Coarse-Grained Modeling and Simulations of Thermoresponsive …
61
143–146]. It has been found that inter-chain interactions are favored when h-bonding
functional groups along each polymer chain in the blend are optimally separated [139,
144–146]. Furthermore, a flexible polymer chain can also coil onto itself to make
intra-chain h-bonds, thus, reducing inter-chain bonds and miscibility between blend
components [147]. Similarly, in the case of PNCs, an h-bond-driven reversible phase
transition from nanoparticle dispersion to nanoparticle aggregation in a polymer
matrix has been observed with increasing temperature in PNCs comprised of gold
nanoparticles with poly(styrene-r-2-vinylpyridine) grafts in a poly (stryrene-r-4-vinyl
phenol) matrix [2]. In another study, dispersion of single walled carbon nanotubes in
a polymer matrix composed of a copolymer of styrene and vinyl phenol was found
to depend on the composition of vinyl phenol in the polymer matrix, the optimal
composition of which maximized inter-molecular h-bonds [148, 149].
In contrast to the many experimental studies, computational studies probing the
effects of h-bonds on the phase behavior in polymer blends and PNCs are relatively
limited. For example, the dynamic behavior of unentangled polyamide-66 melt has
been studied using molecular dynamics (MD) simulations with atomistic force fields.
This study found that the global dynamics of polymer relaxation is linked to the local
dynamics of h-bonds quantified by their relaxation time calculated from the correlation of h-bonds over time [150]. In a follow-up study using a CG model with
effective isotropic potentials derived from the atomistic radial distribution functions,
the same authors found that the lack of directionality in the CG model led to differences in dynamic behavior of polyamide-66 obtained from the CG model compared
to atomistic model, establishing the importance of incorporating the directionality
of h-bonds in CG models to accurately reproduce dynamics of polymers [151].
In another study, Gowers and Carbone [152] used a multiscale/hybrid approach to
model h-bonds in polyamide melt. They used atomistic resolution for atoms involved
in h-bond formation to accurately model the directionality of h-bonding interactions
and for the remaining atoms used a CG representation to enhance the speed of the
simulations [152]. Such hybrid atomistic/CG approaches are valuable but require
careful treatment of CG and atomistic regions in the simulation by using two separate thermostats to maintain temperature [152], defining separate cut-off distances
and creating two neighbor lists for the atom and CG bead interactions to bring about
an effective reduction in degrees of freedom and simulation times in the hybrid model
[153]. Moreover, h-bond formation around atoms can be hindered by the surrounding
bulky CG groups in the hybrid model [152]. This can make the implementation of
such hybrid approaches too complex for quick computational screening of materials to guide experiments Therefore, studies using pure CG models tuned to capture
directional and specific interactions are a suitable alternative to all-atom or hybrid
atomistic-CG models in polymers owing to their ease of implementation and low
computational cost.
In the following subsections, we first describe our CG model for PNCs comprised
of polymer grafted nanoparticles placed in a polymer matrix [154] that mimic the
chemistries studied experimentally by Hayward and coworkers where h-bonds are
formed between the monomers of poly(styrene-r-2-vinylpyridine) grafts on gold
nanoparticles and the monomers of the poly (stryrene-r-4-vinyl phenol) chains in
61
143–146]. It has been found that inter-chain interactions are favored when h-bonding
functional groups along each polymer chain in the blend are optimally separated [139,
144–146]. Furthermore, a flexible polymer chain can also coil onto itself to make
intra-chain h-bonds, thus, reducing inter-chain bonds and miscibility between blend
components [147]. Similarly, in the case of PNCs, an h-bond-driven reversible phase
transition from nanoparticle dispersion to nanoparticle aggregation in a polymer
matrix has been observed with increasing temperature in PNCs comprised of gold
nanoparticles with poly(styrene-r-2-vinylpyridine) grafts in a poly (stryrene-r-4-vinyl
phenol) matrix [2]. In another study, dispersion of single walled carbon nanotubes in
a polymer matrix composed of a copolymer of styrene and vinyl phenol was found
to depend on the composition of vinyl phenol in the polymer matrix, the optimal
composition of which maximized inter-molecular h-bonds [148, 149].
In contrast to the many experimental studies, computational studies probing the
effects of h-bonds on the phase behavior in polymer blends and PNCs are relatively
limited. For example, the dynamic behavior of unentangled polyamide-66 melt has
been studied using molecular dynamics (MD) simulations with atomistic force fields.
This study found that the global dynamics of polymer relaxation is linked to the local
dynamics of h-bonds quantified by their relaxation time calculated from the correlation of h-bonds over time [150]. In a follow-up study using a CG model with
effective isotropic potentials derived from the atomistic radial distribution functions,
the same authors found that the lack of directionality in the CG model led to differences in dynamic behavior of polyamide-66 obtained from the CG model compared
to atomistic model, establishing the importance of incorporating the directionality
of h-bonds in CG models to accurately reproduce dynamics of polymers [151].
In another study, Gowers and Carbone [152] used a multiscale/hybrid approach to
model h-bonds in polyamide melt. They used atomistic resolution for atoms involved
in h-bond formation to accurately model the directionality of h-bonding interactions
and for the remaining atoms used a CG representation to enhance the speed of the
simulations [152]. Such hybrid atomistic/CG approaches are valuable but require
careful treatment of CG and atomistic regions in the simulation by using two separate thermostats to maintain temperature [152], defining separate cut-off distances
and creating two neighbor lists for the atom and CG bead interactions to bring about
an effective reduction in degrees of freedom and simulation times in the hybrid model
[153]. Moreover, h-bond formation around atoms can be hindered by the surrounding
bulky CG groups in the hybrid model [152]. This can make the implementation of
such hybrid approaches too complex for quick computational screening of materials to guide experiments Therefore, studies using pure CG models tuned to capture
directional and specific interactions are a suitable alternative to all-atom or hybrid
atomistic-CG models in polymers owing to their ease of implementation and low
computational cost.
In the following subsections, we first describe our CG model for PNCs comprised
of polymer grafted nanoparticles placed in a polymer matrix [154] that mimic the
chemistries studied experimentally by Hayward and coworkers where h-bonds are
formed between the monomers of poly(styrene-r-2-vinylpyridine) grafts on gold
nanoparticles and the monomers of the poly (stryrene-r-4-vinyl phenol) chains in