Hybrid lattice model

In the following, we first discuss the substrate specificity of heteropolymer adhesion by employing a simple hybrid lattice model [284, 303, 306, 309, 318]. After having gained this qualitative insight into the structural binding behavior of heteropolymers, an exemplary realistic hybrid peptide-semiconductor system is investigated to verify the sequence specificity of peptide adsorption [274-276,340]. 

As an example for the importance of substrate-specific properties upon polymer adsorption, we will now investigate conformational transitions of a nongrafted hydrophobic-polar heteropolymer with 103 residues in the vicinity of different substrates [303]. 

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A similar study on a somewhat more complex 310-hybrid lattice model of an idealized Greek-key fold has been performed by Kolinski et al. 

Eventually, let us compare the adsorption behavior with what we had found in Chapter 13 for simplified hybrid lattice models of polymers and peptides near attractive substrates. The adhesion of the jjeptides at the Si(lOO) substrate exhibits very similar features. Exemplified for peptide S3, Fig. 14.13 shows the plot of the canonical probability distributionpcan E, q) 8 E — E(X))S(q — q(X))) at room temperature (T = 300 K). The peak at E, q) (80.5 kcal/mole, 0.0) corresponds to conformations that are not in contact with the substrate. It is separated from another peak near (E, q) (74.5 kcal/mole, 0.2) and belongs to conformations with about 17% of the heavy atoms with distances < 5 A from the substrate surface (compare with Fig. 14.12). That means adsorbed and desorbed conformations coexist and the gap in between the peaks separates the two pseudophases in g -space, which causes a kinetic free-energy barrier. Thus, the adsorption transition is a first-order-like pseudophase transition in q, but since both structural phases (adsorbed and desorbed) coexist almost at the same energy, the transition in E space is weakly of first order. ... 

The Oishi-Prausnitz model cannot be defined strictly as a lattice model. The combinatorial and residual terms in the original UNIFAC and UNIQUAC models can be derived from lattice statistics arguments similar to those used in deriving the other models discussed in this section. On the other hand, the free volume contribution to the Oishi-Prausnitz model is derived from the Flory equation of state discussed in the next section. Thus, the Oishi-Prausnitz model is a hybrid of the lattice-fluid and free volume approaches. 

The simplest, but very instructive model of a hybrid system is shown in Fig. 13.1. As in the discussion of general folding properties of polymers and proteins, employing a minimalistic simple-cubic (sc) lattice model [39] allows for a systematic analysis of the conformational phases experienced by a nongrafted polymer in a cavity with one adhesive surface. The polymer can move between the two infinitely extended parallel planar walls, separated by a distance expressed in lattice units. The substrate is short-range attractive to the monomers of the polymer chain, while the influence of the other wall is purely steric. 

There are cases where non-regular lattices may be of advantage [36,37]. The computational effort, however, is substantially larger, which makes the models less flexible concerning changes of boundary conditions or topological constraints. Another direction, which may be promising in the future, is the use of hybrid models, where for example local attachment kinetics are treated on a microscopic atomistic scale, while the transport properties are treated by macroscopic partial differential equations [5,6]. 

Figure 7.16. Comparison of Ni-Al Phase diagrams obtained by (a) using a hybrid CVM-CALPHAD approach (Tso 1992, Cacciamani 1997) and (b) CALPHAD approach incorporating a sub-lattice ordering model (Ansaia et al. 1995).

Fig. 8. Difference in the inelastic neutron scattering data between LaFe4Sb 2 and CeFe4Sb 2 vs. energy loss (Keppens et al., 1998). CeFe4Sbi2 was used as a reference compound since the neutron scattering cross section of Ce is much smaller than that of La. The difference spectra therefore reflect the vibrational density of states (DOS) associated with the La atoms. The peak at 7 meV (78 K) corresponds to the quasi-localized La mode. The second broader peak at about 15 meV corresponds to the hybridization of La and Sb vibrational modes. Both peaks can be accounted for using lattice dynamic models based on first-principles calculations (Feldman et al., 2000).

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