Dielectric response of polar liquids in narrow slit pores

Based on molecular dynamics (MD) simulations and a simple (Stockmayer) model we investigate the static and dynamic dielectric response of polar liquids confined to narrow slit pores. The MD simulations are used to calculate the time-dependent polarization fluctuations along directions parallel and perpendicular to the walls, from which the components of the frequency-dependent dielectric tensor can be derived via linear response theory. Our numerical results reveal that the system's response is strongly anisotropic. The parallel dielectric function, epsilonparallel(omega), has Debye-like character very similar to the corresponding isotropic bulk function, epsilonbulk(omega), at the same chemical potential. Indeed, the main confinement effect on epsilonparallel(omega) consists in a shift toward smaller values relative to the bulk function. On the other hand, in the perpendicular direction we observe a characteristic peak in the absorption part of the dielectric function, epsilonperpendicular(omega). This peak is absent in the bulk system and reflects strongly pronounced, damped oscillations in the polarization fluctuations normal to the walls. We discuss two possible origins of the oscillations (and the resulting absorption peak), that is collective oscillations of dipoles in clusters formed parallel to the walls, and the existence of a "dipolaron mode" previously observed in MD simulations of bulk polar fluids.     

A method for treating the passage of a charged hard sphere ion as it passes through a sharp dielectric boundary

In the implicit solvent models of electrolytes (such as the primitive model (PM)), the ions are modeled as point charges in the centers of spheres (hard spheres in the case of the PM). The surfaces of the spheres are not polarizable which makes these models appropriate to use in computer simulations of electrolyte systems where these ions do not leave their host dielectrics. The same assumption makes them inappropriate in simulations where these ions cross dielectric boundaries because the interaction energy of the point charge with the polarization charge induced on the dielectric boundary diverges. In this paper, we propose a procedure to treat the passage of such ions through dielectric interfaces with an interpolation method. Inspired by the "bubble ion" model (in which the ion's surface is polarizable), we define a space-dependent effective dielectric coefficient, ε(eff)(r), for the ion that overlaps with the dielectric boundary. Then, we replace the "bubble ion" with a point charge that has an effective charge q/ε(eff)(r) and remove the portion of the dielectric boundary where the ion overlaps with it. We implement the interpolation procedure using the induced charge computation method [D. Boda, D. Gillespie, W. Nonner, D. Henderson, and B. Eisenberg, Phys. Rev. E 69, 046702 (2004)]. We analyze the various energy terms using a spherical ion passing through an infinite flat dielectric boundary as an example.     

Short-range forces between glass surfaces in aqueous solutions

We found that the force between glass surfaces measured with an atomic force microscope (AFM) has universal character in the short range, less than approximately 1 nm or about 3-4 water molecules, independent of solution conditions, that is, electrolyte ion size, charge and concentration and pH. Our results suggest that the excess DLVO force, obtained by subtracting the DLVO theory with a charge regulation model from the AFM force data, essentially does not change with the electrolytes Na, Ca, and Al, in the range of concentration from 10(-6) to 10(-2) M and the range of pH from 3.1 to 7.9. Single force curves for a glass-silica system in a 10-4 M aqueous NaCl solution at pH approximately 5.1 show oscillations with a period of about 0.25 nm, roughly the diameter of a water molecule. We postulate that the excess force between glass surfaces arises from a surface-induced solvent effect, from the creation of a hydrogen-bonding network at the surface level, rather than from a solvent-induced surface steric hindrance.     

Molecular dynamics study of screening at ionic surfaces

Molecular dynamics simulations of NaCl fluid are used to understand the behavior of ionic fluid to screen the field generated by charges on the ionic crystal surfaces in absence of any external electric field. The NaCl fluid in the strongly coupled regime (corresponding to the melt) in contact with the charged octopolar (111) NaCl surface shows that the spatial correlations decay in an oscillatory manner, with a screening length lambdaQ given by the envelope of the damped oscillations. By contrast to the Debye-Huckel theory, in the strongly coupled regime, lambdaQ increases with increasing coupling strength (also seen in bulk ionic simulations). The NaCl fluid confined between neutral (100) NaCl surfaces also shows weak oscillatory charge decay near the surface. Similar oscillatory exponential decay was seen when the NaCl fluid was confined between two analytically smooth neutral walls. The origin of these oscillations was due to the difference in ion sizes. NaCl fluid confined between neutral octopolar (110) and dipolar (110) surface show stronger density oscillations than (100) surface but comparatively very weak charge oscillations. This paper shows that the strength of the charges on the crystal surfaces is enough to induce a characteristic spatial distribution of charges in the contacting fluid and the extent of distribution depends on the type of surface.     

