Brush Thickness Research Articles

Brush Layer Charge Characteristics of a Biomimetic Polyelectrolyte-Modified Nanoparticle Surface.

Nanoparticle surface charge regulation technology plays an important role in ion rectification, drug delivery, and cell biology. The biomimetic polyelectrolyte can be combined with nanoparticles by nanomodification technology to form a layer of coating, which is called the brush layer of nanoparticles. In this study, based on the Poisson-Nernst-Planck (PNP) equation system, a theoretical model considering a bionic electrolyte brush layer with charge density regulated by a chemical reaction is constructed. The charge properties of brushed nanoparticles are studied by changing the sizes of nanoparticles, the pH value of the solution, background salt solution concentration, and brush layer thickness. The result shows that the charge density of brushed nanoparticles increases with the increase of particle size. The isoelectric point (IEP) of the equilibrium reaction against the brush layer is pH = 5.5. When the pH < 5.5, the charge density of the particle brush layers decreases with the increase of pH, and when the pH > 5.5, the charge density of the particle brush layer increases with the increase of pH. By comparing the charge density of different brush thicknesses, it is found that the larger the brush thickness, the smaller the charge density of the brush layer. This research provides theoretical support for the change of the through pore velocity when macromolecular organic compounds pass through nanopores.

Inhibition of turbulent methane/air premixed bunsen flames by dimethyl methylphosphonate

There is little knowledge about the inhibition efficiency of dimethyl methylphosphonate (DMMP) against turbulent flames, in which vortices of different sizes corrugate and stretch the flame front. This study is to investigate the performance and the mechanism of DMMP in inhibiting turbulent methane/air premixed Bunsen flames. Several important parameters are chosen to characterize the combustion of the flames, including flame brush height, flame brush thickness and turbulent burning velocity. It is found that the flame brush expands both horizontally and vertically with the increase of turbulent intensity. For all the flames, the centerline mean flame brush thickness increases linearly with flame height. Turbulent burning velocity decreases monotonically with the increasing of DMMP addition. However, the normalized turbulent burning velocity increases with the normalized turbulent intensity. Compared with the performance in laminar premixed flames, the inhibition efficiency depends on the turbulent intensity. For low-intensity turbulent flames, the inhibition efficiency is higher than that in laminar premixed flames, but the relative inhibition efficiency decreases with DMMP addition. This can be attributed to the relative size of the vortices and the flame front thickness: when the Kolmogorov length scale is less than the preheat zone thickness but greater than the reaction zone thickness, vortices reduce the burning velocity; when the Kolmogorov length scale is less than the reaction zone thickness, vortices facilitate the combustion. The trend is opposite in high-intensity turbulent flames, which is mainly attributed to the generating of the flame pockets in the flame tips.

Reynolds number scaling of burning rates in spherical turbulent premixed flames

Abstract

Enrichment of Charged Monomers Explains Non-monotonic Polymer Volume Fraction Profiles of Multi-stimulus Responsive Copolymer Brushes.

Multi-stimulus responsive poly(2-(2-methoxyethoxy)ethyl methacrylate-co-2-(diethylamino)ethyl methacrylate) [P(MEO2MA-co-DEA)] 80:20 mol % copolymer brushes were synthesized on planar silica substrates via surface-initiated activators continuously regenerated via electron transfer atom transfer radical polymerization. Brush thickness was sensitive to changes in pH and temperature as monitored with ellipsometry. At low pH, the brush is charged and swollen, while at high pH, the brush is uncharged and more collapsed. Clear thermoresponsive behavior is also observed with the brush more swollen at low temperatures compared to high temperatures at both high and low pH. Neutron reflectometry was used to determine the polymer volume fraction profiles (VFPs) at various pH values and temperatures. A region of lower polymer content, or a depletion region, near the substrate is present in all of the experimental polymer VFPs, and it is more pronounced at low pH (high charge) and less so at high pH (low charge). Polymer VFPs calculated through numerical self-consistent field theory suggest that enrichment of DEA monomers near the substrate results in the experimentally observed non-monotonic VFPs. Adsorption of DEA monomers to the substrate prior to initiation of polymerization could give rise to DEA segment-enriched region proximal to the substrate.

