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REVIEW 2 major objections 5 minor 71 references

Size Effect of Monovalent Ions on Polyelectrolyte Brushes

T0 review · 2 major / 5 minor · reviewed 2026-07-11 · grok-4.5

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Pith's one-line read Counterion size controls low-salt brush collapse; co-ion size and dual-size reduction drive high-salt scaling deviations and reentrant swelling.

desk verdict Solid monovalent CG scan that cleanly separates counterion, co-ion, and joint size effects and documents non-classical scaling plus high-salt reentrant swelling; incremental but useful and referee-ready. read the letter →

arxiv 2607.04897 v1 pith:77VZT5EH submitted 2026-07-06 cond-mat.soft

Xianggui Zhou , Nengjie Cao , Xiang-Meng Jia , Jinyuan Mao , Jiajia Zhou This is my paper · ORCID
classification cond-mat.soft
keywords polyelectrolytebrushesionsizeeffectscounterionsco-ionsosmoticbrushsaltedscalinglawscoarse-grainedmoleculardynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Polyelectrolyte brushes are expected to stay roughly constant height at low salt (osmotic regime) and shrink as salt to the minus one-third at high salt (salted regime). Molecular simulations often deviate from that ideal. This paper uses coarse-grained molecular dynamics to show that monovalent ion size is a main source of the deviation. Smaller counterions penetrate the brush more easily at low salt, improve local charge compensation, and produce stronger collapse; at high salt the height becomes largely insensitive to counterion size while the scaling exponent itself softens. Co-ion size acts more indirectly: smaller co-ions weaken local charge compensation and suppress collapse, an effect that grows with salt. When both counterions and co-ions are made smaller together, the low-salt response remains counterion-dominated, but high salt produces enhanced ion penetration, altered coordination, and reentrant swelling with scaling exponents that can fall almost to zero. The work supplies a microscopic picture of how ion size and salt concentration together set brush structure and generate non-classical scaling.

What carries the argument

Systematic coarse-grained MD protocols that independently and jointly vary monovalent counterion and co-ion diameters (0.3σ–1.0σ) across a wide salt range, quantified by brush height H, density and net-charge profiles, chain-end statistics, radial distribution functions, and condensed-ion state fractions (isolated / intrachain / interchain).

What would settle it

Measure brush height versus monovalent salt concentration for chemically similar ions that differ mainly in hydrated radius (e.g., Li+ vs Cs+, or F− vs I−) at fixed grafting density and chain length; the claimed size-driven low-salt collapse, high-salt co-ion suppression, and reentrant swelling at small dual sizes should appear if the effective-size picture is sufficient.

Watch

Extended reading notes

Core claim

Counterion size dominates ion penetration and local coordination with PE monomers: smaller counterions strengthen low-salt collapse while high-salt height becomes largely size-insensitive and scaling deviates from the classical H ∝ c_s^{-1/3}. Co-ion size acts mainly by weakening local charge compensation and suppressing collapse (stronger at high salt). Simultaneous reduction of both ion sizes produces a coupled response that remains counterion-dominated at low salt but yields reentrant swelling and strongly reduced scaling exponents at high salt.

Load-bearing premise

Ion diameter in the implicit-solvent model is treated as a pure effective steric size that already includes bare radius plus partial hydration, with no explicit water, polarizability, or specific ion chemistry.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This paper uses coarse-grained Langevin MD (WCA, FENE, PPPM) of strong PE brushes (N=30, σ_g=0.1 σ^{-2}) to map how monovalent counterion and co-ion diameters (0.3–1.0σ) reshape brush structure and H(c_s) scaling from the osmotic to the salted regime. Three protocols are compared: reducing σ_C at fixed σ_T=1; reducing σ_T at fixed σ_C=1; and reducing both with σ_C=σ_T. The central claim is that counterion size dominates low-salt penetration and collapse (smaller σ_C → stronger collapse), while at high salt H becomes largely size-insensitive but the effective exponent α deviates from −1/3; co-ion size acts more indirectly by weakening local charge compensation and suppressing collapse, especially at high salt; simultaneous size reduction yields a coupled response with a high-salt crossover (described as reentrant swelling) and strongly reduced α (down to ≈−0.02 at σ=0.3). Support comes from density and net-charge profiles, end-monomer statistics, RDFs, and counterion state fractions, with tabulated H(c_s) in the SI.

