Liquid-liquid and liquid-solid phase separation and flocculation for a charged colloidal dispersion

Formation of stable clusters in colloidal suspensions

The experimental evidence and theoretical explanations of stable cluster formation in colloidal suspensions are reviewed. The clusters form in the intermediate range between a stable suspension built up by singlets and the irreversible coagulation or gelation of the suspension. The stable clusters develop as a result of a balance between competing short range attraction and long range repulsion between colloidal particles or due to reversible flocculation in the shallow secondary potential well. Heteroaggregation in binary colloids can also result in formation of stable clusters.

Thermal response of a microgel system

Recent experimental studies [Z. Wu, B. Zhou, Z.B. Hu, Phys. Rev. Lett. 90 (2003) 048304] on an uncharged aqueous poly-N-isopropylacrylamide (PNIPAM) dispersion have shown that this microgel system is sensitive to temperature. This system was also experimentally found to be modeled quite well by microgel particles interacting via a hard-sphere repulsive plus an inverse power (temperature-dependent) attractive potential. To understand theoretically this thermally responsive PNIPAM dispersion, we apply a novel approach [G.F. Wang, S.K. Lai, Phys. Rev. E 70 (2004) 051402] to calculate its thermodynamic phase diagram. Differing from the conventional method in which the boundaries of the coexisting phases are the ultimate target, the present work places emphasis on crosshatching colloidal domains which include the homogeneous phase (gas, liquid or solid), two coexisting phases and perhaps also multi-phases in coexistence. Strategically, this was done by treating the coexisting phases as one composite system whose Helmholtz free energy density is written as the sum of constituent free energy densities each of which is weighed by its respective volume proportion. We show here that by minimizing the composite system's free energy density the phase-diagram domains can all be determined in addition to the phase boundaries customarily obtained by imposing the conditions of equal pressure and equal chemical potential. Also, we present the theoretically predicted phase diagram of PNIPAM dispersion and compare it with the one observed experimentally.

Secondary Minimum Coagulation in Charged Colloidal Suspensions from Statistical Mechanics Methods

A statistical mechanics approach is applied to predict the critical parameters of coagulation in the secondary minimum for charged colloidal suspensions. This method is based on the solution of the reference hypernetted chain (RHNC) integral equation, and it is intended to estimate only the locus of the critical point instead of the full computation of the "gas-liquid" coexistence. We have used an extrapolation procedure due to the lack of solution of the integral equation in the vicinity of the critical point. Knowing that the osmotic isothermal compressibility of the colloidal system should ideally diverge in the critical point, we work out the critical salt concentration for which the inverse of the compressibility should be zero. This extrapolation procedure is more rapid than that previously proposed by Morales and co-workers [Morales, V.; Anta, J. A.; Lago, S. Langmuir 2003, 19, 475], and it is shown to give equivalent results. We also present experimental results about secondary minimum coagulation for polystyrene latexes and use our method to reproduce the experimental trends. The comparison between theory and experiment is quite good for all colloidal diameters studied.

Theoretical studies of the early stage coagulation kinetics for a charged colloidal dispersion

We study the early stage coagulation kinetics for a charged colloidal dispersion which is here modeled by an effective two-body colloid-colloid potential. The colloidal system was physically prepared by choosing sets of colloidal parameters varying in particular the Hamaker constant and the particle's size. The kinetics of coagulation process was driven by the addition of an indifferent electrolyte and assumed to proceed in two quasi-steady steps. In the first step, colloidal particles are destabilized by the presence of a second potential minimum to diffuse from a bulk-stabilized liquid phase to a flocculated phase. In the second step, we assume that different entities are found in the second potential minimum. The entities comprise secondary dimers, secondary dimers undergoing redispersion, and monomers still in singlet states. If, under favorable condition, this kind of interaction-driven diffusive motion continues, a fraction of the secondary dimers will be induced to undergo primary dimers formation in the first deep minimum. Whether or not the latter process occurs is determined either energetically by the potential barrier falling below a prescribed value, say of 15k(B)T, or/and the second potential minimum becoming negligibly small (with a magnitude <k(B)T). A prototype example to exhibit this kind of the coagulation kinetics phenomenon is an aqueous dispersion of polystyrene latex particles. Our detailed analysis on this system showed the connection between the change of rate constants and the reversible flocculation<==>coagulation transition and would throw a fresh light on the use of both the energy and the kinetic criteria for understanding the colloidal stability such as those observed in the liquid-liquid coexistence.

Heterogeneity in styrene-butadiene latex films

Low-Tg styrene-butadiene (SB) latex films were investigated by noncontact atomic force microscopy and scanning electric potential microscopy, revealing a number of different morphologies and electric potential patterns across films cast from the same SB latex dispersions under the same conditions. Surface leveling and charge dispersion throughout the films are, thus, restrained even at temperatures above Tg and the minimum film-formation temperature. An unprecedented electric pattern is observed, in which the particle cores are more positive than the contacting particle outer layers. Different packing patterns, including cubic and hexagonal arrays, coexist in neighboring areas. Zonal centrifugation of the SB latex in sucrose density gradient shows that particles cover a broad range of densities. Thus, film surface heterogeneity is at least partly due to particle heterogeneity. Fractal dimensions of topographic profiles are lower than those of the electric potential profiles, showing that charge mobility is much more restrained than polymer chain motion at the film surface and that it imposes a limit to the charged chain-ends motion.

Domains of phase separation in a charged colloidal dispersion driven by electrolytes

We put forth the idea of treating coexisting phases as a composite system and express its free energy as the average of its constitutent free energies weighted by their respective volume proportions. As a result, the theoretical study of charged colloidal phase separation in the presence of electrolytes reduces to optimizing solely the entities pertaining to colloids and small ions. As concrete illustrations, we demarcated the boundaries of coexisting phases for the simplest colloidal dispersion driven by salts at moderate to high concentrations and compared the results with those obtained in the usual manner to numerically show the robust efficiency of the present theory. Also, for a charged colloidal dispersion at very low ionic strength, we crosshatched both the homogeneous one phase and coexisting phases, and used the domains of coexisting phases to interpret an anomalous "transition" of phase diagrams exhibited in dilute colloidal dispersions induced by salts on dilution.