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 ${W}^{$-${}1/$\nu${}}$, where the exponent $$\nu${}=1/2$ for ideal chains and $$\nu${}$\approx${}3/5$ for self-avoiding walks. Lattice corrections for finite $W$ are incorporated in the analytical prediction of the ideal chain theory ${U}_{c}$\approx${}(\frac{{$\pi${}}^{2}}{24}){(W+1/2)}^{$-${}2}$ 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 $1$\le${}W$\le${}10$ 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 $$\theta${}$ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: $$\theta${}(N,U,W)=$\theta${}(N{U}_{c},U/{U}_{c})$. 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 $$\langle${}{R}_{g$\perp${}}^{2}$\rangle${}/$\langle${}{R}_{g$\parallel${}}^{2}$\rangle${}=0.320\ifmmode\pm\else\textpm\fi{}0.003$ only at $N$\sim${}5000$. Finite-$N$ corrections for this ratio turn out to be of the opposite sign for $W=1$ and for $W$\ge${}2$. We also study the $N$ dependence of the apparent crossover exponent ${$\phi${}}_{\mathrm{eff}}(N)$. Strong corrections to scaling of order ${N}^{$-${}0.5}$ are observed, and the extrapolated value $$\phi${}=0.483\ifmmode\pm\else\textpm\fi{}0.003$ 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 ${$\phi${}}_{\mathrm{eff}}(N)$ 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.

Dendron brushes are molecular structures built up of treelike macromolecules, with multiple generations of branches, grafted with a root segment to a surface (particle) or to a backbone chain (dendronized polymer) with a sufficiently high grafting density so that the dendrons interact laterally. Recent advances in the theory of dendron brushes are highlighted and complemented by insights from numerical self-consistent field modelling. Our focus is on controversial issues, which are still under debate, such as, the strain distribution in individual dendrons and the appearance of distinct populations with a different extent of stretching for dendrons in planar brushes. We anticipate that dendritic brushes (i) show a strong resistance against bending, which may manifest in a high apparent persistence length of dendronized polymers, and (ii) have an unusually large beneficial effect on the colloidal stability due to the sharp steric repulsive interaction observed when these surface layers are pushed towards the overlap.