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Martens CM, Tuinier R, Vis M. Depletion interaction mediated by semiflexible polymers. J Chem Phys 2022; 157:154102. [PMID: 36272806 DOI: 10.1063/5.0112015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present a simple mean-field theory to describe the polymer-mediated depletion attraction between colloidal particles that accounts for the polymer's chain stiffness. We find that for fixed polymer radius of gyration and volume fraction, the strength of this attraction increases with increasing chain stiffness in both dilute and semidilute concentration regimes. In contrast, the range of attraction monotonically decreases with chain stiffness in the dilute regime, while it attains a maximum in the semidilute regime. The obtained analytical expressions for the depletion interaction were compared with numerical self-consistent field lattice computations and shown to be in quantitative agreement. From the interaction potential between two spheres, we calculated the second osmotic virial coefficient B2, which appears to be a convex function of chain stiffness. A minimum of B2 as a function of chain stiffness was observed both in the numerical self-consistent field computations and the analytical theory. These findings help explain the general observation that semiflexible polymers are more effective depletants than flexible polymers and give insight into the phase behavior of mixtures containing spherical colloids and semiflexible polymers.
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Affiliation(s)
- C M Martens
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - R Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - M Vis
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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Martens CM, van Leuken SHM, Opdam J, Vis M, Tuinier R. The depletion thickness in solutions of semi-flexible polymers near colloidal surfaces: analytical approximations. Phys Chem Chem Phys 2022; 24:3618-3631. [PMID: 35103732 PMCID: PMC8827050 DOI: 10.1039/d1cp05026e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
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.
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Affiliation(s)
- C M Martens
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
| | - S H M van Leuken
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
| | - J Opdam
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
| | - M Vis
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. .,Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - R Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. .,Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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Mehta S, Bahadur J, Sen D, Aswal VK, Kohlbrecher J. Unravelling Polyethylenimine Mediated Non-monotonic Stability Behaviour of Silica Colloids: Role of Competing Electrostatic and Entropic Interactions. Phys Chem Chem Phys 2022; 24:21740-21749. [DOI: 10.1039/d2cp02699f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Polymer-mediated interactions play an important role in the stability of the colloids and therefore, are paramount for both fundamental as well as scientific interests. The stability of the colloids in...
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