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Active particles write lasting structure into fluid droplets

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2026-07-10 00:57 UTC pith:SM5PLTC7

load-bearing objection Real phenomenon, but the 'topological' mechanism is undersupported on 12-monomer chains the 3 major comments →

arxiv 2607.08048 v1 pith:SM5PLTC7 submitted 2026-07-09 cond-mat.soft

Active Particles Imprint Persistent Percolating Networks in Polymer Condensates

Ligesh Theeyancheri , Jennifer L. Ross , J. M. Schwarz This is my paper
classification cond-mat.soft PACS 05.40.-a64.75.Yz
keywords condensatesactiveactivityexchangefluidinterchainnetworksparticles
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper claims that a bath of self-propelling particles can permanently reshape polymer condensates—droplet-like clusters formed by sticky molecular chains—into sprawling, system-spanning networks. The mechanism works through three coupled effects: the active particles stretch individual chains open, force neighboring chains into contact with one another, and wind chains around each other at topological junction points. The key claim is that once this network forms, it survives even after every active particle is removed, because the interchain winding creates topological constraints that the chains cannot easily undo. The condensate remains fluid—individual chains still exchange in and out of the network—but the overall branched architecture persists as a kind of structural memory written by activity into a system that would otherwise forget its history. The authors demonstrate this through simulations of sticker-spacer polymers, using controlled stepwise removal of the active particles followed by extended relaxation, showing that the network does not collapse back into a compact droplet.

Core claim

The central finding is that activity from excluded-volume particles imprints persistent topological memory into fluid polymer condensates. Active particles drive a transition from compact droplets to percolated networks by suppressing intrachain contacts, enhancing interchain contacts, and creating interchain winding that acts as topological constraints. These constraints outlast the active driving itself: after complete removal of active particles and continued evolution for twice the passive coalescence time, the network remains spatially extended rather than collapsing back to a droplet, even though individual polymer chains continue to exchange dynamically. The memory is thus stored not在

What carries the argument

The load-bearing mechanism is the interplay of three activity-induced effects: (1) active Brownian particles of intermediate size (1.5× the monomer diameter) suppress intrachain self-contacts by sterically opening individual chains, (2) the same particles drive interchain contact formation by pushing extended chains into one another, and (3) the resulting interchain encounters produce topological winding—chains wrap around bridging segments at junction points, creating constraints that cannot be removed without chain crossing. The persistence of the network after activity removal is attributed to these topological constraints, quantified via primitive path analysis showing increased entangl

Load-bearing premise

The claim of persistence rests on observing the network for twice the characteristic coalescence time of the passive system after removing all active particles. If the network is actually metastable and would collapse on longer timescales, the memory claim would be weakened. Additionally, the chains are only 12 monomers long, which raises the question of whether the topological winding is genuinely robust or whether it depends on the limited chain length and simulation box.

What would settle it

Run the depletion protocol for significantly longer than twice the passive coalescence time—e.g., 10× or 100×—and check whether the percolated network eventually collapses into a compact droplet. If it does, the memory is metastable rather than persistent. Alternatively, test with longer polymer chains to determine whether the topological winding mechanism scales or is an artifact of short chains.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • If activity can write structural memory into fluid condensates, biological cells may exploit active processes (motor-driven flows, enzymatic activity) to encode information about past states in condensate architecture without sacrificing the exchange dynamics that make condensates functional.
  • The finding that network formation requires an intermediate particle-size regime suggests design rules for synthetic active materials: particle size must be large enough to open chains but small enough to allow interchain winding, constraining the parameter space for engineering persistent active gels.
  • The coexistence of liquid-like chain exchange with solid-like topological persistence in the same condensate suggests a new class of materials with tunable memory: fluid at the molecular level but architecturally stable at the mesoscale.
  • The proposed scaling condition—active persistence length comparable to both the network mesh size and the polymer radius of gyration—provides a testable criterion for distinguishing persistent network formation from transient activity-induced swelling.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This manuscript uses molecular dynamics simulations of sticker-spacer polymers (Np = 12 monomers) in a bath of active Brownian particles (ABPs) to show that activity can drive a structural transition from compact condensate droplets to system-spanning percolated networks. The authors report that this network persists after ABPs are removed, despite continued polymer exchange, and attribute the persistence to topological constraints imprinted via interchain winding. The claim is supported by multiple metrics: largest connected component analysis, contact network compactness, interchain vs. intrachain contact statistics, contact retention fractions, primitive path entanglement analysis (Z1+ algorithm), and controlled ABP depletion protocols at two rates. The central question—whether activity can write structural memory into a fluid condensate—is timely and well-motivated.

