Increasing Grafting Density Research Articles

Adsorption of amphiphilic graft copolymers in solvents selective for the grafts on a lyophobic surface: a coarse-grained simulation study.

The sorption of graft copolymers on surfaces attractive only for the backbone and its effect on the conformational behavior of adsorbed/desorbed chains in solvents good for the grafts and poor for the backbone was studied by coarse-grained computer simulations. It was found that the sorption and conformational behavior are very complex and are results of an intricate interplay of solvent quality (polymer-solvent interactions) and solvent strength (polymer-surface vs. solvent-surface interactions). Increasing grafting density and length of grafts protect the backbone against adsorption, but the behavior is non-trivial. A decrease in solvent quality promotes the adsorption, because it lowers the overall solubility, but the backbone collapses and the probability of backbone-surface contacts decreases, which simultaneously hinders the adsorption. The results of simulations are presented in the form of phase diagrams depicting the decisive features of the conformational and sorption behavior.

Controllable preparation of polymer brushes from mesoporous silica SBA-15 via surface-initiated ARGET ATRP

Surface-initiated activators regenerated by electron transfer atom transfer radical polymerization (ARGET ATRP) was employed for controlled grafting of poly(glycidyl methacrylate) (PGMA) and poly(glycidyl methacrylate)-b-poly(methyl methacrylate) (PGMA-PMMA) brushes from mesoporous silica SBA-15. Initiator 2-bromoisobutyryl bromide (BiBB) was immobilized onto the inner surface of SBA-15 by reaction with free silanol groups. The polymerizations were conducted in the mixed solvents cyclohexanone /N, N-dimethylformamide. The strategy of utilizing mixed solvents gave rise to a suitable polymerization rate and resulted in a good control of the PGMA growth within the SBA-15 framework and could obtain polymer chains with well-preserved chain end functionality. Molecular weight of grafted polymer, structure, morphology, and composition of the functionalized SBA-15 were characterized by using gel permeation chromatography (GPC), X-ray powder diffraction (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM), N2 adsorption/desorption measurements, fourier transform infrared spectroscope (FT-IR), and thermogravimetry analysis (TGA), respectively. The thickness, polymer grafting density and molecular weight of the grafted polymer can be controlled by adjusting the polymerization time. The deactivator cannot efficient diffuse to convert the propagating chains to the dormant species when the pores are nearly completely filled with the polymer, therefore, increasing grafting density resulted in higher molecular weight and polydispersity index (PDI) values for the grafted polymer chains. This work provides a facile route for preparation of well-defined mesoporous silica/polymer hybrids.

Ionic liquid-SnO2 nanoparticle hybrid electrolytes for secondary charge storage devices: Physicochemical and electrochemical studies

A series of nanoscale hybrid ionic fluids (NHIFs) has been prepared by tethering 1-ethyl-3-(3-trimethoxysilylpropyl)-imidazolium bis(trifluoromethanesulfonyl) imide ionic liquids to the surface of SnO2 nanoparticle, at different grafting densities. Investigations reveal that SnO2 nanocores with uniform particle size of 14–17 nm are uniformly dispersed in different NHIF matrices through strong covalent attachment. Thermal stability and mechanical properties of NHIFs are found to improve with increasing grafting density. Temperature dependent electrochemical cycling behaviour of NHIF at different grafting densities are thoroughly investigated. In comparison to pure ionic liquid, the hybrid ionic fluids show substantial enhancement in electrochemical properties, which further improve with increasing grating density. The electrochemical cell containing NHIFs as electrolytes show very good capacitance retentivity (>90%) and long term cyclic stability above room temperature. Results obtained from the study demonstrate the applicability of these hybrid ionic fluids as promising electrolytes in secondary charge storage devices.

