Macroion Charges Research Articles

Screening of a Small Spherical Macroion by Oppositely Charged Flexible Polyelectrolyte

Electrostatic interactions play important roles in the assembly, the structureand the functions of many biological as well as soft matter systems. In the presence of a macro-ion in aqueous solution, oppositely charged molecules mobilize around it to screen out its electrostatic potential. In this paper, we focus on screening of small macroion by a flexible polyelectrolyteusing Monte-Carlo simulation. It is shown that the condensation of the polyelectrolyte around the macroion shows a first order phase transition from a dense to a dilute concentration of monomers. The width of the condensed region increases with stronger screening or with smaller macro-ion charges. For small macro-ion charge, or when the Coulomb interactions are strongly screened, no complexation between the polyelectrolyte and the macro-ion happens.Additionally, long polyelectrolyte protrudes both tails and loops from the macroion. This is quite different from the case of large macroions where only tails appear. Our results can be used to explain various experimental trends.

Charge regulation in ionic solutions: thermal fluctuations and Kirkwood-Schumaker interactions.

We study the behavior of two macroions with dissociable charge groups, regulated by local variables such as pH and electrostatic potential, immersed in a monovalent salt solution, considering cases where the net charge can either change sign or remain of the same sign depending on these local parameters. The charge regulation in both cases is described by the proper free-energy function for each of the macroions, while the coupling between the charges is evaluated on the approximate Debye-Hückel level. The charge correlation functions and the ensuing charge fluctuation forces are calculated analytically and numerically. Strong attraction between like-charged macroions is found close to the point of zero charge, specifically due to asymmetric, anticorrelated charge fluctuations of the macroion charges. The general theory is then implemented for a system of two proteinlike macroions, generalizing the form and magnitude of the Kirkwood-Schumaker interaction.

Effect of Discrete Macroion Charge Distributions on Electric Double Layer of a Spherical Macroion

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on the structure of electric double layer (EDL) of a spherical macroion has been investigated by Monte Carlo (MC) simulations. Two discrete models have been investigated in addition to the central macroion charge: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both models have been studied with fixed and mobile macroion charges. The radial functions of local densities and electrostatic potential in EDL, are calculated and compared to the results obtained for the central macroion charge distribution. It is concluded that the model of charge distribution significantly affects the EDL structure close to the macroion, while the effect is much weaker at larger distances. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion, as a result the absolute values of surface potential ϕ0 and zeta ξ potential are decreased. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the absolute values of ϕ0 and ξ potentials are increased.

Bridging Like-Charged Macroions through Long Divalent Rodlike Ions

Like-charged macroions in aqueous electrolyte solution can attract each other because of the presence of inter- and/or intramolecular correlations. Poisson-Boltzmann theory is able to predict attractive interactions if the spatially extended structure (which reflects the presence of intramolecular correlations) of the mobile ions in the electrolyte is accounted for. We demonstrate this for the case of divalent, mobile ions where each ion consists of two individual charges separated by a fixed distance. Variational theory applied to this symmetric 2:2 electrolyte of rodlike ions leads to an integro-differential equation, valid for arbitrary rod length. Numerical solutions reveal the existence of a critical rod length above which electrostatic attraction starts to emerge. This electrostatic attraction is distinct from nonelectrostatic depletion forces. Analysis of the orientational distribution functions suggests a bridging mechanism of the rodlike ions to hold the two macroions together. For sufficiently large rod length, we also observe "overcharging", that is, an over-compensation of the macroion charges by the diffuse layer of mobile rodlike ions. Our results emphasize the importance of the often rodlike internal structure that condensing agents such as polyamines, peptides, or polymer segments exhibit. The results were compared with Monte Carlo simulations.

Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.