Significance. The paper addresses a genuinely interesting question: can a fluid condensate retain structural information written by activity after the activity ceases? The use of multiple independent diagnostics (LCC, contact networks, Z1+ entanglement analysis, depletion protocols) is a strength, and the depletion protocol is a clean experimental design. The scaling discussion in the Supplemental Material (competing length scales: sigma_s/sigma_p, Rg, active persistence length, mesh size) provides a useful physical framework even if not yet a predictive theory. The finding that interchain contacts are self-renewing (R(t) ~ 1) while intrachain contacts are suppressed is a nontrivial and falsifiable result. The connection to PopZ condensates and recent rigidity transition experiments is appropriate.

major comments (3)
  1. The claim of 'topological imprinting' rests on Z1+ primitive path analysis of 12-monomer chains (Fig. 3c-d, Fig. S7). In polymer physics, the entanglement molecular weight Me is typically far larger than 12 repeat units, so Z1+ kinks on such short chains may represent geometric contacts rather than topological constraints resistant to chain end-retraction. This distinction is load-bearing: if the kinks are not topological, the network persistence after ABP depletion (Fig. 4b, Fig. 5a-ii) could be a kinetic/metastable effect rather than topological memory. The paper does not verify that <Z> scales with chain length as expected for true entanglements, nor does it test whether detected constraints survive end-retraction. A chain-length study (e.g., Np = 24, 48) showing that <Z> increases proportionally would substantially strengthen the topological claim. Alternatively, the authors should直接
  2. The persistence test evolves the system for 'twice the characteristic coalescence time of the polymer-only system' after complete ABP depletion (main text, paragraph describing depletion protocol; Fig. S8). This assumes that 2x passive coalescence time is sufficient to distinguish true persistence from slow metastable relaxation. However, the relevant timescale for rearrangement of an extended 12-mer network may be much longer than droplet coalescence, especially if the network is kinetically arrested rather than topologically stabilized. The paper should either (a) provide evidence that the relaxation time has been sampled sufficiently (e.g., show that the contact renewal rate R(t) has reached steady state in Fig. 5b, or report the actual coalescence time in simulation units for comparison), or (b) soften the claim from 'persistent' to 'long-lived' if the timescale separation cannot be
  3. The chain length Np = 12 is very short relative to typical entangled polymer systems. While the authors acknowledge this is a sticker-spacer model with implicit spacers (FENE springs, R0 = 10 nm), the physical interpretation of 'interchain winding' and 'topological constraints' for chains of this length needs more careful justification. The FENE springs have R0 = 10 nm, which is 5x the monomer diameter (sigma_p = 2 nm), so the effective chain contour length is substantial. However, the paper should discuss whether the sticker-spacer architecture (with specific A-B binding at epsilon_AB = 6 kBT) creates effective topological constraints that differ from standard polymer entanglement, and whether the Z1+ analysis is appropriate for this type of bonded network.
minor comments (6)
  1. Fig. 3 caption: panel labels in the caption text (b, c) do not match the figure description. The caption mentions '(b) mean number of topological constraints per chain <Z>' and '(c) primitive path contour length <L_pp>', but the text also references '(b) Schematic illustration...' which appears to be a separate panel. Clarify panel labels.
  2. The Peclet number definition (Eq. 6) uses sigma_s in the numerator, but the ratio of active to thermal forces would naturally use the relevant length scale for the driven object. Since ABPs interact with polymers via WCA, the relevant length scale for the force ratio might be sigma_p or the interaction range. Clarify why sigma_s is the appropriate length scale.
  3. The bath density parameter rho_M is defined as Ns/(Np*N) in the main text but as N_ABP/N_mon in the Supplemental Material. These are equivalent but the notation should be consistent.
  4. Fig. S3: the percolation threshold S_threshold = 0.85 is stated but not justified. Why 85% rather than, e.g., 50% or 95%?
  5. The paper mentions 'five independent simulation replicates' (SM) but does not report error bars or uncertainty estimates in the main text figures. Adding error bars or confidence intervals would strengthen the quantitative claims.
  6. The reference list includes several 2025-2026 preprints (Refs. 23, 24, 30, 31). Ensure these are properly cited and that the manuscript does not depend on unpublished results as load-bearing premises.

