The role of counterions on the elasticity of highly charged lamellar phases: a small-angle x-ray and neutron-scattering determination

The structure and fluctuations of the swollen L(alpha) lamellar phase of highly charged surfactant didodecyldimethylammonium halide fluid bilayers (DDA+X-) are studied using high-resolution small-angle x-ray scattering and medium-resolution, high-contrast small-angle neutron-scattering. The Caille parameter eta, as a function of the swelling (L(alpha) periodicity d), was determined from the full q-range fits of the measured scattering profiles for three different counterions (X- = Cl-, Br-, and NO3-). This parameter quantifies the amplitude of the membrane fluctuations within the Landau-de Gennes smectic-A linear elasticity theory. The different anions used gave strong specific effects at the maximum swelling of the L(alpha) phase, while at lower swellings a two-phase coexistence of swollen and collapsed lamellae (d approximately 30 and approximately 80 angstroms) was observed for bromide and nitrate ions. Over the intermediate dilution range for all three counterions, a single L(alpha) phase can be continuously swollen with pure water which is governed by an equation of state (i.e., osmotic pressure versus period) and thermally excited fluctuation amplitudes that can be well described by the same Poisson-Boltzmann calculation. The membranes were found to be slightly stiffer than predicted by purely electrostatic repulsions, and this is tentatively attributed to an extra bending rigidity contribution from the surfactant chains.     

Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)].     

Aqueous suspensions of natural swelling clay minerals. 1. Structure and electrostatic interactions

In this article, we present a general overview of the organization of colloidal charged clay particles in aqueous suspension by studying different natural samples with different structural charges and charge locations. Small-angle X-ray scattering experiments (SAXS) are first used to derive swelling laws that demonstrate the almost perfect exfoliation of clay sheets in suspension. Using a simple approach based on geometrical constraints, we show that these swelling laws can be fully modeled on the basis of morphological parameters only. The validity of this approach was further extended to other clay data from the literature, in particular, synthetic Laponite. For all of the investigated samples, experimental osmotic pressures can be properly described by a Poisson-Boltzmann approach for ionic strength up to 10(-3) M, which reveals that these systems are dominated by repulsive electrostatic interactions. However, a detailed analysis of the Poisson-Boltzmann treatment shows differences in the repulsive potential strength that are not directly linked to the structural charge of the minerals but rather to the charge location in the structure for tetrahedrally charged clays (beidellite and nontronites) undergoing stronger electrostatic repulsions than octahedrally charged samples (montmorillonites, laponite). Only minerals subjected to the strongest electrostatic repulsions present a true isotropic to nematic phase transition in their phase diagrams. The influence of ionic repulsions on the local order of clay platelets was then analyzed through a detailed investigation of the structure factors of the various clay samples. It appears that stronger electrostatic repulsions improve the liquidlike positional local order.     

Optimal linearized Poisson-Boltzmann theory applied to the simulation of flexible polyelectrolytes in solution

Optimal linearized Poisson-Boltzmann (OLPB) theory is applied to the simulation of flexible polyelectrolytes in solution. As previously demonstrated in the contexts of the cell model [H. H. von Grunberg, R. van Roij, and G. Klein, Europhys. Lett. 55, 580 (2001)] and a particle-based model [B. Beresfordsmith, D. Y. C. Chan, and D. J. Mitchell, J. Colloid Interface Sci. 105, 216 (1985)] of charged colloids, OLPB theory is applicable to thermodynamic states at which conventional, Debye-Huckel (DH) linearization of the Poisson-Boltzmann equation is rendered invalid by violation of the condition that the electrostatic coupling energy of a mobile ion be much smaller than its thermal energy throughout space, |nu(alpha)e psi(r)|相似文献   

Wetting transitions of ionic solutions

Cahn's phenomenological theory of wetting of a solid substrate by a saturated vapor is generalized to the case where the substrate is charged and the wetting film contains counterions, with or without added salt. The electrostatic contribution to the grand potential associated with these ions is calculated within a nonlinear Poisson-Boltzmann theory. In the salt-free case, when the wetting film includes only counterions released by the substrate, the wetting transition is always first order, regardless of its nature in a neutral system. When salt is present, other wetting scenarios may arise, depending on the salt concentration and substrate surface charge. Over a restricted range of salt concentrations, a wetting scenario similar to that of prewetting, is predicted to occur along the liquid-vapor coexistence line. This scenario includes a discontinuous wetting transition between microscopic and mesoscopic film thicknesses, followed by a continuous divergence of the film thickness at higher temperatures.     

