The growth of charged platelets.

Growth models of charged nanoplatelets are investigated with Monte Carlo simulations and simple theory. In a first model, 2-dimensional simulations in the canonical ensemble are used to demonstrate that the growth of a single weakly charged platelet could be limited by its own internal repulsion. The short range attractive interaction in the crystal is modeled with a square well potential while the electrostatic interactions are described with a screened Coulomb potential. The qualitative behavior of this case can also be described by simply balancing the attractive crystal energy with the screened Coulomb repulsion between the crystal sites. This repulsion is a free energy term dominated by counterion entropy and of course reduced by added salt. For a strongly coupled system, that is with high charge density and divalent counterions as in calcium silicate hydrate, the main product of cement hydration, the screened Coulomb approximation becomes inadequate and the growth behavior has to be described with the full primitive model. In this case, the energetic interactions become relatively more important and the entropy of the system plays a minor role. As a consequence, the electrostatic interactions gradually become less of a hindrance for aggregation and in extreme cases electrostatics actually promote the growth. This is manifested as an increased aggregation with, for example, increasing surface charge density. In the presence of divalent calcium ions and at the high negative surface charge density typical for calcium silicate hydrate, electrostatic interactions are not a hindrance for an infinite growth of the particles. By combining experimental and simulated data we can show that the limited sized platelets found in cement paste is due to a very fast nucleation rate compared to the growth rate.

Interaction of nanometric clay platelets.

The free energy of interaction between two nanometric clay platelets immersed in an electrolyte solution has been calculated using Monte Carlo simulations as well as direct integration of the configurational integral. Each platelet has been modeled as a collection of charged spheres carrying a unit charge the face of a platelet contains negative charges, and the edge, positive charges. The calculations predict that a configuration of "overlapping coins" is the global free energy minimum at intermediate salt concentrations (10-100 mM). A second weaker minimum, corresponding to the well-known "house of cards" configuration, also appears in this salt interval. At low salt concentrations the electrostatic repulsion dominates, while at intermediate concentrations electrostatic interactions alone can create a net attraction between the platelets. At sufficiently high salt content (>200 mM), the van der Waals interaction takes over and the net interaction becomes attractive at essentially all separations. From the calculated free energy and its derivative, we can derive a yield stress and elasticity modulus in fair agreement with experiment. The roughness of the platelets affects the quantitative behavior of the free energy of interaction but does not alter the results in a qualitative way. From the variation of the free energy of interaction, we would tentatively describe the phase behavior as follows: At low salt, the interaction is strongly repulsive and the dispersion should appear as a solid ("repulsive gel"). With increasing salt concentration, the repulsion is weakened and a liquid phase appears ("sol"). A further increase of the salt content leads a second solid phase ("attractive gel") governed by attractive interactions between the platelets. Finally, at sufficiently high salinity, the clay precipitates due to van der Waals forces.

Repulsion between oppositely charged macromolecules or particles.

The interaction of two oppositely charged surfaces has been investigated using Monte Carlo simulations and approximate analytical methods. When immersed in an aqueous electrolyte containing only monovalent ions, two such surfaces will generally show an attraction at large and intermediate separations. However, if the electrolyte solution contains divalent or multivalent ions, then a repulsion can appear at intermediate separations. The repulsion increases with increasing concentration of the multivalent salt as well as with the valency of the multivalent ion. The addition of a second salt with only monovalent ions magnifies the effect. The repulsion between oppositely charged surfaces is an effect of ion-ion correlations, and it increases with increasing electrostatic coupling and, for example, a lowering of the dielectric permittivity enhances the effect. An apparent charge reversal of the surface neutralized by the multivalent ion is always observed together with a repulsion at large separation, whereas at intermediate separations a repulsion can appear without charge reversal. The effect is hardly observable for a symmetric multivalent salt (e.g., 2:2 or 3:3).

Controlling the cohesion of cement paste.

The main source of cohesion in cement paste is the nanoparticles of calcium silicate hydrate (C-S-H), which are formed upon the dissolution of the original tricalcium silicate (C(3)S). The interaction between highly charged C-S-H particles in the presence of divalent calcium counterions is strongly attractive because of ion-ion correlations and a negligible entropic repulsion. Traditional double-layer theory based on the Poisson-Boltzmann equation becomes qualitatively incorrect in these systems. Monte Carlo (MC) simulations in the framework of the primitive model of electrolyte solution is then an alternative, where ion-ion correlations are properly included. In addition to divalent calcium counterions, commercial Portland cement contains a variety of other ions (sodium, potassium, sulfate, etc.). The influence of high concentrations of these ionic additives as well as pH on the stability of the final concrete construction is investigated through MC simulations in a grand canonical ensemble. The results show that calcium ions have a strong physical affinity (in opposition to specific chemical adsorption) to the negatively charged silicate particles of interest (C-S-H, C(3)S). This gives concrete surprisingly robust properties, and the cement cohesion is unaffected by the addition of a large variety of additives provided that the calcium concentration and the C-S-H surface charge are high enough. This general phenomenon is also semiquantitatively reproduced from a simple analytical model. The simulations also predict that the affinity of divalent counterions for a highly and oppositely charged surface sometimes is high enough to cause a "charge reversal" of the apparent surface charge in agreement with electrophoretic measurements on both C(3)S and C-S-H particles.