Significance. If the reported size-dependent penetration, co-ion-mediated compensation, and non-classical α hold within the stated CG model, the work supplies a clear, systematic microscopic account of why monovalent PE-brush simulations often miss H∝c_s^{−1/3} and how co-ions—usually under-discussed—matter at high salt. Strengths include a clean three-protocol design, mutually consistent observables (profiles, RDFs, bridging fractions, H tables with error bars from three runs), an SI box-height check (L_z=60 vs 100), and explicit acknowledgment that ion diameter is an effective steric parameter in implicit solvent. The contribution is incremental but useful for soft-matter theory and for interpreting ion-specific brush experiments, provided the effective-size limitation is kept in view when transferring to real electrolytes.

major comments (2)
  1. [Results (Figs. 3b, 8b, 11b); Tables S1–S3] The non-classical scaling claim is central, but the manuscript never states the c_s windows, functional form, or fitting procedure used to extract α (e.g. α≈−0.33 for σ_C=1.0, −0.25 for σ_C=0.3, −0.14 for σ_T=0.3, −0.02 for σ_C=σ_T=0.3 in Figs. 3b, 8b, 11b). Because max accessible c_s also depends on ion size (Tables S1–S3; reference system limited to c_s≈0.45), different effective windows could shift the reported exponents. Please specify fit ranges, whether log–log linear regression or other methods were used, and report uncertainties on α so the deviations from −1/3 can be assessed quantitatively.
  2. [Decrease σ_C and σ_T simultaneously; Abstract; Fig. 11; Table 3] The simultaneous-reduction section and abstract describe a “reentrant swelling” at high salt (c_s>0.80). Table 3 and Fig. 11 show that for σ_C=σ_T=0.3, H largely plateaus (≈14.9→≈14.5) rather than increasing, while the main crossover is that small-ion brushes become taller than large-ion ones because the latter continue to collapse. That relative crossover is interesting and supported, but “reentrant swelling” overstates the absolute H(c_s) trend. Please rephrase to match the data (e.g. suppressed collapse / relative re-swelling vs larger ions) and, if absolute re-swelling is intended, show a clear upturn with error bars.
minor comments (5)
  1. [Supporting Information title] SI title has a typo: “Polyelectrolte” → “Polyelectrolyte”.
  2. [Figs. 2–5, 7–12 captions] Several figure captions note missing red curves because the reference system cannot reach c_s=0.70. Consider marking the maximum accessible c_s per series on the log–log H plots themselves so readers do not misread truncated series as full high-salt asymptotes.
  3. [Pair Correlation Analysis; Fig. 6] The cutoff R_c=√2(D_P+D_C)/2 for condensation/bridging is stated but not motivated beyond “end of the first RDF peak.” A short sensitivity check (or reference to prior validation) would strengthen the f_iso / f_intra / f_inter analysis.
  4. [Conclusions] Conclusions correctly flag implicit solvent and missing Hofmeister chemistry; a brief forward-looking sentence on which experimental monovalent series (e.g. alkali cations with similar co-ions) would best test the predicted low-salt σ_C trend would improve impact.
  5. [Simulation Model and Methods] Notation mixes σ_C/σ_T for ion diameters with σ_g for grafting density and σ as the LJ length unit; a one-line glossary early in Methods would reduce ambiguity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: results are direct CG-MD outputs compared to external classical scaling benchmarks.

