Complexation between multiple weak polyacid chains and a positively charged spherical nanoparticle has been studied by means of Monte Carlo simulations. By considering titration curves, it is found that variations in the polyacid chain length and concentration, and the polyacid-to-nanoparticle mixing ratio influences the ionization of the system. For larger mixing ratios and longer chain lengths, the titration curves start to exhibit complex shapes with multiple inflection points. We also find that in some cases it is possible to differentiate between free and adsorbed chains, based on the charge probability distribution and the probability distribution of the gyration radius. Furthermore, the adsorption of weak polyacids has been compared with that of strong polyacids and the fraction of adsorbed monomers is found 1 to be slightly larger for the strong polyacids. In addition, the fraction of adsorbed chains can be much lower for the weak polyacids due to their ability to concentrate charge in few chains.

Systems comprised of polyelectrolytes and charged nanoparticles are of great technological interest, being common components in formulations among other uses. The colloidal stability of formulations is an important issue, and thus a large effort has been made to study the interactions of individual components in these systems. Here, the complexation and adsorption of an annealed (pH-dependent) polyelectrolyte to two spherical nanoparticles has been studied using coarse-grained Monte Carlo simulations. This has been done mainly by varying the solution pH and separation distance (concentration) between the nanoparticles. The polyelectrolyte charge distribution is seen to vary with nanoparticle separation distance and its ability to bridge both nanoparticles changes with pH. The flexible polyelectrolyte creates compact, multi-link bridges at short nanoparticle separation distances, and evolves to a stretched single-link bridge at longer distances, where a larger fraction of the polyelectrolyte wraps around the nanoparticles. The annealed polyelectrolyte is also compared with a quenched polyelectrolyte of similar fixed fractional charge. Here, it is found a difference in adsorption ability at low pH/ionization due to the ability of the annealed polyelectrolytes to concentrate charges in the vicinity of the nanoparticle. At intermediate polyelectrolyte charge fractions and with increasing nanoparticle separation distances, the annealed system is able to link nanoparticles at larger distances as compared to the quenched, in good agreement with experimental observations. The results in this work contribute to the understanding of the effect of annealed polyelectrolytes and pH variations in the phase behaviour of polyelectrolyte-nanoparticle systems, potentially aiding in the design and optimization of pH-responsive systems.

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In many experimental studies of polymer electrolyte membranes (PEMs), the electro‐osmotic drag coefficient is a property of primary interest. When protons are the only type of mobile ion present in the system, the coefficient is typically defined as the ratio between the molar water flux and the molar proton flux across the PEM. While most, if not all, experimental results suggest a value of order one, experimentalists have yet to arrive at a consensus regarding its exact value for a specific PEM at specific operating conditions. One reason for the variance in reported results could lie in the misinterpretation of the electro‐osmotic drag. This contribution uses physical models to clarify what a consistent definition and measurement of electro‐osmotic drag coefficients entails, thereby providing guidance for experimental studies of these membranes.