Properties of star-branched polymer brushes

A simple model of a polymer brush was constructed. The star polymers with three arms were terminally attached with one arm (the stem) to an impenetrable surface with the other two arms (branches) free. The excluded volume effect was included into the model as the only interaction. Therefore, the system was studied in good solvent conditions. The simulations were carried out by means of the dynamic Monte Carlo method using the local changes of chain conformations to sample efficiently the conformational space. The influence of both the number of chains (the grafting density) and the length of chains on the static properties of the polymer brush was studied. The internal and local structure of a formed polymer layer was determined. It was shown that the size of the stems increased rapidly with the increase of the grafting density, while the size of the branches diminished. The changes of the spatial orientations of the stems and the branches for different grafting densities were shown and discussed.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

Properties of grafted amphiphilic chains. A computer simulation study

The model of a heteropolymer film formed by polypeptide chains was used for theoretical considerations. The linear chains consisting of amino acid residues were approximated by alpha carbon chains. Each chain was constructed on a very flexible [310] lattice. The inter- and intramolecular interactions consisted of the long-range contact potential between residues. The chains were built of hydrophilic and hydrophobic residues. Chains were terminally attached to an impenetrable surface with lateral motions possible. The Monte Carlo simulations of this model were carried out by using the Metropolis algorithm. The influence of the grafting density, the sequence of the amino acid residues, and the temperature on the static properties of the formed layer were studied and discussed. It was shown that homopolymer chains collapsed at higher temperature than the heteropolymers. The size of the polymers forming brush was smaller for homopolymers than for heteropolymers. The structure of the resulting polymer film and of its external surface was determined. The block copolymers formed well defined hydrophobic and hydrophilic layers, while for the amphiphilic case the composition of the brush layers changed continuously at high temperature. It was observed that the latter effect vanished at the collapsed amphiphilic copolymer.     

Free Energy of a Non‐Gaussian Polymer Brush

An analytical theory describing layers of polymer chains grafted to a planar surface (i.e. polymer brush) is developed. We consider a brush of chains with finite extensibility (or non‐Gaussian brush) within the framework of molecular field theory. An analytical solution for free energy of the brush and a few other brush characteristics are obtained and studied. Comparison with other known models of a brush is also made.

Chain extensibility E(x, y) for Gaussian model (dashed lines) and BCC model (solid lines) for a few chain end positions y (numbers near curves).     

Dynamics of grafted star-branched polymers. A Monte Carlo study

Monte Carlo simulations of simple models of star-branched polymers were carried out. The model chains were confined to simple cubic lattice and consisted of f = 3 branches of equal length and the total number of polymer segments as well as the density of grafted chains on the surface were varied. The chains have had one arm end attached to an impenetrable plate. The simulations were performed by employing the set of local micromodifications of the chain conformations. The model chains were athermal, i.e. good solvent conditions were modeled, the excluded volume effect was present at the model. The density of grafted chains on the surface was varied from a single chain up to 0.3. The static and dynamic properties of the system were studied. The influence of polymer concentration as well as the polymer length on static and dynamic properties of the system studied was shown. The relation between the structure and short-time dynamics (relaxation times) was discussed.     

Normal and Lateral Deformation of Lyotropically Ordered Polymer Brush

Summary: Planar polymer brush formed by semirigid chains of freely jointed rigid segments and immersed into a solvent is considered. Brush collapse induced by deterioration of the solvent quality and its deformation by external normal or lateral force is studied. It is demonstrated that these three different situations can be described in the framework of the common approach. It is shown that the collapse is accompanied by liquid‐crystalline (LC) ordering within the brush. The LC transition can be jump‐like (the first order) or continuous, depending on the segment's aspect ratio and grafting density. Transition point is investigated in detail, the corresponding phase diagrams are calculated. It is shown that the phase diagrams of a normally deformed brush have different structures, with a narrow ‘leg’ in the good solvent region for sparsely grafted brush, with two coexistence regions and a triple point, in addition, for shorter segment length or without these features if the chains are densely grafted. For the laterally deformed brush, phase diagrams have similar structures with a critical point in the good solvent regime.

Polymer brush subjected to deformation by normal (top) and lateral (bottom) external force.     

