Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

Critical adsorption and charge reversal in polyelectrolyte solutions: Analytical mean-field theory

An analytical linearized mean-field theory is presented to describe the adsorption behavior of polyelectrolytes near charged colloidal surfaces with additional short-ranged non-electrostatic interactions. The coupling between the polyelectrolyte segment density and electrostatic potential is explicitly accounted for in a self-consistent manner. This coupling gives rise to highly non-linear behavior, such as oscillations of the electrostatic potential. We derive analytical expressions for the critical surface charge density σc, after which adsorption takes place, and recover the well-known σc∼ns3/2 scaling regime, where ns is the salt concentration. In addition, the theory yields a new ns1 scaling regime if the surface is hard and a unified ns1 scaling regime if the surface also possesses some short-ranged attraction with the polyelectrolyte. Furthermore, we derive an analytical expression to describe the critical polyelectrolyte concentration φc to achieve complete charge reversal, which is found to scale as φc ∼ σ2/(f2c2), where c is related to the magnitude of short-ranged interactions and f is the average charge per monomer of the polyelectrolyte. It is observed that within our theory, complete charge reversal can only take place if the short-ranged interactions are sufficiently strong to completely compensate for the entropy loss of adsorption.

Critical adsorption of multiple polyelectrolytes onto a nanosphere: splitting the adsorption-desorption transition boundary

Employing extensive Monte Carlo computer simulations, we investigate in detail the properties of multichain adsorption of charged flexible polyelectrolytes (PEs) onto oppositely charged spherical nanoparticles (SNPs). We quantify the conditions of critical adsorption-the phase-separation curve between the adsorbed and desorbed states of the PEs-as a function of the SNP surface-charge density and the concentration of added salt. We study the degree of fluctuations of the PE-SNP electrostatic binding energy, which we use to quantify the emergence of the phase subtransitions, including a series of partially adsorbed PE configurations. We demonstrate how the phase-separation adsorption-desorption boundary shifts and splits into multiple subtransitions at low-salt conditions, thereby generalizing and extending the results for critical adsorption of a single PE onto the SNP. The current findings are relevant for finite concentrations of PEs around the attracting SNP, such as the conditions for PE adsorption onto globular proteins carrying opposite electric charges.

Adsorption and encapsulation of flexible polyelectrolytes in charged spherical vesicles

We present a theory of adsorption of flexible polyelectrolytes on the interior and exterior surfaces of a charged vesicle in an electrolyte solution. The criteria for adsorption and the density profiles of the adsorbed polymer chain are derived in terms of various characteristics of the polymer, vesicle, and medium, such as the charge density and length of the polymer, charge density and size of the vesicle, electrolyte concentration and dielectric constant of the medium. For adsorption inside the vesicle, the competition between the loss of conformational entropy and gain in adsorption energy results in two kinds of encapsulated states, depending on the strength of the polymer-vesicle interaction. By considering also the adsorption from outside the vesicle, we derive the entropic and energy contributions to the free energy change to transfer an adsorbed chain in the interior to an adsorbed chain on the exterior. In this paper, we have used the Wentzel-Kramers-Brillouin (WKB) method to solve the equation for the probability distribution function of the chain. The present WKB results are compared with the previous results based on variational methods. The WKB and variational results are in good agreement for both the interior and exterior states of adsorption, except in the zero-salt limit for adsorption in the exterior region. The adsorption criteria and density profiles for both the interior and exterior states are presented in terms of various experimentally controllable variables. Calculation of the dependencies of free energy change to transfer an adsorbed chain from the interior to the exterior surface on salt concentration and vesicle radius shows that the free energy penalty to expel a chain from a vesicle is only of the order of thermal energy.

