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. 2024 Nov 11;25(11):7361-7376.
doi: 10.1021/acs.biomac.4c01037. Epub 2024 Oct 21.

Reentrant Condensation of Polyelectrolytes Induced by Diluted Multivalent Salts: The Role of Electrostatic Gluonic Effects

Huaisong Yong  1   2   3
Affiliations

Reentrant Condensation of Polyelectrolytes Induced by Diluted Multivalent Salts: The Role of Electrostatic Gluonic Effects

Huaisong Yong. Biomacromolecules. .

Abstract

We explore the reentrant condensation of polyelectrolytes triggered by multivalent salts, whose phase-transition mechanism remains under debate. We propose a theory to study the reentrant condensation, which separates the electrostatic effect into two parts: a short-range electrostatic gluonic effect because of sharing of multivalent ions by ionic monomers and a long-range electrostatic correlation effect from all ions. The theory suggests that the electrostatic gluonic effect governs reentrant condensation, requiring a minimum coupling energy to initiate the phase transition. This explains why diluted salts with selective multivalency trigger a polyelectrolyte phase transition. The theory also uncovers that strong adsorption of multivalent ions onto ionic monomers causes low-salt concentrations to induce both collapse and reentry transitions. Additionally, we highlight how the incompatibility of uncharged polyelectrolyte moieties with water affects the polyelectrolyte phase behaviors. The obtained results will contribute to the understanding of biological phase separations if multivalent ions bound to biopolyelectrolytes play an essential role.

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Conflict of interest statement

The author declares no competing financial interest.

Figures

Figure 1
Figure 1
(a) Sketch description of the reentrant condensation of polyelectrolytes induced by diluted multivalent salts. In the figure, the typical values of the multivalent salt concentration for collapse and reentry transitions are quoted from refs., Notice that the reentrant condensation is not necessary to be symmetric with respect to multivalent salt concentrations. (b) A sketch description of preferential adsorption of multivalent ions by ionic monomers (filled blue circles) and forming “physical cross-links” between ionic monomers by sharing multivalent ions (filled red circles). Here, the role of the multivalent ion is just like a glue to bind different ionized monomers. In the figure, the pink lines represent polymer chains and open black circles represent background ions in polyelectrolyte solutions.
Figure 2
Figure 2
Minimum coupling energy (γε2) with respect to the fraction of charged monomer (p) according to eq 13 for typical values of the parameter εFH,2 with lB/a = 2, εFH,1 = 0.45, and N → ∞ for (a) εFH,2 > 1/2 and (b) 0 ≤ εFH,2 ≤ 1/2.
Figure 3
Figure 3
Minimum coupling energy (γε2) with respect to the fraction of charged monomers (p) according to eq 12 for various polyelectrolyte chain lengths (N) with lB/a = 2 and εFH,1 = 0.45 for (a) εFH,2 = 0.78 and εFH,2 > formula image; panel (b) for the case of and εFH,2 = 0.45 and 0 ≤ εFH,2 ≤ formula image.
Figure 4
Figure 4
Osmotic pressure of polyelectrolyte solution as a function of the inverse volume fraction of monomers according to eq 21 for the case of lB/a = 2.5, εFH,1 = 0.45, and N = 500 for (a) p = 0.05, εFH,2 = 0.75, μ = −5, ε1 = 5, and γε2 = 10 and (b) p = 0.2, εFH,2 = 0.45, μ = −5, ε1 = 5, and γε2 = 25. The coexistence pressures by the Maxwell construction are indicated by the horizontal dotted lines in the figure, and the spinodal points are indicated by filled circles in the figure.
Figure 5
Figure 5
Spinodal phase diagrams of polyelectrolyte in the dilute solution of multivalent salts according to eq 22 for various polyelectrolyte chain lengths (N) with lB/a = 2.5 and εFH,1 = 0.45 for (a) p = 0.2, εFH,2 = 0.55, ε1 = 6, and γε2 = 20 and (b) p = 0.2, εFH,2 = 0.45, ε1 = 6, and γε2 = 25.
Figure 6
Figure 6
Spinodal phase diagrams of polyelectrolytes in the dilute solution of multivalent salts according to eq 22 for various values of the electrostatic gluonic effect (γε2) with infinite chain length (N → ∞), lB/a = 2.5, and εFH,1 = 0.45 for (a) p = 0.2, εFH,2 = 0.55, and ε1 = 6 and (b) p = 0.2, εFH,2 = 0.45, and ε1 = 6.
Figure 7
Figure 7
Osmotic pressure of polyelectrolyte solution as a function of the inverse volume fraction of monomers according to eq 21 for the case of infinite chain length (N → ∞), lB/a = 2.5, εFH,1 = 0.45, εFH,2 = 0.55, ε1 = 5, γε2 = 15, and μ = −5 for (a) p = 8 × 10–4 and (b) p = 1 × 10–4. The coexistence pressures by the Maxwell construction are indicated by the horizontal dotted line in the figure, and the spinodal points are indicated by filled circles in the figure. Notice that the spinodal with a negative osmotic pressure in the figure is thermodynamically forbidden for polymer solutions.
Figure 8
Figure 8
Diagram of the parameter space according to eq 24 toward the coexistence of a dilute and condensed polymer phases in the phase transition of polyelectrolyte, if εFH,2 > 1/2 and the polyelectrolyte chain is very long (N → ∞). In the figure, the value of ε1 is chosen to be 5.0. By variations of salt concentration in phase transition (such as the region IV in the figure), it is possible to see a change from the coexistence of two polymer phases to the existence of only a condensed polymer phase.
Figure 9
Figure 9
Illustration of the effect of nonassociative pairwise-like electrostatic interactions from the long-range correlation of all ions on the phase behavior of polyelectrolyte solution according to eq 22 by variations of the parameter lB/a. The existence of long-range pairwise-like electrostatic interaction shifts the coexistence region of collapse transition to lower concentrations of multivalent salts but shifts the coexistence region of reentry transition to higher concentrations of multivalent salts. In the figure, the parameters for the spinodal phase diagrams are chosen as infinite chain length (N → ∞), p = 0.2, εFH,1 = 0.45, εFH,2 = 0.72, ε1 = 6, and γε2 = 32.
Figure 10
Figure 10
By variations of εFH,1 according to eq 22, an illustration of the confluence effect of nonelectrostatic interactions between solvent (water) and charged (εFH,1) and uncharged (εFH,2) monomers in the multivalent salt-induced reentrant condensation of polyelectrolytes. The parameters for the spinodal phase diagrams are chosen as infinite chain length (N → ∞), lB/a = 2.5, p = 0.2, εFH,2 = 0.52, ε1 = 6, and γε2 = 18.
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References

