Percolation theory phenomena modeled

Sequences folding into the same structure form neutral networks in sequence space. A mathematical model based on random graph theory was designed [16] in order to allow for the derivation of analytical expressions. Neutral networks are represented by graphs in sequence space that show an interesting percolation phenomenon depending on the... 

Universal interfacial energy constant (this model assumes that all systems percolate at a universally valid threshold value of the interfacial energy Ag [28]), The merit of this work is that they have drawn attention to the role of the interfaces, even if they have failed to develop any ideas about the nature of the interaction at the interfaces, or the percolation structures, or the mechanisms of formation. For this reason it is not immediately obvious that two cornerstones of this theory, namely Ag and the influence of polymer viscosity, are not sufficiently well founded experimentally and cannot explain the percolation phenomenon. 

The phenomenon of surface-enhanced infrared absorption (SEIRA) spectroscopy involves the intensity enhancement of vibrational bands of adsorbates that usually bond through contain carboxylic acid or thiol groups onto thin nanoparticulate metallic films that have been deposited on an appropriate substrate. SEIRA spectra obey the surface selection rule in the same way as reflection-absorption spectra of thin films on smooth metal substrates. When the metal nanoparticles become in close contact, i.e., start to exceed the percolation limit, the bands in the adsorbate spectra start to assume a dispersive shape. Unlike surface-enhanced Raman scattering, which is usually only observed with silver, gold and, albeit less frequently, copper, SEIRA is observed with most metals, including platinum and even zinc. The mechanism of SEIRA is still being discussed but the enhancement and shape of the bands is best modeled by the Bruggeman representation of effective medium theory with plasmonic mechanism pla dng a relatively minor role. At the end of this report, three applications of SEIRA, namely spectroelectrochemical measurements, the fabrication of sensors, and biochemical applications, are discussed. 

The experimental results presented here, below and beyond the gel point, show clearly that the formation of polyurethane gel by polycondensation is a critical phenomenon which cannot be described by the mean-field theory. The good agreement of exponent values found experimentally and calculated by Monte Carlo simulations shows that this type of polycondensation process can be described by the percolation model. Recent experimental results " performed on different kinds of gelation process seem to indicate that, more generally, percolation and gelation, with permanent crosslinks, belong to the same class of universality. 

---