Comparative discussion of structural fluctuations

In our previous discussion of the lattice model of adsorption, we have already made use of the components of the radius of gyration as excellent measures for the globular compactness of polymer conformations parallel [see Figs. 13.9(a,b)] and perpendicular [Figs. 13.9(c,d)] to the surface, respectively. These components are particularly helpful for the identification of structural changes induced by the presence of an attractive substrate. 

For example, for g 3.4, (R ) vanishes at low temperatures, while attains small values at lower attraction strengths g. The vanishing of R ) corresponds to conformations, where the polymer is spread out flat on the surface without any extension into the third dimension. The associated pseudophases are the adsorbed compact (ACl) and adsorbed expanded (AEl) phases. The phases ACl and AEl are separated by a freezing transition. Polymer sfructures in AC 1 are maximally compact at lower temperatures, while AEl conformations are less compact and more flexible but still he rather planar at the surface. 

In order to verify that conformations in ACl are indeed maximally compact single layers, we can use the same simple argument as in Section 13.4.3. The most compact shape in the two-dimensional (2D) continuous space is the circular disk. Thus one can calculate R ) for a disk and compare it with the value obtained in the simulation of the adsorption model. Assuming, for simplicity, Nmonomers (each assumed to occupy an area a = 1 in the 

In the wetting transition, elastic polymers with stretchable bonds can form perfectly icosahedral morphologies. This would additionally stabilize the polymer conformation and 

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