(4au) Multiscale Chemical Product Design Using the Reverse Problem Formulation
The National Research Council (NRC) has recently recognized the importance of developing integrated formulated product design tools. In response, it created the Committee on Integrated Computational Materials Engineering (CICME) which developed and published a road map for what it termed a ?Grand Challenge? . In the report, the committee noted that in order to alleviate strain put on U.S. manufacturers from the swiftly changing and increasingly global marketplace, integrated design closely coupling computational models with manufacturing processes would be required. The term ?integrated' recognizes that the properties of products are controlled by a multitude of separate and often competing mechanisms that operate over a wide range of length and time scales. It is the linkage of the scales that remains the ?Grand Challenge' . In response to this call from CICME, the design research community has shifted focus from developing only the physical form, function, and aesthetics of assembled products to the design of chemically formulated products . Chemically formulated products are products designed at the molecular level to deliver a specific desired attribute that may exist at multiples scales such as the quantum-, nano-, meso-, macro-, and mega-scales. Examples of formulated products include pharmaceuticals , proteins , organic semi-conductors , nano-structured materials  and many more product types.
Using today's technology, designing these optimized molecules for a specific end-use has never more attainable. Recent achievements owe much of their successes to increased computational speeds and the advent of novel algorithms that improved the transfer of information between the formulated scales . One type of promising new algorithm utilizes the reverse problem formulation which has been shown to significantly reduce the complexity and required computational time of product design problems. For example, Eden et al.  and Eljack et al.  demonstrated the ability of the reverse problem formulation to decouple product design problems from constitutive equations so that molecules can be designed prior to verification at the macro scale process simulation, effectively reducing the computational complexity. Furthermore, Satyanarayana et al.  recently demonstrated the use of the reverse problem formulation combined with grid technology for polymer design with long range order approaching the meso-scale. While each of these applications of the reverse problem formulation has incorporated elements of multi-scale product design, the integration of the reverse problem formulation into the complete multi-scale framework has yet to be achieved.
The main objective for this research was to demonstrate how the reverse problem formulation algorithm could include aspects of each of the length scales, thereby creating a framework where product design could be achieved with significantly reduced computational time. The plan to achieve the objective entailed the following: (1) the development of a centralized framework, (2) the development of an algorithm that chooses the appropriate properties to bridge each of the length scales, (3) the successful implementation of a property clustering algorithm to load the property descriptions into the framework. Independent validation steps were built in to the method and verified using published experimental results because of the ?profound importance of experimental results to calibrate and validate computational methods and fill gaps in the theoretical understanding? . Due to the size of this project, proof-of-concept case studies initially focused on experimentally derived parameters. Information from the molecular scale on short range order, such as group structure, conformation, and stereoregularity, have been combined with information from the microscale on long range order, such as the structure of the lattice, polymorph form, and particle size, in the design of excipients for direct compressed acetaminophen tablets.
The developed method's success in combining characterization data from the micro-scale with the molecular scale suggested it could be applied to other characterization based chemical product designs, such as those with nanoscale architectures. Based on this inference, I authored and received a grant from the Alabama EPSCoR Graduate Research Scholars Program (GRSP) for a proof-of-concept application example regarding the design of green functional groups that improve dispersion of single walled carbon nanotubes (SWNTs). In this work, systems techniques for utilizing IR/NIR spectroscopic based combinatorial methods were used to identify suitable environmentally benign functional groups, sizes, and orientations that improved the dispersion of SWNTs in polypropylene in order to quantify experimental results found by the Davis Laboratory at Auburn University .
