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We present a convex-splitting scheme for the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson equation of state for pure substance. The semi-implicit scheme is proven to be uniquely solvable, mass conservative, unconditionally energy stable and L∞ convergent with the order of 
. The numerical results verify the effectiveness of the proposed algorithm and also show good agreement of the numerical solution with laboratory experimental results.