Controlling Polyelectrolyte Adsorption onto Carbon Nanotubes by Tuning Ion-Image Interactions

Understanding and controlling polyelectrolyte adsorption onto carbon nanotubes is a fundamental challenge in nanotechnology. Polyelectrolytes have been shown to stabilize nanotube suspensions through adsorbing onto the nanotube surface, and polyelectrolyte-coated nanotubes are emerging as building blocks for complex and addressable self-assembly. Conventional wisdom suggests that polyelectrolyte adsorption onto nanotubes is driven by specific chemical or van der Waals interactions. We develop a simple mean-field model and show that ion-image attraction significantly effects adsorption onto conducting nanotubes at low salt concentrations. Our theory suggests a simple strategy to selectively and reversibly functionalize carbon nanotubes on the basis of their electronic structures, which in turn modify the ion-image attraction.

Shaping membrane vesicles by adsorption of a semiflexible polymer

The adsorption of polymers onto fluid membranes is a problem of fundamental interest in biology and soft materials, in part because the flexibility of membranes can lead to nontrivial coupling between polymer and membrane configurations. Here, we use Monte Carlo computer simulations to study the adsorption of a semiflexible polymer onto a fluid membrane vesicle. Polymer adsorption can significantly impact both the vesicle and polymer shapes, and we identify distinct classes of configurations that emerge as a function of polymer persistence length, membrane bending rigidity, adsorption strength, and vesicle size. Large-scale deformations of the vesicle include invaginations of the membrane that internalize the polymer in a membrane bud. The buds range from disk-like shapes surrounding a collapsed polymer to tubular deformations enveloping rod-like polymers. For small vesicles, polymer adsorption also induces dumbbell-like vesicle shapes with a narrow membrane constriction circled by the polymer. Vesicles with sufficiently small or large bending rigidities adopt configurations similar to those without the polymer present. We further characterize statistical properties of the membrane and polymer configurations and identify distinct classes of polymer configurations that emerge within membrane buds. Analysis of idealized polymer-membrane configurations provides additional insight into transitions between bud shapes.

Critical adsorption of periodic and random polyampholytes onto charged surfaces

How different are the properties of critical adsorption of polyampholytes and polyelectrolytes onto charged surfaces? How important are the details of polyampholyte charge distribution on the onset of critical adsorption transition? What are the scaling relations governing the dependence of critical surface charge density on salt concentration in the surrounding solution? Here, we employ Metropolis Monte Carlo simulations and uncover the scaling relations for critical adsorption for quenched periodic and random charge distributions along the polyampholyte chains. We also evaluate and discuss the dependence of the adsorbed layer width on solution salinity and details of the charge distribution. We contrast our findings to the known results for polyelectrolyte adsorption onto oppositely charged surfaces, in particular, their dependence on electrolyte concentration.

Conformational properties of block-polyampholytes adsorbed on charged cylindrical surfaces

Polyampholytes are polymers that have positive and negative monomers along their chain. The adsorption of polyampholytes on charged surfaces has been the subject of a large number of theoretical, computational and experimental studies due to its importance in a variety of bio and nanothechnological systems. However, computational studies focusing on interaction between polyampholytes and cylindrical charged surfaces are rather scarce. This study, therefore, aims to investigate the conformational properties of block-polyampholytes in the presence of a negatively charged cylinder by means of Metropolis Monte Carlo simulations. Adopting a simplified model in which the electrolyte solution is treated at the Debye-Hückel level, the effects of the ionic strength, the linear charge density of the cylinder and the block length on monomers distributions have been investigated. It was found that increasing the salt concentration promotes a transition from a conformation characterized by large loops to a necklace-like conformation parallel to the surface. It was also shown that, at low cylinder charge density, the increase in salt concentration and the length of the blocks lead to a change in the orientation of the adsorbed chain.

Molecular Dynamics Simulations of Adsorption of Poly(acrylic acid) and Poly(methacrylic acid) on Dodecyltrimethylammonium Chloride Micelle in Water: Effect of Charge Density