Swelling of a polymer brush by a poor solvent

The addition of a small amount of a poor solvent impurity (methanol) to a theta solvent (cyclohexane) is found to cause appreciable swelling (≈30% increase of the average brush height) in a model end‐grafted polystyrene (PS) brush layer. This unusual type of swelling is not observed if octadecyltrichlorosilane (OTS) is first grafted to the portion of the silicon substrate uncovered by the grafting end‐groups of the PS chains. Brush swelling in the absence of OTS surface protection is interpreted as arising from a segregation of methanol to the solid substrate and the resulting modification of the polymer–surface interaction. We also observe that the addition of a small amount of methanol to an adsorbed PS layer exposed to cyclohexane causes rapid film delamination from the silicon substrate. Together these observations imply a strong influence of surface active impurities on the structure and adhesive stability of polymer layers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4126–4131, 2004     

Degradable cellulose‐based polymer brushes with controlled grafting densities

Cellulose‐based polymer brushes with variable grafting densities and low dispersity were synthesized by grafting poly(n‐butyl acrylate) (PBA) side chains from cellulose‐derived backbones via ATRP. Esterification of commercially available cellulose acetate with 2‐bromoisobutyryl bromide (2‐BiBB) in NMP provided cellulose‐based macroinitiators averaging one initiation site per double glucose unit. ATRP macroinitiators averaging up to 6 initiation sites per repeating double glucose unit were prepared by acylation of microcrystalline cellulose (MCC) in LiCl/DMAc solvent system with 2‐BiBB. A series of linear macroinitiators with narrow MWD were obtained by fractional precipitation process. The content of initiating sites was determined by elemental analysis. (Meth)acrylate side chains were then grafted from the cellulose‐based macroinitiators. The prepared cellulose‐based polymer brushes showed tunable degradation rates dependent on grafting density of the brush, following two different degradation pathways, either cleavage of the main chain or detachment of the side chains. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2426–2435     

Structure and Surface Properties of High-density Polyelectrolyte Brushes at the Interface of Aqueous Solution

Zwitterionic and cationic polyelectrolyte brushes were prepared by surface-initiated atom transfer radical polymerization of 2-methacryloyloxy- ethyl phosphorylcholine (MPC) and 2-(N,N-dimethylamino)ethyl methacrylate (DMAEMA), respectively. The poly(DMAEMA) brush was treated with methyl iodide to form poly[2-(methacryloyloxy) ethyltrimethylammonium iodide] [poly(METAI)]. The effects of ionic strength on brush structure and surface properties of densely grafted polyelectrolyte brushes were analyzed by contact angle measurements, neutron reflectivity (NR) and macroscopic friction tests. Both polyelectrolyte brushes exhibited hydrophilic properties. The contact angle of the poly(MPC) brush surface against water was ca. 0° in air and the contact angle of the air bubble in water was ca. 170°. The air bubble in water hardly attached to the poly(MPC) brush surface, indicating super hydrophilic characteristics. NR measurements of poly(MPC) and poly(METAI) brushes showed that the grafted polymer chains were extended from the substrate surface in a good solvent such as water. Interestingly, NR study did not reveal the shrinkage of the brush chain in salt solution. The polyelectrolyte brushes immersed in both water and NaCl solution at various concentrations showed a low friction coefficient and low adhesion force.     

Solvent response of mixed polymer brushes

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.     

Monte Carlo simulation study of the kinetics of brush formation by irreversible adsorption of telechelic polymers onto a solid substrate

The irreversible adsorption of telechelic polymer chains from solution and melts onto solid substrates has been studied using the bond fluctuation Monte Carlo model. Complex brush formation kinetics dominated by diffusion of chains to the substrate at short times (diffusion-limited regime or DLR) and by penetration of chains through the maturing brush at longer times (penetration-limited regime or PLR) were observed. During the entire adsorption process, the rate of chain adsorption decreases monotonically with time. In the DLR, characterized by a maximum in the concentration of singly bound chains and a rapidly increasing fraction of doubly bound chains (loops), this decrease is due primarily to the depletion of free chains near the substrate and the formation of concentration gradients of free (nonadsorbed) chains in the bulk solution. The DLR and PLR are separated by an intermediate regime during which the brush becomes dominated by doubly bound chains and both penetration of the maturing brush and diffusion of chains to the brush surface play a role in determining the kinetics of brush growth. The PLR is characterized by steep gradients of free chains within the growing brush and the disappearance of concentration gradients for free chains in the bulk solution. In the PLR, the concentration of singly bound chains is low and decreases slowly while surface coverage and the fraction of doubly bound chains increase slowly. The rates of adsorption of new chains and the formation of loops in the PLR slow dramatically with increasing surface coverage and increasing chain length and less dramatically with decreasing bulk concentration.     

