Multiscale Approaches and Perspectives to Modeling Aqueous Electrolytes and Polyelectrolytes - Multiscale Molecular Methods in Applied Chemistry - page 275

3.2.4 Towards Systematic Coarse Graining of Polyelectrolytes in Solution

Polyelectrolytes in aqueous solution are frequently modeled with generic CG
models rather than with systematically coarse-grained ones. The Bjerrum length
in these systems is, however, small and contributions of the explicit water mole-
cules to the effective forces between the ions cannot be neglected, in particular in
systems where polyelectrolyte concentrations are large. Systematic coarse graining
techniques can be used to account for these contributions in the short range part
of an effective (implicit solvent) ion-ion potential. A so far non-existing implicit
solvent CG model for polystyrene sulfonated (PSS) may be obtained using the
isolated chain approach to molecular coarse graining [ 98 ]. To this end, the PS
mapping scheme of Fig. 8 can be used (alternative mapping schemes may also be
chosen), augmented with a CG bead that represents the sulfonate group connected
to the phenyl bead. Conformational sampling with isolated atomistic PSS chains
in vacuum provides the bonded potentials of the CG model. At this stage, the
electrostatic interactions between the sulfonate groups may be set to zero (e.g., by
using a SO 3 H group instead of the charged SO 3 group); hence the CG bonded
potentials are not influenced by the electrostatic condition, which is described by
nonbonded potentials determined independently. The nonbonded implicit solvent
potentials between the various PSS beads can be obtained from pair potential of
mean force calculations in explicit water, using chemical compounds resembling
the CG beads, along the lines investigated previously for small peptides [ 94 ]. This
approach, however, does not account for the bead being part of a polymer chain,
nor does it take into account that the hydration properties of isolated chemical
compounds are different from those of the corresponding chemical groups within a
macromolecule. It is, for example, unclear to what extent the effective nonbonded
interaction between two benzene molecules in water resembles the effective inter-
action between two phenyl beads on PSS chains in water. To account for both bead
connectivity and differences in aqueous hydration, the approach in Fig. 9 can be
invoked. Note that, in this case, not only the direct interactions between atoms
contained by the central beads of the two solutes are switched off in the lower part
of Fig. 9 , but also the interactions between these atoms and the solvent. Hence,
unlike in the gas phase, the effective potential V eff

( R

!1 6¼

0 and is determined
by the conditional hydration free energy of the central bead, the condition being that
interactions between the atoms in this bead and the solvent are introduced in an
environment that has the solute atoms connected to the central bead already
“dissolved.” Standard thermodynamic integration or thermodynamic perturbation
techniques can be used to calculate the conditional hydration free energy. By means
of the way described here, the effects of the solvent, counter ions, and salt on the
conformations of the CG polyelectrolyte in solution are modeled through the
nonbonded CG interactions, as required. Note that this will not necessarily be
the case when alternative coarse graining methods are used. With the inverse
Monte Carlo or IBI methods, the effects of the nonbonded interactions at the
atomistic scale will be “mixed” between the CG bonded and CG nonbonded
potentials, in effect limiting the transferability of the polyelectrolyte model thus

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