Tetrahedral-lattice model

The inadequacy of the so-called mathematical models led to a second class of distribution functions, which incorporated the specific conformational transitions available to a particular polymer system. These models, the so-called diamond or tetrahedral-lattice models, were generated by considering a three- or four-... 

Very recently Monnerie31 has described Monte Carlo calculations for a quite realistic lattice model nonintersecting chains confined to tetrahedral lattices performing local stochastic processes involving the simultaneous motion of three or four bonds. Without volume exclusion and with no correlations in the orientation probabilities of neighboring bonds, the model has also been treated analytically,32 with application to the fluorescence depolarization experiment. It is easy to show that this model also leads to the long-time Rouse spectrum. 

In the model proposed by Valeur, Jarry, Geny and Monnerie (VJGM), the chain is assumed to perform 3-bond motions on a tetrahedral lattice, to account for... 

However, Valeur and coworkers used a lattice rotational-isomeric tetrahedral chain model for the interpretation of the data on PL (with the aid of a pulsed method and quenching, in labeled polystyrene. 

Dubois-Violette, Monnery, Geny et al. and Taran have developed a theory of PL for the rotational-isomeric tetrahedral lattice chain model A rela-... 

In addition to determining the time scales for several local motions in polyformal, two different interpretational models for segmental motion will be employed. An older model by Jones and Stockmayer (7 ), based on the action of a three bond jump on a tetrahedral lattice is compared with a new model by Weber and Hel-fand (8), based on computer simulations of polyethylene type chains. These two models for segmental motion have been compared before (5 ) for two polycarbonates but somewhat different results are seen in the polyformal interpretation. 

Lattice models have provided many insights into the behaviour of polymers despite the obvious approximations involved. The simplicity of a lattice model means that many states can be generated and examined very rapidly. Both two-dimensional and three-dimensional lattices are used. The simplest models use cubic or tetrahedral lattices in which successive monomers occupy adjacent lattice points (Figure 8.7) The energy models are usually very simple, in part to reflect the simplicity of the representation but also to permit the rapid calculation of the energy. 

Our new approach includes fractal geometry in describing complexity of the spatial distribution of BaTiOs grains. The best fractal model is a sponge model, or and it is more correct to say. a kind of three -dimensional lacunary set (a set with voids). The structure of tetrahedral influence may be established in each spatial sense, which means that one has a tetrahedral lattice that fills the space. 

The data for the Kerr-effect and dielectric relaxations for the solutes of Table 1 and for TnBP suggest that the cooperative a-process occurring just above Tg involves many molecules, and their motions are Just like those of a system of enmeshing cogs. The fluctuation-relaxation model, where c(t) is described by a defect-diffusion model, rationalizes our observations. However, other models may also give the result Ki(t) = K2(t) e.g. the diffusional motions of a bond on a tetrahedral lattice (94). 

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