pith. sign in

arxiv: 2605.20882 · v1 · pith:4V27IAMMnew · submitted 2026-05-20 · ❄️ cond-mat.soft

Monte Carlo simulation of selective adsorption in a binary hard-disk mixture on patterned adhesive surfaces

Nazar Kukarkin , Taras Patsahan This is my paper

Pith reviewed 2026-05-21 02:37 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords selective adsorptionhard-disk mixturepatterned adhesive surfacesgrand canonical Monte Carloaffinity-driven selectivitydomain size effectsbinary mixture adsorption
0
0 comments X

The pith

Surface geometry with domains sized like the particles controls selectivity in binary hard-disk adsorption.

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

The paper uses grand canonical Monte Carlo simulations to examine how a binary mixture of equal-sized hard disks adsorbs selectively onto a surface patterned with adhesive circular domains. The species differ only in their attraction strength to the domains while sharing the same diameter and bulk chemical potential. Selectivity proves highest when domain diameters match the particle size at low and intermediate chemical potentials because this geometry maximizes overlap between particles and attractive regions. Larger domains still deliver strong selectivity at low chemical potentials, while shrinking domains further improves selectivity by making the surface behave like a uniform layer with effective affinities for each species.

Core claim

Grand canonical Monte Carlo simulations of a two-dimensional binary hard-disk mixture on patterned adhesive surfaces demonstrate that selectivity depends strongly on surface geometry. When the two species have equal diameters and equal bulk chemical potentials but different attraction strengths to the domains, domains comparable to the particle size enhance selectivity by creating adsorption regions with large particle-domain overlap. Larger domains can provide high selectivity at low chemical potentials, and further reduction in domain size also increases selectivity as the system approaches a uniform attractive surface with the corresponding effective affinity parameters of the species.

What carries the argument

Grand canonical Monte Carlo simulations on surfaces patterned with circular adhesive domains whose size, surface coverage, and ordered or disordered arrangement are varied to isolate geometric effects on affinity-driven selectivity.

If this is right

  • Domain diameters comparable to particle size maximize selectivity at low to intermediate chemical potentials through improved particle-domain overlap.
  • Larger domains sustain high selectivity specifically in the low-chemical-potential regime.
  • Very small domains recover selectivity by converging to the effective affinities of a uniform attractive surface.
  • Both ordered and disordered domain arrangements influence the overall adsorption behavior and selectivity curves.
  • Geometric tuning separates affinity-driven selectivity from effects of size asymmetry or unequal chemical potentials.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The reported trends could inform design of 2D patterned substrates for size-independent separation of colloidal mixtures that differ only in surface affinity.
  • Similar Monte Carlo protocols might be applied to soft or three-dimensional particles to test whether domain-size rules survive when interactions are no longer strictly hard.
  • Optimal domain size likely shifts with operating chemical potential, suggesting a practical map for choosing patterns in different concentration ranges.
  • The approach isolates pure geometric control, which could be tested by comparing results against continuum theories that average over domain arrangements.

Load-bearing premise

The two species have equal diameters and equal bulk chemical potentials but differ only in attraction strength to the adhesive domains.

What would settle it

Running the same simulations with domains whose size is fixed but particle diameters made unequal, or measuring adsorption isotherms experimentally on lithographically patterned substrates and finding no peak in selectivity near domain size equal to particle diameter.

Figures

Figures reproduced from arXiv: 2605.20882 by Nazar Kukarkin, Taras Patsahan.

