Molecular dynamics simulations of the monomer density profiles of knotted ring polymer chains confined in a slit of two parallel walls with one attractive and another repulsive surface.

Abstract

We have used Molecular Dynamics simulations to obtain the monomer density profiles for real linear and ring polymer chains of 360 monomers length with different topological structures such as simple knots: 31, 61, 91, 10124, complex knots 313151 and twisted knots with n = 10 and n = 20 in a slit geometry of two parallel walls with one attractive and another repulsive surface. We have used Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software to perform simulations with the Verlet integration algorithm. The interactions between monomers were simulated as Lennard-Jones 12-6 potential, for bonds we have used Finitely Extensible Nonlinear Elastic (FENE) potential and the interaction with the walls was taken into account via Lennard-Jones 9-3 potential. We observed that topologically complex polymers have lower monomer density profiles near the attractive wall, but at some distance in the direction to the repulsive wall this tendency changes to the opposite. We showed that most complex twisted knots have two maxima in narrow slits. In the wide slits we do not observe such relation for twisted knots at higher temperatures. These results are important for better understanding the nature of the depletion forces which arise in a slit geometry of two parallel walls with one attractive and one repulsive wall.

Entropic force in a dilute solution of real ring polymer chains with different topological structures in a slit of two parallel walls with mixed boundary conditions

“…The slit width 𝑧 is on the horizontal axis and is scaled to 1. Narrow slit corresponds to the width of 4.81𝜎 (𝐿 < 2𝑅 𝑔 ) and wide slit corresponds to 19.24𝜎 (𝐿 > 2𝑅 𝑔 ) [28].…”

“…This suggests that in wide slits, the interaction with the opposite side may be limited, thereby reducing the force exerted on the opposite wall. The density profiles of polymers with varying knot structures are discussed in [28], where it was demonstrated that the wide slit space penetration diminishes with the knot complexity, see figure 3. Conversely, in narrow slits, where the distance is short, both complex and simple polymers can directly influence the opposite slit sides [28].…”

“…The calculations were performed for the adsorption temperature 𝑇 = 2.30 [27]. We used a model similar to [28]. The interaction between the non-neighbouring monomers was modelled with the 12-6 Lennard-Jones potential:…”