the fluorophore changes from the ground state to the excited state. The reaction rate constant is expressed as the number per second, the starting materials are converted to products.

From this excited state, the fluorophore can return to the ground state via several routes:

In (A) the fluorophore passes through the emission of a photon in the ground state ( fluorescence) in (B ) is the energy of the excited state by other processes going radiation, through heat and in (C) is the excited state radiationless by the quencher transferred to the ground state. In this case, the quencher absorbs the energy of the excited state of the fluorophore, symbolized by Q '.

The three reaction routes ( A), ( B) and (C) have the respective speed constants and.

The fluorescence quantum yield is defined as:

Here, the number of fluorescence photons emitted by per unit time and the number of absorbed photons per unit time by the fluorophore.

The number of photons emitted per unit time is determined by (A ) from the concentration of the excited fluorophore and:

(see also: first-order reaction )

The number of absorbed photons can be analogous to, determine the concentration of the fluorophore F and the rate constant. As the excited fluorophore F * by the above processes (A), (B) and (C) returning to the initial state, the two processes are the absorption and loss of the excitation energy through the three processes ( A), ( B) and ( C) in the equilibrium state of equal size:

In this case, the reactions (A) and (B), first-order reactions, during the reaction (C ) is a second-order reaction.

And by replacing the quantum yield of fluorescence after reduction is to:

In the absence of the quencher - i.e. - Is the quantum yield equal to:

The ratio is equal to:

The fluorescence lifetime of the excited state in the absence of quencher is the inverse sum of the two reaction rates and. Reaction constants of the first order are in units of [1 / s] (pronounced per second) rate constants of the second order are in units of [1 / (mol s ) ] (pronounced per second and mol):

In the absence of the quencher - i.e. - Is the fluorescence lifetime of the same:

If the fluorescence lifetime used in the ratio, we obtain after changing the equation:

If, however, and used in the ratio as follows:

Because of the direct proportionality of the quantum yield of the fluorescence to the intensity of fluorescence follows:

And:

The Stern- Volmer constant for static quenching

Also referred to as static quenching or static quenching - - In the static fluorescence quenching forms from the fluorophore and the quencher, a complex which does not fluoresce themselves. This can be described by using a chemical equation:

The chemical equilibrium between the fluorophore and the quencher to the complex of Fluororphor and quencher is formed by the mass action law and is equal to the Stern-Volmer constant:

Here, the concentration of the complex of the fluorophore and the quencher, the concentration of the unbound fluorophore and the quencher, the concentration of the unbound.

In static quenching, the ratio is out and, in contrast to the dynamic fluorescence quenching, equal to one:

This is because that in the case of static quenching, only the number of excitable fluorophores will be reduced, whereas in the dynamic quenching of the excited state, the life is reduced. Therefore, the ratio of the lifetimes remain constant in the static fluorescence quenching. This circumstance is an important differentiating factor for both types of fluorescence quenching.

For the same concentration of the quencher increases, the temperature rises, wherein the static quenching, the value of the principle on. That is, the quencher deletes worse than at lower temperatures, at higher temperatures: At a higher temperature of the quencher at the fluorophore is bound worse than at a lower temperature, therefore, the number of Quenchvorgänge decreases with increasing temperature. This is an important feature to distinguish static from dynamic fluorescence quenching because it behaves in principle in the dynamic quenching vice versa.

Derivation

The association constant is:

The total concentration of the fluorophore is the sum of the concentration of unbound fluorophore and the concentration of bound fluorophore with the quencher:

Is changed in accordance with this equation and then substituted into the equation of the association constant, the result is:

This equation is now changed by:

Due to the direct proportionality between the fluorescence intensity of the fluorophore to its concentration follows:

Stern-Volmer equation with simultaneous dynamic and static fluorescence quenching

If dynamic and static fluorescence quenching occur simultaneously, the Stern-Volmer equation in its above form can not be applied. Here is the Stern-Volmer equation, the combined deletion must be used:

Here is the Stern-Volmer constant for the dynamic and the Stern-Volmer constant of the static fluorescence quenching. The plot of the Stern- Volmer equation is no longer linear for the combined deletion. A nonlinear behavior of the Stern-Volmer plots has therefore indicate the combined deletion.

Because of the relationship between dynamic fluorescence quenching and the fluorescence lifetime of the Stern-Volmer equation, the combined deletion can also be written as:

The value of the ratio of the lifetimes must lie in the combined deletion between the value for the dynamic and static fluorescence quenching:

This behavior is therefore also an indication of the combined fluorescence quenching.

If the ratio of the lifetimes are known, the equilibrium constant of the static fluorescence quenching can be determined using the Stern-Volmer equation for the combined deletion.

By rearranging the Stern-Volmer equation for the combined deletion to obtain a linearized form of the equation:

Plotting the left-hand term of the equation against the concentration on, you'll obtain the Stern-Volmer plot turn a simple linear relationship. Then the values ​​of and can be determined from the slope and intercept.

Applications of the Stern-Volmer equation

In macromolecules such as proteins, can be fluorophores, such as the amino acid tryptophan, vary easily accessible for different quencher. This accessibility of the fluorophore depends, among other things, the charge and the size of the quencher.

As a tryptophan residue in proteins for the loaded quencher I- iodide is only accessible when the tryptophan residue at the surface ranges of the protein in the aqueous medium. In hydrophobic regions iodide can penetrate poorly. For the quencher acrylamide, a tryptophan residue can be achieved only when it is on the surface and in any case too small: Acrylamide can not penetrate due to its size in each "corner" of the protein. The quencher O2 ( bimolecular oxygen ), however, can also delete tryptophan residues that are buried deep in the protein, because it is small enough and uncharged.

This knowledge can be used to, determine the relative position of fluorophores such as tryptophan in proteins. To the Stern-Volmer plots for various quenchers can be compared, or the protein is examined, in the folded and in the unfolded state, so that previously inaccessible fluorophores with the unfolding of the protein for the quencher used are available.