  We present an investigations on the influence of dynamical quintessence field
models on the formation of non-linear structures. In particular, we focus on
the structure traced by the mass function. Our contribution builds on previous
studies by considering two potentials not treated previousy and investigating
the impact of the free parameters of two other models. Our approach emphasises
the physical insight into the key role of the evolution of the equation of
state. We use the variations in the spherical non-linear collapse caused by
quintessence as a function of the model's potential in a Press Schechter scheme
to obtain the differences in halo mass functions. The comparison is also done
with the more usual scenario $\Lambda$CDM. We conclude the method should be
promissing for discrimination using cluster mass determination and that the key
role lies within the evolution of the equation of state.
