Disordered structure models Carlo

The example illustrates how Monte Carlo studies of lattice models can deal with questions which reach far beyond the sheer calculation of phase diagrams. The reason why our particular problem could be studied with such success Hes of course in the fact that it touches a rather fundamental aspect of the physics of amphiphilic systems—the interplay between structure and wetting behavior. In fact, the results should be universal and apply to all systems where structured, disordered phases coexist with non-struc-tured phases. It is this universal character of many issues in surfactant physics which makes these systems so attractive for theoretical physicists. 

Modeling studies are most useful when experimentally detenriined structures are of modest quality and suitable force-field potentials and modeling software are available. Although statistical methods such as Monte Carlo and molecular dynamics would be preferred in solution or other disordered states, we feel that energy minimization criteria are valid for static, ordered structures such as crystals. 

INVESTIGATION OF THE STRUCTURAL DISORDER D4 ICE Ih USING NEUTRON DIFFRACTION AND REVERSE MONTE CARLO MODELLING... 

Fig. 45. Normalized position of the structure factor maximum, x (e,N) = q Rg(e,N), plotted vs eN for N — 20 (squares) and N = 40 (triangles), for the model of block copolymers with only repulsive interactions between nearest neighbor A, B-pairs on the simple cubic lattice with < >v = 0.2. Note that the order-disorder transition is estimated to occur for eN w 7-8 in this Monte Carlo simulation (due to finite size effects and equilibration problems for eN S 6 no more accurate estimation was possible). From Fried and Binder [325].

Reversible energy transfer between monomeric and dimeric forms of rhoda-mine 6G in ethylene glycol has been observed" and the concentration dependence of the overall fluorescence quantum yield has been modelled by Monte-Carlo simulations. Triplet energy transfer in disordered polymers has been analyzed on the basis of Bassler s model in which the trap energies have a Gaussian distribution." Energy transfer has also been observed in mono-layers and for photoswitchable molecular triads." The structural requirements for efficient energy transfer from a carotenoid to chlorophyll have been... 

In their Monte Carlo studies, A. Bunde et al. considered the effects of structural disorder and long-range Coulomb interactions systematically [23, 24]. In particular, they reproduced the frequent occurrence of correlated forward-backward hopping sequences, which are the main cause of the first-universality phenomenon. Disorder and interactions were also taken into account in the Counterion Model developed by W. Dieterich et al., who derived realistic spectra, a(v), from their numerical simulations [25]. 

Amorphous catalysts do not have the regular or structured morphology dealt with above. Yet, a more representative model of the structure is required for an accurate prediction of their performance, in particular when the structure is modified during its application, e.g., through pore blockage by poisons carried by the feed or by coke formed by the process itself. A pore medium can evidently be considered as a network of channels — preferably 3-dimensional — with a size distribution, but the disorder also has to be included. The problem is two-fold a structure has to be generated and the operation and performance of such a structure has to be described. Two frequently used methods are briefly described here the Monte-Carlo generation and simulation and the Effective Medium Approximation. 

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