Free Energy of Homogeneous Nucleation in the Supersaturated Vapor Phase

用蒙特卡罗方法对饱和Lennard-Jones气相进行了模拟，估计了均匀成核的自由能。对每一个粒子数目n固定的系统进行计算，并假设周期边界条件。在伦纳德-琼斯体系中，每个粒子的体积是43.2单位。不含载气颗粒。温度范围为0.01至1.00，单位为伦纳德-琼斯系统。初始构型是扭曲的立方晶格，将样品冷却到低温，所有分子成为一个大簇。在第二阶段，加热使其汽化，得到单体相。在第三次运行中，在蒙特卡罗模拟中不允许簇分解的条件下加热低温样本。通过热力学积分得到了簇相和单体相的自由能。所得到的临界尺寸与载气粒子的分子动力学模拟相适应。

The free energy of homogeneous nucleation is estimated by the Monte Carlo simulations on the saturated Lennard-Jones vapor phase. The calculation is performed on the each system with a fixed number of particles N. The periodic boundary condition is assumed. The volume per a particle is 43.2 in units of Lennard-Jones system. No carrier gas particles are included. The range of temperature is form 0.01 up to 1.00 in units of Lennard-Jones system. The initial configuration is distorted cubic lattice, and the sample is cooled to low temperature, where all molecules become a large cluster. In the second stage, it is heated to vaporize, where the monomer phase is obtained. In the third run, the low temperature samples is heated with a condition that the cluster is not allowed to decompose in the Monte Carlo simulations. The free energies of the cluster phase and the monomer one is obtained by the thermodynamic integration. The obtained critical size is compatible to the molecular dynamics simulation with the carrier gas particles.