Polymer capture by electro-osmotic flow of oppositely charged nanopores

The authors have addressed theoretically the hydrodynamic effect on the translocation of DNA through nanopores. They consider the cases of nanopore surface charge being opposite to the charge of the translocating polymer. The authors show that, because of the high electric field across the nanopore in DNA translocation experiments, electro-osmotic flow is able to create an absorbing region comparable to the size of the polymer around the nanopore. Within this capturing region, the velocity gradient of the fluid flow is high enough for the polymer to undergo coil-stretch transition. The stretched conformation reduces the entropic barrier of translocation. The diffusion limited translocation rate is found to be proportional to the applied voltage. In the authors' theory, many experimental variables (electric field, surface potential, pore radius, dielectric constant, temperature, and salt concentration) appear through a single universal parameter. They have made quantitative predictions on the size of the adsorption region near the pore for the polymer and on the rate of translocation.     

Solvated calcium ions in charged silica nanopores

Hydroxyl surface density in porous silica drops down to nearly zero when the pH of the confined aqueous solution is greater than 10.5. To study such extreme conditions, we developed a model of slit silica nanopores where all the hydrogen atoms of the hydroxylated surface are removed and the negative charge of the resulting oxygen dangling bonds is compensated by Ca(2+) counterions. We employed grand canonical Monte Carlo and molecular dynamics simulations to address how the Ca(2+) counterions affect the thermodynamics, structure, and dynamics of confined water. While most of the Ca(2+) counterions arrange themselves according to the so-called "Stern layer," no diffuse layer is observed. The presence of Ca(2+) counterions affects the pore filling for strong confinement where the surface effects are large. At full loading, no significant changes are observed in the layering of the first two adsorbed water layers compared to nanopores with fully hydroxylated surfaces. However, the water structure and water orientational ordering with respect to the surface is much more disturbed. Due to the super hydrophilicity of the Ca(2+)-silica nanopores, water dynamics is slowed down and vicinal water molecules stick to the pore surface over longer times than in the case of hydroxylated silica surfaces. These findings, which suggest the breakdown of the linear Poisson-Boltzmann theory, provide important information about the properties of nanoconfined electrolytes upon extreme conditions where the surface charge and ion concentration are large.     

Ionic exclusion phase transition in neutral and weakly charged cylindrical nanopores

A field theoretic variational approach is introduced to study ion penetration into water-filled cylindrical nanopores in equilibrium with a bulk reservoir [S. Buyukdagli, M. Manghi, and J. Palmeri, Phys. Rev. Lett. 105, 158103 (2010)]. It is shown that an ion located in a neutral pore undergoes two opposing mechanisms: (i) a deformation of its surrounding ionic cloud of opposite charge, with respect to the reservoir, which increases the surface tension and tends to exclude ions from the pore, and (ii) an attractive contribution to the ion self-energy due to the increased screening with ion penetration of the repulsive image forces associated with the dielectric jump between the solvent and the pore wall. For pore radii around 1 nm and bulk concentrations lower than 0.2 mol/l, this mechanism leads to a first-order phase transition, similar to capillary "evaporation," from an ionic-penetration state to an ionic-exclusion state. The discontinuous phase transition exists within the biological concentration range (～0.15 mol/l) for small enough membrane dielectric constants (ε(m) < 5). In the case of a weakly charged pore, counterion penetration exhibits a nonmonotonic behavior and is characterized by two regimes: at low reservoir concentrations or small pore radii, coions are excluded and counterions enter the pore to enforce electroneutrality; dielectric repulsion (image forces) remain strong and the counterion partition coefficient decreases with increasing reservoir concentration up to a characteristic value. For larger reservoir concentrations, image forces are screened and the partition coefficient of counterions increases with the reservoir concentration, as in the neutral pore case. Large surface charge densities (>2 × 10(-3) e/nm(2)) suppress the discontinuous transition by reducing the energy barrier for ion penetration and shifting the critical point toward very small pore sizes and reservoir concentrations. Our variational method is also compared to a previous self-consistent approach and yields important quantitative corrections. The role of the curvature of dielectric interfaces is highlighted by comparing ionic penetration into slit and cylindrical pores. Finally, a charge regulation model is introduced in order to explain the key effect of pH on ionic exclusion and explain the origin of observed time-dependent nanopore electric conductivity fluctuations and their correlation with those of the pore surface charge.     

