Mobility reversal of polyelectrolyte-grafted colloids in monovalent salt solutions

Inertial migration of polymer micelles in a square microchannel

Using a hybrid simulation approach that combines a lattice-Boltzmann method for fluid flow and a molecular dynamics model for polymers, we investigate the inertial migration of star-like and crew-cut polymer micelles in a square microchannel. It is found that they exhibit two types of equilibrium positions, which shift further away from the center of the microchannel when the Reynolds number (Re) increases, as can be observed for soft particles. What differs from the behaviors of soft particles is that here, the blockage ratio is no longer the decisive factor. When the sizes are the same, the star-like micelles are always relatively closer to the microchannel wall as they gradually transition from spherical to disc-like with the increase of Re. In comparison, the crew-cut micelles are only transformed into an ellipsoid. Conversely, when the hydrophobic core sizes are the same, the equilibrium position of the star-like micelles becomes closer to that of the crew-cut micelles. Our results demonstrate that for polymer micelles with a core-shell structure, the equilibrium position is no longer solely determined by their overall dimensions but depends on the core and shell's specific dimensions, especially the hydrophobic core size. This finding opens up a new approach for achieving the separation of micelles in inertial migration.

Nonmonotonic electrophoretic mobility of rodlike polyelectrolytes by multivalent coions in added salt

It is well established that when multivalent counterions or salts are added to a solution of highly charged polyelectrolytes (PEs), correlation effects can cause charge inversion of the PE, leading to electrophoretic mobility (EM) reversal. In this work, we use coarse-grained molecular-dynamics simulations to unravel the less understood effect of coion valency on EM reversal for rigid DNA-like PEs. We find that EM reversal induced by multivalent counterions is suppressed with increasing coion valency in the salt added and eventually vanishes. Further, we find that EM is enhanced at fixed low salt concentrations for salts with monovalent counterions when multivalent coions with increasing valency are introduced. However, increasing the salt concentration causes a crossover that leads to EM reversal which is enhanced by increasing coion valency at high salt concentration. Remarkably, this multivalent coion-induced EM reversal persists even for low values of PE linear charge densities where multivalent counterions alone cannot induce EM reversal. These results facilitate tuning PE-PE interactions and self-assembly with both coion and counterion valencies.

Swelling and shrinking of two opposing polyelectrolyte brushes

Salt concentration and confinement effects affect the configuration of polyelectrolyte (PE) brushes due to electrostatic interactions. In this work, we develop a new theoretical model to analyze the electrostatics and swelling-shrinking behavior of two opposing PE brushes. By comparing three length scales, i.e., equilibrium brush height, separation distance, and Debye length, we obtain distinct scaling laws for brush height in different regimes. We provide explanations for the anomalous shrinkage of the PE brush with added salt reported in experiments and simulations, the applicability of the homogeneous brush assumption, and the confinement effect on the brush height. Our model can be used to shed light on the configuration and functionalities of PE-grafted interfaces, which play important roles in ion selective membranes and organism lubrication. We also anticipate that our method will be useful to understand the functionalities of other charged soft matter systems, such as hydrogel swelling and colloidal stability.

Electroosmotic flow velocity in DNA modified nanochannels

Electroosmotic flow (EOF) is systematically investigated in DNA grafted hard PDMS (h-PDMS) channels with size ranging from 50 nm to 2.5 μm by using the current-slope method. The effects of the DNA types, the incubation time in the process of surface modification, and the pH value, ionic concentration of electrolyte solutions, and the UV (ultraviolet) illumination on the velocity of electroosmotic flow are experimentally studied. It is found that the DNA type and the incubation time of DNAs affect the grafting density and the surface charge on the channel walls, thus influencing the EOF velocity. In the DNA modified channels, the pH effects on EOF velocity become less prominent compared with that in the pristine channels. On the contrary, UV illumination can increase the EOF velocity significantly in the DNA modified channels, whereas takes unapparent effects on EOF velocity in the pristine channels. The effects of ionic concentration on EOF are also studied in this paper. It is observed that EOF velocity is dependent on the channel size when the ionic concentration is low even without overlapped electric double layer (EDL) and is essentially independent of the channel size when the ionic concentration is high. Furthermore, with high ionic concentration and thin EDL, the EOF velocity can be enhanced by the coated DNA brushes on the channel surface.