Figure 1
Figure 1. Figure 1: Schematic representation of a functionalized disk-like particle adsorbing on a surface patterned [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Representative fragments of snapshots for a two-dimensional binary hard-disk mixture ad [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Adsorption isotherms of a binary mixture of disk-like particles on a patterned adhesive surface [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Adsorption selectivity S1/2 = σ1/σ2 for a binary mixture of disk-like particles on a patterned adhesive surface with domain surface coverage σd = 0.349 (panel a) and σd = 0.503 (panel b). The line colours and styles correspond to the same parameters as in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

Selective adsorption in a two-dimensional model of a binary hard-disk mixture on patterned adhesive surfaces is studied using grand canonical Monte Carlo simulations. The two species have equal diameters and equal bulk chemical potentials, but different attraction strengths to adhesive domains. Thus, affinity-driven selectivity is separated from particle-size asymmetry and unequal chemical potentials. The surface pattern is defined by domain size, domain surface coverage, and ordered or disordered arrangement of circular domains. The results show that selectivity depends strongly on surface geometry, especially at low and intermediate chemical potentials. Domains comparable to the particle size enhance selectivity by forming adsorption regions with large particle-domain overlap, whereas larger domains can provide high selectivity at low chemical potentials. For small domains, further reduction in size can also increase selectivity as the system approaches a uniform attractive surface with corresponding effective affinity parameters of the species.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript reports grand canonical Monte Carlo simulations of selective adsorption for a binary hard-disk mixture on surfaces patterned with circular adhesive domains. The two species are assigned equal diameters and equal bulk chemical potentials but different attraction strengths to the domains, allowing the study to isolate affinity-driven selectivity. Selectivity is examined as a function of domain size, surface coverage, and ordered versus disordered domain arrangements, with the central finding that geometry strongly modulates selectivity, particularly at low and intermediate chemical potentials, with enhancements when domain size is comparable to particle diameter.

Significance. If the reported trends prove robust, the work supplies concrete, simulation-based design rules for using domain geometry to enhance selective adsorption in two-dimensional mixtures while cleanly separating affinity effects from size or chemical-potential asymmetry. The direct, parameter-controlled Monte Carlo sampling of an explicit hard-disk plus domain-attraction Hamiltonian is a strength that avoids circularity and permits falsifiable comparison with future experiments or theory.

major comments (1)
  1. [Simulation Methods] The manuscript supplies no information on Monte Carlo run lengths, equilibration diagnostics, statistical error estimation, or finite-size corrections. These omissions are load-bearing for the central claim that selectivity depends strongly on domain size and ordering, because grand-canonical adsorption and selectivity ratios can exhibit slow relaxation and large fluctuations at low chemical potentials. Without these controls it is impossible to judge whether the trends shown for small versus large domains are statistically reliable.
minor comments (1)
  1. [Abstract] The abstract states that domains 'comparable to the particle size enhance selectivity' but does not specify the numerical range of reduced chemical potentials or the precise form of the adhesive potential (square-well depth and range) used to generate the data; adding these details would improve reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive comment on the simulation methods. We address the point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Simulation Methods] The manuscript supplies no information on Monte Carlo run lengths, equilibration diagnostics, statistical error estimation, or finite-size corrections. These omissions are load-bearing for the central claim that selectivity depends strongly on domain size and ordering, because grand-canonical adsorption and selectivity ratios can exhibit slow relaxation and large fluctuations at low chemical potentials. Without these controls it is impossible to judge whether the trends shown for small versus large domains are statistically reliable.

    Authors: We agree that these methodological details are essential for assessing the statistical reliability of the selectivity trends, particularly at low and intermediate chemical potentials where grand-canonical fluctuations can be large. In the revised manuscript we will add an explicit subsection to the Simulation Methods describing the Monte Carlo run lengths, the equilibration diagnostics employed (monitoring of particle numbers, energies, and adsorption isotherms until convergence), the procedure for statistical error estimation (block averaging over independent equilibrated segments), and finite-size checks performed by comparing results across different system sizes under periodic boundary conditions. These additions will directly address the concern and allow readers to evaluate the robustness of the geometry-dependent selectivity findings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results follow directly from explicit Monte Carlo sampling

