The Formation and Salt Induced Melting of a Highly Viscoelastic Mixture of Two Oppositely Charged Polyelectrolytes

A quick and convenient route to prepare a highly viscoelastic mixture of two oppositely charged polyelectrolytes is presented. The investigation was essentially performed at a fixed total polyelectrolyte concentration. The phase behaviour was studied at varying ratios between the two oppositely charged polyions. The mixtures phase separated associatively at mixing ratios in the vicinity of overall charge neutrality, while by screening the attractive forces with NaCl the precipitate could be dissolved. At certain mixing ratios off charge neutrality the mixtures were highly viscoelastic single-phase solutions in the absence of screening electrolyte. When NaCl was added to such a solution the viscoelasticity decreased strongly since the attractive forces between the oppositely charged polyions were screened. Therefore, by contacting an initially salt free mixture of polyions with a brine solution of known concentration, the diffusion of salt into the polyion matrices could be monitored by following the rheology of the mixture as a function of the contact time. It is shown that the transport of NaCl inside the polyion matrices was diffusion controlled.     

Phase diagrams of binary mixtures of oppositely charged colloids

Phase diagrams of binary mixtures of oppositely charged colloids are calculated theoretically. The proposed mean-field-like formalism interpolates between the limits of a hard-sphere system at high temperatures and the colloidal crystals which minimize Madelung-like energy sums at low temperatures. Comparison with computer simulations of an equimolar mixture of oppositely charged, equally sized spheres indicate semiquantitative accuracy of the proposed formalism. We calculate global phase diagrams of binary mixtures of equally sized spheres with opposite charges and equal charge magnitude in terms of temperature, pressure, and composition. The influence of the screening of the Coulomb interaction upon the topology of the phase diagram is discussed. Insight into the topology of the global phase diagram as a function of the system parameters leads to predictions on the preparation conditions for specific binary colloidal crystals.     

Phase behavior of mixtures of oppositely charged nanoparticles: heterogeneous Poisson-Boltzmann cell model applied to lysozyme and succinylated lysozyme

We study the phase behavior of mixtures of oppositely charged nanoparticles, both theoretically and experimentally. As an experimental model system we consider mixtures of lysozyme and lysozyme that has been chemically modified in such a way that its charge is nearly equal in magnitude but opposite in sign to that of unmodified lysozyme. We observe reversible macroscopic phase separation that is sensitive not only to protein concentration and ionic strength, but also to temperature. We introduce a heterogeneous Poisson-Boltzmann cell model that generally applies to mixtures of oppositely charged nanoparticles. To account for the phase behavior of our experimental model system, in addition to steric and electrostatic interactions, we need to include a temperature-dependent short-ranged interaction between the lysozyme molecules, the exact origin of which is unknown. The strength and temperature dependence of the short-ranged attraction is found to be of the same order of magnitude as that between unmodified lysozyme molecules. The presence of a rather strong short-ranged attraction in our model system precludes the formation of colloidal liquid phases (or complex coacervates) such as those typically found in mixtures of globular protein molecules and oppositely charged polyelectrolytes.     

Mean spherical model for a mixture of charged spheres and hard dipoles

A solution to the mean spherical model for a mixture of charged hard spheres of equal concentration and opposite charge, and hard dipoles, all of equal size, is given. The excess thermodynamic properties and the structure of the system depend on only 3 parameters, which are the solution of a set of 3 nonlinear, algebraic equations.     

Charge renormalization of charged spheres based on thermodynamic properties

At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles, effective charge Z(*) is therefore invoked in the models based on Debye-Huckel approximation, such as the Derjaguin-Landau-Verwey-Overbeek potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to obtain various thermodynamic properties omega in a spherical Wigner-Seitz cell. The effect of dielectric discontinuity is examined. We show that at the same particle volume fraction, counterions around a highly charged sphere with Z may display the same value of omega as those around a weakly charged sphere with Z(*), i.e., omega(Z)=omega(Z(*)). There exists a maximally attainable value of omega at which Z=Z(*). Defining Z(*) as the effective charge, we find that the effective charge passes through a maximum and declines again due to ion-ion correlation as the number of counterions is increased. The effective charge is even smaller if one adopts the Debye-Huckel expression omega(DH). Our results suggest that charge renormalization can be performed by chemical potential, which may be observed in osmotic pressure measurements.     

