Adsorption of a single polymer chain on a surface: Effects of the potential range

Abstract

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value U(c) corresponding to the adsorption transition scales as W(-1/ν), where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory U(c)≈(π(2)/24)(W+1/2)(-2) and in the best-fit equation for the MC simulation data U(c)=0.585(W+1/2)(-5/3). Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NU(c),U/U(c)). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value <R(g[perpendicular])(2)>/<R(g[parallel])(2)>=0.320±0.003 only at N~5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent φ(eff)(N). Strong corrections to scaling of order N(-0.5) are observed, and the extrapolated value φ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of φ(eff)(N) were identified as the asymptotic value for the crossover exponent.

Stimuli-Responsive Brushes with Active Minority Components: Monte Carlo Study and Analytical Theory

“…It is known that for weak adsorption, the free energy per monomer is determined by the crossover exponent φ : µ ∼ (ε−ε c ) 1/φ . For an ideal chain, φ = 1/2 while the value for a chain with excluded volume was a subject of extensive investigations and prolonged debates [48,49]. For any practical purposes, the adsorption of relatively short chains is very accurately described by the ideal value φ = 1/2.…”

Microcanonical simulations of adsorbing self-avoiding walks

“…Physically, E(a) is the density of visits per unit length, and C(a) is the rate of change in E(a) as a function of changes in log a (it has a maximum at a + c ). For adsorbing walks it is thought that φ = 1 2 in all dimensions d ≥ 2 [2,9], and numerical evidence supporting this in dimensions lower than d = 4 (the upper critical dimension) are available in references [4,23,27,29,31]. If φ = 1 2 , then α = 0, so, for example, the specific heat has scaling C n (a) = h c (n φ (a−a + c )), and plotting measurements of C n (a) against the rescaled variable τ = n φ (a−a + c ) for small values of τ should collapse the curves to a limiting curve (with some finite size corrections to scaling), exposing the scaling function h c .…”

Critical adsorption of an end-grafted diblock copolymer on a flat surface

“…9 The behavior of polymers near attractive surfaces has been extensively studied in theory and by computer simulation. [10][11][12][13] A single homogeneous polymer interacting with a flat surface has been well investigated to identify the phase transition from a desorbed state to an adsorbed state with a temperature decrease beyond a critical adsorption point (CAP) T c . [11][12][13][14][15][16][17][18][19] Crossover scaling laws for a variety of quantities below, above and at the CAP have been formulated and verified by Monte Carlo (MC) simulation of self-avoiding walks.…”