Disordered molecular systems

The long-time balance between recombination and drift of carriers as expressed by the y/n ratio has been analyzed using a Monte Carlo simulation technique and shown to be independent of disorder [40]. Consequently, the Langevin formalism would be expected to obey recombination in disordered molecular systems as well. However, the time evolution of y is of crucial importance if the ultimate recombination event proceeds on the time scale comparable with that of carrier pair dissociation (Tc/Td l). The recombination rate constant becomes then capture—rather than diffusion-con-trolled, so that Thomson-like model would be more adequate than Langevin-type formalism for the description of the recombination process (cf. Sec. 5.4). 

In the following we will show that the charge carrier transport in these materials can be described by the conventional models mentioned before, which have been developed for the characterization of disordered molecular systems. 

The radial distribution function describes how the atomic density varies as a function of the distance from one particular atom. It provides a particularly effective way of describing the average structure of disordered molecular systems such as liquids. The mathematical formula of the radial distribution function, gir), is... 

Gartstein YN, Conwell EM (1995) High-field hopping mobility in molecular systems with spatially correlated energetic disorder. Chem Phys Lett 245 351... 

The tendency of things to get "messed up" is common in everyday life. You may rake the leaves on your lawn into an orderly pile, but after a few windy days the leaves are again scattered randomly. The reverse process is nonspontaneous the wind never blows the randomly disordered leaves into a neatly arranged pile. Molecular systems behave similarly Molecular systems tend to move spontaneously to a state of maximum randomness or disorder. 

For molecular systems at surfaces, one must take into account that STM may interfere with natural assembly. That is, the tip-molecule interaction may induce disorder during scanning operation. In other words, defined molecular 2D crystals can be distorted by this method, not allowing true geometric analysis. Again, low temperatures in UHV or saturated monolayer systems, in general, help to circumvent this problem. 

Proceedings available as special issue (Diffusion and Relaxation in Disordered Complex Systems) of Journal of Molecular Liquids 114, No. 1-3 (2004), guest editor W. T. Coffey. 

Narayana PA, Bowman MK, Kevan L. (1975) Electron spin echo envelope modulation of trapped radicals in disordered glassy systems Application to the molecular structure around excess electrons in y-irradiated lOM sodiiun hydroxide alkaline ice glass. J Chem Phys 63 3365-3371. 

An electrode covered with several molecular layers of dye could be made to adsorb all of the visible light, and obviate the need for the multielectrode stack. Very thick dye layers have tended not to be conductive or highly photoconductive so that their photoelectrochemical efficiencies are no better and perhaps worse than those seen on electrodes modified with very thin dye films. Molecular disorder of the dye appears to be the dominant reason for lack of conductivity in thick films of fluorescein-type, cyanine-type, and phthalocyanine-type dyes (12). It has been shown however that ordered molecular systems (mainly conjugated, highly unsaturated hydrocarbons) have considerable potential as conductive media, and that these ordered systems may be used to chemically modify electrode surfaces (12, 15). 

Anisotropic molecules show optically isotropic behavior in the bulk when they are disordered and randomly oriented, for instance in solutions or liquid crystal above the transition temperature. Under the influence of a strong beam, the induced dipole moment of the molecules feels a torque that tends to orient the molecule. The reorientation of the molecular dipoles induces a change in the refractive index. The typical values for molecular susceptibilities and the time-responses vary depending on the type of systems. For small anisotropic molecular systems, x 10 esu, with a time response 10 s. However, in the nematic phase, liquid crystal molecules are strongly correlated, resulting in much higher values, x 10 esu,... 

Figure II. Density of states (DOS) of vibrational and electronic excitation in condensed matter systems and in molecular systems. The DOS for electronic and vibrational excitation in condensed matter systems is continuous, and is characterized by van Hove topological singularities for ordered structures and by exponential Mott tails for disordered materials. The DOS for electronic excitation of molecular systems is discrete below the first ionization potential. In molecular systems the vibrational DOS is discrete, while in large molecules a quasicontinuum of vibrational states exists at high energies.

Hendrickson and co-workers have continued to probe the dynamics of electron transfer in molecular systems in the solid state. Mossbauer and specific-heat data on biferrocenium [(C5H5)Fe(C5H4 C5H4)Fe(C5H5)] salts indicate that intramolecular electron transfer is controlled by lattice dynamics. The tri-iodide salts show valence localization up to 350 K by Mbssbauer data. The room-temperature crystal structure is centrosymmetric and evidently disordered. 

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