Planar Brushes Research Articles

Attraction between Opposing Planar Dipolar Polymer Brushes.

We use a field theory approach to study the effects of permanent dipoles on interpenetration and free energy changes as a function of distance between two identical planar polymer brushes. Melts (i.e., solvent-free) and solvated brushes made up of polymers grafted on nonadsorbing substrates are studied. In particular, the weak coupling limit of the dipolar interactions is considered, which leads to concentration-dependent pairwise interactions, and the effects of orientational order are neglected. It is predicted that a gradual increase in the dipole moment of the polymer segments can lead to attractive interactions between the brushes at intermediate separation distances. Because classical theory of polymer brushes based on the strong stretching limit (SSL) and the standard self-consistent field theory (SCFT) simulations using the Flory's χ parameter always predicts repulsive interactions at all separations, our work highlights the importance of dipolar interactions in tailoring and accurately predicting forces between polar polymeric interfaces in contact with each other.

Synthesis and characterization of gibbsite nanoplatelet brushes by surface-initiated atom transfer radical polymerization

An efficient method for the polymer modification of gibbsite (γ-Al(OH)3) nanoplatelet particles with poly(methyl methacrylate) (PMMA) by surface-initiated atom transfer radical polymerization (SI-ATRP) was developed. A newly developed initiator system based on 12-(2-bromoisobutyramido) dodecanoic acid (BiBADA) enable grafting densities in excess of 0.4 nm−2 with minimal amount of free homopolymer impurities and narrow molecular weight distribution. The gibbsite brush nanoplatelets were shown to organize into transparent films with nacre-like lamellae morphology. A significant increase of the glass transition temperature (as compared to pristine PMMA) was observed and attributed to the increase of steric confinement in planar brush architectures. The applicability of the presented methodology to a wide range of ATRP-compatible chemistries could be a basis for the development of novel functional materials in which properties depend on the directionality of brush nanoplatelet orientation and interaction.

Cleaning Efficacy of Manual Toothbrushes Around Brackets - A Pilot Randomised Control Trial.

To test the cleaning efficacy of different manual toothbrushes in orthodontic patients in a single-blind randomised clinical trial. The brushes tested were selected based on previous in vitro tests. Thirty-five regular orthodontic patients with a minimum of six bonded brackets on the maxillary anterior teeth were randomly assigned to three experimental groups: staged (2-level) (Candida Parodin, 12 patients) and V-shaped (Oral-B Ortho, 12 patients) toothbrush head designs were compared in a two-phase study to planar control brushes (Paro M 43, 11 patients). First, all participants were advised to brush their teeth twice daily for 2 min for 3 weeks. Prior to the start and at the end of the study, the gingival index was assessed to evaluate the level of oral hygiene. Afterwards, cleaning efficacy was assessed planimetrically by disclosing the respective teeth after two days of not performing any oral hygiene measures. Of the initial 35 participants, two did not attend after 3 weeks and had to be excluded. After 3 weeks, the control (5 out of 180 sites or -2.8% with GI ≥ 2) and staged groups (16 out of 216 sites or 7.5% with GI ≥ 2) showed minor improvement in the oral hygiene level. In contrast, the V-shaped group (29 out of 198 sites or 14.6 % with GI ≥ 2) showed a statistically significant improvement of the oral hygiene level. Planimetric evaluation, however, showed no superior cleaning efficacy of any of the tested head designs. The use of V-shaped and staged toothbrush head designs might be beneficial in patients with inadequate oral hygiene undergoing orthodontic treatment with a fixed appliance. Further large-scale investigations are, however, necessary to validate the presented results.

Self-assembly in densely grafted macromolecules with amphiphilic monomer units: diagram of states.

By means of computer modelling, the self-organization of dense planar brushes of macromolecules with amphiphilic monomer units was addressed and their state diagram was constructed. The diagram of states includes the following regions: disordered position of monomer units with respect to each other, strands composed of a few polymer chains and lamellae with different domain spacing. The transformation of lamellae structures with different domain spacing occurred within the intermediate region and could proceed through the formation of so-called parking garage structures. The parking garage structure joins the lamellae with large (on the top of the brushes) and small (close to the grafted surface) domain spacing, which appears like a system of inclined locally parallel layers connected with each other by bridges. The parking garage structures were observed for incompatible A and B groups in selective solvents, which result in aggregation of the side B groups and dense packing of amphiphilic macromolecules in the restricted volume of the planar brushes.