Responsive Polymer Brush Design and Emerging Applications for Nanotheranostics.

Responsive polymer brushes are a category of polymer brushes that are capable of conformational and chemical changes in response to external stimuli. They offer unique opportunities for the control of bio-nano interactions due to the precise control of chemical and structural parameters such as the brush thickness, density, chemistry, and architecture. The design of responsive brushes at the surface of nanomaterials for theranostic applications has developed rapidly. These coatings can be generated from a very broad range of nanomaterials, without compromising their physical, photophysical, and imaging properties. Although the use of responsive brushes for nanotheranostic remains in its early stages, in this review, the aim is to present how the systems developed to date can be combined to control sensing, imaging, and controlled delivery of therapeutics. The recent developments for such design and associated methods for the synthesis of responsive brushes are discussed. The responsive behaviors of homo polymer brushes and brushes with more complex architectures are briefly reviewed, before the applications of responsive brushes as smart delivery systems are discussed. Finally, the recent work is summarized on the use of responsive polymer brushes as novel biosensors and diagnostic tools for the detection of analytes and biomarkers.

Real-Time Measurement of Polymer Brush Dynamics Using Silicon Photonic Microring Resonators: Analyte Partitioning and Interior Brush Kinetics.

Polymer brushes are found in biomedical and industrial technologies, where they exhibit functionalities considerably dependent on polymer brush-solvent-analyte interactions. It remains a difficult challenge to quickly analyze solvent-swollen polymer brushes, both at the solvent-polymer brush interface and in the brush interior, as well as to monitor the kinetics of interaction of solvent-swollen brushes with key analytes. Here, we demonstrate the novel use of silicon photonic microring resonators to characterize in situ swollen polymer brush-analyte interactions. By monitoring resonant wavelength shifts, we find that brush-solvent-analyte interaction parameters can be extracted from a single set of data or from successive analyte introductions using a single brush-coated sensor. The partition coefficient of three industrially relevant plasticizers into hydrophobic and hydrophilic brushes was determined and found to be in agreement with known solubility trends. We found that the diffusion coefficient of the plasticizer into the brush decreases as brush thickness increases, supporting a model of a dense inner brush layer and diffuse outer layer. pKa's of pH-sensitive brushes were determined on the microring resonator platform; upon increasing the dry brush thickness, the pKa for poly(2-dimethylamino ethyl methacrylate) decreased from 8.5 to approach the bulk material pKa of 7.3 and showed dependence on the presence and concentration of salt. These proof-of-concept experiments show how the surface-sensitive nature of the microring resonator detection platform provides valuable information about the interaction of the polymer brushes with the solvents and analytes, not easily accessed by other techniques.

Polymer Brushes via Surface-Initiated Electrochemically Mediated ATRP: Role of a Sacrificial Initiator in Polymerization of Acrylates on Silicon Substrates.

Silicon wafers as semiconductors are essential components of integrated circuits in electronic devices. For this reason, modification of the silicon surface is an important factor in the manufacturing of new hybrid materials applied in micro- and nanoelectronics. Herein, copolymer brushes of hydrophilic poly(2-hydroxyethyl acrylate) (PHEA) and hydrophobic poly(tert-butyl acrylate) (PtBA) were grafted from silicon wafers via simplified electrochemically mediated atom transfer radical polymerization (seATRP) according to a surface-initiated approach. The syntheses of PHEA-b-PtBA copolymers were carried out with diminished catalytic complex concentration (successively 25 and 6 ppm of Cu). In order to optimize the reaction condition, the effect of the addition of a supporting electrolyte was investigated. A controlled increase in PHEA brush thickness was confirmed by atomic force microscopy (AFM). Various other parameters including contact angles and free surface energy (FSE) for the modified silicon wafer were presented. Furthermore, the effect of the presence of a sacrificial initiator in solution on the thickness of the grafted brushes was reported. Successfully fabricated inorganic–organic hybrid nanomaterials show potential application in biomedicine and microelectronics devices, e.g., biosensors.

