  Recently introduced invariant energy quadratization (IEQ) and scalar
auxiliary variable (SAV) approaches have proven to be very powerful ways to
construct energy stable schemes for phase field models. Both methods require an
assumption which the energy potential or energy is bounded from below. Under
this assumption, a positive constant $C$ need to be added to keep the square
root reasonable. However, it seems that it maybe more reasonable in both
physics and mathematics if the energy potential or energy is arbitrary.
Furthermore, if the bounded value from below is not obvious exactly, we are not
easy to give a proper constant $C$ before calculation. In this paper, by adding
a positive preserving function ($M(\phi)$ in IEQ and $E_0(\phi)$ in SAV )
instead of the positive constant in square root, we can improve this situation.
The main contribution of this article is we proved that the positive preserving
function can always be found for polynomial type $F(\phi)$. We also proved the
unconditional energy stability for all semi-discrete schemes carefully and
rigorously. A comparative study of classical IEQ, SAV, MIEQ and MSAV approaches
is considered to show the accuracy and efficiency. Finally, we present various
2D numerical simulations to demonstrate the stability and
