Modeling Polymers in Molecular Simulations

If generic properties of polymers need to be determined, it is often sufficient to rely on lattice models. For comparison with experiments of particular melts and blends, more sophisticated off-lattice models are typically applied. These models are described by force fields that determine the interactions between atoms or groups of atoms, and the quality of the modeling is essential for the predictive quality of the simulations. Force field parameters can be derived from direct comparison with experimental data, from quantum mechanical calculations, or both. In the first part of this section, we present generic polymer models that are commonly used in molecular simulations without focussing on any particular substance. Emphasis is placed on lattice and simple off-lattice models that will also be discussed in the next three sections. Section 1.5 is dedicated to chemically realistic descriptions. 

The first model that took into account excluded volume effects was the selfavoiding-walk (SAW), which was introduced about 60 years ago [65, 66]. Each monomer occupies a lattice site on a simple cubic lattice. The bond length between adjacent monomers is fixed by the lattice constant and the bond angles are restricted by the geometry of the lattice. This model is well-suited to describe generic polymers in dilute, good solvent conditions and exhibits the correct scaling behavior 

A simple and very popular example of a coarse-grained off-lattice model is given by the bead-spring chain of Kremer and Grest [70,7 Ij. In this model monomers interact via a Lennard-Jones potential  

To increase computational efficiency the Lennard-Jones potential usually is cut and shifted at either twice the minimum value, or 2.5a. The constant in Eq. (1.9) is chosen such that Vy is continuous at r = r. The value of e sets the scale of energy (and temperature T, which is often normalized as T = kBT/e), and the size a of effective monomers sets the scale of length. In addition, adjacent beads interact with the so-called FENE potential  

Constants in Eq. (1.10) are chosen such that the most favorable distance between bonded monomers is slightly smaller than the distance between non-bonded monomers to prevent crystallization. Alternatively, a harmonic potential can be used for bonded monomers instead of Eqs. (1.9,1.10). As indicated for lattice models, polymer blends can be implemented by adjusting the interaction strength e for monomers of 

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