Absorbed weak polyelectrolytes: Impact of confinement,topology, and chemically specific interactions on ionization,conformation free energy,counterion condensation,and absorption equilibrium

Absorption of weak polyelectrolytes impacts on properties such as ionization, conformations, and counterion (CI) condensation that are important in several areas of applied and fundamental science. We used a weak polyelectrolyte model and Monte Carlo simulations to investigate how the mentioned properties depend on pH or the size of a spherical cavity (SC) permeable to CIs but not to polyelectrolytes; the latter have either linear or starlike topologies and may be allowed to form charged hydrogen bonds (c? H‐bonds) between ionized and neutral monomers. Average ionization decreases upon increasing the number of arms at a constant number of monomers; it instead increases with the arm length in large SC due to CI screening. The way SC size, c? H‐bonds, and pH values interrelate to define ionization is instead more complicate due to arm pairing or clustering when c? H‐bonds are possible. These induce oscillations in the arm local ionization and impact on both monomer and CI distributions in the complete simulation cell in a way that also depends on polymer topology. The impact of ionization on the confinement free energy is also estimated; this highlighted that c? H‐bonding may enhance absorption compared with neutral chains. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 491–510     

Modulation of ionization and structural properties of weak polyelectrolytes due to 1D, 2D,and 3D confinement

What is the impact of reducing the space available to molecules onto their properties is a fundamental question for capillary systems, molecular biology and transport, protein and material sciences. Possibly influenced by space restriction, ionization degree has rarely been studied for confined polyelectrolytes; Monte Carlo titrations and coarse‐grained models are thus used to investigate structural and ionization changes induced on a single polyelectrolyte chain by confinement into slit (1D), cylindrical (2D), or spherical (3D) cavities. Four polyelectrolyte models differing in chain stiffness and the possible formation of charged hydrogen bonds (c? H? bonds) are studied. Low pH effective ionization constants (pK_a ) of confined chains are lower than for the free species if c? H? bonds can be formed. This is especially evident for 3D‐confined stiff chains, a finding rationalized by the impact of global compression onto chain conformations. If no c? H? bonds are allowed, chain ionization is largely unaffected by 1D or 2D confinement, while it is depressed by 3D. Chain confinement Helmholtz energy (ΔA _conf) was computed as a function of both pH and confining width (W) to gauge the impact of ionization‐induced stiffening onto ΔA _conf versus W behavior, the partition coefficient governing absorption, and the average number of c? H? bond formed. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 1088–1102     

Chain stiffness, salt valency, and concentration influences on titration curves of polyelectrolytes: Monte Carlo simulations

Monte Carlo simulations have been used to study two different models of a weak linear polyelectrolyte surrounded by explicit counterions and salt particles: (i) a rigid rod and (ii) a flexible chain. We focused on the influence of the pH, chain stiffness, salt concentration, and valency on the polyelectrolyte titration process and conformational properties. It is shown that chain acid-base properties and conformational properties are strongly modified when multivalent salt concentration variation ranges below the charge equivalence. Increasing chain stiffness allows to minimize intramolecular electrostatic monomer interactions hence improving the deprotonation process. The presence of di and trivalent salt cations clearly promotes the chain degree of ionization but has only a limited effect at very low salt concentration ranges. Moreover, folded structures of fully charged chains are only observed when multivalent salt at a concentration equal or above charge equivalence is considered. Long-range electrostatic potential is found to influence the distribution of charges along and around the polyelectrolyte backbones hence resulting in a higher degree of ionization and a lower attraction of counterions and salt particles at the chain extremities.     

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment

Monte Carlo simulations, experimental titrations and fluorescence correlation spectroscopy experiments were used to investigate the conformational and electrical properties of polyacrylic acids (PAA). On the one hand, titration curves were calculated to get an insight into the role of pH on the degree of ionization and conformation of PAA chains. On the other hand, experimental potentiometric titrations of PAA were also achieved for different PAA molecular weights and compared to the calculated titration curves obtained by Monte Carlo coarse grained simulations. It was found that for a large range at intermediate PAA ionizations, a good correlation is obtained between experimental and simulations data thanks to the prominence of electrostatic interactions in this domain. The effect of ionic concentration and PAA molecular weight on the titration curves was also investigated. In order to get a better understanding of PAA conformational behavior, we also investigated PAA diffusion properties in aqueous solutions as a function of pH and ionic strength by fluorescence correlation spectroscopy (FCS), thanks to its high sensitivity to measure diffusion coefficients of tracer solutes. Good qualitative agreements were observed between experimental diffusivities and polymer properties calculated from MC simulations. It was shown that the high molecular weight PAA chains display more significant changes in diffusivity in agreement with the ionization degrees and conformational changes observed in the simulations.     