The role of pH, metal ions and their hydroxides in charge reversal of protein-coated nanoparticles

In this study, we investigated charge inversion of protein-coated Au nanoparticles caused by the addition of metal ions. Adsorbed metal hydroxides were identified to cause the charge inversion of the NPs by using a combination of cryo-TEM, EFTEM andζ-potential measurements.

Remarkable reversal of electrostatic interaction forces on zwitterionic soft nanointerfaces in a monovalent aqueous electrolyte: an AFM study at the single nanoparticle level

Soft (nano)colloids are increasingly used in medical applications due to the versatile options they offer in terms of e.g. tunable chemical composition, adaptable physical properties and (bio)functionalization perspectives. Obtaining a clear understanding of the nature of the interaction forces that such particles experience with neighboring charged (bio)surfaces is a mandatory prerequisite to draw a comprehensive and mechanistic picture of their stability and reactivity and to further optimize their current functionalities. In this study, adopting an original strategy for nanoparticle attachment to atomic force microscopy (AFM) tips, we demonstrate that the sign of electrostatic forces between carboxylate-terminated poly(amidoamine) nanodendrimers (∼9 nm in diameter) and planar cysteamine-coated gold surfaces can be tailored under fixed pH conditions upon the sole variation of the monovalent salt concentration in solution. The origin of this unconventional electrostatic force reversal is deciphered upon confrontation between AFM force measurements and mean-field force evaluation performed beyond the Derjaguin approximation by integrating the dendrimer and cysteamine electrostatic properties derived independently from electrokinetic measurements. It is shown that the electrostatic force reversal (i) originates from the zwitterionic character of the nanodendrimer-solution interphase, and (ii) becomes operational under the strict condition that the sub-nanometric separation distance between peripheral carboxylate groups and intraparticulate amines is of the order of the characteristic electric Debye layer thickness. The possibility to mediate - via suitable adjustment of monovalent salt content in solution - both the magnitude and sign of the electrostatic forces acting on soft interfaces with zwitterionic functionality paves the way for the design of innovative strategies to control the stability of nanoparticles against aggregation, and to modulate their adhesion onto inorganic surfaces or living organisms.

Assessing numerical methods for molecular and particle simulation

We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss the characteristics of different algorithms, including their essential conservation properties, the convergence of averages, and the accuracy of numerical discretizations. Formulations of the equations of motion which are suited to both equilibrium and nonequilibrium simulation include Langevin dynamics, dissipative particle dynamics (DPD), and the more recently proposed "pairwise adaptive Langevin" (PAdL) method, which, like DPD but unlike Langevin dynamics, conserves momentum and better matches the relaxation rate of orientational degrees of freedom. PAdL is easy to code and suitable for a variety of problems in nonequilibrium soft matter modeling; our simulations of polymer melts indicate that this method can also provide dramatic improvements in computational efficiency. Moreover we show that PAdL gives excellent control of the relaxation rate to equilibrium. In the nonequilibrium setting, we further demonstrate that while PAdL allows the recovery of accurate shear viscosities at higher shear rates than are possible using the DPD method at identical timestep, it also outperforms Langevin dynamics in terms of stability and accuracy at higher shear rates.

A dsDNA model optimized for electrokinetic applications

We present a coarse-grained (CG) model of a charged double-stranded DNA immersed in an electrolyte solution that can be used for a variety of electrokinetic applications. The model is based on an earlier rigid and immobile model of Weik et al. and includes now semi-flexibility and mobility, so that DNA dynamics can be sufficiently captured to simulate a full nanopore translocation process. To this end we couple the DNA hydrodynamically via a raspberry approach to a lattice-Boltzmann fluid and parametrize the counterions with a distant dependent friction. The electrokinetic properties of the CG DNA model inside an infinite cylinder is fitted against experimental data from Smeets et al. and all-atom simulation data from Kesselheim et al. The stiffness of our CG DNA is modeled via a harmonic angle potential fitted against experimental data of Brunet et al. Finally, the quality of our tuned parameters is tested by measuring the electrophoretic mobility of our DNA model for various numbers of base pairs and salt concentrations. Our results compare excellently with the experimental data sets of Stellwagen et al. and Hoagland et al.