Influence of ionic charges on the bilayers of lamellar phases

The influence of ionic charges on the mesophases in the ternary system of C(12-16)E(6) (LA 070), ethylhexylglycerid (EHG), and water was studied. The charge was introduced by adding the ionic surfactant SDS (sodium dodecyl sulfate). The single lamellar phase (5 wt % LA 070 and 240 mM EHG in water) yields a bluish homogeneous solution. With the addition of SDS, the samples become more and more clear. Rheology measurements indicate that increased charge density increases the storage modulus G', and the lamellar phases show typical behavior of a viscoelastic fluid with a yield stress at higher SDS concentration. SAXS measurements show that the interlamellar distance D decreases with SDS concentration. The addition of ionic surfactants suppresses the Helfrich undulations, flattens the bilayers, and decreases interbilayer spacing due to electrostatic repulsions of the ionic surfactant head groups. Furthermore, the L(alpha) phase transforms into vesicle phases as the SDS concentration is increased. Second, it is shown that with added NaCl electrolyte the phase with charged surfactant behaves again in the same way as the initial uncharged system. The addition of salt screens the electrostatic interaction, which leads to a higher flexibility of the bilayers and a decrease of the storage modulus G'. Theoretical calculations show that the shear moduli of the L(alpha) phases are much smaller than the osmotic pressure of the systems. Several models are proposed for the explanation of the shear moduli. The model due to Lekkerkerker for the electric contribution of the bending constant of the bilayer seems to yield good results for the transition to vesicles.     

Ion adsorption and lamellar-lamellar transitions in charged bilayer systems

Using a primitive model approach, we analyze the influence of ion specific adsorption on the phase behavior of charged lamellar systems. The presence of a weak short-ranged surface potential, attracting monovalent counterions, induces a phase separation, where the separate phases have different repeat distance. If the adsorption potential is very weak, the more narrow phase never forms. An opposite behavior is found for strong surface affinities. Both Monte Carlo simulations and a recently developed correlation-corrected Poisson-Boltzmann theory are adopted, with a nearly quantitative agreement between the approaches. Different counterions are discriminated by the adsorption potential strength, and with physically reasonable values, experimental observations on these systems are well reproduced. The study highlights the importance of electrostatic correlations, even though only monovalent ions are present.     

Simulation of phase equilibria in lamellar surfactant systems

The coexistence of two lamellar liquid crystalline phases has been investigated by means of Monte Carlo simulations. The surfaces of the negatively charged bilayers formed by the surfactant molecules are modeled as planar infinite walls with a uniform surface charge density. Water is treated as a dielectric continuum, and only electrostatic interactions are considered. The counterions are mono- and divalent point ions, and their ratio is allowed to vary. Monovalent counterions lead to a repulsive osmotic pressure at all separations, while an attractive region exists when the counterions are divalent. In the latter case, one would expect a phase separation to take place, although it is not observed experimentally due to the limited stability of the lamellar phase at high water content. In a system with mixed counterions, however, the osmotic pressure exhibits a van der Waals loop under such conditions that two phases can coexist. A phase diagram is constructed, and the agreement with experimental data is excellent.     

Electrostatic Repulsion in Concentrated Disperse Systems

Electrostatic interactions are considered in the framework of the cell model to predict the osmotic pressure in concentrated disperse systems. A procedure was developed to represent the osmotic pressure as a function of two parameters, namely, the dispersed phase volume fraction and the electric potential attributed to the interface between the continuous and dispersed phases. The procedure is based on a general formula which was derived to express the electrostatic contribution to the osmotic pressure through the electric potential at the cell boundary. The potential of the cell boundary is predicted from the solution of the Poisson-Boltzmann problem which was specified for the cell model approach. The Poisson-Boltzmann problem is solved by a perturbation technique using a normalized interface potential as the perturbation parameter. Three leading terms were obtained in the expansion of the osmotic pressure in terms of the normalized interface potential. Two options for the formation of the interface electric potential are discussed in the analysis of the interface potential dependency on the volume fraction of the dispersed phase. The first one is associated with the difference between the individual ionic distribution coefficients characterizing the equilibrium ratio between the concentrations in the bulk of the constituent phases. The second one deals with preferential adsorption of the carriers having a given electric charge sign. The dependency of the osmotic pressure on the system parameters is discussed and interrelated with other relevant theories. Special discussion is presented concerning the theory's application for the study of hydrocarbon disperse systems, e.g., water-in-oil emulsions. Copyright 2001 Academic Press.     