full rationale

The paper reports coarse-grained molecular dynamics simulations of PE brushes under monovalent salt, systematically varying counterion and co-ion diameters. Brush height H is computed from the first moment of the monomer density (Eq. 9), density profiles, RDFs, and counterion state fractions (isolated/intra/inter) are measured observables, and scaling exponents α are obtained by fitting the simulated H(cs) curves. Classical osmotic (α≈0) and salted-brush (α≈−1/3) relations are external theoretical benchmarks used for comparison, not fitted inputs that force the measured exponents. Self-citations supply context on related PE-brush phenomenology and do not load-bear the size-scan outcomes. No self-definitional loop, fitted-input-called-prediction, uniqueness import, or ansatz smuggling is present; the derivation chain is self-contained simulation phenomenology.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claims are simulation phenomenology under a standard Kremer–Grest-style PE-brush model. Load-bearing inputs are conventional CG force-field choices and classical scaling benchmarks, not new particles or fitted universal constants. Free parameters are simulation control knobs (sizes, N, σ_g, T*) chosen to access salted-brush conditions, not fitted to force the reported exponents.

free parameters (4)
  • counterion/co-ion diameters σ_C, σ_T ∈ {0.3,0.5,0.7,1.0}σ
    Hand-chosen discrete sizes that define the three protocols; the reported size trends depend on this grid.
  • chain length N=30 and grafting density σ_g=0.1 σ^{-2}
    Chosen for computational access to high c_s; short N limits how asymptotic the salted-brush regime can be.
  • reduced temperature T*=1.2 and reduced charge q*=1.0 (l_B/σ≈0.83)
    Sets electrostatic coupling strength; standard but not derived from a uniqueness condition for this system.
  • maximum accessible salt concentration per ion-size set
    Capped by packing/stability (e.g. reference system only to c_s=0.45); affects which high-salt exponents can be measured.
assumptions (5)
  • domain assumption Classical osmotic/salted PE-brush scaling (H∝c_s^0 then H∝c_s^{-1/3}) is the correct asymptotic benchmark for monovalent salt under mean-field assumptions.
    Used throughout Introduction and Results as the reference against which α deviations are judged (Pincus/Zhulina framework).
  • domain assumption WCA (purely repulsive LJ) nonbonded interactions represent good solvent conditions for monomers and ions.
    Simulation Model and Methods; excludes attractive solvent-quality collapse channels.
  • ad hoc to paper Implicit solvent plus effective ion diameter adequately captures monovalent size effects without explicit water or polarizability.
    Stated in Methods and Conclusions; ion size is interpreted as bare radius plus partial hydration.
  • domain assumption Brush height H equals twice the first moment of the monomer density profile.
    Eq. (9); standard for roughly uniform brushes, used for all scaling plots.
  • domain assumption Condensation/bridging cutoff R_c=√2(D_P+D_C)/2 correctly partitions isolated, intra-, and interchain counterion states.
    Following Miao et al.; used for f_iso, f_intra, f_inter analysis.

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Pith. "Pith review of Size Effect of Monovalent Ions on Polyelectrolyte Brushes." pith.science (2026). https://pith.science/paper/77VZT5EH

@misc{pith2026260704897,
  author       = {Pith},
  title        = {Pith review of: Size Effect of Monovalent Ions on Polyelectrolyte Brushes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/77VZT5EH}},
  note         = {Machine review of arXiv:2607.04897}
}
abstract

The conformation of polyelectrolyte (PE) brushes is highly sensitive to external conditions, particularly salt concentration and ion-specific effects. As salt concentration increases, PE brushes transition from an osmotic brush regime at low salt ($H \propto c_\mathrm{s}^{0}$) to a salted brush regime at high salt ($H \propto c_\mathrm{s}^{-1/3}$). However, deviations from this ideal scaling behavior are frequently observed in molecular simulations. In this work, we employ coarse-grained molecular dynamics simulations to systematically investigate how the sizes of counterions and co-ions affect the structural evolution and scaling behavior of PE brushes over a broad range of salt concentrations. Our results show that counterion size plays a dominant role in regulating ion penetration and coordination with PE monomers. At low salt concentration, smaller counterions penetrate more easily into the brush, leading to enhanced local charge compensation and stronger brush collapse. At high salt concentration, however, the brush height becomes largely insensitive to counterion size, while deviations from the classical scaling relation emerge. On the other hand, co-ion size mainly affects the system indirectly by modifying ion distributions and the local electrostatic environment. Smaller co-ions weaken local charge compensation and suppress brush collapse, with this effect becoming more pronounced at high salt concentration. When the sizes of counterions and co-ions are reduced simultaneously, the system exhibits a coupled response. Collectively, this work provides a microscopic understanding of how ion size and salt concentration jointly govern the structural response of PE brushes and the emergence of non-classical scaling behavior in realistic solution environments.

