Suspensions Of Charged Spheres Research Articles

Porous crystals in charged sphere suspensions by aggregate-driven phase separation.

The kinetics of phase transition processes often governs the resulting material microstructure. Using optical microscopy, we here investigate the formation and stabilization of a porous crystalline microstructure forming in low-salt suspensions of charged colloidal spheres containing aggregates comprising some 5-10 of these colloids. We observe the transformation of an initially crystalline colloidal solid with homogeneously incorporated aggregates to individual, compositionally refined crystallites of perforated morphology coexisting with an aggregate-enriched fluid phase filling the holes and separating individual crystallites. A preliminary kinetic characterization suggests that the involved processes follow power laws. We show that this route to porous materials is neither restricted to nominally single component systems nor to a particular microstructure to start from. However, it necessitates an early rapid solidification stage during which the aggregates become trapped in the bulk of the host-crystals. The thermodynamic stability of the reconstructed crystalline scaffold against melting under increased salinity was found comparable to that of pure phase crystallites grown very slowly from a melt. Future implications of this novel route to porous colloidal crystals are discussed.

Salt-concentration-dependent nucleation rates in low-metastability colloidal charged sphere melts containing small amounts of doublets

We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concentration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while postsolidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The full data set, however, shows an unexpected scaling of the nucleation rate densities with metastability times the number density of particles. Parameterization of our results in terms of classical nucleation theory reveals unusually low interfacial free energies of the nucleus surfaces and nucleation barriers well below the thermal energy. We tentatively attribute our observations to the presence of doublets introduced by the employed conditioning technique. We discuss the conditions under which such small seeds may induce nucleation.

Non-monotonic concentration dependence of the electro-phoretic mobility of charged spheres in realistic salt free suspensions.

Using super-heterodyne Doppler velocimetry with multiple scattering correction, we extend the optically accessible range of concentrations in experiments on colloidal electro-kinetics. Here, we measured the electro-phoretic mobility and the DC conductivity of aqueous charged sphere suspensions covering about three orders of magnitude in particle concentrations and transmissions as low as 40%. The extended concentration range for the first time allows the demonstration of a non-monotonic concentration dependence of the mobility for a single particle species. Our observations reconcile previous experimental observations made on other species over restricted concentration ranges. We compare our results to the state-of-the-art theoretical calculations using a constant particle charge and the carefully determined experimental boundary conditions as input. In particular, we consider the so-called realistic salt free conditions, i.e., we respect the release of counterions by the particles, the solvent hydrolysis, and the formation of carbonic acid from dissolved neutral CO2. We also compare our results to previous results obtained under similarly well-defined conditions. This allows identification of three distinct regions of differing density dependence. There is an ascent during the build-up of double layer overlap, which is not expected by theory, an extended plateau region in quantitative agreement with theoretical expectation based on a constant effective charge and a sudden decrease, which occurs way before the expected gradual decrease. Our observations suggest a relation of the non-monotonic behavior to a decrease in particle charge, and we tentatively discuss possibly underlying mechanisms.

Colloidal electro-phoresis in the presence of symmetric and asymmetric electro-osmotic flow.

We characterize the electro-phoretic motion of charged sphere suspensions in the presence of substantial electro-osmotic flow using a recently introduced small angle super-heterodyne dynamic light scattering instrument (ISASH-LDV). Operation in integral mode gives access to the particle velocity distribution over the complete cell cross-section. Obtained Doppler spectra are evaluated for electro-phoretic mobility, wall electro-osmotic mobility and particle diffusion coefficient. Simultaneous measurements of differing electro-osmotic mobilities leading to asymmetric solvent flow are demonstrated in a custom made electro-kinetic cell fitting standard microscopy slides as exchangeable sidewalls. The scope and range of our approach are discussed demonstrating the possibility of an internal calibration standard and using the simultaneously measured electro-kinetic mobilities in the interpretation of a microfluidic pumping experiment involving an inhomogeneous electric field and a complex solvent flow pattern.

