Dependence of the polymer adsorption transition on chain stiffness and surface interaction range: A partition-function-zero analysis.

Abstract

The reversible adsorption of a polymer chain to an attractive surface is an important problem in materials science and biophysics. The location of this transition (T_{c}) is sensitive to both polymer flexibility (l_{p}) and the range of the attractive surface potential (λ) and, for long chains, simple scaling arguments predict T_{c}∼(l_{p})^{a}(λ)^{b} with different power-law exponents for different regimes of l_{p} and λ. Verification of these scaling laws for semiflexible polymers via computer simulation is challenging due to the long chain lengths (N) required to reach the asymptotic scaling regime. Here we propose a finite-size-scaling method using partition function zeros to obtain adsorption transition temperatures in the long-chain limit from simulations of chains of moderate length. By combining the real and imaginary parts of the leading partition function zeros it is possible to eliminate the size- and flexibility-dependent scaling function that describes the N→∞ approach of these leading zeros to the critical point in the complex inverse-temperature plane. Our model polymer is a flexible tangent-hard-sphere chain (sphere diameter σ) with a local bond angle restriction that sets a persistence length l_{p}. The chain is end-tethered to a flat surface that has a square-well attractive potential of range λσ. We use a Wang-Landau simulation algorithm to obtain the density of states for chains up to length N=2560 with 1≤l_{p}/σ≤13,100 and 0.01≤λ≤20. We distinguish three distinct scaling regimes over this wide parameter space: (i) worm-like-chain behavior for l_{p}/σ>max(10,10λ), (ii) expanded-coil behavior for λ>1 with l_{p}/σ<λ, and (iii) a single-bead-interaction region for λ<1 with l_{p}/σ<10, and we find scaling laws consistent with simple scaling expectations for each of these regions. In the rigid-rod limit (l_{p}→∞), an exact solution of the model shows that T_{c}^{*}→∞ for N→∞.