National Technical University of Athens
School of Chemical Engineering
Department of Materials Science and Engineering
Computational Materials Science and Engineering Group (Co.M.S.E.)

On the 17th of September 2017, Prof. Doros N. Theodorou was awarded with the European Materials Medal, in recognition of development of new statistical mechanics-based molecular and multiscale simulation methods for the calculation of thermodynamic, structural, interfacial, and permeability properties of polymeric materials, and zeolites.

Sincerest congratulations to our Master thesis student Dora Argyropoulou on winning a postgraduate studies scholarship of the Bodossaki Foundation.

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Polymer-matrix nanocomposites

Polymer-matrix nanocomposites, i.e. nanoparticle-filled polymers, offer huge potential for future applications and energy savings, and are considered as an important branch of the emerging field of nanotechnology. The observation that, other things being equal, the effectiveness of the filler increases with an increase in surface to volume ratio has provided large impetus for a shift from micron- to nanosized filler particles.

Figure 1: Levels of modeling developed for the study of polymer matrix nanocomposites, methods employed in each one and main simulation observables.

Four interconnected levels of representation have been developed for polymer-matrix nanocomposites (Figure 1):

(a) An atomistic one, where both nanoparticles and polymer chains are represented in terms of detailed atomistic force fields. Fullerenes (C60) are dispersed in PS matrix and atomistic Molecular Dynamics (MD) simulations are undertaken to uncover details of packing and to quantify (local and global) segmental dynamics and (atomic and local) stresses (Figure 2).

Figure 2: Quantification of many-particle influence on polymer dynamics via a Voronoi tessellation of the simulation box (left figure). Mean-square atomic displacements (MSD) of PS backbone carbon atoms as a function of time for pure PS and PS + 1% C60 (right-hand side figure). In the case of fullerene nanocomposites, an analysis of the dependence of backbone MSD on confinement is also presented for most and least confined Voronoi cells. External links:,

(b) A coarse-grained representation, in which each repeat unit is mapped onto a single "superatom", and each nanoparticle is viewed as a solid object interacting with the polymer superatoms and other nanoparticles via Hamaker-type potentials. Equilibration of coarse-grained polymer-nanoparticle systems at all length scales is achieved via connectivity-altering Monte Carlo (MC) moves. These simulations are important for generating well-equilibrated initial configurations for atomistic MD through reverse mapping.

(c) A Field Theory-inspired Monte Carlo (FT-i MC) level, where polymer chains are represented as freely jointed sequences of Kuhn segments. For polymer-polymer interactions, an effective energy function is used, which prevents large departures of the local polymer density from its value in the bulk melt everywhere in the system. This simulation methodology is capable of capturing structural features at length scales on the order of hundreds of nanometers. Brush thickness and scattering curves from the grafted PS corona of silica particles dispersed in PS have been predicted (Figure 3).

Figure 3: The calculated brush thickness (using two estimates indicated in the left figure) is plotted versus the square root of the degree of polymerization of grafted chains, Ng, times the fourth root of the grafting density, σ. Points correspond to systems containing an 8-nm-radius silica particle grafted with PS chains and dispersed in PS matrix. External links:,

(d) A slip-spring network representation where cross-links, entanglements and chain ends are the degrees of freedom of the polymeric matrix. From the thermodynamic point of view, the system under study is fully described by a Helmholtz energy function which accounts for the entropic springs connecting cross-links or entanglements, non-bonded interactions (derived from any appropriate equation of state, e.g. the Sanchez-Lacombe) and Hamaker interactions between nodal points - nanoparticles and nanoparticles - nanoparticles. Brownian simulations at this level, operating at the length scales of up to 1 μm and time scales up to 1 ms, account for changes in segmental mobility induced by the nanoparticles and track elementary events of chain slippage across entanglements, chain entanglement and re-entanglement.

Relevant publications

[1] Vogiatzis, G. G.; Voyiatzis, E.; Theodorou, D. N. "Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system" Eur. Polym. J. 2011, 47, 699-712.,
[2] Vogiatzis, G. G.; Theodorou, D. N. "Structure of Polymer Layers Grafted to Nanoparticles in Silica - Polystyrene Nanocomposites" Macromolecules 2013, 46, 4670-4683.,
[3] Vogiatzis, G. G.; Theodorou, D. N. "Local Segmental Dynamics and Stresses in Polystyrene - C60 Mixtures" Macromolecules 2014, 47, 387-404.,

Relevant projects

[1] EU NANOMODEL, Multi-scale modeling of nano-structured polymeric materials: from chemistry to materials performance.
[2] EU COMPNANOCOMP, Multiscale computational approach to the design of polymer-matrix nanocomposites.