Kern and Frenkel patchy model

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The Kern and Frenkel [1] patchy model published in 2003 is an amalgamation of the hard sphere model with attractive square well patches (HSSW). The model was originally developed by Bol (1982),[2] and later Chapman (1988) [3] [4] reinvented the model as the basis for numerous articles describing properties of associating particles from molecular simulation and theory. The computational advantage of Bol's model is that only a simple dot product is required to determine if a particle is in the bonding orientation.

The potential has an angular aspect, given by (Eq. 1)

where the radial component is given by the square well model (Eq. 2)

and the orientational component is given by (Eq. 3)

where is the solid angle of a patch () whose axis is (see Fig. 1 of Ref. 1), forming a conical segment.

Multiple patches[edit]

The "two-patch" and "four-patch" Bol (Chapman or Kern and Frenkel) model was extensively studied by Chapman and co-workers for bulk and interfacial systems using hard sphere and Lennard-Jones reference systems. Later other groups, including Sciortino and co-workers, considered stronger association energies for the "two-patch" hard sphere reference [5][6][7].

Four patches[edit]

Main article: Anisotropic particles with tetrahedral symmetry


If the two parameters and fullfil the condition

then the patch cannot be involved in more than one bond. Enforcing this condition makes it possible to compare the simulations results with Wertheim theory [3][5][7]

Hard ellipsoid model[edit]

The hard ellipsoid model has also been used as the 'nucleus' of the Kern and Frenkel patchy model [8].


Related reading