full rationale

The paper reports grand-canonical Monte Carlo simulations of a binary hard-disk mixture with explicitly stated rules: equal particle diameters, equal bulk chemical potentials, and species-dependent surface attractions on domains whose size, coverage, and ordering are varied as input parameters. Selectivity measures are computed as direct averages over sampled configurations under the defined Hamiltonian; no parameters are fitted to a subset of data and then invoked as predictions of related quantities, no self-citations supply load-bearing uniqueness theorems, and no ansatz or renaming reduces the central trends to the inputs by construction. The model premise is introduced transparently to isolate affinity effects and does not create internal self-reference. The reported geometry-dependent selectivity therefore constitutes an independent computational experiment rather than a tautological restatement of the simulation protocol.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central observations rest on standard hard-disk exclusion rules and grand-canonical sampling assumptions plus the explicit choice of differing attraction strengths as input parameters; no new entities are postulated.

free parameters (1)
  • species-specific attraction strengths to adhesive domains
    These are chosen input values that define the affinity difference between the two species while keeping diameters and bulk chemical potentials equal.
axioms (2)
  • domain assumption Hard disks interact only by excluded-volume repulsion with no overlaps allowed
    Standard modeling choice for 2D hard-particle systems invoked throughout the simulation description.
  • domain assumption Grand canonical ensemble correctly samples adsorption at fixed chemical potential
    Core assumption of the Monte Carlo method used to generate the reported occupancy and selectivity data.

pith-pipeline@v0.9.0 · 5667 in / 1339 out tokens · 40180 ms · 2026-05-21T02:37:15.743338+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages · 1 internal anchor

  1. [1]

    A., Reinhoudt D

    Maury P. A., Reinhoudt D. N., Huskens J., Current Opinion in Colloid & Interface Science, 2008, 13, No. 1–2, 74–80,

    work page 2008

  2. [2]

    van Dommelen R., Fanzio P., Sasso L., Advances in Colloid and Interface Science, 2018,251, 97–114

    work page 2018

  3. [3]

    J., Fuchsberger K., Nisch W., Stelzle M., In: Lithography, InTech, 2010

    Burkhardt C. J., Fuchsberger K., Nisch W., Stelzle M., In: Lithography, InTech, 2010

    work page 2010

  4. [4]

    Xing X., Man Z., Bian J., Yin Y., Zhang W., Lu Z., Nature Communications, 2020,11, 6002

    work page 2020

  5. [5]

    V., Sundaravadivelan B., Sun A., Xu W., Yang S., Kannan A

    Jambhulkar S., Ravichandran D., Zhu Y., Thippanna V., Ramanathan A., Patil D., Fonseca N., Thummalapalli S. V., Sundaravadivelan B., Sun A., Xu W., Yang S., Kannan A. M., Golan Y., Lancaster J., Chen L., Joyee E. B., Song K., Small, 2024,20, No. 6, 2306394

    work page 2024

  6. [6]

    G., Results in Surfaces and Interfaces, 2024,17, 100326

    Rao S. G., Results in Surfaces and Interfaces, 2024,17, 100326

    work page 2024

  7. [7]

    J., Genzer J., Journal of Chemical Physics, 2003,119, No

    Semler J. J., Genzer J., Journal of Chemical Physics, 2003,119, No. 10, 5274–5280

    work page 2003

  8. [8]

    J., Genzer J., Macromolecular Theory and Simulations, 2004,13, No

    Semler J. J., Genzer J., Macromolecular Theory and Simulations, 2004,13, No. 3, 219–229

    work page 2004

  9. [9]

    I., Heinrich G., The Journal of Chemical Physics, 2006,125, No

    Chervanyov A. I., Heinrich G., The Journal of Chemical Physics, 2006,125, No. 8, 084703

    work page 2006

  10. [10]

    5, 903–908

    Nitta T., Kiriyama H., Shigeta T., Langmuir, 1997,13, No. 5, 903–908

    work page 1997

  11. [11]

    41, 13051–13058

    Talbot J., Tarjus G., Viot P., The Journal of Physical Chemistry B, 2008,112, No. 41, 13051–13058

    work page 2008

  12. [12]