Excluded volume effects in macromolecular forces and ion-interface interactions

A charged Yukawa liquid confined in a slit nanopore is studied in order to understand excluded volume effects in the interaction force between the pore walls. A previously developed self-consistent scheme [S. Buyukdagli, C. V. Achim, and T. Ala-Nissila, J. Stat. Mech. 2011, P05033] and a new simpler variational procedure that self-consistently couple image forces, surface charge induced electric field, and pore modified core interactions are used to this aim. For neutral pores, it is shown that with increasing pore size, the theory predicts a transition of the interplate pressure from an attractive to a strongly repulsive regime associated with an ionic packing state, an effect observed in previous Monte Carlo simulations for hard core charges. We also establish the mean-field theory of the model and show that for dielectrically homogeneous pores, the mean-field regime of the interaction between the walls corresponds to large pores of size d > 4 ?. The role of the range of core interactions in the ionic rejection and interplate pressure is thoroughly analyzed. We show that the physics of the system can be split into two screening regimes. The ionic packing effect takes place in the regime of moderately screened core interactions characterized with the bare screening parameter of the Yukawa potential b ? 3/l(B), where l(B) is the Bjerrum length. In the second regime of strongly screened core interactions b ? 3/l(B), solvation forces associated with these interactions positively contribute to the ionic rejection driven by electrostatic forces and enhance the magnitude of the attractive pressure. For weakly charged pores without a dielectric discontinuity, core interactions make a net repulsive contribution to the interplate force and also result in oscillatory pressure curves, whereas for intermediate surface charges, these interactions exclusively strengthen the external pressure, thereby reducing the magnitude of the net repulsive interplate force. The pronounced dependence of the interplate pressure and ionic partition coefficients on the magnitude and the range of core interactions indicates excluded volume effects as an important ion specificity and a non-negligible ingredient for the stability of macromolecules in electrolyte solutions.     

Counterion volume effects in mixed electrical double layers

When a monolayer of negatively charged surfactant molecules is brought in contact with an aqueous solution containing mixtures of counterions of different size and valency, very large deviations from Poisson-Boltzmann theory (PBT) develop at a high surface charge, with the smaller counterion outcompeting the larger one (even if divalent) near the interface, leading to counterion segregation [V.L. Shapovalov, G. Brezesinski, J. Phys. Chem. B 110 (2006) 10032]. We use a modified PBT that empirically includes an extended Carnahan-Starling equation-of-state to describe hard-sphere interactions in electrical double layers containing ions of different size and charge. Model calculations are made for ion concentration profiles, free energies, surface pressures, and differential capacities. At high surface charge, volume interactions become important, leading to significant deviations from PBT. In contrast to PBT, at high surface charge, contributions to energy and pressure are no longer mainly entropic, but instead volume and electrostatic field effects now dominate. When the hydrated size of the divalent ion is used as an adjustable parameter, the theory is in good agreement with the experimental data.     

Monte Carlo studies of polyelectrolyte solutions. Effect of polyelectrolyte charge density

The influence of the polyion charge density on the osmotic behavior of linear polyelectrolytes is studied by the Monte Carlo method and by the modified Poisson-Boltzmann equation. The polyion is assumed to be either a uniformly or discretely charged cylinder placed along the axis of the cylindrical cell containing only counterions. As a result, osmotic saturation is observed at high polyion charge density. In simulations of solutions with divalent counterions the maximum in the osmotic pressure versus degree of ionization is observed in analogy with recent studies of spherical and planar systems. The correlation between the osmotic coefficient and the acceptance rate observed in simulations is reported.     

Electrostatic interaction of neutral semi-permeable membranes

We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semi-permeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte molecules permeate into the gap and lead to a steric charge separation. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure. From the solution of the nonlinear Poisson-Boltzmann equation, we obtain the distribution of the potential and of ions. We then derive an explicit formula for the pressure exerted on the membranes and show that it deviates from the classical van't Hoff expression for the osmotic pressure. This difference is interpreted in terms of a repulsive electrostatic disjoining pressure originating from the overlap of counterion clouds inside the gap. We also develop a simplified theory based on a linearized Poisson-Boltzmann approach. A comparison with simulation of a primitive model for the electrolyte is provided and does confirm the validity of the theoretical predictions. Beyond the fundamental result that the neutral surfaces can repel, this mechanism not only helps to control the adhesion and long-range interactions of living cells, bacteria, and vesicles, but also allows us to argue that electrostatic interactions should play enormous role in determining behavior and functions of systems bounded by semi-permeable membranes.     