Nonlinear effects in charge stabilized colloidal suspensions

Molecular-dynamics simulations are used to study the effective interactions in charged stabilized colloidal suspensions. We focus on highly charged macroions in the limit of low salt concentrations. Within this regime, nonlinear corrections to Debye-Hückel (DH) theory have to be considered. For non-bulk-like systems, such as isolated pairs or triples of macroions, we show that nonlinear effects can become relevant, which cannot be described by the charge renormalization concept [S. Alexander, J. Chem. Phys. 80, 5776 (1984)]. For an isolated pair of macroions, we find an almost perfect qualitative agreement between our simulation data and DH theory. However, on a quantitative level, neither DH theory nor the charge renormalization concept can be confirmed in detail. This seems mainly to be related to the fact that for small ion concentrations, microionic layers can strongly overlap, whereas, simultaneously, excluded volume effects are less important. In the case of isolated triples, where we compare between coaxial and triangular geometries, we find attractive corrections to pairwise additivity in the limit of small macroion separations and salt concentrations. These triplet interactions arise if all three microionic layers around the macroions exhibit a significant overlap. In contrast to the case of two isolated colloids, the charge distribution around a macroion in a triple is found to be anisotropic.

Free isotropic-nematic interfaces in fluids of charged platelike colloids

Bulk properties and free interfaces of mixtures of charged platelike colloids and salt are studied within the density-functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model. The charges of the particles are concentrated in their center. The density functional is derived by functional integration of an extension of the Debye-Hückel pair distribution function with respect to the interaction potential. For sufficiently small macroion charges, the bulk phase diagrams exhibit one isotropic and one nematic phase separated by a first-order phase transition. With increasing platelet charge, the isotropic and nematic binodals are shifted to higher densities. The Donnan potential between the coexisting isotropic and nematic phases is inferred from bulk structure calculations. Nonmonotonic density and nematic order parameter profiles are found at a free interface interpolating between the coexisting isotropic and nematic bulk phases. Moreover, electrically charged layers form at the free interface leading to monotonically varying electrostatic potential profiles. Both the widths of the free interfaces and the bulk correlation lengths are approximately given by the Debye length. For fixed salt density, the interfacial tension decreases upon increasing the macroion charge.

Effect of discrete macroion charge distributions in solutions of like-charged macroions

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on structural properties of aqueous solutions of like-charged macroions has been investigated by Monte Carlo simulations. Two discrete charge distributions have been considered: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both discrete charge distributions have been examined with fixed and mobile macroion charges. Different boundary conditions have been applied to examine various properties. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion and the effect increases with counterion valence. As a consequence, with mono- and divalent counterions the potential of mean force between two macroions becomes less repulsive and with trivalent counterions more attractive. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the potential of mean force between two macroions becomes more repulsive/less attractive.

Polyelectrolyte–macroion complexation. I. Effect of linear charge density, chain length, and macroion charge

The complexation between a linear flexible polyelectrolyte and one or several oppositely charged macroions was examined by employing a simple model system with focus on the electrostatic interactions. The composition and the structure of the complex as well as conformational data of the polyelectrolyte were obtained by using Monte Carlo simulations. These properties were investigated at different linear charge densities of the polyelectrolyte, different chain lengths of the polyelectrolyte, and different macroion charges, all at different numbers of macroions at constant volume. The binding isotherms obtained are Langmuir type, and in excess of macroions the polyelectrolyte–macroion complex displays a charge reversal. Upon complexation, the polyelectrolyte extension first reduces and thereafter increases as the number of complexed macroions increases, the minimal extension appearing for a neutral complex. Macroions prefer to complex to central polyelectrolyte segments, but for a neutral or an overcharged complex the entire polyelectrolyte chain is involved. In the complex, the macroions are able to come into direct contact with each other, despite their mutual electrostatic repulsion. The distribution of the small ions is also presented.

Effective interactions and volume energies in charged colloids: linear response theory

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out the degrees of freedom of all microions from the partition function, and assuming a linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the Derjaguin-Landau-Verwey-Overbeek screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy-a natural consequence of the one-component reduction-contributes to the total free energy, and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.

Monte Carlo simulations of a mixture of an asymmetric electrolyte and a neutral species

The equilibrium properties of a charge and size asymmetric, multicomponent mixture of macroions, counterions, and neutral particles are characterized through Monte Carlo simulations. Particular emphasis is paid to considering the influence on these properties of macroion concentration, neutral component concentration, macroion charge, and counterion charge. A significant result of the simulations is that sufficient increase in the neutral species concentration leads to a gradual change in the qualitative nature of the interaction between two macro-ions from repulsive to attractive. This occurs for all the counterion charges, macroion charges, and macroion concentrations. Overall, the structure and thermodynamics are shaped by the collective and often competing effects of the species. The simulations are supplemented by theoretical calculations using the symmetric Poisson—Boltzmann, the modified Poisson-Boltzmann, and the hypernetted chain approaches. The theories show reasonable consistency, both among themselves and with the simulations, overall, although the level of agreement with the simulations varies.

