Nonradiative Singlet Energy Transfer

Electronic excitation on one chromophore (the donor) can sometimes be transferred to another chromophore (the acceptor), which might exist on the same molecule, or on another molecule. One of the most important mechanisms for this transfer in polymeric systems is nonradiative singlet energy transter. It is sometimes called Forster transfer, in honor of the person who described its mechanism some 50 years ago.

Efficiency

The efficiency of nonradiative singlet energy transfer depends on the distance, R, between the two chromophores as

Efficiency = R₀⁶/(R₀⁶+R⁶)

The efficiency (see MS Fig. II-3) is

• 1/2 when R = R₀, where R₀ is a constant (known as the Forster radius) for a given system.
• very close to 1 for distances less than 1/2 of R₀.
• nearly zero for distances larger than twice R₀.

Forster showed that the value of R₀ for a donor-acceptor pair depends on properties that can be measured separately for the donor and the acceptor:

• Fluorescence quantum yield for the donor, Q_D
• Extinction coefficient for the acceptor, e_A
• Overlap of the emission from the donor and the excitation of the acceptor, as measured by an overlap integral, O
• Refractive index of the medium, n

R₀⁶ = Q_De_AOn^-4

Pairs of chromophores are known with R₀ covering the range 1-10 nm. Therefore this photophysical effect is operative over much larger distances than is excimer formation.

Experimental Observation

The experiment begins with excitation of the donor. In absence of the acceptor, we can measure the intensity of the fluorescence by the donor. After addition of the acceptor, nonradiative singlet energy transfer will produce

• A reduction in the intensity of the fluorescence from the donor, because that emission is quenched by the acceptor.
• The appearance of fluorescence from the acceptor, not as a result of direct excitation of the acceptor, but instead indirectly, as a consequence of the excitation of the donor.

Experimental Verification of Forster's Mechanism

Experimental verification for Forster's formula for the efficiency of nonradiative singlet energy transfer has been achieved by attaching the donor and acceptor to a rigid molecule, so that the distance R is known. This rigid framework can be a steroid nucleus. Or it can be a polymer that has a strong preference for the formation of a helix of known geometry, with the donor attached at one end, and the acceptor attached at the other end. This helix provides a particularly strong test, because polymers of different molecular weight will form helices of different lengths.

A particularly nice study was performed using poly(L-proline) as the polymer. In the solvent system used for this work, poly(L-proline) forms a left-handed helix with 3 units per turn, and a length of 0.30 nm per unit. The samples studied had degrees of polymerization ranging from 5 to 12, with the donor (naphthyl) at one end, and the acceptor (dansyl) at the other end. Forster's equation yields an R₀ of 2.72 nm for this donor-acceptor pair. The measured efficiencies were in good agreement with theoretical prediction. Reference: Stryer, L.; Haugland, R. P. "Energy Transfer: A Spectroscopic Ruler" Proc. Natl. Acad. Sci. USA 1967, 58, 719-726.

Examples in polymer systems.

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