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

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 ranges of l_p and λ. Verification of these scaling laws for semi-flexible polymers via computer simulation is challenging due to the long chain lengths 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 modest length. By combining the real and imaginary parts of the leading partition function zeros it is possible to eliminate the size/flexibility dependent scaling function that describes the approach, with increasing chain length, 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 ≤ 13,000 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 < 10λ, 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.