Reactive spheres

MC simulations based on the SRS model were pioneered by Ma et al. to explain the peculiar spreading profiles of PEPEs on amorphous carbon surfaces shown in Eig. 3 via the adoption of four different interactions molecule/molecule, molecule/surface, end-group/end-group, and end-group/surface (a molecule is denoted as a backbone in the absence of polar end-groups). Molecules are approximated as reactive spheres, where a spin S = I is assigned to an occupied lattice site (for a vacant site, S = 0). 

Smoluchowski and Debye investigated the problem of diffusion controlled reactions between uniformly reactive spheres in the absence (1 ) and presence (2 ) of centrosymmetric Coulombic forces. Since these pioneering works, there has been a proliferation of theoretical studies based on more refined models. These have considered the inclusion of hydrodynamic interaction, (3-4) solvent... 

Two Spheres. The steady state diffusion controlled rate constant for two uniformly reactive spheres interacting via a centrosymmetric potential of mean force can be solved numerically and in special cases analytically as given by Eq. 2. For a potential of mean force of zero and no hydrodynamic interaction (NHI), Eq. 2 reduces to the Smoluchowski result (1)... 

We compare and contrast 7.B and AB dynamics through treatments based on those of Sinolucliowski-Colliits Kimball (SCK) 67.68 and Noyes 69-72. Kxccpt where otherwise noted, we treat ideal cases. Molecules A and B are modeled as hard, spin-lice, isotropically-reactive spheres surfaces /. arc hard, uniform planes media are structureless, uniform, and isotropic surfaces and media extend to inlinily in all possible directions and Pick s Laws govern diffusion. 

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