Effect of Filler–Polymer Interface on Elastic Properties of Polymer Nanocomposites: A Molecular Dynamics Study

ABSTRACT A coarse-grained model has been built to study the effect of the interfacial interaction between spherical filler particles and polymer on the mechanical properties of polymer nanocomposites. The polymer is modeled as bead-spring chains, and nano-fillers grafted with coupling agent are embedded into the polymer matrix. The potential parameters for polymer and filler are optimized to maximally match styrene-butadiene rubber reinforced with silica particles. The results indicated that, to play a noticeable role in mechanical reinforcement, a critical value exists for the grafting density of the filler–polymer coupling agent. After reaching the critical value, the increase of grafting density can substantially enhance mechanical properties. It is also observed that the increase of grafting density does not necessarily increase the amount of independent polymer chains connected to fillers. Instead, a significant amount of increased grafting sites serve to further strengthen already connected polymer and filler, indicating that mechanical reinforcement can occur through the locally strengthened confinement at the filler–polymer interface. These understandings based on microstructure visualization shed light on the development of new filler polymer interfaces with better mechanical properties.

PEGylation on mixed monolayer gold nanoparticles: Effect of grafting density, chain length, and surface curvature

PEGylation on nanoparticles (NPs) is widely used to prevent aggregation and to mask NPs from the fast clearance system in the body. Understanding the molecular details of the PEG layer could facilitate rational design of PEGylated NPs that maximize their solubility and stealth ability without significantly compromising the targeting efficiency and cellular uptake. Here, we use molecular dynamics (MD) simulation to understand the structural and dynamic the PEG coating of mixed monolayer gold NPs. Specifically, we modeled gold NPs with PEG grafting densities ranging from 0–2.76chain/nm2, chain length with 0–10 PEG monomers, NP core diameter from 5nm to 500nm. It is found that the area accessed by individual PEG chains gradually transits from a “mushroom” to a “brush” conformation as NP surface curvature become flatter, whereas such a transition is not evident on small NPs when grafting density increases. It is shown that moderate grafting density (∼1.0chain/nm2) and short chain length are sufficient enough to prevent NPs from aggregating in an aqueous medium. The effect of grafting density on solubility is also validated by dynamic light scattering measurements of PEGylated 5nm gold NPs. With respect to the shielding ability, simulations predict that increase either grafting density, chain length, or NP diameter will reduce the accessibility of the protected content to a certain size molecule. Interestingly, reducing NP surface curvature is estimated to be most effective in promoting shielding ability. For shielding against small molecules, increasing PEG grafting density is more effective than increasing chain length. A simple model that includes these three investigated parameters is developed based on the simulations to roughly estimate the shielding ability of the PEG layer with respect to molecules of different sizes. The findings can help expand our current understanding of the PEG layer and guide rational design of PEGylated gold NPs for a particular application by tuning the PEG grafting density, chain length, and particle size.

Synthesis of Nanoparticle Copolymer Brushes via Surface-Initiated seATRP

Synthesis of densely grafted (co)polymer brushes, including poly(tert-butyl acrylate) (PtBA), poly(tert-butyl acrylate)-b-poly(styrene) (PtBA-b-PS), and poly(tert-butyl acrylate)-b-poly(butyl acrylate) (PtBA-b-PBA), from 15.8 nm silica nanoparticles (NPs) via a surface-initiated simplified electrochemically mediated atom transfer radical polymerization (SI-seATRP) under constant potential electrolysis conditions is reported for the first time. The rate of polymerization was enhanced by applying more negative potentials, which resulted in an increase in grafting density, up to 0.93 nm–2. Furthermore, temporal control over the polymerization was achieved by adjustment of the applied potential. The polymers showed narrow molecular weight distributions (Đ = 1.20–1.32), and polymer-grafted nanoparticles had excellent size uniformity. Dispersions in suitable solvents were stable without any nanoparticle aggregation. Microstructures observed in thin films of densely block copolymer tethered silica NPs suggested ...

