Two-body repulsion

Here the first term reproduces the effective two-body repulsion and the second the effective two-body van der Waals attraction, is the interatomic distance, whereas A, p and C are constants that are usually determined empirically. The repulsive term is steeply increasing at low interatomic distances but quickly becomes negligible beyond the nearest neighbour distance. 

The nonbonded interactions commonly consist of a sum of two-body repulsion and dispersion energy terms between atoms that are often of the Lennard-Jones form in addition to the energy from the interactions between fixed partial atomic or ionic charges (Coulomb interaction)... 

When the problem is only the study of the behaviour of polymers in good solvents, we may content ourselves with the model with two-body repulsive interaction (z > 0, y = 0). Then, by looking at (9.1.7), we immediately see that dimension d = 4 plays a special role. In this case, there is only one dimensionless parameter. In particular, the size of an isolated chain is given by the mean square end-to-end distance which can be written as follows... 

Let us now compare the interactions, when we have only two-body repulsive interactions. For each model, let us consider a set of chains. A weight... 

Moreover, these results remain valid when the two-body repulsive interaction between polymer segments diminishes. In particular, de Gennes pointed out in 1975 that for polymer solutions, Flory s 0 point (T = TF) is a tri-critical point and must be treated as such. Thus, the Lagrangian theory can be used not only to describe the behaviour of solutions in the repulsive domain where excluded volume is dominant, but also in the attractive domain. 

The above method can be extended to the 0-point, where the above two-body repulsion (0(c )) is exactly balanced by the attractive interaction and three-body interaction (0(c )) comes into play. Hence, here F R) + (R /N). Again from energy... 

Total force between two bodies = repulsion forces + attraction forces... 

For the MC calculations, Sutton-Chen multi-atomic potential is applied with an annealing method to simulate the pseudo-equilibrium atomic repartition of each stracture. This potential provides the total nanoparticle energy Uas the addition of terms that describes the two-body repulsive interaction between the atoms / and... 

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