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The interaction of plasma particles with dust grains leads to their charging. An equilibrium grain potential depends on a plasma environment, as well as on the grain composition, size, shape, and charging history. We present results of calculations of the equilibrium potential of the grain immersed in the plasma simulating a lunar environment. In calculations, we apply a modified model of the secondary electron emission from dust grains, which takes into account grain sizes, their material, and surface roughness. Since this model describes the increase in the secondary emission yield caused by a finite dimension of the dust grain, the calculations provide a realistic estimation of the dust grain charge in the near-Earth environment. We show that the grain surface potential is a descending function of the grain size and this effect can even lead to opposite polarities of small and large grains.