Compression and interpenetration of adsorption-active brushes.

Compression and interpenetration of two opposing polymer brushes formed by end-grafted adsorption-active chains are studied by the numerical self-consistent field approach and by analytical theory. For sufficiently strong polymer-surface attraction, a fraction of chains in the adsorption-active brush condenses into a near-surface layer, while the remaining ones form the outer brush with reduced effective grafting density. Analysis shows that the normal pressure in adsorption-active brushes can be understood in terms of the effective grafting density concept although the pressure at small separations is affected by the presence of the dense adsorbed phase. We propose a simple theory modification that accounts for this effect. We also formulate a procedure for extracting the value of the effective grafting density directly from the pressure vs separation curves by inverting the equation of state. In contrast to the normal pressure, the interpenetration of the two opposing adsorption-active brushes demonstrates a much more intricate behavior. At weak to moderate compressions, the effective grafting density concept works well but fails spectacularly at small interbrush separations. We identify two interpenetration regimes for adsorption-active brushes: (i) at separations larger than the ideal Gaussian coil size N1/2, the overlap of the two brushes is concentrated in the mid-plane region, in the same way as in brushes grafted onto non-attractive surfaces; (ii) at separations less than N1/2, the brush overlap is strongly enhanced in the wall regions where the attractive interaction plays an important role both in generating the dense layer for the "proper" brush and in attracting the "foreign" chains.

Adsorption-active polydisperse brush with tunable molecular mass distribution.

Recently, a novel class of responsive uncharged polymer brushes has been proposed [Klushin et al., J. Chem. Phys. 154(7), 074904 (2021)] where the brush-forming chains have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush with a reduced grafting density. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly as a response to changes in environmental parameters. In this paper, we use numerical self-consistent field calculations to study this phenomenon in polydisperse brushes. Our results reveal an unexpected effect: Although all chains are chemically identical, shorter chains are adsorbed preferentially. Hence, with the increase in the surface affinity parameter, a reduction in the surface grafting density of the residual brush is accompanied by a change in the shape of its molecular mass distribution (MMD). In particular, an originally bidisperse brush can be effectively transformed into a nearly monodisperse one containing only the longer chain fraction. We introduce a method of assigning different chain conformations to one or the other microphase, based on analyzing tail length distributions. In a polydisperse brush with a uniform MMD, short chains are relegated to the adsorbed phase, leading to a narrower effective MMD in the residual brush. Preferential adsorption is not absolute, and longer chains are also partially involved in adsorption. As a result, not only the width of the distribution decreases but also its shape evolves away from the initial uniform distribution. We believe that the effect of preferential adsorption stems from a fundamental property of a polydisperse brush, which is characterized by a spectrum of chemical potential values for monomers belonging to chains of different lengths. Hence, preferential adsorption is also expected in polyelectrolyte brushes; moreover, brush polydispersity would affect coexistence with any other condensed phase, not necessarily related to adsorption.

Branched versus linear lactide chains for cellulose nanoparticle modification: an atomistic molecular dynamics study.

We studied the structure of brushes consisting of branched oligolactide (OLA) chains grafted onto the surface of cellulose nanoparticles (CNPs) in polylactide (PLA) and compared the outcomes to the case of grafting linear OLA chains using atomistic molecular dynamics simulations. The systems were considered in a melt state. The branched model OLA chains comprised one branching point and three branches, while the linear OLA chains examined had a molecular weight similar to the branched chains. It was shown that free branches of the branched OLA chains tend to fold back toward the CNPs due to dipole-dipole interactions within the grafted layer, in contrast to the well-established behavior of the grafted uncharged branched chains. This result, however, is in qualitative agreement with the conformational behavior known for linear OLA chains. At the same time, no significant difference in the effectiveness of covering the filler surface with grafted branched or linear OLA chains was found. In terms of the expelling ability of the grafted chains and the interaction between PLA and CNP or OLA, the linear chains were broadly similar (sparse grafting) or better (intermediate or dense grafting) compared to the branched ones. Thus, the grafted lactide chains with a linear architecture, rather than their branched counterpart, may be preferable for the covalent modification of cellulose nanoparticles.

Polymer brushes with reversibly tunable grafting density.

We propose a novel class of responsive polymer brushes, where the effective grafting density can be controlled by external stimuli. This is achieved by using end-grafted polymer chains that have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly and in a controlled way as a response to changes in environmental parameters. The effect is demonstrated by numerical self-consistent field calculations and analyzed by scaling arguments. Since the thickness of the denser layer is about a few monomer sizes, its capacity to form a microphase is limited by the product of the brush chain length and the grafting density. We explore the range of chain lengths and grafting densities where the effect is most pronounced. In this range, the SCF studies suggest that individual chains inside the brush show large rapid fluctuations between two states that are separated by only a small free energy barrier. The behavior of the brush as a whole, however, does not reflect these large fluctuations, and the effective grafting density varies smoothly as a function of the control parameters.

Cascades of unfolding transitions in amphiphilic molecular brushes.

Using a combination of self-consistent field theory with coarse-grained Brownian dynamics simulations, we studied mechanical unfolding of an amphiphilic molecular brush in a solvent that was poor for the side chains but good for the main chain of the brush. In striking contrast to earlier theoretical predictions [O. V. Borisov and A. Halperin, Europhys. Lett. 34, 657 (1996)] made for amphiphilic graft copolymers, we discovered that in a partially unfolded molecular brush, a globular core co-exists, at equilibrium, with a necklace of smaller sized intra-molecular micelles, each comprising a few side chains connected by stretched main chain strands (bridges). A progressive increase in the main chain end-to-end distance of the brush triggers a sequence of discrete events of generation of new intramolecular micelles, giving rise to a sawtooth pattern in the restoring force-deformation curve.

