Association in electrolyte solutions: Rodlike polyelectrolytes in multivalent salts

A route to self-assemble suspended DNA nano-complexes

Highly charged polyelectrolytes can self-assemble in presence of condensing agents such as multivalent cations, amphiphilic molecules or proteins of opposite charge. Aside precipitation, the formation of soluble micro- and nano-particles has been reported in multiple systems. However a precise control of experimental conditions needed to achieve the desired structures has been so far hampered by the extreme sensitivity of the samples to formulation pathways. Herein we combine experiments and molecular modelling to investigate the detailed microscopic dynamics and the structure of self-assembled hexagonal bundles made of short dsDNA fragments complexed with small basic proteins. We suggest that inhomogeneous mixing conditions are required to form and stabilize charged self-assembled nano-aggregates in large excess of DNA. Our results should help re-interpreting puzzling behaviors reported for a large class of strongly charged polyelectrolyte systems.

Load-collapse-release cascades of amphiphilic guest molecules in charged dendronized polymers through spatial separation of noncovalent forces

The ability to pack guest molecules into charged dendronized polymers (denpols) and the possibility to release these guest molecules from subsequently densely aggregated denpols in a load-collapse-release cascade is described. Charged denpols, which constitute molecular objects with a persistent, well-defined envelope and interior, are capable of incorporating large amounts of amphiphilic guest molecules. Simultaneously, multivalent ions can coordinate to the surfaces of charged denpols, leading to counterion-induced aggregation of the already guest-loaded host structures. Thus, although the local guest concentration in denpol-based molecular transport might already be initially high due to the dense guest packing inside the dendritic denpol scaffolding, the "local" guest concentration can nonetheless be further increased by packing (through aggregation) of the host-guest complexes themselves. Subsequent release of guest compounds from densely aggregated dendronized polymers is then possible (e.g., through increasing the solution concentration of imidazolium-based ions). Augmented with this release possibility, the concept of twofold packing of guests, firstly through hosting itself and secondly through aggregation of the hosts, gives rise to a load-collapse-release cascade that strikingly displays the high potential of dendronized macromolecules for future molecular transport applications.

Correlated electrolyte solutions and ion-induced attractions between nanoparticles

Simple expressions are presented for the equations of state of a correlated electrolyte solution, calculated straightforwardly within a full nonlinear Debye-Hückel approach in terms of the mean potential at contact, that predict quantitatively different phase behavior from the popular Debye-Hückel limiting law. The theory includes pair correlations accurately and may provide a basis for a quantitative theoretical study of organic or multivalent ionic solutions. As an example, cohesive effects are addressed of strong couplings between ions on the effective interactions between nanoparticles.

Charged particles on surfaces: coexistence of dilute phases and periodic structures at interfaces

We consider a mixture of two immiscible oppositely charged molecules strongly adsorbed to an interface, with a neutral nonselective molecular background. We determine the coexistence between a high density ionic periodic phase and a dilute isotropic ionic phase. We use a strong segregation approach for the periodic phase and determine the one-loop free energy for the dilute phase. Lamellar and hexagonal patterns are calculated for different charge stoichiometries of the mixture. Molecular dynamics simulations exhibit the predicted phase behavior. The periodic length scale of the solid phase is found to scale as epsilon/(lB psi3/2), where psi is the effective charge density, lB is the Bjerrum length, and epsilon is the cohesive energy.

Monte Carlo simulations of a charged dendrimer with explicit counterions and salt ions

Static properties of a dendrimer with generation g = 5 with positively charged terminal groups in an athermal solvent are studied by lattice Monte Carlo simulations using the cooperative motion algorithm as the tossing scheme. The calculations are performed both for a salt-free system with neutralizing counterions and for a small amount of added monovalent and divalent salt. The full Coulomb potential and the excluded volume interactions between ions and beads are taken explicitly into account with the reduced temperature tau, the number of salt cations (anions) n(s), and salt valence z(s) as the simulation parameters. The bahaviour of the systems is analyzed by the mean effective charge per end-bead <Q>, Coulomb mean energy <E>, mean-square radius of gyration <R(g)(2)>, pair correlation functions g(alphabeta), and charge density rho(ch). The simulations show that for n(s)> or = 0 and decreasing tau: (a) there is encapsulation in the dendrimer and condensation onto the terminal groups of anions accompanied by a monotonic decrease in <Q> and <E> and by subsequent swelling and shrinking of the molecule; (b) encapsulation, condensation and shrinking are the most significant and swelling weaker for |z(s)| = 2; (c) penetration of salt cations into the dendrimer is minor when compared to that of anions; (d) rho(ch) is reduced and becomes negative close to the center of mass of the dendrimer and on its periphery; (e) for the considered n(s) > 0, unlike divalent salt ions the monovalent ones cause slight effects when compared to the salt-free case.

