Single-particle thermal diffusion of charged colloids: Double-layer theory in a temperature gradient

The double-layer contribution to the single-particle thermal diffusion coefficient of charged, spherical colloids with arbitrary double-layer thickness is calculated and compared to experiments. The calculation is based on an extension of the Debye-Hückel theory for the double-layer structure that includes a small temperature gradient. There are three forces that constitute the total thermophoretic force on a charged colloidal sphere due to the presence of its double layer: i) the force F _W that results from the temperature dependence of the internal electrostatic energy W of the double layer, ii) the electric force F _el with which the temperature-induced non-spherically symmetric double-layer potential acts on the surface charges of the colloidal sphere and iii) the solvent-friction force F _sol on the surface of the colloidal sphere due to the solvent flow that is induced in the double layer because of its asymmetry. The force F _W will be shown to reproduce predictions based on irreversible-thermodynamics considerations. The other two forces F _el and F _sol depend on the details of the temperature-gradient-induced asymmetry of the double-layer structure which cannot be included in an irreversible-thermodynamics treatment. Explicit expressions for the thermal diffusion coefficient are derived for arbitrary double-layer thickness, which complement the irreversible-thermodynamics result through the inclusion of the thermophoretic velocity resulting from the electric- and solvent-friction force.     

Scaling in dispersion rheology

Summary A nonequilibrium fluid lattice model of concentrated colloidal dispersions is presented to predict the effects of the microstructure, particle interactions, volume fraction (ϕ), frequency (ω), and the longest viscoelastic relaxation time on the complex shear viscosity. In addition to the pair interactions between colloidal particles, the many-body interactions between the particles and the equilibrium microstructure have to be included in the analysis. As ϕ approaches a critical valueφ _c, the fluidity of concentrated dispersions slows down drastically. This percolation thresholdφ _c scales ad (AP)^−0.5, whereA andP are related to the repulsive interparticle potential and microstructure, respectively. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Measuring colloidal forces with the magnetic chaining technique

In 1994 Leal Calderon et al. (Phys. Rev. Lett. 72, 2959 (1994)) introduced the magnetic chaining technique to directly probe the force-distance profile between colloidal particles. In this paper, we revisit this approach in two ways. First, we describe a new experimental design which allows us to utilize sample volumes as low as a few microliters, involving femtomoles of surface active macromolecules. Secondly, we extensively describe the characterization and preparation of the magnetic colloids, and we give a quantitative evaluation of performance and resolution of the technique in terms of force and interparticle separation.     

Phase behaviour of a dispersion of charge-stabilised colloidal spheres with added non-adsorbing interacting polymer chains

We present a theory for the phase behaviour of mixtures of charge-stabilised colloidal spheres plus interacting polymer chains in good and θ -solvents within the framework of free-volume theory. We use simple but accurate combination rules for the depletion thickness around a colloidal particle and for the osmotic pressure up to the semi-dilute concentration regime. Hence, we obtain expressions for the free energy for mixtures of charged colloidal particles and non-adsorbing interacting polymers. From that, we calculate the phase behaviour, and discuss its topology in dependence on the competition between the charge-induced repulsion and the polymer-induced attraction. The homogeneous mixture of colloids and polymers becomes more stabilised against demixing when increasing the electrostatic repulsion. This charge-induced stabilisation is strongest for small polymer-to-colloid size ratios and is more pronounced for charged colloids mixed with polymers in a good solvent than for polymers in a θ -solvent. For the weakly charged regime we find that the phase diagram becomes salt-concentration-independent in the protein limit for charged colloids plus polymers in a θ -solvent. The liquid window, i.e., the concentration regimes where a colloidal liquid exists, is narrowed down upon increasing the charge-induced repulsion. Also this effect is more pronounced when charged colloids are mixed with polymer chains in a good solvent. In summary, we demonstrate that the solvent quality significantly influences the phase behaviour of mixtures of charged colloids plus non-adsorbing polymers if the range of the screened electrostatic repulsion becomes of the order of the range of the depletion-induced attraction.     