Control of electro‐osmotic flow by mixed polymer brushes: Molecular dynamics simulations

Molecular dynamics simulations of electro‐osmotic flow through a channel coated by a mixed polymer brush reveal the modulation of electro‐osmotic flow. The mixed polymer brush consists of two types of neutral chains, denoted as PA and PB chains, respectively. The effect of the interaction strength between PA and PB monomers on fluid transport is studied. It was found that the PA‐PB interaction plays an important role in controlling the flow. The mixed polymer brush adopts a layered structure owing to the difference in solvent‐polymer interactions. Stronger shear force from the solvent flow leads to larger extension of polymer chains on the top layer (or PA chains). Such layering structure also causes different coupling between polymer conformational dynamics and fluid dynamics. At high grafting densities, there are remarkable differences in the velocity profiles for different PA‐PB interactions. For repulsive and attractive interactions, the increase of grafting density leads to reduced fluid transport. However, when the attraction between PA and PB interactions becomes stronger, the flow behavior is more complicated depending on the grafting density. Our simulation results indicate the change of ionic distribution induced by the conformational transition due to the PA‐PB interaction has significant contributions to the flow controlling. POLYM. ENG. SCI., 57:1293–1300, 2017. © 2017 Society of Plastics Engineers

Scaling features of the tribology of polymer brushes of increasing grafting density around the mushroom-to-brush transition.

Nonequilibrium coarse-grained, dissipative particle dynamics simulations of complex fluids, made up of polymer brushes tethered to planar surfaces immersed in a solvent yield nonmonotonic behavior of the friction coefficient as a function of the polymer grating density on the substrates, Γ, while the viscosity shows a monotonically increasing dependence on Γ. This effect is shown to be independent of the degree of polymerization, N, and the size of the system. It arises from the composition and the structure of the first particle layer adjacent to each surface that results from the confinement of the fluid. Whenever such layers are made up of as close a proportion of polymer beads to solvent particles as there are in the fluid, the friction coefficient shows a minimum, while for disparate proportions the friction coefficient grows. At the mushroom-to-brush transition (MBT) the viscosity scales with an exponent that depends on the characteristic exponent of the MBT (6/5) and the solvent quality exponent (ν=0.5, for θsolvent), but it is independent of the polymerization degree (N). On the other hand, the friction coefficient at the MBT scales as μ∼N^{6/5}, while the grafting density at the MBT scales as Γ∼N^{-6/5} when friction is minimal, in agreement with previous scaling theories. We argue these aspects are the result of cooperative phenomena that have important implications for the understanding of biological brushes and the design of microfluidics devices, among other applications of current academic and industrial interest.

Insight into the Dispersion Mechanism of Polymer-Grafted Nanorods in Polymer Nanocomposites: A Molecular Dynamics Simulation Study

Coarse-grained molecular dynamics simulations are performed to investigate the dispersion behavior and the underlying dispersion mechanism of polymer-grafted nanorods (NRs) in a polymer matrix. The influences of grafting density, grafted chain length, and the miscibility between grafted chains and matrix chains are systematically analyzed. The simulation results indicate that the dispersion state of grafted NRs is determined primarily by the excluded volume effect of grafted NRs and the interface between grafted chains and matrix chains. It is found that increasing grafting density and/or grafted chain length induces the conformational transition of grafted chains from mushroom to brush, enlarges the excluded volume of grafted NRs, and enhances the brush/matrix interface in the brush regime, resulting in the improvement of the NR dispersion state. By tuning the interaction strength between grafted chains and matrix chains in a wide range, three general categories of NR spatial organization are found: macroscopic phase separation of the NRs and polymer matrix, homogeneous dispersion of the NRs, and “tele-bridging” of the NRs via the matrix chains. The transition from a “wet” to “dry” brush is observed at the strong brush/matrix interaction. In addition, for the polymer brush grafted on the surface of NRs, the dependence of the brush thickness Tb on either grafting density Σ or grafted chain length Lg is always weaker than that of polymer brush grafted on flat surface or spherical surface, mainly due to the broader range of moving and the less stretching of polymer chains grafted to NRs. The Tb scales with Σ and Lg as Tb ∼ ΣαLgβ, where the ratio β/α is a constant equal to 3, independent of the grafted surface. In general, this work offers a deep insight into the dispersion mechanism of grafted NRs and thus is believed to provide some guidance on the design and preparation of high-performance polymer nanocomposites with tailored dispersion of NRs.

