From the beginning of life with the information-containing polymers until the present era of a plethora of water-based materials in health care industry and biotechnology, polyelectrolytes are ubiquitous with a broad range of structural and functional properties. The main attribute of polyelectrolyte solutions is that all molecules are strongly correlated both topologically and electrostatically in their neutralizing background of charged ions in highly polarizable solvent. These strong correlations and the necessary use of numerous variables in experiments on polyelectrolytes have presented immense challenges toward fundamental understanding of the various behaviors of charged polymeric systems. This Perspective presents the author’s subjective summary of several conceptual advances and the remaining persistent challenges in the contexts of charge and size of polymers, structures in homogeneous solutions, thermodynamic instability and phase transitions, structural evolution with oppositely charged polymers, dynamics in polyelectrolyte solutions, kinetics of phase separation, mobility of charged macromolecules between compartments, and implications to biological systems.

We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.

Many ssRNA/ssDNA viruses bind their genome by highly basic semiflexible peptide arms of capsid proteins. Here, we show that nonspecific electrostatic interactions control both the length of the genome and genome conformations. Analysis of available experimental data shows that the genome length is linear in the net charge on the capsid peptide arms, irrespective of the actual amino acid sequence, with a proportionality coefficient of 1.61 ± 0.03. This ratio is conserved across all ssRNA/ssDNA viruses with highly basic peptide arms, and is different from the one-to-one charge balance expected of specific binding. Genomic nucleotides are predicted to occupy a radially symmetric spherical shell detached from the viral capsid, in agreement with experimental data.

Conditions of rapid processing often drive polymers to adopt nonequilibrium molecular conformations, which, in turn, can give rise to structural, dynamical, and mechanical properties that are significantly different from those in thermodynamic equilibrium. However, despite the possibility to control the desired nonequilibrium properties of polymers, a rigorous microscopic understanding of the processing–property relations is currently lacking. In an attempt to stimulate progress along this topical direction, we focus here on three prototypical and apparently different cases: spin-coated polymer films, rapidly drawn polymer fibers, and sheared polymer melts. Inspired by the presence of common observations in the chosen cases, we search for order parameters as, for example, topological correlations and heterogeneities, which may allow characterizing the processing-induced behavior of polymers. We highlight that such approaches, necessitating concerted efforts from theory, simulations, and experiments, can provide a profound understanding leading to predictable and tunable properties of polymers.

The translocation of macromolecules through a nanopore requires the impingement of the molecules at the pore followed by threading through the pore. While most of the discussion on the translocation phenomenon focused so far on the threading process, the phenomenology on the frequency of encounters between the polymer and the pore exhibits diverse features in terms of polymer length, solution conditions, driving force, and pore geometry. We derive a general theory for the capture rate of polyelectrolyte molecules and the probability of successful translocation through a nanopore, under an externally imposed electric field. By considering the roles of entropic barrier at the pore entrance and drift of the polyelectrolyte under the electric field, we delineate two regimes: (a) entropic barrier regime and (b) drift regime. In the first regime dominated by the entropic barrier for the polyelectrolyte, the capture rate is an increasing nonlinear function in the electric field and chain length. In the drift regime, where the electric field dwarfs the role of entropic barriers, the capture rate is independent of chain length and linear in electric field. An analytical formula is derived for the crossover behavior between these regimes, and the general results are consistent with various experimentally observed trends.

The counterion distribution around an isolated flexible polyelectrolyte in the presence of a divalent salt is evaluated using the adsorption model [M. Muthukumar, J. Chem. Phys. 120, 9343 (2004)] that considers the Bjerrum length, salt concentration, and local dielectric heterogeneity as physical variables in the system. Self-consistent calculations of effective charge and size of the polymer show that divalent counterions replace condensed monovalent counterions in competitive adsorption. The theory further predicts that at modest physical conditions for a flexible polyelectrolytes such as sodium polystyrene sulfonate in aqueous solutions polymer charge is compensated and reversed with increasing divalent salt. Consequently, the polyelectrolyte shrinks and reswells. Lower temperatures and higher degrees of dielectric heterogeneity between chain backbone and solvent enhance condensation of all species of ions. Complete diagrams of states for the effective charge calculated as functions of the Coulomb strength and salt concentration suggest that (a) overcharging requires a minimum Coulomb strength and (b) progressively higher presence of salt recharges the polymer due to either electrostatic screening (for low Coulomb strengths) or coion condensation (for high Coulomb strengths). Consideration of ion-bridging by divalent counterions leads to a first-order collapse of polyelectrolytes in modest presence of divalent salts and at higher Coulomb strengths. The authors’ theoretical predictions are in agreement with the generic results from experiments and simulations.