Comparison with lattice results

In order to identify the limitations of both the lattice model for a rather long polymer (N= 179 monomers) and the continuum model of a short polymer (A7= 20), it is instructive to compare the phase diagrams obtained from the sc lattice and the off-lattice models (Figs. 13.2 and 13,12), 

The energy of the lattice system is given by Eq, (14,1), which we rewrite here as 

Pseudophase diagram of a lattice polymer with 179 monomers as in Fig. Z2, but here parametrized by the surface attraction strength e and the temperature 7. The color encodes the specific-heat profile the darker the color, the larger Its value. From [304]. 

This also explains why the wetting transition is more difficult to observe in adsorption studies on regular lattices. On the other hand, AC2 conformations at low T and for q between the adsorption and the single-double layering transitions can be observed in both models. Similarly, in both models there exists the AG pseudophase of surface-attached globules. 

While for the off-lattice system, apart from the wetting transition, there is only the transition from AC2a (semi-spherical shaped) to AC2b (double-layer stmctures), on the lattice AC2 comprises a wide range of higher-layer subphase transitions (see Fig. 13,6). 

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The random A1 siting method of reference (7) was used to compute 29Si NMR intensities for comparison with experimental results reported in reference (2). The results in Table II show clearly some discrepancy between the experimental and calculated results. The variance a2 ranges from 35 to 329. The discrepancy is greatest at higher Si/Al ratios where the experimental distribution is much sharper than is expected of the maximum probability distribution of silicon and aluminum atoms. These results imply some ordering of the aluminum atoms in the lattice. 

Having developed and parameterized potential models, the final stage before their use in a simulation study should be their evaluation. Nonempirically derived potentials should be evaluated by reference to their ability to predict empirical crystal properties. For empirical potentials, it is clearly necessary to use data outside the range employed in the parameterization. We have already referred to the use of lattice dynamical data. Comparison with the results of high-pressure studies, in particular the variation of structural and elastic properties with pressure, is also of great value and... 

Table 4.8 Equilibrium lattice constant a, cohesive energy and bulk modulus B of FCC Al Exact exchange in comparison with LDA results.

We have re-analyzed the available data in comparison with the results of band structure calculation to provide the basis for an understanding of the electronic structure of the four principal forms of poly aniline the fuUy reduced leucoemeraldine, (1 A)n the partially oxidized emeraldine base, [(1 A)(2A)]n the oxidized and fully protonat emeraldine salt, [IS] (A )n and the fully oxidized bipolaron lattice, (-B-NH+=Q=NH+-)n. 

The elaborated in [R. V. Chepulskii, Analytical method for calculation of the phase diagram of a two-component lattice gas, Solid State Commun. 115 497 (2000)] analytical method for calculation of the phase diagrams of alloys with pair atomic interactions is generalized to the case of many-body atomic interactions of arbitrary orders and effective radii of action. The method is developed within the ring approximation in the context of a modified thermodynamic perturbation theory with the use of the inverse effective number of atoms interacting with one fixed atom as a small parameter of expansion. By a comparison with the results of the Monte Carlo simulation, the high numerical accuracy of the generalized method is demonstrated in a wide concentration interval. 

The relaxation rates of the individual nuclei can be either measured or estimated by comparison with other related molecules. If a molecule has a very slow-relaxing proton, then it may be convenient not to adjust the delay time with reference to that proton and to tolerate the resulting inaccuracy in its intensity but adjust it according to the average relaxation rates of the other protons. In 2D spectra, where 90 pulses are often used, the delay between pulses is typically adjusted to 3T] or 4Ti (where T] is the spin-lattice relaxation time) to ensure no residual transverse magnetization from the previous pulse that could yield artifact signals. In ID proton NMR spectra, on the other hand, the tip angle 0 is usually kept at 30°-40°. 

Calibration of the MC time step in the simulation on the 2nnd lattice can be achieved by comparison of rr or DN with the results from a conventional MD simulation (as in the second and third columns of Table 4.8), or via comparison with a translational diffusion coefficient obtained from experiment with a... 

A comparison of the results using this method and the rate of electroless copper deposition determined gravimetrically shows that the best results are obtained with the Le Roy equation applied to the polarization data in the anodic range. It is interesting to note that here, in the metal deposition as in the corrosion (9), the partial reaction, which does not involve destruction or building of a crystal lattice of metal substrate, gives better results (this is hardly surprising, of course). 

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