Figures

Figures reproduced from arXiv: 2607.04897 by the authors.

Figure 1
Figure 1. Schematic illustration of the PE brush model. (a) Simplified model, (b) MD simulation snapshot at a salt concentration of cs = 0.01. system with counterion and co-ion diameters of 1.0 σ. Based on this system, three simulation protocols were considered: (i) decreasing the counterion diameter while fixing the co-ion diameter at 1.0 σ; (ii) decreasing the co-ion diameter while fixing the counterion diameter at 1.0 σ; (… view at source ↗
Figure 2
Figure 2. Density profiles of PE monomers (solid circles), counterions (triangles), and co￾ions (open circles) along the direction normal to the grafting surface for different counterion size σC with fixed co-ion size σT = 1.0 at different salt concentrations: cs = 0 (a), 0.05 (b), 0.40 (c), and 0.70 (d). Panels (e–h) show the corresponding local net charge distributions. Solid lines represent smoothed profiles obtained by co… view at source ↗
Figure 3
Figure 3. PE brush height H as a function of salt concentration cs for different σC at σT = 1.0: (a) linear scale; (b) log–log scale. As shown in Figure 3a, the brush height decreases monotonically with increasing salt concentration for all counterion sizes, indicating progressive brush collapse. Smaller coun￾terions consistently lead to lower brush heights, suggesting enhanced penetration into the brush and stronger electros… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Dependence of characteristic parameters of the PE chain-end monomer density distribution on salt concentration cs for different σC at σT = 1.0: (a) peak position zmax, (b) peak height ρmax, and (c) full width at half maximum (FWHM). As shown in Figure 4a, zmax decrease…
Figure 5
Figure 5. Figure 5: Radial distribution functions (RDFs) between PE monomers and counterions (a–c) or co-ions (d–f) for different σC at σT = 1.0 under various salt concentrations. The red curve for cs = 0.70 is absent because the maximum accessible salt concentration in the reference syst…
Figure 6
Figure 6. Figure 6: Fractions of different counterion states as functions of salt concentration for different σC at σT = 1.0: (a) isolated (fiso), (b) intrachain condensation (fintra), and (c) interchain bridging (finter). Error bars are smaller than the symbol size. is governed by the co…
Figure 7
Figure 7. Figure 7: Density profiles of PE monomers, counterions, and co-ions along the direction normal to the grafting surface for different co-ion size σT with fixed counterion size σC = 1.0 at different salt concentrations: cs = 0.05 (a), 0.40 (b), and 0.70 (c). The red curve for cs =…
Figure 8
Figure 8. Figure 8: PE brush height H as a function of salt concentration cs for different σT at σC = 1.0: (a) linear scale; (b) log–log scale. and S7c) exhibit similar trends. In the low-salt regime (cs ≲ 0.025), ρmax and FWHM nearly overlap for different co-ion sizes, consistent with th…
Figure 9
Figure 9. Figure 9: RDFs between PE monomers and counterions (a–c) or co-ions (d–f) for different σT at σC = 1.0 under various salt concentrations. The red curve for cs = 0.70 is absent because the maximum accessible salt concentration in the reference system is cs = 0.45. To elucidate th…
Figure 10
Figure 10. Figure 10: Density profiles of PE monomers, counterions, and co-ions along the direction normal to the grafting surface when counterions and co-ions decrease simultaneously (σC = σT) at different salt concentrations: cs = 0.05 (a), 0.40 (b), 0.70 (c), and 1.00 (d). Panels (e–h) …
Figure 11
Figure 11. Figure 11: PE brush height H as a function of salt concentration cs when counterions and co-ions decrease simultaneously (σC = σT): (a) linear scale; (b) log–log scale. We further analyze the distribution of chain-end particles under simultaneous reduction of both ion sizes. The…
Figure 12
Figure 12. Figure 12: RDFs between PE monomers and counterions (a–c) or co-ions (d–f) when counterions and co-ions decrease simultaneously (σC = σT). The red curve for cs = 0.70 is absent because the maximum accessible salt concentration in the reference system is cs = 0.45. 30 [PITH_FULL…

