Energetic and structural quantities for phase characterization by canonical statistical analysis

2 Energetic and structural quantities for phase characterization by canonical statistical analysis 

In order to understand as much as possible about the canonical equihbrium behavior of a polymer adsorbed at a substrate, the following suitable cpiantities O will be considered in the following. Besides the canonical expectation values (0 , the fluctuations about these averages, as represented by the temperature derivative d 0)/dT= (OE) — (O) (E)) jT (A b = 1), are required to identify transition points. Apart from energetic fluctuations such as the specific heat cy= E)d E) jdT and fluctuations of structural quantities like the parallel and perpendicular components of the gyration tensor, andf x. respectively [cf Eqs. (13.6) and (13.7)], clear evidence that the polymer is moving freely in the box, or whether it is very close to the surface, can be provided by the average distance of the center of mass of the polymer Ifom the surface, (zcm) = i ( i) 

Another useful quantity is the mean number of monomers docked to the surface. A single-layer stracture is formed if all monomers are attached at the substrate if none is attached, the polymer is quasi-free (desorbed) in solvent. The surface potential is a continuous potential and in order to distinguish monomers docked to the substrate from those not being docked, it is necessary to introduce a cutoff Zc. A monomer i is defined to be docked if Zi Zc The corresponding measured quantity is the average ratio ( ) of 

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