Tag Archives: Modeling

How to define particle size?

Particle size is a very important property in the research field of cementitious materials, e.g. modeling, reaction kinetics.

Particles are 3-dimensional objects, and unless they are perfect spheres, e.g. emulsions or bubbles, they cannot be fully described by a single dimension such as a radius or diameter.

In order to simplify the measurement process, it is often convenient to define the particle size using the concept of equivalent spheres. In this case the particle size is defined by the diameter of an equivalent sphere having the same property as the actual particle such as volume or mass for example.

It is important to realize that different measurement techniques use different equivalent sphere models and therefore will not necessarily give exactly the same result for the particle diameter.

Below is a schematic figure illustrating the definition of particle size based on different equivalent spheres.

Definition of particle size

Hydration Mechanisms of Portland Cement: Topochemical or Through-Solution Reaction?

When we simulate the hydration process of Portland cement, it is of significant importance to know the hydration mechanisms. Basically, there are two mechanisms for the hydration of Portland cement, viz. Topochemical and Through-Solution Reaction.

1 Topochemical Reaction Concept

Immediately after the first contact of the cement with water a calcium-rich silicious clinker would liberate Ca2+ ions into the solution. A calcium-poor skeleton is left which reacts with the calcium-rich solution which is accompanied by swelling of the hydration products compared with the original volume of the anhydrous cement.

The topochemical concept was launched by Michaelis at the beginning of last century. Since then topochemical phenomena have been reported for the hydration of both C3S and Portland cement.

Schematic representation of proposed hydration mechanisms

2 Through-Solution Concept

In the through-solution concept dissolution of the anhydrous grain after contact of the cement with water is considered to be followed by hydration in the solution. The hydration products then precipitate on the grain surface.

The through-solution concept was first formulated by Le Chatelier for plaster and Portland cement in the first decade of this century. The concept has been supported by many reserachers, Regourd et al., Brunauer and Gauglitz, Williamson and Dron et al.

The debate on whether cement hydration proceeds topochemically or according to a through-solution mechanism dates back to the very beginning of cement chemistry. The subject is of significant importance in view of mathematical modeling of both the hydration process and structural formation. As such, a so-called Simultaneously Operating Mechanisms is proposed to account for the debate.

3 Simultaneously Operating Mechanisms

According to Neville the controversy between the topochemical and through-solution concept can largely be reduced to a matter of terminology. Shebl et al. explains that hydration of C3S involves both through-solution reactions and topochemical reactions (solid-state reaction). The water/solid ratio would be an important factor in this respect. For low water/solid ratios the reaction would be predominantly topochemical, whereas for high water/solid ratios the through-solution mechanism would be more important. Both reactions could occur simultaneously.

The concept of simultaneously operating mechanisms is plausible indeed if the outer products, i.e. the products which are formed outside the original grain boundaries in a relatively water-rich environment, are formed by a through-solution mechanism, while the inner products, formed inside the original grain boundaries, are the result of a topochemical reaction.

From a literature survey on this topic Daimon concluded that it is very difficult to determine which mechanism has marred. The fact that we are dealing with a poly-size system significantly contributes to the complexity of the subject. Probably the effect of the particle size distribution also explains why Kalousek found many contradictions between different authors on this point.

The conclusion is that the mechanism of cement hydration depends on the water/solid ratio, viz. low water/solid ratios lead to topochemical reaction, while through-solution mechanism is more important at high water/solid ratios, and both reactions could occur simultaneously.

Reference: Simulation of hydration and formation of structure in hardening cement-based materials, by K. Van Breugel, TuDelft.