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Works this paper leans on

71 extracted references · 1 canonical work pages

  1. [1]

    Soft Matter , volume=

    Polyelectrolyte brushes: theory, modelling, synthesis and applications , author=. Soft Matter , volume=. 2015 , publisher=

    2015

  2. [2]

    Chemical Communications , volume=

    All-atom molecular dynamics simulations of polymer and polyelectrolyte brushes , author=. Chemical Communications , volume=. 2024 , publisher=

    2024

  3. [3]

    2022 , school=

    Atomistic exploration of densely-grafted polyelectrolyte brushes: effect of applied electric field and multivalent screening counterions , author=. 2022 , school=

    2022

  4. [4]

    Polyelectrolytes with defined molecular architecture I , pages=

    Polyelectrolyte brushes , author=. Polyelectrolytes with defined molecular architecture I , pages=. 2004 , publisher=

    2004

  5. [5]

    Chemistry--An Asian Journal , volume=

    Structure and functionality of polyelectrolyte brushes: a surface force perspective , author=. Chemistry--An Asian Journal , volume=. 2018 , publisher=

    2018

  6. [6]

    Macromolecules , volume=

    Unveiling the layered structure of sulfobetaine polymer brushes through bimodal atomic force microscopy , author=. Macromolecules , volume=. 2023 , publisher=

    2023

  7. [7]

    Polymer , volume=

    Polyelectrolyte brushes in monovalent and multivalent salt solutions , author=. Polymer , volume=. 2014 , publisher=

    2014

  8. [8]

    Langmuir , volume=

    Ion-specific effects of divalent ions on the structure of polyelectrolyte brushes , author=. Langmuir , volume=. 2019 , publisher=

    2019

Show all 71 references
  1. [9]

    Langmuir , volume=

    Inverse and reversible switching gradient surfaces from mixed polyelectrolyte brushes , author=. Langmuir , volume=. 2004 , publisher=

    2004

  2. [10]

    Journal of Applied Physics , volume=

    Electroosmotic transport in polyelectrolyte-grafted nanochannels with pH-dependent charge density , author=. Journal of Applied Physics , volume=. 2015 , publisher=

    2015

  3. [11]

    The Journal of chemical physics , volume=

    Polymer brushes in solvents of variable quality: Molecular dynamics simulations using explicit solvent , author=. The Journal of chemical physics , volume=. 2007 , publisher=

    2007

  4. [12]

    Giant , volume=

    Synergistic regulation of polyelectrolyte brush conformations by solvent quality and trivalent ions , author=. Giant , volume=. 2025 , publisher=

    2025

  5. [13]

    ACS Nano , volume=

    Overscreening, co-ion-dominated electroosmosis, and electric field strength mediated flow reversal in polyelectrolyte brush functionalized nanochannels , author=. ACS Nano , volume=. 2021 , publisher=

    2021

  6. [14]

    Macromolecules , volume=

    Charge-density-specific response of grafted polyelectrolytes to electric fields: Bending or tilting? , author=. Macromolecules , volume=. 2022 , publisher=

    2022

  7. [15]

    Macromolecules , volume=

    All-atom molecular dynamics simulations of the temperature response of densely grafted polyelectrolyte brushes , author=. Macromolecules , volume=. 2021 , publisher=

