The depletion thickness in solutions of semi-flexible polymers near colloidal surfaces: analytical approximations

C.M. Martens, Stijn van Leuken, Joeri Opdam, Mark Vis (Corresponding author), Remco Tuinier (Corresponding author)

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We derive a simple, yet accurate approximate mean-field expression for the depletion thickness δsf of a solution of dilute semi-flexible polymers next to a hard surface. In the case of a hard wall this equation has the simple form δsf = δ0[1 − tanh(psf/δ0)], where psf accounts for the degree of flexibility and δ0 is the depletion thickness in the case of fully flexible polymers. For fixed polymer coil size, increasing the chain stiffness leads to a decrease in the depletion thickness. The approach is also extended to include higher polymer concentrations in the semidilute regime. The analytical expressions are in quantitative agreement with numerical self-consistent field computations. A remarkable finding is that there is a maximum in the depletion thickness as a function of the chain stiffness in the semidilute concentration regime. This also means that depletion attractions between colloidal particles reach a maximum for a certain chain stiffness, which may have important implications for the phase stability of colloid–polymer mixtures. The derived equations could be useful for the description of interactions in- and phase stability of mixtures of colloids and semi-flexible polymers.
Original languageEnglish
Pages (from-to)3618-3631
Number of pages14
JournalPhysical Chemistry Chemical Physics
Issue number6
Publication statusPublished - 14 Feb 2022


J. O. gratefully acknowledges the financial support from the Dutch Ministry of Economic Affairs of the Netherlands via the Top-consortium Knowledge and Innovation (TKI) roadmap Chemistry of Advanced Materials (No. CHEMIE.PGT.2018.006). M. V. acknowledges the Netherlands Organization for Scientific Research (NWO) for a Veni grant (No. 722.017.005). S. H. M. van Leuken acknowledges the financial support of the InScite HiperBioPol project. The authors acknowledge Professor Frans Leermakers for the sfbox software package and useful discussions on SCF theory. Additionally, the authors would like to thank a helpful referee for pointing out the wall-induced nematization in depleted polymer solutions.

FundersFunder number
Dutch Ministry of Economic Affairs
Top-consortium Knowledge and InnovationCHEMIE.PGT.2018.006
Nederlandse Organisatie voor Wetenschappelijk Onderzoek722.017.005


    • Depletion
    • Depletion interaction
    • polymers


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