Related papers: Phase transitions in solvent dependent polymer ads…
This is a rather personal review of the problem of self-avoiding walks and polygons. After defining the problem, and outlining what is known rigorously and what is merely conjectured, I highlight the major outstanding problems. I then give…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
We investigate the phase diagram of a two-component associating fluid mixture in the presence of selectively adsorbing substrates. The mixture is characterized by a bulk phase diagram which displays peculiar features such as closed loops of…
In recent work [PRE 100, 022121 (2019)] evidence was found that the surface adsorption transition of interacting self-avoiding trails (ISATs) placed on the square lattice displays a non-universal behavior at the special adsorption point…
We study a generalized interacting self-avoiding walk (ISAW) model with nearest- and next nearest-neighbor (NN and NNN) interactions on the square and cubic lattices. In both dimensions, the phase diagrams show coil and globule phases…
A linear polymer grafted to a hard wall and underneath an AFM tip can be modelled in a lattice as a grafted lattice polymer (or self-avoiding walk) compressed underneath a piston approaching the wall. As the piston approaches the wall the…
Adsorption of polymers to surfaces is crucial for understanding many fundamental processes in nature. Recent experimental studies indicate that the adsorption dynamics is dominated by non-equilibrium effects. We investigate the adsorption…
Polymer chains with hard-core interaction on a two-dimensional lattice are modeled by directed random walks. Two models, one with intersecting walks (IW) and another with non-intersecting walks (NIW) are presented, solved and compared. The…
The self-avoid random walk algorithm has been extensively used in the study of polymers. In this work we study the basic properties of the trajectories generated with this algorithm when two interactions are added to it: contact and folding…
In a recent letter, a simple method was proposed to generate solvable models that predict the critical properties of statistical systems in hyperspherical geometries. To that end, it was shown how to reduce a random walk in $D$ dimensions…
We provide an introductory account of a tricritical phase diagram, in the setting of a mean-field random walk model of a polymer density transition, and clarify the nature of the density transition in this context. We consider a…
We solve a model of self-avoiding walks which allows for a site to be visited up to two times by the walk on the Husimi lattice. This model is inspired in the Domb-Joyce model and was proposed to describe the collapse transition of polymers…
We analyze equilibrium properties and adsorption desorption phase transition behaviour of a linear semiflexible copolymer chain under constrained geometrical situation on square lattice in a good solvent. One dimensional stair shaped line…
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…
Self-avoiding walk (SAW) represents linear polymer chain on a large scale, neglecting its chemical details and emphasizing the role of its conformational statistics. The role of the latter is important in formation of agglomerates and…
Polymer adsorption on fractally rough walls of varying dimensionality is studied by renormalization group methods on hierarchical lattices. Exact results are obtained for deterministic walls. The adsorption transition is found continuous…
Generalized-ensemble simulations enable the study of complex adsorption scenarios of a coarse-grained model polymer near an attractive nanostring, representing an ultrathin nanowire. We perform canonical and microcanonical statistical…
We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous…
If the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half-space and in a sphere. The ensembles of SAW's used to define these hitting densities involve walks…
We investigate semi-stiff interacting self-avoiding walks on the square lattice with random impurities. The walks are simulated using the flatPERM algorithm and the inhomogeneity is realised as a random fraction of the lattice that is…