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Multiscale Molecular Modeling

 
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The concept of Multiscale Molecular Modeling and its application

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.