Neutron reflectometry yields distance-dependent structures of nanometric polymer brushes interacting across water.

The interaction between surfaces displaying end-grafted hydrophilic polymer brushes plays important roles in biology and in many wet-technological applications. In this context, the conformation of the brushes upon their mutual approach is crucial, because it affects interaction forces and the brushes' shear-tribological properties. While this aspect has been addressed by theory, experimental data on polymer conformations under confinement are difficult to obtain. Here, we study interacting planar brushes of hydrophilic polymers with defined length and grafting density. Via ellipsometry and neutron reflectometry we obtain pressure-distance curves and determine distance-dependent polymer conformations in terms of brush compression and reciprocative interpenetration. While the pressure-distance curves are satisfactorily described by the Alexander-de-Gennes model, the pronounced brush interpenetration as seen by neutron reflectometry motivates detailed simulation-based studies capable of treating brush interpenetration on a quantitative level.

Surface Fluctuations of Polymer Brushes Swollen in Good Solvent Vapor

Swollen polymer brushes are found in various applications including biomedical coatings where the brush provides stability against harsh environmental conditions and mediates interactions with the surroundings. The surface height fluctuations of planar polystyrene brushes (0.04–0.61 chains/nm2) highly swollen in toluene vapor are so strongly slowed by the tethering of the chains that they are unobservable in the current experimental window of length and time. This is the case despite the fact that the segmental dynamics of the brush chains should be very fast due to the substantial plasticization by the solvent. With respect to thermally stimulated fluctuations, the surfaces of these swollen brushes are solidlike on time scales and length scales pertinent to many practical applications.

Vertical Phase Segregation Induced by Dipolar Interactions in Planar Polymer Brushes

We present a generalized theory for studying structural properties of a planar dipolar polymer brush immersed in a polar solvent. We show that an explicit treatment of the dipolar interactions yields a macroscopic concentration dependent effective “chi” (the Flory–Huggins-like interaction) parameter. Furthermore, it is shown that the concentration dependent chi parameter promotes phase segregation in polymer solutions and brushes so that the polymer-poor phase consists of a finite/nonzero polymer concentration. Such a destabilization of the homogeneous phase by the dipolar interactions appears as vertical phase segregation in a planar polymer brush. In a vertically phase segregated polymer brush, the polymer-rich phase near the grafting surface coexists with the polymer-poor phase at the other end. Predictions of the theory are directly compared with prior reported experimental results for dipolar polymers in polar solvents. Excellent agreements with the experimental results are found, hinting that the di...

Phase transitions in brushes of homopolymers

Polymer brushes formed by identical macromolecules anchored at the solid-liquid interface may undergo conformational transitions resulting in formation of layered structures with abrupt variation of polymer density (”vertical stratification”) or in lateral decomposition that gives rise to nano-patterned interfaces. The intra-brush nanoscale segregation is governed by a balance of intermolecular interactions with conformational entropy of the brush-forming chains and may be triggered by external stimuli that affect the strength of the inter-chain interactions. Both vertical and lateral segregation in the brushes have important implication for applications of brushes for modification of physico-chemical and (bio)interactive properties of interfaces, as well as in biological functions of biopolymer brushes widely found in living nature. While the effects of microphase segregation in polymer brushes are well understood on the basis of existing theories, experimental observation and characterization of such structures using surface-sensitive techniques often remains challenging. Here we present an overview of the state-of-the-art in experimental work on high-resolution structural characterization of polymer brushes in relation to the existing theoretical predictions. The review focusses on planar and spherical brushes. Moreover, consequences for the related case of bottle brush polymers are discussed.