Let a Hundred Polymers Bloom: Tunable Wetting of Photografted Polymer-Carbon Nitride Surfaces

Sunlight is widely used by plants to produce chemical energy fundamental for all life, a process that also serves as an inspiration for science. Recently, light-harvesting semiconductor materials, here, carbon nitrides, have been widely used in photochemistry to catalyze reactions under visible light illumination. We exploited photoactive carbon nitride thin films as a metal-free platform for one-step photografting from polymers on the surface. Here, we observe photoswitchable wetting properties of polystyrene-grafted carbon nitride, which are independent of any classical photoswitchable groups. Dense and thick polymer brush formation with a tunable thickness (up to 700 nm) was obtained, allowing for tailor surface properties. Furthermore, exploiting the reciprocal insolubility of water–dimethylacrylamide and pentane–styrene solutions, we provide a general method for the synthesis of centimeter-scale carbon nitride-based Janus asymmetric films. It is thought that the simple experimental design based on cheap and common chemicals provides a novel dimension of carbon nitride materials with advanced surface properties.

Ultrastructure of the Midgut Adult, Trachyderma philistina (Coleoptera: Tenebrionidae)

In the anterior part of the midgut adult Trachyderma philistina, the apical part showed microvilli in the form of membrane with folds and also microvilli appeared slender and uniform. Between these folds of microvilli appeared a lot of ribosomes and rough endoplasmic reticulum. Secretory vesicles are discharged from part of midgut. A well-developed oval nucleus appeared in the cytoplasm near the apical part of the cell. The nucleus is surrounded by a lot of free ribosomes and rough endoplasmic reticulum. Mitochondria appeared near the apical part of the cell. A well-developed thick basement membrane appeared in the basal part of the anterior midgut of adult beetle Trachyderma philistina. In the middle part of the midgut, a very thick well-developed brush border microvilli appeared. Mitochondria and numerous tracheae appeared through cytoplasm. Rough endoplasmic reticulum appeared throughout the cytoplasm. A lot of secretory vacuoles were observed directed apically. A well-developed oval and circular nucleus appeared near the basal part of the cell and surrounded by numerous rough endoplasmic reticulum A well-developed muscle fiber appeared apically and basally. A very thin basement membrane appeared in the basal part of the cell. The peritrophic membrane is absent in the midgut of adult stage Trachyderma philistine while regenerative cells appeared in the basal part of the middle midgut cell. In the posterior part of the midgut, microvilli appeared in the form of membranes due to the presence of numerous organelles that are discharging into the lumen. Lipid spheres and aggregations of glycogen are present throughout the cell. A thin basement membrane was observed.

Glycopolymer Brushes by Reversible Deactivation Radical Polymerization: Preparation, Applications, and Future Challenges.

The cellular surface contains specific proteins, also known as lectins, that are carbohydrates receptors involved in different biological events, such as cell–cell adhesion, cell recognition and cell differentiation. The synthesis of well-defined polymers containing carbohydrate units, known as glycopolymers, by reversible deactivation radical polymerization (RDRP) methods allows the development of tailor-made materials with high affinity for lectins because of their multivalent interaction. These polymers are promising candidates for the biomedical field, namely as novel diagnostic disease markers, biosensors, or carriers for tumor-targeted therapy. Although linear glycopolymers are extensively studied for lectin recognition, branched glycopolymeric structures, such as polymer brushes can establish stronger interactions with lectins. This specific glycopolymer topology can be synthesized in a bottlebrush form or grafted to/from surfaces by using RDRP methods, allowing a precise control over molecular weight, grafting density, and brush thickness. Here, the preparation and application of glycopolymer brushes is critically discussed and future research directions on this topic are suggested.