Complexation and overcharging of polyelectrolyte stars and charged colloids

We examine the complexation behavior of polyelectrolyte stars on oppositely charged colloidal particles with similar sizes by means of computer simulations employing the molecular dynamics approach. In particular the overcharging phenomenon is considered and its dependence on the charge and functionality of the stars. The complexes thus formed are a realization of inverse patchy particles (Bianchi et?al 2011 Soft Matter 7 8313) for which both the number of patches and the total charge can be tuned.     

Partial clustering prevents global crystallization in a binary 2D colloidal glass former

A mixture of two types of super-paramagnetic colloidal particles with long-range dipolar interaction is confined by gravity to the flat interface of a hanging water droplet. The particles are observed by video microscopy and the dipolar interaction strength is controlled via an external magnetic field. The system is a model system to study the glass transition in 2D, and it exhibits partial clustering of the small particles (N. Hoffmann et al., Phys. Rev. Lett. 97, 078301 (2006)). This clustering is strongly dependent on the relative concentration of big and small particles. However, changing the interaction strength reveals that the clustering does not depend on the interaction strength. The partial clustering scenario is quantified using Minkowski functionals and partial structure factors. Evidence that partial clustering prevents global crystallization is discussed.     

Phase behaviour of colloid-polymer mixtures

Summary We review the phase behaviour of mixtures of colloids and non-adsorbing polymers. The exclusion of polymer molecules from overlapping ?depletion zones? between two neighbouring colloidal particles results in an unbalanced osmotic pressure pushing the particles together. This depletion potential is separately tunable in range and depth. Theory predicts that the resulting phase behaviour is sensitive to ξ=r _g/R, the ratio of the radius of gyration of a polymer molecule, to the radius of the colloid. At large ξ, a stable colloidalliquid phase becomes possible. This has been confirmed by recent experiments. The formation of non-equilibrium ?transient gel? states when the size ratio is small (≈0.08) is also introduced briefly. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Effect of colloidal charge discretization in the primitive model

The effect of fixed discrete colloidal charges in the primitive model is investigated for spherical macroions. Instead of considering a central bare charge, as it is traditionally done, we distribute discrete charges randomly on the sphere. We use molecular dynamics simulations to study this effect on various properties such as overcharging, counterion distribution and diffusion. In the vicinity of the colloid surface the electrostatic potential may considerably differ from the one obtained with a central charge. In the strong Coulomb coupling, we showed that the colloidal charge discretization qualitatively influences the counterion distribution and leads to a strong colloidal charge-counterion pair association. However, we found that charge inversion still persists even if strong pair association is observed. Received 30 June 2000 and Received in final form 28 November 2000     

Macroions in salty water with multivalent ions: giant inversion of charge

Screening of a strongly charged macroion by oppositely charged colloidal particles, micelles, or short polyelectrolytes is considered. Because of strong lateral repulsion such multivalent counterions form a strongly correlated liquid at the surface of the macroion. This liquid provides correlation-induced attraction of multivalent counterions to the macroion surface. As a result even a moderate concentration of multivalent counterions in the solution inverts the sign of the net macroion charge. We show that at high concentration of monovalent salt the absolute value of inverted charge can be larger than the bare one. This giant inversion of charge can be observed in electrophoresis.     

Dielectrophoresis of nanocolloids: A molecular dynamics study

Dielectrophoresis (DEP), the motion of polarizable particles in non-uniform electric fields, has become an important tool for the transport, separation, and characterization of microparticles in biomedical and nanoelectronics research. In this article we present, to our knowledge, the first molecular dynamics simulations of DEP of nanometer-sized colloidal particles. We introduce a simplified model for a polarizable nanoparticle, consisting of a large charged macroion and oppositely charged microions, in an explicit solvent. The model is then used to study DEP motion of the particle at different combinations of temperature and electric field strength. In accord with linear response theory, the particle drift velocities are shown to be proportional to the DEP force. Analysis of the colloid DEP mobility shows a clear time dependence, demonstrating the variation of friction under non-equilibrium. The time dependence of the mobility further results in an apparent weak variation of the DEP displacements with temperature.     

