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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 /=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.

We propose a design for polymer-based sensors and switches with sharp switching transition and fast response time. The switching mechanism involves a radical change in the conformations of adsorption-active minority chains in a brush. Such transitions can be induced by a temperature change of only about ten degrees, and the characteristic time of the conformational change is less than a second. We present an analytical theory for these switches and support it by self-consistent field calculations and Brownian dynamics simulations.Multicomponent polymer brushes offer promising perspectives for the design of smart responsive materials with a wide range of applications in nano-and biotechnology [1,2]. For example, mixed polymer brushes comprising approximately equal amounts of hydrophobic and hydrophilic polymers have been used to fabricate surfaces with switchable wettability [3,4]. If the polymers phase separate along the direction perpendicular to the brush, the surface properties can switch between the properties of the two polymer species. The transition occurs on a temperature interval of ∆T ≈ 30K. However, the response times are relatively slow on the time scale of minutes to hours, due to the existence of kinetically frozen metastable states with lateral nanoscale segregation.In this letter we propose a new class of brush-based switches, which rely on a radical conformational change of adsorption-active minority chains in a brush. The basic mechanism of the transition is illustrated in Fig. 1a). Consider a brush of polymers with chain length N b containing a small amount of minority chains with length N > N b , which undergo an adsorption transition on the substrate. In the absence of the brush, the adsorption transition (in the limit N → ∞) is continuous. Due to the interaction with the brush, it becomes first order at N, N b → ∞, and at finite chain length the chain end distribution of the minority chain becomes bimodal. A small change in temperature or solvent composition may thus lead to a sharp transition from an adsorbed state, where the switch chain is completely hidden inside the brush, to an exposed state, where the free end of the switch chain is localized at the outer surface of the brush. If each minority chain has an active group attached to its free end, the brush switches between two states: one where all active groups are fully hidden inside the brush, near the solid substrate, and one where they are exposed at the outer brush surface. The active end-groups can serve as sensors triggering an immune-like response or a detectable change in optical properties.The proposed switches possess two main advantages.First, the transition is sharp and can be induced by a temperature change of only about ten degrees, as attested and utilized by polymer chromatography in mixed eluents [5]. Second, the characteristic time scale for conformational changes is small; below, we estimate it to be well below a second. Hence the rate of change in brush properties is limited by the rate of change in the external c...