  The configurational entropy of several H-disordered ice polymorphs is
calculated by means of a thermodynamic integration along a path between a
totally H-disordered state and one fulfilling the Bernal-Fowler ice rules. A
Monte Carlo procedure based on a simple energy model is used, so that the
employed thermodynamic path drives the system from high temperatures to the
low-temperature limit. This method turns out to be precise enough to give
reliable values for the configurational entropy of different ice phases in the
thermodynamic limit (number of molecules N --> infinity). The precision of the
method is checked for the ice model on a two-dimensional square lattice.
Results for the configurational entropy are given for H-disordered arrangements
on several polymorphs, including ices Ih, Ic, II, III, IV, V, VI, and XII. The
highest and lowest entropy values correspond to ices VI and XII, respectively,
with a difference of 3.3\% between them. The dependence of the entropy on the
ice structures has been rationalized by comparing it with structural parameters
of the various polymorphs, such as the mean ring size. A particularly good
correlation has been found between the configurational entropy and the
connective constant derived from self-avoiding walks on the ice networks.
