We will discuss the asymptotical limit of the isotropic-nematic interface problem within the Landau-de Gennes Q-tensor framework. In particular, the effect of a negative anisotropic elastic coefficient L_2 will be considered. We will show, when the transition layer width goes to zero, the minimizers converge to a minimizer of a free boundary problem for the Oseen-Frank energy with homeotropic free boundary condition in the sense of Gamma-convergence.