Molecular dynamics simulations of polyelectrolyte brushes: from single chains to bundles of chains

Using molecular dynamics simulations in combination with scaling analysis, we have studied the effects of the solvent quality and the strength of the electrostatic interactions on the conformations of spherical polyelectrolyte brushes in salt-free solutions. The spherical polyelectrolyte brush could be in one of four conformations: (1) a star-like conformation, (2) a "star of bundles" conformation in which the polyelectrolyte chains self-assemble into pinned cylindrical micelles, (3) a micelle-like conformation with a dense core and charged corona, or (4) a conformation in which there is a thin polymeric layer uniformly covering the particle surface. These different brush conformations appear as a result of the fine interplay between electrostatic and monomer-monomer interactions. The brush thickness depends nonmonotonically on the value of the Bjerrum length. This dependence of the brush thickness is due to counterion condensation inside the brush volume. We have also established that bundle formation in poor solvent conditions for the polymer backbone can also occur in a planar polyelectrolyte brush. In this case, the grafted polyelectrolyte chains form hemispherical aggregates at low polymer grafting densities, cylindrical aggregates at an intermediate range of the grafting densities, and vertically oriented ribbon-like aggregates at high grafting densities.     

Polymer brushes in solvents of variable quality: molecular dynamics simulations using explicit solvent

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.     

Conformations of molecular brushes based on polyimide and poly(methyl methacrylate) in selective solvents: Experiment and computer simulation

The effect of solvent quality with respect to main and side chains on the conformations of molecular brushes is investigated by the methods of molecular hydrodynamics and optics as well as by computer simulation. Copolymers with a polyimide backbone and poly(methyl methacrylate) side chains are studied in solvents featuring strongly different thermodynamic qualities (chloroform, ethyl acetate, and 3-heptanone). The studied samples have close total molecular masses and backbone lengths but differ in grafting densities and lengths of side chains: a brush with densely grafted and relatively short side chains versus a brush with loosely grafted but very long side chains. For both types of brushes, similar changes in hydrodynamic behavior with improvement in the solvent quality are found experimentally. Computer simulation shows that these changes have different origins. In the former case, macromolecules are elongated, and their volumes grow simultaneously, while in the latter case, the shape of the macromolecules remains close to spherical and the changes in hydrodynamic parameters are mainly due to an increase in the volume of macromolecules.     

Swelling‐Induced Chain Stretching Enhances Hydrolytic Degrafting of Hydrophobic Polymer Brushes in Organic Media

Hydrophilic polymer brushes grown via surface‐initiated polymerization from silicon oxide surfaces can detach or degraft in aqueous media. Degrafting of these chain end‐tethered polymers is believed to involve hydrolysis of bonds at the polymer–substrate interface. Degrafting so far has not been reported for hydrophobic polymer brushes in non‐aqueous media. This study has investigated the degrafting and swelling properties of poly(tert‐butyl methacrylate) (PtBMA) brushes in different water‐miscible, organic solvents, viz. DMF, acetone and THF. In the presence of a sufficient quantity of water in the organic solvent, degrafting was also observed for PtBMA brushes. More importantly, however, the rate of degrafting depended on the nature of the organic solvent and the apparent initial rate constant of the degrafting reaction was found to correlate with the swelling ratio of the polymer brush in the different solvents. This correlation is first, direct evidence in support of the hypothesis that degrafting is facilitated by a tension that acts on the bond(s) that tether the polymer chains to the surface and which is amplified upon swelling of the polymer brush.     

Effect of end-group sticking energy on the properties of polymer brushes: comparing experiment and theory

Using surface force balance measurements we have established that polystyrene chains bearing three zwitterionic groups have a higher end-group sticking energy than equivalent chains bearing a single zwitterionic group. In a good solvent, polystyrene chains end-functionalized with three zwitterionic groups form brushes of a higher surface coverage than those bearing a single zwitterion. The increase in surface coverage is slow compared with the initial formation of the brush. Measurements of the refractive index allow us to directly quantify the variation of surface coverage, permitting comparison with models for the kinetics of brush formation based on scaling theory and an analytical self-consistent field. We find qualitative support for associating the kinetic barrier with the energy required for an incoming chain to stretch as it penetrates the existing brush.     