Monte Carlo simulations of a polyelectrolyte chain with added salt: effect of temperature and salt valence

Using the cooperative motion algorithm, the effect of salt valence z(s) and of the reduced temperature T* on a single polyelectrolyte chain as well as on counterions and salt ions themselves is studied. The calculations show that both parameters strongly influence the polymer, causing it to undergo conformational changes. For a given number of the added salt cations (anions) n(s) and temperature T*, the chain takes more and more compact forms as z(s) increases (z(s) > 0). For fixed z(s), in turn, the polymer size reduces sharply as T* drops down from intermediate to low. For high T* configurational the entropy dominates the chain statistics and the mean-square radius of gyration (s2)1/2(T*,n(s),z(s)) approaches its athermal value. The low-temperature polymer collapse is also accompanied by a drop in the effective mean charge per monomer q*(T*,n(s),z(s)) (condensation of ions onto the chain) and the total inner energy e*(T*,n(s),z(s)). Furthermore, the local structure of the system is analyzed by means of pair-correlation functions g(ab)(r,T*,n(s),z(s)). At lower T* they possess sharp local maxima at small interparticle distances r that disappear as T* grows. The former observation indicates that at lower T* the ions tend to group themselves close to each other. In particular, it is concluded that the condensation is dominated by the multivalent salt ions carrying charges of opposite sign to that of monomers.

Polynucleotide adsorption to negatively charged surfaces in divalent salt solutions

Polynucleotide adsorption to negatively charged surfaces via divalent ions is extensively used in the study of biological systems. We analyze here the adsorption mechanism via a self-consistent mean-field model that includes the pH effect on the surface-charge density and the interactions between divalent ions and surface groups. The adsorption is driven by the cooperative effect of divalent metal ion condensation along polynucleotides and their reaction with the surface groups. Although the apparent reaction constants are enhanced by the presence of polynucleotides, the difference between reaction constants of different divalent ions at the ideal condition explains why not all divalent cations mediate DNA adsorption onto anionic surfaces. Calculated divalent salt concentration and pH value variations on polynucleotide adsorption are consistent with atomic force microscope results. Here we use long-period x-ray standing waves to study the adsorption of mercurated-polyuridylic acid in a ZnCl2 aqueous solution onto a negatively charged hydroxyl-terminated silica surface. These in situ x-ray measurements, which simultaneously reveal the Hg and Zn distribution profiles along the surface normal direction, are in good agreement with our model. The model also provides the effects of polyelectrolyte line-charge density and monovalent salt on adsorption.

Computer simulations of a polyelectrolyte chain with a mixture of multivalent salts

Diluted solutions of a single, electrically charged polymer chain, its monovalent counterions and two kinds of multivalent salts are investigated. In particular, the influence of the salt concentrations and valences on the mean effective charge per monomer, total inner energy, radius of gyration and various pair correlation functions of the monomers and free ions are analysed. The calculations show that it is the four-valent and three-valent ions, oppositely charged to the monomers, that mostly occupy the space around the polymer and tremendously increase their number there compared to that in the bulk. Furthermore, reductions in the polymer size and effective charge per monomer appear, especially for increasing amount of the four-valent salt. Thus, there is an evidence for polymer conformational changes associated with the ion condensation onto the chain.