Simulating (electro)hydrodynamic effects in colloidal dispersions: Smoothed profile method

Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent (Phys. Rev. E 71, 036707 (2005)). An improved formulation called the “Smoothed Profile (SP) method” is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporate multi-component fluids, allowing systems such as charged colloids in electrolyte solutions to be studied. The dynamics of the colloidal dispersions are solved with the same computational cost as required for solving non-particulate flows. Numerical results which assess the hydrodynamic interactions of colloidal dispersions are presented to validate the SP method. The SP method is not restricted to particular constitutive models of the host fluids and can hence be applied to colloidal dispersions in complex fluids.     

A Two-Dimensional One Component Plasma and a Test Charge: Polarization Effects and Effective Potential

We study the effective interactions between a test charge Q and a one-component plasma, i.e. a complex made up of mobile point particles with charge q, and a uniform oppositely charged background. The background has the form of a flat disk, in which the mobile charges can move. The test particle is approached perpendicularly to the disk, along its axis of symmetry. All particles interact by a logarithmic potential. The long and short distance features of the effective potential—the free energy of the system for a given distance between Q and the disk—are worked out analytically in detail. They crucially depend on the sign of Q/q, and on the global charge borne by the discotic complex, that can vanish. While most results are obtained at the intermediate coupling Γ≡βq ²=2 (β being the inverse temperature), we have also investigated situations with stronger couplings: Γ=4 and 6. We have found that at large distances, the sign of the effective force reflects subtle details of the charge distribution on the disk, whereas at short distances, polarization effects invariably lead to effective attractions.     

Poisson–Boltzmann for oppositely charged bodies: an explicit derivation

The interaction between two parallel charged plates in ionic solution is a general starting point for studying colloidal complexes. An intuitive expression of the pressure exerted on the plates is usually proposed, which includes an electrostatic plus an osmotic contribution. We present here an explicit and self-consistent derivation of this formula in the only framework of the Poisson–Boltzmann (PB) theory. We also show that, depending on external constraints, the correct thermodynamic potential can differ from the usual PB free energy. For asymmetric, oppositely charged plates, the resulting expression predicts a non-trivial equilibrium position with the plates separated by a finite distance. The depth of this energy minimum is decisive for the stability of the complex. It is therefore crucial to obtain its explicit dependence on the charge densities of the plates and on the ion concentration. Analytic expressions for the position and depth of the energy minimum were derived in 1975 by Ohshima [Colloid Polym. Sci. 253, 150 (1975)] but, surprisingly, these important results seem to have been overlooked. We retrieve these expressions in a simpler formalism, more familiar to the physics community, and give a physical interpretation of the observed behavior.     

Effective interactions of colloids on nematic films

The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations d. The elastic interaction is repulsive and of quadrupolar type, varying as d^-5. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to d^-5 as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically varying capillary attractions. However, their strength turns out to be too small to be of importance for the recently observed pattern formation of colloidal droplets on nematic films.     

Nanotitania-coated multi-walled carbon nanotube composite by facile colloidal processing route for photocatalytic applications

Multi-walled carbon nanotubes (MWCNTs) and titanium dioxide nanocomposites (MWCNTs/TiO₂) were fabricated by a simple novel colloidal processing route and tested as a photocatalyst for degradation of methylene blue under UV irradiation. The novel idea behind this work is to make MWCNTs and TiO₂ nanoparticle suspensions separately highly oppositely charged and utilize the electrostatic force of attraction between two entities to deposit nanotitania onto MWCNTs surface. Particle charge detector, scanning electron microscopy, transmission electron microscope, energy dispersive X-rays, X-rays diffraction (XRD), and Raman spectroscopy were used to characterize the composite. XRD and Raman spectroscopic analysis showed the crystalline structure of deposited TiO₂ over MWCNTs surface structure as anatase phase. It was found that MWCNTs/TiO₂ composite structure have much higher photocatalytic activity compared to TiO₂ nanoparticles. The composite material developed may find potential applications in the degradation of organic pollutants in aqueous medium under UV irradiation.     