Potential of average force between two ions in a solvent of polarizable hard spheres

A method of obtaining the potential of average force between two ions immersed in a polarizable hard sphere fluid is described. The ions and the solvent particles may have different hard sphere diameters. For large values of the reduced polarizability of the solvent particles, ^*, the potential of average force rises near contact much more steeply than the primitive model would permit and also has maxima and minima vanishing at larger distances, in semiquantitative agreement with the similar results of Patey and Valleau. The oscillating character of the potential of average force is due above all to the oscillations of the radial distribution function between the ion and polarizable hard sphere.     

Influence of atomistic physics on electro-osmotic flow: an analysis based on density functional theory

Molecular density profiles and charge distributions determined by density functional theory (DFT) are used in conjunction with the continuum Navier-Stokes equations to compute electro-osmotic flows in nanoscale channels. The ion species of the electrolyte are represented as centrally charged hard spheres, and the solvent is treated as a dense fluid of neutral hard spheres having a uniform dielectric constant. The model explicitly accounts for Lennard-Jones interactions among fluid and wall molecules, hard sphere repulsions, and short range electrical interactions, as well as long range Coulombic interactions. Only the last of these interactions is included in classical Poisson-Boltzmann (PB) modeling of the electric field. Although the proposed DFT approach is quite general, the sample calculations presented here are limited to symmetric monovalent electrolytes. For a prescribed surface charge, this DFT model predicts larger counterion concentrations near charged channel walls, relative to classical PB modeling, and hence smaller concentrations in the channel center. This shifting of counterions toward the walls reduces the effective thickness of the Debye layer and reduces electro-osmotic velocities as compared to classical PB modeling. Zeta potentials and fluid speeds computed by the DFT model are as much as two or three times smaller than corresponding PB results. This disparity generally increases with increasing electrolyte concentration, increasing surface charge density and decreasing channel width. The DFT results are found to be comparable to those obtained by molecular dynamics simulation, but require considerably less computing time.     

Density-functional theory of spherical electric double layers and zeta potentials of colloidal particles in restricted-primitive-model electrolyte solutions

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high.     

Dielectric saturation of the ion hydration shell and interaction between two double helices of DNA in mono- and multivalent electrolyte solutions: foundations of the epsilon-modified Poisson-Boltzmann theory

Potentials of mean force between single Na+, Ca2+, and Mg2+ cations and a highly charged spherical macroion in SPC/E water have been determined using molecular dynamics simulations. Results are compared to the electrostatic energy calculations for the primitive polarization model (PPM) of hydrated cations describing the ion hydration shell as a dielectric sphere of low permittivity (Gavryushov, S.; Linse, P. J. Phys. Chem. B 2003, 107, 7135). Parameters of the ion dielectric sphere and radius of the macroion/water dielectric boundary were extracted by means of this comparison to approximate the short-range repulsion of ions near the interface. To explore the counterion distributions around a simplified model of DNA, the obtained PPM parameters for Na+ and Ca2+ have been substituted into the modified Poisson-Boltzmann (MPB) equations derived for the PPM and named the epsilon-MPB (epsilon-MPB) theory. epsilon-MPB results for DNA suggest that such polarization effects are important in the case of 2:1 electrolyte and highly charged macromolecules. The three-dimensional implementation of the epsilon-MPB theory was also applied to calculation of the energies of interaction between two parallel macromolecules of DNA in solutions of NaCl and CaCl2. Being compared to results of MPB calculations without the ion polarization effects, it suggests that the ion hydration shell polarization and inhomogeneous solvent permittivity might be essential factors in the experimentally known hydration forces acting between charged macromolecules and bilayers at separations of less than 20 A between their surfaces.     

Water molecule clusters measured at water/air interfaces using atomic force microscopy

During the tip approach to hydrophobic surfaces like the water/air interface, the measured interaction force reveals a strong attraction with a range of approximately 250 nm at some points along the interface. The range of this force is approximately 100 times larger than the measured for gold (approximately 3 nm) and 10 times larger than the one for hydrophobic silicon surfaces (approximately 25 nm). At other points the interface exerts a medium range repulsive force growing stepwise as the tip approaches the interface plane, consequently the hydrophobic force is a strong function of position. To explain these results we propose a model where the force on the tip is associated with the exchange of a small volume of the interface with a dielectric permittivity epsilon(int) by the tip with a dielectric permittivity epsilon(tip). By assuming a oscillatory spatial dependence for the dielectric permittivity it is possible to fit the measured force profiles. This dielectric spatial variation was associated with the orientation of the water molecules arrangement in the interfacial region. Small nanosized hydrogen-bond connected cages of water molecules present in bulk water at the interface are oriented by the interfacial electric field generated by the water molecules broken bonds, one broken hydrogen bond out of every four. This interfacial field orients small clusters formed by approximately 100 water molecules into larger clusters (approximately 100 nm). In the limit of small (less than 5 nm thick) water molecule cages we have modeled the static dielectric permittivity (epsilon) as the average response of those cages. In these regions the dielectric permittivity for water/air interfaces decreases monotonically from the bulk value epsilon approximately 80 to approximately 2 at the interface. For regions filled with medium size cages, the tip senses the structure of each cage and the static dielectric permittivity is matched to the geometrical features of these cages sized approximately 25 to 40 nm. Interfacial electric energy density values were calculated using the electric field intensity and the dielectric permittivity obtained by the fitting of the experimental points. The integration of the electric energy density along the interfacial region gives a value of 0.072 J m(-2) for interfacial energy density for points where the hydrophobic force has a range of approximately 250 nm. Regions formed by various clusters result in lower values of the interfacial energy density.     