Molecular dynamics simulations of polymer crystallization under confinement: Entanglement effect

We carried out molecular dynamics simulations to study the crystallization of polymer melts subjected to confinement between two parallel walls. Two types of walls, bare and grafted walls, are studied. The bare walls are slippery for chain motions, and the interactions between polymer chains and the walls are moreover chosen either attractive or repulsive. The crystallization in the case of bare walls generally consists of surface-induced processes close to the walls followed by homogeneous nucleation in both the boundary and middle regions. In the case of grafted walls, parts of polymer chains residing close to the walls are adhesive to the surfaces and become permanent graft points. We find that the surface-induced crystallization is increasingly suppressed with increasing grafting density. At high grafting densities, only crystallization in the middle regions is observed. We calculated the spatial distribution of entanglement lengths and related it to the crystallization behavior. The entanglement length close to the walls is found to decrease with increasing grafting density, as the adhesion points act as effective entanglement knots. In light of our recent results that less entangled polymer melts lead to faster crystallization and higher crystallization order, we now show that this conclusion stands also for the case of confined polymer melts. Our results suggest entanglements to be an universal factor towards the understanding of polymer crystallization under different situations, in particular at supercooling.

Swelling and Surface Interactions of End-Grafted Poly(2-vinylpyridine) Layers in Acidic Solution: Influence of Grafting Density and Salt Concentration.

In previous studies, the authors found that end-grafted layers of the weak polybase poly(2-vinylpyridine) (P2VP) in aqueous solutions do not only swell and collapse if the pH value and salt concentration are varied but also exhibit a pH- and salinity-dependent adhesion to microsized silica spheres. For a better understanding of these effects, in situ force measurements using the AFM colloidal probe technique were applied to end-grafted P2VP layers of different grafting densities in NaCl solutions at pH 2.5. Although a mushroom-to-brush transition could be seen in the dry state, the layers were in the brush regime in aqueous solutions at all NaCl concentrations and grafting densities. We observed an increase of the brush height with increasing grafting density and a salinity-dependent collapse and reswelling of the brushes. The adhesion between the P2VP layer and a silica sphere depended on both grafting density and salinity. At low salt concentrations, the adhesion reached its highest value at the intermediate grafting density and disappeared with denser brushes. Maximum adhesion was obtained for high NaCl concentrations and the lowest grafting density. From a detailed analysis of the experiments, we gained insight into chain stretching and density profiles under complex ionic conditions and into the mechanism of adhesion of polyelectrolytes to solid surfaces.

Increasing the Thermal Conductivity of Graphene-Polyamide-6,6 Nanocomposites by Surface-Grafted Polymer Chains: Calculation with Molecular Dynamics and Effective-Medium Approximation

By employing reverse nonequilibrium molecular dynamics simulations in a full atomistic resolution, the effect of surface-grafted chains on the thermal conductivity of graphene-polyamide-6.6 (PA) nanocomposites has been investigated. The interfacial thermal conductivity perpendicular to the graphene plane is proportional to the grafting density, while it first increases and then saturates with the grafting length. Meanwhile, the intrinsic in-plane thermal conductivity of graphene drops sharply as the grafting density increases. The maximum overall thermal conductivity of nanocomposites appears at an intermediate grafting density because of these two competing effects. The thermal conductivity of the composite parallel to the graphene plane increases with the grafting density and grafting length which is attributed to better interfacial coupling between graphene and PA. There exists an optimal balance between grafting density and grafting length to obtain the highest interfacial and parallel thermal conductivity. Two empirical formulas are suggested, which quantitatively account for the effects of grafting length and density on the interfacial and parallel thermal conductivity. Combined with effective medium approximation, for ungrafted graphene in random orientation, the model overestimates the thermal conductivity at low graphene volume fraction (f < 10%) compared with experiments, while it underestimates it at high graphene volume fraction (f > 10%). For unoriented grafted graphene, the model matches the experimental results well. In short, this work provides some valuable guides to obtain the nanocomposites with high thermal conductivity by grafting chain on the surface of graphene.

Control of Cell Attachment and Spreading on Poly(acrylamide) Brushes with Varied Grafting Density.