Interactions between charged spherical macroions

Monte Carlo (MC) simulations were used to study the screened interactions between charged spherical macroions surrounded by discrete counterions, and to test previous theories of screening. The simulations were performed in the primitive cell of the bcc lattice, and in the spherical Wigner–Seitz cell that is commonly used in approximate calculations. We found that the Wigner–Seitz approximation is valid even at high volume fractions φ and large macroion charges Z, because the macroion charge becomes strongly screened. Pressures calculated from Poisson–Boltzmann theory and local density functional theory deviate from MC values as φ and Z increase, but continue to provide upper and lower bounds for the MC results. While Debye–Hückel (DH) theory fails badly when the bare charge is used, MC pressures can be fit with an effective DH charge, ZDH, that is nearly independent of volume fraction. As Z diverges, ZDH saturates at zψmaxRm/λ, where z is the counterion charge, Rm is the macroion radius, λ is the Bjerrum length, and ψmax is a constant of order 10.

Brownian Motion in Polydisperse Charged Colloidal Suspensions

The effect of combined intrinsic size and charge polydispersity on the tracer diffusion in bimodal suspensions of strongly charged macroparticles is investigated both theoretically and experimentally. The measurable wavenumber-dependent mean squared displacement and the partial mean squared displacements are calculated based on a bimodal Schulz distribution for the particle sizes and charges, using both a single relaxation time approximation for the memory function (SEXP) and the multicomponent Brownian Dynamics (BD) simulation technique. It is found that intrinsic polydispersity has a significant effect on tracer diffusion. The partial static structure functions, which are required as an input for the single relaxation time approximation, are obtained by using the multicomponent hypernetted chain approximation. The predictions of the SEXP approximation and BD simulations are compared with data from large-wave-number dynamic light scattering (DLS) experiments on binary suspensions of strongly interacting polystyrene spheres. Good agreement between SEXP, BD, and DLS data is found within the experimentally scanned time window. However, at intermediate to large times, it is found that the mean squared displacements calculated from the SEXP approximation deviate significantly from results obtained from BD simulations, especially for systems with substantial polydispersity in macroion sizes and charges. We also discuss the range of validity for a simple extension of the substitutional model applicable to intrinsically polydisperse bimodal suspensions.

Dynamics in BSA solutions at low ionic strengths as observed by holographic relaxation spectroscopy

Holographic relaxation techniques (HRS) were used to study dynamics in solutions of bovine serum albumin (BSA) labeled with azobenzene-p-isothiocyanate (ABITC). The ionic strengths ranged from 0.5 to 100 mM and the protein concentrations were 3 to 50 g/L. A single diffusive component was observed above 25 mM salt, but at lower ionic strengths two components were resolved. Also, electrophoresis combined with holographic relaxation spectroscopy (EHRS) showed two components. A photoionization model, in which the net charge of the BSA-ABITC molecule is altered by the writing laser pulse, is proposed to explain the results. The coupled diffusion problem for the bleached and unbleached macroions and the counter and coions is solved to obtain the concentration and ionic strength dependences of the diffusion coefficients. Also, effective diffusion coefficients for the components in EHRS are obtained. Overall, there is good agreement between this simple model and experiment; however, the macroion charges required in the theory are roughly a factor of two lower than those found by titration and electrolysis.

Electrophoretic charge of a cylindrical macroion in aqueous 1 : 1 electrolyte

AbstractThe potential problem is formulated for rodlike macroions and reduced to a single dimensionless equation with appropriate boundary conditions. A method of solution based on piecewise linearization of the potential equation is detailed and compared with two other approaches. It is suggested that the present method yields improved estimates of macroion charges. Some numerical results are included, and the relation between electrophoretic charge and macroion charge is considered.