Circularity Check

0 steps flagged

No significant circularity; simulation-based claims verified by direct measurement of independent observables

full rationale

This paper is a simulation study whose central claims are verified by direct measurement of simulation observables, not by fitting parameters and then predicting the same data. The transition from droplet to percolated network (Fig. 1c) is directly observed. The mechanistic claims—enhanced interchain contacts (Fig. 2c), suppressed intrachain contacts (Fig. 2b), increased topological constraints ⟨Z⟩ via Z1+ analysis (Fig. 3c), and continued chain exchange (Fig. 3a)—are each measured by independent analysis tools applied to simulation configurations. The persistence claim is tested by a controlled ABP depletion protocol (Fig. 4, Fig. 5), which is an experimental intervention within the simulation, not a circular re-derivation. The contact retention fraction χ_RC and renewal rate R(t) are computed directly from trajectory frames, not predicted from a fitted model. The scaling picture in the SM is explicitly disclaimed as non-predictive ('Although the present work does not establish a predictive scaling theory'). Self-citations exist (Ref. 30, overlapping authors with Schwarz and Ross; Ref. 37, overlapping with Theeyancheri) but are used as motivation for model choices and background context, not as load-bearing premises for the central result. The skeptic's concern about whether Z1+ detects true topological constraints vs. geometric kinks for 12-monomer chains is a validity/correctness concern, not a circularity concern—the paper does not define its observables in terms of its own predictions or smuggle in an ansatz via self-citation. No step in the derivation chain reduces to its inputs by construction.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

No new physical entities are postulated. The paper introduces no new particles, forces, or fields. The 'topological imprinting' is a descriptive label for an emergent phenomenon, not a new entity.

free parameters (5)
  • epsilon_AB = 6 kBT
    Binding affinity strength chosen by hand; not fitted to experimental data but selected to ensure phase separation.
  • sigma_s/sigma_p ratio = 1.5
    Ratio of ABP diameter to monomer diameter chosen as 3nm/2nm; the paper argues this must be in an intermediate regime but does not systematically scan this parameter.
  • rho_M = 0.5-2.5
    Bath density ratio scanned over a range; the main results use rho_M=2.0 without justification for this specific choice beyond showing trends.
  • Pe = 0-2.0
    Peclet number scanned; the transition appears between Pe=0.5 and Pe=1.0 but no critical Pe is identified.
  • N_p = 12
    Chain length fixed at 12 monomers; not varied, and the shortness of chains is a potential limitation for the topological argument.
axioms (4)
  • domain assumption Sticker-spacer polymer model with A-B heterotypic binding captures essential physics of biomolecular condensates
    Invoked throughout as the model framework (Ref 32, 33). Standard in the field but a simplification of real condensate chemistry.
  • domain assumption Overdamped Langevin dynamics with ABP self-propulsion correctly models the active bath
    Eq. 1 and SM Eq. 5. Standard active matter modeling, but real active baths (enzymes, motors) have different force-generation mechanisms.
  • ad hoc to paper Twice the passive coalescence time is sufficient to demonstrate network persistence
    Depletion protocol in main text and Fig. S8. This is the load-bearing timescale assumption; no argument is given for why this is the right timescale rather than, e.g., 10x or 100x.
  • domain assumption Primitive path analysis (SMDP algorithm) correctly identifies topological constraints in short (12-monomer) chains
    Z1+ package applied to chains of N_p=12. The algorithm is designed for entangled polymer melts; its applicability to very short chains is assumed but not validated.

