Molecular modelling and simulation combines methods that cover a range of
size scales in order to study material and bio systems. These range from the
sub-atomic scales of quantum mechanics (QM), to the atomistic level of molecular
mechanics MM), molecular dynamics (MD) and Monte Carlo (MC) methods, to the
micrometer focus of mesoscale modelling. Quantum mechanical methods have
undergone enormous advances in the past ten years, enabling simulation of
systems containing several hundred atoms. Molecular mechanics is a faster and
more approximate method for computing the structure and behaviour of molecules,
bio molecules or materials. It is based on a series of assumptions that greatly
simplify chemistry, e.g., atoms and the bonds that connect them behave like
balls and springs. The approximations make the study of larger molecular systems
feasible, or the study of smaller systems, still not possible with QM methods,
very fast. Using MM force fields to describe molecular-level interactions, MD
and MC methods afford the prediction of thermodynamic and dynamic properties
based on the principles of equilibrium and non equilibrium statistical
mechanics. Mesoscale modelling uses a basic unit just above the molecular scale,
and is particularly useful for studying the behaviour of polymers and soft
materials. It can model even larger molecular systems, but with the commensurate
trade-off in accuracy. Furthermore, it is possible to transfer the simulated
mesoscopic structure to finite elements modelling tools for calculating
macroscopic properties for the systems of interest.

The figure shows the class of models that are available at each single scale.
There are many levels at which modelling can be useful, ranging from the highly
detailed ab-initio quantum mechanics, through classical molecular modelling to
process engineering modelling. These computations significantly reduce wasted
experiments, allow products and processes to be optimized, and permit large
numbers of candidate materials to be screened prior to production. QM, MM and
mesoscale techniques cover many decades of both length and time scale, and can
be applied to arbitrary materials: solids, liquids, interfaces, self-assembling
fluids, gas phase molecules and liquid crystals, to name but a few. There are a
number of factors, however, which need to be taken care of to ensure that these
methods can be applied routinely and successfully. First and foremost of course
are the validity and usability of each method on its own, followed by their
interoperability in a common and efficient user environment. Of equal importance
is the integration of the simulation methods with experiment.

Multiscale simulation can be defined as the enabling technology of science
and engineering that links phenomena, models, and information between various
scales of complex systems. The idea of multiscale modelling is straightforward:
one computes information at a smaller (finer) scale and passes it to a model at
a larger (coarser) scale by leaving out, i.e., coarse-graining, degrees of
freedom. The ultimate goal of multiscale modelling is then to predict the
macroscopic behaviour of a process from first principles, i.e., starting from
the quantum scale and passing information into molecular scales and eventually
to process scales. Thus, based on accurate QM calculations, a force field (FF)
is determined, which includes charges, force constants, polarization, van der
Waals interactions and other quantities that accurately reproduce the QM
calculations. With the FF, the dynamics is described with Newton's equations
(MD), instead of the Schrödinger Equation. The MD level allows predicting the
structures and properties for systems much larger in terms of number of atoms
than for QM, allowing direct simulations for the properties of many interesting
systems. This leads to many relevant and useful results in materials design;
however, many critical problems in this filed still require time and length
scales far too large for practical MD. Hence, the need to model the system at
the mesoscale (a scale between the atomistic and the macroscopic) and to pass
messages from the atomistic scale to the mesoscale and to the macro scale. This
linking through the mesoscale in which the microstructure can be described is
probably the greatest challenge to developing reliable first principles methods
for practical materials' design applications. Only by establishing this
connection from micro scale to mesoscale it is possible to build first
principles methods for describing the properties of new materials and (nano)
composites. The problem here is that the methods of coarsening the description
from atomistic to mesoscale or mesoscale to continuum is not as obvious as it is
in going from electrons to atoms. For example, the strategy for polymers seems
quite different than for metals, which seem different from ceramics or
semiconductors. In other words, the coarsening form QM to MD relies on basic
principles and can be easily generalized in a method and in a procedure, while
the coarsening at higher scales is system specific. Multiscale Molecular
Modeling: detailed description Scale integration in specific contexts in the
field of material and bio modelling can be done in different ways. Any ‘recipe’
for passing information from one scale to another (upper) scale is based on the
definition of multiscale modeling which consider ‘objects’ that are relevant at
that particular scale, disregard all degrees of freedom of smaller scales and
summarize those degrees of freedom by some representative parameters. All
approaches are initially based on the application of a Force field that
transfers information from quantum chemistry to atomistic simulation. From
atomistic simulation to mesoscale one can use a traditional approach based on
the estimation of the characteristic ratio, the Kuhn length, and the Flory
Huggins interaction parameter. This approach for determining the input
parameters for mesoscale simulation is based on the following information: (i)
the bead size and Gaussian chain architecture, (ii) the bead mobility M, and
(iii) the effective Flory-Huggins X interaction parameters.