Amphiphilic polymer brush in a mixture of incompatible liquids

An analogue of the Alexander‐DeGennes box model is used for theoretical investigation of polymer brushes in a mixture of two solvents. The basic solvent A and the admixture B are assumed to be highly incompatible (Flory‐Huggins parameter χ_AB = 3.5). Thermodynamics of a polymer in the solvents A and B are described by parameters χ_B < χ_A ≤ 1/2. The equilibrium behavior of a brush is investigated in dependence on solvent composition, grafting density, polymer‐solvents and solvent‐solvent interactions. The possibility of a phase transition related with a strong preferential solvation of a brush by a minor solvent component with higher affinity to polymer is shown and examined. Microphase segregation inside a brush is also demonstrated despite overestimating of the brush homogeneity given by the box model. A further simplification of the model permits to obtain scaling formulas and to investigate main regularities in the brush behavior. This offers a clear physical picture of the phase segregation inside a brush in correlation with the phase state of a bulk solvent.     

Polyelectrolyte brushes

The simple scaling theory of weakly-charged polyelectrolyte brush (the layer of polyelectrolyte chains grafted at one end onto an impermeable surface) immersed into a good solvent has been developed.The asymptotic scaling dependences of the free layer thickness on charge density and solvent strength are obtained. The behavior of polyelectrolyte brush subjected to normal and tangential external forces is considered. New “polyelectrolyte effect” is predicted: shear of a free polyelectrolyte brush leads to a decrease in brush thickness in contrast to the case of a free neutral brush. Such behavior is equivalent to that of a neutral brush subjected to external normal stretching force. This force in the case of polyelectrolyte brush is created by the osmotic pressure of mobile counterions neutralizing grafted chain charges.     

Directed motion of a polyelectrolyte micelle along tethered chains of oppositely charged polyelectrolyte brush

The complexation of different single polyelectrolyte (PE) micelles formed by linear diblock copolymers with oppositely charged brushes with varying grafting densities and charge content was studied by means of molecular dynamics simulations using the primitive model. We found that all micelles perform a directed motion along the vertical z axis on the grafted surface where they trapped while on the other axes the motion is restricted in a circle in which the diameter decreases with the increase of the hydrophilic length of the linear diblock copolymer. The motion of micelles is characterized as super diffusion inside brushes with low densities and low charge content. At high grafting densities and charge content the diffusion becomes Fickian or slightly subdiffusive. The number of the absorbed brush chains on the micelle corona increases almost monotonically with the increase of brush grafting density or with the decrease of charge content. The distance from the surface in which the micelle is trapped can be controlled by the charge density along the grafted PE chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 621–631     

Evaluation of an atomic force microscopy pull-off method for measuring molecular weight and polydispersity of polymer brushes: effect of grafting density

The accuracy of the molecular weights Mn and polydispersities of polymer brushes, determined by stretching the grafted chains using atomic force microscopy (AFM) and measuring the contour length distribution, was evaluated as a function of grafting density sigma. Poly(N,N-dimethylacrylamide) brushes were prepared by surface initiated atom transfer radical polymerization on latex particles with sigma ranging between 0.17 and 0.0059 chains/nm2 and constant Mn. The polymer, which could be cleaved from the grafting surface by hydrolysis and characterized by gel permeation chromatography (GPC), had a Mn of 30,600 and polydispersity (PDI) of 1.35. The Mn determined by the AFM technique for the higher density brushes agreed quite well with the GPC results but was significantly underestimated for the lower sigma. At high grafting density in good solvent, the extended structure of the brush increases the probability of forming segment-tip contacts located at the chain end. When the distance between chains approached twice the radius of gyration of the polymer, the transition from brush to mushroom structure presumably enabled the formation of a larger number of segment-tip contacts having separations smaller than the contour length, which explains the discrepancy between the two methods at low sigma. The PDI was typically higher than that obtained by GPC, suggesting that sampling of chains with above average contour length occurs at a frequency that is greater than their spatial distribution.