  Ion-exchange is commonly used to chemically strengthen glasses, by replacing
small atoms by larger ones at sub T$_g$ temperature, thereby inducing a
compressive stress. However, the resulting expansion of the glass remains lower
than that predicted by the difference of molar volumes of the as-cooled
glasses, an anomaly that remains poorly understood. Here, based on molecular
dynamcis simulations of permanently densified sodium silicate glasses coupled
with topological constraint theory, we show that the rigidity of the network
controls the extent of the dilatation. Isostatic networks, which are rigid but
free of eigenstress, show maximal expansion and, therefore, appear to be an
attractive option to improve the toughness of glass.