With this approach, the Flory-Huggins X parameters between two components of
the coarse-grained molecular models in the mesoscopic simulation are estimated
through the atomistic simulation, and a mesoscopic structure is predicted using
these parameters. Mesoscopic simulations are performed using a coarse-grained
molecular model as shown in the figure: the particle in mesoscopic simulation is
related to a group of several atoms in the atomistic simulation. Mesodyn and DPD
mesoscale theory and simulation protocols are fully described in the literature.
The traditional approach can be enhanced and improved by considering the
detailed structure at the interface macromolecule–nanofiller. If one resorts to
a particle based method for describing the system at mesoscale, atomistic MD
simulation gives the necessary details of the interface with a particular
attention to the binding energies among components. Mapping of the binding
energies on mesoscale beads by means of a combinatorial approach to repulsive
parameter for particles is then carried out and the system is simulated at
mesoscale. If both particle based and field based methods are to be used at
mesoscale, then an hybrid method can be adopted in which particles are treated
as described above and field interaction is calculated from pair–pair
distribution function. Mesoscale simulation typical result is the morphology and
the structure of the matter at nanoscale level at the desired conditions of
temperature, composition and shear. For the representation of flow of polymeric
materials on a processing scale, one must employ a hydrodynamic description and
incorporate phenomena occurring on mesoscopic to macroscopic length and time
scales. For example, to capture the non-Newtonian properties of polymer flow
behaviour one can either use special models for the materials stress tensor, or
obtain it from a molecular simulation using the instantaneous flow properties of
the hydrodynamic fields as input. In the area of high-performance materials and
devices, polymer composites are finding a widespread application, and the
modelling of these materials was until recently done primarily through finite
element methods (FEM), and are beyond the realm of application of molecular
modelling approaches. Nonetheless, a real problem in using FEM is the definition
of the physical property of a complex material such as a polymer blend with
phase segregation and/or a polymer with micro inclusion of nanosized platelets.
Mesoprop technique is a method based on finite elements for estimating
properties of a complex material starting from the density distribution at
mesoscale. The method uses the results of a mesoscale simulation under the form
of three dimensional density maps, and transforms such information into a fixed
grid that is used for the integration of the equations to determine macroscopic
properties. Palmyra is a different method that allows the simulation at FEM
level with a variable grid methodology that allows to extend the size of the
system studied.

The figure shows how the mapping from mesoscale to macroscale is done. At FEM
level each finite element corresponds to one phase, with property tensor Pi, at
mesoscale (MesoDyn or DPD) each element contains mixture of phases, with
concentration Ci. It is necessary to perform a geometry mapping by converting
MesoDyn cubic elements to Palmyra tetrahedrons. Once this is done, Laplace
equation is solved directly for obtaining direct properties such as electric
conductance, diffusion, permeability,.. Local deformation allows the calculation
of mechanical properties. Integration between these methods (from mesoscale to
macroscale) is of paramount importance for the estimation of the properties of
the materials.