Electrostatics and aggregation: How charge can turn a crystal into a gel

Abstract

The crystallization of proteins or colloids is often hindered by the appearance of aggregates of low fractal dimension called gels. Here we study the effect of electrostatics upon crystal and gel formation using an analytic model of hard spheres bearing point charges and short range attractive interactions. We find that the chief electrostatic free energy cost of forming assemblies comes from the entropic loss of counterions that render assemblies charge-neutral. Because there exists more accessible volume for these counterions around an open gel than a dense crystal, there exists an electrostatic entropic driving force favoring the gel over the crystal. This driving force increases with increasing sphere charge, but can be counteracted by increasing counterion concentration. We show that these effects cannot be fully captured by pairwise-additive macroion interactions of the kind often used in simulations, and we show where on the phase diagram to go in order to suppress gel formation.

Novel kinetic trapping in charged colloidal clusters due to self-induced surface charge organization

“…Another possibility is that the counterion entropy acts to stablise the 4D clusters, as these are less compact than 4A. This may hold for aqueous systems where the ionic strength is higher than is the case here and the transition to more compact clusters significantly reduces the space available to the counterions, as they are bound to a region of order a Debye length from the colloids35. However, here the number of ions is very small, and the Debye length is so large (~ 2 σ ) that the relative change in volume accessible to the ions in the 4D → 4A transition is so small that this mechanism has a rather limited contribution (somewhat less than k B T for our parameters).…”

“…While we do not capture the full experimental parameters, we argue that these features are generic to the ion condensation (weak charging) regime. This mechanism is reminiscent of ion condensation in polyelectrolytes39 and may also be relevant to aggregation/crystallisation in proteins35. Stablisation of 4D clusters may be achieved by such an anisotropic charge distribution as follows.…”

Dynamics of confined depletion mixtures of polymers and bidispersed colloids

“…Such systems, however, may serve as better models of particle-laden complex fluids ubiquitously used in confined geometries. Particles suspended in organic 3 solvents may also exhibit electrostatic repulsions, and mixtures of charged particles and depleting polymers have been extensively studied as models for gelation in the presence of competing interparticle interactions [32][33][34][35][36][37][38][39] . One particularly convenient model system for attractive complex fluids is a mixture of particles and non-adsorbing polymers [26][27][28][29][30][31] , in which the range and strength of the effective depletion attraction between particles are governed by the polymer-to-particle size ratio and the polymer concentration, respectively.…”

Growth Rates of Protein Crystals

“…11 This approximation is likely to fail for larger proteins where the aqueous cavities are much larger than the Debye length. In these cases a linearized 16 or numerical treatment may be more appropriate. The average potential can be determined from the charge neutrality condition for the crystal $$q=-{\nu }_w(c_{+}-c_{-})=2{\nu }_w{c}_0\sinh \stackrel{false‒}{\psi }.$$…”