Solvent-mediated nonelectrostatic ion-ion interactions predicting anomalies in electrophoresis

We study the effects of solvent-mediated nonelectrostatic ion-ion interactions on electrophoretic mobility of a charged spherical particle. To this end, we consider the case of low surface electrostatic potential resulting in the linearization of the governing equations, which enables us to deduce a closed-form analytical solution to the electrophoretic mobility. We subsequently compare our results to the standard model using Henry's approach and report the changes brought about by the nonelectrostatic potential. The classical approach to determine the electrophoretic mobility underpredicts the particle velocity when compared with experiments. We show that this issue can be resolved by taking into account nonelectrostatic interactions. Our analysis further reveals the phenomenon of electrophoretic mobility reversal that has been experimentally observed in numerous previous studies.

Importance of core electrostatic properties on the electrophoresis of a soft particle

The impact of the volumetric charged density of the dielectric rigid core on the electrophoresis of a soft particle is analyzed numerically. The volume charge density of the inner core of a soft particle can arise for a dendrimer structure or bacteriophage MS2. We consider the electrokinetic model based on the conservation principles, thus no conditions for Debye length or applied electric field is imposed. The fluid flow equations are coupled with the ion transport equations and the equation for the electric field. The occurrence of the induced nonuniform surface charge density on the outer surface of the inner core leads to a situation different from the existing analysis of a soft particle electrophoresis. The impact of this induced surface charge density together with the double-layer polarization and relaxation due to ion convection and electromigration is analyzed. The dielectric permittivity and the charge density of the core have a significant impact on the particle electrophoresis when the Debye length is in the order of the particle size. We find that by varying the ionic concentration of the electrolyte, the particle can exhibit reversal in its electrophoretic velocity. The role of the polymer layer softness parameter is addressed in the present analysis.

Specific ion effects on the electrokinetic properties of iron oxide nanoparticles: experiments and simulations

We report experimental and simulation studies on ion specificity in aqueous colloidal suspensions of positively charged, bare magnetite nanoparticles. Magnetite has the largest saturation magnetization among iron oxides and relatively low toxicity, which explain why it has been used in multiple biomedical applications. Bare magnetite is hydrophilic and the sign of the surface charge can be changed by adjusting the pH, its isoelectric point being in the vicinity of pH = 7. Electrophoretic mobility of our nanoparticles in the presence of increasing concentrations of different anions showed that anions regarded as kosmotropic are more efficient in decreasing, and even reversing, the mobility of the particles. If the anions were ordered according to the extent to which they reduced the particle mobility, a classical Hofmeister series was obtained with the exception of thiocyanate, whose position was altered. Monte Carlo simulations were used to predict the diffuse potential of magnetite in the presence of the same anions. The simulations took into account the ion volume, and the electrostatic and dispersion forces among the ions and between the ions and the solid surface. Even though no fitting parameters were introduced and all input data were estimated using Lifshitz theory of van der Waals forces or obtained from the literature, the predicted diffusion potentials of different anions followed the same order as the mobility curves. The results suggest that ionic polarizabilities and ion sizes are to a great extent responsible for the specific ion effects on the electrokinetic potential of iron oxide particles.

Recent Progress and Perspectives in the Electrokinetic Characterization of Polyelectrolyte Films

The analysis of the charge, structure and molecular interactions of/within polymeric substrates defines an important analytical challenge in materials science. Accordingly, advanced electrokinetic methods and theories have been developed to investigate the charging mechanisms and structure of soft material coatings. In particular, there has been significant progress in the quantitative interpretation of streaming current and surface conductivity data of polymeric films from the application of recent theories developed for the electrohydrodynamics of diffuse soft planar interfaces. Here, we review the theory and experimental strategies to analyze the interrelations of the charge and structure of polyelectrolyte layers supported by planar carriers under electrokinetic conditions. To illustrate the options arising from these developments, we discuss experimental and simulation data for plasma-immobilized poly(acrylic acid) films and for a polyelectrolyte bilayer consisting of poly(ethylene imine) and poly(acrylic acid). Finally, we briefly outline potential future developments in the field of the electrokinetics of polyelectrolyte layers.

The raspberry model for hydrodynamic interactions revisited. I. Periodic arrays of spheres and dumbbells

The so-called "raspberry" model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy this problem by adding internal coupling points. Finally, we examine a non-convex shape, namely, a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in de Graaf et al. [J. Chem. Phys. 143, 084108 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.

