Atomistic Simulation studies of the Cement Paste Components

Atomistic Simulation studies of the Cement Paste Components
not only in its local stability, but also in its stability with respect to their neighbouring
sizes. The stability index of an alumino-silicate chain with the length m evaluates the
stability of that chain with respect to the addition or removal of one alumino-silicate
unit. It is the chemical potential of the system against the number of particles. This
methodology is generally employed in the study of the stability with the cluster sizes
[216], and it has been applied successfully to investigate the stable lengths of silicate
chains [128]. To calculate the stability index, all the possible growing mechanism must
be identified and taken into account. A silicate chain of length m might grow reacting
with other silicon monomer Si(OH) 4 , an aluminium monomer Al(OH) - 4 , or even with a
charged silicon monomer Si(OH) 3 O - [215]. If only one charged silicon tetrahedra unit or
one aluminium per chain are considered, the chains of length m +1 could continue
growing by adding neutral silicon monomer. The same reasoning can be applied to the
inverse process, when a silicate chain losses a unit. All the possible growth paths that
were considered in this study are given in figure 4.2.1. It must be noted that once the
aluminium enters the chain, the next Si(OH) 4 may be incorporated in both sides of the
chain. Then, they are several growth paths due to the asymmetry arising from the
presence of aluminium. In order to deal with a unique growth path, the -Al(OH) - 4 unit
was always located at the end of the chain, assuming that subsequent silicon units would
react in the opposite chain side.
The neutral and charged silicate chains (orange, blue and red paths of figure 4.2.1) were
explored in a previous work by Ayuela and co-workers [128]. They found that the stable
chains were those which fulfil the 3n – 1 rule, in agreement with the experimental data
[6, 8, 52], and that the charged chains contribute more than the neutral ones to the global
stability. In this work, the growing paths involving aluminium (green and purple in
figure 4.2.2) were studied. The stability index of these new channels is defined as:
( ) ( 1) ( 1) ( 1) 3 ( )
S m = Em− + Em+ + Em− − ⋅ Em
(4.2.2)
Al Al Al Si Al
where the subscript denotes a silicate ( Si ) or alumino-silicate chain ( Al ), the term in
parenthesis indicates the length of the chain, and E is the energy of the corresponding
chain. A detailed derivation of the stability index from reaction transition rates and the
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