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.