(702b) A Complete Multiscale Modeling Approach for Nanocomposites
Blending molten polymer and inorganic clays can result in a class of new materials, in which nanoscale clay particles, generally layered silicates, are molecularly dispersed within the polymeric matrix. Such polymer-clay nanocomposites (or PCNs) exhibit dramatic increases in several properties, including mechanical strength and heat resistance, and decrease in gas permeability, when compared to the polymeric matrix alone. Importantly, the improvement in these properties is achieved at very low loadings of the inorganic component, typically, 1-10 weight %, thus rendering PCNs lighter in weight than any other conventionally filled polymer. These unique features make PCNs ideal materials for applications such as high-barrier for food or pharmaceutical packaging, to strong, heat resistant automotive components, just to name a few. Fabricating these materials in an efficient and cost-effective manner, however, poses significant synthetic challenges. To appreciate these challenges, let us discuss briefly the structure of layered silicates by considering montmorillonite (MMT) as a prime example. This inorganic clay consists in stacked silicate sheets, each approximately 200 nm long and 1 nm thick. The spacing between each sheet (or gallery) is also of the order of 1 nm, and this quantity is clearly smaller than the average radius of gyration of any conventional polymer. Therefore, entropy generally constitutes a large barrier that prevents the polymer from penetrating these galleries and become an intercalated material. Accordingly, there is a number of critical issues that need to be addressed in order to optimize the design and production of PCNs. Of foremost importance is the isolation of the conditions that result in a promotion of the polymer penetration into the narrow clay galleries. If, however, the sheets ultimately phase-separate from the polymer matrix, the mixture will not exhibit improved strength, heat resistance, or barrier properties mentioned above. Accordingly, it is also essential to determine the factors that control the macroscopic phase behavior of the mixture. Finally, the properties of the PCN commonly depend on the structure of the material; thus, it is of particular interest to establish the morphology of the final composite.
To date, there are few theories to pinpoint the critical parameters or to predict the thermodynamic stability of a PCN system, forcing synthetic chemists to synthesize all possible mixtures in order to isolate the desired system. Therefore, in order to develop new materials and composites with designed new properties, it is essential for these properties to be predicted before preparation, processing, and experimental characterization. Despite the tremendous advances made in the modeling of structural, thermal, mechanical and transport properties of materials at the macroscopic level (finite element (FE) analysis of complicated structures), there remains a tremendous uncertainty about how to predict many critical properties related to performance. The fundamental problem here is that these properties depend on the atomic level of interactions and chemistry, dealing with the electronic and atomic level of description and at a length/time scale of nanometers and nanoseconds. The material designer, however, needs answers from macroscopical modeling (the finite element paradigm) of components having scales of centimeters and milliseconds, if not larger. To substantially advance the ability to design useful high performance materials, it is then essential that we insert the chemistry into the mesoscopic (MS) and macroscopic (FE) modeling. Currently, atomistic level simulations such as molecular dynamics (MD) or Monte Carlo (MC) techniques allows to predict the structure and properties for systems of considerably large number of atoms and time scales of the order of microseconds. Although this can lead to many relevant results in material design, many critical issues in materials design still require time and length scales far too large for practical MD/MC simulations. Therefore, we need to develop methods treating the mesoscale in between the atomistic length and time scales of MD/MC and the macroscopic length and time scales (microns to mm, and ?Ýs to s) pertaining to FE analysis. This linking through the mesoscale, in which we can describe a system microstructure, is probably the greatest challenge to developing reliable first principles methods for practical and effective material design. Indeed, only by establishing this connection from microscale to mesoscale it is possible to build first principles methods for describing the properties of new materials and composites.
One of our major aims is to reach the domain of materials science and engineering by building from fundamental principles of physics and chemistry. Thus, for fundamental predictions to play a direct role in materials innovation and design, it is essential to fill the micro-meso gap. The problem here is that the current methods of coarsening the description from atomistic to mesoscale (as well as MS to FE) are not as obvious as they are from going to the quantum mechanics (QM) to the atomistic level, being strongly system-dependent and, hence, hardly generalizable. Indeed, it is quite clear that the strategy for polymers should be rather different from that adopted for metals, and again different from that conceivable for ceramic systems.
Given these concepts, it is than necessary to carry out calculations for realistic time scales fast enough to be useful in design. This requires developing techniques useful to design engineers, by incorporating the methods and results of the lower scales (e.g., MD) to mesoscale simulations. In this work, we developed a hierarchical procedure for bridging the gap between atomistic and mesoscopic simulation for PCN design. The Mesoscopic Bead-Field (MBF) hybrid method is adopted as the simulation technique, and all necessary parameters of the mesoscopic model are estimated by a step-by-step procedure involving a) the matching of the atomistic and mesoscopic pair correlation functions to determine the best mesoscopic topology for the organic modifiers, b) the mapping of interaction energies obtained from atomistic simulations onto the mesoscopic bead-bead interaction parameters, and c) the matching of the atomistic and polymer density profiles to calculate the bead-field coupling parameters. Finally, the mesoscopic simulated structures are passed on to the FEM calculations, to estimate the macroscopic properties of the PCN (e.g., Young modulus, diffusivity, etc.).
The global perspective of our work is the complete integration of all available simulation scales, in a hierarchical procedure to provide an efficient and robust simulation protocol for the successful design of PCNs of industrial interest and the prediction of their final performance.