  We present a molecular dynamics simulation study of the liquid-solid
transition in a two dimensional system consisting of particles of two different
sizes interacting via a truncated Lennard-Jones potential. We work with equal
number of particles of each kind and the dispersity $\Delta$ in the sizes of
the particles is varied by changing the ratio of the particle sizes only. For
the monodisperse case ($\Delta = 0$) and for small values of $\Delta$, we find
a first order liquid-solid transition on increasing the volume fraction $\rho$
of the particles . As we increase $\Delta$, the first-order transition
coexistence region weakens gradually and completely disappears at high
dispersities around $\Delta = 0.10$ . At these values of dispersity the high
density phase lacks long range translational order but possesses orientational
order with a large but finite correlation length. The consequences of this
effect of dispersity on the glass transition and on the melting transition in
general are discussed.