Nonuniform electro-osmotic flow on charged strips and its use in particle trapping

In this article, we investigate theoretically electro-osmotic flow set up by charged strips on an otherwise uncharged surface. Starting with a single-strip problem we demonstrate that for simple polynomial surface charge distributions several basic solutions can be derived in closed forms constituted by the analogous idea-flow solutions, which provide a more lucid way of revealing the flow features. These solutions reveal two types of flow topology: simple draining-in/pumping-out streaming and a pair of microvortices for symmetric and antisymmetric surface charge distributions, respectively. For an arbitrary surface charge distribution, more complicated flow structures can be found by the superposition of these basic solutions. We further extend the analysis to two uniformly charged strips and show how the flow characteristics vary with the strips' dimensions and surface zeta potentials. The far-field velocity behavior is also asymptotically identified and indicates that the hydrodynamic nature of the flow is typically long-range. An application to particle trapping with electro-osmotic vortices is also investigated theoretically for the first time. We show that in collaboration with short-range attraction effects the trapping can be facilitated by symmetric vortices with a converging stagnation point, but not by asymmetric vortices.     

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.     

Nanofracture on fused silica microchannel for Donnan exclusion based electrokinetic stacking of biomolecules

Due to Donnan exclusion, charged molecules are prohibited from passing through a channel of electrical double layer scale (nanometers), even though the molecules are smaller than the lowest dimension of the channel. To employ this effect for on-chip pre-concentration, an ion channel of nanometer scale has to be introduced. Here we introduced a simple method of generating a fracture (11-250 nm) directly on the commercially available open tubular fused silica capillary, and a chip comprised of the capillary with the nanofracture was prepared. A ring-disk model of the fracture was derived with which the fracture width can be easily characterized online without any damage to the chip, and the result was validated by a scanning electron microscope (SEM). The fractures can be used directly as a nanofluidic interface exhibiting an obvious ion concentration polarization effect with high current flux. On-chip electrokinetic stacking of SYBR Green I labeled λDNA inside the capillary was successfully demonstrated, and a concentration factor close to the amplification rate of the polymerase chain reaction (PCR) was achieved within 7 min. The chip is inexpensive and easy to prepare in common chemistry and biochemistry laboratories without limitations in expensive microfabrication facilities and sophisticated expertise. More applications of this interface could be found for enhancing the detectability of capillary based microfluidic analytical systems for the analysis of low concentrated charged species.     

Aqueous NaCl and CsCl solutions confined in crystalline slit-shaped silica nanopores of varying degree of protonation

All-atom molecular dynamics simulations were conducted to study the dynamics of aqueous electrolyte solutions confined in slit-shaped silica nanopores of various degrees of protonation. Five degrees of protonation were prepared by randomly removing surface hydrogen atoms from fully protonated crystalline silica surfaces. Aqueous electrolyte solutions containing NaCl or CsCl salt were simulated at ambient conditions. In all cases, the ionic concentration was 1 M. The results were quantified in terms of atomic density distributions within the pores, and the self-diffusion coefficient along the direction parallel to the pore surface. We found evidence for ion-specific properties that depend on ion-surface, water-ion, and only in some cases ion-ion correlations. The degree of protonation strongly affects the structure, distribution, and the dynamic behavior of confined water and electrolytes. Cl(-) ions adsorb on the surface at large degrees of protonation, and their behavior does not depend significantly on the cation type (either Na(+) or Cs(+) ions are present in the systems considered). The cations show significant ion-specific behavior. Na(+) ions occupy different positions within the pore as the degree of protonation changes, while Cs(+) ions mainly remain near the pore center at all conditions considered. For a given degree of protonation, the planar self-diffusion coefficient of Cs(+) is always greater than that of Na(+) ions. The results are useful for better understanding transport under confinement, including brine behavior in the subsurface, with important applications such as environmental remediation.     

Long-time self-diffusion of charged colloidal particles: electrokinetic and hydrodynamic interaction effects

The authors analyze the long-time self-diffusion of charge-stabilized colloidal macroions in nondilute suspensions using a mode-coupling scheme developed for multicomponent suspensions of interacting Brownian spheres. In this scheme, all ionic species, including counterions and electrolyte ions, are treated on an equal footing as charged hard spheres undergoing overdamped Brownian motion. Hydrodynamic interactions between all ions are accounted for on the far-field level. We show that the influence on the colloidal long-time self-diffusion coefficient arising from the relaxation of the microionic atmosphere surrounding the colloids, the so-called electrolyte friction effect, is usually insignificant in comparison with the friction contributions arising from direct and hydrodynamic interactions between the colloidal particles. This finding is true even for small colloid concentrations unless the mobility difference between colloidal particles and microions is not large. Furthermore, we observe an interesting nonmonotonic density dependence of the colloidal long-time self-diffusion coefficient in suspensions with low amount of added salt. We show that this unusual density dependence is due to colloid-colloid hydrodynamic interactions.     