Interfacial Energy Measurement on the Reconstructive Polymer Surface: Dynamic Polymer Brush by Segregation of Amphiphilic Block Copolymers.

Herein, the interfacial energy of a reconstructive polymer surface formed by segregation is analyzed by measuring the change in the size of elastomer thin films floating on water. When a system in which amphiphilic diblock copolymers are mixed with the hydrophobic elastomer is in contact with water, surface reconstruction is triggered by the segregation of copolymers with a gain in the hydration energy of the hydrophilic blocks. The hydrophilic brush layer spontaneously formed at the elastomer-water interface is named the dynamic polymer brush. Although it is anticipated that the interfacial energy will significantly decrease in the dynamic polymer brush system, a direct measurement of the interfacial energy of the reconstructive interface is a challenge. We propose a novel method to measure the interfacial energy of a reconstructive polymer surface by measuring the deformation of elastomer thin films floating on water and apply it to the dynamic polymer brush system. The interfacial energy of the dynamic polymer brush formed by the segregation of amphiphilic diblock copolymers with longer hydrophilic chains drastically decreased to zero due to the high hydration energy of hydrophilic chains. Based on the neutron reflectometry results, the graft density and thickness of the dynamic polymer brush system floating on water were found to be lower than those of the system fixed onto solid substrates. This indicates that the floating system can respond to an external environment with a high degree of freedom (graft density, brush thickness, and interface area).

Variations in the Morphology, Mechanics and Adhesion of Persister and Resister E. coli Cells in Response to Ampicillin: AFM Study.

Persister bacterial cells are great at surviving antibiotics. The phenotypic means by which they do that are underexplored. As such, atomic force microscope (AFM) was used to quantify the contributions of the surface properties of the outer membrane of multidrug resistance (MDR)-Escherichia coli Strains (A5 and A9) in the presence of ampicillin at minimum inhibitory concentration (MIC) (resistant cells) and at 20× MIC (persistent cells). The properties quantified were morphology, root mean square (RMS) roughness, adhesion, elasticity, and bacterial surface biopolymers’ thickness and grafting density. Compared to untreated cells, persister cells of E. coli A5 increased their RMS, adhesion, apparent grafting density, and elasticity by 1.2, 3.4, 2.0, and 3.3 folds, respectively, and decreased their surface area and brush thickness by 1.3 and 1.2 folds, respectively. Similarly, compared to untreated cells, persister cells of E. coli A9 increased their RMS, adhesion and elasticity by 1.6, 4.4, and 4.5 folds, respectively; decreased their surface area and brush thickness by 1.4 and 1.6 folds, respectively; and did not change their grafting densities. Our results indicate that resistant and persistent E. coli A5 cells battled ampicillin by decreasing their size and going through dormancy. The resistant E. coli A9 cells resisted ampicillin through elongation, increased surface area, and adhesion. In contrast, the persistent E. coli A9 cells resisted ampicillin through increased roughness, increased surface biopolymers’ grafting densities, increased cellular elasticities, and decreased surface areas. Mechanistic insights into how the resistant and persistent E. coli cells respond to ampicillin’s treatment are instrumental to guide design efforts exploring the development of new antibiotics or renovating the existing antibiotics that may kill persistent bacteria by combining more than one mechanism of action.

The Thickness of Surface Grafting Layer on Bio-materials directly Mediates the Immuno-reacitivity of Macrophages in vitro.