Self‐sustained entropy‐driven flow in nano‐confined polymer melts

We present a Monte Carlo simulation study of the Brownian motion of polymer chains in a melt confined in a periodically asymmetric channel of nanometric dimensions. We assume no friction between the chains and the channel. A detailed analysis of the conformations of the chains reveals the presence of a favorable entropy gradient along the easy flow direction. For high molecular weight chains, this gradient is seen to drive a self‐sustained polymer flow with Peclet numbers as high as 0.9, which makes our observation experimentally accessible. Much weaker efficiences are observed at low molecular weights. We show that the unexpected directed Brownian motion of polymers in confined geometries is of significant importance in the design and stabilization of platelet nanocomposites which typically age over time under quiescent conditions. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 869–875     

Loose complexation of weakly charged microemulsion droplets and a polyelectrolyte

The effect of polyelectrolyte addition on the properties of an oil-in-water (O/W) microemulsion of weakly charged spherical micelles is studied. The 81 A radius O/W droplets in this system can be charged by the partial substitution of the nonionic surfactant by a cationic surfactant. The effect of the addition of poly(acrylic acid) (PAA), which is a charged pH-dependent polyelectrolyte, on the interactions between charged or noncharged droplets has been investigated using SANS. We have characterized the phase behavior of this pH-smart system as a function of the microemulsion and the polyelectrolyte concentration and the number of charges per droplet at three pH values: pH = 2, 4.5, and 12. In particular, an associative phase separation due to the bridging of the droplets by the neutral PAA chains through H-bonds is observed with extremely low PAA addition at low pH. At the opposite, an addition of PAA at pH = 4.5 generates a strong repulsive contribution between neutral droplets. Electrostatic bonds between charged droplets and PAA, controlled by the number of charges per droplet, are responsible for a pH drift and then for an associative phase separation similar to that observed at low pH. Finally, at high pH, the creation of electrostatic bonds between fully charged PAA and charged droplets liberates sufficiently counterions in solution at high droplet charge density to screen the electrostatic interactions and to allow an associative phase separation.     

Simulations and scattering functions of polyelectrolyte–macroion complexes

Using Monte Carlo simulations of complex formation between a polyelectrolyte chain and an oppositely charged macroion, we calculated the scattering function of the polyelectrolyte chain. We investigated the case of the isolated polyelectrolyte chain and studied the effect and influence of key parameters such as the ionic concentration of the solution, polyelectrolyte length and intrinsic rigidity on the scattering function. Then, we focused on the polyelectrolyte–macroion complex by calculating the structure factor S(q) of the adsorbed polyelectrolyte chain. Typical conformations ranging from coils, extended chains to solenoids are revealed and the corresponding S(q) analysed. The effects of ionic concentration, chain length and intrinsic rigidity and relative size ratio between the polyelectrolyte and the macroion are investigated. Important effects on the structure factor of the adsorbed polyelectrolyte are observed when the macroion is partially or totally wrapped by the polyelectrolyte. Distance correlations between the polyelectrolyte monomer positions at the surface of the macroion induce the formation of peaks in the fractal regime of S(q). For semiflexible chains, when solenoid conformations are observed, the position of the peaks in the fractal regime corresponds directly to the separation distance between the turns. The formation of a protruding tail in solution is also observed through the formation in the fractal regime of a linear domain.This revised version was published online in November 2004 with corrections to the authors.     

Molecular dynamics simulations of end‐grafted polymers with charged side chains

We report molecular dynamics simulations on bottle‐brush polyelectrolytes end‐grafted to a planar surface. For each bottle‐brush polyelectrolyte, flexible charged side chains are anchored to one neutral main chain. The effects of the counterion valence and the grafting density on the density profiles and the structural characteristics of the brush were studied in this work. It is found that the electrostatic repulsion between charged monomers in the side chains leads an extended conformation of the brush in a solution containing monovalent counterions, while strong electrostatic binding of multivalent counterions to the side chains has a significant contribution to the collapse of the brush. For the trivalent case, the distribution of end monomers in the main chains becomes broader upon decreasing the grafting density, as compared with the monovalent case. However, the position of the distribution for the monovalent case is relatively insensitive to the change of the grafting density. Additionally, with increased counterion valence, enhanced electrostatic correlation between counterions and charged side chains also weakens the diffusive ability of counterions. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Surface forces mediated by charged polymers: effects of intrinsic chain stiffness

The strength and range of surface forces in a system consisting of charged polymers with variable intramolecular stiffness confined between two charged planar surfaces have been investigated by Monte Carlo simulations. The negatively charged surfaces are neutralized by polymers carrying charges of opposite sign. Introducing the intermediate intrinsic stiffness of the chains gives rise to a weaker, but more long-ranged attraction between the surfaces. In the limit of infinitely stiff chains, this bridging attraction is lost, but it is replaced by a strong correlation attraction at short distances. Comparisons with predictions by a correlation-corrected polyelectrolyte Poisson-Boltzmann theory are made. The theory predicts surface attractions that are somewhat too weak, but all qualitative features are correctly reproduced. Given the crudeness of the model, the quantitative agreement is satisfactory.     

