Effect of Counterion Size on Knotted Polyelectrolyte Conformations.

Using Langevin dynamics simulations and a coarse-grained primitive model of electrolytes, we show that the behavior of knotted circular strong polyelectrolytes (PEs) in diluted aqueous solution is largely affected by the diameter of the counterions (CIs), σCI. Indeed, we observe that both gyration radius and knot length vary nonmonotonically with σCI, with both small and bulky CIs favoring knot localization, while medium-sized ones promote delocalized knots. We also show that the conformational change from delocalized to tight knots occurs via the progressive coalescence of the knot's essential crossings. The emerging conformers correspond to the minima of the free energy landscape profiled as a function of the knot length or PE size. We demonstrate that different conformational states can coexist, the transition between them appearing first-order-like and controlled by the enthalpic and entropic trade-off of the amount of CIs condensed on the PE. Such balance can be further altered by varying CI concentrations, thus providing an additional and more convenient tuning parameter for the system properties. Our results lay the foundation for achieving broader and more precise external adjustability of knotted PE size and shape by choosing the nature of its CIs. Thus, they offer new intriguing possibilities for designing novel PE-based materials that are capable of responding to changes in ionic solution properties.

Interaction between surfaces decorated with like-charged pendants: Unravelling the interplay between energy and entropy leading to attraction.

HYPOTHESIS: The stronger motional coupling between monovalent counterions neutralizing homogeneously like-charged surfaces induced by an increase in charge density is known to foster inter-surface attraction. Compared to a uniformly distributed charge, point-like charges generate locally more intense fields, so that the correlation induced between counterions may be even stronger despite an identical total charge. It should thus be possible to induce surface attraction at lower charge densities than commonly expected. EXPERIMENTS: Monte Carlo simulations on primitive electrolyte models have been exploited to compute potential of mean force profiles and mobile ion densities for systems composed of two parallel surfaces bearing surface-tethered monovalent like-charged pendants as a function of the surface distance and pendant densities. FINDINGS: Surfaces bearing like-charged pendants are found to attract each other over a wide range of distances despite the presence of very low charge densities. Notwithstanding the attractive contribution to the inter-surface forces provided by electrostatic interactions, the entropic component of the system Helmholtz energy is found to play the key role in defining the overall magnitude. The latter finding appears justified by an increase in the relative delocalization of counterions upon decreasing the surface distance.

Inducing pH control over the critical micelle concentration of zwitterionic surfactants via polyacids adsorption: Effect of chain length and structure.

HYPOTHESIS: The critical concentration above which micelles form from zwitterionic surfactant solutions and their thermodynamic stability is affected by the interaction with weak Brønsted polyacid chains (An) via the formation of charged hydrogen bonds between the latter and anionic moieties. EXPERIMENTS: The interaction between zwitterionic micelles and polyacids capable of forming hydrogen bonds, and its dependence on the environmental pH and polymer structure, has been studied with constant-pH simulations and a restricted primitive model for all electrolytes. FINDINGS: At low pH, the formation of polyacid/micelle complexes is witnessed independently of the polymer size or structure, so that the concentration above which micelles form is substantially decreased compared to polyacid-free cases. Upon rising pH, polymer desorption takes place within a narrow range of pH values, its location markedly depending on the size and structure of polyacids, and on the relative disposition between headgroup charged moieties. Thus, the desorption onset for long linear polyacids (A60) interacting with sulphobetainic headgroups is roughly two pH units higher than for six decameric chains (6A10) adsorbed onto micelles bearing phosphorylcholinic headgroups. This effect, together with the preferential desorption of chain ends at intermediate pH, may be exploited for drug delivery purposes or building advanced metamaterials.

Tunable Knot Segregation in Copolyelectrolyte Rings Carrying a Neutral Segment.

