  Using analytical models and cosmological N-body simulations, we study the
free-free radio emission from ionized gas in clusters and groups of galaxies.
The results obtained with the simulations are compared with analytical
predictions based on the mass function and scaling relations. Earlier works
based on analytical models have shown that the average free-free signal from
small haloes (galaxies) during and after the reionization time could be
detected with future experiments as a distortion of the CMB spectrum at low
frequencies ($\nu <$ 5 GHz). We focus on the period after the reionization time
(from redshift $z=0$ up to $z=7$) and on haloes that are more massive than in
previous works (groups and clusters). We show how the average signal from
haloes with $M > 10^{13} h^{-1} M_{\odot}$ is less than 10% the signal from the
more abundant and colder smaller mass haloes. However, the individual signal
from the massive haloes could be detected with future experiments opening the
door for a new window to study the intracluster medium.