Self-consistent field model of brushes formed by root-tethered dendrons

We present an analytical self-consistent field (scf) theory that describes planar brushes formed by regularly branched root-tethered dendrons of the second and third generations. The developed approach gives the possibility for calculation of the scf molecular potential acting at monomers of the tethered chains. In the linear elasticity regime for stretched polymers, the molecular potential has a parabolic shape with the parameter k depending on architectural parameters of tethered macromolecules: polymerization degrees of spacers, branching functionalities, and number of generations. For dendrons of the second generation, we formulate a general equation for parameter k and analyze how variations in the architectural parameters of these dendrons affect the molecular potential. For dendrons of the third generation, an analytical expression for parameter k is available only for symmetric macromolecules with equal lengths of all spacers and equal branching functionalities in all generations. We analyze how the thickness of dendron brush in a good solvent is affected by variations in the chain architecture. Results of the developed scf theory are compared with predictions of boxlike scaling model. We demonstrate that in the limit of high branching functionalities, the results of both approaches become consistent if the value of exponent bin boxlike model is put to unity.In conclusion, we briefly discuss the systems to which the developed scf theory is applicable. These are: planar and concave spherical and cylindrical brushes under various solvent conditions (including solvent-free melted brushes) and brush-like layers of ionic (polyelectrolyte) dendrons.

Numerical study of weak polybase brushes grafted on neutral or charged spherical surface by the self-consistent field theory.

The self-consistent field theory (SCFT) is employed to numerically study the response of weak polybase type polymer chains grafted on a sphere to electric fields generated by the uniform positive or negative charges on the grafting substrate in the planar polyelectrolyte brush limit. Also the effect of curvature of the grafting sphere on the brush height of weak polybase brushes in the absence of surface charges is investigated. The numerical study reveals interesting and nontrivial dependence of the brush height on the radius of the grafting substrate. Consistent with experimental results, in the parameter range of the surface charge density examined, the brush height is found to be independent of the applied electric field at intermediate and high grafting densities. At relatively low grafting density, the applied negative surface charge which is termed as negative bias in this study results in a reduction of the brush height. At rather low grafting density, the positive bias corresponding to applied positive surface charges can lead to a slight increase in the brush height. The underlining mechanism governing the response of weak polybase brushes to the applied electric field is elucidated.

Self-assembly of polymer brushes in the presence of a surfactant: A system of strands

This theoretical study is focused on the formation of a cylindrical microstructure in a planar polymer brush in the presence of a surfactant. It is assumed that the brush may be nonuniform in the direction along the grafting plane and that there are regions with constant concentrations of monomer units and regions occupied only by the surfactant. The surfactant molecule is simulated by a dimer whose parts interact in a different manner with the monomer units of the polymer. At the interface between these regions, dimer molecules are oriented mainly perpendicularly to this interface and the surface tension is reduced. If the surface energy becomes negative, the formation of a structured brush is more favorable in terms of energy than that of a uniform brush. As a result, there may appear a cylindrical microstructure in which grafted macromolecules are united into strands perpendicular to the grafting plane. The stretching of macromolecules and their interaction with the solvent within the strands are described by the Alexander-de Gennes model, whereas the surface energy is calculated with allowance for the surface curvature of strands at a high degree of amphiphilicity of the surfactant molecules. It is shown that the arising strands have radii of the order of the surfactant-molecule length, while the number of macromolecules per strand is proportional to the surface density of their grafting. With an increase in the grafting density, the strand length increases initially, while the volume fraction of the polymer in a strand remains constant. Furthermore, strands start to shorten and their density grows. Structural characteristics are calculated as a function of the parameter characterizing the degree of amphiphilicity of the solvent molecules, their sizes, and their average energy of interaction with monomer units.

Self-organized polyelectrolyte end-grafted layers under nanoconfinement.

Layers of end-grafted weak polyelectrolytes in poor solvent self-organize into a rich variety of structures (such as micelles, micelles coexisting with nonaggregated chains, stripes and layers with solvent-filled holes) due to the subtle competition among hydrophobic, electrostatic and steric interactions and the chemical acid-based equilibria of the weak polyelectrolyte. In this work, a molecular theory has been used to systematically study how nanoconfinement modulates the competition among these interactions and, therefore, dictates the morphology of the self-assembled layer. Two different types of confinement were considered and compared: (i) soft lateral confinement due to increasing surface coverage in a planar polyelectrolyte brush and (ii) hard vertical confinement due to the interaction of a planar polyelectrolyte brush with an opposing surface, as typically found in AFM-colloidal-tip and surface-force-apparatus experiments. It is shown that increasing the surface coverage (soft lateral confinement) or compressing the layer with an opposing wall (hard vertical confinement) have a similar qualitative effect on the morphology of the system: both types of nanoconfinement increase the stability of morphologies that extend in one or two dimensions (such as the homogeneous brush, holes and stripes) over nonextended aggregates (such as hemispherical micelles). However, vertical confinement can also lead to pillar-like structures that are not observed in the absence of the opposing wall. Interestingly, the pillar structures, which bridge the grafting and opposing surfaces, may coexist with metastable structures collapsed to the grafting surface only. This coexistence may help to understand the hysteresis commonly observed in surface-force experiments.