Highly charging of nanoparticles through electrospray of nanoparticle suspension

Patterned deposition of nanoparticles is a prerequisite for the application of unique properties of nanoparticles in future nanodevices. Recent development of nanoxerography requires highly charged aerosol nanoparticles to avoid noise deposition due to random Brownian motion. However, it has been known that it is difficult to charge aerosol nanoparticles with more than two elementary charges. The goal of this work is to develop a simple technique for obtaining highly charged monodisperse aerosol nanoparticles by means of electrospray of colloidal suspension. Highly charged aerosol nanoparticles were produced by electrospraying (ES) and drying colloidal suspensions of monodisperse gold nanoparticles. Size and charge distributions of the resultant particles were measured. We demonstrate that this method successfully charges monodisperse nanoparticles very highly, e.g., 122 elementary charges for 25.0 nm, 23.5 for 10.5 nm, and 4.6 for 4.2 nm. The method described here constitutes a convenient, reliable, and continuous tool for preparing highly charged aerosol nanoparticles from suspensions of nanoparticles produced by either wet chemistry or gas-phase methods.     

Sugar-based gemini surfactant with a vesicle-to-micelle transition at acidic pH and a reversible vesicle flocculation near neutral pH

A sugar-based (reduced glucose) gemini surfactant forms vesicles in dilute aqueous solution near neutral pH. At lower pH, there is a vesicle-to-micelle transition within a narrow pH region (pH 6.0-5.6). The vesicles are transformed into large cylindrical micelles that in turn are transformed into small globular micelles at even lower pH. In the vesicular pH region, the vesicles are positively charged at pH < 7 and exhibit a good colloidal stability. However, close to pH 7, the vesicles become unstable and rapidly flocculate and eventually sediment out from the solution. We find that the flocculation correlates with low vesicle zeta-potentials and the behavior is thus well predicted by the classical DLVO theory of colloidal stability. Surprisingly, we find that the vesicles are easily redispersed by increasing the pH to above pH 7.5. We show that this is due to a vesicle surface charge reversal resulting in negatively charged vesicles at pH > 7.1. Adsorption, or binding, of hydroxide ions to the vesicular surface is likely the cause for the charge reversal, and a hydroxide ion binding constant is calculated using a Poisson-Boltzmann model.     

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.     

Phase coexistence in polydisperse charged hard-sphere fluids: mean spherical approximation

Taking advantage of the availability of the analytic solution of the mean spherical approximation for a mixture of charged hard spheres with an arbitrary number of components we show that the polydisperse fluid mixture of charged hard spheres belongs to the class of truncatable free energy models, i.e., to those systems where the thermodynamic properties can be represented by a finite number of (generalized) moments of the distribution function that characterizes the mixture. Thus, the formally infinitely many equations that determine the parameters of the two coexisting phases can be mapped onto a system of coupled nonlinear equations in these moments. We present the formalism and demonstrate the power of this approach for two systems; we calculate the full phase diagram in terms of cloud and shadow curves as well as binodals and discuss the distribution functions of the coexisting daughter phases and their charge distributions.     

Nanoparticle-mediated epitaxial assembly of colloidal crystals on patterned substrates

We have studied the assembly of 3-D colloidal crystals from binary mixtures of colloidal microspheres and highly charged nanoparticles on flat and epitaxially patterned substrates created by focused ion beam milling. The microspheres were settled onto these substrates from dilute binary mixtures. Laser scanning confocal microscopy was used to directly observe microsphere structural evolution during sedimentation, nanoparticle gelation, and subsequent drying. After microsphere settling, the nanoparticle solution surrounding the colloidal crystal was gelled in situ by introducing ammonia vapor, which increased the pH and enabled drying with minimal microsphere rearrangement. By infilling the dried colloidal crystals with an index-matched fluorescent dye solution, we generated full 3-D reconstructions of their structure including defects as a function of initial suspension composition and pitch of the patterned features. Through proper control over these important parameters, 3-D colloidal crystals were created with low defect densities suitable for use as templates for photonic crystals and photonic band gap materials.     

