Coarse-Grained Modeling for Macromolecular Chemistry - Multiscale Molecular Methods in Applied Chemistry - page 302

whereas IL-MS2 agrees better with the position of the peak at higher q . This can be
understood by looking at the different details retained in the two mapping schemes:
IL-MS1, which describes the aromatic ring with more details using three different
beads and preserving its flat shape, predicts a better position of the lower q peak,
which in fact is due to the interactions between the rings [ 24 - 26 ]. In contrast,
IL-MS2, which describes the alkyl tail more accurately with two beads instead
of one, predicts better the position of the peak at 1.5A 1 , which arises from the
tail-tail interactions [ 24 - 26 ].
In addition to the positions of the superatoms, their number is also important.
The number of real atoms collected into one superatom is often referred to as the
degree of coarse-graining. It cannot be chosen completely arbitrarily, or else the
essential physics of the polymer may be lost, as the following example shows.
If polyethylene were to be coarse-grained, one could combine 1, 2, 3, or n CH 2 units
into one superatom. For efficiency, one should opt for a high degree of coarse-
graining n . The volume of the spherical superatom has to be approximately the sum
of the volumes of the constituting methylene units, which fixes its diameter. For
large enough n , this will lead to neighboring superatoms whose excluded volumes
no longer overlap. As a consequence, polymer chains can cut through each other in
a simulation and are not forced to reptate through the tubes formed by their
neighbors. It is obvious that the dynamics of such a polymer melt will be qualita-
tively wrong, so that no diffusion coefficients, viscosities, elastic, or rheological
parameters can be obtained. In the case of polyethylene, the largest possible n is 3.
If the polymer has bulkier, more spherical subunits then n can be considerably
larger. An example is the above-mentioned PS model where a styrene repeat unit
(16 atoms) can be combined into one superatom without any harm to the dynamics
because PS has a much fatter envelope than polyethylene.
The choice of the number and position of the superatoms is the responsibility of
the human researcher. Guidelines can be given, but it cannot be automated. One
possible principle for selecting the superatom center is that the bonds between
superatoms can be represented by a single harmonic potential. One can calculate the
bond distributions between the beads for different possible positions of the center of
the superatom. Mapping schemes with a more localized bond length distribution are
often preferred for technical reasons. For example, in the case of PA-66 (Fig. 1a ),
the main concern is on the M3 bead and we can consider two possibilities for the
center of the bead: the center of mass (CM) of the bead or the central carbon atom.
Figure 4 compares the distributions for the two different mapping schemes. As
shown in this figure, the mapping with beads centered on the CM of M3 gives a
three-peaked bond length distribution, whereas a more localized, double peak is
found in the case of the beads centered on the second carbon atom of M3. In the
light of this result, we locate the M3 center on the carbon atom of the backbone
(rather than in the CM of the bead).
Another criterion that needs to be taken into account relates to the statistical
correlations of internal degrees of freedom. The mapping scheme should be chosen
such that these correlations are as weak as possible so that the intramolecular
potentials can be separated, to a good approximation, into bond stretching, bond