Dendron brushes and dendronized polymers: a theoretical outlook

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.

Swelling of chemical and physical planar brushes of gradient copolymers in a selective solvent

We propose a mean-field theory of chemical and physical planar brushes of linear gradient copolymers swollen in a selective solvent. The polymer chains are grafted to the substrate by the ends with the excess of insoluble monomer units, and the majority of the soluble units are located near the free ends of the chains. The grafting points are considered to be immobile (chemical brush) and mobile in-plane (physical brush). In the latter case the grafting density is determined from the equilibrium conditions (minimum of the free energy). A common peculiarity of the brushes of both types is that the polymer concentration gradually changes from a relatively high value near the substrate (collapsed region of the brush) to a small value near the free surface (swollen region of the brush). In the case of the chemical brush, a polymer depletion zone can appear in the middle of the brush if incompatibility between insoluble and soluble (A and B) units is high enough. Here the polymer density is even lower than near the free surface of the brush. The grafting density of the physical brush is inversely proportional to the chain length and increases with the decrease of the solvent quality for the insoluble (A) units. The latter can be accompanied by shrinkage of the brush thickness due to broad distribution of the insoluble units through the chain: a minor fraction of insoluble units near the free ends can aggregate with a major fraction of them near the substrate. As a result, the concentration of the soluble (B) units can have a maximum in the middle of the brush rather than near the free surface.

Dynamics of Macromolecules Grafted in Spherical Brushes under Good Solvent Conditions

Spherical polymer brushes have a structure intermediate between star polymers and polymer brushes on flat substrates, and are important building blocks of polymer nanoparticles. Molecular dynamics simulations are presented for isolated spherical polymer brushes under good solvent conditions, varying the grafting density as well as the chain length, using a coarse-grained bead–spring model of flexible chains. We complement previous work on the static properties of the same model by analyzing the chain dynamics, studying the motions of monomers in relation to their position along the grafted chains, and extract suitable relaxation times. A qualitative discussion in terms of the Rouse model is given, as well as a comparison to corresponding work on planar brushes. We find that the end monomers relax faster than monomers further inside along the chain, as previously observed for planar brushes, but at variance with theoretical expectations. The relevance of our findings for experimental work is briefly discussed.

Self-assembly and elasticity of hierarchical proteoglycan–hyaluronan brushes

Spatially confined yet strongly hydrated assemblies made from the proteoglycan aggrecan and the polysaccharide hyaluronan (HA) are major, functionally important components of the pericellular space around chondrocytes, and in cartilage. To better understand, how mechanical properties arise from the supramolecular structure and dynamics of such assemblies, we have studied the effect of aggrecan on the physico-chemical properties of well-defined, planar HA brushes. From interaction studies by quartz crystal microbalance with dissipation monitoring and spectroscopic ellipsometry, and compression studies by combined colloidal probe atomic force/reflection interference contrast microscopy, we find that aggrecan readily intercalates into HA brushes in a reversible manner. Aggrecan induces a drastic swelling of HA brushes, generating self-assembled films of several micrometers in thickness that are highly hydrated (>99%), elastic and very soft. The Young modulus in the linear compression regime is well below 100 Pa, and reaches several kPa at strong compression. The implications of these findings for biological function are discussed.

