Replicas problems

The mean field treatment of such a model has been presented by Forgacs et al. [172]. They have considered the particular problem of the effects of surface heterogeneity on the order of wetting transition. Using the replica trick and assuming a Gaussian distribution of 8 Vq with the variance A (A/kT < 1), they found that the prewetting transition critical point is a function of A and... 

Replication avoids the problem of sample deterioration in the instrument, but it is destructive in that reaction of the material cannot be continued after the replica has been prepared. Transitory features cannot be detected unless a series of preparations are examined corresponding to increasing progress of the reaction considered. The textures of replicas have been shown [220] to be in satisfactory agreement with those of the original surface as viewed in the scanning electron microscope. The uses and interpretations of observations made through sample replication procedures are illustrated in the studies of decomposition of metal carboxyl-ates by Brown and co-workers [97,221—223]. 

Nowadays synthesis of mesoporous materials with zeolite character has been suggested to overcome the problems of week catalytic activity and poor hydrothermal stability of highly silicious materials. So different approaches for the synthesis of this new generation of bimodal porous materials have been described in the literature like dealumination [4] or desilication [5], use of various carbon forms as templates like carbon black, carbon aerosols, mesoporous carbon or carbon replicas [6] have been applied. These mesoporous zeolites potentially improve the efficiency of zeolitic catalysis via increase in external surface area, accessibility of large molecules due to the mesoporosity and hydrothermal stability due to zeolitic crystalline walls. During past few years various research groups emphasized the importance of the synthesis of siliceous materials with micro- and mesoporosity [7-9]. Microwave synthesis had... 

Most research on the structure of skeletal catalysts has focused on nickel and involved methods such as x-ray diffraction (XRD), x-ray absorption spectroscopy (XAS), electron diffraction, Auger spectroscopy, and x-ray photoelectron spectroscopy (XPS), in addition to pore size and surface area measurements. Direct imaging of skeletal catalyst structures was not possible for a long while, and so was inferred from indirect methods such as carbon replicas of surfaces [54], The problem is that the materials are often pyrophoric and require storage under water. On drying, they oxidize rapidly and can generate sufficient heat to cause ignition. 

Therefore, the central technical problem is the calculation of averaged value of F = — InZ this can be done using the so-called replica trick ... 

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