Introducing the surface grafting layers to regulate bio-compatibility and bio-function is an important step in the tissue engineering field. However, whether the thickness variation of the introduced biomimetic layer impacts the behavior of the adhered immune effector cells is yet to be dissected fully. In this study, we used a surface-induced atom transfer radical polymerization (SI-ATRP) method to synthetize and graft poly-phenoxyethyl methacrylate (PHEMA) brushes having different lengths on the glass substrates. Primary murine peritoneal macrophages were collected and cultured on the PHEMA brushes and we investigated the influence of polymer brushes having different lengths on macrophages phenotype and function. Our results demonstrated that the thicker brushes (200 nm and 450 nm) are superior to the thinner layers (50 nm) for macrophages survival, proliferation, cell elongation and migration. Moreover, the thicker brushes are more beneficial for macrophage’s activities and functions, presented by the increased production of M1-associated cytokines IL-6 and MCP-1, the elevated cell phagocytosis and the activation molecule F4/80 expression, and the reduced macrophages apoptosis in thicker brushes-sustained macrophages. Our data suggests that the thickness of the substrate grafting layer directly impacts macrophages recruitment and pro-inflammatory function, which is important in determining the intrinsic immuno-compatibilities of the surface modified-biomaterials and mediates material-host interactions in vivo.

Synergistic Charge Reversal with Hierarchical Architecture for Self-Adaptive Antibacterial Surface of Polymer Substrate

The responsive antibacterial efficacy of hierarchical polymer brushes has been well recognized for the treatment of device-associated infection. However, in the previous work, the nanometer-scale thickness of polymer brushes is prone to damage and the reported silicon substrate is not close to practical application. To address these challenges, a self-adaptive antibacterial polymer surface is facilely proposed and designed. Herein, a two-layered polymer brush is first constructed onto the polymer surface, the inner layer of which is conjugated by dimethylmaleic anhydride (DMMA) to produce charge-reversal function, subsequently loading antimicrobial peptides (AMP), and the outer layer of which is a hydrated brush to provide anti-biomass adhesion function. It's worth noting that the micrometer-scale thickness of the inner layer presents the excellent AMP loading capacity. Compared with the charge-neutralization surface, the charge-reversal surface can more sensitively and controllably release AMP triggered by the acidic environment arising from the metabolism of bacteria and may still be bactericidal after AMP is completely released due to the exposure of the primary amino group, thus the long-term antibacterial of the surface is readily obtained. More importantly, in a mice model the charge-reversal surface demonstrates the highly effective anti-infection and excellent biocompatibility, which implies a promising strategy for the clinical prevention of device-associated infections.

Electroresponsive Polyelectrolyte Brushes Studied by Self-Consistent Field Theory.

End-grafting of polyelectrolyte chains to conducting substrates offers an opportunity to fabricate electro-responsive surfaces capable of changing their physical/chemical properties (adhesion, wettability) in response to applied electrical voltage. We use a self-consistent field numerical approach to compare the equilibrium properties of tethered strong and weak (pH-sensitive) polyelectrolytes to applied electrical field in both salt-free and salt-containing solutions. We demonstrate that both strong and weak polyelectrolyte brushes exhibit segregation of polyions in two populations if the surface is oppositely charged with respect to the brush. This segregation gives rise to complex patterns in the dependence of the brush thickness on salt concentration. We demonstrate that adjustable ionization of weak polyelectrolytes weakens their conformational response in terms of the dependence of brush thickness on the amplitude of the applied voltage.

Modelling of a turbulent lean premixed combustor using a Reynolds-averaged Navier–Stokes approach