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.     

Hydration force between mica surfaces in aqueous KCl electrolyte solution

Liquid-vapor molecular dynamics simulations are performed to study the interaction forces between two mica surfaces in an aqueous KCl electrolyte solution. Strong repulsive hydration force is obtained within a distance of ~2 nm between the two mica surfaces, which cannot be explained by the continuum theory of double-layer repulsion. We find that this short-range repulsive hydration force is much stronger than the double-layer force between mica surfaces. Whereas the simulation system is much smaller than the surface force measurement system, fundamental mechanisms of repulsive hydration force are revealed. In particular, important features of the step-like force oscillatory behavior during normal compression and force hysteresis during retraction are observed. Detailed analysis of the ionic density distributions shows that the "forced adsorption" of diffusive K(+) ions onto mica surfaces during compression and the subsequent "slow desorption" of the absorbed K(+) ions from mica surfaces upon retraction are responsible for the hysteresis phenomenon. From a mechanics point of view, we attribute the load bearing capacity of the dense electrolyte to the very hard hydration shells of K(+) metal ions under confinement. We find that the hydrated K(+) ions and Cl(-) co-ions remain very diffusive in the aqueous film. Water molecules in the hydration layer are also very fluidic, in the sense that the diffusion constant of water molecules is less than its bulk value by at most 3 orders of magnitude under the extreme confinement.     

Oscillatory forces of nanoparticle suspensions confined between rough surfaces modified with polyelectrolytes via the layer-by-layer technique

This paper addresses the systematic study of surface roughness effects on the internal structuring of silica nanoparticle suspensions under confinement. The confining surfaces are modified by physisorption of layers of oppositely charged polyelectrolytes with the so-called layer-by-layer technique. The layer-by-layer technique modifies the surface roughness without changing the surface potential of a multilayer with the same outermost layer, by increasing the number of constituent layers and ionic strength of the polyelectrolyte solutions and by selecting an appropriate pair of polyelectrolytes. The oscillatory forces of nanoparticle suspensions with a particle diameter of 26 nm are measured by a colloidal-probe atomic force microscope (CP-AFM). The characteristic lengths of the oscillatory force, i.e., wavelength, which indicates interparticle distance, and decay length, or particle correlation length, are not affected by the surface roughness. The corresponding reduction in the oscillatory amplitude and the shift in the phase correlate with an increase in surface roughness. Increasing surface roughness further induces a disappearance of the oscillations, and both confining surfaces contribute to the effect of surface roughness on the force reduction. In order to show an oscillatory force, the particles have to show positional correlation over a reasonably long range perpendicular to the surface, and the correlation function should be the same over a larger lateral area. This requires that both the particles and the surfaces have a high degree of order or symmetry; otherwise, the oscillation does not occur. A roughness of a few nanometers on a single surface, which corresponds to about 10% of the nanoparticle diameter, is sufficient to eliminate the oscillatory force.     

The influence of discrete surface charges on the force between charged surfaces

The force between two parallel charged flat surfaces, with discrete surface charges, has been calculated with Monte Carlo simulations for different values of the electrostatic coupling. For low electrostatic coupling (small counterion valence, small surface charge, high dielectric constant, and high temperature) the total force is dominated by the entropic contribution and can be described by mean field theory, independent of the character of the surface charges. For moderate electrostatic coupling, counterion correlation effects lead to a smaller repulsion than predicted by mean field theory. This correlation effect is strengthened by discrete surface charges and the repulsive force is further reduced. For large electrostatic coupling the total force for smeared out surface charges is known to be attractive due to counterion correlations. If discrete surface charges are considered the attractive force is weakened and can even be turned into a repulsive force. This is due to the counterions being strongly correlated to the discrete surface charges forming effective, oppositely directed, dipoles on the two walls.     