Macromolecular Crowding and the Sizes of Neutral Flexible Polymer Chains: The Role of Colloids Sizes and Concentrations

In the present work, we revisit the effect of macromolecular crowding on the sizes of flexible neutral polymer chains. Motivated by recent experimental measurements on crowding effects on neutral flexible polymers chains, we perform Monte Carlo simulations on a model system consisting of hard spheres (HS) and a neutral flexible polymer chain. We find that, depending on the ratio of the sizes of the colloidal particles to the sizes of the polymer chain, and thus, on the extent of the colloid partitioning among the chain segments and the solution, the flexible polymeric coil may be either continuously compressed, or initially compressed followed by a reswelling at high enough colloid concentration. The chain behavior is thus nonmonotonic, a point which, apart from the work of Khalatur et al., has not so far been stressed in simulations of flexible polymer chains under crowding conditions. A thermodynamic model for the polymer–colloid interactions based on the Gibbs–Duhem equation and on a “Flory‐type” argument is also presented, emphasizing the indirect influence of macromolecular crowding on the monomers chemical potential. We show explicitly that under crowding conditions, the colloids are driven into the most compact coil states. These analytical results are compared with the results of the potential of mean force between the chain center of mass and the colloids obtained from the Monte Carlo simulations, and a reasonable agreement is found. The implications of the aforementioned results are further discussed in the context of biological systems, specially those for which macromolecular crowding is supposed to play the important role of including preferentially other (charged) macromolecules into the colloid‐compressed polymer phase.

     

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.     

Phase equilibrium and charge fractionation in polyelectrolyte solutions

A new type of phase separation in the polyelectrolyte solutions consisting of several types of charged macromolecules differing in their degree of ionization is presented. Via a general thermodynamic consideration we show that even a small difference in the degree of ionization of otherwise equivalent high‐molecular components results in their spatial separation occurring upon decreasing the temperature much earlier than precipitation of any of the pure components from the solution. Some implications of charge fractionation are discussed, including the separation of DNA (or RNA) strands interacting with different proteins and the appearance of heterogeneities in polyelectrolyte solutions of partially charged hydrophobic chains with polydispersed charge distributions such as sodium polystyrene sulfonate. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3003–3009, 2007     

Self-recognition and aggregation between diblock (charged/neutral) polyelectrolytes by Monte Carlo simulations

The self-recognition between oppositely charged polyelectrolyte-neutral diblock copolymers and aggregate formation is investigated by Monte Carlo simulations. Both matched lengths and charge numbers are critical conditions for self-recognition. The optimum self-recognition occurs between oppositely charged chains with matched charged block lengths and charge numbers. The size of aggregates increases, as the total length and the ratio of charged to neutral beads become larger. Polyelectrolyte networks were observed in some cases containing unmatched chains. The molecular configurations of the entire chains and of the charged and neutral blocks as well as the radial distribution functions of the charged beads are also investigated.     

Computer Study of Stimuli-Responsive Polyelectrolyte Micelles in Aqueous Media. Comparison of Monte Carlo and Self-Consistent Field Approaches

The behavior of polyelectrolyte micelles with kinetically frozen hydrophobic cores in aqueous solutions was studied by Monte Carlo (MC) simulations and self-consistent field (SCF) calculations. Some results have already been published. The structure of water-soluble shells formed by weak polyelectrolytes, both pure and containing a low fraction of strongly hydrophobic units arranged either in a short sequence or distributed uniformly in the shell-forming chains was studied in detail. In the case of sequenced system, the analysis of concentration profiles of individual species reveals strong segregation and important self-organization of hydrophobic units in the shell. A comparison and critical analysis of results of MC and SCF methods is presented.     

DNA and surfactants in bulk and at interfaces

Recent investigations of the DNA interactions with cationic surfactants and catanionic mixtures are reviewed. Several techniques have been used such as fluorescence microscopy, dynamic light scattering, electron microscopy, and Monte Carlo simulations.

