We present Monte Carlo simulations on annealed polyelectrolytes in poor solvent. Increasing the chemical potential of the charges, which is equal to the pH of the solution except for a trivial additive constant, we find the first-order phase transition between a weakly charged globule and a highly charged extended chain predicted by theory. Starting from an elongated highly charged conformation and increasing the coupling strength u = λB/b, the degree of stretching of the chain at first increases similarly to quenched polyelectrolytes. However, on reaching some upper threshold u * , the chain collapses back into a weakly charged state.

Using (semi-)grand canonical Monte Carlo simulations of a polyelectrolyte chain of length N where the charges are in contact with a reservoir of constant chemical potential µ given by the solution pH, we study the behavior of annealed polyelectrolytes in a poor solvent. We focus on the conformational properties in the close-to-Θ-point regime τ < τ* ∼ N -1/5 u -3/5 , which can be reached either by reducing electrostatic interaction strength u ) λ B /b or by improving solvent quality, i.e., by reducing τ ) (Θ -T)/Θ. We investigate the conformations with regard to parameters u, τ, and µ and explore in which conditions pearl-necklace-like structures are stable. Most of the pearl-necklace parameters are found to obey the scaling relations predicted for quenched polyelectrolytes. However, similarly to the behavior known for this class of polyelectrolytes, we obtain large fluctuations in pearl number and size. In agreement with theoretical predictions we find a nonuniform charge distribution between pearls and strings. For τ , 1 and moderate interaction strength we demonstrate that a cascade of pearl-necklace transitions can be initiated by changing µ, i.e., by tuning the solution pH.

Using molecular dynamics, we study the self-assembly of phenylalanine with charged end-groups at various temperatures and concentrations. As in the case of diphenylalanine, we observe the formation of nanotubes; however, phenylalanine aggregates in layers of four, not six, molecules. The observed aggregates are consistent with recent experimental measurements of fibrils obtained from mice with phenylketonuria. We investigate the stability and the mechanism by which these tubular structures form and discuss potential toxicity mechanisms.

Common structures identified in the assembly of aromatic amino acids and their mixtures include the four-fold tube (a and b) and the zig-zag structure (c and d).

Using grand canonical Monte Carlo simulations of a polyelectrolyte chain where the charges are in contact with a reservoir of constant chemical potential given by the solution pH, we study the behavior of weak polyelectrolytes in a poor solvent. We address the influence of variable screening of the electrostatic interaction on the chain structure for rather poor solvents as well as in the close-to-Θ-point regime. For the latter case, we demonstrate that a fine tuning of the chain structure is attainable by varying screening. With growing screening length, that is, by reducing the salt concentration, the degree of charging is reduced and the pearl distribution can be shifted toward a smaller number of pearls. In addition, we find that pearl necklaces can also occur at high charging provided the screening is very strong. In the rather-poor-solvent regime, the position of the discrete transition from a highly charged, stretched chain to a weakly charged globule can be shifted by the variation of screening. By reducing the screening of electrostatic repulsion, we observe in both regimes a nonmonotonic stretching of the polyelectrolyte. After reaching a maximum of stretching, the chains relax back to an asymptotic value at vanishing screening, which depends on pH. For rather poor solvents, at large screening lengths, the chains collapse into an almost uncharged globule provided that high ionization is not pinned by a large chemical potential of the charges.

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