Lattice Monte Carlo simulations of a charged polymer chain: Effect of valence and concentration of the added salt

The configurational properties of a single polyelectrolyte chain accompanied by counterions and added salt are simulated using the cooperative motion algorithm on the face-centered cubic lattice. In particular, a greater emphasis is put on the effect of valence z(s) and concentration of the added positive (negative) salt ions n(s) on the polymer behavior. This is achieved by inspecting two families of systems with widely varying numbers n(s) of monovalent (z(s)=1) or multivalent (z(s)=4) salt ions at two fixed reduced temperatures T*=0.5, 1. The calculations indicate that especially at the lower temperature the addition of some amount of multivalent salt has a tremendous impact on chain conformations compared to the situation with monovalent salt. Even for relatively low concentrations of the former, the mean radius of gyration <s2>(1/2) and the mean end-to-end distance <R2>(1/2) decrease sharply, i.e., the polymer exists in strongly collapsed forms. This reduction of polymer size is also accompanied by a drop in the system inner energy e* and the effective mean charge per monomer q*. The analysis of various pair-correlation functions g(ab)(r) indicates that the latter effect-caused by condensation of ions onto the chain-is dominated by the multivalent ones. Furthermore, it is found that for z(s)=4, the uncondensed salt ions tend to group themselves into small clusters.

Molecular multivalent electrolytes: microstructure and screening lengths

We study small rod-like molecular electrolytes solutions with their corresponding atomic counterions. The asymptotic length scales (decay length and wavelength) of the structural correlations are analyzed using the formalism of the dressed interaction site theory (DIST). The correlation functions are determined using the reference interaction site model equation complemented with a mixed approach in which the hypernetted-chain closure is used for the repulsive interactions, and the mean spherical approximation is used for the attractive interactions. The results from this scheme are in good agreement with the Monte Carlo computer simulations reported here. The asymptotic properties of the correlation functions of this molecular system are compared against those corresponding to two related simple (atomic) electrolyte models. The main conclusion is that the molecular structure of the ions lowers by two orders of magnitude the concentration at which the transition from monotonic to oscillatory decay occurs.

Effect of mono- and multivalent salts on angle-dependent attractions between charged rods

Using molecular dynamics simulations we examine the effective interactions between two like-charged rods as a function of angle and separation. In particular, we determine how the competing electrostatic repulsions and multivalent-ion-induced attractions depend upon concentrations of simple and multivalent salts. We find that with increasing multivalent salt, the stable configuration of two rods evolves from isolated rods to aggregated perpendicular rods to aggregated parallel rods; at sufficiently high concentration, additional multivalent salt reduces the attraction. Monovalent salt enhances the attraction near the onset of aggregation and reduces it at a higher concentration of multivalent salt.

Phase diagram of charged dumbbells: a random phase approximation approach

The phase diagram of the charged hard dumbbell system (hard spheres of opposite unit charge fixed at contact) is obtained with the use of the random phase approximation (RPA). The effect of the impenetrability of charged spheres on charge-charge fluctuations is described by introduction of a modified electrostatic potential. The correlations of ions in a pair are included via a correlation function in the RPA. The coexistence curve is in good agreement with Monte Carlo simulations. The relevance of the theory to the restricted primitive model is discussed.

Thermoreversible crosslinking of polyelectrolyte chains

Thermoreversible crosslinking of polyelectrolyte chains via short-range attractions such as hydrogen bonding induced by uncharged or charged particles is studied within the Flory model of ideal association. Electrostatic interactions between the charges at different linking fractions are taken into account by using a generalized random phase approximation approach which includes the network connectivity. We find that at certain concentration of linking agents an infinitely large polymer network is formed. We calculate the structural gelation lines for linkers of different charges and functionalities.

Precipitation of oppositely charged polyelectrolytes in salt solutions

We study phase separation in symmetric solutions of weakly charged flexible chains of opposite sign. Precipitation is caused by effective attractions due to charge fluctuations and by short-range attractions between monomers. The contribution from charge fluctuations is computed within the random phase approximation (RPA), which takes into account the connectivity of charges in the polyions. The impenetrability of the ions is accounted for by using a modified Coulomb potential in the RPA. In good solvent conditions the precipitate monotonically swells and eventually dissolves upon addition of salt. However, near the theta-solvent condition, but still in the good solvent, the precipitate can be stable at any salt concentration. Moreover, the density of the precipitate after initial decrease can increase with addition of salt. This effect is a result of redistribution of salt between the precipitate and the supernatant, which is due to an interplay of electrostatic and hardcore interactions. For not too weakly charged polyions the precipitate properties become strongly dependent on temperature even in good solvent conditions.