The conformational behaviour of large DNA molecules in the presence of cationic surfactant was followed by fluorescence microscopy and also by dynamic light scattering. These techniques were in good agreement and it was possible to observe a discrete transition from extended coils to collapsed globules and their coexistence for intermediate amphiphile concentrations. The dependence on the surfactant alkyl chain was also monitored by fluorescence microscopy and, as expected, lower concentrations of the more hydrophobic surfactant were required to induce DNA compaction, although an excess of positive charges was still required.

Monte Carlo simulations on the compaction of a medium size polyanion with shorter polycations were performed. The polyanion chain suffers a sudden collapse as a function of the concentration of condensing agent, and of the number of charges on the polycation molecules. Further increase in the concentration increases the degree of compaction. The compaction was found to be associated with the polycations promoting bridging between different sites of the polyanion. When the total charge of the polycations was lower than that of the polyanion, a significant translational motion of the compacting agent along the polyanion was observed, producing only a small-degree of intrachain segregation, which can explain the excess of positive charges necessary to compact DNA.

Dissociation of the DNA–cationic surfactant complexes and a concomitant release of DNA was achieved by addition of anionic surfactants. The unfolding of DNA molecules, previously compacted with cationic surfactant, was shown to be strongly dependent on the anionic surfactant chain length; lower amounts of a longer chain surfactant were needed to release DNA into solution. On the other hand, no dependence on the hydrophobicity of the compacting agent was observed. The structures of the aggregates formed by the two surfactants, after the interaction with DNA, were imaged by cryogenic transmission electron microscopy. It is possible to predict the structure of the aggregates formed by the surfactants, like vesicles, from the phase behaviour of the mixed surfactant systems.

Studies on the interactions between DNA and catanionic mixtures were also performed. It was observed that DNA does not interact with negatively charged vesicles, even though they carry positive amphiphiles; however, in the presence of positively charged vesicles, DNA molecules compact and adsorb on their surface.

Finally Monte Carlo simulations were performed on the adsorption of a polyelectrolyte on catanionic surfaces. It was observed that the mobile charges in the surface react to the presence of the polyelectrolyte enabling a strong degree of adsorption even though the membrane was globally neutral. Our observations indicate that the adsorption behaviour of the polyelectrolyte is influenced by the response given by the membrane to its presence and that the number of adsorbed beads increases drastically with the increase of flexibility of the polymer. Calculations involving polymers with three different intrinsic stiffnesses showed that the variation is non-monotonic. It was observed also that a smaller polyanion typically adsorbs more completely than the larger one, which indicates that the polarisation of the membrane becomes less facilitated as the degree of disruption increases.     

Electrostatic self-assembly of neutral and polyelectrolyte block copolymers and oppositely charged surfactant

We investigated the phase behavior and the microscopic structure of the colloidal complexes constituted from neutral/polyelectrolyte diblock copolymers and oppositely charged surfactant by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The neutral block is poly(N-isopropylacrylamide) (PNIPAM), and the polyelectrolyte block is negatively charged poly(acrylic acid) (PAA). In aqueous solution with neutral pH, PAA behaves as a weak polyelectrolyte, whereas PNIPAM is neutral and in good-solvent condition at ambient temperature, but in poor-solvent condition above approximately 32 degrees C. This block copolymer, PNIPAM-b-PAA with a narrow polydispersity, is studied in aqueous solution with an anionic surfactant, dodecyltrimethylammonium bromide (DTAB). For a low surfactant-to-polymer charge ratio Z lower than the critical value ZC, the colloidal complexes are single DTAB micelles dressed by a few PNIPAM-b-PAA. Above ZC, the colloidal complexes form a core-shell microstructure. The core of the complex consists of densely packed DTA+ micelles, most likely connected between them by PAA blocks. The intermicellar distance of the DTA+ micelles is approximately 39 A, which is independent of the charge ratio Z as well as the temperature. The corona of the complex is constituted from the thermosensitive PNIPAM. At lower temperature the macroscopic phase separation is hindered by the swollen PNIPAM chains. Above the critical temperature TC, the PNIPAM corona collapses leading to hydrophobic aggregates of the colloidal complexes.     

Static field ionization of the spherically confined hydrogen atom

The ionization of the hydrogen atom confined in a spherical potential well and subjected to a static electric field is studied, using the diffusion Monte Carlo (DMC) method. Atomic ionization within a potential well is found to be a stationary, gradual, and reversible process. The value of the electric field at the onset of ionization is of the order of 0.1 atomic units, and depends on the symmetry of the atomic wave function and on the confinement dimension. By decreasing the confinement sphere, the difference between the bound and ionized states disappears, showing that strict confinement leads to pressure ionization of the atom. The off-center case is studied characterizing the potential energy surface (PES), and the transition between field-induced and pressure-induced ionization is confirmed. Except for very weak fields, the minimum of the PES is reached when the proton is in contact with the boundary of the well.     

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.