Bond fluctuation model

Polymers have many interesting mesoscopic properties that can adequately represented through coarse-grained models. Lattice models are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided.

The bond fluctuation model has been used in the recent past to simulate a great variety of polymer systems (see Ref.s 1 and 2). It represents 8-site non-overlapping beads placed in a simple cubic lattice. Bonds linking the beads may have lengths ranging between 2 and ${\sqrt {1}}0$ lattice length units but bonds vectors of the type (2,2,0) are excluded to avoid bond crossing during the simulation.

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This model exhibits some advantages with respect to more conventional representations of the polymer in a lattice, such as fixed-bond self-avoiding walk chains on a simple cubic or tetrahedral lattice:

• It is somehow more consistent with the theoretical description of the chain through Gaussianly distributed statistical segments. This description has been employed in the past to obtain useful analytical expression for equilibrium properties and its dynamical version corresponds to the Rouse model.
• A variety of bond lengths alleviate the restrictions due to the lattice constraints and, therefore, the model is more similar to the continuum behavior.
• It is possible to perform simulations by using a single type elementary bead jumps. A bead jump is a simple translation of the bead to one of the six contiguous lattice units along the x, y or z axis.This is a difference with respect to the simple cubic lattice model where a combination of bent and crankshaft elementary moves involving two or three beads has to be used as the simplest local level. The implication is that one can generate dynamic trajectories with the bond fluctuation model by using a simple and natural type of bead jumps, which intuitively resembles the stochastic behavior of Brownian particles.
• The elementary jump moves can directly used in polymers with branch points (stars, combs, dendrimers).

References

1. K. Binder (ed.) “Monte Carlo and Molecular Dynamics Simulations in Polymer Science”, Oxford University Press (1995)
2. I. Carmesin and Kurt Kremer "The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions", Macromolecules pp. 2819 - 2823 (1988)