Self-avoiding walks pulled at an angle

TL;DR

This work analyzes self-avoiding walks pulled at an angle to an interacting surface, mapping the angle–temperature–force phase diagram via Monte Carlo simulations. Using a canonical lattice model with partition function $Z_n(T,F,\theta)$ weighted by $\kappa$, $\lambda$, and $\tau$, the authors identify two phases—adsorbed and desorbed—and show that the phase boundary shifts strongly with the pulling angle $\theta$, including a $T$-reentrant desorbed region in 3D for near-vertical pulling. The study develops scaling arguments near the adsorption point and contrasts the SAW results with partially directed walk (PDW) models, finding qualitative agreement but important entropy-driven differences in the adsorbed phase. The results illuminate how force direction influences polymer-surface adhesion and provide a lattice-grounded benchmark for interpreting AFM experiments and PDW theory, while highlighting lattice-specific effects and avenues for future refinement.

Abstract

We investigate polymers pulled away from an interacting surface, where the force is applied to the untethered endpoint and at an angle $θ$ to the surface. We use the canonical self-avoiding walk model of polymers and obtain the phase diagram of the model using Monte Carlo simulations for a range of angles, temperatures and force magnitudes. The phase diagram of the model displays re-entrance at low temperatures for three-dimensional walks when the pulling is more vertical than horizontal. Our results agree with various exactly solvable lattice models that have been previously studied.

Figures (6)

• Figure 1: The schematic phase diagram of pulled walks based on the solution to partially-directed walk models. The adsorbed phase is always on the left and the desorbed phase is always on the right but the boundary between them depends on the angle of the applied force.
• Figure 2: A self-avoiding walk pulled at an angle $\theta$ by a force $F$. There are $m=3$ vertices in the surface and the endpoint is at $(a,h) = (5,3)$.
• Figure 3: The order parameters for $d = 2$ SAWs pulled at an angle $\theta = 0^\circ, 45^\circ, 90^\circ$ (left to right). From top to bottom are the adsorbed fraction $\langle m \rangle / n$, average horizontal position of the endpoint $\langle a \rangle / n$ and average vertical position of the endpoint $\langle h \rangle / n$. For all angles, the desorbed phase lies on the right of the boundary, and the adsorbed phase lies on the left side.
• Figure 4: The order parameters for $d = 3$ SAWs, with same parameters as fig:OrderParameters2D.
• Figure 5: The phase boundaries of the SAW model indicated by regions of high covariance $\log\chi$. The top panel is for $d = 2$ and the bottom panel is for $d = 3$.