The role of grains in evolution of accretion disc is an important issue in astrophysics. In this paper, we study the effect of vapor pressure of grains in the dead zones of protoplanetary discs. Our study is limited to some particular observed cases in which evaporation of grains would be important and their vapor gas are constrained to an approximately isolated case. Here, we use the Einstein model to investigate the thermodynamics of vapor pressure. The results show that there is a critical temperature as a function of oscillation frequency and binding energy of particles. For temperatures greater than this critical value, the system goes into unstable mode. We show that the dead zone of the disc may reach to enough conditions to condense via instability caused by vapor pressure of grains. This mechanism may play an important role in the formation of planetesimals through protoplanetary disc.
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