100
M. H. Köhler et al.
and simulations have also been coupled with experiments to develop more robust and
stiffer nanomaterials. This is the case of a recent finite element analysis combined
with a two-photon lithography used to produce carbon nanostructures stronger than
diamonds [95].
Possible computational approaches for nanofluidics and nanomaterials include
quantum mechanics (QM) calculations, molecular dynamics (MD) simulations, and
hybrid methods such as QM/MM—a link between quantum and classical world
providing relevant chemical and physical insights. At the QM level, electronic interactions are described by solving the Schrödinger wave equation either directly or by
employing functionals with approximations at various levels, such as in the Density
Functional Theory (DFT). For instance, these methods are used in calculations of the
energy barrier of individual molecules permeating nanopores. Unfortunately, a high
computational cost associated with the many-body problem makes it unsuitable for
systems with more than a few hundred atoms.
MD simulations are computationally cheaper, allowing for direct observation of
kinetic processes of much larger systems—including a 64 million atoms HIV capsid
[96]—during widely representative timescales up to μs. A typical MD framework is
based on a predetermined distribution of atomic positions and partial charges. While
the latter does not change during the simulation, the former evolves in time following
Newton’s equations of motion. MD simulations on 2D membrane separation usually
start from two gas or water reservoirs separated by a nanoporous structure. Then,
a pressure gradient is applied, so that the solute/solvent flux can be monitored and
further analyzed. Intermolecular interactions are described through empirical force
fields based on simple potential functions, which means that chemical interactions
involving electronic degrees of freedom are neglected.
The best of both worlds would be a combination where atomic motion is determined by Newton’s law and interatomic forces calculated using quantum mechanics.
Although further theoretical advancements are needed to make QM/MM suitable
for membrane separation simulations, QM and MD approaches are regularly used
together to predict mechanical properties. While QM calculations based on first
principles have long been considered for elastic evaluation of nanomaterials, reactive force fields implemented in MD simulations can also be used to predict failure
mechanisms and deformation. Currently, the adaptive intermolecular reactive empirical bond order (AIREBO) [97], a Tersoff-type potential, is one of the most popular
reactive force fields used to compute mechanical properties of graphene and various
carbon allotropes. The salient feature of this potential is that the bond order term
only depends on the local coordination without the need to consider explicit charges
and long-range Coulombic interactions, allowing for excellent computational performance as fast Fourier transforms (FFT) calculations are not needed [98]. However,
the cutoffs of the switching functions in AIREBO terms must be carefully selected.
ReaxFF [99] is another reactive force field used for hydrocarbon systems, where
atomic charges are dynamically optimized during the simulations. It makes ReaxFF
more transferable and suitable for complex chemical reactions, such as interactions
between graphyne and other molecules in various environments.
M. H. Köhler et al.
and simulations have also been coupled with experiments to develop more robust and
stiffer nanomaterials. This is the case of a recent finite element analysis combined
with a two-photon lithography used to produce carbon nanostructures stronger than
diamonds [95].
Possible computational approaches for nanofluidics and nanomaterials include
quantum mechanics (QM) calculations, molecular dynamics (MD) simulations, and
hybrid methods such as QM/MM—a link between quantum and classical world
providing relevant chemical and physical insights. At the QM level, electronic interactions are described by solving the Schrödinger wave equation either directly or by
employing functionals with approximations at various levels, such as in the Density
Functional Theory (DFT). For instance, these methods are used in calculations of the
energy barrier of individual molecules permeating nanopores. Unfortunately, a high
computational cost associated with the many-body problem makes it unsuitable for
systems with more than a few hundred atoms.
MD simulations are computationally cheaper, allowing for direct observation of
kinetic processes of much larger systems—including a 64 million atoms HIV capsid
[96]—during widely representative timescales up to μs. A typical MD framework is
based on a predetermined distribution of atomic positions and partial charges. While
the latter does not change during the simulation, the former evolves in time following
Newton’s equations of motion. MD simulations on 2D membrane separation usually
start from two gas or water reservoirs separated by a nanoporous structure. Then,
a pressure gradient is applied, so that the solute/solvent flux can be monitored and
further analyzed. Intermolecular interactions are described through empirical force
fields based on simple potential functions, which means that chemical interactions
involving electronic degrees of freedom are neglected.
The best of both worlds would be a combination where atomic motion is determined by Newton’s law and interatomic forces calculated using quantum mechanics.
Although further theoretical advancements are needed to make QM/MM suitable
for membrane separation simulations, QM and MD approaches are regularly used
together to predict mechanical properties. While QM calculations based on first
principles have long been considered for elastic evaluation of nanomaterials, reactive force fields implemented in MD simulations can also be used to predict failure
mechanisms and deformation. Currently, the adaptive intermolecular reactive empirical bond order (AIREBO) [97], a Tersoff-type potential, is one of the most popular
reactive force fields used to compute mechanical properties of graphene and various
carbon allotropes. The salient feature of this potential is that the bond order term
only depends on the local coordination without the need to consider explicit charges
and long-range Coulombic interactions, allowing for excellent computational performance as fast Fourier transforms (FFT) calculations are not needed [98]. However,
the cutoffs of the switching functions in AIREBO terms must be carefully selected.
ReaxFF [99] is another reactive force field used for hydrocarbon systems, where
atomic charges are dynamically optimized during the simulations. It makes ReaxFF
more transferable and suitable for complex chemical reactions, such as interactions
between graphyne and other molecules in various environments.