    2021

  8. [16]

    Polymers , volume=

    Hysteretic swelling/deswelling of polyelectrolyte brushes and bilayer films in response to changes in pH and salt concentration , author=. Polymers , volume=. 2021 , publisher=

    2021

  9. [17]

    Science , volume=

    Neuromorphic functions with a polyelectrolyte-confined fluidic memristor , author=. Science , volume=. 2023 , publisher=

    2023

  10. [18]

    Soft Matter , volume=

    Improved ionic current rectification utilizing cylindrical nanochannels coated with polyelectrolyte layers of non-uniform thickness , author=. Soft Matter , volume=. 2024 , publisher=

    2024

  11. [19]

    Langmuir , volume=

    Highly efficient conversion of salinity difference to electricity in nanofluidic channels boosted by variable thickness polyelectrolyte coating , author=. Langmuir , volume=. 2024 , publisher=

    2024

  12. [20]

    Science , volume=

    Multivalent counterions diminish the lubricity of polyelectrolyte brushes , author=. Science , volume=. 2018 , publisher=

    2018

  13. [21]

    Langmuir , volume=

    Oil-in-water emulsions stabilized by highly charged polyelectrolyte-grafted silica nanoparticles , author=. Langmuir , volume=. 2005 , publisher=

    2005

  14. [22]

    Langmuir , volume=

    Wettability and antifouling behavior on the surfaces of superhydrophilic polymer brushes , author=. Langmuir , volume=. 2012 , publisher=

    2012

  15. [23]

    Environmental Science & Technology , volume=

    Antifouling thin-film composite membranes by controlled architecture of zwitterionic polymer brush layer , author=. Environmental Science & Technology , volume=. 2017 , publisher=

    2017

  16. [24]

    Chemistry of Materials , volume=

    An antimicrobial polymer brush coating to fabricate high-performance, durable, self-sterilization, and recyclable face masks , author=. Chemistry of Materials , volume=. 2023 , publisher=

    2023

  17. [25]

    Bioconjugate Chemistry , volume=

    Disulfide-containing brushed polyethylenimine derivative synthesized by click chemistry for nonviral gene delivery , author=. Bioconjugate Chemistry , volume=. 2012 , publisher=

    2012

  18. [26]

    Polymers , volume=

    A polycationic brush mediated co-delivery of doxorubicin and gene for combination therapy , author=. Polymers , volume=. 2019 , publisher=

    2019

  19. [27]

    Soft Matter , volume=

    Amphiphilic copolymer brush with random pH-sensitive/hydrophobic structure: synthesis and self-assembled micelles for sustained drug delivery , author=. Soft Matter , volume=. 2012 , publisher=

    2012

  20. [28]

    Facile incorporation of biorecognition elements into nanoconfined geometries , author=

    Biosensing and supramolecular bioconjugation in single conical polymer nanochannels. Facile incorporation of biorecognition elements into nanoconfined geometries , author=. Journal of the American Chemical Society , volume=. 2008 , publisher=

    2008

  21. [29]

    Angewandte Chemie International Edition , volume=

    Building bio-inspired artificial functional nanochannels: From symmetric to asymmetric modification , author=. Angewandte Chemie International Edition , volume=. 2012 , publisher=

    2012

  22. [30]

    Matter , volume=

    Dynamically modulated gating process of nanoporous membrane at sub-2-nm speed , author=. Matter , volume=. 2022 , publisher=

    2022

  23. [31]

    Chemistry of Materials , volume=

    High lithium transference number electrolytes via creation of 3-dimensional, charged, nanoporous networks from dense functionalized nanoparticle composites , author=. Chemistry of Materials , volume=. 2013 , publisher=

    2013

  24. [32]

    Spherical polyelectrolyte brushes templated hollow

    Xie, Dongjiu and Jouini, Oumeima and Mei, Shilin and Quan, Ting and Xu, Yaolin and Kochovski, Zdravko and Lu, Yan , journal=. Spherical polyelectrolyte brushes templated hollow. 2022 , publisher=

