Concept of the proposed work

This project concerns the study of hybrid complex materials through a combination of simulation techniques and mathematical approaches. The main challenge in the study of complex systems, both from the scientific and technological point of view, is to *relate the microstructure in a molecular level with mesoscopic structures-patterns and macroscopic properties*. The principal focus of the proposed work is along these lines, i.e. finding the basic underlying principles that govern the macroscopic behavior of hybrid complex materials through* novel mathematical and computational approaches*. The ultimate goal is the *design and optimization (virtual experiments) of hybrid complex materials*. Here we will focus on graphene based polymer nanocomposites [1,2].

In more detail, the main goal of the present proposal is to provide, a *fundamental quantitative study of the coupling between microstructure and macroscopic properties *of hybrid multi-phase complex systems and at the same time to develop a *novel set of enabling mathematical and computational tools for the design* of such systems.

Scientific and Technological Objectives

In the following we shortly describe the objectives of the project defining scientific aims and expected results. The goals of the project are divided into two thematic areas:

**A) Design of novel hybrid complex materials:**

*Coupling between ab-initio, microscopic, mesoscopic scale and macroscopic properties:*Direct investigation of hybrid complex systems by means of a single simulation method is impossible due to the large length and time scales characterizing them. Thus, hierarchical modelling schemes that involve more than one simulation level are critical to the modelling of realistic systems [2-17]. Here such a scheme will be pursued along the following directions:

- First, detailed ab-initio (density functional theory, DFT) calculations of small fragments of hybrid multi-phase systems (here a monomer with a single, or multiple, graphene layers) will be performed. The strength of the interaction between the small molecules and the graphene layers as well as an accurate classical force field will be obtained.
- Second, microscopic MC and MD simulations will be performed on hybrid complex systems of relevant short polymer chains adsorbed on graphene layers. The microstructure and the short time dynamics especially in the interfacial region will be predicted. A CG model capable of reproducing the characteristics of the coarse variables as they are obtained from the atomistic simulations will be also constructed.
- Finally, larger hybrid complex systems will be modelled through the mesoscopic CG simulations. This will allow us to study realistic systems relating directly microstructure with macroscopic properties.

*Graphene based nanocomposites:*In 2010, two physicists, A. Geim and K. Novoselov, working at the University of Manchester, received the Nobel Prize for Physics for isolating and characterizing graphene which constitutes of a 2D monolayer of graphitic carbon [13]. Graphene is in effect a sheet of carbon atoms of macroscopic dimensions but of atomic thickness. It has already been found to possess remarkable physical properties that can revolutionise our way of thinking in many areas and can lead to novel applications in the long term. The electrical charge carriers in graphene move, unimpeded, at speeds 10–100 times faster than in today’s silicon chips – and at normal temperatures. Furthermore, graphene is stable in air and transparent. Its mechanical performance is a unique combination of high strength and stiffness but not at the expense of ductility, as is the norm for conventional materials. Since it consists of just carbon atom the source materials can be cheap and plentiful. Already there is a major mobilization of researchers in academia and industry in an attempt to understand the basic behaviour of graphene but also to start designing new applications [1,13,18].

A main objective of the proposed work is to study graphene/polymer nanocomposites, through the novel hierarchical methodology discussed above, over a broad range of length and time scales. Our goal is to predict macroscopic properties (structure, conformations, dynamics and elastic constants) and relate them with the microstructure of such complex systems, under equilibrium and non-equilibrium-flowing (shear, uniaxial tensile) conditions.

** **

**B) Innovative mathematical and computational approaches:**

*Novel mathematical rigorous CG strategies:*The development of innovative mathematical approaches for the modeling of complex systems is a crucial issue. Here we propose a general new mathematical approach to obtain CG models and to properly treat many-body effects in the mesoscopic description. The methodology is based on recently developed mathematical schemes for the CG of stochastic lattice systems which provide a clear way to obtain the CG interactions and accurate error quantification [14,15]. These approaches will be generalized to more realistic, and complicated, hybrid multi-phase systems in continuum description.*Parallel numerical algorithms:*The rapid progress in building cost-efficient parallel-computing platforms, based on clusters of multi-core processors or many-core graphics processing units provides both new opportunities and challenges in the treatment of complex interacting particle systems. One type of modern processor architecture is the Graphical Processing Unit (GPU). Here we propose novel parallel algorithms for such computing systems.*Development of general computational tools for the design of novel hybrid materials:*Finally, an important objective is to generalize and combine together the new mathematical and computational methods developed in the framework of the proposed work, in order to obtain a set of software tools capable of modeling hybrid complex multi-phase multi-component systems.

** **

Added Value

The added value and the benefit expected to emerge from the project implementation are along the following directions:

- Impact on research will be strong through the development of advanced novel hierarchical modeling approaches that combine molecular simulations and mathematical approaches.
- Economic benefit will be crucial, in the long term, from the “virtual” design of cost effective novel hybrid materials.
- Taking into account that the design of novel complex systems has a large potential for further development and considering the variety of problems they can be applied to, our project has a life-span exceeding the duration of the proposal setting the foundations of a long term activity in the area. Therefore, it will help Greece to retain state-of-the-art knowledge in this so competitive area.