Dynamics of energy transport in ternary molecular solids. II. Time evolution of naphthalene fluorescence

Abstract

The spectrally resolved rime-evolution of free and trapped singlet c&tons was ohtsincd II liquid-helium temperature for ternary cestals of perdeuteronaphthalene/naphrhalene/betamsth\-Inaphthalrms (host/_eue~r/supsr:rsp). The nsphthalenc guest (donor) concentration varied between 0.30 and 0.99 mole fraction. while the supertrap (acceptor1 concentrations were lO-'-lO-5. AI the lower guest concentrations (0.50 and below) the naphthalene-esciton decay time approaches the natural lifetime (= 122 ns). At higher concentrations. the decay is much shorter and sxtremcl\-non-exponentid. This behavior is inconsistent with simple homogeneous kinetics schemes that use a time-independent rate consrant for energy transport. Above the percolation concentration (0.60 naphthalens) we fitted the esperimental results with a random-flight-kinetic model. incorporating correlated random walks on the percolating guest cluster. The best fit was obtained for a-coherence length" (mean free path) of = 10' lattice units. These results are in good agrscmcm \vith previous srccdy-s~ste studies on the same samples, and seem to indicate a partial coherence of the exiton transport in holh pure and substitutionally disordered crystals at these low temperatures.

Persistent random walk on a site-disordered one-dimensional lattice: Photon subdiffusion

“…From Eqs. ( 5) and ( 6) (10) hence we can immediately transform Eq. ( 8) to an equivalent integral equation for P ± (z, θ).…”

“…For example, the vacancy mechanism of atom diffusion in solids incorporates a correlation effect, since an atom has a larger probability to move backward to the hole it just vacated rather than onward [7]. Correlations also arise in diffusion of guest molecules in zeolite channels [8], electron hopping in Coulomb glass [9], motion of excitons at low temperatures in mixed naphthalene crystals [10], etc. Among the correlated walks, the persistent random walk is possibly the simplest one to incorporate a form of momentum in addition to random motion [3,4].…”

Exciton trapping by emitting two phonons at impurities in molecular crystals

“…For acoustic phonons the eigenvalue &(K) is obtained as [7]&(K) = E(K) * [ E @ ( K ) -E,) + B2(E(K)/2 -E0)]1/2r-1n,(16) where E(K) is the energy of an exciton with wave vector K. Eo is the energy of the center of the unperturbed exciton band with a width of 2B, and t = Iv2, v being the velocity of sound in the crystal, and I the mass coefficient of the host molecules.In the final state the exciton gets trapped at the impurity (p), and two phonons are emitted. The eigenvectors of the final state can be expressed asI P ;~ = C G,B:b:b:-,lO;n),9 where G, is a normalization constant given byThe conservation of momenta of the system in its initial and final states is taken care of by the two phonon! emitted.…”