Rod-like polyelectrolyte adsorption onto charged surfaces in monovalent and divalent salt solutions

We analyze the adsorption of strongly charged polyelectrolytes onto weakly charged surfaces in divalent salt solutions. We include short-range attractions between the monomers and the surface and between condensed ions and monomers, as well correlations among the condensed ions. Our results are compared with the adsorption in monovalent salt solutions. Different surface charge densities (σ), and divalent (m) and monovalent (s) salt concentrations are considered. When the Wigner-Seitz cells diameter (2R) is larger than the length of the rod, the maximum amount of adsorption scales like n_max ∼ σ^4/3 in both monovalent and divalent solutions. For homogeneously charged surfaces, the maximum adsorption occurs at s* ∼ σ² when s* > ϕ, where ϕ is the monomer concentration, the counterpart for divalent salt solution, m* roughly scales as σ^2.2 when m* > ϕ. The effective surface charge density has a maximum absolute value at m′ < m*. A discrete surface charge distribution and short-range attractions between monomers and surface charge groups can greatly enhance surface charge inversion especially for high salt concentration. The critical salt concentration for adsorption in divalent salt solution roughly scales as m_c ∼ bσ^1.9, where b is the distance between two neighboring charged monomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3642–3653, 2004     

Structure and dynamics of water confined in silica nanopores

We report the results of molecular simulation of water in silica nanopores at full hydration and room temperature. The model systems are approximately cylindrical pores in amorphous silica, with diameters ranging from 20 to 40 ?. The filled pores are prepared using grand canonical Monte Carlo simulation and molecular dynamics simulation is used to calculate the water structure and dynamics. We found that water forms two distinct molecular layers at the interface and exhibits uniform, but somewhat lower than bulk liquid, density in the core region. The hydrogen bond density profile follows similar trends, with lower than bulk density in the core and enhancements at the interface, due to hydrogen bonds between water and surface non-bridging oxygens and OH groups. Our studies of water dynamics included translational mean squared displacements, orientational time correlations, survival probabilities in interfacial shells, and hydrogen bond population relaxation. We found that the radial-axial anisotropy in translational motion largely follows the predictions of a model of free diffusion in a cylinder. However, both translational and rotational water mobilities are strongly dependent on the proximity to the interface, with pronounced slowdown in layers near the interface. Within these layers, the effects of interface curvature are relatively modest, with only a small increase in mobility in going from the 20 to 40 ? diameter pore. Hydrogen bond population relaxation is nearly bulk-like in the core, but considerably slower in the interfacial region.     

Melting and freezing of water in cylindrical silica nanopores

Freezing and melting of H(2)O and D(2)O in the cylindrical pores of well-characterized MCM-41 silica materials (pore diameters from 2.5 to 4.4 nm) was studied by differential scanning calorimetry (DSC) and (1)H NMR cryoporometry. Well-resolved DSC melting and freezing peaks were obtained for pore diameters down to 3.0 nm, but not in 2.5 nm pores. The pore size dependence of the melting point depression DeltaT(m) can be represented by the Gibbs-Thomson equation when the existence of a layer of nonfreezing water at the pore walls is taken into account. The DSC measurements also show that the hysteresis connected with the phase transition, and the melting enthalpy of water in the pores, both vanish near a pore diameter D* approximately equal to 2.8 nm. It is concluded that D* represents a lower limit for first-order melting/freezing in the pores. The NMR spin echo measurements show that a transition from low to high mobility of water molecules takes place in all MCM-41 materials, including the one with 2.5 nm pores, but the transition revealed by NMR occurs at a higher temperature than indicated by the DSC melting peaks. The disagreement between the NMR and DSC transition temperatures becomes more pronounced as the pore size decreases. This is attributed to the fact that with decreasing pore size an increasing fraction of the water molecules is situated in the first and second molecular layers next to the pore wall, and these molecules have slower dynamics than the molecules in the core of the pore.     