We use Langevin dynamics simulations to study the knotting properties of copolyelectrolyte rings carrying neutral segments. We show that by solely tuning the relative length of the neutral and charged blocks, one can achieve different combinations of knot contour position and size. Strikingly, the latter is shown to vary nonmonotonically with the length of the neutral segment; at the same time, the knot switches from being pinned at the block's edge to becoming trapped inside it. Model calculations relate both effects to the competition between two adversarial mechanisms: the energy gain of localizing one or more of the knot's essential crossings on the neutral segment and the entropic cost of such localization. Tuning the length of the neutral segment sets the balance between the two mechanisms and hence the number of localized essential crossings, which in turn modulates the knot's size. This general principle ought to be useful in more complex systems, such as multiblock copolyelectrolytes, to achieve a more granular control of topological constraints.

Can oppositely charged polyelectrolyte stars form a gel? A simulational study.

We present a Langevin molecular dynamics study of an equimolar mixture of monodispersed oppositely charged di-block four-armed polyelectrolyte stars. We used an implicit solvent coarse-grained representation of the polyelectrolyte stars, and varied the length of the terminal charged blocks that reside on each arm. By varying the polymer concentration, we computed PV diagrams and determined the free-swelling equilibrium concentration with respect to a pure water reservoir as a function of the charged block length. We investigated various structural properties of the resulting equilibrium structures, like the number of ionic bonds, dangling arms, isolated stars, and cluster sizes. The ionic bonds featured a broad distribution of the number of arms involved and also displayed a distribution of net charges peaked around the neutral ionic bond. Our main result is that for charged block length equal to 4 and 5 ionized beads the resulting macro-aggregate spans the box and forms a network phase. Furthermore, we investigated the restructuring dynamics of ionic bonds; the results suggested both short bond lifetimes and a high frequency of ballistic association/dissociation events. Bonds result strong enough to yield a stable gel phase, but they are still weak enough to allow network restructuring under thermal fluctuations.

On the distribution of hydrophilic polyelectrolytes and their counterions around zwitterionic micelles: the possible impact on the charge density in solution.

Despite their charge neutrality, micelles composed of surfactants with zwitterionic headgroups selectively accumulate anions at their hydrophobic core/solution interphase due to electrostatic interactions if headgroup positive moieties are the innermost. This tendency may be markedly enhanced if polyions substitute simple ions. To investigate this possibility, solutions composed of zwitterionic micelles and hydrophilic polyanions have been investigated with Monte Carlo simulations representing the studied systems via primitive electrolyte models. Structural and energetic properties are obtained to highlight the impact of connecting simple ions into polyions on the interactions between electrolytes and micelles. Despite the latter, polyanions conserve their conformational properties. A marked increase in the concentration of charged species inside the micellar corona is, instead, found when polyions are present independently of their charge sign or the headgroup structure. Thus, polyelectrolytes act as "shuttle" for all charged species, with the potential of increasing reactions rates involving the latter due to mass effects. Besides, results for the polyions/micelles mixing free energy and Helmholtz energy profiles indicate that the critical micelle concentration is impacted minimally by hydrophilic polyelectrolytes, an outcome agreeing with experiments. This finding is entirely due to weak enthalpic effects while mixing hydrophilic polyions and micelles. A strong reduction in the screening of the micelle negative charge, acquired following the adsorption of anions in the corona and due to counterions layering just outside it (the so called "chameleon effect"), is forecasted when polyanions substitute monovalent anions.

Interface Counterion Localization Induces a Switch between Tight and Loose Configurations of Knotted Weak Polyacid Rings despite Intermonomer Coulomb Repulsions.

Stochastic simulations have been used to investigate the conformational behavior of knotted weak polyacid rings as a function of pH. Different from the commonly expected ionization-repulsion-expansion scheme upon increasing pH, theoretical results suggest a nonmonotonic behavior of the gyration radius Rg2. Polyelectrolyte recontraction at high ionization is induced by the weakening of Coulomb repulsion due to counterions (CIs) localizing at the interphase between the polymer and solvent, and the more marked it appears, the more complex is the knot topology. Compared with strong polyelectrolytic species of identical ionization, weak polyacids present tighter knots due to their ability to localize neutral monomers inside the tangled part. Increasing the solvent Bjerrum length enhances CIs localization, lowering the pH at which polyacids start decreasing their average size. A similar effect is also obtained by increasing the amount of "localizable" cations by adding salts.