    1. Nordenskiöld L.; Shi X.; Korolev N.; Zhao L.; Zhai Z.; Lindman B. Liquid-liquid phase separation (LLPS) in DNA and chromatin systems from the perspective of colloid physical chemistry. Adv. Colloid Interface Sci. 2024, 326, 103133.10.1016/j.cis.2024.103133. - DOI - PubMed
    1. Sołtys K.; Tarczewska A.; Bystranowska D. Modulation of biomolecular phase behavior by metal ions. Biochimica Et Biophysica Acta (BBA) - Molecular Cell Res. 2023, 1870 (8), 119567.10.1016/j.bbamcr.2023.119567. - DOI - PubMed
    1. Herrera S.; Agazzi M. L.; Apuzzo E.; Cortez M. L.; Marmisollé W.; Tagliazucchi M.; Azzaroni O. Polyelectrolyte-multivalent molecule complexes: physicochemical properties and applications. Soft Matter 2023, 19, 2013–2041. 10.1039/D2SM01507B. - DOI - PubMed
    1. Stala Ł.; Ulatowska J.; Polowczyk I. A review of polyampholytic ion scavengers for toxic metal ion removal from aqueous systems. Water Res. 2021, 203, 117523.10.1016/j.watres.2021.117523. - DOI - PubMed
    1. Wurm F.; Rietzler B.; Pham T.; Bechtold T. Multivalent Ions as Reactive Crosslinkers for Biopolymers—A Review. Molecules 2020, 25 (8), 1840.10.3390/molecules25081840. - DOI - PMC - PubMed

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