Mixed brushes consisting of oppositely charged Y-shaped polymers in salt free,monovalent, and divalent salt solutions

The conformation and the internal stratification of mixed brushes formed from oppositely charged Y(−) and Y(+)-shaped chains in salt free, monovalent, and divalent salt solutions were studied by means of molecular dynamics simulations using the primitive model. Scaling relations of mixed brush height with respect to the grafting surface per chain, the ratio of the total positive to the total negative charge of polyelectrolyte chains, and salt concentrations were obtained. The simulations predicted that mixed brushes show a unique response to divalent salt (1:2) solutions. For symmetric brushes having the same spacer lengths, number of chains and charged units fractions the increase of the salt concentration leads to the enrichment of the outer brush surface with Y(+) units and the lamella microphase separation. For asymmetric brushes in high salt concentration cylindrical domain microphases are formed.     

Ion size effects on the dielectric and electrokinetic properties in aqueous colloidal suspensions

One of the main assumptions of the classical theory most widely used to characterize electrokinetic phenomena is that ions behave as point-like entities. While the realization of the importance of the finite ion size goes back to Stern, 1924, it was Bikerman who presented in 1942 the first expression for the steric interactions among ions. Even now, this is the most often used expression, mainly due to its analytic simplicity. However, once ions are considered to have a finite size, other consequences besides the steric interactions have to be considered. For example, the finite closest approach distance of ions to the interface, the dielectrophoretic force acting on ions in a non-uniform electric field, the variation of the electrolyte solution permittivity with the local ion concentration, and the corresponding Born force acting on the ions, have to be taken into account. In this work, we examine these items in detail and discuss the main contributions made in this field. They show that even for the relatively low surface charge and electrolyte concentration values encountered in colloidal suspension studies, corrections to the classical theory due to ion size effects are far from negligible.     

The detachment of nylon particles from quartz plate by electro-osmotic flow

The direct application of electrokinetic phenomena to detergency was investigated. Experiments were carried out to remove particles from substrate by electro-osmosis. A model system which consisted of spherical nylon particles of 5m in mean diameter, a quartz plate, and wash liquid were used in analyzing the kinetic process of particle removal from substrate. When an electric field was applied to the system, electro-osmotic flow took place, and hence the particles were removed from the quartz surface. The -potentials of nylon particles and quartz plate were measured by electrophoresis. The rate constants of removal,, were obtained from the changes with time in the ratio of particle residue by applying the first-order reaction scheme. The value of increased with increasing electric field and with increasing concentration of surfactant. The total force of interaction between particle and plate was calculated on the basis of heterocoagulation theory of colloid stability.It was found from results thus obtained that the hydrodynamic force due to the electro-osmotic flow worked effectively as a mechanical force on the removal process and the adhesion force of particle to substrate reduced by adding surfactant.     

Scan-rate-dependent ion current rectification and rectification inversion in charged conical nanopores

Herein we report a theoretical study of diode-like behavior of negatively charged (e.g., glass or silica) nanopores at different potential scan rates (1-1000 V·s(-1)). Finite element simulations were used to determine current-voltage characteristics of conical nanopores at various electrolyte concentrations. This study demonstrates that significant changes in rectification behavior can be observed at high scan rates because the mass transport of ionic species appears sluggish on the time scale of the voltage scan. In particular, it explains the influence of the potential scan rate on the nanopore rectifying properties in the cases of classical rectification, rectification inversion, and the "transition" rectification domain where the rectification direction in the nanopore could be modulated according to the applied scan rate.     

Electrolyte exclusion from charged adsorbent: replica Ornstein-Zernike theory and simulations

Structural and thermodynamic properties of the restrictive primitive model +1:-1 electrolyte solution adsorbed in a disordered charged media were studied by means of the Grand Canonical Monte Carlo simulation and the replica Ornstein-Zernike theory. Disordered media (adsorbent, matrix) was represented by a distribution of negatively charged hard spheres frozen in a particular equilibrium distribution. The annealed counterions and co-ions were assumed to be distributed within the nanoporous adsorbent in thermodynamic equilibrium with an external reservoir of the same electrolyte. In accordance with the primitive model of electrolyte solutions, the solvent was treated as a dielectric continuum. The simulations were performed for a set of model parameters, varying the net charge of the matrix (i.e., concentrations of matrix ions) and of annealed electrolyte, in addition to the dielectric constant of the invading solution. The concentration of adsorbed electrolyte was found to be lower than the corresponding concentration of the equilibrium bulk solution. This electrolyte "exclusion" depends strongly on the dielectric constant of the invading solution, as also on concentrations of all components. The most important parameter is the net charge of the matrix. Interestingly, the electrolyte rejection decreases with increasing Bjerrum length for the range of parameters studied here. The latter finding can be ascribed to strong inter-ionic correlation in cases where the Bjerumm length is high enough. To a minor extent, the adsorption also depends on the spacial distribution of fixed charges in adsorbent material. The replica Ornstein-Zernike theory was modified to cater for this model and tested against the computer simulations. For the range of parameters explored in this work, the agreement between the two methods is very good. These calculations were also compared with the results of the classical Donnan theory for electrolyte exclusion.     

