Minimalistic modeling and simulation of hybrid interfaces

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. 

Denoting the number of nearest-neighbor, but nonadjacent monomer-monomer contacts by n and the number of nearest-neighbor monomer-substrate contacts by the energy of the hybrid system can be expressed in the simplest model [295] as 

In the following, we will focus mainly on the conformational transitions the polymer experiences under different environmental conditions [301,302]. More specifically, we are interested in how energetic and structural quantities depend on temperature T and reciprocal solubility 5 in equilibrium. The probability (per unit area) for a conformation with surface and itm monomer-monomer contacts at temperature T and reciprocal solubility s is given by 

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 gyration radius is then simply the trace of the gyration tensor, R - 

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