The key milestones in understanding the fluctuation effects and phase transitions in weakly charged polyelectrolytes

The purpose of the lecture is to demonstrate a variety of scenarios according to which the confrontation between the long-range Coulomb and short-range van der Waals interactions in polyelectrolytes results in destroying the homogeneous (disordered) state and formation of ordered phases and complexes. The basic issues to be discussed in the lecture are as follows.
1. Polyelectrolytes are the area of fluctuation effects: if the fluctuations were absent the total charge profile would be zero (due to electroneutrality) and, thus, electrostatic energy would equal zero either.
2. The electrostatic blob notion and distinction between the weakly and strongly charged polyelectrolytes (the blob is big in weakly charged ones).
3. Screening by non-point-like objects and different types of screening in polyelectrolytes (conventional screening, recharging and oscillating screening).
4. Polyelectrolytes in poor solvent: microphase vs macrophase separation. Phase diagrams.
5. Macrophase separation in polyelectrolyte solutions and polyelectrolyte complexes as the minimal droplets of the condensed phase.
5. Why could be the Debye-Hückel estimate of the electrostatic energy not always correct. The necessary extension.
6. Polyelectrolyte complexes and ordered polyelectrolyte complexes. Phase diagrams.
7. The polydispersity effects and charge fractionation. Why and how the polyelectrolyte polydispersity with respect to the linear charge density leads to the fact that the microphase separation is accompanied by the macrophase separation into the stronger and weaker charged polyelectrolyte chains (with the corresponding counter-ion dendities).
8. Necklace model and microphase separation.

 

High swelling of polyelectrolytes (PEs) in comparison with neutral counterparts in aqueous media is usually ascribed to the presence of ionic groups capable of dissociation. In macroscopic polymer gels counterions are trapped within the network interior and create exerting osmotic pressure providing high gel swelling. Single chains in dilute solutions obtain non-zero charge owing to release of counterions, and their extended conformations are the consequence of Coulomb repulsion of ionic groups. Immersed in organic solvents, both PE gels and single chains collapse. The reason of this phenomenon is counterion binding with charges in polymer chains, which is more favourable in low polar media due to higher energy gain from ion association.

It is natural to start consideration of counterion association in PEs with the case of macroscopic gels owing to their electroneutrality. Association/dissociation equilibrium in low-molecules-weight electrolytes (AB ↔ A⁺ + B⁻) is well understood, and the law of mass action defines concentrations of all species in the solution. However, this approach cannot be directly applied to PE gels because of following reasons:

(i)       Concentration of ionic groups within the gel is not fixed. Their dissociation favours network swelling and results in a decrease of their concentration. In turn, it promotes further dissociation as well as further gel swelling;

(ii)    Gel shrinking/swelling is accompanied by changes in a gel media polarity because a dielectric constant of a dry polymer is usually much lower than that of a pure solvent. Thus, energy gain from ion pairing depends on the state of the gel, swollen or collapsed;

(iii)  Each counterion electrostatically interacts not only with the respective charge in polymer chain but also with its spatial neighbors. Manning condensation of counterions in swollen networks and multiplet formation within the collapsed gels are manifestations of this fact.           

In highly swollen PE gels it is useful to describe ion association as a two-step process with the first step being Manning condensation and the second being ion pairing. Retaining of a part of counterions within PE microgel or micelle with PE corona can be treated as a third step of ion association. Type of counterion strongly influences PEs swelling, though counterion specifity directly affects only one ion association step, namely ion pairing.