Theory of volume transition in polyelectrolyte gels with charge regularization

Hua, Jing; Mitra, Mithun K.; Muthukumar, M.

doi:10.1063/1.3698168

Cited by 70 publications

(68 citation statements)

References 93 publications

(129 reference statements)

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“…48 to treat polyelectrolyte gels created by divalent ions, with the main focus being sol-gel transition and liquid-liquid phase separation. Because the combinatorics treatment of associating bonds is equivalent to the Flory model, the new element is the concentration fluctuations, which are also treated in other works using replica formalism and charge regularization (55,56). The relative merits of these advances are yet to be explored.…”

Section: Discussionmentioning

confidence: 99%

Ordinary–extraordinary transition in dynamics of solutions of charged macromolecules

Muthukumar

2016

Proc. Natl. Acad. Sci. U.S.A.

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The occurrence of the ubiquitous and intriguing "ordinary-extraordinary" behavior of dynamics in solutions of charged macromolecules is addressed theoretically by explicitly considering counterions around the macromolecules. The collective and coupled dynamics of macromolecules and their counterion clouds in salt-free conditions are shown to lead to the "ordinary" behavior (also called the "fast" mode) where diffusion coefficients are independent of molar mass and polymer concentration and are comparable to those of isolated metallic ions in aqueous media, in agreement with experimental facts observed repeatedly over the past four decades. The dipoles arising from adsorbed counterions on polymer backbones can form many pairwise physical cross-links, leading to microgel-like aggregates. Balancing the swelling from excluded volume effects and counterion pressure with elasticity of the microgel, we show that there is a threshold value of a combination of polymer concentration and electrolyte concentration for the occurrence of the "extraordinary" phase (also called the "slow" mode) and the predicted properties of diffusion coefficient for this phase are in qualitative agreement with well-known experimental data.ordinary-extraordinary transition | slow mode | fast mode | polyelectrolyte dynamics | polyelectrolyte aggregation T he "ordinary-extraordinary" transition has been known over the past four decades from dynamic light-scattering (DLS) experiments on aqueous solutions of charged macromolecules such as DNA, polylysine, polystyrene sulfonate, polyvinyl pyridine, etc. (1-22). In the so-called "ordinary" behavior, the diffusion coefficient D determined from DLS increases, from the value D SE expected from the Stokes-Einstein law for dilute polyelectrolyte solutions at high enough monovalent salt concentrations c s sufficient to screen electrostatic interactions, to even higher values upon a decrease in c s . This observation is already intriguing, because the chain swells due to stronger intrachain electrostatic repulsion at lower values of c s and hence D is expected to decrease according to the Stoke-Einstein law. However, D actually increases! Even more strangely, upon further decrease in c s , an additional diffusion coefficient with very small values emerges, suggesting the presence of large aggregates. It is surprising that similarly charged, and hence electrostatically repulsive, polymers would aggregate at all and that they would break apart when electrostatic repulsion is screened by added electrolyte. In view of this mysterious nature, this behavior is called "extraordinary." In addition to these tantalizing facts, the occurrence of the ordinaryextraordinary behavior for solutions of charged macromolecules completely undermines the utility of the Stokes-Einstein law, which is the routine methodology for characterizing uncharged macromolecules in solutions.The diffusional modes corresponding to the ordinary and extraordinary behaviors are also called "fast" and "slow" modes, with their respective diffusio...

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Section: Discussionmentioning

confidence: 99%

Ordinary–extraordinary transition in dynamics of solutions of charged macromolecules

Muthukumar

2016

Proc. Natl. Acad. Sci. U.S.A.