pith-pipeline@v1.1.0-glm · 17497 in / 3695 out tokens · 171366 ms · 2026-07-10T00:57:12.207032+00:00 · methodology

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Cite this review

Pith. "Pith review of Active Particles Imprint Persistent Percolating Networks in Polymer Condensates." pith.science (2026). https://pith.science/paper/SM5PLTC7

@misc{pith2026260708048,
  author       = {Pith},
  title        = {Pith review of: Active Particles Imprint Persistent Percolating Networks in Polymer Condensates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SM5PLTC7}},
  note         = {Machine review of arXiv:2607.08048}
}
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read the original abstract

Fluid condensates readily exchange components and reorganize, and in doing so typically erase structural history. Using simulations of sticker-spacer polymers in an active particle bath, we show that activity drives condensates from compact droplets into system-spanning percolated networks by enhancing interchain connectivity, suppressing intrachain collapse, and increasing topological constraints through interchain winding. The network persists after the active particles are removed, despite continued polymer exchange and contact turnover, revealing a fluid-like state with activity-induced topological imprinting. Hence, activity can write long-lived structural organization and memory into fluid condensates.

Figures

Figures reproduced from arXiv: 2607.08048 by Jennifer L. Ross, J. M. Schwarz, Ligesh Theeyancheri.

Figure 1
Figure 1. Figure 1: Activity-driven transition from polymer droplets to percolated networks. (a) Sticker-spacer polymer model (A/B monomers) with active Brownian particles (ABPs) as the bath, (b) interaction scheme, and (c) representative steady states: (i) polymer-only (no bath), forming a compact droplet; (ii) passive bath (Pe = 0), yielding compact dense clusters; (iii) active bath (Pe = 1.0), producing a percolated networ… view at source ↗
Figure 2
Figure 2. Figure 2: Increasing Pe percolates the network, enhanc￾ing interchain contact (IC) formation and retention while suppressing nonbonded intrachain (NB) contacts. Prob￾ability distributions of (a) network compactness ΓComp, (b) NB, and (c) IC contacts, for ρM = 2.0 with increas￾ing Pe. (d) Mean contact retention fraction ⟨χRC ⟩ as a function of Pe. ΓComp as the average closeness centrality of the network, ΓComp = ⟨Cne… view at source ↗
Figure 3
Figure 3. Figure 3: Dynamic chain exchange and topological robustness of the percolated network. (a) Distribution of the exchange fraction fexch. (b) Schematic illustration of primitive path analysis using the SMDP algorithm for two entangled polymer chains (α and β). Distributions of (b) mean number of topological constraints per chain ⟨Z⟩, and (c) primitive path contour length ⟨Lpp⟩ for different Pe (ρM = 2.0). of ABPs, the… view at source ↗
Figure 4
Figure 4. Figure 4: Activity-driven structural transition from a com￾pact condensate to a spatially extended network. Repre￾sentative snapshots of the system for (a) Pe = 0 and (b) Pe = 1.0, showing a compact dense condensate and a spa￾tially extended network structure, respectively. (c) Dis￾tribution of ΓComp and (d) radial polymer density profile ⟨ρp (|r−rCOM|)⟩ as a function of distance from the center of mass of the syste… view at source ↗
Figure 5
Figure 5. Figure 5: Activity drives a self-renewing condensate net￾work that persists after depletion. (a) Time evolution of IC and NB contacts and (b) renewal rate distributions R(t) for (i) Pe = 0 and (ii) Pe = 1.0. Dashed vertical lines mark successive ABP depletion (ρM = 2.0, λ = 0.1) events D1-D10 in (a) and the mean R(t) for each contact type in (b). active bath case, for Pe = 1.0, IC contacts remain largely stable, exh… view at source ↗

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