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conditions with varying solution concentrations. This question has been addressed
in a recent study of benzene-water mixtures [
84
]. There, the authors investigated
the variation of the solute (benzene) activity coefficient with a detailed-atomistic
and a CG model in the entire range of stable solution concentrations varying
between high solute dilution up to the solubility limit where large density fluctua-
tions and corresponding hydrophobic benzene clusters were observed. To this end,
the authors developed a CG single-site benzene-benzene pair potential, based on
the benzene-benzene pair potential of mean force obtained from detailed-atomistic
simulations at high benzene dilution. The CG pair potential contained a hydropho-
bic contribution in additional to the contribution of direct benzene-benzene van
der Waals interactions. It could be illustrated that the thermodynamic changes and
benzene clustering obtained with the CG model matched almost perfectly with
the predictions of the corresponding atomistic model in the entire range of stable
solution concentrations [
84
]. This result indicates that the hydrophobic interactions
in this system are pairwise additive, supporting the ideas of an earlier study by Wu
and Prausnitz [
96
] who examined a larger set of hydrophobic solutes.
3.2.3 Coarse-Grained Polymer Models
Hierarchical modeling of polymers has made significant progress in recent years.
The coarse-grained models discussed in this section consist of “united atoms,”
which typically merge 5-15 real atoms [
55
,
56
,
97
,
98
]. Figure
8
shows an example
of a polystyrene (PS) fragment in which two coarse grained beads are used to
represent the chemical repeat unit. Effective pair potentials are used to describe the
non-bonded interactions between CG beads, the bonded interactions including
potentials for bond stretching, angle bending, and torsional rotations along CG
bonds [
56
]. Molecular dynamics simulations of polymer melts with these types
of CG models are typically four orders of magnitude more efficient than detailed-
atomistic models [
99
]. Hence, long enough time scales are achieved, required to
Fig. 8 Coarse-grained poly(styrene) model [
98
]. The
gray beads
represent the dangling phenyl
groups,
red beads
represent the aliphatic (backbone) part of the chemical repeat unit.
Red
and
gray
beads
are connected by coarse-grained bonds. Atomistic details can be reinserted in the coarse
grained beads (“inverse mapping”), allowing for scale-hopping between the different resolution
levels
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