    Oleyar C., Talbot J., Physica A: Statistical Mechanics and its Applications, 2007,376, 27–37

    work page 2007

  13. [13]

    Cadilhe A., Ara´ ujo N. A. M., Privman V., Journal of Physics: Condensed Matter, 2007,19, No. 6, 065124

    work page 2007

  14. [14]

    Ara´ ujo N. A. M., Cadilhe A., Privman V., Physical Review E, 2008,77, No. 3, 031603

    work page 2008

  15. [15]

    F., Lima A

    Marques J. F., Lima A. B., Ara´ ujo N. A. M., Cadilhe A., Physical Review E, 2012,85, No. 6, 061122

    work page 2012

  16. [16]

    24, 244704

    Privman V., Yan H., The Journal of Chemical Physics, 2016,144, No. 24, 244704

    work page 2016

  17. [17]

    L., Vrhovac S

    Stojiljkovi´ c D. L., Vrhovac S. B., Physica A: Statistical Mechanics and its Applications, 2017,488, 16–29. 8

    work page 2017

  18. [18]

    16, 7335–7341

    Nieszporek K., Szabelski P., Drach M., Langmuir, 2005,21, No. 16, 7335–7341

    work page 2005

  19. [19]

    O., Garcia G

    Sanchez-Varretti F. O., Garcia G. D., Pasinetti P. M., Ramirez-Pastor A. J., Adsorption, 2014,20, No. 7, 855–862

    work page 2014

  20. [20]

    O., Bulnes F

    Sanchez-Varretti F. O., Bulnes F. M., Ramirez-Pastor A. J., Adsorption, 2019,25, No. 7, 1317–1328

    work page 2019

  21. [21]

    V., Late R., Banpurkar A

    Wagaskar K. V., Late R., Banpurkar A. G., Limaye A. V., Shelke P. B., Journal of Statistical Physics, 2020,181, 2191–2205

    work page 2020

  22. [22]

    9, 095001

    Lebovka N., Cie´ sla M., Petrone L., Vygornitskii N., Journal of Physics A: Mathematical and Theo- retical, 2024,57, No. 9, 095001

    work page 2024

  23. [23]

    7, 074705

    Darjani S., Koplik J., Pauchard V., Banerjee S., The Journal of Chemical Physics, 2021,154, No. 7, 074705

    work page 2021

  24. [24]

    15, 3523–3531

    Steinbach A., Paust T., Pluntke M., Marti O., Volkmer D., ChemPhysChem, 2013,14, No. 15, 3523–3531

    work page 2013

  25. [25]

    Beggiato M., Rastogi R., Dupont-Gillain C., Krishnamoorthy S., Sensors and Actuators B: Chemical, 2022,366, 131945

    work page 2022

  26. [26]

    17, 4581– 4587

    Kumar N., Parajuli O., Hahm J.-I., The Journal of Physical Chemistry B, 2007,111, No. 17, 4581– 4587

    work page 2007

  27. [27]

    F., Tabrizian M., Lab on a Chip, 2010,10, No

    Didar T. F., Tabrizian M., Lab on a Chip, 2010,10, No. 22, 3043–3053

    work page 2010

  28. [28]

    Badenhorst R., Makaev S. V., Parker M., Marunych R., Reukov V., Bedzinska A., Korchynskyi O., Kalyuzhnyi O., Yaremchuk D., Ilnytskyi J., Patsahan T., Minko S., ACS Applied Materials & Interfaces, 2025,17, No. 35, 49193–49209

    work page 2025

  29. [29]

    Kukarkin N., Patsahan T., Equilibrium adsorption of hard disks on patterned adhesive surfaces: A Monte Carlo simulation study, 2026, arXiv:2605.02671

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  30. [30]

    P., Tildesley D

    Allen M. P., Tildesley D. J., Computer simulation of liquids, Oxford university press, 2017. 9

    work page 2017