Ionic effects in collapse of polyelectrolyte brushes

We investigated the effect of counterion valence on the structure and swelling behavior of polyelectrolyte brushes using a nonlocal density functional theory that accounts for the excluded-volume effects of all ionic species and intrachain and electrostatic correlations. It was shown that charge correlation in the presence of multivalent counterions results in collapse of a polyelectrolyte brush at an intermediate polyion grafting density. At high grafting density, the brush reswells in a way similar to that in a monovalent ionic solution. In the presence of multivalent counterions, the nonmonotonic swelling of a polyelectrolyte brush in response to the increase of the grafting density can be attributed to a competition of the counterion-mediated electrostatic attraction between polyions with the excluded-volume effect of all ionic species. While a polyelectrolyte brush exhibits an "osmotic brush" regime at low salt concentration and a "salted brush" regime at high salt concentration regardless of the counterion valence, we found a smoother transition as the valence of the counterions increases. As observed in recent experiments, a quasi-power-law dependence of the brush thickness on the concentration ratio can be identified when the monovalent counterions are replaced with trivalent counterions at a fixed ionic strength.     

Charged Semi-Permeable Shell with Encapsulated Polyions: Concentration Profile,Surface Potential,and Electrostatic Pressure

Summary: We study theoretically the electrostatic equilibrium for a charged shell filled with a suspension of polyions (e.g., colloids, polyelectrolytes, etc.) and immersed in an infinite salt-free reservoir. The shell is impermeable for polyions, but allows free diffusion of counterions. From the solution of the linearized Poisson-Boltzmann equation we obtain the distribution of the potential and concentration profiles for polyions. We then derive explicit formulas for the electrostatic pressure exerted by the shell. If the overall charge of the filled shell has the same sign as the surface alone the pressure on the shell increases with increase of the surface charge density. Otherwise the surface charge density suppresses the electro-osmotic pressure due to the electrostatic attraction between the oppositely charged polyions and shell.     

Concentration Polarization of Interacting Solute Particles in Cross-Flow Membrane Filtration

A theoretical approach for predicting the influence of interparticle interactions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presented. The Ornstein-Zernike integral equation is solved using appropriate closures corresponding to hard-spherical and long-range solute-solute interactions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, namely the osmotic pressure and the diffusion coefficient, are determined on the basis of the radial distribution function at different solute concentrations. Incorporation of the concentration dependence of these two properties in the concentration polarization model comprising the convective-diffusion equation and the osmotic-pressure governed permeate flux equation leads to the coupled prediction of the solute concentration profile and the local permeate flux. The approach leads to a direct quantitative incorporation of solute-solute interactions in the framework of a standard theory of concentration polarization. The developed model is used to study the effects of ionic strength and electrostatic potential on the variations of solute diffusivity and osmotic pressure. Finally, the combined influence of these two properties on the permeate flux decline behavior during cross-flow membrane filtration of charged solute particles is predicted. Copyright 1999 Academic Press.     

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.     

The Effect of Surface Charge on Adsorption of a Cationic Polyelectrolyte

The regularities of adsorption of a cationic polyelectrolyte, poly(diallyldimethylammonium chloride), on the surface of fused quartz are studied at different values of solution pH by capillary electrokinetics. It is shown that the polyelectrolyte adsorption on a negatively charged surface depends on the value of the surface charge and increases with its growth. At a low charge value (pH 3.8), the polyelectrolyte adsorption increases the quartz surface charge. The driving forces of the adsorption are both electrostatic interaction and forces of nonelectrostatic nature, probably hydrophobic interactions and a change in entropy due to the displacement of counterions from a double layer. The adsorption of poly(diallyldimethylammonium chloride) on quartz from alkaline and neutral solutions is irreversible, which indicates the key role of the electrostatic interaction. At low values of the surface charge, the nonelectrostatic interactions play the main role, thereby resulting in polyelectrolyte desorption.     

The Poisson-Boltzmann model for tRNA: Assessment of the calculation set-up and ionic concentration cutoff

Using tRNA molecule as an example, we evaluate the applicability of the Poisson-Boltzmann model to highly charged systems such as nucleic acids. Particularly, we describe the effect of explicit crystallographic divalent ions and water molecules, ionic strength of the solvent, and the linear approximation to the Poisson-Boltzmann equation on the electrostatic potential and electrostatic free energy. We calculate and compare typical similarity indices and measures, such as Hodgkin index and root mean square deviation. Finally, we introduce a modification to the nonlinear Poisson-Boltzmann equation, which accounts in a simple way for the finite size of mobile ions, by applying a cutoff in the concentration formula for ionic distribution at regions of high electrostatic potentials. We test the influence of this ionic concentration cutoff on the electrostatic properties of tRNA.