Percolation excitation

Here we limit ourselves to excitation percolation in very... 

One of the most interesting aspects of energy transport is the excitation percolation transition (, and its similarity (10) to magnetic phase transitions and other critical phenomena (, 8). In its simplest form the problem is one of connectivity. In a binary system, made only of hosts and donors, the question is can the excitation travel from one side of the material to the other The implicit assumption is that there are excitation-transfer-bonds only between two donors that are "close enough", where "close enough" has a practical aspect (e.g. defined by the excitation transfer probability or time). Obviously, if there is a succession of excitation-bonds from one edge of the material to the other, one has "percolation", i.e. a connected chain of donors forming an excitation conduit. We note that the excitation-bonds seldom correspond to real chemical bonds rather more often they correspond to van-der-Walls type bonds and most often they correspond to a dipole-dipole or equivalent quantum-mechanical interaction. 

We believe that excitation percolation will be a common occurrence in many complex heterogeneous systems, both synthetic and natural. Excitation percolation has been proposed for the... 

Organic acid fluorescence. In a similar manner to trace constituents, such as Mg, Sr and P, concentrations of organic acids present in speleothem calcite are sufficient to observe variation at temporal scales of less than annual in some cases (e.g.. Baker et al. 1993, Shopov et al. 1994). Organic acids (humic and fulvic) are formed in the soil by humification, and transported to the cave void by percolating waters where they are entrapped in precipitating carbonates. Under certain circumstances, where precipitation patterns are strongly seasonal and the nature of vadose percolation is such that seasonal mixing is incomplete, bands with different luminescent intensities can be differentiated after excitation with UV radiation. In other cases, bands are not observable but secular... 

Excitation spectroscopy Monitoring of the surface emission allows one to discriminate the upper excited surface states and their relaxation dynamics. Problems such as surface reconstruction, or quantum percolation of surface excitons upon thermal and static disorder, are connected with high accuracy to changes of the exciton spectra.61118,119,121... 

From now on, we wish, in the spirit of the site percolation in electrokinetics (Section IV.C.4.a), to neglect the bond correlations. Thus, we consider an effective medium around the energy vA where the excitation will propagate it is clear that this medium correctly describes the propagation, but that it will not correctly describe, for example, the density-of-states distribution, since it contains also fictitious B sites at the energy vA. Therefore, by means of this restriction, the HCPA method is then directly transferable to the naphthalene triplet lattice, with probability cL = cA of having a passing bond (4.83). The curves of Fig. 4.18 are likewise transferable, but, because of the fictitious B sites, the density of states around vA is not normalized at the real concentration of the A sites (as was possible for the CPA cases cf. Fig. 4.11). 

Fig. 7.2. Schematic representation of the forward reactions (steps 1-4, indicated by plain arrows) and recombination routes (steps 5-7, indicated by dotted arrows) taking place in the nc-DSC. (1) Optical excitation of the sensitizer. (2) Electron injection from the excited sensitizer (S ) to the conduction band of Ti02. (3) Electron percolation through the network of Ti02 particles. (4) regeneration of the oxidized sensitizer (S+) by iodide (I ). (5) Deactivation of the excited state of the sensitizer (S ). (6) Recombination of injected electrons with oxidised sensitizer (S+). (7) Recombination of conduction band electrons with triiodide (Ig ) in the electrolyte. Al/max is the maximum voltage that can be generated under illumination and corresponds to the difference between the Fermi level of the conduction band of TiC>2 under illumination and the electrochemical potential of the electrolyte...

For percolating microemulsions, the second and the third types of relaxation processes characterize the collective dynamics in the system and are of a cooperative nature. The dynamics of the second type may be associated with the transfer of an excitation caused by the transport of electrical charges within the clusters in the percolation region. The relaxation processes of the third type are caused by rearrangements of the clusters and are associated with various types of droplet and cluster motions, such as translations, rotations, collisions, fusion, and fission [113,143]. 

The third relaxation process is located in the low-frequency region and the temperature interval 50°C to 100°C. The amplitude of this process essentially decreases when the frequency increases, and the maximum of the dielectric permittivity versus temperature has almost no temperature dependence (Fig 15). Finally, the low-frequency ac-conductivity ct demonstrates an S-shape dependency with increasing temperature (Fig. 16), which is typical of percolation [2,143,154]. Note in this regard that at the lowest-frequency limit of the covered frequency band the ac-conductivity can be associated with dc-conductivity cio usually measured at a fixed frequency by traditional conductometry. The dielectric relaxation process here is due to percolation of the apparent dipole moment excitation within the developed fractal structure of the connected pores [153,154,156]. This excitation is associated with the selfdiffusion of the charge carriers in the porous net. Note that as distinct from dynamic percolation in ionic microemulsions, the percolation in porous glasses appears via the transport of the excitation through the geometrical static fractal structure of the porous medium. 

Mid-temperature process II This process extends over mid-range temperatures (300-400 K) and over low to moderate frequencies (up to 105 Hz). The mid-temperature process was associated with the percolation of charge excitation within the developed fractal structure of connected pores at low... 

A detailed description of the relaxation mechanism associated with an excitation transfer based on a recursive (regular) fractal model was introduced earlier [47], where it was applied for the cooperative relaxation of ionic microemulsions at percolation. 

The fractal dimensions of the excitation paths in samples D, F, and G lie between 2 and 3. Thus, percolation of the charge carriers (protons) is also moving through the Si02 matrix because of the availability of an ultra-small porous structure that occurs after special chemical and temperature treatment of the initial glasses [156]. 

Thus, the non-Debye dielectric behavior in silica glasses and PS is similar. These systems exhibit an intermediate temperature percolation process associated with the transfer of the electric excitations through the random structures of fractal paths. It was shown that at the mesoscale range the fractal dimension of the complex material morphology (Dr for porous glasses and porous silicon) coincides with the fractal dimension Dp of the path structure. This value can be obtained by fitting the experimental DCF to the stretched-exponential relaxation law (64). 

The exponent p in Eq. (7.91) depends on the physical situation and is typically calculated to be in the range 1-2. At elevated temperatures the carriers are thermally excited over the potential fluctuations and the application of percolation theory is less clear. 

As can be deduced from numerous experimental studies of superconducting cuprates, the hole excitations in the CUO2 layers are characterized by a spatially inhomogeneous distribution with a tendency to quasi one-dimensional structurization in the form of stripes [1,2]. This nanoscale segregation is found to be more pronounced in underdoped curates [3] with npcritical temperature Tcifip) on the threshold line enclosing the protectorate of percolation superconductivity. 

Anomalous subdiffusion occurs on percolation clusters or on objects that in a statistical sense can be described as fractal, by which we mean that selfsimilarity describes simply the scaling of mass with length. Connections between v, the fractal dimension of the cluster, D, and the spectral dimension, d, have been established, relations that were originally derived by Alexander and Orbach [35], who developed a theory of vibrational excitations on fractal objects which they called fractons. An elegant scaling argument by Rammal and Toulouse [140] also leads to these relations, and we summarize their results. 

Excitation spectrum In fluorescence spectroscopy, a plot of fluorescence intensity as a function of excitation wavelength. Exhaustive extraction A cycle in which an organic solvent, after percolation through an aqueous phase containing the solute of interest, is distilled, condensed, and again passed through the aqueous phase. 

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