To achieve spatial control of fibroblast cell attachment and spreading on a biocompatible polymer coating, the effect of poly(acrylamide) (PAAm) brushes with varied grafting density was investigated. The synthesis of the brushes was performed by surface-initiated atom transfer radical polymerization (SI-ATRP). Gold substrates were modified with binary self-assembled monolayers (SAMs) of an initiator and 16-mercaptohexadecanoic acid (MHDA) as an "inert" thiol to initiate the ATRP of AAm. By using different mixtures for the binary SAMs, a series of polymer brushes with varied grafting densities were prepared. The fractional coverage of surface bound initiator was determined by grazing incidence Fourier transform infrared (FTIR) spectroscopy, X-ray photoelectron spectroscopy (XPS), time-of-flight secondary ion mass spectrometry (ToF-SIMS), and contact angle measurements. A linear relationship between the Br/S ratio determined by XPS and ToF-SIMS versus the fraction of initiator on the surface determined by water contact angle measurements was observed. The varied initiation concentration on the gold substrates yielded PAAm brushes with different thicknesses, indicating a transition from mushroom to brush regimes with increasing grafting density. Thereby we achieved exquisite control of the degree of cell adhesion. Cell attachment experiments with NIH 3T3 fibroblast cells revealed cell spreading on PAAm brushes with low grafting densities (initiator fractional coverage <0.2) as well as a complete passivation by polymer brushes with higher grafting densities.

High density silanization of nano-silica particles using γ-aminopropyltriethoxysilane (APTES)

A novel and efficient process was developed for high density silanization of nano-silica particles using APTES, in which 13.48APTESnm−2 was achieved. This process comprises three stages, namely, aqueous mixing, spray drying and thermal treatment. After the successive stages, the APTES conversions were 25.3%, 50.7% and 80.6%. In the aqueous mixing stage, the chemical reaction was fast and quite limited. In the spray drying stage, APTES was distributed on the surface of nano-silica particles uniformly by both physical and chemical adsorption. In the thermal treatment stage, the processing temperature (T) and time in the thermal treatment had large effects on the grafting density, and the reaction was reversible. When T<300°C, the reverse reaction dominated, causing a decrease of APTES grafting density. When T>300°C, the forward reaction dominated, leading to increased grafting density. The optimum processing temperature and time for high grafting density were 360°C and 30min, respectively.

Reactive melt modification of polyethylene by ethyl acrylate/acrylic acid copolymers: rheology, morphology and thermal behavior

Polyethylene (PE) was in situ grafted and blended with ethyl acrylate and acrylic acid copolymer units and the rheology, morphology and thermal behavior of samples were investigated and correlated to grafting efficiency. The ethyl acrylate and acrylic acid monomers were copolymerized in three different amounts of monomers (i.e., 5, 15 and 25 wt%) and three different amounts of 2,2′-azobisisobutyronitrile (AIBN) initiator (i.e., 0.2, 0.3 and 0.4 wt%). The reactive melt blending of the synthesized copolymers, PE and dicumyl peroxide (DCP) were carried out in a co-rotating, 40 L/D twin screw extruder. The grafting percentage, determined by using chemical titration and Fourier transform infrared (FTIR) methods, increased at higher amounts of reactive monomers and AIBN and a maximum of 6 % was achieved. The thermal behavior of PE were studied by differential scanning calorimeter (DSC) and no remarkable changes was observed in melting (T m = 127.0 ± 2 °C) and crystallization (T c = 113.6 ± 2 °C) temperatures. The crystallinity of PE decreased from 53.5 to 43.8 %, with increase in grafting density. Investigating the gel content showed that only in samples that contained the highest amounts of acrylic monomer, i.e., 25 wt%, an increase in gel content was observed by increasing the total peroxide. The maximum value of gel content was 23.6 %. Increase in acrylate and AIBN percentages showed increase in viscosity and damping factor and decrease in storage modulus in rheological study of the samples and the results were proved by morphological study of the samples using scanning emission microscopy (SEM).

