# how to determine timescale with characterization methods?

There are 4 different timescales on material characterization (as classified in the Atkins textbook ): a)Time during which a quantum of radiation or a particle can interact with a molecule.

b)Lifetime of excited state of a molecule.

c)Minimum lifetime species must have to be seen as a distinct species.

d)Total time of experiment in which the species is observed.

Now the question is how to determine each of these? Say I have a certain compound and want to know what is the time of interaction of a photon with the molecule (part a). Is there an experimental method or instrument to determine that? How about the lifetime of excited state? or other ones?( c and d?)

The absorption of a photon en route to an electronically excited Franck-Condon state typically typically proceeds in the femtosecond range.

The lifetime of an electronically excited singlet state mostly is in the range of several nanoseconds. In some cases, however, fluorescence lifetimes in the range of several tenth of nanoseconds have been observed.

In cases where the initial excited singlet state undergoes intersystem crossing to a triplet state, much longer phosphorescence lifetimes (seconds range) are observed.

In order to detect a transient, its lifetime must be longer than the laser pulse needed to generate it.

Once you've populated a state, you may either use

• time-resolved absorption spectroscopy to record it's spectrum and the decay of the absorption at a particular wavelength over time or

• use time-resolved emission spectroscopy to measure the decrease of fluorescence (or phosphorescence emission) intensity at a particular wavelength over time.

The time to interact with a photon is only a few femtoseconds (1 fs = $10^{-15}$ s) as this is the time for the excited state to be distinct from the ground state. Before that time the molecule is in a superposition of the two states with the photon.

Fluorescence is generally short lived as it is a spin allowed process, excited singlet state to ground singlet state. The fluorescence lifetimes range from a few picoseconds e.g. bilirubin, to several hundred nanoseconds, e.g. pyrene.

Intersystem crossing from a singlet state produced a triplet state and as the transition the the ground state is spin forbidden (triplet to singlet)then phosphorescence has a longer lifetime than fluorescence in the same molecule. Phosphorescence lifetimes vary from tens of nanoseconds (rare) to several seconds.

It is possible to measure decay times shorter than the light pulse (usually laser ) used to excite the molecules. This involves the mathematical process of convolution and is routinely performed in fluorescence decay measurements.

Measuring excited state decays by absorption is done by the pump-probe method (formerly called Flash-Photolysis). In this method a pump pulse excites the sample and a probe photon beam measures the change in absorption at a later time. The pump-probe process is repeated at different time delays until the time profile is mapped out.

Fluorescence decays are usually measured by time correlated single photon counting. In this method a short pulse excites the sample and the time delay after excitation at which a single photon is measured is recorded. This is repeated many thousand of times and a histogram of the recorded times represents the fluorescence decay time.