Phase transitions in DNA-linked nanoparticle assemblies: a decorated-lattice model

We use decorated-lattice models to explore the phase behavior of two types of DNA-linked colloidal mixtures: systems with identical nanoparticles functionalized with two different DNA strands (mixture Aab) and mixtures involving two types of particles each one functionalized with a different DNA strand (mixture Aa-Ab). The model allows us to derive the properties of the mixtures from the well-known behavior of underlying spin-n Ising models with temperature and activity dependent effective interactions. The predicted evolution of the dissolution profiles for the colloidal assemblies as a function of temperature and number of single DNA strands on a nanoparticle M is in qualitative agreement with that observed in real systems. According to our model, the temperature at which the assemblies dissolve can be expected to increase with increasing M only for concentrations of colloids below a certain threshold. For more concentrated solutions, the dissolution temperature is a decreasing function of M. Linker-mediated interactions between Aa and Ab particles in the Aa-Ab mixture render the phase separation involving disordered aggregates metastable with respect to a phase transition between a solvent-rich and an ordered phase. The stability of the DNA-linked assembly is enhanced by the ordering of the colloidal network and the ordered aggregates dissolve at higher temperatures. Our results may explain the contrasting evolution of the dissolution temperatures with increasing probe size in Aab and Aa-Ab mixtures as observed experimentally.     

Analytical solution of Poisson–Boltzmann equation for interacting plates of arbitrary potentials and same sign

Efficient calculation of electrostatic interactions in colloidal systems is becoming more important with the advent of such probing techniques as atomic force microscopy. Such practice requires solving the nonlinear Poisson–Boltzmann equation (PBE). Unfortunately, explicit analytical solutions are available only for the weakly charged surfaces. Analysis of arbitrarily charged surfaces is possible only through cumbersome numerical computations. A compact analytical solution of the one-dimensional PBE is presented for two plates interacting in symmetrical electrolytes. The plates can have arbitrary surface potentials at infinite separation as long they have the same sign. Such a condition covers a majority of the colloidal systems encountered. The solution leads to a simple relationship which permits determination of surface potentials, surface charge densities, and electrostatic pressures as a function of plate separation H for different charging scenarios. An analytical expression is also presented for the potential profile between the plates for a given separation. Comparison of these potential profiles with those obtained by numerical analysis shows the validity of the proposed solution.     

Surface functionalization of silica nanoparticles supports colloidal stability in physiological media and facilitates internalization in cells

The influence of the surface functionalization of silica particles on their colloidal stability in physiological media is studied and correlated with their uptake in cells. The surface of 55 ± 2 nm diameter silica particles is functionalized by amino acids or amino- or poly(ethylene glycol) (PEG)-terminated alkoxysilanes to adjust the zeta potential from highly negative to positive values in ethanol. A transfer of the particles into water, physiological buffers, and cell culture media reduces the absolute value of the zeta potential and changes the colloidal stability. Particles stabilized by L-arginine, L-lysine, and amino silanes with short alkyl chains are only moderately stable in water and partially in PBS or TRIS buffer, but aggregate in cell culture media. Nonfunctionalized, N-(6-aminohexyl)-3-aminopropyltrimethoxy silane (AHAPS), and PEG-functionalized particles are stable in all media under study. The high colloidal stability of positively charged AHAPS-functionalized particles scales with the ionic strength of the media, indicating a mainly electrostatical stabilization. PEG-functionalized particles show, independently from the ionic strength, no or only minor aggregation due to additional steric stabilization. AHAPS stabilized particles are readily taken up by HeLa cells, likely as the positive zeta potential enhances the association with the negatively charged cell membrane. Positively charged particles stabilized by short alkyl chain aminosilanes adsorb on the cell membrane, but are weakly taken up, since aggregation inhibits their transport. Nonfunctionalized particles are barely taken up and PEG-stabilized particles are not taken up at all into HeLa cells, despite their high colloidal stability. The results indicate that a high colloidal stability of nanoparticles combined with an initial charge-driven adsorption on the cell membrane is essential for efficient cellular uptake.     

