Pseudophase transition, structural

At this point, the challenge for theoretical physics, in particular, is twofold first, the modeling and analysis of specific molecular structures at atomic scales and second, the generalization of the conformational (pseudophase) transitions accompanying structure formations processes within a mesoscopic frame. Both approaches facilitate the systematic understanding of molecular processes that is typically difficult to achieve in experiments. 

Although the two contact parameters are sufficient to describe the macrostate of the system and their fluctuations characterize the main pseudophase transition lines, it is often useful to also introduce non-energetic quantities such as the end-to-end distance and the gyration tensor for gaining more detailed structural information of the polymer. For our... 

The adsorption of the peptides at the semiconductor surface is a conformational pseudophase transition and accompanied by structural changes of the peptides during the adsorption process. The energetic response of the peptides upon binding can be obtained from Fig. 14.9, where the specific heat curves are plotted for each of the peptides. The peaks for SI and S3 and the increase toward lower temperatures for S3 and SI indicate energetic activity that signals the onset of a crossover between random-coil structures in solvent and adsorbed conformations at the substrate. 

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 Icolor code in Fig, 13,2 encodes the value of the specific heat and the brighter the shading, the larger the value of cy. Black and white lines emphasize the ridges of the profile. The specific heat profile typically is a reasonable quantity for the identification of pseudophases and, therefore, these ridges mark pseudophase boundaries. As expected, the pseudophase diagram is divided into two main parts - the phases of adsorption and desorption. The two desorbed pseudophases DC (desorbed-compact conformations) and DE (desorbed-expanded structures) are separated by the collapse transition line which... 

Furthermore, highlighted by white fines, there are transitions in between the major phases. These subphases are dominated by finite-size effects and do not survive in the thermodynamic limit. This concerns, e.g., the higher-order layering transitions among the compact pseudophases AC2ai -d. In the following sections we will analyze the properties of the structural phases in detail. 

The contact numbers and can be considered as system parameters appropriately describing the state of the system and are therefore useful to identify the pseudophases. Peaks and dips in the external-parameter dependence of self-correlations ( j)c, n )c and cross-correlations nsn )c indicate activity in the contact-number fluctuations and, analyzing the expectation values (%) and ( ) in these active regions of the external parameters T and s, allow for an interpretation of the respective conformational transitions between the structural phases. 

We will now take a closer look at the adsorption transition in the phase diagram (Fig. 13.12) and we do this by a microcanonical analysis [307, 308]. As we have discussed in detail in Section 2,7, the microcanonical approach allows for a unique identification of transition points and a precise description of the energetic and entropic properties of structural transitions in finite systems. The transition bands in canonical pseudophase diagrams are replaced by transition lines. Figure 13.15 shows the microcanonical entropy per monomer s e)=N lng e) as a function of the energy per monomer e=EfN for a polymer with N=, 20 monomers and a surface attraction strength = 5, as obtained from multicanonical simulations of the model described in Section 13.6. 

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