    2022

  25. [33]

    Journal de Physique , volume=

    Scaling theory of polymer adsorption , author=. Journal de Physique , volume=. 1976 , publisher=

    1976

  26. [34]

    Journal de Physique , volume=

    Adsorption of chain molecules with a polar head a scaling description , author=. Journal de Physique , volume=. 1977 , publisher=

    1977

  27. [35]

    Journal de Physique , volume=

    Remarks on polyelectrolyte conformation , author=. Journal de Physique , volume=. 1976 , publisher=

    1976

  28. [36]

    Macromolecules , volume=

    Colloid stabilization with grafted polyelectrolytes , author=. Macromolecules , volume=. 1991 , publisher=

    1991

  29. [37]

    Journal de Physique II , volume=

    Collapse of grafted polyelectrolyte layer , author=. Journal de Physique II , volume=. 1991 , publisher=

    1991

  30. [38]

    Macromolecules , volume=

    Theory of ionizable polymer brushes , author=. Macromolecules , volume=. 1995 , publisher=

    1995

  31. [39]

    Macromolecules , volume=

    Charged polymeric brushes: structure and scaling relations , author=. Macromolecules , volume=. 1994 , publisher=

    1994

  32. [40]

    Physical Review E , volume=

    Swelling and shrinking of two opposing polyelectrolyte brushes , author=. Physical Review E , volume=. 2023 , publisher=

    2023

  33. [41]

    Physical Review Letters , volume=

    Influence of salt on the viscosity of polyelectrolyte solutions , author=. Physical Review Letters , volume=. 2020 , publisher=

    2020

  34. [42]

    Journal of Rheology , volume=

    Electrostatics, conformation, and rheology of unentangled semidilute polyelectrolyte solutions , author=. Journal of Rheology , volume=. 2021 , publisher=

    2021

  35. [43]

    Macromolecules , year=

    Ionization of Semidilute Weak Polyelectrolytes in Equilibrium with a Reservoir , author=. Macromolecules , year=

  36. [44]

    Macromolecules , volume=

    Effects of ion valency on polyelectrolyte brushes: a unified theory , author=. Macromolecules , volume=. 2022 , publisher=

    2022

  37. [45]

    Macromolecules , volume=

    Structure of polyelectrolyte brushes in the presence of multivalent counterions , author=. Macromolecules , volume=. 2016 , publisher=

    2016

  38. [46]

    Macromolecules , year=

    A scaling theory for polyelectrolyte brushes: Insights from intermonomer electrostatic interactions , author=. Macromolecules , year=. doi:10.1021/acs.macromol.6c00048 , publisher=

    doi

  39. [47]

    Macromolecules , volume=

    Polyelectrolyte brushes with added salt , author=. Macromolecules , volume=. 2005 , publisher=

    2005

  40. [48]

    Macromolecules , volume=

    Strongly charged polyelectrolyte brushes: a molecular dynamics study , author=. Macromolecules , volume=. 2000 , publisher=

    2000

  41. [49]

    Macromolecules , volume=

    Strongly stretched polyelectrolyte brushes , author=. Macromolecules , volume=. 2003 , publisher=

    2003

  42. [50]

    The Journal of Physical Chemistry B , volume=

    Mesoscale modeling of polyelectrolyte brushes with salt , author=. The Journal of Physical Chemistry B , volume=. 2010 , publisher=

    2010

  43. [51]

    Macromolecules , volume=

    Ionic strength and curvature effects in flat and highly curved polyelectrolyte brushes , author=. Macromolecules , volume=. 1998 , publisher=

    1998

  44. [52]

    Macromolecules , volume=

    Ionic strength effects in polyelectrolyte brushes: The counterion correction , author=. Macromolecules , volume=. 1998 , publisher=

    1998

  45. [53]

    Macromolecules , volume=

    A systematic study on trivalent salt cationic specificity through polyelectrolyte brushes , author=. Macromolecules , volume=. 2025 , publisher=

