The spinodal instabilities in hot asymmetric nuclear matter and some important critical parameters derived thereof are studied using six different families of relativistic mean-field ( RMF ) models .
The slopes of the symmetry energy coefficient vary over a wide range within each family .
The critical densities and proton fractions are more sensitive to the symmetry energy slope parameter at temperatures much below its critical value ( T _ { c } \sim 14-16 MeV ) .
The spread in the critical proton fraction at a given symmetry energy slope parameter is noticeably larger near T _ { c } , indicating that the warm equation of state of asymmetric nuclear matter at sub-saturation densities is not sufficiently constrained .
The distillation effects are sensitive to the density dependence of the symmetry energy at low temperatures which tend to wash out with increasing temperature .