This work aims to characterize lean premixed turbulent swirling flames representative of gas turbines and jet engines via a numerical study of flame topologies in a laboratory-scale burner. The state of the art of the numerical studies concerning these types of flames is first reviewed, with respect to Reynolds-averaged Navier–Stokes and large eddy simulations. Then, a turbulent, isothermal flow study is performed within the radial swirler. The impact of mesh refinement levels and boundary conditions on the swirl number and overall flow structure is investigated. The mesh refinement level and slip wall boundary condition alter the computed swirl number significantly. The computed swirl number converges to a value of 0.7, which is larger than the geometrical one, 0.4. Furthermore, using Reynolds-averaged Navier–Stokes transport equations, closed by the realizable $$k-\epsilon$$ model, coupled with a two-equation premixed combustion model for methane/air mixtures, two combustion regimes are analysed. These regimes correspond to the outer recirculation zone flame and an unstable regime. The flow structure is characterized in terms of velocity fields, turbulence and combustion properties. A reaction progress variable comparison is also performed, using existing experimental results, yielding qualitatively similar structures for both studied regimes. Some discrepancies between numerical and experimental results concerning the stable regime may be observed: The computed progress variable at the outer recirculation zone, 0.5, is smaller than the experimental value, 0.8, and the average flame brush thickness, 1 mm, is found to be smaller than the measured, 3 mm.

Poly(diethylene glycol methylether methacrylate) Brush-Functionalized Anodic Alumina Nanopores: Curvature-Dependent Polymerization Kinetics and Nanopore Filling.

We report on the synthesis and characterization of poly(diethylene glycol methylether methacrylate) (PDEGMA) brushes by surface-initiated atom transfer radical polymerization inside ordered cylindrical nanopores of anodic aluminum oxide with different pore radii between 20 and 185 nm. In particular, the dependence of polymerization kinetics and the degree of pore filling on the interfacial curvature were analyzed. On the basis of field emission scanning electron microscopy data and thermal gravimetric analysis (TGA), it was concluded that the polymerization rate was faster at the pore orifice compared to the pore interior and also as compared to the analogous reaction carried out on flat aluminum oxide substrates. The apparent steady-state polymerization rate near the orifice increased with decreasing pore size. Likewise, the overall apparent polymerization rate estimated from TGA data indicated stronger confinement for pores with increased curvature as well as increased mass transport limitations due to the blockage of the pore orifice. Only for pores with a diameter to length ratio of ∼1, PDEGMA brushes were concluded to grow uniformly with constant thickness. However, because of mass transport limitations in longer pores, incomplete pore filling was observed, which leads presumably to a PDEGMA gradient brush. This study contributes to a better understanding of polymer brush-functionalized nanopores and the impact of confinement, in which the control of polymer brush thickness together with grafting density along the nanopores is key for applications of PDEGMA brushes confined inside nanopores.

How Dissociation of Carboxylic Acid Groups in a Weak Polyelectrolyte Brush Depend on Their Distance from the Substrate.

A weak polyelectrolyte brush is composed of a layer of polyacids or polybases grafted by one end of their chains to a substrate surface. For such brush layers immersed in an aqueous solution, the dissociation behavior of the acidic or basic groups and the structural and physical properties of the brush layer will thus be strongly dependent on the environmental conditions. For a polyacid brush layer consisting of, e.g., poly(acrylic acid), this means that the chains in the brush layer will be charged at high pH and uncharged at low pH. However, theoretical scaling laws not only foresee the structural changes occurring in response to the pH-induced dissociation behavior but also how the dissociation behavior of the brush layer depends on the ionic strength of the aqueous solution and the density of acidic groups within the brush layer. We have herein employed spectroscopic ellipsometry and a quartz crystal microbalance with dissipation monitoring (QCM-D) to experimentally evaluate the theoretically predicted dissociation and structural behavior of PAA brushes. Spectroscopic ellipsometry allows us to study the brush thickness as a function of pH and ionic strength, while QCM-D gives us an opportunity to investigate the swelling behavior of PAA brushes at various penetration depths of propagating acoustic waves. Our studies show that the dissociation degree of the carboxylic acid groups in a PAA brush increases with increasing distance from the substrate. Moreover, the ionic strength enhances carboxylic acid dissociation, such that a higher ionic strength leads to a narrower distribution and higher average dissociation degree. In conclusion, our results provide an experimental verification of the theoretically predicted gradient in the degree of dissociation of the acid groups in weak polyacid brush layers and shows that at a pH value equal to approximately the average pKa value of the brush, the state of the acid groups varies from being almost uncharged to almost fully dissociated depending on the ionic strength and vertical position in the brush.