We have investigated the interaction of dodecyltrimethylammonium chloride (DoTA) micelle with weak polyelectrolytes, poly(acrylic acid) and poly(methacrylic acid). Anionic as well as un-ionized forms of the polyelectrolytes were studied. Polyelectrolyte-surfactant complexes were formed within 5-11 ns of the simulation time and were found to be stable. Association is driven purely by electrostatic interactions for anionic chains whereas dispersion interactions also play a dominant role in the case of un-ionized chains. Surfactant headgroup nitrogen atoms are in close contact with the carboxylic oxygens of the polyelectrolyte chain at a distance of 0.35 nm. In the complexes, the polyelectrolyte chains are adsorbed on to the hydrophilic micellar surface and do not penetrate into the hydrophobic core of the micelle. Polyacrylate chain shows higher affinity for complex formation with DoTA as compared to polymethacrylate chain. Anionic polyelectrolyte chains show higher interaction strength as compared to corresponding un-ionized chains. Anionic chains act as polymeric counterion in the complexes, resulting in the displacement of counterions (Na(+) and Cl(-)) into the bulk solution. Anionic chains show distinct shrinkage upon adsorption onto the micelle. Detailed information about the microscopic structure and binding characteristics of these complexes is in agreement with available experimental literature.

Inverted critical adsorption of polyelectrolytes in confinement

What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density σc-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of σc for the concave interfaces versus the Debye screening length 1/κ and the extent of confinement a for these three interfaces for small κa values. For large κa the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/κ. We also rationalize how σc(κ) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.

Global analysis of the ground-state wrapping conformation of a charged polymer on an oppositely charged nano-sphere

We investigate the wrapping conformations of a single, strongly adsorbed polymer chain on an oppositely charged nano-sphere by employing a reduced (dimensionless) representation of a primitive chain-sphere model. This enables us to determine the global behavior of the chain conformation in a wide range of values for the system parameters including the chain contour length, its linear charge density and persistence length as well as the nano-sphere charge and radius, and also the salt concentration in the bathing solution. The structural behavior of a charged chain-sphere complex can be described in terms of a few distinct conformational symmetry classes separated by continuous or discontinuous transition lines which are determined by means of appropriately defined (order) parameters. Our results can be applied to a wide class of strongly coupled polymer-sphere complexes including, for instance, complexes that comprise a mechanically flexible or semiflexible polymer chain or an extremely short or long chain and, as a special case, include the biologically relevant example of DNA-histone complexes.

Critical adsorption of polyelectrolytes onto charged Janus nanospheres

The conditions of critical polyelectrolyte adsorption onto spherical charged Janus nano-particles are exploited by Monte-Carlo computer simulations and theoretically.

Packing of charged chains on toroidal geometries

We study a strongly adsorbed flexible polyelectrolyte chain on tori. In this generalized Thomson problem, the patterns of the adsorbed chain are analyzed in the space of the toroidal coordinates and in terms of the orientation of each chain segment. Various patterns are found, including double spirals, disclination-like structures, Janus tori, and uniform wrappings, arising from the long-range electrostatic interaction and the toroidal geometry. Their broken mirror symmetry is quantitatively characterized by introducing an order parameter, an integral of the torsion. The uniform packing, which breaks the mirror symmetry the least, has the lowest value of the order parameter. In addition, it is found that the electrostatic energy of confined chains on tori conforms to a power law regardless of the screening effect in some typical cases studied. Furthermore, we study random walks on tori that generate chain configurations in the large screening limit or at large thermal fluctuation; some features associated with the toroidal geometry are discussed.

The bridging force between colloidal particles in a polyelectrolyte solution

The presence of a polyelectrolyte in a colloidal dispersion affects the interaction between colloidal particles through electrostatic and bridging interactions. In this paper, using a self-consistent field approach, a simple theory is developed which allows for the calculation of the bridging force between two plates and two colloidal particles. The present approach differs from the previous ones, since the contribution of the plate-solution interfacial tension to the free energy is taken into account in the calculation. The interfacial tension between solvent and plate depends on the nature of the particles and the concentration of the segments of the polymer at the surface. The surface-segment interaction has a significant effect on the segment concentration profile. When the segment-surface interaction is repulsive, the bridging force is weak because few polyelectrolyte chains are adsorbed onto the surface. When the segment-surface interaction is attractive, various segment concentration profiles could be identified. Depending upon the concentration of polyelectrolyte, the electrostatic plus bridging forces can be attractive or repulsive. The bridging force between two plates which is attractive has a longer range than the van der Waals interaction.

