FIG. 4.
(a) Two solute molecules of diameters σ1 and σ2, part of a larger system of solute molecules enclosed in some containing region Ω, are at time t0 separated from the other molecules in Ω by an imaginary surface Σ and possibly a portion of the system boundary ∂Ω. The surfaces Σ1 and ∂Ω1 (dashed lines) are formed by tracing the positions of the center of molecule 1 when that molecule is rolled around on the insides of Σ and ∂Ω, respectively. The surfaces Σ2 and ∂Ω2 are formed in a similar way by the center of molecule 2. (b) After subdividing the corralling region enclosed by the larger of the Σ1 and Σ2 surfaces (Σ1 in this case) into cubic voxels of edge length h < min (σ1, σ2), the SVTA assumes that the centers of molecules 1 and 2 are distributed randomly and uniformly inside the particular voxels in which they respectively reside; those two voxels are shown here in gray, and are labeled VC1 and VC2, respectively. The surfaces Σ1, ∂Ω1, Σ2, and ∂Ω2 are replaced by their voxelated counterparts VΣ1 (in green), V∂Ω1 (in pink), VΣ2 (in yellow), and V∂Ω2 (in red). Although in this pictorial representation VΣ1 and VΣ2 do not have any voxels in common, they will if σ1 ≈ σ2, and in fact they will be identical if σ1 = σ2. Likewise for V∂Ω1 and V∂Ω2.