Polymer chains inside a model mesopore were associated with faster passage of suspended particles under one favorable condition, even though the added material might seem likely to obstruct the channel. In the reported good-solvent example, polymer fringes were associated with a 3.3-fold reduction in external resistance and a 10-fold reduction in total resistance compared with a bare pore. Here, resistance means the modeled opposition to diffusive movement, so a lower value corresponds to a higher predicted permeation rate.
The result is a model prediction built around two competing effects. The framework combined the mobility reduction associated with a polymer meshwork with attractive recruitment of colloids, particles suspended in liquid, into the pore. That setup allowed the calculation to ask when capture by the brush could outweigh the loss of mobility.
The calculation balanced obstruction and attraction
Researchers represented the channel as a cylindrical mesopore with an end-grafted flexible polymer brush. They calculated polymer-density profiles and used them to estimate the free-energy cost of inserting a colloid as it moved through the pore. The colloid was treated as a nonperturbing probe, and direct on-axis SF-SCF calculations showed good quantitative agreement with the analytical insertion estimate.
To translate that energy landscape into transport, the study used the stationary Smoluchowski equation, a description of diffusive movement through a changing environment. It calculated resistance analytically and checked the result with a direct numerical solution.
Changing affinity changed the gate
The model did not predict that attraction always helps. As colloid affinity changed, it predicted a sharp transition between facilitated and impeded permeation. Once the impeded regime was reached, internal resistance dominated.
Solvent quality moved that boundary. Increasing the model's solvent-quality parameter shifted the resistance curve toward stronger interaction values and extended the facilitation range to more weakly interacting colloids.
One comparison showed how strongly the assumed interaction mattered. For a colloid of modeled size 8, a polymer-colloid interaction parameter of -1.25, and a solvent parameter of 0.5, the attractive case had resistance about five times the bare-pore value. The same-size inert case was displayed in the extracted result as approximately 104 times the bare-pore reference, but the review flags that notation as potentially affected by formatting.
A filter with a size threshold
The model also predicted concentration enrichment at steady state. The calculated concentration was about 20 times the bulk value near the pore entrance and about 10 times the bulk value inside the pore. Those figures apply only to sufficiently low bulk concentrations because colloid crowding was left out of the calculation.
Size produced a less straightforward pattern than a simple bigger-is-worse rule. For attractive colloids, resistance could rise to a local maximum and then fall to a local minimum as size increased. Under the reported strong-attraction condition, with a polymer-colloid parameter of -1.4, resistance rose sharply above a modeled colloid size of approximately 24.
A cautious comparison with nuclear pores
The authors also tested the framework against published transport data from non-sticky nuclear pore complexes, or NPCs. That comparison covered two orders of magnitude in molecular mass and five orders of magnitude in transport rate. The reported size comparison matched the resistance trends very well, and the best-fit diffusion prefactor was 5.5, a value then fixed for the rest of the analysis.
The biological comparison was a calibration exercise, not a controlled test of a new pore. The paper notes experimental scatter and differences between assay systems, and reports no confidence interval for the fit. It also found that the interaction pattern mattered: a homogeneous model fit non-sticky and weakly attractive colloids but overestimated transport for strongly attractive ones, while a single-sticky-patch limit matched the stronger-attraction data better.
A design idea still awaiting a device test
That last result is important for the design idea, but it comes with a narrow interpretation. The single-sticky-patch calculation is an idealized limiting case, not a measurement of how interaction sites are distributed across an actual surface. More broadly, the pore geometry and polymer arrangement were simplified, so the results describe the selected model architecture rather than a universal recipe.
The central practical question remains open: whether a fabricated polymer-filled mesopore would deliver the predicted rate gain and selective gating. The study offers a mechanism and a set of model conditions to test, not evidence that a manufactured device or a living biological system will behave in exactly the same way.
Paper data and sources
Original title: How a polymer filling enhances the rate and selectivity of colloid permeation across mesopores
Authors: Mikhail Y. Laktionov, Frans A. M. Leermakers, Ralf P. Richter et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
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