Non-equilibrium interaction between catalytic colloids: Boundary conditions and penetration depth

Alexander Y. Grosberg, Yitzhak Rabin

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Spherical colloids that catalyze the interconversion reaction A ⇋ B between solute molecules A and B whose concentration at infinity is maintained away from equilibrium effectively interact due to the non-uniform fields of solute concentrations. We show that this long range 1/r interaction is suppressed via a mechanism that is superficially reminiscent but qualitatively very different from electrostatic screening: catalytic activity drives the concentrations of solute molecules towards their equilibrium values and reduces the chemical imbalance that drives the interaction between the colloids. The imposed non-equilibrium boundary conditions give rise to a variety of geometry-dependent scenarios; while long-range interactions are suppressed (except for a finite penetration depth) in the bulk of the colloid solution in 3D, they can persist in quasi-2D geometry in which the colloids but not the solutes are confined to a surface, resulting in the formation of clusters or Wigner crystals, depending on the sign of the interaction between colloids.

Original languageEnglish
Pages (from-to)7414-7420
Number of pages7
JournalSoft Matter
Issue number31
StatePublished - 21 Aug 2020

Bibliographical note

Publisher Copyright:
© The Royal Society of Chemistry.


We would like to thank Alexandra Zidovska and Paul Chaikin for valuable discussions. We are also indebted to Ramin Golestanian for helpful comments and suggestions, and thank Siegfried Dietrich and Mihail Popescu for useful correspondence. YR’s work was supported by grants 178/16 from the Israel Science Foundation and 1902/12 from the Israeli Centers for Research Excellence program of the Planning and Budgeting Committee. YR would like to acknowledge the hospitality of the Center for Soft Matter Research of New York University where part of this work was done. AYG’s research is supported in part by the MRSEC Program of the National Science Foundation under Award DMR-1420073. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 and by the National Institutes of Health under Grant No. R25GM067110.

FundersFunder number
National Science FoundationPHY-1748958, DMR-1420073
National Institutes of Health
Directorate for Mathematical and Physical Sciences1420073
Israel Science Foundation1902/12


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