Effects of structural properties of the Stern layer on the electrophoretic migration of a highly charged spherical macroion

The electrophoretic migration of a highly charged spherical macroion suspended in an aqueous solution of NaCl is studied using the molecular dynamic method. The objective is to examine the effects of the colloidal surface charge density on the electrophoretic mobility (μ) of the spherical macroion. The bare charge and the size of the macroion are varied separately to induce changes in the colloidal surface charge density. Our results indicate that μ depends on colloidal surface charge density in a nonmonotonic manner, but that this relationship is independent of the way the surface charge density is varied. It is found that an increase in colloidal surface charge density may lead to the formation of new sublayers in the Stern layer. The μ profile is also found to have a local maximum for a bare charge at which a new sublayer is formed in the Stern layer, and a local minimum for a bare charge at which the outer sublayer becomes relatively dense. Finally, the electrophoretic flow caused by the migration of the spherical macroion is studied to find that one decisive factor causing the electrophoretic flow is the ability of the macroion to carry anions in the electrolyte solution.     

Theoretical study of catalytic effects in micellar solutions

The catalytic effect of charged micelles as manifested through the increased collision frequency between the counterions of an electrolyte in the presence of such micelles is explored by the Monte Carlo simulation technique and various theoretical approaches. The micelles and ions are pictured as charged hard spheres embedded in a dielectric continuum with the properties of water at 298 K with the charge on micelles varying from zero to z(m) = 50 negative elementary charges. Analytical theories such as (i) the symmetric Poisson-Boltzmann theory, (ii) the modified Poisson-Boltzmann theory, and (iii) the hypernetted-chain integral equation are applied and tested against the Monte Carlo data for micellar ions (m) with up to 50 negative charges in aqueous solution with monovalent counterions (c; z(c) = +1) and co-ions (co; z(co) = -1). The results for the counterion-counterion pair correlation function at contact, g(cc)(sigma(cc)), are calculated in a micellar concentration range from c(m) = 5 x 10(-)(6) to 0.1 mol/dm(3) with an added +1:-1 electrolyte concentration of 0.005 mol/dm(3) (for most cases), and for various model parameters. Our computations indicate that even a small concentration of a highly charged polyelectrolyte added to a +1:-1 electrolyte solution strongly increases the probability of finding two counterions in contact. This result is in agreement with experimental data. For low charge on the micelles (z(m) below -8), all the theories are in qualitative agreement with the new computer simulations. For highly charged micelles, the theories either fail to converge (the hypernetted-chain theory) or, alternatively, yield poor agreement with computer data (the symmetric Poisson-Boltzmann and modified Poisson-Boltzmann theories). The nonlinear Poisson-Boltzmann cell model results yield reasonably good agreement with computer simulations for this system.     

Thoughts on the ideal behavior of mixed micelles and the appropriate application of regular solution theory (RST)

Solutions of mixed surfactants are often considered as solvent mixtures. Usually, mixed micellar aggregates are considered as a homogeneous mixture of solvents dispersed in a solution. But the transposition of the usual thermodynamic models of solvent mixtures to mixed micelles is not always so obvious. We discussed this point in this paper by considering several cases of surfactant mixtures. A major problem is to define the molar fraction of each surfactant in the aggregate especially when a charged surfactant is employed in the mixture, because possible dissociation of the components of the mixture must be considered in the bulk as well in the micelle. This definition is crucial especially for the characterization of the ideal behavior which is usually described by the Clint relation, as well as for the application of regular solution theory (RST) which is the most frequently applied model for interpreting the behavior of surfactant mixtures. We show in this paper how the definition of the molar fraction can change the equations and the interpretations.     