Unfolding of a comb-like polymer in a poor solvent: translation of macromolecular architecture in the force-deformation spectra.

A numerical self-consistent field modeling approach was employed to study the mechanical unfolding of a globule made by comb-like polymers in a poor solvent with the aim of unraveling how the macromolecular architecture affects the shape of the single-molecule force-deformation curves. We demonstrate that the dependence of the restoring force on the imposed extension of the main chain of the comb-like polymer exhibits a characteristic oscillatory shape in the intermediate deformation range. Theoretical arguments are developed that enable us to relate the shape of the patterns on the force-deformation curves to the molecular architecture (grafting density and length of the side chains) and interaction parameters. Thus, the results of our study suggest a new approach for the determination of macromolecular topology from single-molecule mechanical unfolding experiments.

Sharp and fast: sensors and switches based on polymer brushes with adsorption-active minority chains.

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.

Coil-bridge transition in a single polymer chain as an unconventional phase transition: theory and simulation.

The coil-bridge transition in a self-avoiding lattice chain with one end fixed at height H above the attractive planar surface is investigated by theory and Monte Carlo simulation. We focus on the details of the first-order phase transition between the coil state at large height H ⩾ Htr and a bridge state at H ⩽ Htr, where Htr corresponds to the coil-bridge transition point. The equilibrium properties of the chain were calculated using the Monte Carlo pruned-enriched Rosenbluth method in the moderate adsorption regime at (H/Na)tr ⩽ 0.27 where N is the number of monomer units of linear size a. An analytical theory of the coil-bridge transition for lattice chains with excluded volume interactions is presented in this regime. The theory provides an excellent quantitative description of numerical results at all heights, 10 ⩽ H/a ⩽ 320 and all chain lengths 40 < N < 2560 without free fitting parameters. A simple theory taking into account the effect of finite extensibility of the lattice chain in the strong adsorption regime at (H/Na)tr ⩾ 0.5 is presented. We discuss some unconventional properties of the coil-bridge transition: the absence of phase coexistence, two micro-phases involved in the bridge state, and abnormal behavior in the microcanonical ensemble.

Random copolymer adsorption onto a periodic heterogeneous surface: A partially directed walk model.

The adsorption of a single AB random copolymer (RC) chain onto an inhomogeneous ab surface with a regular periodic pattern is studied theoretically. The problem is considered within the simplest model of a partially directed random walk in two dimensions by using the method of generating functions and the annealed approximation for the averaging over disorder in the RC sequence. The existence of the "optimal" RC composition and the degree of correlation in the monomer sequence, at which the inverse transition temperature has a local minimum, is shown. This is characteristic for symmetric and weakly asymmetric surfaces, whereas for surfaces with pronounced asymmetry there is no such local minimum. The best adsorbate for a strongly asymmetric surface is the homopolymer composed of monomer units that are complimentary to the majority sites on the surface. The results for the adsorption transition point obtained in the annealed approximation are compared with the numerical results for random-periodic AB-copolymers with a long period being a quenched random sequence of A and B units. The comparison shows that the annealed approximation provides a very good quantitative estimate of the adsorption transition point.

Formation of a "Hollow" Interior in the Fourth-Generation Dendrimer with Attached Oligomeric Terminal Segments.

By using the Scheutjens-Fleer self-consistent field approach, the structure of the fourth-generation dendrimer with attached terminal chemically different oligomeric segments is studied theoretically. It is demonstrated that an incompatibility of terminal segments with inner dendrimer units leads to formation of a "hollow" core with reduced polymer density in the dendrimer center. This effect is enhanced with a deterioration in the solvent quality for terminal segments. This observation is in accordance with experimental results and molecular dynamics simulation data for an analogous system. It is established that the main factor determining the hollow core formation is the segregation between inner and terminal units because the main driving force for the effect is the localization of the terminal segments at the dendrimer periphery. The influence of structural parameters of dendrimer such as the number of generations and length of the terminal chain on this effect is also studied.

Adsorption of a single polymer chain on a surface: effects of the potential range.

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.

Mechanical desorption of a single chain: unusual aspects of phase coexistence at a first-order transition.

The phase transition occurring when a single polymer chain adsorbed at a planar solid surface is mechanically desorbed is analyzed in two statistical ensembles. In the force ensemble, a constant force applied to the nongrafted end of the chain (that is grafted at its other end) is used as a given external control variable. In the z-ensemble, the displacement z of this nongrafted end from the surface is taken as the externally controlled variable. Basic thermodynamic parameters, such as the adsorption energy, exhibit a very different behavior as a function of these control parameters. In the thermodynamic limit of infinite chain length the desorption transition with the force as a control parameter clearly is discontinuous, while in the z-ensemble continuous variations are found. However, one should not be misled by a too-naive application of the Ehrenfest criterion to consider the transition as a continuous transition: rather, one traverses a two-phase coexistence region, where part of the chain is still adsorbed and the other part desorbed and stretched. Similarities with and differences from two-phase coexistence at vapor-liquid transitions are pointed out. The rounding of the singularities due to finite chain length is illustrated by exact calculations for the nonreversal random walk model on the simple cubic lattice. A new concept of local order parameter profiles for the description of the mechanical desorption of adsorbed polymers is suggested. This concept give evidence for both the existence of two-phase coexistence within single polymer chains for this transition and the anomalous character of this two-phase coexistence. Consequences for the proper interpretation of experiments performed in different ensembles are briefly mentioned.