Polyelectrolyte adsorption onto oppositely charged interfaces: image-charge repulsion and surface curvature

We analyze theoretically the influence of low-dielectric boundaries on the adsorption of flexible polyelectrolytes onto planar and spherical oppositely charged surfaces in electrolyte solutions. We rationalize to what extent polymer chains are depleted from adsorbing interfaces by repulsive image forces. We employ the WKB (Wentzel-Kramers-Brillouin) quantum mechanical method for the Green function of the Edwards equation to determine the adsorption equilibrium. Scaling relations are determined for the critical adsorption strength required to initiate polymer adsorption onto these low-dielectric supports. Image-force repulsion shifts the equilibrium toward the desorbed state, demanding larger surface charge densities and polyelectrolyte linear charge densities for the adsorption to take place. The effect is particularly pronounced for a planar interface in a low-salt regime, where a dramatic change in the scaling behavior for the adsorption-desorption transition is predicted. For the adsorbed state, polymers with higher charge densities are displaced further from the interface by image-charge repulsions. We discuss relevant experimental evidence and argue about possible biological applications of the results.

Critical polyelectrolyte adsorption under confinement: planar slit, cylindrical pore, and spherical cavity

We explore the properties of adsorption of flexible polyelectrolyte chains in confined spaces between the oppositely charged surfaces in three basic geometries. A method of approximate uniformly valid solutions for the Green function equation for the eigenfunctions of polymer density distributions is developed to rationalize the critical adsorption conditions. The same approach was implemented in our recent study for the "inverse" problem of polyelectrolyte adsorption onto a planar surface, and on the outer surface of rod-like and spherical obstacles. For the three adsorption geometries investigated, the theory yields simple scaling relations for the minimal surface charge density that triggers the chain adsorption, as a function of the Debye screening length and surface curvature. The encapsulation of polyelectrolytes is governed by interplay of the electrostatic attraction energy toward the adsorbing surface and entropic repulsion of the chain squeezed into a thin slit or small cavities. Under the conditions of surface-mediated confinement, substantially larger polymer linear charge densities are required to adsorb a polyelectrolyte inside a charged spherical cavity, relative to a cylindrical pore and to a planar slit (at the same interfacial surface charge density). Possible biological implications are discussed briefly in the end.

Biocompatible nanoparticles trigger rapid bacteria clustering

This study reveals an exciting phenomenon of stimulated bacteria clustering. Rapid aggregation and microbial arrest are shown to occur in Escherichia coli solutions of neutral pH when chitosan nanoparticles with positive zeta potential are added. Because chitosan nanoparticles can easily be dispersed in aqueous buffers, the rapid clustering phenomenon requires only minuscule nanoparticle concentrations and will be critical in developing new methods for extricating bacterial pathogens. This work establishes the dominant role of electrostatic attraction in bacteria-nanoparticle interactions by varying the nanoparticle zeta potential from highly positive to strongly negative values, and by exploring concentration effects. For strongly negative nanoparticles, no clusters form, while aggregates are small and loose at intermediate conditions. In addition, optical density measurements indicate that over 90% of the suspended bacteria flocculate within seconds of being mixed with chitosan nanoparticles of a highly positive surface charge. Finally, the nanoparticles are significantly more efficient as a clustering agent compared to an equal mass of molecular chitosan in solution, as the bacteria-nanoparticle clusters formed are substantially larger. The bacteria-nanoparticle aggregation effect demonstrated here promises a rapid separation method for aiding pathogen detection and for flocculation of bacteria in fermentation processes.

Electrostatics in soft matter

Recent progress in understanding the effect of electrostatics in soft matter is presented. A vast number of materials contain ions, ranging from the molecular scale (e.g. electrolyte) to the meso/macroscopic one (e.g. charged colloidal particles or polyelectrolytes). Their (micro)structure and physico-chemical properties are especially dictated by the famous and redoubtable long-ranged Coulomb interaction. In particular, theoretical and simulational aspects, including the experimental motivations, will be discussed.