Ion transport and molecular organization are coupled in polyelectrolyte-modified nanopores

Chemically modified nanopores show a strong and nontrivial coupling between ion current and the structure of the immobilized species. In this work we study theoretically the conductance and structure in polymer modified nanopores and explicitly address the problem of the coupling between ion transport and molecular organization. Our approach is based on a nonequilibrium molecular theory that couples ion conductivity with the conformational degrees of freedom of the polymer and the electrostatic and nonelectrostatic interactions among polyelectrolyte chains, ions, and solvent. We apply the theory to study a cylindrical nanopore between two reservoirs as a function of pore diameter and length, the length of the polyelectrolyte chains, their grafting density, and whether they are present or not on the outer reservoir walls. In the very low applied potential regime, where the distribution of polyelectrolyte and ions is similar to that in equilibrium, we present a simple analytical model based on the combination of the different resistances in the system that describes the conductance in excellent agreement with the calculations of the full nonequilibrium molecular theory. On the other hand, for a large applied potential bias, the theory predicts a dramatic reorganization of the polyelectrolyte chains and the ions. This reorganization results from the global optimization of the different interactions in the system under nonequilibrium conditions. For nanopores modified with long chains, this reorganization leads to two interesting physical phenomena: (i) control of polyelectrolyte morphology by the direction and magnitude of ion-fluxes and (ii) an unexpected decrease in system resistance with the applied potential bias for long chains due to the coupling between polyelectrolyte segment distribution and ion currents.     

Structural characterization of surfactant aggregates adsorbed in cylindrical silica nanopores

The self-assembly of nonionic surfactants in the cylindrical pores of SBA-15 silica with a pore diameter of 8 nm was studied by small-angle neutron scattering (SANS) at different solvent contrasts. The alkyl ethoxylate surfactants C(10)E(5) and C(12)E(5) exhibit strong aggregative adsorption in the pores as indicated by the sigmoidal shape of the adsorption isotherms. The SANS intensity profiles can be represented by a sum of two terms, one accounting for diffuse scattering from surfactant aggregates in the pores and the other for Bragg scattering from the pore lattice of the silica matrix. The Bragg reflections are analyzed with a form factor model in which the radial density profile of the surfactant in the pore is approximated by a two-step function. Diffuse scattering is represented by a Teubner-Strey-type scattering function which indicates a preferred distance between adsorbed surface aggregates in the pores. Our results suggest that adsorption starts with formation of discrete surface aggregates which increase in number and eventually merge to interconnected patches as the plateau value of the adsorption isotherm is approached. A grossly different behavior, viz. formation of micelles as in solution, is found for the maltoside surfactant C(10)G(2), in agreement with the observed weak adsorption of this surfactant in SBA-15.     

Effect of linear surface-charge non-uniformities on the electrokinetic ionic-current rectification in conical nanopores

The electrokinetic ionic-current rectification in a conical nanopore with linearly varying surface-charge distributions is studied theoretically by using a continuum model composed of a coupled system of the Nernst-Planck equations for the ionic-concentration field and the Poisson equation for the electric potential in the electrolyte solution. The numerical analysis includes the electrochemistry inside reservoirs connected to the nanopore, neglected in previous studies, and more precise accounts of the ionic current are provided. The surface-charge distribution, especially near the tip of the nanopore, significantly affects the ionic enrichment and depletion, which, in turn, influence the resulting ionic current and the rectification. It is shown that non-uniform surface-charge distribution can reverse the direction, or sense, of the rectification. Further insights into the ionic-current rectification are provided by discussing the intriguing details of the electric potential and ionic-concentration fields, leading to the rectification. Rationale for future studies on ionic-current rectification, associated with other non-uniform surface-charge distributions and electroosmotic convection for example, is discussed.