Monte Carlo simulations of antibody adsorption and orientation on charged surfaces

Monte Carlo simulations were performed to study the adsorption and orientation of antibodies on charged surfaces based on both colloidal and all-atom models. The colloidal model antibody consists of 12 connected beads representing the 12 domains of an antibody molecule. The structure of the all-atom antibody model was taken from the protein databank. The effects of the surface charge sign and density, the solution pH and ionic strength on the adsorption and orientation of different colloidal model antibodies with different dipole moments were examined. Simulation results show that both the 12-bead and the all-atom models of the antibody, for which the dipole moment points from the Fc to (Fab)2 fragments, tend to have the desired "end-on" orientation on positively charged surfaces and undesired "head-on" orientation on negatively charged surfaces at high surface charge density and low solution ionic strength where electrostatic interactions dominate. At low surface charge density and high solution ionic strength where van der Waals interactions dominate, 12-bead model antibodies tend to have "lying-flat" orientation on surfaces. The orientation of adsorbed antibodies results from the compromise between electrostatic and van der Waals interactions. The dipole moment of an antibody is an important factor for antibody orientation on charged surfaces when electrostatic interactions dominate. This charge-driven protein orientation hypothesis was verified by our simulations results in this work. It was further confirmed by surface plasmon resonance biosensor and time-of-flight secondary ion mass spectrometry experiments reported elsewhere.     

Microbicides for HIV/AIDS. 2. Electrophoretic fingerprinting of CD4+ T-cell model systems

New measurements of the dependence of the surface charge on the pH and electrolyte concentration for three living human white blood cell lines that are the principal targets of the HIV-1 virus are reported. Comparison of the electrophoretic fingerprint (EF) pattern, especially the line of zero mobility, with that of reference colloids establishes the separate individual identities and shows that all three exhibit a zwitterionic surface. With the EF results as a guide, preliminary biological infectivity measurements showed that small polyvalent cations modulate the negative charge on the T-cell surface in a way that strongly affects the infection kinetics. H9 cells were exposed to an infectious virus (X4), and the data showed that HIV interaction with target cells is enhanced by physiological fluids. The nondestructive methodology described is generally applicable to characterization of the surface charge and determination of the colloidal stability of any aqueous charged colloidal system without reference to any model of the double layer.     

Theoretical analysis of factors affecting the formation and stability of multilayered colloidal dispersions

A mathematical analysis of the major factors influencing the formation and stability of colloidal dispersions containing spherical particles surrounded by multilayered polymeric interfacial membranes formed by the layer-by-layer electrostatic deposition technique is carried out. The mathematical model assumes that (i) the colloidal dispersion initially consists of a mixture of electrically charged monodisperse spherical particles and oppositely charged polymer molecules, (ii) the adsorption of polymer molecules to the particle surfaces is diffusion-limited, and (iii) the dominant particle-particle collision mechanism is Brownian motion. This approach was used to produce stability maps that highlight conditions under which bridging flocculation, multilayer formation, or depletion flocculation occurs. The stability maps are derived from calculations of the critical polymer concentrations required to (i) saturate the particle surfaces (C(Sat)), (ii) ensure that polymer adsorption is faster than particle collisions (C(Ads)), and (iii) promote depletion flocculation (C(Dep)). In addition, the influence of interfacial properties on the stability of multilayer colloidal dispersions was assessed by calculating the colloidal interactions between the coated particles (i.e., van der Waals, electrostatic, steric, and depletion). These calculations indicated that the major factors are the interfacial charge and composition rather than the interfacial thickness. This article provides useful insights into the factors affecting the formation of stable multilayer colloidal dispersions.     

Effect of charge asymmetry and charge screening on structure of superlattices formed by oppositely charged colloidal particles

Colloidal suspensions made up of oppositely charged particles have been shown to self-assemble into substitutionally ordered superlattices. For a given colloidal suspension, the structure of the superlattice formed from self-assembly depends on its composition, charges on the particles, and charge screening. In this study we have computed the pressure-composition phase diagrams of colloidal suspensions made up of binary mixtures of equal sized and oppositely charged particles interacting via hard core Yukawa potential for varying values of charge screening and charge asymmetry. The systems are studied under conditions where the thermal energy is equal or greater in magnitude to the contact energy of the particles and the Debye screening length is smaller than the size of the particles. Our studies show that charge asymmetry has a significant effect on the ability of colloidal suspensions to form substitutionally ordered superlattices. Slight deviations of the charges from the stoichiometric ratio are found to drastically reduce the thermodynamic stability of substitutionally ordered superlattices. These studies also show that for equal-sized particles, there is an optimum amount of charge screening that favors the formation of substitutionally ordered superlattices.