Generalized electrostatic model of the wrapping of DNA around oppositely charged proteins

Histonelike proteins in prokaryotes and histone octamers in eukaryotes carry large positive charges, which are responsible of strong electrostatic interactions with DNA. As a result, DNA wraps around proteins and genetic information is condensed. We describe a generalized model of these electrostatic interactions mediated by salt that explains the wrapping of DNA around the nucleosome octamer, around remodeling factors in eukaryotes and around histonelike proteins in prokaryotes. It comes out that small changes in protein dimension and charge produce large effects in the supramolecular DNA-protein architecture.

Adsorption of DNA onto positively charged amidine colloidal spheres and the resultant bridging interaction

The complexation behaviour of duplex linear DNA (negatively charged) with amidine functionalised sub-micron latex spheres (positively charged) was studied using dynamic light scattering (DLS) and a PALS interferrometric zeta potential sizer. Four types of DNA-sphere complex were investigated as a function of component concentration by combining amidine functionalised polystyrene microspheres with radii of 10.5 nm and 60 nm, and herring DNA of lengths of 35 nm and 85 nm. At low DNA concentrations (c(DNA)), the undercharged complexes showed a small increase in measured hydrodynamic radius (R(h)) and a decrease in zeta potential with increasing c(DNA). Within a critical DNA concentration range R(h) was seen to peak sharply, and the zeta potentials were approximately 0 mV, corresponding to the formation of unstable neutral complexes. Immediately above this concentration region the measured R(h) values became comparable with those at low c(DNA), and the zeta potential became negative, indicating the formation of stable overcharged complexes. The small and large spheres formed multi-sphere and single sphere overcharged aggregates respectively, which is thought to be determined by the relative magnitude of the chain persistence length (approximately 50 nm) and the sphere radius, switching on or off the DNA bridging interaction.

Electrostatics of DNA Complexes with Cationic Lipid Membranes

We present the exact solutions of the linear Poisson-Boltzmann equation for several problems relevant to electrostatics of DNA complexes with cationic lipids. We calculate the electrostatic potential and electrostatic energy for lamellar and inverted hexagonal phases, concentrating on the effects of dielectric boundaries. We compare our results for the complex energy with the known results of numerical solution of the nonlinear Poisson-Boltzmann equation. Using the solution for the lamellar phase, we calculate the compressibility modulus and compare our findings with the experimental data available. Also, we treat charge-charge interactions across, along, and between two low-dielectric membranes. We obtain an estimate for the strength of electrostatic interactions of one-dimensional DNA smectic layers across the lipid membrane. We discuss in the end some aspects of two-dimensional DNA condensation and DNA-DNA attraction in the DNA-lipid lamellar phase in the presence of di- and trivalent cations. We analyze the equilibrium DNA-DNA separations in lamellar complexes using the recently developed theory of electrostatic interactions of DNA helical charge motifs.

Adsorption of Weakly Charged Polyelectrolytes onto Oppositely Charged Spherical Colloids

The adsorption of a long weakly charged flexible polyelectrolyte in a salt solution onto an oppositely charged spherical surface is investigated. An analytical solution for Green's function is derived, which is valid for any sphere radius and consistently recovers the result of a planar surface in the limit of large sphere radii, by substituting the Debye-Hückel potential via the Hulthén potential. Expressions for critical quantities like the critical radius and the critical surface charge density are provided. In particular, we find a universal critical line for the sphere radius as a function of the screening length separating adsorbed from desorbed states. Moreover, results for the monomer density distribution, adsorbed layer thickness, and the radius of gyration are presented. A comparison of our theoretical results with experiments and computer simulations yields remarkably good agreement.

Spontaneous stretching of DNA in a two-dimensional nanoslit

DNA molecules in silicon dioxide-glass fluidic nanoslits spontaneously extend at the lateral sidewalls of the slit. The nanoslit geometry, however, physically confines polymer molecules to two spatial dimensions; further reduction in configurational entropy resulting in axially stretched molecules arises spontaneously and appears to be electrostatically mediated. The observations not only shed light on electrostatic interactions of charged soft matter with like-charged confining walls but also offer a new method to stretch DNA in solution.