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“…This term is similar to the "dielectric mismatch" term introduced by Muthukumar et al in a theoretically description of counterion condensation to polyelectrolytes. [35][36][37] The dielectric function of polymers is usually in the range of ε p ∈ (2, 10) whereas water has a higher value of w = 78.5. Hence, β G s (z) will be positive.…”

Section: B Molecular Theory: Weak Polyelectrolytesmentioning

confidence: 99%

Born energy, acid-base equilibrium, structure and interactions of end-grafted weak polyelectrolyte layers

Nap

Tagliazucchi

Szleifer

2014

The Journal of Chemical Physics

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This work addresses the effect of the Born self-energy contribution in the modeling of the structural and thermodynamical properties of weak polyelectrolytes confined to planar and curved surfaces. The theoretical framework is based on a theory that explicitly includes the conformations, size, shape, and charge distribution of all molecular species and considers the acid-base equilibrium of the weak polyelectrolyte. Namely, the degree of charge in the polymers is not imposed but it is a local varying property that results from the minimization of the total free energy. Inclusion of the dielectric properties of the polyelectrolyte is important as the environment of a polymer layer is very different from that in the adjacent aqueous solution. The main effect of the Born energy contribution on the molecular organization of an end-grafted weak polyacid layer is uncharging the weak acid (or basic) groups and consequently decreasing the concentration of mobile ions within the layer. The magnitude of the effect increases with polymer density and, in the case of the average degree of charge, it is qualitatively equivalent to a small shift in the equilibrium constant for the acid-base equilibrium of the weak polyelectrolyte monomers. The degree of charge is established by the competition between electrostatic interactions, the polymer conformational entropy, the excluded volume interactions, the translational entropy of the counterions and the acid-base chemical equilibrium. Consideration of the Born energy introduces an additional energetic penalty to the presence of charged groups in the polyelectrolyte layer, whose effect is mitigated by down-regulating the amount of charge, i.e., by shifting the local-acid base equilibrium towards its uncharged state. Shifting of the local acid-base equilibrium and its effect on the properties of the polyelectrolyte layer, without considering the Born energy, have been theoretically predicted previously. Account of the Born energy leads to systematic, but in general small, corrections to earlier theoretical predictions describing the behavior of weak polyelectrolyte layers. However, polyelectrolyte uncharging results in a decrease in the concentration of counterions and inclusion of the Born Energy can result in a substantial decrease of the counterion concentration. The effect of considering the Born energy contribution is explored for end-grafted weak polyelectrolyte layers by calculating experimental observables which are known to depend on the presence of charges within the polyelectrolyte layer: inclusion of the Born energy contribution leads to a decrease in the capacitance of polyelectrolyte-modified electrodes, a decrease of conductivity of polyelectrolyte-modified nanopores and an increase in the repulsion exerted by a planar polyelectrolyte layer confined by an opposing wall.

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“…Although there are no doubts regarding the importance of both mechanisms for swelling of polyelectrolyte gels, analysis of experimental data is traditionally grounded on the assumption that ionic pressure plays the key role, while the effect of interaction between bound charges is subordinate (in a number of studies it is referred to in order to explain discrepancies between observations and their predictions; see [9] for a discussion). This approach may be explained by the absence of simple expressions for the energy of electrostatic repulsion of bound changes to be employed in fitting observations [10][11][12][13],…”

Section: Introductionmentioning

confidence: 99%

Swelling ofpH-sensitive hydrogels

Drozdov

Christiansen

2015

Phys. Rev. E

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A model is derived for the elastic response of polyelectrolyte gels subjected to unconstrained and constrained swelling. A gel is treated as a three-phase medium consisting of a solid phase (polymer network), solvent (water), and solutes (mobile ions). Transport of solvent and solutes is modeled as their diffusion through the network accelerated by an electric field formed by ions and accompanied by chemical reactions (dissociation of functional groups attached to the chains). Constitutive equations (including the van't Hoff law for ionic pressure and the Henderson-Hasselbach equation for ionization of chains) are derived by means of the free energy imbalance inequality. Good agreement is demonstrated between equilibrium swelling diagrams on several pH-sensitive gels and results of simulation. It is revealed that swelling of polyelectrolyte gels is driven by electrostatic repulsion of bound charges, whereas the effect of ionic pressure is of secondary importance.

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Theory of volume transition in polyelectrolyte gels with charge regularization

Cited by 70 publications

References 93 publications

Ordinary–extraordinary transition in dynamics of solutions of charged macromolecules

Ordinary–extraordinary transition in dynamics of solutions of charged macromolecules

Born energy, acid-base equilibrium, structure and interactions of end-grafted weak polyelectrolyte layers

Swelling ofpH-sensitive hydrogels

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