Interactions between a polystyrene particle and hydrophilic and hydrophobic surfaces in aqueous solutions

The interaction between a colloidal polystyrene particle mounted on an AFM cantilever and a hydrophilic and a hydrophobic surface in aqueous solution is investigated. Despite the apparent simplicity of these two types of systems a variety of different types of interactions are observed. The system containing the polystyrene particle and a hydrophilic surface shows DLVO-like interactions characteristic of forces between charged surfaces. However, when the surface is hydrophobized the interaction changes dramatically and shows evidence of a bridging air bubble being formed between the particle and the surface. For both sets of systems, plateaus of constant force in the force curves are obtained when the particle is retracted from the surface after being in contact. These events are interpreted as a number of individual polystyrene molecules that are bridging the polystyrene particle and the surface. The plateaus of constant force are expected for pulling a hydrophobic polymer in a bad (hydrophilic) solvent. The plateau heights are found to be of uniform spacing and independent of the type of surface, which suggests a model by which collapsed polymers are extended into the aqueous medium. This model is supported by a full stretching curve showing also the backbone elasticity and a stretching curve obtained in pentanol, where the plateau changes to a nonlinear force response, which is typical for a polymer in a good or neutral solvent. We suggest that these polymer bridges are important in particular for the interaction between polystyrene and the hydrophilic surface, where they to some extent counteract the long-range electrostatic repulsion.     

Effect of surface roughness and softness on water capillary adhesion in apolar media

The roughness and softness of interacting surfaces are both important parameters affecting the capillary condensation of water in apolar media, yet are poorly understood at present. We studied the water capillary adhesion between a cellulose surface and a silica colloidal probe in hexane by AFM force measurements. Nanomechanical measurements show that the Young's modulus of the cellulose layer in water is significantly less (~7 MPa) than in hexane (~7 GPa). In addition, the cellulose surface in both water and hexane is rather rough (6-10 nm) and the silica probe has a comparable roughness. The adhesion force between cellulose and silica in water-saturated hexane shows a time-dependent increase up to a waiting time of 200 s and is much (2 orders of magnitude) lower than that expected for a capillary bridge spanning the whole silica probe surface. This suggests the formation of one or more smaller bridges between asperities on both surfaces, which is confirmed by a theoretical analysis. The overall growth rate of the condensate cannot be explained from diffusion mediated capillary condensation alone; thin film flow due to the presence of a wetting layer of water at both the surfaces seems to be the dominant contribution. The logarithmic time dependence of the force can also be explained from the model of the formation of multiple capillary bridges with a distribution of activation times. Finally, the force-distance curves upon retraction show oscillations. Capillary condensation between an atomically smooth mica surface and the silica particle show less significant oscillations and the adhesion force is independent of waiting time. The oscillations in the force-distance curves between cellulose and silica may stem from multiple bridge formation between the asperities present on both surfaces. The softness of the cellulose surface can bring in additional complexities during retraction of the silica particle, also resulting in oscillations in the force-distance curves.     

Density functional theory for planar electric double layers: closing the gap between simple and polyelectrolytes

We report a nonlocal density functional theory (NLDFT) for polyelectrolyte solutions within the primitive model; i.e., the solvent is represented by a continuous dielectric medium, and the small ions and polyions by single and tangentially connected charged hard spheres, respectively. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for hard-sphere repulsion, an extended first-order thermodynamic perturbation theory for chain connectivity, and a quadratic functional Taylor expansion for electrostatic correlations. With the direct and cavity correlation functions of the corresponding monomeric systems as inputs, the NLDFT predicts the segment-level microscopic structures and adsorption isotherms of polyelectrolytes at oppositely charged surfaces in good agreement with molecular simulations. In particular, it faithfully reproduces the layering structures of polyions, charge inversion, and overcharging that cannot be captured by alternative methods including the polyelectrolyte Poisson-Boltzmann equation and an earlier version of DFT. The NLDFT has also been used to investigate the influences of the small ion valence, polyion chain length, and size disparity between polyion segments and counterions on the microscopic structure, mean electrostatic potential, and overcharging in planar electric double layers containing polyelectrolytes.     

Direct measurement of depletion and structural forces in polydisperse, charged systems

The effect of polydispersity in macromolecule size or surface potential on the depletion interaction between a spherical silica particle and a silica flat in solutions containing two different types of nonadsorbing charged spherical macromolecules was studied with an atomic force microscope (AFM). The macromolecules used here were negatively charged nanospheres of either polystyrene or silica. To investigate the effect of size polydispersity, experiments were performed under the condition of either constant macromolecule number density or constant volume fraction as the relative proportions of smaller and larger polystyrene nanospheres in the suspension were varied. Similarly, for the experiments with surface potential polydispersity, the suspensions contained varying fractions of more highly charged (polystyrene) and less highly charged (Ludox silica) nanospheres at constant number density. The experimental results were compared to the predictions of the modified force-balance model of Piech and Walz and semiquantitative agreement was found. In particular, the maximum attraction and repulsion observed in the measured force profiles were found to agree with the predicted trends as the makeup of the macromolecules was varied. The trend in the maximum attraction was also consistent with predictions made using a simple "scaling" analysis derived using the equation for hard-sphere interactions.