Facile Fabrication of Bio- and Dual-Functional Poly(2-oxazoline) Bottle-Brush Brush Surfaces.

Poly(2‐oxazoline)s (POx) bottle‐brush brushes have excellent biocompatible and lubricious properties, which are promising for the functionalization of surfaces for biomedical devices. Herein, a facile synthesis of POx is reported which is based bottle‐brush brushes (BBBs) on solid substrates. Initially, backbone brushes of poly(2‐isopropenyl‐2‐oxazoline) (PIPOx) were fabricated via surface initiated Cu0 plate‐mediated controlled radical polymerization (SI‐Cu0CRP). Poly(2‐methyl‐2‐oxazoline) (PMeOx) side chains were subsequently grafted from the PIPOx backbone via living cationic ring opening polymerization (LCROP), which result in ≈100 % increase in brush thickness (from 58 to 110 nm). The resultant BBBs shows tunable thickness up to 300 nm and high grafting density (σ) with 0.42 chains nm−2. The synthetic procedure of POx BBBs can be further simplified by using SI‐Cu0CRP with POx molecular brush as macromonomer (M n=536 g mol−1, PDI=1.10), which results in BBBs surface up to 60 nm with well‐defined molecular structure. Both procedures are significantly superior to the state‐of‐art approaches for the synthesis of POx BBBs, which are promising to design bio‐functional surfaces.

Analytical strong-stretching theory of polyelectrolyte brushes loaded with charged nanoparticles

Nanoparticles can be used to tune the properties of polyelectrolyte brushes, and polyelectrolyte brushes can be used to control the interaction between nanoparticles and substrates. In the present paper, we investigate the polyelectrolyte brushes immersed in a nanoparticle solution within the analytical strong-stretching theoretical framework. The theoretical model does not take the excluded volume interaction between any two components into account. When there is no nanoparticle loaded, the polyelectrolyte brush is assumed to be an osmotic brush. Local electroneutral approximation is assumed to be still valid after the nanoparticles have been loaded. The loaded nanoparticles are not big enough to deform the grafted polyelectrolyte chains laterally. Analytical formulae for density profiles of each component and brush thickness are derived. The loaded nanoparticles always compress the polyelectrolyte brush. By analyzing the limiting case, a scaling-type diagram for behaviors of the nanoparticle-loading polyelectrolyte brush is constructed. Two characteristic nanoparticle controlling regimes are shown. When the charge of the nanoparticle, &lt;i&gt;Z&lt;/i&gt;, is not very large, charged nanoparticles penetrate into the brush and the brush thickness is scaled by &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$H \sim (Z\varPhi)^{-1/3}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M5.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M5.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, where &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$\varPhi$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M6.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; is the nanoparticle volume fraction. When the nanoparticle charge &lt;i&gt;Z&lt;/i&gt; is large enough, nanoparticles are mainly distributed outside the brush and the brush thickness is scaled by &lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}$H \sim (Z\varPhi)^{-1}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M7.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M7.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. In the former case, the Coulombic repulsion between the grafted polyelectrolyte chains is screened by the counterions and the nanoparticles, and the brush behavior is determined by the balance between the chain elasticity and the osmotic pressure of the counterions and the nanoparticles. In the latter case, the electrostatic screening is executed by the counterions, and the chain elasticity is balanced by the osmotic pressure of the counterions. The two regimes are divided into subregimes which are dominated respectively by electrostatic or non-electrostatic interaction. The effects of size polydispersity of the nanoparticles are also investigated. It is found that the behaviors of the grafted polyelectrolyte chains are mainly determined by the ratio between the first two moments of the nanoparticle size distribution function. The polyelectrolyte brush is compressed more by the polydispere nanoparticles than by the monodisperse ones. Possible improvement in the present theory is discussed in the conclusion section.