Confinement effect of graphene nanoplatelets on atom transfer radical polymerization of styrene: grafting through hydroxyl groups

Dual characteristics polystyrene chains were synthesized by “grafting through” atom transfer radical polymerization in the presence of surface-modified graphene nanoplatelets. After oxidation of graphene, it was functionalized by different amounts of 3-(trimethoxysilyl) propyl methacrylate (MPS) through the surface hydroxyl groups. Polymerization of styrene in the presence of modified graphene and initiator, ethyl alpha-bromoisobutyrate, was accomplished at 110 C. Then, the effects of various graft densities and different graphene loadings on the heterogeneous graft and free polystyrene chains’ characteristics and also their kinetics of polymerization were studied by gas- and gel-permeation chromatographies. Linear increase of ln(M 0/M) with time for all the samples shows that polymerization proceeds in a living manner. By increasing graphene content, M n increases, and polydispersity index (PDI) decreases for free chains. However, a reverse behavior was observed for attached chains. Increasing graft density resulted in higher M n and lower PDI values for free chains. Similar to the effect of graphene content, a reverse behavior was observed for the attached chains. Efficiency of grafting reactions along with the graft contents was studied by X-ray photoelectron spectroscopy (XPS), elemental analysis, and thermogravimetry analysis. The grafting ratio of MPS modifier was calculated to be 9.7 % via the data of Si contents in the XPS survey scan data. Finally, the morphology of the functionalized graphene was studied by transmission electron microscopy.

How does a polymer brush repel proteins?

The captioned question has been addressed by the steric effect; namely, the adsorption of proteins on a surface grafted with linear polymer chains decreases monotonically as the grafting density increases. However, there is no quantitative and satisfactory explanation why the adsorption starts to increase when the grafting density is sufficiently high and why polyethylene glycol (PEG) still remains as one of the best polymers to repel proteins. After considering each grafted chain as a molecular spring confined inside a “tube” made of its surrounding grafted chains, we estimated how its free energy depends on the grafting density and chain length, and calculated its thermal energy-agitated chain conformation fluctuation, enabling us to predict an adsorption minimum at a proper grafting density, which agrees well with previous experimental results. We propose that it is such a chain fluctuation that slows down the adsorption kinetically.

Substrate Effect on the Phase Behavior of Polymer Brushes with Lattice Density Functional Theory

The lattice density functional theory (LDFT) is used to describe the substrate effect on the phase behavior of polymer brush grafted on different substrates. The LDFT predicts that: both attractive and repulsive interactions between the substrate and the polymer chains have effects on the thickness of brushes; when the short-range monomer–substrate interaction is larger than a certain value, the thickness and density profiles of polymer brushes almost do not change. And also an attractive substrate can increase the critical grafting density of pancake to brush transition. For temperature responsive polymer brushes, the temperature transition points are almost the same with different substrates, however, an attractive substrate can increase the swelling ratio and a repulsive substrate can decrease the swelling ratio. We also find that an increasing grafting density can decrease the substrate effect on the swelling behavior of temperature responsive polymer brushes.

Modeling lower critical solution temperature behavior of associating polymer brushes with classical density functional theory

We study the lower critical solution temperature (LCST) behavior of associating polymer brushes (i.e., poly(N-isopropylacrylamide)) using classical density functional theory. Without using any empirical or temperature-dependent parameters, we find the phase transition of polymer brushes from extended to collapsed structure with increasing temperature, indicating the LCST behavior of polymer brushes. The LCST behavior of associating polymer brushes is attributed to the interplay of hydrogen bonding interactions and Lennard-Jones attractions in the system. The effect of grafting density and molecular weight on the phase behavior of associating polymer brushes has been also investigated. We find no LCST behavior at low grafting density or molecular weight. Moreover, increasing grafting density decreases the LCST and swelling ratio of polymer brushes. Similarly, increasing molecular weight decreases the LCST but increases the swelling ratio. At very high grafting density, a partial collapsed structure appears near the LCST. Qualitatively consistent with experiments, our results provide insight into the molecular mechanism of LCST behavior of associating polymer brushes.

On the Two-Population Structure of Brushes Made of Arm-Grafted Polymer Stars

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.