Monte Carlo study of the effects of macroion charge distribution on the ionization and adsorption of weak polyelectrolytes and concurrent counterion release.

HYPOTHESIS: Adsorption of weak polyelectrolytes onto charged nanoparticles, and concurrent effects such as spatial partitioning of ions may be influenced by details of the polyelectrolyte structure (linear or star-like) and size, by the mobility of the nanoparticle surface charge, or the valence of the nanoparticle counterions. EXPERIMENTS: Ionization and complexation of weak polyelectrolytes on spherical macroions with monovalent and divalent countrions has been studied with constant-pH Monte Carlo titrations and primitive electrolyte models for linear and star-like polymers capable, also, of forming charged hydrogen bonds. Nanoparticles surface charge has been represented either as a single colloid-centered total charge (CCTC) or as surface-tethered mobile monovalent spherical charges (SMMSC). FINDINGS: Differences in the average number of adsorbed polyelectrolyte arms and their average charge, and in the relative amount of macroion counterions (m-CI's) released upon polymer adsorption are found between CCTC and SMMSC nanoparticles. The amount of the counterions released also depends on the polymer structure. As CCTC adsorbs a lower number of star-like species arms, the degree of condensation of polymer counterions (p-CI's) onto the polyelectrolyte is also substantially higher for the CCTC colloid, with a concurrent decrease of the osmotic coefficient values.

Impact of Charge Correlation, Chain Rigidity, and Chemical Specific Interactions on the Behavior of Weak Polyelectrolytes in Solution.

In this work, we performed titration simulations of weak linear polyelectrolytes via the Monte Carlo method and the constant pH ensemble aiming to understand how polyelectrolyte concentration, chain rigidity, and the formation of intra- and inter-chain charged hydrogen bonds (c-H-bonds) impact on ionization and conformations of polyacidic species, counterions (CIs) distribution, and system Helmholtz energy. Increasing polyelectrolyte concentration resulted in enhanced acidity for all cases investigated due to the increased screening of chain charges by CIs and, when possible, the formation of interchain c-H-bonds. Our simulations also evidenced that polyelectrolytes able to form c-H-bonds can populate simultaneously two conformational states (aggregated and unfolded) in a range of pH, the transition between the two appearing first order-like. To better understand how properties of two polyelectrolytic chains are modified by their relative distance, we performed window sampling (WS) simulations, which highlighted nontrivial features in the ionization and conformational behaviors. As byproducts of WS simulations, we obtained also the potential of mean force between two chains; from this, it emerges that the reversible work needed to reach a specific interchain distance does not always increase with the pH, especially for c-H-bonds forming semirigid chains brought at short distances.

Out of Equilibrium Self-Assembly of Janus Nanoparticles: Steering It from Disordered Amorphous to 2D Patterned Aggregates.

Solvent evaporation driven self-assembly of Janus nanoparticles (J-NPs) has been simulated employing lattice-gas models to investigate the possible emergence of new superlattices. Depending on the chemical nature of NP faces (hence solvophilicity and relative interaction strength), zebra-like or check-like patterns and micellar agglomerates can be obtained. Vesicle-like aggregates can be produced by micelle-based corrals during heterogeneous evaporation. Patterns formed during aggregation appear to be robust against changes in evaporation modality (i.e., spinodal or heterogeneous) or interaction strengths, and they are due to a strictly nanoscopic orientation of single J-NPs in all cases. Due to the latter feature, the aggregate size growth law N(t) ∝ ta has its exponent a markedly depending on the chemical nature of the J-NPs involved in spite of the unvaried growth mechanism. We interpret such a finding as connected to the increasingly stricter orientation pre-requirements for successful (binding) NP landing upon going from isotropic (a ≃ 0.50), to "zebra" (a ≃ 0.38), to "check" (a ≃ 0.23), and finally to "micelle" (a = 0.15-0.17) pattern forming NPs.