Brushes of strong polyelectrolytes in mixed mono- and tri-valent ionic media at fixed total ionic strengths

This paper describes the structure and properties of end-tethered anionic polyelectrolyte brushes containing counterions of tri-valent ruthenium hexamine (Ru(NH3)63+) and mono-valent sodium (Na+). Detailed studies of these planar brushes composed of the strong polyelectrolyte, poly(sodium styrenesulfonate), were performed via electrochemical experiments using cyclic voltametry (CV) and surface force experiments using the Surface Forces Apparatus (SFA). A comparison between electrochemical and force measurements provided physical information regarding polyelectrolyte brush height and the population of tri-valent Ru(NH3)63+ counterions inside a brush. Polyelectrolyte brushes were observed to transform from extended brushes dominated by the presence of mono-valent counterions, to collapsed brushes saturated with tri-valent counterions. This transformation occurred as a result of Ru(NH3)63+ replacement of Na+ counterions in the polyelectrolyte brushes. This Ru(NH3)63+ uptake was seen to be limited by either the diffusion of tri-valent ions in low ionic strength solutions or the equilibrium between mono and tri-valent ions at higher fixed ionic strengths. The collapsed state, seen only with brushes dominated by multi-valent counterions, also corresponded to an observed adhesive state between brushes. Adhesion was never seen with exclusively mono-valent ions present in solution. Ru(NH3)63+ was observed to be released from saturated brushes when placed in a purely mono-valent salt solution of sufficiently high ionic strength. All SFA and CV experiments were performed in solutions of three separate fixed ionic strengths, with brush collapse/saturation occurring more sudden and producing higher adhesion at lower total ionic strength.

Repulsive Forces between Spherical Polyelectrolyte Brushes in Salt-Free Solution

Abstract Interaction forces between two colloidal spherical polyelectrolyte brushes in salt-free solution are calculated within Derjaguin approximation on the basis of self-consistent field Poisson–Boltzmann theory of a planar polyelectrolyte brush (E. B. Zhulina, O. V. Borisov, J. Chem. Phys. 107 (1997) 5952). It is demonstrated that at large separations the force-distance curve has a universal form which is independent of the charge density of the brush. At small separations the repulsive force is controlled by osmotic pressure of the counterions confined inside compressed brush. The crossover between these two regimes corresponds to the distance between the surfaces comparable to (double) thickness of a brush and occurs either continuously or with abrupt variation in the magnitude of the repulsive force. The latter is the case if the interacting brushes are found in the osmotic regime, that is, most of the counterions are retained in the intra-brush volume.

Charge regulation and local dielectric function in planar polyelectrolyte brushes

Understanding the effect of inhomogeneity on the charge regulation and dielectric properties, and how it depends on the conformational characteristics of the macromolecules is a long-standing problem. In order to address this problem, we have developed a field-theory to study charge regulation and local dielectric function in planar polyelectrolyte brushes. The theory is used to study a polyacid brush, which is comprised of chains end-grafted at the solid-fluid interface, in equilibrium with a bulk solution containing monovalent salt ions, solvent molecules, and pH controlling acid. In particular, we focus on the effects of the concentration of added salt and pH of the bulk in determining the local charge and dielectric function. Our theoretical investigations reveal that the dipole moment of the ion-pairs formed as a result of counterion adsorption on the chain backbones play a key role in affecting the local dielectric function. For polyelectrolytes made of monomers having dipole moments lower than the solvent molecules, dielectric decrement is predicted inside the brush region. However, the formation of ion-pairs (due to adsorption of counterions coming from the dissociation of added salt) more polar than the solvent molecules is shown to increase the magnitude of the dielectric function with respect to its bulk value. Furthermore, an increase in the bulk salt concentration is shown to increase the local charge inside the brush region.

Perpendicular Domain Orientation in Dense Planar Brushes of Diblock Copolymers

Dense planar brushes of diblock copolymers physically attached to the substrate by end groups are studied by the dissipative particle dynamics simulation technique. We predict stability of spatially ordered perpendicularly oriented domains which are separated from the substrate and the free surface of the film by homogeneous layers of different type. Depending on composition of the copolymer, various structures including hexagonally ordered “golf holes”, parallel “gullies” and “ridges”, and “stalactites” ordered with the symmetry of hexagonal lattice can be stable. We analyze regimes of good and poor solvents for both blocks (nonselective solvents). Physical reasons for perpendicular domain orientation are discussed. In the case of low “grafting” density, our results coincide with those reported in the literature.