Self-similarity of nonlinear screening in asymmetric complex plasmas

In this paper, two-component electroneutral systems of finite-sized macroions and oppositely charged point-like microions in the average spherical electroneutral Wigner–Seitz cell with a central macroion are studied. We investigate the self-similarity of nonlinear screening of highly charged macroions by microions in a classical asymmetrically charged complex plasma. This work is devoted to the problem of the relationship between the effective (‘visible’) charge of the macroion Z^* and its initial charge Z taking into account the effect of the nonlinear screening. It is analysed how the form of the dependence Z^*(Z) changes. The self-similarity of this dependence has been demonstrated for various characteristic system temperatures, macroion concentrations, and macroion sizes.     

Sequential deposition of polydisperse particles with double layer interactions: An integral-equation theory

Adsorption of charged colloidal particles to oppositely charged surfaces is usually an irreversible process. The interaction between a pair of particles can be modeled with an exponentially decaying potential originating from double layer interactions. This work explored the effect of the Debye length on monolayer structures using the integral-equation theory which was successfully developed based on a binary-mixture approximation to include the effect of particle size polydispersity. The theoretical results from the integral equations with a Percus-Yevick closure showed that upon increasing the Debye length, the radial distribution functions, g(r), as well as the structure factor, S(k), decreased, in good agreement with simulation results. When the effect of size distributions was investigated, the prominent peak of the radial distribution function increased non-linearly with the product κσ_av, which followed the same trend as was reported for the case of the jamming coverage of the monolayer film.     

Dynamics in dense suspensions of charge-stabilized colloidal particles

The dynamic behavior of charge-stabilized colloidal particles in suspension was studied by photon correlation spectroscopy with coherent X-rays (XPCS). The short-time diffusion coefficient, D(Q) , was measured for volume concentrations φ ⩽ 0.18 and compared to the free particle diffusion constant D₀ and the static structure factor S(Q) . The data show that indirect, hydrodynamic interactions are relevant for the system and hydrodynamic functions were derived. The results are in striking contrast to the predictions of the PA (pairwise-additive approximation) model, but show features typical for a hard-sphere system. The observed mobility is however considerably smaller than the one of a respective hard-sphere system. The hydrodynamic functions can be modelled quantitatively if one allows for an increased effective viscosity relative to the hard-sphere case.     

AC field induced two-dimensional aggregation of multilamellar vesicles

The aggregation of 2D colloidal crystals can be performed by applying an AC field to a colloidal dispersion. This technique is used in this work for assembling multilamellar vesicles in suspension. The dynamics of the aggregation is followed by real-time recording of the pictures of the microsphere assembly through a phase contrast microscope. The influence of both the frequency and the amplitude of the alternating field on the dynamical evolution of the concentration of layered particles is discussed with respect to their size. A phenomenological model of double layer induced trapping of the particles is proposed and an electroconvective instability of the fluid surrounding the particles is suggested from the observation of the local dynamics of the particles, in accordance with a very recent argument of Yeh et al. [#!Yeh:97!#]. Received: 4 December 1997 / Revised: 24 March 1998 / Accepted: 4 May 1998     

The Effect of ζ‐Potential and Hydrodynamic Size on Nanoparticle Interactions in Hydrogels

The ζ‐potential and hydrodynamic size (d_h) of nanoparticles (NPs) are systematically controlled by capping gold NPs (AuNPs) with polymers having different charges and treating them in NaCl solutions of diverse concentrations. Interactions between AuNPs in hydrogel are caused by chemical reactions induced by 1,4‐dithiothreitol. The effect of ζ‐potential is clear, as negatively charged AuNPs can be aggregated in neutral agarose gel, but the amount of aggregation is significantly affected by the magnitude of the negative surface charge on the AuNPs. However, all positively charged AuNPs show negligible aggregation in agarose gel with slightly negative polarity. The effect of d_h on AuNP aggregation is different from that of ζ‐potential. Although AuNPs with small d_h generally show more aggregation than those with large d_h, the amount of AuNP capping layer is critical. Thus, the amount of polymer present on NP surface needs to be considered to investigate the effect of d_h on AuNP aggregation. Through extended Derjaguin, Landau, Verwey, Overbeek (XDLVO) theory, it is shown that the charges of the AuNPs and the hydrogel, as well as the d_h of the NPs, are related to electrostatic repulsion and steric hindrance, which affect AuNP aggregation in hydrogel.