Formation of a transient amorphous solid in low density aqueous charged sphere suspensions

Colloidal glasses formed from hard spheres, nearly hard spheres, ellipsoids and platelets or their attractive variants, have been studied in great detail. Complementing and constraining theoretical approaches and simulations, the many different types of model systems have significantly advanced our understanding of the glass transition in general. Despite their early prediction, however, no experimental charged sphere glasses have been found at low density, where the competing process of crystallization prevails. We here report the formation of a transient amorphous solid formed from charged polymer spheres suspended in thoroughly deionized water at volume fractions of 0.0002–0.01. From optical experiments, we observe the presence of short-range order and an enhanced shear rigidity as compared to the stable polycrystalline solid of body centred cubic structure. On a density dependent time scale of hours to days, the amorphous solid transforms into this stable structure. We further present preliminary dynamic light scattering data showing the evolution of a second slow relaxation process possibly pointing to a dynamic heterogeneity known from other colloidal glasses and gels. We compare our findings to the predicted phase behaviour of charged sphere suspensions and discuss possible mechanisms for the formation of this peculiar type of colloidal glass.

An empirical correction for moderate multiple scattering in super-heterodyne light scattering.

Frequency domain super-heterodyne laser light scattering is utilized in a low angle integral measurement configuration to determine flow and diffusion in charged sphere suspensions showing moderate to strong multiple scattering. We introduce an empirical correction to subtract the multiple scattering background and isolate the singly scattered light. We demonstrate the excellent feasibility of this simple approach for turbid suspensions of transmittance T ≥ 0.4. We study the particle concentration dependence of the electro-kinetic mobility in low salt aqueous suspension over an extended concentration regime and observe a maximum at intermediate concentrations. We further use our scheme for measurements of the self-diffusion coefficients in the fluid samples in the absence or presence of shear, as well as in polycrystalline samples during crystallization and coarsening. We discuss the scope and limits of our approach as well as possible future applications.

Equilibrium fluid-crystal interfacial free energy of bcc-crystallizing aqueous suspensions of polydisperse charged spheres.

The interfacial free energy is a central quantity in crystallization from the metastable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from these data effective nonequilibrium values for the interfacial free energy between the emerging bcc nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory (CNT). A strictly linear increase of the interfacial free energy was observed as a function of increased metastability. Here, we further analyze these data for five aqueous suspensions of charged spheres and one binary mixture. We utilize a simple extrapolation scheme and interpret our findings in view of Turnbull's empirical rule. This enables us to present the first systematic experimental estimates for a reduced interfacial free energy, σ(0,bcc), between the bcc-crystal phase and the coexisting equilibrium fluid. Values obtained for σ(0,bcc) are on the order of a few k(B)T. Their values are not correlated to any of the electrostatic interaction parameters but rather show a systematic decrease with increasing size polydispersity and a lower value for the mixture as compared to the pure components. At the same time, σ(0) also shows an approximately linear correlation to the entropy of freezing. The equilibrium interfacial free energy of strictly monodisperse charged spheres may therefore be still greater.

Structure and transport properties of charged sphere suspensions in (local) electric fields

Motivated by both still open fundamental theoretical questions as well as novel applications, the electro-kinetics of highly charged model colloids have attracted considerable interest in the last few years. The present paper reviews corresponding new developments and trends emerging mainly from novel instrumentations for both strongly interacting and extremely dilute systems. We also highlight recent uses of local electric fields and electro-kinetic currents to realize complex micro-swimmers or prescribe crystal micro-structures.

Transient Moiré rotation patterns in thin colloidal crystals

A high resolution optical microscopy study on low salt charged sphere suspensions settling under gravity reveals the formation of AB-stacked triangular layers via different transient structures. In particular, metastable triangular Moire rotation patterns (formally corresponding to 1 × 1 Rα super structures) with rotation angles α = 27.8° and α = 38.2° are identified.

Microscopic investigations of homogeneous nucleation in charged sphere suspensions

We studied the homogeneous nucleation kinetics of an aqueous suspension of charged colloidal spheres under de-ionized conditions. Samples of equilibrium crystalline structure were shear molten and the metastable melt left to solidify after cessation of shear. At low particle number densities n, corresponding to low metastability of the melt, nucleation was monitored directly via video microscopy. We determined the nucleation rates gamma(t) by counting the number of newly appearing crystals in the observation volume per unit time. Using a suitable discrete adaptation of Avrami's [J. Chem. Phys. 7, 1003 (1939); ibid.8, 212 (1940); ibid.9, 177 (1941)] model for solidification via homogeneous nucleation and subsequent growth, we calculate the remaining free volume VF(t) to obtain the rate densities J(t) = gamma(t)/VF(t). We observe J(t) to rise steeply, display a plateau at a maximum rate density Jmax, and to decrease again. With increased n the plateau duration shrinks while Jmax increases. At low to moderate number densities fully solidified samples were analyzed by microscopy to obtain the grain-size distribution and the average crystallite size angle brackets(L). Under the assumption of stationarity, we obtained the nucleation rate density J(Avr), which increased strongly with increasing n. Interestingly, J(Avr) agrees quantitatively to Jmax and to J(Avr) as obtained previously from scattering data taken on the same sample at large n. Thus, by combination of different methods, reliable nucleation rate densities are now available over roughly one order of magnitude in n and eight orders of magnitude in J.

