Monte Carlo simulation of 3-star lattice polymers pulled from an adsorbing surface

Abstract

We study uniform 3-star polymers with one branch tethered to an attractive surface and another branch pulled by a force away from the surface. Each branch of the 3-star lattice is modelled as a self-avoiding walk on the simple cubic lattice with one endpoint of each branch joined at a common node. Recent theoretical work [1] found four phases for this system: free, fully adsorbed, ballistic and mixed. The mixed phase occurs between the ballistic and fully adsorbed phase. We investigate this system by using the flatPERM Monte Carlo algorithm with special restrictions on the endpoint moves to simulate 3-stars up to branch length 128. We provide numerical evidence of the four phases and in particular that the ballistic-mixed and adsorbed-mixed phase boundaries are first-order transitions. The position of the ballistic-mixed and adsorbed-mixed boundaries are found at the expected location in the asymptotic regime of large force and large surface-monomer interaction energy. These results indicate that the flatPERM algorithm is suitable for simulating star lattice polymers and opens up new avenues for numerical study of non-linear lattice polymers.

Copolymeric stars adsorbed at a surface and subject to a force: a self-avoiding walk model

“…There are extra complications in the square lattice (where d = 2) because arms can shield other arms from the surface [4]. The cubic lattice case (where d = 3) has also been investigated by Monte Carlo methods [6].…”

“…These problems have also been investigated numerically by exact enumeration methods [9,32] and using Monte Carlo techniques [5,27,28]. Other polymer architectures have been considered, including star polymers [4,6,25,26], and other branched polymers such as combs [26].…”

Force-induced desorption of 3-star polymers in two dimensions

“…In two dimensions the situation is more difficult but Beaton [3] has given an essentially complete solution for staircase polygons in two dimensions. Various models of branched polymers have also been investigated [4,16,17].…”

“…By keeping track of how many vertices are in the surface and the height of the vertex where the force is applied we can map out the phase diagram of the system. This has been carried out for 3-stars in three dimensions both rigorously [16] and using Monte Carlo methods [4]. In three dimensions we have a considerable amount of information available about the phase diagram [4,16].…”

“…This has been carried out for 3-stars in three dimensions both rigorously [16] and using Monte Carlo methods [4]. In three dimensions we have a considerable amount of information available about the phase diagram [4,16]. In two dimensions the situation seems more complicated since it is not possible for the star to lie entirely in the surface at which adsorption occurs.…”