    2025

  46. [54]

    The Journal of Physical Chemistry C , volume=

    Reversible adhesion with polyelectrolyte brushes tailored via the uptake and release of trivalent lanthanum ions , author=. The Journal of Physical Chemistry C , volume=. 2015 , publisher=

    2015

  47. [55]

    ChemPhysChem , volume=

    Counterion specificity of polyelectrolyte brushes: role of specific ion-pairing interactions , author=. ChemPhysChem , volume=. 2018 , publisher=

    2018

  48. [56]

    Macromolecules , volume=

    Quantification of mono- and multivalent counterion-mediated bridging in polyelectrolyte brushes , author=. Macromolecules , volume=. 2021 , publisher=

    2021

  49. [57]

    The Journal of Physical Chemistry B , volume=

    Specific ion and electric field controlled diverse ion distribution and electroosmotic transport in a polyelectrolyte brush grafted nanochannel , author=. The Journal of Physical Chemistry B , volume=. 2022 , publisher=

    2022

  50. [58]

    Macromolecules , volume=

    Size effect of multivalent counterions on polyelectrolyte brushes in different polar solvents , author=. Macromolecules , volume=. 2023 , publisher=

    2023

  51. [59]

    Faraday Discussions , volume=

    Ionic specific effects on the structure, mechanics and interfacial softness of a polyelectrolyte brush , author=. Faraday Discussions , volume=. 2013 , publisher=

    2013

  52. [60]

    Soft matter , volume=

    Numerical modelling of non-ionic microgels: an overview , author=. Soft matter , volume=. 2019 , publisher=

    2019

  53. [61]

    Progress in polymer science , volume=

    Theory of polyelectrolytes in solutions and at surfaces , author=. Progress in polymer science , volume=. 2005 , publisher=

    2005

  54. [62]

    Physical Review E , volume=

    Polyelectrolyte brushes: Counterion distribution and complexation properties , author=. Physical Review E , volume=. 1999 , publisher=

    1999

  55. [63]

    Journal of the American Chemical Society , volume=

    Synthesis of poly (styrene sulfonate) brushes , author=. Journal of the American Chemical Society , volume=. 2001 , publisher=

    2001

  56. [64]

    Polymers , volume=

    Synthesis of poly (2-Acrylamido-2-methylpropanesulfnoinc Salt) modified carbon spheres , author=. Polymers , volume=. 2023 , publisher=

    2023

  57. [65]

    arXiv preprint arXiv:1402.4565 , year=

    Nanofriction on Sodium Polystyrene Sulfonate Brushes in Water , author=. arXiv preprint arXiv:1402.4565 , year=

    arXiv

  58. [66]

    Effective radii of hydrated ions , author=

    Phenomenological theory of ion solvation. Effective radii of hydrated ions , author=. The Journal of Physical Chemistry , volume=. 1959 , publisher=

    1959

  59. [67]

    Journal of Computational Chemistry , volume=

    GALAMOST: GPU-accelerated large-scale molecular simulation toolkit , author=. Journal of Computational Chemistry , volume=

  60. [68]

    The Journal of Chemical Physics , volume=

    Role of repulsive forces in determining the equilibrium structure of simple liquids , author=. The Journal of Chemical Physics , volume=. 1971 , publisher=

    1971

  61. [69]

    The Journal of Chemical Physics , volume=

    Dynamics of entangled linear polymer melts: a molecular-dynamics simulation , author=. The Journal of Chemical Physics , volume=. 1990 , publisher=

    1990

  62. [70]

    Macromolecules , volume=

    Heterogeneous morphology and dynamics of polyelectrolyte brush condensates in trivalent counterion solution , author=. Macromolecules , volume=. 2017 , publisher=

    2017

  63. [71]

    Macromolecules , volume=

    Surface morphologies of planar ring polyelectrolyte brushes induced by trivalent salts , author=. Macromolecules , volume=. 2020 , publisher=

    2020

Pith tools

Reviewed July 11, 2026 · model on record in the stance chip above.