Dielectric functions of the double layer polarization theory of a charged colloidal suspension

The double layer polarization theory is analyzed, where the dielectric storage ε′(ω) and the dielectric loss ε″(ω) are expressed in terms of the free energy stored and the free energy dissipation. The dielectric functions are further put into the canonical form of the sum of the contributions from the elementary excitations. The excitations obey the extremal dissipation principle, subjected to the appropriate constraint. We calculate the dielectric function of the suspension of charged spheres as an example, where a simple algebraic formula is obtained.

A study on the homogeneous nucleation kinetics of model charged spheresuspensions

We investigated the kinetics of homogeneous nucleation from a shear melt for amodel system of deionized aqueous suspensions of charged spheres. With the aidof nearly index-matched perfluorinated particles of low polydispersity,we extended previous studies into the regime of large metastability andnucleation-dominated solidification. With increasing particle number densityn,the solidification time determined by the appearance of a finite shearmodulus decreased from minutes to milliseconds. Nucleation rate densitiesJ werederived from the width of the principal peak in the static structure factoras measured by means of light scattering after complete solidification.Jwas observed to increase approximately exponentially withn asexpected from classical nucleation theory in the absence of a kinetic glasstransition. Additional measurements of the elastic and dynamic behaviour,however, show that for the largest concentrations, the sample properties areglass-like.

Sedimentation Velocity and Potential in Concentrated Suspensions of Charged Spheres with Arbitrary Double-Layer Thickness

The sedimentation in a homogeneous suspension of charged spherical particles with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model. Overlap of the double layers of adjacent particles is allowed, and the polarization effect in the double layer surrounding each particle is considered. The electrokinetic equations that govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. An analytical expression for the settling velocity of the charged sphere in closed form is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged spheres is also derived by using the requirement of zero net electric current. Our results demonstrate that the effects of overlapping double layers are quite significant, even for the case of thin double layers.

Calculation of the collective diffusion coefficient of electrostatically stabilised colloidal particles

The collective diffusion of concentrated suspensions of charged spheres is theoretically investigated. The analysis is based on a fundamental calculation of colloidal interactions between particles expressed in terms of osmotic pressure. The osmotic pressure accounts for multiparticle electrostatic interactions, dispersion forces, and configurational entropy effects. This osmotic pressure is used in the generalised Stokes–Einstein equation to derive the collective diffusion coefficient. This allows the prediction of the concentration dependence of the collective diffusion coefficient for various physicochemical conditions, such as particle size, surface charge or potential and electrolyte concentration. Results are compared with existing experimental data on the collective diffusion coefficient of bovine serum albumin, and to other dilute theories. Very good quantitative agreement is found.

Electrical conductivity of suspensions of charged particles in ionic solutions

A theory for the electrical conductivity of dilute suspensions of charged spheres in ionic solutions is constructed starting with a description of processes around a single particle followed by averaging over a representative volume to obtain the average current and the effective conductivity. On the small scale, electrokinetic effects due to the transport of charge by convection (electro-osmosis) and deformation of the equilibrium double-layer are taken into account along with alterations in the local conductivity due to the distribution of ions in the double-layer. The effective conductivity consists of the bulk conductivity of the ionic solution plus contributions arising from: (a) polarization of the applied field by the nonconducting spheres, (b) polarization due to electrokinetic effects, (c) alterations in the distribution of ions, (d) transport of ions by electro-osmosis, and (e) electrophoresis of the particles. These contributions are proportional to the volume fraction of particles. Effects due to the particles can be interpreted in terms of what is often termed the surface conductivity. Analytical solutions for symmetrical electrolytes are obtained using a perturbation method and these are employed to derive a formula for the conductivity, correct to the second order in the surface charge or ζ-potential. Numerical evaluations of the various expressions show how the conductivity depends on, for example, the double-layer thickness. Contributions arising from polarization of the charge cloud are found to be substantial and these, coupled with effects due to curvature, cause the conductivity to differ substantially from that calculated using the Bikerman formula which omits such effects. Considering the fact that the analytical theory is formulated for small surface charge (or ζ-potential) the degree of agreement with experiments by Watillon and StoneMasui [ J. Electroanal. Chem. 37, 143 (1972)] is remarkable.