It is my belief that based on the preliminary results of this research, a new multi-scale design method can be developed that offers many advantages over existing approaches. One of the most beneficial advantages is a reduction in the computational expense needed to solve multi-scale design problems. For example the traditional method of solving a design problem has been to compute information at smaller length scales and pass it to models at larger length scales by removing degrees of freedom (coarse-graining) with the objective being to predict macroscopic properties from molecular information . While often the most accurate method for predicting properties, simulation has two limitations: (1) it has an immense computational cost due to hierarchical nesting and (2) it utilizes a priori knowledge of the molecular architecture (i.e. the number and types of atoms or electrons present). The large computational cost typically prevents an accurate modeling of mesoscopic structure such as the morphology of polymers without the use of constraints that significantly limit the degrees of freedom in the simulation (e.g. it may take a supercomputer six weeks to generate a single data point) . Furthermore, when these models are integrated within a product-process design framework, such as those presented in the senior-design course, the computational intensiveness exponentially increases because each projected molecular architecture must now be simulated to determine its physico-chemical properties . To minimize the computational cost in these types of problems, the property prediction simulations are typically approximated with constitutive equations based on structure descriptor models such as property based group contribution (GCM), quantitative structure property/activity relationships (QSPR/QSAR) using topological indices (T.I.), or chemometric based models. The introduction of structure descriptor models improves computational efficiency by avoiding nested simulation at the cost of prediction accuracy. However, these structure descriptor models are still too computationally expensive when utilized in design algorithms because of their often highly nonlinear nature. It has been shown that the reverse problem formulation can be used to minimize this issue by decoupling the constitutive equations from the constraint and balance equations to identify the property solution domain without committing to any components a priori . Making use of this significant find in addition to parallel programming could dramatically improve the computational efficiency of multi-scale product and process design problems, especially those with significant architecture influences at the nano-, micro-, and meso-scales. Hence, I believe we can begin to transform chemical product and process design from a candidate selection problem to a true candidate DESIGN problem that identifies the optimum molecular architecture from ALL possibilities. To achieve this goal, my research plan consists of the development of cutting edge computation reduction approaches in two main research thrusts: (1) characterization studies using empirical structure models to establish information work flows between scales using the reverse problem formulation and (2) simulation studies using coarse-grained beads to investigate parallel computation algorithmic efficiency, accuracy, and applicability. The domains studied will include both physically relevant properties, such as cohesive energy density, and mathematical constructs, such as latent properties in decomposition techniques. Applications of this research include the development of SWNT-polymer structured products, drug-delivery mechanisms for pharmaceuticals and therapeutics, and reaction network flow sheet designs for the conversion of biomass to structured chemical products beyond biofuels.
 Committee on Integrated Computational Materials Engineering, National Research Council (2008). Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security. The National Academies Press, USA.
 Hill, M. (2004) Product and Process Design for Structured Products. AIChE Journal, 50(8), pp. 1656-1661.
 Solvason C.C., Chemmangattuvalappil N.G., Eden M.R. (2009) Decomposition Techniques for Multi-Scale Structured Product Design: Molecular Synthesis. Computer Aided Chemical Engineering (In Press).
 Floudas C.A., Fung H.K., McAllister S.R., Monningmann, M., Rajgaria R. (2006) Advances in protein structure prediction and de novo protein design: A review. Chemical Engineering Science, 61(3), pp.966-988.
 Farhang A.R and Deeter T. (1999) Theoretical characterization of phenylene-based oligomers, polymers, and dendrimers. Synthetic Metals, 100(1), pp. 141-162.
 Fermeglia M. and Pricl S. (2009) Multiscale molecular modeling in nanostructured material design and process system engineering. Computers & Chemical Engineering (In Press).
 Eden M.R., Jergensen S.B., Gani R., and El-Halwagi M.M. (2003) Reverse problem formulation based techniques for process and product synthesis and design. Computer Aided Chemical Engineering, 15(1), pp. 451-456.
 Eljack F.T., Eden M.R., Vasiliki K., Kazantzi Q., and El-Hawagi M.M. (2007) Simultaneous process and molecular design - A property based approach. AIChE Journal, 53(5), pp. 1232-1239.
 Satyanarayana K.C., Abildskov J., and Gani, R. (2009) Computer-aided polymer design using group contribution plus property models. Computers & Chemical Engineering, 33, pp. 1004-1013.
 Radhakrishnan V.K., Davis E.W., Davis V.A. (2010). Influence of Initial Mixing Methods on Melt Extruded Single-Walled Carbon Nanotube-Polypropylene Nanocomposites. Polymer Engineering and Science, (accepted for publication 12/8/09).