The zero-phonon line and the phonon sideband jointly constitute the line shape of individual light absorbing and emitting molecules (chromophores) embedded into a transparent solid matrix. When the host matrix contains many chromophores, each will contribute a zero-phonon line and a phonon sideband to the absorption and emission spectra. The spectra originating from a collection of identical chromophores in a matrix is said to be inhomogeneously broadened because each chromophore is surrounded by a somewhat different matrix environment which modifies the energy required for an electronic transition. In an inhomogeneous distribution of chromophores, individual zero-phonon line and phonon sideband positions are therefore shifted and overlapping.
Figure 1 shows the typical line shape for electronic transitions of individual chromophores in a solid matrix. The zero-phonon line is located at a frequency ω’ determined by the intrinsic difference in energy levels between ground and excited state as well as by the local environment. The phonon sideband is shifted to a higher frequency in absorption and to a lower frequency in fluorescence. The frequency gap Δ between the zero-phonon line and the peak of the phonon side band is determined by Franck–Condon principles.
The distribution of intensity between the zero-phonon line and the phonon side band is strongly dependent on temperature. At room temperature there is enough thermal energy to excite many phonons and the probability of zero-phonon transition is close to zero. For organic chromophores in organic matrices, the probability of a zero-phonon electronic transition only becomes likely below about 40 kelvins, but depends also on the strength of coupling between the chromophore and the host lattice.
https://en.wikipedia.org/wiki/Zero-phonon_line_and_phonon_sideband
Line shape[edit]
The shape of the zero-phonon line is Lorentzian with a width determined by the excited state lifetime T10 according to the Heisenberg uncertainty principle. Without the influence of the lattice, the natural line width (full width at half maximum) of the chromophore is γ0 = 1/T10 . The lattice reduces the lifetime of the excited state by introducing radiationless decay mechanisms. At absolute zero the lifetime of the excited state influenced by the lattice is T1. Above absolute zero, thermal motions will introduce random perturbations to the chromophores local environment. These perturbations shift the energy of the electronic transition, introducing a temperature dependent broadening of the line width. The measured width of a single chromophore's zero phonon line, the homogeneous line width, is then γh(T) ≥ 1/T1 .
The line shape of the phonon side band is that of a Poisson distribution as it expresses a discrete number of events, electronic transitions with phonons, during a period of time. At higher temperatures, or when the chromophore interacts strongly with the matrix, the probability of multiphonon is high and the phonon side band approximates a Gaussian distribution.
The distribution of intensity between the zero-phonon line and the phonon sideband is characterized by the Debye-Waller factor α.
Analogy to the Mössbauer effect[edit]
The zero-phonon line is an optical analogy to the Mössbauer lines, which originate in the recoil-free emission or absorption of gamma rays from the nuclei of atoms bound in a solid matrix. In the case of the optical zero-phonon line, the position of the chromophore is the physical parameter that may be perturbed, whereas in the gamma transition, the momenta of the atoms may be changed. More technically, the key to the analogy is the symmetry between position and momentum in the Hamiltonian of the quantum harmonic oscillator. Both position and momentum contribute in the same way (quadratically) to the total energy.
See also[edit]
Shpolskii systems are low-temperature host–guest systems – they are typically rapidly frozen solutions of polycyclic aromatic hydrocarbons in suitable low molecular weight normal alkanes. The emission and absorption spectra of lowest energy electronic transitions in the Shpolskii systems exhibit narrow lines instead of the inhomogeneously broadened features normally associated with spectra of chromophoresin liquids and amorphous solids. The effect was first described by Eduard Shpolskii in the 1950s[1] and 1960's[2][3][4] in the journals Transactions of the U.S.S.R. Academy of Sciences and Soviet Physics Uspekhi.
Subsequent detailed studies of concentration and speed of cooling behavior of Shpolskii systems by L. A. Nakhimovsky and coauthors led to a hypothesis that these systems are metastable segregationalsolid solutions formed when one or more chromophores replace two or more molecules in the host crystalline lattice. The solid state quasi-equilibrium solubility in most Shpolskii systems is very low. When the Shpolskii effect is manifested, the solid state solubility increases two to three orders of magnitude.[5][6] Isothermic annealing of the supersaturated rapidly frozen solutions of dibenzofuran in heptane was performed, and it was shown that the return of the metastable system to equilibrium in time reasonable for laboratory observation required the annealing temperature to be close to the melting temperature of the metastable frozen solution.[7] Thus the Shpolskii systems are an example of a persistent metastable state.
A good match between the chromophore and the host lattice leads to a uniform environment for all the chromophores and hence greatly reduces the inhomogeneous broadening of the electronic transition's pure electronic and vibronic lines. In addition to the weak inhomogeneous broadening of the transitions, the quasi-lines observed at very low temperatures are phonon-less transitions.[8] Since phonons originate in the lattice, an additional requirement is weak chromophore-lattice coupling. Weak coupling increases the probability of phonon-less transitions and hence favors the narrow zero phonon lines.[9] The weak coupling is usually expressed in terms of the Debye-Waller factor, where a maximum value of one indicates no coupling between the chromophore and the lattice phonons. The narrow lines characteristic of the Shpolskii systems are only observed at cryogenic temperatures because at higher temperatures many phonons are active in the lattice and all of the amplitude of the transition shifts to the broad phonon sideband. The original observation of the Shpolskii effect was made at liquid nitrogen temperature (77 kelvins), but using temperatures close to that of liquid helium (4.2 K) yields much sharper spectral lines and is the usual practice.
Low molecular weight normal alkanes absorb light at energies higher than the absorption of all pi-pi electronic transitions of aromatic hydrocarbons. They interact weakly with the chromophores and crystallize when frozen. The length of the alkanes is often chosen to approximately match at least one of the dimensions of the chromophore, and are usually in the size range between n-pentane and n-dodecane.
https://en.wikipedia.org/wiki/Shpolskii_matrix
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