The structure of a brush made of arm-grafted polymer stars is investigated using the Scheutjens–Fleer self-consistent field method. By using the “probe macromolecule” approach, conditional distributions of end- and branching points were obtained, which allowed for a detailed analysis of intramolecular correlations in the brush. Results strongly support a previously suggested “two population” picture of the star structure: stars in the brush are divided into two populations (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended toward the solvent. The stars in the “stretched” population have no arms that fold back toward the grafting surface and their free arms form a new sub-brush with effective grafting density determined solely by the total surface loading: molecular mass of polymer grafted onto unit area. With increasing grafting density or/and number of star arms the fraction of stars in the “stretched” population grows. The degree of backfolding of arms is estimated, the total fraction of backfolded arms is invariably small and decreases with increasing grafting density; only stars of the weakly extended population contribute to backfolding. The free ends within a given star are correlated: the ends of different arms are located approximately at the same distance from the grafting plane. Comparison of conditional ends distributions at fixed position of the branching points at different grafting densities reveals a conformational universality of grafted stars belonging to the weakly stretched population: the shape of the ends distribution does not depend on the grafting density but is determined solely by the position of the branching point. We also present analytical arguments showing that this effect is due to universal parabolic self-consistent potential acting on monomer units in the star brush, this potential is independent of the grafting density and the number of star arms.

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.

Equilibrium structural properties of polymer brushes formed by dendritic polymer chains (dendrons) are studied by means of Scheutjens-Fleer self-consistent field (SF-SCF) modeling and scaling analysis. Limiting cases of minimal and maximal possible losses of conformational entropy corresponding to different assumptions concerning distribution of elastic tension in the end-grafted dendrons are analyzed on the basis of the Flory-type scaling approach. The numerical SCF modeling indicates that the effective exponent of the power-law dependence for the height of dendritic brush on the grafting density differs from that derived within the Flory-type approximation. This is explained by changing of the intramolecular elastic tension distribution upon an increase in grafting density. The distributions of end and branching points are wide and exhibit multiple maxima, pointing to a broad distribution in the chain stretching. This distribution leads to monotonically decreasing overall density profiles. The theoretical results are in line with experimental findings on linear and dendritic poly(ethylene glycol) layers end-grafted onto TiO 2 surfaces.

We present a theory of a conformational collapse-to-swelling transition that occurs in aqueous dispersions of multiresponsive (pH-and thermoresponsive) microgels upon variation of ionic strength, temperature, or pH. Our theory is based on osmotic balance arguments and explicitly accounts for ionization equilibrium inside microgel partices. The theory predicts complex patterns in the dependence of the microgel particle dimensions on the control parameters: An increase in temperature leads to worsening of the solvent quality for the gel forming LCST-polymers and to concomitant decrease in the dimensions of the gel particles. This collapse of the gel particles provoked by an increase in temperature occurs either smoothly (at high or low ionic strength), or may exhibit a jump-wise character at intermediate ionic strength. The theory further predicts that the degree of swelling of microgel particles varies nonmonotonously and exhibits a maximum as a function of salt concentration at a pH close to the pK. This nonmonotonous variation of the particle dimensions occurs continuously at temperatures below or slightly above LCST (good or marginal poor solvent strength conditions, respectively), whereas at higher temperatures the jump-wise swelling of the gel particles is followed by either continuous or jump-wise collapse induced by progressive increase in the salt concentration. A decrease/increase in pH leads to deswelling of the weak polyacid/polybase gel particles, which occurs smoothly at temperatures below LCST, but may exhibit a discontinuity above LCST. These theoretical predictions can be used for design of smart stimuliresponsive microgels.

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...