Corona charge regulation in nanoparticle electrophoresis

Nanoparticle (NP) size and charge play key roles in bioconjugation chemistry, imaging and drug delivery. Although the electrophoretic mobility and hydrodynamic size are routinely measured, interpreting these data can be extremely difficult. Here, the challenge is addressed via an electrokinetic model for spheres bearing a soft amphoteric corona, the charge of which is regulated by a multi-component electrolyte. The model is applied to NPs with a metallic core to which are grafted poly(ethylene glycol) chains with either weak acid or amphiprotic end groups. The results elucidate the separate roles of electrolyte pH and ionic strength on the electrophoretic mobility and diffusion coefficient. In this study, the forces were evaluated directly, rather than from the Stokeslet velocity disturbances. While the second-order convergence was demonstrated by both methods, the direct approach, which uses only the inner part of the global solution, furnished superior accuracy and robustness. This may benefit future attempts to model the dielectric and electroacoustic properties of these complex nanoparticulates.

Nonlinear electro-osmosis of dilute non-adsorbing polymer solutions with low ionic strength

Nonlinear electro-osmotic behaviour of dilute non-adsorbing polymer solutions with low salinity is investigated using Brownian dynamics simulations and a kinetic theory. In the Brownian simulations, the hydrodynamic interaction between the polymers and a no-slip wall is considered using the Rotne-Prager approximation of the Blake tensor. In a plug flow under a sufficiently strong applied electric field, the polymer migrates toward the bulk, forming a depletion layer thicker than the equilibrium one. Consequently, the electro-osmotic mobility increases nonlinearly with increasing electric field and becomes saturated. This nonlinear mobility does not depend qualitatively on the details of the rheological properties of the polymer solution. Analytical calculations using the kinetic theory for the same system quantitatively reproduce the results of the Brownian dynamics simulation well.

Computer simulations of single particles in external electric fields

Applying electric fields is an attractive way to control and manipulate single particles or molecules, e.g., in lab-on-a-chip devices. However, the response of nanosize objects in electrolyte solution to external fields is far from trivial. It is the result of a variety of dynamical processes taking place in the ion cloud surrounding charged particles and in the bulk electrolyte, and it is governed by an intricate interplay of electrostatic and hydrodynamic interactions. Already systems composed of one single particle in electrolyte solution exhibit a complex dynamical behaviour. In this review, we discuss recent coarse-grained simulations that have been performed to obtain a molecular-level understanding of the dynamic and dielectric response of single particles and single macromolecules to external electric fields. We address both the response of charged particles to constant fields (DC fields), which can be characterized by an electrophoretic mobility, and the dielectric response of both uncharged and charged particles to alternating fields (AC fields), which is described by a complex polarizability. Furthermore, we give a brief survey of simulation algorithms and highlight some recent developments.

Remarkable electrokinetic features of charge-stratified soft nanoparticles: mobility reversal in monovalent aqueous electrolyte

The electrokinetic behavior of G6.5 carboxylate-terminated poly(amidoamine) (PAMAM) starburst dendrimers (8 ± 1 nm diameter) is investigated over a broad range of pH values (3-9) and NaNO3 concentrations (c(∞ )= 2-200 mM). The dependence of nanodendrimer electrophoretic mobility μ on pH and c(∞) is marked by an unconventional decrease of the point of zero mobility (PZM) from 5.4 to 5.5 to 3.8 upon increase in salt concentration, with PZM defined as the pH value at which a reversal of the mobility sign is reached. The existence of a common intersection point is further evidenced for series of mobility versus pH curves measured at different NaNO3 concentrations. Using soft particle electrokinetic theory, this remarkable behavior is shown to originate from the zwitterionic functionality of the PAMAM-COOH particles. The dependence of PZM on c(∞) results from the coupling between electroosmotic flow and dendrimeric interphase defined by a nonuniform distribution of amine and carboxylic functional groups. In turn, μ reflects the sign and distribution of particle charges located within an electrokinetically active region, the dimension of which is determined by the Debye length, varied here in the range 0.7-6.8 nm. In agreement with theory, the electrokinetics of smaller G4.5 PAMAM-COOH nanoparticles (5 ± 0.5 nm diameter) further confirms that the PZM is shifted to higher pH with decreasing dendrimer size. Depending on pH, a mobility extremum is obtained under conditions where the Debye length and the particle radius are comparable. This results from changes in particle structure compactness following salt- and pH-mediated modulations of intraparticle Coulombic interactions. The findings solidly evidence the possible occurrence of particle mobility reversal in monovalent salt solution suggested by recent molecular dynamic simulations and anticipated from earlier mean-field electrokinetic theory.