Contribution of convection, diffusion and migration to electrolyte transport through nanofiltration membranes.

Transport mechanisms through nanofiltration membranes are investigated in terms of contribution of convection, diffusion and migration to electrolyte transport. A Donnan steric pore model, based on the application of the extended Nernst-Planck equation and the assumption of a Donnan equilibrium at both membrane-solution interfaces, is used. The study is focused on the transport of symmetrical electrolytes (with symmetric or asymmetric diffusion coefficients). The influence of effective membrane charge density, permeate volume flux, pore radius and effective membrane thickness to porosity ratio on the contribution of the different transport mechanisms is investigated. Convection appears to be the dominant mechanism involved in electrolyte transport at low membrane charge and/or high permeate volume flux and effective membrane thickness to porosity ratio. Transport is mainly governed by diffusion when the membrane is strongly charged, particularly at low permeate volume flux and effective membrane thickness to porosity ratio. Electromigration is likely to be the dominant mechanism involved in electrolyte transport only if the diffusion coefficient of coions is greater than that of counterions.

Evaluation of the "DSPM" model on a titania membrane: measurements of charged and uncharged solute retention, electrokinetic charge, pore size, and water permeability.

The DSPM (Donnan steric partitioning pore model) was evaluated in the case of a titania membrane with "nanofiltration properties" by measuring the electrokinetic charge, pore size, and water permeability of the membrane, along with charged and uncharged solute retention. The zeta potential values (zeta) were determined from measurements of the electrophoretic mobility (EM) of titania powder forming the filtering layer of the membrane. Zeta potential values were converted into membrane volume charge (X) by assuming two limiting cases: a constant surface charge (sigma(s)(cst)) and a constant surface potential (psi(s)(cst)). The mean pore radius and thickness/porosity ratio of the membrane were determined by permporometry and from water permeability measurements, respectively. Retention measurements were carried out as a function of the permeate volume flux for both neutral solutes (polyethylene glycol PEG of different size) and salts (KCl, MgSO4, K2SO4, and MgCl2) at various pH values. Ionic retentions showed minimum values near the IEP of the membrane. Retention data were analyzed using the DSPM. Very good agreement was found between the pore radius calculated by the model and that determined by permporometry. X values calculated from fitting retention data using the DSPM were also in satisfactorily agreement with X values calculated from EM measurements assuming a constant surface potential for a large pH range. Furthermore, the DSPM leads to X values (X(DSPM)) between those calculated from EM (X(EM)) using the two limiting bounds. In other words, X(DSPM) was higher than X(EM) assuming psi(s)(cst) at pH values far from the isoelectric point (IEP) and lower than X(EM) assuming sigma(s)(cst). These results show that the DSPM is in qualitative agreement with the charge regulation theory (increase of the pore surface potential and decrease of the pore surface charge density with decreasing the pore size). On the other hand, the thickness/porosity ratio of the membrane calculated from solute retention data differed significantly from that determined from water permeability measurements. Moreover, a single value of Deltax/Ak could not be determined from PEG and salt retention data. This means that the Deltax/Ak parameter loses its physical meaning and includes physical phenomena which are not taken into account by the DSPM. Nevertheless, the model satisfactorily predicted the limiting retention, as this is not influenced by the Deltax/Ak parameter.

Determining the Zeta Potential of Porous Membranes Using Electrolyte Conductivity inside Pores.

The zeta potential is an important and reliable indicator of the surface charge of membranes, and knowledge of it is essential for the design and operation of membrane processes. The zeta potential cannot be measured directly, but must be deduced from experiments by means of a model. The possibility of determining the zeta potential of porous membranes from measurements of the electrolyte conductivity inside pores (lambda(pore)) is investigated in the case of a ceramic microfiltration membrane. To this end, experimental measurements of the electrical resistance in pores are performed with the membrane filled with KCl solutions of various pHs and concentrations. lambda(pore) is deduced from these experiments. The farther the pH is from the isoelectric point and/or the lower the salt concentration is, the higher the ratio of the electrolyte conductivity inside pores to the bulk conductivity is, due to a more important contribution of the surface conduction. Zeta potentials are calculated from lambda(pore) values by means of a space charge model and compared to those calculated from streaming potential measurements. It is found that the isoelectric points are very close and that zeta potential values for both methods are in quite good agreement. The differences observed in zeta potentials could be due to the fact that the space charge model does not consider the surface conductivity in the inner part of the double layer. Measurements of the electrolyte conductivity within the membrane pores are proved to be a well-adapted procedure for the determination of the zeta potential in situations where the contribution of the surface conduction is significant, i.e., for small and charged pores. Copyright 2001 Academic Press.